Efficient HydroelectricGeneration Using NovelBalance SchemesbyMilad Fekri MoghadamB.Sc., Sharif University of Technology, 2008M.Sc., Amirkabir University of Technology, 2010A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Electrical and Computer Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2015© Milad Fekri Moghadam 2015AbstractIn order to control frequency and interchange schedules in electric powersystems, a permanent balance between generation and demand is necessary.Following electric demand has traditionally been realized by control of flexiblegeneration resources. As a consequence, conventional generation units areutilized in lower maximum output power and less efficient operating points.Transition toward increased penetration of intermittent Distributed EnergyResources (DER) requires more balancing capacity in power systems whichmakes frequency control a more challenging issue.Demand Side Management (DSM) is a main ingredient of Smart Grid(SG)s to improve efficiency and reliability. Some industrial processes haveinherent flexibilities making them capable of virtually storing enough energyto immediately and continuously respond to control signals of transmissionsystem operator. These loads, when equipped with advanced metering, com-munication and control infrastructure, can realize participation of DemandSide Storage (DSS) in sub-hourly time steps of grid balance.In order to fairly distribute the benefits of interconnection among all con-trol areas, frequency control standards are defined and proposed by reliabil-ity coordinators e.g. NERC. Once new standards become effective,BalancingAuthorities (BA)s modify their Automatic Generation Control (AGC) andreal-time balance logic to comply with the new requirements.This research is dedicated to finding novel balance structures in sub-hourly dispatch and real-time operation. The objectives of the proposedbalance structures are to increase hydroelectric generation efficiency and re-duce unit maneuvering leading to mechanical wear and tear.iiAbstractA new Demand Dispatch (DD) application for industrial flexible loads anda new sub-hourly balance structure based on use of DSS are developed in thisthesis. Also in real-time operation, a novel AGC logic is proposed to max-imize the benefits of a hydroelectric dominated Balancing Authority basedon latest frequency control standards. It is shown through mathematicalmodeling, static scheduling optimization formulations and dynamic simula-tions that utilizing 5% of system peak demand as sub-hourly dispatched DSSsaves up to 2% in generation efficiency and utilizing the proposed real-timeAGC logic leads to generation efficiency saving of up to 1.3%. Both proposedmethods also significantly reduce mechanical wear and tear.iiiPrefaceThe chapters of this thesis were prepared and written by the author withthe help and supervision of university supervisor Dr. William G. Dunford,university co-supervisor Dr. Ebrahim Vaahedi and industry supervisor Mal-colm Metcalfe. Some of the research results are already published/acceptedas journal articles, conference proceedings and/or submitted for peer review.In all chapters and paper publications, the author was responsible fordeveloping the ideas, mathematical formulations, implementing the mod-els, conducting the simulations, compiling the results and concluding thework. All manuscripts are prepared by the author while university supervi-sors Dr. William G. Dunford and Dr. Ebrahim Vaahedi have provided super-visory comments and corrections during the process of studies and writingthe manuscripts.The industrial supervisor helped the author during this research by pro-viding real industrial load data and general information about demand sidemanagement and the potential benefits for utilities and load owners.My contributions during the PhD has resulted in the following publica-tions and conference presentations.A version of Chapter 3 and part of Chapter 2 is published as a journalpaper. M. Fekri Moghadam, M. Metcalfe, W. Dunford and E. Vaahedi, ”De-mand Side Storage to Increase Hydroelectric Generation Efficiency,”IEEE Trans. Sustain. Energy, vol. 6, n. 1, pp. 1-12, 2014.ivPrefaceTwo conference presentations were also based on primitive results of thesechapters. M. F. Moghadam, W. G. Dunford, E. Vaahedi, and M. Metcalfe, “Us-ing industrial load flexibility to increase hydroelectric generation effi-ciency,” in IEEE PES General Meeting, Conf. Expo., July 2014, pp.1-5. M. F. Moghadam, W. G. Dunford, E. Vaahedi, and M. Metcalfe, “Op-timizing Generator Efficiency Using An Optimized Network of Loads,”in AIChE 2013 Annual meeting, Nov. 2013.A version of Chapter 4 is submitted to a peer review journal. M. Fekri Moghadam, M. Metcalfe, W. Dunford and E. Vaahedi, ”In-creasing Hydroelectric Generation Efficiency Using NERC’s BRD Fre-quency Control Standards,” Submitted to IEEE Trans. Sustain. En-ergy.Some other results of this part is accepted for presentation in a conference. M. F. Moghadam, W. G. Dunford, E. Vaahedi, and M. Metcalfe, “Eval-uation of NERC’s BRD Frequency Control Standard in HydroelectricGeneration ,” Accepted for IEEE PES General Meeting, Conf. Expo.,July 2015.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivNomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xixDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.1 Generation-Demand Balance . . . . . . . . . . . . . . 31.2.2 Frequency Control Tasks . . . . . . . . . . . . . . . . 41.2.3 Frequency Control Standards . . . . . . . . . . . . . . 51.2.4 Demand Side Management . . . . . . . . . . . . . . . 6viTable of Contents1.2.5 Demand Side Energy Storage - Demand Dispatch . . . 91.3 State-of-the-Art Research . . . . . . . . . . . . . . . . . . . . 111.3.1 Frequency Control . . . . . . . . . . . . . . . . . . . . 111.3.2 Aggregator Design . . . . . . . . . . . . . . . . . . . . 121.3.3 Residential Load Control . . . . . . . . . . . . . . . . 131.3.4 Power System Support . . . . . . . . . . . . . . . . . . 151.3.5 Market Operation . . . . . . . . . . . . . . . . . . . . 151.4 Research Objectives and Anticipated Impacts . . . . . . . . . 161.4.1 Objective 1: Modeling Industrial Flexible Loads as De-mand Side Storage (DSS) . . . . . . . . . . . . . . . . 161.4.2 Objective 2: Demand Side Storage as a Sub-hourlyDemand Dispatch Product . . . . . . . . . . . . . . . 171.4.3 Objective 3: An AGC Logic Based on Maximum Ben-efits From BRD Draft Standards . . . . . . . . . . . . 181.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . 192 Generation-Demand Balance . . . . . . . . . . . . . . . . . . . 212.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.2 Balance Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . 242.2.1 Unit Commitment (UC) . . . . . . . . . . . . . . . . . 252.2.2 Economic Dispatch (ED) . . . . . . . . . . . . . . . . 252.2.3 Frequency Regulation . . . . . . . . . . . . . . . . . . 272.3 Hydroelectric Generation Efficiency . . . . . . . . . . . . . . . 282.3.1 Generation Loss Function . . . . . . . . . . . . . . . . 292.3.2 Start-up and Shut-down Costs . . . . . . . . . . . . . 332.4 Hydro Unit Commitment . . . . . . . . . . . . . . . . . . . . 342.4.1 Problem Formulation . . . . . . . . . . . . . . . . . . 342.4.2 Dynamic Programming (DP) . . . . . . . . . . . . . . 352.4.3 Solution Technique . . . . . . . . . . . . . . . . . . . . 402.5 Hydro Economic Dispatch . . . . . . . . . . . . . . . . . . . . 412.5.1 Problem Formulation . . . . . . . . . . . . . . . . . . 41viiTable of Contents2.5.2 Transmission Loss Effect . . . . . . . . . . . . . . . . 442.5.3 Transmission Line Flows . . . . . . . . . . . . . . . . . 452.5.4 Solution Technique . . . . . . . . . . . . . . . . . . . . 462.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 Demand Side Storage as Sub-hourly Balance Resource . . 483.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.2 Proposed Control Strategy . . . . . . . . . . . . . . . . . . . 503.2.1 Grid Balance . . . . . . . . . . . . . . . . . . . . . . . 503.2.2 Control Structure . . . . . . . . . . . . . . . . . . . . 513.2.3 Grid interface . . . . . . . . . . . . . . . . . . . . . . . 543.3 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.3.1 Framework . . . . . . . . . . . . . . . . . . . . . . . . 543.3.2 Water Pumps in Drinking Water Storage Systems . . 563.4 Balance Logic Formulation . . . . . . . . . . . . . . . . . . . 603.4.1 System-wide Balance . . . . . . . . . . . . . . . . . . 603.4.2 Local DSS Optimization . . . . . . . . . . . . . . . . . 623.4.3 Mixed Integer Linear Programming . . . . . . . . . . . 633.5 Numerical Results & Discussion . . . . . . . . . . . . . . . . . 653.5.1 Simulation Environment . . . . . . . . . . . . . . . . . 653.5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . 693.5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . 774 Frequency Control in BRD Standard Paradigm . . . . . . . 814.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.2 NERC’s Frequency Control Standards . . . . . . . . . . . . . 824.2.1 Control Performance Standards (CPS) . . . . . . . . . 824.2.2 Balance Resource and Demand (BRD) Standard . . . 834.3 Proposed Real-time ACE Control . . . . . . . . . . . . . . . . 874.3.1 Economic Dispatch Control . . . . . . . . . . . . . . . 874.3.2 Real-time ACE Control . . . . . . . . . . . . . . . . . 88viiiTable of Contents4.4 Simulation Environment . . . . . . . . . . . . . . . . . . . . . 904.4.1 Power System . . . . . . . . . . . . . . . . . . . . . . 904.4.2 Dynamic Model . . . . . . . . . . . . . . . . . . . . . 934.4.3 Static Scheduling Model . . . . . . . . . . . . . . . . . 954.4.4 Load Data . . . . . . . . . . . . . . . . . . . . . . . . 954.5 Simulation Results and Discussion . . . . . . . . . . . . . . . 964.5.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . 965 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . 1055.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 1055.1.1 Objective 1 . . . . . . . . . . . . . . . . . . . . . . . . 1065.1.2 Objective 2 . . . . . . . . . . . . . . . . . . . . . . . . 1065.1.3 Objective 3 . . . . . . . . . . . . . . . . . . . . . . . . 1075.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 108Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110AppendixA Transmission System Data . . . . . . . . . . . . . . . . . . . . 124ixList of Tables3.1 Generation Unit Locations . . . . . . . . . . . . . . . . . . . . 663.2 24 Hour Unit Commitment Schedule of Swing Power Plant . . 683.3 Daily results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.1 Generation capacities of BA1 & BA2 . . . . . . . . . . . . . . 934.2 24 Hour UC Schedule of Swing Power Plants of BA1 & BA2 . 964.3 AGC logics of each BA in each study case . . . . . . . . . . . 974.4 Average daily CPM score . . . . . . . . . . . . . . . . . . . . . 1004.5 Efficiency gains compared to the benchmark . . . . . . . . . . 102A.1 Transmission Lines Data of IEEE 24 BUS Reliability Test Sys-tem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124xList of Figures1.1 Classification of Demand Side Management . . . . . . . . . . . 81.2 Classification of Demand Response . . . . . . . . . . . . . . . 82.1 Spinning reserve capacity compared to generation capacity insub-hourly control time steps . . . . . . . . . . . . . . . . . . 232.2 Regulation reserve capacity compared to generation capacityin sub-hourly control time steps . . . . . . . . . . . . . . . . . 232.3 Control hierarchy in power system operation . . . . . . . . . . 262.4 Regulation up and Regulation down capacity and PreferredOperating Point . . . . . . . . . . . . . . . . . . . . . . . . . . 362.5 Typical efficiency curve of a single hydroelectric generation unit 372.6 Algorithm to calculate total power generation loss function ina multi-unit hydroelectric plant . . . . . . . . . . . . . . . . . 382.7 Generation loss curve of the modeled plant when differentnumbers of units are in operation . . . . . . . . . . . . . . . . 392.8 Effects of N = 3 and X = 5 control variables on search spacein forward Dynamic Programming . . . . . . . . . . . . . . . 403.1 Proposed control structure . . . . . . . . . . . . . . . . . . . . 533.2 Demand granularity (left) and resource granularity (right) . . 533.3 Scheme of a water storage facility . . . . . . . . . . . . . . . . 553.4 Hourly generation schedule of base-loaded plants and swingplant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683.5 Individual and aggregate demand of loads in Normal mode . . 70xiList of Figures3.6 Swing plant loading in Normal and Smart modes . . . . . . . 713.7 Aggregate DSS power consumption in Normal and Smart modes 723.8 Volume of a sample tank in Normal and Smart modes . . . . 733.9 Smart operation of 4 pumps in one storage system . . . . . . . 743.10 Total hourly average of Regulation Up and Regulation Downcapacity for different lengths of scheduling time window . . . . 753.11 Daily average water savings in different DSS penetration . . . 764.1 BA’s BAAL and CPM limits . . . . . . . . . . . . . . . . . . . 864.2 Control scheme of proposed AGC logic . . . . . . . . . . . . . 864.3 Combined efficiency curve of a multi-unit hydroelectric plant . 894.4 Interconnection comprised of N BAs . . . . . . . . . . . . . . 924.5 Results of Economic Dispatch for BA1 and BA2 . . . . . . . . 974.6 ACE1 and BAALl, BAALh and CPS2 limits for BA1 in Case 1 984.7 ACE1 and BAALl, BAALh and CPS2 limits for BA2 in Case 1 994.8 ACE1 and BAALl, BAALh and CPS2 limits for BA1 in Case 21004.9 ACE1 and BAALl, BAALh and CPS2 limits for BA2 in Case 21014.10 Number of generation control swings in BA1 in Case1 (upperfigure) and in Benchmark (lower figure) . . . . . . . . . . . . 1034.11 Number of generation control swings in BA2 in Case2 (upperfigure) and in Benchmark (lower figure) . . . . . . . . . . . . 104A.1 Single Line Diagram of IEEE 24 BUS Reliability Test System 125xiiList of Algorithms1 Unit Commitment via Forward Dynamic Programming . . . . 362 Real-time BAAL Control Module Logic . . . . . . . . . . . . . 913 Real-time CPM Control Module Logic . . . . . . . . . . . . . 91xiiiGlossaryACE Area Control Error. 6, 81–83, 87, 89, 95, 105, 107AGC Automatic Generation Control. ii, iii, vii, x, xii, 3, 5, 6, 10, 12, 17–20,24, 27, 28, 80, 81, 86–89, 92, 93, 96, 97, 101, 105, 107, 109BA Balancing Authority. ii, iii, 5, 6, 18, 19, 81, 83–85, 87, 89BAAL Balancing Authority ACE Limit. 6, 84, 85, 87, 107BRD Balance Resource and Demand. vii, viii, 5, 6, 16, 18–20, 81, 83, 89,96, 99, 101, 105, 107CPM Control Performance Measure. 83–85, 87, 107CPS Control Performance Standards. viii, 81–85, 87, 98, 107DD Demand Dispatch. iii, vii, 10, 16–20, 49, 105, 106, 108DER Distributed Energy Resources. ii, 51, 52, 66DLC Direct Load Control. 11, 13, 17, 50–52, 107DP Dynamic Programming. vii, xi, xiii, 35–37, 40DR Demand Response. xi, 7–11, 15–17, 48, 49, 51, 52, 54, 66, 108DSM Demand Side Management. ii, xi, 6–8, 11, 15–17, 19, 48DSS Demand Side Storage. ii, iii, vii, viii, xii, 10, 16, 17, 48–52, 54, 59–63,66, 71–77, 79, 80, 105–109xivGlossaryEBO Energy Balance Optimizer. 51, 52, 54, 59, 60, 62, 69, 75, 77–80ED Economic Dispatch. vii, 3, 4, 17, 18, 21, 22, 25, 27, 28, 33, 41, 42, 45–47,49, 50, 81, 82, 85, 87, 95, 107ESS Energy Storage Systems. 9, 11, 19, 48–50, 109GDF Generation Distribution Factor. 45, 46, 62ISO Independent System Operator. 11, 12, 17, 54, 108, 109MILP Mixed-Integer Linear Programming. 64, 65, 69, 107NERC North American Electric Reliability Corporation. ii, 5, 7, 19, 20, 82,83, 105, 107POP Preferred Operating Point. xi, 28, 36, 79, 80, 106, 109QP Quadratic Programming. 46, 47, 62SG Smart Grid. ii, 1, 6, 16, 48UC Unit Commitment. vii, xiii, 3, 4, 21, 22, 25, 27, 28, 33, 34, 36, 43, 47,67, 76, 77, 82, 87, 88, 95, 107V2G Vehicle-to-Grid. 12, 13, 15, 109VIU Vertically Integrated utility. 11, 16, 17, 19, 20, 49–51, 54, 79, 81, 105,107–109VPP Virtual Power Plant. 50, 106xvNomenclatureβi,j Penstock loss constant, s2/m5.δg(t) Vector of limits of generator ramp rates.δl(t) Vector of maximum limit of pump ramp rates.δs(t) Vector of limits of DSS ramp rates.δp,s Ramp rate limit of pump p in storage s, MW/s.ηg,i,j Generator efficiency of hydroelectric unit i in plant j, %.ηt,i,j Turbine efficiency of unit i in plant j, %.F Vector of active power flow limits.Lmax(t) Vector of limit on maximum pump power.Lmin(t) Vector of limit on minimum pump power.Pmax(t) Vector of limits on maximum hydro generation.Pmin(t) Vector of limits on minimum hydro generation.Smax(t) Vector of limits on maximum DSS consumption.Smin(t) Vector of limits on minimum DSS consumption.V ts Normalized volume of storage s at time t.ρ Water specific weight, kg/m3.xviNomenclaturen̂ts Ideal number of pumps to be “on at time t.ap,s Coefficient of linear term of fitted discharge curve for pump p instorage s.bp,s Coefficient of constant term of fitted linear discharge curve forpump p in storage s.Dte Effective demand at time t, MW.di,j Water discharge in unit i in plant j, m3/s.Es,T Total energy consumption in storage s, MWh.Etotal Total energy consumption of all DSSs in system-wide balanceproblem.fp,s Pumping rate function of pump p in storage s.g Acceleration of gravity, m/s2.he,i,j Effective water head of unit i in plant j, m.hf,j Forebay elevation of plant j, m.hp,j Penstock loss effect of plant j, m.ht,j Tailrace effect of plant j, m.kj Number of units in hydroelectric plant j.N Number of control buses.nts Real number of pumps to be “on at time t.Nb Number of storage systems in bus b.Ng Number of dispatchable power plants.xviiNomenclatureNs Number of pumps in storage s.P tj,sch Capacity of the largest committed unit in the system at t, MW.Pi,j Generation in hydroelectric unit i in plant j, MW.pp,s,max Maximum power consumption limit of pump p in storage s, MW.pp,s,min Minimum power consumption limit of pump p in storage s, MW.ptp,s Power consumption of pump p in storage s at time t, MW.Qp,s Water inflow rate from pump p to storage s at highest mechanicalefficiency, m3/s.qtp,s Water inflow rate from pump p to storage s at time t, m3/s.qts Total water inflow rate to storage s at time t, m3/s.rts Water outflow rate from storage s at time t, m3/s.RRt Total regulation reserve requirement at time t.sj Water Spillage through dam in hydroelectric plant j, m3/s.SRt Total spinning reserve requirement at time t.uj Water release of hydroelectric plant j, m3/s.Vs,max Maximum volume limit of storage s, m3.Vs,min Minimum volume limit of storage s, m3.V 0s Initial volume of storage s, m3.V ts Volume of storage s at time t, m3.xviiiAcknowledgementsI would have not been able to do this work without the help and assistance ofmy supportive advisor Dr. William G. Dunford and co-advisor Dr. EbrahimVaahedi. I would also like to thank Malcolm Metcalfe, my industry supervisorwhose ideas encouraged me during this work. Great thanks to knowledgeablecolleagues at Power System Group of ECE department at the University ofBritish Columbia.I would also like to thank to University of British Columbia (UBC), Nat-ural Sciences and Engineering Research Council of Canada (NSERC), andEnbala Power Networks®for their financial support throughout my PhDstudies.Great thanks to my friends Nima Mohseni Kiasari, Omid Namvar Gharehshi-ran, Maziyar Hamdi and Mahdi Ramezani who helped me a lot during thisjourney.Special thanks to my parents, who have supported me throughout myyears of education, both morally and financially.xixDedicationTo my family...xxChapter 1Introduction1.1 MotivationThe existing electricity industry is unidirectional in nature. It converts onlyone-third of fuel energy into electricity and almost 8% of its output is lostalong its transmission lines, while 20% of its generation capacity exists tomeet peak demand only (i.e. in use only 5% of the time) [1]. Moreover, dueto hierarchical topology of the equipment and their control structure, failuresand effects of malfunctions penetrate to upstream and downstream regions.Advanced Metering Infrastructure necessitate realization of Smart Grid (SG)through enhanced demand side participation and bidirectional flow of powerand information between supply and demand resources to overcome the grow-ing power system challenges [2, 3]. Future grid requires high penetration ofrenewable energy resources, strict limits on greenhouse gas emissions andelectrification of transportation systems. These factors drive transition fromtraditional grid to Smart Grid [4]. Smart Grid aims to increase power sys-tem efficiency, reliability and sustainability while maximizing utilization ofcurrent assets to delay investments required to meet increasing future energyneeds [5, 6].Permanent balance between generation and demand in real-time is thekey to stable and reliable operation of electric power systems. Electric powersystem demand follows seasonal to daily cycles, which are predictable usingdemand forecasting methods. But the very short term and real-time compo-nent of system demand has stochastic characteristics imposing mismatchesbetween generation and demand. In order to keep these mismatches within11.1. Motivationpermitted levels while reducing balancing costs, a hierarchy of different bal-ancing tasks is designed in Energy Management Systems (EMS) of operationcenters. Generation resources are committed and dispatched economicallyto meet the demand. Since electric demand is a non-controllable stochasticfluctuating quantity, flexible generation units have traditionally been usedas balancing tools to follow the demand. However, there are technical andeconomic constraints on the generation side that reduce generation flexibilityand make energy balance a challenging task. Unexpected outages of loads,generation units as well as transmission and distribution lines also aggravatethe problem. As renewable energy penetration increases, the variable anduncertain characteristics of demand become even more severe to handle. Ac-cording to the report on annual energy outlook in [7], by 2035 the combinedintermittent and non-dispatchable non-hydroelectric energy resources are ex-pected to deliver 14% of total generation in electric energy. The consequentoutcome of increasing this percentage is the need for installing/committingmore expensive operating reserves and sub-hourly load-following capacity ingeneration units, increased wear and tear of thermal, gas and hydroelectricgeneration units and carbon footprint of non-renewable units.Each generation unit has an efficiency characteristic for generating re-sources showing the efficiency of produced electricity in each operating point(output power). This efficiency characteristic is the most important elementused in scheduling and dispatch routines to maximize the benefits of utilizedresources. Operating reserves are provided by leaving a part of plant capacityfor reserve, thus reducing the total achievable output power and operatingthe plant at lower efficiency than that of most efficient point. Thus genera-tion unit owners suffer from lost opportunity costs associated with reducedcapacity, increased mechanical wear and tear as well as generation efficiencyloss.It is widely accepted in industry and academia that these challenges inbalancing generation and demand should be addressed and new measures21.2. Backgroundmust be proposed and developed to facilitate the transition toward adoptionof more renewable energy resources and operating the assets near their “knee”points. In other words, any attempt to increase asset utilization and genera-tion efficiency would contribute in following the energy and utility industryroad maps. These measures include new generation control architecture, bal-ance logics and use of demand side response in different control time scalesi.e. from primary frequency response to short-term and even long-term gen-eration and demand scheduling routines. Proposing and developing thesemeasures must be compatible with the state-of-the art technology in termsof metering, control and communication infrastructure to be accepted andadopted in electric energy industry. In other words, ideas and methods thatare not economic neither compatible with today’s utility standards will havea very low chance of being adopted in real world.1.2 Background1.2.1 Generation-Demand BalanceAs the electric power system demand changes or a deviation happens in gen-eration from its schedule, an imbalance occurs in the system, which leadsto operating in a new frequency deviated from nominal frequency [8]. Inorder to keep system frequency within reliable margins, different frequencycontrol measures in different time frames are utilized in power systems. Au-tonomous and manual, centralized and decentralized generation and demandadjustments are implemented both ahead of time i.e. day-ahead and hour-ahead Unit Commitment (UC) and hour-ahead or in real-time i.e. EconomicDispatch (ED) and Load Frequency Control (LFC) [9].The function of real-time Automatic Generation Control (AGC) in powersystem is to realize LFC and Economic Dispatch of generation units. LFCor frequency regulation is done in 2s-4s time steps to maintain system fre-quency within allowable limits by tracking the deviations of real-time system31.2. Backgrounddemand from forecasted demand and unintended fluctuations in generatoroutputs and matching the tie-line flows with the schedules [10]. EconomicDispatch is performed in sub-hourly time intervals (normally 5 min) to eco-nomically load different resources to minimize the generation costs subjectto static and dynamic unit constraints and system-wide constraints [11]. De-pending on type and characteristics of the dispatchable generation portfolio,the Unit Commitment program schedules hourly sets of committed genera-tion resources to be dispatched in real-time and meet the system forecasteddemand, regulation and contingency reserves.1.2.2 Frequency Control TasksThere are three types of frequency control: primary, secondary and tertiaryfrequency control [12]. Primary frequency control happens right after imbal-ances and includes effects of droop-based automatic response of governors,sensitivity of loads and frequency responsive load control. This type of con-trol is fast and takes place in less than 1 min. If this response is not enoughto bring frequency back to the desired range, centrally coordinated secondaryfrequency control takes place which is realized through maneuvering of flex-ible generation and loads to respond AGC signals. AGC signal is updatedin 2s-4s time steps and economically dispatched among AGC assigned units.The response time is around 1-2 min. Tertiary frequency control is centrallycoordinated dispatch of dispatchable resources in longer time steps to followsystem slower demand variations. This task is also called “load following” or“ramping” service and takes place in Economic Dispatch time frame.In interconnected power systems, utilities are synchronized through ACtie-lines. Tie-lines realize energy exchange between utilities and possibility ofinteractive frequency control support [10, 13]. Therefore, in interconnectedoperation mode, frequency related reliability risks are less than isolated op-eration mode. Interconnected operation has also provided utilities with highsavings in balancing costs. Besides these benefits, control areas in each inter-41.2. Backgroundconnection are responsible to continually adjust their generation and respon-sive demand to meet their internal demand and energy exchange obligationas well as the share of interconnection frequency control support. Since obli-gations change much faster than flexible generation and responsive demand,only the trend of them is followed by balancing tools. Therefore, frequencyand interchange power fluctuate around their schedule [8, 9]. Accumula-tion of mismatches in frequency and unintended interchange power must becontrolled to stay within permitted levels.1.2.3 Frequency Control StandardsIn order to fairly distribute the benefits of interconnection among all con-trol areas, frequency control standards are defined by reliability coordinators[14, 12, 15]. Reliability coordinators continually monitor compliance of con-trol areas and aim to develop new balance standards to increase the economicbenefits of the interconnected operation while keeping reliability of inter-connection in acceptable level. North American Electric Reliability Council(NERC) enforces reliability standards and regulations for all interconnectionsin North America under which each control area should be operated. Thesestandards affect real-time frequency control measure of areas i.e. AGC. Oncethe new standards become effective, areas modify their AGC logic and bal-ancing strategies to comply with the new requirements [16, 17]. Researchersalso study the effects of new standards on dynamic and long-term statisticalperformance of generation control and evaluate benefits associated with thenew limits and targets [18, 19, 20, 21].Based on North American Electric Reliability Corporation’s latest fre-quency control draft known as Balance Resource and Demand (BRD) (BAL007-01-1), each Balancing Authority is responsible “to maintain intercon-nection frequency within predefined limits under all conditions (i.e., normaland abnormal)”. As of Feb. 2013, 13 Balancing Authorities in the EasternInterconnection, 26 in the Western Interconnection, the Electric Reliabil-51.2. Backgroundity Council of Texas (ERCOT) and Quebec were under field trial for thisstandard and reliability coordinators continue to monitor the performanceof participating Balancing Authorities [22]. This standard mandates Bal-ancing Authoroties to maintain clock-minute average of their Area ControlError (ACE) within frequency-dependent Balancing Authority ACE Limit(BAAL).Wider ACE bounds allow system operator to make less costly genera-tion maneuvering in real-time. In other words, less regulation capacity isneeded to stay within new ACE limits. This leads to operation in more ef-ficient points and less deviations in AGC assigned generation units. Doingso, a Balancing Authority could benefit from rotational energy storage insynchronous generators of interconnection.Implementation of new AGC logics based on BRD standards, could accel-erate adoption of more renewable energy resources and reduce overall systembalance costs.1.2.4 Demand Side ManagementThe relatively low average plant utilization and advances in communication,control and network infrastructures necessitate realization of a significantscope of Smart Grid i.e. Demand Side Management (DSM). DSM as a toolto shift system demand from peak periods to off-peak periods includes every-thing that is done on the demand side of energy system. Shaping the systemdemand would reduce the need for installing new generation capacity and asmentioned in part 1.1, new generation-based operating reserves. DSM alsoincreases the utilization and efficiency of existing generation capacity [23, 24].The target of DSM as an alternative to conventional generation adjustmentpractices is to maximize economic benefits of power system while fulfillingreliability concerns in terms of maintaining frequency error within tolerablelimits [4, 25, 26].Electric energy infrastructure is very expensive and power system plan-61.2. Backgroundners tend to reduce and/or defer huge capital investments to meet the grow-ing electric demand. So the new philosophy of power system operation is tokeep demand fluctuations as small as possible to decrease the needed flexi-bility and increase system efficiency. Adding communication infrastructureand intelligent decision making tools to current power systems to achieveresponsive demand does not require huge investments compared to conven-tional alternatives i.e. making new generation, transmission and distributioninfrastructures, so demand manipulation is believed to be economic and reli-able resource in power system operation. Historically, under frequency, undervoltage and fast manual load shedding have been used by operators in emer-gencies, but the utility-level nature of these acts make them disruptive forcustomers, so operators hesitate to implement them frequently.NERC defines DSM as an important element among all required resourcesto meet the increasing demands for electricity in North America [27]. As seenin Figure 1.1, based on [27] DSM includes two components: Energy Efficiency(EE) and Demand Response (DR). Energy Efficiency programs aim to re-duce overall energy consumption in all hours of a day by putting stress onend-user energy solutions in order to solve long-term problems e.g. environ-mental effects of burning fossil fuels. In addition to energy savings, EnergyEfficiency can reduce peak demand and avoid/defer new investments. Short-term problems, on the other hand, can be handled by demand managementprograms which are referred to as Demand Response. Demand Response isdefined as responsiveness of customers to price or control signals from utilityto change the timing, level of demand or total energy consumption. DemandResponse can be exercised in different time intervals from seconds to severalhours or an entire day to serve utility as well as consumers. Demand Re-sponse programs aim to influence system reliability through peak demandreduction in periods of high market prices or low-reserve conditions ratherthan reduction in overall energy consumption [6, 28, 29].Figure 1.2 demonstrates classification of Demand Response. NERC clas-71.2. BackgroundDemand Side Management Demand Response Energy Efficiency Figure 1.1: Classification of Demand Side ManagementDemand Response Dispatch ab l e N on- Dispatch ab l e Time of use Critical Peak Pricing Controllbale Economic Time-Sensitive Pricing Ancillary Energy-Volountry Capacity Emergency Spinning Reserve Direct Load Control Non-Spinning Reserve Regulation Interruptible Demand Energy Price Demand Bidding Figure 1.2: Classification of Demand Response81.2. Backgroundsifies Demand Response programs as Dispatchable and Non-Dispatchable[27]. Non-Dispatchable Demand Response programs motivate end users toreduce their total energy consumption or shift their consumption to low risktime intervals to reduce costs or increase reliability. Dispatchable DemandResponse programs are implemented through customer response to directcontrol signals from utility for better asset utilization and running in betteroperating points to enhance reliability and efficiency. The Federal EnergyRegulatory Commission (FERC) order 719 [30] and order 745 [31] promoteparticipation in Demand Response programs and discuss compensation rulesand initiatives. Current Demand Response programs in electricity marketsare based on voluntary or directly controlled load curtailments or load re-ductions to support the power grid while providing a revenue stream forparticipating customers and aggregators [6, 28]. Demand Response providesexcellent opportunities to avoid/defer investments required to meet the cur-rent fluctuating demand and reduce the overall energy price. However, loadcurtailments or load reductions cause temporary discomfort for the partici-pants. This inconvenience limits their deployment frequency and duration.1.2.5 Demand Side Energy Storage - DemandDispatchSince demand manipulations of Demand Response programs are not able toserve power system continuously, there always have been efforts to find so-lutions to fix demand fluctuations problem. One solution could be addingstorage capacity to power grid. Energy Storage Systems (ESS) such as bat-teries, super capacitors, flywheels and Superconducting Magnetic EnergyStorage (SMES), etc. have been suggested for facilitating intermittent gen-eration integration, improving grid reliability and power quality, enablingenergy arbitrage, transmission distribution investment deference and provid-ing ancillary services in [32, 33, 34, 35]. The main drawback of using thesestorage systems with a power electronics interface is their high capital cost,91.2. Backgroundlow energy density, low cycle efficiency and potential adverse environmentaleffects [34].In contrast, inherent storage and flexibility of some residential, commer-cial and industrial loads make them capable of immediately and continuouslyresponding to control signals of the system operator significantly faster andmore accurately than conventional generation resources [36]. These loads canbe called Demand Side Storage (DSS) and used as Demand Response prod-ucts in control hierarchy of power generation to enhance generation efficiencyand system reliability. The capability to permanently aggregate and controlloads rather than just at peak times is called Demand Dispatch (DD). De-mand Dispatch is an important enabling technology to increase penetrationof intermittent renewable generation through providing grid balance service[26, 37, 38, 39, 40]. Industrial processes such as water pumping in drinkingwater storage systems, aeration in wastewater treatment plants, industrialheating and refrigeration have an inherent flexibility within their existingassets [41]. This flexibility provides required storage to be used in activepower manipulation tasks such as AGC. These processes have enough powercapacity, energy storage and no adverse reactive effect on the grid that makethem suitable resources for grid balance applications. Their cycle efficiencyis also very close to 100%. These loads can be used to provide real-timeservices to power system while fulfilling their primary obligation.Some electricity markets have accepted loads to provide regulation as aregular indefinite response service [6]. Midwest Independent System Oper-ator (MISO) [42] and Southwest Power Pool (SPP) [43] have also acceptedbehind the meter generation or controllable load among energy, reserve andregulation resources as long as the loads comply with telemetry standards andcan follow dispatch commands. In this thesis, fast, continuous and indefiniteresponse of the loads is called Demand Dispatch.101.3. State-of-the-Art Research1.3 State-of-the-Art ResearchApplications of DSM or Demand Response in Generation-Demand balance inIndependent System Operator (ISO) and Vertically Integrated utility (VIU)environments have drawn considerable attention in the literature in recentyears. Some researchers have focused on the concepts and general aspectsof DSM and Demand Response while others have seen the problem fromwholesale markets or retailers point of views.DSM can be implemented by scheduling charging Electric Vehicles (EV)sand ESSs, consumption of home appliances, Heating, Ventilation and Air-Conditioning (HVAC) loads in office areas and flexible industrial processeswith inherent storage. Direct Load Control (DLC) and Smart Pricing (SP)are two main approaches used to affect system demand profile to follow inter-mittent energy feed-ins, reduce peak demand and limit the imported powerfrom main grid connections. These approaches aim to flatten system demandby shifting consumption from peak times to off-peak times. Inefficient load-ing and committing extra local fossil-based generation units could also beavoided by demand manipulations.1.3.1 Frequency ControlBenefits of Demand Response in grid balance have been studied in differentfrequency control levels and time frames.Primary Frequency ResponseAn adaptive frequency restoration plan based on Demand Response designedin [44] to affect primary frequency response in contingency events. Authorsin [45] proposed a method to directly control domestic loads by smart metersto improve primary frequency response of the power system. The effect ofdynamic demand control on system frequency stability is studied in [46] andit is concluded that incorporating controllable frequency-dependant loads111.3. State-of-the-Art Researchcould result in a delay in frequency fall and reduction in backup rapid gener-ation capacity in contingency events. Pourmousavi et al. proposed real-timecentral demand response scheme to improve primary frequency response insmart Microgrids [47].secondary frequency responseKeyhani presented a new AGC structure based on response times of differentassets in power system to overcome the drawback of intermittency in smartpower grid [25]. Cheng et al. proposed a dynamic model to distribute AGCsignal among utility level energy storage systems to increase their perfor-mance [48].1.3.2 Aggregator DesignThere are many papers in the literature on optimal scheduling and charg-ing strategies of EVs in Vehicle-to-Grid (V2G) connections and design ofaggregation schemes to provide ancillary services e.g. regulation reserve orspinning reserve in ISO environment and improve power quality. The objec-tives are maximizing the benefits of aggregators and reducing the discomfortfor load owners.Ancillary ServicesOptimal charging of grid connected EVs to maximize the benefits of aggre-gators is considered in several recent publications. Sortomme et al. proposedunidirectional [49, 50] and bidirectional [51] charging strategies by dedicatingcapacities of Vehicle-to-Grid connections to spinning reserve and regulationreserve services to be sold in electricity markets. Han et al. also proposeda dynamic programming based aggregation design for frequency regulationproviders [52]. A two-level optimization is proposed in [53] to minimize thetotal cost of electric vehicles charging and discharging in stations. Han et al.121.3. State-of-the-Art Researchproposed a method of estimating the available power capacity from Vehicle-to-Grid to be used in aggregation design for regulation reserve providers [54].Dallinger et al. designed a regulation reserve aggregation scheme for Vehicle-to-Grid based on dynamic simulation of mobility behavior [55].Power QualityOnce the adoption of EVs and Vehicle-to-Grid connections become consid-erable, the effects of charging and discharging on distribution feeders arecritical. Shahidinejad et al. studied profile of charging Vehicle-to-Grid loadson the grid using a large database of field-recorded driving cycles, parkingtimes and locations [56]. A realistic driving habit pattern is estimated basedon this information and effects on hourly load pattern is modeled. Authorsin [56] proposed a coordinated charging algorithm for EVs to minimize powerlosses and voltage deviations on distribution feeders.1.3.3 Residential Load ControlDirect Load ControlDLC approach is based on a central Energy Management System whichschedules and remotely controls the operation and energy consumption ofeach controllable asset. This can be implemented via smart meters enabledwith two-way digital communication with EMS [2, 3]. Depending on theutility or market type, different optimization problems are formulated andsolved. In residential DLC schemes, system operator controls operation andenergy consumption of appliances e.g. residential air-conditioning [57, 58],space heating [58, 59], electric water heating [60] and EVs [61].References [62, 63, 64] proposed models for loads participating in DLCand solved optimization problems to find the savings in generation costs. Nget al. in [65] introduced a method to determine the number of groups ofpower customers to maximize the profits of utility. Chu et al. [66] presented131.3. State-of-the-Art Researchan objective function to minimize the amount of load reductions to reduceinconvenience of customers while taking advantage of load reduction in util-ities. Scheduling the interruptible and curtailable loads from aggregatorspoint of view is considered in [67]. However, all these contributions are inload reduction framework.Smart PricingSP as another approach motivates end-users to shift their consumption frompeak times to off-peak times. Following this scheme, consumers change theirconsumption pattern voluntarily without losing their privacy. Doing so, res-idential consumers tend to reduce their energy bills while enabling utilitiesand retailers to benefit from reduced peak demand and wholesale energycosts. Decentralized approaches in SP schemes are based on individual de-cision makings which may be optimal based on amount of information usedin coordination algorithms. Lack of knowledge to properly schedule resi-dential energy consumption and Advanced Metering Infrastructure are mainchallenges to fully utilize SP measures [68].Conejo et al. in [69] presented an optimization model to adjust hourlyconsumption of a customer in response to hourly prices of energy. The ob-jective of the model is to maximize the utility of the consumer subject toa minimum daily energy-consumption level, maximum and minimum hourlyload levels, and ramping limits on such load levels. A power consumptionscheduling module is proposed in [70] to provide economic benefits for cus-tomers. In this work, price of electricity is assumed to be time-varying. Thescheduler has access to past and current prices, but only statistical knowledgeabout future prices, which it uses to make an optimal decision in each timeperiod. Mohsenian Rad in [68] proposed an optimal energy scheduling unitand a price predictor unit for a residential customer in retail market environ-ment. This design is based on a two-way communication capability betweenindividual end-users and utility which enables receiving updated price in-141.3. State-of-the-Art Researchformation [3, 2]. It is shown that in a general SP environment, not onlyPeak-to-Average Ratio of aggregate response is decreased, but also user’spayments are significantly reduced which consequently provide incentives forresidential consumers to follow prescriptions of energy scheduling system. In[71] same author argues that DSM based on individual interactions betweenutility and each user does not necessarily lead to best solution in energyconsumption problem. Alternatively, an energy scheduling design based ondesired aggregate load response is designed and it is assumed that interac-tions among all users are enabled via two-way digital communication.1.3.4 Power System SupportOnce the volume of Demand Response in the power system reaches to a con-siderable level, effects of Demand Response on distribution and transmissionnetwork will be a contributing factor in Demand Response scheduling. Med-ina et al. in [72] modeled the distribution network in DR scheduling problem.They proposed changing the business process of Demand Response schedul-ing and implementation by integrating Demand Response with distributiongrid topology. An event-driven load reduction scheme is proposed in [73] toenhance system security. Coordinated Vehicle-to-Grid charging is proposedin [74, 75] to minimize distribution system losses.1.3.5 Market OperationA summary of Demand Response implementation in electricity markets isreported in [6] and [28]. Nguyen et al. in [76] proposed a concept of De-mand Response exchange to optimize the overall benefit of Demand Responseby enabling the participants to deal with other DR-involved players in themarket. Authors in [77] proposed a market-clearing tool which offers con-sumers the opportunity to reduce their energy costs by submitting shiftingbids. Parvania et al. in [78] proposed a stochastic Security Constrained Unit151.4. Research Objectives and Anticipated ImpactsCommitment (SCUC) model for scheduling conventional energy and reserveunits as well as Demand Response resources providing operating reserves inelectricity market environment.1.4 Research Objectives and AnticipatedImpactsThe main research goal in this thesis is to reach alternative approaches inGeneration-Demand balance task of a VIU e.g. BC Hydro. The main ob-jectives in reaching alternative approaches are increasing hydroelectric gen-eration efficiency and reducing mechanical wear and tear on conventionalgeneration units. These approaches are based on existing and future balancestandards. In order to achieve these goals, two criteria are considered: Generation-Demand balance using DSM as an important ingredient ofSmart Grid paradigm Generation-Demand balance with generation units under new limitsimposed by BRD draft standardObjectivesThe detailed research objectives and contributions of this PhD thesis are asfollows:1.4.1 Objective 1: Modeling Industrial FlexibleLoads as Demand Side Storage (DSS)There are some publications that introduce Demand Dispatch as a valuablealternative to traditional balancing resources [38, 79, 37, 26]. The continu-ous, repeated and non-interrupted service characteristic of flexible loads thatdoes not lead to discomfort for the owners is highlighted in these publications.161.4. Research Objectives and Anticipated ImpactsHowever, the exact modeling of Demand Dispatch resources in different bal-ancing time frames i.e. Economic Dispatch and AGC is not reported in theliterature. In other words, all published works are based on the “possibility”of using the inherent flexibility of some industrial loads as Demand Dispatchbalancing tools. The focus in this research has been exact modeling of thisflexibility.The communication infrastructure, metering and control technology ofmaking a network of flexible industrial loads under remote control is avail-able and the sponsor of this research is one example. One economic loadwhich is under operation for providing regulation reserve in ISO environ-ment is water pumping in drinking water storage systems. Using this kind offlexible load as balancing tool in DLC formulation and VIU environment isone main contribution of this thesis. In order to use this load as a DemandDispatch balancing tool, the inherent storage is modeled based on character-istic curve, efficiency model, physical and operational limits. Real physicaland operational data of this load was given by the sponsor of the research.1.4.2 Objective 2: Demand Side Storage as aSub-hourly Demand Dispatch ProductAlthough Generation-Demand balance with DSM is topic of many researchprojects in recent years, to the best of our knowledge, there is no workreported in area of grid balance structure based on Demand Dispatch in VIUs.In other words, all of the published works have focused on curtailable DemandResponse programs and load-based operating reserve capacity aggregationformulations to find the benefits for the customers and/or the aggregators.In VIU framework however, application of industrial load based DemandDispatch has not been considered in published research works.This flexibility of industrial loads provides required storage to be used inactive power manipulation tasks such as Economic Dispatch. These processeshave enough power capacity, energy storage and no adverse reactive effect171.4. Research Objectives and Anticipated Impactson the grid that make them suitable resources for grid balance applications.Their cycle efficiency is also very close to 100%. These loads can be usedto provide ongoing services to power system while fulfilling their primaryobligation. This flexibility however, is limited to different operational andphysical constraints. The most important one is “limited energy” that couldbe absorbed or released in Economic Dispatch time frame. In traditionalpractices of power system operation, there is no constraint on produced en-ergy in generation units. Designing a balance logic which includes “energyconstraints” for responsive loads is necessary to add Demand Dispatch re-sources to dispatchable assets in Economic Dispatch time frame. Formulationof a system-wide balance structure is another contribution of this thesis.1.4.3 Objective 3: An AGC Logic Based onMaximum Benefits From BRD Draft StandardsFrequency control standards have evolved during decades of interconnectedoperation to fairly distribute the benefits among all tied Balancing Authori-ties. These benefits include increasing the frequency reliability and reducingthe balancing costs in a fairly manner. Adoption of each new standard is re-ported to realize millions of dollars of savings in balancing costs for BalancingAuthorities [12, 14].Once a standard becomes accepted, researchers in academia and industryfocus on evaluating the existing AGC logics under new standards. Their goalis to ensure compliance with new standards and find the amount of resourcesrequired to be dedicated to frequency control. The other goal is to increaseBalancing Authorities benefits in terms of less generation maneuvering andmore generation efficiency. Although reliability coordinators tend to decreasebalancing costs for all utilities in a fairly manner, it is the responsibilityof each Balancing Authority to asses the existing AGC logics under newstandards and improve their benefits by developing new AGC logics whilemeeting the requirements of the new standards.181.5. Thesis OutlineAlthough lots of Balancing Authotities in all North American intercon-nections are under field trial of NERC’s draft standard BRD, to the best ofour knowledge there is no published work in this area in the literature. Noevaluation study is reported and no new AGC logic is proposed based onBRD standards. Since Balancing Authorities could consider new wide lim-its of BRD standards as an alternative to investments on utilizing differentbalancing resources e.g. DSM and ESSs, the second part of this thesis isfocused on this topic. One main contribution of this thesis is to propose anAGC logic to gain new limits and maximize the benefits of a hydroelectricdominated Balancing Authority e.g. BC Hydro. A heuristic AGC logic isproposed to maximize the hydroelectric generation efficiency and decreasethe mechanical wear and tear.Anticipated ImpactsThe outcome of this thesis regarding objective 1 is introducing another appli-cation for a State-of-the-Art technology of using a network of water pumpingloads in drinking water storage systems. Regarding objective 2, the outcomeis introducing a sub-hourly balance logic formulation which maximizes thehydroelectric generation while not compromising the operation of flexibleloads as Demand Dispatch resources. Proposing a new AGC logic based onBRD which is elaborated as objective 3, would impact the existing AGC log-ics and be implemented to reduce the balancing costs. All these applicationscould be implemented in a hydroelectric dominated VIU e.g. BC Hydro.1.5 Thesis OutlineThis thesis consists of 5 chapters. The current chapter introduces the moti-vation and objectives of this work as well as a brief background on the topics.A literature review is also included in this chapter which introduces the mainrelated works in this area. Chapter 2 provides a detailed description of themodels used as prerequisites to the proposed generation control schemes in191.5. Thesis Outlinethis work. In other words, materials of chapter 2 are used to implement thebalance schemes which are tied to the proposed balance schemes. In chap-ter 3, a sub-hourly Generation-Demand balance control structure based onDemand Dispatch is proposed. The balance logic is formulated to increasehydroelectric generation efficiency and not to compromise the main opera-tion of the loads. Moreover, an industrial flexible load is modeled for thisapplication. Chapter 4 describes a real-time generation control method basedon NERC’s BRD standards. In this chapter, an AGC logic is developed tomaximize the benefits of a hydroelectric dominated VIU. Finally, chapter 5presents a summary of the contributions of the work and comments brieflyon the future directions.20Chapter 2Generation-Demand Balance2.1 IntroductionDue to the randomness of the demand in power systems and different op-erative characteristics of different generating resources, there is a consistentmismatch between total generation and total demand in electric power sys-tem. Any imbalance between generation and demand will induce a devia-tion in system frequency from the nominal frequency value (60 Hz in NorthAmerica). The dynamic and magnitude of this deviation depends on thecharacteristics of constantly fluctuating loads and intermittent generationresources and dynamic of rotating masses in the power systems i.e. rotors ofgenerators. Permanent balance between generation and demand in real timeis the key to reliable operation of the electric power system. In order to keepthese variations within permitted levels, three different operation planningprocesses are used: Unit Commitment, Economic Dispatch and FrequencyRegulation. Each process has different time scale and must consider adequatereserve [80, 81, 82].Operating reserve is the generating capacity available to the system op-erator within a short interval of time to meet the demand in case a generatorgoes down or there is another disruption to the supply. Regulation reserveis defined as a generation capacity within which output power of some gen-erators can swing to compensate for the error between total demand plusinterchange power and generation in a specific multi-area interconnection11Multi-area interconnection is comprised of regions, or areas, that are interconnectedby tie-lines.212.1. IntroductionFigures 2.1 and 2.2 illustrate the concept of spinning reserve and regula-tion reserve in a generation unit. Each generation unit has a maximum anda minimum operating point. Depending on the current generation level andramping capability of the unit, part of the generation capacity is available asspinning reserve. As shown in Figure 2.1, in each operating interval the unitis loaded in a base point. The green area in each operating interval shows theamount of feasible increment in output power from the base point in casesof emergencies i.e. spinning reserve. Since the base point is near maxiumunit capacity in interval 1, there is less room for increment in output power.Therefore, the spinning reserve is less than intervals 2 and 3. Figure 2.2 il-lustrates the same concept for regulation reserve capacity of units where darkand light orange areas show the room for regulation down and regulation upin each sub-hourly interval, respectively.In this chapter, hierarchy of balance tasks in power systems is introduced.Different tasks and their objectives are described in section 2.2. Sub-hourlyand real-time generation control schemes proposed in this thesis are tied tothe classic tasks of hydro Unit Commitment and hydro Economic Dispatch,respectively. In order to model and implement the proposed generation con-trol schemes in a simulation environemnt, Unit Commitment and EconomicDispatch modules in a hydroelectric dominated utility should also be imple-mented. Section 2.3 describes exact modeling of generation loss function inhydroelectric generation units. This loss function as the main driving factor,is used in hydro Unit Commitment and hydro Economic Dispatch modelsused in this thesis. Hydro Unit Commitment model of section 2.4 is used inboth sub-hourly and real-time generation control schemes of chapters 3 and4. In other words, the output of Unit Commitment model of section 2.4, isfed to the input of the proposed sub-hourly and real-time models. The out-put of hydro Economic Dispatch model of section 2.5 is fed to input of theproposed real-time model of chapter 3. Therefore, this chapter is dedicated toelaboration of the concepts and mathematical models of Generation-Demand222.1. Introductionspinning reservemax unit capacitymax spinning reserveinterval 1 interval 2 interval 3MinUnitcapacitybase point(generation level)tFigure 2.1: Spinning reserve capacity compared to generation capacity insub-hourly control time stepsR eg. upinterval 1 interval 2 interval 3max Unitcapacitybase point(generation level)R eg. d ow nMinUnitcapacitytFigure 2.2: Regulation reserve capacity compared to generation capacity insub-hourly control time steps232.2. Balance Hierarchybalance tasks and generation loss functions used in this thesis.2.2 Balance HierarchyEach utility uses different generating resources to meet the total demandof the power system. For example, BC Hydro operates 31 hydroelectricfacilities and three thermal generating plants, totaling 12,000MW of installedgenerating capacity. Over 95% of the total generated electricity is fromhydroelectric facilities which are located throughout the Peace, Columbiaand Coastal regions of Advanced Metering Infrastructure and three thermalgenerating plants provide the remaining [83].As the competition in power industry increases, each utility realizes tomaximize the value of their resources at different levels of planning. Thehierarchical approach for maximizing the benefits of resources is divided toseveral operation planning models with different time steps and computa-tional burden. Advanced Metering Infrastructure Hydro uses three levels ofoperation planning to maximize its benefits [84]: Strategic long-term operation planning which covers 1 to 4 years witha monthly time step Medium-term optimization over a daily or weekly time step for up toa year Short-term optimization with an hourly or sub-hourly time step withtwo components. Short Term Optimization Model (STOM), whichproduces an optimal plant schedule for up to a week [85]; and the Dy-namic Unit commitment and Loading model (DUCL) [84], which takesSTOMs optimal plant generation schedule and produces an optimalDUCL schedule covering every time stepOn top of this operation planning tasks, real-time frequency regulation isimplemented in 2s-4s time steps through AGC.242.2. Balance HierarchyFigure 2.3 illustrates the hierarchy of control tasks and their executionfrequency and time steps in a typical power system generation-demand bal-ance scheme.2.2.1 Unit Commitment (UC)Unit Commitment is a day-ahead (or hour-ahead) decision making tool whichhas complex computational models, technical and operational constraints tooptimize generating units to be scheduled for next day to meet the hourlyforecasted demand at minimum cost. This process also schedules the ad-ditional required units for operating reserve while considering enough regu-lation reserve capacity for frequency control which are required for reliableand secure operation of power system. Therefore, depending on the costsof generation and reserve resources, Unit Commitment model can select themost economic solution among all available and possible states to supplytotal forecasted demand and required reserve capacity.For example, Advanced Metering Infrastructure Hydro uses STOM tomaximize the benefits of its resources. This is subject to meeting the do-mestic load demand and making optimal trade-off between present benefitsand the potential expected long-term value of resources [85]. The output ofthis model is hourly plant schedules, which are passed to DUCL model thatminimizes the use of water in hydroelectric facilities based on water usageand start-up/shut-dwon costs and the value of energy and reserves in sub-hourly time steps [84]. This model selects the most economic commitmentand loading in each time step and leaves enough space for regulation andoperating reserves [86, 87, 88, 89, 90].2.2.2 Economic Dispatch (ED)Economic Dispatch is the process of allocating loads among committed gen-eration units in an economic way subject to static and dynamic constraints252.2. Balance HierarchyU nit C ommitmentEconomic DispatchRegu l ationDay- ah eadH ou r- ah eadH ou r- ah eadO nl ineO nl ine 2 s- 4 s5 min- 1 5 min6 0 min- 1 5 minFigure 2.3: Control hierarchy in power system operation262.2. Balance Hierarchyof units and transmission system [11, 91, 92]. Although Economic Dispatchcan be a separate program in real-time Energy Management System of powersystems, some utilities have Unit Commitment programs including EconomicDispatch program that dispatches the load economically among committedunits. Another target of real-time Economic Dispatch program is to compen-sate the load forecast error, which is not available in day-ahead or real-timeload forecast models. The output of this program is the operating pointsof generating units in sub-hourly time steps e.g. 5 min. Depending on theconstraints considered in Economic Dispatch process, different terminologiesare used in literature e.g. Dynamic Economic Dispatch (DED) [93], ReserveConstrained Economic Dispatch (RCED) [94] and Security Constrained Eco-nomic Dispatch (SCED) [95]. Also mathematical modeling and optimizationalgorithms highly depend on characteristics of cost curves and types of con-straints. Since load forecast modules can be run in sub-hourly time steps,some papers suggest implementing a real-time Dynamic Economic Dispatch(DED) based on the most updated load forecast [96]. As the communica-tion infrastructure and computation speed of optimization routines improve,the balancing tasks can be done in smaller time steps. For example, Real-time Unit Commitment (RTUC) and Real-time Dispatch (RTD) processestake place in 15 min and 5 min time steps in California Independent SystemOperator to handle the 5 min to 5 min energy imbalances.2.2.3 Frequency RegulationRegulation is the function used to track the minute-to-minute fluctuations insystem load and unintended fluctuations in generator output, in conjunctionwith ramp-up and ramp-down load-following process to comply with reliabil-ity standards. AGC is the system that each interconnection in power systemshould be equipped with to implement regulation [10]. Regulation demandof the system is usually met by leaving some generation capacity for AGCassigned units and running generation units in operating points lower than272.3. Hydroelectric Generation Efficiencymost efficient points. In other words, AGC assigned units will be online,spinning and produce electricity at certain points called Preferred OperatingPoint (POP), which have enough space to move up and down, based on op-erating control signals (2-4 seconds signals) as shown in Figure 2.4. Giventhe regulation reserve capacity, Unit Commitment and Economic Dispatchmodels leave the required space for AGC assigned units to swing up anddown. As the average total demand of the system changes over longer timeperiods (5 to 10 min), the AGC units may have insufficient space to compen-sate for load fluctuations in shorter time periods. Therefore, a ramp-up orramp-down load-following action is required to re-establish the AGC units inbetter set-points [9].2.3 Hydroelectric Generation EfficiencyIn hydroelectric dominated utilities with multiple reservoirs, various schedul-ing modules (long-term, short-term and real-time) with different time framesare implemented to maximize the value of water resources [84]. Short-termhydro scheduling models produce optimal daily plant generation, water dis-charge/spillage and energy/reserve import/export schedules for up to a week[86, 87]. In real-time dynamic Unit Commitment models, most efficient orwater constrained units are base-loaded at the optimal schedules obtainedfrom short-term models while less efficient ones are partially loaded in swingmode to meet the required reserve capacity to realize load-following and reg-ulation. The proposed generation control method in this thesis is tied tothe real-time operation of swing plants/units which are already selected inshort-term hydro scheduling models. So the short-term scheduling modelsare excluded from the study. Moreover, it is assumed that swing plants arenot constrained to discharge maximum water to avoid spillage.282.3. Hydroelectric Generation Efficiency2.3.1 Generation Loss FunctionIn any generation scheduling and operation practice, power loss in hydro-electric generation is the main driving factor of the optimization routines.Generation of a unit in a multi-unit hydroelectric power plant is a functionof turbine efficiency, generator efficiency, water discharge and effective waterhead as [86]:Pi,j = g · ρ · ηt,i,j · ηg,i,j · he,i,j · di,j · 106 (2.1)where Pi,j (MW ) is generated power in unit i in plant j, g (m/s2) is ac-celeration of gravity, ρ (kg/m3) is water specific weight, ηt,i,j (%) is turbineefficiency of unit i in plant j, ηg,i,j (%) is the efficiency of generator i in plantj, he,i,j (m) is the effective water head of unit i in plant j and di (m3/s) iswater discharge in unit i in plant j.The effective water head he,i,j of unit i in plant j depends on forebayelevation, tailrace elevation and penstock head loss as:he,i,j = hf,j − ht,j − hp,j (2.2)where hf,j, ht,j and hp,j are forebay elevation (m), tailrace elevation (m) andpenstock head loss (m) of plant j, respectively.As seen in the equations, the power generation in hydroelectric units de-pends on many variables. The most important variable is water dischargedi (m3/s). Output power generation is controlled through changing valveposition in turbines which affect water discharge through the turbine. There-fore, generated power in a hydroelectric units is often expressed as an input-output ratio of water discharge-generated power in (MW/m3/s) which inturn depends on effective head effect and turbine efficiency.There are different ways of modeling hydroelectric generation efficiencyamong which representing generation loss in different output powers of planthas been adopted more in the literature [86, 88, 89]. In order to model gen-eration efficiency by a generation loss function, the influence of each variable292.3. Hydroelectric Generation Efficiencyof (2.1) on power generation is considered.Forebay ElevationForebay elevation is an important factor in mid-term and long-term opera-tional planning of hydroelectric reservoirs. As mentioned in part 2.2, mid-term and long-term operational planning consider a time period of one ormore years in weekly or monthly time steps and optimize water level in thereservoirs. On the other hand, in short-term operation planning and real-time dispatch, changes in water level in the reservoirs are negligible. Thisassumption is more valid in the case of larger reservoirs like the ones inAdvanced Metering Infrastructure. Since the proposed generation controlschemes of chapters 3 and 4 are in sub-hourly dispatch and real-time oper-ation and the reservoirs are assumed to be large as the ones in AdvancedMetering Infrastructure, the forebay elevation is assumed to be constant inevaluating generation loss functions.Tailrace ElevationUnlike forebay elevation, tailrace elevation could change considerably de-pending on the amount of released water in the power plant. Increasing theamount of released water through the dam leads to an increase in tailraceelevation. Increasing tailrace elevation decreases the effective water head asin (2.2), consequently.The tailrace elevation of the plant depends on the released water as [87]:ht,j = a0 + a1uj + a2u2j + a3u3j + a4u4j (2.3)where ak is the kth degree term coefficient of the 4-degree polynomial modeland uj is the water release of plant j. The water release is related to waterdischarge as:uj = dj + sj (2.4)302.3. Hydroelectric Generation Efficiencywhere dj and sj are the total water discharge and water spillage in plant j,respectively. Total discharge of a plant is the sum of unit discharges:dj =kj∑i=1di,j (2.5)where kj is the number of units in hydroelectric plant j.Penstock LossPenstock head loss hp,j represents frictional loss in the penstock and is mod-eled as a quadratic function of water discharge [87]:hp,j = βi,j · d2i,j (2.6)where βi,j is penstock loss constant in (s2/m5).Turbine EfficiencyTurbine efficiency ηt,i,j of each unit is a measure of the relation between thepotential energy of water discharge in the unit and the output mechanicalproduced energy. Turbine efficiency is usually expressed as a function of theunit discharged water or unit output power, usually known as “hill-curve”.Figure 2.5 shows a typical efficiency curve of a single hydroelectric unit.As seen in the figure, as the discharge of water increases, the efficiencyincreases up to a maximum value ηmax (point B) and then starts to decreaseafterwards. To avoid vibration and cavitation, a permissible operating rangedmin-dmax is defined for each effective water head which is between points Aand C in Figure 2.5.Reduction in turbine efficiency leads to an equivalent generation loss.This generation loss in a given forebay elevation, can be calculated based ondeviations from maximum efficiency ηmax of point B as a reference point.312.3. Hydroelectric Generation EfficiencyOperation of turbine in points other than point B leads to generation loss:pηt,i,j = g · ρ · (ηt,i,j − ηt,i,j,max) · he,i,j · di,j · 106 (2.7)where pηt,i,j (MW ) is the generation loss due to drop in efficiency of turbineof unit i in plant j and ηt,i,j,max (%) is the maximum turbine efficiency ofunit i in plant j.Generator EfficiencyGenerator efficiency ηg,i,j is a measure between input mechanical energy tothe generator and output electric power. In this range of operation, generatorefficiency changes by 2% according to [86]. This can be assumed to be a linearchange between 96.5% and 98.5%. However, upon availability of real data,exact values of generator efficiency could be obtained by interpolating amonggenerator efficiency data points.Total Power Generation LossAfter evaluating the effects of each variable of (2.1) in generation efficiency,the total power generation loss function for a multi-unit hydroelectric plantwith identical units is calculated by algorithm shown in Figure 2.6. As seenin the flowchart, calculation of generation loss starts from an initial waterdischarge of plant. Since the units are identical, water discharge of the unitsare simply found as:di,j = dj/kj (2.8)However, if the units are different, total plant discharge should be distributedoptimally among various units.After calculations based on Figure 2.6, a polynomial function could be fit-ted to the obtained points. The non-linear Least Squares curve fitting tool ofMATLAB [97] was used to fit a polynomial function to the obtained curve. A2-degree polynomial (quadratic curve) is selected because of relatively good322.3. Hydroelectric Generation Efficiencyaccuracy and simplicity. For a multi-unit hydroelectric power plant, a gen-eration loss curve is derived for every unit combination [86]. These curvescould be used in models of Unit Commitment, Economic Dispatch and theproposed generation control schemes of chapters 3 and 4. As expected, thegeneration loss curve represents combined efficiency losses from tailrace ele-vation effect, penstock friction effect and overall turbine-generator efficiencycharacteristics at different loadings of the plant.Figure 2.7 depicts total generation loss curve for a 4-unit plant whendifferent numbers of units are in operation. It is seen that the plant hashigher combined efficiency when more units are operated. For example, unit1 has about 3 MW of generation loss at 150 MW of generation. This pointcorresponds to maximum mechanical efficiency of one turbine. However, thecombined generation loss when 2 identical units are operated has minimumloss of slightly more than 4 MW, which is more efficient than running 2 unitsindependently (at 2 different reservoirs). Moreover, the combined efficiencycurve at higher number of “on” units is wider. This means that, for a specificconstant deviation from optimal points in generation axis, generation loss hasless increase in higher number of “on” units compared to the lower numberof “on” units.Efficiency and unit characteristics given in [88] are used here. The curvesare convex and a quadratic function could be fitted to each one.2.3.2 Start-up and Shut-down CostsIt is obvious that starting up or shutting down of turbines in generation unitshave negative effect on their maintenance costs and service life. However,exact modeling of these costs is almost impossible. Reference [98] describesthe main cost factors of start-up and shut-down of hydroelectric generatingunits based on experience of major electric energy producers in Sweden.This reference also evaluates the associated costs and effects on short-termoperation planning of hydroelectric units. In this thesis, we scale the costs332.4. Hydro Unit Commitmentevaluated in [98] to the size of considered generation units.2.4 Hydro Unit CommitmentIn this section, the objective of minimizing the number of start-ups andshut-downs of generating units is combined with the objective of minimizingpower generation losses through formulation of the hydro Unit Commitmentproblem.2.4.1 Problem FormulationThe problem of scheduling the number of generating units in operation on anhourly basis in a multi-unit hydroelectric plant is formulated as a dynamicdiscrete optimization model. A trade-off between hydroelectric generation ef-ficiency and the start-up and shut-down of generating units can be expressedby an objective function containing both elements. The problem of optimiz-ing the number of operating units in a multi-unit power plant on an hourlybasis can be formulated as [86]:minnh,Ph24∑h=1{cap · |∆nh|+ cp ·GL(nh, P h)} (2.9)s.t. nh = nh−1 + ∆nh (2.10)nhmin ≤ nh ≤ nhmax (2.11)where nh, nhmin and nhmax are the number of “on” units in plant, minimumand maximum number of “on” units in operation in hour h, respectively.Parameters cap and cp are start-up or shut-down unit cost ($/start−up) andpower generation loss cost ($/MWh), respectively. GL is the generation lossfunction of plant when nh units are in operation in hour h and P h is thehourly generation of plant in (MWh). Generation loss function was modeled342.4. Hydro Unit Commitmentin section 2.3. After scaling the costs evaluated in [98], values of cp and capare considered to be 50 $/MWh and 1200 $ per start-up or shut-down for a200 MW unit.Problem (2.9)-(2.11) is non-convex and mixed-integer. Different solutionmethods have been suggested in the literature among which Dynamic Pro-gramming (DP) is selected in thesis. This method have also been used inDUCL model of BC Hydro based on [84].2.4.2 Dynamic Programming (DP)In the Dynamic Programming approach that follows, we assume: A state consists of an array of units among which specific units are inoperation and the rest are off-line The start-up or shut-down cost of a unit does not depend on the unit’shistory of operation. In other words, the unit start-up or shut-downcost is a fixed amount. This assumption is always valid in hydroelectricunits. In each interval i.e. hour, a specified minimum amount of generationcapacity must be on-line.A feasible state in each period is one in which the committed units can supplythe required hourly forecasted demand, spinning and regulation reserves andthe minimum amount of the generation capacity.We set up the algorithm in a forward manner so that it starts from theinitial hour and runs to the final hour. If the start-up (or shut-down) cost ofgeneration units depend on the time they have been off (or on), then startingfrom initial hour is a more suitable approach than starting from last hour.The other advantages are possibility of specifying the initial conditions andmoving the computations forward in time as needed. A forward DynamicProgramming algorithm is shown in Algorithm 1.352.4. Hydro Unit CommitmentPower (kW)T ime( s) TP O P Regu l ation U P C apacityRegu l ation Dow n C apacityFigure 2.4: Regulation up and Regulation down capacity and Preferred Op-erating PointAlgorithm 1 Unit Commitment via Forward Dynamic Programming1: K=12: {I} = X feasible states in stage 13: for all states I in stage 1 do4: Fcost(1, I) = min{L}[Pcost(1, I) + Scost(0, L : 1, I)]5: end for6: save N lowest cost strategies in {L}7: K = K + 18: {I} = X feasible states in stage K9: for all states I in stage K do10: Fcost(K, I) = min{L}[Pcost(K, I)+Scost(K−1, L : K, I)+Fcost(K−1, L)]11: end for12: save N lowest cost strategies in {L}13: if K = M (last hour) then14: trace optimal trajectory15: else16: go to line 717: end if362.4. Hydro Unit CommitmentDisch arge ( m^ 3 / s)Efficiency (%)ηmaxdminABCηmindmaxFigure 2.5: Typical efficiency curve of a single hydroelectric generation unitThe recursive algorithm to compute the minimum cost in hour K withcombination I is formulated as:Fcost(K, I) = min{L}[Pcost(K, I)+Scost(K−1, L : K, I)+Fcost(K−1, L)] (2.12)where Fcost(K, I) is the minimum total cost from initial point to reach to state(K, I), Pcost(K, I) is the production cost in state (K, I) and Scost(K − 1, L :K, I) is the cost of transition from state (K − 1, L) to state (K, I).In this formulation, state (K, I) is the I th combination of possibilities inhour (stage) K. In order to move from one state in one hour to anotherstate in next hour in forward Dynamic Programming, a transition strategy372.4. Hydro Unit CommitmentI nitial iz e pl ant disch argeI ncrease pl ant disch arge and find u nit disch argeC al cu l ate tail race el ev ation, penstock h ead l oss and effectiv e w ater h eaddmin < d< dmaxF ind total generation l ossY esY sF ind P min and P max of pl antStartEndN oNd> dmaxN oNd< dminA dj u st a q u adratic fu nction to th e fou nd v al u esF ind overall turbine-generator efficiency Figure 2.6: Algorithm to calculate total power generation loss function in amulti-unit hydroelectric plant382.4. Hydro Unit Commitment0 100 200 300 400 500 600 700 8002468101214161820Generation (MW)Loss (MW) 1 unit2 units3 units4 unitsFigure 2.7: Generation loss curve of the modeled plant when different num-bers of units are in operationis selected. In this strategy, two control variables are defined. The firstcontrol variable is X which is the number of states to search at each period.This variable shrinks the search space. The other variable is N which is thenumber of paths to save at each hour (stage). In other words, among Xsearched states, only N paths are made and saved for each stage. Therefore,tuning these two variables controls the computational effort. The maximumvalue for X and N is 2n − 1 which is for complete enumeration where n isthe number of units. Reducing the number N leads to neglecting the highestcost paths at each time interval and saving only the N lowest cost paths.Figure 2.8 depicts the restrictions variables X and N impose on searchpaths in forward DP algorithm. As seen in the figure, in interval K, the392.4. Hydro Unit CommitmentI ntervalK - 1I ntervalKI ntervalK + 1 XNNXXFigure 2.8: Effects of N = 3 and X = 5 control variables on search space inforward Dynamic Programmingsearch space is restricted to 5 combinations out of many possibilities. Alsoamong these 5 combinations, the 3 lowest cost paths are selected and savedfor reference to the next interval.2.4.3 Solution TechniqueThe problem of (2.9)-(2.11) can be solved efficiently by a forward DynamicProgramming technique described in section 2.4.2 where each interval is anhour, the state variable is the number of generating units in operation for402.5. Hydro Economic Dispatcheach interval, and the control variable X is the number of start-ups or shut-downs of generating units in each interval. The state space is defined by theset of natural numbers between the minimum and maximum of generatingunits which are able to generate the forecasted hourly demand and providethe required spinning and regulation reserves.The corresponding equations for the problem of (2.9)-(2.11) are:f 1(n1) = cap · |∆n1|+ cp ·GL(n1, P 1) (2.13)For t = 2, . . . , 24fh(nh) = min cap · |∆nh|+ cp ·GL(nh, P h) + fh−1(nh − 1) (2.14)nh = nh−1 + ∆nh (2.15)nhmin ≤ nh ≤ nhmax (2.16)where fh(nh) is the cumulative minimum cost from the first interval to in-terval h for state nh.2.5 Hydro Economic DispatchIn this section, the objective of minimizing total generation loss or maximiz-ing total generation efficiency of a given set of committed units in sub-hourlytime intervals is addressed. The optimization is subject to static and dynamicconstraints on generating units and system-wide constraints. This problemis addressed through formulation of a hydro Economic Dispatch problem.2.5.1 Problem FormulationThe traditional Economic Dispatch problem assumes that the amount ofpower to be supplied by committed sets of generation units is constant. Sinceone main constraint is avoiding mechanical stress on equipment, the rate ofincrease or decrease in the output of generators are restricted to acceptable412.5. Hydro Economic Dispatchlimits. These ramp-rate constraints change the traditional Economic Dis-patch problem to a Dynamic Economic Dispatch (DED) problem. The otherconcern is to avoid compromising security constraints of transmission sys-tem. In other words, an optimized solution which maximizes the generationefficiency should not jeopardize transmission lines’ power flow limits. Secu-rity limits of transmission lines change the Economic Dispatch to a SCEDproblem. As mentioned earlier in this chapter, spinning and regulation re-serve constraints also could be included in Economic Dispatch and turn itto RCED. The hydro Economic Dispatch problem of this section, considersall constraints mentioned above. This problem is formulated for sub-hourlytime steps of t with length of ∆t for a time window of 1h as:minP tj ,StjCT =T∑t=1Nj∑j=1Cj(Ptj ) (2.17)s.t.N∑j=1P tj = Dt + Losst (t = 1, 2, . . . , T ) (2.18)DRtj ·∆t ≤ Pt+1j − Ptj ≤ URtj ·∆t (j ∈ Nj, t = 1, 2, . . . , T ) (2.19)P tj + Stj ≤ Ptj,max (j ∈ Nj, t = 1, 2, . . . , T ) (2.20)P tj ≥ Ptj,min (j ∈ Nj, t = 1, 2, . . . , T ) (2.21)0 ≤ Stj ≤ URtj (j ∈ Nj, t = 1, 2, . . . , T ) (2.22)Nj∑j=1Stj ≥ SRt (t = 1, 2, . . . , T ) (2.23)−Fmaxl ≤ Ftl ≤ Fmaxl (l = 1, 2, . . . , L) (2.24)In objective function of (2.17), CT is total cost of generation from t = 1to t = T . Since the time window is 1h, CT is the total hourly generation costwhich is to be minimized in this formulation. In hydro Economic Dispatch,generation cost could be equivalent to the cost of lost generation due to devi-ation from maximum efficiency which was modeled in section 2.3. Therefore,422.5. Hydro Economic Dispatchthe elements of (2.17) which are summed over a time window of 1h are gen-eration loss functions found in part 2.3. Depending on the output of hydroUnit Commitment problem of section 2.4, generation loss functions couldchange for different hours of the day. Therefore,Cj(Ptj ) = GL(UCtj , Pj) (2.25)where UCtj is the status of Unit Commitment of plant j at time t. In otherwords, the number of “on” units determines the cost curve (function) asshown in Figure 2.7. If quadratic curves such as those shown in Figure 2.7are used, the objective function of (2.17) will also be quadratic.The minimization problem of (2.17)-(2.24) is subject to the followingconstraints:Equation (2.18) models the generation-demand balance in time step twhere Dt is the total demand and losses in transmission system in time stept. The sum of the demand and loss represents the effective system demand.Constraint (2.19) limits the ramp-up and ramp-down rates of plant j in timestep t where URtj and DRtj are maximum ramp-up and ramp-down rates ofplant j in time step t. The ramp-up and ramp-down rates of plants dependon the number of “on” units, their characteristics and loading in previoustime step. Constraint (2.20) limits the generation and reserve of plant jto the maximum plant capacity P tj,max. Maximum reserve contribution of aplant is limited by its ramp-up rate as in (2.22). System total reserve is thesummation over the reserve contributions of plants. Constraint (2.23) ensuresthat the total reserve of the system in time step t is greater than minimumrequired number of SRt. Security of the system is satisfied through condition(2.24) by restricting line flows to the limit of Fmaxl in both directions, wherel is the index of transmission lines and L is the total number of lines in thetransmission system.432.5. Hydro Economic Dispatch2.5.2 Transmission Loss EffectThe transmission losses of system Losst are related to the generation in plantsP tj through:Nj∑j=1βj · Ptj = Dte (2.26)Dte = Dt + Losst (2.27)where Dte is effective system demand and βj is inverse penalty factor. If thetransmission loss is known for the time step before t, the loss for the tth timestep could be calculated as:Losst = Losst−1 + ∆Losst (2.28)where ∆Losst represents the incremental loss from time step t− 1 to t. Thetransmission loss could be modeled as function of injected power in all buses.Therefore, ∆Losst is derived as:∆Losst =Nj∑j=1∂Losst−1∂P t−1j[P tj − Pt−1j ]−Nk∑k=1∂Losst−1∂dt−1k[dtk − dt−1k ] (2.29)where Nk is the number of load buses (PQ buses) in the transmission systemand dtk is the demand in load bus k at time step t. The total system demandis sum of demand in load buses:Dt =Nk∑k=1dtk (2.30)In (2.29), ∂Losst−1∂P t−1jis the incremental loss due to 1MW generation in plant jand ∂Losst−1∂dt−1kis the incremental loss due to 1MW consumption at bus k bothat time step t − 1. It is assumed that the incremental loss does not change442.5. Hydro Economic Dispatchin the entire dispatch window of t = 1 to t = T . Since in a real situation thischange is not considerable, this assumption is valid.Using the transmission loss equation of (2.29) in constraint (2.18) leadsto:Dte = Dt + Losst−1 −Nj∑j=1∂Losst−1∂P t−1j· P t−1j −Nk∑k=1∂Losst−1∂dt−1k[dtk − dt−1k ] (2.31)where βj can be defined as:βj = (1−∂Losst−1∂P t−1j) (2.32)2.5.3 Transmission Line FlowsIn order to obtain a secure dispatch of generation, constraint (2.24) is addedto the Economic Dispatch model. Power flow calculations can relate flowsin transmission lines to the generation in power plants through concept ofGeneration Distribution Factor (GDF) [99, 100]. GDFs only depend on thetransmission network and are able to establish line flows independent of gen-eration or demand in different buses.The set of GDFs is defined as:Fl =Nj∑j=1ρl,j · Pj (2.33)where Fl are real power flow on line l and ρl,j is GDF for line l due to gen-eration unit j. Coefficient ρl,j represents the portion of generation suppliedby generation unit j which flows on line l.It should be pointed out that although (2.33) can be used to calculateline flows based on bus generations, it does not uniquely define GDFs. Inorder to find GDFs, procedure in [99] is followed and implemented.452.5. Hydro Economic DispatchUsing the GDFs of (2.33), the line flow constraint of (2.24) becomes:− F´l ≤Nj∑j=1ρl,j · (Ptj + Stj) ≤ F´l (2.34)where F´l is the real power flow limit on line l after adjusting the effect ofdemand distribution.2.5.4 Solution TechniqueDepending on the characteristics of the objective function, the optimizationproblem formulated in (2.17)-(2.24) needs different solution methods. Asmentioned in part 2.3.1, a quadratic function is fitted to the generation losscurve. Doing so, the hydro ED problem formulated in this section is convexand can be expressed as a Quadratic Programming (QP) [101].For simplicity, the above problem can be written in the form of a standardQuadratic Programming as:minx12x>Hx + f>x (2.35)s.t. Ax ≤ b (2.36)Aeqx = beq (2.37)lb ≤ x ≤ ub (2.38)where x is the variables vector, H is a symmetric matrix which represents thequadratic terms of the objective function. The linear terms of the objectivefunctions are modeled with vector f . Matrix A and vector b implement theinequality constraint (2.36). Matrix Aeq and vector beq model the equalityconstraint (2.37). Vectors lb and ub are numbers of lower bound and upperbound for constraint (2.38), respectively.Different algorithms are used to solve this problem among which InteriorPoint method has been widely accepted in power system optimization and462.6. SummaryEconomic Dispatch problems [102]. In this thesis, we use quadprog function[103] of Optimization Toolbox [104] of MATLAB [105] to to solve QuadraticProgramming problems including hydro Economic Dispatch problem.2.6 SummaryIn this chapter, the concept of generation-demand balance in power systemsis breifly described. Generation-based spinning and regulation reserves aredefined. The balance hierachy in power systems is covered and the differ-ent balancing tasks are introduced. The main driving factor in power systembalance decission making tools is generation efficiency. Therefore, the deriva-tion method of the generation loss in hydroelectric units is elaborated. Theintegration method of generation loss curves into the generations schedulingand dispatch modules is also presented. The novel balance structure andlogic presented in this thesis are tied to the main balancing tasks of powersystems. Therefore, the hydro Unit Commitment and the hydro EconomicDispatch models should be implemented as prerequisites to the proposedschemes. The prerequisite models used in this thesis are described and theformulated problems are elaborated in this chapter. The solution techniquesto solve the formulated optiization problems are also breifly explained.47Chapter 3Demand Side Storage asSub-hourly Balance Resource3.1 IntroductionDSM and ESS are two main ingredients of smart power grids to improveefficiency and reliability of the grid by reducing demand peak and variability[5]. A Smart Grid is expected to have improved monitoring and control,system resiliency against component failures and natural disasters as wellas increased renewable energy penetration [4]. DSM in general and morespecificaly Demand Response can be exercised in different time intervals fromseconds to several hours or an entire day to serve utility by reducing peakdemands and customers by providing a revenue stream.The fundamental drawback of ESS and interruptible loads in the DemandResponse context is that their response duration and frequency are verylimited. Load reductions/interruptions cause inconvenience for customers, sothese loads are only suitable to serve the power system in contingency eventsas a reliability resource and in wholesale market price spikes as economicresource. ESS can also provide frequency regulation which does not requirehigh average energy consumption or release.Some industrial processes e.g. water pumping in drinking water storagesystems, aeration in wastewater treatment plants, industrial heating and re-frigeration have inherent flexibilities which make them capable of virtuallystoring enough energy to immediately and continuously respond to controlsignals of transmission system operator. In other words, the energy is not483.1. Introductionphysically stored in these loads in another forms like the case in ESS. How-ever, the possibility of shifting the power consumption in these loads let themfunction as an energy storage asset. Their response time and quality is sig-nificantly faster and more accurate than conventional generation resources[38, 36]. These loads can realize participation of DSS in longer time steps ofgrid balance because of high energy density and power capacity. Althoughsome papers reported the capability of industrial responsive loads to provideregulation and spinning reserve without compromising their main function,to the best of our knowledge, no similar “energy-intact” Demand Dispatchscheme in sub-hourly time frame is reported in the literature.This chapter deals with improving the generation efficiency of hydroelec-tric units by optimal scheduling and dispatch of pumps in drinking waterstorage systems. At the time of this study, the only sub-hourly DemandResponse program in electricity energy markets is based on load reductions[6]. On the other hand, in this chapter a method is proposed to transforma certain amount of energy usage from individual large industrial loads toa scheduled aggregated load profile. The method is based on maximizingcustomer comfort by maintaining the energy consumption of loads equal totheir normal non-responsive operation mode. The industrial responsive loadsare scheduled in a sub-hourly (Economic Dispatch) time frame to enhancehydroelectric generation efficiency. The remaining storage of these loads canstill be used for “low-energy” balance task of frequency regulation. Thisformulation can be implemented in VIUs.This chapter addresses the following: A new generation/load scheduling method based on the combined useof DSS and conventional hydroelectric generation units Modelling the flexibility of water pumping in water storage systemsbased on their inherent constraints and water delivery requirements Modelling the integration of DSS assets in a power system transmission493.2. Proposed Control Strategynetwork as Virtual Power Plant (VPP)s [106] A system-wide optimal scheduling problem considering generation units,DSS and transmission system constraints with the objective of increas-ing hydroelectric generation efficiency A local operation optimization which maximizes the efficiency of pumpsin storage systemsStorage and operation data of a DSS system which already provides regu-lation reserve service in market environment are used. The new formulationand simulations are done to find the achievable flexibility in sub-hourly timesteps in a VIU. Since these loads are already used in 4s regulation time steps,the assumptions of available control and communication network infrastruc-ture in sub-hourly time steps is also valid.The proposed scheme is based on a centralized generation control andDLC in Economic Dispatch time frame. Utility level ESS do not have acommon modelling framework in grid balance. The current control structuresof power grids in VIUs and ESSs are based on meeting power balance andreserves in real-time operation. However in the presence of DSS, the controlstructure should be modified to include the “energy constraints” of loads ontop of the traditional “power and reserve constraints”.3.2 Proposed Control Strategy3.2.1 Grid BalanceThe traditional practice of power system operation is based on dispatchinggeneration units in different time intervals to meet real-time “power balance”and there is no constraint on produced energy especially in market-orienteddispatch. Generation units are divided to dispatchable and non-dispatchableunits. If the unit is converting stored fuel to electricity, there is no constraint503.2. Proposed Control Strategyon produced energy unless the fuel is limited. In hydroelectric units, depend-ing on the levels of reservoirs, the total amount of released water is limited.This constraint limits the amount of produced energy. In the case of intermit-tent Renewable Energy Resources (RES), predicted renewable generation isincluded in day-ahead or hour-ahead generation scheduling modules as nega-tive demand while in real-time operation, the deviations from predicted RESpower productions are handled by flexible resources or curtailments/spillageof intermittent injected power. Depending on the dominant type of gener-ation resources, every utility designs its own generation scheduling moduleswith different time steps and level of detailed modeling. In a hydroelectricdominated grid, the common practice is operating the units on hourly timesteps derived from hydroelectric generation scheduling modules [86]- [87] andputting the less efficient units on swing mode to realize load-following andregulation.3.2.2 Control StructureFigure 3.1 illustrates proposed generation control structure in a VIU withbase-loaded generation, flexible generation, DER, DSS and Demand Re-sponse. Without loss of generality, Demand Response is assumed to be ofDLC type. The generation control scheme is based on an optimizer calledthe Energy Balance Optimizer (EBO) and a Process Model module. EBOincludes characteristics of flexible generation units i.e. economic generationlimits, ramp rates, cost/efficiency curves. It also contains status and char-acteristics of responsive loads (DSS and Demand Response) i.e. storage andpower limits, ramp rates, efficiency curves, etc.The inputs to EBO are: Balance demand forecast Expected energy consumption of DSS Status and generation of flexible generation units513.2. Proposed Control Strategy Status and operation data of Demand Response Status and operation data of DSSBalance Demand Forecast module sends the most updated balance de-mand and reserve schedule to the EBO. This schedule should be met bythe commitment and dispatch of flexible generation units, dispatch of DSSresources as well as load reduction/interruption through DLC Demand Re-sponse. To find this, the generation schedule of base-loaded units and theexpected generation of DER are subtracted from total demand schedule. Fig-ure 3.2 illustrates this concept. The expected energy consumption of DSS isfound by the Process Model module based on the forecast of the load processand sent to the EBO.The expected energy consumption of DSS determines the amount of al-lowed energy consumption by DSS. This can be done by modelling normaloperation of DSS loads based on current storage and expected process datacoming from DSS resources. Doing so, total energy consumption of DSSresources in responsive operation could be set to be same as the amountthat would be consumed in non-responsive operation. Therefore, EBO doesnot cause additional energy costs and the amount of energy consumption isintact. The amount of energy consumption could also be set manually byload owners. This will be further explained in section 3.5. It is assumed thatenergy cost is constant during scheduling time window of the EBO.The commitment status and current generation of flexible generationunits are used to find static and dynamic constraints of the EBO logic for thescheduling time window. Availability status and operation data of DSS areused to calculate remaining energy storage of DSS for the next schedulingtime window which appear in storage constraints of the EBO logic.The outputs of EBO are: Dispatch signals to flexible generation units Process control signals to DSS523.2. Proposed Control Strategy Figure 3.1: Proposed control structure Figure 3.2: Demand granularity (left) and resource granularity (right)533.3. Modelling Load reduction/interruption signal to Demand ResponseDispatch signals to the flexible generation units are selected optimallyto increase generation efficiency. Process control signals to DSS determinepower consumption of loads to affect generation/demand balance. ProcessModel is described in section 3.3.3.2.3 Grid interfaceThe challenge of aggregating many DSSs to make a single operating profilefitting in current operating frameworks, is met by using the concept of VPP[106]. In this thesis, since the control structure is different from currentcontrol frameworks in VIUs and ISOs and each DSS has considerable energyand power density, we treat each one as a single controllable asset whichis directly controlled and enabled to communicate with the EBO. The DCpower flow equations are used to model the transmission system. Each DSS istreated as a generator with negative controlled generation, which is connectedto a transmission bus. The concept of Generalized Generation DistributionFactors [99] is used to find the active power flow in the transmission lines dueto positive or negative power injections by the generation units and DSS.3.3 Modelling3.3.1 FrameworkIn order to include the flexibility of DSS in grid balance applications, the firststep is to obtain a model which transforms the power/energy of the loadsto their main function during the scheduling time window. Doing so, thephysical operation flexibility could be transformed to a virtual energy storagecapable of consuming (absorbing) and not-consuming (releasing) real ,power.The amount and dynamics of the power/energy of the load is determined bythe consumption process and variables representing the operating condition.543.3. ModellingNatural outflow(r)Regulated inflow (q)Main inflowControl SignalVmaxVminFigure 3.3: Scheme of a water storage facilityOnce the model is obtained, the permissible operating range of each loadis translated to equivalent power/energy equations as well as power/energyconstraints. Then these equations and constraints are used in optimizationroutines of the proposed control strategy to realize efficient grid balance.The behaviour of each asset under different operating conditions results indifferent power and energy constraints.There are two types of constraints: “dynamic constraints” and “storageconstraints”. Dynamic constraints are determined based on power ratings,ramp rates and power to asset rate conversion. Storage constraints are inte-gral constraints which couple different control time intervals. These couplingconstraints require look-ahead capability over a time window which is satis-fied through forecasting the operating condition of each load during operatingperiod. Since operation of each load follows cycles, historical data of oper-ating conditions give necessary information on operating condition duringconsidered operating time window.553.3. Modelling3.3.2 Water Pumps in Drinking Water StorageSystemsFigure 3.3 shows scheme of a drinking water storage facility which has anumber of controllable input pumps. For simplicity, only one pump is shown.The water outflow is non-controllable and depends on the water consumptionpattern of consumers. On the other hand, water inflow is controlled by theoperator. Based on the inflow and the outflow rates of storage s, the storagelevel V ts is updated as:V ts = Vt−1s + (qts − rts) ·∆t (3.1)whereqts =Ns∑p=1qtp,s =Ns∑p=1fp,s(pp,s, Vs, t) (3.2)where fp,s is a generic nonlinear function that transforms the power con-sumption of each pump to its water pumping rate. The water inflow rateinto storage s is sum of individual inflow rates of pumps into storage s.Normal OperationThe normal operation model is used in the Process Model module to updatethe demand forecast and expected energy consumption as in Figure 3.1. Eachindustrial water pump has a characteristic curve that relates the amount ofpower consumption to water pumping rate. The curve is generally nonlinearand each pump is normally operated at the peak efficiency point in its ”on”state or not operated at all. In normal operation, a simple “on/off” controlalgorithm could be used to maintain enough water in the tank. At eachcontrol time step, based on available water in the tank, a binary numberrepresenting the ideal “on/off” states of the pumps is found:n̂ts = Ns − floor(V ts × (Ns + 1)) (3.3)563.3. ModellingThe volume of the tank is normalized by dividing to Ns+1 segments. Hence,according to (3.3) the number of ”on” pumps linearly increases as the waterlevel approaches to Vmin and vice versa. A dead-band of (3.4) is used to avoidexcessive switching of pumps to reduce wear and tear:nts ={nt−1s if |n̂ts − nt−1s | < 1n̂ts else(3.4)This logic leads to operating ns pump at their highest mechanical efficiency:qts = nts ×Qp,s (3.5)Smart OperationIf each water pump is enabled with a Variable Frequency Drive (VFD) thatcan operate the pump at speeds lower than nominal speed, a continuous rangeof flexibility is achieved. In smart operation, the VFD controls the waterinflow rate and isolates the frequency response of the load from the grid.This pump is enabled to respond to dispatch signals from the control centreto change its pumping speed immediately to achieve the desired pumpingrate and power consumption. Based on the affinity laws of a centrifugalpump for a fixed wheel diameter, pumping rate q, head H and power P indifferent speeds of N1 and N2 follow:q2/q1 = N2/N1 (3.6)H2/H1 = (N2/N1)2 (3.7)P2/P1 = (N1/N2)3 (3.8)If the pump head is constant and the speed is reduced below the rated speedof the motor, the mechanical efficiency drops. Using the pump operationdata, pumping rate, mechanical efficiency and total efficiency are found in573.3. Modellingdiscrete increments of mechanical input power. Then a curve is fitted tothese points which relates pumping rate to electric power. Calculations basedon real data show mechanical efficiency highly drops below 80% of nominalspeed. So the pumps are not allowed to operate below that point. Totalefficiency equals mechanical efficiency times electrical efficiency, which is as-sumed to be constant in this range. The curve is generally nonlinear but inthe operating range of 80% to 100% of nominal speed, it is adequate to beindependent of tank volume and operation time. For example, for a 550kWand 1200rpm pump, the fitted curve is linear between 222kW and 550kW .The curve is modelled as:fp,s(pp,s, Vs, t) ' ap,s · ptp,s + bp,s (3.9)where fp,s is linear approximately and ap,s and bp,s are constants.Dynamic constraints are defined by power ratings and ramp rates of pumpas:pp,s,min ≤ ptp,s ≤ pp,s,max (3.10)− δp,s ·∆t ≤ ptp,s − pt−1p,s ≤ δp,s ·∆t (3.11)Storage constraints are determined by minimum and maximum operatinglimits of tank and operating condition. The expected water consumptionvalues can be calculated from historical data. The storage constraints arefound as follows:The volume of water in the tank should be between minimum and maxi-mum operation limits during each control interval:Vs,min ≤ Vts ≤ Vs,max (3.12)If V 0s at the beginning of scheduling time window (t = 1, ..., T ) is known, by583.3. Modellingusing (3.1) and (3.2) the storage level at each time step is updated as:V ts = V0s +t∑k=1(Ns∑p=1qkp,s − rks ) ·∆t (3.13)substituting (3.13) in (3.12) yields:t∑k=1Ns∑p=1pkp,s ·∆t ≥Vs,min − V 0s − (t · bp,s −∑tk=1 rks ) ·∆t)ap,st∑k=1Ns∑p=1pkp,s ·∆t ≤Vs,max − V 0s − (t · bp,s −∑tk=1 rks ) ·∆t)ap,s(3.14)The left-hand sides of (3.14) represent the energy consumption of pumpsbetween dispatch intervals 1 and t in storage s which couples the controlvariables in different time steps. The right-hand sides define the minimumand maximum energy storage limits based on the expected storage wateroutflow rs.The other storage constraint is total amount of energy consumption ofload in Smart operation mode during the scheduling time window:Ns∑p=1T∑t=1ptp,s = Es,T (3.15)where Es,T is the total energy that would be consumed in storage s if expectedoutflow rs was happened during the scheduling time window. This constraintensures that the total amount of energy consumption remains intact.Once the total consumption in each DSS is found by system-wide logicof EBO, pumps should be optimally turned “on” and “off” and operated intheir continuous range to minimize the efficiency drop.593.4. Balance Logic Formulation3.4 Balance Logic FormulationIn what follows we define two optimization problems of EBO: System-wide balance which minimizes the generation loss in hydroelec-tric plants. Local operation optimization which maximizes the efficiency of pumpsin each DSS.3.4.1 System-wide BalanceIn a power system with N control buses, Ng hydroelectric power plants andNb DSS at each control bus, the objective of the system-wide EBO logicis to minimize the sum of generation loss in the hydroelectric swing plantsduring scheduling time window (t = 1, 2, ..., T ). The variables of the opti-mization problem are generation of hydroelectric swing plants P(t), reserveof hydroelectric swing plants R(t) and total power consumption in each stor-age system S(t). Elements of diagonal matrix α(t) and row vector β(t) arecoefficients of quadratic and linear terms of the fitted functions to hourly gen-eration loss curves of hydroelectric swing plants, respectively. As depictedin Figure 2.7, depending on the number of “on” units, the generation losscurves change so the elements of diagonal matrix and row vector of the ob-jective function are time-dependent. Constant terms of the fitted curves do603.4. Balance Logic Formulationnot affect the optimization.minP,R,ST∑t=1[P(t)> ×α(t)×P(t) + β(t)×P(t)](3.16)s.t. 1> × S(t) = Etotal (3.17)for t = 1, . . . , T :P(t)> × 1− 1> × S(t)× 1 = Dte (3.18)R(t)> × 1 + 1> × S(t)× 1 ≥ SRt +RRt (3.19)P(t) ≥ Pmin(t) (3.20)P(t) + R(t) ≤ Pmax(t) (3.21)0 ≤ R(t) ≤ Rmax(t) (3.22)Smin ≤ S(t) ≤ Smax (3.23)Emin(t) ≤ E× S(t) ≤ Emax(t) (3.24)− δg(t) ≤ P(t)−P(t− 1) ≤ δg(t) (3.25)− δs(t) ≤ S(t)− S(t− 1) ≤ δs(t) (3.26)− F ≤ Γ(GEN(t) + RES(t)) ≤ F (3.27)whereP(t) =[P1(t), . . . , PNg(t)]>S(t) =[S1(t), . . . , SNg(t)]>α(t) = diag(α1(t), . . . , αNg (t))β(t) =[β1(t), . . . , βNg (t)]R(t) =[R1(t), . . . , RNg(t)]Constraint (3.17) limits the total consumption of DSS loads to Etotalwhich is found by summation of Es,T for all s as in (3.15). Equation (3.18) isthe generation/demand balance constraint. Effective system demand repre-sents the Balance Demand Forecast described in part 3.2.2. System spinningand regulation reserve is met by constraint (3.19). In hydroelectric plants,spinning and regulation reserves are treated the same. The spinning reserve613.4. Balance Logic Formulationcapacity is modeled as a function of demand uncertainties and the capacityof the largest committed unit in the system as [95]:SRt = αdDte + αg ×max(Ptj,sch) (3.28)where αd and αg are constant values. Regulation reserve capacity is chosen tobe a constant percentage of maximum system demand. Constraints (3.20)-(3.23) limit the maximum and minimum power generation, reserve and DSSconsumption. Constraint (3.24) limits the integral of power consumptionfrom first interval to t-th interval according to (3.14). Matrix E includeslower unitriangular matrices with all non-zero elements equal to “1”, andEmin(t) and Emax(t) include right-hand side of (3.14). Constraints (3.25)-(3.26) limit the ramp-rate of power generation in hydroelectric swing plantsand power consumption in DSSs. Power flows in the lines are determinedbased on the DC power system model through matrix Γ where Γlb is theGDF of line l with respect to bus b [99]. The net injected power in each busGEN(t) equals to the generation of each bus minus the total consumptionof DSS. The net reserve in each bus RES(t) equals to the generation-basedreserve plus DSS-based reserve of each bus.According to the model of (3.16)-(3.27), the objective function (3.16) isquadratic while the constraints are linear. Quadratic Programming can beused to solve this optimization problem.3.4.2 Local DSS OptimizationIn DSS system s with Ns pumps, the objective of the local EBO operationis to maximize the efficiency of pumps during scheduling time window (t =1, 2, ..., T ). The variables of the optimization problem are “on/off” states of623.4. Balance Logic Formulationpumps U(t) and their power consumption L(t).maxU,LT∑t=1[U(t)> · Fs> × L(t)](3.29)s.t. for t = 1, . . . , T :Lmin ≤ L(t) ≤ Lmax (3.30)− δl ≤ L(t)− L(t− 1) ≤ δl (3.31)U(t)> × L(t) = Ss(t) (3.32)whereU(t) = [U1(t), . . . , UNs(t)]>L(t) = [L1(t), . . . , LNs(t)]>Fs(t) = [F1(t), . . . , FNs(t)]>Vector Fs in objective function (3.29) contains linear terms of linear ef-ficiency curves of pumps (1, . . . , Ns) in storage system s. Constant termsof the efficiency curves of the pumps do not affect the optimization. Ele-ments of vector U(t) are 1 in “on” state and 0 in “off” state of each pump.Elements of vector L(t) are continuous and in the range of (3.10) which isensured through constraint (3.30). Constraint (3.31) models the ramp ratelimit of individual pumps as in (3.11). Finally, constraint (3.32) ensures thatthe total power consumption of pumps is equal to the DSS power of storages found in the system-wide problem.According to the model of (3.29)-(3.32), the problem is mixed integerlinear.3.4.3 Mixed Integer Linear ProgrammingIn the problem formulated in section 3.4.2, some of the variables (status ofpumps) are restricted to integers while the objective function and the con-straints are linear. Therefore, the problem of defining the “on” and “off”633.4. Balance Logic Formulationstates of the pumps and the amount of power consumption in each pumpcould be formulated as a MILP [9]. Among different solution method, La-grange multiplier and dual optimization technique is used to solve the prob-lem. This procedure is explained below for a simple case. The same procedureis applicable for the bigger problem of section 3.4.2.The primal problem could be simply stated as:minx1,x2f(x1, x2)s.t. w(x1, x2) = 0 (3.33)where its Lagrangian function is:ϕ(x1, x2, λ) = f(x1, x2) + λw(x1, x2) (3.34)If we define a dual function, q(λ) as:q(λ) = minx1,x2ϕ(x1, x2, λ) (3.35)then the dual problem is to find:q∗(λ) = maxλ≥0q(λ) (3.36)The solution procedure involves solving two separate optimization problems.The first problem starts with initial value(s) for λ (set of λs). Then in thenext step, the value of λ is held as a constant and the second problem isformulated and solved for x1 and x2 to minimize ϕ(x1, x2, λ). After this step,the value of λ is adjusted so that q(λ) is moved from its current value towardsa larger value. A simple way to do this to use a gradient adjustment so that:λ1 = λ0 + [ddλq(λ)]α (3.37)643.5. Numerical Results & Discussionwhere α adjusts the behavior of the gradient. A good way for applying thegradient technique is to lower the rate of λ update in downward direction.For example:α = 0.5 whenddλq(λ) > 0α = 0.1 whenddλq(λ) < 0 (3.38)This process is iterated to find the solution. The closeness to the solutionin a dual optimization problem is measured by size of the gap between theprimal and the dual functions. The difference between the solutions of theprimal and the dual functions is called duality gap as:g =J∗ − q∗q∗(3.39)where J∗ is the optimal value of the primal function in one iteration and q∗ isthe value of dual function in the same iteration. For a convex problem withcontinuous variables, the duality gap will become zero at the final solutionbut in our non-convex MILP problem it will never actually become zero.The simple method mentioned above is used to attack MILP of localoperation optimization of part 3.4.2.3.5 Numerical Results & Discussion3.5.1 Simulation EnvironmentThe balance logic developed was tested on IEEE 24 bus Reliability TestSystem [107]. The single line diagram of the test system is shown in theAppendix. The transmission network consists of 24 bus locations, 20 of whichare PQ, PV or slack (control buses) which are connected by 34 transmissionlines or transformers. The generation unit data of considered benchmark653.5. Numerical Results & DiscussionTable 3.1: Generation Unit LocationsPlant Bus Unit 1 Unit 2 Nuclear1 1 6 0 02 13 0 4 03 18 0 0 14 21 0 0 15 22 6 0 06 23 0 0 1power system is changed to a system with 3 hydroelectric plants and 3 nuclearplants. Two hydroelectric unit types are called (Hydro 1 and Hydro 2). Dataof Hydro 1 and nuclear units are given in [107] and data of Hydro 2 are usedfrom a real case. The plant locations and number of units in each locationis presented in Table 3.1.Daily peak demand is 2650MW . Plant 1 is base-loaded at 100MW andthe rest of the capacity is dedicated to provide spinning reserve. Plant 5is operated at its maximum capacity during hours 8:00-22:00 and is on-lineat other times only to provide reserve. Nuclear plants are base-loaded at400MW . Plant 2 is operated in swing mode and meets the rest of the systemdemand and reserve requirements.System net demand (system demand minus DER generation e.g. windpower,...) is simulated and reproduced from trend and variations of a realcase for 24 hours with 5 min resolution. No Demand Response consideredin this study and all responsive loads are of DSS type. The distribution ofnon-responsive loads in different PQ bus locations follow 17 bus Load Distri-bution Coefficients (LDC) of the benchmark transmission system which aregiven in [107]. On the other hand, responsive loads (DSS in this study) aredistributed in the transmission system arbitrarily. Without loss of generality,in this study it is assumed that each control bus contains equal number ofDSSs. Bus demand values are assumed to have the same proportional rela-663.5. Numerical Results & Discussiontion to maximum system demand for times other than peak hour. Spinningreserve requirement of (3.28) is found taking αd = 0.05 and αg = 0.25. Theregulation reserve requirement is taken as 1% of the peak demand.Depending on the variation of total system demand and variations ingeneration/reserve of other plants, hourly scheduled generation and reserveof swing plant varies. As a result, the number of ”on” units of swing powerplant in each hour is different. An hourly UC is solved for the entire dayto find the number of units in operation based on forecasted demand andreserve to be followed by swing power plant.The Unit Commitment problem of section 2.4 is formulated and solvedfor this system. The results are shown in Table 3.2. Hourly generation of allunits are given in Figure 3.4.In this simulation, it is assumed that 3 water storage facilities are fed byeach of 20 control buses. Each storage system has 4 pumps and only swingplant is dispatched, so N ,Ng, Nb and Ns are 20, 1, 3 and 4, respectively. Inthis research, the industry partner provided access to real field data of onestorage system which is already providing regulation service. The data of thisstorage system is used for this new formulation. Data of water tank volume,pump characteristic curves and pump power ratings of real case is used forall storage systems. Since limited data was available, operational data ofthis storage system for different days of year is used as operation data ofdifferent storages in 1 day of this simulation. This provides one sample pathwhich makes the simulations deterministic. However, whenever operationaldata of all storage systems is available, Monte Carlo simulations could beused to better treat the uncertainty of the water outflow. The minimum andmaximum limits of tank volume are 20% and 80%, respectively. Total tankvolume is 60.5 km3 and rating of each pump is 550kW .The scheduling time step ∆t is 5 min, while time window T of differentlengths are used in simulations. It is assumed that the optimizer has accessto all needed data during each time window i.e. storage, outflow and con-673.5. Numerical Results & DiscussionTable 3.2: 24 Hour Unit Commitment Schedule of Swing Power PlantHour # of Units Hour # of Units Hour # of Units1 1 9 3 17 22 1 10 3 18 33 1 11 3 19 34 1 12 3 20 35 2 13 3 21 36 2 14 3 22 37 2 15 2 23 38 3 16 2 24 20 5 10 15 20020040060080010001200Time (hour)Loading (MW) Plant 1Plant 2Plant 3Plant 4Plant 5Plant 6Figure 3.4: Hourly generation schedule of base-loaded plants and swing plant683.5. Numerical Results & Discussionsumption data. The 24 hours of day is divided to T segments. Doing so,24/T runs are needed for 24 hours. For example in the case of T = 1 h, thefirst run is for hour 1:00 to 2:00 and the second run is for hour 2:00 to 3:00and so on.The model is implemented in a MATLAB environment. Depending onT , model statistics change. For example, in the case of a 1h scheduling timewindow and for the considered system, the system-wide balance model ofEBO has 1224 variables, 2314 inequality constraints, 13 equality constraintsand 2448 bound constraints. The local operation optimization model of EBOhas 96 variables half of which are of integer type, 88 inequality constraints,1 equality constraint and 8 bound constraints.MATLAB Optimization Toolbox is used to solve QP of system-wide bal-ance optimization. Lagrangian method described in part 3.4.3 is used tosolve the MILP of local operation optimization. In each iteration of solveddual optimization [9], Linear Programming (LP) problems are solved withMATLAB Optimization Toolbox. The corresponding time to solve 24 of thefirst and 60 of the second problem is: 77.61s on a system with Intel Corei5-2400 3.1GHz CPU.3.5.2 ResultsTwo cases are compared: the first case is when all pumps are in Normal modeso all loads of system are non-responsive. In this case, only generation unitsare controlled and dispatched to meet generation/demand balance. The sec-ond case is where all pumps work in Smart mode and are following dispatchrequest signals coming from the EBO. In this case, the power consumptionof the loads are treated as control variables. Obviously, the rest of systemloads are still non-responsive.693.5. Numerical Results & DiscussionNormal OperationIn this mode, base-loaded plants generate based on their hourly schedule andonly swing plant is dispatched to meet the remaining demand and reserverequirements. The power consumption of the pumps is simulated based onlogic given in section 3.3.2. Figure 3.5 shows individual and simulated diver-sified demand of a sample bus with 5 water storage system for an entire dayin Normal operation. This simulated demand is used in Demand ForecastModule to calculate effective demand in (3.18).0 500 1000 1500−1012345678Time (min)Power (MW) Storage 1Storage 2Storage 3Storage 4Storage 5TotalFigure 3.5: Individual and aggregate demand of loads in Normal mode703.5. Numerical Results & DiscussionSmart OperationIn this mode, base-loaded plants still generate based on their hourly scheduleand DSSs are scheduled to be dispatched together with swing plant. TheDispatchable Demand Forecast module described in 3.2.2 is used to find Dtein (3.18). Figure 3.6 shows the loading of swing power plant in both modeswith scheduling time step and window of 5 min and 1 h, respectively. Tobetter show the difference, only a time span between hour 10:00 to 14:00 isillustrated.600 650 700 750 8004005006007008009001000Time (min)Swing Plant Loading (MW) Normal CaseSmart CaseBest EfficiencyFigure 3.6: Swing plant loading in Normal and Smart modesLoading of the swing plant has less variation in Smart mode comparedto Normal mode. According to Table 3.2, UC does not change during thesehours. Therefore, the best efficiency point which is the minimum of curve713.5. Numerical Results & Discussionwith 3 units in Fig. 2.7 is constant and around 450 MW. The balance logickeeps loading of power plant near hourly optimum points and variations ofsystem demand are transferred to the DSS side rather than the plant side.Figure 3.7 shows aggregate power consumption of DSS in Normal andSmart modes of operation for the same time span of Figure 3.6. It is seenthat the aggregated DSS power is constrained to its maximum limit at t = 720min and to its minimum at t = 605 min. Mechanical wear and tear will alsobe reduced due to less variation in swing plant side.600 650 700 750 800020406080100120140Time (min)DSS Power (MW) Normal CaseSmart CaseFigure 3.7: Aggregate DSS power consumption in Normal and Smart modesFigure 3.8 shows the volume of a sample tank in the same time span.At the end of hour 13:00, the volume of the tank reaches to the maximumlimit in Normal mode. However, constraint 3.10 guarantees tank volume to723.5. Numerical Results & Discussionalways remain below this limit in Smart mode.600 650 700 750 8000102030405060Time (min)Tank volume (km3 ) MaximumMinimumNormal CaseSmart CaseFigure 3.8: Volume of a sample tank in Normal and Smart modesFigure 3.9 shows how 4 pumps in one DSS are operated based on localoperation optimization.Among all 4 pumps of one sample storage system, the efficiency curve ofpump 1 is the most flat one while pump 4 has the steepest efficiency curve.In other words, if the consumed power (i.e. speed) of all pumps drop equallybelow their rated power, the efficiency of pump 1 drops less than that ofpump 2 and so on. In this scenario, pump 1 is a better choice for partialloading compared to pump 2 because partial loading of pump 2 incurs moreefficiency loss. If pump 1 has the most flat efficiency curve (most efficientin partial loadings) and pump 4 has the steepest one (less efficient in partial733.5. Numerical Results & Discussion600 650 700 750 80000.10.20.30.40.50.6Time (min)Pump Power (MW) Pump 1Pump 2Pump 3Pump 4Figure 3.9: Smart operation of 4 pumps in one storage systemloadings) among all 4 pumps, pump 1 has the tendency to be more partiallyloaded than others and pump 4 has the least. As see in Figure 3.9, thelocal optimization problem of part 3.4.2 gives the same results. The red line(pump 1) is more partially loaded than other pumps and the grey line (pump4) is almost always “on” or “off” and not partially loaded at all. Doing sothe overall operation efficiency of pumps is maximized.After scheduling the Preferred Operating Points (POPs) [26] of DSSs in5 min time steps, the remaining up and down storage capacities of each DSSare calculated. Figure 3.10 shows the total hourly average of load-based upand down reserve capacities obtained in different scheduling time windows.Water release and generation loss of swing plant are also calculated based743.5. Numerical Results & Discussion10 11 12 13050100150Reg. Up Capacity (MW) 10 11 12 13050100150Time (Hour)Reg. Down Capacity (MW) 1h 6h 24hFigure 3.10: Total hourly average of Regulation Up and Regulation Downcapacity for different lengths of scheduling time windowon hydroelectric generation model of part 2.3 and compared to the Normalcase. Table 3.3 shows total daily savings in water release and generationloss compared to the Normal case in different lengths of scheduling timewindow. Although consumed electric energy of DSS system is guaranteed tobe the same as in the Normal mode, less pumping efficiency leads to moreenergy consumption for pumping the same amount of water. Therefore ifEBO restricts energy consumption of DSS to the Normal case, less wateris pumped into the tanks and the customer comfort is jeopardized. Theremaining water could be pumped into the tank by running one of the idlepumps in its maximum efficiency point. This incurs extra consumption ofenergy in the DSS side. The amount of extra energy consumption due toefficiency loss in DSS side is also shown in last column of Table 3.3.Fig. 3.11 shows the daily water savings in different DSS penetration. Thex-axis represents the power capacity of DSS and the y-axis presents the sav-753.5. Numerical Results & Discussionings in discharged water. For example, if the total capacity of all DSS assetsin the simulated system is 60 MW and the scheduling time window is 1h,0.8% less water discharge is required to generate the same amount of energythat would be generated when these loads are operated in Normal mode.The maximum DSS capacity is 132 MW which is a realistic assumption ofpenetration of water pumping loads in a real power system as also describedin the simulated case mentioned in section 3.5.1.0 20 40 60 80 100 120 14000.20.40.60.811.21.41.61.82DSS capacity (MW)Daily average water savings (%) 1h6h24hFigure 3.11: Daily average water savings in different DSS penetrationAs seen in the figure, the amount of savings monotonically increases asDSS penetration increases. However, the incremental savings vary in dif-ferent DSS penetration. As mentioned earlier, the savings are calculatedbased on generation loss functions which are dependent to Unit Commitment763.5. Numerical Results & DiscussionTable 3.3: Daily resultsTime Window Water Savings Energy Savings DSS Loss(h) (%) (MWh) (MWh)1 1.73 258.17 82.426 1.93 288.54 66.9024 1.95 291.34 91.16status of the system. As the DSS penetration changes, the Unit Commit-ment could also change which imposes different generation loss curves, con-sequently. Therefore, the amount of savings and incremental savings highlydepend on the status of Unit Commitment which is already dependent tomany factors e.g. system demand, unit availability, water constraints, ... .Theoretically, increasing the DSS capacity leads to more savings in thegeneration efficiency. The theoretical limit for efficiency improvement iswhere all generation units are operated at their maximum efficiency pointsand all the swings are transferred to DSS side. Although this seems ideal,it is not practical. Because the cost of changing all flexible loads to respon-sive DSS could exceed the benefits of savings in generation efficiency. Theother reason is that there is a practical limit for DSS penetration capacityas all loads in a power sysyem territory are not potentially flexible. Morediscussion about the results are presented in the following.3.5.3 DiscussionThe amount of savings highly depends on Unit Commitment, demand andreserve obligations. As described in section 2.3, the number of “on” unitsdefines the hourly generation loss curves and affect the objective function of(3.16). The length of scheduling time window also influences the savings ingeneration efficiency. Through constraint (3.17), the EBO logic limits thetotal energy consumption of DSSs. Therefore as the length of schedulingtime window (T in objective function) increases, the feasible region of the773.5. Numerical Results & Discussionoptimization problem expands. In other words, the equality constraint isless restrictive. Therefore, the optimal solution has lower objective functionvalue in longer scheduling time windows.Because of hard constraint (3.17), mathematically, there could be a casewhen a feasible region does not exist. In this case, the problem will be infea-sible and have no solution. The virtual energy storage of loads is equivalentto real water storage in the tanks. If for a scheduling time window, tankoverflow or lack of water is avoided according to the model of Normal op-eration, feasibility is guaranteed in Smart mode of operation for the samescheduling time window. Thus, the feasibility of the problem depends on themodel of Normal operation which gives the hard equality constraints. Asload aggregator adds more storage systems to the control network, feasibleregion is expanded. Increasing the length of scheduling time window alsoexpands the feasible region. Moreover, a safety margin of 20% for maximumand minimum volume limits of tanks is considered to compensate for theerrors associated with water outflow forecast.”As seen in Figure 3.10, the scheduling time window also affects the averagehourly load-based regulation reserve. Since the objective of EBO logic is tomaximize generation efficiency, load-based reserve capacity is not necessarilyequal in up and down directions. It is observed that the average hourlycapacities of regulation reserve in up and down directions are equal for thetime window of 1 h. Because the scheduling time horizon is same as theaveraging time horizon of regulation reserve capacity, which is 1 h. Howeverin other T s, this is not true and the up and down reserve capacities are notequal.The system-wide and the local problems of EBO are decoupled to sim-plify the optimization problem. If “on/off” status of individual pumps andtheir efficiency characteristics are considered in the system-wide problem, thescheduling problem would be large mixed-integer and quadratic. Althoughsolving the large Mixed-Integer Nonlinear Programming (MINP) problem783.5. Numerical Results & Discussiongives the optimal result, the number of variables highly increases and exe-cution time will be orders of magnitude higher than the proposed decoupledscheme. On the other hand, the sub-optimal results of the decoupled schemehas the benefit of fewer variables and very short execution time. The mod-eling proposed in this chapter is based on inherent virtual energy storage ofpumps in drinking water facilities. However, other large industrial loads e.g.aeration in wastewater treatment plants, industrial heating and refrigerationcould also be added to DSS network. Depending on the nonlinearity of theconsumption models of these loads, the coupled approach would have muchhigher complexity.Since the savings are in generation side and the costs are in DSS side, inthe proposed formulation customer discomfort and the generation efficiencysavings are not lumped together in the system-wide objective function. DSSowners would prefer to tolerate the discomfort or predict the equivalent en-ergy of the discomfort and input the amount in EBO problem through (3.15).If the benefits are to be split between DSS owner and utility, the bilateralagreement defines how the discomfort is managed. In the VIU environment,load aggregators can sign bilateral contracts with individual large industrialload owners and utility operator/owner. The benefits of shown energy sav-ings could be split between the load owners, the aggregators and the utility.As long as the normal load process is intact or slightly jeopardized, customerscould benefit directly from new revenue stream by allowing aggregators/VIUoperator to use the flexibility of their loads. Aggregators use their com-munication, control and network infrastructure and exchange the requiredinformation with VIU operator and individual loads operators.Because of the scheduling nature of the proposed problem, the look-aheadcapability and full future knowledge is required. On the other hand, load fore-cast error in large scheduling time windows is more than short scheduling timewindows. However, the operating point of any flexible resource would devi-ate from sub-hourly POPs to realize frequency regulation in 4s time steps.793.5. Numerical Results & DiscussionThe amount which these deviations occur highly depends on frequency ofthe interconnection, AGC logic and balancing behaviour of other BalancingAuthotities in the interconnection. So the real efficiency gain could be calcu-lated after real-time operation. As a very important implementation issue,any proposed generation control strategy should be compatible with utili-ties’ generation control practices including load forecast execution frequency.Thus if the load-forecast and sub-hourly dispatch are hourly updated, theproposed method with 1-h scheduling time window would be more compati-ble. The other benefit of 1-h scheduling over longer scheduling time windowsis less forecast error.Although 5 min POP of DSSs are scheduled in EBO, DSSs still havevirtual stored energy that could be used as regulation reserve or spinningreserve. The value of this reserve capacity is on top of efficiency savingsobtained from scheduling POPs of DSSs. In real-time operation, dependingon the frequency of the interconnection and frequency control standards,AGC driven operating points deviate from 5 min schedules.80Chapter 4Frequency Control in BRDStandard Paradigm4.1 IntroductionIn hydroelectric dominated power systems or systems with enough hydroelec-tric resources, load-following and AGC are less costly. However, tight ACEcontrol deviates the real-time AGC operating points of the units from thescheduled optimal ones in Economic Dispatch (ED) time frame. Avoidingthese deviations increases the generation efficiency and mechanical wear andtear of the units.This chapter proposes a heuristic real-time frequency control method tomaximize the benefits of a hydroelectric dominated BA in real-time genera-tion control under BRD frequency control standards. The performance of themethod is assessed through modeling and simulation of primary, secondaryand tertiary frequency control of a Balancing Authority operated in an in-terconnection. This method is based on the flexibility of hydroelectric unitsand could be implemented without fundamental changes to the AGC logicsbased on CPS limits. The performance of this method is evaluated againstan AGC logic based on CPS standards and a classic AGC logic.This chapter addresses the followings: A new real-time generation control strategy in a VIU based on wideACE bounds to maximize the efficiency of hydroelectric generationunits.814.2. NERC’s Frequency Control Standards Dynamic simulation of the primary and the secondary frequency controltogether with Economic Dispatch and Unit Commitment modules. Evaluation of new draft standards under scenarios where maximumbenefits of wider bounds are gained.4.2 NERC’s Frequency Control Standards4.2.1 Control Performance Standards (CPS)In interconnected power systems, frequency and interchange power control re-sponsibility is realized through tie-line biased control scheme [10]. Each areahas obligation consisting of local demand and losses, scheduled interchangeand share of interconnection frequency control support. In the presence ofinternal generation and primary frequency control, ACE measures the degreeto which each areas meets its obligation. ACE is calculated as:ACE = NIa −NIs − 10B(Fa − Fs) (4.1)where NI and F are net interchange power and frequency and subscripts aand s stand for “actual” and “scheduled” values, respectively. B is the area’sfrequency bias coefficient in MW/0.1Hz which is based on system naturalresponse β.In order to maintain frequency reliability of an interconnection, mag-nitude and average of frequency error ∆F should be kept within tolerablelimits. During decades of interconnected operation, frequency control stan-dards have been used to specify the amount which each BA should control itsACE to fairly share the benefits of interconnected operation. NERC’s Con-trol Performance Standards (CPS1 and CPS2) became effective in 1997 anddescribed by Jaleeli and VanSlyck in [18, 108]. These statistical criteria tendto maximize and fairly distribute the benefits of interconnected operation824.2. NERC’s Frequency Control Standardsamong BAs.In the rest of this chapter, y-min average of X will be noted as Xy. It isshown in [108] that if ACEs of Balancing Authoritys are random and non-coincident, Root-Mean-Square (RMS) of ∆FT will decay at rate of 1/√T .CPS1 aims to maintain RMS of ∆F1 within a statistically defined target 1which is found based on data stratification of experienced ∆F in the intercon-nection at different time intervals and applying proper decay rates. Keepingthis decaying rate ensures randomness of ACEs of Balancing Authoritys andfairly distributes the benefits of interconnected operation. Ideally RMS of∆FT at all T s should be limited at a rate of 1/√T to make ACEs random andnon-coincident but in real situation this is not the case. So the experiencedACEs are coincident and ∆F have a structure. CPS1 is non-sensitive to ac-cumulation of ∆F and is not able to make ACEs random in larger averagingtime intervals.CPS2 meant to limit inadvertent interchanges by limiting RMS of ACEover longer averaging time intervals i.e. 10 min. Technically defensible sta-tistical tolerance limits for CPS2 were found in [108]. However, it was ar-gued both by industry and academia that under typical conditions in NorthAmerican interconnections, CPS1 and CPS2 are redundant and once CPS1is satisfied, CPS2 is not required [18, 19].4.2.2 Balance Resource and Demand (BRD)StandardNERC proposed BRD standards in 2006. Currently most Balancing Author-ities of North America are under field trial for this standard. Based on thesestandards, Balancing Authoritys are required to balance their resources anddemand so that: 12-months rolling average of their Control Performance Measure (CPM)is more than 100%.834.2. NERC’s Frequency Control Standards Real-time ACE1 does not exceed their interconnection frequency de-pendent Balancing Authority ACE Limit (BAAL) for more than 30consecutive clock-minutes.Long-term performanceCPM measure is same as old CPS1. It assigns each Balancing Authoritya share of steady-state frequency control directly proportional to BalancingAuthority frequency bias B. For each 1-min period, CPM Compliance Factorof area i is calculated as:CFi = (ACEi−10Bi)× (∆F21) (4.2)where 1 is constant statistical target on RMS of interconnection ∆F1. Clock-minute CPM is then calculated as:CPMi = (2− CFi)× 100% (4.3)Once clock-minute CPMs are calculated, one-month average and rolling 12-month average of all of the 12 preceding months’ clock-minute CPMs can becalculated at the end of each month. Each BA shall maintain its 12-monthrolling average of clock-minute CPMs at least at 100%.Based on (4.2) and (4.3), if ACE1 and ∆F1 have opposite signs, areaCPM has a value more than 200%. So a positive ACE1 when frequency islow and negative ACE1 when frequency is high is a good strategy to get highCPM score. On the other hand, same signs for ACE1 and ∆F1 will get CPMscores less than 200%.844.2. NERC’s Frequency Control StandardsReal-time performanceBalancing Authority ACE Limits of high and low ∆F1 for area i are definedas:BAALl,i = −10Bi × (FTLl,i − Fs,i)×(FTLl,i − Fs,i)Fa,i − Fs,i(4.4)BAALh,i = −10Bi × (FTLh,i − Fs,i)×(FTLh,i − Fs,i)Fa,i − Fs,i(4.5)where FTLh,i and FTLl,i are high and low constant Frequency Trigger Limit(FTL) established for each interconnection i, respectively. They are calcu-lated as:FTLl,i = Fs,i − 31 (4.6)FTLh,i = Fs,i + 31 (4.7)If a BA operates outside these limits, it will contribute more than its shareof risk to the interconnection reliability.Figure 4.1 shows real-time BAAL limits and long-term 100% CPM scorefor positive and negative frequency error when Fs = 60Hz and no TimeError Correction is scheduled. Based on this standard, there is an accept-able ∆F − ACE operation region within which Balancing Authorities canmaintain their ACE1. Shaded area in Figure 4.1 shows the acceptable re-gion. If ∆F > 0, ACE can be negative to assist interconnection frequencyor be less than BAALh and if ∆F < 0, ACE can be positive to assist in-terconnection frequency or be less than BAALl. Long-term average CPMCompliance Factor still should be less than limits shown in the figure. Non-zero ACE brings the benefit of less unit maneuvering and less deviationsfrom Economic Dispatch set points. If ACE is large in 1st and 3rd quadrants,CPM CF will be low. However, operating in 2nd and 4th quadrants alwaysaccumulates high CPM CF score and assists BA to bring average CPM CFto an acceptable level.These new limits are intended to be replacement to previous CPS2 and854.2. NERC’s Frequency Control Standardsf (Hz)BAALhBAALlACE (MW)Frequency Bias line60HzCPMFigure 4.1: BA’s BAAL and CPM limitsReal - T ime B A A L C ontrolEconomic Dispatch C ontrolA C EǻFSw ing P l ant O b l igationǻP c raise/ l ow er signal to gov ernorP ED ED O u tpu tFigure 4.2: Control scheme of proposed AGC logic864.3. Proposed Real-time ACE Controlenhance the reliability of interconnection by keeping frequency within prede-fined limits in all conditions. The CPS2 was designed to limit accumulationof inadvertent interchange of Balancing Authorities by limiting average oftheir ACE within defined bounds [18]. Unlike CPS2, BAALs are dynamic,address the interconnection frequency and do not allow Balancing Author-ity’s ACE to be unbounded for 10% of the time i.e. 72 hours per month. Onthe other hand, BAALs of high and low frequency sides, depending on theinterconnection frequency, allow Balancing Authorities to deviate their clock-minute ACE average from zero more freely compared to CPS2. BalancingAuthorities are still required to comply with long-term CCPM.4.3 Proposed Real-time ACE ControlFigure 4.2 illustrates the proposed generation control scheme for AGC as-signed hydroelectric units. This generation control scheme has an EconomicDispatch module and a Real-Time BAAL Control module. Economic Dis-patch module finds the economic operating points of generation unit in sub-hourly time intervals. This module works in coordination with Unit Com-mitment program which schedules hourly “on/off” states of the unit. UCprogram is not shown in the control scheme since it is not run online.Real-time BAAL Control logic is based on monitoring ∆F1 and ACE1and finding required generation raie/lower signal ∆Pc sent to speed governorof the units. Real-time operating point of generation units are obtained byadding generation adjustment ∆Pc to sub-hourly ED operating point PED.4.3.1 Economic Dispatch ControlThis control module runs Economic Dispatch optimization problem based onmost updated real-time demand forecast and finds operating points of AGCassigned units in sub-hourly intervals. Generation schedule of base-loadedunits are subtracted from system local demand and interchange schedule and874.3. Proposed Real-time ACE Controlan optimization problem is solved to minimize system generation efficiencyloss as described in section 2.2.2. The minimization is subject to static,dynamic and system-wide constraints. Hourly sets of available units arefound through Unit Commitment problem described in section 2.2.1.4.3.2 Real-time ACE ControlReal-time ACE control consists of two control modules: BAAL control mod-ule and CPM control module. These modules track compliance with real-timeand long-term limits, respectively and are coordinated to make a single gen-eration adjustment at each control time step. BAAL control module rampsthe hydroelectric plant to the desired operating region and has higher prior-ity since it directly affects interconnection frequency. CPM control modulemakes smaller generation adjustments when BAAL control module is idle.In other words, BAAL control module has higher priority than CPM controlmodule.BAAL Control ModuleThis module is designed to maintain BA’s ACE1 within acceptable operatingregion of Figure 4.1. It tracks ACE1 and ∆F1 and makes minimum necessaryunit maneuvering while maximizing the generation efficiency as follows:Figure 4.3 shows a typical combined efficiency curve of a multi-unit hy-droelectric plant with 4 different commitment combinations. Depending onthe number of “on” units, one of the curves at a time is effective. PointsA, B, C and D are local maximums in combined efficiency-power curve fordifferent numbers of “on” units. For example, point A represents peak ef-ficiency point in “hill-curve” characteristics of 1 “on” unit while point Bshows the power (discharge) at which 2 hydroelectric turbines are at theirpeak efficiency points and so on [86, 87]. If the plant is operated in “swing”mode to realize load-following and AGC, the operating points deviate from884.3. Proposed Real-time ACE Controllocal maximums and generation efficiency is lost. Shaded area of the curveshows efficiency drop because of deviations from local maximums.Power (MW)Efficiency(%)A B C DFigure 4.3: Combined efficiency curve of a multi-unit hydroelectric plantAssume a case where the interconnection ∆F is negative and BA’s ACEwill be zero by loading the plant somewhere between B and C. The balancelogic ramps the plant to point C to build positive ACE, operate in safe regionof 2nd quadrant of ∆F − ACE plane of Figure 4.1 and get high CPM CFwhile generating at optimum efficiency. As Balancing Authority is support-ing interconnection by positive Area Control Error, ∆F will move towardpositive region and the operating point will shift towards 1st quadrant whichis bounded by BAALh. Wide ACE bound in 1st quadrant allows BA to stilloperate at C and “lean” on the interconnection without ACE control. AsBalancing Authority’s ACE or ∆F increase, the operating point will reachBAALh. According to BRD frequency control standard, BA must bring theACE back below BAALh within 30 consecutive clock minutes.Generation adjustment is obtained by Algorithm 2 where δi,j(t) is ramprate capacity of AGC plant i with j committed units and C is the BAALviolation counter. This algorithm ramps the plant toward another optimumefficiency point while making negative ACE to compensate the poor CPM CFof operating in 1st quadrant. In the assumed case, the balance logic moves894.4. Simulation Environmenttoward left in Figure 4.3 and stops at B or A depending on the size of units.This is equivalent to operating somewhere in the 4th quadrant of ∆F −ACEwhere BA “assists” the interconnection and get high CPM CF. With largenegative ACE, ∆F will be pushed toward negative values where BA is limitedby BAALl in 3rd quadrant. BA can still “lean” on the interconnection withlow CPM CF score up to reaching to the BAALl and triggering the BAALviolation counter.CMP Control ModuleThis module calculates clock-minute moving average of CPM CF based onACE and ∆F as:cpm = MAVG1−min(ACE−10B1)×MAVG1−min(∆F1) (4.8)where MAVG1−min(Y ) denotes 1-min moving average of Y . Then cpm iscompared to a predetermined threshold Cth. If a control action is needed∆Pc is set to integral of ACE, otherwise ∆Pc = 0. Control threshold Cth isselected so that very poor instantaneous CPM CF is avoided. This logic ispresented in Algorithm 3 where c(t) denotes the control signal.4.4 Simulation EnvironmentThe effectiveness of the proposed real-time ACE control method is studiedin a simulation environment described as follows:4.4.1 Power SystemA power system with N Balancing Authorities is considered in simulationswhich are interconnected as shown in Figure 4.4. The first and second areas(BA 1 and BA 2) are studied in detail considering system-wide scheduling anddispatch models together with system level and individual dynamic models904.4. Simulation EnvironmentAlgorithm 2 Real-time BAAL Control Module Logic1: Calculate ACE1(t) & ∆F1(t)2: if |ACE1(t)| < |BAAL(t)| then3: P (t+ 1) = P (t) , t← t+ 1, C = 0 go to line 14: else5: C ← C + 16: if C < 30 min then7: P (t+ 1) = P (t) , t← t+ 1, go to line 18: else9: if ACE1(t) > 0 then10: while P (t) < Pn do11: t = t+ 1 , P (t+ 1) = P (t) + ∆t · δi,j(t)12: end while13: go to line 114: else15: while P > Pp do16: t = t+ 1 , P (t+ 1) = P (t)−∆t · δi,j(t)17: end while18: end if19: end if20: end if21: go to line 1Algorithm 3 Real-time CPM Control Module Logic1: Calculate cpm as in (4.8)2: if cpm < Cth then3: c(t+ 1) = KI ·´ACE(t).dt4: else5: c(t+ 1) = 06: end if914.4. Simulation Environmentof real-time AGC. BAs (3, ..., N) are modeled as a 3 large equivalent units.Total generation capacity and peak demand of areas are shown in Figure 4.4.BA 1 is all hydroelectric while BA 2 has hydroelectric units, thermal unitswith reheat steam turbine and thermal units with non-reheat turbine. Thecapacity of equivalent units of BAs (3, ..., N) is selected to be 30% nuclear,50% thermal and 20% hydroelectric. Types and number of units in BA1and BA2 are shown in Table 4.1. The generation capacities of unit typesT1 to T6 are 500MW , 400MW , 250MW , 300MW , 200MW and 1000MW ,respectively.BA 3BA 4BA1NBA (3 , … , N)Total1Generation: 60000 MWPeak1Demand: 54000 MW BA 1Total1Generation: 10500 MWPeak1Demand: 9500 MWf of1Units: 23BA 2Total1Gen: 4200 MWPeak1Demand: 3600 MWf of1Units: 17Figure 4.4: Interconnection comprised of N BAsIn BA1 nuclear units are base-loaded at their maximum capacity while T2and T3 hydroelectric units are base-loaded at their best efficiency points. A 5-unit hydroelectric plant of type T1 is operated in swing mode to realize load-following and AGC. In BA2 thermal units are base-loaded at their maximumcapacity and a 4-unit hydroelectric plant of type T3 is operated in swing924.4. Simulation EnvironmentTable 4.1: Generation capacities of BA1 & BA2Area Hydro Th. w reh. Th. w/o reh. Nuclear1 5T1 + 5T2 + 8T3 - - 4T62 4T3 6T4 7T5 -mode to realize load-following and AGC.4.4.2 Dynamic ModelDynamic models of generation units, load damping, speed governors andturbines are obtained from [8, 109]. Inertia response of all units in one areatogether with load damping effect are lumped as a single equivalent rotatingmachine and a single damping factor representing overall frequency responseperformance. This model is adequate since in AGC studies inter-machineoscillations within each area are neglected [8, 9].Equivalent inertia Heq,i for area i is calculated as [48]:Heq,i =∑nj=1Mij ·Hi,j∑nj=1Mi,j(4.9)where Mij and Hi,j are MVA base and inertia constant of generator j in thearea i, respectively.A model of constant 5% primary frequency regulation is considered for allunits. For equivalent units of areas (3, ..., N), equivalent primary frequencyregulation (droop) Req,i is calculated as [48]:Req,i = (n∑j=11Ri,j)−1 (4.10)where Ri,j is primary frequency regulation of unit j in area i. Constant 1.5%load-damping is considered for all areas. Governor dead-bands selected to be0.036Hz for thermal units and 0.012Hz for hydroelectric units. Ramp rate934.4. Simulation Environmentof units are selected based on their typical ramping capability.Since the new ACE limits are based on the interconnection frequency andaddress the whole frequency control efforts of BAs normal and abnormal con-ditions, the primary and the secondary control should be jointly considered insimulations and performance assessments. As suggested by NERC, frequencybias coefficient B of BAs should be at least equal to the primary frequencyresponse β [110]. Therefore finding the “proper” value of BA’s β is of highimportance. Commitment, generation level, maximum capacity, ramp rateand reserve allocation restrict the amount of up-reserve or “headroom” ofunits and BA’s primary frequency response, consequently. Therefore, themethod suggested in NERC standard BAL-003-01 was simulated to find the“proper” β in the presence of all these nonlinearities [110]. Large step dis-turbances which lead to large frequency deviations (greater than 0.036Hz)were applied to the simulation model. Interchange errors were used to findβ of each BA. Then Bs of BAs were selected to be same as found βs to tuneBAs share of the interconnection frequency control support. The amount ofregulation reserve capacity of each BA is considered to be 1% of system peakdemand.The amount of spinning reserve of each BA is chosen to be dependent tohourly demand Dt and the capacity of largest committed unit in the systemP tj,sch as [95]:SR = αdDt + αg ×max(Ptj,sch) (4.11)where αd and αg are constant values. Spinning and regulation reserves aremet by non-base loaded units in BA1 and BA2 and by model of equivalentunit in the rest of interconnection.Model of synchronizing torque is used to tie the BAs and the value ofsynchronizing torques were selected to represent tie-lines capacity and ratioof BA sizes.944.5. Simulation Results and Discussion4.4.3 Static Scheduling ModelThe simulation environment involves modules of day-ahead Unit Commit-ment and hour-ahead Economic Dispatch for BA1 and BA2. Base-loadedunits are excluded fromUnit Commitment and Economic Dispatch. The UnitCommitment model of section 2.4 is used to find the number of operatingunits in a multi-unit power plant in each hour. Based on the results, thecombined efficiency curves of the units are found in each hour to be usedin the proposed real-time ACE control of section 4.3. Inputs to the UnitCommitment model are units’ data e.g. efficiency curves, generation capac-ity, ramp rate. They also include cost of power generation loss, start-up andshut-down costs as well as requirements of hourly generation, spinning andregulation reserves. Real efficiency data is used for hydroelectric plants ofBA1 and BA2. The unit cost of power generation loss and switching costsare 50$/MWh and 1200$ per start-up or shut-down for a 200MW unit.4.4.4 Load DataShort-term and random load fluctuations drive the primary and the sec-ondary frequency control and load-following control of BAs. Real 5-mingeneration data of a utility was scaled to the size of each area and used astheir short-term load. A random Gaussian noise with zero mean and stan-dard deviation proportional to square-root of BA’s size [20] was also addedto each area’s short-term load as random load fluctuations.Generation of base-loaded units was taken out from total area load tofind swing plant load. Therefore, swing plant load consists of short-term andrandom fluctuations which should be followed by generation maneuvering.954.5. Simulation Results and DiscussionTable 4.2: 24 Hour UC Schedule of Swing Power Plants of BA1 & BA2Hour BA1 BA2 Hour BA1 BA2 Hour BA1 BA21 4 3 9 3 5 17 5 32 5 3 10 3 5 18 5 33 5 2 11 4 5 19 5 34 4 2 12 3 5 20 5 35 3 3 13 3 5 21 5 36 5 3 14 3 5 22 5 37 5 3 15 3 4 23 5 38 5 3 16 3 4 24 4 34.5 Simulation Results and Discussion4.5.1 ResultsTable 4.2 shows the UC schedule of swing plants in BA1 and BA2. Sincethe units are identical, the value of each row of table shows the number ofhourly “on” units in swing plants of BA1 and BA2. These numbers definethe plant capacity, ramp rate and maximum efficiency points in each hour.Figure 4.5 shows the results of ED module and maximum efficiency pointsfor swing plants of BA1 and BA2. It is seen that following sub-hourly de-mand, even with ED logic, leads to deviations of operating points from max-imum efficiency points. In the real-time operation, however, the operatingpoints in AGC time frame are defined based on frequency control logic ofBAs and control manner of the rest of the interconnection.The AGC logic proposed in section 4.3 is simulated for two study casesand the results are compared with a benchmark logic in terms of CPM perfor-mance, generation efficiency and unit maneuvering. The AGC logics of eachBA in study cases and benchmark are presented in Table 4.3 where BAALrefers to the proposed method based on maximum benefits from BRD stan-dard and CPS refers to the method proposed in [16] based on maximum964.5. Simulation Results and Discussion0 100 200 300 400 500 600 70005001000150020002500Time (min)Power (MW)ED BA1Max Eff. BA1ED BA2Max Eff. BA2Figure 4.5: Results of Economic Dispatch for BA1 and BA2Table 4.3: AGC logics of each BA in each study caseBA Case 1 Case 2 Benchmark1 BAAL BAAL CPS2 BAAL CPS CPS(3, ..., N) Generic Generic Genericbenefits from CPS standards. The AGC logic of the rest of the intercon-nection is a generic AGC which models negative frequency error during loadpick-up hours and positive frequency error during load drop-off hours.Case 1In this case, BA1 and BA2 are operated under AGC logic proposed in thischapter and the results are compared with the benchmark. Figure 4.6 shows974.5. Simulation Results and Discussion0 200 400 600 800 1000 1200 1400−1000−50005001000Time (min)ACE Limits (MW)BAALHBAALLACE1 Case 1ACE1 BenchmarkL10(+)L10( )Figure 4.6: ACE1 and BAALl, BAALh and CPS2 limits for BA1 in Case 1ACE1 in Case 1 and the benchmark, BAALH , BAALL and CPS2 limitsfor BA1 in Case 1. Depending on the interconnection frequency and ACE1i.e. operating quadrant of Figure 4.1, only one of BAALH , BAALL may beactive in each clock minute. Based on CPS2 standard, ACE10 of each BAmust be less than constant number L10 [16]. As seen in Figure 4.6, ACE1is less restricted by BAAL limits than L10. Because of very large valuesof BAALH and BAALL in some clock minutes, only the values between1000MW and -1000MW are shown. Although large bounds of BAAL are lessrestrictive compared to CPS2 requirement, large instantaneous ACE valueslead to poor CPM score. In other words, large temporary deviations of ACEare tolerable only if tighter ACE control in the future brings the averageCPM score within the required number of (4.3). The CPM Control Moduleof section 4.3 ensures the clock-minute values of CPM remain bounded. As984.5. Simulation Results and Discussion0 200 400 600 800 1000 1200 1400−1000−50005001000Time (min)ACE Limits (MW)BAALHBAALLACE1 Case 1ACE1 BenchmarkL10(+)L10( )Figure 4.7: ACE1 and BAALl, BAALh and CPS2 limits for BA2 in Case 1seen in Figure 4.6 although ACE is loosely controlled, BAAL limits are notviolated.Figure 4.7 shows ACE1 in Case 1 and the benchmark, BAALH , BAALLand CPS2 limits for BA2 in Case 1. As seen in the figure, ACE1 of BA2reaches to BAALH and BAALL limits 13 times during the day but the logicBAAL Control Module brings makes large generation maneuvering to bringACE1 to acceptable region. According to BRD standard, ACE1 should notviolate BAALH or BAALL for more than 30 consecutive clock minutes. Inthis simulation, conservatively ACE1 is brought back in far less than 30consecutive clock minutes. This is done not to compromise interconnectionfrequency reliability because of gaining generation efficiency. However, BAscan still tolerate violated BAALH or BAALL for about 30 consecutive clockminutes. Although magnitude of ACE1 can be as high as BAALH or BAALL994.5. Simulation Results and Discussionfor 30 consecutive clock minutes, very poor CPM score will built up duringthis time. In this case, CPM Control Module makes small generation ad-justments to avoid very poor CPM score. As seen in Table 4.4, CPM scorefor BA1 and BA2 in Case 1 are above 100%. This means gaining efficiencyhas not compromised CPM compliance level over the simulated time i.e. 24hours.Case 20 200 400 600 800 1000 1200 1400−1000−50005001000Time (min)ACE Limits (MW)BAALHBAALLACE1 Case 2ACE1 BenchmarkL10(+)L10( )Figure 4.8: ACE1 and BAALl, BAALh and CPS2 limits for BA1 in Case 2Table 4.4: Average daily CPM scoreBA Case 1 Case 21 109.75% 111.5%2 171.3% 122.1%1004.5. Simulation Results and Discussion0 200 400 600 800 1000 1200 1400−1000−50005001000Time (min)ACE Limits (MW)BAALHBAALLACE1 Case 2ACE1 BenchmarkL10(+)L10( )Figure 4.9: ACE1 and BAALl, BAALh and CPS2 limits for BA2 in Case 2In this case, BA1 and BA2 are operated under AGC logic proposed in thischapter and the one in [16] respectively and the results are compared withthe Benchmark. Figure 4.8 and Figure 4.9 show ACE1 in Case 2 and theBenchmark as well as BAALH , BAALL and CPS2 limits for BA1 and BA2in Case 2. According to the results, BA1 can tolerate large ACE within itsterritory and gain efficiency. Since BA2 is operating under CPS, ACE varia-tions will be in the order of the Benchmark, as demonstrated in Figure 4.9.As seen in Table 4.4, average CPM score for Case 2 is also compliant withBRD standard. BA2 has higher CPM score since its logic does not focus onefficiency and more generation maneuvering is done.Table 4.5 shows average daily efficiency gains in BA1 and BA2 comparedto the Benchmark. Efficiency gains are calculated based on total generationand discharged water in hydroelectric units using efficiency curves. In Case1,1014.5. Simulation Results and Discussionsince the BAAL logic keeps the generation on optimum efficiency points andsmall generation adjustments are minimized, efficiency is improved in bothareas. However in Case2, CPS logic of BA2 leads to more generation ad-justments while BAAL logic in BA1 leads to more interconnection frequencydeviation. More frequency deviations in the interconnection leads to morerequired generation adjustments in BA2 and aggravates the overall efficiencyin BA2.Table 4.5: Efficiency gains compared to the benchmarkBA Case 1 Case 21 0.65% 1.3%2 0.41% -0.61%Figure 4.10 compares generation adjustments in BA1 for Case1 and theBenchmark. In the upper figure, generation adjustments of CPM moduleof BAAL logic are shown while in the lower figure, those of CPS logic inthe Benchmark are demonstrated. Generation maneuvering capacity of bothmodules are set to be 150MW both in up and down directions. As seenin the figure, BAAL logic leads to extremely lower number of generationadjustments both in up and down directions which in turn leads to lowermechanical wear and tear on hydroelectric units. According to Figure 4.11,the number of generation pulses in Case2 for BA2 is more than the Bench-mark. The reason is less generation control in BA1 which is operated underBAAL logic.1024.5. Simulation Results and Discussion−150 −100 −50 0 50 100 150050100150Swing (MW)BA1Case1−150 −100 −50 0 50 100 150050100150Swing (MW)BA1BenchmarkFigure 4.10: Number of generation control swings in BA1 in Case1 (upperfigure) and in Benchmark (lower figure)1034.5. Simulation Results and Discussion−150 −100 −50 0 50 100 1500204060Swing (MW)BA2Case2−150 −100 −50 0 50 100 1500204060Swing (MW)BA2BenchmarkFigure 4.11: Number of generation control swings in BA2 in Case2 (upperfigure) and in Benchmark (lower figure)104Chapter 5Conclusion and Future Work5.1 ContributionsThis work focuses on finding new “strategies” that hydroelectric dominatedVIUs can deploy using Demand Side Management and the newly proposedNERC AGC standard to make hydroelectric generation more efficient.In this thesis, different balance tasks in a hydroelectric dominated VIUsare described. Also derivation of hydroelectric generation loss function asthe main contributing factor in generation scheduling decision making toolsis elaborated. The flexibility of water pumping load in drinking water storagefacilities is modeled as a Demand Dispatch resource. Moreover, two differentgeneration control schemes are proposed. The first one is based on utiliz-ing DSS through aggregation and direct control of flexible industrial loads.This generation control method is based on a sub-hourly balance logic andcombined use of hydroelectric generation units and responsive loads. Thesecond generation control method is a real-time AGC logic based on takingmaximum advantage of wide ACE bounds in NERC’s latest draft standardi.e. BRD frequency control standard.In general, one contribution of this thesis is to provide an approach to dothe cost benefit analysis of different strategies. With respect to the initialobjectives of this research, the contributions of this works can be summarizedas follows:1055.1. Contributions5.1.1 Objective 1In Chapter 3, the inherent flexibility of water pumping in drinking water stor-age systems is modeled as a Demand Dispatch resource. Operation of pumpsin Normal and Smart modes are described and mathematically modeled. Amathematical model which transforms the power/energy constraints of thisload to its main function in both modes of operation is developed. The per-missible operating range of the load is translated to equivalent power/energyequations which could be used in any scheduling optimization as static anddynamic constraints. Dynamic constraints are derived based on power rat-ings, ramp rates and power to asset rate conversion. Storage constraintsare modeled as integral constraints coupling different operating control timesteps. Storage constraints are added to ensure energy-neutrality of the bal-ance logic. In other words, the power consumption of loads in Smart modeof operation does not exceed the value of energy consumption Normal oper-ation mode. Doing so, customer comfort is maintained and Smart operationis justified more. This model is general and could be used in any centralizedbalance logic or aggregation design method.5.1.2 Objective 2The fluctuating system demand and generation capacity set aside for oper-ating reserves, reduces the efficiency of hydroelectric power generation. InChapter 3, a new sub-hourly generation/load balance structure and schedul-ing optimization is proposed. This method is based on the outcomes regard-ing to the Objective 1. Integration of DSS assets in power system transmis-sion network is realized through the concept of VPP. A system-wide opti-mal scheduling problem is formulated considering generation units, DSS andtransmission system constraints. The objective of system-wide balance is tomaximize hydroelectric generation efficiency while minimizing the customerdiscomfort. Therefore, POP of swing power plant and DSSs are scheduled1065.1. Contributionsto be dispatched in 5 min time steps. The formulation is a DLC scheme andbased on centralized control of generation and DSSs. Customer comfort ismaximized by equalizing total energy consumption of responsive loads withtheir normal water serving requirements, which is modeled as Objective 1. Alocal operation optimization in the form of MILP is also designed to minimizeefficiency drops in Smart mode of operation for the modeled DSSs. Simu-lations were done on a benchmark power system (IEEE 24 BUS ReliabilityTest System shown in Appendix) using real data of hydroelectric generationand responsive loads. In the simulated system, through replacement of about5% of system peak demand with continuous-range controlled DSS, up to 2%savings in hydroelectric generation efficiency in swing-mode is achieved.5.1.3 Objective 3Based on NERC’s latest frequency standard, Balancing Authorities can toler-ate larger ACE within their areas and practice less generation maneuvering.According to BRD standard, Balancing Authorities are responsible to keeptheir ACE within frequency dependent limits i.e. BAAL. The heuristic real-time frequency control method proposed in Chapter 4 of this thesis is basedon taking maximum advantage of new draft standards i.e. BRD standards.A two-layer AGC logic is designed where the first layer i.e. BAAL Con-trol Module implements large generation swings and the second layer i.e.CPM Control Module implements 4s deviations from optimum points. Theeffectiveness of the proposed method is assessed through modeling of UnitCommitment and Economic Dispatch as well as dynamic simulation of thenovel real-time AGC logic in hydroelectric dominated VIUs. The proposedAGC logic is tested for different study cases on two Balancing Authoritieswith different sizes which are tied in an interconnection. The results are com-pared with a benchmark case where all Balancing Authorities are operatedunder CPS standards. It is demonstrated that under BRD standards, hy-droelectric generation efficiency is increased up to 1.3%. Also, deviations of1075.2. Future Workgeneration units from scheduled optimum operating points are significantlyreduced which leads to decreased wear and tear on hydroelectric units. Itis shown that, regardless of DSS-based approaches, using the AGC standardcan provide significant benefit to utilities if they play the game properly.5.2 Future WorkAs the next steps of this study, the author would like to point out thesedirections and tasks. Although water pump in drinking water storage systems is modeled asDSS to realize Demand Dispatch, there are other loads with inherentstorages that could also be turned into DSS by adding metering, controland communication infrastructure. Aeration in wastewater treatmentplants, industrial heating and refrigeration have large amount of virtualenergy storage within their assets making them capable of providingsub-hourly Demand Dispatch. The method proposed in Chapter 3 issuggested to be investigated for development of DSS models for theseindustrial loads. The centralized generation control scheme of Chapter 3 is based on VIUstructure. In ISO framework however, it is the responsibility of aggre-gator to transform a certain amount of energy usage to a scheduled loadresponse and bid into Ancillary Services market as Demand Responseproducts e.g. load-based regulation and spinning reserve. Therefore,the structure is no longer centralized among responsive loads and gen-eration units. Because the load aggregator is a market participant andthere is no common benefit between Generation Company (GENCO),Distribution Company (DISCO), aggregator and ISO. In this frame-work, DSSs could be modeled as standard Demand Response products.The objective is maximizing the benefits of aggregator while maintain-ing customer comfort. Related works such as [49, 50, 53, 51, 52] are1085.2. Future Workabout optimal charging and discharging strategies for V2Gs to maxi-mize the benefits of aggregators. Extending this concept to industrialDSS is suggested as a research topic which looks promising for academiaand industry. Scheduling the POP of DSSs in sub-hourly time frame defines their Upand Down regulation capacity such as the case shown in Figure 3.10.This capacity still can be used for real-time balance in AGC time frame.In real-time operation, ISOs split the AGC signal among selected re-sources based on market clearing status. On the other hand, the AGCsignal could be split among different resources also in VIU frameworkwhere load-based regulation could also be one of these resources. Ifthe operator owns the generation, the energy efficiency/fuel cost is alegit reason to use load-based flexibility. Another legit reason is freeingup the capacity of tie-lines dedicated to import/export of energy andnot to import/export regulation. A dynamic AGC signal distributionmethod which maximizes the benefits of VIUs in terms of generationefficiency is suggested as a future step of this study. 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(MVA)1 2 0.146 175 11 13 0.488 5001 3 0.2253 175 11 14 0.0426 5001 5 0.0907 350 12 13 0.488 5002 4 0.1356 175 12 23 0.0985 5002 6 0.0205 175 13 23 0.0884 5003 9 0.1271 175 14 16 0.0594 5003 24 0.084 400 15 16 0.0172 5004 9 0.111 175 15 21 0.0249 10005 10 0.094 350 15 24 0.0529 5006 10 0.642 175 16 17 0.0263 5007 8 0.0652 350 16 19 0.0234 5008 9 0.1762 175 17 18 0.0143 5008 10 0.1762 175 17 22 0.1069 5009 11 0.084 400 18 21 0.0132 10009 12 0.084 400 19 20 0.0203 100010 11 0.084 400 20 23 0.1112 100010 12 0.084 400 21 22 0.0692 500124Appendix A. Transmission System DataFigure A.1: Single Line Diagram of IEEE 24 BUS Reliability Test System125
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Efficient hydroelectric generation using novel balance schemes Fekri Moghadam, Milad 2015
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Title | Efficient hydroelectric generation using novel balance schemes |
Creator |
Fekri Moghadam, Milad |
Publisher | University of British Columbia |
Date Issued | 2015 |
Description | In order to control frequency and interchange schedules in electric power systems, a permanent balance between generation and demand is necessary. Following electric demand has traditionally been realized by control of flexible generation resources. As a consequence, conventional generation units are utilized in lower maximum output power and less efficient operating points. Transition toward increased penetration of intermittent Distributed Energy Resources (DER) requires more balancing capacity in power systems which makes frequency control a more challenging issue. Demand Side Management (DSM) is a main ingredient of Smart Grid (SG)s to improve efficiency and reliability. Some industrial processes have inherent flexibilites making them capable of virtually storing enough energy to immediately and continuously respond to control signals of transmission system operator. These loads, when equipped with advanced metering, communication and control infrastructure, can realize participation of Demand Side Storage (DSS) in sub-hourly time steps of grid balance. In order to fairly distribute the benefits of interconnection among all control areas, frequency control standards are defined and proposed by reliability coordinators e.g. NERC. Once new standards become effective, Balancing Authorities (BA)s modify their Automatic Generation Control (AGC) and real-time balance logic to comply with the new requirements. This research is dedicated to finding novel balance structures in sub-hourly dispatch and real-time operation. The objectives of the proposed balance structures are to increase hydroelectric generation efficiency and reduce unit maneuvering leading to mechanical wear and tear. A new Demand Dispatch (DD) application for industrial flexible loads and a new sub-hourly balance structure based on use of DSS are developed in this thesis. Also in real-time operation, a novel AGC logic is proposed to maximize the benefits of a hydroelectric dominated Balancing Authority based on latest frequency control standards. It is shown through mathematical modeling, static scheduling optimization formulations and dynamic simulations that utilizing 5% of system peak demand as sub-hourly dispatched DSS saves up to 2% in generation efficiency and utilizing the proposed real-time AGC logic leads to generation efficiency saving of up to 1.3%. Both proposed methods also significantly reduce mechanical wear and tear. |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | eng |
Date Available | 2015-08-24 |
Provider | Vancouver : University of British Columbia Library |
Rights | Attribution-NonCommercial-NoDerivs 2.5 Canada |
DOI | 10.14288/1.0166630 |
URI | http://hdl.handle.net/2429/54605 |
Degree |
Doctor of Philosophy - PhD |
Program |
Electrical and Computer Engineering |
Affiliation |
Applied Science, Faculty of Electrical and Computer Engineering, Department of |
Degree Grantor | University of British Columbia |
GraduationDate | 2015-09 |
Campus |
UBCV |
Scholarly Level | Graduate |
Rights URI | http://creativecommons.org/licenses/by-nc-nd/2.5/ca/ |
AggregatedSourceRepository | DSpace |
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