Applied Science, Faculty of
Electrical and Computer Engineering, Department of
DSpace
UBCV
Bogado, German
Master of Applied Science - MASc
University of British Columbia
Remote off-grid communities rely on diesel for generating electricity. In addition to the greenhouse gas emissions, diesel generators require a constant fuel supply leading to transportation and logistics issues over the lifespan of the project. On the other hand, PV-BESS microgrids offer a suitable alternative to provide clean and sustainable energy to the communities due to their decreasing cost, small size, versatility for interconnection and low maintenance. Conventional methods determine the required PV-BESS installed capacity utilizing simple models to assess the financial aspects of the systems. However, they do not provide information about the implementation, thus requiring an additional stage to select available commercial devices and the correct series-parallel interconnection of the PV, BEES and power converters. Consequently, the overall cost of the system increases, while the performance drifts away from the predicted behaviour. In this work, a novel sizing methodology is proposed, reducing the cost of the system by 23%, the installed PV and BESS by 9% and the necessary power converters by 58%. The proposed approach facilitates a comprehensive study of the scenario, incorporating advanced models in the optimization problem, maintaining the financial goals, and adding new goals to a multi-objective optimal energy management strategy (EMS). The proposed optimal solution provides the number of series-parallel interconnected PV and BESS, and the required number of power converters, which eliminates the need for an additional implementation stage. The developed tool provides a comprehensive understanding of standalone microgrids, closing the gap between the optimal solution and industrial implementation.
Improved Sizing of PV-BESSDC Microgrids: AMixed-Integer OptimizationbyGerman BogadoIng., Universidad Nacional del Comahue, 2016A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Electrical & Computer Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)December 2019c© German Bogado 2019The following individuals certify that they have read, and recommend to the Faculty ofGraduate and Postdoctoral Studies for acceptance, the thesis entitled:Improved Sizing of PV-BESS DC Microgrids: A Mixed-Integer Optimizationsubmitted by German Nahuel Bogado in partial fulfillment of the requirements forthe degree of Master of Applied Sciencein Electrical and Computer EngineeringExamining Committee:Dr. Martin Ordonez, Electrical and Computer EngineeringSupervisorDr. William Dunford, Electrical and Computer EngineeringSupervisory Committee MemberDr. Hermann Dommel, Electrical and Computer EngineeringSupervisory Committee MemberiiAbstractRemote off-grid communities rely on diesel for generating electricity. In addition to the green-house gas emissions, diesel generators require a constant fuel supply leading to transportationand logistics issues over the lifespan of the project. On the other hand, PV-BESS microgridsoffer a suitable alternative to provide clean and sustainable energy to the communities due totheir decreasing cost, small size, versatility for interconnection and low maintenance. Conven-tional methods determine the required PV-BESS installed capacity utilizing simple models to assess the financial aspects of the systems. However, they do not provide information about the implementation, thus requiring an additional stage to select available commercial devices and the correct series-parallel interconnection of the PV, BEES and power convert-ers. Consequently, the overall cost of the system increases, while the performance drifts away from the predicted behaviour. In this work, a novel sizing methodology is proposed, reducing the cost of the system by 23%, the installed PV and BESS by 9% and the nec-essary power converters by 58%. The proposed approach facilitates a comprehensive study of the scenario, incorporating advanced models in the optimization problem, maintaining the financial goals, and adding new goals to a multi-objective optimal energy management strategy (EMS). The proposed optimal solution provides the number of series-parallel inter-connected PV and BESS, and the required number of power converters, which eliminates the need for an additional implementation stage. The developed tool provides a comprehensive understanding of standalone microgrids, closing the gap between the optimal solution and industrial implementation.iiiLay SummaryAccess to clean and renewable electricity is necessary to ensure the sustainable developmentof remote communities. Providing clean and reliable energy can be achieved by deployingnew standalone microgrids, incorporating photovoltaic (PV) energy as a renewable resource,and battery energy storage systems (BESS) to supply the power when the solar resourceis not available. However, there is no go-to solution for determining the optimal size of aPV-BESS microgrid.This work proposes a sizing methodology that incorporates the detailed interconnectedmodels of the system into an optimization problem formulation. The proposed methodallows obtaining a solution that maintains the performance of the microgrid while requiringless capital investment, less PV-BESS capacity installed, and fewer power conversion stageswhen compared to the traditional methods.ivPrefaceThis work is based on research performed at the Electrical and Computer Engineering de-partment of the University of British Columbia by German Bogado, under the supervision of Dr. Martin Ordonez.A first version of this work was presented in the IEEE Applied Power Electronics Confer-ence, APEC 2019 [1].As the first author of these publications, the author of this thesis developed the theoret-ical contribution, the simulation models, and performed the sensitivity results. The author received advice and technical support from Dr. Ordonez and members of his research team.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.1 Optimal Sizing Problems . . . . . . . . . . . . . . . . . . . . . . . . 21.2.2 Algorithms for Optimal Sizing Problems . . . . . . . . . . . . . . . . 61.3 Contribution of the Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10viTable of Contents2 Interconnected Detailed Modeling . . . . . . . . . . . . . . . . . . . . . . . 122.1 Irradiation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2 Microgrid Element Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2.1 PV Panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2.2 Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.2.3 DC/DC Converters . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.3 The Energy Management Strategy for the Microgrid . . . . . . . . . . . . . 272.4 Optimization Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.1 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48viiList of Tables2.1 Microgrid Devices Characteristics and Cost . . . . . . . . . . . . . . . . . . . 293.1 Solution based on installed power capacity . . . . . . . . . . . . . . . . . . . 343.2 Solution based on the selected devices . . . . . . . . . . . . . . . . . . . . . . 34viiiList of Figures1.1 Description of the sizing problem illustrating the advantages of the proposedapproach (P) in contrast to the conventional implementation (CI); consideringthe same requirements, the proposed approach achieves Ê fewer panels andbatteries installed, Ë fewer power converters, Ì reduced costs of the imple-mented system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Comparison between the conventional design approach (CD), where simplifiedmodels for the storage, PV panels, and power converters are used targetingonly financial goals, requiring an additional implementation stage (CI) to selectthe devices and interconnection, in contrast to the proposed methodology (P),where detailed models of different parts are brought into the optimization withmultiple objectives; the proposed approach allows to craft accurate solutionsto the financial problem, as well as targeting different objectives obtaining animproved system that eliminates the need of an additional stage. . . . . . . . 31.3 Genetic Algorithm (GA) basic principle. The GA utilizes the evolutionarypattern to calculate the next generation and population. . . . . . . . . . . . 82.1 Plane of array irradiation (POA); the direct, diffuse and reflected irradiationsources are shown, together with the angle of incidence (AOI) in a PV collectorsurface tilted by Σ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14ixList of Figures2.2 Solar angles. Altitude β, azimuth φ, tilt angle Σ, and the collector azimuthφc are displayed. The direction of the true south (S) is shown as a reference. 142.3 Sun path over the full year; summer and winter solstice are shown as referencetogether with paths for the 21st of each month corresponding to the locationof Edmonton, Alberta latitude 53.5◦. . . . . . . . . . . . . . . . . . . . . . . 162.4 DNI, GHI, zenith, albedo, and temperature are shown for a remote locationin Edmonton, Alberta. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.5 Plane of array irradiation (POA); the added available energy at the surface ofthe PV collector is shown together with the average yearly irradiation. . . . 182.6 Equivalent circuit model of a PV cell (a); Output power Ppv for differentirradiation conditions @ 20 ◦C (b), and temperature conditions @ 1000 W/m2(c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.7 Equivalent circuit model of a Lithium-Ion battery; the voltage-current charac-teristics are calculated as a function of the discharging current iBAT , and theactual charge of the battery it. . . . . . . . . . . . . . . . . . . . . . . . . . . 232.8 Discharge characteristics of a single battery considering the proposed mod-elling approach; the conventional approach neglects the insight provided bythese curves considering the battery as a recipient of energy. . . . . . . . . . 242.9 Proposed topology for the bidirectional DC/DC converter; VIN represents thevoltage of the BESS or PV arrangement; when PV is connected, the converteroperates uniquely in boosting mode, while the BESS is connected bucking andboosting modes are possible. . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.10 Safe Operating Area (SOA) for the DC-DC bidirectional converter as a func-tion of input voltage and power; boost and buck regions are indicated, theefficiency surfaces are projected within the region, and the peak efficiency ofthe converter is highlighted. . . . . . . . . . . . . . . . . . . . . . . . . . . . 26xList of Figures3.1 Load profile used as the input of the optimization problem; the year-round, Êsummer solstice and Ë winter solstice profile are shown; the average power isindicated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.2 Operating points of the optimal solution for the PV array connected to thepower converter; the operating points are a combination of MPPT and LPPTconditions depending on the instantaneous demand. . . . . . . . . . . . . . . 353.3 Occurrences for the PV array working at MPP and LPP; the proposed ap-proach shows that the system works at the LPP condition at higher powerratings, providing the bulk energy to the load under this condition. . . . . . 363.4 Operating points of the optimal solution for the battery array connected to thepower converter; it can be noticed how the converter limits the charging/dis-charging power producing a limited operating mode typically neglected in theconventional approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.5 Power profiles for the proposed solution and conventional design; From top tobottom, the PV input power for the MPP and LPP when there is no other pathfor the energy, input power at the battery, and battery pack charge capacity. 383.6 Power profiles for the conventional design and implementation solutions; Fromtop to bottom, the PV input power for the MPP and LPP when there is noother path for the energy, input power at the battery, and battery pack chargecapacity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.7 Comparison between the conventional design (CD), conventional implementa-tion (CI), and Proposed approach (P). The proposed approach achieves thesame performance while having a smaller design, obtaining a 23.4% reductionof the final cost compared against the CI Stage. . . . . . . . . . . . . . . . . 41xiList of Figures3.8 Sensitivity analysis for different uncertainties on the load profile forecastingwith the same overall average power (a); for different the load profile fore-casting maintaining the measurement uncertainty but with different averagepower (b); and for cost of the optimum system as a function of the shortagerequirement (c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43xiiAcknowledgementsFirst, I would like to thank Dr. Martin Ordonez for his supervision, guidance and continuoussupport during the Master’s program. His inspiring example of leadership and mentoringexpanded my professional skills in ways beyond my expectations.Next, I would like to thank my lab colleagues, all the members of Dr. Ordonez’s researchteam. Their support, collaboration and feedback were essential for the success of this work.I take with me strong friendships that will last forever. They took care of me as a memberof their family, and I consider them as part of mine.I would also like to thank the University of British Columbia, the Faculty of Graduateand Postdoctoral Studies and the Electrical and Computer Engineering Department for thecontinuous support received during this time.I feel especially grateful to my girlfriend Victoria for her moral and financial supportduring this time. Her constant encouragement makes me become a better person each day.My love goes to her for enlightening the right path with her smile.I would also like to thank my mother Claudia, my brother Gonzalo, my grandpa Emilio foralways believing in me and supporting me with all the decisions that I make for my future.I would like to thank all my friends across the globe. I feel fortunate to have so manymeaningful friendships, with people that are always supporting and helping me in their ways.A lifetime is not enough to give back all the love and support that I receive through them.Finally, I would like to thank you for taking the time to read this work.xiiiTo Emilio and Victoria.xivChapter 1Introduction1.1 MotivationTechnological advancements, population growth, and electricity dispatch to off-grid areasare the largest contributors to the ever-increasing societal energy demand. Currently, theconventional electricity generation methods, such as oil and gas, are insufficient to meetprojected future demands [2, 3]. Providing reliable electricity to communities is essentialto ensure their development. In this context, there are multiple alternatives to provide asolution to this issue. All of them require increasing the installed generation capacity. Oneoption is increasing developing expansions to the existing facilities. However, many of thesefacilities use fossil fuels. Electricity production based on fossil fuels generates large amountsof greenhouse gas emissions contributing to climate change [4, 5]. Additionally, extendingthe existing grid to remote areas may be prohibitive due to the large capital investmentsrequired. In Canada, there are 292 off-grid remote communities, and 251 depend on dieselas the main generation source [6]. In order to ensure meeting the future demand, the newfacilities in these remote locations need to generate energy in a clean, renewable, reliable andsustainable manner. The development of PV-BESS DC stand-alone microgrids is a suitablealternative. They provide all the necessary characteristics to minimize environmental impact.Additionally, they offer high versatility from an interconnected and distributed prospective.This work investigates how to optimally determine the size of PV-BESS DC stand-alonemicrogrids in order to guarantee minimum capital investment.11.2. Literature ReviewIsolated Community Loadsand Performance RequirementsNcBAT NsBAT NpBAT DCDCBESS Array and ConvertersNsPV DCDCNcPV PV Array and ConvertersPCI9%1PCI58%2DCDC23%PCI3cost $NpPV Figure 1.1: Description of the sizing problem illustrating the advantages of the proposedapproach (P) in contrast to the conventional implementation (CI); considering the samerequirements, the proposed approach achieves Ê fewer panels and batteries installed, Ëfewer power converters, Ì reduced costs of the implemented system.1.2 Literature ReviewDetermining the size of a PV-BESS DC microgrid system requires to define an optimizationproblem from the model of the system. However, the problem definition is independent ofthe algorithms that find a solution. In this section, first, the literature review for microgridmodelling and problem formulation is introduced. Then, the optimization algorithms usedby the conventional and proposed approaches are discussed.1.2.1 Optimal Sizing ProblemsThe deployment of microgrids incorporating distributed renewable generation and energystorage is a suitable alternative, thus providing a solution to the aforementioned challenges[7]. However, there is no go-to solution for sizing new stand-alone renewable energy systems.21.2. Literature Review$$$$$$NcBAT NsBAT NpBAT DCDCNsPV NpPV DCDCNcPV NcBAT NsBAT NpBAT DCDCNsPV NpPV DCDCNcPV Conventional Design (CD) Simple Models Medium complexityAccuracySimple EMSOversized convertersAdditional stage neededAvailable ProductsConventional Implementation Stage (CI)StandardInterconnection SuboptimalInterconnecteddesignHighComplexityAvailableProductsFlexibleInterconnectionProposed Approach (P)AccurateAdvancedModelsOptimalPerformanceEMSFewer 1Fewer 2DCDCCost-effective System3Figure 1.2: Comparison between the conventional design approach (CD), where simplifiedmodels for the storage, PV panels, and power converters are used targeting only financialgoals, requiring an additional implementation stage (CI) to select the devices and intercon-nection, in contrast to the proposed methodology (P), where detailed models of different partsare brought into the optimization with multiple objectives; the proposed approach allows tocraft accurate solutions to the financial problem, as well as targeting different objectivesobtaining an improved system that eliminates the need of an additional stage.Figure 1.1 depicts the microgrid sizing problem. Considering a microgrid with photo-voltaicenergy (PV), and a battery energy storage system (BESS), the objective is to determinethe array size of PV panels interconnected in series NsPV , in parallel NpPV and connectedto each power converter, and the total number of subsystems in parallel NcPV . Similarly,the number of batteries interconnected in series NsBAT , in parallel NpBAT and connectedto each power converter, and the total number of subsystems in parallel NcBAT , are cal-31.2. Literature Reviewculated to determine the BESS array. Additionally, the main advantages of the proposedapproach in contrast with the conventional implementation are shown in Figure 1.1. Utiliz-ing the methodologies later discussed in this work, it is possible to comply with the systemrequirements utilizing fewer solar panels and batteries, fewer power conversion stages and upto 23% less capital investment. The industry best practices estimate the size of the systembased on the average annual consumption, weather indicators dependent on the location,such as the yearly average irradiation to size the PV side, and backup time for the BESS[8]. This approach provides a fast calculation that accounts for security factors leading to anoversized system, thus being sub-optimal from a financial perspective. Alternatively, differ-ent optimization problems have been formulated for a numerous variety of system topologiestargeting financial objectives only [9–12]. These approaches represent the elements in themicrogrid utilizing simple models, described from a high-level perspective, thus neglectingsome of the real operating conditions. Simple models are typically exhaustive to provide a fi-nancial assessment, and limited describing the electrical behavior, assuming maximum powerpoint tracking (MPPT) for PV generation [13–15], considering energy storage capacity lim-its for BESS [16–18], and considering flat efficiency profiles in the power conversion stages[19–21], while overlooking the voltage and current profiles and safe operating area (SOA) ofthe devices. Consequently, the energy management strategy (EMS), the core of the problemcomputation, is formulated either following sub-optimal hard rules based on power flow pri-oritization [22, 23] or optimized in terms of high-level variables inherent to the limitations ofeach model within the system [24–26]. In [27] detailed models for the PV panels, as well aslistings of commercially available devices, are incorporated into the design of the simplifiedmicrogrid topology grid-tied PV plant obtaining improved results. Furthermore, [28] and[29] perform the optimal sizing of the storage systems for microgrid applications consideringdifferent technologies for the batteries but not from a electrical interconnection and perfor-mance perspective. Industry-standard practices and the optimization approaches for sizing41.2. Literature Reviewrenewable microgrids both result in a simplified solution. This solution provides the requiredPV kW and BESS kWh installed capacity. Since the PV kW and BESS kWh are consideredcontinuous variables in the conventional design (CD), the output of the optimization problemcannot be represented as an integer combination of the panels and batteries. Consequently,obtaining a symmetrically interconnected solution requires additional PV and BESS installedcapacity. From this perspective, the CD provides the input requirements for an additionalimplementation stage. This conventional implementation stage (CI) selects the candidate de-vices from the market availability and decides the interconnection of the elements to obtaina finalized system design. As a result, candidates for each device, and the interconnectionare decided outside the optimization environment, thus leading to discrepancies between themodelled CD and implemented CI solutions.On the other hand, great effort has been placed in developing models for the PV panels[30], batteries [31, 32] and power converters [33, 34] yet they are not commonly broughtto the optimization problem, favouring a high-level approach. The implementation of thesemodels is challenging since they need to be translated in a way that can suit the optimizationalgorithms, and the difficulty increases with the number of elements in the microgrid.In summary, there exists a gap between the conventional optimization approach (CD)and system implementation (CI). This gap can be fulfilled following the standard practices,resulting in a new system with different behaviour and increasing the overall costs of thesystem. On the other hand, incorporating an extra layer of detail in the system modelling,including the device selection and interconnection of the system into the optimal problemformulation is a feasible solution that has not been investigated before. Figure 1.2 showsan outline of the proposed modelling of the microgrid compared to the conventional model.The conventional approach utilizes simple models and a high-level EMS to find the optimalsolution. Consequently, the optimization is formulated utilizing continuous variables suchas the installed PV-BESS capacity in kW and kWh, respectively. Additionally, the power51.2. Literature Reviewconversion stages are sized in terms of those variables in a way that they can manage the powerflow assuming MPPT for the PV, and rated charging/discharging power for the BESS. Oncethe system has been sized, the additional implementation stage (CI) is necessary to selectavailable products and to define the interconnection following the standard practices. Themain drawback of this additional stage is that the installed capacity of PV-BESS establishedby the CD stage cannot be reached utilizing an integer number of devices, thus incorporatingmore devices for completion and symmetry. On the other hand, the proposed approachshifts the analysis to the discrete domain by defining the decision variables as the integerinterconnected elements NsPV , NpPV , and NcPV for the PV array, and NsBAT , NpBAT , andNcBAT for the BESS array. The discrete nature of these variables transforms the problem intoa mixed-integer optimization. In order to satisfy the additional requirements, the selection ofthe devices and the optimal interconnection are decided by the optimization algorithm to findthe best fit. Furthermore, an additional level of detail is introduced in the models to obtaininsights on the current-voltage waveforms, and power losses in the system, in contrast to thehigh-level power flow analysis and constant efficiency utilized by the conventional approach.Incorporating such detail requires a low-level performance EMS that is able to control thesetpoints at the current and voltage levels, which has not been investigated before. Finally,the proposed approach predicts that the system can achieve the desired performance utilizingÊ fewer PV-BESS devices, Ë fewer power converters, and Ì less capital investment.1.2.2 Algorithms for Optimal Sizing ProblemsOne of the key differences between the proposed and conventional approaches is the opti-mization algorithm selection to optimize the size of the system. The optimization algorithmsintend to find the global maximum or minimum of an objective function for a set of inputvariables valid in a constrained domain. In this work, the input variables of the optimiza-tion algorithm are the PV and BESS installed capacity, the objective is to minimize the61.2. Literature Reviewnet present value of the capital investment, and the constraints are related to the maximumshortage of energy allowed in the system. A specific combination of PV and BESS is not validwhen the maximum allowed shortage of energy is larger than the reference value, typically10%. The conventional approach considers that the power conversion stages can handle themaximum PV and BESS rated outputs, thus the size of the conversion stages is directlycalculated from that requirement. On the other hand, the proposed approach allows theEMS to decided the working setpoint, allowing limited power point tracking (LPPT) on thePV Plant or limited charging/discharging in the BESS. Consequently, the conversion stagesbecome independent variables, and they need to be included as a variable in the optimiza-tion formulation. Another important aspect is that the conventional approach allows the PVand BESS to be continuous variables, obtaining an optimization problem that is non-linearprogramming (NLP). This facilitates the algorithm selection and implementation due to theavailability of possible algorithms to solve a problem of this nature, including particle swarm[35, 36], active-set [37], Sequential Quadratic Programming (SQP) [38, 39], and interior-point[40], among others. The variety of algorithms simplifies the programming and calculation ofthe result. However, the conventional method delivers an output that requires an additionalimplementation stage to define the quantities and interconnection of series and parallel PVor BESS to a single power converter, and the total amount of power converters. As discussedin the previous section, this additional stage increases the overall cost of the system and theperformance deviates from the expectation.In contrast, the proposed approach defines the number of series-parallel elements for thePV-BESS arrays, and the number of power converters as the input variables. These are therequired elements to complete the design for each block as shown in Figure 1.1. Therefore, thedecision variables of the optimal sizing problem formulation are six integer variables NsPV ,NpPV , and NcPV for the PV array, and NsBAT , NpBAT , and NcBAT for the BESS array. Thisis a major challenge, since the aforementioned algorithms cannot solve for integer variables,71.2. Literature ReviewX1 1 2 3 1 5 1X2 2 2 5 2 3 1X3 1 2 3 1 2 3PopulationGeneChromosomeX4 2 2 5 1 5 1X5 1 2 3 2 3 1New OffspringX2 2 2 5 2 3 1X1 1 2 3 1 5 1Cross Over PointMutationX5 1 2 3 2 3 1 X6 1 5 1 7 3 1Figure 1.3: Genetic Algorithm (GA) basic principle. The GA utilizes the evolutionary patternto calculate the next generation and population.and new optimization algorithms need to be used. In this sense, the proposed approachreformulates the sizing problem in the discrete domain obtaining a Mixed-Integer Non-LinearProgramming (MINLP). The algorithm used in this work is known as genetic algorithm (GA)[41–43], and is the only one fully tested, trusted and supported by MATLAB R© that offersall the characteristics required to formulate the problem. The size of the interconnectedsystem can be determined utilizing this technique, avoiding an additional implementationstage. This comes at the cost of increasing the programming complexity and the convergencetime. Since the optimal sizing runs only one single time at the design stage, it is affordableto implement this approach enabling the discrete nature of the problem formulation, whichis a major contribution of this work.81.2. Literature ReviewFigure 1.3 shows a block diagram of the standard terminology utilized in the GA. Start-ing from an initial generation, the population is given by a set of possible solution vectorscalled chromosomes. Each chromosome is composed of genes, and they represent the decisionvariables of the problem. In the context of this work, there are six genes that represent thenumber of series and parallel solar panels, batteries and the respective power converters asshown in Figure 1.1. In this sense, a chromosome is any feasible combination of those sixvariables. The population typically contains 50 chromosomes, that are individually evaluatedto determine the objective function, representing the net present cost (NPC) in this work.Once all the chromosomes have been evaluated and compared to each other, the best per-formers are labelled as the parents for the next generation. The parents are utilized to createa new generation following two possible rules: creating a new offspring based on crossingover genes, or mutation. As shown in Figure 1.3, the new offspring is created crossing overthe genes of two possible parents by interchanging them around a cross over point creating anew set of children. A mutation happens when some of the children have a random geneticalteration changing the original value of the genes. The process is repeated setting a limitof 50 generations that is rarely reached since the algorithm converges with different criteria.The combination of new offspring and mutated children have different purposes. The newoffspring children allow the GA to explore the area closer to the best performers. The mu-tated children allow the GA to identify better performers in a different region that mightnot be reached with the offspring children when the domain is not convex which is often thecase. A domain is convex when all the intersecting points of a single line segment belong tothat domain, as long as the segment is formed by two points in the domain. If any segmentformed by two points of that domain contains a single point outside the domain, then is notconvex.91.3. Contribution of the Work1.3 Contribution of the WorkIn this work, a mixed-integer optimization procedure for the design of a microgrid based ondetailed models of the components is presented. Figure 1.2 shows how the proposed modelincludes further details of the electrical behaviour of the system allowing a comprehensiveassessment, deciding the size of the system as a function of the number and interconnectionof each element in the microgrid. This representation enables detailed and realistic operationof the system to be modelled contributing with:• Novel optimized energy management strategy accounting for voltage and current char-acteristics and limitations of the system, such as the safe operating area of the powerconverters.• New variables and constraints for the optimization algorithm in the mixed-integer spacethat eliminates the need of an additional implementation stage.• Multi-objective optimization taking into account physical variables at the EMS opti-mization as well as financial variables at the system level.• Solution based on the selected equipment and electrical interconnection.The proposed approach eliminates the need of an additional stage to finalize the systemdesign, ensuring the optimality of the implemented solution, while decreasing Ê the overallcost of the implemented system, Ë the installed capacity of PV and BESS, and Ì powerconversion stages, thus reducing the financial and environmental impact of the implementedsolution.1.4 Thesis OutlineThis thesis is organized as follows:101.4. Thesis Outline• In Chapter 2, the detailed models of the devices are presented. First, the solar out-put power is calculated. Then the battery behaviour is introduced. Next, the powerconverter topology, losses and safe operating area are introduced. All these modelsare compared to the conventional approach highlighting the advantages and drawbacksin each section. Once the main models are explained, the novel energy managementstrategy is discussed and formulated as a non-linear optimization problem. Finally, theoptimal sizing mixed-integer problem is formulated and compared to the conventionalapproach.• In Chapter 3, the simulation results are presented illustrating and discussing the dif-ferences between the proposed and conventional methodologies. The procedure is com-pared utilizing the same case scenario in both methodologies. The proposed approachis extensively validated through the presented examples. Additionally, sensitivity anal-ysis is presented. The three main assumptions of the proposed approach are tested indifferent scenarios to provide a strong statistical behaviour of the proposed method-ology. The impact of each variable is analyzed including a discussion on overcomingpossible but unlikely extreme scenarios.• In Chapter 4, the summary, conclusions and future work are presented. All the findingsare summarized highlighting the main advantages of the proposed procedures.11Chapter 2Interconnected Detailed ModelingIn this chapter, the solar irradiation models are presented. These models are valid for theconventional approach as well as for the proposed approach methodology for sizing the system.Addtionally, the models of the different elements in the microgrid are presented, jointly withthe proposed low-level EMS and the formulation of the optimization problem.2.1 Irradiation modelIn order to model the energy generated by a solar panel at each time of the day, the incidentirradiation on the collector surface needs to be calculated. The plane of array irradiationPOA in W/m2 is given byPOA = POAdirect + POAdiff,sky + POAdiff,refl, (2.1)where POAdirect is the direct beam irradiation, POAdiff,sky is the isotropic model for skydiffuse irradiation, and POAdiff,refl ground reflected diffuse irradiation given byPOAdiff,refl = ρ GHI1− cos (Σ)2, (2.2)where ρ is the ground surface albedo, Σ is the tilt angle of the panel, and GHI is the globalhorizontal irradiation in W/m2. The sky diffuse irradiation is calculated as122.1. Irradiation modelPOAdiff,sky = DHI1 + cos (Σ)2, (2.3)where DHI is the diffuse horizontal irradiation in W/m2. The direct beam irradiation isrepresented asPOAdirect = DNI cos (AOI) , (2.4)where DNI is the direct normal irradiation in W/m2, and AOI is the angle of incidencecalculated fromcos (AOI) = cos (ζ) cos (Σ) + sin (ζ) sin (Σ) cos (φ− φc) , (2.5)where ζ is the zenith angle, φ is the solar azimuth angle, and φc is the panel azimuth angle.The altitude angle is complementary to the zenith angle and can be calculated asβ = 90◦ − ζ (2.6)Typically, weather databases provide the measurements of albedo, GHI, DNI, and DHI.Sometimes, only DNI or DHI are available, and the following expression can be utilized tocalculate the undetermined parameterDHI = GHI −DNI cos (ζ) . (2.7)Figure 2.1 depicts the different sources of irradiation arriving to the panel collector surface.The direct beam irradiation has the largest influence in the total irradiation. The diffuseirradiation is the resultant of the beams that have a larger trajectory in the sky, and theenergy of the electromagnetic wave is distributed in all directions equally. The reflected beamrepresents the reflection of the solar rays in the ground. The reflected beam is polarized in132.1. Irradiation modelFigure 2.1: Plane of array irradiation (POA); the direct, diffuse and reflected irradiationsources are shown, together with the angle of incidence (AOI) in a PV collector surface tiltedby Σ.Figure 2.2: Solar angles. Altitude β, azimuth φ, tilt angle Σ, and the collector azimuth φcare displayed. The direction of the true south (S) is shown as a reference.all directions. However, the largest percentage of the reflected energy comes polarized in thedirection parallel to the reflecting surface.142.1. Irradiation modelFigure 2.2 depicts all the solar angles for a collector arbitrarily placed facing towards thesouth with a deviation of φc from the real south. The sun rises from the east and sets in thewest. The position of the sun and the trajectory can be represented by two angles, altitudeβ, and azimuth φ.Figure 2.3 shows the variation of altitude β as a function of the azimuth φ for a full year inEdmonton, Alberta at latitude 53.5◦. The hours of the day when the sun is up are depictednormalized with respect to the solar time. The highest and lowest altitude of the sun atnoon happen at summer and winter solstice respectively. The illustrated sun path curvesrepresent the 21st of each month, and each one is valid for two different months of each year.For example, the curve under the summer solstice is valid for May and July 21st, and thecurve above winter solstice is valid for November and January 21st. As seen in the previousequations, knowing the position of the sun at all times of the year is critical to calculating theincident irradiation on the surface of the collector, as well as the required distance betweenthe solar panels. The tilt angle is selected to match the latitude angle to maximize theyear-round average irradiation on the surface of the collector. As a design standard practice,the distance between solar panels in a PV installation is calculated to avoid self-shadingfrom 9 a.m. to 3 p.m. year-round. The worst-case scenario happens when the sun is atits lowest point, thus the angles corresponding to winter solstice are utilized for the design.Furthermore, a negative angle for the altitude represents that the sun is not visible from thatregion, being night time at that latitude. Positive angles for azimuth represent the positionof the sun towards the east before solar noon, while negative represents the angle towardswest after solar noon. It can be noticed how the sun rises around 8:30 a.m. and sets around3:30 p.m. in the winter solstice. On the other hand, the sun rises before 4 a.m., and setsafter 8 p.m. in the summer solstice. Every other day of the year, the sunrise and sunsettimes are within the limits of summer and winter solstice.152.1. Irradiation model-150-100-50050100150010203040506034567891011 12 131415161718192021Solar Azimuth, [°]Solar Altitude, [°]hours of the daySun Path SummerSolsticeSun Path WinterSolsticeFigure 2.3: Sun path over the full year; summer and winter solstice are shown as referencetogether with paths for the 21st of each month corresponding to the location of Edmonton,Alberta latitude 53.5◦.Figure 2.4 depicts the information provided by weather databases for Edmonton, Alberta.From top to bottom, the direct normal irradiation, global horizontal irradiation, solar zenithangle, albedo, and temperature are depicted. It can be noticed how the zenith angle, com-plementary to the altitude, reaches its highest value at the winter solstice, and its lowestpoint at the summer solstice. Furthermore, the albedo that represents the reflectance of theground surface, reaches about 0.85 during winter due to the presence of the snow, and 0.2 insummer where the ground is clear of snow. Due to the high albedo for long periods of time,this particular location is preferable for installing bi-facial solar panels to improve energyharvesting. However, to the extent of the work, the bi-facial technology is not incorporatedsince is an emerging technology that is yet to settle. Additionally, the contributions of this162.1. Irradiation model05001000DNI [W/m2 ]50100150Zenith, [°]00.51Albedo, [°]01-Jan 21-Mar 21-Jun 21-Sep 21-Dec-40-2002040Time, [days]T [ °C]05001000GHI [W/m2 ]winter spring summer fallFigure 2.4: DNI, GHI, zenith, albedo, and temperature are shown for a remote location inEdmonton, Alberta.172.1. Irradiation model01-Jan 21-Mar 21-Jun 21-Sep 21-Dec05001000Time, [days]POA [W/m2 ]winter spring summer fallAverage IrradiationFigure 2.5: Plane of array irradiation (POA); the added available energy at the surface ofthe PV collector is shown together with the average yearly irradiation.work are independent of the particular technology selected for each one of the devices, andthe proposed techniques are equally valid for all devices.Figure 2.5 shows the POA aggregated irradiation together with the year-round averageirradiation. It can be noticed the influence of the reflected and diffuse components, particu-larly towards the beginning of spring where the solar irradiation is higher than 1000 W/m2.The average irradiation is 184 W/m2, which is equivalent to 1612 hours of full sun for oneyear. In other words, the sun provides the equivalent energy to the full sun irradiation 1000W/m2 in 1612 hours in one year, which represents 18.4 % of the 8760 hours in a year. Thisis the input profile utilized to calculate the photo-generated power of the PV panels in thesystem. The conventional approach utilizes this information to estimate the maximum poweroutput. On the other hand, the proposed approach leaves that decision to the EMS allowinga limited power point operation when convenient.182.2. Microgrid Element Models2.2 Microgrid Element Models2.2.1 PV PanelsEnabling limited power point tracking (LPPT), in contrast to MPPT used by the conventionalapproach, is of vital importance to ensure that the power electronics operate within thepower limitations, avoiding overvoltage in the DC bus side, and overcharging of the BESS.Additionally, LPPT allows for higher predictability of the output of the system, and enhancedstability for the output of the converter, at the cost of increasing the complexity of the controlloop [44–46]. Moreover, working at LPP implies typically two possible operating conditionsfor the PV array, and selecting which one is adequate at each time step depends on the EMS.In this work, the proposed detail modelling approach enables the selection of the operatingpoint that produces the best performance of the system in terms of energy harvested andconverter efficiency which is formulated as an optimization problem within the EMS.Figure 2.6 (a) depicts the equivalent circuit model of a PV panel that allows any operatingcondition. Since the panels are built from a combination of Ns series and Np parallel cells,the current-voltage behaviour of the panel is given byIPV = Np(Iirr − ID − VDRpNs), (2.8)Iirr is the irradiation current; VD and ID are the voltage and current in the anti-parallel dioderespectively, given byVD = VPV + IPVRsNs/Np, (2.9)ID = I0(eqVDnkT − 1), (2.10)192.2. Microgrid Element Modelswhere q is the elementary charge, n is the ideality factor (n = 1.3 for silicon), and k is theBoltzman constant.I0 is the reverse saturation current of the anti-parallel diode, calculated asI0 = I0,ref(TTref)3e(qEg,refnkTref− qEgnkT), (2.11)where the subscript ref describes the value of the variable at standard test conditions (STC),T is the cell temperature in ◦C and Eg is the bandgap energy in eV and it depends on thematerial of the cell. Considering silicon cells the bandgap energy can be expressed asEg = 1.16− 7.02× 10−4(T 2T + 1108). (2.12)I0,ref can be obtained from the open-circuit voltage VOC and the short-circuit current ISCcurrent asI0,ref = ISC/(eqVOCnkNOCT − 1). (2.13)The irradiation current Iirr as a function of the solar irradiation G in kW/m2 is describedbyIirr = Iirr ref(GGref)[1 + αT (T − Tref )] , (2.14)where the constant αT is the temperature coefficient in %/◦C, and it is provided by themanufacturer.The temperature of the cell is dependent on the solar irradiation and can be calculated asT = Tamb +(NOCT − 20 ◦C0.8)G, (2.15)202.2. Microgrid Element ModelsRPRSIDIPVVD VPVIirrGEquivalent PV circuit(a)1 kW/m20.5 kW/m20.6 kW/m2ConventionalVpv [V]P pv [kW](b)0 10 20 30 40 50 00.10.20.30.420 °C60 °C40 °CVpv [V]Conventional(c)P pv [kW]0 10 20 30 40 50 00.10.20.30.4Figure 2.6: Equivalent circuit model of a PV cell (a); Output power Ppv for different irradi-ation conditions @ 20 ◦C (b), and temperature conditions @ 1000 W/m2 (c).212.2. Microgrid Element Modelswhere Tamb is the ambient temperature in◦C, and NOCT is the nominal operating celltemperature in ◦C.I0 = I0,ref(TTref)3e(qEg refnkTref− qEgnkT), (2.16)I0,ref can be obtained from the open-circuit voltage VOC and the short-circuit current ISCcurrent asI0 ref = ISC/(eqVOCnkNOCT − 1), (2.17)The presented approach models all the possible operating points of the PV panels incontrast with the MPP model used by the conventional approach. Figure 2.6 (b) showsthe output power of the PV array (Ppv) in terms of the output voltage (Vpv) at 20◦C, forirradiation conditions of 1, 0.6 and 0.5 kW/m2. Furthermore, Fig. 2.6 (c) shows Ppv in termsof Vpv for different temperature conditions. It can be noticed how this model describes thecharacteristic of the solar panels for a wide range of conditions, while the conventional modelonly traces the MPP operating condition. The proposed approach provides insight into thecurrent and voltage waveforms, while the conventional approach only predicts the maximumoutput power of the array.2.2.2 BatteriesThe voltage of the lithium batteries is dependant on the internal parameters and the dischargecurrent is given byVBAT = E0 − VPol −R · iBAT + Ae−B·it −RPol · i∗, (2.18)222.2. Microgrid Element ModelsvocRinternalLow Pass FilterModel CalculationsiBATiBATVBATiti*Figure 2.7: Equivalent circuit model of a Lithium-Ion battery; the voltage-current character-istics are calculated as a function of the discharging current iBAT , and the actual charge ofthe battery it.where E0 is the battery constant voltage, R is the internal resistance, iBAT is the batterydischarging current, and charging current when iBAT is negative, B is the exponential-zonetime-constant inverse, A is the exponential-zone amplitude, it is the actual charge of thebattery, and i∗ is the average of the current. The polarization voltage is given byVPol = KQQ− it · it (2.19)where K is the polarization constant in V/Ah and Q is the battery nominal capacity in Ah.Finally, the polarization resistance is given byRPol =K QQ−it if DischargingK Qit−0.1Q if Charging(2.20)Figures 2.7 and 2.8 illustrate the proposed modelling approach, providing full detail ofthe battery voltage-current behaviour, while the conventional approach is only based on thepower profile and total energy storage capacity requirement. In the proposed case, the batteryvoltage can be calculated at each time step from the charge/discharge characteristic, whilethe conventional approach considers the battery as a container of energy. In consequence,232.2. Microgrid Element Models0 20 40 60 80 100 120 1403237.242.447.652.858Discharge Capacity [Ah]Voltage [V]0.3C0.5C1CFigure 2.8: Discharge characteristics of a single battery considering the proposed modellingapproach; the conventional approach neglects the insight provided by these curves consideringthe battery as a recipient of energy.the conventional approach does not predict the voltage-current behaviour of the battery andcannot be expressed in terms of the power converters. Moreover, the proposed model accountsfor the power losses in the battery by using the internal resistance, while the conventionalmodels consider a constant efficiency for the charging and discharging cycles.2.2.3 DC/DC ConvertersAfter determining the operating voltage and current of the PV panels and batteries, the realoperating point of the associated converter can be determined, thus calculating the instantefficiency at each time step.Figure 2.9 presents a synchronous bidirectional topology. VIN represents the input voltagethat can either come from the PV array or the BESS array. The converter can operate inboost mode when the PV panels are generating energy or when the BESS array is dischargingenergy to the load, and buck mode when the BESS is charging. The switch S1 controls thebuck mode limiting the charging current, while S2 controls the boost mode limiting thedischarging current, or performing MPPT and LPPT for the PV array. In either operatingmode, the switches work in complementary to each-other maintaining VBUS constant.242.2. Microgrid Element ModelsL VBUSS2 D2D1S1CCiINVINFigure 2.9: Proposed topology for the bidirectional DC/DC converter; VIN represents thevoltage of the BESS or PV arrangement; when PV is connected, the converter operatesuniquely in boosting mode, while the BESS is connected bucking and boosting modes arepossible.The power losses in S1,S2, are given byPcond = VON · Iaverage +RON · I2rms, (2.21)where Pcond is the conduction loss on the switch or diode, VON and RON are the parameters ofthe IGBT or diode model. The inductor ohmic losses are proportional to I2rms. The switchinglosses can be obtained asPsw =1Ts∫ Ts0Esw dωt, (2.22)where Ts is the switching period, and Esw is the switching energy. Finally, the efficiency ofthe converter at each operating point is given byηconv =Pin − Pcond − PswPin. (2.23)where Pin is the input power of the converter. This model provides the efficiency profile andconsiders the real operating points of the converter, in contrast with the constant efficiencymodel used in the conventional approach.252.2. Microgrid Element Modelsmax max 200 300 400 500Vin [V]-20-15-10-505101520Pin [kW]0.910.9150.920.9250.930.9350.940.945EfficiencyBoostModeBuckModemax= 0.9471SOAFigure 2.10: Safe Operating Area (SOA) for the DC-DC bidirectional converter as a functionof input voltage and power; boost and buck regions are indicated, the efficiency surfaces areprojected within the region, and the peak efficiency of the converter is highlighted.Figure 2.10 shows the SOA on boost and buck mode. As a reference, the boost modedefines the positive sign for the current IIN . The peak efficiency is found to be ηmax = 0.9471working at 18.5% of rated power, and 91.3% of rated voltage in either operating mode. Itcan be noticed that the proposed model provides a family of efficiency curves dependenton the voltage and power, in contrast to the conventional approach that assumes constantefficiency for all operating conditions of the converter. Additionally, the SOA of the converterestablishes a hard limit for the operation of the devices that are usually neglected in thetraditional approach.262.3. The Energy Management Strategy for the Microgrid2.3 The Energy Management Strategy for theMicrogridThe energy dispatch strategy is an optimization problem by itself. The proposed EMScontrols the operating point of the PV array and battery storage in order to minimize theinstantaneous shortage of energy. The proposed approach enables constraints to be addedrelated to the electrical limitations of the system and SOA of the converters that cannot beincorporated in the conventional approach. Additionally, the decision variables, the currentof the storage system and the voltage of the PV array, are neglected in the conventionalapproach. Considering the multiobjective functions f1 for shortage and f2 for PV efficiencygiven byf1 (VPV , iBAT ) = Pload − ηPV (VPV )PPV (VPV )− ηBAT (iBAT )PBAT (iBAT ) , (2.24)f2 (VPV ) = 1/ηPV (VPV ) (2.25)where Pload is the loading requirement, ηBAT and ηPV are the efficiencies of the convertersassociated with the batteries and PV array respectively. The EMS optimization problem isdefined by272.4. Optimization ProblemminVPV , iBAT{|f1 (VPV , iBAT ) |, f2 (VPV )}s.t. SOCmin ≤ SOC ≤ SOCmax,0 ≤ |iBAT | ≤ iBAT,max,0 ≤ VPV ≤ VOC,array,0 ≤ Pconv ≤ PSOA,conv,(2.26)where SOC is the state of charge of the battery pack, VOC,array is the open-circuit voltageof the PV array connected to the converter, and Pconv is the input power of the differentconverters that must be contained within the SOA denoted by PSOA,conv.2.4 Optimization ProblemIn this section, the system sizing optimization problem is formulated. The proposed approachenables constraints associated with the electrical design that are contemplated within theEMS. At the system-level design, these constraints translate into two main indicators: totalenergy shortage, caused by the different times of the year that the load cannot be matched,and total number of panels, allowing the PV array to be oversized, as long as the converteris able to handle the DC disconnect short circuit current, thus the raw size of the PV respectthe output power of the converter is limited. The decision variables are the output of theproblem establishing the final size of the system given in terms ofX = [NsPV NpPV NcPV NsBAT NpBAT NcBAT ], (2.27)where NsPV , NpPV and NcPV are the panels connected in series, parallel and the number ofconverters needed for the PV plant respectively. NsBAT , NpBAT and NcBAT are the batteriesconnected in series, parallel and the number of converters needed for the BESS respectively.282.4. Optimization ProblemTable 2.1: Microgrid Devices Characteristics and CostDescriptionLifetime Replacement Ccap CO&M Poweryears units $/unit $/kW − y kW/unitSolar Panels 20 0 205 15 0.335Power Converters 10 1 5400 5 20Lithium-Ion Batteries 7 2 6656 10 6656This vector provides a full determined design and connection schedule, while the conventionalapproach leaves this decision for the implementation stage, moving the final solution awayfrom the optimal design.The formulation of the optimal sizing problem is given byminXCcap + CO&M + Creps.t. 0 ≤ Eshortage ≤ 10% Eload,0 ≤ NsPV NpPV ≤ NtPV,max,NsPV,min ≤ NsPV ≤ NsPV,max,NpPV,min ≤ NpPV ≤ NpPV,max,NcPV,min ≤ NcPV ≤ NcPV,max,NsBAT,min ≤ NsBAT ≤ NsBAT,max,NpBAT,min ≤ NpBAT ≤ NpBAT,max,NcBAT,min ≤ NcBAT ≤ NcBAT,max,(2.28)where Ccap is the capital cost, CO&M is the operation and maintenance cost (O&M), Crep isthe replacement cost, Eshortage is the shortage of energy of the design considering the totalload requirement Eload, and NtPV,max is the maximum total number of panels that a singleconverter can disconnect.292.5. SummaryThe detailed representation of the microgrid enables the objective function to representspecific characteristics of the system, such as power losses, harvested energy, efficiency, amongothers. These characteristics are considered in the EMS optimization, working jointly withall the conventional financial variables at the system sizing optimization level. The financialaspect typically depends on installation costs, O&M costs, replacement costs, or net profit,among others. In this case, the objective function targets to maximize the efficiency of thepower converter, while minimizing the shortage of energy and the net present value of allthe devices installed. This definition illustrates how different aspects of the microgrid canbe included in the optimization objective, which is usually overlooked by the conventionalapproach.Finally, the optimization algorithms utilized are different for EMS optimization and theoptimal size problem. Since the variables of the EMS are continuous, the active-set methodis selected to solve the problem at each time step. On the other hand, the decision variablesof the optimal sizing problem are constrained to be positive integer numbers which limitthe options of the feasible algorithms; for this problem, the genetic search algorithm withmix-integer capability is selected. Table 2.1 shows the lifetime considered for each one of thedevices in years, as well as the number of replacement for the time span of the project, andthe cost scheme utilized to compute the objective function accounting for a 10% discountrate per year. The replacement cost is calculated as the net present value considering theactual capital cost, the lifetime and the discount rate.2.5 SummaryIn this chapter, an improved optimal sizing methodology was presented. The proposedmethod incorporates extended capabilities into the optimal sizing problem formulation. First,solar irradiation models are presented. They allow determining the density of solar energy at302.5. Summarya collector surface combining the direct, sky-diffuse and reflected irradiation sources. Thesemodels are valid for the proposed and conventional approaches. Then, the models of eachelement of the microgrid are introduced.The proposed approach allows the PV panels to operate at any operating point by in-troducing the voltage-current characteristics in the model. However, only maximum powerpoint operation (MPP) is considered in the proposed approach. Moreover, the proposed ap-proach incorporates the voltage-current characteristics for the batteries, while the proposedapproach utilizes a simplified kinetic model representing the power flow only. Finally, thepower converters are modelled calculating the detail losses. This allows obtaining a preferredinterconnection design, in contrast to the conventional approach that considers flat efficiency.The proposed approach incorporates the safe area of operation of the power converters, whichis typically overlooked in the conventional approach. The extended capabilities of the pro-posed methodology enable the formulation of a low-level EMS that controls the setpoints atthe current-voltage level which has not been investigated before.The formulation of the optimization problem uses the number of interconnected elementsas decision variables incorporating the power converters into the design space. The formu-lated problem requires a mixed-integer optimization that can be solved utilizing the geneticalgorithm.The proposed approach provides an extended understanding of microgrids, obtaining asolution based on the interconnected design, eliminating the need for an additional imple-mentation stage. The proposed methodology is validated in the next chapter of this thesis.31Chapter 3Results and Discussion3.1 Simulation ResultsThe PV plant is optimized considering the profile of a typical meteorological year (TMY)in Edmonton, Alberta. The optimization is performed over a 20 years lifetime period. Thesolar panels are considered to be facing south with a tilt equal to the latitude to maximizethe year-round average irradiation on the surface.The load can be represented as a combination of DC and AC loads. The total load of thesystem is depicted in Fig. 3.1 for the full calendar year, where Ê is the summer solstice and Ëis the winter solstice profile. The load profile is winter peaking having the peak consumptiontowards the beginning of the year. Finally, the initial charge of the battery pack correspondsto the remaining charge of the batteries in steady state, considering the same irradiationprofile every year, and the performance requirements considering (2.24) and (2.28) allows fora maximum shortage of 10%. Table 3.1 this compares the results of the sizing following thedifferent methodologies and the costs in millions of dollar (M$). The CD stage, presents atotal PV plant of 432.12 kW connected to a power converter of 484.39 kW , a total storagecapacity of 767.69 kWh with a power converter of 330.12 kW . This system has a predictedcost of 2.3254 M$ and a predicted shortage of 9.95 %. Since this power rating cannot beachieved as an integer combination of the selected devices, the additional CI stage is required.The design was obtained by following the best practices, resulting in the system presented inTable 3.2. It can be observed that the real cost of this configuration is 2.6575 M$, producing323.1. Simulation Results201-Jan 21-Mar 21-Jun21-Jun21-Sep 21-Dec21-Dec050100150Time [days]Power [kW]0 6 12 18 24020406080Time [h]Power [kW]0 6 12 18 24020406080Time [h]Power [kW]Demanded Power Average PowerSummerSolsticeWinterSolstice211Figure 3.1: Load profile used as the input of the optimization problem; the year-round, Êsummer solstice and Ë winter solstice profile are shown; the average power is indicated.a shortage of 5.42 %. This reinforces the impact of the additional implementation stage,producing a suboptimal system, and the performance of the final implementation drift fromthe expected value. On the other hand, the proposed approach reduces the cost of the systemby 12.4 % at the CD stage, and 23.35 % at the CI stage, providing a solution that accountsfor the interconnection of the devices, thus eliminating the need for an additional design333.1. Simulation ResultsTable 3.1: Solution based on installed power capacityMethod kWPV kWConv,PV kWhBAT kWConv,BAT Cost M$CD 432.12 484.39 767.69 330.12 2.3254CI 469 500 905.22 340 2.6575Proposed 422.1 200 745.47 140 2.0370Table 3.2: Solution based on the selected devicesMethod NsPV NpPV NcPV NsBAT NpBAT NcBATCD - - - - - -CI 7 8 25 8 1 17Proposed 6 21 10 8 2 7stage. The proposed approach bridges the gap between the traditional optimal formulationand the finalized implementation, typically neglected in the design, by combining both stagesinto a unified problem.Moreover, the solution space is not symmetrical due to the inclusion of the non-financialobjectives in the EMS optimization objective constraint to the real operating conditions.Consequently, the PV panel and the battery arrays are not a trivial decision. For example,considering the optimal solution where the PV array has 126 panels per converter, the con-figuration 6x21 produces a shortage of 9.99%, performing better than the configuration 7x18that is obtained following the best practices, producing a shortage of 10.42%, thus being anunfeasible solution for the reference shortage requirements. Additionally, it can be inferredthat re-arranging the PV array can increase the harvested energy up to 0.43%, thus increasingthe average efficiency of the power conversion stages. Furthermore, the configuration 21x6 isnot a feasible solution, yet all these configurations nominally would generate the same powerat the same cost in the conventional approach. Similar behaviour is observed in the batteryarrangement, where the configuration 8x2 corresponding to the optimal, performs better thanthe configuration 4x4 that does not comply with the shortage requirement. This derivation343.1. Simulation Results200 300 400 500050100150200VPV [V]Pin,PV [kW]0.910.9150.920.9250.930.9350.940.945EfficiencyLPPTDominantRegionMPPT DominantRegionLPPTMPPTFigure 3.2: Operating points of the optimal solution for the PV array connected to the powerconverter; the operating points are a combination of MPPT and LPPT conditions dependingon the instantaneous demand.illustrates the importance of the proposed approach in comparison with the conventionalmodel.Figure 3.2 depicts all the operating points of the PV array within the SOA of the converter.Each point is coloured according to its efficiency. The proposed approach provides furtherinsight into the voltage-current characteristic, and the efficiency of each operating point iscomputed independently. Consequently, the search space of the optimization algorithm isasymmetrical, reinforcing the fact that the configuration of the different arrays is not trivial.Figure 3.3 compares the number of occurrences of the PV array under MPP and LPP,as a function of the input power. In the study case, the optimum result implies a ratio of2.11 kWpv/kWconverter, thus the converter operates clipping the output power when the PV353.1. Simulation Results0 0.2 0.4 0.6 0.8 1Pin,PV / PR,converter051510Time usage [%]LPPMPPEtotal = 326 MWhEtotal, MPP = 35.2 %Etotal, LPP = 64.8 %TimeMPP = 46.1 %TimeLPP = 53.9 %4.1 MWh23.4 MWhFigure 3.3: Occurrences for the PV array working at MPP and LPP; the proposed approachshows that the system works at the LPP condition at higher power ratings, providing thebulk energy to the load under this condition.is under full irradiation. In this case, the PV array operates in LPP with a higher frequencywhen the power is around 20% of rated power. LLP is also predominant when the systemoperates closer to the full rated power. This is associated with the BESS limiting the chargingpower due to the SOA of the converters. Finally, the proposed system shows an operationthat is mostly dominated by the LPP condition 53.9% of the time contributing with 64.8%of the total energy delivered to the load and BESS, in contrast to the conventional approachthat only allows MPP, and in case of excess energy a dump load assumption is considered.The proposed approach highlights the added benefits of allowing the installed PV capacityto exceed the rated power of the power converters.Figure 3.4 shows similar behaviour for the BESS array. It can be noticed how the convert-ers limit the charging power at different operating conditions and it discharges freely most ofthe time. In all cases, the proposed approach allows the converters to clip the power, avoidingthe need for a larger converter usually utilized in the conventional approach. Comparing tothe conventional approach, both methods derive in the same number of interconnected bat-teries in series. However, the proposed approach has twice the number of parallel batteries,363.1. Simulation Results200 300 400 500VBAT [V]-100-50050100Pin,BAT [kW]0.910.9150.920.9250.930.9350.940.945EfficiencyBoostModeBuckModeFigure 3.4: Operating points of the optimal solution for the battery array connected to thepower converter; it can be noticed how the converter limits the charging/discharging powerproducing a limited operating mode typically neglected in the conventional approach.thus requiring half of the power converters to charge/discharge the same total number ofbatteries.Figures 3.5 and 3.6 depicts the PV and BESS power profile, and the energy profile for theBESS comparing P, CD and CI. The limits of the power converters are indicated, as well asthe total PV and BESS installed capacity. The proposed approach allows the PV plant tooperate at LPP, allowing the converter to clip the output power. The clipping effect is alsoallowed in the BESS profile, which results in a system that requires a lower total installedcapacity, thus decreasing the total cost of the system. The proposed method achieves thesame performance utilizing Ê less installed BESS and PV capacity, Ë fewer installed powerconversion stages, and Ì less capital investment.373.1. Simulation Resultswinter spring summer fallwinter spring summer fall0200400600-400-200020040002004006008001000Proposed Approach Conventional Design Stage01-Jan 21-Mar 21-Jun 21-SepTime [days] Time [days]01-Jan 21-Mar 21-Jun 21-Sep 21-Dec21-DecPin,PV [kW]Pin,BAT [kW]EnergyBAT [kWh]MPP 422 kWPV, installedPin, PV 200 kWConv, PVMPPPin, PV485 kWConv, PV432 kWPV, installedPin, BAT 330 kWConv, BATPin, BATclippedpower140 kWConv, BATCapacity BAT745 kWh BAT, installed 85% SOC15% SOCCapacity BAT768 kWh BAT, installed 85% SOC15% SOCFigure 3.5: Power profiles for the proposed solution and conventional design; From top tobottom, the PV input power for the MPP and LPP when there is no other path for theenergy, input power at the battery, and battery pack charge capacity.383.1. Simulation Results0200400600-400-20002004000200400600800100001-JanPin,PV [kW]Pin,BAT [kW]EnergyBAT [kWh]winter spring summer fall winter spring summer fallConventional Design Stage Conventional Implementation StageTime [days]21-Mar 21-Jun 21-Sep 21-Dec 01-Jan 21-Mar 21-Jun 21-Dec21-SepTime [days]MPPPin, PV485 kWConv, PV432 kWPV, installedPin, BAT 330 kWConv, BATCapacity BAT768 kWh BAT, installed 85% SOC15% SOCCapacity BAT905 kWh BAT, installed 85% SOC15% SOCPin, BAT 340 kWConv, BATMPPPin, PV500 kWConv, PV469 kWPV, installedFigure 3.6: Power profiles for the conventional design and implementation solutions; Fromtop to bottom, the PV input power for the MPP and LPP when there is no other path forthe energy, input power at the battery, and battery pack charge capacity.393.1. Simulation ResultsFigures 3.7 summarizes the key information by comparing the proposed (P), conventionaldesign stage (CD), and conventional implementation stage (CI) approaches. The majordifferences between them come from the capability of the proposed approach to track LPPoperation, the consideration of the real operating limits of the devices in the microgrid, aswell as clipping capability in the power conversion stages. It can be noticed that even ifthe MPP power generated in the CD and P approaches are similar, the rated power of theconverters is 2.5 times lower in P compared to CD. However, after the CI stage, the ratedpower is slightly higher than in CD, thus the PV MPP power is larger to accommodate for theminimum required power following the best practices for interconnection. On the other hand,the proposed approach implements the solution utilizing fewer panels, allowing any arbitraryelectrical interconnection, and deriving in the optimum when the problem is solved. Similarobservations can be done by comparing CD and CI against P, where the proposed approachallows the converter to clip the power during the charge of the batteries, opposed to theCD where the converters are sized to manage the full power specifications of the system.Moreover, the rated capacity for the BESS is slightly lower in P compared to CD; however,it increases considerably after the CI stage. This advantage of the proposed model comesfrom allowing the system to have any arbitrary interconnection in compliance with the SOAof the converters. All in all, the proposed approach allows the operating conditions of thesystem at LPP and power clipping, resulting in reduced requirements in the power conversionstages when compared against the conventional approach. This enables the system to haveless PV and BESS installed capacity connected to less than half of the power converters.Additionally, the system allows any arbitrary interconnection in the proposed approach,performing closer to the requirements, and maintaining the optimality of the design afterimplementation. Finally, the proposed approach incorporates the aforementioned featuresinto the optimal design, obtaining the optimal size of the system providing the interconnectedsolution. In contrast, the conventional approach requires both CD and CI stages to obtain the403.2. Sensitivity AnalysiskWPV kWConv,BAT cost M$PCICD PCICD PCICD+ 8.5%4323302.33- 9.9%+ 14.3%- 23.4%+ 3%- 58.8%kWhBATPCICD768 + 17.9%- 17.6%kWConv, PVPCICD484 + 3.2%- 60%Fewer 1 Fewer 2 DCDC ReducedCost3Figure 3.7: Comparison between the conventional design (CD), conventional implementation(CI), and Proposed approach (P). The proposed approach achieves the same performancewhile having a smaller design, obtaining a 23.4% reduction of the final cost compared againstthe CI Stage.interconnected design. From this contribution, the proposed methodology achieves reducingthe total costs up to 12.4% compared to the CD stage, and up to 23.35% compared to andCI stage.3.2 Sensitivity AnalysisOnce the system has been optimally sized, it is interesting to understand the resiliency androbustness of the design. In this section, three different cases are presented to validate theproposed approach.Firstly, both sizing methodologies require a known load profile as input. Typically, fore-casting the load profile is not straightforward and the real instant value might be differentthan the predicted value. Under this condition, the optimal solution is required to meet theload up to some degree of uncertainty in the forecast of the load. Figure 3.8 (a) depicts theshortage response of the optimal solution to different levels of uncertainties in the forecast-413.2. Sensitivity Analysising of the loading condition while maintaining the same average consumption. The level ofuncertainty is introduced as noise using a uniform distribution proportional to the real valueof the load. In this case, it can be observed that the system is resilient to load forecastingerrors with an uncertainty of 20%. Within this range, the system will meet the shortage re-quirements. Furthermore, considering an uncertainty between 20− 60%, the performance ofthe system deviates a maximum of 0.5% from the desired shortage. Finally, for a maximumuncertainty of 100% the added shortage of the system is almost 1% added to the designedvalue. Therefore, the optimal solution is robust to the uncertainty introduced in the loadforecasting as long as the average consumption remains invariant.Secondly, the optimal solution presents the desired performance when the total consumedenergy is equal to or lower than the expected value. However, if the load increases, theoptimum solution reduces its performance. Figure 3.8 (b) shows the shortage response of thesized system when the load increases up to 100%. It can be observed that when the totalconsumed energy increases by 20% the shortage of the system drops an additional 10%, andwhen the load duplicates the expected value, the shortage increases to 70%. This behaviourindicates that if the load is underestimated, the optimally sized system can provide a part ofthe excess load, at the cost of a deteriorated performance. Therefore, the uncertainty on thetotal energy demanded by the load needs to be accounted for in the design of the system.Finally, in a stand-alone microgrid, the maximum shortage allowed is of importance toguarantee energy supply to a critical load. However, the allowed value can have a significantimpact on the cost of the system. Figure 3.8 (c) shows the cost of the optimum systemrespect to the base case, as a function of the shortage requirement. It can be noticed thatallowing a 5%, 10%, and 25% additional shortage to the 10% reference case, results in acost reduction of 15%, 20%, and 25%, respectively. In this sense, the marginal financial gainin reducing the performance of the system is higher when the shortage requirements vary423.2. Sensitivity Analysis(a)0 20 40 60 80 1009.51010.511Uncertainty [%]Shortage [%]20 %20 to 60 %GoodPerformanceΔsh = +0.5%Δsh, max < +1%(c)10 15 20 25 30 357580859095100Shortage [%]cost / cost optimum [%]Δcost = - 15%Δcost = - 5%Δcost, max = - 25%Δsh = + 5%Δsh = + 5%(b)1 1.2 1.4 1.6 1.8 2020406080PLoad / P Load,refShortage [%]+20 %Δsh, max < +70%Δsh < +10%Figure 3.8: Sensitivity analysis for different uncertainties on the load profile forecasting withthe same overall average power (a); for different the load profile forecasting maintaining themeasurement uncertainty but with different average power (b); and for cost of the optimumsystem as a function of the shortage requirement (c).433.3. Summarybetween 10− 20%. Therefore, understanding the critical loads of the system accurately canlead to further financial improvements establishing the performance requirements.3.3 SummaryIn this chapter, the optimal sizing of DC PV-BESS stand-alone microgrids is validated.The proposed approach is compared to the conventional design through specific examples.The results show that the proposed approach achieves the same performance in the microgriddesign utilizing up to 9.9% less installed PV-BESS capacity, up to 60% fewer power conversionstages, and up to 23.35% less capital investment when compared to the conventional designand implementation.The proposed methodology achieves this performance by allowing the system to work atlimited power point operation (LPP), introducing the safe operating area of power converters,and formulation of the optimization problem as a function of the interconnected variables.The proposed methodology provides a further understanding of the microgrids, eliminat-ing the need for an additional implementation stage typically required by the conventionalapproach.The sensitivity analysis shows that the obtained design maintains the performance up to20% of uncertainty in the instant load forecasting. It also provides additional robustnesswhen the overall consumption increases deviating up to 10% from the required performancewhen the load increases by 20%. Finally, the sensitivity analysis presents how the capitalinvestment of the project can be reduced up to an additional 15% increasing the shortagerequirements by an extra 5%.44Chapter 4Conclusions4.1 SummaryThis work introduces an optimization methodology utilizing a comprehensive model of themicrogrid for optimal sizing of PV generation and battery energy storage systems (BESS)in stand-alone applications. The proposed methodology considers commercially availabledevices, including the voltage-current characteristics into the design, as well as the safe op-erational limits of the devices and comprehensive behaviour of the energy conversion stages.Additionally, the system is designed in terms of the interconnectivity of the PV and BESSarray with the power converters, thus reducing the gap between the optimal sizing problemand the industrial implementation. Moreover, limited power point tracking for the PV plantis allowed in the design to improve the performance of the microgrid. The detailed modellingapproach introduces new constraints to the optimization problem reducing the search space.Furthermore, the formulation of the problem enables the inclusion of new optimization con-straints and objectives related to the real operational conditions of the system resulting ina novel energy management strategy for microgrid application. The simulation shows thatthe proposed approach reduces the cost of the sized system by 12.4% in the design stage anda total of 23.35% after the implementation stage. Additionally, the results show that thePV and BESS arrangement is not trivial, obtaining an extra 0.43% efficiency in the energyconversion stages by optimizing the configuration, and the algorithm provides the numberof parallels and series PV-BESS required. Finally, the proposed approach presents high re-454.2. Future Worksiliency for the load forecasting allowing an uncertainty of 20% without compromising theperformance of the system and producing a maximum deviation of 1% when the uncertaintyin the predicted instant power is closer to 100%.4.2 Future WorkThis work introduces an optimal sizing methodology incorporating the implementation tech-niques into the optimal design, shifting the problem formulation from a non-linear optimiza-tion to a mixed-integer non-linear formulation. The technique developed has been appliedto specific examples, and it can be extended to a large number of applications. This workanalyzes the influence of stage in the problem formulation process, and how they impact thesolution. The results indicate that the accurate modelling of PV, BESS and power conver-sion stages influence the online operation of the system, obtaining a 0.5% improvement in theefficiency of different configurations. As a consequence, the system can maintain the overallperformance utilizing up to 17.6% fewer PV and BESS capacity installed. The inclusion ofthe interconnectivity model closes the gap between the conventional optimal sizing formula-tion, and the industrial implementation eliminating the need for an additional stage. Finally,the proposed methodology includes the power conversion stages into the design, allowing theenergy management strategy (EMS) to decide the operating set points in a current-voltagelevel. This extended capability enables the limited power point tracking (LPPT) operationof the PV plant. Consequently, the results show how the performance of the system can beachieved by utilizing up to 60% fewer power converters.The advantages of the proposed approach enable a new research space for the optimaldesign of microgrids. The proposed methodology can be utilized to size any architecture andto improve the EMS control, accessing extended capabilities. The future work utilizing theproposed technique can be extended, but not limited to optimally sizing of any stand-alone464.2. Future Workor grid-connected microgrid architecture, improved low-level EMS control of microgrids, andfinancial benefits of allowing LPPT operation in systems that include PV and BESS.47Bibliography[1] G. N. Bogado, F. Paz, I. G. Zurbriggen, and M. 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Thesis/Dissertation
eng
Electrical and Computer Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Improved sizing of PV-BESS DC microgrids : a mixed-integer optimization
Text