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Improved power loss estimation for device- to system-level analysis Amyotte, Matthieu 2019

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Improved Power Loss Estimation for Device- to System-Level AnalysisbyMatthieu AmyotteB.Sc., University of Alberta, 2013A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of Applied ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Electrical & Computer Engineering)The University of British Columbia(Vancouver)July 2019© Matthieu Amyotte, 2019The following individuals certify that they have read, and recommend to the Faculty of Graduate and Post-doctoral Studies for acceptance, the thesis entitled:Improved Power Loss Estimation for Device- and System-Level Analysissubmitted by Matthieu Amyotte 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 MemberiiAbstractPower converters are found nearly everywhere electric power is used and are ubiquitous in renewable energygeneration and electric vehicles. All power converters suffer from losses, Modern power converters havevery high efficiency, often reaching peak efficiency ≥ 95%. However, the losses in these systems are stillsignificant and must be considered for thermal and financial purposes. To enable maximum loss reduction,accurate estimation of the losses at the design stage is mandatory.Gallium Nitride (GaN) power switches are an emerging technology due to their high efficiency operationand smaller size compared to traditional Silicon (Si) devices. To date, simplistic power loss models havebeen employed for loss predication and thermal management design with Gallium Nitride (GaN). How-ever, these simplistic models do not provide accurate loss prediction, resulting in over-design of the thermalmanagement systems. This work proposes a comprehensive method to predict losses in GaN devices us-ing high-accuracy thermal measurement. The proposed model is validated experimentally and provides afour-fold increase in loss predication accuracy compared to traditional methods.Having established accurate converter-level loss prediction, a higher level of abstraction is then consid-ered. Existing system-level analysis focuses on distribution losses and oversimplifies converter losses byassuming fixed efficiency. In reality, converter losses are highly variable under different operating condi-tions. In this work, the Rapid Loss Estimation equation (RLEE) is proposed to provide computationallysimple loss prediction under all operating conditions. The RLEE extracts detailed loss behavior from multi-domain simulation into a computationally simple parametric equation. Using the RLEE high accuracy andhigh speed loss estimation is obtained, as demonstrated in a DC microgrid with three different converters.Ultimately, the tools developed in this work improve loss estimation in power converters from the com-ponent level up to the system level. The proposed techniques, while explained through specific examples,are widely applicable and can be readily implemented to other devices, topologies and systems. Improvedloss estimation is valuable at all levels, from designing thermal management systems for individual devicesin a converter to optimizing the financial outcomes of a complex grid with multiple power converters.iiiLay SummaryPower converters are a fundamental technology for renewable energy generation and transportation elec-trification, among many other applications. However, these devices are subject to unwanted power losses.Reduction of losses, particularly in high power systems, can result in significant energy and cost savings.For this reason, it is critical to develop tools to better predict these losses and reduce them.In this work, detailed models are developed to better predict the losses in power converters. First, thelosses in the individual switches inside the converter are investigated. The developed models allow for accu-rate loss prediction of the next generation of power converters. Secondly, the losses in the whole converterare considered. The developed Rapid Loss Estimation Equation can be used for fast and accurate simulationof complex systems with high renewable energy integration. The proposed techniques are widely applicable,allowing for easy application by electrical engineers as they develop the energy systems of the future.ivPrefaceThis work is based on research performed at the Electrical and Computer Engineering Department at theUniversity of British Columbia by Matthieu Amyotte, under the supervision of Dr. Martin Ordonez.A version of Chapter 2 was presented and published at the Institute of Electrical and Electronics Engineers(IEEE) Energy Conversion Conference & Congress (ECCE) 2018 [1]. Additional detail has been added herefor completeness. Chapter 3 is based on work that has been submitted for publication, and is currently underreview.As the first author of the above-mentioned publications, the author of this thesis developed the theoreticalconcepts and procedures, designed the experiments and wrote the documents. Technical advice and guidancewas provided by Dr. Martin Ordonez throughout the process. Furthermore, the work in Chapter 2 wassupported by Ettore Scabeni Glitz and Maria Celeste Garcia Perez, who assisted in the development of thecharacterization procedure. They are acknowledged as secondary authors on the associated publication [1].vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.1 Design of Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2.2 Gallium Nitride Power Switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.3 Power Loss Analysis in Power Switches . . . . . . . . . . . . . . . . . . . . . . . . 61.2.4 System-Level Power Loss Prediction . . . . . . . . . . . . . . . . . . . . . . . . . 81.3 Contribution of the Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10vi2 Power Loss Characterization of Gallium Nitride Power Switches . . . . . . . . . . . . . . . . 112.1 Conduction Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.1.1 Datasheet Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.1.2 Characterization with Design of Experiments . . . . . . . . . . . . . . . . . . . . . 132.2 Loss Determination with Thermal Measurement . . . . . . . . . . . . . . . . . . . . . . . . 162.2.1 Test Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2.2 Thermal Resistance Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.3 Power Loss Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3 Switching Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.1 Double Pulse Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3.2 Switching Cycle Losses using Thermal Measurement . . . . . . . . . . . . . . . . . 232.3.3 Characterization with Design of Experiments . . . . . . . . . . . . . . . . . . . . . 242.4 Loss Prediction for GaN Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.4.1 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.4.2 Experimental Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 The Rapid Loss Estimation Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.1 Loss Model Development Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.2 Converter Topologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.2.1 Boost Converter for PV Generation . . . . . . . . . . . . . . . . . . . . . . . . . . 333.2.2 LLC Converter for EV Chargers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.2.3 Bidirectional DC-DC Converter for Battery Energy Storage . . . . . . . . . . . . . 423.3 System-Level Loss Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.3.1 EVCS Load Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.3.2 System Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.3.3 Loss Prediction Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53viiBibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54viiiList of TablesTable 2.1 Test Points for Conduction Loss Characterization of a GaN enhancement-mode high elec-tron mobility transistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Table 2.2 Boost Converter Design Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Table 2.3 Average Loss Prediction Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Table 3.1 Comparison of Loss Prediction Techniques for the Boost Converter . . . . . . . . . . . . 38Table 3.2 Operating Range of a 6.6 kW LLC electric vehicle (EV) Battery Charger . . . . . . . . . 40Table 3.3 Comparison of Loss Prediction Techniques for the LLC Converter . . . . . . . . . . . . 42Table 3.4 Operational Limits of the 12 kW Bidirectional DC-DC Converter . . . . . . . . . . . . . 43Table 3.5 Comparison of Loss Prediction Techniques for the direct current (DC)-DC BidirectionalConverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Table 3.6 Statistical Data for a 2-Stall Public Charging Station in Vancouver, Canada . . . . . . . . 46Table 3.7 Simulation Time for One-Year Simulation of the DC Microgrid . . . . . . . . . . . . . . 49Table 3.8 Percent Error for One-Year Simulation of the DC Microgrid . . . . . . . . . . . . . . . . 50ixList of FiguresFigure 1.1 Omnipresece of Power Converters in Energy Systems . . . . . . . . . . . . . . . . . . . 2Figure 1.2 Comparison of Traditional Silicon Devices with Emerging Wide Bandgap Devices . . . 5Figure 1.3 Overview of Electrical and Thermal Measurement Techniques for Power Losses . . . . 7Figure 2.1 On-State Drain-to-Source Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Figure 2.2 Conduction Loss Characterization Circuit . . . . . . . . . . . . . . . . . . . . . . . . . 13Figure 2.3 Normalized Test Points for the face-centered central composite design (FCCCD) . . . . . 14Figure 2.4 Response Surface of the On-State Resistance from the Detailed Characterization . . . . 15Figure 2.5 Overview of Thermal Measurement for Thermal Characterization of Losses . . . . . . . 16Figure 2.6 Test Setup used for Thermal Characterization of Power Losses . . . . . . . . . . . . . . 17Figure 2.7 Thermal Resistance Calibration Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 18Figure 2.8 Loss Measurement using Thermal Imaging . . . . . . . . . . . . . . . . . . . . . . . . 19Figure 2.9 Introduction to Switching Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Figure 2.10 Introduction to Losses from Ringing caused by Parasitic Elements in the Circuit . . . . . 22Figure 2.11 Overview of the Double-Pulse Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Figure 2.12 Boost Converter and Waveforms for Switching Cycle Loss Characterization . . . . . . . 24Figure 2.13 Response Surfaces for the Switching Cycle Losses . . . . . . . . . . . . . . . . . . . . 25Figure 2.14 Boost Converter for Validation of the Proposed Model . . . . . . . . . . . . . . . . . . 26Figure 2.15 Comparison of Results for Different Device Loss Prediction Techniques . . . . . . . . . 27Figure 3.1 Introduction to Microgrids with Distributed Energy Resources . . . . . . . . . . . . . . 29Figure 3.2 Overview of the Proposed Rapid Loss Estimation Equation . . . . . . . . . . . . . . . . 31Figure 3.3 Procedure to Develop the Rapid Loss Estimation Equation . . . . . . . . . . . . . . . . 32Figure 3.4 Solar Resource in Vancouver, Canada . . . . . . . . . . . . . . . . . . . . . . . . . . . 34xFigure 3.5 Operational Limits of the photovoltaic (PV) Boost Converter . . . . . . . . . . . . . . . 35Figure 3.6 DOE test conditions for the PV Boost converter . . . . . . . . . . . . . . . . . . . . . . 36Figure 3.7 The RLEE for the PV Boost Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Figure 3.8 Predicted vs Actual Plot for the PV Boost Converter . . . . . . . . . . . . . . . . . . . . 38Figure 3.9 Battery Charge Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Figure 3.10 The RLEE for the LLC EV Charger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 3.11 Predicted vs Actual Plot for the LLC EV Charger . . . . . . . . . . . . . . . . . . . . . 41Figure 3.12 The RLEE for the DC-DC Bidirectional Converter for battery energy storage (BES) . . . . 43Figure 3.13 Predicted vs Actual Plot for the BES DC-DCConverter . . . . . . . . . . . . . . . . . . . 44Figure 3.14 The DC Microgrid for Evaluation of the RLEE . . . . . . . . . . . . . . . . . . . . . . . 45Figure 3.15 Operating Conditions of the EV Charger in One Year . . . . . . . . . . . . . . . . . . . 46Figure 3.16 Electric Vehicle Charging Station Operating Conditions for One Week . . . . . . . . . . 47Figure 3.17 Process Flow for Simulation of DC Microgrid . . . . . . . . . . . . . . . . . . . . . . . 48Figure 3.18 Annual Operating Conditions for the BES DC-DC Converter . . . . . . . . . . . . . . . . 48Figure 3.19 Comparison of Loss Prediction Techniques for System-Level Simulation . . . . . . . . 50Figure 3.20 Summary of the Advantages of the RLEE . . . . . . . . . . . . . . . . . . . . . . . . . 51xiGlossaryAC alternating currentBES battery energy storageDC direct currentDER distributed energy resourcesDOE design of experimentsDPT double pulse testDUT device-under-testECCE Energy Conversion Conference & CongresseHEMT enhancement-mode high electron mobility transistorEMI electromagnetic interferenceEV electric vehicleEVCS electric vehicle charging stationFCCCD face-centered central composite designGaN Gallium NitrideHEMT high electron mobility transistorIEEE Institute of Electrical and Electronics EngineersIR infraredxiiMOSFET metal-oxide semiconductor field-effect transistorMPP maximum power pointMPPT maximum power point trackingNREL National Renewable Energy LaboratoryPCB printed circuit boardPFC power factor correctorPV photovoltaicRLEE Rapid Loss Estimation equationRTD resistance temperature detectorSi SiliconSiC Silicon CarbideSOC state of chargeSPICE Simulation Program with Integrated Circuit EmphasisWBG wide-bandgapxiiiAcknowledgmentsFirst and foremost, I want to graciously acknowledge the continued support of Dr. Martin Ordonez. Throughhis guidance, my technical knowledge and research abilities have expanded well beyond my expectations.Not only did he provide technical direction, but he emphasized a well-rounded graduate experience. Hisleadership provided a strong example for many of the extracurricular activities I pursued throughout my timeat UBC, and will continue to guide my career in the years to come.Next, I would like to thank my lab mates who have become strong friends during the time we’ve spenttogether. Their encouragement and collaboration greatly contributed to the success of this work. Moreimportantly, their friendship made the graduate experience truly memorable.I would also like to recognize my family, especially my parents, who taught me the value of education.Their support has been invaluable through my entire academic career, and was particularly meaningful whenthey supported my return for graduate studies.Finally, I owe an overwhelming thank you to my wife, Kristen, who has supported me throughout thisentire journey. From challenging me to think critically about our impact on the world, to being my dailysupport through this journey, I could not have done this without you. Thank you for everything that you are.xivDedicationTo Kristen,For inspiring me in more ways than I can count.xvChapter 1Introduction1.1 MotivationRenewable energy generation and transportation electrification are emerging fields that will play an essentialrole in addressing climate change. These technologies, in combination with myriad other solutions, will beneeded to meet the targets outlined in the Paris Agreement, which formally came into effect in November2016 [2]. Power converters are a critical component in all renewable energy generation and transportationelectrification systems. Power converters transform electricity between alternating current (AC) and directcurrent (DC) and change voltage levels. A sample energy system with distributed renewable energy gener-ation and various electrified loads is shown in Fig. 1.1. From the diversity of applications, it is clear thatpower converters will be omnipresent in the creation of a sustainable future.In addition to new technology, efficiency improvements in existing systems are also needed [3]. High ef-ficiency (≥ 95%) is not uncommon in modern power converters [4, 5]. However, incremental improvements,particularly in high-power electronics, still yield significant energy and cost savings. For example, increasingthe efficiency from 98% to 99% (only 1% change in efficiency) corresponds to a loss reduction of 50%. Thiscould be the difference between an active (expensive and unreliable) cooling system or a passive coolingsystem. It also allows for significant size reduction, which is particularly valuable for space-constrained ap-plications, like electric vehicles. Thus, to better understand converter efficiency, it is necessary to investigatethe underlying challenge: power losses.Power losses occur in the individual components of power converters, particularly in the power converterswitches. Silicon (Si) switches are currently the standard for power converters, having been used for over40 years [6]. However, Si devices are quickly approaching their physical limits, slowing the evolution of1DCACDCACACDCDCDCDCDCSolar GenerationBattery StoragePublic EVChargingACDCACDCACDCACACWind GenerationDCACACACACDCHome EVChargingRooftop SolarConsumerElectronicsClimateControlAC DistributionNetworkElectric ShippingFigure 1.1: Power converters will be omnipresent in a sustainable future from generating renewableenergy to charging electric vehicles and powering zero-emission homes.power converter technology. In order to achieve lower losses and the associated benefits, wide-bandgap(WBG) devices must be used. These WBG devices, namely Silicon Carbide (SiC) and Gallium Nitride (GaN),have substantially lower losses than Si devices [7]. WBG devices are also capable of operating at highertemperatures, which allows for simplified cooling systems that use less (or no) power [7]. However, GaNdevices are still a new technology and their loss performance is not well understood [7]. There exists a needfor high accuracy power loss estimation in GaN devices to enable the next generation of power converterdesign.Shortcomings in power loss estimation extend into the design of energy systems, as well. As more powerconverters are added, system complexity grows rapidly. Existing simulation tools used for converter-levelanalysis are too computationally intensive for large systems. Traditional system-level simulation relies onoversimplifications, effectively eliminating any insight into the converter’s actual loss behavior. To effec-tively design the next generation of energy systems, loss models that are both accurate and computationallysimple are required.This work addresses the shortcomings of power loss estimation at all levels, from GaN switches to energysystems. First, an improved loss prediction model for GaN devices is developed through the use of thermalmeasurement to characterize device performance under different operating conditions. Using the developedhigh-accuracy device-level models, it is possible to analyze losses at the converter level. Then, the accurate2converter-level behavior is extracted for use in system-level simulation. The proposed Rapid Loss Estimationequation is a computationally-simple parametric equation for system-level loss prediction in all operatingconditions. Ultimately, the improved loss prediction provided by this work enables the next generation ofpower converters and energy systems.1.2 Literature ReviewIn order to place this work within a larger research context and to identify the contributions, it is importantto first consider the existing work. In this section, a comprehensive literature review is provided.Throughout this work, design of experiments (DOE) is used for statistical analysis. DOE is a powerfulstatistical technique used to intelligently design experiments with multiple variables. An introduction tothis technique and a literature review of its use in different power electronic applications is presented inSection 1.2.1.A literature review of the development and early implementation of GaN power switches is presented inSection 1.2.2. The many benefits that GaN devices provide compared to traditional Si devices is presented.Furthermore, through this early work, a number of challenges were identified. The particular challengeof interest, power loss prediction for GaN devices, is investigated in further detail. Existing solutions arepresented and their shortcomings are highlighted.Next, a review of existing techniques for power loss analysis of power switches is presented in Sec-tion 1.2.3. A number of traditional electrical and thermal loss measurement techniques are presented andtheir strengths and weaknesses are identified. Many of these techniques were implemented in early work toevaluate their utility for GaN devices. Ultimately, the disadvantages discussed here proved too significant toallow for accurate power loss characterization of GaN devices.Finally, a literature review of converter loss prediction at the system-level is provided in Section 1.2.4.While existing system-level investigations of distribution losses have been performed regularly, it is commonto oversimplify converter losses using the fixed efficiency approximation. Some recent work has shown thatby including more detailed converter loss considerations for photovoltaic (PV) inverters, benefits can be seenin system optimization and reliability studies.1.2.1 Design of ExperimentsDesign of Experiments is a statistical technique used for intelligently designing experiments with multiplevariables. In particular, DOE serves two important purposes. First, it optimally selects specific operating con-3ditions to test. In this way, the number of experiments needed for a statistically valid model is minimized.Secondly, DOE applies statistical analysis to generate a parametric equation. This parametric equation ac-curately predicts the response under all operating conditions within the tested range [8]. In particular, itgenerates an equation of the formF(Y ) = a0+n∑i=1aixi+n∑i=1n∑j=1bi jxix j +n∑i=1n∑j=1n∑k=1ci jkxix jxk. (1.1)Where Y is the response; F(Y ) is a mathematical transform of the response (e.g. square root or naturallogarithm); x1...xn are the experimental variables; a0 is the overall average of the response; ai are linearregression coefficients; bi j are quadratic regression coefficients; and, ci jk are cubic regression coefficients.Design of Experiments can be used for design evaluation, model development and optimization problems.By running a small number of experiments, it is often possible to quickly identify which variables have astatistically significant impact on a response [8]. In [9–13], DOE is used extensively to understand, modeland optimize different aspects of planar magnetics, such as trace and winding geometry.Loss characterization using DOE was first proposed in [14], and has since been further investigated forSi metal-oxide semiconductor field-effect transistors (MOSFETS) [15–17]. In [15, 16], the losses in the SiMOSFETS of an LLC resonant converter are characterized using DOE techniques. Similarily, in [17], thelosses in the semi-bridgeless power factor corrector (PFC) are investigated. This work expands on existingDOE loss characterization by developing models for emerging GaN devices [1]. In particular, this work usesDOE to capture the complex non-linear switch behavior into an easily implemented loss prediction model.Energy resource modeling has also been performed using DOE. Direct methanol fuel cells are consideredin [18] and wind turbine rotors are investigated in [19]. In these works, the focus is on the energy resource,rather than the power converter. In this work, the power converter is considered and a loss prediction methodis developed using DOE to allow for computationally simple loss prediction in system-level simulation. Inparticular, DOE is used to extract detailed loss prediction behavior from complicated converter models into acomputationally simple meta-model that can be effectively applied to system-level simulation.1.2.2 Gallium Nitride Power SwitchesTraditionally, power electronics have relied on Si-based switches; however, Si devices are nearing their the-oretical limits. As an alternative, WBG devices have emerged, offering better switching performance, higherblocking voltage, and higher operating temperatures as outlined in Fig. 1.2a [7]. Based on manufacturingcapabilities, Silicon Carbide has emerged as the dominant player for high-voltage and high-power applica-47NormalizedtoSi1234560ElectronVelocityThermalConductivityMeltingPointElectricFieldEnergyGapVoltageFrequency TemperatureSiCGaN(a)10MPower[W]Switching Frequency [Hz]100 1k 100k10k 1M1001k10k100k1M10MSiCTraditional Si GaN(b)Figure 1.2: a) Comparison of material properties of SiC and GaN compared to traditional Si. The con-nection to operating parameters, shown on the x-axis, highlights how WBG devices outperformSi in power electronic applications. b) Overview of the power electronics market to illustrate theoperating niche that each material will occupy. GaN will be predominantly used in high-frequencylow-to-medium power applications.tions, while GaN is a front-runner in the high-frequency, low-to-medium power market. The expected marketfor each of the three device technologies is highlighted in Fig. 1.2b. Silicon devices will remain competitivein the low-frequency, low-power category because of their very low cost, while SiC and GaN will be neededto push the boundaries of what is possible in power electronics.The first commercially-available GaN devices were normally-on GaN high electron mobility transistors(HEMTS) [7]. While these devices exhibited the expected performance benefits over Si, their applicability waslimited. To create the normally-off devices needed for power electronics, two main solutions have emerged.Firstly, cascode structures are created by adding a normally-off low-voltage Si transistor in series with thenormally-on GaN HEMT [7, 20]. This cascode structure provides normally-off behavior, but reintroducessome of the restrictions that arise with Si devices, such as limited temperature performance. The alternativestructure is the enhancement-mode high electron mobility transistor (eHEMT), which modifies the originalHEMT structure to allow for normally-off behavior [21]. In this way, the benefits of GaN are maintained.GaN eHEMTS are now commercially available from a number of manufacturers [5, 21]. When comparedto similarly rated Si MOSFETS, GaN eHEMTS provide better performance through two main improvements:faster switching and no reverse recovery [21]. The improved switching speed has been leveraged to develophigh efficiency power converters at high frequency, such as the 97.8% efficient 1MHz boost in [22] and the597.5% efficient 500kHz LLC in [23], among many others [24, 25]. The lack of reverse recovery, however, hasproven even more interesting by enabling the totem-pole PFC topology, which was not previously possiblewith Si MOSFETS [4, 26]. Significant effort has been invested in this topology, as it exhibits performance andcost benefits compared to other PFC topologies [26–29].Despite the many advancements occurring with GaN, there are still challenges that must be addressed.Firstly, reliability of this new technology is a work-in-progress [5, 7]. In order to better understand the relia-bility, the loss performance and thermal management must be considered [5]. Reliability is also compromisedby the sensitivity to parasitic elements. Because GaN devices can be so small, external elements, such as cir-cuit board traces and driver selection, now play a larger role in the performance of the switch [30, 31]. Thisis problematic as adding measurement devices, such as oscilloscope probes, can change the switches’ per-formance. Furthermore, electrical measurement is susceptible to electromagnetic interference (EMI) whichincreases with switching frequency [32]. Instead, thermal measurement can be used to avoid the need forelectrical measurement in power loss measurement [31, 32].1.2.3 Power Loss Analysis in Power SwitchesAnalysis of power losses in semiconductor devices is a critical part of power converter design. By comparingthe losses in different devices, it is possible to select the best device for a particular application [33]. Further-more, the converter efficiency can be determined in order to compare different topologies [15, 34, 35]. Lossanalysis is also valuable in thermal management design, which is particularly necessary for GaN devicesbecause of their small thermal mass [1, 35]. To this end, significant efforts have been made to develop lossmodels from experimental techniques using electrical and thermal measurement.Fundamentally, power losses, Ploss, occur anytime there is both a drain current, Id , and a drain-to-sourcevoltage, Vds, present in the device, as described byPloss = IdVds (1.2)In GaN devices, this occurs in two instances: conduction losses (when the switch is turned on) andswitching losses (when the switch is changing from on-to-off or vice-versa). These two loss mechanisms areillustrated in their simplest form in Fig. 1.3a. Conduction losses are relatively easy to measure, as they occurin a steady-state condition. Switching losses, on the other hand, are very difficult to measure as they occurvery quickly. Therefore, most research efforts focus on the characterization of switching losses.Loss characterization using electrical measurement attempts to capture more accurate current and voltage6dIdsVlossPONOFF OFFConduction LossTurn-on Loss Turn-off Loss(a)inToutT T∆Thermally Isolated Test SetupDeviceUnderTestlossPCooling Fluid(b)Figure 1.3: a) Simplified Vds and Id waveforms and the resultant Ploss during turn-on, conduction andturn-off instances. The real waveforms are significantly more complicated than those depictedhere. b) At its simplest level, thermal loss measurement determines power losses from the differ-ence in temperature at two points. Commonly, a calorimeter, shown here, is used to isolate thethermal behavior of the DUT.waveforms, compared to the simplified version used in Fig. 1.3a. The approach described in [36] considersthe effect of the MOSFETS parasitic capacitance on the speed and timing of the rise/fall of the Id and Vdswaveforms. This is a common approach in industry, as all the necessary information is available on thedatasheet. This approach was further improved by [37, 38] by considering the parasitics in the circuit whichcause ringing at the MOSFET gate. For the most accurate understanding of the Id and Vds waveforms, thedouble pulse test can be used, as in [39, 40].All of these electrically-based techniques provide valuable insight into the switching behavior of thedevice; however, they have one significant limitation. At high frequencies, as are typically seen in modernpower converters, the accuracy of electrical measurement quickly degrades [35, 41]. Electrical measurementis particularly problematic for GaN devices where the addition of probes can alter the circuit performanceby introducing unwanted parasitics [30]. Device manufacturers provide best practices [40] for electricalmeasurement, but even the models developed by manufacturers are not necessarily accurate [1].An alternative to electrical techniques is to use thermal measurements, which are generally consideredmore accurate [41]. The fundamental principle of thermal measurement is to determine the heat (losses)produced by the device by measuring the temperature at two different points. As illustrated in Fig. 1.3b,this is commonly done using a calorimeter, where the DUT is thermally isolated from the environment and acooling fluid is heated by the losses [41]. Alternatively, the temperature change of the DUT can be used for theloss calculation. Thermal measurement has been applied at the device level in [42, 43], but is more generally7applied to converter level study because of the challenges associated with isolating the DUT [35, 41, 43]. Inaddition to the difficulty of isolating the individual device, thermal measurement can also be very slow asthe system must reach thermal equilibrium before a measurement can be taken [41].1.2.4 System-Level Power Loss PredictionAs described above, power loss analysis is critical in the design of power converters. The importance ex-tends to system-level studies as converters are increasingly installed into distributed energy resources (DER)systems. In [44, 45], a solar PV plant is optimized and advanced modeling of the inverters is considered.Both conclude that consideration of the detailed inverter behavior is necessary for accurate results. In par-ticular, [44] is able to increase the financial benefit by 1%, reduce payback period by 6.95% and increaseharvested energy by 9.3%. Furthermore, [5, 46] uses advanced loss modeling to study life-cycle reliability.These works recognize that converters operate under a wide range of operating conditions throughout theirlife-cycle, and that consideration of the losses under these diverse conditions is critical.The primary challenge with loss prediction at a system-level is computation speed which is directlyrelated to computational complexity. In order to study large time scales, such as years, simulations must bevery fast. However, power electronic simulation tools, such as Plexim’s PLECS and Powersim’s PSIM, arevery computationally complex as they study the individual switching transitions in a converter [47, 48]. Witha frequency of 100kHz, there would be more than three trillion switching transitions when simulating oneyear. Even simulating a few seconds to reach thermal equilibrium can take significant time.Traditionally, computationally simple models have been used by assuming the fixed-efficiency method.In this approach, a fixed value is used to calculate the losses usingPloss = Pin(1−η f ixed). (1.3)This approach is used by [49–52] for a variety of DER and microgrid optimization problems. [52] considersthe efficiency of different converters in the system, but still uses a fixed efficiency for each.The European efficiency, ηeuro, can also be considered [53, 54]. This is a weighted efficiency whichaccounts for the efficiency change as Pin changes, as defined byηeuro = 0.03η5%+0.06η10%+0.13η20%+0.1η30%+0.48η50%+0.2η100% (1.4)where ηx% is the efficiency x% of the rated load. Still, this approach uses a fixed value in the system-8level simulation that does not consider how the losses dynamically change as the operating conditions varythroughout the year.Then, there exists a gap where existing system-level loss prediction is computationally simple, but overlysimplified; and, converter-level simulation is accurate but too computationally complex. This work addressesthis gap by developing accurate computationally simple loss prediction by extracting converter-level detailusing DOE.1.3 Contribution of the WorkThrough the above literature review, a number of shortcomings are evident in power loss analysis for powerconversion. The work proposes solutions to improve loss analysis from the device level to the system level,as outlined below.• The first contribution of this work is the development of a characterization procedure for GaN eHEMTS.This procedure uses thermal measurement to accurately determine the losses of the GaN device undera variety of different operating conditions. By using different circuit configurations, conduction andswitching losses can be characterized independently.• Using the loss characterization, a loss model for the GaN eHEMT is created. By applying DOE, a mini-mum number of test conditions can be used to model the loss behavior under all operating conditions.The proposed model can easily be implemented in PLECS for accurate loss prediction in any powerconverter topology. The model is validated through experiment with a boost converter and the resultsare compared to other common loss-prediction practices. The loss prediction error is improved from50% using current best practices to 12% with the developed model.• Moving to a higher level of abstraction, loss prediction at the system level is also considered. TheRapid Loss Estimation equation (RLEE) is developed to allow for accurate converter loss predictionunder the diverse operating conditions seen in system-level simulation. The RLEE uses DOE to extractdetailed converter behavior into a computationally-simple parametric equation.• Finally, the RLEE is applied to the analysis of a DER DC microgrid. For this study, the RLEE is devel-oped for three different converter topologies to highlight its versatility and ease of use. The microgridis simulated for one year to compare the performance of the RLEE and the traditional fixed-efficiencymethod. It is found that the RLEE has very fast simulation speed and provides improved accuracy inloss prediction.9Ultimately, the greatest contribution of this work is the procedures developed. While demonstrated forparticular devices and converters in this work, these methods can be applied to any power electronic device,converter topology and/or energy system.1.4 Thesis OutlineThis work is outlined in the remainder of this document as follows.• In Chapter 2, the device characterization procedure and its application for loss prediction in a boostconverter is presented. First, the loss mechanisms of GaN devices are introduced. Then, the thermalcharacterization procedure is explained, including the circuits used to isolate the individual loss mech-anisms. design of experiments is introduced and applied to the development of a loss prediction modelfor the GaN eHEMT. Finally, the loss model is applied in a boost converter, where its performance isvalidated.• In Chapter 3, the Rapid Loss Estimation equation is presented. First, the procedure to develop theRLEE is presented. This procedure is applied to three different converters that are commonly used forDER. Through these examples, the ability of the RLEE to consider different operating conditions ishighlighted. The three converters are included in the design of a DC microgrid, which is simulated forone year. The simulation validates the computational simplicity of the RLEE, while demonstrating thepitfalls of the traditional fixed-efficiency method of loss prediction at system level.• In Chapter 4, the experimental and simulation results are summarized and conclusions are drawn onthe impact of the presented work. Finally, future work is presented to apply the developed techniquesin the continued advancement of power conversion.10Chapter 2Power Loss Characterization of GalliumNitride Power SwitchesGaN power switches provide multiple benefits over traditional Si MOSFETS, such as lower losses, higherswitching frequencies and increased power density. To date, multiple converter topologies have been demon-strated using GaN transistors; however, GaN devices are still a developing technology. Their small physicalsize and low thermal capacitance are particularly challenging to deal with. Significant emphasis must beplaced on thermal management of the heat generated by the losses in the device. To this end, accurate powerloss prediction is needed to properly design the thermal management system and reach the full benefits ofGaN technology.In order to characterize the loss behavior of GaN eHEMTS, it is necessary to consider the two loss mech-anisms in the device, as first presented in Fig. 1.3a in 1.2.3. For eHEMTS, there are only two main lossmechanisms: conduction losses and switching losses. Unlike Si MOSFETS, there is no anti-parallel diode,and so there are no reverse recovery losses to consider. The individual loss mechanisms and the techniquesused to isolate them from each other are described in the subsequent sections. For each of the two lossmechanisms, it is necessary to be able to test the loss performance under a variety of realistic operatingconditions.In this work, experimental characterization of the switch using thermal measurement allows for the cre-ation of a high accuracy power loss model. First, the conduction losses are evaluated through a simpleexperimental procedure. During this procedure, the thermal behavior of the system is also characterized.Using this thermal characterization, the switching losses can then be evaluated experimentally. Using theexperimental results from select operating conditions, a power loss model for the GaN switch can be created11gdsONdIdsVdsdIdsVcondPds,onRFigure 2.1: When the eHEMT is turned on, a parasitic resistance between drain and source exists, Rds,on.When current Id flows through Rds,on, conduction losses, Pcond , predict the losses under any operating conditions. The developed model is applied to the simulation of thelosses in a boost converter. Experimental validation is performed on the simulated converter to demonstratethe performance benefit of the proposed model over traditional loss estimation techniques.2.1 Conduction LossesThe first loss mechanism, and the simplest to characterize, is conduction loss. Conduction losses, Pcond , arecaused by the resistive behavior of the device between the drain and source, Rds,on, when the eHEMT is turnedon, as shown in Fig. 2.1.When the device is on and current, id , flows, the conduction losses, Pcond , are given bypcond(t) = vds(t) · id(t) (2.1)where vds is the voltage between drain and source. Assuming that variations of the current and voltage arenegligible in the conduction interval, the average values can be assumed, Vds and Id for voltage and current,respectively. Then, Rds,on is defined such thatPcond =VdsId = Rds,onI2d (2.2)and soRds,on =VdsId. (2.3)122.1.1 Datasheet ModelRds,on is provided by the manufacturer on the datasheet, however, the provided model lacks detail. Often,the dependence of Rds,on on the junction temperature, Tj is provided, but only for a specific value of Id .For GaN Systems’ GS66508B, considered throughout this work, a relatively detailed model is provided.As is common, the dependence of Rds,on on Tj is given, normalized to the value at Tj = 25oC. In addition,the dependence of Rds,on on Id is given for Tj = 25oC and Tj = 150oC. Then, the datasheet value of Rds,onfor a given operating point can be obtained by assuming a linear interpolation between the Tj = 25oC andTj = 150oC curves for a given value of Id .2.1.2 Characterization with Design of ExperimentsGiven (2.2), it is easy to determine the conduction losses if Id and Vds can be measured. The circuit usedfor testing conduction losses is given in Fig. 2.2. A DC current supply is used to generate Id and the DUT isturned on by a constant Vgs = 6V. Two highly accurate (error ≤ ±0.01% of the reading) digital multimeters[55] are used to measure Id and Vds. The multimeter is used to measure Id as the precision of the currentsupply is limited. As these are DC measurements, there are none of the challenges for electrical measurementmentioned in 1.2.3.The Tj, however, cannot be measured as the junction is concealed by the device’s case. Instead, the casetemperature, Tc, is used as a proxy because it can easily be measured. Tj can readily be found from Tc usingTj = Tc+PlossRθ , jc (2.4)Where Rθ , jc is the thermal resistance between the junction and case given on the device datasheet. Tc iscontrolled by placing the DUT in a thermal chamber. A thermocouple is mounted to the case with thermally-conductive epoxy and the temperature value is directly fed to the thermal chamber controller. AdditionalgsVsource−dIAmeasured−dIVmeasured−dsVcTFigure 2.2: Id is applied by a DC source and Id and Vds are measured with high accuracy.131x2x(-1,-1)(-1,0)(-1,1)(0,1)(0,0)(0,-1) (1,-1)(1,0)(1,1)Operating AreaTest PointsCenter Point -Multiple ReplicatesFigure 2.3: Normalized test points for the FCCCD design. While two independent variables are shownhere, the design can be mathematically extended to any number of independent variables. This de-sign methodology allows for robust characterization of 2nd-order behavior with a minimal numberof experimental test points.details on the test setup are given in 2.2.1.As described in 1.2.1, design of experiments can be used to intelligently select specific test conditions.From these specific test conditions, the behavior under all operating conditions can be expressed as a para-metric equation. For the conduction losses a face-centered central composite design (FCCCD) was selectedfor the DOE analysis. In this design approach, the boundary conditions of the operating area are considered,as well as multiple replicates of the center point. Each independent variable, xi, can be considered to have anormalized range of −1 ≤ xi ≤ 1. Then, the test conditions can be represented graphically in Fig. 2.3. Forthe FCCCD with two variables, 13 test points are needed including 5 replicates at the center point. Thesereplicates are used to quantify the random error that is present in any experimental measurement.For the conduction loss characterization, the operational limits were selected based on the 1.85kW boostconverter in 2.4, which was designed using the GS66508B GaN devices. Id is limited to 1 A≤ Id ≤ 6 A, andTc is limited to 25oC≤ Tc ≤ 110oC. The test points and characterization results are given in Table 2.1.From the measured Id and Vds, Rds,on and Pcond can be calculated using (2.3) & (2.2). As Rds,on is typicallygiven on the datasheet, it is the focus of the DOE analysis. Using DOE software to analyze the FCCCD runs,a parametric equation for Rds,on was found. Given in (2.5), the equation can be used to predict Rds,on (andsubsequently Pcond) for any combination of Id and Tc within the tested limits.Rds,on = 46.1+0.3Tc−2.3Id +0.02IdTc+2.9×10−3T 2c +0.4I2d [mΩ] (2.5)14Table 2.1: Test Points for Conduction Loss Characterization of a GaN enhancement-mode high electronmobility transistorNormalized Values Operating Conditions ResponsesId Tc Id Tc Rds,on Pcond ∆Tcb[norm.] [norm.] [A] [oC] [mΩ] [W] [oC]0 -1 3.5 30 51.8 0.62 3.00 0 3.5 70 73.7 0.88 3.71 -1 6 30 54.7 1.93 9.51 0 6 70 79.4 2.81 13.11 1 6 110 114.9 4.05 18.80 0 3.5 70 75.2 0.89 3.70 0 3.5 70 72.9 0.87 3.70 0 3.5 70 72.0 0.85 3.80 1 3.5 110 105.5 1.25 4.5-1 -1 1 30 50.1 0.05 0.1-1 0 1 70 73.4 0.07 0.3-1 1 1 110 101.8 0.09 0.50 0 3.5 70 73.6 0.87 3.5Figure 2.4 shows the DOE characterization of Rds,on graphically and compares the result to the datasheetmodel (as described in 2.1.1). There is a significant portion of the operating region that is not accurately de-scribed by the datasheet model from 2.1.1. This is because the linear interpolation required by the datasheetmodel fails to capture the complexity of Rds,on, which is non-linear. By performing the experimental char-acterization presented here and applying DOE a much more accurate model of Rds,on is obtained. Then is itpossible to accurately predict Pcond using the improved Rds,on model and (2.2).1234560246810+11030[A]dI C]o[cTDatasheetError[%]505070709090[mΩ]ds,onR110130Figure 2.4: Response surface for the actual Rds,on showing considerable error when compared to thedatasheet model, particularly under heavy load (high Id) where losses are highest.15lossPcTjTθjcR θcbRbT(a)cbCo45Co35Co25Co30Co40(b)Figure 2.5: a) The thermal behavior of the system can be represented as an equivalent electrical circuit.Based on this circuit, Ploss can be calculated using (2.6). b)Visible and thermal camera images ofthe GaN eHEMT showing the two points used for temperature measurement.2.2 Loss Determination with Thermal MeasurementIn order to avoid the pitfalls of electrical measurement, thermal measurement can be used. The underlyingprincipal of thermal measurement is that the losses in the device are converted into heat. The losses can beexpressed as an electrical circuit, shown in Fig. 2.5a, where Ploss is analogous to current; the temperature ofa specific point (x), Tx, is synonymous to voltage; and, the thermal resistance between two points (x and y),Rθxy is synonymous to electrical resistance. Shown in Fig. 2.5b, the two points of interest in this work arethe eHEMT case, c, and another point, b, on the board near the eHEMT. Then, if Rθcb, Tc and Tb are known,Ploss can be found inPloss =∆TcbRθcb=Tc−TbRθcb. (2.6)To determine the value of Rθcb for the selected points, a calibration is performed in the first part of themethodology. By performing this calibration, the choice of c and b are flexible. This was verified by testinga variety of points at different locations on the device and board. The measured losses for each combinationof points was found to be within experimental error. This calibration stage, which is done in parallel withthe conduction loss calibration in 2.1.2, is detailed in Test SetupA number of temperature measurement devices were considered for thermal measurement. Electrical-basedtemperature sensors are a common choice. Thermocouples are cheap and readily available, but have limitedaccuracy. resistance temperature detectors (RTDS) are still relatively low cost but provide improved accuracy.However, it was found that when placed in close proximity to a device switching at high frequency, theseelectrical-based sensors were susceptible to EMI. While the EMI did not compromise the controller of the161(a)1234(b)35(c)35678(d)Figure 2.6: a) ¶ The flexible power platform for GaN eHEMT. b) The PCB is · mounted verticallyand installed in ¸ the thermal chamber to provide temperature regulation. ¹ is the IR transparentwindow to allow c) º the thermal camera, mounted to the thermal chamber, to view the DUT. d)» The power supply, ¼ electronic load, and ½ digital multimeters.thermal chamber, the more sensitive thermometers being used for temperature measurement of Tc and Tbwere rendered ineffective. To mitigate EMI effects, a thermal camera was used. While expensive, the thermalcamera is immune to EMI and is non-invasive (i.e. it does not need to be in contact with the DUT).Given the above considerations, the test setup in Fig. 2.6 was built. The test circuits given in Fig. 2.2 andFig. 2.12a for both conduction losses and switching losses, respectively, were implemented using the GaNflexible power platform in Fig. 2.6a. The printed circuit board (PCB) was mounted vertically and positionedin the thermal chamber, as shown in Fig. 2.6b. Using the thermal chamber it was possible to control the Tcof the DUT. The thermal camera was mounted to look into the chamber through an infrared (IR) transparentwindow, as shown in Fig. 2.6c, giving the view shown in Fig. 2.5b. Finally, the digital multimeters, powersupply and load were connected outside the chamber, as shown in Fig. 2.6d.17θcbRCalibratedlossPbT−cT=θcbRthermal cameraMeasurewithbT&cTDC power lossdsVdI=lossPHigh-accuracy123(a)0 0.5 1 1.5 2 2.5 302468101214[W]lossPC]o [cbT∆123(b)Figure 2.7: a) The three steps of the calibration procedure. b) By measuring ∆Tcb and Ploss under DCconditions, Rθcb is found from the slope of the line. As shown by the excellent fit, Rθcb is constantunder diverse operating conditions.2.2.2 Thermal Resistance CalibrationThe characterization procedure can be divided into two steps: thermal resistance calibration and powerloss measurement. Thermal resistance calibration, outlined in Fig. 2.7a can be done in parallel with theconduction loss characterization in 2.1.2.During the conduction loss characterization, Pcond was measured, which is the power loss under a spe-cific operating condition (step 1 in Fig. 2.7). Ploss is known with very high accuracy because of the digitalmultimeters used to measure Id and Vds. The two temperature points Tc and Tb were also measured (step 2 inFig. 2.7). The temperature difference between these two points can then be calculated, ∆Tcb = Tc−Tb.Next, ∆Tcb vs Ploss is plotted, as shown in Fig. 2.7b. The data points are fitted with a linear regression,the slope of which is Rθcb, as can be found from rearranging (2.6) asRθcb =∆TcbPloss(2.7)25 data points (13 from the Pcond characterization and 12 additional Rθcb validation points), are plotted inFig. 2.7b. It can be seen that there is good agreement with the Rθcb calibration line for all points, with an R2value of 0.9978.18123ApplyθcbRcalibratedthermal cameraMeasurewithbT&cTMeasured lossesθcbRbT−cT=lossP(a)0 0.5 1 1.5 2 2.5 302468101214[W]lossPC]o [cbT∆123(b)Figure 2.8: a) The three steps of the measurement procedure. b) By measuring only Tc and Tb, ∆Tcband the calibrated Rθcb can be used to find Ploss without any electrical measurement.2.2.3 Power Loss MeasurementOnce Rθcb has been calibrated, it is possible to analyze the losses under any operating condition with noelectrical measurement. Again, a simple three step procedure is used, as outlined in Fig. 2.8a.In this measurement stage, only the temperature at the two specified points, Tc and Tb are measured(step 1). The same two points must be used in order for the Rθcb calibration to remain valid. Using thismeasurement, and the calibrated Rθcb (step 2), Ploss can be calculated with (2.6) (step 3). This is showngraphically in Fig. 2.8b.2.3 Switching LossesUsing the developed thermal measurement technique, it is possible to measure the losses under any operatingcondition. However, in order to generate a loss model, it is desirable to isolate the switching losses. In thisway, the two loss mechanisms (conduction and switching) can be modeled independently.The more complicated of the two loss mechanisms, switching losses occur when the switch transitionsfrom the on to off or vice versa. The theoretical switching waveforms and resulting losses are shown inFig. 2.9. When the switch is off, no current can flow so Id is zero, and Vds is high. When the switch is on,current can flow so Id is high and Vds is low (but non-zero because of Rds,on described in 2.1).Consider the turn-on transition with ideal waveforms shown in Fig. 2.9a. First, Id begins to increase to19its final value during the current rise time tri. Once tri is complete, Vds begins to fall during the voltage falltime t f v. Once Vds reaches its final value, the switch is said to be turned on and the transition is complete.During this switching transition, the instantaneous power loss, psw, is given bypsw(t) = id(t)vds(t) (2.8)where id(t) and vds(t) are the time varying values of Id and Vds, respectively.From the instantaneous power, the energy of the turn-on transition, Esw,on can be found inEsw,on =∫ t0+tri+t f vt0psw(t)dt (2.9)If the ideal waveforms of Fig. 2.9a are considered, Esw,on is given byEsw,on =12IdVds (tri+ t f v) (2.10)For a given switching frequency, fsw, the average turn on losses, Psw,on, can be found fromPsw,on = Esw,on fsw (2.11)The turn-off transition behaves symmetrically, as shown in Fig. 2.9b. In this case, Vds increases firston−swPTurn-ondIdsVONOFF0trit fvton−swE(a)rvt fitoff−swPTurn-off OFFdsVdION0toff−swE(b)Figure 2.9: Shown with simplified waveforms, in a) turn on losses occur as the eHEMT begins con-ducting (Id increases) before Vds decreses. Similarily, in b), turn off losses occur as Vds increasesbefore Id decreases.20during the voltage rise time trv and then Id falls to zero during the current fall time t f i. When the currentreaches zero, the switch is off. During the turn-off transition, the instantaneous losses are again given by(2.8), while the switching energy, Esw,o f f and average power losses, Psw,o f f are given in (2.12) and (2.13),respectively.Esw,o f f =∫ t0+trv+t f it0psw(t)dt (2.12)Psw,o f f = Esw,o f f fsw (2.13)If the ideal waveforms of Fig. 2.9a are considered, Esw,on is given byEsw,o f f =12IdVds (trv+ t f i) (2.14)The total switching energy, Esw, and total switching losses, Psw, are the sum of the turn-on and turn-offlosses, as given in (2.15) and (2.16).Esw = Esw,on+Esw,o f f (2.15)Psw = Psw,on+Psw,o f f (2.16)Generally, the values of tri, t f v, trv, and t f i are given by the device manufacturer on the datasheet. Then,it would appear, that switching loss estimation is quite easy. However, the real Id and Vds waveforms varysignificantly from the theoretical values, as shown in Fig. 2.10a. The overshoot and subsequent ringing ofthe waveforms during the transition occur because of parasitic inductance and capacitance present in thecircuit. During this ringing period, there are additional ringing losses given by (2.17) and (2.18) and shownin Fig. 2.10b.Ering =∫ringing timeid(t)vds(t)dt (2.17)Pring = Ering fsw (2.18)2.3.1 Double Pulse TestThe electrical loss measurement techniques in 1.2.3 attempt to capture this ringing. The dominant techniquefor electrical measurement of switching losses is the double pulse test (DPT). In the DPT, the switchingwaveforms of a single switching cycle (turn on and turn off) are studied under specific operating conditions.In this way, there is no self-heating of the DUT and Tc can be controlled very easily.21gsVdsVdIlossP(a)swEdIdsVlossPringEcondE(b)Figure 2.10: a) Oscilloscope capture of the ringing in Id and Vds during the turn-on transition of aGaN eHEMT. b) Illustration of Pring, the losses which occur because of this ringing. This lossmechanism is generally ignored in simple switching loss calculations.To generate the switching transition, the circuit in Fig. 2.11a is used. First, the DUT, S1 is turned on andthe inductor current, iL charges linearly based on the DC voltage, Vds−set . Once iL reaches the desired testcurrent, Id−set , S1 is turned off. This provides the Id and Vds waveforms for the turn-off transition. Afterturn-off, iL remains constant as it freewheeling through the diode. By turning S1 on, the waveforms for theturn-on transition can be captured. The waveforms of iL, Id , and Vds are illustrated in Fig. 2.11b.Using the DPT results id(t) and vds(t), Esw,on, Esw,o f f , and Ering can be found using (2.9), (2.12), andset−dsVLdI1SdsVLi(a)dIdsVlossPLisw,onEsw,offEringEON OFF ON(b)Figure 2.11: a) Circuit schematic used for the double pulse test. b) Illustration of the waveforms pro-duced by the DPT. However, these waveforms are very hard to capture accurately with electricalmeasurement.22(2.17), respectively. Then, Psw,on and Psw,o f f can be found from (2.11) and (2.13). Psw is given by (2.16).Finally, Pring can be found using (2.18).The DPT can be applied either in simulation or experiment. Manufacturers often provide Simulation Pro-gram with Integrated Circuit Emphasis (SPICE) models for their devices, which allow for circuit simulationof the DPT procedure. While these models provide high accuracy of the switch behavior, they neglect theparasitic elements that arise from surrounding circuitry when the switch is installed on a PCB. As a result,SPICE simulation of the DPT often has poor results.2.3.2 Switching Cycle Losses using Thermal MeasurementThis work avoids high-frequency electrical measurement of the switching transition; instead relying on non-invasive thermal measurement as described in 2.2. In this approach, the individual Psw,on, Psw,o f f and Pringcannot be isolated, so the combined switching cycle losses is proposed Psw−cycle, as given inPsw−cycle = Psw,on+Psw,o f f +Pring (2.19)In most converter applications, for every turn-on, there is a corresponding turn-off under very similar op-erating conditions. In this case, combining the losses into Psw−cycle does not compromise loss prediction.Therefore, the inability to isolate Psw,on, Psw,o f f , and Pring is deemed an acceptable trade-off for the elimina-tion of low accuracy electrical measurement.To measure Psw−cycle independently from Pcond , the boost converter in Fig. 2.12a is used. The DUT is theboost switch, S1, and the duty cycle, D, is very low. The low duty cycle is set in such a way as to immediatelyturn the switch off as soon as it is fully turned on, as shown in the oscilloscope capture of Fig. 2.12b. In thisway, the switch experiences no Pcond , thus isolating Psw−cycle.The boost converter is supplied by a DC voltage source, Vin, and an electronic load is applied to the output.Vds is equal to the boost converter’s output voltage,calculated using (2.20) and controlled via the DC source.Vds =Vout =Vin1−D (2.20)If D is very small, (2.20) simplifies toVds =Vout ≈Vin (2.21)Id is the boost converter’s input current Iin. By over-sizing the inductor, ripple is minimized, so Iin is canbe approximated as constant. Then, Id can be controlled by changing the electronic load resistance, Rload23inI CL2SdI1SinVdsVloadRoutVcycle−swP(a)dsVdIlossP(b)Figure 2.12: a) A boost converter is used to test Psw−cycle under different operating conditions. Vin andRload are controlled and thermal measurement is used for the losses from S1. b)Oscilloscopecapture of Id , Vds, and Psw−cycle in the boost converter during Psw−cycle testing. As soon as theswitch is fully on, it is immediately turned off so that Pcond is negligible. It can also be seen thatelectrical measurement of Ploss is inaccurate.according toId = Iin =V 2outRloadVin(2.22)With control over Id , Vds and Tc (using the thermal chamber) it is possible to determine the Psw−cycle underany operating conditions.2.3.3 Characterization with Design of ExperimentsSimilar to the Rds,on model used for conduction losses, DOE is employed in the development of a model forEsw−cycle =Psw−cyclefswin the GaN eHEMT. A FCCCD was selected for the three variables of interest: Id , Vds andTc, which required 17 test points, including 5 center points. Again, the operational limits were selected basedon the 1.85kW boost converter in 2.4. Id is limited to 1 A≤ Id ≤ 6 A, Vds is limited to 250 V≤Vds ≤ 450 V,and Tc is limited to 30oC≤ Tc ≤ 110oC. The switching frequency was fsw = 100 kHz.Using DOE software to analyze the Psw−cycle characterization results, a parametric equation for Esw−cyclewas found. Given in (2.23), the equation can be used to predict Esw−cycle (and subsequently Psw−cycle) for anycombination of Id , Vds, and Tc within the tested limits. Figure 2.13 shows (2.23) graphically.Esw−cycle =−252.2+6.1Tc+1.7Vds+20.1Id−4.4×10−2TcVds−0.3TcId+1.4×10−2T 2c −2.6×10−3V 2ds+6.6×10−5TcV 2ds (2.23)24DatasheetModel12345610002040608030 507011090J]µ[cycle−swEC]o[cT[A]dI(a)02040608010025030035040045030 507011090J]µ[cycle−swEC]o[cT[V]dsVDatasheetModel(b)Figure 2.13: Response surfaces for the proposed model and the datasheet model under typical operatingconditions: a) Vds = 350 V, and b) Id = 3.5 A. The proposed model shows a higher-order responseto the relevant variables and predicts much larger losses than the datasheet.For comparison, Esw calculated by the datasheet is also shown. Two differences stand out. First, the DOEmodel provides a higher-order response. That is, the DOE model shows second- and third-order behavior andinteractions, while the datasheet model is linear. Also, it is clear that the datasheet significantly underesti-mates the switching losses. By not including Ering, the datasheet cannot accurately account for the effects ofparasitics in the circuit.2.4 Loss Prediction for GaN DevicesFor the purposes of validating the proposed thermal characterization method, a 1.85 kW boost converter isdesigned using the GS66508B GaN eHEMT. The boost converter is chosen as it is a fundamental powerelectronics topology and is often used in advanced converters, such as PFCS and solar inverters. The relevantspecifications for the test boost converter are provided in Table 2.2 and the schematic is given in SimulationMulti-domain power electronics software can be used to predict the losses in different circuit topologies.These software tools simulate the individual switching transitions within the circuit and evaluate the lossesat each transition. Then, the losses in the GaN eHEMT are calculated as the total of conduction losses andswitching losses.For the boost converter, three different approaches are considered:25Table 2.2: Boost Converter Design SpecificationsSpecification ValueSwitch GS66508BRated Power, Pr 1.85 kWOutput Voltage, Vout 250 - 450 V†Input Voltage, Vin 90 - 325 VInput Current, Iin 1 - 6 ASwitch Temperature, Tc 30 - 110 oC† Vin <Vout for all operating conditionsinI CL2SdI1SinVdsVloadRoutVlossPFigure 2.14: A boost converter is used for validating the proposed model. Ploss of S1 is measured underdifferent operating conditions and compared to the different loss prediction techniques.1. The datasheet model uses the datasheet information for both the conduction and switching loss mod-els.2. The double-pulse-test model also uses the datasheet information for conduction losses. For switchinglosses, the DPT was performed using the SPICE model and DPT circuit provided by GaN Systems. Anumber of DPT tests were performed and a lookup table was created. For test conditions that were notconsidered, the linear interpolation is used within the lookup table.3. The proposed DOE model uses the Rds,on characterization from 2.1.2 for conduction losses. Forswitching losses, the Esw−cycle characterization from 2.3.3 is used.Using each of these models, the predicted power losses under different operating conditions can be obtained.Furthermore, the conduction and switching losses can be estimated individually. This provides additionalinsight into the nature of Ploss for different operating conditions.26PowerLosses[W]: 150 WoutP : 500 WoutP : 1.5 kWoutP : 1.85 kWoutP: 90 VinV : 170 VinV : 325 VinV: 295 VinV43%17% 67% 52%2%57% 50%7% 61% 56%74%15%Proposed Model(best accuracy) (worst accuracy)Datasheet Model(also inaccurate)SPICE ModelMeasured Losses012345678910Figure 2.15: Comparison of experimental results with loss prediction from the datasheet model, SPICEdouble-pulse-test model and the proposed model. The dark color shows the low conductionlosses, while the lighter color shows the much greater switching losses. The datasheet model isthe least accurate, while the SPICE model is only marginally better. The proposed model is muchmore accurate under all operating conditions.2.4.2 Experimental ValidationThe designed boost converter is implemented in hardware to allow for experimental validation of the pro-posed method. Different operating conditions are applied and Ploss is measured using the thermal measure-ment technique described in 2.2. In the selected operating conditions, both conduction and switching lossesare present; however, the two losses cannot be separated in experiment. A sample of the operating conditionswith Vout = 350 V is given in Fig. 2.15, while the average error in Ploss prediction is given in Table 2.3.Table 2.3: Average Loss Prediction ErrorMethod Average Error [%]Datasheet 65Double-Pulse Test 50Proposed 12From the experimental results, the proposed method had an average error for only 12%, while thedatasheet model’s average error was 65% and the double-pulse-test model’s was 50%. It is clear that theexisting methods (both datasheet and DPT) are inadequate for accurate loss prediction. Furthermore, from27the loss breakdown in Fig. 2.15, it can be seen that switching losses comprise the majority of the losses forthe selected switch. This further highlights the detrimental impact of neglecting ringing losses caused byparasitic circuit elements. The proposed model, by considering the parasitic effects in the characterizationprocess, is able to provide significantly improved loss prediction.2.5 SummaryIn this chapter, an improved loss prediction model for GaN eHEMTS was developed. The proposed modeluses accurate thermal loss measurement to characterize the eHEMT under specific operating conditions. First,Pcond is characterized using very accurate DC measurement. During this step, Rθcb is also calibrated. Usingthe Rθcab calibration, Esw−cycle is characterized. DOE is used for both characterizations to develop twoparametric equations: one for conduction losses and one for switching cycle losses. Finally, the losses underany operating condition can be predicted using mulit-domain power electronic simulation software.The developed method was compared to a number of traditional loss prediction techniques. The datasheetmodel is very fast to apply since the data is readily available; however, it lacks accuracy with an averageerror of 65% in the tested boost converter. While more accurate than the datasheet model (average errorof 50%), the DPT model uses electrical measurement which is unreliable for high switching frequencies.Existing calorimetric methods require complicated test setups and are difficult to build, without providingdevice-level detail. The proposed method uses thermal measurement to provide accurate (average error of12%) measurements at high frequency. Meanwhile, DOE is used to minimize the number of tests needed forcharacterization, allowing for relatively fast model creation.The increased accuracy provided by the proposed model is an invaluable tool in estimating efficiencyand planning effective thermal management systems. Through improved thermal management, maximizedpower density will be achieved as GaN devices become increasingly viable for commercial development inthe power electronics industry.28Chapter 3The Rapid Loss Estimation EquationGrowth in distributed energy resources (DER) has led to increasingly complex systems with more powerconverters. As highlighted in Fig. 3.1, many converters are present in a DER microgrid and each converterwill experience a diverse range of operating conditions throughout its lifetime. Given the expanded role ofpower converters, it is necessary to consider converter performance in system-level analysis. In particular,the power losses in the converter should be considered for accurate financial and reliability evaluation.Converter-level simulation typically employs multi-domain power electronic simulations, as seen intpvVtpvPtSoCtratedCDC MicrogridtbatPtSoCFigure 3.1: An example DC microgrid with PV generation, BES and EVCS. There is a large number ofpower converters, each of which experiences a wide variety of operating conditions (one weekshown).29Chapter 2. While accurate, these simulations are very computationally complex, requiring long simulationtimes to analyze even a few seconds of converter performance. Conversely, existing system-level simulationof DER uses the fixed-efficiency method which is overly simplified. This work addresses this gap by provid-ing accurate and computationally simple converter loss prediction: Rapid Loss Estimation equation (RLEE).To develop the RLEE, the relevant operating conditions must be determined. Then, detailed converterbehavior is extracted from multi-domain simulation. Using DOE, the loss performance of the converterunder any operating condition can then be predicted. The detailed model development procedure, as well asits application to three converter topologies is detailed in this chapter. Finally, the proposed RLEE is used insystem-level simulation of a DER DC microgrid designed for Vancouver, Canada. The results are comparedto existing loss prediction techniques.3.1 Loss Model Development ProcedureIn order to accurately predict the losses in each converter of a complex system, a computationally-simpleloss model is needed. It is necessary to distill the detailed converter behavior, which involves trillions ofswitching actions per year, into a simple parametric equation: the Rapid Loss Estimation equation (RLEE).This concept is highlighted in Fig. 3.2a and the resulting benefit in system-level simulation is illustratedin Fig. 3.2b. The RLEE is represented as a loss surface to demonstrate the variability of losses at differentoperating conditions. The high-level development process of the RLEE is given in Fig. 3.3.The first step in the development of the RLEE is the identification of the system-level variables. In general,converter-level simulation relies on electrical variables: voltage, current and power. However, from a system-level perspective, these are often not the variables of interest. For example, when working with batteries,the state of charge (SOC) is often more relevant than the battery voltage. These system-level variables arevaluable in defining the operating conditions of the associated converters.In order to generate a set of DOE test conditions, the operational limits of the system-level variables mustbe determined. DOE software is used to select specific test conditions within these operational limits. Theprovided list of test conditions is optimized to provide the best possible model with the minimum numberof points. Once the relevant test conditions are established, the system-level variables can be translated intovoltage, current and power for use at the converter-level.In addition to identifying the system-level variables, it is also necessary to select a specific convertertopology for the given application. For a selected topology, the translated converter-level variables canbe used to design the converter for the defined system-level operational limits. In this way, the converter30design is focused on the realistic operating conditions, rather than constraints on converter-level variableswhich may have no system-level meaning. The designed converter is then implemented in multi-domainsimulation software to allow for accurate loss modeling.With the variables established (at both system and converter level) and the converter simulation built,the DOE test conditions can be simulated. This simulation, using multi-domain software, provides highlyaccurate power loss prediction for the given operating condition. While accurate, this simulation is much tooslow to simulate all possible operating conditions, which justifies the selection of specific conditions usingDOE.Finally, the high-accuracy simulation results from the select test conditions can be processed using DOEsoftware to generate a parametric equation of the general form given in (1.1). This is the Rapid Loss Es-timation equation (RLEE). The RLEE describes the effect of each system-level variable on the converterlosses. This equation is valid within the entire operating region defined in the initial system-level variableidentification. The RLEE is computationally simple, but extracts detailed converter behavior for accurate lossprediction in system-level simulation. In the subsequent sections, the RLEE is demonstrated for three uniqueconverter topologies.lossPpvPpvVoutVoutIinVinIL 2S1SinVoutVinIoutIdIdsVDetailed Converter Simulation in PLECSFASTSLOW!RLE Equation(a)Traditional ProposedPV EVBatteryLossesConverter ERROR!SimpleComputationallyLoss PredictionDetailedConverterBehaviorRealOperatingConditionslossPpvPpvVProposed:fixedηTraditional:OversimplifiedConverterModel(b)Figure 3.2: a) The proposed method transforms computationally-complex multi-domain simulationsinto the computationally-simple RLEE. b) The RLEE considers both real operating conditions anddetailed converter behavior for accurate system-level loss prediction.311 234Identify system-levelvariables subject tochange during operationTranslate system-levelvariables intoconverter-level variablesImplement convertersimulation inmulti-domain softwareDesign converterfor expectedoperating conditionsSelectconvertertopologymulti-domain softwareSimulate DoE testconditions inAnalyze test resultswith DoE softwarefor system-level variablesGenerate DoE test conditionsusing DoE softwarelossPpvPpvV), ...2, x1x(f=lossPRapid LossEstimation EquationFigure 3.3: The RLEE creation procedure can be summarized in four stages. ¶ Identification and anal-ysis of the system-level variables. · Selection and implementation of the converter in multi-domain simulation software. ¸ Simulation of DOE test conditions. ¹ Analysis of DOE results togenerate the RLEE323.2 Converter TopologiesEach application within a DC microgrid requires a unique converter topology, tailored to the particular de-mands and opearting conditions of that application. While there are infinite choices for each converter, threecommon topologies are considered here a illustrative examples.3.2.1 Boost Converter for PV GenerationPV generation is highly variable throughout the year. The output of the PV panels is dependent on theirradiance and the panel temperature. However, the RLEE is derived for the boost converter, and thereforeshould be independent from the selection of PV panel. Then, the irradiance and panel temperature must firstbe converted into variables that effect the boost converter: PV panel voltage, Vpv, and power, Ppv.In this work, solar irradiance data is obtained from the National Renewable Energy Laboratory (NREL)National Solar Radiation Database Data Viewer [56]. This resource provides the direct normal irradiance,DNI; global horizontal irradiance, GHI; zenith angle, θZ; ground albedo, ρ; and, air temperature, Tair. Thepanels are titled at an angle equal to the latitude of their installation θtilt = L = 49o for Vancouver. Then, itis necessary to calculate the plane-of-array irradiance, POA, to know the actual irradiance perpendicular tothe panels throughout the year. POA is given byPOA = POAdirect +POAre f lected +POAdi f f use (3.1)where POAdirect is the direct irradiance found in (3.2); POAre f lected is the irradiance reflected off the groundin (3.5); and, POAdi f f use is the diffuse irradiance from the atmosphere in (3.6).POAdirect = DNIcos(AOI) (3.2)Where AOI is the angle of incidence of direct irradiance on the panel incos(AOI) = cos(θZ)cos(θtilt)+ sin(θZ)sin(θtilt)cos(θhour) (3.3)Where θhour is the hour angle, given in (3.4), which describes how the sun moves from east to west throughthe day.θhour = 15o(12−hr) (3.4)Where hr is the hour of the current time of day.33Jan Mar May July Sept Nov0246PVPower[kW](a)Time of Day [hr]PVPower[kW]012345108 12 14 16 186 20SunnyWinterRainySpringSunnySummer(b)Figure 3.4: a) Ppv throughout the year in Vancouver with the weekly average power overlaid. b)Zoomed view of seasonal power generation of the PV array on representative days. It can beseen that PV generation changes significantly throughout the year.POAre f lected = GHIρ1− cos(θtilt)2(3.5)POAdi f f use = DHI1+ cos(θtilt)2(3.6)Where DHI is the direct horizontal irradiance found inDHI = GHI−DNIcos(θZ) (3.7)Using the NREL data and above equations, the POA and Tamb are known in half-hour increments through-out the year. Then, Vpv and Ppv must be found for the year. The BP365 65 Watt panel is selected as ademonstrative panel in this work and is installed in an array with 15 panels in series per string and 6 stringsin parallel. For the given panel, the maximum power point (MPP) of the panel for each POA and Tamb operat-ing condition can be found using a manufacturer provided lookup table. The annual Ppv profile in vancouveris given in Fig. 3.4a, and three representative days of different seasons are shown in Fig. 3.4b. In this work,it is assumed that the boost converter always works at the MPP. This is an acceptable assumption as modernmaximum power point tracking (MPPT) systems are very good [57, 58]. Furthermore, if the converter is notat the MPP it is expected to be very close, so the difference in power losses will not be significant.For the selected array, a 4 kW boost converter was selected as the DC-DC converter for PV generation.The boost converter is a well-established technology for DC-DC systems and often makes up the input stageof PV inverters for AC-DC conversion as well. In the boost converter, the input voltage is the PV MPP voltage,Vin =Vpv, and the input power will be the PV MPP power, Pin = Ppv. The output voltage will be fixed by the34SunnyWinterSunnySummerRainySpringPV BoostLimitsPVPower[kW]PV Voltage [V]0123450 100 200 300Figure 3.5: The operational limits of the 4 kW boost converter are shown in the power-voltage plane.Seasonal opearting points are shown to highlight how Vpv and Ppv change throughout the day andyear.DC bus to be Vout =Vbus = 400 V and the output power will follow the input power. Since the converter maybe installed outside, Tamb should also be considered. Then, the relevant system-level variables for the DOEare Vpv, Ppv and Tamb.With the variables identified, the operational limits must also be considered, as highlighted in Fig. 3.5.Firstly, Vin must be constrained to ensure balanced utilization of the low-side and high-side switches inthe boost converter. If th input is too low or too high, one switch carries the majority of the current andwill be prone to failure. In this case, the lower limit is set to 80 V, which corresponds to an 80% dutycycle from (2.20). Similarily, the upper limit is set to 320 V, which corresponds to a 20% duty cycle. So80 V≤Vin ≤ 320 V and outside of these limits the converter cannot operate.The power is also limited. While the maximum rated power of the converter is 4 kW, this is only validfor input voltages above 200 V. At Vin = 200 V and Ppv = 4 kW, the input current is 20 A. This is the currentlimit for the converter which is enforced to prevent overheating of the selected switches. Then, if the inputvoltage is below 200 V, the maximum power will be limited by the maximum current. If at any point Ppvexceeds the rated input power, the solar generation is reduced to the rated power by adjusting the voltageaway from the MPP. As mentioned earlier, it is assumed that the shift in Vpv from this adjustment is small andhas a negligible effect on the loss behavior of the converter. Then, the operating limits of the converter can beexpressed as a single piece-wise function given in (3.8). Fig. 3.5 shows the various operating conditions thatare experienced by the boost converter in the three sample days of Fig. 3.4b in comparison to the operationallimits. It can be seen that during peak production (sunny summer at midday), the array power exceeds the35power rating of the converter and must be curtailed.Pin ≤0 Vin ≤ 80V20A ·Vin 80V≤Vin ≤ 200V4kW 200V≤Vin ≤ 320V0 Vin ≥ 320V(3.8)Based on the expected operating conditions and and operational limits, a DOE was developed for the threeindependent variables mentioned above: Vpv, Ppv and Tamb. Tamb is considered for −25oC ≤ Tamb ≤ 50oCto account for operation in most climates. Since the operational area is constrained by (3.8), the FCCCDused in Chapter 2 is not ideal. In this case, the DOE software was used to create an optimal design thatwould allow for a cubic regression. This optimal design, shown in Fig. 3.6, ensures that no PV operatingconditions are tested that would violate the input limits of the boost converter. 27 unique operating conditionswere identified for this design. Note that no duplicated center points are needed because the response is theresult of simulation and is not subject to random experimental error. Where there are duplicate points in thepower-voltage plane of Fig. 3.6, these correspond to different temperature conditions. These conditions weresimulated in multi-domain software to accurately capture the boost converter’s loss behavior.Using the simulation results, the DOE software performed statistical analysis to develop the parametricPVPower[kW]PV Voltage [V]0123450 100 200 300Figure 3.6: Optimized test points are generated by DOE software to generate the best result in theconstrained operating area of the boost converter. Where points are close together in the power-voltage plane, different temperatures were considered.36RLE Equation fixedηTraditional[W]lossP[V]pvV100 150200 250300134050100150[kW]pvP2Figure 3.7: The RLEE shown graphically for the PV boost converter. The traditional fixed-efficiencymethod is shown for comparison. The RLEE is able to capture complex loss behavior that is lostin the fixed-efficiency method.equation in (3.9). From the analysis, it was found that Tamb was not significant when predicting the losses.That is, whether the ambient temperature was -25oC or 50oC, the losses did not change by a statisticallysignificant amount. Still, the RLEE is valid for the effects of Vpv and Ppv and is illustrated in Fig. 3.7.Ploss−boost = 70−1.8Vpv+0.15Ppv−1.1×10−3VpvPpv+1.1×10−2V 2pv+3.3×10−6P2pv+2.1×10−6V 2pvPpv−4.1×10−8VpvP2pv−1.9×10−5V 3pv+1.8×10−9P3pv [W ] (3.9)The RLEE result can be compared to the traditional fixed-efficiency method introduced in 1.2.4. If theefficiency is fixed, the losses can be found using (1.3). As the boost converter is being used for PV generation,the European efficiency, ηeuro will be used, as defined in (1.4). ηeuro neglects the variability of losses with Vpv,so the center point is used, Vpv = 200 V. For the boost converter, this gives a fixed efficiency of ηboost−euro =97.7%. The fixed-efficiency loss surface is also plotted in Fig. 3.7 for comparison with the RLEE. It caneasily be seen that the fixed-efficiency method fails to capture the complexity of the converter’s losses underdifferent operating conditions. In particular, the losses are highly dependent on Vpv, especially at high power.In order evaluate the two methods, 40 additional evenly-distributed operating conditions were simulated,giving a total for 67 evaluation points. A comparison of the multi-domain simulation (actual) values and thepredicted values is given in Fig. 3.8 and is summarized in Table 3.1. In this figure, the distance from theideal case represents the error in the prediction technique. It is immediately clear that the RLEE provides37PredictedLosses[W]15010050015010050Actual Losses [W]0!ERRORProposed RLEE fixedηTraditionalFigure 3.8: Predicted vs actual plot of the boost converter losses. The proposed RLEE equation showsmuch less deviation from the ideal (black line) than the traditional fixed-efficiency method.Table 3.1: Comparison of Loss Prediction Techniques for the Boost ConverterTechniqueAverage MaximumError Error[W] [W]Traditional ±17 88Fixed-EfficiencyProposed RLEE ±4 14much better loss prediction than the fixed-efficiency method. In particular, the fixed-efficiency method withthe ηeuro is prone to either over or under predict the losses. When a year’s worth of operation is consideredin 3.3, it will be shown that the over and under prediction are not balanced and do not cancel out to give anaccurate prediction. The fixed-efficiency method had an average error of ±17 W and a maximum error of88 W. By contrast, the RLEE is much more accurate with an average error of only ±4 W and a maximumerror of 14 W.Through this validation, it is verified that the proposed RLEE provides improved accuracy over the tradi-tional fixed-efficiency method. The parametric equation obtained by the DOE and the operational limits arecomputationally simple and can easily be implemented in system-level simulation, as demonstrated later in3.3. The result is a computationally-simple method for accurate loss prediction of the boost converter for PVgeneration.384.50 50 1002.533.54020406080State of Charge [%]100ChargeCurrent[%rated]SingleCellVoltage[V](a)370 380 390 400 410 420[kW]outP024610% 20%30%40% 50%60%70%80%90%[V]outV(b)Figure 3.9: a) Charging current and single cell voltage as a function of state of charge. The charge cur-rent is expressed as a percentage of the battery’s maximum rated charge current. b) The trajectoryin the power-voltage plane of a Crated = 15 A, 100-cell EV battery as it charges from SoC = 10%to SoC = 90%. The converter’s operating conditions vary constantly as the battery charges.3.2.2 LLC Converter for EV ChargersIn modern electric vehicles (EVS), the primary battery technology is lithium-ion. Lithium-ion batteries havea well defined ideal charge profile that defines the current and voltage as the battery charges. This profile isshown for a single cell battery in 3.9a. It can be seen that the battery voltage, Vbat , and the battery current,Ibat , are both a function of the battery’s state of charge, SoC. Ibat is expressed as a percentage of the battery’smaximum rated current, Crated .For the EV battery charger, the converter-level variables would be the output voltage, Vout =Vbat , and theoutput power, Pout =VoutIout =VbatIbat . However, the system-level variables that correspond to Vbat and Ibatare SoC and Crated . Figure 3.9b shows how the converter-level variables change in response to SoC. If Cratedis lower, a similar trend is observed but at a lower Pout . The converter input voltage is fixed by the DC busand the input power follows the output power.The LLC resonant converter is a popular battery charger topology because of its high efficiency [59,60]. In this system, a 6.6 kW LLC converter is used in the EVCS. Based on the converter- and system-level variables above, the operational limits for the EV charger are given in Table 3.2. SoC is limited from10% to 90% as operation outside this range is detrimental to battery longevity and be avoided. In thisparticular charger, the rated power (6.6 kW) exceeds the maximum loading condition (6.0 kW) , so noadditional constraints are needed on the converter-level variables. The diverse operating conditions that willbe encountered as different EVS plug in to charge is explored further in 3.3.1. As in 3.2.1, an ambienttemperature range for most climates is also considered.Using the system-level variables, SoC, Crated , and Tamb, an optimized DOE was generated with 30 test39[%]SoC[A]ratedC[W]lossP510151030507090100150200250300Co25Co0Co25−Co50Figure 3.10: The RLEE shown graphically for the LLC EV charger shows significant variation in lossesunder different operating conditions. For the LLC, ambient temperature has a significant effecton the loss behavior.points. Each test point was evaluated in multi-domain simulation and the results were analyzed to createthe RLEE given in (3.10). Unlike the PV boost converter, temperature has a significant effect on the lossperformance. Figure 3.10 plots the RLEE across different temperatures to illustrate the effect.Ploss−LLC = 108+0.43SoC+2.6Crated +0.20Tamb+9.8×10−2SoC ·Crated +2.6×10−2SoC ·Tamb+6.2×10−2Crated ·Tamb−1.0×10−3SoC2−4.5×10−4SoC ·Crated ·Tamb−1.3×10−3SoC2 ·Crated−2.2×10−4SoC2 ·Tamb [W ] (3.10)Similar to the boost converter, 40 additional points across the design space were used for validating theTable 3.2: Operating Range of a 6.6 kW LLC EV Battery ChargerVariable Lower Limit Upper LimitSoC [%] 10 90Crated [A] 5 15Tamb [oC] -25 50†Vout [V] 374 416‡Pout [W] 495 6023† Vout is a result of SoC and is not a separate variablein the DoE.‡ Pout is a result of SoC and Crated and is not a sepa-rate variable in the DoE.40PredictedLosses[W]Actual Losses [W]RLEE peakη load−fullη0 100 200 3000100200300Figure 3.11: Predicted vs actual plot of the LLC converter losses. The proposed RLEE equation showsmuch less deviation from the ideal (black line) than the traditional fixed-efficiency method.RLEE. The predicted versus actual plot is given in Fig. 3.11 and the error results are summarized in Table 3.3.In the case of EV chargers, there is no euro-efficiency equivalent for a weighted average. Instead, theefficiency from a single operating point can be considered. There are two values that are commonly used:the peak efficiency, ηpeak (i.e. the highest efficiency the converter has under any operating condition), and thefull-load efficiency, η f ull−load (i.e. the efficiency when the converter is operating it its rated power). For the6.6 kW LLC used here, ηpeak = 98.4% and η f ull−load = 97.5%, based on the efficiency at room temperature(25oC). These two fixed-efficiency values are also considered in Fig. 3.11 and Table 3.3. Both of the fixed-efficiency selections exhibits very poor prediction accuracy compared to the RLEE. Only a few select pointshave accurate loss predictions, which are the conditions at which the fixed efficiency is defined. Otherwise,the fixed efficiency drastically under-predicts the losses. This is due to two major shortcomings of the fixed-efficiency approach. First, the the converter efficiency drops significantly under light-loading conditionswhich are completely ignored by the fixed-efficiency approach. Secondly, the effect of temperature on theloss behavior is completely ignored. By comparison, the RLEE extracts accurate loss behavior from themulti-domain simulation including under light load conditions and at various ambient temperatures.From these results, it is clear that the operating conditions have a significant impact on the loss per-formance of the LLC resonant converter when used as an EV charger. The RLEE effectively captures thevariability of losses in a computationally-simple parametric equation.41Table 3.3: Comparison of Loss Prediction Techniques for the LLC ConverterTechniqueAverage MaximumError Error[W] [W]Fixed ηpeak ±92 173Fixed η f ull−load ±89 172Proposed RLEE ±2 93.2.3 Bidirectional DC-DC Converter for Battery Energy StorageFor battery energy storage systems, many battery options are available since the high energy density oflithium-ion is less critical. Still, lithium-ion is a common choice because of their widespread availability andpopularity. Then, the same dependency of Vbat on SoC seen in Fig. 3.9 can be expected for the BES converteroutput voltage VBES = Vbat . The input voltage will again be fixed by the DC bus. In this case, however, thepower, PBES, will be dictated by the difference between the PV generation power, PPV , and the EVCS loadpower, PEVCS, as described inPBES = PPV −PEVCS (3.11)In this case, the converter must be bidirectional: able to charge the BES when PPV > PEVCS and ableto discharge when PPV < PEVCS. A 12 kW bidirectional DC-DC converter works well for this application;operating in buck mode to charge the batteries and boost mode to supply the DC bus. This power ratingallows for the converter to supply to EV chargers at the EVCS without PV support.The relevant variables will then be SoC, PBES, Tamb and direction of power flow, with the limits outlinedin Table 3.4. Again, 10% ≤ SoC ≤ 90% to ensure the longevity of the batteries. With this charge limit, thebattery voltage will not change significantly, so the system is designed for full power at all battery voltages;i.e. there is no power de-rating for low voltage as was seen in the PV boost converter. This also highlights acrucial benefit of considering system-level variables in the DOE. For a 65-cell battery, Vbat will only changefrom 240 V to 270 V as it charges from 10 to 90%. If converter-level variables were considered without thisinsight, the DOE would likely consider converter voltages in the range of 80 V ≤ VBES ≤ 320 V (similar tothe PV boost); but, most of these voltages would never be seen in the BES application. Instead, by focusingonly on actual operating conditions for the system-level variables, a more accurate model can be generatedusing the same number of test points.A DOE with 30 test points was performed with different Ploss responses for charging and discharging42Table 3.4: Operational Limits of the 12 kW Bidirectional DC-DC ConverterVariable Lower Limit Upper LimitSoC [%] 10 90PBES [kW] 1.2* 12Tamb [oC] -25 50†Direction Charging Discharging‡VBES [V] 240 270* PBES is not tested below 1.2 kW as losses below thispoint are not statistically significant. For operationbelow 1.2 kW, the 1.2 kW loss value is assumed as aworst-case assumption.† The direction (charge vs discharge) was found tohave a negligible impact on the loss behavior.‡ VBES is a result of SoC and is not a separate variablein the DOE.operation. It was found that the direction had an insignificant effect on the loss performance, and thus couldbe neglected moving forward. This is a reasonable result, as the buck and boost modes are symmetrical, sothe magnitude of the currents and voltages on the switches will be the same in both charge and dischargemodes. The RLEE for the bidirectional DC-DC converter for the BES system isPloss−BES = 18+0.28SoC−1.2×10−2Pstorage−0.44Tamb−7.2×10−5SoC ·Pstorage+1.5×10−4Pstorage ·Tamb−3.1×10−3SoC2+4.4×10−6P2storage−9.1×10−3T 2amb+9.7SoC2 ·Pstorage−1.0×10−8SoC ·P2storage−1.2×10−8P2storage ·Tamb+2.6×10−4T 3amb [W ] (3.12)[W]lossP[kW]BESP [%]SoC20406080639120100200300400Figure 3.12: The RLEE shown graphically for the DC-DC bidirectional converter for the BES showssignificant variation in losses under different operating conditions.43PredictedLosses[W]Actual Losses [W]RLEE peakη load−fullη0 100 200 300 400 5000100200300400500Figure 3.13: Predicted vs actual plot of the DC-DC bidirectional converter losses. The proposedRLEE equation shows much less deviation from the ideal (black line) than the traditional fixed-efficiency method.Table 3.5: Comparison of Loss Prediction Techniques for the DC-DC Bidirectional ConverterTechniqueAverage MaximumError Error[W] [W]Fixed ηpeak ±92 211Fixed η f ull−load ±85 149Proposed RLEE ±4 14Much like the converters above, the RLEE was validated using 40 additional test points and comparedto the fixed-efficiency method. Again both ηpeak = 99.4% and η f ull−load = 96.4% were considered forthe fixed-efficiency method. The results are presented in the predicted-versus-actual graph in Fig. 3.13and summarized in Table 3.5. From the predicted-versus-actual graph, it can be seen that both the fixed-efficiency methods are very inaccurate. The peak efficiency generally results in a significant under-predictionof the losses, while the full-load efficiency generally results in a significant over-prediction of the losses. Incomparison, the RLEE consistently provides accurate loss estimation under all operating conditions.For all three converters considered investigated here, the RLEE provides more accurate loss predictionacross all of the diverse operating conditions. The parametric equation is computationally simple, but cap-tures the detailed converter behavior of the multi-domain simulation. Thus, the RLEE is well positioned foruse in simulation of large systems, as shown in the following section.44Test DC Microgrid6×Figure 3.14: The DC microgrid used for evaluation of the RLEE with PV generation, BES and EVCS. 6PV arrays provide power for the EVCS with two EV chargers. Two BES converters allow for fastenergy storage when PV generation is high.3.3 System-Level Loss PredictionTo demonstrate the performance of the RLEE, a multi-converter energy system is analyzed over one year. TheDC microgrid for this simulation is shown in Fig. 3.14. This system uses multiples of the three convertersinvestigated in 3.2: 6 parallel PV arrays, a BES with two parallel strings and an EVCS with two charge ports,each of which sees a different charge profile.For PV generation, the BP365 65 W panel is used with 15 panels in series and 6 parallel strings perarray. 6 arrays, each with a corresponding PV boost converter, provide adequate energy generation for themicrogrid. The BES system is designed with 2 DC-DC converters to capture all the generated energy form the6 PV boost converters at full power. Each converter is connected to 2.5 MWh of storage capacity providedby 65-cell strings (to match the voltage range considered in 3.2.3). This configuration allows for no energyshortage throughout the year. Note that this configuration has not been optimized; it was selected simply tomeet the basic requirements and highlight the functionality of the RLEE.3.3.1 EVCS Load ProfileOne of the challenges of simulating public EVCSS is that the load profile is poorly defined and highly random.SoC, Crated and time spent charging can very significantly as different cars plug in. For this investigation,statistical data was obtained for a 2-stall public charging station in Vancouver from [61]. Shown in Table 3.6,the data was used to create a random, normally-distributed EV charge profile. Using the half-hour time step,cars would randomly arrive with varying likelihood based on the time of day. If a charger was available,the car would park and being charging. Each car that charged would have a random SoC, Crated and chargeduration. It was assumed that all cars have a 100-cell battery for consistency with the DOE performed in45Table 3.6: Statistical Data for a 2-Stall Public Charging Station in Vancouver, CanadaVariable MeanStandardDeviationAnnual Vehicles 4072 N/ATime of Day 13:45 4hrDuration [hr] 1.46 1†SoC at plug-in [%] 50 13†Crated [A] 10 2† SoC and Crated mean and standard deviation wereselected for consistency with the LLC parametersconsidered earlier and were not provided with theEVCS data.Occurrences20406080050100150200[A]ratedC[%]SoC51015Figure 3.15: Distribution of the many different operating conditions seen by the EV charger in oneyear, based on a normally-distributed random profile.3.2.2; however, this could be an additional variable in future work. As the car remained charging, SoCwould increase and the remaining charge time would decrease. If the car was fully charged before the timecompleted, the charger would turn off, but the port remained full. An example of one week of chargingdata is given in Fig. 3.16. This charging approach resulted in the operating condition distribution shown inFig. 3.15. From this sample profile, it is very clear that the EV chargers in the EVCS experience a wide varietyof operating conditions.46EVPresent YesNoSat SunMon Tues Wed FriThurSun050100[%]SoC051015[A]ratedCFigure 3.16: One week of EVCS data generated using a normally-distributed random profile. As differ-ent vehicles plug in to charge, the operating conditions vary significantly.3.3.2 System SimulationWith the operating conditions established through the PV and EVCS profiles above, one year of systemoperation was simulated in half-hour time steps. As the primary goal of the simulation is to evaluate theRLEE, a relatively simple simulation is used, as outlined in Fig. 3.17. For each time step, the generation ofthe PV arrays is calculated first. The PV panel data is established as described in 3.2.1. The PV data providesthe energy generated during that time step using (3.13), as well as the system-level operating conditions usedto calculate the losses in the boost converter.EPV = NarrayPpvtstep (3.13)where Narray is the number of solar arrays in the system and tstep is the length of the simulation time step(0.5 hr in this case).Next, the EVCS load is calculated for the two EV chargers based on the profile described in 3.3.1. Fromthe EV profile, the energy demand of the EVCS, EEV is calculated for each charger. SoC and Crated are alsogiven by the profile and used to calculate the losses in the two LLC EV chargers.Finally, the BES status can be evaluated for the time step. The energy balance, that is if there is netgeneration or net consumption is calculated usingEBES = EPV −EEV (3.14)47PVE- Calculateboost−lossP- CalculatePV GenerationEVCS LoadEVE- CalculateLLC−lossP- CalculateBES SystemEVE−PVE=BESE- CalculateSoC- UpdateDCDC−lossP- CalculateLoopfor1 yearFigure 3.17: Process flow for simulating the DC microgrid for evaluation of the RLEE. The PV genera-tion and EV consumption are calculated and the BES provides energy accordingly. The converterlosses are evaluated at each time step to consider the diverse operating conditions seen through-out the year.If EBES > 0, then there is net generation. In this case, if the batteries are not fully charged, the generatedenergy is added. If the batteries are fully charged, this energy is assumed to be wasted. If EBES < 0, thenthere is net consumption. In this case, the batteries are discharged to power the load. In both the generationand consumption cases, the SoC of the batteris is updated and the losses in the BES DC-DC converter arecalculated. Figure 3.18 shows the performance of the BES system throughout the year. It can be seen thatthe battery is sized in such a way that the load can always be met. Furthermore, it can be seen that the BESis routinely charging and discharging throughout the year with a large variety of operating conditions. Thisprocess is repeated for each time step for one year of system operation.20406080Jan Mar May July Sept Nov[%]SoC(a)-60612Jan Mar May July Sept Nov[kW]BESP(b)Figure 3.18: a) The annual SoC of the complete BES throughout the year. b) The annual PBES of oneDC-DC bidirectional converter in the BES system. The operating conditions vary significantlythroughout the year, particularly when the SoC drops due to low generation in winter.483.3.3 Loss Prediction EvaluationThere are two key considerations for evaluation of loss prediction techniques: speed (i.e. computationalsimplicity) and accuracy. The RLEE excels in both of these categories, as demonstrated in the subsequentanalysis.Computational simplicity is needed in order to ensure rapid simulation at the system-level when multipleconverters are present. While there are many factors that effect simulation speed, the simplified simulationpresented in 3.3.2 was used to evaluate both the proposed RLEE and the fixed-efficiency method. The sim-ulation was run repeatedly 1000 times, with only the equation used for loss prediction changing for the twocases. The results are given in Table 3.7. From this result, it is clear that the RLEE is not significantly morecomplex than the fixed-efficiency method; however, as demonstrated in 3.2 the RLEE is significantly moreaccurate. If multi-domain simulation were used, the expected simulation time would be approximately 120days. This is assuming one-second of converter operation (to reach thermal steady-state) is simulated ateach half-hour time step. If a continuous simulation was desired, the required time would be much larger.Clearly the RLEE provides very fast simulation, while multi-domain simulation is unusable for system-levelloss prediction.The second consideration in evaluating the proposed RLEE is the accuracy of the loss prediction. Basedon the validation in 3.2, the error of the RLEE is shown to be significantly less than the error of the fixed-efficiency approach. This is also highlighted in the predicted-versus-actual graphs (Fig. 3.8, 3.11 & 3.13).The extreme error in loss prediction of the fixed-efficiency methods extends to system-level simulation whereit compounds throughout the year. The total annual losses predicted by each method are given in Fig. 3.19,where the compounding error can be seen from the error bars. The percent error of the different fixed-efficiency methods relative to the RLEE prediction is given in Table 3.8. The large discrepancy both in termsTable 3.7: Simulation Time for One-Year Simulation of the DC MicrogridMethod Mean [s]StandardDeviation [s]Fixed-efficiency 0.14 0.01†Multi-domain 120 days N/AProposed RLEE 0.15 0.01† The multi-domain simulation time is estimated basedon the simulation time for a one-second simulation ateach half-hour time step. Due to the length, simulationfor a full year is impossible.49AnnualLosses[kWh]PV BoostProposed RLEE euroηFixed load−fullηFixed peakηFixedBES DC-DCEV LLC0100020003000Figure 3.19: Comparison of predicted annual losses via the proposed RLEE and the traditional fixed-efficiency method. Significant discrepancy between the two mehtods is observed, regardless ofthe fixed-efficiency value used. The LLC EV charger and the BES DC-DC have particularly higherror.of predicted value and cumulative error, between the accurate RLEE and the fixed-efficiency method is clear.Regardless of which efficiency is considered, the annual loss result deviates significantly from that pre-dicted by the RLEE. When ηpeak is assumed, the fixed-efficiency method grossly underestimates the lossesin the system. This is not surprising, as the converter cannot be expected to operate at it’s peak efficiencyunder all operating conditions. Still, this value is often quoted on manufacturer datasheets and marketingmaterials. While providing a different result, η f ull−load does not necessarily provide a better result. Theconverters often operate under light- or partial-loading conditions where the efficiency varies significantlyTable 3.8: Percent Error for One-Year Simulation of the DC MicrogridPercent Error [%]Fixed PV Boost EV LLC BES DC-DCEfficiency LLCηeuro 35 N/A N/Aηpeak -30 -67 -37η f ull−load 76 -49 277† All fixed efficiency approaches have significant error whencompared to the RLEE. Both over (positive percent error) andunder (negative) prediction can be detrimental to system de-sign.50from that at full-load. In the case of the boost converter, even ηeuro does not provide a better result as it is nomore accurate than ηpeak in this case.It is clear that the fixed-efficiency method is severely lacking in accuracy and so cannot be relied upon forsystem-level loss prediction. Similarly, multi-domain simulation is unusable because of the incredibly longsimulation times. The proposed RLEE is an ideal solution. The computationally simple parametric equationallows for high-speed system-level simulation while providing accurate loss prediction. In doing so, accuratesystem design is made possible.3.4 SummaryIn this chapter, the Rapid Loss Estimation equation was presented. The RLEE is a computationally-simpleloss prediction tool for system-level analysis. It extracts detailed converter behavior to accurately predictlosses under all operating conditions. The benefits compared to the traditional fixed-efficiency method andmulti-domain simulation are highlighted in Fig. 3.20. While the traditional fixed-efficiency method is inac-curate, the proposed RLEE is very accurate. While multi-domain simulation is slow, the proposed RLEE isvery fast. The exceptional performance was demonstrated in a sample DC microgrid where the RLEE wasapplied to three different converter topologies. Ultimately, the RLEE allows for fast system-level simulationwith accurate converter-level detail.lossPpvPpvV), ...2, x1x(f=lossPRapid LossEstimation EquationFAST ACCURATEeuroηpeakηload−fullηTraditionalFixed-EfficiencyL 2S1SMulti-domainSimulationSLOW!WRONG!Figure 3.20: Traditional fixed-efficiency simulation is inaccurate, while the proposed RLEE is accurate.Similarily, the RLEE is very fast, while multi-domain simulation is too slow for system-levelsimulation.51Chapter 4Conclusion4.1 SummaryIn this work, techniques for improved power loss prediction in power converters are developed. At the devicelevel, GaN eHEMTS are characterized in detail to provide accurate power loss prediction in converter-levelsimulation. The two loss mechanisms, conduction and switching, are studied independently to allow for lossprediction under any operating condition. Conduction loss characterization provides improved modelingcompared to the manufacturer datasheet and also provides the thermal resistance calibration necessary foraccurate thermal measurement. The switching losses are characterized to include the ringing that occurs as aresult of parasitic elements in the circuit. By including the effects of the parastics, significantly improved lossprediction is obtained. The developed characterization is applied through DOE to build an accurate model oflosses under any operating conditions. Finally, the developed model is validated through experiment and isdemonstrated to provide significantly more accurate loss prediction in converter-level simulation.At the converter level, the Rapid Loss Estimation equation is developed to provide fast and accurate powerloss prediction in system-level simulation. The RLEE is developed by identifying the relevant system-levelvariables that define the operating conditions of the different converters in a system. Then, DOE is appliedto select key operating conditions, which are simulated in multi-domain software to extract the detailed lossbehavior. Ultimately, the RLEE is created as a parametric equation which accurately reflects the converter’sloss behavior under any operating condition. The RLEE is developed for three different converters in aDC microgrid to highlight the procedure. System-level simulation of the microgrid demonstrates the highaccuracy and computational simplicity that the RLEE provides.In conclusion, the power loss prediction techniques developed in this work allow for improved estimation52of power losses at different levels of power converter simulation. The proposed techniques actively accountfor the large variety of operating conditions seen by power converters in any application. At the converterlevel, improved loss prediction ensures effective thermal management design and optimal topology selection.At the system-level, rapid and accurate loss prediction enables optimization of cost, energy collection andreliability. Ultimately, the proposed tools will allow power electronics and power systems engineers furtheradvance the adoption of new technology and renewable energy systems.The contribution to the scientific community is proven through the presentation and publication of oneconference paper at the Institute of Electrical and Electronics Engineers (IEEE) Energy Conversion Con-ference & Congress (ECCE) [1]. It is further supported by the submission of a journal publication to IEEETransactions on Industrial Electronics, which is currently under peer review.4.2 Future WorkIn this work, the methodology for developing accurate power loss prediction is developed. Though specificexamples are considered in this work, the proposed methodologies are completely generic. They can readilybe applied to any are of power electronics where loss prediction is of value.The thermal characterization of GaN eHEMTS provides accurate loss models for an emerging class ofdevices. The developed models could readily be applied to the development of new converter topologiesusing GaN devices. Furthermore, as new devices come to the market, the developed process can be used todevelop highly accurate loss models for these new devices. Similarly, the same methodology can be used fordevices made with other materials such as Si and SiC.The RLEE is also a process that can readily be applied to different applications. The selection of convertertopologies used in this work is arbitrary. Once the RLEE has been applied for a given set of converters, theaccurate loss prediction it provides is invaluable. 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