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Metoda optimiranja trorazinskoga pretvarača za pomoćna napajanja tračničkih vozila : doktorski rad /

by Kovačić, Marinko; Šunde, Viktor [ths].
Type: materialTypeLabelBookPublisher: Zagreb : M. Kovačić; Fakultet elektrotehnike i računarstva, 2017Description: 243 str. : ilustr. u bojama ; 30 cm. + CD.Summary: U disertaciji je razvijena nova metoda optimiranja pretvarača pomoćnih napajanja za tračnička vozila. Metoda implicira pretvarač kao cjelinu sastavljenu od izmjenjivača i izlaznog filtra uzimajući u obzir njihove međusobne uzročno-posljedične veze. Za potrebe višekriterijske optimizacije pretvarača izrađeni su računalno nezahtjevni modeli izmjenjivača i filtra. Ubrzanje izračuna strujno-naponskih odnosa unutar izmjenjivača i filtra postignuto je spajanjem fazorskog modela, usrednjenog modela i sklopnog modela u tzv. hibridni model. U ovaj model uključena je i nelinearnost magnetskog materijala jezgre prigušnice filtra. U radu su razvijeni usrednjeni modeli strujnog opterećenja poluvodičkih sklopki dvaju tipova višerazinskih izmjenjivača, tj. trorazinskog izmjenjivača T-tipa i diodno pritegnutog trorazinskog izmjenjivača. Ovi modeli povezani su s modelom gubitaka i toplinskim modelom poluvodičkih sklopki. Rezultati simulacije ovih računalno nezahtjevnih modela uspoređeni su s rezultatima simulacije sklopnog nelinearnog modela pretvarača. Na temelju zadane geometrije magnetske jezgre, poznatog magnetskog materijala i broja zavoja te valnog oblika struje i magnetskog toka prigušnice računaju se gubitci prigušnice koji uključuju gubitke uzrokovane harmoničkim izobličenjem izlaznog napona izmjenjivača. Kako bi se utvrdila granična vrijednost gubitaka razvijen je računalno nezahtjevni dvodimenzionalni toplinski model lončaste prigušnice temeljen na ekvivalentnim toplinskim otporima. Razvijena optimizacijska metoda kao kriterije koristi volumen izlaznog filtra i ukupne gubitke pretvarača. Za rješavanje ovako definiranog višekriterijskog optimizacijskog problema s mješovito cjelobrojnim varijablama odluke prethodno je modificiran metaheuristički optimizacijski algoritam kolonije mrava. Također je razvijena metoda odabira težinskih faktora za skaliranje funkcija cilja koja omogućuje izračun gustog skupa Pareto-optimalnih rješenja. Prema jednom od rješenja optimizacije napravljen je prototip pretvarača pomoćnih napajanja s trorazinskim izmjenjivačem T-tipa. Kako bi se potvrdili u radu postavljeni modeli, na prototipu su napravljena detaljna ispitivanja gubitaka u filtru i izmjenjivaču. Mjerenjima je pokazano da su korišteni modeli zadovoljavajuće točni za upotrebu u projektiranju pretvarača. Mjerenja su također pokazala da je razvijeni pretvarač veće djelotvornosti, manje mase i izmjera od prethodno korištenog pretvarača pomoćnih napajanja s klasičnim dvorazinskim izmjenjivačem. Ključne riječi: višerazinski izmjenjivači, pomoćna napajanja tračničkih vozila, računalno nezahtjevni modeli, višekriterijska optimizacija, algoritam kolonije mrava Summary: Abstract Design optimization method of three level inverter for auxiliary power supplies in railway vehicles A new method for the design optimization of the auxiliary power supply for railway vehicles has been developed in the dissertation. Modern railway vehicles have increased requirements for supplying auxiliary loads such as air-conditioning compressors, ventilation systems, passenger equipment, etc. This work is related to the design of auxiliary power supplies for three phase loads. Main components of such supply are power inverter and output filter. Motivation Classical methods for design of the auxiliary power supply for railway vehicles are mainly based on observing inverter and output filter as two devices. Inverter components and operational parameters are chosen according to load requirements and thermal stress of the components. Filter components are usually chosen to conform regulatory requirements set by the international standards. Filter inductor value is determined by the maximum current ripple limitation, and capacitor value is chosen to reduce the output voltage distortion to the required level. Development of new inverter topologies, magnetic materials, and passive components increase the difficulty of the task that is set in front of the designer. The highlight of this work is to observe inverter, filter and modulation parameters as one mutually coupled system. Choice of inverter components and modulation affects behavior and sizing of the filter and vice-versa. Eg. increased switching frequency will result in the increased loss in the inverter, but the usage of the smaller filter will reduce filter loss. The sensitivity of both components to design parameters gives space for some of the mathematical optimization methods in solving the problem. The idea is to use mathematical optimization in the process of choosing components for both, inverter and output filter in order to reduce total power loss and filter dimensions. Due to the multidisciplinary nature of the problem, usage of the mathematical optimization coupled to accurate models of the inverter and filter becomes promising approach in the design of auxiliary power supply converter. To reduce total loss and dimensions of the output filter at the same time, one of multi-objective optimization methods has to be employed. Multi-objective methods usually require a large number of objective function evaluations to produce solutions that are acceptable to the designer. Due to the need for a large number of evaluations of the objective functions, it is desirable to use models that are computationally efficient. Hypotesis The basic hypothesis of the dissertation is that there is an additional space for the enchantments of the method for the design of auxiliary power converter for railway vehicles using multi-objective mathematical optimization method in order to reduce total loss and dimensions of the output filter. Computationally efficient models of the electrical and thermal behavior of the inverter and output filter have to be developed to solve the optimization problem in a reasonable amount of time. Design method developed in this work will reduce the time between the input data definition and choice of actual components of the converter. Dissertation structure The doctoral dissertation is divided into nine chapters. Chapter 1 provides an introduction to the application of multilevel inverters in the industry and electric traction. The current state of the research in the field of the design of multilevel inverters and optimization of power converters with the output filter is shown. The basics of the problem of designing the auxiliary power supply for traction vehicles are described. The motivation for usage of a multi-objective optimization method in the design procedure and the hypothesis is laid out in this chapter. Chapter 2 describes the basic structures and topologies of auxiliary power supplies for railway vehicles. The topology of auxiliary supply supplied from the traction transformer is recognized as the best candidate for the reduction of filter dimensions trough optimization techniques as it lacks low-frequency transformer at the output. This chapter also deals with the international standards that have to be followed in the design procedure. Chapter 3 brings the historical development, review, and systematization of multilevel inverter topologies. For each of the topologies, the advantages and disadvantages are defined together with a desirable area of the application. Usage of one of the multilevel inverter topologies is attractive for auxiliary power supply design due to its inherently low output voltage distortion. Chapter 4 provides a review of metaheuristic optimization methods focusing on the ant colony optimization algorithm. As optimization has to choose between of shelf components, the problem is defined as mixed integer non-linear programming (MINLP) problem. Mixed integer distributed ant colony algorithm (MIDACO) is recognized as powerful optimization algorithm in solving this type of problems. The application and results of the optimization method, as well as the extension that enables the implementation of multi-objective optimization with MIDACO, are described. The quality measures of the optimization process based on hypervolume and frontal distance are defined. Chapter 5 is the most important contribution of this work. A detailed description of the computationally efficient models of the inverter and the output filter used in the design of the auxiliary power inverter is presented. The expressions that describe a non-linear magnetic material in the phasor model of the auxiliary supply are derived. A generalized switching model of the neutral point connected three level inverter is defined. Averaged model for a three level inverter is derived from switching model. Averaged switching functions are used to derive current load on the semiconductor components for three level neutral point clamped (NPC) and three level T-type inverter. The calculated current load is used in the semiconductor loss model to obtain power loss distribution in the inverter components. To calculate a thermal stress of the semiconductor components calculated power loss is used in the semiconductor module thermal model. Phasor and averaged models cannot describe high-frequency inductor current ripple that is necessary to obtain inductor loss and output voltage distortion. To overcome this drawback, a hybrid model based on the combination of phasor model averaged model and switching model is proposed. One of the important features of the hybrid model is the computationally efficient calculation of inductor current waveform by taking into account nonlinearities of the magnetic material. A speedup of three orders of magnitude, compared to classical time domain simulation, was achieved by using proposed hybrid model. Inductor current and flux ripple, calculated by the hybrid model of the supply, are used in loss model of the inductor to obtain high-frequency loss component. Improved generalized Steinmetz method (iGSE) was used to calculate core loss at high-frequency. Beside core loss, an influence of high-frequency current ripple on skin and proximity loss in foil winding was discussed through finite element method approach. An important constraint of the optimization is a temperature in the inductor's winding. For this purpose, a thermal model of the pot core inductor with two dimensions of thermal flow was developed using the thermal equivalent circuit. This model was verified with finite element method using several loss excitations. Chapter 6 describes the method of multi-objective optimization of the auxiliary power supply project. Multi-objective optimization is based on the MIDACO optimization algorithm described in Chapter 4 and the computationally efficient models developed for the inverter and output filter described in the Chapter 5. Decision variables, objective functions, and constraint functions are defined. A detailed description of the implementation of multi-objective optimization and the modifications of optimization algorithm that improve the quality of Pareto solution set is presented. The optimization results for the auxiliary power supply rated at 60 kVA are shown in objective function space. A method of selection of the solution from the Pareto optimal set is discussed in this chapter. In the Chapter 7, the construction of a prototype of the auxiliary power supply is explained in detail. The prototype was constructed based on the solution chosen from the multi-objective optimization. Mechanical construction, DC-link design, choice of DC-link capacitors and IGBT drivers is elaborated. The basic characteristics of the digital control system and the necessary modifications of the hardware have been described. In addition to the hardware, the operation of the control algorithm developed for the inverter test purposes is described, and the modulation algorithm implementation is given in detail. Chapter 8 refers to the experimental verification of the computationally efficient auxiliary power supply models used in the optimization process. Special attention is paid to the filter inductor loss measurement method and the comparison of the results obtained by the electrical and calorimetric loss measurements. In addition to the inductor loss measurement, the total loss of inverter was measured to confirm the semiconductor loss simulation. For each of the measurement methods, an accuracy of the measurement procedure was discussed. The measured results were compared with the simulated results. Chapter 9 is a final chapter in which a review of the entire work is given, and the conclusions that were made during the work are presented. Recommendations for further improvements and upgrades of the proposed method of auxiliary power supply design as well as for new areas of application are given. Conclusion The design optimization of auxiliary power supply for railway vehicle involved solving problems in the field of optimization theory, power electronics, electromagnetism, and heat transfer. From the aspect of optimization, the auxiliary power converter is observed as a single device composed of two essential components: the inverter and the output filter. To justify conduction of the optimization procedure, it is necessary to establish a link between these components. The connection is achieved through the dependence of the filter loss on the distortion of the output voltage of the inverter. To perform the optimization procedure, it is necessary to create the accurate models of the auxiliary power supply components. These models are executed within the optimization procedure that requires a large number of simulation iterations with different input parameters. For this reason, all models are tailored to be computationally efficient. The largest impact on the simulation speed was achieved by using hybrid model for filter inductor current waveform calculation. By comparing the time of execution of the proposed hybrid model and the equivalent Matlab SimPowerSystems model, the average acceleration factor was about 800 times with retained accuracy. The calculated waveforms of the inductor current and flux are used as input data for the calculation of inductor's loss. It has been shown that the inductor loss can be calculated using the data from the magnetic material manufacturer datasheet. Comparison of the simulation results of the inductor loss with the measured results showed a very good arrangement. The waveform of the inductor current is also used to calculate the distortion of the output voltage. The simulations of voltage distortion were compared with the measured distortion, and very good agreement was found in the range of the amplitude modulation index between 0.8 and 1. To get a better agreement at lower amplitude modulation indices, the model has to include an effect of dead-time. A comparison of the proposed auxiliary power supply model with the model created in the Matlab SimPowerSystems was performed to evaluate the gain in the calculation speed. Both models included calculation of electrical, loss and thermal parameters. The proposed model was 286 times faster than the equivalent Matlab SimPowerSystems model. The high calculation speed of the proposed model enabled usage of the optimization method. The multi-objective optimization is performed to minimize two conflicting objectives: total auxiliary power supply loss and filter volume. Decision variables were indices of IGBT module, capacitor, magnetic core, magnetic material, the number of turns of the inductor's winding and switching frequency. Since decision variables are mainly discrete, a metaheuristic method of optimization based on an ant colony algorithm has been used. The optimization method has been expanded from single-objective to multi-objective optimization. Each objective is scaled by certain weight and combined in a single objective. A method for calculation of scaling factors that leads to a better quality of Pareto optimal solution set is elaborated. Usage of computationally efficient auxiliary supply models, with 150,000 objective and constraint function evaluations, enabled the optimization process to complete in less than 10 hours. For example, if standard switching model implemented in one of the commercial computer simulation tools such as Matlab SimPowerSystems was used, the time of optimization would be 119 days. It can be concluded that without the computationally efficient models of the power supply, optimization procedure would be infeasible. It has been shown that multi-objective optimization is a very powerful tool that, besides selecting components of the inverter and filter, can also be used for additional insights such as usage of different topologies, types of magnetic materials, and core dimensions. By analyzing the results of multi-objective optimization in the objective function space, it is possible to make additional conclusions that can be used by the designer in the faster and better development of new projects. According to one of the Pareto optimal solutions, a prototype of auxiliary power supply for railway vehicle rated at 60 kVA was built. The power supply prototype was used to verify the accuracy of computationally efficient models used in the design. The basic concept of model verification was the comparison of the simulated and measured inverter and filter loss. Measurements showed very good consistency with the simulation results. The procedure for selecting the correct equipment regarding its accuracy and bandwidth is described for each of the critical measurements. Particular attention was paid to the electrical measurement of the inductor loss. It has been shown that because of the low cosφ, the relative angular error between the measured voltage and current signal becomes the main source of measurement error. To overcome this, a compensation method is proposed. To verify the compensation method, a simple experimental setup with a calorimeter was made. Results of calorimetric loss measurement justified the further use of the electrical method of measuring the inductor loss. Also, a special experimental setup for measuring the efficiency of the inverter based on the measurements of input and output power was made. Due to high efficiency (greater than 98 %) very accurate measurements of input and output power had to be done to calculate system loss. For this purpose current sensors based on fluxgate technology were used. Usage of a T-type three level inverter in combination with the optimization method in selection of the inverter and filter components resulted in a prototype with smaller filter and higher efficiency compared to an existing two-level auxiliary power supply. The weight of the filter components was reduced by the factor of 3.7, the output filter volume was reduced by factor of 3.5, and the total efficiency was increased from 97.9 % to 98.2 %. Keywords: three level inverter, auxiliary power supplies for railway vehicles, computationally efficient models, loss models, multi-objective optimization, ant colony optimization
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Bibliografija str. 213-221.

U disertaciji je razvijena nova metoda optimiranja pretvarača pomoćnih napajanja za tračnička vozila. Metoda implicira pretvarač kao cjelinu sastavljenu od izmjenjivača i izlaznog filtra uzimajući u obzir njihove međusobne uzročno-posljedične veze.
Za potrebe višekriterijske optimizacije pretvarača izrađeni su računalno nezahtjevni modeli izmjenjivača i filtra. Ubrzanje izračuna strujno-naponskih odnosa unutar izmjenjivača i filtra postignuto je spajanjem fazorskog modela, usrednjenog modela i sklopnog modela u tzv. hibridni model. U ovaj model uključena je i nelinearnost magnetskog materijala jezgre prigušnice filtra. U radu su razvijeni usrednjeni modeli strujnog opterećenja poluvodičkih sklopki dvaju tipova višerazinskih izmjenjivača, tj. trorazinskog izmjenjivača T-tipa i diodno pritegnutog trorazinskog izmjenjivača. Ovi modeli povezani su s modelom gubitaka i toplinskim modelom poluvodičkih sklopki. Rezultati simulacije ovih računalno nezahtjevnih modela uspoređeni su s rezultatima simulacije sklopnog nelinearnog modela pretvarača.
Na temelju zadane geometrije magnetske jezgre, poznatog magnetskog materijala i broja zavoja te valnog oblika struje i magnetskog toka prigušnice računaju se gubitci prigušnice koji uključuju gubitke uzrokovane harmoničkim izobličenjem izlaznog napona izmjenjivača. Kako bi se utvrdila granična vrijednost gubitaka razvijen je računalno nezahtjevni dvodimenzionalni toplinski model lončaste prigušnice temeljen na ekvivalentnim toplinskim otporima.
Razvijena optimizacijska metoda kao kriterije koristi volumen izlaznog filtra i ukupne gubitke pretvarača. Za rješavanje ovako definiranog višekriterijskog optimizacijskog problema s mješovito cjelobrojnim varijablama odluke prethodno je modificiran metaheuristički optimizacijski algoritam kolonije mrava. Također je razvijena metoda odabira težinskih faktora za skaliranje funkcija cilja koja omogućuje izračun gustog skupa Pareto-optimalnih rješenja.
Prema jednom od rješenja optimizacije napravljen je prototip pretvarača pomoćnih napajanja s trorazinskim izmjenjivačem T-tipa. Kako bi se potvrdili u radu postavljeni modeli, na prototipu su napravljena detaljna ispitivanja gubitaka u filtru i izmjenjivaču. Mjerenjima je pokazano da su korišteni modeli zadovoljavajuće točni za upotrebu u projektiranju pretvarača. Mjerenja su također pokazala da je razvijeni pretvarač veće djelotvornosti, manje mase i izmjera od prethodno korištenog pretvarača pomoćnih napajanja s klasičnim dvorazinskim izmjenjivačem.
Ključne riječi: višerazinski izmjenjivači, pomoćna napajanja tračničkih vozila, računalno nezahtjevni modeli, višekriterijska optimizacija, algoritam kolonije mrava

Abstract
Design optimization method of three level inverter for auxiliary power supplies in railway vehicles
A new method for the design optimization of the auxiliary power supply for railway vehicles has been developed in the dissertation.
Modern railway vehicles have increased requirements for supplying auxiliary loads such as air-conditioning compressors, ventilation systems, passenger equipment, etc. This work is related to the design of auxiliary power supplies for three phase loads. Main components of such supply are power inverter and output filter.
Motivation
Classical methods for design of the auxiliary power supply for railway vehicles are mainly based on observing inverter and output filter as two devices. Inverter components and operational parameters are chosen according to load requirements and thermal stress of the components. Filter components are usually chosen to conform regulatory requirements set by the international standards. Filter inductor value is determined by the maximum current ripple limitation, and capacitor value is chosen to reduce the output voltage distortion to the required level. Development of new inverter topologies, magnetic materials, and passive components increase the difficulty of the task that is set in front of the designer.
The highlight of this work is to observe inverter, filter and modulation parameters as one mutually coupled system. Choice of inverter components and modulation affects behavior and sizing of the filter and vice-versa. Eg. increased switching frequency will result in the increased loss in the inverter, but the usage of the smaller filter will reduce filter loss. The sensitivity of both components to design parameters gives space for some of the mathematical optimization methods in solving the problem. The idea is to use mathematical optimization in the process of choosing components for both, inverter and output filter in order to reduce total power loss and filter dimensions. Due to the multidisciplinary nature of the problem, usage of the mathematical optimization coupled to accurate models of the inverter and filter becomes promising approach in the design of auxiliary power supply converter.
To reduce total loss and dimensions of the output filter at the same time, one of multi-objective optimization methods has to be employed. Multi-objective methods usually require a large number of objective function evaluations to produce solutions that are acceptable to the designer. Due to the need for a large number of evaluations of the objective functions, it is desirable to use models that are computationally efficient.
Hypotesis
The basic hypothesis of the dissertation is that there is an additional space for the enchantments of the method for the design of auxiliary power converter for railway vehicles using multi-objective mathematical optimization method in order to reduce total loss and dimensions of the output filter. Computationally efficient models of the electrical and thermal behavior of the inverter and output filter have to be developed to solve the optimization problem in a reasonable amount of time. Design method developed in this work will reduce the time between the input data definition and choice of actual components of the converter.
Dissertation structure
The doctoral dissertation is divided into nine chapters. Chapter 1 provides an introduction to the application of multilevel inverters in the industry and electric traction. The current state of the research in the field of the design of multilevel inverters and optimization of power converters with the output filter is shown. The basics of the problem of designing the auxiliary power supply for traction vehicles are described. The motivation for usage of a multi-objective optimization method in the design procedure and the hypothesis is laid out in this chapter.
Chapter 2 describes the basic structures and topologies of auxiliary power supplies for railway vehicles. The topology of auxiliary supply supplied from the traction transformer is recognized as the best candidate for the reduction of filter dimensions trough optimization techniques as it lacks low-frequency transformer at the output. This chapter also deals with the international standards that have to be followed in the design procedure.
Chapter 3 brings the historical development, review, and systematization of multilevel inverter topologies. For each of the topologies, the advantages and disadvantages are defined together with a desirable area of the application. Usage of one of the multilevel inverter topologies is attractive for auxiliary power supply design due to its inherently low output voltage distortion.
Chapter 4 provides a review of metaheuristic optimization methods focusing on the ant colony optimization algorithm. As optimization has to choose between of shelf components, the problem is defined as mixed integer non-linear programming (MINLP) problem. Mixed integer distributed ant colony algorithm (MIDACO) is recognized as powerful optimization algorithm in solving this type of problems. The application and results of the optimization method, as well as the extension that enables the implementation of multi-objective optimization with MIDACO, are described. The quality measures of the optimization process based on hypervolume and frontal distance are defined.
Chapter 5 is the most important contribution of this work. A detailed description of the computationally efficient models of the inverter and the output filter used in the design of the auxiliary power inverter is presented. The expressions that describe a non-linear magnetic material in the phasor model of the auxiliary supply are derived. A generalized switching model of the neutral point connected three level inverter is defined. Averaged model for a three level inverter is derived from switching model. Averaged switching functions are used to derive current load on the semiconductor components for three level neutral point clamped (NPC) and three level T-type inverter. The calculated current load is used in the semiconductor loss model to obtain power loss distribution in the inverter components. To calculate a thermal stress of the semiconductor components calculated power loss is used in the semiconductor module thermal model.
Phasor and averaged models cannot describe high-frequency inductor current ripple that is necessary to obtain inductor loss and output voltage distortion. To overcome this drawback, a hybrid model based on the combination of phasor model averaged model and switching model is proposed.
One of the important features of the hybrid model is the computationally efficient calculation of inductor current waveform by taking into account nonlinearities of the magnetic material. A speedup of three orders of magnitude, compared to classical time domain simulation, was achieved by using proposed hybrid model.
Inductor current and flux ripple, calculated by the hybrid model of the supply, are used in loss model of the inductor to obtain high-frequency loss component. Improved generalized Steinmetz method (iGSE) was used to calculate core loss at high-frequency. Beside core loss, an influence of high-frequency current ripple on skin and proximity loss in foil winding was discussed through finite element method approach.
An important constraint of the optimization is a temperature in the inductor's winding. For this purpose, a thermal model of the pot core inductor with two dimensions of thermal flow was developed using the thermal equivalent circuit. This model was verified with finite element method using several loss excitations.
Chapter 6 describes the method of multi-objective optimization of the auxiliary power supply project. Multi-objective optimization is based on the MIDACO optimization algorithm described in Chapter 4 and the computationally efficient models developed for the inverter and output filter described in the Chapter 5. Decision variables, objective functions, and constraint functions are defined. A detailed description of the implementation of multi-objective optimization and the modifications of optimization algorithm that improve the quality of Pareto solution set is presented. The optimization results for the auxiliary power supply rated at 60 kVA are shown in objective function space. A method of selection of the solution from the Pareto optimal set is discussed in this chapter.
In the Chapter 7, the construction of a prototype of the auxiliary power supply is explained in detail. The prototype was constructed based on the solution chosen from the multi-objective optimization. Mechanical construction, DC-link design, choice of DC-link capacitors and IGBT drivers is elaborated. The basic characteristics of the digital control system and the necessary modifications of the hardware have been described. In addition to the hardware, the operation of the control algorithm developed for the inverter test purposes is described, and the modulation algorithm implementation is given in detail.
Chapter 8 refers to the experimental verification of the computationally efficient auxiliary power supply models used in the optimization process. Special attention is paid to the filter inductor loss measurement method and the comparison of the results obtained by the electrical and calorimetric loss measurements. In addition to the inductor loss measurement, the total loss of inverter was measured to confirm the semiconductor loss simulation. For each of the measurement methods, an accuracy of the measurement procedure was discussed. The measured results were compared with the simulated results.
Chapter 9 is a final chapter in which a review of the entire work is given, and the conclusions that were made during the work are presented. Recommendations for further improvements and upgrades of the proposed method of auxiliary power supply design as well as for new areas of application are given.
Conclusion
The design optimization of auxiliary power supply for railway vehicle involved solving problems in the field of optimization theory, power electronics, electromagnetism, and heat transfer.
From the aspect of optimization, the auxiliary power converter is observed as a single device composed of two essential components: the inverter and the output filter. To justify conduction of the optimization procedure, it is necessary to establish a link between these components. The connection is achieved through the dependence of the filter loss on the distortion of the output voltage of the inverter.
To perform the optimization procedure, it is necessary to create the accurate models of the auxiliary power supply components. These models are executed within the optimization procedure that requires a large number of simulation iterations with different input parameters. For this reason, all models are tailored to be computationally efficient.
The largest impact on the simulation speed was achieved by using hybrid model for filter inductor current waveform calculation. By comparing the time of execution of the proposed hybrid model and the equivalent Matlab SimPowerSystems model, the average acceleration factor was about 800 times with retained accuracy.
The calculated waveforms of the inductor current and flux are used as input data for the calculation of inductor's loss. It has been shown that the inductor loss can be calculated using the data from the magnetic material manufacturer datasheet. Comparison of the simulation results of the inductor loss with the measured results showed a very good arrangement.
The waveform of the inductor current is also used to calculate the distortion of the output voltage. The simulations of voltage distortion were compared with the measured distortion, and very good agreement was found in the range of the amplitude modulation index between 0.8 and 1. To get a better agreement at lower amplitude modulation indices, the model has to include an effect of dead-time.
A comparison of the proposed auxiliary power supply model with the model created in the Matlab SimPowerSystems was performed to evaluate the gain in the calculation speed. Both models included calculation of electrical, loss and thermal parameters. The proposed model was 286 times faster than the equivalent Matlab SimPowerSystems model. The high calculation speed of the proposed model enabled usage of the optimization method.
The multi-objective optimization is performed to minimize two conflicting objectives: total auxiliary power supply loss and filter volume. Decision variables were indices of IGBT module, capacitor, magnetic core, magnetic material, the number of turns of the inductor's winding and switching frequency. Since decision variables are mainly discrete, a metaheuristic method of optimization based on an ant colony algorithm has been used. The optimization method has been expanded from single-objective to multi-objective optimization. Each objective is scaled by certain weight and combined in a single objective. A method for calculation of scaling factors that leads to a better quality of Pareto optimal solution set is elaborated.
Usage of computationally efficient auxiliary supply models, with 150,000 objective and constraint function evaluations, enabled the optimization process to complete in less than 10 hours. For example, if standard switching model implemented in one of the commercial computer simulation tools such as Matlab SimPowerSystems was used, the time of optimization would be 119 days. It can be concluded that without the computationally efficient models of the power supply, optimization procedure would be infeasible.
It has been shown that multi-objective optimization is a very powerful tool that, besides selecting components of the inverter and filter, can also be used for additional insights such as usage of different topologies, types of magnetic materials, and core dimensions. By analyzing the results of multi-objective optimization in the objective function space, it is possible to make additional conclusions that can be used by the designer in the faster and better development of new projects.
According to one of the Pareto optimal solutions, a prototype of auxiliary power supply for railway vehicle rated at 60 kVA was built. The power supply prototype was used to verify the accuracy of computationally efficient models used in the design. The basic concept of model verification was the comparison of the simulated and measured inverter and filter loss. Measurements showed very good consistency with the simulation results.
The procedure for selecting the correct equipment regarding its accuracy and bandwidth is described for each of the critical measurements. Particular attention was paid to the electrical measurement of the inductor loss. It has been shown that because of the low cosφ, the relative angular error between the measured voltage and current signal becomes the main source of measurement error. To overcome this, a compensation method is proposed. To verify the compensation method, a simple experimental setup with a calorimeter was made. Results of calorimetric loss measurement justified the further use of the electrical method of measuring the inductor loss.
Also, a special experimental setup for measuring the efficiency of the inverter based on the measurements of input and output power was made. Due to high efficiency (greater than 98 %) very accurate measurements of input and output power had to be done to calculate system loss. For this purpose current sensors based on fluxgate technology were used.
Usage of a T-type three level inverter in combination with the optimization method in selection of the inverter and filter components resulted in a prototype with smaller filter and higher efficiency compared to an existing two-level auxiliary power supply. The weight of the filter components was reduced by the factor of 3.7, the output filter volume was reduced by factor of 3.5, and the total efficiency was increased from 97.9 % to 98.2 %.
Keywords: three level inverter, auxiliary power supplies for railway vehicles, computationally efficient models, loss models, multi-objective optimization, ant colony optimization

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