As the world moves further into the 21st century, the electricity demand worldwide continues to rapidly grow. The power systems that supply this growing demand continue to be pushed closer to their limits. When those limits are exceeded, system blackouts occur that have massive societal and economical impact. Power system protection relays make up a piece of these limits and can be important factors in preventing or causing a system blackout. The purpose of this thesis is to present a working implementation of an adaptive protection scheme known as the adaptive voting scheme, used to alter the security/dependability balance of protection schemes. It is argued that as power system conditions change, the ability of protection relays to adjust the security/dependability balance based on those conditions can allow relays to play a part in preventing power system catastrophes. It is shown that the adaptive voting scheme can be implemented on existing protection technology given Wide Area Measurements (WAMs) provided by Phasor Measurement Units (PMUs). The proposed implementation characteristics allow numerous existing protection practices to be used without changing the basic operation of the practices. / Master of Science

This report presents a simulation of a real-time phasor measurement unit (PMU) using Matlab, designed to adhere to the IEEE C.37.118 standard. A PMU utilizes measured voltage or current on the power grid and calculates the phasor, frequency and rate of change of frequency (ROCOF). They are crucial in smart grid applications, used to minimize losses and prevent damage to hardware and blackouts. The project was issued by Hitachi Energy with the purpose of utilizing the model for simulating and analyzing real-time data, assessing the PMU's response to different scenarios on the power grid. The results are intended to verify their current system's implementation. The Matlab implementation correctly calculated the phasor, phase-shift, frequency and ROCOF within the requirements of the standard. The associated Total Vector Error (TVE) also complied with the standard. However, the real-time aspect of the PMU did not comply with the standard for several reasons. Specifically the Hilbert transform and FIR filter introduced calculation and filtering delays in addition to internet transmission delays associated with the UDP-interface in Matlab. However, Matlab support confirmed that there are known performance issues with the UDP-interface. It was concluded that the model provided a solid groundwork for its intended use, though the model has yet to be tested with real data from the grid, and would benefit from additional work on optimization.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-12-07T12:33:00Z No. of bitstreams: 1 lucianacarvalhoacacio.pdf: 3829408 bytes, checksum: 88a83782335531c4be76d1544699c7bb (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-12-22T11:27:58Z (GMT) No. of bitstreams: 1 lucianacarvalhoacacio.pdf: 3829408 bytes, checksum: 88a83782335531c4be76d1544699c7bb (MD5) / Made available in DSpace on 2017-12-22T11:27:58Z (GMT). No. of bitstreams: 1 lucianacarvalhoacacio.pdf: 3829408 bytes, checksum: 88a83782335531c4be76d1544699c7bb (MD5) Previous issue date: 2017-08-25 / Este trabalho propõe um método baseado em algoritmos genéticos para alocação ótima de medidores na rede. A partir da alocação dos medidores, é verificado a assertividade alcançada na detecção de defeitos monofásicos, por área, com impedância na média tensão de sistemas de distribuição. Assim, é avaliado o desempenho da metologia de alocação ótima dos medidores. A saída do algoritmo, indica as posições que os medidores devem ser alocados, que formarão as respectivas áreas de observações para detecção. Para realizar a detecção de defeitos em sistemas de distribuição foi desenvolvido também um método utilizando redes neurais artificiais, que é utilizado como rotina interna do método de alocação de medidores, onde as entradas são grandezas elétricas de tensão e corrente, podendo ser medições fasoriais e/ou não-fasoriais, oriundas dos medidores definidos no método de alocação. Esta variação de tipos de medições serviu para analisar o desempenho na detecção do defeito do emprego de diferentes tipos de equipamentos de medição. A escolha da detecção de defeitos monofásicos é baseada no fato de que estes são a grande maioria nos sistemas de distribuição. O método desenvolvido consegue detectar defeitos monofásicos com resistência de arco variando entre 0 a 200 ohms, considerando ainda, variação do carregamento do sistema. O método proposto para alocação, bem como a rotina para detecção de falhas foi desenvolvido no ambiente MatLab®. Os testes foram realizados em sistemas do IEEE, apresentando bons resultados. / The proposal of this work is to develop a method based on genetic algorithms for optimal allocation of measurements units the distribution grid, which aims to detect monophasic defects with impedance in the medium voltage of distribution systems. The detection is performed by artificial neural networks. The developed methodology for optimal distribution of meters indicates as output the positions that the units should be allocated, creating detection areas. Artificial neural networks were used to perform fault detection in distribution systems, which is an internal routine of the measurement units distribution method. The inputs of the artificial neural networks are voltage and current. These electrical parameters can be either phasor measurements and/or non-phasor, depending on the category of meters defined in the allocation algorithm. The performance of different types of measurement equipment was executed by the analysis of different measurement types. It was selected single-phase defects due to the fact that these are the vast majority of faults in distribution systems. The developed method is able to identify single-phase defects with arc resistance ranging from 0 to 200 ohms, and it is also capable of correctly detect faults when considering load variation. The method of measurement unit allocation and the fault detection algorithm were developed in the software MatLab®. Tests were performed in IEEE systems, presenting good results.

Real-time monitoring of electromechanical oscillations is of great significance for power system operators; to this aim, software solutions (algorithms) that use synchrophasor measurements have been developed for this purpose. This thesis investigates different approaches for improving mode estimation process by offering new methods and deepening the understanding of different stages in the mode estimation process. One of the problems tackled in this thesis is the selection of synchrophasor signals used as the input for mode estimation. The proposed selection is performed using a quantitative criterion that is based on the variance of the critical mode estimate. The proposed criterion and associated selection method, offer a systematic and quantitative approach for PMU signal selection. The thesis also analyzes methods for model order selection used in mode estimation. Further, negative effects of forced oscillations and non-white noise load random changes on mode estimation results have been addressed by exploiting the intrinsic power system property that the characteristics of electromechanical modes are predominately determined by the power generation and transmission network. An improved accuracy of the mode estimation process can be obtained by intentionally injecting a probing disturbance. The thesis presents an optimization method that finds the optimal spectrum of the probing signals. In addition, the probing signal with the optimal spectrum is generated considering arbitrary time domain signal constraints that can be imposed by various probing signal generating devices. Finally, the thesis provides a comprehensive description of a practical implementation of a real-time mode estimation tool. This includes description of the hardware, software architecture, graphical user interface, as well as details of the most important components such as the Statnett’s SDK that allows easy access to synchrophasor data streams. / <p>The Doctoral Degrees issued upon completion of the programme are issued by Comillas Pontifical University, Delft University of Technology and KTH Royal Institute of Technology. The invested degrees are official in Spain, the Netherlands and Sweden, respectively.</p><p>QC 20160218</p> / FP7 iTesla

This thesis describes the generic modeling of a Doubly-Fed Induction Generator (DFIG) based wind turbine. The model can also represent a wind plant with a group of similar wind turbines lumped together. The model is represented as a controlled current source which injects the current needed by the grid to supply the demanded real and reactive power. The DFIG theory is explained in detail as is the rationale for representing it by a regulated current source. The complete model is then developed in the time-domain and phasor domain by the interconnection of various sub-systems, the functions of which have been described in detail. The performance of the model is then tested for steady-state and dynamic operation. The model developed can be used for bulk power system studies and transient stability analysis of the transmission system. This thesis uses as its basis a report written for NREL [1]. / text

The motivation for this research is to leverage the increasing deployment of the phasor measurement unit (PMU) technology by electric utilities in order to improve situational awareness in power systems. PMUs provide unprecedentedly fast and synchronized voltage and current measurements across the system. Analyzing the big data provided by PMUs may prove helpful in reducing the risk of blackouts, such as the Northeast blackout in August 2003, which have resulted in huge costs in past decades. In order to provide deeper insight into early warning signs (EWS) of catastrophic events in power systems, this dissertation studies changes in statistical properties of high-resolution measurements as a power system approaches a critical transition. The EWS under study are increases in variance and autocorrelation of state variables, which are generic signs of a phenomenon known as critical slowing down (CSD). Critical slowing down is the result of slower recovery of a dynamical system from perturbations when the system approaches a critical transition. CSD has been observed in many stochastic nonlinear dynamical systems such as ecosystem, human body and power system. Although CSD signs can be useful as indicators of proximity to critical transitions, their characteristics vary for different systems and different variables within a system. The dissertation provides evidence for the occurrence of CSD in power systems using a comprehensive analytical and numerical study of this phenomenon in several power system test cases. Together, the results show that it is possible extract information regarding not only the proximity of a power system to critical transitions but also the location of the stress in the system from autocorrelation and variance of measurements. Also, a semi-analytical method for fast computation of expected variance and autocorrelation of state variables in large power systems is presented, which allows one to quickly identify locations and variables that are reliable indicators of proximity to instability.

A medição fasorial sincronizada é utilizada hoje como forma de aprimorar a operação de um Sistema Elétrico de Potência (SEP), empregando unidades de medição fasorial estrategicamente localizadas e instaladas. Estas realizam a aquisição do sinal elétrico e posteriormente a estimação dos fasores de tensão e corrente sincronizados no tempo, os quais indicam o comportamento do SEP em uma localidade específica. Este trabalho multidisciplinar propõe a análise e implementação de um método computacional evolutivo, o Algoritmo Genético Compacto Multiobjetivo (AGCM) aplicado ao problema de medição fasorial, amplamente utilizado por exemplo, no monitoramento de um SEP, comportando-se assim como uma unidade medidora de fasor, ou Phasor Measurement Unit (PMU). O AGCM aqui apresentado tem como principal característica a análise multiobjetiva do problema. Pelo fato de todo SEP ser trifásico, é proposto esta nova abordagem, onde é considerando para a estimação fasorial as três fases de forma conjunta, e não mais estimadas independentemente. Assim o AGCM proposto considera em seu mapeamento genético dos indivíduos, as características do sinais das três fases, diferentemente da abordagem mono-objetivo, onde cada fase do SEP é modelada sobre um indivíduo diferente. Posteriormente para garantir a eficácia do método evolutivo quando em operação em um cenário de tempo real, é proposto uma plataforma de aquisição de dados e processamento, inspirada em trabalhos anteriormente desenvolvidos, permitindo a integração de todos os módulos que formarão um PMU para análise fasorial em tempo real. Aqui um sistema de Global Positioning System (GPS) existente é proposto como forma de sincronismo entre os PMUs, sincronizando uma gama de equipamentos em um única referência de tempo, com a precisão necessária. Para auxiliar na integração dos módulos necessários, uma biblioteca de funções desenvolvida no LSEE será expandida permitindo a execução do método evolutivo diretamente em uma interface Field Programmable Gate Array (FPGA) a qual atuará como um coprocessador genético da plataforma de tempo real. Os resultados aqui apresentados foram obtidos seguindo especificações normativas, através de sinais gerados sinteticamente, e também utilizando o Alternative Transient Program (ATP), permitindo assim ensaios mais realísticos para a validação dos métodos evolutivos. / The synchronized phasor measurement is used today as a way to enhance the operation of an Electric Power System (EPS), using phasor measurement units strategically located and installed. They perform the acquisition of the electrical signal and then, the estimation of the voltage and current phasors, synchronized in time, which indicates the SEPs behavior in a specific location. This multidisciplinary work proposes the analysis and implementation of an evolutionary computing method, the Multibjective Compact Genetic Algorithm (MCGA) applied to the phasor estimation method used in EPS, known as an Phasor Measurement Units (PMUs). The MCGA presented here has as a main characteristic the multiobjective analysis of the problem. Because all EPSs have three phases, this new approach is proposed , which is considering the phasor estimation for the three phases together, instead of doing it for each phase independently.Thus the proposed MCGA includes in its genetic mapping of individuals, the characteristics of the signals of the three phases, unlike the monoobjective where each phase of the Electric Power System (EPS) is modeled using a different individual. In order to ensure the effectiveness of the evolutionary method when operating in a real time scenario, a platform for data acquisition and processing is proposed, inspired by previous work, allowing the integration of all the modules that composes a PMU for real-time phasor analysis. A Global Positioning System (GPS) is proposed as a way to synchronize different PMUs, integrating pieces of equipment in a single time reference, with the precision required. In order to assist in the integration of the required modules, a library of functions developed in the Laboratory of Electric Power Systems will be expanded allowing the execution of the evolutionary method directly on a Field Programmable Gate Array (FPGA) interface, which will act as a genetic co-processor of a real-time platform. The results presented here were obtained following normative specifications, through signals generated synthetically, and also using the Alternative Transient Program (ATP), allowing more realistic tests to validate the evolutionary methods.

A medição fasorial sincronizada é utilizada hoje como forma de aprimorar a operação de um Sistema Elétrico de Potência (SEP), empregando unidades de medição fasorial estrategicamente localizadas e instaladas. Estas realizam a aquisição do sinal elétrico e posteriormente a estimação dos fasores de tensão e corrente sincronizados no tempo, os quais indicam o comportamento do SEP em uma localidade específica. Este trabalho multidisciplinar propõe a análise e implementação de um método computacional evolutivo, o Algoritmo Genético Compacto Multiobjetivo (AGCM) aplicado ao problema de medição fasorial, amplamente utilizado por exemplo, no monitoramento de um SEP, comportando-se assim como uma unidade medidora de fasor, ou Phasor Measurement Unit (PMU). O AGCM aqui apresentado tem como principal característica a análise multiobjetiva do problema. Pelo fato de todo SEP ser trifásico, é proposto esta nova abordagem, onde é considerando para a estimação fasorial as três fases de forma conjunta, e não mais estimadas independentemente. Assim o AGCM proposto considera em seu mapeamento genético dos indivíduos, as características do sinais das três fases, diferentemente da abordagem mono-objetivo, onde cada fase do SEP é modelada sobre um indivíduo diferente. Posteriormente para garantir a eficácia do método evolutivo quando em operação em um cenário de tempo real, é proposto uma plataforma de aquisição de dados e processamento, inspirada em trabalhos anteriormente desenvolvidos, permitindo a integração de todos os módulos que formarão um PMU para análise fasorial em tempo real. Aqui um sistema de Global Positioning System (GPS) existente é proposto como forma de sincronismo entre os PMUs, sincronizando uma gama de equipamentos em um única referência de tempo, com a precisão necessária. Para auxiliar na integração dos módulos necessários, uma biblioteca de funções desenvolvida no LSEE será expandida permitindo a execução do método evolutivo diretamente em uma interface Field Programmable Gate Array (FPGA) a qual atuará como um coprocessador genético da plataforma de tempo real. Os resultados aqui apresentados foram obtidos seguindo especificações normativas, através de sinais gerados sinteticamente, e também utilizando o Alternative Transient Program (ATP), permitindo assim ensaios mais realísticos para a validação dos métodos evolutivos. / The synchronized phasor measurement is used today as a way to enhance the operation of an Electric Power System (EPS), using phasor measurement units strategically located and installed. They perform the acquisition of the electrical signal and then, the estimation of the voltage and current phasors, synchronized in time, which indicates the SEPs behavior in a specific location. This multidisciplinary work proposes the analysis and implementation of an evolutionary computing method, the Multibjective Compact Genetic Algorithm (MCGA) applied to the phasor estimation method used in EPS, known as an Phasor Measurement Units (PMUs). The MCGA presented here has as a main characteristic the multiobjective analysis of the problem. Because all EPSs have three phases, this new approach is proposed , which is considering the phasor estimation for the three phases together, instead of doing it for each phase independently.Thus the proposed MCGA includes in its genetic mapping of individuals, the characteristics of the signals of the three phases, unlike the monoobjective where each phase of the Electric Power System (EPS) is modeled using a different individual. In order to ensure the effectiveness of the evolutionary method when operating in a real time scenario, a platform for data acquisition and processing is proposed, inspired by previous work, allowing the integration of all the modules that composes a PMU for real-time phasor analysis. A Global Positioning System (GPS) is proposed as a way to synchronize different PMUs, integrating pieces of equipment in a single time reference, with the precision required. In order to assist in the integration of the required modules, a library of functions developed in the Laboratory of Electric Power Systems will be expanded allowing the execution of the evolutionary method directly on a Field Programmable Gate Array (FPGA) interface, which will act as a genetic co-processor of a real-time platform. The results presented here were obtained following normative specifications, through signals generated synthetically, and also using the Alternative Transient Program (ATP), allowing more realistic tests to validate the evolutionary methods.

Series compensation of transmission lines is an effectiveand cheap method of improving the power transmission systemperformance. Series capacitors virtually reduces the length ofthe line making it easier to keep all parts of the power systemrunning in synchronism and to maintain a constant voltage levelthroughout the system. In Sweden this technology has been inuse since almost 50 years. The possibility to improve the performance of the ACtransmission system utilizing power electronic equipment hasbeen discussed a lot since about ten years. Some newsemiconductor based concepts have been developed beside thesince long established HVDC and SVC technologies. The ThyristorControlled Series Capacitor (TCSC) is one such concept. Byvarying the inserted reactance an immediate and well-definedimpact on the active power flow in the transmission line isobtained. Several potential applications, specifically poweroscillation damping, benefit from this capability. The conceptimplied the requirement to design a semiconductor valve, whichcan be inserted directly in the high-voltage power circuit.This certainly presented a technical challenge but thestraightforward approach appeared to be a cost-effectivealternative with small losses. It was also realized that the TCSC exhibits quite differentbehaviour with respect to subsynchronous frequency componentsin the line current as compared to the fixed series capacitorbank. This was a very interesting aspect as the risk ofsubsynchronous resonance (SSR), which just involves such linecurrent components, has hampered the use of series compensationin power systems using thermal generating plants. The thesis deals with the modelling and control aspects ofTCSC. A simplifying concept, the equivalent, instantaneousvoltage reversal, is introduced to represent the action of thethyristor controlled inductive branch, which is connected inparallel with the series capacitor bank in the TCSC. The idealvoltage reversal is used in the thesis in order to describe andexplain the TCSC dynamics, to investigate its apparentimpedance at various frequencies, as a platform forsynthesizing the boost control system and as the base elementin deriving a linear, small-signal dynamical model of thethree-phase TCSC. Quantitative Feedback Theory (QFT) then hasbeen applied to the TCSC model in order to tune its boostregulator taking into account the typical variation ofparameters that exists in a power system. The impact of theboost control system with respect to damping of SSR is finallybeing briefly looked at. <b>Keywords:</b>Thyristor Controlled Series Capacitor, TCSC,FACTS, reactive power compensation, boost control, phasorestimation, Quantitative Feedback Theory, subsynchronousresonance, SSR.

Multi-level inverters play a significant role in high power drive systems for induction motors. Interest in multi-level inverters started with the three-level, neutral point clamped (NPC) inverter. Now there are many topologies for higher number of levels such as the, flying capacitor and cascaded H-bridge etc. The advantage of multi-level inverters is the reduced voltage stress on the switching devices, lower dv/dt and lower harmonic content. The voltage space vector structure in a multi-level inverter has a hexagonal periphery similar to that in a two-level inverter. In the over-modulation region in multi-level inverters, there is the presence of lower order harmonics such as 5th and 7th in the output voltage, and this can be avoided by using a voltage space vector scheme with more than six polygonal voltage space vectors such as 12, 18, 24 etc. These polygonal voltage space vectors can be generated by using multi-level inverter topologies, by cascading two-level inverter structures with asymmetric DC-links. This thesis deals with the development of 12-sided and 18-sided polygonal voltage space vector schemes for induction motor drives. With the 12-sided polygonal structure, all the 5th and 7th harmonic orders and 6n±1, n=1, 3, 5.. are absent throughout the modulation range, and in the 18-sided voltage space vector scheme, 5th, 7th, 11th and 13th harmonics are absent throughout the modulation range. With the absence of the low order frequencies in the proposed polygonal space vector structures, high frequency PWM schemes are not needed for voltage control. This is an advantage over conventional schemes. Also, due to the absence of lower order harmonics throughout the modulation range, special compensated synchronous reference frame PI controllers are not needed in current controlled vector control schemes in over-modulation. In this thesis a method is proposed for generating 12-sided polygonal voltage space vectors for an induction motor fed from one side. A cascaded combination of three two-level inverters is used with asymmetrical DC-links. A simple space vector PWM scheme based only on the sampled reference phase amplitudes are used for the inverter output voltage control. The reference space vector is sampled at different sampling rates depending on the frequency of operation. The number of samples in a sector is chosen to keep the overall switching frequency around 1kHz, in order to minimize switching losses. The voltage space vectors that make up the two sides of the sector in which the reference vector lies, are time averaged using volt-sec balance, to result in the reference vector. In the proposed 12-sided PWM scheme all the harmonics of the order 6n±1, n=1, 3, 5... are eliminated from the phase voltage, throughout the modulation range. In multi-level inverters steps are taken to eliminate common-mode voltage. Common-mode voltage is defined as one third of the sum of the three pole voltages of the inverter for a three phase system. Bearings are found to fail prematurely in drives with fast rising voltage pulses and high frequency switching. The alternating common-mode voltage generated by the PWM inverter contributes to capacitive couplings from stator body to rotor body. This generates motor shaft voltages causing bearing currents to flow from rotor to stator body and then to the ground. There can be a flashover between the bearing races. Also a phenomenon termed EDM (Electro-discharge machining) effect occurs and may damage the bearings. Common-mode voltage has to be eliminated in order to overcome these effects. In multi-level inverters redundancy of space vector locations is used to eliminate common-mode voltages. In the present thesis a 12-sided polygonal voltage space vector based inverter with an open-end winding induction motor is proposed, in which the common-mode voltage variation at the poles of the inverter is eliminated. In this scheme, there is a three-level inverter on each side of the open-end winding of the induction motor. The three-level inverter is made by cascading two, two-level inverters with unequal DC-link voltages. Appropriate space vectors are selected from opposite sides such that the sum of the pole voltages on each side is a constant. Also during the PWM operation when the zero vector is applied, identical voltage levels are used on both sides of the open-end windings, in order to make the phase voltages zero, while the common-mode voltage is kept constant. This way, common-mode voltage variations are eliminated throughout the modulation range by appropriately selecting the voltage vectors from opposite ends. In this method all the harmonics of 6n±1, n=1, 3, 5.. and triplen orders are eliminated. In the 12-sided polygonal voltage space vector methods, the 11th and 13th harmonics though attenuated are not eliminated. In the 18-sided polygonal voltage space vector method the 11th and 13th harmonics are eliminated along with the 5th and 7th harmonics. This scheme consists of an open-end winding induction motor fed from one side by a two-level inverter and the other side by a three-level inverter comprising of two cascaded two-level inverters. Asymmetric DC-links of a particular ratio are present. The 12-sided and 18-sided polygonal voltage space vector methods have been first simulated using SIMULINK and then verified experimentally on a 1.5kW induction motor drive. In the simulation as well as the experimental setup the starting point is the generation of the three reference voltages v, vB and vC . A method for determining the sector in which the reference vector lies by comparing the values of the scaled sampled instantaneous reference voltages is proposed. For the reference vector lying in a sector between the two active vectors, the first vector is to be kept on for T1 duration and the second vector for T2 duration. These timing durations can be found from the derived formula, using the sampled instantaneous values of the reference voltages and the sector information. From the pulse widths and the sector number, the voltage level at which a phase in the inverter has to be maintained is uniquely determined from look-up tables. Thus, once the pole voltages are determined the phase voltages can be easily determined for simulation studies. By using a suitable induction motor model in the simulation, the effect of the PWM scheme on the motor current can be easily obtained. The simulation studies are experimentally verified on a 1.5kW open-end winding induction motor drive. A V/f control scheme is used for the study of the drive scheme for different speeds of operation. A DSP (TMS320LF2407A) is used for generating the PWM signals for variable speed operation. The 12-sided polygonal voltage space vector scheme with the motor fed from a single side has a simple power bus structure and it is also observed that the pole voltage is clamped to zero for 30% of the time duration of one cycle of operation. This will increase the overall efficiency. The proposed scheme eliminates all harmonics of the order 6n±1, n=1, 3, 5…for the complete modulation range. The 12-sided polygonal voltage space vector scheme with common-mode elimination requires the open-end winding configuration of the induction motor. Two asymmetrical DC-links are required which are common to both sides. The leg of the high voltage inverter is seen to be switched only for 50% duration in a cycle of operation. This will also reduce switching losses considerably. The proposed scheme not only eliminates all harmonics of the order 6n±1, n=1, 3, 5…for the complete modulation range, but also maintains the common-mode voltage on both sides constant. The common-mode voltage variation is eliminated. This eliminates bearing currents and shaft voltages which can damage the motor bearings. In the 18-sided polygonal voltage space vector based inverter, the 11th and 13th harmonics are eliminated along with the 5th and 7th. Here also an open-end winding induction motor is used, with a two-level inverter on one side and a three-level inverter on the other side. A pole of the two-level inverter is at clamped to zero voltage for 50% of the time and a pole of the three-level inverter is clamped to zero for 30% of the time for one cycle of operation. The 18-sided polygonal voltage space vectors show the highest maximum peak fundamental voltage in the 18-step mode of 0.663Vdc compared to 0.658Vdc in the 12-step mode of the 12-sided polygonal voltage space vector scheme and 0.637Vdc in the six-step mode of a two-level inverter or conventional multi-level inverter (where Vdc is the radius of the space vector polygon). Though the schemes proposed are verified on a low power laboratory prototype, the principle and the control algorithm development are general in nature and can be easily extended to induction motor drives for high power applications.