From the early days of HVDC system applications, the importance of mathematical modelling of the dynamics of Line Commutated Converter (LCC) HVDC systems has been appreciated. There are essentially two methodologies used to develop mathematical models of dynamic systems. One methodology is to define the properties of the system by the “laws of nature” and other well-established relationships. Basic techniques of this methodology involve describing the system’s processes using differential equations. This methodology is called “Deductive Modelling”. The other methodology used to derive mathematical models of a dynamic system is based on experimentation. Input and output signals from the original system are recorded to infer a mathematical model of the system. This methodology is known as “Inductive Modelling”. A review of the current state of the art of modelling LCC HVDC systems indicates that majority of the techniques utilized to develop mathematical models of LCC HVDC systems have used the “Deductive Modelling” approach. This methodology requires accurate knowledge of the ac systems and the dc system and involves complicated mathematics. In practice, it is nearly impossible to obtain accurate knowledge of the ac systems connected to LCC HVDC systems. The main aim of this thesis is to present an “Inductive Modelling” methodology to calculate the plant transfer functions of LCC HVDC systems. Due to the uncertain nature of the effective short circuit ratio of rectifier and inverter converter stations, generic ranges of parametric uncertainties of the developed plant transfer functions were determined. Based on the determined range of HVDC plant parametric uncertainty, Quantitative Feedback Theory (QFT) methodology was used to design the parameters of the LCC HVDC control system. The stability of the start-up and step responses for varying ac system conditions validated the “Inductive Modelling” technique and the QFT design methodology. The thesis presents the following, which are considered to be scientific advancements and contributions to the body of knowledge: · Novel LCC HVDC Step Response (HSR) equations were developed using an “Inductive Modeling” technique. · The range of parametric variations of the LCC HSR equations were determined for various rectifier and inverter ac system effective short circuit ratios. · The LCC HSR equations were used to develop the LCC HVDC plant transfer functions for various rectifier and inverter effective short circuit ratios. · The LCC HVDC plant transfer functions were utilized to design an LCC HVDC control system for varying ac system conditions using Quantitative Feedback Theory (QFT) methodology. The main contributions of this thesis relate to LCC HVDC systems. This thesis does not attempt to advance control theory however this thesis does apply existing classical control theory to LCC HVDC control systems. Index Terms: Line Commutated Converter, HVDC, inductive modelling, power system, transient analysis. / Thesis (Ph.D.)-University of KwaZlu-Natal, Durban, 2011.

Thesis (Ph. D.)--Ohio University, August, 1993. / Title from PDF t.p.

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Simulations of two types of constant-frequency resonant power converters using SPICE-2/I-G SPICE are performed. The first one is a parallel resonant converter (PRC) using a controlled output rectifier. The PRC is operated at a constant frequency and its output voltage is regulated by controlling the firing angle of the output rectifier. The other circuit is the phase-controlled dual resonant converter (DRC) which employs two PRCs with their output (Capacitor voltages) connected in series. In the scheme, again the PRCs are operated at a constant frequency. By controlling the phase delay of the two PRCs, regulation of the output voltage is achieved. The behaviors of these two types of constant frequency resonant converters have been analyzed in details recently by Tsai and documented in his thesis. The objectives of the present work is to verify some of Tsai's key findings via computer simulations. First of all, the DC output characteristics of the parallel resonant converter (PRC) using the conventional acontrol (phase control) scheme and the new a-control scheme are simulated. The a-control scheme is implemented by monitoring the delay angle of the output controlled rectifier and the zero-crossing of the resonant capacitor voltage waveform while the a control is implemented by monitoring the delay angle of the output controlled rectifier with respect to the switching instance of the input inverter. The current and voltage ratings of different circuit components as a function of the control parameter-a angle are shown. The control-to-output characteristics are verified. The advantages of acontrol scheme is demonstrated. Simulation results of the phase-controlled dual resonant converter (DRC) are presented under various operating conditions. A comprehensive understanding of the behavior complex of the DRC are obtained. The ability to regulate the link voltage of the DRC is demonstrated. Boundary conditions of the DRC for natural commutation ( line or load) of the power devices are also verified. Some comments on SPICE-2/I-G SPICE simulation of the resonant circuits are presented. / M.S.

Thesis (PhD)--University of Stellenbosch, 2004. / ENGLISH ABSTRACT: Multilevel converters were developed as a result of a growing need for higher power converters. This dissertation addresses a specific multilevel topology called the multicell topology. A problem associated with this topology is cell capacitor voltage unbalance. This dissertation addresses the issue of natural balancing of multicell converters. The topology is mathematically analysed and a theory is developed to explain the natural balancing mechanism. The study of the natural balancing property includes a detailed harmonic-, steady-state- and time constant analysis. The theory is verified by a comparison between the theoretical-, simulated- and experimental results. / AFRIKAANSE OPSOMMING: Veelvlakkige omsetters het ontstaan as gevolg van ’n behoefte aan ho¨er drywing omsetters. Hierdie proefskrif handel spesifiek oor die veelsellige omsetter topologie. ’n Probleem wat met hierdie topologie geassosieer word is selkapasitor onbalans. Hierdie proefskrif ondersoek die natuurlike balansering van veelsellige omsetters. Die topologie word wiskundig geanaliseer en ’n teorie word geformuleer om die natuurlike balanseringsmeganisme te verduidelik. Die ondersoek van die natuurlike balanseringseienskap bevat ’n volledige harmoniese-, bestendige toestand- en tydkonstante analise. Die teorie is gekontroleer deur teoretiese-, simulasie- en eksperimentele resultate te vergelyk.

Thesis (MScIng)--University of Stellenbosch, 2004. / ENGLISH ABSTRACT: The thesis discusses the analysis and design of a three-phase-to-three-phase direct AC-AC matrix converter. A background study of the various matrix converter topologies and their modulation strategies are presented. The associated PWM strategy of each matrix converter topology is investigated. In addition, a detailed explanation of the three safe commutation strategies is presented. The research focuses on the design and analysis of the direct AC-AC matrix converter topology. That includes the design of the main bi-directional power converter circuit, gate drive circuit, current direction detection circuit, voltage measurement circuit and protection circuitry. Moreover, it covers the development of the direct control algorithm based on the four-step safe current commutation- and the two-step voltage commutation strategy. A “PEC33” controller board is used to implement the developed control algorithm. Furthermore, simulation results of the direct and the indirect matrix converter topologies are presented. The results obtained from the experimental test performed on the direct AC-AC matrix converter topology are also presented. The conclusion drawn is discussed at the final stage of the report. / AFRIKAANSE OPSOMMING: Hierdie tesis bevat die analise en ontwerp van ‘n drie-fase na drie-fase direkte WS-WS matriksomsetter. ‘n Agtergrondstudie van verskeie ander matriksomsetter topologieë word aangebied. Die ge-assosieerde PWM beheerstrategie van elke matriksomsetter topologie is ondersoek. Hierby word ‘n gedetaileerde verduideliking van drie veilige kommutasie strategieë ingesluit. Die navorsing fokus op die ontwerp en analise van die direkte WS-WS matriksomsetter topologie. Dit sluit die volgende in: die ontwerp van die hoof bi-direksionele drywingsomsetterbaan; die hek aandryfbaan; die stroomrigting deteksiebaan; die spanningsmeetbaan en die beveiliging stroombane. Dit dek ook die ontwikkeling van die direkte beheeralgoritme wat gebasseer is op die vier-stap veilige stroomkommutasie- en die twee-stap spanningskommutasie strategie. ‘n “PEC33” beheerkaart is gebruik om hierdie beheeralgoritme te implementer. Simulasie resultate van beide die direkte sowel as die indirekte matriksomsetter topologieë word ingesluit. Die eksperimentele resultate wat met die direkte WS-WS matriksomsetter topologie verkry is word aangebied en bespreek. Die gevolgtrekking word in die finale afdeling van die verslag bespreek.

M.Ing.

Energy security concerns and the impact of traditional sources of power generation on the climate have prompted a rise in renewable energy expansion around the world. Power transmission from remote generation sites to consumers over long distance is most efficient using High-Voltage Direct Current (HVDC) transmission lines. Consequently, HVDC and the integration of renewable resources are considered as key perspectives in the improvement of sustainable energy systems capable of secure and stable electric power supply. With the intention of huge energy demand in the future, the multi-terminal DC grid concept is proposed based on various converter topologies like Line Commutated Converter (LCC), Voltage Sourced Converter (VSC), and Modular Multilevel Converter (MMC) HVDC technologies. These converters play a vital role in integrating remotely-located renewable generation and reinforcing existing power systems. The MMC has become increasingly popular in HVDC transmission compared to conventional line commutated converters, two-level and multilevel voltage source converters. Low generation of harmonics, a low switching frequency of semiconductors, sine formed AC voltages and currents, black start capability and higher overall efficiency are a few of the unique features of MMC. The MMC is characterised by a modular arm structure, formed by a cascade connection of a vast number of simple cells with floating DC capacitors. These cells are called Sub-Modules (SMs) and can be easily assembled into a converter for high voltage power conversion systems. Compared with traditional VSCs, the analytical modelling of MMC is more challenging. This is because of technical issues such as higher order system, the discontinuous and non-linear nature of signal transfer through converters, the complexity of the interaction equations between the AC and DC variables, and harmonic frequency conversion through AC side and DC side of the converter. This work intends to resolve these challenges by developing a detailed non-linear model using fundamental switching Selective Harmonic Elimination (SHE) modulation technique, an average MMC model in DQ0 frame and an analytical dynamic MMC model, which can be suitable for small-signal stability studies, and control design. Firstly, the detailed model of MMC using fundamental switching SHE modulation scheme has been developed using PSCAD/EMTDC (Power systems computer aided design Electromagnetic transients for DC) software. The basic terms and equations of the MMC have been presented along control loops. The significance of the switching frequency on the performance of the MMC has been studied as well as the relation between the switching frequency, the Total Harmonic Distortion (THD) and the number of output voltage levels. Detailed representation of MMC systems in PSCAD/EMTDC programs incorporates the modelling of Insulated-Gate Bipolar Transistor (IGBT) valves and should typically utilise small integration time-steps to represent fast switching events precisely. Computational burden introduced by such detailed models make the study of steady-state and transient events more complex, highlighting the need to implement more efficient models that provide comparative behaviour and dynamic response. Secondly, average DQ0 models has been implemented to accurately replicate the steady-state, dynamic and transient behaviour of MMC in PSCAD/EMTDC programs. These simplified models represent the average response of switching devices and converters by using averaging techniques involving controlled sources and switching functions. Developing the MMC average model in DQ0 frame was a challenging task because of the multiplication terms in the MMC average model in ABC frame. The proposed approach to overcome this challenge is considering generic form for the product variables and multiplying them in ABC frame and then transferring only the DC and fundamental frequency components of the results to DQ0 frame. The comparisons between detailed model and the average model validated the effectiveness of the average model in representing the dynamics of MMC. It is at least one hundred times faster than the detailed model for the same simulation time step. Finally, a dynamic analytical MMC model and associated controls have been proposed. To enable the model application to a broad range of system configurations and various dynamic studies, the model is built on a modular modelling approach using four sub-systems; an AC system, Phase Locked Loop (PLL) system, MMC system and a DC arrangement. The developed MMC system model has been linearized and implemented in state-space form. To select the best open-loop controller gains, eigenvalue analysis is performed for each particular test system. The rationality and correctness of the proposed model are verified against non-linear PSCAD/EMTDC simulations, and good accuracy is obtained in the time domain analysis. Further, the model is also verified in the frequency domain, and it is concluded that the developed model can be employed for dynamic analysis below 300 Hz.

The frequency response analysis of switched networks plays a very important part in designing various kinds of power converter circuits. In this thesis two frequency response techniques for analyzing switching power converters are discussed. One method provides a mathematical description which treats the converter as a periodic time varying system. A linearized small signal model is subsequently derived. The major part of the thesis concentrates on this accurate exact small-signal technique. The derivation involves state space representation and the use of the time varying transfer function. A Fourier analysis is performed to show the relationship between the frequency response of the network and the time varying transfer function. The obtained expressions are in closed form. The method has proven to be exact. The complexity of this technique is overcome by automating its derivation in conjunction with a circuit simulator. An alternative method, relying only on a sampled-data representation, is also derived, which provides a less complicated algorithm. However the accuracy of this method suffers, particularly at high frequencies. The accuracy of the exact small-signal technique is verified by experimentation.

Switch-mode power supplies (SMPS's) not only convert energy, they also consume it. Typical operational efficiencies are approximately 25 to 60% for linear power supplies, and approximately 50-90% for switching power supplies. This means that products whose end-use electronics are dc, such as televisions and DVD players, could consume 50% less power when operating if the power supply were upgraded from 40% efficiency to 80% efficiency. Savings can occur not only from using SMPS's instead of linear power supplies, but also from specifying highly efficient switching power supplies. In many cases, efficiencies are still lagging to keep costs down, since the power consumption is considered to be relatively low (40W-700W range). Over time, however, efficiency improvement strategies will pay back based on the cost of energy. Therefore three common flyback converter topologies have been studied through this thesis in the Low (15W), Medium (40W), and High (150W) Power levels. Efficiency analysis on the three power level topologies showed that the greatest opportunity for efficiency improvement existed in the 40W (medium power) topology. Efficiency improvement and measurement approaches are investigated and an optimized medium-power flyback converter is proposed and implemented resulting in an efficiency improvement from 57.8% to 83.6%. / Graduation date: 2004