Due to the increasing trend towards energy saving of white goods appliances and the commercial viability of power electronic components, there has been an expansion in the use of solid state electronics and variable frequency drive motors in these applications. However, a major drawback of using such energy efficient loads is the introduction of current harmonics onto the local distribution grid. Furthermore, the proliferation of such devices elevates the harmonic content of the supply voltage and the ensuing potential impact on residential distribution networks. This thesis investigates the harmonic content generated by some representative household appliances and suggests a solution to minimize current harmonics by means of active filtering. An active filter circuit is proposed and simulations will be undertaken to compare filter performance when used as an active front end versus a feeder input compensator. Further, a hardware design of the filter was implemented to experimentally verify the filter operation. / Thesis / Master of Applied Science (MASc)

In this dissertation, the problem of multi-area load frequency control in large power systems is investigated. The load frequency control problem is concerned with the minimization of the deviations in the frequencies of the different areas and in the tie line power exchange between these areas, and is a problem of major importance in the satisfactory operation of large power systems. Some new techniques for designing load frequency control systems are presented through the use of concepts from singular perturbation and hierarchical system theory. To provide appropriate vehicles for the design of the new control systems, state variable models for power systems are developed. These models progress from a two-area interconnected power system model to large scale models comprising of N areas. Two centralized state feedback schemes are proposed for the load frequency control by utilizing the separation of the system models into two time scales. In the first scheme, composite controls and reduced order controls are developed to meet the required performance specifications by. The second scheme is obtained by using the theory of variable structure systems where the existence of a sliding regime leads to the design of a single discontinuous state feedback controller that meets the performance requirements. In order to further improve the performance of the closed loop system, a two level hierarchical control scheme is developed. This consists of a set of local controllers that are designed using either the singular perturbation approach or the variable structure system approach as before and a set of global control functions provided by a higher level controller that attempts to coordinate the local controllers. The interaction prediction principle is used as a tool in the design of the global controller. The performance of the presently developed control schemes is examined in detail for the illustrative cases of a two-area and a three-area power system. From this analysis, it is shown that these controllers provide an improved performance compared to the existing control schemes in reducing the frequency and tie line power deviations.

A research report submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Science in Engineering, 2016 / The power system frequency must be kept as close as possible to the nominal value. This is due to the inherent design of electrical equipment to operate efficiently at the nominal frequency. Frequency regulation in an interconnected power system is the duty of all members of the interconnection. However, in the Eskom-ZESA interconnected power system Eskom engineers ignore the contribution of the ZESA system to primary frequency control. This is mainly due to the prevalent assumption that the ZESA control area is small relative to the Eskom control area and its contribution to primary frequency control of the interconnected power system is negligible. This document presents a project that examines the validity of this assumption via determination of the contribution of the ZESA system to the interconnected power system’s primary frequency control. The interconnected power systems background was studied to understand the theory behind the operation of two or more interconnected power systems. System frequency disturbances deemed to be a good representation of the Eskom-ZESA interconnected power system’s performance were selected and analysed to validate the current assumption. The results show that there is a significant support from ZESA during a system frequency disturbance. This proves that the existing assumption is not valid anymore. Furthermore; the generator model that mimics the Eskom-ZESA tie-line governing behaviour was developed. Two different types of governor models were employed; firstly the IEEEG1 governor was tuned to control generator output to match the tie-line performance and then the TGOV5 governor model was used. The IEEEG1 governor model is a simplified governor representation; as a result, it is not easy to tune the parameters to match tie-line response. However, the performance is acceptable and it can be used to represent the tieline governor response. The TGOV5 governor model is very complex as discussed in section 4.2. The model includes boiler dynamics, and this improves performance such that it is possible to tune the parameters to follow the tie-line performance as close as necessary. / GR2016

Este trabalho apresenta algumas estratégias de controle das malhas de rastreamento de tensão e corrente no lado CA de conversores do tipo fonte de tensão com filtro L ou LC. A topologia escolhida para o controle de tensão CA do inversor é a de duas malhas de controle em cascata: malha de tensão e malha de corrente, sendo esta última mais interna no sistema de controle. A metodologia de trabalho utilizada consiste na modelagem do sistema (sistema controlado e controladores), ajuste dos parâmetros do controlador, simulação computacional do sistema \"inversor + controlador\", implementação de alguns controladores propostos utilizando um DSP e testes em um sistema real com inversor. O estudo das técnicas de controle concentra-se inicialmente na estratégia de realimentação de dois estados no domínio de tempo contínuo, evoluindo para estratégias em tempo discreto que consideram o atraso na atuação do inversor devido ao tempo de cálculo do algoritmo de controle. Em tempo discreto, são analisados controladores preditivos para as malhas de tensão e corrente, bem como o emprego de controladores Proporcional-Integral (PI) na malha de tensão. Os dois últimos controladores são testados em um inversor PWM de baixa potência para diversos tipos de carga, com tensão de referência de inversor senoidal em 60Hz e referência contendo harmônicas. / This work presents some control strategies to achieve voltage and current tracking at the AC side of Voltage Source Converters with L or LC output filters. The topology of voltage control is the Multi-loop control with two loops: Voltage (outer loop) and Current Loop (inner loop). The proposed methodology consists in modeling the control system (plant and controllers), tuning of the controller parameters, simulating the complete system including inverter and controller, implementation of the proposed control strategies on a Digital Signal Processor (DSP) and tests in a power converter. The thesis is initially focused on a state variable continuous time controller with two states and then discrete-time strategies which consider the actuation delay due to the time required to evaluate the control algorithm are studied. In these discrete-time models, predictive controllers in voltage and current loops are analyzed, as well as the use of Proportional- Integral (PI) controllers in the Voltage Loop. These two last control topologies are tested in a low-power inverter for several load conditions with sinusoidal 60Hz inverter reference voltage and with harmonic distortion in the inverter reference voltage.

本论文开发出了一个全新的理论和算法框架用於无线网络的分布式功率控制。我们提出两种快速分布式功率控制算法，并对此作了深入的研究。 此种算法相当普适，比如适用于目前热门的LTE和认知无线电网络。 它在解的最优性以及收敛速度等方面击败了著名的高通公司的"荷载溢出型分布式功率控制算法" (收录于重要论文[HandeRanganChiangWu08] )以及"分布式加权比例型信干噪比均衡算法" (收录于重要论文[TanChiangSrikant 11)。 / 作为一个重要而富有挑战性的研究课题，通过分布式功率控制达至无线网络效用的最大化一直受到业界的普遍关注。 这方面的研究通常把问题表述为一个最优化问题，即在某些功率约束条件下，优化整体系统的效用函数。 (其中，系统的效用函数通常是各无线收发链路的信干噪比的增函数。 )此问题已经有了不错的集中式解决方案，但成本更低廉、更易于布置、更为实用的分布式解决方案则欠奉，尤其是经严格证明可行的分布式解决方案。 这是因为分布式算法一般只适用于相对简单或者有特殊结构的优化问题。 而无线设备之间的相互干扰和各自信号功率之间的复杂关系使得分布式求解极其困难。 在算法设计上，很小的疏漏就可能导致解决方案无效或者不收敛。 例如，尽管论文[HandeRanganChiangWu08] 和[TanChiangSrikant 11] 都声称各自的分布式算法提供了问题的最优解，但我们通过大量的仿真实验以及理论研究发现并非如此。 我们发现"荷载溢出型分布式功率控制算法"时常要么无法收敛，要么收敛得极其慢。而"分布式加权比例型信干噪比均衡算法"则经常在几次迭代之後就已经发散。 / 我们开发出了全新的分析和算法框架，并将其推广到适用于一般线性功率约束的情况。(前述论文的分析框架是基于某些非常特殊的线性功率约束。)在此基础上，我们逐一找出了前述算法中的错漏之处，并设计出我们的分布式梯度投影功率控制算法，以及与之相匹配的步长规则。 我们严格证明了该步长规则的有效性和算法的收敛性、最优性，并给出了算法复杂度的分析。(相较之下， [HandeRanganChiangWu08] 在算法收敛性证明上语焉不详，在其它方面则付之阙如;而[TanChiangSrikant 11] 的算法收敛性证明存在明显错误，在其它方面同样付之阙如。 )在某些情况下，我们的算法可以进一步提速并提升运行性能。 大量的仿真实验证实我们的算法在解的最优性和运行速度两方面都较前述算法优越。在某些情况下，我们算法的收敛速度上百倍快于前述算法。 / 总而言之，本论文成功解决了重要的效用优化问题并取得比前述论文更好的结果。它开发出全新的理论和算法框架，完全解决了步长规则和收敛性、最优性这些难题。展望未来，我们相信，本论文为快速功率控制在无线和移动解决方案中的应用打下了坚实的理论基础。 我们期待该理论框架能够提供更多問題的解決方案。 / This thesis develops a new theoretical and algorithmic framework for practical distributed power control in wireless networks. It proposes and investigates fast optimal distributed power control algorithms applicable to LTE as well as cognitive radio. The proposed algorithms beat the well-known Qualcomm's load-spillage distributed power control algorithm in [HandeRan-ganChiangWu08] and the distributed weighted proportional SINR algorithm in [TanChiangSrikant11] in terms of both the optimality of the solution and the convergence speed. / Wireless network utility maximization via distributed power control is a classical and challenging issue that has attracted much research attention. The problem is often formulated as a system utility optimization problem under some transmit power constraints, where the system utility function is typically an increasing function of link signal-to-interference-plus-noise-ratio (SINR). This problem is complicated by the fact that these wireless devices may interfere with each other. In particular, the wireless devices are affected by each other's transmit power, and the transmit powers and interferences experienced by the devices are interwoven in a complex manner. / Despite that, there have been good centralized algorithms for solving the problem. "Decentralized" solutions, on the other hand, are a different story. In practice, decentralized algorithms in which the devices interact with each other in a loosely coupled manner to improve the network utility, are easier to deploy than centralized algorithms. However, the design of workable (and provably workable in the mathematical sense) solution is very challenging. Small neglects can lead to solutions that are invalid or non-convergent. For example, although both papers [HandeRanganChiangWu08] and [TanChiangSrikant11] claim their distributed algorithms to be optimal, we discover some experimental evidence suggesting that certain parts of these algorithms are not quite right. Oftentimes, the former fails to converge or converges extremely slowly, while the latter could diverge in the first few iterations. / To fix these glitches and to broaden the scope of the problem, we develop a new analytical and algorithmic framework with a more general formulation. With this framework, we can identify the sources of the defects and shortcomings of prior algorithms. We further construct an optimal distributed (sub)gradient projection algorithm with provably valid step size rules. Rigorous convergence proof and complexity analysis for our algorithm are given (note: convergence proof and complexity analysis were missing in [HandeRanganChiangWu08] and incorrect in [TanChiangSrikant11]). In some scenarios, our algorithm can be further accelerated to yield even better performance. Extensive simulation experiments confirm that our algorithms always outperform the prior algorithms, in terms of both optimality and efficiency. Specifically, simulation demonstrates at least 100 times faster convergence than the prior algorithms under certain scenarios. / In summary, this thesis solves the important SINR-based utility maximization problem and achieves significantly better results than existing work. It develops a new theoretical an dalgorithmic framework which completely addresses the difficult convergence and step-size issues. Going forward, we believe the foundation established in this work will open doors to other fast distributed wireless and mobile solutions to problems beyond the power control problem addressed here. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Zhang, Jialiang. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 83-87). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Overview --- p.1 / Chapter 1.2 --- Thesis Organization --- p.6 / Chapter 1.3 --- Notations --- p.7 / Chapter 2 --- System Model and Problem Formulation --- p.8 / Chapter 2.1 --- System Model --- p.8 / Chapter 2.2 --- Nonnegative Linear Power Constraints --- p.9 / Chapter 2.3 --- Network Utility --- p.10 / Chapter 2.4 --- Problem Formulation --- p.11 / Chapter 2.5 --- Characterization of T[subscript c] --- p.13 / Chapter 2.6 --- Multiple Constraints --- p.16 / Chapter 3 --- Nice Properties of SINR Constraints --- p.18 / Chapter 3.1 --- Convexity, Differentiability and Monotonicity --- p.19 / Chapter 3.2 --- Fast Distributed Gradient Computation --- p.20 / Chapter 3.2.1 --- Distributed SINR-Driven Single-Constrained Power Control --- p.21 / Chapter 3.2.2 --- Network Duality --- p.23 / Chapter 3.3 --- The Case of Multiple Constraints --- p.27 / Chapter 4 --- Network Utility Maximization in Log-SINR Domain --- p.32 / Chapter 4.1 --- Single Active Constraint and Ascent Directions --- p.34 / Chapter 4.2 --- Multiple Constraints and Subgradient Projection --- p.39 / Chapter 4.3 --- Unconstrained Equivalence and Complexity results of M = 1 --- p.46 / Chapter 4.4 --- Simulation Experiments --- p.52 / Chapter 4.4.1 --- Simulation Settings --- p.52 / Chapter 4.4.2 --- Negative results of algorithm 6 in [7] --- p.54 / Chapter 4.4.3 --- Negative results of Qualcomm’s load-spillage algorithm in [25] --- p.56 / Chapter 4.4.4 --- More results of our algorithms --- p.62 / Chapter 5 --- Related Work --- p.64 / Chapter 6 --- Conclusion --- p.68 / Chapter 7 --- Appendix --- p.72

Lu, Lian. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 91-95). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.

Este trabalho apresenta algumas estratégias de controle das malhas de rastreamento de tensão e corrente no lado CA de conversores do tipo fonte de tensão com filtro L ou LC. A topologia escolhida para o controle de tensão CA do inversor é a de duas malhas de controle em cascata: malha de tensão e malha de corrente, sendo esta última mais interna no sistema de controle. A metodologia de trabalho utilizada consiste na modelagem do sistema (sistema controlado e controladores), ajuste dos parâmetros do controlador, simulação computacional do sistema \"inversor + controlador\", implementação de alguns controladores propostos utilizando um DSP e testes em um sistema real com inversor. O estudo das técnicas de controle concentra-se inicialmente na estratégia de realimentação de dois estados no domínio de tempo contínuo, evoluindo para estratégias em tempo discreto que consideram o atraso na atuação do inversor devido ao tempo de cálculo do algoritmo de controle. Em tempo discreto, são analisados controladores preditivos para as malhas de tensão e corrente, bem como o emprego de controladores Proporcional-Integral (PI) na malha de tensão. Os dois últimos controladores são testados em um inversor PWM de baixa potência para diversos tipos de carga, com tensão de referência de inversor senoidal em 60Hz e referência contendo harmônicas. / This work presents some control strategies to achieve voltage and current tracking at the AC side of Voltage Source Converters with L or LC output filters. The topology of voltage control is the Multi-loop control with two loops: Voltage (outer loop) and Current Loop (inner loop). The proposed methodology consists in modeling the control system (plant and controllers), tuning of the controller parameters, simulating the complete system including inverter and controller, implementation of the proposed control strategies on a Digital Signal Processor (DSP) and tests in a power converter. The thesis is initially focused on a state variable continuous time controller with two states and then discrete-time strategies which consider the actuation delay due to the time required to evaluate the control algorithm are studied. In these discrete-time models, predictive controllers in voltage and current loops are analyzed, as well as the use of Proportional- Integral (PI) controllers in the Voltage Loop. These two last control topologies are tested in a low-power inverter for several load conditions with sinusoidal 60Hz inverter reference voltage and with harmonic distortion in the inverter reference voltage.

Dissertation submitted for Masters of Science degree in Mathematical Statistics in the Faculty of Science, School of Statistics and Actuarial Science, University of the Witwatersrand Johannesburg May 2016 / Electricity demand in South Africa exhibit some randomness and has some important implications on scheduling of generating capacity and maintenance plans. This work focuses on the development of a short term probabilistic forecasting model for the 19:00 hours daily demand. The model incorporates deterministic influences such as; temperature effects, maximum electricity demand, dummy variables which include the holiday effects, weekly and monthly seasonal effects. A benchmark model is developed and an out-of-sample comparison between the two models is undertaken. The study further assesses the residual demand analysis for risk uncertainty. This information is important to system operators and utility companies to determine the number of critical peak days as well as scheduling load flow analysis and dispatching of electricity in South Africa. Keywords: Semi-parametric additive model, generalized Pareto distribution, extreme value mixture modelling, non stationary time series, electricity demand

<p>Controlling the power flow in transmission systems has recently gained increased interest. The difficulties of building new lines and the pressure of having a high utilization of existing assets, makes the flexibility of grid systems increasingly important.</p><p>This master thesis work investigates induction regulators as control devices for active power flow in a transmission system. A small change in angle of the rotor affects both the amplitude and the phase of the voltage. The magnetic coupling in the induction regulator can be controlled by changing the permeability of a thermo magnetic material such as gadolinium and can hence give a second independent controlling parameter. An analytical model and calculations in the</p><p>FEM software AceTripleC together with Matlab, is used to simulate the influence of the regulators connected to a simple grid in case1, a 400 kV scenario and case 2, a 45 kV scenario.</p><p>The analysis was carried out on a small transmission system consisting of two parallel transmission lines connected to source and load. The induction regulators are connected to one of the parallel transmission lines. The regulators modelled in case 1 must be able to control the active power flow in the regulated line to vary between 50 and 150 % of the original power flow through this line.</p><p>This shall be done over a range of 0 to 800 MW transmitted power. The regulators modelled in case 2 must be able to control the active power flow in</p><p>the regulated line to vary between 0 and 30 MW, if this does not cause the power flow in the parallel line to exceed 30 MW. This shall be done over a range of 0 to</p><p>50 MW transmitted power.</p><p>The regulators are designed as small and inexpensive as possible while still fulfilling requirements regarding the active power flow controllability in the grid, current density in windings and maximum flux density in core and gap.</p><p>The results indicate that the size of the 400 kV solution has to be reduced to become competitive whereas for the 45 kV solution the relative difference to existing solution is smaller. Advantages with the proposed design over a phase shifting transformer are mainly a simpler winding scheme and the absence of a tap changer.</p>

When large disturbances occur in interconnected power systems, there exists the danger that the power system states may leave an associated region of stability, if timely corrective action is not taken. Open-loop remedial control actions such as field-forcing, line-tripping, switching of series-capacitors, energizing braking resistors, etc., are helpful in reducing the effects of the disturbance, but do not guarantee that the post-fault power system will be stabilized. Linear controllers are widely used in the power industry, and provide excellent damping when the power system state is close to the equilibrium. In general, they provide conservative regions of stability. This study focuses on the development of nonlinear controllers to enhance the stability of interconnected power systems following large disturbances, and allow stable operation at high power levels. There is currently interest in the power industry in using thyristor-controlled series-capacitors for the dual purpose of exercising tighter control on steady-state power flows and enhancing system stability. This device is used to implement the nonlinear controller in this dissertation. A mathematical model of the power system controlled by the thyristor-controlled series-capacitor is developed for the purpose of controller design. Discrete-time, nonlinear predictive controllers are derived by minimizing criterion functions that are quadratic in the output variables over a finite-horizon of interest, with respect to the control variables. The control policies developed in this manner are centralized in nature. The stabilizing effect of such controllers is discussed. A potential drawback is the need to have large prediction horizons to assure stability. In this context, a coordinated-control policy is proposed, in which the nonlinear predictive controller is designed with a small prediction horizon. For a class of disturbances, such nonlinear predictive controllers return the power system state to a small neighborhood of the post-fault equilibrium, where linear controllers provide asymptotic stabilization and rapid damping. Methods of coordinating the controllers are discussed. Simulation results are provided on a sample four-machine power system model. There exists considerable uncertainty in power system models due to constantly shifting loads and generations, line-switching following disturbances, etc. The performance of fixed-parameter controllers may not be good when the plant description changes considerably from the reference. In this context, a bilinear model-based self-tuning controller is proposed for the stabilization of power systems for a class of faults. A class of generic predictive controllers are presented for use with the self-tuning controller. Simulation results on single-machine and multimachine power systems are provided. / Graduation date: 1995