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

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

Digitized by Kansas Correctional Industries

Advanced technologies, a world-wide trend to deregulation of power systems and environmental constraints have attracted increasing interest in the operation of electric power systems with multiple storage resources. Under the competitive pressure of the deregulation, new efficient solution techniques to adapt quickly to the changing marketplace are in demand. This thesis presents a new evolutionary method, Constructive Evolutionary Programming (CEP), for minimising the system operational cost of scheduling electric power systems with multiple storage resources. The method combines the advantages of Constructive Dynamic Programming and Evolutionary Programming. Instead of evolving the "primal" variables such as storage content releases and thermal generator outputs, CEP evolves the piecewise linear convex cost-to-go functions (i.e. the storage content value curves). The multi-stage problem of multi-storage power system scheduling is thus decomposed into many smaller one-stage subproblems with evolved cost-to-go functions. For each evolutionary individual, linear programming is used in the forward pass process to solve the dispatch subproblems and the total system operational cost over the scheduling period is assigned to its fitness. Case studies demonstrate that the proposed method is robust and efficient for multi-storage power systems, particularly large complex hydrothermal system with cascaded and pumped storages. Although the proposed method is in the early stage of development, relying on assumptions of piecewise linear convexity in a deterministic environment, methods for the incorporation of stochastic models, electrical network and nonlinear, non-convex and non-smooth models are discussed. In addition, a number of possible improvements are also outlined. Due to its simplicity but robustness and efficiency, there are potential research directions for the further development of this evolutionary optimisation method.

Thesis (Ph. D. in electrical engineering)--Washington State University, December 2007. / Includes bibliographical references (p. 135-146).

Advanced technologies, a world-wide trend to deregulation of power systems and environmental constraints have attracted increasing interest in the operation of electric power systems with multiple storage resources. Under the competitive pressure of the deregulation, new efficient solution techniques to adapt quickly to the changing marketplace are in demand. This thesis presents a new evolutionary method, Constructive Evolutionary Programming (CEP), for minimising the system operational cost of scheduling electric power systems with multiple storage resources. The method combines the advantages of Constructive Dynamic Programming and Evolutionary Programming. Instead of evolving the "primal" variables such as storage content releases and thermal generator outputs, CEP evolves the piecewise linear convex cost-to-go functions (i.e. the storage content value curves). The multi-stage problem of multi-storage power system scheduling is thus decomposed into many smaller one-stage subproblems with evolved cost-to-go functions. For each evolutionary individual, linear programming is used in the forward pass process to solve the dispatch subproblems and the total system operational cost over the scheduling period is assigned to its fitness. Case studies demonstrate that the proposed method is robust and efficient for multi-storage power systems, particularly large complex hydrothermal system with cascaded and pumped storages. Although the proposed method is in the early stage of development, relying on assumptions of piecewise linear convexity in a deterministic environment, methods for the incorporation of stochastic models, electrical network and nonlinear, non-convex and non-smooth models are discussed. In addition, a number of possible improvements are also outlined. Due to its simplicity but robustness and efficiency, there are potential research directions for the further development of this evolutionary optimisation method.

Advanced technologies, a world-wide trend to deregulation of power systems and environmental constraints have attracted increasing interest in the operation of electric power systems with multiple storage resources. Under the competitive pressure of the deregulation, new efficient solution techniques to adapt quickly to the changing marketplace are in demand. This thesis presents a new evolutionary method, Constructive Evolutionary Programming (CEP), for minimising the system operational cost of scheduling electric power systems with multiple storage resources. The method combines the advantages of Constructive Dynamic Programming and Evolutionary Programming. Instead of evolving the "primal" variables such as storage content releases and thermal generator outputs, CEP evolves the piecewise linear convex cost-to-go functions (i.e. the storage content value curves). The multi-stage problem of multi-storage power system scheduling is thus decomposed into many smaller one-stage subproblems with evolved cost-to-go functions. For each evolutionary individual, linear programming is used in the forward pass process to solve the dispatch subproblems and the total system operational cost over the scheduling period is assigned to its fitness. Case studies demonstrate that the proposed method is robust and efficient for multi-storage power systems, particularly large complex hydrothermal system with cascaded and pumped storages. Although the proposed method is in the early stage of development, relying on assumptions of piecewise linear convexity in a deterministic environment, methods for the incorporation of stochastic models, electrical network and nonlinear, non-convex and non-smooth models are discussed. In addition, a number of possible improvements are also outlined. Due to its simplicity but robustness and efficiency, there are potential research directions for the further development of this evolutionary optimisation method.

Today's power systems are undergoing dynamic changes in their operation. The high cost of capital improvements that include new generation and transmission projects has prompted power system planners to look for other alternatives in dealing with increased loads and overall system growth. A dynamic braking resistor is a device that allows for an increased rating of a transmission system's transient stability limit. This allows increased power flows over existing transmission lines without the need to build additional transmission facilities. This thesis investigates the application of dynamically controlled resistive braking in the Pacific Northwest power system. Specifically, possible control alternatives, to replace the present dynamic brake control system at Chief Joseph station, are examined. This examination includes determination of appropriate locations for control system input, development of control algorithms, development of computer and laboratory power system models, and testing and recommendations based upon the developed control algorithms. / Graduation date: 1995

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

Future development of electric power systems must pursue anumber of different goals. The power system should beeconomically efficient, it should provide reliable energysupply and should not damage the environment. At the same time,operation and development of the system is influenced by avariety of uncertain and random factors. The planner attemptsto find the best strategy from a large number of possiblealternatives. Thus, the complexity of the problems related topower systems planning is mainly caused by presence of multipleobjectives, uncertain information and large number ofvariables. This dissertation is devoted to consideration of themethods for development planning of a certain subsystem, i.e.the distribution network. The dissertation first tries to formulate the networkplanning problem in general form in terms of Bayesian DecisionTheory. However, the difficulties associated with formulationof the utility functions make it almost impossible to apply theBayesian approach directly. Moreover, when approaching theproblem applying different methods it is important to considerthe concave character of the utility function. Thisconsideration directly leads to the multi-criteria formulationof the problem, since the decision is motivated not only by theexpected value of revenues (or losses), but also by theassociated risks. The conclusion is made that the difficultiescaused by the tremendous complexity of the problem can beovercome either by introducing a number of simplifications,leading to the considerable loss in precision or applyingmethods based on modifications of Monte-Carlo or fuzzyarithmetic and Genetic Algorithms (GA), or Dynamic Programming(DP). In presence of uncertainty the planner aims at findingrobust and flexible plans to reducethe risk of considerablelosses. Several measures of risk are discussed. It is shownthat measuring risk by regret may lead to risky solutions,therefore an alternative measure - Expected Maximum Value - issuggested. The general future model, called fuzzy-probabilistictree of futures, integrates all classes of uncertain parameters(probabilistic, fuzzy and truly uncertain). The suggested network planning software incorporates threeefficient applications of GA. The first algorithm searchessimultaneously for the whole set of Pareto optimal solutions.The hybrid GA/DP approach benefits from the global optimizationproperties of GA and local search by DP resulting in originalalgorithm with improved convergence properties. Finally, theStochastic GA can cope with noisy objective functions. Finally, two real distribution network planning projectsdealing with primary distribution network in the large city andsecondary network in the rural area are studied.