The electric power distribution system usually operates a radial configuration, with tie switches between circuits to provide alternate feeds. The losses would be minimized if all switches were closed, but this is not done because it complicates the system's protection against overcurrents. Whenever a component fails, some of the switches must be operated to restore power to as many customers as possible. As loads vary with time, switch operations may reduce losses in the system. Both of these are applications for reconfiguration. The problem is combinatorial, which precludes algorithms that guarantee a global optimum. Most existing reconfiguration algorithms fall into two categories. In the first, branch exchange, the system operates in a feasible radial configuration and the algorithm opens and closes candidate switches in pairs. In the second, loop cutting, the system is completely meshed and the algorithm opens candidate switches to reach a feasible radial configuration. Reconfiguration algorithms based on linearized transshipment, neural networks, heuristics, genetic algorithms, and simulated annealing have also been reported, but not widely used. These existing reconfiguration algorithms work with a simplified model of the power system, and they handle voltage and current constraints approximately, if at all. The algorithm described here is a constructive method, using a full nonlinear power system model that accurately handles constraints. The system starts with all switches open and all failed components isolated. An optional network power flow provides a lower bound on the losses. Then the algorithm closes one switch at a time to minimize the increase in a merit figure, which is the real loss divided by the apparent load served. The merit figure increases with each switch closing. This principle, called discrete ascent optimal programming (DAOP), has been applied to other power system problems, including economic dispatch and phase balancing. For reconfiguration, the DAOP method's greedy nature is mitigated with a backtracking algorithm. Approximate screening formulas have also been developed for efficient use with partial load flow solutions. This method's main advantage is the accurate treatment of voltage and current constraints, including the effect of control action. One example taken from the literature shows how the DAOP-based algorithm can reach an optimal solution, while adjusting line voltage regulators to satisfy the voltage constraints. / Ph. D.

The high cost of grid extension to rural areas, often characterized by scattered communities with low load densities, requires the use of low cost electrification technologies to ensure economic viability. In Single Wire Earth Return (SWER) power distribution networks, the earth itself forms the current return path of the single phase system leading to significant cost savings on conductors, poles and poletop hardware compared to conventional systems. However, challenges exist in SWER with regard to earthing and safety as well as the dependence on earth conductivity to supply consumer loads. This work presents models for the optimal planning of SWER distribution networks. The earth return path is modeled as a conductor based on the Carson line model taking into consideration specific ground properties of the considered location. A load flow algorithm for radial SWER networks is subsequently formulated whereby both overhead line and ground voltages and currents are determined. First, heuristic planning models are developed based on the SWER load flow model. The objective of the heuristic models is to determine the optimum feeder configuration and overhead conductor subject to SWER load flow constraints and load growth over several time periods. Whereas the resulting solutions are good, they may not necessarily be globally optimum. Optimization models are then developed using mixed integer non-linear programming (MINLP) with the aim of obtaining global solutions to the SWER network planning problem. Since the MINLP formulations are limited to the accurate analysis of limited size networks, considerations and approximations for the analysis of larger networks are presented. The developed models are applied to a case study in Uganda to test their practical application. In addition, comparative studies are done to determine how the proposed optimization models compare with previous distribution planning models. The numerical analysis includes the impact of deterministic distributed generation on the SWER planning problem. Results showed consistent performance of the proposed heuristic and optimization models, which also compared well with conventional models. The optimization models gave more cost-effective solutions to the SWER planning problem than the heuristic models. However, the former models had higher computational cost than the latter. The inclusion of distributed generation allowed for cheaper network solutions to be obtained. The models are applicable to the planning of Single Wire Earth Return networks for isolated mini-grids, grid-extension to previously un-electrified rural areas as well as the upgrade of SWER feeders in existing installations. / <p>QC 20121207</p> / Sustainable Technological Development in the Lake Victoria Region

Orientador: José Roberto Sanches Mantovani / Resumo: Neste trabalho propõem-se formulações matemáticas e metodologias para resolver o problema de planejamento da expansão e operação de sistemas de distribuição de energia elétrica de longo prazo com instalação de geração distribuída despachável, renovável e dispositivos armazenadores de energia, considerando as incertezas nos parâmetros e variáveis envolvidas no comportamento do sistema. No modelo de otimização desenvolvido considera- se uma formulação com espaço de busca convexo como um problema de programação cônica inteira de segunda ordem. Como primeira metodologia de solução para o modelo matemático proposto, usam-se solvers de otimização comerciais através de linguagem de programação matemática. Em segundo lugar é proposta a técnica de otimização meta-heurística VND combinada com um solver de otimização para resolver o modelo de otimização desenvolvido. Os algoritmos e modelos matemáticos de otimização usados para resolver o planejamento de sistemas de distribuição são implementados em AMPL e testados em sistemas presentes na literatura. Finalmente são comparadas as metodologias segundo a solução obtida e desempenho em tempo computacional. / Abstract: This work proposes mathematical formulations and methodologies to solve the long-term electric power distribution system operation and expansion planning with distributed renewable energy sources and energy storage devices, considering the uncertainties in the involved parameters and variables in the system behavior. In the developed optimization model, a convex formulation is considered as integer second-order conic programming problem. The first solution methodology for the proposed mathematical model, the commercial optimization solvers that uses mathematical modelling language is used. In the second way, the VND meta-heuristic optimization technique is proposed combined with the optimization solver to analyze the obtained solutions of the search through optimal neighborhoods. The mathematical optimization model and the proposed algorithm used to solver the planning of distribution systems are implemented in AMPL and tested in literature’s systems. Finally, the methodologies according to the obtained solution and computational time performance are compared. / Doutor