Multiobjective optimal power flow using a semidefinite programming-based model

In spite of the significant advance achieved in the development of optimal power flow (OPF) programs, most of the solution methods reported in the literature have considerable difficulties in dealing with different-nature objective functions simultaneously. By leveraging recent progress on the semidefinite programming (SDP) relaxations of OPF, in the present article, attention is focused on modeling a new SDP-based multiobjective OPF (MO-OPF) problem. The proposed OPF model incorporates the classical ϵ-constraint approach through a parameterization strategy to handle the multiple objective functions and produce Pareto front. This article emphasizes the extension of the SDP-based model for MO-OPF problems to generate globally nondominated Pareto optimal solutions with uniform distribution. Numerical results on IEEE 30-, 57-, 118-bus, and Indian utility 62-bus test systems with all security and operating constraints show that the proposed convex model can produce the nondominated solutions with no duality gap in polynomial time, generate efficient Pareto set, and outperform the well-known heuristic methods generally used for the solution of MO-OPF. For instance, in comparison with the obtained results of NSGA-II for the 57-bus test system, the best compromise solution obtained by SDP has 1.55% and 7.42% less fuel cost and transmission losses, respectively.©2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.fi=vertaisarvioitu|en=peerReviewed

Despacho óptimo de potencia reactiva basado en programación no lineal entera mixta y restricciones de cargabilidad de líneas de transmisión

El despacho óptimo de potencia reactiva en los sistemas eléctricos de potencia llega a ser esencial, pues permite operar el sistema eléctrico de manera óptima y estable, al encontrar la asignación más apropiada de potencia reactiva tanto para los generadores como para los elementos de compensación. Sin embargo, al optimizarse los despachos de potencia reactiva los costos de generación se ven en aumento, por lo que es necesario garantizar una optimización multiobjetivo que permita mejorar las características técnicas como económicas de los sistemas eléctricos. Es así como en el presente trabajo, se desarrolla e implementa un algoritmo de optimización multiobjetivo en el software GAMS, sujeto a varias restricciones operativas que mantienen estable el sistema eléctrico, garantizando un despacho óptimo de potencia reactiva sin aumentar en gran medida los costos de generación. El algoritmo propuesto será evaluado y validado mediante la simulación en el software Power Factory Digsilent sobre los sistemas eléctricos de prueba del IEEE de 14 y 30 barras respectivamente.The optimal reactive power dispatch in electrical power systems becomes essential, since it allows the electrical system to operate in an optimal and stable way, by finding the most appropriate allocation of reactive power for both generators and compensation elements. However, as reactive power dispatches are optimized, generation costs are increasing, so it is necessary to guarantee a multi-objective optimization that allows improving the technical and economic characteristics of the electrical systems. Thus, at the present work, a multi-objective optimization algorithm is developed and implemented in the GAMS software, subject to several operational restrictions that keep the electrical system stable, guaranteeing an optimal reactive power dispatch without greatly increasing generation costs. The proposed algorithm will be evaluated and validated by simulation in Power Factory Digsilent software on the IEEE 14-, and 30- bus test system respectively

Despacho ótimo de potência reativa com controladores discretos usando o algoritmo branch and bound : uma abordagem por relaxação semidefinida

Orientador: Marcos Julio Rider FloresDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Recentemente, vários relaxamentos convexos foram aplicados com sucesso para resolver o problema do fluxo de potência ótimo de CA (OPF), o que chamou a atenção da comunidade científica. Dentre esses relaxamentos, destaca-se um relaxamento baseado em programação semidefinida (SDP). Nesse sentido, neste trabalho é proposta uma metodologia para resolver o despacho ótimo de potência reativa (ORPD) em sistemas elétricos de potência(SEP), considerando controladores discretos. Controladores discretos, como a posição de tap dos transformadores de comutação em carga (OLTC) e compensação de shunt reativa comutável, são otimizados pelo método proposto. Uma relaxação semidefinida(SDR) do problema ORPD e um algoritmo branch-and-bound (B&B) foram totalmente implementados. O algoritmo B&B personalizado lida com a natureza discreta das variáveis de controle binárias. Além disso, a fim de melhorar a convexificação, desigualdades válidas chamadas de cortes não lineares elevados (LNCs) são implementadas no SDR. Além disso, uma técnica de decomposição de cordas é usada para melhorar o desempenho computacional. Finalmente, o algoritmo B&B é usado para resolver o problema de programação semidefinida inteira mista. Vários sistemas de referência foram usados para mostrar a precisão e escalabilidade do método proposto, e a análise de convergência mostraque soluções ótimas quase globais são geradas com pequenas brechasAbstract: Recently, several convex relaxations has been successfully applied to solve the AC optimal power flow (OPF) problem, which has caught the attention of the research community. Among these relaxations, a relaxation based on semidefinite programming (SDP) stands out. Accordingly, in this work a methodology to solve the optimal reactive power dispatch (ORPD) in electric power systems (EPS), considering discrete controllers, is proposed. Discrete controllers, such as the tap position of on-load tap changing (OLTC) transformers and switchable reactive shunt compensation, are optimized by the proposed method. A semidefinite relaxation (SDR) of the ORPD problem and a branch-and-bound (B&B) algorithm has been fully deployed. The customized B&B algorithm deals with the discrete nature of the binary control variables. Moreover, in order to enhance the convexification, valid inequalities called lifted non-linear-cuts (NLC) are implemented in the SDR. Addition-ally, a chordal decomposition technique is used to improve the computational performance. Finally, the B&B algorithm is used to solve the mixed-integer semidefinite programming problem. Several benchmarks have been used to show the accuracy and scalability of the proposed method, and convergence analysis shows that near-global optimal solutions are generated with small relaxation gapsMestradoEnergia ElétricaMestre em Engenharia Elétrica88882.329400/2019-1CAPE