Optimal VAr planning by approximation method for recursive mixed-integer linear programming
TL;DR: An algorithm for solving reactive power planning problems based on a recursive mixed-integer programming technique using an approximation method so that the number of capacitor or reactor units can be treated as a discrete variable in solving large-scale VAr (volt-ampere reactive) planning problems.
Abstract: The authors propose an algorithm for solving reactive power planning problems. The optimization approach is based on a recursive mixed-integer programming technique using an approximation method. A fundamental feature of this algorithm is that the number of capacitor or reactor units can be treated as a discrete variable in solving large-scale VAr (volt-ampere reactive) planning problems. Numerical results have verified the validity and efficiency of the algorithm. >
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TL;DR: A solution to the reactive power dispatch problem with a novel particle swarm optimization approach based on multiagent systems (MAPSO) is presented and it is shown that the proposed approach converges to better solutions much faster than the earlier reported approaches.
Abstract: Reactive power dispatch in power systems is a complex combinatorial optimization problem involving nonlinear functions having multiple local minima and nonlinear and discontinuous constraints. In this paper, a solution to the reactive power dispatch problem with a novel particle swarm optimization approach based on multiagent systems (MAPSO) is presented. This method integrates the multiagent system (MAS) and the particle swarm optimization (PSO) algorithm. An agent in MAPSO represents a particle to PSO and a candidate solution to the optimization problem. All agents live in a lattice-like environment, with each agent fixed on a lattice point. In order to obtain optimal solution quickly, each agent competes and cooperates with its neighbors, and it can also learn by using its knowledge. Making use of these agent-agent interactions and evolution mechanism of PSO, MAPSO realizes the purpose of optimizing the value of objective function. MAPSO applied to optimal reactive power dispatch is evaluated on an IEEE 30-bus power system and a practical 118-bus power system. Simulation results show that the proposed approach converges to better solutions much faster than the earlier reported approaches. The optimization strategy is general and can be used to solve other power system optimization problems as well.
550 citations
Cites methods from "Optimal VAr planning by approximati..."
...Aoki et al. [ 9 ] addressed the issue of discrete variables by an approximation-search method for recursive mixed-integer programming in solving large-scale VAR planning problems....
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TL;DR: Optimal power flow (OPF) has become one of the most important and widely studied nonlinear optimization problems as mentioned in this paper, and there is an extremely wide variety of OPF formulations and solution methods.
Abstract: Over the past half-century, Optimal Power Flow (OPF) has become one of the most important and widely studied nonlinear optimization problems. In general, OPF seeks to optimize the operation of electric power generation, transmission, and distribution networks subject to system constraints and control limits. Within this framework, however, there is an extremely wide variety of OPF formulations and solution methods. Moreover, the nature of OPF continues to evolve due to modern electricity markets and renewable resource integration. In this two-part survey, we survey both the classical and recent OPF literature in order to provide a sound context for the state of the art in OPF formulation and solution methods. The survey contributes a comprehensive discussion of specific optimization techniques that have been applied to OPF, with an emphasis on the advantages, disadvantages, and computational characteristics of each. Part I of the survey (this article) provides an introduction and surveys the deterministic optimization methods that have been applied to OPF. Part II of the survey examines the recent trend towards stochastic, or non-deterministic, search techniques and hybrid methods for OPF.
483 citations
TL;DR: In this paper, the main challenges to the security constrained optimal power flow (SCOPF) computations are discussed, focusing mainly on: approaches to reduce the size of the problem by either efficiently identifying the binding contingencies and including only these contingencies in the SCOPF or by using approximate models for the post-contingency states, and the handling of discrete variables.
393 citations
TL;DR: Wang et al. as discussed by the authors proposed a two-stage robust optimization model to coordinate the discrete and continuous reactive power compensators and find a robust optimal solution that can hedge against any possible realization within the uncertain wind power output.
Abstract: Traditional reactive power optimization aims to minimize the total transmission losses by control reactive power compensators and transformer tap ratios, while guaranteeing the physical and operating constraints, such as voltage magnitudes and branch currents to be within their reasonable range. However, large amounts of renewable resources coming into power systems bring about great challenges to traditional planning and operation due to the stochastic nature. In most of the practical cases from China, the wind farms are centrally integrated into active distribution networks. By the use of conic relaxation based branch flow formulation, the reactive optimization problem in active distribution networks can be formulated as a mixed integer convex programming model that can be tractably dealt with. Furthermore, to address the uncertainties of wind power output, a two-stage robust optimization model is proposed to coordinate the discrete and continuous reactive power compensators and find a robust optimal solution that can hedge against any possible realization within the uncertain wind power output. Moreover, the second order cone programming-based column-and-constraint generation algorithm is employed to solve the proposed two-stage robust reactive power optimization model. Numerical results on 33-, 69- and 123-bus systems and comparison with the deterministic approach demonstrate the effectiveness of the proposed method.
290 citations
Cites methods from "Optimal VAr planning by approximati..."
...The other as the conventional methods included gradient-based optimization algorithms [17], quadratic programming [18], successive linear programming [19], successive quadratic programming [20], Newton’s method [21], interior-point methods [22] and mixedinteger programming [23] as well as some decomposition methods [24]....
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TL;DR: A comparative study for three evolutionary algorithms (EAs) to the optimal reactive power planning (ORPP) problem: evolutionary programming, evolutionary strategy, and genetic algorithm.
Abstract: This paper presents a comparative study for three evolutionary algorithms (EAs) to the optimal reactive power planning (ORPP) problem: evolutionary programming, evolutionary strategy, and genetic algorithm. The ORPP problem is decomposed into P- and Q-optimization modules, and each module is optimized by the EAs in an iterative manner to obtain the global solution. The EA methods for the ORPP problem are evaluated against the IEEE 30-bus system as a common testbed, and the results are compared against each other and with those of linear programming.
290 citations
Cites methods from "Optimal VAr planning by approximati..."
...Various mathematical optimization algorithms have been developed for the ORPP, which in most cases, use nonlinear [l], linear [2], or mixed integer programming [ 3 ], and decomposition methods [4-7]....
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References
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TL;DR: A detailed description of an efficient, reliable SLP algorithm along with a convergence theorem for linearly constrained problems and extensive computational results show that SLP compares favorably with the Generalized Reduced Gradient Code GRG2 and with MINOS/GRG.
Abstract: Successive Linear Programming SLP, which is also known as the Method of Approximation Programming, solves nonlinear optimization problems via a sequence of linear programs. This paper reports on promising computational results with SLP that contrast with the poor performance indicated by previously published comparative tests. The paper provides a detailed description of an efficient, reliable SLP algorithm along with a convergence theorem for linearly constrained problems and extensive computational results. It also discusses several alternative strategies for implementing SLP. The computational results show that SLP compares favorably with the Generalized Reduced Gradient Code GRG2 and with MINOS/GRG. It appears that SLP will be most successful when applied to large problems with low degrees of freedom.
177 citations
TL;DR: This paper introduces a new approach to solve the var optimization problem that computes the desired optimal solution on-line and is applicable to large system deviations, without the need of an OPF.
Abstract: This paper introduces a new approach to solve the var optimization problem. It computes the desired optimal solution on-line and is applicable to large system deviations, without the need of an OPF. Problem non-linearities are retained. The overall problem is decomposed into subproblems which are solved separately using a suitable NLP Method. These results are then coordinated. This process is repeated until it converges to an overall optimum point.
108 citations
TL;DR: In this article, an integrated methodology for VAr sources expansion planning is described, which extends and generalizes a previously proposed two-level hierarchical approach to represent multiple load levels and multiple contingencies, calculate the trade-off between investment cost and supply reliability, and select the most adequate set of candidate nodes for expansion.
Abstract: An integrated methodology for VAr sources expansion planning is described. The methodology extends and generalizes a previously proposed two-level hierarchical approach to represent multiple load levels and multiple contingencies, calculate the trade-off between investment cost and supply reliability, and select the most adequate set of candidate nodes for expansion. Case studies with the IEEE-118 bus system are used to illustrate the capabilities of the approach. >
90 citations
TL;DR: In this article, a two-level hierarchical approach for optimum allocation of reactive volt ampere (VAR) sources in large scale power system planning is presented, which takes advantage of the natural distinction between var dispatch in system operation and var allocation in system planning.
Abstract: A two-level hierarchical approach for optimum allocation of reactive volt ampere (VAR) sources in large scale power system planning is presented in this paper. The approach takes advantage of the natural distinction between var dispatch in system operation (Level 1) and var allocation in system planning (Level 2). The two levels are related together using the Generalized Benders Decomposition. The methodology has been implemented in the form of a prototype computer program which can be applied to large scale power systems with up to 1500 buses. The results of testing the package with practical power systems of different sizes and characteristics indicate that the technique is a valuable tool for reactive source allocation.
66 citations
TL;DR: In this article, a new methodology for planning future reactive compensation for large scale systems is presented, based on a restructuring of the network model and a special formulation of the revised simplex method.
Abstract: A new methodology for planning future reactive compensation for large scale systems is presented. The planning technique is based on a restructuring of the network model and a special formulation of the revised simplex method. A preprocessor is incorporated for correcting systems which are not able to converge using conventional power flow or optimal power flow programs. A 600 bus example is provided which considers 285 transmission contingencies.
63 citations