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.

A multiagent-based particle swarm optimization approach for optimal reactive power dispatch

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.

Optimal power flow: a bibliographic survey I

State-of-the-art, challenges, and future trends in security constrained optimal power flow

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.

A Two-Stage Robust Reactive Power Optimization Considering Uncertain Wind Power Integration in Active Distribution Networks

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.

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Optimal reactive power planning using evolutionary algorithms: a comparative study for evolutionary programming, evolutionary strategy, genetic algorithm, and linear programming

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. >

Optimal VAr planning by approximation method for recursive mixed-integer linear programming

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A VAR Planning Method with Multiple Power Flow Conditions

The goal of reactive power (VAR) planning is to find the minimum cost installation plan of new reactive power sources so that the system voltage is maintained within an acceptable level. The consideration of multiple contingency states, together with the discrete nature of VAR facilities, creates a large-scale nonlinear mixed-integer programming (MIP) problem.



To overcome the discrete nature of VAR facilities, an approximate method for the MIP problem is employed since the method is linear-programming based and thus efficient for large-scale problems. To treat the multiple contingencies, a resource directive decomposition approach is used in the proposed algorithm. If the number of installed VAR sources is fixed, the overall problem can be reduced to independent subproblems. Then subproblems are coordinated to give a VAR installation pattern in which installation cost becomes less than before. The algorithm proposed is tested for a 135-node real-size system and the results show the validity and effectiveness of the algorithm.

A VAR planning method with multiple power-flow states

This paper presents a new algorithm to solve an optimal power flow problem which can take into consideration the discrete nature of some facilities in power systems. The optimal power flow problem is formulated as a nonlinear mixed-integer programming problem in which the number of transformer taps and the number of shunt capacitor units and reactor units are treated as discrete variables.



This paper attempts to solve such a large-scale nonlinar mixed-integer programming problem by some effective programming techniques. The optimization procedure of the algorithm is that the nonlinear mixed-integer programming problem is linearized iteratively and solved by an approximation method for linear mixed-integer programming.



A fundamental feature of the algorithm is that it can guarantee a solution which is discrete, feasible and near-optimal. The validity and efficiency of the algorithm is demonstrated by the numerical results of real-scale optimal power flow problems.

Akimine Nishikori

Papers

Optimal VAr planning by approximation method for recursive mixed-integer linear programming

A VAR Planning Method with Multiple Power Flow Conditions

A VAR planning method with multiple power-flow states

An algorithm for discrete optimal power flow

Constrained Power Flow Using Nonlinear Programming