| With the growing demand for electricity,power industry has a swift and big development.lt makes the scale and structure of the modern power grid to become larger and more complicated,which will have higher requests to power quality and economic operation. Reactive power has an important influence on the voltage loss and power loss in power system,so a rational reactive power optimization can keep voltage stability,improve voltage quality and reduce power loss that is able to reduce energy consumption and cost.Reactive power optimization problem is a nonlinear programming problem which has the characteristics of complicated constraints and multi-variables including continuous variables and discrete variables. Many scholars have put forward kinds of algorithms.Interior point method is one of the traditional mathematical methods.lt received widespread attention because it is not sensitive to initial values selection and has good robustness and convergence, and,its calculaton will not increase obviously with the scale of power system’s expansion. This paper studies the application in reactive power optimization by Primal-Dual Interior Point Method (PDIPM)and Branch-Bound Method(BBM).This algorithm is based on the mathematical model which selects the least active power loss as objective function.Primal-Dual Interior Point Method is a combination of barrier function method, Lagrange function method and Newton-Raphson method.This paper explain PDIPM’s principle in detail.That is first using slack variables which only meet the conditions of greater than zero to convert function inequality constraints into equality constraints,using barrier parameter to convert objective function into barrier function,then using Lagrange multiplier method to solve the optimization problem which only contains equality constraints,after deducing the Karush-Kuhn-Tucker (KKT) conditions,last using Newton-Raphson method to solve the deduced nonlinear equations.This paper gives the algorithm’s specific implementation steps including relevant matrix element expressions,selection of barrier parameter, iteration steps and initial values.In order to correspond the optimization and feasibility, this paper also introduces the principle of Predictor-Corrector Primal—Dual Interior Point Method and demonstrate that its convergence ability is improved.This paper also discusses ways how to resolve discrete variables in reactive power optimization problem,such as taps of transformer and groups of capacitor.This paper introduces the principle of PDIPM with embedded penalty function and focus on the BBM’s application in reactive power optimization.The essence of BBM is based on "slack","brunch","delimit" and "cut",constantly dividing the region of the primal problem’s feasible solution,converting primal problem’s optimization into several slack sub problems’optimization. Combined with the characteristics of practical power system, this paper studies how to sort the brunch variables and uses PDIPM and a simple BBM based on heuristic method to solve reactive power optimization problem.In order to further test the validity of PDIPM and BBM to solve reactive power optimization problem, this paper introduces the principle of Genetic Algorithm(GA) and Particle Swarm Optimization Algorithm(PSO) which are choosed in artificial intelligence algorithms and makes programming of Standard Particle Swarm Optimization Algorithm (SPSO).This paper finally uses MATLAB language for programming and simulation and tests it on IEEE14and IEEE30standard systems. The compared results of PDIPM+BBM and SPSO applied to the reactive power optimization indicates that PDIPM has a reliable convergence and its iterations will not increase obviously with the scale of power system’s expansion,combining BBM to regulate discrete variables, can accurately solve the reactive power optimization problem.PDIPM+BBM can improve voltage quality and reduce power loss and its power loss is less than that with SPSO. |
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