Security Region Based Optimal Power Flow Of Power Systems

In the past decades, a great deal of achievements had been made in optimal powerflow (OPF) research of power systems. However, normal OPF can't take transientstability and voltage stability constraints into account. Additionally, computationspeed of OPF based on traditional "point-wise" approach is not fast enough for on lineapplications. These problems become more serious under the environment ofelectricity market, such that we must adopt new theories and methods to deal withOPF with stability constrains in modern power systems. Different from the "point-wise" approach, "security region approach" is abrand-new method which can give power system engineers systematic and globalinformation about the stability margins in different directions in power injection spaceor in cut-set power space. In order to include steady state security constraints (busvoltage constrains of nodes, branch thermo stability limit constrains and powerinjection limits of nodes), static voltage stability constrains and transient stabilityconstrains into the OPF formulation, this paper presents a novel mathematics modeland an efficient algorithm based on security region methodology that can minimizetotal generation cost with considering both 1st order and 2nd order terms of generationcost function. We derive a new affine mapping between angles of tree branches andactive power injections of networks. Then, a mathematics model of OPF is proposedwhich takes branch angles as optimization variables instead of power injections asusual, such that all the security constraints are linear inequalities and the OPF can besolved easily and rapidly by basic optimization methods. The feasibility andeffectiveness of the proposed mathematics model and algorithm have been validatedin the 39-bus New-England System and an 845-bus real power system of China. Atthe same time, the visualization of OPF is explored which can provide dispatcherinformation about security margins of power systems effectively for correctivelymaking decision of preventive control.