Research On Optimal Power Flow Problem Using A Dynamical System Based Method

With the vigorous development of smart grid technology and new energy industry,the operating conditions and scheduling strategies of power systems become more and more complex.How to optimize the existing power systems on the basis of ensuring their safety and reliability,so as to realize the economical and efficient operation of the systems is the primary goal and main challenge of the electricity market.As a basic tool in the power systems,the optimal power flow(OPF)problem constitutes the foundation of other optimization problems.Moreover,solving the OPF problem will play a leading role in the solutions of other extended applications in the power systems.In this paper,we will discuss the convergence problem and global optimization problem of OPF in a novel and in-depth way.In summary,this paper develops and presents:(1)Substantial efforts have been directed into the OPF problem.However,few articles involve a fundamental and important issue in solving the OPF problem—the feasible region.Because of the existence of nonlinear constraints,the feasible region of the OPF problem is complex.This paper proposes a non-hyperbolic dynamical system model and the stable equilibrium manifolds(SEMs)of this system are used to completely characterize the feasible region of the OPF problem.To address the issue associated with visualization of the feasible region of high-dimensional OPF problems,the notion of local feasible region is presented.In addition,the impacts of varying constraint parameters on the alteration of the feasible region are demonstrated via the alteration of the SEMs of the non-hyperbolic dynamical system;(2)The computation of OPF problem remains difficult.When solving OPF problem using a numerical method like interior point method(IPM),if a divergence occurs,it is difficult to figure out whether it is because the numerical method fails to find the optimum or there exists no feasible region to the set of equalities and inequalities imposed at all.In this paper,a trajectory based approach to identify the feasibility of OPF problem is proposed.In order to reduce the computation burden of the proposed approach,the active-set method and pseudo-transient continuation method are respectively employed to simplify the model and accelerate the integration process;(3)Local bifurcations occur in power systems,causing changes in power system dynamic behaviors.This paper presents a new type of bifurcation that can occur in the OPF problem.This new type of bifurcation,termed pseudo pitchfork-bifurcation,involves the coalescing of feasible components of the OPF problem.The main features of this special type of bifurcation are demonstrated on several power systems with different loading condition parameters and different inequality constraint parameters.Then the computation consideration and the physical meaning of the pseudo-pitchfork bifurcation are roughly discussed;(4)An effective algorithm to find the global optimum of OPF problem is still challenging and it is the direction we are heading towards.In this paper,a trajectory-based unified method to globally search for the solutions of OPF problem is proposed.It combines IPM,SDP method and exerts each method's advantages.By studying the theoretical basis and the complete algorithm of the trajectory-based unified method in detail,the numerical studies are carried out in several standard examples and several difficult examples to verify the effectiveness and robustness of the method.