Solution Of Optimal Power Flow Problems By Mixed Cone Linear Programming

Power system is a huge and complicated engineering system.The production and consumption of power energy,the distance between them can amount to thousands of kilometers,but they must keep balance in every minute.Hence,guaranteeing the security and stability of system operation,enhancing operation efficiency and reducing power loss,are the objective of electricity workers and researchers all the time.As a powerful tool for power system secutity and economy,optimal power flow(OPF)has never stopped the research steps since its birth.Based on mixed cone linear programming(MCLP),this dissertation presents an innovative method to solve OPF problems,namely MCLP-OPF.By using the mixed cone structure of MCLP,several MCLP-OPF models can be built.To solve MCLP-OPF sucessfully and effectively,two algorithms including homogeneous self-dual interior point method(HSDIPM)and simplified alternating direction method of multipliers(SADMM)are presented.Research results are as follows:1)By exploiting the structure characteristics of OPF problem,three MCLP-OPF models are presented to solve the OPF problems based on mixed cone linear programming method.These models adopt different kinds of conic variables to construct cone relaxation models of the original OPF problem.The conic variables can be taken from semi-definite cones,second-order cones and nonnegative polyhedral cones simultaneously.Comparing to semi-definite programming(SDP)using a single cone structure,the mixed cone structure applied can make the establishment of MCLP-OPF not confined to the matrix form of semi-definite cone variables and full use of the vector space of second-order cone variables and nonnegative cone variables to reduce the complexity of modeling.Consequently,it can avoid the big matrix variable form of SDP-OPF and improve the modeling efficiency.In addition,the variable size of MCLP-OPF is far less than that of SDP-OPF.This feature makes MCLP-OPF have higher efficiency of solution and storage and apply to large-scale power system problems.2)For some MCLP-OPF models which can not be solved directly by interior point method(IPM),an improved method of IPM,HSDIPM,is presented to deal with this problem.By introducing a concept of "thickness" in regard to the feasible region of MCLP-OPF,the relation between the "thickness" and the solving efficiency of IPM and HSDIPM is investigated.According to this relation,an algorithmic selection mechanism to enhance the solution robustness and efficiency of MCLP-OPF is devised.3)Employing IPM to solve MCLP-OPF problems,a dense Schur complement matrix factorization is inevitable.This brings difficulty to the solution of large-scale MCLP-OPF problems by IPM.To this end,an algorithm using simplified alternating direction method of multipliers is presented.SADMM can avoid the dense matrix factorization,and just need once factorization in the whole iteration process by applying factorization caching technique.Therefore,SADMM can improve the solving efficiency of MCLP-OPF,and make MCLP more scalable to large-scale OPF problems.There are seven chapters in this dissertation.The main contents are as follows:.In chapter 1,the classical OPF problem and its extension are discussed briefly.Besides,introduction on the mathematical form and solving method of OPF are conducted.In chapter 2,detailed introduction on the related contents of linear conic programming(LCP),involve the standard model,the optimality theorems and some concepts such as convex set and cone.In addition,the computable LCP model including linear programming,second-order cone programming and SDP are emphatically discussed.In chapter 3,concrete introduction on MCLP theory,involves the primal model and dual model of MCLP,IPM applied to solve the MCLP problems,initial point setting and step length calculation etc.In chapter 4,by exploiting the structure characteristics of OPF problem,the linear terms of OPF problem are handled by using the nonnegative cones,and the quadratic terms of OPF problem are handled by using the semi-definite cones or second-order cones.Then,based on MCLP,three kinds of MCLP-OPF models are established and solved by IPM.The results of 6 test systems such as C-703 show that,MCLP-OPF possesses higher solution efficiency and storage efficiency compared to SDP.In chapter 5,HSDIPM is used to solve the MCLP-OPF problems.By introducing a concept of "thickness" with respect to the feasible region of MCLP-OPF,the relation between the "thickness" and the solving efficiency of IPM and HSDIPM is investigated.According to this relation,an algorithmic selection mechanism is devised.In chapter 6,SADMM is used to solve the MCLP-OPF problems.First,the reason of forming the dense Schur complement matrix is analyzed.Then,Algorithm steps of SADMM are discussed in detail.Last,to acquire the solvable form of SADMM,the transform method via MCLP-OPF is presented.In chapter 7,the main research results of this dissertation are summarized.Several further follow-up studies are pointed out as well.