Optimal Power Flow Research Based On Second-Order Cone Programming Relaxation Method And Quadratic Programming Algorithms

In this paper,the second order cone programming relaxation(SOCP relaxation)and quadratic programming(QP)are combined to solve the optimal power flow problem of power system,which can effectively solve the problem that SOCP relaxation is not strictly feasible,and the problem that QP algorithm is sensitive to initial values,so as to ensure the convergence of the algorithm and improve the computational efficiency.The basic strategy of this paper is to introduce relaxation variables and use SOCP relaxation technology to convex relaxation of inequality constraints and quadratic equality constraints with relaxation variables to form second-order cone constraints,and then replace variables in power flow equation with square terms,so as to transform the orig:inal non-linear equation into linear equation.The strategy successfully transforms the original OPF model into a convex SOCP relaxation model,which not only theoretically guarantees the global optimality of the optimization results,but also provides a good lower bound for the original problem,and can reasonably evaluate the advantages and disadvantages of the solution.The model provides the initial value near the global optimal solution for the output of generating units and the voltage amplitude and angle of all nodes,which can satisfy the requirement of QP algorithm for the initial value.Firstly,the original optimal power flow model and the SOCP relaxation model are simulated and analyzed by using the IEEE-14 mesh network system.The comparison results show that the SOCP relaxation model does not get the optimal solution of the original problem,but its lower bound value.It shows that the relaxation model of SOCP does have the possibility of inaccurate relaxation.On the basis of this conclusion,this paper combines SOCP relaxation method with QP algorithm,and uses four systems such as IEEE-300 to complete simulation analysis.The results show that the QP algorithm initialized by SOCP relaxation method can obtain feasible solutions.Compared with the QP algorithm initialized by flat-start method,it can jump out of the local optimal solution quickly and effectively,reduce the calculation time and iteration times,and achieve higher computational efficiency.At the same time,the results of the QP algorithm initialized by SOCP relaxation method are basically consistent with those of the interior point non-linear programming,which further shows that the global optimization of the final solution can be guaranteed.In addition,the lower bounds of the global optimal solution given by the SOCP relaxation model can also reasonably measure the merits and demerits of the final solution.The smaller the relative error between the final solution and its lower bound,the closer the final solution is to the global optimal solution and the better the solution quality is.At the same time,based on the original deterministic optimal power flow problem,this paper introduces uncertain variables such as wind power,and adopts the affine adjustable strategy robust optimization method to deal with the uncertainty of wind power.The numerical results show that the proposed method can still solve the problem successfully when wind power is connected to the power system,and the corresponding unit output plan can be made according to the uncertainty level of wind power to balance the uncertainty of wind power.It is proved that this method not only takes into account the security and economy of the system,but also has universality and expansibility.