Towards The Construction Of Feasible Region For OPF Problems With Discrete Control Variables

The Optimal Power Flow(OPF)problem is a fundamental optimization problem in power system.Because of the nonlinearity of OPF,the OPF problems is generally hard to solve.Studying feasible region can help us better understanding the solving of optimal power flow and can help us design better optimal power flow solvers.Therefore,,this paper proposed a method based on a nonlinear dynamical system to construct the feasible region of optimal power flow problems considering discrete variables.The main contribution of this paper is concluded as follow:(1)This thesis proposed a method to construct the feasible region of OPF problem based on a Quotient Gradient System(QGS).A relevant feasible region construction method based on QGS is proposed that can obtain a series of feasible solutions toward given direction until reaching the boundary of feasible region.Based on the relevant feasible region construction method,we further propose a Local Feasible Solution Searching(LFSS)method to construct the feasible region in given space.For a better computing speed,we further proposed a method to construct the boundary of feasible region.Since this method combining the use of interior point method and QGS,both the robustness and the computing efficiency can be guaranteed.On the other hand,we design a heuristic rule based on the convexity of the feasible region boundary to realize the computation of feasible region boundary of different shaped.By constructing the feasible region for OPF problems with different scale,we testify the computing efficiency and the accuracy of the methods in this paper.(2)This thesis studies the non-convexity of the feasible region of large scale OPF problems.First,we observe the cross sections of feasible region and discover the nonconvexity of feasible region.Then,a visualization method for feasible region based on Principle Component Analysis is proposed.By studying a feasible region of a 118 bus case with multiple feasible solutions,we discover that the feasible region of large scale OPF problems could also be composed of different feasible components.At last,we study the variation of different feasible components with the load condition and conclude the empirical conclusion about he reasons for the disappearance of different feasible components.(3)This thesis studies the construction of feasible region for OPF problems considering discrete variables.We first mathematically characterize the feasible region of OPF problems with relaxed discrete variables based on QGS.Then,to construct the original feasible region of OPF problems with discrete variables,we propose a discretization method based on the branching and prune procedure to find the feasible discrete values of the discrete variables.The feasible region construction method is applied to a 9-bus system and a 118-bus system.The computing result prove the accuracy of the method in this thesis.At last,we conclude the influence of the variation of discrete variables to the feasible region though the observation of feasible region.