Semi-Infinite Programming With Application To OTS Problems

Semi-infinite programming (SIP) is an important branch in the field of Nonlinear programming, which comprises finite variables with infinite constraints. The studies of methods have been developed fast because it's wide applied in engineering technique and control system and so on. We propose an effective iterative method in this paper firstly. The algorithm has global convergence in theory. Then SIP is applied to optimal power flow (OPF) in electric power systems. Numerical results are shown that the new method in this paper is effective. The main contents are as follows:In the first section, we mainly introduce both the development and current situation of semi-infinite programming and the main ideas of its existing methods, propose a different theory of SIP algorithm with its KKT system in this paper and briefly describe the optimal power flow with transient stability constraints. In addition, our researches of this paper are also introduced compactly.In the second section, we apply the new SIP theory to the optimal power flow with transient stability constraints. By using the functional transformation technology, the OTS is converted into a semi-infinite programming problem firstly. Then an iterative method is presented for the reformulated SIP problem. The new iterative method uses an active set strategy to obtain its finite approximation,(called the subproblem of SIP). This subproblem is typical nonlinear programming problems and can be solved by ordinary methods. The algorithm has global convergence in theory. Two practical OTS examples are presented. Both are shown that the new method in this paper is effective.In the third section, we tentatively apply a generalized semi-infinite programming (GSIP) to OTS which is armed at a fault clearing time. By using the functional transformation technology, this OTS is converted into a GSIP problem. Numerical results show the feasibility of the iterative method.