Research On Direct Dynamic Optimization Method For Optimal Coordinated Voltage Control

The modern electric power system, taking into account the constraints of decling investment, environmental contamination, etc, is operating much closer to its physical limits. With the increasing development of inter-tie, higher transmission voltage level, heavier load and longer distance from power resources to the sinks, voltage stability has become a serious problem which can no longer be ignored. The coordinated voltage control has been being considered of the research interest and engineering concern for the academic groups and utility companies. In this work, we propose a optimal coordinated voltage control strategy combining the secondary and tertiary voltage control and explore the numerical solution methods.According to the long-term voltage stability scenarios, based on quasi-steady state model, the optimal coordinated voltage control model is formulated as an objective function, minimizing both the voltage magnitude deviation of the load buses and control cost of various control schemes in terms of generator AVR setpoints, switchable capacitor banks, on load tap changers and load shedding, subjected to a series of differential-algebraic equations describing the dynamics of the system including the self-restoration of the load. The research time interval is divided into finite elements and the state variables, algebraic variables and control variables in each elements are approximated by a family of polynomials using Radau collocation. The dynamic optimization problem is then converted into a nonlinear programming model with continuous discrete variables. The quadratic penalty function is introduced to treat the discrete control variables and it is integrated with the nonlinear interior point method to obtain the approximate optimal solution.Nonlinear interior point method is indeed the combination of barrier function, Lagrangian function and Newton method. The most computational intensive parts of the algorithm is actually the formulation of Hessian, correction step length and the correction direction. The correction direction, which is derived from the KKT condition by first order Taylor series, is a large scale sparse matrix. Multifrontal method is introduced to enhance the computational efficiency with reordering the matrix by Approximate Minimum Degree method. The direct strategy is compared with the iterative method GMRES in the test results.Unlike the traditional descent method, line search based filter method is introduced to minimize either the objective or the constraints instead of minimizing the combination of both the objective and the constraints, namely merit function. The proposed filter method can enhance the stability and robustness of the interior point method and, with line search, it can converge to the optimum faster while obtaining a larger correction step length.