مطالعات بهره برداری بهینه از سیستم برق از طریق تجزیه و تحلیل حساسیت

This paper presents an optimal operation study of the power system via sensitivity analysis. This study is based on perturbation of optimum theorem, which works with a Lagrangian function associated with the perturbed problem. Starting from an optimal operating point obtained by solution of an optimal power flow problem, the new optimal operating point is calculated directly satisfying the constraints and optimising the objective function after making a small perturbation in the loads. Test results are presented to demonstrate the efficiency of the approach.

An important question that often arises in the utilization of mathematical programming algorithms is how much the optimum changes when changes are made in the constraints. An answer to this question is available if the appropriated assumptions are made about conditions holding in the optimum point [1]. This study takes us to general parametric programming problem. The sensibility of the solution for parameter variations, that is, perturbation, has been largely studied since the approach proposed by Dillon [2]. Carpentier et al. [3] applied parametric quadratic programming to the real power economic dispatch problem. Galiana et al. [4] proposed a parametric technique for the optimal power flow (OPF) problem, based on the varying limit strategy. Almeida et al. [5] presented an extension and generalization of the studies described in [4]. Gribik et al. [6] described a parametric OPF formulation to perform sensitivity analysis on incremental losses with respect to the load. The authors determined the sensitivity of the OPF solution to the perturbation in the load, ɛ, by calculating the perturbed Lagrangian. The sensibility matrix obtained is symmetric and does not contain information on the inequality constraints. Several algorithms have been proposed for sensitivity analysis [7], [8], [9] and [10]. In this paper, we will make use of the optimal point perturbation theorem, introduced by Fiacco [1]. Applying a small perturbation to an optimal state, it is possible, on the basis of the theorem, to estimate a new optimal state satisfying all the constraints, by optimising the objective function of the problem, and the behavior of the primal and dual system variables can also be studied. While this theorem permits analysis of the effects of perturbations of the objective function and of the inequality and equality constraints, in this study we will only consider the effects of equality constraint perturbations, such as a variation in demand. The paper is organized as follows: first, the optimal power flow problem is presented, followed by the analysis of optimum perturbation by non-linear programming. Next, an application of this approach is then described. The results obtained from tests on three systems (14, 162, 300 buses) are reported. Finally, some concluding remarks are made.

The optimal power flow is a large-scale, non-convex, non-linear programming problem with non-linear constraints. This paper reports an investigation into the optimal operation of the power system with sensitivity analysis. In most of the cases studied, it was shown that an optimal solution could be safely estimated for perturbations of the system load in the order of 1%, by the sensitivity technique. The estimate of the Lagrange multipliers (spot prices) for load perturbations, under minimization of costs of generation (objective function), could help network managers take decisions based on optimal criteria. It should be stressed that even when the system has no OPF solution, or a power flow solution using sensitivity, it is always possible to estimate the behavior of active and reactive power in the network. It was found that after load perturbation the optimum point stays in the same region of convergence, preventing large leaps in the solution. The tests demonstrated the effectiveness of the proposed method.