This paper presents studies of cases in power systems by Sensitivity Analysis (SA) oriented by Optimal Power Flow (OPF) problems in different operation scenarios. The studies of cases start from a known optimal solution obtained by OPF. This optimal solution is called base case, and from this solution new operation points may be evaluated by SA when perturbations occur in the system. The SA is based on Fiacco’s Theorem and has the advantage of not be an iterative process. In order to show the good performance of the proposed technique tests were carried out on the IEEE 14, 118 and 300 buses systems.
One of the main tasks of a power system operator is to manage the system in such a way that its operation be safe and reliable. The availability of tools that aid the operator in its task of maintaining the system operating safely is of fundamental importance for utilities. Studies of the present and future system conditions should be carried out and, furthermore, in many cases they should be done rapidly and precisely in order that decisions may be taken. In this context, Sensitivity Analysis (SA) emerges as an efficient instrument for studies of the planning of power electrical system operations given that it demonstrates the future performance of the system in different situations.
In specialized literature, there are very few proposals about the application of SA in power systems. One of the first papers on this line of research is the one proposed by Peschon et al. [1], in which studies of sensitivity between the magnitude of voltage and the injection of reactive in certain buses of the system were carried out. The Jacobian matrix, calculated in the system operation point, provided the sensitivity relations that were of interest to the study. Kishore and Hill [2], using the sensitivity matrix showed in [1], elaborated a technique for optimal reactive allocation in power systems. Wojciechowski [3] applied the Tellegen Theorem aiming at developing an efficient SA method. Gribik et al. [4] and Belati et al. [5] made a study of SA oriented by Optimal Power Flow (OPF) problems. The OPF problem widely divulged in literature [6], [7], [8], [9] and [10] has the objective of minimizing a function and, at the same time, of satisfying a set of physical and operational constraints in power systems. As a solution, it provides the optimal operation point for the electrical network for a given generation and load configuration of the system. If perturbations occur in the electrical system, such as a variation in demand or alterations in operational limits, a new operation point should be obtained. This new point can be founded by running again the OPF program or by a SA technique applied to the OPF. SA oriented by OPF requires a known optimal point, which is obtained from the OPF program. The solution provided by the OPF is called base case solution and after perturbations occur new optimal points can be obtained via SA. The main advantage of using the SA approach is that, unlike the OPF, it is not iterative and it does not demand to estimate the initial barrier parameter and its correction factor. Thus, it allows not only to follow the load variations, but also to analyze, fast and efficiently, different strategies of adjustments.
In this paper we presented the SA oriented by OPF to accomplish studies of cases in power system for different operation scenarios. The OPF was solved by primal–dual logarithmic barrier method [11] and [12] and the SA formulation is based on a theorem proposed by Fiacco [13]. The developed models of both optimization problems – OPF and SA – were the same. The minimized objective function was active power losses in the transmission system. The set of constraints was given by: balance equations and operational limits of magnitude voltage, LTC’ taps, active and reactive power generations and active power flow in transmission lines. Aiming at avoiding the complexity of the problem, transmission line constraints are usually avoided in studies [4], but we chose to implement this constraint in order to verify the efficiency of SA when the model of the problem contains a greater number of constraints. We also point out in this work the complete implementation of Fiacco’s Theorem, with the possibility of perturbing equality and inequality constraints. Studies of cases were carried out in the IEEE 14, 118 and 300 buses systems, where the efficiency of the presented technique was verified. This paper is organized as follows: the OPF problem and a brief review of the primal–dual logarithmic barrier method are presented, next the formulation used for the SA is shown and, finally, the studies of cases and the conclusions are presented.
The aim of this paper was to accomplish studies of cases in power systems by SA technique, which is based on the Fiacco’s Theorem. The base case solution used as start point in SA, was obtained by OPF. The OPF problem was solved by the primal–dual logarithmic barrier method. The transmission line constraint was considered in the OPF and in the SA model.
Perturbations were introduced in the limit of the active transmission line constraint and in the load of the system. It was observed that the feasible operation points for the studied system provided by the SA and OPF are very similar. The error for the balance equations, evaluated by SA, was accepted for a given tolerance. The SA allows verifying the power system performance as long as perturbations occur, without the need to execute an OPF for each perturbation. The results obtained showed the efficiency of this technique in the studies of system planning. The main advantage of the SA approach is that, unlike the OPF, it is not iterative and it does not demand to estimate the initial barrier parameter and its correction factor. Thus, it allows not only to follow the load variations, but also to analyze, fast and efficiently, different strategies of adjustments.
