# A Multi-Period Optimal Reactive Power Dispatch Approach Considering Multiple Operative Goals
## 1 Introduction
Under real-time circumstances, solutions provided by traditional ORPD models may not be practical because the number of control actions would be too large to be executed in actual power system operation [32]; furthermore, the computing time plays a key role in such applications. The multi-period ORPD (MP-ORPD) was originally proposed in [33]; its main focus is dealing with different loading conditions for a given future time interval instead of a single snapshot of the power network. The set of desirable features for real implementations of the MP-ORPD programs is extensive and can make the solution of the model a complex task. In this case, the control actions must be valid within a given time horizon, the improvement of the voltage profile can be achieved by resorting to pilot nodes, and the number of control actions must not be excessive. A compilation of such features is presented in [34]. Compared with its traditional or static counterpart, the MP-ORPD is a more complex optimization problem involving multiple local minima as well as nonlinear and discontinuous constraints [32]. Relatively few studies have approached the dynamic MP-ORPD. In this case, the most common objective function corresponds to the minimization of power losses. In [35], a day-ahead reactive power dispatch was proposed with the aim of minimizing active power losses for wind power plants. In [36], the authors approached the ORPD problem by considering the time-varying demand and renewable energy uncertainty. In this case, the authors implemented the so called Rao-3 algorithm to solve the MP-ORPD problem. In [37], the MP-ORPD was approached through chance-constrained programming. In [38], a dynamic optimal reactive power flow considering several time intervals was carried out, taking into account voltage stability. In this case, the problem was solved by means of a branch and bound primal-dual interior point method and different areas were considered. In [39; 40], the authors also proposed ORPD schemes for power loss reductions over a 24 h time horizon. This paper presents a novel approach to solve the MP-ORPD problem. The main features and contributions that differentiate this study from other papers reported in the literature are as follows:  
* The proposed MP-ORPD is envisaged from the point of view of a power system operator; in this case, a single objective function is not pursued as such, but instead a set of goals regarding the minimization of deviations from desired operational values are considered;
* The main goal of the MP-ORPD is guaranteeing operative feasibility throughout a given time horizon, while minimizing the number of maneuvers carried out in reactive power devices and transformers taps, preserving their useful life and reducing eventual maintenance costs;
* Instead of considering all buses to enforce voltage limit constraints, only a set of pilot nodes are taken into account. Furthermore, dynamic limits are considered in these buses to mimic real-life operation. This results in low computational effort, which encourages real-life applications of the methodology. This work is organized as follows. Section 1 presents a literature review of the ORPD problem. Section 2 describes the relevant aspects of the proposed model and other considerations taken into account. Section 3 presents the tests and results with the IEEE 57-bus and IEEE 118-bus test systems. Finally, the conclusions are presented in Section 4.