One methodology for optimal compensation of reactive energy of a TS 110/x kV consumption
Authors: Kovačević Branka 
Published: August 2024

When considering the task of optimal compensation of reactive energy in the distribution network of some TS 110/X kV, the aim is to optimally locate capacitor banks. The mathematical model of the distribution network theoretically allows treating each node of the network as a potential location for the installation of capacitor banks. However, it is clear that this is not the case in practice. Therefore, when choosing potential locations for the installation of capacitor banks, attention should be paid to objective limitations, such as the type of node (busbar, line node), the existence of already installed capacitor banks, available cells and space both in the medium voltage transformer substations and in the TS X/0.4 kV, availability (ownership) of the observed node (bus). In addition to these objective limitations, in models of distribution networks characterized by a particularly large number of nodes, it is convenient to preliminarily select a narrower set of potential locations based on the analysis of sensitivity and voltage conditions. In this way, the application of the algorithm for the optimal distribution and sizing of capacitor banks becomes practically feasible in the case of such networks. In order to be able to assess the suitability of a solution when solving optimization tasks, a suitable criterion function is defined. The value of the criterion function, for the given values of the parameters, that is, for the potential solution of the task, is a reflection of how successfully the given solution fulfils the requirements of the optimization task. In this way, it is possible to see the relative advantage of a solution compared to others. On the other hand, the value of the criterion function for the optimal solution provides information about the cost of the investment that is necessary for the realization of the optimal solution, as well as about the investment payback time. The criterion function is usually defined as a total cost, when the goal is to minimize this total cost, or as a difference between savings and investment cost, when the goal is to maximize this difference. Since it is easier to implement, the total cost criterion function was used in this case. As an algorithm for the optimal distribution and sizing of capacitor batteries in the distribution network, from the point of view of usability for needs, as well as convenience for implementation, an algorithm based on the method of local variations was used. The method of local variations is based on the simple idea that for each of the previously selected candidate nodes for the installation of capacitor banks, the suitability of a given position in the network and the corresponding capacity of the capacitor bank is iteratively tested. Eligibility is monitored via the resulting value of the criterion function. The algorithm gradually adds capacitor batteries to the network from iteration to iteration, until the moment when the value of the criterion function in the next iteration does not achieve a more favorable value compared to the previous iteration or if the previously selected maximum number of iterations is reached. The method of local variations is supplemented by one step which, in the case of medium voltage networks with a large number of nodes, enables the determination of a narrower set of potential nodes for the installation of capacitor banks. This step is optional and can be skipped for networks of a standard size of a few hundred nodes. What should be noted is that the described algorithm has the possibility of self-correction, since in subsequent iterations it checks the adequacy of the compensation level of the node where the installation of the capacitor battery was previously proposed. In order to enable the most appropriate solution proposal for a certain distribution consumption, in the implementation of the algorithm it is possible to choose the type of capacitor battery that can be proposed as part of the optimization procedure. Thus, the choice between fixed capacitor batteries, capacitor batteries of variable power and mixed type (a system of capacitor batteries composed of a fixed and a variable part) is foreseen. The algorithm is implemented within the DPL programming language, which is an integral part of the DIgSILENT PowerFactory software tool.