Networks of 0.4 kV are characterized by a large unbalance of loads in phases. Current unbalance leads to voltage unbalance and additional losses of electrical energy. As a result, the voltage at the consumer may not meet the quality standards of electrical energy. In addition, due to unbalance, the service life of electrical equipment is reduced. Since the effect of stress balancing significantly depends on the place of balancing loads on the line, the paper proposes to determine the places of balancing loads by solving a multicriteria optimization problem. The paper proposes an objective function that minimizes active power losses and contains the total index of active power losses and indices of voltage unbalance coefficients in the negative and zero sequence.
The purpose of the study is to obtain an effective objective function for determining the places of balancing loads and voltages in the network, which ensures a minimum of active power losses and the values of the voltage unbalance factors within the required limits; conduct a study of balancing loads and voltages depending on the places of balancing.
Materials and methods. In the work, methods for calculating electrical networks were used, taking into account voltage losses and active power. To study the places of balancing loads and voltages, the method of multicriteria optimization with restrictions was used. The study of the objective function was carried out on a mathematical model of a low voltage overhead line. All calculations were carried out in MATLAB.
Research results. A review and analysis of modern tools and methods for balancing loads and voltages in low voltage networks has been carried out. As a result of the analysis, it was concluded that there is no algorithm for determining the places of load balancing in low-voltage networks that provide minimal active power losses and the values of the voltage unbalance factors within the required limits. The task of finding places for balancing loads and voltages is a multiobjective optimization problem with constraints. Therefore, an objective function was proposed that minimizes active power losses in the network and contains the total index of active power losses and indices of voltage unbalance coefficients for the reverse and zero sequence. To study the proposed objective function, a model overhead line of a 0.4 kV network with specified phase loads and voltages was used. For the model line, the calculation of active power losses and the values of the voltage unbalance coefficients in the initial mode before balancing was carried out. All calculations were carried out for each phase separately. At the first stage, the calculation of the sensitivity coefficients of active power losses and the sensitivity coefficients for the voltage unbalance coefficients was carried out. To study the balancing of loads, nodes were selected that have the maximum values of the sensitivity coefficients. It follows from the calculation results that the best effect from balancing is observed when balancing loads simultaneously in two nodes: in the node with the highest value of the total sensitivity factor of active power losses, and in the node with the maximum value of the phase sensitivity factor of active power losses. When balancing loads in only one of the nodes, the most optimal of the selected ones will be the node most remote from the TS. We also obtained weight coefficients that provide a minimum of the objective function.
Conclusions. The proposed objective function is effective for determining the places of load and voltage balancing in low voltage networks. In this case, the best effect is observed when balancing loads in nodes that have the highest values of the sensitivity coefficients of total active power losses and by phases. The node most remote from the TP will be more optimal. When balancing loads in places determined using the proposed objective function, it is possible to reduce power losses and ensure the values of the unbalance coefficients in the nodes on the line less than the maximum allowable value.
