Unbalanced and Reactive Currents Compensation in Three-Phase Four-Wire Sinusoidal Power Systems

Abstract

In an unbalanced linear three-phase electrical system, there are inefficient powers that increase the apparent power supplied by the network, line losses, machine malfunctions, etc. These inefficiencies are mainly due to the use of unbalanced loads. Unlike a three-wire unbalanced system, a four-wire system has zero sequence currents that circulate through the neutral wire and can be compensated by means of compensation equipment, which prevents it from being delivered by the network. To design a compensator that works with unbalanced voltages, it is necessary to consider the interactions between it and the other compensators used to compensate for negative-sequence currents and positive-sequence reactive currents. In this paper, through passive compensation, a new method is proposed to develop the zero sequence current compensation equipment. The method does not require iteration algorithms and is valid for unbalanced voltages. In addition, the interactions between all compensators are analyzed, and the necessary modifications in the calculations are proposed to obtain a total compensation. To facilitate the application of the method and demonstrate its validity, a case study is developed from a three-phase linear four-wire system with unbalanced voltages and loads. The results obtained are compared with other compensation methods that also use passive elements.

An Alternate Representation of the Vector of Apparent Power and Unbalanced Power in Three-Phase Electrical Systems

“…The main objective of this paper is to propose the vector expressions necessary to quantify the unbalanced powers and, as a consequence, the total apparent powers of an unbalanced three-phase linear system. These expressions are valid for perfectly analysing systems with balanced and unbalanced voltages y, and in both cases, it allows us to develop passive compensators for unbalance powers due to negative and zero-sequence currents [21,22]. The modulus of the total apparent power obtained at any node in the system coincides with the apparent power of Buchholz.…”

“…As described in the previous sections, from the symmetric components of voltages, any unbalanced linear three-phase system is divided into three linear three-phase systems. S v+ , S v− , and S v0 are the apparent powers in each of these three systems, and their RMS values are calculated from (19), (22), and (23). Each of these expressions can be expressed in vector form three apparent power vectors: positive-sequence voltage apparent power vector − − → S v+ , negative-sequence voltage apparent power vector − − → S v− , and zero-sequence voltage apparent power vector − − → S v0 .…”

“…Furthermore, the decomposition of the apparent powers in different sequences helped the authors to obtain a passive compensator for the negative sequence current [21], treating the reactive power Q z− z+ in a similar way to the compensation of the positive-sequence reactive power. It was also applied to the development of a passive compensator for the zero-sequence current consumed by the load [22]. These compensators respond correctly for both balanced and unbalanced voltages.…”

Passive Reactive Power Compensators for Improving the Sustainability of Three-Phase, Four-Wire Sinusoidal Systems Supplied by Unbalanced Voltages

“…Topology and elements of all reactive power compensators mentioned above have been determined by applying Ohm's law and Fortescue's theorem [11] under the consideration these devices must supply fundamental-frequency reactive currents of positive, negative and zero sequences. The use of Fortescue's theorem is the key that determines topology differences between our compensators and the industrial capacitor banks, Jeon's compensators, and similar passive devices described in [21,22]. Since Fortescue's theorem is not applied to implement latter passive compensators, these can only compensate the Topology and elements of all reactive power compensators mentioned above have been determined by applying Ohm's law and Fortescue's theorem [11] under the consideration these devices must supply fundamental-frequency reactive currents of positive, negative and zero sequences.…”

“…Since Fortescue's theorem is not applied to implement latter passive compensators, these can only compensate the Topology and elements of all reactive power compensators mentioned above have been determined by applying Ohm's law and Fortescue's theorem [11] under the consideration these devices must supply fundamental-frequency reactive currents of positive, negative and zero sequences. The use of Fortescue's theorem is the key that determines topology differences between our compensators and the industrial capacitor banks, Jeon's compensators, and similar passive devices described in [21,22]. Since Fortescue's theorem is not applied to implement latter passive compensators, these can only compensate the total reactive powers, but they are not able to compensate separately each of the reactive power components.…”