The compensation of an electrical system from passive compensators mainly focuses on linear systems where the consumption of charges does not vary significantly over time. In three-phase three-wire systems, when the network voltages are unbalanced, negative-sequence voltages and currents appear, which can significantly increase the total apparent power supplied by the network. This also increases the network losses. This paper presents a method for calculating the compensation of the positive-sequence reactive power and unbalanced powers caused by the negative-sequence line currents using reactive elements (coils and/or capacitors). The compensation is applied to three-phase three-wire linear systems with unbalanced voltages and loads, which are connected to an infinite power network. The method is independent of the load characteristics, where only the line-to-line voltages and line currents, at the point where compensation is desired, need to be known in advance. The solution obtained is optimal, and the system observed from the network behaves as one that only consumes the active power required by a load with a fully balanced current system. To understand the proposed method and demonstrate its validity, a case study of a three-phase three-wire linear system connected to an infinite power network with unbalanced voltages and currents is conducted.Appl. Sci. 2020, 10, 113 2 of 17 these inefficient powers. According to [13,14], imbalances at one point in the system can help offset some of the imbalances at another point. Such situations cannot be analyzed if only the modules of voltages and currents are known.The application of electronics, in the compensation of electrical systems, indicates that most industries today mainly focus on the use of active compensators. The advantages of these compensators or filters cannot be denied, especially for the compensation of non-linear systems. As compared to passive compensators, the active compensators are more expensive, less robust, and consume more energy. In certain situations, for linear systems, where the load does not vary with time, the use of passive compensators is a good alternative. They are configured from reactive elements (coils and/or capacitors). In this study, passive compensators are used to compensate for the reactive and unbalanced power resulting from the negative-sequence current of any three-wire system.The concept of compensation of an electrical system by passive compensators is not new. Steinmetz [15] developed a passive compensator to obtain a system of balanced line currents. He used a single-phase load with known data, and compensated it with a coil and capacitor and we believe that the voltages in the study were balanced. This study has been extended by many authors [16][17][18][19][20][21][22][23][24].Gyugyi et al.[25] studied compensation through passive compensators for a three-wire linear system with unbalanced load and balanced voltages. For this purpose, they categorised the line currents into symmetric component values, and proposed...

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.

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For analysis of three-wire three-phase linear systems, the transformations 'wye-delta' and 'delta-wye' from Kennelly's theorem are used. These transformations can be applied to balanced systems but not to unbalanced systems. Depending on the type of connection that is used, zero-sequence voltages and currents appear in generators and loads and are not transferred over the network. The zero-sequence voltage in a delta-connected load and the zero-sequence current that is obtained using Kennelly's theorem in a star-connected load, or vice versa, cause different imbalance effects. In this work, the equivalent circuit for any point of the system is developed. The impedances of the equivalent circuit in any node are calculated using line-to-line voltages and line currents. This equivalent circuit incorporates all energetic phenomena, including the imbalance. For its calculation, the phasor unbalance power is used.

Low-voltage distribution systems are typically unbalanced. These inefficiencies cause unbalanced powers that can significantly increase the apparent power of the system. Analysing and measuring these inefficient powers appropriately allows us to compensate for them and obtain a more efficient system. Correcting the imbalance at some nodes can worsen the rest of the system; therefore, it is essential that all nodes are analysed such that action can be taken when necessary. In most studies, the unbalanced power is measured from the modulus. Other more recent studies have proposed phasor expressions of unbalanced powers; however, in both cases, these are not enough to address the compensation of unbalanced powers in systems with unbalanced voltages. In this work, a different representation of the vector expressions for analysis of the unbalanced powers and the apparent powers of the three-phase linear systems is proposed. Additionally, these vector expressions are extended to nonlinear systems to quantify the harmonic apparent powers. These expressions have been formulated from the power of Buchholz and are valid for systems with unbalanced voltages and currents. To help understand the use of the proposed formulation, a practical case of a three-phase four-wire system with unbalanced loads and voltages is demonstrated.