Abstract
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.
Highlights
The majority of low-voltage distribution systems are unbalanced, mainly owing to the use of single-phase loads
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
If we extend the vector expressions (28)–(30) that have been defined in previous sections for m = n = 1 to the remaining harmonic combinations of m and n, that is, for each m, n and m = n, 1, we obtain the harmonic vectors expressions according to (66)–(68)
Summary
The majority of low-voltage distribution systems are unbalanced, mainly owing to the use of single-phase loads. It presents the same problem as [16] since they use the unbalance factors δ− and δ0 to consider the unbalance power caused by the unbalanced voltages Other authors extend their studies to the analysis of non-linear three-phase systems [19,20]. 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].
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