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On electrical power evaluation in dq coordinates under sinusoidal unbalanced conditions


On electrical power evaluation in dq coordinates under sinusoidal unbalanced conditions (2014)


This study develops a phasor-based analytical expression for the reactive power in dqo coordinates, which exhibits compatibility with IEEE Standard 1459-2010 under sinusoidal unbalanced conditions. The dqo coordinates are often employed in power systems, for instance in machine modelling, but the power expressions are provided in the IEEE Standard only in terms of the abc coordinates and the sequence components. In addition, the usual complex product vdqi*dq for power evaluation in the dqo coordinates does not exhibit reactive power consistency with the IEEE standard but for the balanced case. Such consistency becomes a central issue in the context of distributed generation systems since they are often subject to voltage/current imbalance, and the active power, the reactive power, and the power factor are important control variables and, as such, require calculation and measurement. This study provides a complete set of phasor-based analytical expressions (including the instantaneous, active, reactive, complex and apparent powers) in dqo coordinates which help stability and control developments of unbalanced distributed generation systems. An example of a distributed generation system with sinusoidal unbalanced voltage is given to illustrate the contribution.

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