On electrical power evaluation in dq coordinates under sinusoidal unbalanced conditions

• Published in: IET generation, transmission & distribution Vol. 8; no. 5; pp. 976 - 982
• Main Authors: Reginatto, Romeu, Ramos, Rodrigo A
• Format: Journal Article
• Language: English
• Published: Stevenage The Institution of Engineering and Technology 01.05.2014; Institution of Engineering and Technology; The Institution of Engineering & Technology
• Subjects: abc coordinates; Active control; active power; Applied sciences; Consistency; Control systems; control variables; Distributed generation; distributed power generation; dqo coordinates; Electric potential; Electric power generation; Electric power plants; Electrical engineering. Electrical power engineering; Electrical power engineering; electrical power evaluation; Exact sciences and technology; Exact solutions; IEEE 1459‐2010 standard; machine modelling; Mathematical analysis; Mathematical models; Miscellaneous; phasor measurement; phasor‐based analytical expression; power evaluation; power expressions; power factor; Power networks and lines; power system stability; power systems; Reactive power; sequence components; sinusoidal unbalanced conditions; sinusoidal unbalanced voltage; unbalanced distributed generation systems; voltage‐current imbalance; abc coordinates; power system stability; control variables; distributed power generation; power evaluation; voltage-current imbalance; power factor; dqo coordinates; electrical power evaluation; sinusoidal unbalanced voltage; sequence components; power expressions; sinusoidal unbalanced conditions; reactive power; phasor-based analytical expression; IEEE 1459-2010 standard; active power; power systems; phasor measurement; machine modelling; unbalanced distributed generation systems; Sinusoidal conditions; Phasor; Unbalanced conditions; Distributed power generation; Distributed system; Absorbing boundary condition; Modeling; Reactive power; Electrical network; Analytical method; Power factor; IEEE standards; Electric power production; Apparent power; Compatibility
• ISSN: 1751-8687; 1751-8695
• DOI: 10.1049/iet-gtd.2013.0532

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.