Constraints of instantaneous reactive power p-q theory

The instantaneous reactive power (IRP) p-q theory can be acknowledged as the first concept that provided fundamentals for switching compensator control and very often such a control is satisfactory. There are situations when this control can result in objectionable effects, however. Instantaneous active and reactive powers, p and q, defined in the IRP p-q theory, were introduced with the emphasis that the definitions of these powers are valid for any three-phase system, without any constraints as to the system properties with respect to the load structure and the supply voltages and load currents waveform. This may imply a conclusion that the instantaneous powers p and q specify the power properties of the three-phase systems regardless of such systems properties. This assurance regarding the lack of constraints has contributed to the dissemination of the IRP p-q theory, especially as a fundamental of the algorithms for switching compensator control. This study shows that such a conclusion has no ground, however. In fact, only at very specific properties of the three-phase system some conclusions on its power properties can be derived from the values of the instantaneous active and reactive powers. Also, it shows that the IRP p-q theory identifies the power properties of the three-phase loads correctly only on the condition that such loads are supplied with symmetrical and sinusoidal voltage.