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.