The p-q theory uses a b 0 transformations and various definitions of active and reactive powers. The transformation of 3-Phase quantities (a-b-c) of stationary reference frame into 2-Phase quantities (a Ь 0) stationary reference frame is achieved by applying Clark’s transformation.

Performance Analysis-2Performance Analysis-3

Let the instantaneous real, imaginary and zero sequence power denoted by p, q and P0 respectively. Then the three phase instantaneous power is given by

Performance Analysis-4

The zero sequence components of the voltages and currents do not contribute to the instantaneous powers P and q .The instantaneous imaginary power, q is defined as

Fig2Performance Analysis

Fig. 2 : Block Diagram of IRP theory

It represents an energy that may be constant or not and that is being exchanged between the phases of the system. This implies that q does not contribute to the energy transfer between the source and the load at any time. From Eq. (2.20)-(2.21), we write p and q as following.

Performance Analysis-6

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