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For emolument of current harmonics (if any), the instantaneous resoluteness of different active and reactive powers is utilized - the active and reactive powers are computed utilizing p-q theory. No restrictions are imposed on the voltage or current wave forms, and it can be applied to three-phase systems with or without a neutral wire for three-phase generic voltage and current wave forms. Thus, it is valid not only in steady state, but withal in transient states.
The p-q Theory first transforms voltages and currents from the a-b-c to α-β-o coordinates, and then defines instantaneous power on these coordinates. Hence, this theory always considers the three-phase system as a unit, not a superposition or sum of three single-phase circuits. The p-q Theory utilizes the α-β-o transformation, additionally kenned as the Clarke transformation, which consists of an authentic matrix that transforms three-phase voltages and currents into the α-β-o stationary reference frames, given by:
[█(V_0@V_α@V_β )]=√3/2 [■(1/√2&1/√2&1/√2@1&-1/√2&-1/√3@0&√3/2&-√3/2)][█(V_a@V_b@V_c )]
[█(i_L0@i_Lα@i_Lβ )]=√3/2 [■(1/√2&1/√2&1/√2@1&-1/√2&-1/√3@0&√3/2&-√3/2)][█(i_La@i_Lb@i_Lc )]
By utilizing the α-β-o transformation the zero-sequence component can be disunited from the a-b-c phase components. The α and β axes make no contribution to zero-sequence components. If the three-phase system has three wires (no neutral conductor), no zero-sequence current components are present and i0 can be eliminated

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