基于Hilbert变换的非正弦电路无功及瞬时无功功率定义

非正弦电路无功功率及瞬时无功功率尚无统一的定义。文中从传统单相正弦电路功率的另一种表述出发，给出了基于Hilbert变换、适用非正弦单相电路的无功功率以及瞬时无功功率定义。其中，无功功率定义为电压Hilbert变换与电流共同作用产生的平均功率，瞬时无功功率定义为电压Hilbert变换与电流无功分量瞬时值的乘积，而电流无功分量定义为电流在电压Hilbert变换上的投影。该定义满足功率定义的一般要求，具有与有功功率及瞬时有功功率定义相同的表示形式和特性，同时满足方向性和平均性条件。最后通过具体算例验证了其正确性。

AVERAGE AND INSTANTANEOUS REACTIVE POWER OF NON-SINUSOIDAL CIRCUIT BASED ON HILBERT TRANSFORMATION

So far there have been no widely accepted definitions of average and instantaneous reactive power for non-sinusoidal alternating-current.(AC) circuit. A new definition of reactive power for sinusoidal circuit is discussed. Then the definitions of average and instantaneous reactive power based on Hilbert transforrnation for non-sinusoidal circuit are presented. The average reactive power is defihed as average power between current and voltage after Hilbert transforrnation. The instantaneous reactive power is defined as product of reactive component of current and voltage after Hilbert transforrnation. The reactive component of current is defined as projection of current on voltage aiter Hilbert transformation. These new definitions satisfy the general requirements of power, conform to definitions and characteristics of average and instantaneous active power, and meet the requirements of average and directionally. An application example is given to verify the new definitions.