Generalization of reactive power definition for periodical waveforms

Abstract

The article presents a selection of reactive power definitions, which are applicable for implementation in energy meters. For sinusoidal current and voltage waveforms, all provided dependencies yield equivalent reactive power values. However, in the presence of distorted current and voltage, the power values are determined by the applied method (algorithm). Standardization requirements for reactive energy meters stipulate metrological verification under sinusoidal conditions. The selection of an optimal reactive power definition remains a problematic and ongoing subject of debate within the field. The paper shows that a generalized unique definition of additive reactive power derives from the definition of active power. Unlike active power, reactive power must be independent of the conversion of electric energy into work and heat. This independence is achieved if one of the waveforms – the current in the scalar voltage and current product (specifying active power) – is replaced by a special orthogonal waveform. An orthogonal waveform can be derived through either differentiation or integration. Reactive power obtained by this method is an additive within the system. When differentiation is employed, the reactive power for a nonlinear resistive load with a unique, time-invariant current-voltage characteristic will be zero. Some other properties of reactive power defined in this way are presented. This method is straightforward to implement in reactive energy meters.