Active Currents, Power Factor, and Apparent Power for Practical Power Delivery Systems

Concepts of apparent power and power factor as measures of a system's power delivery capability are over a century old but have not been defined in one general, rigorous and acceptable way. Instantaneous power is defined precisely, and average power measured over a selected period is widely accepted. The many ways of defining and measuring reactive and apparent power in single and three phase systems are based on different assumptions and give different results in real cases. Building on definitions in the IEEE Standard 1459-2010, this paper formulates in vector space linear algebra and the frequency domain, the active wire currents as those that cause the minimum losses in a network for the power delivered. Power factor measures the relative efficiency of power delivery as defined by the losses. Apparent power consistent with early terminology is the maximum power that can be sourced for the same original line losses and has the unit of power: Watt. It is identified without requiring the contentious concept of reactive and non-active power components. Measurements based on this approach are independent of assumptions about sinusoidal waveform, voltage and current balance, and frequency-dependent wire resistances, and apply to power delivery systems with any number of wires. The rigor of this novel general formulation is important for technical design of compensators and inverters; analyzing power system losses, delivery efficiency and voltage stability; and electricity cost allocation and pricing.