Abstract
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.
Highlights
Power theory has scientific, engineering and economic relevance
Since the power factor (PF) and apparent power (AP) can be identified with measurement made at a point of connection or common coupling (PCC) of a power supply to a load or other network, this power theory has many potential applications, such as in converters, loss reduction in delivery systems and loads, dispatching of embedded or distributed generation (DG) into systems, and in electricity trading and tariffs
The relation, derived from the fundamental and harmonic voltages measured at the PCC, was reproduced in many publications, extended to three-phase loads and adopted in IEEE definitions and standards [2], [42] without referring to the delivery system impedances
Summary
Power theory has scientific, engineering and economic relevance It identifies the relationships between parameters of power systems, such as voltages, currents, delivered power and the losses incurred, as explored in the literature review section. This paper presents a new, more general formulation of power theory for any poly-phase systems, including a neutral or without it, with any periodic non-sinusoidal waveforms and dc components, voltage and current unbalance, and unequal and/or frequency-dependent wire impedances. Since the PF and AP can be identified with measurement made at a point of connection or common coupling (PCC) of a power supply to a load or other network, this power theory has many potential applications, such as in converters, loss reduction in delivery systems and loads, dispatching of embedded or distributed generation (DG) into systems, and in electricity trading and tariffs.
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