On the definition of power factor and apparent power in unbalanced polyphase circuits with sinusoidal voltage and currents

Abstract

This paper advocates much needed definitions for the apparent power S and f o r the power factor PF, in unbalanced polyphase circuits with sinusoidal waveforms. It is proved that the definition S2 = (V: + + V:)(Z; + I : + 1:) has a definite physical meaning, lending itself to a convenient resolution in positive, negative and zero sequence, nonactive and active powers. Zt is suggested to represent the power factor with the help of the ratio P + / S , where P+ is the positive sequence active power.

Error Analysis for Networks Supplying Unbalanced Nonlinear Load

“…This has been traditionally expressed through the concept of a power factor K that is defined in single-phase situations as the ratio between the average active power P and the apparent power S, with the latter being the product of the rms values of the voltage and current. However, in a non sinusoidal situation, the concept of power factor above has been proved to be misleading [9], [10]. Moreover, a universally accepted definition of the power factor in polyphase situations has been lacking and hotly debated for almost a century [11], [12].…”

“…In contrast, the apparent power S has no physical meaning since it does not consider the corresponding values of the voltage and current at each instant. Only in the special case when the instantaneous voltage bears a constant ratio to the instantaneous current does the apparent power equal P and, hence, acquires the physical meaning of the latter [10]. All the inadequacies and ambiguities above can be circumvented when the physical entity directly responsible for a poor utilization of the power capacity at the mains fundamental frequency is considered.…”

“…The ever-growing proliferation of power switching devices for source conditioning and motion control in single-phase and three-phase modern industrial applications has increased the eventuality of unbalanced currents, unacceptable harmonic levels, and poor power factor in threephase distribution systems. It is remarked that a low power transfer quality could be caused either by the power supply (through unbalanced supply voltages and/or voltage harmonics), by the load (nonlinear and/or unbalanced load), or by both [10]. The newly suggested PQF has the advantage of evaluating the power quality at any selected point in a distribution network by means of a single indicator rather than separately comparing a multitude of factors with their recommended values, which thus considerably simplifies the rate structures.…”

An improved design of virtual output impedance loop for droop-controlled parallel three-phase voltage source inverters

“…7 shows the block diagram of the dynamically-tuned negative resistance loop. A proportional relationship between the negative-sequence reactive power Q N , i [20] and the negative-sequence virtual resistance is introduced, so that the inverter with higher negative-sequence reactive power can furnish a higher negative-sequence resistance. The values of proportional coefficients for all inverters need to meet the following condition where k i is the coefficient of the proportional relationships in the i-th inverter.…”

Significado y medida de los fenómenos de desfase en los sistemas trifásicos desequilibrados, lineales. Aplicación a la medida en sistemas con conductor neutro

“…De entre sus numerosas publicaciones, en [41] y [43], pone de manifiesto su rechazo a que oscilaciones de energía, en el término de la potencia instantánea, debidas a asimetrías de carga puedan dar lugar a un incremento de la potencia aparente, lo que si acepta A. Emanuel [76] y [77].…”