Electromagnetic compatibility - General - Part 7: Power factor in single-phase systems under non-sinusoidal conditions
1 Scope
This document provides definitions of various electrical power quantities and the relationship between them under non-sinusoidal conditions, in order to give clear information on both components in the power factor: the fundamental power factor, which is due to the phase difference between the voltage and current at the fundamental frequency, and the non-fundamental power factor, which is related to the distortion of the voltage and/or current.
This document is applicable only to single-phase systems.
This document provides definitions for the three following cases:
——the general case where the voltage and current are both distorted (Clause 5),
——the case where the voltage is assumed to be sinusoidal and the current is only distorted with harmonic components (Clause 6),
——the particular case where the voltage and current are both sinusoidal (Annex A).
Annex B gives information on the fundamental active factor, which is used to describe the behaviour of a piece of equipment as a load or a generator.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
root-mean-square value
r.m.s. value
effective value
for a time-dependent quantity, positive square root of the mean value of the square of the quantity taken over a given time interval
Note 1: The root-mean-square value of a periodic quantity is usually taken over an integration interval the range of which is the period multiplied by a natural number.
Note 3: The root-mean-square value of a quantity may be denoted by adding one of the subscripts eff or rms to the symbol of the quantity.
Note 4 to entry: In electrical technology, the root-mean-square values of electric current i(t) and voltage u(t) are usually denoted I and U, respectively.
[SOURCE: GB/T 2900.92-2015, 103-02-03]
3.2
direct component
mean value of a quantity taken over a given time interval
[SOURCE: GB/T 2900.92-2015, 103-06-05, modified - definition extended to quantities
containing interharmonic components.]
3.3
sinusoidal
pertaining to an alternating quantity represented by the product of a real constant and a sine or cosine function whose argument is a linear function of the independent variable
Note 1: The real constant may be a scalar, vector or tensor quantity.
[SOURCE: GB/T 2900.92-2015, 103-07-01]
3.4
initial phase
phase angle
value of the phase of a sinusoidal quantity when the value of the independent variable is zero
[SOURCE: GB/T 2900.92-2015, 103-07-05]
3.5
periodic conditions
state of an electric circuit element or electric circuit that is characterized by the electric currents and voltages all being periodic functions of time with the same period T
[SOURCE: GB/T 2900.74-2008, 131-11-27, modified - addition of symbol T for the period.]
3.6
sinusoidal conditions
state of a linear electric circuit element or electric circuit that is characterized by the electric currents and voltages all being sinusoidal functions of time with the same frequency
[SOURCE: GB/T 2900.74-2008, 131-11-28]
3.7
instantaneous power
p(t)
for a two-terminal element or a two-terminal circuit with terminals A and B, product of the
voltage uAB between the terminals and the electric current i in the element or circuit
p(t) = uAB(t) ⋅ i(t)
where uAB is the line integral of the electric field strength from A to B, and where the electric current in the element or circuit is taken positive if its direction is from A to B and negative if its direction is from B to A
Note 1: The direction of electric current is as defined in GB/T 2900.74-2008, 131-11-29.
Note 2: In circuit theory the electric field strength is generally non-rotational and thus uAB = VA - VB, where VA and VB are the electric potentials at terminals A and B, respectively.
Note 3: The coherent SI unit of instantaneous power is watt, W.
Note 4: A two-terminal element or circuit refers to a single-phase equipment or system.
[SOURCE: IEC 60050-131 :2013, 131-11-30, modified - a new note 4 has been added.]
3.8
apparent power
S
product of the r.m.s. voltage U between the terminals of a two-terminal element or two-terminal circuit and the r.m.s. electric current I in the element or circuit
S = UI
Note 1: The coherent SI unit for apparent power is voltampere, VA.
Note 2: A two-terminal element or circuit refers to a single-phase equipment or system.
[SOURCE: IEC 60050-131:2013, 131-11-41, modified - the existing note 1 has been removed and a note 2 has been added.]
3.9
active power
P
under periodic conditions, mean value, taken over one period T, of the instantaneous power p(t)
Note 1: The coherent SI unit for active power is watt, W.
Note 2: When the voltage or current contain interharmonic components, often their waveforms are no more periodic. In this document, the active power is approximated by the mean value of the instantaneous power, taken over an integer number of periods of the a.c. power supply system (see 5.3.1 and 5.1.4). This definition is also used under periodic conditions in this document (see 6.3 and Clause A.3).
[SOURCE: IEC 60050-131:2013, 131-11-42, modified - the existing note 1 has been removed and a note 2 has been added.]
3.10
non-active power
Q~
for a two-terminal element or a two-terminal circuit under periodic conditions, quantity equal to the square root of the difference of the squares of the apparent power S and the active power P
Note 1: The coherent SI unit for non-active power is voltampere, VA. The special name "var" and its symbol "var" are also used. See IEC 60050-131:201 3, 131-11-45.
Note 2: A two-terminal element or circuit refers to a single-phase equipment or system.
[SOURCE: IEC 60050-131:2013, 131-11-43, modified - the existing note 1 has been removed and a note 2 has been added.]
3.11
reactive power
Q
for a linear two-terminal element or two-terminal circuit, under sinusoidal conditions, quantity equal to the product of the apparent power S and the sine of the displacement angle φ
Q = S X sinϕ
Note 1: The coherent SI unit for reactive power is voltampere, VA. The special name var and its symbol var are also used. See IEC 60050-131:2013, 131-11-45.
Note 2: A two-terminal element or circuit refers to a single-phase equipment or system.
Note 3: When the conditions are not sinusoidal, there is no international consensus on a definition of the reactive power. Instead, several definitions of the reactive power exist. In some documents, the reactive power is taken as the non-active power, but there are many other formulae.
[SOURCE: IEC 60050-131 :2013, 131-11-44, modified - the existing note 1 has been removed and notes 2 and 3 have been added.]
3.12
power factor
λ
ratio of the absolute value of the active power P to the apparent power S
Note: Under sinusoidal conditions, the power factor is the absolute value of the active factor.
[SOURCE: IEC 60050-131:2002, 131-11-46, modified - definition extended to quantities containing interharmonic components.]
3.13
displacement angle
phase difference angle
φ
under sinusoidal conditions, phase difference between the voltage applied to a linear two-terminal element or two-terminal circuit and the electric current in the element or circuit
