|
|
| (11 intermediate revisions by 5 users not shown) |
| Line 1: |
Line 1: |
| {{Menu_Power_factor_correction_and_harmonic_filtering}} | | {{Menu_Power_Factor_Correction}} |
| __TOC__
| | The Power Factor is an indicator of the quality of design and management of an electrical installation. It relies on two very basic notions: active and apparent power. |
|
| |
|
| == Definition of power factor ==
| | The '''active power P (kW)''' is the real power transmitted to loads such as motors, lamps, heaters, and computers. The electrical active power is transformed into mechanical power, heat or light. |
|
| |
|
| {| cellspacing="1" cellpadding="1" width="65%" border="1"
| | In a circuit where the applied r.m.s. voltage is V<sub>rms</sub> and the circulating r.m.s. current is I<sub>rms</sub>, the '''apparent power S (kVA)''' is the product: V<sub>rms</sub> x I<sub>rms</sub>. |
| |-
| |
| | bgcolor="#0099cc" | The power factor is the ratio of kW to kVA. The closer the power factor approaches its maximum possible value of 1, the greater the benefit to consumer and supplier.<br>PF = P (kW) / S (kVA)<br>P = Active power<br>S = Apparent power
| |
| |}
| |
|
| |
|
| The power factor of a load, which may be a single power-consuming item, or a number of items (for example an entire installation), is given by the ratio of P/S i.e. kW divided by kVA at any given moment.<br>The value of a power factor will range from 0 to 1.<br>If currents and voltages are perfectly sinusoidal signals, power factor equals cos <span class="texhtml">φ</span>.<br>A power factor close to unity means that the reactive energy is small compared with the active energy, while a low value of power factor indicates the opposite condition. | | The apparent power is the basis for electrical equipment rating. |
|
| |
|
| == Power vector diagram ==
| | The '''Power Factor''' λ is the ratio of the active power P (kW) to the apparent power S (kVA): |
|
| |
|
| *Active power P (in kW)
| | <math> \lambda = \frac {P(kW)}{S(kVA)}</math> |
|
| |
|
| - Single phase (1 phase and neutral): P = V I cos <span class="texhtml">φ</span> <br> - Single phase (phase to phase): P = U I cos <span class="texhtml">φ</span><br> - Three phase (3 wires or 3 wires + neutral): P = <math>\sqrt 3</math> U I cos <span class="texhtml">φ</span>
| | The load may be a single power-consuming item, or a number of items (for example an entire installation). |
|
| |
|
| *Reactive power Q (in kvar)
| | The value of power factor will range from 0 to 1. |
| | |
| - Single phase (1 phase and neutral): P = V I sin <span class="texhtml">φ</span><br>- Single phase (phase to phase): Q = U I sin <span class="texhtml">φ</span><br>- Three phase (3 wires or 3 wires + neutral): P = <math>\sqrt 3</math> U I sin <span class="texhtml">φ</span>
| |
| | |
| *Apparent power S (in kVA)
| |
| | |
| - Single phase (1 phase and neutral): S = V I<br> - Single phase (phase to phase): S = U I<br> - Three phase (3 wires or 3 wires + neutral): P = <math>\sqrt 3</math> U I <br>where:<br>V = Voltage between phase and neutral<br>U = Voltage between phases<br>I = Line current<br><span class="texhtml">φ</span> = Phase angle between vectors V and I. <br> - For balanced and near-balanced loads on 4-wire systems
| |
| | |
| == Current and voltage vectors, and derivation of the power diagram ==
| |
| | |
| The power “vector” diagram is a useful artifice, derived directly from the true rotating vector diagram of currents and voltage, as follows: | |
| | |
| The power-system voltages are taken as the reference quantities, and one phase only is considered on the assumption of balanced 3-phase loading.
| |
| | |
| The reference phase voltage (V) is co-incident with the horizontal axis, and the current (I) of that phase will, for practically all power-system loads, lag the voltage by an angle <span class="texhtml">φ</span>.
| |
| | |
| The component of I which is in phase with V is the “wattful” component of I and is equal to I cos <span class="texhtml">φ</span>, while VI cos <span class="texhtml">φ</span> equals the active power (in kW) in the circuit, if V is expressed in kV.
| |
| | |
| The component of I which lags 90 degrees behind V is the wattless component of I and is equal to I sin <span class="texhtml">φ</span>, while VI sin<span class="texhtml">φ</span> equals the reactive power (in kvar) in the circuit, if V is expressed in kV.
| |
| | |
| If the vector I is multiplied by V, expressed in kV, then VI equals the apparent power (in kVA) for the circuit.
| |
| | |
| The simple formula is obtained: S<sup>2</sup> = P<sup>2</sup> + Q<sup>2</sup>
| |
| | |
| The above kW, kvar and kVA values per phase, when multiplied by 3, can therefore conveniently represent the relationships of kVA, kW, kvar and power factor for a total 3-phase load, as shown in '''Figure L3'''.
| |
| | |
| | |
| [[Image:FigL03.jpg|none]]
| |
| '''''Fig. L3:''''' ''' Power diagram'''
| |
| | |
| | |
| == An example of power calculations (see '''Fig. L4''') ==
| |
| | |
| | |
| {| style="width: 797px; height: 177px" cellspacing="1" cellpadding="1" width="797" border="1"
| |
| |-
| |
| | bgcolor="#0099cc" colspan="2" | '''Type of circuit'''
| |
| | bgcolor="#0099cc" | '''Apparent power S (kVA)'''
| |
| | bgcolor="#0099cc" | '''Active power P (kW)'''
| |
| | bgcolor="#0099cc" | '''Reactive power Q (kvar)'''
| |
| |-
| |
| | colspan="2" | Single-phase (phase and neutral)
| |
| | S = VI
| |
| | P = VI cos <span class="texhtml">φ</span>
| |
| | Q = VI sin <span class="texhtml">φ</span>
| |
| |-
| |
| | colspan="2" | Single-phase (phase to phase)
| |
| | S = UI
| |
| | P = UI cos φ
| |
| | Q = UI sin <span class="texhtml">φ</span>
| |
| |-
| |
| | valign="top" rowspan="2" | Example
| |
| | 5 kW of load
| |
| | valign="top" rowspan="2" | 10 kVA
| |
| | valign="top" rowspan="2" | 5 kW
| |
| | valign="top" rowspan="2" | 8.7 kvar
| |
| |-
| |
| | cos <span class="texhtml">φ</span> = 0.5
| |
| |-
| |
| | colspan="2" | Three phase 3-wires or 3-wires + neutral
| |
| | S = <math>\sqrt 3</math> UI
| |
| | P = <math>\sqrt 3</math> UI cos <span class="texhtml">φ</span>
| |
| | Q = <math>\sqrt 3</math> UI sin <span class="texhtml">φ</span>
| |
| |-
| |
| | valign="top" rowspan="3" | Example
| |
| | Motor Pn = 51 kW
| |
| | valign="top" rowspan="3" | 65 kVA
| |
| | valign="top" rowspan="3" | 56 kW
| |
| | valign="top" rowspan="3" | 33 kvar
| |
| |-
| |
| | cos <span class="texhtml">φ</span>= 0.86
| |
| |-
| |
| | <span class="texhtml">ρ</span>= 0.91 (motor efficiency)
| |
| |}
| |
| | |
| '''''Fig. L4:''''' '' Example in the calculation of active and reactive power''
| |
| | |
| [[ru:Коэффициент мощности]]
| |
| [[zh:功率因数]]
| |
The Power Factor is an indicator of the quality of design and management of an electrical installation. It relies on two very basic notions: active and apparent power.
The active power P (kW) is the real power transmitted to loads such as motors, lamps, heaters, and computers. The electrical active power is transformed into mechanical power, heat or light.
In a circuit where the applied r.m.s. voltage is Vrms and the circulating r.m.s. current is Irms, the apparent power S (kVA) is the product: Vrms x Irms.
The apparent power is the basis for electrical equipment rating.
The Power Factor λ is the ratio of the active power P (kW) to the apparent power S (kVA):
[math]\displaystyle{ \lambda = \frac {P(kW)}{S(kVA)} }[/math]
The load may be a single power-consuming item, or a number of items (for example an entire installation).
The value of power factor will range from 0 to 1.
