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| {{Menu_Power_factor_correction_and_harmonic_filtering}} | | {{Menu_Power_Factor_Correction}} |
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| | 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. |
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| | 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
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| '''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. |
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| 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.
| | 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>. |
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| '''Power vector diagram'''
| | The apparent power is the basis for electrical equipment rating. |
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| *Active power P (in kW)
| | The '''Power Factor''' λ is the ratio of the active power P (kW) to the apparent power S (kVA): |
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| - 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>
| | <math> \lambda = \frac {P(kW)}{S(kVA)}</math> |
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| *Reactive power Q (in kvar)
| | The load may be a single power-consuming item, or a number of items (for example an entire installation). |
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| - 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>
| | The value of power factor will range from 0 to 1. |
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| *Apparent power S (in kVA)
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| - 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
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| '''Current and voltage vectors, and derivation of the power diagram'''<br>The power “vector” diagram is a useful artifice, derived directly from the true rotating vector diagram of currents and voltage, as follows:<br>The power-system voltages are taken as the reference quantities, and one phase only is considered on the assumption of balanced 3-phase loading.<br>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>.<br>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.<br>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.<br>If the vector I is multiplied by V, expressed in kV, then VI equals the apparent power (in kVA) for the circuit.<br>The simple formula is obtained: S<sup>2</sup> = P<sup>2</sup> + Q<sup>2</sup><br>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'''.
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| <br>[[Image:FigL03.jpg|left]] <br><br><br><br><br><br><br><br><br><br><br>'''''Fig. L3:'''''<i> Power diagram</i>
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| '''An example of power calculations '''(see '''Fig. L4)'''
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| | bgcolor="#0099cc" colspan="2" | '''Type of circuit'''
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| | bgcolor="#0099cc" | '''Apparent power S (kVA)'''
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| | bgcolor="#0099cc" | '''Active power P (kW)'''
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| | bgcolor="#0099cc" | '''Reactive power Q (kvar)'''
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| | colspan="2" | Single-phase (phase and neutral)
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| | S = VI
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| | P = VI cos <span class="texhtml">φ</span>
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| | Q = VI sin <span class="texhtml">φ</span>
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| | colspan="2" | Single-phase (phase to phase)
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| | S = UI
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| | P = UI cos φ
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| | Q = UI sin <span class="texhtml">φ</span>
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| | valign="top" rowspan="2" | Example
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| | 5 kW of load
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| | valign="top" rowspan="2" | 10 kVA
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| | valign="top" rowspan="2" | 5 kW
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| | valign="top" rowspan="2" | 8.7 kvar
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| | cos <span class="texhtml">φ</span> = 0.5
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| | colspan="2" | Three phase 3-wires or 3-wires + neutral
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| | S = <math>\sqrt 3</math> UI
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| | P = <math>\sqrt 3</math> UI cos <span class="texhtml">φ</span>
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| | Q = <math>\sqrt 3</math> UI sin <span class="texhtml">φ</span>
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| | valign="top" rowspan="3" | Example
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| | Motor Pn = 51 kW
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| | valign="top" rowspan="3" | 65 kVA
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| | valign="top" rowspan="3" | 56 kW
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| | valign="top" rowspan="3" | 33 kvar
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| | cos <span class="texhtml">φ</span>= 0.86
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| | <span class="texhtml">ρ</span>= 0.91 (motor efficiency)
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| '''''Fig. L4:'''''<i> Example in the calculation of active and reactive power</i>
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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.
