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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.
The value of a power factor will range from 0 to 1. If currents and voltages are perfectly sinusoidal signals, power factor equals cos ϕ.
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.
Power vector diagram
- Active power P (in kW)
- Single phase (1 phase and neutral): P = V x I x cos ϕ
- Single phase (phase to phase): P = U x I x cos ϕ
- Three phase (3 wires or 3 wires + neutral): P = √3 x U x I x cos ϕ
- Reactive power Q (in kvar)
- Single phase (1 phase and neutral): P = V x I x sin ϕ
- Single phase (phase to phase): Q = UI sin ϕ
- Three phase (3 wires or 3 wires + neutral): P = √3 x U x I x sin ϕ
- Apparent power S (in kVA)
- Single phase (1 phase and neutral): S = VI
- Single phase (phase to phase): S = UI
- Three phase (3 wires or 3 wires + neutral): P = √3 x U x I
where:
V = Voltage between phase and neutral
U = Voltage between phases
- For balanced and near-balanced loads on 4-wire systems
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.
PF = P (kW) / S (kVA)
P = Active power
S = Apparent power
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 ϕ. The component of I which is in phase with V is the wattful component of I and is equal to I cos ϕ, while VI cos ϕ equals the active power (in kV) 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 ϕ, while VI sin ϕ 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 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 K3 .
SOURCE: Schneider Electric
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Related articles
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All inductive machines i.e. electromagnetic and devices that operate on AC systems convert electrical energy from the powersystem generators into mechanical work and heat. This energy is measured by kWh meters, and is referred to as active or wattful energy. In order to perform this conversion, magnetic fields have to be established in the machines, and these fields are associated with another form of energy to be supplied from the power system, known as reactive or wattless energy.
The reason for this is that inductive plant cyclically absorbs energy from the system (during the build-up of the magnetic fields) and re-injects that energy into the system (during the collapse of the magnetic fields) twice in every power-frequency cycle.
The effect on generator rotors is to (tend to) slow them during one part of the cycle and to accelerate them during another part of the cycle. The pulsating torque is stricly true only for single-phase alternators. In three-phase alternators the effect is mutually cancelled in the three phases, since, at any instant, the reactive energy supplied on one (or two) phase(s) is equal to the reactive energy being returned on the other two (or one) phase(s) of a balanced system. The nett result is zero average load on the generators, i.e. the reactive current is “wattless”.
An exactly similar phenomenon occurs with shunt capacitive elements in a power system, such as cable capacitance or banks of power capacitors, etc. In this case, energy is stored electrostatically. The cyclic charging and discharging of capacitive plant reacts on the generators of the system in the same manner as that described above for inductive plant, but the current flow to and from capacitive plant is in exact phase opposition to that of the inductive plant. This feature is the basis on which powerfactor improvement schemes depend.
It should be noted that while this “wattless” current (more accurately, the wattless component of a load current) does not draw power from the system, it does cause power losses in transmission and distribution systems by heating the conductors.
In practical power systems, wattless components of load currents are invariably inductive, while the impedances of transmission and distribution systems are predominantly inductively reactive. The combination of inductive current passing through an inductive reactance produces the worst possible conditions of voltage drop (i.e. in direct phase opposition to the system voltage).
For these reasons, viz:
- Transmission power losses and
- Voltage drop
The power-supply authorities reduce the amount of wattless (inductive) current as much as possible. Wattless (capacitive) currents have the reverse effect on voltage levels and produce voltage-rises in power systems.
The power (kW) associated with “active” energy is usually represented by the letter P. The reactive power (kvar) is represented by Q. Inductively-reactive power is conventionally positive (+ Q) while capacitively-reactive power is shown as a negative quantity (- Q). S represents kVA of “apparent” power.
Figure 1 shows that the kVA of apparent power is the vector sum of the kW of active power plus the kvar of reactive power.
Alternating current systems supply two forms of energy:
- Active energy measured in kilowatt hours (kWh) which is converted into mechanical work, heat, light, etc
- Reactive energy, which again takes two forms:
- “Reactive” energy required by inductive circuits (transformers, motors, etc.),
Plant and appliances requiring reactive energy
All AC plant and appliances that include electromagnetic devices, or depend on magnetically-coupled windings, require some degree of reactive current to create magnetic flux. The most common items in this class are transformers and reactors, motors and discharge lamps (i.e. the ballasts of).
The proportion of reactive power (kvar) with respect to active power (kW) when an item of plant is fully loaded varies according to the item concerned being:
- 65-75% for asynchronous motors
- 5-10% for transformers
SOURCE: Schneider Electric
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