6 Chapter 1 • Conductors and cables
In a three-phase circuit; S = 3 × Vph
Iph
Where Vph
VL
= 3 VL = phase voltage, 1.3.2 True power
When the current and voltage are not in phase, as illustrated in fig. 1.1, the current can be resolved into two components, one in phase with the voltage and the other in quadrature (90˚) with it.
Te actual power (P), also known as true power or active power is, however, a product of the voltage and the in-phase (with the voltage) component, I x cos ϕ, of the current, fig. 1.1 (b). Power (true power) in a single-phase circuit is therefore expressed as:
P = V × I cos ϕ watts .............................................................................................. (1.2)
Tis in-phase component of the current is also known as the energy component of the current and is always smaller than the actual current “I”. Te power (true power) of a circuit in which the current is not in phase with the voltage, is therefore smaller than the apparent power.
In a three-phase circuit; P = 3 × Vph
Iph cos ϕ = 3 VL
1.3.3 Power factor (cos ϕ) D
Definition 1.1 Power factor Power factor is the ratio of the true power to the apparent power.
Power factor pf
= V × I cos ϕ ∴pf = cos ϕ ................................... (1.3) V × I
IL cos ϕ watts
IL Iph = line voltage, and IL
VA
= phase current = line current
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