Concept of power factor, real, reactive and complex power: Complex Power is defined as the product of Voltage phasor and conjugate of current phasor
If S is the complex power then,
S = V . I
*
V is the phasor representation of voltage and I* is the conjugate of current phasor.
So if V is the reference phasor then V can be written as |V|
∠
0.
(Usually one phasor is taken reference which makes zero degrees with real axis. It eliminates
the necessity of introducing a non zero phase angle for voltage)
Let current lags voltage by an angle φ, so I = | I |
∠
-φ
(current phasor makes -φ degrees with real axis)
I
*
= | I |
∠
φ
So,
S = |V| | I |
∠
(0+φ) = |V| | I |
∠
φ
(For multiplication of phasors we have considered polar form to facilitate calculation)
Writing the above formula for S in rectangular form we get
S = |V| | I | cos φ + j |V| | I | sin φ
The real part of complex power S is |V| | I | cos φ which is the real power or average
power and the imaginary part |V| | I | sin φ is the reactive power.
So, S = P + j Q
Where P = |V| | I | cos φ and Q = |V| | I | sin φ
P is measured in watt and Q is measured in VoltAmp-Reactive or VAR. In power systems
instead of these smaller units larger units like Megawatt, MVAR and MVA is used.
The ratio of real power and apparent power is the power factor
power factor = Cos φ = |P| / |S|
= |P| / √(P
2
+Q
2
)
ELECTRICAL CIRCUITS UNIT-IV NETWORK THEOREMS
Thevenin’s Theorem
Norton’s Theorem
Maximum Power Transfer Theorem