12 Electrical Power Systems
LF =
P2 ´ t + P1 ´ (T - t) P2 ´ T
LF =
P1 t + × P2 T
or
FG T - t IJ HTK
...(1.25)
The loss factor is LLF =
Lavg Lmax
=
Lavg L2
...(1.26)
where Lmax = maximum power loss = L2 From Fig. 1.6, we obtain
Lavg = average power loss.
L2 ´ t + L1 ´ (T - t) T From eqns. (1.26) and (1.27), we get Lavg =
LLF =
L2 ´ t + L1 ´ (T - t) L2 ´ T
...(1.27)
...(1.28)
where t = peak load duration (T t) = off-peak load duration. The copper losses are the function of associated loads. Therefore, the loss at off-peak and peak load can be expressed as: L1 = K × P12
...(1.29)
L2 = K × P22
...(1.30)
From eqns. (1.28), (1.29) and (1.30), we get,
t + LLF = T
FG P IJ FG T - t IJ HP K H T K 1
2
2
...(1.31)
By using eqns. (1.25) and (1.31), the load factor can be related to loss factor for three different cases: Case-1: Off-peak load is zero. Here, P1 = 0 and L1 = 0, therefore, from eqns. (1.25) and (1.31), we have
t T That is load factor is equal to loss factor and they are equal to t/T constant. LF = LLF =
....(1.32)