Electrical Power Systems

Optimal System Operation 423
Now we will consider the transmission losses for determining l. One common practice is to
express the total transmission loss as a quadratic function of the generator power outputs. The
simplest quadratic form is
m
m
PL = å å Pgi BijPgj ...(16.54)
i=1 j=1
Derivation of the loss formula is presented in next section.
rom eqn . (16.30), we get,
dC
dP
i
gi
+ l P
P
rom eqn. (16.54), we have
P
P
L
gi
L
gi
= l, i = 1, 2, ..., m ...(16.55)
m
= 2å BijPgj ...(16.56)
j=1
rom eqns. (16.55) and (16.56), we get,
bi + 2diPgi +
2lå BijPgj = l
m
j=1
m
\ bi + 2diPgi + 2lBiiPgi + 2l
j=1
j¹ i
å BijPgj = l
At K-th iteration, eqn.(16.57) is expressed as:
m
å
l-bi -2l
BijPgj DPgi =
j=1
j¹ i
2bdi + lBiig
... (16.57)
(K)
Pgi =
At K-th iteration, eqn.(16.23) is written as
m
(K)
P (K)
å gi = PD + PL i=1
( K)
i
m
( K)
å
j=1
l -b -2l
B P
j¹ i
(K) 2edi+ l Biij
Substituting eqn. (16.58) in eqn. (16.59), we get,
(K)
ij gj
...(16.58)
...(16.59)