Electrical Power Systems

Optimal System Operation 443
B 11 = 0.011, B 22 = 0.03, B 33 = 0.04, B 12 = 0.001, B 23 = 0.0004, B 31 = –0.001
\ P L = 0.011(1) 2 + 0.03(2) 2 + 0.04(4) 2 + 2(0.001) × 1 × 2
+ 2 (0.0004) × 2 × 4 + 2(– 0.001) × 4 × 1
\ P L = 0.7734 pu.
Incremental loss rates with respect to plant q,
\
\
P
P
L
q
P
P
L
1
P
P
L
2
P
P
L
3
P
P
L
1
P
P
L
2
P
P
L
3
=
3
å
p=1
2B P
pq p
= 2P 1 B 11 + 2B 21 P 2 + 2B 31 P 3
= 2P 2 B 22 + 2B 12 P 1 + 2B 32 P 3
= 2B 33P 3 + 2B 13P 1 + 2B 23P 2
= 2 × 1 × 0.011 + 2 × 0.001 × 2 + 2 × (– 0.001) × 4.0
= 0.016 pu
= 2 × 2 × 0.03 + 2 × 0.001 × 1.0 + 2 × 0.0004 × 4.0
= 0.1252 pu
= 2 × 0.04 × 4 + 2 × (– 0.001) × 1 + 2 × (0.0004) × 2
= 0.3196 pu
EXERCISE–16
16.1 Input-output characteristic of a generating unit is
= (75 + 1.25P g + 1.625 P g 2 + 0.025 Pg 3 ) × 10 5 K Cal/hr
Determine the increase in input to raise the output from 7 MW to 9 MW.
Ans: 6.415 × 10 6 K Cal/hr.
16.2 Incremental fuel costs in Rs/MWhr for a generating plant consisting two units are:
IC1 = 20 + 0.10 Pg1 IC2 = 15 + 0.12 Pg2