Electrical Power Systems

408 Electrical Power Systems
\ uel cost function is given by
c(P g) = 222.24 + 20.44 P g + 0.142 P g 2
(b) at 25% rating, P g = 12.5 MW
\ C(P g = 12.5) = 222.24 + 20.44 × 12.5 + 0.142 × (12.5) 2
\ C(P g = 12.5) = 500 Rs/hr
at 40% rating, P g = 20 MW
\ C(P g = 20) = 222.24 + 20.44 × 20 + 0.142 × (20) 2
\ C(P g = 20) = 688 Rs/hr.
at 100% rating, P g = 50 MW
C(P g = 50) = 222.24 + 20.44 × 50 + 0.142 × (50) 2
\ C(P g = 50) = 1599 Rs/hr.
(c) The incremental cost
dC
dP g
= IC = (20.44 + 0.284 P g ) Rs/MWhr
(d) at 100% rating, P g = 50 MW.
\ IC = (20.44 + 0.284 × 50)
\ IC = 34.64 Rs/MWhr.
Approximate cost of fuel to deliver 51 MW is C(P g = 50) + IC × DP g
DP g = (51 – 50) = 1 MW
C(P g = 50) = 1599 Rs/hr
\ Approximate cost = 1599 + 34.64 × 1
= 1633.64 Rs/hr.
Exact cost
C(P g = 51) = 222.24 + 20.44 × 51 + 0.142 × (51) 2
= 1634 Rs/hr.
16.3 GENERAL PROBLEM ORMULATION
Consider a system with m generators committed and all the loads P di given, find P gi and |V i|,
i = 1, 2, ..., m, to minimize the total fuel cost
m
CT = å Ci( Pgi)
... (16.6)
i=1
Subject to the satisfaction of the power flow equations and the following inequality constraints
on generator power, voltage magnitude and line power flow.
1. P gi min < Pgi < P gi max , i = 1, 2, ..., m
2. V i
min max
< Vi < V , i = 1, 2, ..., m
i
3. P ij < P ij
max
, for all lines.
Brief explanation on the problem formulation is given below.
1. The power flow or load flow equations must be satisfied. They are equality constraint in
the optimization process.