408
Electrical Power Systems
\ Fuel cost function is given by c(Pg) = 222.24 + 20.44 Pg + 0.142 Pg2 (b) at 25% rating, Pg = 12.5 MW \ C(Pg = 12.5) = 222.24 + 20.44 × 12.5 + 0.142 × (12.5)2 \ C(Pg = 12.5) = 500 Rs/hr at 40% rating, Pg = 20 MW \ C(Pg = 20) = 222.24 + 20.44 × 20 + 0.142 × (20)2 \ C(Pg = 20) = 688 Rs/hr. at 100% rating, Pg = 50 MW C(Pg = 50) = 222.24 + 20.44 × 50 + 0.142 × (50)2 \ C(Pg = 50) = 1599 Rs/hr. (c) The incremental cost
dC = IC = (20.44 + 0.284 Pg) Rs/MWhr dPg (d) at 100% rating, Pg = 50 MW. \ IC = (20.44 + 0.284 × 50) \ IC = 34.64 Rs/MWhr. Approximate cost of fuel to deliver 51 MW is C(Pg = 50) + IC × DPg DPg = (51 50) = 1 MW C(Pg = 50) = 1599 Rs/hr \ Approximate cost = 1599 + 34.64 × 1 = 1633.64 Rs/hr. Exact cost C(Pg = 51) = 222.24 + 20.44 × 51 + 0.142 × (51)2 = 1634 Rs/hr.
16.3 GENERAL PROBLEM FORMULATION Consider a system with m generators committed and all the loads Pdi given, find Pgi and |Vi|, i = 1, 2, ..., m, to minimize the total fuel cost m
CT =
å Ci ( Pgi ) i=1
... (16.6)
Subject to the satisfaction of the power flow equations and the following inequality constraints on generator power, voltage magnitude and line power flow. 1. Pgimin < Pgi < Pgimax , i = 1, 2, ..., m 2. Vi
min
< Vi < V i
3. Pij < Pij
max
max
, i = 1, 2, ..., m
, 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.