Question

Home Work-5 (Chapter-5) Incremental fuel costs (ROMWhr) for a power plant consisting two generating units are: * = 0,36 Pe +32 and generator limits are: 32 MW Pris 180 MW 22 MW Pas 130 MW. Determine P.P and values ofà for the variation of load from 54 MW to 310 MW. Assume that both generating units are operating at all times. Both by using (i) Analytical Technique and (ii) Iterative method.

Answer 1

(i) Analytical method

By equating two incremental fuel costs,

0.18Pg1+41 = 0.36Pg2+32

0.18Pg1-0.36Pg2 = -9 ............(eq-1)

Load (PL) = Pg1 + Pg2 ............(eq-2)

From above equations, by varing load (PL) and solving equations we get values Pg1 & Pg2, those values we get in table,

PL(MW)	Pg1 (MW)	Pg2 (MW)	$\lambda$
54	32**	22**	39.92#
70	32	41	46.76
100	50	50	50
183.34	105.56	77.78	60
266.66	161.107	105.55	70
295	180	115	73.4
299.44	180**	119.44**	75
310	180**	130**	78.8

* $\lambda$ value can be obtained by substuting either Pg1 or Pg2 in their incremental costs.

e.g. For Pg1=32MW, $\lambda$ = dC1/dPg1 = 0.18(32)+41 = 46.76 RMWh

# For Pg1 = 32MW, $\lambda$ = 46.76 RMWh and Pg2 = 22MW, $\lambda$ = 39.92 RMWh

So, lowest value of $\lambda$ = 39.92 RMWh is considered.

** Min & Max values of generator limits are considered.

*** Decimal values are considered calculation purpose.

(ii) Iterative method:

For Pg1 = 32MW, $\lambda$ = 46.76 RMWh and

Pg2 = 22MW, $\lambda$ = 39.92 RMWh

The incremental fuel cost is more for generator-1 and less for generator-2.

So, For  $\lambda$ = dC2/dPg2 = 46.76 = 0.36Pg2+32

Pg2 = 41MW.

Until $\lambda$ = 46.76 RMWh, the generator-2 gives optimum value of incremental cost as compared to genrator-2.

Further, $\lambda$ increases to 50 gives the Pg1 = 50MW, Pg2 = 50MW.

The tables gives by increasing values of $\lambda$ is,

$\lambda$	Pg1 (MW)	Pg2 (MW)	PL(MW)
39.92	32	22	54
46.76	32	41	70
50	50	50	100
60	105.56	77.78	183.34
70	161.107	105.55	266.66
73.4	180	115	295
75	180	119.44	299.44
78.8	180	130	310

By increasing various values of $\lambda$ we get Pg1 & Pg2 and PL.

At $\lambda$ = 73.4 generator-1 gives its maximum value of generation.

At $\lambda$ = 78.8 both generators 1 & 2 gives the maximum outputs.