A lossless power system has to serve a load of 250 MW. There

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A lossless power system has to serve a load of 250 MW. There are two generators (G₁ and G₂) in the system with cost curves C₁ and C₂ respectively defined as follows:
C₁ (P_G1) = P_G1 + 0.055 × P_G1²
C₂ (P_G2) = 3P_G2 + 0.03 × P_G2²
where P_G1 and P_G2 are the MW injections from generator G₁ and G₂ respectively. Then the minimum cost dispatch will be

1. P_G1 = 250 MW; P_G2 = 0 MW
2. P_G1 = 150 MW; P_G2 = 100 MW
3. P_G1 = 100 MW; P_G2 = 150 MW
4. P_G1 = 0 MW; P_G2 = 250 MW

Correct Option: C

C₁ (P_G1) = P_G1 + 0.055 × P_G1²

∴	dC₁	= 1 + 0.11PG₁
	dP_G1

C₂ (P_G2) = P_G2 + 0.03 × P_G2²

∴	dC₂	= 3 + 0.06 PG₂
	dP_G2

For minimum cost analysis

	dC₁	=	dC₂
	dP_G1		dP_G2

⇒ 1 + 0.11 P_G1 = 3 + 0.006 P_G2
or 0.11 P_G1 – 0.06 P_G2 = 2 ...(1)
and P_G1 + P_G2 = 250 MW ...(2)
Solving equations (1) and (2), we get
P_G1 = 100 MW and P_G2 = 150 MW