GATE 2015 EE – SET 2 – Question 40

Solution :

$$\frac{dc_{1}}{dp_{1}}$$ = 0.2$$P_{1} $$+ 50

$$\frac{dc_{1}}{dp_{1}} $$= 76$$\frac{Rs}{MWh}$$

0.2$$P_{1} $$+ 50 = 76
$$P_{1} $$= 130 MW

$$\frac{dc_{2}}{dP_{2}} $$= 0.24$$P_{2}$$ + 40

$$\frac{dc_{2}}{dP_{2}} $$= 68.8$$\frac{Rs}{MWh}$$

0.24$$P_{2} $$+ 40 = 68.8
$$P_{2} $$= 120 MW

$$P_{1} + P_{2} $$ = 250 Mw   —————(1)

0.2$$P_{1}$$ + 50 = 0.24 $$P_{2}$$ + 40

0.2$$P_{1}$$  – 0.24 $$P_{2}$$ = -10 ———(2)

$$P_{1}$$ = 113.636 MW

$$P_{2}$$ = 136.36 MW