The generator data arc given in Table 1 and tin load and res

The generator data arc given in Table 1 and tin; load and reserve data arc given in Table 2. The fuel cost functions of the generating units arc linear F(P) = a + b * P($). The unit shutdown costs and the system losses are assumed to be zero. Assume that the relative duality gap to convergence is 0.2, and the step sizes for updating Lagrangian multipliers are k1 = 0.01 and k2 = 0.004. In addition, set J = 10,000 if the ED is infeasible based on a given commitment. Use the LR method to solve the following UC problems. (a) Ignoring the reserve requirements and the minimum ON/OFF lime limits. (b) Considering the reserve requirements and ignoring the minimum ON/OFF time limits. (c) Optional: considering the reserve requirements and the minimum ON/OFF time limits.

Solution

Pmin<Ps<Pmax

F(a)= a + bP

dC1/dP = dC2/dP

P =PI + P2

a) P =PI + P2 = 100

b)P =PI + P2 = 170

c) P =PI + P2 = 140