Consider a 3-Bus system below, Ga $90/MWh A B La Z Lb 120MW OMW 2Z GC $50/MWh LO C 100MW The 3-Bus system information: Assume Generator A and Generator C have infinite generating capacity and OMW minimum output. Marginal Cost of Generator A: $90/MWh Marginal Cost of Generator C: $50/MWh Line 1(f) Limit: 75MW Line 2(f2) Limit: 65MW Line 3(f;) Limit: 45MW Load on node B: 120MW Load on node C: 100MW Below is the PTDF matrix of the 3-bus system with bus A as the reference bus. Line I PTDFA PTDFBI PTDFCI 1 = 1 0 -3/4 -1/4 1 = 2 0 1/4 -1/4 1 =3 0 -1/4 -3/4 PTDFA : Power Transfer Distribution Factor for line I for the net injection from bus n to the reference bus R.3a) Solve for the optimal dispatch. List the generators' outputs and all line flows. Show your work. Hint: Generator C should generate as much as the line limits allow since it is cheaper than Generator A. Additional hint: Reformulate the DCOPF in 3a) to produce the bounds for Go from transmission constraints. f3 Optimal Cost f1 f2 Ga 3b) Change the demand at bus B to be 121MW. Determine the new optimal dispatch, line flows, and optimal cost. Optimal Cost f2 Gc fi f3 Ga