Only Need 6.8 Answered, since it needs the answers from 6.5 - 6.7 I will include them below 6.5 Answer: PA=0MW; PB=0MW; PC=120MW; PD=400MW; 1 = 2 = 3 = 10 $/MWh 6.6 Answer: F21 = 120 MW; F31 = 280 MW; F32 = 200 MW; Line 13 is overloaded by 30MW. 6.7 Answer: Method 1: PA = 0 MW; PB = 48 MW; PC = 72 MW; PD = 400 MW F21 = 102 MW; F31 = 250 MW; F32 = 182 MW Increase in cost: $240 Method 2: PA = 80 MW; PB = 0 MW; PC = 40 MW; PD = 400 MW F21 = 150 MW; F31 = 250 MW; F32 = 150 MW Increase in cost: $160 Method 2 is preferable because it is cheaper.

65 Consider the three-bus power system shown in Figure P6.5 The table below shows the data about the generators connected to this system. Calculate the unconstrained economic dispatch and the nodal prices for the loading conditions shown in Figure P6.5. 6.5 PROBLEMS 203 B A 400 MW 80 MW 2 40 MW D Figure P6.5 Three-bus power system for Problems 6.5 to 6.9 and 6.12 to 6.17 Generator Capacity (MW) Marginal cost (S/MWh) B D 150 200 150 400 12 15 10 8 6.6 The table below gives the branch data for the three-bus power system of Prob- lem 6.5. Using the superposition principle, calculate the flow that would result if the generating units were dispatched as calculated in Problem 6.5. Identify all the violations of security constraints. Branch Reactance (P..) 1-2 1-3 2-3 0.2 0.3 0.3 Capacity (MW) 250 250 250 6.7 Determine two ways of removing the constraint violations that you identified in Problem 6.6 by redispatching generating units. Which redispatch is preferable? 6.8 Calculate the nodal prices for the three-bus power system of Problems 6.5 and 6.6 when the generating units have been optimally redispatched to relieve the constraint violations identified in Problem 6.7. Calculate the merchandising sur- plus and show that it is equal to the sum of the surpluses of each line. 65 Consider the three-bus power system shown in Figure P6.5 The table below shows the data about the generators connected to this system. Calculate the unconstrained economic dispatch and the nodal prices for the loading conditions shown in Figure P6.5. 6.5 PROBLEMS 203 B A 400 MW 80 MW 2 40 MW D Figure P6.5 Three-bus power system for Problems 6.5 to 6.9 and 6.12 to 6.17 Generator Capacity (MW) Marginal cost (S/MWh) B D 150 200 150 400 12 15 10 8 6.6 The table below gives the branch data for the three-bus power system of Prob- lem 6.5. Using the superposition principle, calculate the flow that would result if the generating units were dispatched as calculated in Problem 6.5. Identify all the violations of security constraints. Branch Reactance (P..) 1-2 1-3 2-3 0.2 0.3 0.3 Capacity (MW) 250 250 250 6.7 Determine two ways of removing the constraint violations that you identified in Problem 6.6 by redispatching generating units. Which redispatch is preferable? 6.8 Calculate the nodal prices for the three-bus power system of Problems 6.5 and 6.6 when the generating units have been optimally redispatched to relieve the constraint violations identified in Problem 6.7. Calculate the merchandising sur- plus and show that it is equal to the sum of the surpluses of each line