Please answer (1)

Fig. 1 depicts a three-bus system. Suppose the three units are always running, with the following characteristics: Unit 1: $40/MWh, Poin = OMW, P = 820MW Unit 2: $50/MWh, P=OMW, P = 600MW Unit 3: $55/MWh, P = OMW, P. = 610MW The total demand for three hours is: 1000, 1100, 900 MW. The load distribution always has a ratio of: D1:02:D3 = 200:350:450, which means the total load will be allocated to D1, D2 and D3 by this ratio. For example, in hour 2, D1 = 1100*200/(200 + 350+450) D2 = 1100*350/200 + 350+450) D3 = 1100*450/(200 + 350+450). Loads in other hours can be obtained similarly. Transmission line impedances in per unit and constraints in MW are labeled in the figure. Sbase = 100 MW. The transmission line constraints are L1 = 250 MW, L2=200 MW, L3 = 200 MW. G1 G2 Bus! 0.lj LI MW Bus2 0.23 0.125j L2 MW L3 MW Bus3 ID3 63 O Fig. 1 A three-bus power system. Bus 1 is chosen as the reference bus. DC load flow is utilized. Let d2 and d3 represent the voltage angles of bus 2 and bus 3, respectively. (1) Formulate the Linear Programming (LP) problem for each hour. Define variables and write down your formulated problem in lp format, i.e., identify all the matrices and vectors to represent the problem. (2) Develop a program in Matlab or any other language of your choice to obtain the optimal unit outputs and total cost for each hour. You can use Matlab function linprog function