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Briefly explain the three main methods for allocating the cost of transmission. 5 (a) [3 marks Consider the two-bus power system shown in Figure 3. Assume that (b) demand is constant and insensitive to price, and energy is sold at its marginal cost of production. There are no limits on the output of the generators. The marginal cost of generation units A and B are given by the following expressions respectively MCA = 20 +0.03PA + 0.00001P; E/MWh MC = 10 + 0.02P, + 0.00001P E/MWh D2000 MW 4-1000 MW Figure 3 (1) Determine the transmission demand function for the system. The flow along the transmission line is assumed to be FBA. (ii) Calculate the generation output of the two systems when they are operated as a single market. (iii) Calculate the maximum revenue of the transmission line. (iv) Use a diagram to illustrate the change of the line revenue with respect to its capacity. [9 marks Assume that the periods of high, medium and low load coincide at both buses. The duration and load levels of the three periods are given in Table 8. (c) Table 8 Load at B (MW) 3000 1000 500 Duration (hour) 2000 Load at A Period High Medium Low (MW) 2000 2000 1000 3000 3760 (i) Build the load duration curve for the system in a diagram. Clearly label load levels and duration periods. (ii) Derive generation cost for the two generation units according to the marginal cost functions defined in part (b). (i) Determine the unconstrained and constrained economic dispatches for the high load system condition, indicated in Table 8. In the constrained dispatch, the transmission capacity is assumed to be 200MW. Quantify the constrained cost. [8 marks