Consider the three-bus power system shown in Figure P5.23a. Two identical circuits of equal impedance and equal MW capacity connect each pair of buses. The reactance and MW capacity of each circuit are given in Table P5.23. 6 Paradox (Noun): A statement, proposition, or situation that seems to be absurd or contradictory, but in fact is or may be true. Table P5.23 Characteristics of the circuits in Problem 5.23. From bus 1 1 2 To bus 2 3 3 Circuit reactance (p.u.) Circuit capacity (MW) 0.2 0.4 0.2 Figure P5.23b shows the marginal cost curves of the two generators. Startup and no-load costs are assumed negligible. A DC (linear) transmission model is deemed acceptable. a Calculate the economic dispatch ignoring network constraints. b Check that this economic dispatch does not violate any transmission constraint when all the circuits are in service. 120 180 250 c Assuming that all generators bid at their marginal cost, what is the locational marginal price at each node under these conditions? The system operator must operate this system in a way that guarantees N - 1 security, i.e. there should be no line overload in the event of the outage of any transmission circuit. (We do not consider generation contingencies.) d For each branch, determine the single circuit contingencies that would result in a flow constraint violation if this economic dispatch were implemented. (Take into account the fact that the transmission capacity and reactance of a branch change if one of its circuit is disconnected.) Identify the contingency that would cause the worst violation of a flow constraint and the circuit or branch that would be overloaded. e Determine the least cost generation dispatch that would avoid a line overload for the critical contingency identified in part (d). Assume that no postcontin- gency redispatch is allowed. f What is the locational marginal price at each node under these conditions? 500 MW 3 2 Figure P5.23a Three-bus power system for Problem 5.23. B 1