A 3 bus locational marginal pricing electricity market consists of buses A, B and C. Bus A is connected to bus C by line 1, bus A is connected to bus B by line 2, and bus B is connected to bus C by line 3. Line 1 has a reactance of 0.4 pu, line 2 has a reactance of 0.5 pu, and line 3 has a reactance of 0.6 pu. A load of 270 MW is placed at bus A, and a further load of 190 MW is placed at bus C. Generator 1 is located at bus A, has a capacity of 240 MW, and bids €40/MWh. Generator 2 is located at bus B, has a capacity of 180 MW, and bids €25/MWh. Finally, generator 3 is located at bus C, has a capacity of 150 MW, and bids €55/MWh.

Assuming a DC load flow model, and taking bus A as the reference bus, determine the line sensitivity matrix for the system.

Assuming that there are no transmission line limits, determine the optimal dispatch subject to all unit constraints, the power flows on the lines and the locational marginal price at each bus.

Transmission lines 1, 2 and 3 have flow limits of 70 MW, 85 MW and 90 MW respectively. Determine the optimal dispatch subject to all constraints, the power flows on the lines, the locational marginal price at each bus, the market surplus and the multiplier values for all active constraints