Power Market Economics and Security

Problem 1: The generator data are given in Table 1 and the load and reserve data are given inTable 2. The fuel consumption functions of the generating units are quadratic H(P) = af + bf * P

cf * P2(MBtu). The fuel prices are all 1 $/MBtu. The unit shutdown costs and the systemlosses are assumed to be zero. Unit 3 has a fuel contract of 2000 MBtu. The initial Lagrangianmultipliers for power balance and reserve requirements are given in Table 3. The initialmultiplier  for Unit 3’s fuel constraint is zero. The adjustment steps of multipliers are given inTable 4. Set Γ=10,000 if the ED is infeasible based on a given commitment. Use the LR methodto solve the UC problem. Obtain two different feasible solutions and show the correspondingrelative duality gaps.Table 1: Generator dataUnit af(MBtu)bf(MBtu/MW)cf(MBtu/MW2)Pmin(MW)Pmax(MW)MinON(h)MinOFF(h)StartupCost ($)InitialStatus(h)/(MW)1 2000 62.3 0.06 100 400 2 2 2000 ON 4 /3002 2100 64 0.07 80 400 2 1 1500 ON 4 /2003 1900 59 0.05 40 200 1 2 0 OFF 4 /0Table 2: Load and reserve dataHour Load (MW) Reserve (MW)1 500 502 700 703 800 804 400 40Table 3: Initial  and Hour  (Power balance)  (Reserve requirements)1 75 02 100 03 110 04 70 0Table 4: Adjustment steps of Lagrangian multipliersLagrangian Multiplier k1 k2 (Power balance) 0.02 0.01 (Reserve requirements) 0.02 0.005 (Fuel constraint for unit 3) 0.005 0.001

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