Power Market Economics and Security

Problem 1: The generator data are given in Table 1 and the load and reserve data are given in
Table 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 $/MBtu. The unit shutdown costs and the system
    losses are assumed to be zero. Unit 3 has a fuel contract of 2000 MBtu. The initial Lagrangian
    multipliers for power balance and reserve requirements are given in Table 3. The initial
    multiplier  for Unit 3’s fuel constraint is zero. The adjustment steps of multipliers are given in
    Table 4. Set Γ=10,000 if the ED is infeasible based on a given commitment. Use the LR method
    to solve the UC problem. Obtain two different feasible solutions and show the corresponding
    relative duality gaps.
    Table 1: Generator data
    Unit af
    (MBtu)
    bf
    (MBtu/MW)
    cf
    (MBtu/MW2
    )
    Pmin
    (MW)
    Pmax
    (MW)
    Min
    ON
    (h)
    Min
    OFF
    (h)
    Startup
    Cost ($)
    Initial
    Status
    (h)/(MW)
    1 2000 62.3 0.06 100 400 2 2 2000 ON 4 /300
    2 2100 64 0.07 80 400 2 1 1500 ON 4 /200
    3 1900 59 0.05 40 200 1 2 0 OFF 4 /0
    Table 2: Load and reserve data
    Hour Load (MW) Reserve (MW)
    1 500 50
    2 700 70
    3 800 80
    4 400 40
    Table 3: Initial  and 
    Hour  (Power balance)  (Reserve requirements)
    1 75 0
    2 100 0
    3 110 0
    4 70 0
    Table 4: Adjustment steps of Lagrangian multipliers
    Lagrangian Multiplier k1 k2
     (Power balance) 0.02 0.01
     (Reserve requirements) 0.02 0.005
     (Fuel constraint for unit 3) 0.005 0.001

Sample Solution

ACED ESSAYS