Publication record · 18.cifr/2006.carrion.thermal-uc-milp

A Computationally Efficient Mixed-Integer Linear Formulation for the Thermal Unit Commitment Problem

v1.0.0

M. Carrion (Universidad de Castilla-La Mancha), J.M. Arroyo (Universidad de Castilla-La Mancha)

RAI18.cifr/2006.carrion.thermal-uc-milp

IEEE Transactions on Power Systems· 2006· doi:10.1109/TPWRS.2006.876672

A computationally efficient mixed-integer linear programming (MILP) formulation for the thermal unit commitment (UC) problem is presented. The proposed formulation is based on a set of tighter constraints for the minimum up and down time conditions, leading to a significantly improved LP relaxation. Startup costs are modeled using binary variables that track unit transitions, avoiding auxiliary continuous variables. Numerical results on standard test systems demonstrate order-of-magnitude speedups over previous MILP-based UC formulations while guaranteeing global optimality.

unit commitmentmixed-integer linear programmingthermal schedulingpower systemsstartup cost

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Problem solved

The thermal unit commitment problem requires deciding which generators to commit each hour to meet demand at minimum cost — an NP-hard combinatorial problem. Prior MILP formulations had weak LP relaxations requiring huge search trees. Power system operators needed a provably optimal MILP that solves in practical time for real-sized systems.

Novelty

Introduces tighter rolling-window binary inequality constraints for minimum up/down times and a startup-cost linearization using transition binaries, yielding a much tighter LP relaxation than prior MILP formulations. This dramatically reduces branch-and-bound tree size and enables solution of real-sized instances (up to 100 units, 168 hours) to proven optimality.

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Canvas contract1-in / 1-out · unpacked into generators, system_params legacy ports

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sha256:6800c5d29bf6cb0e873ed7a1659a8572d0dac02d95d7f475b16ceb1de75c59a4

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Pre-filled with the paper's canonical scenario. Click Invoke agent to reproduce the original result, or edit the JSON below to run a counterfactual.

inputapplication/jsonoptional

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{
  "generators": {
    "generators": [
      {
        "id": "G1",
        "p_min": 150,
        "p_max": 455,
        "min_up_time": 8,
        "min_down_time": 8,
        "ramp_up": 120,
        "ramp_down": 120,
        "startup_cost": 4500,
        "shutdown_cost": 0,
        "cost_coefficients": [
          [
            150,
            1000
          ],
          [
            305,
            2000
          ],
          [
            455,
            3000
          ]
        ],
        "initial_status": 8
      },
      {
        "id": "G2",
        "p_min": 100,
        "p_max": 300,
        "min_up_time": 5,
        "min_down_time": 5,
        "ramp_up": 100,
        "ramp_down": 100,
        "startup_cost": 2000,
        "shutdown_cost": 0,
        "cost_coefficients": [
          [
            100,
            800
          ],
          [
            200,
            1600
          ],
          [
            300,
            2500
          ]
        ],
        "initial_status": 5
      }
    ]
  },
  "system_params": {
    "time_periods": 6,
    "demand": [
      400,
      500,
      600,
      580,
      520,
      430
    ],
    "reserve": [
      40,
      50,
      60,
      58,
      52,
      43
    ]
  }
}

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