Multi-objective Economic-Environmental Load Dispatch

MOED.py

"""
## GAMSSOURCE: https://www.gams.com/latest/psoptlib_ml/libhtml/psoptlib_MOED.html
## LICENSETYPE: Demo
## MODELTYPE: QCP


Multi-objective Economic-Environmental Load Dispatch

For more details please refer to Chapter 3 (Gcode3.4), of the following book:
Soroudi, Alireza. Power System Optimization Modeling in GAMS. Springer, 2017.
--------------------------------------------------------------------------------
Model type: QCP
--------------------------------------------------------------------------------
Contributed by
Dr. Alireza Soroudi
IEEE Senior Member
Email: alireza.soroudi@gmail.com
We do request that publications derived from the use of the developed GAMS code
explicitly acknowledge that fact by citing
Soroudi, Alireza. Power System Optimization Modeling in GAMS. Springer, 2017.
DOI: doi.org/10.1007/978-3-319-62350-4
"""

from __future__ import annotations

import os

import pandas as pd
from gamspy import (
    Card,
    Container,
    Equation,
    Model,
    Parameter,
    Set,
    Sum,
    Variable,
)


def reformat_df(dataframe):
    return dataframe.reset_index().melt(
        id_vars="index", var_name="Category", value_name="Value"
    )


def data_records():
    # data records table
    cols = ["a", "b", "c", "d", "e", "f", "Pmin", "Pmax"]
    inds = [f"g{i}" for i in range(1, 6)]
    data = [
        [3.0, 20.0, 100.0, 2.0, -5.0, 3.0, 28, 206],
        [4.05, 18.07, 98.87, 3.82, -4.24, 6.09, 90, 284],
        [4.05, 15.55, 104.26, 5.01, -2.15, 5.69, 68, 189],
        [3.99, 19.21, 107.21, 1.1, -3.99, 6.2, 76, 266],
        [3.88, 26.18, 95.31, 3.55, -6.88, 5.57, 19, 53],
    ]
    data_recs = reformat_df(pd.DataFrame(data, columns=cols, index=inds))

    return data_recs


def main():
    m = Container(
        system_directory=os.getenv("SYSTEM_DIRECTORY", None),
    )

    # SETS #
    gen = Set(m, name="gen", records=[f"g{i}" for i in range(1, 6)])
    counter = Set(m, name="counter", records=[f"c{i}" for i in range(1, 12)])

    # PARAMETERS
    report = Parameter(m, name="report", domain="*")
    rep = Parameter(m, name="rep", domain=[counter, "*"])
    rep2 = Parameter(m, name="rep2", domain=[counter, gen])
    data = Parameter(m, name="data", domain=[gen, "*"], records=data_records())

    # SCALARS
    load = Parameter(m, name="load", records=400)
    Elim = Parameter(m, name="Elim")

    # VARIABLES #
    P = Variable(m, name="P", domain=gen)
    TE = Variable(m, name="TE")
    TC = Variable(m, name="TC")

    # EQUATIONS #
    eq1 = Equation(m, name="eq1", type="regular")
    eq2 = Equation(m, name="eq2", type="regular")
    eq3 = Equation(m, name="eq3", type="regular")

    eq1[...] = (
        Sum(
            gen,
            data[gen, "a"] * P[gen] * P[gen]
            + data[gen, "b"] * P[gen]
            + data[gen, "c"],
        )
        == TC
    )
    eq2[...] = Sum(gen, P[gen]) >= load
    eq3[...] = (
        Sum(
            gen,
            data[gen, "d"] * P[gen] * P[gen]
            + data[gen, "e"] * P[gen]
            + data[gen, "f"],
        )
        == TE
    )

    P.lo[gen] = data[gen, "Pmin"]
    P.up[gen] = data[gen, "Pmax"]

    END1 = Model(
        m,
        name="END1",
        equations=[eq1, eq2, eq3],
        problem="qcp",
        sense="min",
        objective=TC,
    )
    END1.solve()
    report["maxTE"] = TE.l
    report["minTC"] = TC.l

    END2 = Model(
        m,
        name="END2",
        equations=[eq1, eq2, eq3],
        problem="qcp",
        sense="min",
        objective=TE,
    )
    END2.solve()
    report["maxTC"] = TC.l
    report["minTE"] = TE.l

    for idx, cc in enumerate(counter.toList()):
        Elim[...] = (report["maxTE"] - report["minTE"]) * (idx) / (
            Card(counter) - 1
        ) + report["minTE"]
        TE.up[...] = Elim
        END1.solve()
        rep[cc, "TC"] = TC.l
        rep[cc, "TE"] = TE.l
        rep2[cc, gen] = P.l[gen]

    print("rep  \n", rep.pivot().round(4))
    print("rep2  \n", rep2.pivot().round(4))

    import math

    assert math.isclose(END1.objective_value, 131454.0003, rel_tol=0.001)


if __name__ == "__main__":
    main()