Dynamic Economic Load Dispatch

DED.py

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


Dynamic Economic Load Dispatch

For more details please refer to Chapter 4 (Gcode4.1), 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 numpy as np
import pandas as pd
from gamspy import Container, Equation, Model, Parameter, Set, Sum, Variable
from gamspy.math import sqr


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


def data_records():
    # gendata records table
    cols = ["a", "b", "c", "d", "e", "f", "Pmin", "Pmax", "RU0", "RD0"]
    inds = [f"g{i}" for i in range(1, 5)]
    data = [
        [0.12, 14.80, 89, 1.2, -5.0, 3.0, 28, 200, 40, 40],
        [0.17, 16.57, 83, 2.3, -4.24, 6.09, 20, 290, 30, 30],
        [0.15, 15.55, 100, 1.1, -2.15, 5.69, 30, 190, 30, 30],
        [0.19, 16.21, 70, 1.1, -3.99, 6.2, 20, 260, 50, 50],
    ]
    gen_recs = reformat_df(pd.DataFrame(data, columns=cols, index=inds))

    # Demand data
    demand_recs = np.array(
        [
            510,
            530,
            516,
            510,
            515,
            544,
            646,
            686,
            741,
            734,
            748,
            760,
            754,
            700,
            686,
            720,
            714,
            761,
            727,
            714,
            618,
            584,
            578,
            544,
        ]
    )

    return gen_recs, demand_recs


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

    # SETS #
    t = Set(
        m,
        name="t",
        records=[f"t{i}" for i in range(1, 25)],
        description="hours",
    )
    i = Set(
        m,
        name="i",
        records=[f"g{i}" for i in range(1, 5)],
        description="thermal units",
    )

    # PARAMETERS #
    demand = Parameter(m, name="demand", domain=t, records=data_records()[1])
    gendata = Parameter(
        m,
        name="gendata",
        domain=[i, "*"],
        records=data_records()[0],
        description="generator cost characteristics and limits",
    )

    # VARIABLES #
    p = Variable(
        m,
        name="p",
        type="free",
        domain=[i, t],
        description="power generated by thermal power plant",
    )
    EM = Variable(
        m, name="EM", type="free", description="emission calculation"
    )

    p.up[i, t] = gendata[i, "Pmax"]
    p.lo[i, t] = gendata[i, "Pmin"]

    # EQUATIONS #
    Genconst3 = Equation(m, name="Genconst3", type="regular", domain=[i, t])
    Genconst4 = Equation(m, name="Genconst4", type="regular", domain=[i, t])
    balance = Equation(m, name="balance", type="regular", domain=t)
    EMcalc = Equation(m, name="EMcalc", type="regular")

    costThermal = Sum(
        [t, i],
        gendata[i, "a"] * sqr(p[i, t])
        + gendata[i, "b"] * p[i, t]
        + gendata[i, "c"],
    )

    Genconst3[i, t] = p[i, t.lead(1)] - p[i, t] <= gendata[i, "RU0"]

    Genconst4[i, t] = p[i, t.lag(1)] - p[i, t] <= gendata[i, "RD0"]

    balance[t] = Sum(i, p[i, t]) >= demand[t]

    EMcalc[...] = (
        Sum(
            [t, i],
            gendata[i, "d"] * sqr(p[i, t])
            + gendata[i, "e"] * p[i, t]
            + gendata[i, "f"],
        )
        == EM
    )

    DEDcostbased = Model(
        m,
        name="DEDcostbased",
        equations=m.getEquations(),
        problem="qcp",
        sense="min",
        objective=costThermal,
    )

    DEDcostbased.solve()

    import math

    assert math.isclose(
        DEDcostbased.objective_value, 647964.4601, rel_tol=0.001
    )

    # Export results to excel
    p.pivot().round(4).to_excel("DEDcostbased.xlsx")


if __name__ == "__main__":
    main()