"""
## GAMSSOURCE: https://www.gams.com/latest/psoptlib_ml/libhtml/psoptlib_DED-PB.html
## LICENSETYPE: Demo
## MODELTYPE: QCP
Price based Dynamic Economic Load Dispatch
For more details please refer to Chapter 4 (Gcode4.5), 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 gamspy.math as gams_math
import numpy as np
import pandas as pd
from gamspy import 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():
# gendata records table
cols = ["a", "b", "c", "d", "e", "f", "Pmin", "Pmax", "RU0", "RD0"]
inds = ["p1", "p2", "p3", "p4"]
data = [
[0.12, 14.80, 89, 1.2, -5, 3, 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))
# data records table
cols = ["lamda", "load"]
inds = [f"t{i}" for i in range(1, 25)]
data = [
[32.71, 510],
[34.72, 530],
[32.71, 516],
[32.74, 510],
[32.96, 515],
[34.93, 544],
[44.9, 646],
[52.0, 686],
[53.03, 741],
[47.26, 734],
[44.07, 748],
[38.63, 760],
[39.91, 754],
[39.45, 700],
[41.14, 686],
[39.23, 720],
[52.12, 714],
[40.85, 761],
[41.2, 727],
[41.15, 714],
[45.76, 618],
[45.59, 584],
[45.56, 578],
[34.72, 544],
]
data_recs = reformat_df(pd.DataFrame(data, columns=cols, index=inds))
return gen_recs, data_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"p{i}" for i in range(1, 5)],
description="thermal units",
)
# SCALAR #
lim = Parameter(m, name="lim", records=np.inf)
# PARAMETERS #
gendata = Parameter(
m,
name="gendata",
domain=[i, "*"],
records=data_records()[0],
description="generator cost characteristics and limits",
)
data = Parameter(
m, name="data", domain=[t, "*"], records=data_records()[1]
)
# VARIABLES #
costThermal = Variable(
m, name="costThermal", type="free", description="cost of thermal units"
)
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])
costThermalcalc = Equation(m, name="costThermalcalc", type="regular")
balance = Equation(m, name="balance", type="regular", domain=t)
EMcalc = Equation(m, name="EMcalc", type="regular")
EMlim = Equation(m, name="EMlim", type="regular")
costThermalcalc[...] = costThermal == Sum(
[t, i],
gendata[i, "a"] * gams_math.power(p[i, t], 2)
+ 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]) <= data[t, "load"]
EMcalc[...] = (
Sum(
[t, i],
gendata[i, "d"] * gams_math.power(p[i, t], 2)
+ gendata[i, "e"] * p[i, t]
+ gendata[i, "f"],
)
== EM
)
EMlim[...] = lim >= EM
# Objective Function
OF = Sum([i, t], 1 * data[t, "lamda"] * p[i, t]) - costThermal
DEDPB = Model(
m,
name="DEDPB",
equations=m.getEquations(),
problem="qcp",
sense="max",
objective=OF,
)
DEDPB.solve()
import math
assert math.isclose(DEDPB.objective_value, 99552.6661, rel_tol=0.001)
# Export results to an excel file
p.pivot().round(3).to_excel("DEDPB.xlsx")
if __name__ == "__main__":
main()
