"""
Cost based Dynamic Economic Dispatch integrated with Energy Storage and Wind
For more details please refer to Chapter 7 (Gcode7.2), of the following book:
Soroudi, Alireza. Power System Optimization Modeling in GAMS. Springer, 2017.
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Model type: QCP
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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
import gamspy.math as gams_math
from gamspy import Container
from gamspy import Equation
from gamspy import Model
from gamspy import Ord
from gamspy import Parameter
from gamspy import Set
from gamspy import Sum
from gamspy import 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 = [f"p{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))
# data records table
cols = ["lamda", "load", "wind"]
inds = [f"t{i}" for i in range(1, 25)]
data = [
[32.71, 510, 44.1],
[34.72, 530, 48.5],
[32.71, 516, 65.7],
[32.74, 510, 144.9],
[32.96, 515, 202.3],
[34.93, 544, 317.3],
[44.9, 646, 364.4],
[52.0, 686, 317.3],
[53.03, 741, 271.0],
[47.26, 734, 306.9],
[44.07, 748, 424.1],
[38.63, 760, 398.0],
[39.91, 754, 487.6],
[39.45, 700, 521.9],
[41.14, 686, 541.3],
[39.23, 720, 560.0],
[52.12, 714, 486.8],
[40.85, 761, 372.6],
[41.2, 727, 367.4],
[41.15, 714, 314.3],
[45.76, 618, 316.6],
[45.59, 584, 311.4],
[45.56, 578, 405.4],
[34.72, 544, 470.4],
]
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),
delayed_execution=int(os.getenv("DELAYED_EXECUTION", False)),
)
# SETS #
t = Set(
m,
name="t",
records=[f"t{i}" for i in range(1, 25)],
description="hours",
)
g = Set(
m,
name="g",
records=[f"p{i}" for i in range(1, 5)],
description="thermal units",
)
# PARAMETERS #
gendata = Parameter(
m,
name="gendata",
domain=[g, "*"],
records=data_records()[0],
description="generator cost characteristics and limits",
)
data = Parameter(
m, name="data", domain=[t, "*"], records=data_records()[1]
)
# VARIABLES #
cost = Variable(
m, name="cost", type="free", description="cost of thermal units"
)
p = Variable(
m,
name="p",
type="free",
domain=[g, t],
description="power generated by thermal power plant",
)
SOC = Variable(m, name="SOC", type="free", domain=t)
Pd = Variable(m, name="Pd", type="free", domain=t)
Pc = Variable(m, name="Pc", type="free", domain=t)
Pw = Variable(m, name="Pw", type="free", domain=t)
PWC = Variable(m, name="PWC", type="free", domain=t)
p.up[g, t] = gendata[g, "Pmax"]
p.lo[g, t] = gendata[g, "Pmin"]
# SCALARS #
SOC0 = Parameter(m, name="SOC0", records=100)
SOCmax = Parameter(m, name="SOCmax", records=300)
eta_c = Parameter(m, name="eta_c", records=0.95)
eta_d = Parameter(m, name="eta_d", records=0.9)
VWC = Parameter(m, name="VWC", records=50)
SOC.up[t] = SOCmax
SOC.lo[t] = 0.2 * SOCmax
SOC.fx["t24"] = SOC0
Pc.up[t] = 0.2 * SOCmax
Pc.lo[t] = 0
Pd.up[t] = 0.2 * SOCmax
Pd.lo[t] = 0
Pw.up[t] = data[t, "wind"]
Pw.lo[t] = 0
PWC.up[t] = data[t, "wind"]
PWC.lo[t] = 0
# EQUATIONS #
Genconst3 = Equation(m, name="Genconst3", type="regular", domain=[g, t])
Genconst4 = Equation(m, name="Genconst4", type="regular", domain=[g, t])
costThermalcalc = Equation(m, name="costThermalcalc", type="regular")
constESS = Equation(m, name="constESS", type="regular", domain=t)
balance = Equation(m, name="balance", type="regular", domain=t)
wind = Equation(m, name="wind", type="regular", domain=t)
costThermalcalc[...] = cost == Sum(t, VWC * PWC[t]) + Sum(
[t, g],
gendata[g, "a"] * gams_math.power(p[g, t], 2)
+ gendata[g, "b"] * p[g, t]
+ gendata[g, "c"],
)
Genconst3[g, t] = p[g, t.lead(1)] - p[g, t] <= gendata[g, "RU0"]
Genconst4[g, t] = p[g, t.lag(1)] - p[g, t] <= gendata[g, "RD0"]
constESS[t] = (
SOC[t]
== SOC0.where[Ord(t) == 1]
+ SOC[t.lag(1)].where[Ord(t) > 1]
+ Pc[t] * eta_c
- Pd[t] / eta_d
)
balance[t] = Pw[t] + Sum(g, p[g, t]) + Pd[t] >= data[t, "load"] + Pc[t]
wind[t] = Pw[t] + PWC[t] == data[t, "wind"]
DEDESScostbased = Model(
m,
name="DEDESScostbased",
equations=m.getEquations(),
problem="qcp",
sense="min",
objective=cost,
)
DEDESScostbased.solve()
import math
assert math.isclose(
DEDESScostbased.objective_value, 223360.0645, rel_tol=0.001
)
# Reporting parameter
rep = Parameter(m, name="rep", domain=[t, "*"])
rep[t, "Pth"] = Sum(g, p.l[g, t])
rep[t, "SOC"] = SOC.l[t]
rep[t, "Pd"] = Pd.l[t]
rep[t, "Pc"] = Pc.l[t]
rep[t, "Pw"] = Pw.l[t]
rep[t, "Pwc"] = PWC.l[t]
rep[t, "Load"] = data[t, "load"]
# Export results to an excel file
writer = pd.ExcelWriter("DEDESScostbased.xlsx", engine="openpyxl")
p.pivot().round(4).to_excel(writer, sheet_name="Pthermal")
rep.pivot().round(4).to_excel(writer, sheet_name="rep")
# close writer agent
writer.close()
if __name__ == "__main__":
main()
