"""
## GAMSSOURCE: https://www.gams.com/latest/psoptlib_ml/libhtml/psoptlib_TEP.html
## LICENSETYPE: Demo
## MODELTYPE: MIP
Transmission Expansion Planning
For more details please refer to Chapter 9 (Gcode9.1), of the following book:
Soroudi, Alireza. Power System Optimization Modeling in GAMS. Springer, 2017.
--------------------------------------------------------------------------------
Model type: MIP
--------------------------------------------------------------------------------
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 (
Alias,
Container,
Domain,
Equation,
Model,
Options,
Ord,
Parameter,
Set,
Smax,
Sum,
Variable,
)
def reformat_df(dataframe):
return dataframe.reset_index().melt(
id_vars="index", var_name="Category", value_name="Value"
)
def data_records():
# GenD records table
cols = ["b", "Pmin", "Pmax"]
inds = [f"g{g}" for g in range(1, 4)]
data = [[20, 0, 400], [30, 0, 400], [10, 0, 600]]
GenD_recs = reformat_df(pd.DataFrame(data, columns=cols, index=inds))
# BD records table
cols = ["Pd"]
inds = ["1", "2", "3", "4", "5"]
data = [[80], [240], [40], [160], [240]]
BD_recs = reformat_df(pd.DataFrame(data, columns=cols, index=inds))
# Branch records table
cols = ["X", "LIMIT", "Cost", "stat"]
inds = [
("1", "2"),
("1", "4"),
("1", "5"),
("2", "3"),
("2", "4"),
("2", "6"),
("3", "5"),
("4", "6"),
]
data = [
[0.4, 100, 40, 1],
[0.6, 80, 60, 1],
[0.2, 100, 20, 1],
[0.2, 100, 20, 1],
[0.4, 100, 40, 1],
[0.3, 100, 30, 0],
[0.2, 100, 20, 1],
[0.3, 100, 30, 0],
]
inds = pd.MultiIndex.from_tuples(inds, names=["Index1", "Index2"])
B_recs = pd.DataFrame(data, columns=cols, index=inds)
B_recs.reset_index(inplace=True)
B_recs = B_recs.melt(
id_vars=["Index1", "Index2"], value_vars=["X", "LIMIT", "Cost", "stat"]
)
return (
GenD_recs,
BD_recs,
B_recs,
)
def main():
m = Container(
system_directory=os.getenv("SYSTEM_DIRECTORY", None),
)
# SETS #
bus = Set(m, name="bus", records=[str(buses) for buses in range(1, 7)])
slack = Set(m, name="slack", domain=bus, records=["1"])
Gen = Set(m, name="Gen", records=[f"g{g}" for g in range(1, 4)])
k = Set(m, name="k", records=[f"k{k}" for k in range(1, 5)])
GBconect = Set(
m,
name="GBconect",
domain=[bus, Gen],
records=[("1", "g1"), ("3", "g2"), ("6", "g3")],
description="connectivity index of each generating unit to each bus",
)
conex = Set(
m,
name="conex",
domain=[bus, bus],
description="bus connectivity matrix",
)
# ALIAS #
node = Alias(m, name="node", alias_with=bus)
# SCALARS #
Sbase = Parameter(m, name="Sbase", records=100)
M = Parameter(m, name="M")
# PARAMETERS #
GenData = Parameter(
m,
name="GenData",
domain=[Gen, "*"],
records=data_records()[0],
description="generating units characteristics",
)
BusData = Parameter(
m,
name="BusData",
domain=[bus, "*"],
records=data_records()[1],
description="demands of each bus in MW",
)
branch = Parameter(
m,
name="branch",
domain=[bus, node, "*"],
records=data_records()[2],
description="network technical characteristics",
)
conex[bus, node].where[branch[bus, node, "x"]] = True
conex[bus, node].where[conex[node, bus]] = True
branch[bus, node, "x"].where[branch[node, bus, "x"]] = branch[
node, bus, "x"
]
branch[bus, node, "cost"].where[branch[node, bus, "cost"]] = branch[
node, bus, "cost"
]
branch[bus, node, "stat"].where[branch[node, bus, "stat"]] = branch[
node, bus, "stat"
]
branch[bus, node, "Limit"].where[branch[bus, node, "Limit"] == 0] = branch[
node, bus, "Limit"
]
branch[bus, node, "bij"].where[conex[bus, node]] = (
1 / branch[bus, node, "x"]
)
M[...] = Smax(
Domain(bus, node).where[conex[bus, node]],
branch[bus, node, "bij"] * 3.14 * 2,
)
# VARIABLES #
OF = Variable(m, name="OF", type="free")
Pij = Variable(m, name="Pij", type="free", domain=[bus, node, k])
Pg = Variable(m, name="Pg", type="free", domain=Gen)
delta = Variable(m, name="delta", type="free", domain=bus)
LS = Variable(m, name="LS", type="free", domain=bus)
alpha = Variable(m, name="alpha", type="binary", domain=[bus, node, k])
alpha.l[bus, node, k] = 1
alpha.fx[bus, node, k].where[
(conex[bus, node]) & (Ord(k) == 1) & (branch[node, bus, "stat"])
] = 1
# EQUATIONS #
const1A = Equation(
m, name="const1A", type="regular", domain=[bus, node, k]
)
const1B = Equation(
m, name="const1B", type="regular", domain=[bus, node, k]
)
const1C = Equation(
m, name="const1C", type="regular", domain=[bus, node, k]
)
const1D = Equation(
m, name="const1D", type="regular", domain=[bus, node, k]
)
const1E = Equation(
m, name="const1E", type="regular", domain=[bus, node, k]
)
const2 = Equation(m, name="const2", type="regular", domain=bus)
const3 = Equation(m, name="const3", type="regular")
const1A[bus, node, k].where[conex[node, bus]] = Pij[bus, node, k] - branch[
bus, node, "bij"
] * (delta[bus] - delta[node]) <= M * (1 - alpha[bus, node, k])
const1B[bus, node, k].where[conex[node, bus]] = Pij[bus, node, k] - branch[
bus, node, "bij"
] * (delta[bus] - delta[node]) >= -M * (1 - alpha[bus, node, k])
const1C[bus, node, k].where[conex[node, bus]] = (
Pij[bus, node, k]
<= alpha[bus, node, k] * branch[bus, node, "Limit"] / Sbase
)
const1D[bus, node, k].where[conex[node, bus]] = (
Pij[bus, node, k]
>= -alpha[bus, node, k] * branch[bus, node, "Limit"] / Sbase
)
const1E[bus, node, k].where[conex[node, bus]] = (
alpha[bus, node, k] == alpha[node, bus, k]
)
const2[bus] = LS[bus] + Sum(
Gen.where[GBconect[bus, Gen]], Pg[Gen]
) - BusData[bus, "pd"] / Sbase == Sum(
Domain(k, node).where[conex[node, bus]], Pij[bus, node, k]
)
const3[...] = (
10
* 8760
* (
Sum(Gen, Pg[Gen] * GenData[Gen, "b"] * Sbase)
+ 100000 * Sum(bus, LS[bus])
)
+ 1e6
* Sum(
Domain(bus, node, k).where[conex[node, bus]],
0.5
* branch[bus, node, "cost"]
* alpha[bus, node, k].where[
(Ord(k) > 1) | (branch[node, bus, "stat"] == 0)
],
)
<= OF
)
loadflow = Model(
m,
name="loadflow",
equations=m.getEquations(),
problem="mip",
sense="min",
objective=OF,
)
LS.up[bus] = BusData[bus, "pd"] / Sbase
LS.lo[bus] = 0
Pg.lo[Gen] = GenData[Gen, "Pmin"] / Sbase
Pg.up[Gen] = GenData[Gen, "Pmax"] / Sbase
delta.up[bus] = np.pi / 3
delta.lo[bus] = -np.pi / 3
delta.fx[slack] = 0
Pij.up[bus, node, k].where[conex[bus, node]] = (
1 * branch[bus, node, "Limit"] / Sbase
)
Pij.lo[bus, node, k].where[conex[bus, node]] = (
-1 * branch[bus, node, "Limit"] / Sbase
)
loadflow.solve(options=Options(relative_optimality_gap=0, mip="CPLEX"))
print("Objective Function Value: ", round(loadflow.objective_value, 3))
if __name__ == "__main__":
main()
