# Optimal power flow for a Five-bus system#

`OPF5bus.py`

```"""
## GAMSSOURCE: https://www.gams.com/latest/psoptlib_ml/libhtml/psoptlib_OPF5bus.html
## MODELTYPE: LP

Optimal power flow for a Five-bus system

For more details please refer to Chapter 6 (Gcode6.3), of the following book:
Soroudi, Alireza. Power System Optimization Modeling in GAMS. Springer, 2017.
--------------------------------------------------------------------------------
Model type: LP
--------------------------------------------------------------------------------
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,
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():
# GenD records table
cols = ["b", "Pmin", "Pmax"]
inds = [f"g{gg}" for gg in range(1, 6)]
data = [
[14, 0, 40],
[15, 0, 170],
[30, 0, 520],
[40, 0, 200],
[10, 0, 600],
]
GenD_recs = reformat_df(pd.DataFrame(data, columns=cols, index=inds))

# BD records table
cols = ["Pd"]
inds = ["2", "3", "4"]
data = [[300], [300], [400]]
BD_recs = reformat_df(pd.DataFrame(data, columns=cols, index=inds))

# Branch records table
cols = ["x", "limit"]
inds = [
("1", "2"),
("1", "4"),
("1", "5"),
("2", "3"),
("3", "4"),
("4", "5"),
]
data = [
[0.0281, 400],
[0.0304, 400],
[0.0064, 400],
[0.0108, 400],
[0.0297, 400],
[0.0297, 240],
]
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"]
)

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, 6)])
slack = Set(m, name="slack", domain=bus, records=["1"])
Gen = Set(m, name="Gen", records=[f"g{gg}" for gg in range(1, 6)])
conex = Set(
m,
name="conex",
domain=[bus, bus],
records=[
("1", "2"),
("2", "3"),
("3", "4"),
("4", "1"),
("4", "5"),
("5", "1"),
],
description="bus connectivity matrix",
)
GBconect = Set(
m,
name="GBconect",
domain=[bus, Gen],
records=[
("1", "g1"),
("1", "g2"),
("3", "g3"),
("4", "g4"),
("5", "g5"),
],
description="connectivity index of each generating unit to each bus",
)

# ALIASES #
node = Alias(m, name="node", alias_with=bus)

conex[bus, node].where[conex[node, bus]] = 1

# SCALARS #
Sbase = Parameter(m, name="Sbase", records=100)

# 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",
)

branch[bus, node, "x"].where[branch[bus, node, "x"] == 0] = branch[
node, bus, "x"
]
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"]
)

# VARIABLES #
OF = Variable(m, name="OF")
Pij = Variable(m, name="Pij", domain=[bus, node])
Pg = Variable(m, name="Pg", domain=Gen)
delta = Variable(m, name="delta", domain=bus)

# EQUATIONS #
const1 = Equation(m, name="const1", type="regular", domain=[bus, node])
const2 = Equation(m, name="const2", type="regular", domain=bus)
const3 = Equation(m, name="const3", type="regular")

const1[bus, node].where[conex[bus, node]] = Pij[bus, node] == branch[
bus, node, "bij"
] * (delta[bus] - delta[node])

const2[bus] = Sum(Gen.where[GBconect[bus, Gen]], Pg[Gen]) - BusData[
bus, "pd"
] / Sbase == Sum(node.where[conex[node, bus]], Pij[bus, node])

const3[...] = Sum(Gen, Pg[Gen] * GenData[Gen, "b"] * Sbase) <= OF

m,
equations=[const1, const2, const3],
problem="lp",
sense="min",
objective=OF,
)

Pg.lo[Gen] = GenData[Gen, "Pmin"] / Sbase
Pg.up[Gen] = GenData[Gen, "Pmax"] / Sbase
delta.up[bus] = np.pi
delta.lo[bus] = -np.pi
delta.fx[slack] = 0
Pij.up[bus, node].where[conex[bus, node]] = (
1 * branch[bus, node, "Limit"] / Sbase
)
Pij.lo[bus, node].where[conex[bus, node]] = (
-1 * branch[bus, node, "Limit"] / Sbase
)

#  REPORTING PARAMETERS
report = Parameter(m, name="report", domain=[bus, "*"])
Congestioncost = Parameter(m, name="Congestioncost")
report[bus, "Gen(MW)"] = (
Sum(Gen.where[GBconect[bus, Gen]], Pg.l[Gen]) * Sbase
)
report[bus, "Angle"] = delta.l[bus]
report[bus, "LMP(\$/MWh)"] = const2.m[bus] / Sbase
Congestioncost[...] = (
Sum([bus, node], Pij.l[bus, node] * (-const2.m[bus] + const2.m[node]))
/ 2
)

print("report:  \n", report.pivot().round(4), "\n")
print("Pij:  \n", Pij.pivot().round(4), "\n")
print("Congestioncost:  ", Congestioncost.toValue())
print("Objective Function Value:  ", round(OF.toValue(), 4))

if __name__ == "__main__":
main()
```