# Multi-period AC-OPF for IEEE 24-bus network considering wind and load shedding#

`MultiperiodACOPF24bus.py`

```"""
## GAMSSOURCE: https://www.gams.com/latest/psoptlib_ml/libhtml/psoptlib_MultiperiodACOPF24bus.html
## MODELTYPE: NLP

Multi-period AC-OPF for IEEE 24-bus network considering wind and load shedding

For more details please refer to Chapter 6 (Gcode6.7), of the following book:
Soroudi, Alireza. Power System Optimization Modeling in GAMS. Springer, 2017.
--------------------------------------------------------------------------------
Model type: NLP
--------------------------------------------------------------------------------
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 math
import os

import gamspy.math as gams_math
import pandas as pd
from gamspy import (
Alias,
Card,
Container,
Equation,
Model,
Ord,
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():
# GenD records table
cols = ["pmax", "pmin", "b", "Qmax", "Qmin", "Vg", "RU", "RD"]
inds = ["1", "2", "7", "13", "15", "16", "18", "21", "22", "23"]
data = [
[152, 30.4, 13.32, 192, -50, 1.035, 21, 21],
[152, 30.4, 13.32, 192, -50, 1.035, 21, 21],
[350, 75.0, 20.7, 300, 0, 1.025, 43, 43],
[591, 206.85, 20.93, 591, 0, 1.02, 31, 31],
[215, 66.25, 21.0, 215, -100, 1.014, 31, 31],
[155, 54.25, 10.52, 155, -50, 1.017, 31, 31],
[400, 100.0, 5.47, 400, -50, 1.05, 70, 70],
[400, 100.0, 5.47, 400, -50, 1.05, 70, 70],
[300, 0.0, 0.0, 300, -60, 1.05, 53, 53],
[360, 248.5, 10.52, 310, -125, 1.05, 31, 31],
]
GenD_recs = reformat_df(pd.DataFrame(data, columns=cols, index=inds))

# BD records table
cols = ["Pd", "Qd"]
inds = [str(ii) for ii in range(1, 25)]
data = [
[108, 22],
[97, 20],
[180, 37],
[74, 15],
[71, 14],
[136, 28],
[125, 25],
[171, 35],
[175, 36],
[195, 40],
[0, 0],
[0, 0],
[265, 54],
[194, 39],
[317, 64],
[100, 20],
[0, 0],
[333, 68],
[181, 37],
[128, 26],
[0, 0],
[0, 0],
[0, 0],
[0, 0],
]
BD_recs = reformat_df(pd.DataFrame(data, columns=cols, index=inds))

# LN records table
cols = ["r", "x", "b", "limit"]
inds = [
("1", "2"),
("1", "3"),
("1", "5"),
("2", "4"),
("2", "6"),
("3", "9"),
("3", "24"),
("4", "9"),
("5", "10"),
("6", "10"),
("7", "8"),
("8", "9"),
("8", "10"),
("9", "11"),
("9", "12"),
("10", "11"),
("10", "12"),
("11", "13"),
("11", "14"),
("12", "13"),
("12", "23"),
("13", "23"),
("14", "16"),
("15", "16"),
("15", "21"),
("15", "24"),
("16", "17"),
("16", "19"),
("17", "18"),
("17", "22"),
("18", "21"),
("19", "20"),
("20", "23"),
("21", "22"),
]
data = [
[0.0026, 0.0139, 0.4611, 175],
[0.0546, 0.2112, 0.0572, 175],
[0.0218, 0.0845, 0.0229, 175],
[0.0328, 0.1267, 0.0343, 175],
[0.0497, 0.192, 0.052, 175],
[0.0308, 0.119, 0.0322, 175],
[0.0023, 0.0839, 0.0, 400],
[0.0268, 0.1037, 0.0281, 175],
[0.0228, 0.0883, 0.0239, 175],
[0.0139, 0.0605, 2.459, 175],
[0.0159, 0.0614, 0.0166, 175],
[0.0427, 0.1651, 0.0447, 175],
[0.0427, 0.1651, 0.0447, 175],
[0.0023, 0.0839, 0.0, 400],
[0.0023, 0.0839, 0.0, 400],
[0.0023, 0.0839, 0.0, 400],
[0.0023, 0.0839, 0.0, 400],
[0.0061, 0.0476, 0.0999, 500],
[0.0054, 0.0418, 0.0879, 500],
[0.0061, 0.0476, 0.0999, 500],
[0.0124, 0.0966, 0.203, 500],
[0.0111, 0.0865, 0.1818, 500],
[0.005, 0.0389, 0.0818, 500],
[0.0022, 0.0173, 0.0364, 500],
[0.00315, 0.0245, 0.206, 1000],
[0.0067, 0.0519, 0.1091, 500],
[0.0033, 0.0259, 0.0545, 500],
[0.003, 0.0231, 0.0485, 500],
[0.0018, 0.0144, 0.0303, 500],
[0.0135, 0.1053, 0.2212, 500],
[0.00165, 0.01295, 0.109, 1000],
[0.00255, 0.0198, 0.1666, 1000],
[0.0014, 0.0108, 0.091, 1000],
[0.0087, 0.0678, 0.1424, 500],
]
inds = pd.MultiIndex.from_tuples(inds, names=["Index1", "Index2"])
LN_recs = pd.DataFrame(data, columns=cols, index=inds)
LN_recs.reset_index(inplace=True)
LN_recs = LN_recs.melt(
id_vars=["Index1", "Index2"], value_vars=["r", "x", "b", "limit"]
)

# WD records table
cols = ["w", "d"]
inds = [f"t{tt}" for tt in range(1, 25)]
data = [
[0.0786666666666667, 0.684511335492475],
[0.0866666666666667, 0.644122690036197],
[0.117333333333333, 0.6130691560297],
[0.258666666666667, 0.599733282530006],
[0.361333333333333, 0.588874071251667],
[0.566666666666667, 0.5980186702229],
[0.650666666666667, 0.626786054486569],
[0.566666666666667, 0.651743189178891],
[0.484, 0.706039245570585],
[0.548, 0.787007048961707],
[0.757333333333333, 0.839016955610593],
[0.710666666666667, 0.852733854067441],
[0.870666666666667, 0.870642027052772],
[0.932, 0.834254143646409],
[0.966666666666667, 0.816536483139646],
[1.0, 0.819394170318156],
[0.869333333333333, 0.874071251666984],
[0.665333333333333, 1.0],
[0.656, 0.983615926843208],
[0.561333333333333, 0.936368832158506],
[0.565333333333333, 0.887597637645266],
[0.556, 0.809297008954087],
[0.724, 0.74585635359116],
[0.84, 0.733473042484283],
]
WD_recs = reformat_df(pd.DataFrame(data, columns=cols, index=inds))

return GenD_recs, BD_recs, LN_recs, WD_recs

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

# SETS #
i = Set(
m,
name="i",
records=[str(ii) for ii in range(1, 25)],
description="network buses",
)
slack = Set(m, name="slack", domain=i, records=[13])
t = Set(m, name="t", records=[f"t{tt}" for tt in range(1, 25)])

# ALIAS #
j = Alias(m, name="j", alias_with=i)

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

# PARAMETERS
GenD = Parameter(
m,
name="GenD",
domain=[i, "*"],
records=data_records()[0],
description="generating units characteristics",
)
BD = Parameter(
m,
name="BD",
domain=[i, "*"],
records=data_records()[1],
description="demands of each bus in MW",
)
LN = Parameter(
m,
name="LN",
domain=[i, j, "*"],
records=data_records()[2],
description="network technical characteristics",
)
WD = Parameter(m, name="WD", domain=[t, "*"], records=data_records()[3])
Wcap = Parameter(
m,
name="Wcap",
domain=i,
records=[("8", 200), ("19", 150), ("21", 100)],
)
cx = Parameter(m, name="cx", domain=[i, j])

LN[i, j, "x"].where[LN[i, j, "x"] == 0] = LN[j, i, "x"]
LN[i, j, "r"].where[LN[i, j, "r"] == 0] = LN[j, i, "r"]
LN[i, j, "b"].where[LN[i, j, "b"] == 0] = LN[j, i, "b"]
LN[i, j, "Limit"].where[LN[i, j, "Limit"] == 0] = LN[j, i, "Limit"]
LN[i, j, "bij"].where[LN[i, j, "Limit"]] = 1 / LN[i, j, "x"]
LN[i, j, "z"].where[LN[i, j, "Limit"]] = gams_math.sqrt(
sqr(LN[i, j, "x"]) + sqr(LN[i, j, "r"])
)
LN[j, i, "z"].where[LN[i, j, "z"] == 0] = LN[i, j, "z"]
LN[i, j, "th"].where[
(LN[i, j, "Limit"]) & (LN[i, j, "x"]) & (LN[i, j, "r"])
] = gams_math.atan(LN[i, j, "x"] / (LN[i, j, "r"]))
LN[i, j, "th"].where[
(LN[i, j, "Limit"]) & (LN[i, j, "x"]) & (LN[i, j, "r"] == 0)
] = math.pi / 2
LN[i, j, "th"].where[
(LN[i, j, "Limit"]) & (LN[i, j, "r"]) & (LN[i, j, "x"] == 0)
] = 0
LN[j, i, "th"].where[LN[i, j, "Limit"]] = LN[i, j, "th"]

cx[i, j].where[(LN[i, j, "limit"]) & (LN[j, i, "limit"])] = 1
cx[i, j].where[cx[j, i]] = 1

# VARIABLES #
OF = Variable(m, name="OF")
Pij = Variable(m, name="Pij", domain=[i, j, t])
Qij = Variable(m, name="Qij", domain=[i, j, t])
Pg = Variable(m, name="Pg", domain=[i, t])
Qg = Variable(m, name="Qg", domain=[i, t])
Va = Variable(m, name="Va", domain=[i, t])
V = Variable(m, name="V", domain=[i, t])
Pw = Variable(m, name="Pw", domain=[i, t])

# EQUATIONS #
eq1 = Equation(m, name="eq1", type="regular", domain=[i, j, t])
eq2 = Equation(m, name="eq2", type="regular", domain=[i, j, t])
eq3 = Equation(m, name="eq3", type="regular", domain=[i, t])
eq4 = Equation(m, name="eq4", type="regular", domain=[i, t])
eq5 = Equation(m, name="eq5", type="regular")
eq6 = Equation(m, name="eq6", type="regular", domain=[i, t])
eq7 = Equation(m, name="eq7", type="regular", domain=[i, t])

eq1[i, j, t].where[cx[i, j]] = (
Pij[i, j, t]
== (
V[i, t] * V[i, t] * gams_math.cos(LN[j, i, "th"])
- V[i, t]
* V[j, t]
* gams_math.cos(Va[i, t] - Va[j, t] + LN[j, i, "th"])
)
/ LN[j, i, "z"]
)

eq2[i, j, t].where[cx[i, j]] = (
Qij[i, j, t]
== (
V[i, t] * V[i, t] * gams_math.sin(LN[j, i, "th"])
- V[i, t]
* V[j, t]
* gams_math.sin(Va[i, t] - Va[j, t] + LN[j, i, "th"])
)
/ LN[j, i, "z"]
- LN[j, i, "b"] * V[i, t] * V[i, t] / 2
)

eq3[i, t] = Pw[i, t].where[Wcap[i]] + Pg[i, t].where[GenD[i, "Pmax"]] - WD[
t, "d"
] * BD[i, "pd"] / Sbase == Sum(j.where[cx[j, i]], Pij[i, j, t])

eq4[i, t] = Qg[i, t].where[GenD[i, "Qmax"]] - WD[t, "d"] * BD[
i, "qd"
] / Sbase == Sum(j.where[cx[j, i]], Qij[i, j, t])

eq5[...] = (
Sum([i, t], Pg[i, t] * GenD[i, "b"] * Sbase.where[GenD[i, "Pmax"]])
<= OF
)

eq6[i, t].where[(GenD[i, "Pmax"]) & (Ord(t) > 1)] = (
Pg[i, t] - Pg[i, t.lag(1)] <= GenD[i, "RU"] / Sbase
)

eq7[i, t].where[(GenD[i, "Pmax"]) & (Ord(t) < Card(t))] = (
Pg[i, t] - Pg[i, t.lead(1)] <= GenD[i, "RD"] / Sbase
)

m,
equations=[eq1, eq2, eq3, eq4, eq5, eq6, eq7],
problem="nlp",
sense="min",
objective=OF,
)

Pg.lo[i, t] = GenD[i, "Pmin"] / Sbase
Pg.up[i, t] = GenD[i, "Pmax"] / Sbase
Qg.lo[i, t] = GenD[i, "Qmin"] / Sbase
Qg.up[i, t] = GenD[i, "Qmax"] / Sbase

Va.up[i, t] = math.pi / 2
Va.lo[i, t] = -math.pi / 2
Va.l[i, t] = 0
Va.fx[slack, t] = 0

Pij.up[i, j, t].where[cx[i, j]] = 1 * LN[i, j, "Limit"] / Sbase
Pij.lo[i, j, t].where[cx[i, j]] = -1 * LN[i, j, "Limit"] / Sbase
Qij.up[i, j, t].where[cx[i, j]] = 1 * LN[i, j, "Limit"] / Sbase
Qij.lo[i, j, t].where[cx[i, j]] = -1 * LN[i, j, "Limit"] / Sbase

V.lo[i, t] = 0.9
V.up[i, t] = 1.1
V.l[i, t] = 1
Pw.up[i, t] = WD[t, "w"] * Wcap[i] / Sbase
Pw.lo[i, t] = 0

# Reporting Parameters
report = Parameter(m, name="report", domain=[t, i, "*"])
report2 = Parameter(m, name="report2", domain=[i, t])
report3 = Parameter(m, name="report3", domain=[i, t])

report[t, i, "V"] = V.l[i, t]
report[t, i, "Angle"] = Va.l[i, t]
report[t, i, "Pg"] = Pg.l[i, t] * Sbase
report[t, i, "Gg"] = Qg.l[i, t] * Sbase
report[t, i, "LMP_P"] = eq3.m[i, t] / Sbase
report[t, i, "LMP_Q"] = eq4.m[i, t] / Sbase
report2[i, t] = Pg.l[i, t] * Sbase
report3[i, t] = Qg.l[i, t] * Sbase
print("report  \n", report.pivot().round(4))

writer = pd.ExcelWriter("results.xlsx", engine="openpyxl")

report.pivot().round(4).to_excel(writer, sheet_name="classic")
report2.pivot().round(4).to_excel(writer, sheet_name="classic2")
report3.pivot().round(4).to_excel(writer, sheet_name="classic3")

writer.close()

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