"""
## GAMSSOURCE: https://www.gams.com/latest/psoptlib_ml/libhtml/psoptlib_PMU-OBI.html
## LICENSETYPE: Demo
## MODELTYPE: MIP
Maximizing the network observability using a limited number of PMU for IEEE 14 network without considering zero injection nodes
For more details please refer to Chapter 8 (Gcode8.4), 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
from gamspy import (
Alias,
Container,
Equation,
Model,
Options,
Parameter,
Sense,
Set,
Sum,
Variable,
)
def main():
m = Container(
system_directory=os.getenv("SYSTEM_DIRECTORY", None),
)
# Set
bus = Set(m, name="bus", records=[str(idx) for idx in range(1, 15)])
node = Alias(m, name="node", alias_with=bus)
conex = Set(
m,
name="conex",
records=[
("1", "2"),
("1", "5"),
("2", "3"),
("2", "4"),
("2", "5"),
("3", "4"),
("4", "5"),
("4", "7"),
("4", "9"),
("5", "6"),
("6", "11"),
("6", "12"),
("6", "13"),
("7", "8"),
("7", "9"),
("9", "10"),
("9", "14"),
("10", "11"),
("12", "13"),
("13", "14"),
],
domain=[bus, node],
description="Bus connectivity matrix",
)
conex[bus, node].where[conex[node, bus]] = 1
# Data
NPMU = Parameter(m, name="NPMU", records=10)
# Variable
PMU = Variable(m, name="PMU", domain=bus, type="Binary")
alpha = Variable(m, name="alpha", domain=bus, type="Binary")
# Equation
eq1 = Equation(m, name="eq1")
eq1[...] = Sum(bus, PMU[bus]) <= NPMU
eq2 = Sum(node, alpha[node])
eq3 = Equation(m, name="eq3", domain=bus)
eq3[bus] = (
PMU[bus] + Sum(node.where[conex[bus, node]], PMU[node]) >= alpha[bus]
)
placement3 = Model(
m,
name="placement3",
equations=m.getEquations(),
problem="MIP",
sense=Sense.MAX,
objective=eq2,
)
counter = Set(m, "counter", records=[f"c{idx}" for idx in range(1, 5)])
report = Parameter(m, "report", domain=[bus, counter])
OBIrep = Parameter(m, "OBIrep", domain=counter)
for idx, iter, _ in counter.records.itertuples():
NPMU[...] = idx + 1
placement3.solve(options=Options(relative_optimality_gap=0))
report[bus, iter] = PMU.l[bus]
OBIrep[iter] = placement3.objective_value
print("Report:\n", report.pivot())
if __name__ == "__main__":
main()
