# Ramp rate sensitivity analysis for Dynamic Economic Load Dispatch#

`RampSenDED.py`

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

Ramp rate sensitivity analysis for Dynamic Economic Load Dispatch

For more details please refer to Chapter 4 (Gcode4.2), of the following book:
Soroudi, Alireza. Power System Optimization Modeling in GAMS. Springer, 2017.
--------------------------------------------------------------------------------
Model type: QCP
--------------------------------------------------------------------------------
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 Container, Equation, Model, 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():
# 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],
]
gendata_recs = reformat_df(pd.DataFrame(data, columns=cols, index=inds))

# demand records list
demands_recs = np.array(
[
510,
530,
516,
510,
515,
544,
646,
686,
741,
734,
748,
760,
754,
700,
686,
720,
714,
761,
727,
714,
618,
584,
578,
544,
]
)

return gendata_recs, demands_recs

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

# SETS #
t = Set(
m,
name="t",
records=[f"t{t}" for t in range(1, 25)],
description="hours",
)
i = Set(
m,
name="i",
records=[f"p{i}" for i in range(1, 5)],
description="thermal units",
)

# PARAMETERS #
gendata = Parameter(
m,
name="gendata",
domain=[i, "*"],
records=data_records()[0],
description="generator cost characteristics and limits",
)
demand = Parameter(m, name="demand", domain=t, records=data_records()[1])

# VARIABLES #
p = Variable(
m,
name="p",
domain=[i, t],
description="power generated by thermal power plant",
)
EM = Variable(m, name="EM", description="emission calculation")

p.up[i, t] = gendata[i, "Pmax"]
p.lo[i, t] = gendata[i, "Pmin"]

# EQUATIONS #
Genconst3 = Equation(m, name="Genconst3", type="regular", domain=[i, t])
Genconst4 = Equation(m, name="Genconst4", type="regular", domain=[i, t])
balance = Equation(m, name="balance", type="regular", domain=t)
EMcalc = Equation(m, name="EMcalc", type="regular")

# Objective Function; cost of thermal units
costThermalcalc = Sum(
[t, i],
gendata[i, "a"] * sqr(p[i, t])
+ gendata[i, "b"] * p[i, t]
+ gendata[i, "c"],
)

Genconst3[i, t] = p[i, t.lead(1)] - p[i, t] <= gendata[i, "RU"]
Genconst4[i, t] = p[i, t.lag(1)] - p[i, t] <= gendata[i, "RD"]
balance[t] = Sum(i, p[i, t]) >= demand[t]
EMcalc[...] = (
Sum(
[t, i],
gendata[i, "d"] * sqr(p[i, t])
+ gendata[i, "e"] * p[i, t]
+ gendata[i, "f"],
)
== EM
)

DEDcostbased = Model(
m,
name="DEDcostbased",
equations=m.getEquations(),
problem="qcp",
sense="min",
objective=costThermalcalc,
)

# COUNTER SET
counter = Set(m, name="counter", records=[f"c{c}" for c in range(1, 22)])

# SCALAR
Rscale = Parameter(m, name="Rscale", records=1)

# REPORTING PARAMETER
report1 = Parameter(m, name="report1", domain=[counter, "*"])

for idx, c in enumerate(counter.toList()):
Rscale[...] = 1 - (idx) * 0.02
gendata[i, "RU"] = gendata[i, "RU0"] * Rscale
gendata[i, "RD"] = gendata[i, "RD0"] * Rscale
DEDcostbased.solve()
report1[c, "Scale"] = Rscale
report1[c, "TC"] = DEDcostbased.objective_value
report1[c, "EM"] = EM.l

print("report1:  \n", report1.pivot().round(4))

report1.pivot().round(4).to_excel(
"DEDcostbased.xlsx", sheet_name="Pthermal"
)

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