import logging
from pathlib import Path
import numpy as np
import pandas as pd
from amplpy import AMPL
from matpowercaseframes import CaseFrames
from scipy.optimize import minimize
[docs]
def compute(args):
return max(args, key=len)
# TODO: Remove compute function at some point
def array2dict(array):
"""Convert a 2D numpy array to a dictionary."""
return {(i, j): array[i, j] for i in range(array.shape[0]) for j in range(array.shape[1])}
[docs]
class PowerSystem:
"""PowerSystem class for solving optimal power flow problems."""
[docs]
def __init__(self, case_file: str):
"""Initialize the power system with a MATPOWER case file."""
print(f"=======Initializing the power system with case file: {case_file}")
self.case_file = case_file
self.max_angle = np.pi / 2
self.min_angle = -np.pi / 2
self.load_data()
self.summary()
self.compute_matrices()
self.initialize()
self.compute_initial_bigm_dc()
self.compute_initial_bigm_ac()
[docs]
def load_data(self):
"""Load MATPOWER case data into DataFrames and convert to per unit."""
try:
case = CaseFrames(self.case_file)
# Load data for each component
self.baseMVA = case.baseMVA
self.buses = case.bus
self.buses.reset_index(drop=True, inplace=True)
self.buses["BUS_I"] -= 1
self.generators = case.gen
self.generators.reset_index(drop=True, inplace=True)
self.generators["GEN_BUS"] -= 1
self.branches = case.branch
self.branches.reset_index(drop=True, inplace=True)
self.branches["F_BUS"] -= 1
self.branches["T_BUS"] -= 1
self.gencost = case.gencost
self.gencost.reset_index(drop=True, inplace=True)
self.nbus = len(self.buses)
self.nlin = len(self.branches)
self.ngen = len(self.generators)
# Add default values for generator costs if not provided
if "COST_2" not in self.gencost.columns:
self.gencost["COST_2"] = 0
# Minimum and maximum voltage limits
self.max_voltage = self.buses["VMAX"].max()
self.min_voltage = self.buses["VMIN"].min()
self.buses["AMAX"] = self.max_angle
self.buses["AMIN"] = self.min_angle
# Convert to per unit
self.buses["PD"] /= self.baseMVA
self.buses["QD"] /= self.baseMVA
self.buses["GS"] /= self.baseMVA
self.buses["BS"] /= self.baseMVA
self.generators["PG"] /= self.baseMVA
self.generators["QG"] /= self.baseMVA
self.generators["PMAX"] /= self.baseMVA
self.generators["PMIN"] /= self.baseMVA
self.generators["QMAX"] /= self.baseMVA
self.generators["QMIN"] /= self.baseMVA
self.branches["RATE_A"] /= self.baseMVA
self.branches["RATE_B"] /= self.baseMVA
self.branches["RATE_C"] /= self.baseMVA
# Set default branch limit if not provided
self.default_branch_limit = np.sqrt(self.buses["PD"].sum() ** 2 + self.buses["QD"].sum() ** 2)
for line_index in range(self.nlin):
if self.branches.loc[line_index, "RATE_A"] == 0:
self.branches.loc[line_index, "RATE_A"] = self.default_branch_limit
except Exception as e:
logging.error(f"Error loading data from {self.case_file}: {e}")
raise
[docs]
def compute_matrices(self):
"""Calculate the admittance matrices (yff, ytf, yft, ytt) for the network."""
# Initizalize matrices
self.yff = np.zeros(self.nlin, dtype=complex)
self.ytf = np.zeros(self.nlin, dtype=complex)
self.yft = np.zeros(self.nlin, dtype=complex)
self.ytt = np.zeros(self.nlin, dtype=complex)
self.cf = np.zeros((self.nlin, self.nbus)) # Connection for F_BUS
self.ct = np.zeros((self.nlin, self.nbus)) # Connection for T_BUS
self.cg = np.zeros((self.ngen, self.nbus)) # Connection for generators
# Compute admittance matrices
for line_index in range(self.nlin):
branch = self.branches.iloc[line_index] # Access branch data
r = branch["BR_R"]
x = branch["BR_X"]
b = branch["BR_B"]
tau = branch["TAP"] if branch["TAP"] != 0 else 1 # Handle TAP=0 case
theta = branch["SHIFT"]
# Calculate Y series and shunt admittance
ys = 1 / (r + 1j * x)
# Store the admittance components
self.yff[line_index] = (ys + 1j * 0.5 * b) / (tau**2)
self.yft[line_index] = -ys / (tau * np.exp(-1j * theta))
self.ytf[line_index] = -ys / (tau * np.exp(1j * theta))
self.ytt[line_index] = ys + 1j * 0.5 * b
# Update bus connection matrices
f_bus, t_bus = int(branch["F_BUS"]), int(branch["T_BUS"]) # Ensure indices are integers
self.cf[line_index, f_bus] = 1
self.ct[line_index, t_bus] = 1
# Compute additional matrices
self.yf = np.dot(np.diag(self.yff), self.cf) + np.dot(np.diag(self.yft), self.ct)
self.yt = np.dot(np.diag(self.ytf), self.cf) + np.dot(np.diag(self.ytt), self.ct)
self.ysh = self.buses["GS"].values + 1j * self.buses["BS"].values
self.yb = np.dot(np.transpose(self.cf), self.yf) + np.dot(np.transpose(self.ct), self.yt) + np.diag(self.ysh)
# Include admittance values in the branch DataFrame
self.branches["GFF"] = np.real(self.yff)
self.branches["BFF"] = np.imag(self.yff)
self.branches["GFT"] = np.real(self.yft)
self.branches["BFT"] = np.imag(self.yft)
self.branches["GTF"] = np.real(self.ytf)
self.branches["BTF"] = np.imag(self.ytf)
self.branches["GTT"] = np.real(self.ytt)
self.branches["BTT"] = np.imag(self.ytt)
# Compute generator connection matrix
for g in range(self.ngen):
bus = int(self.generators.iloc[g]["GEN_BUS"]) # Ensure index is an integer
self.cg[g, bus] = 1
[docs]
def initialize(self, voltages=None, angles=None):
"""Initialize the voltage magnitudes, angles, flows, and generation levels."""
if voltages is None:
voltages = np.ones(self.nbus)
if angles is None:
angles = np.zeros(self.nbus)
self.buses["VOL0"] = voltages
self.buses["ANG0"] = angles
self.buses["VOLR0"] = voltages * np.cos(angles)
self.buses["VOLI0"] = voltages * np.sin(angles)
# Compute flows
v = voltages * np.exp(1j * angles)
sf = (self.cf @ v) * np.conj(self.yf @ v)
st = (self.ct @ v) * np.conj(self.yt @ v)
self.branches["PF0"] = np.real(sf)
self.branches["QF0"] = np.imag(sf)
self.branches["PT0"] = np.real(st)
self.branches["QT0"] = np.imag(st)
# Compute generator outputs
sd = self.buses["PD"].values + 1j * self.buses["QD"].values
sb = v * np.conj(self.yb @ v)
sg = sb + sd
self.generators["PG0"] = np.dot(np.real(sg), self.cg.T)
self.generators["QG0"] = np.dot(np.imag(sg), self.cg.T)
[docs]
def summary(self):
"""Print summary of the network."""
print(f"Number of buses: {self.nbus}")
print(f"Number of lines: {self.nlin}")
print(f"Number of generators: {self.ngen}")
print(f"baseMVA: {self.baseMVA}")
print("\nBuses:")
print(self.buses.head())
print("\nGenerators:")
print(self.generators.head())
print("\nBranches:")
print(self.branches.head())
print("\nGenerator Costs:")
print(self.gencost.head())
[docs]
def compute_initial_bigm_dc(self):
"""Compute Big-M values for DC the different lines and return them in a DataFrame."""
print("=======Computing initial bigM values for DC power flow")
self.branches["PFUPDC"] = (1 / self.branches["BR_X"]) * (self.cf @ self.buses["AMAX"] - self.ct @ self.buses["AMIN"])
self.branches["PFLODC"] = (1 / self.branches["BR_X"]) * (self.cf @ self.buses["AMIN"] - self.ct @ self.buses["AMAX"])
# print(self.branches[["PFUPDC", "PFLODC"]])
[docs]
def compute_initial_bigm_ac(self):
"""Compute Big-M values for AC the different lines and return them in a DataFrame."""
print("=======Computing initial bigM values for AC power flow")
self.branches["PFUPAC"] = np.zeros(self.nlin)
self.branches["PFLOAC"] = np.zeros(self.nlin)
self.branches["PTUPAC"] = np.zeros(self.nlin)
self.branches["PTLOAC"] = np.zeros(self.nlin)
self.branches["QFUPAC"] = np.zeros(self.nlin)
self.branches["QFLOAC"] = np.zeros(self.nlin)
self.branches["QTUPAC"] = np.zeros(self.nlin)
self.branches["QTLOAC"] = np.zeros(self.nlin)
self.branches["COSFTMAX"] = np.zeros(self.nlin)
self.branches["COSFTMIN"] = np.zeros(self.nlin)
self.branches["SINFTMAX"] = np.zeros(self.nlin)
self.branches["SINFTMIN"] = np.zeros(self.nlin)
for lin_index in range(self.nlin): # Changed 'lin' to 'lin_index'
f_bus = int(self.branches.loc[lin_index, "F_BUS"])
t_bus = int(self.branches.loc[lin_index, "T_BUS"])
amaxf = self.buses.loc[f_bus, "AMAX"]
aminf = self.buses.loc[f_bus, "AMIN"]
amaxt = self.buses.loc[t_bus, "AMAX"]
amint = self.buses.loc[t_bus, "AMIN"]
vmaxf = self.buses.loc[f_bus, "VMAX"]
vminf = self.buses.loc[f_bus, "VMIN"]
vmaxt = self.buses.loc[t_bus, "VMAX"]
vmint = self.buses.loc[t_bus, "VMIN"]
x0 = [(vmaxf + vminf) / 2, (vmaxt + vmint) / 2, (amaxf + aminf) / 2, (amaxt + amint) / 2]
def pfac(x, lin_index=lin_index):
return (
self.branches.loc[lin_index, "GFF"] * x[0] * x[0]
+ self.branches.loc[lin_index, "GFT"] * x[0] * x[1] * np.cos(x[2] - x[3])
+ self.branches.loc[lin_index, "BFT"] * x[0] * x[1] * np.sin(x[2] - x[3])
)
def ptac(x, lin_index=lin_index):
return (
self.branches.loc[lin_index, "GTT"] * x[1] * x[1]
+ self.branches.loc[lin_index, "GTF"] * x[0] * x[1] * np.cos(x[3] - x[2])
+ self.branches.loc[lin_index, "BTF"] * x[0] * x[1] * np.sin(x[3] - x[2])
)
def qfac(x, lin_index=lin_index):
return (
-self.branches.loc[lin_index, "BFF"] * x[0] * x[0]
- self.branches.loc[lin_index, "BFT"] * x[0] * x[1] * np.cos(x[2] - x[3])
+ self.branches.loc[lin_index, "GFT"] * x[0] * x[1] * np.sin(x[2] - x[3])
)
def qtac(x, lin_index=lin_index):
return (
-self.branches.loc[lin_index, "BTT"] * x[1] * x[1]
- self.branches.loc[lin_index, "BTF"] * x[0] * x[1] * np.cos(x[3] - x[2])
+ self.branches.loc[lin_index, "GTF"] * x[0] * x[1] * np.sin(x[3] - x[2])
)
def cosft(x):
return x[0] * x[1] * np.cos(x[2] - x[3])
def sinft(x):
return x[0] * x[1] * np.sin(x[2] - x[3])
self.branches.loc[lin_index, "PFUPAC"] = (
-1 * minimize(lambda x: -pfac(x), x0, bounds=[(vminf, vmaxf), (vmint, vmaxt), (aminf, amaxf), (amint, amaxt)]).fun
)
self.branches.loc[lin_index, "PFLOAC"] = minimize(
pfac, x0, bounds=[(vminf, vmaxf), (vmint, vmaxt), (aminf, amaxf), (amint, amaxt)]
).fun
self.branches.loc[lin_index, "PTUPAC"] = (
-1 * minimize(lambda x: -ptac(x), x0, bounds=[(vminf, vmaxf), (vmint, vmaxt), (aminf, amaxf), (amint, amaxt)]).fun
)
self.branches.loc[lin_index, "PTLOAC"] = minimize(
ptac, x0, bounds=[(vminf, vmaxf), (vmint, vmaxt), (aminf, amaxf), (amint, amaxt)]
).fun
self.branches.loc[lin_index, "QFUPAC"] = (
-1 * minimize(lambda x: -qfac(x), x0, bounds=[(vminf, vmaxf), (vmint, vmaxt), (aminf, amaxf), (amint, amaxt)]).fun
)
self.branches.loc[lin_index, "QFLOAC"] = minimize(
qfac, x0, bounds=[(vminf, vmaxf), (vmint, vmaxt), (aminf, amaxf), (amint, amaxt)]
).fun
self.branches.loc[lin_index, "QTUPAC"] = (
-1 * minimize(lambda x: -qtac(x), x0, bounds=[(vminf, vmaxf), (vmint, vmaxt), (aminf, amaxf), (amint, amaxt)]).fun
)
self.branches.loc[lin_index, "QTLOAC"] = minimize(
qtac, x0, bounds=[(vminf, vmaxf), (vmint, vmaxt), (aminf, amaxf), (amint, amaxt)]
).fun
self.branches.loc[lin_index, "COSFTMAX"] = (
-1 * minimize(lambda x: -cosft(x), x0, bounds=[(vminf, vmaxf), (vmint, vmaxt), (aminf, amaxf), (amint, amaxt)]).fun
)
self.branches.loc[lin_index, "COSFTMIN"] = minimize(
cosft, x0, bounds=[(vminf, vmaxf), (vmint, vmaxt), (aminf, amaxf), (amint, amaxt)]
).fun
self.branches.loc[lin_index, "SINFTMAX"] = (
-1 * minimize(lambda x: -sinft(x), x0, bounds=[(vminf, vmaxf), (vmint, vmaxt), (aminf, amaxf), (amint, amaxt)]).fun
)
self.branches.loc[lin_index, "SINFTMIN"] = minimize(
sinft, x0, bounds=[(vminf, vmaxf), (vmint, vmaxt), (aminf, amaxf), (amint, amaxt)]
).fun
# print(self.branches[["PFUPAC", "PFLOAC", "PTUPAC", "PTLOAC", "QFUPAC", "QFLOAC", "QTUPAC", "QTLOAC"]])
[docs]
def solve_opf(self, opf_type="dc", switching="off", connectivity="off", solver="gurobi", options="outlev=1 timelimit=3600"):
"""Solve the optimal power flow problem using AMPL.
Parameters:
opf_type (str): Type of optimal power flow ('dc', 'acrect', 'acjabr')
switching (str): Switching strategy ('off', 'nl', 'bigm')
connectivity (str): Connectivity for topology solutions ('off', 'on')
solver (str): Solver to use ('gurobi', 'cplex', 'cbc')
options (str): Options for the solver
Returns:
dict: Results of the optimal power flow problem
"""
# set the status of the lines
if isinstance(switching, np.ndarray):
self.branches["BR_STATUS"] = switching
elif switching == "off":
self.branches["BR_STATUS"] = 1
elif switching == "nl":
self.branches["BR_STATUS"] = 2
elif switching == "bigm":
self.branches["BR_STATUS"] = 3
print(
f"=======Solving OPF ({opf_type}) with switching {switching} and connectivity {connectivity} with solver {solver} and options {options}"
)
ampl = AMPL()
ampl.reset()
ampl.read(Path(__file__).parent / "opf.mod")
ampl.set_data(self.buses, "N")
ampl.set_data(self.generators, "G")
ampl.set_data(self.branches, "L")
ampl.set_data(self.gencost)
ampl.param["CF"] = array2dict(self.cf)
ampl.param["CT"] = array2dict(self.ct)
ampl.param["CG"] = array2dict(self.cg)
ampl.param["OPF_TYPE"] = opf_type
ampl.param["CONNECTIVITY"] = connectivity
ampl.param["BASEMVA"] = self.baseMVA
ampl.param["MAXVOL"] = self.max_voltage
ampl.param["MINVOL"] = self.min_voltage
ampl.option["mp_options"] = options
ampl.solve(solver=solver)
solver_status = ampl.solve_result
if solver_status == "solved" or solver_status == "limit":
# Get the generation results
Pg = ampl.get_variable("Pg").get_values().to_pandas().values.flatten()
Qg = ampl.get_variable("Qg").get_values().to_pandas().values.flatten()
Pg_viol = (
100
* np.maximum(0, Pg - self.generators["PMAX"].values, self.generators["PMIN"].values - Pg)
/ (self.generators["PMAX"].values - self.generators["PMIN"].values)
)
Qg_viol = (
100
* np.maximum(0, Qg - self.generators["QMAX"].values, self.generators["QMIN"].values - Qg)
/ (self.generators["QMAX"].values - self.generators["QMIN"].values)
)
gen_df = pd.DataFrame(
{"Pg": Pg, "Qg": Qg, "Pg_viol": Pg_viol, "Qg_viol": Qg_viol},
index=ampl.get_variable("Pg").get_values().to_pandas().index,
)
# Get the line results
switching = ampl.get_variable("status").get_values().to_pandas().values.flatten()
Pf = ampl.get_variable("Pf").get_values().to_pandas().values.flatten()
Pt = ampl.get_variable("Pt").get_values().to_pandas().values.flatten()
Qf = ampl.get_variable("Qf").get_values().to_pandas().values.flatten()
Qt = ampl.get_variable("Qt").get_values().to_pandas().values.flatten()
Sf = Pf + 1j * Qf
St = Pt + 1j * Qt
Sf_viol = (
100
* np.maximum(0, abs(Sf) - self.branches["RATE_A"].values, -self.branches["RATE_A"].values - abs(Sf))
/ (2 * self.branches["RATE_A"].values)
)
St_viol = (
100
* np.maximum(0, abs(St) - self.branches["RATE_A"].values, -self.branches["RATE_A"].values - abs(St))
/ (2 * self.branches["RATE_A"].values)
)
line_df = pd.DataFrame(
{
"switching": switching,
"Pf": Pf,
"Pt": Pt,
"Qf": Qf,
"Qt": Qt,
"Sf": abs(Sf),
"St": abs(St),
"Sf_viol": Sf_viol,
"St_viol": St_viol,
},
index=ampl.get_variable("status").get_values().to_pandas().index,
)
# Get the voltage results
if opf_type == "acrect":
volr = ampl.get_variable("Vr").get_values().to_pandas().values.flatten()
voli = ampl.get_variable("Vi").get_values().to_pandas().values.flatten()
Vm = np.sqrt(volr**2 + voli**2)
Va = np.arctan2(voli, volr)
elif opf_type == "acjabr":
vol2 = ampl.get_variable("V2").get_values().to_pandas().values.flatten()
Vm = np.sqrt(vol2)
vfvtcosft = ampl.get_variable("cosft").get_values().to_pandas().values.flatten()
vfvt = np.array([Vm[int(self.branches.loc[i, "F_BUS"])] * Vm[int(self.branches.loc[i, "T_BUS"])] for i in range(self.nlin)])
cosft = np.maximum(-1, np.minimum(1, vfvtcosft / vfvt))
# Compute angles for all buses
Va = np.full(self.nbus, np.nan) # Initialize angles with NaN
Va[0] = 0 # Reference bus angle is 0
# Iteratively compute angles
visited = {0} # Start with the reference bus
while len(visited) < self.nbus:
for line_index in range(self.nlin):
f_bus = int(self.branches.loc[line_index, "F_BUS"])
t_bus = int(self.branches.loc[line_index, "T_BUS"])
if f_bus in visited and np.isnan(Va[t_bus]):
Va[t_bus] = Va[f_bus] + np.arccos(cosft[line_index])
visited.add(t_bus)
elif t_bus in visited and np.isnan(Va[f_bus]):
Va[f_bus] = Va[t_bus] - np.arccos(cosft[line_index])
visited.add(f_bus)
else:
Vm = ampl.get_variable("Vm").get_values().to_pandas().values.flatten()
Va = ampl.get_variable("Va").get_values().to_pandas().values.flatten()
Vm_viol = (
100
* np.maximum(0, Vm - self.buses["VMAX"].values, self.buses["VMIN"].values - Vm)
/ (self.buses["VMAX"].values - self.buses["VMIN"].values)
)
Va_viol = (
100
* np.maximum(0, Va - self.buses["AMAX"].values, self.buses["AMIN"].values - Va)
/ (self.buses["AMAX"].values - self.buses["AMIN"].values)
)
# Computation of power injections
Sd = self.buses["PD"].values + 1j * self.buses["QD"].values
Sg = Pg + 1j * Qg
Ssh = self.buses["GS"].values * Vm**2 - 1j * self.buses["BS"].values * Vm**2
S_viol = Sg @ self.cg - Sd - Ssh - Sf @ self.cf - St @ self.ct
P_viol = 100 * np.real(S_viol) / sum(self.buses["PD"].values)
Q_viol = 100 * np.imag(S_viol) / sum(self.buses["QD"].values)
bus_df = pd.DataFrame(
{
"Vm": Vm,
"Va": Va,
"Vm_viol": Vm_viol,
"Va_viol": Va_viol,
"P_viol": P_viol,
"Q_viol": Q_viol,
},
index=ampl.get_variable("Vm").get_values().to_pandas().index,
)
return {
"obj": ampl.get_objective("total_cost").value(),
"time": ampl.get_value("_solve_time"),
"gen": gen_df,
"bus": bus_df,
"lin": line_df,
"status": "solved",
}
else:
return {"obj": None, "time": None, "gen": None, "bus": None, "lin": None, "status": solver_status}