import logging
from pathlib import Path
import numpy as np
import pandas as pd
from amplpy import AMPL
from matpowercaseframes import CaseFrames
from amplpower.utils import find_min_max
[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, max_voltage_angle: float = np.pi / 2, min_voltage_angle: float = -np.pi / 2):
"""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 = max_voltage_angle
self.min_angle = min_voltage_angle
self.load_data()
self.summary()
self.compute_matrices()
self.initialize()
self.compute_voltage_bounds()
self.compute_bigm_dc()
self.compute_bigm_ac()
self.compute_ptdf()
self.compute_lodf()
[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)
# Create a mapping for bus numbers
self.bus_mapping = {bus: idx for idx, bus in enumerate(self.buses["BUS_I"])}
self.reverse_bus_mapping = {idx: bus for bus, idx in self.bus_mapping.items()}
self.buses["BUS_I"] = self.buses["BUS_I"].map(self.bus_mapping)
self.generators = case.gen
self.generators.reset_index(drop=True, inplace=True)
self.generators["GEN_BUS"] = self.generators["GEN_BUS"].map(self.bus_mapping)
self.branches = case.branch
self.branches.reset_index(drop=True, inplace=True)
self.branches["F_BUS"] = self.branches["F_BUS"].map(self.bus_mapping)
self.branches["T_BUS"] = self.branches["T_BUS"].map(self.bus_mapping)
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 limits for voltage angle and real/imaginary voltage variables
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
# Define PFMAX and PFMIN for branches
self.branches["PFMAX"] = self.branches["RATE_A"]
self.branches["PFMIN"] = -self.branches["RATE_A"]
self.branches["QFMAX"] = self.branches["RATE_A"]
self.branches["QFMIN"] = -self.branches["RATE_A"]
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
pg_split = np.zeros(self.ngen)
qg_split = np.zeros(self.ngen)
for bus in range(self.nbus):
gen_indices = self.generators[self.generators["GEN_BUS"] == bus].index
if len(gen_indices) > 0:
pmax_total = self.generators.loc[gen_indices, "PMAX"].sum()
if pmax_total > 0:
pg_split[gen_indices] = np.real(sg[bus]) * self.generators.loc[gen_indices, "PMAX"] / pmax_total
qg_split[gen_indices] = np.imag(sg[bus]) * self.generators.loc[gen_indices, "PMAX"] / pmax_total
self.generators["PG0"] = pg_split
self.generators["QG0"] = qg_split
[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_voltage_bounds(self):
"""Compute bounds for the real and imaginary parts of voltage."""
print("=======Computing voltage bounds")
for bus in range(self.nbus):
vmin = self.buses.loc[bus, "VMIN"]
vmax = self.buses.loc[bus, "VMAX"]
amin = self.buses.loc[bus, "AMIN"]
amax = self.buses.loc[bus, "AMAX"]
v_critical = [vmin, vmax]
a_critical = [amin, amax]
for ac in [0, np.pi / 2, np.pi, -np.pi / 2, -1 * np.pi]:
if amin <= ac <= amax:
a_critical.append(ac)
vrmin = float("inf")
vrmax = float("-inf")
vimin = float("inf")
vimax = float("-inf")
for v in v_critical:
for a in a_critical:
vrmin = min(vrmin, v * np.cos(a))
vrmax = max(vrmax, v * np.cos(a))
vimin = min(vimin, v * np.sin(a))
vimax = max(vimax, v * np.sin(a))
self.buses.loc[bus, "VRMIN"] = vrmin
self.buses.loc[bus, "VRMAX"] = vrmax
self.buses.loc[bus, "VIMIN"] = vimin
self.buses.loc[bus, "VIMAX"] = vimax
[docs]
def compute_bigm_dc(self):
"""Compute Big-M values for DC power flow."""
print("=======Computing Big-M values for DC power flow")
weights = self.branches["PFMAX"] * self.branches["BR_X"]
bound_lp = weights.nlargest(self.nlin - 1).sum()
self.branches["PFUPDC"] = bound_lp / self.branches["BR_X"]
self.branches["PFLODC"] = -bound_lp / self.branches["BR_X"]
self.branches["PFUPDC"] = np.ceil(self.branches["PFUPDC"] * 100) / 100
self.branches["PFLODC"] = np.floor(self.branches["PFLODC"] * 100) / 100
[docs]
def compute_bigm_ac(self):
"""Compute Big-M values for active and reactive power flows."""
print("=======Computing Big-M values for AC power flow using find_min_max")
for lin_index in range(self.nlin):
branch = self.branches.iloc[lin_index]
f_bus = int(branch["F_BUS"])
t_bus = int(branch["T_BUS"])
vmaxf, vminf = self.buses.loc[f_bus, "VMAX"], self.buses.loc[f_bus, "VMIN"]
vmaxt, vmint = self.buses.loc[t_bus, "VMAX"], self.buses.loc[t_bus, "VMIN"]
amaxf, aminf = self.buses.loc[f_bus, "AMAX"], self.buses.loc[f_bus, "AMIN"]
amaxt, amint = self.buses.loc[t_bus, "AMAX"], self.buses.loc[t_bus, "AMIN"]
# Active power flow at "from" bus
pf_min, pf_max = find_min_max(
branch["GFF"], branch["GFT"], branch["BFT"], vminf, vmaxf, vmint, vmaxt, aminf - amaxt, amaxf - amint
)
self.branches.loc[lin_index, "PFLOAC"] = np.floor(pf_min * 100) / 100
self.branches.loc[lin_index, "PFUPAC"] = np.ceil(pf_max * 100) / 100
# Active power flow at "to" bus
pt_min, pt_max = find_min_max(
branch["GTT"], branch["GTF"], branch["BTF"], vmint, vmaxt, vminf, vmaxf, amint - amaxf, amaxt - aminf
)
self.branches.loc[lin_index, "PTLOAC"] = np.floor(pt_min * 100) / 100
self.branches.loc[lin_index, "PTUPAC"] = np.ceil(pt_max * 100) / 100
# Reactive power flow at "from" bus
qf_min, qf_max = find_min_max(
-branch["BFF"], -branch["BFT"], branch["GFT"], vminf, vmaxf, vmint, vmaxt, aminf - amaxt, amaxf - amint
)
self.branches.loc[lin_index, "QFLOAC"] = np.floor(qf_min * 100) / 100
self.branches.loc[lin_index, "QFUPAC"] = np.ceil(qf_max * 100) / 100
# Reactive power flow at "to" bus
qt_min, qt_max = find_min_max(
-branch["BTT"], -branch["BTF"], branch["GTF"], vmint, vmaxt, vminf, vmaxf, amint - amaxf, amaxt - aminf
)
self.branches.loc[lin_index, "QTLOAC"] = np.floor(qt_min * 100) / 100
self.branches.loc[lin_index, "QTUPAC"] = np.ceil(qt_max * 100) / 100
# Cosine of angle difference
cos_min, cos_max = find_min_max(0, 1, 0, vminf, vmaxf, vmint, vmaxt, aminf - amaxt, amaxf - amint)
self.branches.loc[lin_index, "COSFTMAX"] = np.ceil(cos_max * 100) / 100
self.branches.loc[lin_index, "COSFTMIN"] = np.floor(cos_min * 100) / 100
# Sine of angle difference
sin_min, sin_max = find_min_max(0, 0, 1, vminf, vmaxf, vmint, vmaxt, aminf - amaxt, amaxf - amint)
self.branches.loc[lin_index, "SINFTMAX"] = np.ceil(sin_max * 100) / 100
self.branches.loc[lin_index, "SINFTMIN"] = np.floor(sin_min * 100) / 100
[docs]
def compute_ptdf(self):
"""
Compute the PTDF (Power Transfer Distribution Factor) matrix and store it in self.ptdf.
The slack bus is the one with BUS_TYPE == 3 in self.buses dataframe.
"""
nlin = self.nlin
nbus = self.nbus
# Find reference bus (BUS_TYPE == 3)
ref_bus_idx = self.buses.index[self.buses["BUS_TYPE"] == 3][0]
ref_bus_pos = list(self.buses.index).index(ref_bus_idx)
# Build branch-to-node incidence matrix A (nlin x nbus)
A = self.cf - self.ct # shape (nlin, nbus)
# Remove slack bus column
keep = [i for i in range(nbus) if i != ref_bus_pos]
A_red = A[:, keep] # shape (nlin, nbus-1)
# Diagonal matrix of line reactances
X = np.diag(self.branches["BR_X"].values) # shape (nlin, nlin)
Xinv = np.linalg.inv(X)
# Compute B = A_red.T @ Xinv @ A_red
B = A_red.T @ Xinv @ A_red # shape (nbus-1, nbus-1)
B_inv = np.linalg.inv(B)
# Compute PTDF: Xinv @ A_red @ B_inv
PTDF_red = Xinv @ A_red @ B_inv # shape (nlin, nbus-1)
# Insert zeros for slack bus column
PTDF = np.zeros((nlin, nbus))
PTDF[:, keep] = PTDF_red
self.ptdf = PTDF
[docs]
def compute_lodf(self):
"""
Compute the LODF (Line Outage Distribution Factor) matrix and store it in self.lodf.
Uses the PTDF matrix already stored in self.ptdf.
"""
nlin = self.nlin
PTDF = self.ptdf # shape (nlin, nbus)
# Build branch-to-node incidence matrix A (nlin x nbus)
A = self.cf - self.ct # shape (nlin, nbus)
# H = PTDF @ A.T (A.T is nbus x nlin)
H = PTDF @ A.T # shape (nlin, nlin)
h = np.diag(H)
denom_mat = np.ones((nlin, nlin)) - np.outer(np.ones(nlin), h)
LODF = H / denom_mat
np.fill_diagonal(LODF, 0)
LODF = LODF - np.eye(nlin)
self.lodf = LODF
[docs]
def set_switching(self, switching):
"""Set the switching status of the branches.
Explanations:
- 'off': All lines are connected (no switching, all BR_SWITCH=1).
- 'nl': Use binary variables for line connection with a non-linear formulation (BR_SWITCH=2).
- 'bigm': Use binary variables for line connection with a Big-M formulation (BR_SWITCH=3).
- 'df': Use the values already stored in BR_SWITCH (do not modify).
- numpy.ndarray: Directly set BR_SWITCH to the provided array.
Switching statuses:
0: The line is off.
1: The line is on.
2: The line is switchable and modeled with a non-linear approach.
3: The line is switchable and modeled with a Big-M approach.
Parameters:
switching (str or np.ndarray): The switching strategy or array of statuses.
"""
if isinstance(switching, np.ndarray):
self.branches["BR_SWITCH"] = switching
elif switching == "off":
self.branches["BR_SWITCH"] = 1
elif switching == "nl":
self.branches["BR_SWITCH"] = 2
elif switching == "bigm":
self.branches["BR_SWITCH"] = 3
elif switching == "df":
# Do nothing, use existing BR_SWITCH values
pass
else:
raise ValueError(
f"Unknown switching value: {switching}. "
"Allowed values are 'off' (all lines connected), "
"'nl' (binary variables, non-linear formulation), "
"'bigm' (binary variables, Big-M formulation), "
"'df' (use existing BR_SWITCH), or a numpy array."
)
[docs]
def create_model(self, opf_type="dc", connectivity="off"):
"""Compute the feasible region for the power system.
Parameters:
opf_type (str): Type of optimal power flow ('dc', 'acrect', 'acjabr')
connectivity (str): Connectivity for topology solutions ('off', 'on')
"""
print(f"=======Computing feasible region ({opf_type}) with connectivity {connectivity}")
self.ampl = AMPL()
self.ampl.reset()
self.ampl.read(Path(__file__).parent / "opf.mod")
self.ampl.set_data(self.buses, "N")
self.ampl.set_data(self.generators, "G")
self.ampl.set_data(self.branches, "L")
self.ampl.set_data(self.gencost)
self.ampl.param["CF"] = array2dict(self.cf)
self.ampl.param["CT"] = array2dict(self.ct)
self.ampl.param["CG"] = array2dict(self.cg)
self.ampl.param["OPF_TYPE"] = opf_type
self.ampl.param["CONNECTIVITY"] = connectivity
self.ampl.param["BASEMVA"] = self.baseMVA
[docs]
def solve_model(self, solver="gurobi", options=""):
"""Solve the model using the specified solver.
Parameters:
solver (str): Solver to use ('gurobi', 'cplex', 'cbc')
options (str): Options for the solver
Returns:
dict: Results of the optimization
"""
print(f"=======Solving model with solver {solver} and options {options}")
self.ampl.option[solver + "_options"] = options
self.ampl.solve(solver=solver)
[docs]
def solve_opf(self, opf_type="dc", switching="off", connectivity="off", solver="gurobi", options=""):
"""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
"""
self.set_switching(switching)
self.create_model(opf_type, connectivity)
self.ampl.eval("minimize objective: sum {g in G} (COST_2[g] * (BASEMVA*Pg[g])^2 + COST_1[g] * (BASEMVA*Pg[g]) + COST_0[g]);")
self.ampl.eval("option presolve_eps 1e-10;")
self.solve_model(solver, options)
return self.get_results_opf(opf_type)
[docs]
def get_results_opf(self, opf_type="dc"):
"""Get results from the solved model.
Returns:
object: Results of the optimization with attributes like obj, time, generators, buses, branches, etc.
"""
solver_status = self.ampl.solve_result
# Create a simple object to hold results
results = type("Results", (object,), {})()
# Get the generation results
Pg = self.ampl.get_variable("Pg").get_values().to_pandas().values.flatten()
Qg = self.ampl.get_variable("Qg").get_values().to_pandas().values.flatten()
# Avoid division by zero for Pg_viol
pmax_pmin_diff = self.generators["PMAX"].values - self.generators["PMIN"].values
Pg_viol = np.where(
pmax_pmin_diff == 0,
0,
100 * np.maximum(0, Pg - self.generators["PMAX"].values, self.generators["PMIN"].values - Pg) / pmax_pmin_diff,
)
# Avoid division by zero for Qg_viol
qmax_qmin_diff = self.generators["QMAX"].values - self.generators["QMIN"].values
Qg_viol = np.where(
qmax_qmin_diff == 0,
0,
100 * np.maximum(0, Qg - self.generators["QMAX"].values, self.generators["QMIN"].values - Qg) / qmax_qmin_diff,
)
results.generators = pd.DataFrame(
{"Pg": Pg, "Qg": Qg, "Pg_viol": Pg_viol, "Qg_viol": Qg_viol},
index=self.ampl.get_variable("Pg").get_values().to_pandas().index,
)
# Get the line results
status = self.ampl.get_variable("status").get_values().to_pandas().values.flatten()
Pf = self.ampl.get_variable("Pf").get_values().to_pandas().values.flatten()
Pfa = self.ampl.get_variable("Pfa").get_values().to_pandas().values.flatten()
Pt = self.ampl.get_variable("Pt").get_values().to_pandas().values.flatten()
Pta = self.ampl.get_variable("Pta").get_values().to_pandas().values.flatten()
Qf = self.ampl.get_variable("Qf").get_values().to_pandas().values.flatten()
Qfa = self.ampl.get_variable("Qfa").get_values().to_pandas().values.flatten()
Qt = self.ampl.get_variable("Qt").get_values().to_pandas().values.flatten()
Qta = self.ampl.get_variable("Qta").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)
)
results.branches = pd.DataFrame(
{
"status": status,
"Pf": Pf,
"Pt": Pt,
"Qf": Qf,
"Qt": Qt,
"Sf": abs(Sf),
"St": abs(St),
"Sf_viol": Sf_viol,
"St_viol": St_viol,
"Pfa": Pfa,
"Pta": Pta,
"Qfa": Qfa,
"Qta": Qta,
},
index=self.ampl.get_variable("status").get_values().to_pandas().index,
)
# Get the voltage results
if opf_type == "acrect":
volr = self.ampl.get_variable("Vr").get_values().to_pandas().values.flatten()
voli = self.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 = self.ampl.get_variable("V2").get_values().to_pandas().values.flatten()
Vm = np.sqrt(vol2)
vfvtcosft = self.ampl.get_variable("cosft").get_values().to_pandas().values.flatten()
vfvtsinft = self.ampl.get_variable("sinft").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))
sinft = np.maximum(-1, np.minimum(1, vfvtsinft / vfvt))
# Compute angles for all buses
Va = np.full(self.nbus, np.nan) # Initialize angles with NaN
slack = int(self.buses.index[self.buses["BUS_TYPE"] == 3][0])
Va[slack] = 0
visited = {slack}
# Iteratively compute angles
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"])
angle_diff = np.arctan2(sinft[line_index], cosft[line_index])
if f_bus in visited and np.isnan(Va[t_bus]):
Va[t_bus] = Va[f_bus] - angle_diff
visited.add(t_bus)
elif t_bus in visited and np.isnan(Va[f_bus]):
Va[f_bus] = Va[t_bus] + angle_diff
visited.add(f_bus)
# Rectangular voltage components
volr = Vm * np.cos(Va)
voli = Vm * np.sin(Va)
else:
Vm = self.ampl.get_variable("Vm").get_values().to_pandas().values.flatten()
Va = self.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)
results.buses = pd.DataFrame(
{
"Vm": Vm,
"Va": Va,
"Vr": volr if opf_type == "acrect" or opf_type == "acjabr" else None,
"Vi": voli if opf_type == "acrect" or opf_type == "acjabr" else None,
"Vm_viol": Vm_viol,
"Va_viol": Va_viol,
"P_viol": P_viol,
"Q_viol": Q_viol,
},
index=self.ampl.get_variable("Vm").get_values().to_pandas().index,
)
# Set other attributes
results.obj = self.ampl.get_objective("objective").value()
try:
results.bestbound = self.ampl.get_value("objective.bestbound")
except RuntimeError:
results.bestbound = None
results.time = self.ampl.get_value("_solve_time")
results.total_solve_time = self.ampl.get_value("_total_solve_time")
results.solve_system_time = self.ampl.get_value("_solve_system_time")
results.solver_status = solver_status
results.max_viol = float(
max(
np.max(np.abs(Pg_viol)),
np.max(np.abs(Qg_viol)),
np.max(np.abs(Vm_viol)),
np.max(np.abs(Va_viol)),
np.max(np.abs(Sf_viol)),
np.max(np.abs(St_viol)),
np.max(np.abs(P_viol)),
np.max(np.abs(Q_viol)),
)
)
return results
[docs]
def is_feasible(self, voltages, angles):
"""
Check feasibility of a given voltage and angle vector.
Returns a dictionary with slacks for each constraint.
If a variable is feasible, slack is 0. Otherwise, it is the absolute value needed to make it feasible.
"""
slacks = {}
# 1. Voltage magnitude and angle bounds
vmin = self.buses["VMIN"].values
vmax = self.buses["VMAX"].values
amin = self.buses["AMIN"].values
amax = self.buses["AMAX"].values
Vm_slack = np.maximum(0, vmin - voltages) + np.maximum(0, voltages - vmax)
Va_slack = np.maximum(0, amin - angles) + np.maximum(0, angles - amax)
slacks["Vm_slack"] = Vm_slack
slacks["Va_slack"] = Va_slack
# 2. Compute bus voltages
v = voltages * np.exp(1j * angles)
# 3. Compute branch flows
sf = (self.cf @ v) * np.conj(self.yf @ v)
st = (self.ct @ v) * np.conj(self.yt @ v)
# 4. Branch flow bounds (use RATE_A)
rate_a = self.branches["RATE_A"].values
abs_sf = np.abs(sf)
abs_st = np.abs(st)
Pf_slack = np.maximum(0, abs_sf - rate_a)
Pt_slack = np.maximum(0, abs_st - rate_a)
slacks["Sf_slack"] = Pf_slack
slacks["St_slack"] = Pt_slack
# 5. Power balance at buses: Pg + jQg = Sbus = v * conj(yb @ v) + Sload
sd = self.buses["PD"].values + 1j * self.buses["QD"].values
sb = v * np.conj(self.yb @ v)
sg = sb + sd # total generation at each bus
# 6. Split generator injections among generators at each bus
pg = np.zeros(self.ngen)
qg = np.zeros(self.ngen)
for bus in range(self.nbus):
gen_indices = self.generators[self.generators["GEN_BUS"] == bus].index
if len(gen_indices) > 0:
pmax_total = self.generators.loc[gen_indices, "PMAX"].sum()
if pmax_total > 0:
pg[gen_indices] = np.real(sg[bus]) * self.generators.loc[gen_indices, "PMAX"] / pmax_total
qg[gen_indices] = np.imag(sg[bus]) * self.generators.loc[gen_indices, "PMAX"] / pmax_total
# 7. Generator bounds
pmin = self.generators["PMIN"].values
pmax = self.generators["PMAX"].values
qmin = self.generators["QMIN"].values
qmax = self.generators["QMAX"].values
Pg_slack = np.maximum(0, pmin - pg) + np.maximum(0, pg - pmax)
Qg_slack = np.maximum(0, qmin - qg) + np.maximum(0, qg - qmax)
slacks["Pg_slack"] = Pg_slack
slacks["Qg_slack"] = Qg_slack
return slacks