ac-branch-pi-model

AC Branch Pi-Model + Transformer Handling

Implement the exact branch power flow equations in acopf-math-model.md using MATPOWER branch data:

[F_BUS, T_BUS, BR_R, BR_X, BR_B, RATE_A, RATE_B, RATE_C, TAP, SHIFT, BR_STATUS, ANGMIN, ANGMAX]

Quick start

• Use scripts/branch_flows.py to compute per-unit branch flows.
• Treat the results as power leaving the “from” bus and power leaving the “to” bus (i.e., compute both directions explicitly).

Example:

import json
import numpy as np

from scripts.branch_flows import compute_branch_flows_pu, build_bus_id_to_idx

data = json.load(open("/root/network.json"))
baseMVA = float(data["baseMVA"])
buses = np.array(data["bus"], dtype=float)
branches = np.array(data["branch"], dtype=float)

bus_id_to_idx = build_bus_id_to_idx(buses)

Vm = buses[:, 7]  # initial guess VM
Va = np.deg2rad(buses[:, 8])  # initial guess VA

br = branches[0]
P_ij, Q_ij, P_ji, Q_ji = compute_branch_flows_pu(Vm, Va, br, bus_id_to_idx)

S_ij_MVA = (P_ij**2 + Q_ij**2) ** 0.5 * baseMVA
S_ji_MVA = (P_ji**2 + Q_ji**2) ** 0.5 * baseMVA
print(S_ij_MVA, S_ji_MVA)

Model details (match the task formulation)

Per-unit conventions

• Work in per-unit internally.
• Convert with baseMVA:
  • (P_{pu} = P_{MW} / baseMVA)
  • (Q_{pu} = Q_{MVAr} / baseMVA)
  • (|S|{MVA} = |S|{pu} \cdot baseMVA)

Transformer handling (MATPOWER TAP + SHIFT)

• Use (T_{ij} = tap \cdot e^{j \cdot shift}).
• Implementation shortcut (real tap + phase shift):
  • If abs(TAP) < 1e-12, treat tap = 1.0 (no transformer).
  • Convert SHIFT from degrees to radians.
  • Use the angle shift by modifying the angle difference:
    • (\delta_{ij} = \theta_i - \theta_j - shift)
    • (\delta_{ji} = \theta_j - \theta_i + shift)

Series admittance

Given BR_R = r, BR_X = x:

• If r == 0 and x == 0, set g = 0, b = 0 (avoid divide-by-zero).
• Else:
  • (y = 1/(r + jx) = g + jb)
  • (g = r/(r^2 + x^2))
  • (b = -x/(r^2 + x^2))