Newton–Raphson & Fast-Decoupled Load Flow (NR/FDLF) Solver

Description

This project implements a small power-flow solver for an n-bus system using:

• Full Newton–Raphson (NR) power flow
• Fast-Decoupled Load Flow (FDLF) (B' / B'' method)

It is currently set up to read a FiveBus_PQ-style text file and solve that network for multiple mismatch tolerances.

Created: 11/10/2025

Modified: 12/03/2025

Author: Jeff Dinsmore

Licence: GPL-3.0 license

---

Installation

The Following commands will be used in the terminal using PowerShell or Bash:

• Clone this repository
• Open repository in your preferred code builder program. (This was built in VS Code)
• cd into the Fall2025HW folder
• Check python version
  • python --version
• If no python, download using winget
  • winget install Python.Python.3.12
• Install virtual venv environment
  • python -m venv .venv
• Activate .venv environment
  • source .venv/Scripts/activate
• Upgrade pip version
  • python -m pip install --upgrade pip
• Download packages that are used in this script
  • pip install —upgrade pandas numpy tabulate math cmath matplotlib pprint

---

Features

• Parses a simple text-based system description (SYSTEM, BUS, LINE records)
• Builds the complex Y-bus matrix from per-unit line impedances
• Builds reduced B' (for angles) and B'' (for voltage magnitudes) for FDLF
• Supports SLACK, PQ, and PV bus types
• Runs NR and FDLF for a list of mismatch tolerances EPS = [1e-2, 1e-4, 1e-6]
• Tracks:
  • Mismatch norms and state updates per iteration
  • Per-bus voltage magnitude, angle, P/Q injections by iteration
• Writes results to CSV and plots convergence on a log scale

---

File Overview

Main script (your Python file) contains:

• Global config:
  • EPS – list of mismatch tolerances
  • MAX_ITERS – maximum number of iterations for NR and FDLF
  • Bus type constants: SLACK, PQ, PV
• Parsing / I/O
  • load_system_file(filename) – reads base MVA and BUS records
  • load_line_data(filename, bus_name_to_num) – reads LINE records and builds line impedance dict Z
• Network construction
  • build_Ybus(Z, n=None) – builds complex Y-bus
  • build_B_prime_and_B_double_prime(B_full, buses) – builds B' and B'' for FDLF
  • display_Ybus(Ybus) – pretty-prints Y-bus (optional, for debugging)
• Power flow core
  • PowerVariables class
    • stores reduced P/Q spec and calc vectors
    • builds mismatch vector(s)
    • builds NR state vector
    • constructs all 4 Jacobian blocks J1–J4
    • assembles full Jacobian J
    • solves for Δx and applies state updates to bus data
  • compute_bus_injections(buses, Ybus) – computes full P/Q injections at each bus
  • print_bus_info() – prints final bus voltages / angles / injections and writes final_bus_results.csv
• Solvers
  • run_iterations() – Newton–Raphson solver
  • run_fdlf() – Fast-Decoupled Load Flow solver
• Main
  • Runs NR and FDLF, prints total timings and per-iteration averages

---

Input File Format (FiveBus_PQ-style)

The code expects a text file with blocks like:

% comment lines start with %
SYSTEM  FiveBus_PQ   100   0.05

BUS  Alan   SL  1.00   0.0   0.0   0.0   0.0   0.0
BUS  Betty  PQ  1.00   0.0   0.0   0.9   0.5   0.0
BUS  Clyde  PV  1.01   1.3   0.0   0.0   0.0   0.0
...

LINE  Alan   Betty  0.0  0.10  0.0  0.0  999
LINE  Alan   Clyde  0.0  0.25  0.0  0.0  999
LINE  Betty  Clyde  0.0  0.20  0.0  0.0  999
...

---

Results

---

The Max Bus result of N-R and FDLF for each iteration using ε=1e-06

======================== Running NR with EPS = 1e-06 ========================
Iter 0: max mismatch = 1.9978433598183885, [Δv, Δδ] = 1
Iter 0: ΔV & Δδ not computed yet
Iter 1: max mismatch = 0.19749135582722577, [Δv, Δδ] = 0.11524655390253655
Iter 2: max mismatch = 0.007756691761843459, [Δv, Δδ] = 0.018885424228148255
Iter 3: max mismatch = 0.0007295450521884739, [Δv, Δδ] = 0.0006021531095129415
Iter 4: max mismatch = 6.367679013674632e-05, [Δv, Δδ] = 2.254682865366751e-05
Iter 5: max mismatch = 5.535414396629079e-06, [Δv, Δδ] = 1.9599402516178526e-06
Iter 6: max mismatch = 4.811913369984211e-07, [Δv, Δδ] = 1.7037644364632053e-07
N-R Converged in 6 iterations with ε=1e-06

======================== Running FDLF with EPS = 1e-06 ========================
Iter 0: max mismatch = 1.997843e+00, max [Δv, Δδ] = 1.170425e-01
Iter 1: max mismatch = 3.914411e-01, max [Δv, Δδ] = 3.115791e-02
Iter 2: max mismatch = 5.827013e-02, max [Δv, Δδ] = 2.601853e-03
Iter 3: max mismatch = 6.919409e-03, max [Δv, Δδ] = 1.548606e-04
Iter 4: max mismatch = 1.117655e-03, max [Δv, Δδ] = 2.169311e-05
Iter 5: max mismatch = 1.969816e-04, max [Δv, Δδ] = 8.960917e-06
Iter 6: max mismatch = 4.002192e-05, max [Δv, Δδ] = 1.630399e-06
Iter 7: max mismatch = 5.929995e-06, max [Δv, Δδ] = 1.713213e-07
Iter 8: max mismatch = 1.178264e-06, max [Δv, Δδ] = 4.810994e-08
Iter 9: max mismatch = 1.705961e-07, max [Δv, Δδ] = 7.985301e-09
FDLF Converged in 10 iterations with ε=1e-06

---

Table of N-R results of each bus after each iteration using ε=1e-06

Table 1: Alan Slack bus results

Table 2: Betty PV bus results

Table 2: Clyde PQ bus results

Table 4: Doug PQ bus results

Table 5: Eve PQ bus results

---

Time to process the convergence functions for N-R and FDLF

For 3 N-R iterations and 4 FDLF iterations at ε=1e-02

• N-R iterations time: 0.382310 seconds taking 0.127437 seconds per iteration
• FDLF iteration time: 0.394830 seconds taking 0.098708 seconds per iteration

For 9 N-R iterations and 12 FDLF iterations at ε=1e-09

• N-R iterations time: 0.144251 seconds taking 0.016028 seconds per iteration
• FDLF iteration time: 0.175566 seconds taking 0.013505 seconds per iteration

Total time to process four ε values, EPS = [1e-2, 1e-4, 1e-6, 1e-9]

• N-R total iterations time: 1.159153 seconds
• FDLF total iterations time: 1.179878 seconds

---