Three-Phase OPF with Cross-Phase Inverter Operation

This repository contains the code and data accompanying the work on three-phase optimal power flow (OPF) for unbalanced distribution networks with inverter-based distributed energy resources (DERs), especially photovoltaic (PV) systems and electric vehicle charging stations (EVCSs).

The framework formulates a convex (QP) three-phase OPF in polar coordinates, explicitly models cross-phase power flows enabled by three-phase inverters, and incorporates a data-driven polynomial approximation of the Voltage Unbalance Factor (VUF). It is designed for both radial and heavily meshed distribution networks.

The repository includes all the elements needed to reproduce the test cases and numerical results presented in the associated paper.

✨ Key Features

• Convex three-phase OPF

  • Voltages modeled in polar form (magnitudes and angles).
  • Linearized three-phase power flow equations and line capacity constraints.
  • Single objective function combining operational cost, losses, and a polynomial approximation of VUF.

• Explicit modeling of DERs

  • Three-phase and single-phase PVs.
  • Three-phase and single-phase EV charging stations.
  • DERs participate actively in OPF to:
    • Limit harmful operating conditions.
    • Exploit full converter capability.
    • Improve voltage quality and reduce losses.

• Cross-phase inverter operation

  • Models the ability of three-phase inverters to transfer power across phases.
  • Uses unused phase capacity (active and reactive) to:
    • Reduce operating cost.
    • Improve system conditions.
    • Mitigate current and voltage imbalance.

• Unbalanced distribution networks

  • Fully three-phase unbalanced model including:
    • Self and mutual impedances.
    • Structural and random imbalance sources.
  • Applicable to:
    • IEEE 33-bus radial system.
    • 192-bus heavily meshed test system.

• Reproducible experiments

  • Multiple scenarios and sub-methods:
    • Different device mixes (various PV/EV configurations).
    • Different control/operation modes (with/without cross-phase capability).
  • Comparative results for:
    • Total cost.
    • Network losses.
    • VUF / power quality.

📁 Repository Structure

At a high level, the repository is organized as:

• Libraries/
  Core routines and helper functions used across projects:

  • Data structures and parameter loading.
  • Power flow and OPF model assembly.
  • Linearization and convexification utilities.
  • VUF approximation and evaluation.

• Projects/
  High-level entry points / project scripts to:

  • Build specific test systems (e.g., IEEE 33-bus, 192-bus).
  • Configure scenarios and sub-methods.
  • Call the OPF solver and post-process results (cost, losses, VUF).

• Test Cases/
  Input data for the case studies:

  • Network topology and line parameters.
  • Load profiles and phases.
  • PV and EVCS locations, capacities, and operating constraints.
  • Scenario definitions for radial and meshed systems.

• paper/
  Supporting material related to the paper:

  • Draft/LaTeX, figures, or additional derivations as needed.

• Imbalance_paper.pdf
  PDF of the paper describing the full mathematical formulation, theoretical background, and numerical results.

• README.md
  This file (project overview, usage, and citation information).

• LICENSE
  License information (Apache-2.0).

• *.bat
  Convenience scripts to initialize or push the project on Windows.

If you add or rename core scripts (e.g., main OPF driver, plotting utilities), consider adding them explicitly in the sections below.

🚀 Getting Started

1. Clone the repository

git clone https://github.com/AB-Coder96/threephaseOPF.git
cd threephaseOPF