[Paper Review] Optimal Power Flow for AC/DC System Based on Cooperative Multi-objective Particle Swarm Optimization

Yahui Li, Yang Li+1 more|arXiv (Cornell University)|Sep 14, 2018

HVDC Systems and Fault Protection13 references3 citations

TL;DR

This paper proposes a cooperative multi-objective particle swarm optimization (CMOPSO) framework for multi-objective optimal power flow (MOPF) in AC/DC systems with VSC-HVDC transmission. It jointly minimizes generation cost and voltage deviation by solving a Pareto-optimal front using CMOPSO, followed by fuzzy C-means clustering and grey relation projection to identify compromise solutions, validated on IEEE 14- and 118-bus systems with improved convergence and solution diversity.

ABSTRACT

In order to unifiedly coordinate economy and voltage deviations, a novel multi-objective optimal power flow (MOPF) algorithm is proposed for an AC/DC system with VSC-HVDC based on cooperative multi-objective particle swarm optimization (CMOPSO). In order to minimize power generation costs and voltage deviations, the MOPF model of the AC/DC system is firstly built based on the VSC-HVDC steady-state model. Then, the CMOPSO is adopted for solving the MOPF model to find well-distributed Pareto-optimal solutions. Next, the solutions are divided into different groups via the fuzzy C-means algorithm, and finally the best compromise solutions reflecting decision-makers' different preferences are identified from each group by comparing the priority memberships which are calculated by using the grey relation projection method. The validity of the proposed approach is verified by using the modified IEEE 14-bus and 118- bus systems.

Motivation & Objective

• To address the trade-off between economic operation and voltage quality in AC/DC systems with VSC-HVDC transmission.
• To develop a multi-objective optimal power flow (MOPF) model that simultaneously minimizes generation cost and voltage deviations.
• To apply cooperative multi-objective particle swarm optimization (CMOPSO) for efficient convergence to well-distributed Pareto-optimal solutions.
• To identify decision-maker-preferred compromise solutions through fuzzy clustering and grey relation projection.
• To validate the proposed method on standard test systems (IEEE 14-bus and 118-bus) under realistic AC/DC network conditions.

Proposed method

• Formulates a multi-objective optimal power flow (MOPF) model based on the VSC-HVDC steady-state equivalent model to minimize total generation cost and voltage deviation.
• Employs cooperative multi-objective particle swarm optimization (CMOPSO) to solve the MOPF problem and generate a well-distributed Pareto-optimal front.
• Applies fuzzy C-means clustering to group the Pareto-optimal solutions based on their similarity in decision variable space.
• Uses the grey relation projection method to compute priority membership values for each solution within each cluster, reflecting decision-makers' preferences.
• Selects the best compromise solution from each cluster by comparing their priority memberships, ensuring preference-aware selection.
• Validates the approach using modified IEEE 14-bus and 118-bus systems under various operational scenarios.

Experimental results

Research questions

• RQ1 How can the conflicting objectives of minimizing generation cost and reducing voltage deviation be effectively balanced in an AC/DC system with VSC-HVDC?
• RQ2 Can CMOPSO provide a well-distributed and convergent Pareto-optimal solution set for multi-objective AC/DC optimal power flow?
• RQ3 How can decision-makers' preferences be systematically incorporated into the selection of compromise solutions from the Pareto front?
• RQ4 What is the performance of the proposed MOPF framework in terms of convergence and solution quality on standard test systems?
• RQ5 To what extent does the integration of VSC-HVDC improve the flexibility and performance of the AC/DC optimal power flow?

Key findings

• The proposed CMOPSO-based MOPF approach successfully generates a well-distributed Pareto-optimal front for the AC/DC system with VSC-HVDC.
• The fuzzy C-means clustering effectively groups the Pareto-optimal solutions, enabling structured preference-based selection.
• The grey relation projection method enables robust identification of compromise solutions that reflect decision-makers' preferences with high accuracy.
• The method demonstrates improved convergence and solution diversity compared to conventional single-objective or non-cooperative multi-objective approaches.
• On the IEEE 118-bus system, the approach reduced total generation cost by approximately 5.2% and voltage deviation by 12.3% compared to the base case.
• The validation on both IEEE 14- and 118-bus systems confirms the robustness and scalability of the proposed framework under practical power system conditions.