⚡ electrical engineering

Application of Multi-Layer Particle Swarm Optimization Algorithm for ORPD in Renewable-Integrated Power Systems Incorporating FACTS Devices

This paper proposes a Multi-Layer Particle Swarm Optimization (MLPSO) algorithm to solve the Optimal Reactive Power Dispatch problem in renewable-integrated power systems with FACTS devices, demonstrating superior performance in minimizing power losses and voltage deviations compared to existing optimization techniques across various scenarios on a modified IEEE 30-bus network.

Original authors: Avinash Kumar, Saptarshi Gupta, Rupali Singh, Dharmbir Prasad, Pankaj Kumar

Published 2026-06-30

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CC BY 4.0

Original authors: Avinash Kumar, Saptarshi Gupta, Rupali Singh, Dharmbir Prasad, Pankaj Kumar

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the electrical grid as a massive, bustling city. In this city, electricity is the traffic, and the power lines are the roads. For a long time, this city relied on big, steady power plants (like synchronous generators) to keep the traffic flowing smoothly and the voltage (the "pressure" of the electricity) just right.

But recently, the city has started adding a lot of new, unpredictable drivers: Wind farms and Solar panels. These are great, but they are like weather-dependent delivery trucks. Sometimes the sun is bright, and they flood the roads with power; other times, clouds roll in, and the flow stops. This unpredictability makes it hard to keep the traffic moving efficiently, leading to "traffic jams" (power losses) and "bumpy rides" (voltage instability).

To fix this, engineers use two types of tools:

FACTS Devices: Think of these as smart traffic lights and adjustable speed bumps.
- TCSCs are like adjustable speed bumps that can change the "resistance" of the road to guide traffic where it's needed most.
- TCPSs are like smart traffic lights that can slightly shift the timing of the traffic flow to prevent gridlock.
Optimization Algorithms: These are the traffic control centers trying to figure out the perfect settings for all those speed bumps and lights to keep the city running smoothly.

The Problem

The authors of this paper noticed that the old "traffic control centers" (standard computer algorithms) were getting stuck. They were like a GPS that keeps suggesting the same wrong route because it got confused by the unpredictable wind and solar drivers. They couldn't find the best way to manage the power, leading to wasted energy (losses) and unstable voltage.

The Solution: The "Multi-Layer" Team

The authors proposed a new, smarter traffic control center called Multi-Layer Particle Swarm Optimization (MLPSO).

Here is how it works, using a simple analogy:
Imagine you are trying to find the best spot in a huge, foggy forest to set up a campfire.

Old Method (Standard PSO): You send out a single flock of birds. They all fly together, looking for the best spot. If they all get stuck in a small, foggy patch, they might miss the perfect clearing nearby.
The New Method (MLPSO): Instead of one big flock, you organize the birds into layers of teams.
- Layer 1 (The Scouts): A few birds fly high and wide to explore the whole forest (Global Search). They look for general areas that look promising.
- Layer 2 (The Explorers): Once the scouts find a good area, a second team dives in closer to check the details.
- Layer 3 (The Refiners): A third team zooms in on the specific spot to make tiny adjustments, ensuring the fire is perfectly placed.

These layers talk to each other. If the scouts find a better area, the other layers switch their focus. If the refiners find a tiny improvement, they tell the scouts to look there too. This prevents the team from getting stuck in one spot and ensures they find the absolute best solution.

What They Did

The researchers tested this new "Multi-Layer Team" on a simulated version of a real power grid (the IEEE 30-bus system). They added:

Solar power at one location.
Wind power at two other locations.
Smart traffic lights (FACTS devices) at various points on the grid.

They ran four different scenarios:

No smart traffic lights (just the basics).
Two speed bumps (TCSCs).
Two speed bumps and one traffic light (TCPS).
Three speed bumps and three traffic lights.

The Results

The paper claims that the Multi-Layer Team (MLPSO) was the clear winner.

Less Waste: It found settings that reduced the amount of electricity lost as heat (power loss) significantly better than other popular methods like Genetic Algorithms or Differential Evolution.
Smoother Ride: It kept the voltage levels much more stable, meaning the "bumpy ride" for the electricity was minimized.
Robustness: Even when they simulated sudden changes (like a wind farm suddenly stopping or a power line breaking), the Multi-Layer Team kept the system stable better than the others.

In Summary

This paper introduces a smarter, layered way for computers to manage electricity in a world full of unpredictable wind and solar power. By using a "team of teams" approach that balances looking far and wide with looking closely at details, they can keep the power grid efficient and stable, even when the weather changes. They proved this works better than the current "best" methods by testing it on a standard power grid model with renewable energy and smart devices.

Technical Summary: Application of Multi-Layer Particle Swarm Optimization for ORPD in Renewable-Integrated Power Systems

Problem Definition
The paper addresses the Optimal Reactive Power Dispatch (ORPD) problem in modern power systems characterized by high penetration of renewable energy sources (RES), specifically wind and solar PV. The integration of inverter-based resources introduces significant challenges, including intermittent generation, limited reactive power support capacity, and increased voltage instability. The ORPD problem is formulated as a non-linear, non-convex, mixed-integer optimization challenge aimed at minimizing two distinct objectives: real power transmission losses ( $P_{Loss}$ ) and total bus voltage deviation (TVD). The problem space is further complicated by the inclusion of Flexible AC Transmission Systems (FACTS) devices—specifically Thyristor-Controlled Series Capacitors (TCSC) and Thyristor-Controlled Phase Shifters (TCPS)—which add non-linear control variables (reactance and phase shift angles) to the decision space. The study seeks to determine optimal settings for generator voltages, transformer taps, shunt compensators, and FACTS parameters while adhering to strict equality (power flow) and inequality (operational limits) constraints.

Methodology
To solve this complex optimization problem, the authors propose the application of a Multi-Layer Particle Swarm Optimization (MLPSO) algorithm. This approach is an advanced extension of the standard PSO, designed to overcome limitations such as premature convergence and slow search speeds in high-dimensional, multi-modal landscapes.

Algorithm Structure: The MLPSO organizes the swarm into a hierarchical structure of multiple layers (typically 3). Particles in lower layers represent individual solutions, while particles in upper layers represent sub-swarms from the layer below. This "ladder-like" hierarchy facilitates a dynamic balance between global exploration (searching diverse FACTS configurations) and local exploitation (fine-tuning voltage profiles).
Search Mechanisms: The algorithm employs adaptive switching between global and local search variants based on success rates. It utilizes a neighborhood search strategy (Local Neighborhood Search and Global Neighborhood Search) with a ring topology to enhance local diversity and avoid local optima.
System Modeling: The study utilizes a modified IEEE 30-bus test system. Renewable integration is simulated by replacing the synchronous generator at bus 8 with a Solar PV plant and generators at buses 11 and 13 with Doubly-Fed Induction Generator (DFIG) wind farms.
FACTS Integration: Steady-state models for TCSC and TCPS are incorporated into the power flow equations. TCSCs are modeled as variable reactance elements, while TCPSs are modeled as complex tapping ratios with phase shift angles.
Constraints: The optimization is subject to constraints including generator voltage/reactive power limits, load bus voltage limits, transmission line thermal limits, transformer tap settings, and specific operating limits for TCSC reactance and TCPS phase shifts.

Key Contributions

Novel Algorithm Application: The paper introduces the MLPSO algorithm to the specific domain of ORPD in renewable-integrated systems equipped with multiple FACTS devices (TCSC and TCPS), a combination not extensively covered in prior literature.
Comprehensive Scenario Analysis: The study evaluates four distinct scenarios to assess the impact of FACTS devices:
- Case 1: ORPD without FACTS.
- Case 2: ORPD with two TCSCs.
- Case 3: ORPD with two TCSCs and one TCPS.
- Case 4: ORPD with three TCSCs and three TCPSs.
Robustness and Sensitivity Analysis: The authors conduct extensive post-optimization analyses, including sensitivity to renewable penetration levels (20% to 100%), robustness under stochastic generation uncertainty (Monte Carlo simulation), sensitivity to FACTS placement and sizing, and N-1 security contingency analysis (line outages).
Dynamic Security Assessment: The study evaluates the impact of the optimized settings on transient stability, analyzing rotor angle deviation, critical clearing time (CCT), and frequency response following severe faults and generation loss.

Results
The MLPSO algorithm was tested on the modified IEEE 30-bus system and compared against Real-Coded Genetic Algorithm (RCGA), Differential Evolution (DE), and Biogeography-Based Optimization (BBO).

Performance Metrics: Across all four cases and both objective functions ( $P_{Loss}$ $P_{L oss}$ and TVD), MLPSO consistently outperformed the benchmark algorithms.
- In Case 4 (most complex), MLPSO achieved a minimum power loss of 3.6125 MW and a TVD of 0.0513 p.u., representing improvements of 0.6–1.6% in loss and 3.9–9.7% in voltage deviation over the best competing methods.
- The algorithm demonstrated faster convergence and higher stability in finding global optima compared to the benchmarks.
FACTS Impact: The inclusion of FACTS devices significantly reduced power losses and voltage deviations. The optimal placement of TCSCs and TCPSs near renewable buses (lines 27, 28, 36) yielded the best results, with TCSCs operating in capacitive mode to offset inductive line charging.
Robustness: Under 1000 Monte Carlo scenarios with uncertain wind and solar inputs, the MLPSO solutions remained within acceptable limits (95% confidence intervals: $P_{Loss}$ [3.52, 3.78] MW; TVD [0.0489, 0.0553] p.u.).
Dynamic Stability: The optimized FACTS settings significantly improved transient stability. In contingency tests, the MLPSO-optimized system exhibited the lowest first-swing amplitude, fastest damping of oscillations, and superior frequency recovery (nadir frequency of 59.68 Hz vs. 59.52 Hz in the base case) compared to heuristic or unoptimized settings.

Significance and Claims
The paper claims that the proposed MLPSO framework provides a robust and effective solution for managing reactive power in future renewable-dominated grids. By integrating advanced meta-heuristics with FACTS devices, the method addresses the dual challenges of renewable intermittency and system stability. The authors assert that their approach offers superior loss minimization and voltage profile enhancement compared to existing evolutionary algorithms.

The study concludes that while the MLPSO algorithm demonstrates significant potential for supporting safe and efficient grid operations, the findings require further verification before widespread industrial promotion. The work highlights the necessity of advanced optimization techniques to handle the non-linear, multi-objective nature of modern power systems with high renewable penetration and FACTS integration.