⚡ electrical engineering

A New Hybridization Algorithm For Solving The Non-Convex AC Transmission Expansion Planning Problem Considering Large Scale Systems

This paper proposes a new hybrid DE-GWO algorithm combined with a Search Space Reduction strategy to solve the non-convex AC Transmission Expansion Planning problem for large-scale systems, demonstrating improved optimality and robustness over existing methods in IEEE test systems.

Original authors: Thanh Long Duong, Nguyen Duc Huy Bui, Viet Anh Truong

Published 2026-07-09

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Thanh Long Duong, Nguyen Duc Huy Bui, Viet Anh Truong

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 you are the mayor of a growing city. Your job is to decide where to build new roads and bridges to handle the increasing number of cars (electricity) expected in the future. You want to spend as little money as possible on construction, but you also need to make sure the roads don't get jammed (overloaded) and that traffic flows smoothly without accidents (blackouts).

This is essentially what Transmission Expansion Planning (TEP) is for an electrical grid.

This paper tackles a very specific, difficult version of this problem called ACTEP (AC Transmission Expansion Planning). Here is the breakdown of the problem and the authors' solution, explained simply:

The Problem: The "Perfect Map" vs. The "Rough Sketch"

Most planners use a "rough sketch" (a simplified model called DC) to plan roads. It's fast to calculate, but it ignores important details like the weight of the cars, the steepness of the hills, and the friction on the tires. In electricity terms, this ignores voltage levels and power losses. If you build a grid based only on this sketch, you might end up with a system that looks good on paper but fails in the real world.

To get it right, you need the "perfect map" (the full AC model). This model accounts for every physical detail of how electricity actually behaves. However, this map is incredibly complex. It's like trying to solve a 3D puzzle where the pieces keep changing shape. If you try to solve this puzzle using standard methods, you often get stuck in a "local optima"—a solution that looks good but isn't the best possible one. You might find a path that works, but it costs way more than necessary.

The Solution: A New Hybrid Algorithm (DE-GWO)

The authors created a new "search engine" to find the best road plan. They combined two different strategies, like mixing two types of explorers:

The "Global Wanderer" (Differential Evolution - DE): Imagine a team of explorers who spread out across the entire country to look for new paths. They are great at finding new areas to explore but sometimes lack focus when they get close to a good spot.
The "Local Hunter" (Grey Wolf Optimizer - GWO): Imagine a pack of wolves hunting prey. They are very focused and know how to zero in on a target once they are close. They are great at fine-tuning a solution but might miss a better path if they start in the wrong neighborhood.

The Hybrid (DE-GWO): The authors combined these two. The algorithm uses the "Wanderers" to scan the whole map for promising areas and the "Wolves" to zoom in and perfect the solution once they find a good spot. This prevents the algorithm from getting stuck in a "good enough" solution and helps it find the best solution.

The Shortcut: The "Search Space Reduction" (SSR) Strategy

Even with a great algorithm, checking every single possible road combination on a massive grid (like the IEEE 300-bus system, which is like a huge metropolis) takes too long. It's like trying to read every book in a library to find one specific sentence.

The authors introduced a Search Space Reduction (SSR) strategy. Think of this as using a "rough sketch" (the DC model) first to get a general idea of where the roads probably need to go.

High-Ability Lines: Roads that the sketch says are definitely needed.
Medium-Ability Lines: Roads that are cheap to build.
Low-Ability Lines: Roads that are likely unnecessary.

Instead of checking every possible road, the algorithm focuses its energy on the "High" and "Medium" candidates and only checks a few "Low" ones. This is like telling your construction crew, "Don't build roads in the desert; focus on the city center and the cheap suburbs." This drastically cuts down the time needed to find the answer.

The Results: What Did They Find?

The team tested their new method on three famous electrical grid models (24-bus, 118-bus, and 300-bus systems).

Better Savings: On the largest system (300-bus), their method found a solution that was 9.75% cheaper than the previous best method found in other research.
More Reliable: The new method was much more consistent. While other methods might find the best answer only 20% of the time, the new hybrid method found it much more often (up to 100% in some tests).
Speed: By using the "Search Space Reduction" shortcut, they reduced the time and effort needed to solve the problem significantly, especially for the large cities (118-bus and 300-bus systems).

In Summary

The paper presents a smarter way to plan electrical grids. Instead of using a simplified, inaccurate map, they use a detailed, realistic model. To handle the complexity of this model, they created a "hybrid explorer" algorithm that balances looking far and wide with focusing closely. They also added a "shortcut" strategy to ignore unlikely road options, making the process fast enough to handle massive power grids. The result is a plan that saves money and is more reliable than previous methods.

Technical Summary: A New Hybridization Algorithm for Solving the Non-Convex AC Transmission Expansion Planning Problem Considering Large Scale Systems

Problem Statement
Transmission Expansion Planning (TEP) aims to identify a feasible set of new transmission lines to meet future load demand while minimizing investment costs and satisfying technical constraints. Conventional approaches often rely on simplified DC power flow models or linearized/convexified AC formulations to reduce computational complexity. However, these simplifications neglect critical parameters such as voltage magnitudes, reactive power requirements, and active power losses, often yielding solutions that are physically unrealizable in real-world networks.

The full Alternating Current Transmission Expansion Planning (ACTEP) problem, formulated as a Mixed-Integer Non-Linear Programming (MINLP) problem, offers higher accuracy but presents significant challenges due to its non-linear and non-convex nature. Solving the ACTEP problem directly is computationally burdensome, particularly for large-scale systems, where meta-heuristic algorithms often struggle to balance exploration and exploitation, leading to premature convergence, entrapment in local optima, and insufficient robustness under N-1 contingency conditions.

Methodology
The study proposes a bi-level optimization framework to address the ACTEP problem using a complete non-convex AC model.

Mathematical Formulation:
- Master Problem: Focuses on discrete investment decisions (number of new circuits per right-of-way). The objective is to minimize total cost, comprising line investment costs, system operation costs, and power loss costs.
- Sub-Problem: Utilizes the AC Optimal Power Flow (ACOPF) formulation to evaluate the operational feasibility of the topologies generated by the master problem under both normal and contingency (N-1) conditions.
- Penalty Mechanism: Infeasible solutions (those violating ACOPF constraints or requiring load shedding) are penalized using virtual generators at load buses. A large penalty value is added to the objective function if the ACOPF calculation fails or if operational constraints are violated, guiding the meta-heuristic algorithm toward feasible regions.
Proposed Hybrid Algorithm (DE-GWO):
To overcome the limitations of standard meta-heuristics in large discrete search spaces, the authors introduce a hybrid algorithm combining Differential Evolution (DE) and Grey Wolf Optimizer (GWO).
- DE Component: Provides strong global exploration capabilities through mutation and crossover operations, sharing information among individuals to prevent premature convergence.
- GWO Component: Offers rapid local exploitation (search refinement) guided by the three best solutions (alpha, beta, and delta wolves).
- Hybridization Strategy: The algorithm dynamically selects between DE's mutation process and GWO's hunting mechanism based on a decision parameter ( $\tau_{DE-GWO}$ ). This integration aims to maintain a balance between exploring the vast search space and exploiting promising regions for rapid convergence.
Search Space Reduction (SSR) Strategy:
To mitigate the computational burden of large-scale systems, a novel three-level heuristic-based SSR strategy is introduced. Instead of eliminating candidate lines entirely, the strategy classifies them into three levels based on a preliminary DC model solution:
- High-ability lines: Lines selected in the DC solution, assigned a higher upper bound for circuit addition.
- Medium-ability lines: Low-cost candidate lines (cost $\le$ average DC investment cost), assigned a moderate upper bound.
- Low-ability lines: Remaining lines, assigned a lower upper bound (potentially increased slightly for N-1 security criteria).
  This approach reduces the search space dimensionality while preserving viable low-cost options that might be overlooked by strict elimination methods.

Key Contributions

Novel Hybrid Algorithm: The proposal of the DE-GWO algorithm specifically tailored for the discrete, non-convex ACTEP problem, integrating DE's exploration with GWO's exploitation.
Comprehensive Modeling: Solving the ACTEP problem using a full non-convex AC model that integrates Reactive Power Planning (RPP), N-1 security constraints, power loss costs, and operation costs.
SSR Strategy: The development of a three-level heuristic SSR strategy that reduces computational complexity without discarding potentially optimal low-cost rights-of-way.
Preprocessing Optimization: Implementation of the Objective Function Evaluation Number Reduction (OFENR) strategy and parallel computing to further decrease simulation time by avoiding redundant ACOPF calculations.

Results
The proposed method was validated on three standard test systems: IEEE 24-bus, IEEE 118-bus, and IEEE 300-bus.

Optimality: The DE-GWO algorithm consistently achieved lower or comparable total costs compared to state-of-the-art methods (including IDE-PBILc, BL-ES-MARO, and various single-algorithm approaches). In the IEEE 300-bus system, the proposed method improved optimality by 9.75% compared to the IDE-PBILc method.
Robustness: The hybrid algorithm demonstrated superior robustness (success rate) in finding the global optimum across multiple runs. The SSR strategy significantly enhanced this robustness, increasing it by up to 20% in the IEEE 118-bus system and up to 80% in the IEEE 300-bus system compared to the non-SSR version.
Efficiency: The combination of the SSR strategy and OFENR preprocessing significantly reduced the average number of iterations and ACOPF function evaluations. While some exploitation-focused algorithms (e.g., EHPSGWO) showed faster convergence times, they frequently failed to find the global optimum in large-scale discrete spaces. The proposed method offered a better trade-off between solution quality and computational effort.

Significance and Claims
The paper claims that solving the ACTEP problem with a full non-convex AC model is essential for obtaining realistic and reliable expansion plans, despite the computational challenges. The authors assert that their hybrid DE-GWO algorithm, augmented by the three-level SSR strategy, effectively addresses the trade-off between optimality and robustness in large-scale systems where traditional meta-heuristics often fail.

The study highlights that while simplified models offer speed, they risk physical infeasibility. By integrating RPP and N-1 contingencies into a full AC model, the proposed method ensures that expansion plans are not only cost-effective but also technically secure. The authors conclude that their approach provides a robust framework for large-scale TEP, though they acknowledge that the current SSR strategy relies on static boundaries derived from a DC model. They suggest that future work could focus on dynamic SSR strategies to further enhance global search capabilities, particularly for stochastic TEP problems involving renewable energy integration.

The Problem: The "Perfect Map" vs. The "Rough Sketch"

The Solution: A New Hybrid Algorithm (DE-GWO)

The Shortcut: The "Search Space Reduction" (SSR) Strategy

The Results: What Did They Find?

In Summary

More like this