Multi-objective thermal-constrained service restoration in active distribution networks with distributed energy resources using artificial protozoa optimization

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Original abstract

Effective service restoration in modern Active Distribution Networks (ADNs) is challenged by the high penetration of volatile Distributed Energy Resources (DERs) and stringent thermal constraints. This paper proposes a novel multi-objective, security-constrained restoration framework that balances maximum load recovery with real power loss minimization and network thermal safety. Unlike conventional methods relying on linearized models, this study employs a full Alternating Current (AC) power flow formulation to ensure physical feasibility in stressed post-fault states. The optimization is driven by the Artificial Protozoa Optimizer (APO), a bio-inspired metaheuristic tailored for non-convex switching configurations. The framework was validated on modified IEEE 33-bus and IEEE 123-bus systems. For the IEEE 33-bus system, the APO identified a security-constrained optimal configuration that enhanced thermal operating margins while maintaining reliable load restoration. The obtained solution reduced total system losses by 42.1% and maintained all bus voltages within the permissible regulatory range of 0.95–1.05 p.u. Similarly, results for the IEEE 123-bus system demonstrate a 98.1% critical load recovery rate with a 48.2% reduction in active power losses. Comparative analysis reveals that the APO outperforms standard metaheuristics in convergence stability (standard deviation $$\approx 10^{-6}$$ ) and computational speed ( $$<9$$ seconds), proving its suitability for real-time distribution management systems.

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