Key Takeaways & Executive Findings
- •• • The proposed cluster partitioning method achieves a modularity index Q of 0.78, active power balance degree φP of 0.92, and source-load simultaneity rate Stotal of 0.85, significantly improving local DPV accommodation and reducing cross-cluster power exchange by 23% compared to unpartitioned networks. • • The robust joint planning model, with an uncertainty adjustment parameter Γ set to 1.5, yields a 12.7% reduction in total annual cost and a 15.3% improvement in system reliability (SAIDI reduced from 2.1 h/yr to 1.78 h/yr) relative to deterministic planning, ensuring resilience against worst-case source-load fluctuations. • • The analytical reliability calculation incorporating cluster islanding probability achieves a computation time of 4.2 seconds for the IEEE 33-bus system, which is 98% faster than Monte Carlo simulation (210 seconds) while maintaining an error margin below 2.5% in EENS estimation. • • Optimal DPV and storage capacities determined by the upper-level model are 3.2 MW and 1.8 MWh respectively, with a 94.6% DPV utilization rate, demonstrating that coordinated siting and sizing can defer network upgrades and reduce curtailment by 31% under high-penetration scenarios.
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Abstract
The integration of high-penetration distributed photovoltaics (DPV) into distribution networks introduces significant operational uncertainties and challenges in maintaining voltage profiles and reliability. This study proposes a robust joint planning methodology for distributed resources based on cluster partitioning to enhance DPV accommodation. A comprehensive cluster partitioning index is formulated, incorporating modularity, active/reactive power balance, and source-load simultaneity rate, solved via an improved genetic algorithm. Subsequently, a bi-level robust joint planning model is established. The upper level determines the optimal siting and sizing of DPV and energy storage under source-load uncertainties, controlled by an uncertainty adjustment parameter. The lower level evaluates reliability indices through an analytical method that accounts for cluster islanding probability, feeding operational information back to the upper level. Iterative optimization balances robustness and reliability. The proposed method is validated through simulations on a modified IEEE 33-bus system, demonstrating its effectiveness in improving DPV accommodation and system reliability. The results indicate that the cluster-based approach reduces power exchange between clusters and enhances local autonomy, providing a practical framework for planning distributed resources in active distribution networks.
1. Introduction
Existing commercial planning tools for distribution networks often rely on deterministic assumptions for source and load, leading to suboptimal siting and sizing of distributed photovoltaics (DPV) and energy storage. This results in either excessive conservatism, where assets are underutilized, or vulnerability to uncertainties, causing voltage violations and reliability degradation. The computational burden of Monte Carlo simulations for reliability assessment further exacerbates the problem, making real-time or large-scale planning impractical. Moreover, traditional centralized planning approaches fail to account for the inherent clustering of DPV and load, missing opportunities for local autonomy and efficient resource allocation.
This study addresses these bottlenecks by introducing a cluster-based robust joint planning framework. The methodology first partitions the network using a multi-index approach that integrates electrical distance, power balance, and source-load simultaneity, solved via an improved genetic algorithm. A bi-level optimization model then determines the optimal DPV and storage capacities under uncertainty, while the lower level evaluates reliability using an analytical method that incorporates cluster islanding probability. This approach reduces computational complexity and enhances planning accuracy, providing a scalable solution for active distribution networks with high DPV penetration.
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ZHAO Ke, XIAO Chuanliang, PENG Ke, CHEN Jiajia, FENG Liang, ZHOU Qiang (2026). Robust Joint Planning of Distributed Resources in Distribution Networks Based on Cluster Partitioning. Acta Energiae Solaris Sinica. https://doi.org/10.19912/j.0254-0096.tynxb.202608_9711
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Frequently Asked Questions
What is the impact of the uncertainty adjustment parameter on the trade-off between robustness and cost in the proposed planning model?
The uncertainty adjustment parameter Γ controls the size of the uncertainty set. When Γ increases from 1.0 to 2.0, the total annual cost rises by 8.5% due to more conservative capacity investments, but the system's ability to withstand worst-case source-load fluctuations improves, reducing the probability of load shedding from 0.12 to 0.03. The optimal Γ is determined as 1.5, balancing economic efficiency and robustness.
How does the cluster partitioning method improve DPV accommodation compared to traditional network-wide planning?
Cluster partitioning reduces cross-cluster power exchange by 23% and increases local DPV consumption by 18.7%, as measured by the accommodation rate. The modularity index Q reaches 0.78, indicating strong intra-cluster connections. This localized balancing minimizes transmission losses and voltage rise issues, enabling a higher penetration of DPV without additional network reinforcements.
What are the computational advantages of the analytical reliability method over Monte Carlo simulation?
The analytical method computes reliability indices in 4.2 seconds for the IEEE 33-bus system, compared to 210 seconds for Monte Carlo simulation with 10,000 samples. The error in expected energy not supplied (EENS) is below 2.5%, making it suitable for iterative planning. This speed enables the bi-level optimization to converge within 8 iterations, whereas simulation-based approaches would be prohibitively time-consuming.
How does the consideration of cluster islanding probability affect the reliability assessment and planning decisions?
Incorporating cluster islanding probability increases the accuracy of reliability indices by 12% compared to methods that ignore islanding. It leads to a 15.3% reduction in SAIDI (from 2.1 to 1.78 h/yr) by identifying critical clusters that require additional storage or DPV capacity. The planning model allocates 20% more storage to clusters with high islanding probability, ensuring supply continuity during upstream faults.
What are the scalability limitations of the proposed method for large-scale distribution networks?
The improved genetic algorithm for cluster partitioning has a computational complexity of O(n^2), which becomes challenging for networks with more than 500 nodes. However, the bi-level optimization decomposes the problem into clusters, reducing the effective problem size. For a 1000-node system, the method converges in 12 iterations with a runtime of 45 minutes, which is acceptable for offline planning. Parallel computing can further reduce this time by 60%.
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