arXiv subjects

Omid Mokhtari

Publications and source records attributed to Omid Mokhtari.

4 recordsLinked to original sources

arXiv2026

Data-Driven Power Flow for Radial Distribution Networks with Sparse Real-Time Data

Real-time control of distribution networks requires accurate information about the system state. In practice, however, such information is difficult to obtain because real-time measurements are available only at a limited number of locations. This paper proposes a novel data-driven power flow (DDPF) framework for balanced radial distribution networks. The proposed algorithm combines the behavioral approach with the DistFlow model and leverages offline historical data to solve power flow problems using only a limited set of real-time measurements. To design DDPF under sparse measurement conditions, we develop a sensor placement problem based on optimal network reductions. This allows us to determine sensor locations subject to a predefined sensor budget and to explicitly account for the radial nature of distribution networks. Unlike approaches that rely on full observability, the proposed framework is designed for practical distribution grids with sparse measurement availability. This enables data-driven power flow for real-time operation while reducing the number of required sensors. On several test cases, the proposed DDPF algorithm could demonstrate accurate voltage magnitude predictions, with a maximum error less than 0.001 p.u., with as little as 25% of total locations equipped with sensors.

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arXiv2025

Optimal Kron-based Reduction of Networks (Opti-KRON) for Three-phase Distribution Feeders

This paper presents a novel structure-preserving, Kron-based reduction framework for unbalanced distribution feeders. The method aggregates electrically similar nodes within a mixed-integer optimization (MIP) problem to produce reduced networks that optimally reproduce the voltage profiles of the original full network. To overcome computational bottlenecks of MIP formulations, we propose an exhaustive-search formulation to identify optimal aggregation decisions while enforcing voltage margin limits. The proposed exhaustive network reduction algorithm is parallelizable on GPUs, which enables scalable network reduction. The resulting reduced networks approximate the full system's voltage profiles with low errors and are suitable for steady-state analysis and optimal power flow studies. The framework is validated on two real utility distribution feeders with 5,991 and 8,381 nodes. The reduced models achieve up to 90% and 80% network reduction, respectively, while the maximum voltage-magnitude error remains below 0.003 p.u. Furthermore, on a 1000-node version of the network, the GPU-accelerated reduction algorithm runs up to 15x faster than its CPU-based counterpart.

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arXiv2025

Structure-preserving Optimal Kron-based Reduction of Radial Distribution Networks

Network reduction simplifies complex electrical networks to address computational challenges of large-scale transmission and distribution grids. Traditional network reduction methods are often based on a predefined set of nodes or lines to remain in the reduced network. This paper builds upon previous work on optimal Kron-based reduction of networks, which was formulated as a mixed-integer linear program, to enhance the framework in three aspects. First, the scalability is improved via a cutting plane restriction, tightened Big M bounds, and a zero-injection node reduction stage. Next, we introduce a radiality-preservation step to identify and recover nodes whose restoration ensures radiality. A linearized voltage magnitude error constraint is incorporated to explicitly bound the difference between full and reduced networks. The model is validated through its application to the 533-bus distribution test system and a 3499-bus utility feeder for a set of representative loading scenarios. In the 533-bus system, an 85% reduction was achieved with a maximum voltage error below 0.0025 per unit, while in the 3499-bus feeder, over 94% reduction was obtained with maximum voltage errors below 0.002 per unit. Additionally, we show that the radialization step accelerates the runtime of optimal voltage control problems when applied to Kron-reduced networks.

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arXiv2024

Enhancing Scalability of Optimal Kron-based Reduction of Networks (Opti-KRON) via Decomposition with Community Detection

Electrical networks contain thousands of interconnected nodes and edges, which leads to computational challenges in some power system studies. To address these challenges, we contend that network reductions can serve as a framework to enable scalable computing in power systems. By building upon a prior AC "Opti-KRON" formulation, this paper presents a DC power flow formulation for finding network reductions that are optimal within the context of large transmission analysis. Opti-KRON previously formulated optimal Kron-based network reductions as a mixed integer linear program (MILP), where the number of binary variables scaled with the number of nodes. To improve the scalability of the Opti-KRON approach, we augment the MILP formulation with a community detection (CD) technique that segments a large network into smaller, disjoint, but contiguous sub-graphs (i.e., communities). For each sub-graph, we then (in parallel) apply MILP-based along with a new cutting plane constraint, thus, enhancing scalability. Ultimately, the new DC-based Opti-KRON method can achieve a 80-95\% reduction of networks (in terms of nodes) while statistically outperforming other CD- and Kron-based methods. We present simulation results for the IEEE RTS-96 and the 2383-bus Polish networks.

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