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Distributed Primal-Dual Interior Point Framework for Analyzing Infeasible Combined Transmission and Distribution Grid Networks

Muhammad Hamza Ali, Amritanshu Pandey

Abstract

The proliferation of distributed energy resources has heightened the interactions between transmission and distribution (T&D) systems, necessitating novel analyses for the reliable operation and planning of interconnected T&D networks. A critical gap is an analysis approach that identifies and localizes the weak spots in the combined T\&D networks, providing valuable information to system planners and operators. The research goal is to efficiently model and simulate infeasible (i.e. unsolvable in general settings) combined positive sequence transmission and three-phase distribution networks with a unified solution algorithm. We model the combined T&D network with the equivalent circuit formulation. To solve the overall T&D network, we build a Gauss-Jacobi-Newton (GJN) based distributed primal dual interior point optimization algorithm capable of isolating weak nodes. We validate the approach on large combined T&D networks with 70k+ T and 15k+ D nodes and demonstrate performance improvement over the alternating direction method of multipliers (ADMM) method.

Distributed Primal-Dual Interior Point Framework for Analyzing Infeasible Combined Transmission and Distribution Grid Networks

Abstract

The proliferation of distributed energy resources has heightened the interactions between transmission and distribution (T&D) systems, necessitating novel analyses for the reliable operation and planning of interconnected T&D networks. A critical gap is an analysis approach that identifies and localizes the weak spots in the combined T\&D networks, providing valuable information to system planners and operators. The research goal is to efficiently model and simulate infeasible (i.e. unsolvable in general settings) combined positive sequence transmission and three-phase distribution networks with a unified solution algorithm. We model the combined T&D network with the equivalent circuit formulation. To solve the overall T&D network, we build a Gauss-Jacobi-Newton (GJN) based distributed primal dual interior point optimization algorithm capable of isolating weak nodes. We validate the approach on large combined T&D networks with 70k+ T and 15k+ D nodes and demonstrate performance improvement over the alternating direction method of multipliers (ADMM) method.
Paper Structure (15 sections, 13 equations, 5 figures, 4 tables, 1 algorithm)

This paper contains 15 sections, 13 equations, 5 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries: $IV$-based Transmission and Distribution Modeling
  3. Positive-sequence Transmission Network
  4. Three-phase Distribution Network
  5. Infeasibility Analysis
  6. Coupling Port
  7. Combined T&D Infeasibility Analysis
  8. Centralized approach
  9. Distributed Approach
  10. Experiments
  11. Case Description
  12. Reactive Power Compensation of Infeasible Combined T&D Networks
  13. Analyzing Large Infeasible Combined T&D Networks
  14. Conclusion
  15. Acknowledgement

Figures (5)

  • Figure 1: Illustration of combined positive sequence transmission network and three-phase distribution networks with infeasibility sources at each node.
  • Figure 2: Real and imaginary circuit of coupling port.
  • Figure 3: Combined T&D in BBD structure. Here, A, B, and C represent three distinct distribution networks.
  • Figure 4: A graph representation of the Vermont feeder with a heatmap showing the highest infeasibility current magnitude at each node, based on the L2 (A) and L1 (B) norm formulations. Note that with L2-norm, infeasibility currents are spread throughout the network. With L1 norm, non-zero infeasibility currents are only found in 8 locations.
  • Figure 5: Combined T&D D-PDIP algorithm scalability.