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Enhanced Flexibility Aggregation Using LinDistFlow Model with Loss Compensation

Yanlin Jiang, Xinliang Dai, Frederik Zahn, Veit Hagenmeyer

TL;DR

The paper analyzes the limitations of the LinDistFlow linearization for flexibility aggregation in ITD systems, showing that neglected losses cause boundary errors that accumulate at the PCC. It introduces a loss-compensation method that models losses as quadratic functions of the LinDistFlow exchange variables, yielding a privacy-preserving, quadratic mapping to refine the LinDistFlow-based flexibility set. Simulations on single and multi-DR configurations demonstrate that the compensation substantially improves coordination accuracy and feasibility, closely matching centralized AC-based references and reducing cost discrepancies. The approach enables accurate, scalable, and privacy-preserving ITD coordination in systems with multiple distributed energy resources.

Abstract

With the increasing integration of renewable energy resources and the growing need for data privacy between system operators, flexibility aggregation methods have emerged as a promising solution to coordinate integrated transmissiondistribution (ITD) systems with limited information exchange. However, existing methods face significant challenges due to the nonlinearity of AC power flow models, and therefore mostly rely on linearized models. This paper examines the inherent errors in the LinDistFlow model, a linearized approximation, and demonstrates their impact on flexibility aggregation. To address these issues, we propose an intuitive compensation approach to refine the LinDistFlow-based flexibility set. Simulation results demonstrate the effectiveness of the proposed method in efficiently coordinating ITD systems.

Enhanced Flexibility Aggregation Using LinDistFlow Model with Loss Compensation

TL;DR

The paper analyzes the limitations of the LinDistFlow linearization for flexibility aggregation in ITD systems, showing that neglected losses cause boundary errors that accumulate at the PCC. It introduces a loss-compensation method that models losses as quadratic functions of the LinDistFlow exchange variables, yielding a privacy-preserving, quadratic mapping to refine the LinDistFlow-based flexibility set. Simulations on single and multi-DR configurations demonstrate that the compensation substantially improves coordination accuracy and feasibility, closely matching centralized AC-based references and reducing cost discrepancies. The approach enables accurate, scalable, and privacy-preserving ITD coordination in systems with multiple distributed energy resources.

Abstract

With the increasing integration of renewable energy resources and the growing need for data privacy between system operators, flexibility aggregation methods have emerged as a promising solution to coordinate integrated transmissiondistribution (ITD) systems with limited information exchange. However, existing methods face significant challenges due to the nonlinearity of AC power flow models, and therefore mostly rely on linearized models. This paper examines the inherent errors in the LinDistFlow model, a linearized approximation, and demonstrates their impact on flexibility aggregation. To address these issues, we propose an intuitive compensation approach to refine the LinDistFlow-based flexibility set. Simulation results demonstrate the effectiveness of the proposed method in efficiently coordinating ITD systems.
Paper Structure (14 sections, 1 theorem, 17 equations, 3 figures)

This paper contains 14 sections, 1 theorem, 17 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Model of Transmission Systems
  4. Model of Distribution Systems
  5. DistFlow Model
  6. LinDistFlow Model
  7. Optimal Power Flow for ITD Systems
  8. Flexibility Aggregation Methods
  9. Flexibility Aggregation based on LinDistFlow Model
  10. System Loss Compensation
  11. Simulation
  12. Performance with Different Cost
  13. Overall Performance with Multiple Distribution Systems
  14. Conclusion

Key Result

Proposition 1

Given a radial network, matrix $A$ is invertible.

Figures (3)

  • Figure 1: Coordination framework between TSO-DSO
  • Figure 2: First row: The topology of the radial networks, with DER location and PCC. Second row: Shaded regions represent the LinDistFlow model (red) (i) and the compensation method (green) (ii). Dashed and solid lines mark the exact flexibility bounds, derived from solutions using DistFlow model. Third row: Markers show power flows for different costs, increasing in price from left to right.
  • Figure 3: Performance of aggregating flexibility in a distribution system, considering one TSO connected with $29$ distribution systems, including $9$ case10ba, $16$ case33mg and $4$ case118zh

Theorems & Definitions (6)

  • Remark 1: farivar2013branch
  • Remark 2
  • Remark 3: Lossless Approximation
  • Proposition 1: Prop. 1 in dai2023nmpc
  • Remark 4
  • Remark 5: Data Privacy