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Taylor-Expansion-Based Robust Power Flow in Unbalanced Distribution Systems: A Hybrid Data-Aided Method

Sungjoo Chung, Ying Zhang, Zhaoyu Wang, Fei Ding

TL;DR

The paper tackles robust power flow in unbalanced distribution systems with high DER penetration and measurement outliers. It blends a rotated complex Taylor-series-based linearization with a data-driven SVR to estimate and compensate linearization errors, enabling accurate and robust PF solutions in real time. Case studies on modified 13- and 123-bus feeders show substantial RMSE reductions (up to 15–50x) and online computation times around $0.126$ s, even with bad data, outperforming BFS and pure data-driven methods. This hybrid approach enables reliable PF for active distribution networks without relying on traditional balanced-system assumptions, with potential extensions to DER penetration variability, ZIP loads, and unknown topology.

Abstract

Traditional power flow methods often adopt certain assumptions designed for passive balanced distribution systems, thus lacking practicality for unbalanced operation. Moreover, their computation accuracy and efficiency are heavily subject to unknown errors and bad data in measurements or prediction data of distributed energy resources (DERs). To address these issues, this paper proposes a hybrid data-aided robust power flow algorithm in unbalanced distribution systems, which combines Taylor series expansion knowledge with a data-driven regression technique. The proposed method initiates a linearization power flow model to derive an explicitly analytical solution by modified Taylor expansion. To mitigate the approximation loss that surges due to the DER integration and bad data, we further develop a data-aided robust support vector regression approach to estimate the errors efficiently. Comparative analysis in the 13-bus and 123-bus IEEE unbalanced feeders shows that the proposed algorithm achieves superior computational efficiency, with guaranteed accuracy and robustness against outliers.

Taylor-Expansion-Based Robust Power Flow in Unbalanced Distribution Systems: A Hybrid Data-Aided Method

TL;DR

The paper tackles robust power flow in unbalanced distribution systems with high DER penetration and measurement outliers. It blends a rotated complex Taylor-series-based linearization with a data-driven SVR to estimate and compensate linearization errors, enabling accurate and robust PF solutions in real time. Case studies on modified 13- and 123-bus feeders show substantial RMSE reductions (up to 15–50x) and online computation times around s, even with bad data, outperforming BFS and pure data-driven methods. This hybrid approach enables reliable PF for active distribution networks without relying on traditional balanced-system assumptions, with potential extensions to DER penetration variability, ZIP loads, and unknown topology.

Abstract

Traditional power flow methods often adopt certain assumptions designed for passive balanced distribution systems, thus lacking practicality for unbalanced operation. Moreover, their computation accuracy and efficiency are heavily subject to unknown errors and bad data in measurements or prediction data of distributed energy resources (DERs). To address these issues, this paper proposes a hybrid data-aided robust power flow algorithm in unbalanced distribution systems, which combines Taylor series expansion knowledge with a data-driven regression technique. The proposed method initiates a linearization power flow model to derive an explicitly analytical solution by modified Taylor expansion. To mitigate the approximation loss that surges due to the DER integration and bad data, we further develop a data-aided robust support vector regression approach to estimate the errors efficiently. Comparative analysis in the 13-bus and 123-bus IEEE unbalanced feeders shows that the proposed algorithm achieves superior computational efficiency, with guaranteed accuracy and robustness against outliers.
Paper Structure (9 sections, 18 equations, 5 figures, 4 tables)

This paper contains 9 sections, 18 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Proposed Hybrid SVR-Aided Algorithm
  4. Rotated Complex Taylor Series Expansion
  5. Hybrid SVR-Aided Power Flow Algorithm
  6. Case Study
  7. Computation Accuracy and Time
  8. Robustness Against Bad Data
  9. Conclusion

Figures (5)

  • Figure 1: Three-phase rotation for linearization approximation
  • Figure 2: Flowchart of the proposed hybrid algorithm
  • Figure 3: The modified IEEE 13-node feeder with PV installation.
  • Figure 4: Comparison of three-phase voltage magnitude for the 123-bus test feeder using SVR and the proposed methods.
  • Figure 5: Comparison of voltage angles using SVR and the proposed methods. Limited by space, only C-phase angles are illustrated.