[Paper Review] Accuracy and Application Scope Analysis for Linearized Branch Flow Model in Radial Distribution Systems

Hanyang Lin, Xinwei Shen+2 more|arXiv (Cornell University)|Dec 23, 2021

Optimal Power Flow Distribution4 citations

TL;DR

This paper proposes a linearized branch flow (LBF) model for radial distribution systems that simplifies power flow analysis by using current injection and voltage drop equations, achieving high accuracy in voltage magnitude and computational efficiency. With a proper scaling coefficient, LBF provides lower bounds for voltage and upper bounds for branch flows, making it suitable as a warm start for optimization problems like distribution system expansion planning.

ABSTRACT

An in-depth analysis of linearized branch flow (LBF) model considering current injection and absolute value of impedance is proposed in this paper. The form of LBF model is based on two equations: the current injection to meet KCL and the voltage drop to meet KVL. By representing the absolute value of complex load power with the current injection, LBF model is much simpler than alternating current power flow (ACPF) model. The results on theoretical analysis and numerical studies show that LBF exhibits the high accuracy in bus voltage magnitude but a poor performance in branch flow. Moreover, LBF is also compared with fast decoupled linearized power flow (FDLPF) model to verify its efficiency, thus proving its superiority for fast evaluation of large-scale distribution systems with high accuracy in voltage magnitude. Finally, this paper analyzes three factors to lower LBF's errors of branch flow, as well as LBF's possible application scope.

Motivation & Objective

• To analyze the accuracy and application scope of the linearized branch flow (LBF) model in radial distribution systems.
• To compare LBF with FDLPF and SOCP-based ACOPF models in terms of computational efficiency and accuracy.
• To identify factors affecting LBF's error in branch flow and voltage magnitude for practical deployment.
• To establish conditions under which LBF can serve as a reliable warm start for large-scale distribution network optimization.
• To determine the model's applicability in planning and operational problems such as distribution system expansion planning (DSEP).

Proposed method

• Formulates the LBF model using two core equations: KCL via current injection and KVL via voltage drop, with complex power represented via current injection.
• Introduces a scaling coefficient 'a' in current injection to adjust for approximation errors, enabling bound estimation.
• Employs theoretical analysis to derive error sources, particularly related to reactive power flows and R/X ratios.
• Conducts numerical studies on 33-, 69-, and 141-bus systems to compare LBF with FDLPF and SOCP-based ACOPF.
• Uses linear programming for fast solution, leveraging the model’s simplicity for large-scale system evaluation.
• Analyzes sensitivity of errors to P/Q ratio, R/X ratio, and load levels through case studies.

Experimental results

Research questions

• RQ1 How accurate is the LBF model in estimating bus voltage magnitude and branch power flow compared to AC power flow?
• RQ2 What factors significantly influence the error in branch flow estimation within the LBF model?
• RQ3 Can the LBF model provide conservative bounds (lower for voltage, upper for flow) when a proper scaling coefficient is applied?
• RQ4 Under what system conditions (e.g., high P/Q ratio, high load level) does the LBF model achieve acceptable accuracy?
• RQ5 In what optimization contexts can LBF serve as an effective warm start for distribution network problems?

Key findings

• LBF achieves high accuracy in voltage magnitude estimation, outperforming FDLPF in larger systems due to reduced linearization error in voltage drop equations.
• LBF exhibits poor accuracy in branch flow estimation, with errors increasing rapidly under high reactive power loads.
• With a scaling coefficient a = 1.08, LBF consistently produces negative voltage errors (lower bounds) and positive branch flow errors (upper bounds).
• Errors in branch flow are primarily caused by inaccurate modeling of reactive power flows, especially when the P/Q ratio is low.
• Lower errors in branch flow occur when the R/X ratio is high or the P/Q ratio of loads is increased, indicating better performance in systems with less reactive power.
• At higher load levels, LBF errors decrease due to improved reactive power compensation, suggesting improved accuracy under heavy loading conditions.