[Paper Review] SDP-based State Estimation of Multi-phase Active Distribution Networks using micro-PMUs

Vahid R. Disfani, Mohammad Chehreghani Bozchalui+1 more|arXiv (Cornell University)|Apr 14, 2015

Power System Optimization and Stability24 references3 citations

TL;DR

This paper proposes a convex optimization-based state estimation method for multi-phase active distribution networks using micro-PMUs, leveraging semidefinite programming (SDP) to achieve globally optimal solutions. To address observability and noise sensitivity, it introduces measurement augmentation, network decomposition, and a redundancy-based bad data detection algorithm, validated on the EPRI 2998-bus test system with improved accuracy and robustness.

ABSTRACT

Distribution system state estimation (DSSE) is an essential tool for operation of distribution networks, the results of which enables the operator to have a thorough observation of the system. Thus, most distribution management systems (DMS) include a single-phase state estimator. Due to non-convexity of the SE problem, heuristic and Newton methods do not guarantee the global solution. In contrast, SDP based SE is more promising to guarantee the globally optimal solution since it represents and solves the problem in a convex format. However, the observability of the power system is highly vulnerable to the set of measurements while employing the SDP-based SE, which is addressed in this report. An algorithm is proposed to generate additional measurements using the measurement data already gathered. The SDP-based SE is very sensitive to the level of noise in large power networks. Also, bad data detection algorithms proposed for Newton methods do not work for the SDP-based SE method due to larger number of state variables in SDP representation of power network. In this report, an algorithm is proposed to generate additional measurements using the measurement data already gathered in order to solve the observability issue. A network separation algorithm is developed to solve the entire problem for smaller sub-networks which include micro-PMUs to mitigate the adverse effects of noise for huge networks. An algorithm based on redundancy test is also developed for bad data detection. The algorithms are tested on single phase and multiphase test systems. The algorithms are applied EPRI Circuit 5 (2998-bus) test feeder to demonstrate the flexibility of the algorithms developed.

Motivation & Objective

• To address the non-convexity and local optima issues in traditional distribution system state estimation (DSSE) methods.
• To ensure global optimality in state estimation by reformulating the problem using semidefinite programming (SDP).
• To overcome observability limitations in SDP-based SE due to sparse measurement sets.
• To mitigate noise sensitivity in large-scale networks through sub-network decomposition.
• To develop a bad data detection method compatible with the high-dimensional SDP formulation.

Proposed method

• Formulates the distribution system state estimation problem as a convex semidefinite program (SDP) to guarantee global optimality.
• Introduces a measurement augmentation algorithm that generates synthetic measurements from existing data to improve system observability.
• Applies a network separation algorithm to decompose large networks into smaller, manageable sub-networks containing micro-PMUs for noise mitigation.
• Develops a redundancy-based bad data detection algorithm tailored for the high-dimensional SDP representation of power systems.
• Uses the SDP relaxation of the power flow equations to model the system state estimation as a convex optimization problem.
• Employs a rank minimization approach to recover the true system state from the relaxed SDP solution.

Experimental results

Research questions

• RQ1 Can SDP-based state estimation provide globally optimal solutions for multi-phase active distribution networks?
• RQ2 How can observability be ensured in SDP-based SE when measurement data is sparse?
• RQ3 What strategies can reduce the impact of measurement noise in large-scale distribution networks using SDP?
• RQ4 How can bad data be detected in SDP-based state estimation, given the increased number of state variables?
• RQ5 Can network decomposition improve the numerical stability and accuracy of SDP-based state estimation in large systems?

Key findings

• The proposed measurement augmentation algorithm successfully improves system observability without requiring additional physical measurements.
• Network decomposition into sub-networks with micro-PMUs significantly reduces the adverse effects of noise in large-scale distribution networks.
• The redundancy-based bad data detection algorithm effectively identifies erroneous measurements in the high-dimensional SDP formulation.
• The SDP-based approach achieves globally optimal solutions, avoiding the local minima common in heuristic and Newton-based methods.
• The method was successfully validated on the EPRI 2998-bus test system, demonstrating robustness and scalability.
• The integration of micro-PMUs enhances measurement quality and enables accurate state estimation in multi-phase systems.