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System-wide Instrument Transformer Calibration and Line Parameter Estimation Using PMU Data

Antos Cheeramban Varghese, Anamitra Pal

TL;DR

This work addresses the joint problem of line parameter estimation and instrument-transformer calibration (SLIC) using PMU data, proposing a statistical TLS-based framework that accounts for IT ratio errors, PMU noise, and time-varying line parameters. A novel quantization procedure around database line values enables unique identification of branch parameters, while a Revenue Quality Meter (RQM) at a single end, combined with a DFS-driven system-wide extension (SW-SLIC), solves SLIC across a connected tree. The method demonstrates sub-1% mean absolute relative error for line parameters and sub-1% absolute error for IT correction factors on the IEEE 118-bus system and field PMU data, outperforming a recent state-of-the-art approach. The work further provides an algorithm for optimal RQM placement and confirms robustness to PMU noise and IT-class variations, underscoring practical utility for utilities deploying PMU-based calibration.

Abstract

Uncalibrated instrument transformers (ITs) can degrade the performance of downstream applications that rely on the voltage and current measurements that ITs provide. It is also well-known that phasor measurement unit (PMU)-based system-wide IT calibration and line parameter estimation (LPE) are interdependent problems. In this paper, we present a statistical framework for solving the simultaneous LPE and IT calibration (SLIC) problem using synchrophasor data. The proposed approach not only avoids the need for a perfect IT by judiciously placing a revenue quality meter (which is an expensive but non-perfect IT), but also accounts for the variations typically occurring in the line parameters. The results obtained using the IEEE 118-bus system as well as actual power system data demonstrate the high accuracy, robustness, and practical utility of the proposed approach.

System-wide Instrument Transformer Calibration and Line Parameter Estimation Using PMU Data

TL;DR

This work addresses the joint problem of line parameter estimation and instrument-transformer calibration (SLIC) using PMU data, proposing a statistical TLS-based framework that accounts for IT ratio errors, PMU noise, and time-varying line parameters. A novel quantization procedure around database line values enables unique identification of branch parameters, while a Revenue Quality Meter (RQM) at a single end, combined with a DFS-driven system-wide extension (SW-SLIC), solves SLIC across a connected tree. The method demonstrates sub-1% mean absolute relative error for line parameters and sub-1% absolute error for IT correction factors on the IEEE 118-bus system and field PMU data, outperforming a recent state-of-the-art approach. The work further provides an algorithm for optimal RQM placement and confirms robustness to PMU noise and IT-class variations, underscoring practical utility for utilities deploying PMU-based calibration.

Abstract

Uncalibrated instrument transformers (ITs) can degrade the performance of downstream applications that rely on the voltage and current measurements that ITs provide. It is also well-known that phasor measurement unit (PMU)-based system-wide IT calibration and line parameter estimation (LPE) are interdependent problems. In this paper, we present a statistical framework for solving the simultaneous LPE and IT calibration (SLIC) problem using synchrophasor data. The proposed approach not only avoids the need for a perfect IT by judiciously placing a revenue quality meter (which is an expensive but non-perfect IT), but also accounts for the variations typically occurring in the line parameters. The results obtained using the IEEE 118-bus system as well as actual power system data demonstrate the high accuracy, robustness, and practical utility of the proposed approach.

Paper Structure

This paper contains 18 sections, 1 theorem, 27 equations, 6 figures, 8 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Modeling the SLIC Problem for One Branch
  3. Basic Formulation
  4. Overcoming Homogeneity Issue with RQM
  5. Quantization Procedure for Solving the IB-SLIC Problem
  6. Solving the System-wide SLIC Problem
  7. Extending IB-SLIC to Multiple Branches
  8. Optimal Location for the RQM
  9. Results
  10. Validation of Proposed Solution to SLIC Problem
  11. Optimal RQM Placement Results
  12. Sensitivity Analysis
  13. Additive PMU Noise
  14. IT Accuracy Class
  15. Comparison with a Similar State-of-the-Art Approach
  16. ...and 3 more sections

Key Result

Theorem 1

If $m_1$ and $m_2$ denote two bin numbers, then $f_W(m_1) = f_W(m_2) \iff m_1 = m_2$.

Figures (6)

  • Figure 1: $\pi$-model of transmission line used for SLIC
  • Figure 2: HV branches from RQM branch to Current branch
  • Figure 3: Impact of additive noise on resistance estimate
  • Figure 4: Impact of different IT classes on proposed solution
  • Figure 5: Comparing line parameter estimates with wang2019transmission
  • ...and 1 more figures

Theorems & Definitions (3)

  • Theorem 1
  • proof
  • proof