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Measurement-Based Line-Impedance Estimation in the Absence of Phasor Measurement Units

Plouton Grammatikos, Ali Mohamed Ali, Fabrizio Sossan

Abstract

This paper proposes and compares experimentally several methods to estimate the series resistance and reactance (i.e., the transversal components of the $π$-model of a line) of low-voltage lines in distribution grids. It first shows that if phasor measurements are available and the grid nodal voltages and power injections are known, the problem can be formulated and solved as a conventional load flow with properly adjusted unknowns. To solve this problem, we propose an analytical derivation of the Jacobian matrix. If only RMS values are available, such as from smart meters, integrating information from multiple intervals becomes necessary, ultimately opening to least-squares estimations, widely adopted in the literature. In this context, applying the proposed Jacobian contributes to accelerating the problem resolution of existing algorithms. The methods are compared in terms of estimation performance and convergence by using measurements from an experimental distribution grid interfacing real-world components and with realistic size implemented at the Gridlab at HES-SO Valais.

Measurement-Based Line-Impedance Estimation in the Absence of Phasor Measurement Units

Abstract

This paper proposes and compares experimentally several methods to estimate the series resistance and reactance (i.e., the transversal components of the -model of a line) of low-voltage lines in distribution grids. It first shows that if phasor measurements are available and the grid nodal voltages and power injections are known, the problem can be formulated and solved as a conventional load flow with properly adjusted unknowns. To solve this problem, we propose an analytical derivation of the Jacobian matrix. If only RMS values are available, such as from smart meters, integrating information from multiple intervals becomes necessary, ultimately opening to least-squares estimations, widely adopted in the literature. In this context, applying the proposed Jacobian contributes to accelerating the problem resolution of existing algorithms. The methods are compared in terms of estimation performance and convergence by using measurements from an experimental distribution grid interfacing real-world components and with realistic size implemented at the Gridlab at HES-SO Valais.
Paper Structure (15 sections, 29 equations, 4 figures, 3 tables)

This paper contains 15 sections, 29 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Estimating the Line Parameters
  4. The Newton-Raphson Method
  5. First Method: Using PMUs
  6. Second Method: Without Using PMUs
  7. Least Squares Estimation
  8. Newton-Raphson with an overdetermined system
  9. Quadratic optimization
  10. Experimental Validation
  11. Experimental Setup
  12. Preliminary validation with simulations
  13. Singularity of Jacobian Matrix
  14. Validation in an Experimental Setting
  15. Conclusion

Figures (4)

  • Figure 1: Schematic of district
  • Figure 2: Reciprocal condition number (RCOND) of the Jacobian matrix as a function of the ratio between the power injections of the two time instances.
  • Figure 3: Voltage error reduction percentage as a function of the number of samples for Least-squares with Newton-Raphson (LS-NR) and Trust-region-reflective (TRR) for nodes PM1-PM3.
  • Figure 4: Maximum estimation error of the resistance R and the reactance X achieved by Least-squares with Newton-Raphson (LS-NR) and Trust-region-reflective (TRR) as a function of the ratio $\rho$ given by \ref{['eq:ratio-r']}.