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Uncertainty Error Modeling for Non-Linear State Estimation With Unsynchronized SCADA and $μ$PMU Measurements

Austin Cooper, Arturo Bretas, Sean Meyn, Newton G. Bretas

Abstract

Distribution systems of the future smart grid require enhancements to the reliability of distribution system state estimation (DSSE) in the face of low measurement redundancy, unsynchronized measurements, and dynamic load profiles. Micro phasor measurement units ($μ$PMUs) facilitate co-synchronized measurements with high granularity, albeit at an often prohibitively expensive installation cost. Supervisory control and data acquisition (SCADA) measurements can supplement $μ$PMU data, although they are received at a slower sampling rate. Further complicating matters is the uncertainty associated with load dynamics and unsynchronized measurements-not only are the SCADA and $μ$PMU measurements not synchronized with each other, but the SCADA measurements themselves are received at different time intervals with respect to one another. This paper proposes a non-linear state estimation framework which models dynamic load uncertainty error by updating the variances of the unsynchronized measurements, leading to a time-varying system of weights in the weighted least squares state estimator. Case studies are performed on the 33-Bus Distribution System in MATPOWER, using Ornstein-Uhlenbeck stochastic processes to simulate dynamic load conditions.

Uncertainty Error Modeling for Non-Linear State Estimation With Unsynchronized SCADA and $μ$PMU Measurements

Abstract

Distribution systems of the future smart grid require enhancements to the reliability of distribution system state estimation (DSSE) in the face of low measurement redundancy, unsynchronized measurements, and dynamic load profiles. Micro phasor measurement units (PMUs) facilitate co-synchronized measurements with high granularity, albeit at an often prohibitively expensive installation cost. Supervisory control and data acquisition (SCADA) measurements can supplement PMU data, although they are received at a slower sampling rate. Further complicating matters is the uncertainty associated with load dynamics and unsynchronized measurements-not only are the SCADA and PMU measurements not synchronized with each other, but the SCADA measurements themselves are received at different time intervals with respect to one another. This paper proposes a non-linear state estimation framework which models dynamic load uncertainty error by updating the variances of the unsynchronized measurements, leading to a time-varying system of weights in the weighted least squares state estimator. Case studies are performed on the 33-Bus Distribution System in MATPOWER, using Ornstein-Uhlenbeck stochastic processes to simulate dynamic load conditions.
Paper Structure (7 sections, 18 equations, 4 figures, 1 table)

This paper contains 7 sections, 18 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. Non-Linear State Estimation
  4. Dynamic Load Modeling
  5. Non-Linear Measurement Uncertainty
  6. Case Study
  7. Summary and Conclusions

Figures (4)

  • Figure 1: Proposed Uncertainty Modeling Non-linear SE Flowchart.
  • Figure 2: Comparison of $J_{CME}$ paths when SCADA measurements are synchronized (blue) and unsnychronized with each other (orange).
  • Figure 3: Comparison of $J_{CME}$ paths when weight matrix $\mathbf{W}$ values are static (blue) and when $\mathbf{W}(t)$ values are updated (orange).
  • Figure 4: Comparison of state variable estimate accuracy