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This paper develops a generalized Copula-polynomial chaos expansion (PCE) framework for power system probabilistic power flow that can handle both linear and nonlinear correlations of uncertain power injections, such as wind and PVs. A data-driven Copula statistical model is used to capture the correlations of uncertain power injections. This allows us to resort to the Rosenblatt transformation to transform correlated variables into independent ones while preserving the dependence structure. This paves the way of leveraging the PCE for surrogate modeling and uncertainty quantification of power flow results, i.e., achieving the probabilistic distributions of power flows. Simulations carried out on the IEEE 57-bus system show that the proposed framework can get much more accurate results than other alternatives with different linear and nonlinear power injection correlations.
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Data-Driven Flow and Injection Estimation in PMU-Unobservable Transmission Systems
Fast and accurate knowledge of power flows and power injections is needed for a variety of applications in the electric grid. Phasor measurement units (PMUs) can be used to directly compute them at high speeds; however, a large number of PMUs will be needed for computing all the flows and injections. Similarly, if they are calculated from the outputs of a linear state estimator, then their accuracy will deteriorate due to the quadratic relationship between voltage and power. This paper employs machine learning to perform fast and accurate flow and injection estimation in power systems that are sparsely observed by PMUs. We train a deep neural network (DNN) to learn the mapping function between PMU measurements and power flows/injections. The relation between power flows and injections is incorporated into the DNN by adding a linear constraint to its loss function. The results obtained using the IEEE 118-bus system indicate that the proposed approach performs more accurate flow/injection estimation in severely unobservable power systems compared to other data-driven methods.
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- Award ID(s):
- 2132904
- PAR ID:
- 10535021
- Publisher / Repository:
- IEEE
- Date Published:
- ISBN:
- 978-1-6654-6441-3
- Page Range / eLocation ID:
- 1 to 5
- Format(s):
- Medium: X
- Location:
- Orlando, FL, USA
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/PESGM52003.2023.10252719
