Details
| Original language | English |
|---|---|
| Article number | 110716 |
| Number of pages | 7 |
| Journal | Electric power systems research |
| Volume | 236 |
| Early online date | 23 Jul 2024 |
| Publication status | E-pub ahead of print - 23 Jul 2024 |
Abstract
This paper proposes a novel method rooted in differential geometry to approximate the voltage stability boundary of power systems under high variability of renewable generation. We extract intrinsic geometric information of the power flow solution manifold at a given operating point. Specifically, coefficients of the Levi-Civita connection are constructed to approximate the geodesics of the manifold starting at an operating point along any interested directions that represent possible fluctuations in generation and load. Then, based on the geodesic approximation, we further predict the voltage collapse point by solving a few univariate quadratic equations. Conventional methods mostly rely on either expensive numerical continuation at specified directions or numerical optimization. Instead, the proposed approach constructs the Christoffel symbols of the second kind from the Riemannian metric tensors to characterize the complete local geometry which is then extended to the proximity of the stability boundary with efficient computations. As a result, this approach is suitable to handle high-dimensional variability in operating points due to the large-scale integration of renewable resources. Using various case studies, we demonstrate the advantages of the proposed method and provide additional insights and discussions on voltage stability in renewable-rich power systems.
Keywords
- Differential geometry, Geodesic curves, Levi-Civita connection, Power flow manifold, Variable renewable energy, Voltage stability
ASJC Scopus subject areas
- Energy(all)
- Energy Engineering and Power Technology
- Engineering(all)
- Electrical and Electronic Engineering
Sustainable Development Goals
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In: Electric power systems research, Vol. 236, 110716, 11.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Approximating voltage stability boundary under high variability of renewables using differential geometry
AU - Wu, Dan
AU - Wolter, Franz Erich
AU - Geng, Sijia
N1 - Publisher Copyright: © 2024 Elsevier B.V.
PY - 2024/7/23
Y1 - 2024/7/23
N2 - This paper proposes a novel method rooted in differential geometry to approximate the voltage stability boundary of power systems under high variability of renewable generation. We extract intrinsic geometric information of the power flow solution manifold at a given operating point. Specifically, coefficients of the Levi-Civita connection are constructed to approximate the geodesics of the manifold starting at an operating point along any interested directions that represent possible fluctuations in generation and load. Then, based on the geodesic approximation, we further predict the voltage collapse point by solving a few univariate quadratic equations. Conventional methods mostly rely on either expensive numerical continuation at specified directions or numerical optimization. Instead, the proposed approach constructs the Christoffel symbols of the second kind from the Riemannian metric tensors to characterize the complete local geometry which is then extended to the proximity of the stability boundary with efficient computations. As a result, this approach is suitable to handle high-dimensional variability in operating points due to the large-scale integration of renewable resources. Using various case studies, we demonstrate the advantages of the proposed method and provide additional insights and discussions on voltage stability in renewable-rich power systems.
AB - This paper proposes a novel method rooted in differential geometry to approximate the voltage stability boundary of power systems under high variability of renewable generation. We extract intrinsic geometric information of the power flow solution manifold at a given operating point. Specifically, coefficients of the Levi-Civita connection are constructed to approximate the geodesics of the manifold starting at an operating point along any interested directions that represent possible fluctuations in generation and load. Then, based on the geodesic approximation, we further predict the voltage collapse point by solving a few univariate quadratic equations. Conventional methods mostly rely on either expensive numerical continuation at specified directions or numerical optimization. Instead, the proposed approach constructs the Christoffel symbols of the second kind from the Riemannian metric tensors to characterize the complete local geometry which is then extended to the proximity of the stability boundary with efficient computations. As a result, this approach is suitable to handle high-dimensional variability in operating points due to the large-scale integration of renewable resources. Using various case studies, we demonstrate the advantages of the proposed method and provide additional insights and discussions on voltage stability in renewable-rich power systems.
KW - Differential geometry
KW - Geodesic curves
KW - Levi-Civita connection
KW - Power flow manifold
KW - Variable renewable energy
KW - Voltage stability
UR - http://www.scopus.com/inward/record.url?scp=85199260082&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2310.01911
DO - 10.48550/arXiv.2310.01911
M3 - Article
AN - SCOPUS:85199260082
VL - 236
JO - Electric power systems research
JF - Electric power systems research
SN - 0378-7796
M1 - 110716
ER -