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Voltage collapse in complex power grids.

Simpson-Porco JW, Dörfler F, Bullo F - Nat Commun (2016)

Bottom Line: A large-scale power grid's ability to transfer energy from producers to consumers is constrained by both the network structure and the nonlinear physics of power flow.Violations of these constraints have been observed to result in voltage collapse blackouts, where nodal voltages slowly decline before precipitously falling.We extensively test our predictions on large-scale systems, highlighting how our condition can be leveraged to increase grid stability margins.

View Article: PubMed Central - PubMed

Affiliation: Department of Electrical and Computer Engineering, Engineering Building 5, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.

ABSTRACT
A large-scale power grid's ability to transfer energy from producers to consumers is constrained by both the network structure and the nonlinear physics of power flow. Violations of these constraints have been observed to result in voltage collapse blackouts, where nodal voltages slowly decline before precipitously falling. However, methods to test for voltage collapse are dominantly simulation-based, offering little theoretical insight into how grid structure influences stability margins. For a simplified power flow model, here we derive a closed-form condition under which a power network is safe from voltage collapse. The condition combines the complex structure of the network with the reactive power demands of loads to produce a node-by-node measure of grid stress, a prediction of the largest nodal voltage deviation, and an estimate of the distance to collapse. We extensively test our predictions on large-scale systems, highlighting how our condition can be leveraged to increase grid stability margins.

No MeSH data available.


Related in: MedlinePlus

Stress testing of voltage stability condition for high power factor loading.The horizontal voltage axis is scaled by Vbase=345 kV. The solid black trace is the numerically computed voltage magnitude at node four, while the dotted red trace is given explicitly by , where δ− is determined as below (7). The stability margin Δ is shown in dashed blue.
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f4: Stress testing of voltage stability condition for high power factor loading.The horizontal voltage axis is scaled by Vbase=345 kV. The solid black trace is the numerically computed voltage magnitude at node four, while the dotted red trace is given explicitly by , where δ− is determined as below (7). The stability margin Δ is shown in dashed blue.

Mentions: As a second loading direction for testing, we maintain the direction of the base case, for which the average power factor of loads is approximately 0.88. In this regime reactive power transfers will be less prominent, and we expect the unmodeled coupling between active and reactive power flows to induce voltage collapse at a loading level lower than expected from the simplified model (1). Again as a function of λ, Fig. 4 displays the desired traces. While the trace of continues to lower bound the trace of the node voltage V4, we find in this case that Δ=0.75 when voltage collapse occurs for the coupled equations at λ/λcollapse=1. As expected, in this regime the unmodeled coupled power flow effects become crucial and the simplified decoupled model (1), on which our analysis is based, becomes invalid. Said differently, when reactive power demands in the network are low, our analytic prediction of the point of voltage collapse based on the simplified model (1) is overly optimistic. We comment further on extensions of our analysis to the coupled case in the ‘Discussion' section and in Supplementary Note 5.


Voltage collapse in complex power grids.

Simpson-Porco JW, Dörfler F, Bullo F - Nat Commun (2016)

Stress testing of voltage stability condition for high power factor loading.The horizontal voltage axis is scaled by Vbase=345 kV. The solid black trace is the numerically computed voltage magnitude at node four, while the dotted red trace is given explicitly by , where δ− is determined as below (7). The stability margin Δ is shown in dashed blue.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4759633&req=5

f4: Stress testing of voltage stability condition for high power factor loading.The horizontal voltage axis is scaled by Vbase=345 kV. The solid black trace is the numerically computed voltage magnitude at node four, while the dotted red trace is given explicitly by , where δ− is determined as below (7). The stability margin Δ is shown in dashed blue.
Mentions: As a second loading direction for testing, we maintain the direction of the base case, for which the average power factor of loads is approximately 0.88. In this regime reactive power transfers will be less prominent, and we expect the unmodeled coupling between active and reactive power flows to induce voltage collapse at a loading level lower than expected from the simplified model (1). Again as a function of λ, Fig. 4 displays the desired traces. While the trace of continues to lower bound the trace of the node voltage V4, we find in this case that Δ=0.75 when voltage collapse occurs for the coupled equations at λ/λcollapse=1. As expected, in this regime the unmodeled coupled power flow effects become crucial and the simplified decoupled model (1), on which our analysis is based, becomes invalid. Said differently, when reactive power demands in the network are low, our analytic prediction of the point of voltage collapse based on the simplified model (1) is overly optimistic. We comment further on extensions of our analysis to the coupled case in the ‘Discussion' section and in Supplementary Note 5.

Bottom Line: A large-scale power grid's ability to transfer energy from producers to consumers is constrained by both the network structure and the nonlinear physics of power flow.Violations of these constraints have been observed to result in voltage collapse blackouts, where nodal voltages slowly decline before precipitously falling.We extensively test our predictions on large-scale systems, highlighting how our condition can be leveraged to increase grid stability margins.

View Article: PubMed Central - PubMed

Affiliation: Department of Electrical and Computer Engineering, Engineering Building 5, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.

ABSTRACT
A large-scale power grid's ability to transfer energy from producers to consumers is constrained by both the network structure and the nonlinear physics of power flow. Violations of these constraints have been observed to result in voltage collapse blackouts, where nodal voltages slowly decline before precipitously falling. However, methods to test for voltage collapse are dominantly simulation-based, offering little theoretical insight into how grid structure influences stability margins. For a simplified power flow model, here we derive a closed-form condition under which a power network is safe from voltage collapse. The condition combines the complex structure of the network with the reactive power demands of loads to produce a node-by-node measure of grid stress, a prediction of the largest nodal voltage deviation, and an estimate of the distance to collapse. We extensively test our predictions on large-scale systems, highlighting how our condition can be leveraged to increase grid stability margins.

No MeSH data available.


Related in: MedlinePlus