Limits...
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 low 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. When Δ>1, δ− becomes undefined and the corresponding bound is no longer plotted.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4759633&req=5

f3: Stress testing of voltage stability condition for low 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. When Δ>1, δ− becomes undefined and the corresponding bound is no longer plotted.

Mentions: The above testing procedure obviously depends on the choice of direction for increase in the space of power demands and generation. We select two directions and study them separately, to illustrate the strengths and limitations of our analytic approach based on a simplified power flow model. As a first choice, we select a direction where the mean power factor in the network is decreased 20% to a value of 0.7. (The power factor of the ith load is defined as , where Pi is the active power drawn by the load. If Pi=Qi, then the power factor is 0.707.) This corresponds to a case where loads consume roughly equal amounts of active and reactive power, which in practice is unusually highly reactive power consumption. We therefore expect that instabilities associated with reactive power flow should dominate any unmodeled active power effects, and the simplified model (1) should serve as a good proxy for the coupled active/reactive power flow equations. As a function of λ, Fig. 3 displays the trace of the voltage magnitude at node 4 (solid black), the loading margin Δ (dashed blue), and the bound (dotted red) determined by equation (7). Node 4 was determined through equation (7) to be the most stressed node in the network, and hence the node for which our theoretical bound would be best tested. First, observe that the numerically determined voltage trace is bounded below by the trace of the theoretical bound, as expected. The loading margin Δ increases roughly linearly with λ, with Δ=1 occurring at λ/λcollapse=0.98. Our previous conclusions regarding the necessity of Δ>1 for voltage collapse therefore hold in this highly stressed case for the more complicated coupled active/reactive power flow model, and the gap between the necessary condition Δ>1 and the true point of collapse is a surprisingly small 2%.


Voltage collapse in complex power grids.

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

Stress testing of voltage stability condition for low 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. When Δ>1, δ− becomes undefined and the corresponding bound is no longer plotted.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: Stress testing of voltage stability condition for low 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. When Δ>1, δ− becomes undefined and the corresponding bound is no longer plotted.
Mentions: The above testing procedure obviously depends on the choice of direction for increase in the space of power demands and generation. We select two directions and study them separately, to illustrate the strengths and limitations of our analytic approach based on a simplified power flow model. As a first choice, we select a direction where the mean power factor in the network is decreased 20% to a value of 0.7. (The power factor of the ith load is defined as , where Pi is the active power drawn by the load. If Pi=Qi, then the power factor is 0.707.) This corresponds to a case where loads consume roughly equal amounts of active and reactive power, which in practice is unusually highly reactive power consumption. We therefore expect that instabilities associated with reactive power flow should dominate any unmodeled active power effects, and the simplified model (1) should serve as a good proxy for the coupled active/reactive power flow equations. As a function of λ, Fig. 3 displays the trace of the voltage magnitude at node 4 (solid black), the loading margin Δ (dashed blue), and the bound (dotted red) determined by equation (7). Node 4 was determined through equation (7) to be the most stressed node in the network, and hence the node for which our theoretical bound would be best tested. First, observe that the numerically determined voltage trace is bounded below by the trace of the theoretical bound, as expected. The loading margin Δ increases roughly linearly with λ, with Δ=1 occurring at λ/λcollapse=0.98. Our previous conclusions regarding the necessity of Δ>1 for voltage collapse therefore hold in this highly stressed case for the more complicated coupled active/reactive power flow model, and the gap between the necessary condition Δ>1 and the true point of collapse is a surprisingly small 2%.

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