Model-predictive Cascade Mitigation of
Electric Power Systems with Energy
Storage and Renewable Generation
Mads R. Almassalkhi and Ian A. Hiskens
Department of Electrical Engineering and Computer Science
University of Michigan, Ann Arbor, USA
32nd CNLS Conference
Optimization and Control for Smart Grids
Santa Fe, New Mexico
May 25, 2012
malmassa@umich.edu
Outline
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Motivate cascade mitigation problem
Introduce storage hub model
Discuss optimal energy dispatch
Introduce thermal overload model
Describe MPC cascade mitigation
Simulation and Example
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Motivation
• Cascade is a cycle of flow redistribution and line overloads
• Non-trivial to predict and protect against all failures (N-k schemes)
• Significant economic and human impact (even if rare)
2
Motivation
• Storage devices provide natural protection
against cascade failures
– Buffer against temporary energy shortages or
overflows
– Diminish effect of generator ramp-rate limits
• Progression of cascade is order of minutes
– Difficult for human operator to respond
– Opportunity for feedback control!
• Apply model-predictive scheme to mitigate
cascades in power networks with storage and wind
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Energy Hubs and Storage
• Energy hubs explicitly model couplings between energy
infrastructures.
• Similar to a multi-input, multi-output black box
• Modeling of hubs can be accomplished with MIL formulation1
Example – WGT (with hydrogen storage)
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Energy Hubs and Storage
Another example of storage device as hub:
Example – Lithium-ion battery device
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Energy Hub Network
• Using energy hubs we can construct arbitrarily large coupled
systems and describe through our hub format – Hubert.1
Hydro
Electric
Natural Gas
A Small Multi-energy Carrier Example
1
Wind
Background on energy hubs networks, see Almassalkhi & Hiskens, PSCC, 2011
6
Optimal (Economic) Dispatch
• Satisfy forecasted nominal demand and minimize
the cost of generation by optimal utilization of
available energy storage and expected externally
injected power from hour 1 to hour T
– Obj. function takes a variety of forms (generally
quadratic)
– May include load-shedding and wind-spill relaxation terms
• Subject to:
– storage flows, limits on storage devices
– DC Power flow, limits on network elements, ramp-rate
limits on generators
• Yields MP MIQP formulation11Almassalkhi
and solution
represents
& Hiskens, PSCC, 2011
an optimal energy schedule
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1st attempt at cascade
mitigation
• Energy hubs provide protection against cascade failures
– Coupled energy networks for “shared” loads
– Storage provides buffer against temporary energy shortages
or overflows
• Employed shrinking horizon
MPC
Optimal MPC
schedule
- Able to reject disturbance and
restore load
- Lines are tripped if they are
beyond their power rating after 5
minutes
•
2Almassalkhi
& Hiskens, CDC, 2011
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Thermal Overload Model
• Track overload:
• Cumulative overload yields a simple first-order
estimate of temperature:
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Thermal Overload Model
• Line is tripped based on cumulative overload
– Probabilistic outages:
– Zero flow across switched ‘off’ lines:
– Inactive nodal constraints for switched ‘off’ lines:
decouple phase angles
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MPC: Contingency Dispatch
• Satisfy forecasted nominal demand and
optimally utilize available energy storage
and expected externally injected power to
alleviate line overloads
– Quadratic objective function drives thermal
overloads & load shedding to zero
• Subject to:
– Storage dynamics, limits on storage devices
– Thermal line overload dynamics
– DC Power flow, limits on network elements, ramprate limits on generators
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Cascade Mitigation Scheme
SLOW timescale
optimal schedule
for power system
FAST timescale
receding
horizon MPC
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Cascade Mitigation Scheme
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Base Case Comparison
• Want to model operator during contingency
– Not straight forward!
• Employ simple/crude model
– Snapshot optimizer
– Only aware of overloads, not temperature
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Preliminary Results – Small Example
Small (20-node) electric network with 3 wind hubs with hydrogen storage
• Total of 24 hours considered
• Cumulative overload is over 20 minutes
• Prediction horizon = 25 minutes
• Consumer demand peaks at midday
• Energy prices peak at midday
• Wind-power lowest at midday
• Lines tripped: 2 randomly selected lines at hour 7
• Allow temperatures with 1% chance of tripping
Contingency: If 30 minutes pass without a line trip, MPC = Success
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Cascade Mitigation – Small Example
Small (20-node) electric network with 3 wind hubs with hydrogen storage
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Cascade Mitigation – Small Example
Small (20-node) electric network with 3 wind hubs with hydrogen storage
Timing of cascading outage
MPC sheds enough load to alleviate line temperature!
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Cascade Mitigation – Small Example
Small (20-node) electric network with 3 wind hubs with hydrogen storage
Disturbance rejected!
Load Restored!
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Preliminary Results – Larger
Example
Larger (120-node) electric network
with 10 wind hubs with hydrogen storage
• Total of 24 hours considered
• Cumulative overload is over (W=) 15 minutes
• Prediction/control horizon = 20 minutes
• Consumer demand peaks at midday
• Energy prices peak at midday
• Wind-power lowest at midday
• Lines tripped: 4 randomly selected lines at hour 7
• Allow temperatures with 1% chance of tripping
Contingency: If 20 minutes pass without a line trip, MPC = Success
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Preliminary Results – Larger
Example
Larger (120-node) electric network
with 10 wind hubs with hydrogen storage
Lines tripped on fast time scale
Load shed on fast time scale
Cascading outage
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Preliminary Results – Larger
Example
Larger (120-node) electric network
with 10 wind hubs with hydrogen storage
Disturbance rejected!
Load Restored!
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Conclusion & Future Work
Today •
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Employed a model-predictive cascade mitigation scheme:
– MPC scheme operates on fast timescale and takes into account
generator and storage ramping limits
Included thermal line model and probabilistic line-tripping
Illustrated method with numerical example
– MPC balances energy storage with load shedding to alleviate overloads
– MPC properly rejects disturbances and restores load
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Future
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Include governor-droop control with island-detection scheme
Pursue theoretical developments to analyze the robustness and
stability of MPC scheme
Question the DC power flow for cascade mitigation (LAC?)
Investigate optimal energy position and non-centralized MPC
schemes
Couple fast and slow timescale to achieve optimal cascade
mitigation (i.e. balance economics with reliability)
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Thank you for your attention!
[1] M. Almassalkhi and I. Hiskens, “Optimization framework for the analysis of largescale networks of energy hubs,” Power Systems Computation Conference, Aug 2011.
[2] M. Almassalkhi and I. Hiskens, “Cascade mitigation in energy hub networks,” IEEE
Control and Decision Conference, Dec 2011.
[3] M. Almassalkhi and I. Hiskens, “Impact of Energy Storage on Cascade Mitigation
in Multi-energy Systems,” IEEE PES General Meeting, July 2012.
Mads Almassalkhi
malmassa@umich.edu
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Greatest Achievement
• “If anything shines as an example of how
engineering has changed the world during the
twentieth century, it is clearly the power that we
use in our homes and businesses.” – Neil
Armstrong, 2000
• “Scores of times each day, with the merest flick of
a finger, each one of us taps into vast sources of
energy—deep veins of coal and great reservoirs of
oil, sweeping winds and rushing waters, the
hidden power of the atom and the radiance of the
Sun itself—all transformed into electricity, the
workhorse of the modern world.” – NAE, 2003
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