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 32 nd CNLS Conference Optimization and Control for Smart Grids Santa Fe, New Mexico May 25, 2012

Outline Motivate cascade mitigation problem Introduce storage hub model Discuss optimal energy dispatch Introduce thermal overload model Describe MPC cascade mitigation Simulation and Example 1

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 3

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 formulation 1 Example – WGT (with hydrogen storage) 4

5 Energy Hubs and Storage Example – Lithium-ion battery device Another example of storage device as hub:

Energy Hub Network Using energy hubs we can construct arbitrarily large coupled systems and describe through our hub format – Hubert. 1 A Small Multi-energy Carrier Example Electric Natural Gas Hydro Wind 6 1 Background on energy hubs networks, see Almassalkhi & Hiskens, PSCC, 2011

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 formulation 1 and solution represents an optimal energy schedule 1 Almassalkhi & Hiskens, PSCC,

1 st 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 8 Optimal MPC schedule Employed shrinking horizon MPC - Able to reject disturbance and restore load - Lines are tripped if they are beyond their power rating after 5 minutes 2 Almassalkhi & Hiskens, CDC, 2011

Thermal Overload Model 9 Track overload: Cumulative overload yields a simple first-order estimate of temperature:

Thermal Overload Model 10 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

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, ramp- rate limits on generators 11

Cascade Mitigation Scheme FAST timescale receding horizon MPC SLOW timescale optimal schedule for power system 12

13 Cascade Mitigation Scheme

Base Case Comparison Want to model operator during contingency –Not straight forward! Employ simple/crude model –Snapshot optimizer –Only aware of overloads, not temperature 14

Preliminary Results – Small Example 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 Small (20-node) electric network with 3 wind hubs with hydrogen storage 15 Contingency: If 30 minutes pass without a line trip, MPC = Success

Cascade Mitigation – Small Example 16 Small (20-node) electric network with 3 wind hubs with hydrogen storage

Cascade Mitigation – Small Example 17 Small (20-node) electric network with 3 wind hubs with hydrogen storage MPC sheds enough load to alleviate line temperature! Timing of cascading outage

Cascade Mitigation – Small Example 18 Small (20-node) electric network with 3 wind hubs with hydrogen storage Disturbance rejected! Load Restored!

Preliminary Results – Larger Example 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 Larger (120-node) electric network with 10 wind hubs with hydrogen storage 19 Contingency: If 20 minutes pass without a line trip, MPC = Success

Preliminary Results – Larger Example Larger (120-node) electric network with 10 wind hubs with hydrogen storage 20 Cascading outage Load shed on fast time scaleLines tripped on fast time scale

Preliminary Results – Larger Example Larger (120-node) electric network with 10 wind hubs with hydrogen storage 21 Disturbance rejected! Load Restored!

Conclusion & Future Work 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 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) Today Future 22

Thank you for your attention! Mads Almassalkhi 23 [1] M. Almassalkhi and I. Hiskens, “Optimization framework for the analysis of large- scale networks of energy hubs,” Power Systems Computation Conference, Aug [2] M. Almassalkhi and I. Hiskens, “Cascade mitigation in energy hub networks,” IEEE Control and Decision Conference, Dec [3] M. Almassalkhi and I. Hiskens, “Impact of Energy Storage on Cascade Mitigation in Multi-energy Systems,” IEEE PES General Meeting, July 2012.

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,