Report

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 [email protected] 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 formulation1 Example – WGT (with hydrogen storage) 4 Energy Hubs and Storage Another example of storage device as hub: Example – Lithium-ion battery device 5 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 7 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 8 Thermal Overload Model • Track overload: • Cumulative overload yields a simple first-order estimate of temperature: 9 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 10 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 11 Cascade Mitigation Scheme SLOW timescale optimal schedule for power system FAST timescale receding horizon MPC 12 Cascade Mitigation Scheme 13 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 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 15 Cascade Mitigation – Small Example Small (20-node) electric network with 3 wind hubs with hydrogen storage 16 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! 17 Cascade Mitigation – Small Example Small (20-node) electric network with 3 wind hubs with hydrogen storage Disturbance rejected! Load Restored! 18 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 19 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 20 Preliminary Results – Larger Example Larger (120-node) electric network with 10 wind hubs with hydrogen storage Disturbance rejected! Load Restored! 21 Conclusion & Future Work Today • • • 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 • • • • Future • 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) 22 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 [email protected] 23 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 24