Economic MPC of Thermal Storage for Demand Response American Control Conference, July 1, 2015 Kevin Kircher, kircher.mae.cornell.edu 1 / 19
Background Model Simulation Discussion 2 / 19
Background Model Simulation Discussion 3 / 19
Power system peaks are expensive 2013 NYC load histogram • 95 th percentile: 8.5 GW 500 450 • maximum: 11.5 GW 400 • 1 GW of new peaking Number of hours 350 capacity: $1 billion 300 250 200 150 100 50 0 0 2 4 6 8 10 12 Hourly average load (GW) 4 / 19
Depeaking with thermal storage • peaks happen on hot summer days, driven by AC • curtailing cooling on hot days risks bothering occupants • storage eliminates this risk • why thermal storage? ⋄ electrochemical storage: 1 500-600 $/kWh ⋄ thermal storage: 2 14-20 $/kWh th (equivalent to 35-60 $/kWh with chiller COP of 2.5-3) 1R. Hensley et al. , “Battery Technology Charges Ahead.” McKinsey Quarterly 3 (2012): 5-50. 2A. Arteconi et al. , “State of the Art of Thermal Storage for Demand-Side Management.” Applied Energy 93 (2012): 371-389. 5 / 19
Can MPC handle the incentives that real buildings face? A challenging case study • ConEd’s default rate plan 3 for large commercial buildings ⋄ hourly energy prices determined by wholesale market ⋄ three-tiered demand charge • a ConEd demand response program 4 Main result: yes, but it’s important to include true incentives, particularly demand charge, in MPC objective function 3Rider M - Day-Ahead Hourly Pricing. General Rule 24: Service Classification Riders. ConEd, 2014. 4Commercial System Relief Program. Demand Response Program Details , ConEd, 2014. 6 / 19
Background Model Simulation Discussion 7 / 19
Physics • DOE “large office” prototype 5 (3 floors, 14,000 m 2 ) • quasi-steady model extends seminal work 6 to include ⋄ two chillers ⋄ temperature-varying COPs ⋄ non-ideal tank and heat exchanger efficiencies 5Commercial Building Prototype Models: “Large Office.” Building Energy Codes Program , U.S. Department of Energy. (2011) 6Henze, G. et al. “Development of a Predictive Optimal Controller for Thermal Energy Storage Systems.” HVAC&R Research 3.3 (1997): 233-264. 8 / 19
Physics (continued) x ( k + 1) = A x ( k ) + B ( k ) u ( k ) + G w ( k ) • states ⋄ tank charge ( x 1 , kWh th ) ⋄ cooling deficit ( x 2 , kWh th ) • controls ⋄ ice chiller power ( u 1 , kW) ⋄ cooling from ice ( u 2 , kW th ) ⋄ main chiller power ( u 3 , kW) • disturbances (Gaussian, white) ⋄ cooling demand ( w 1 , kW th ) ⋄ electrical demand ( w 2 , kW) 9 / 19
MPC optimization • 24-hour horizon, half-hour time steps • minimize + energy cost + increase in demand cost + occupant discomfort + terminal cost (tank depletion) − demand response revenue • subject to ⋄ chiller capacity and ramping limits ⋄ tank limit • solved in CVX, driving SDPT3 10 / 19
Background Model Simulation Discussion 11 / 19
Simulation day Temperature and Coefficients of Performance 40 4 Temperature ( ◦ C) 3 COP 30 2 1 Main Chiller Ice Chiller Temperature 20 0 0 0 6 6 12 12 18 18 24 24 Expected Loads and 95% Confidence Intervals 500 500 Other Electric Loads (kW) Cooling Load (kW t h ) 400 400 300 300 200 200 100 100 0 0 0 0 6 6 12 12 18 18 24 24 Time (hours) 12 / 19
Prices Energy and Demand Response Prices 0.4 4 c dr ( k ) ($/kWh) c e ( k ) ($/kWh) 0.2 2 0 0 0 0 6 6 12 12 18 18 24 24 Demand Prices 20 c d ( T i ) ($/kW) 15 10 c d ( T 1 ) 5 c d ( T 2 ) c d ( T 3 ) 0 0 6 12 18 24 Prices of Under- or Over-cooling −3 6 x 10 c u ( k ) ($/kWh 2 ) 4 2 0 0 6 12 18 24 Time (hours) 13 / 19
A typical Monte Carlo run Tank Charge State 2000 x 1 (kWh t h ) 1000 0 0 6 12 18 24 Cooling Load Deficit 500 x 2 (kWh t h ) 0 −500 0 6 12 18 24 Power to Ice Chiller 100 u 1 (kW) 50 0 0 6 12 18 24 Cooling from Ice Melt u 2 (kW t h ) 400 200 0 0 6 12 18 24 Power to Main Chiller 100 u 3 (kW) 50 0 0 6 12 18 24 Time (hours) 14 / 19
A typical Monte Carlo run (continued) Total Power Consumption 300 250 200 kW 150 100 50 MPC Baseline No Storage 0 0 6 12 18 24 Costs 60 40 20 0 $ −20 −40 Energy −60 Demand Response Under-cooling −80 0 6 12 18 24 Time (hours) 15 / 19
Background Model Simulation Discussion 16 / 19
Important to model demand charge Demand Charge Ignored Demand Charge Included 300 300 250 250 Total Power (kW) Total Power (kW) 200 200 150 150 100 100 50 50 0 0 0 6 12 18 24 0 6 12 18 24 Time (hours) Time (hours) Costs with and without Demand Charge in Objective Function 4000 Without g d With g d 3000 2000 $ 1000 0 −1000 Energy Demand Response Demand Under−cooling Tank Depletion 17 / 19
Lots of extensions • optimal tank size? • simulate for a month, study demand charge in depth • other economic incentives ⋄ critical peak pricing ⋄ ancillary services ⋄ contracts with aggregators All code is available by email or at kircher.mae.cornell.edu. 18 / 19
Thanks to. . . • the Consortium for Electric Reliability Technology Solutions (CERTS) for funding • Max Zhang for advising • Santiago Naranjo Palacio, Brandon Hencey, and Eilyan Bitar for ideas and feedback • you for listening! 19 / 19
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