Impact of the controller model complexity on MPC performance evaluation for building climate control

Impact of the controller model complexity on MPC performance evaluation for building climate control Damien Picard a, Ján Drgoňa b, Lieve Helsen a,c, and Michal Kvasnica b a KU Leuven, Department of Mechanical Engineering, Leuven, Belgium b Slovak University of Technology in Bratislava, Slovakia c EnergyVille, Thor Park, Waterschei, Belgium September 14, 216 Acknowledgment: The Authors gratefully acknowledge the contribution of the Slovak Research and Development Agency under the project APVV 551-11. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 1 / 21

Building Control Motivation Problem: EU spends 4 billion EUR/year on energy. 4% goes into thermal comfort in buildings.* Goal: Reduce the energy consumption Solution: MPC-based control * International Energy Agency, Energy efficiency requirements in building codes, energy efficiency policies for new buildings 213 OECD/IEA. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 2 / 21

Building Control Motivation Problem: EU spends 4 billion EUR/year on energy. 4% goes into thermal comfort in buildings.* Goal: Reduce the energy consumption Solution: Thermal comfort control * International Energy Agency, Energy efficiency requirements in building codes, energy efficiency policies for new buildings 213 OECD/IEA. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 2 / 21

Model Predictive Control Pros: Satisfy thermal comfort constraints Minimize energy consumption Obey technological restrictions Cons: Implementation in early stages Need for a good controller model J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 3 / 21

What is the Best Model? J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 4 / 21

Methodology Controller model order MPC Plant model order RBC PID J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 5 / 21

Building Description Floor area [m 2 ] 48.3 Conditioned volume [m 3 ] 13.6 Total exterior surface area [m 2 ] 195 Windows [-] 5 Walls [-] 22 Roof and floor surfaces [-] 12 Thermal zones [-] 6 J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 6 / 21

Linearisation 1 Controller model order MPC Plant model order RBC PID 1 Picard, D., Jorissen, F., and Helsen, L. 215. Methodology for Obtaining Linear State Space Building Energy Simulation Models. In 11th International Modelica Conference, pages 51 58, Paris J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 7 / 21

Linearisation Error 1. Original 1. Renovated 1. Light weight.5.5.5 [K]....5.5.5 1. Zone1 Zone2 Zone3 Zone4 Zone5 Zone6 1. Zone1 Zone2 Zone3 Zone4 Zone5 Zone6 1. Zone1 Zone2 Zone3 Zone4 Zone5 Zone6 Full year open-loop simulation linearization error below 1 K. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 7 / 21

Model Order Reduction 2 Controller model order MPC Plant model order RBC PID Square root balanced truncation algorithm, based on Hankel singular values. 2 Antoulas, A. C. and Sorensen, D. C. 21. Approximation of large-scale dynamical systems: An overview. Applied Mathematics and Computer Science. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 8 / 21

Reduced Order Models Error Bounds Error bounds Error bounds 1 Original Renovated Light weight 1 1 Original Renovated Light weight Error bound [-] 1-5 Error bound [-] 1 1-1 1-1 1-2 5 1 15 2 25 State [-] 5 1 15 2 25 3 State [-] Guarantees of an error bounds and preserves most of the system characteristics in terms of stability, frequency, and time responses. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 9 / 21

Reduced Order Models Open Loop Simulation 25 TZone 1 TZone 2 TZone 3 T [ C] 2 15 25 Orders of ROM: 4 7 1 15 2 3 4 1 SSM TZone 4 TZone 5 TZone 6 T [ C] 2 15 1 2 3 4 5 6 7 1 2 3 4 5 6 7 Time [Day] 1 2 3 4 5 6 7 Single week open loop simulation with realistic control inputs and disturbances. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 9 / 21

Reduced Order Models Prediction Errors 2 1-step ahead 2 1-step ahead 2 4-step ahead 1 1 1-1 -1-1 -2-2 -2-3 -3-3 ROM 4 ROM 7 ROM 1 ROM 15 ROM 2 ROM 3 ROM 4 ROM 1 ROM 4 ROM 7 ROM 1 ROM 15 ROM 2 ROM 3 ROM 4 ROM 1 ROM 4 ROM 7 ROM 1 ROM 15 ROM 2 ROM 3 ROM 4 ROM 1 [K] The central line is the median, the box gives the 1st and 3rd quartiles, the wiskers contain 99.5% of the data, the crosses are the outliers. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 9 / 21

Control Setup Controller model order MPC Plant model order RBC PID J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 1 / 21

Control Scheme r MPC u Building y d Estimator ˆx, ˆp J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 11 / 21

Estimator and Augmented Model ) ˆx k k = ˆx k k 1 + L (y m,k ŷ k k 1 ˆx k+1 k = Aˆx k k + Bu k k + Ed k k ŷ k k = Cˆx k k + Du k k ] [ˆxk+1 ˆp k+1 }{{} x k+1 [ ] ] [ ] [ ] A [ˆxk B E = + u I ˆp k k + }{{}}{{}}{{}}{{} Ã x k B Ẽ ] [ ] [ ] [ˆxk D C F + u k ŷ k = } {{ } C ˆp k }{{} D d k J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 12 / 21

MPC Formulation N 1 min u,...,u N 1 k= ( s k 2 Q s + u k 2 Q u ) s.t. x k+1 = Ax k + Bu k + Ed k y k = Cx k + Du k lb k s k y k ub k + s k u u k u x = ˆx(t) k {,..., N 1} J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 13 / 21

State Condensing x 1 = Ax + Bu + Ed x 2 = A(Ax + Bu + Ed )+Bu 1 + Ed 1. x k+1 = A k+1 x +... [ ] [ ] T A k B... AB B u T... ut k +... [ ] [ ] A k E... AE E d T... dk T T y k = CA k x +... [ ] [ T C A k 1 B... AB B u k 1] T... ut +... [ ] [ T C A k 1 E... AE E d T... dk 1] T + Duk + Fp Significantly reduces the number of the optimization variables. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 14 / 21

Simulation Setup One year performances of RBC, PID, MPC. Three types of 6-zone buildings, with 3 states. [%] 1 98 96 Total comfort level Original Renovated Light weight 2 6 1 14 18 22 26 3 34 38 42 46 [MWh / year] 15 1 5 Total heating cost 2 6 1 14 18 22 26 3 34 38 42 46 prediction horizon [] [1e3 s] CPU time 4 3 2 1 2 6 1 14 18 22 26 3 34 38 42 46 [%] 1 5 1 1 Total comfort level 1 1 1 1 1e+6 1e+7 1e+8 1e+9 1e+1 [MWh / year] 15 1 5 1 1 Total heating cost 1 1 weighting factor [] 1 1 1e+6 1e+7 1e+8 1e+9 1e+1 [1e3 s] 1.3 1.2 1.1 1.9 1 1 CPU time T s = 9, N = 4 steps (i.e., 1 hours), Qs Q u = 1 8. 1 1 1 1 1e+6 1e+7 1e+8 1e+9 1e+1 J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 15 / 21

Disturbance Profiles Temperature disturbances Power disturbances Power per surface disturbances 285 2 45 4 [K] 28 275 [W] 15 1 [W/m 2 ] 35 3 25 2 27 5 15 1 265 2 4 6 time [days] 2 4 6 time [days] 5 2 4 6 time [days] 52 disturbances J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 16 / 21

Control Profiles RBC Indoor temperature Heating 3 6 y 2 [ C] 25 2 u 2 [W] 4 2 1 2 3 4 5 6 7 time [days] 1 2 3 4 5 6 7 time [days] Comfort satisfaction, spanning from 93.9% to 95.2%. Energy savings around xx. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 17 / 21

Control Profiles PID Indoor temperature Heating 3 6 y 2 [ C] 25 2 u 2 [W] 4 2 1 2 3 4 5 6 7 time [days] 1 2 3 4 5 6 7 time [days] Comfort satisfaction, spanning from 95.6% to 99.6%. Energy savings around 6%. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 18 / 21

Control Profiles MPC Indoor temperature Heating 3 6 y 2 [ C] 25 2 u 2 [W] 4 2 1 2 3 4 5 6 7 time [days] 1 2 3 4 5 6 7 time [days] Comfort satisfaction, close to 1.%. Energy savings around 13%. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 19 / 21

Performance Evaluation Total comfort rate Total heating cost 1 2 [%] 5 PID RBC ROM 4 ROM 7 ROM 1 ROM 15 ROM 2 ROM 3 ROM 4 ROM 1 SSM (a) Total one-step ahead prediction error [ MWh / year ] 15 1 5 PID RBC ROM 4 ROM 7 ROM 1 ROM 15 ROM 2 (b) CPU time ROM 3 ROM 4 ROM 1 SSM [1e4 Kh / year ] 2 15 1 5 PID RBC ROM 4 ROM 7 ROM 1 ROM 15 ROM 2 (c) Original Renovated Light weight Original (OSF) Renovated (OSF) Light weight (OSF) ROM 3 ROM 4 ROM 1 SSM [1e3 s] 8 6 4 2 PID RBC ROM 4 ROM 7 ROM 1 ROM 15 ROM 2 (d) ROM 3 ROM 4 ROM 1 SSM J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 2 / 21

Conclusions 1 Influence of controller model accuracy on controller performance. 2 Minimum of 3 states was necessary for 6-rooms house. 3 When a dense formulation is used a CPU time becomes independent of the number of states of the controller model. 4 Use a controller model which emulates the real building as accurately as possible! Acknowledgment: The Authors gratefully acknowledge the contribution of the Slovak Research and Development Agency under the project APVV 551-11. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 216 21 / 21