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

Transcription

1 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 J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, / 21

2 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, / 21

3 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, / 21

4 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, / 21

5 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, / 21

6 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, / 21

7 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, / 21

8 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, / 21

9 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, / 21

10 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, / 21

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

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

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

14 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, / 21

15 Linearisation 1 Controller model order MPC Plant model order RBC PID 1 Picard, D., Jorissen, F., and Helsen, L 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, / 21

16 Linearisation Error 1. Original 1. Renovated 1. Light weight [K] 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, / 21

17 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, / 21

18 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 [-] State [-] 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, / 21

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

20 Reduced Order Models Prediction Errors 2 1-step ahead 2 1-step ahead 2 4-step ahead 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, / 21

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

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

23 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, / 21

24 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, / 21

25 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, / 21

26 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, / 21

27 Simulation Setup One year performances of RBC, PID, MPC. Three types of 6-zone buildings, with 3 states. [%] Total comfort level Original Renovated Light weight [MWh / year] Total heating cost prediction horizon [] [1e3 s] CPU time [%] Total comfort level e+6 1e+7 1e+8 1e+9 1e+1 [MWh / year] Total heating cost 1 1 weighting factor [] 1 1 1e+6 1e+7 1e+8 1e+9 1e+1 [1e3 s] CPU time T s = 9, N = 4 steps (i.e., 1 hours), Qs Q u = e+6 1e+7 1e+8 1e+9 1e+1 J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, / 21

28 Simulation Setup One year performances of RBC, PID, MPC. Three types of 6-zone buildings, with 3 states. [%] Total comfort level Original Renovated Light weight [MWh / year] Total heating cost prediction horizon [] [1e3 s] CPU time [%] Total comfort level e+6 1e+7 1e+8 1e+9 1e+1 [MWh / year] Total heating cost 1 1 weighting factor [] 1 1 1e+6 1e+7 1e+8 1e+9 1e+1 [1e3 s] CPU time T s = 9, N = 4 steps (i.e., 1 hours), Qs Q u = e+6 1e+7 1e+8 1e+9 1e+1 J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, / 21

29 Disturbance Profiles Temperature disturbances Power disturbances Power per surface disturbances [K] [W] 15 1 [W/m 2 ] time [days] time [days] time [days] 52 disturbances J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, / 21

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

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

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

33 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 ] 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 ] 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] 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, / 21

34 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 J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, / 21

35 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 J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, / 21

36 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 J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, / 21

37 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 J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, / 21