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, 2016 Acknowledgment: The Authors gratefully acknowledge the contribution of the Slovak Research and Development Agency under the project APVV 0551-11. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 2016 1 / 21
Building Control Motivation Problem: EU spends 400 billion EUR/year on energy. 40% 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’ 2013 OECD/IEA. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 2016 2 / 21
Building Control Motivation Problem: EU spends 400 billion EUR/year on energy. 40% 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’ 2013 OECD/IEA. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 2016 2 / 21
Building Control Motivation Problem: EU spends 400 billion EUR/year on energy. 40% 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’ 2013 OECD/IEA. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 2016 2 / 21
Building Control Motivation Problem: EU spends 400 billion EUR/year on energy. 40% 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’ 2013 OECD/IEA. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 2016 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, 2016 3 / 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, 2016 3 / 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, 2016 3 / 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, 2016 3 / 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, 2016 3 / 21
What is the Best Model? J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 2016 4 / 21
What is the Best Model? J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 2016 4 / 21
Methodology Controller model order MPC RBC PID Plant model order J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 2016 5 / 21
Building Description [m 2 ] Floor area 48.3 [m 3 ] Conditioned volume 130.6 [m 2 ] Total exterior surface area 195 Windows [-] 5 Walls [-] 22 Roof and floor surfaces [-] 12 Thermal zones [-] 6 J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 2016 6 / 21
Linearisation 1 Controller model order MPC RBC PID Plant model order 1Picard, D., Jorissen, F., and Helsen, L. 2015. 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, 2016 7 / 21
Linearisation Error Original Renovated Light weight 1.0 1.0 1.0 0.5 0.5 0.5 [K] 0.0 0.0 0.0 −0.5 −0.5 −0.5 −1.0 −1.0 −1.0 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 e e e e e e e e e e e e e e e e e e n n n n n n n n n n n n n n n n n n o o o o o o o o o o o o o o o o o o Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Full year open-loop simulation linearization error below 1 K. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 2016 7 / 21
Model Order Reduction 2 Controller model order MPC RBC PID Plant model order Square root balanced truncation algorithm, based on Hankel singular values. 2 Antoulas, A. C. and Sorensen, D. C. 2001. Approximation of large-scale dynamical systems: An overview. Applied Mathematics and Computer Science. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 2016 8 / 21
Reduced Order Models – Error Bounds Error bounds Error bounds Original Original 10 0 Renovated Renovated Light weight Light weight 10 1 Error bound [-] Error bound [-] 10 0 10 -5 10 -1 10 -10 10 -2 50 100 150 200 250 5 10 15 20 25 30 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, 2016 9 / 21
Reduced Order Models – Open Loop Simulation 25 TZone 1 TZone 2 TZone 3 T [ ° C] 20 15 Orders of ROM: 4 7 10 15 20 30 40 100 SSM 25 TZone 4 TZone 5 TZone 6 T [ ° C] 20 15 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Time [Day] Single week open loop simulation with realistic control inputs and disturbances. J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 2016 9 / 21
Reduced Order Models – Prediction Errors 1-step ahead 10-step ahead 40-step ahead 2 2 2 1 1 1 0 0 0 [K] -1 -1 -1 -2 -2 -2 -3 -3 -3 ROM 100 ROM 100 ROM 100 ROM 10 ROM 15 ROM 20 ROM 30 ROM 40 ROM 10 ROM 15 ROM 20 ROM 30 ROM 40 ROM 10 ROM 15 ROM 20 ROM 30 ROM 40 ROM 4 ROM 7 ROM 4 ROM 7 ROM 4 ROM 7 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, 2016 9 / 21
Control Setup Controller model order MPC RBC PID Plant model order J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 2016 10 / 21
Control Scheme y r u Building MPC d Estimator ˆ x , ˆ p J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 2016 11 / 21
Estimator and Augmented Model � � x k | k = ˆ ˆ x k | k − 1 + L y m , k − ˆ y k | k − 1 x k + 1 | k = A ˆ ˆ x k | k + Bu k | k + Ed k | k y k | k = C ˆ ˆ x k | k + Du k | k � � � � � � � � � � x k + 1 ˆ A 0 ˆ x k B E = + u k + d k ˆ 0 ˆ 0 0 p k + 1 I p k � �� � � �� � � �� � ���� ���� x k + 1 ˜ ˜ x k ˜ ˜ ˜ A B E � � � � ˆ � � x k D y k = ˆ + C F u k p k ˆ 0 � �� � ���� ˜ C ˜ D J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 2016 12 / 21
Estimator and Augmented Model � � x k | k = ˆ ˆ x k | k − 1 + L y m , k − ˆ y k | k − 1 x k + 1 | k = A ˆ ˆ x k | k + Bu k | k + Ed k | k y k | k = C ˆ ˆ x k | k + Du k | k � � � � � � � � � � x k + 1 ˆ A 0 ˆ x k B E = + u k + d k ˆ 0 ˆ 0 0 p k + 1 I p k � �� � � �� � � �� � ���� ���� x k + 1 ˜ ˜ x k ˜ ˜ ˜ A B E � � � � ˆ � � x k D y k = ˆ + C F u k p k ˆ 0 � �� � ���� ˜ C ˜ D J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 2016 12 / 21
MPC Formulation N − 1 � � � || s k || 2 Q s + || u k || 2 min Q u u 0 ,..., u N − 1 k = 0 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 0 = ˆ x ( t ) ∀ k ∈ { 0 , . . . , N − 1 } J. Drgoňa (STU Bratislava) EUCCO, Leuven, Belgium September 14, 2016 13 / 21
Recommend
More recommend
