Master Project Scenario-Based Model Predictive Control for Energy-Efficient Building Climate Control

Transcription

1 Master Project Scenario-Based Model Predictive Control for Energy-Efficient Building Climate Control Georg Schildbach, David Sturzenegger, Prof. Dr. Manfred Morari 02.Oktober 2012

2 Outline Introduction Simulation Environment Controller Assessment RMPC with Sample Removal Conclusion 2

3 Outline Introduction Building Control Scenario-Based Optimization Simulation Environment Controller Assessment RMPC with Sample Removal Conclusion 3

4 Energy Usage of Buildings $ '(#$ 40% 47%!" #" HVAC: Worldwide: 40% Europe, US: >70% China: 30% - Heating - Ventilation - Air Conditioning - Lausten, U.S. Dept. of Energy, Int l Energy Agency,

5 Building Control occupancy realization Realization weather realization building state Disturbance δ input U t,0 MPC min U t s.t. C T t U t U t U t (δ) comfort levels: - temperature - illuminance occupancy prediction Planning weather prediction 5

6 Control Objective Minimize energy cost Keep violations low ( 70 Kh/a) à Chance-constrained problem Conventional Non- Predictive Control OptiControl I simulations project significant savings Predictive Control e.g. Rule-Based Controller if-then-else - Gyalistras, Gwerder, Oldewurtel 2011 Det. MPC Stoch. MPC constraint tightening Randomized MPC scenariobased / sampling 6

7 Scenario-Based Optimization disturbance set δ (1) δ (2) δ (M) min U t s.t. C T t U t U t U t (δ) scenario-based programming min U t C T t U t s.t. U t U t (δ (i) ) i =1,...,M If M is chosen appropriately, then the above gives a feasible solution to a chance-constrained program with high confidence: min U t s.t. C T t U t P {δ U t U t (δ)} 1 - Calafiore, Campi, Garatti,

8 Outline Introduction Simulation Environment Building Model Disturbances Controller Assessment RMPC with Sample Removal Conclusion 8

9 Building Model State space model: B xu [x t ]u B vu [v t ]u B xu,1 x t B xu,2 x t... B xu,m x t u B vu,1 v t B vu,2 v t... B vu,m v t u x t+1 = Ax t +(B + B xu [x t ]+B vu [v t ])u t + B v v t y t = Cx t + D[v t ]u t + D v v t - Room temperature: main constraint - Illuminance: adjusted instantaneously Examples of bilinear effects: v solrad u bpos v t =ˆv t + δ t disturbance prediction external influence u bpos x temp u bpos v solrad - Gyalistras, Gwerder, Oldewurtel

10 Disturbances: Weather and IG Weather Real data provided by MeteoSwiss Weather prediction: Realization: v temp ˆv temp MPC 10 Internal Gains Measurements from Actelion building Design data à prediction: Realization: ˆv IG v IG air temperature [degc] v temp ˆv temp Persons v IG ˆv IG time steps [h] time steps [h] 10

11 Chance-Constrained Program Minimize energy cost Keep violations low min U t =(u 0,...,u N 1 ) N 1 t=0 c T t u t s.t. x t+i+1 = Ax t+i +(B + B xu [x t+i ]+B vu [v t+i ])u t+i x t =ˆx t + B v v t+i, bilinear dynamics P {U t U t (δ)} 1 chance constraints 11

12 Linearization I Q1. How to treat stateinput bilinearity? min U t =(u 0,...,u N 1 ) s.t. N 1 t=0 c T t u t x t+i+1 = Ax t+i +(B + B xu [x t+i ]+B vu [v t+i ])u t+i ˆx t x t =ˆx t + B v v t+i, P {U t U t (δ)} 1 A1. Linearize around initial condition 12

13 Linearization II Q2. How to treat disturbanceinput bilinearity? min U t =(u 0,...,u N 1 ) N 1 t=0 c T t u t s.t. x t+i+1 = Ax t+i +(B + B xu [x t+i ]+B vu [v t+i ])u t+i x t =ˆx t + B v v t+i, P {U t U t (δ)} 1 A2. DMPC/SMPC - linearize around prediction RMPC - linearize around multiple samples 13

14 Outline Introduction Simulation Environment Controller Assessment Approaches Simulation Results RMPC with Sample Removal Conclusion 14

15 Controller Assessment Bilinearity: B vu [v t ]u t Additive noise: B v v t Constraint tightening: Deterministic MPC Stochastic MPC Randomized MPC min U t =(u 0,...,u N 1 ) N 1 t=0 c T t u t s.t. x t+i+1 = Ax t+i +(B + B xu [x t+i ]+B vu [v t+i ])u t+i + B v v t+i, x t =ˆx t P {U t U t (δ)} 1 15

16 Controller Assessment: DMPC Bilinearity: B vu [v t ]u t Deterministic MPC Stochastic MPC linearize around prediction B vu [ˆv t ]u t Additive noise: prediction assume δ N (µ, Σ) x B v v t B vˆv t B vˆv t + δ Constraint tightening: constant progressive Randomized MPC room temperature [degc] room temperature [degc] time steps [h] time steps [h] 16

17 Controller Assessment: RMPC Persons Deterministic MPC air temperature [degc] Stochastic MPC Randomized MPC Bilinearity: prediction samples B vu [v t ]u t B vu [ˆv t ]u t B vu [ˆv t + δ (i) ]u t B v v t B vˆv t B vˆv t + δ B vˆv t + δ (i) Additive noise: prediction assume δ N (µ, Σ) x samples Constraint tightening: constant progressive none Sample from past year s uncertainty set δ (i) realization -- prediction time steps [h] time steps [h]

18 DMPC & SMPC HVAC input HVAC cost input [kwh/m cost 2 /a] < 70 Kh/a PB Same linearization DMPC B[ˆv t ] 1.4 SMPC Both apply constraint tightening OL-violation prob tightening factor [degc] Both need tuning SMPC comput more expensive perfect prediction Room temperature violation [Kh/a] Pareto frontier of DMPC and SMPC comparable 18

19 RMPC HVAC input cost [kwh/m 2 /a] < 70 Kh/a # samples 3 2 SMPC RMPC Room temperature violation [Kh/a] 1 Better approx. of bilinearity B[ˆv t + δ (i) ] Few samples: - Theory: 4800 needed - But can exploit slow dynamics Computationally cheap Easy to tune RMPC good at low violations à Sample Removal 19

20 Outline Introduction Simulation Environment Controller Assessment RMPC with Sample Removal Motivation Removal Algorithms Simulation Results Conclusion 20

21 RMPC with Sample Removal min U t C T t U t s.t. U t U t (δ (1) ), U t U t (δ (2) ) U t U t (δ (3) ), U t U t (δ (4) ) Goals: 1. Improve objective value 2. Keep violation low start with 2 samples take 2 more samples remove 1 sample δ (2) δ (3) δ (1) U t (δ (2) ) δ (4) U t (δ (1) ) U t U t (δ (3) ) U t (δ (4) ) C T t U t 21

22 Sample Removal: Algorithms Greedy Removal: Solves all possible problems and takes best value Multiplier Removal: Solves original problem with all samples Removes sample associated to largest multiplier Heuristic: Solves DMPC with no constraint tightening Simulates trajectories with different samples Removes sample that creates most violations Remove 1 sample Greedy: solve M LPs Multiplier: solve 2 LPs Heuristic: solve 2 LPs 22

23 Sample Removal HVAC input cost [kwh/m 2 /a] SMPC RMPC RMPC multiplier 1 RMPC greedy 1 RMPC heuristic 1 Room temperature violation [Kh/a] Greedy - lowest cost - most violations - expensive Multiplier - less aggressive - cheap Heuristic - worst Pareto frontier - cheap Q. What if more samples are removed? 23

24 Sample Removal: More Removal HVAC input cost [kwh/m 2 /a] A. Higher savings possible energy saved SMPC RMPC RMPC multiplier 1 RMPC multiplier 2 RMPC multiplier 3 RMPC multiplier 5 RMPC multiplier 10 RMPC multiplier 20 RMPC multiplier 30 RMPC multiplier 40 RMPC multiplier 50 Multiplier removal Outperforms RMPC, SMPC Higher comput. effort Saturation after 30 removals room temperature violation [Kh/a] 24

25 Outline Introduction Simulation Environment Controller Assessment RMPC with Sample Removal Conclusion 25

26 Conclusion Developed a framework for RMPC that considers uncertainty in weather uncertainty in internal gains RMPC promising method at low violations intuitive and easy to implement computationally tractable Sample removal further improves performance evaluation of 3 removal algorithms RMPC with Sample Removal is method of choice! 26