Explicit Model Predictive Control of a Fuel Cell

Transcription

1 Explicit Model Predictive Control of a Fuel Cell Deepak Ingole, Ján Drgoňa, Martin Kalúz, Martin Klaučo, Monika Bakošová, Michal Kvasnica Faculty of Chemical and Food Technology Slovak University of Technology in Bratislava Slovakia September 12, 2016 Acknowledgment: The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the EU s Seventh Framework Programme under REA grant agreement no (TEMPO). The Authors gratefully acknowledge the contribution of the Slovak Research and Development Agency under the project APVV Deepak Ingole (STU) September 12, / 22

2 Outline 1 Fuel Cell 2 Experimental Set-up 3 PEM Fuel Cell Control 4 Fuel Cell Modeling 5 Experimental Results 6 Conclusions Deepak Ingole (STU) empc of Fuel Cell September 12, / 22

3 Fuel Cell A device which converts the chemical energy from the fuel into electric energy through a chemical reaction Emits heat and pure water Operates like a battery Proton Exchange Membrane (PEM) Deepak Ingole (STU) Fuel Cell September 12, / 22

4 Fuel Cell Power System Day Night Solar Energy Consumers Wind Energy Battery Bank Oxygen Electrolyzer Hydrogen Fuel Cell Water Deepak Ingole (STU) Fuel Cell September 12, / 22

5 Applications of a PEM Fuel Cell Deepak Ingole (STU) Fuel Cell September 12, / 22

6 Motivation Properties of fuel cells Renewable source of energy Silent operation No pollution High Efficiency Consumer market Deepak Ingole (STU) Fuel Cell September 12, / 22

7 Motivation Properties of fuel cells Renewable source of energy Silent operation No pollution High Efficiency Consumer market Control of electrolyzer and fuel cell Deepak Ingole (STU) Fuel Cell September 12, / 22

8 Principle of a Fuel Cell e, Load e Fuel In H + Oxidant In O 2 H 2 H + H + H 2 O Anode Electrolyte Cathode Water Out Deepak Ingole (STU) Fuel Cell September 12, / 22

9 Principle of a Fuel Cell e, Load e Fuel In H + Oxidant In O 2 H 2 H + H + H 2 O Anode Electrolyte H 2 2H + +2e 1 2 O 2 +2H + +2e H 2 O Cathode Water Out Deepak Ingole (STU) Fuel Cell September 12, / 22

10 Components of a Fuel Cell System Heat and Water Clean Exhaust Electricity Fuel Fuel Processor Hydrogen Fuel Cell Stack DC Power Converter AC Air Deepak Ingole (STU) Fuel Cell September 12, / 22

11 Experimental Set-up of a PEM Fuel Cell Host PC Electrolyzer Output Data Monitor FC Stack Input Data Monitor Tank Load Deepak Ingole (STU) Experimental Set-up September 12, / 22

12 PEM Fuel Cell Control Generate desired voltage from the fuel cell stack without violating the electrolyzers input voltage limits Challenges Electrolyzer and fuel cell dynamics Temperature and air flow High resistance at load side Small operating range of electrolyzers Control Model predictive control Disturbance modeling Deepak Ingole (STU) PEM Fuel Cell Control September 12, / 22

13 Implementation of a Real-time MPC Real-time MPC Deepak Ingole (STU) Fuel Cell Modeling September 12, / 22

14 Implementation of a Real-time MPC Plant Model Real-time MPC Deepak Ingole (STU) Fuel Cell Modeling September 12, / 22

15 Implementation of a Real-time MPC Plant Model Plant/Model Mismatch Real-time MPC Deepak Ingole (STU) Fuel Cell Modeling September 12, / 22

16 Implementation of a Real-time MPC Plant Model Plant/Model Mismatch MPC Design Real-time MPC Deepak Ingole (STU) Fuel Cell Modeling September 12, / 22

17 PEM Fuel Cell Modeling + V IN V OUT Voltage Regulator Electrolyzer Hydrogen Canister FC Stack Load Fuel Cell Plant Input: Input voltage (V IN ) Output: Output voltage (V OUT ) Input Constraints: V Deepak Ingole (STU) Fuel Cell Modeling September 12, / 22

18 Model Identification 1.92 Input Voltage [V] Time [s] 2 Output Voltage [V] Time [s] Deepak Ingole (STU) Fuel Cell Modeling September 12, / 22

19 Model Identification 1.92 Input Voltage [V] Time [s] 2 Output Voltage [V] Time [s] Deepak Ingole (STU) Fuel Cell Modeling September 12, / 22

20 Model Validation Model Order Fit To Estimated Data FPE MSE % % % % % Identified fuel cell model: x k+1 = Ax k +Bu k y k = Cx k Deepak Ingole (STU) Fuel Cell Modeling September 12, / 22

21 Disturbance Modeling Sources of model/plant mismatch Temperature and air flow Data monitor Augmented design model x k+1 = Ax k +Bu k d k+1 = d k Luenberger observer [ˆxˆd] [ ] A 0 = 0 I][ˆxˆd k+1 ŷ k = [ C I ][ˆx ] ˆd y k = Cx k +d k k k + [ ] B u 0 k +L(y m,k ŷ k ) Deepak Ingole (STU) Fuel Cell Modeling September 12, / 22

22 MPC Problem min u 0,...,u N 1 N 1 (y k y r ) T Q(y k y r )+ uk T R u k k=0 s.t. x k+1 = Ax k +Bu k y k = Cx k u k = u k u k 1 u k U x 0 = x(t) k = 0,...,N 1 k = 0,...,N 1 k = 0,...,N 1 k = 0,...,N 1 Deepak Ingole (STU) Fuel Cell Modeling September 12, / 22

23 MPC Problem min u 0,...,u N 1 N 1 (y k y r ) T Q(y k y r )+ uk T R u k k=0 s.t. x k+1 = Ax k +Bu k y k = Cx k +d k u k = u k u k 1 u k U d k+1 = d k x 0 = ˆx(t) d 0 = ˆd(t) k = 0,...,N 1 k = 0,...,N 1 k = 0,...,N 1 k = 0,...,N 1 k = 0,...,N 1 Deepak Ingole (STU) Fuel Cell Modeling September 12, / 22

24 Explicit MPC Optimization Problem (mpqp) Deepak Ingole (STU) Fuel Cell Modeling September 12, / 22

25 Explicit MPC Optimization Problem (mpqp) Off-line On-line Explicit Solution (Look-Up Table) ˆx(t), ˆd(t) u (t) Estimation Plant y(t) Deepak Ingole (STU) Fuel Cell Modeling September 12, / 22

26 Sequential Search u (x) A1x b1 A2x b2 A3x b3 A4x b4 A5x b5 A6x b6 A7x b7 R1 R2 R3 R4 R5 R6 R7 F 1 x 0 +g 1 if x 0 R 1 u (x) =. F 7 x 0 +g 7 if x 0 R 7 x Deepak Ingole (STU) Fuel Cell Modeling September 12, / 22

27 Sequential Search u (x) A1x b1 A2x b2 A3x b3 A4x b4 A5x b5 A6x b6 A7x b7 R1 R2 R3 R4 R5 R6 R7 F 1 x 0 +g 1 if x 0 R 1 u (x) =. F 7 x 0 +g 7 if x 0 R 7 x Deepak Ingole (STU) Fuel Cell Modeling September 12, / 22

28 Sequential Search u (x) A1x b1 A2x b2 A3x b3 A4x b4 A5x b5 A6x b6 A7x b7 R1 R2 R3 R4 R5 R6 R7 F 1 x 0 +g 1 if x 0 R 1 u (x) =. F 7 x 0 +g 7 if x 0 R 7 x Deepak Ingole (STU) Fuel Cell Modeling September 12, / 22

29 Sequential Search u (x) A1x b1 A2x b2 A3x b3 A4x b4 A5x b5 A6x b6 A7x b7 R1 R2 R3 R4 R5 R6 R7 F 1 x 0 +g 1 if x 0 R 1 u (x) =. F 7 x 0 +g 7 if x 0 R 7 x Deepak Ingole (STU) Fuel Cell Modeling September 12, / 22

30 Explicit MPC : Pros and Cons Pros Simple implementation: small code, division-free Predictable execution: exact worst-case runtime and memory Verifiable performance: closed-loop stability, feasibility, and safety Cons Only for small scale problems Explicit solutions can be very complex Reducing complexity requires scarifying performance Deepak Ingole (STU) Fuel Cell Modeling September 12, / 22

31 Implementation of a Explicit MPC Prediction horizon: 10 Number of regions: 519 Computational time: 3.58 s u (x) x 2 x 1 Deepak Ingole (STU) Experimental Results September 12, / 22

32 Experimental Results 1.85 Output Voltage [V] Reference Input Voltage [V] Lb/Ub Time [s] Deepak Ingole (STU) Experimental Results September 12, / 22

33 Experimental Results 1.85 Output Voltage [V] Reference Output Input Voltage [V] Lb/Ub Input Time [s] Deepak Ingole (STU) Experimental Results September 12, / 22

34 Conclusions Identification of fuel cell model Disturbance modeling Model predictive control design Verification of explicit MPC on fuel cell system Deepak Ingole (STU) Conclusions September 12, / 22