Experimental RTO of an SOFC

Experimental Real-Time Optimization (RTO) of a Solid Oxide Fuel Cell (SOFC) Stack via Constraint Adaptation : 

Experimental Real-Time Optimization (RTO) of a Solid Oxide Fuel Cell (SOFC) Stack via Constraint Adaptation G.A. Bunina, Z. Wuilleminb, G. Françoisa, A. Nakajob, L. Tsikonisb, and D. Bonvina a Laboratoire d’Automatique, EPFL b Laboratoire d’Énergétique Industrielle, EPFL

Key Goals : 

Key Goals Demonstrate that experimental optimization of SOFC stacks is viable Propose effectiveness of the constraint adaptation methodology “simple yet effective”

Talk Map : 

Talk Map The System Constraint Adaptation Experimental Validation ? Conclusions

Talk Map : 

Talk Map The System Constraint Adaptation Experimental Validation ? Conclusions

The System : 

The System Manipulated Variables nH2: H2 flux nO2: O2 flux I: current Safety Constraints Ucell: cell potential ν: fuel utilization λ: air excess ratio Performance pel: power demand η: electrical efficiency Fuel Air 79% N2 21% O2 Current 97% H2 3% H2O Furnace 6-cell SOFC Stack nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratio pel: power demand η: efficiency O-2 e-

Talk Map : 

Talk Map The System Constraint Adaptation Experimental Validation ? Conclusions nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratio pel: power demand η: efficiency

A Standard Optimization : 

A Standard Optimization The NLP Problem: efficiency performance safety } actuator limits nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratio pel: power demand η: efficiency θ: uncertain parameters Not Implementable!

Where the Model Errs : 

Where the Model Errs nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratio pel: power demand η: efficiency θ: uncertain parameters This is generally where we want to operate!

Modified Problem : 

Modified Problem Original Modified nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratio pel: power demand η: efficiency θ: uncertain parameters ε: modifiers For this system: either ν or Ucell are active at the optimum

The Iterative Scheme : 

The Iterative Scheme nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratio pel: power demand η: efficiency θ: uncertain parameters ε: modifiers K: filter

Talk Map : 

Talk Map The System Constraint Adaptation Experimental Validation ? Conclusions nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratio pel: power demand η: efficiency θ: uncertain parameters ε: modifiers K: filter

Criteria : 

Criteria Power density demand profile: Safety constraints: nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratio pel: power demand η: efficiency θ: uncertain parameters ε: modifiers K: filter RTO iteration every 30 minutes

Results (K=0.4) : 

Results (K=0.4) nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratio pel: power demand η: efficiency θ: uncertain parameters ε: modifiers K: filter Note: - iterative convergence - violations

Using Lower Filters (K=0.7) : 

Using Lower Filters (K=0.7) nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratio pel: power demand η: efficiency θ: uncertain parameters ε: modifiers K: filter

Using Lower Filters (K=1.0) : 

Using Lower Filters (K=1.0) nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratio pel: power demand η: efficiency θ: uncertain parameters ε: modifiers K: filter

Good, But… : 

Good, But… Tracking is slow Modifier terms are only locally valid Change in power demand  new operating point Old modifiers no longer valid  temporary offsets Can alleviate the problem by iterating faster In order to do this, we need: Computationally-friendly model Pseudo-steady state assumption nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratio pel: power demand η: efficiency θ: uncertain parameters ε: modifiers K: filter

“Fast” RTO : 

“Fast” RTO Computationally-friendly model: We have this 30 minutes  10 seconds Pseudo-steady state assumption: Electrochemical time scale (ETC) < 1 second Thermal time scale (TTC) ≈ 30 minutes Gain of ETC >> Gain of TTC nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratio pel: power demand η: efficiency θ: uncertain parameters ε: modifiers K: filter

Using Lower Filters (K=1.0) : 

Using Lower Filters (K=1.0) nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratio pel: power demand η: efficiency θ: uncertain parameters ε: modifiers K: filter

“Fast” RTO : 

“Fast” RTO Computationally-friendly model: We have this 30 minutes  10 seconds Pseudo-steady state assumption: Electrochemical time scale (ETC) < 1 second Thermal time scale (TTC) ≈ 30 minutes Gain of ETC >> Gain of TTC Assumption: Steady state occurs on electrochemical scale Treat thermal effects as “degradation” nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratio pel: power demand η: efficiency θ: uncertain parameters ε: modifiers K: filter

“Fast” RTO : 

“Fast” RTO nH2: H2 flux nO2: O2 flux I: current Ucell: potential ν: fuel utilization λ: air ratio pel: power demand η: efficiency θ: uncertain parameters ε: modifiers K: filter

Talk Map : 

Talk Map The System Constraint Adaptation Experimental Validation ? Conclusions

Conclusions : 

Conclusions Constraint adaptation works Successfully detects the proper constraints Iteratively eliminates offset in constraints Slow convergence improved via “Fast RTO” Caveat: pseudo-steady state assumption Future work will focus on more complex systems More complex models Pseudo-state assumption may not hold Sensitivity-seeking directions become important

Thank You! : 

Thank You! Questions?