This project has received funding from the Fuel Cells and Hydrogen 2 Joint Undertaking under grant agreement No 700101. This Joint Undertaking receives support from the European Union's Horizon 2020 research and innovation programme and Hydrogen Europe and N.ERGHY. Nordic Process Control Workshop NPCW-2019, DTU, Copenhagen 22-23 >August 2019 Relay feedback excitation for identification of Fuel Cell performance parameters Ivar J. Halvorsen, Federico Zenith SINTEF Digital, Trondheim, Norway Relay feedback excitation for identification of fuel cell low frequency resistance3 = impedance at: • Add filter d(s) such that • Filter => when • The filter can be partitioned in to pre- and post-filers e.g: • Bias estimator for handling of slow voltage drift must be included • Require access to DC/DC in FC system for setting fuel cell current References: 1. Ivan Pivac, Dario Bezmalinović, Frano Barbir, Catalyst degradation diagnostics of proton exchange membrane fuel cells using electrochemical impedance spectroscopy, International Journal of Hydrogen Energy, Volume 43, Issue 29, 2018, Pages 13512-13520, https://doi.org/10.1016/j.ijhydene.2018.05.095 2. Aström, Karl Johan, Hägglund ,Tore. PID controllers: Theory, design, and tuning, vol. 2. , NC: Instrument society of America Research Triangle Park; 1995 3. Ivar J. Halvorsen, Ivan Pivac, Dario Bezmalinović, Frano Barbir, Federico Zenith, Electrochemical low-frequency impedance spectroscopy algorithm for diagnostics of PEM fuel cell degradation, International Journal of Hydrogen Energy, 2019, In Press, https://doi.org/10.1016/j.ijhydene.2019.04.004. H(s) 0 2 4 6 8 10 12 14 16 -1.5 -1 -0.5 0 0.5 1 1.5 Z LTI System of FC Relay 0 Constant Scope 0.5s+1 s Transfer Fcn 1 0.5s+1 Transfer Fcn1 1 s Transfer Fcn2 1 s Estimated R Product 100 Gain1 Step Step1 Signal Generator 0.003033 Display Rest -0.0008 Bias relayout To Workspace Im To Workspace1 Um To Workspace2 Rest To Workspace3 1 s Estimated_bias Product1 -0.0008045 Display Bias 1 Gain2 -K- Gain 0 1 2 3 4 5 6 7 8 9 Re(Z(j )) [ ] 10 -3 -2 -1 0 1 2 3 4 5 -Im(Z(j )) [ ] 10 -3 Nyquist Diagram for impedance Z(j ) [ ] R real : 0.0083213 [ ] R est : 0.0083129 [ ] @Im(z)==0: 2.2001 [rad/s] est @Im(z)==0: 2.3102 [rad/s] Nyquist curve Real max R Estimated max R Steady state High freq 0 0.05 0.1 0.15 0.2 0.25 Real(Z) -0.01 0 0.01 0.02 0.03 0.04 0.05 -Imag(Z) Nyquist diagram w=0.126 w=0.314 w=0.628 w=3.14 w=6.3 w=12.6 w=1.71 rad/s 0 100 200 300 400 500 600 57 58 59 60 voltage ConstFreq_0020_mHz 0 100 200 300 400 500 600 220 222 224 226 current Relay feedback creates quickly a stable limit cycle at critical frequency of H(s) Gain can be obtained from data Result can be used e.g. for PID tuning Recorded EIS curves from long term test (ref FESB) From simulation data: Full stack test The EU-project: • Building Hydrogen Fuel Cell range extender for heavy duty transport • Diagnostic, Control, Performance and health monitoring for fuel cells Case introduction: Fuel Cell Impedance – electrical equivalent model Z(s): LFR - A dynamic parameter for ageing indication1: • The low frequency resistance (LFR) at the intercept where increases with ageing. • Challenge: How to identify LFR in a running FC application! ( ) 0 Z jω ∠ = ° Alternatives for on-line identification: • Electrochemical impedance spectroscopy (EIS) – use in lab only • Fixed frequency excitation in relevant range - feasible, tested • Phase locked loop - feasible • Relay feedback excitation – studied here Relay feedback excitation2 180 ( ) 180 H H jω ∠ = − ° ( ) 0 Z jω ∠ = ° ( ) ( ) ( ) H s Z s d s = 2 ( ) 1/ d s s = 180 ( ) 0 H Z jω ∠ = ° 180 ( ) 180 H H jω ∠ = − ° 1 1 2 2 2 1 1 1 1 ( )* ( ) ( ) * 1 T d s d s s d s s s T s + = + = = 180 ( ) H H jω Bias Estimator Relay feedback loop • Bias estimation is based on simple adaption by a gradient method • Data can be post processed for more detailed analysis Testing on a full stack: (ElringKlinger) • Tests have been carried out at a set of fixed frequencies and