**Appendix A**

*Appendix A.1. Figures*

**Figure A1.** The Li-ion Battery—3RC ECM and Simscape models: (**a**)Li-ion battery represented in NI Multisim 14.1 editor (see Figure 6—Part 1); (**b**) Simscape Simulink diagram of Li-ion battery (see Figure A19—Part 1); (**c**) Simscape SAFT Li-ion battery nominal current discharge characteristic @1C (6A) (top side view); @6.5A, 13A and 32.5A. (**d**) Simulink diagram of Li-ion Simscape generic model.

**Figure A2.** EMS—Classical PI Control Strategy setup.

**Figure A3.** SMCAR HEV Powers—Classical PI Control EMS.

**Figure A4.** Fuel cell. (**a**) FC current; (**b**) FC voltage; (**c**) FC consumption.

**Figure A5.** Li-ion battery specific variables. (**a**) Battery current; (**b**) Battery voltage; (**c**) Battery SOC.

**Figure A6.** SC specific variables. (**a**) SC current variation; (**b**) SC voltage.

**Figure A7.** EMS—Equivalent Consumption Minimization Strategy setup.

**Figure A8.** SMCAR HEV Powers—Equivalent Consumption Minimization EMS.

**Figure A9.** Fuel cell. (**a**) FC current; (**b**) FC voltage; (**c**) FC consumption.

**Figure A10.** Li-ion battery specific variables. (**a**) Battery current; (**b**) Battery voltage; (**c**) Battery SOC.

**Figure A11.** SC specific variables. (**a**) SC current variation; (**b**) SC voltage.

• 3RC EMC Li-Ion Battery Model—A EKF SOC Estimator.

**Figure A12.** The MATLAB simulation results for Simulink Simscape Li-ion battery. (**a**) The AEKF SOC value versus battery model SOC true value; (**b**) The AEKF terminal output voltage versus battery model terminal output voltage true value; (**c**) The SOC residual.

**Figure A13.** Robustness to changes in SOC initial value—SOCini = 0.4. (**a**)AEKF SOC estimate versus battery SOC true value; (**b**) SOC residual.

**Figure A14.** Robustness to simultaneous changes, SOCini = 0.4, σ noise = 0.01; (**a**) AEKF SOC value versus battery model true value; (**b**) SOC residual.

*Batteries* **2020**, *6*, 41

• 3 RC AEKF Li-ion Battery Simscape Model.

**Figure A15.** The MATLAB simulation results for Simulink Simscape Li-ion battery. (**a**) The AEKF SOC value versus battery model SOC true value; (**b**) The AEKF terminal output voltage versus battery model terminal output voltage true value; (**c**) The SOC residual.

**Figure A16.** Robustness to changes in SOC initial value—SOCini = 0.4. (**a**)AEKF SOC estimate versus battery SOC true value; (**b**) SOC residual.

**Figure A17.** Robustness to simultaneous changes, SOCini = 0.4, σ noise = 0.01; (**a**) AEKF SOC value versus battery model true value; (**b**) SOC residual.

• AUKF 3RC EMC Li-ion Battery Model

**Figure A18.** The MATLAB simulation results for Simulink 3RC ECM Li-ion battery. (**a**) The AUKF SOC value versus battery model SOC true value; (**b**) The AUKF terminal output voltage versus battery model terminal output voltage true value; (**c**) The SOC residual.

**Figure A19.** Robustness to changes in SOC initial value—SOCini = 0.4. (**a**)AUKF SOC estimate versus battery SOC true value; (**b**) SOC residual.

**Figure A20.** Robustness to simultaneous changes, SOCini = 0.4, σ noise = 0.01; (**a**) AUKF SOC value versus battery model true value; (**b**) SOC residual.

• AUKF Li-ion Battery Simscape Model

**Figure A21.** The MATLAB simulation results for Simulink Simscape Li-ion battery. (**a**) The AUKF SOC value versus battery model SOC true value; (**b**) The AUKF terminal output voltage versus battery model terminal output voltage true value; (**c**) The SOC residual.

**Figure A22.** Robustness to changes in SOC initial value—SOCini = 0.4. (**a**) AUKF SOC estimate versus battery SOC true value; (**b**) SOC residual.

**Figure A23.** Robustness to simultaneous changes, SOCini = 0.4, σ noise = 0.01; (**a**) AUKF SOC value versus battery model true value; (**b**) SOC residual.

• PFE 3RC ECM Li-ion Battery Model

**Figure A24.** The MATLAB simulation results for Simulink Simscape Li-ion battery. (**a**) The PFE SOC value versus battery model SOC true value; (**b**) The PFE terminal output voltage versus battery 3RC ECM model terminal output voltage true value; (**c**) The SOC residual.

**Figure A25.** Robustness to changes in SOC initial value—SOCini = 0.4. (**a**) PFE SOC estimate versus 3RC ECM Li-ion battery SOC true value; (**b**) SOC residual.

**Figure A26.** Robustness to simultaneous changes, SOCini = 0.4, σ noise = 0.01; (**a**) PFE SOC value versus 3RC ECM Li-ion battery model true value; (**b**) SOC residual.

**Figure A27.** The MATLAB simulation results for Simulink Simscape Li-ion battery. (**a**) The PFE SOC value versus battery model SOC true value; (**b**) The PFE terminal output voltage versus battery model terminal output voltage true value; (**c**) The SOC residual.

**Figure A28.** Robustness to changes in SOC initial value—SOCini = 0.4. (**a**) PFE SOC estimate versus battery SOC true value; (**b**) SOC residual.

• Scenario R3: Robustness to simultaneous changes, namely in SOCini (SOCini = 0.4), and measurement noise level, e.g., an increase in noise level 10 times (σ noise = 0.01).

**Figure A29.** Robustness to simultaneous changes, SOCini = 0.4, σ noise = 0.01; (**a**) PFE SOC value versus Simscape battery model true value; (**b**) SOC residual.

*Appendix A.2. Tables*

**Table A1.** Statistical errors—SOC estimates versus Li-ion battery Simscape model SOC values—Scenario R1 (SOCini = 0.4).


**Table A2.** Statistical errors—SOC estimates versus Li-ion battery Simscape model SOC values—Scenario R2: (SOCini = 1, Qnom = 4.2 Ah).



**Table A3.** Statistical errors—SOC estimates versus Li-ion battery Simscape model SOC values—Scenario R3: (SOCini = 0.4, σ noise = 0.01).

**Table A4.** Statistical errors—SOC estimates versus Li-ion battery Simscape model SOC values—Scenario R4: (SOCini = 0.2, temperature effects on Rin and Kp).

