1. Flexible Photovoltaics/Fuel Cell/Wind Turbine (PVFCWT) Hybrid Power System Designs Meng-Han Lin, Vincentius Surya Kurnia Adi, Chuei–Tin Chang Dept. of Chemical Engineering National Cheng Kung University Tainan, Taiwan 70101 1

2. Outline Introduction and the models of system Development of flexibility index Temporal flexibility analysis Computation flowchart Case 1 – Annan, Taiwan Case 2 – Richfield, Idaho, USA Conclusion 2

3. Introduction Each “green” energy source has its pros and cons: Our objective: integrating these units to satisfy power demand in any given standalone application. Power demand 3 PV array Wind Turbine DC H 2 storage Battery equipment load Charge Controller  PV array – inexpensive but uncertain/intermittent  Wind Turbine – inexpensive but uncertain/limited to specific locations  Fuel cell – stable but expensive

4. Wind turbine 4 Ref.: S.L. Dixon, C.A. Hall, Fluid Mechanics and Thermodynamics of Turbomachinery, 7th ed., Elsevier Inc., 2014, ch. 10 characteristic power curve

5. Photovoltaics 5 Ref.: Shen W. X., Choo F. H., Wang P., Loh P. C. and Khoo S. Y., Development of a Mathematical Model for Solar Module in Photovoltaic Systems, 2011 6th ICIEA, 2056-2061, June 2011.

6. Fuel cell 6 Ref.: Hwang J. J., Lai L. K., Wu W. and Chang W. R., Dynamic Modeling of a Photovoltaic Hydrogen Fuel Cell Hybrid System, Int J Hydrogen Energ, 34, 9531– 9542, 2009.

7. Li-ion Battery 7 Ref.: Tremblay O. and Dessaint L., A. Experimental Validation of a Battery Dynamic Model for EV Applications, WEVJ, 3, 1–10, 2009.

8. Simulink ® model 8 Inputs – Wind speed, solar irradiance, hydrogen flow rate, power consumption rate Outputs – power supply of each unit State – Battery’s state of charge

9. Available Flexibility Indices The original flexibility index was defined by Swaney and Grossmann (1985), which provides a measure of the size of the feasible region for a given steady-state operation. → Steady-state flexibility index (FIs) Dimitriadis and Pistikopoulos (1995) developed a computation method to quantitatively evaluate the flexibility of systems that operate dynamically under the influence of time-varying uncertain disturbances. → Dynamic flexibility index (FId) Adi and Chang (2013) considered that the cumulative effects of temporary disturbances in the dynamic systems. → Temporal flexibility index (FIt) 9 Ref: R.E. Swaney, I.E. Grossmann, An index for operational flexibility in chemical process design. Part I: Formulation and theory, AIChE Journal, 31 (1985), pp. 621–630 Ref: V.D. Dimitriadis, E.N. Pistikopoulos, Flexibility analysis of dynamic systems, Industrial & Engineering Chemistry Research, 34 (1995), pp. 4451–4462 Ref: V.S.K. Adi, C.T. Chang, A mathematical programming formulation for temporal flexibility analysis, Comput Chem Eng, 57 (2013), pp. 151–158

10. Temporal Flexibility Index Design target: FI t = 1 d :Design variables z :Control variables x :State variables Uncertain parameters 10

11. Motivation Example: A Buffer Tank 11 Feed rate θ(t) Equality constraint Inequality constraint Uncertain parameter Given Data 5 m 2 5 m 62.5 m 3 800 min Described later

12. Motivation Example: A Buffer Tank 12 Feed rate change with time θ(t) Uncertain parameter Equality constraint Inequality constraint

13. Computation Flowchart – Overall 13

14. Computation Flowchart – Bisection method 14

15. Case 1 – Annan, Taiwan 15 Uncertain parameters: (1) solar irradiance, (2) wind speed Ref.: Taiwan Central Weather Bureau, 2014 Year Data of Annan District, http://www.cwb.gov.tw/V7/, 2014http://www.cwb.gov.tw/V7/ Sun Irradiance 4879 W·h/m 2 4780 W·h/m 2 Wind Speed 131.8 m·h/s 47.4 m·h/s

16. Case 1 – Annan, Taiwan 16 Ref.: EnergyPark, Office energy-saving handbook, 2015 Uncertain parameters: (3) power demand Power consumption 2404.4 W·h 3266.6 W·h

17. Case 1 – Equipment Data 17 Annualized capital costs (ACC) Remarks No hydrogen storage is taken into account for capital cost calculation. Annual hydrogen consumption are 788.4 kg per unit and it cost $985/year. In the current study an annual maintenance cost of 3% of capital cost is used for the wind turbine but for PV and Battery, maintenance cost has been neglected. UnitRated powerCompanyACC / unit Fuel cell8.5 kWENE-FARM$ 4,588 Wind turbine0.7 kWHiVAWT DS-700$ 203 Photovoltaic60 WMSX-60$ 70 Battery10 kWhTesla PowerWall$ 710 Ref: D.B. Nelson, M.H. Nehrir, C. Wang, Unit sizing and cost analysis of stand-alone hybrid wind/PV/fuel cell power generation systems, Renewable Energy, 31 (2006), pp. 1641–1656 Ref: C.E. Thomas, I.F. Kuhn Jr, B.D. James, F.D. Lomax Jr, G.N. Baum, Affordable hydrogen supply pathways for fuel cell vehicles, International Journal of Hydrogen Energy, 6 (1998), pp. 507-516

18. Case 1 – Optimization Results 18 Points above this surface represent feasible designs. Darker area is more favorable because the corresponding TAC is lower. 75% TAC($/year) (%) x10 8

19. Case 2 – Richfield, Idaho, USA 19 Uncertain parameters: (1) solar irradiance, (2) wind speed Ref.: AgriMet, 2014 Year Data of INL - Richfield, Idaho, http://www.usbr.gov/pn/agrimet/webaghrread.html, 2015http://www.usbr.gov/pn/agrimet/webaghrread.html Wind Speed 308.1 m·h/s 171.1 m·h/s Sun Irradiance 4448 W·h/m 2 4288 W·h/m 2

20. Case 2 – Richfield, Idaho, USA 20 Ref.: D.B. Nelson, M.H. Nehrir, C. Wang, Unit sizing and cost analysis of stand-alone hybrid wind/PV/fuel cell power generation systems, Renewable Energy, 31 (2006), p.1641–1656 Uncertain parameters: (3) power demand Power consumption 9.3 W·h

21. Case 2 – Optimization Results 21 Feasible volume in this case is larger than the previous one because the wind and solar irradiance are stronger. TAC($/year) (%)

22. Conclusions Disturbances in the power supplies are only buffered by the battery. Choosing an appropriate battery size and the proper power supply distribution are necessary for flexible operation. Temporal flexibility analysis has been successfully applied to design a flexible hybrid power generation system according to arbitrarily given time-variant demand and supply profiles with uncertain disturbances. Cost analysis is adopted in this research to choose operable and financially feasible designs. 22

23. Thanks for your listening 23