Fig. 1 shows a flow diagram of the analyzed high power SOEC system. Liquid water is fed to pre-vaporizer where it is heated up by the high temperature flow out from fuel heat exchanger (F-HEX). After pre-vaporizer, hot water comes to vaporizer, receiving heat from heat source such as nuclear reactor, concentrated solar panel, etc. vaporizes into steam. This steam recuperates the heat from extremely hot flue gas stream out from SOEC at the F-HEX, before going through an electrical heater (F-heater) which increases the steam temperature to SOEC operating temperature. In the remaining side of SOEC, air is blown to an air heat exchanger (A-HEX) where it receives heat from the outgoing air stream from SOEC, then once again the air stream is heated up by an electrical heater (A-heater) before being supplied to SOEC. Through the electrochemical reaction of SOEC, the supplied electricity and steam are converted into oxygen and hydrogen. Then, mixes with the unconverted steam to be H₂-rich hot stream, exiting SOEC to F-HEX. After transferring heat to cold steam at F-HEX and pre-vaporizer, H₂-rich stream is split into two streams; one stream is recirculated to vaporizer to recover steam and also keep H₂ molar fraction in inlet steam higher than certain value⁶⁾. The remaining flows through condenser where steam condenses, and is removed from gaseous mixture which is finally separated to get pure hydrogen.

Fig. 1. 
Flow diagram of the high power SOEC system

Table 1 summarizes the assumptions used in system modeling and simulation^7-11). The current density is assumed to be 1 A/cm² higher than almost normal SOEC^5,12,13). Beside, operating condition of cell is chosen at 715˚C and 1 atm. Furthermore, the 36 kW stack includes 380 cells. Other essential coefficients such as inverter efficiency, Faraday efficiency, heat loss are set at widely used values: 92%, 92%, and 5%, respectively¹⁰⁾. Lastly, the heat supplied to SOEC system is assumed from a 300˚C waste steam stream with mass flow rate of 15 kg/h.

The analyzed cycle was modeled using the EBSILON^® (Steag, Zwingenberg, Germany) Professional commercial software package¹⁴⁾. Fig. 2 shows a screenshot of the EBSILON software used for the analyzed cycle. During optimization process genetic algorithm is employed to find optimal point. Though genetic algorithm does not guarantee the global optimal point, this result suggests a parameter set for further investigation or analysis.

Fig. 2. 
Screenshot of the EBSILON software used for the simulation

The figures show the system efficiency as function of each parameter in parametric study. In Fig. 3, external steam temperature is proportional to the amount of heat fed to the system, so the system efficiency increases when steam temperature increases, as expected. In the same way, the HEX effectiveness also affects positively to the system efficiency because it performs the heat recuperation of heat exchanger as shown in Fig. 4. Moreover, the dependence of system efficiency to HEX effectiveness is very high; about 10 percent points increases in system efficiency when HEX effectiveness changes from 0.7 to 0.9.

Fig. 3. 
System efficiency depends on the external steam temperature

Fig. 4. 
System efficiency depends on the HEX effectiveness

Fig. 5 shows the system dependence on steam conversion. When steam conversion rate increases, the H₂ content in the output of SOEC stack is also higher, leading to the lower recirculation flow, and then less recovered heat from fuel off-gas. As a result, the fuel heater power increases, causing slightly decrease in system efficiency. In Fig. 6, the effect of hydrogen molar fraction is quite similar to that of steam conversion rate. A higher hydrogen molar fraction in stack inlet stream requires a smaller recirculation flow, leading to less recuperated heat amount. Consequently, the F-heater has to provide more heat to achieve deign temperature, reducing total system efficiency. However, the amplitude is bigger than that in Fig. 5 due to the higher recycle blower power consumption.

Fig. 5. 
System efficiency depends on the steam conversion

Fig. 6. 
System efficiency depends on the H₂ molar fraction

Fig. 7 shows the dependency of system efficiency on Faraday efficiency. The SOEC efficiency increases with Faraday efficiency. However, it affects the heat release from or absorption into SOEC stack, consequently the whole system efficiency does not always increase with Faraday efficiency’s increase. The maximum system efficiency is 89.7% when Faraday efficiency is 0.96. In Fig. 8, system efficiency decreases when cell voltage increases because SOEC works at low faraday efficiency (0.92) that is in exothermic condition. Therefore, the higher voltage makes the higher loss.

Fig. 7. 
System efficiency depends on faraday efficiency

Fig. 8. 
System efficiency depends on the cell voltage

Because Faraday efficiency effect is not monotonous, it is set at discrete values from 0.92 to 0.97 in optimization. Besides, the cell voltage also chosen at 1.285 V where the stack is almost at thermal balance point, neither absorb nor release heat⁹⁾. In addition, the parametric study in the previous section also pointed out the system efficiency is maximum with cell voltage value of 1.285 V.

Table 3 shows the optimization results with Faraday efficiency from 0.92 to 0.97. In all the cases, the optimal results are found at the boundary value of the external steam temperature, 700˚C. However, the result also shows that, though the effect of all parameters are monotonous, the optimal point is not always achieved when the examined variables at the boundary. For example, when Faraday efficiency is 0.97, optimal point is achieved at HEX effectiveness of 0.787, steam conversion rate of 0.57 and hydrogen molar fraction of 0.200. This reveals the combination and correlation effect between the parameters.

Though genetic algorithm does not guarantee the global optimal point, this result suggests a parameter set for further investigation or analysis.