## 3 Results and Discussion
### DC Analysis
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the \(V_{\text{da/c+\Delta OCV}}\) decreased by approximately 50% if considering the initial \(V_{\text{da/c+\Delta OCV}}\) value of 0.56 V. To show how the degradation affects the electric conversion efficiency (\(\eta\)) of the SOFC, the \(\eta\) was evaluated at every \(\Delta t\) = 100 h from 0 to 1000 h, according to the following equation:  
\[\eta=\frac{P_{\text{el}}}{P_{\text{in}}}=\frac{P_{\text{el}}}{\Phi_{\text{in}, \text{H}_{2}}\cdot\Delta H_{\text{H}_{2}}}=\frac{2\cdot F\cdot V_{\text{cell}}} {\Delta H_{\text{H}_{2}}} \tag{24}\]  
The \(P_{\text{el}}\) is electric power density, \(P_{\text{in}}\) is input power density, \(\Phi_{\text{in},\text{H}_{2}}\) is input molar flux of hydrogen. It can be noticed that \(\eta\) depends on the output voltage of SOFC (\(V_{\text{cell}}\)), Faraday constant (\(F\)), and standard enthalpy of formation for hydrogen (\(\Delta H_{\text{H}_{2}}\)) only if it is assumed that each oxidized H\({}_{2}\) contributes two electrons, Equation (2). Figure 8a shows the \(\eta\) of the SOFC as a function of time. The reference conversion efficiency (\(\eta_{\text{Ref. [10]}}\)) dropped rapidly from 0 to 200 h and moderately from 200 h to 1000 h (by approximately 0.07 and 0.04, respectively). A similar trend of the conversion efficiency (\(\eta_{\text{da/c+\Delta OCV}}\)) of SOFC, with degraded anode/cathode and \(\Delta\)OCV, was observed. The absolute degradation rate of \(\eta_{\text{Ref. [10]}}\) from 0 to 1000 h was estimated to be 0.11 kh\({}^{-1}\), whereas the relative degradation rate was about 25% kh\({}^{-1}\). Similar degradation rates of \(\eta_{\text{da/c+\Delta OCV}}\) were noticed. These values were high, but it should be noted that the real SOFC degradation test was performed at high temperature (900 \({}^{\circ}\)C). The details about the experimental test can be found in Ref. [10]. It is important to note that the proposed model reproduces reliable results which are closely related to the measured ones. Figure 8b shows the electric power density (\(P_{\text{cell}}\)) and energy density (\(E_{\text{cell}}\)) of SOFC that can be calculated by Equations (25) and (26). \[P_{\text{cell}}(t)=J_{\text{cell}}(t)\cdot V_{\text{cell}}(t) \tag{25}\]  
\[E_{\text{cell}}(t)=\int\limits_{0}^{t}J_{\text{cell}}(t)\cdot V_{\text{cell}} (t)\cdot dt\
cong\sum\limits_{i=1}^{i=\text{N}}J_{\text{cell}}[\text{i}]\cdot V _{\text{cell}}[\text{i}]\cdot\Delta t \tag{26}\]  
The energy yield of non-degraded cell (\(E_{\text{ref}}\)) equals 25.1 MWh m\({}^{-2}\), whereas the energy yield of degraded cell (\(E_{\text{da/c+\Delta OCV}}\)) equals 15.8 MWh m\({}^{-2}\) at \(t\) = 10,000 h. The yield of electrical energy, generated by the real SOFC over a long time, would be much lower (by approximately 37%) than calculated by considering the initial electric performance (i.e., the non-degraded SOFC). Figure 8: **(a)** Electric conversion efficiency (\(\eta\)) of the SOFC as a function of time from 0 to 1000 h. Degradation is considered in the anode (\(\eta_{\text{da}}\)) layer alone, with drop of open circuit voltage (\(\eta_{\text{da+\Delta OCV}}\)) and in both, anode and cathode layers, with drop of OCV (\(\eta_{\text{da/c+\Delta OCV}}\)). **(b)** Electric power density (\(P_{\text{cell}}\)) and energy yield (\(E_{\text{cell}}\)) of non-degraded (\(P_{\text{ref}}\), \(E_{\text{ref}}\)) and degraded SOFC (\(P_{\text{da/c+\Delta OCV}}\), \(E_{\text{da/c+\Delta OCV}}\)) as a function of time from 0 to 10,000 h.  
As a result, the overall cost per generated MWh of electric energy could be estimated when a high power SOFC generator was considered. This estimation is beyond the scope of the present study since the input data of the model is based on laboratory scale SOFC. The model is very useful tool to predict the degradation rate and is suitable for online monitoring of the SOFC.