# Capacity-Operation Collaborative Optimization for Wind-Solar-Hydrogen Multi-Energy Supply System
## 2 System Description
### Model Construction and Validation  
The mathematical model of PV, WP, CSP, PEME, HST, and PEMFC is introduced in Table 2. Among them, the CSP model includes an SF, TES, and a turbine.  
Where \(V_{\text{cv}}\) is the theoretical minimum electrolytic voltage at which the electrolysis of water occurs; \(V_{\text{act}}\) is the open circuit voltage. \(V_{\text{diff}}\) is the equivalent overpotential due to diffusion, and \(V_{\text{ohm}}\) is the ohmic overpotential due to the proton exchange membrane. More detailed data can be found in [33].  
\begin{table}
\begin{tabular}{p{14.2 pt} p{142.3 pt} p{142.3 pt}} \hline \hline
**Subsystem** & **Main Equations** & **Auxiliary Notes** \\ \hline \multirow{7}{*}{PV} & \(P_{\text{PV}}=GHI\cdot n_{\text{m}}\cdot A_{\text{m}}\cdot\eta_{\text{PV}} \cdot\eta_{\text{inv}}\cdot f_{\text{PV}}\) & Where effective area \(A_{\text{m}}\) and the quantity of PV panels \(n_{\text{m}}\), the inverter’s efficiency \(\eta_{\text{inv}}\), and the derating factor \(f_{\text{PV}}\) are specified. Where \(T_{\text{c}}\) is the PV module’s actual operating temperature; \(T_{\text{a}}\) is the surrounding air’s temperature; \(T_{\text{noct}}\) is the nominal operating cell temperature; \(GHI_{\text{noct}}\) is the assumed level of global irradiation; \(U_{\text{L,noct}}\) and \(U_{\text{L}}\) are heat transfer coefficients at the nominal and actual conditions, respectively; \(\gamma\) is the temperature coefficient, and \(T_{\text{c,ref}}\) is the operating cell temperature under reference condition; \(\eta_{\text{PV}}\) is the actual PV efficiency; and \(\tau\cdot\alpha\) is the transmittance-absorbance coefficient. \\ \hline \multirow{7}{*}{WP} & \(\frac{\eta_{\text{m}}}{\eta_{\text{m}}}=(\frac{h_{\text{m}}}{h_{\text{m}}})^{ k}\) & Where \(\tau_{1}\) is the surface wind speed, \(m/s\); \(v_{2}\) is the wind speed at \(h_{2}=70\) m from ground height, \(m/s\); and \(k\) is the wind shear coefficient, \(k=0.14\eta_{\text{c}}\) is the fan starting wind speed, \(m/s\); \(v_{\text{r}}\) is the rated wind speed of fan, \(m/s\); and \(v_{f}\) is the cut-off wind speed of fan, \(m/s\). \(P_{R}^{\text{r}}\) is the rated output power of fan, MW; \(P_{\text{WP}}\) is the actual output power of fan, MW. \\ \hline \multirow{7}{*}{CSP} & \(Q_{\text{SF}}=\left(Q_{\text{absorb}}-Q_{\text{loss}}-Q_{\text{pipe}}\right) \cdot A\cdot 10^{-6}\) & Where \(Q_{\text{SF}}\) is the heat gain power of heat-conducting oil in the SF, MW; \(Q_{\text{absorb}}\) is the solar heat absorbed with the collector tube, W/m\({}^{2}\); \(Q_{\text{loss}}\) is the heat loss of collector tube, W/m\({}^{2}\); \(Q_{\text{pipe}}\) is the pipe heat loss, \(W/m^{2}\); and \(A\) is the area of SF, m\({}^{2}\). \(\dot{m}_{\text{HTT}}\) is the mass flow of HTF; \(h_{\text{in}}\) and \(h_{\text{out}}\) are the specific enthalpies of the HTF inlet and outlet of the receiver, respectively. \\ \cline{1-1}  & \(\eta_{\text{turb}}=(1-\eta_{\text{red}})\cdot\eta_{\text{ref}}\) & Where \(Q_{\text{SF}}\) is the heat gain power of heat-conducting oil in the SF, MW; \(Q_{\text{absorb}}\) is the solar heat absorbed with the collector tube, W/m\({}^{2}\); \(Q_{\text{loss}}\) is the heat loss of collector tube, W/m\({}^{2}\); \(Q_{\text{pipe}}\) is the pipe heat loss, \(W/m^{2}\); and \(A\) is the area of SF, m\({}^{2}\). \(\dot{m}_{\text{HTT}}\) is the mass flow of HTF; \(h_{\text{in}}\) and \(h_{\text{out}}\) are the specific enthalpies of the HTF inlet and outlet of the receiver, respectively. \\ \cline{1-1}  & \(\dot{m}_{\text{act}}\) is the actual mass flow of steam, \(\dot{m}_{\text{ref}}\) is the reference mass flow of steam in design condition, \(\eta_{\text{red}}\) is the deviation proportion of steam turbine efficiency compared to that in design condition, and \(\eta_{\text{ref}}\) is the reference steam turbine efficiency in design condition. More detailed data can be found in [33]. \\ \hline \hline \end{tabular}
\end{table}
Table 2: The modeling formula of the subsystem (Symbols as shown in Nomenclature).