# Assessment of the Impacts of Climate Change on Power Systems: The Italian Case Study
## 1 Introduction
### Generation and Demand Models
#### 2.2.1 Photovoltaic Power  
For solar energy, variations in cloud cover are one of the causes that dramatically impact the surface downwelling solar radiation. Specifically, in PV systems there is almost a linear relation between the power and the irradiance when the system works at the maximum power point (MPP) [17]. Other meteorological variables, such as wind and ambient temperature, affect the efficiency (and then the power output) of PV systems [18]. In particular, the output power is affected by cell temperature, \(T_{cell}\), whose dependence is quantitatively defined by the coefficient \(\alpha_{\text{PV}}\), that is the power temperature coefficient, whose value depends on the PV cell technology considered. For example, in monocrystalline silicon solar panels, it can range mainly between \(-0.5\) and \(-0.4\%/^{\circ}\text{C}^{-1}\) (e.g., in [13]\(\alpha_{\text{PV}}=-0.5\)). In turn, the cell temperature depends on the ambient variables (e.g., irradiance, temperature and wind speed). In [13], \(T_{cell}\) was modelled, considering the effects of the near-surface temperature (\(T_{a}\)), the 10-m wind speed (\(\
u_{10}\)), and the surface downwelling solar radiation, G [\(W/\text{m}^{2}\)] as the following:  
\[T_{cell}(t)=c_{1}+c_{2}T_{a}(t)+c_{3}\text{G}(t)+c_{4}\
u_{10}(t) \tag{1}\]  
where \(c_{1}=4.3\ ^{\circ}\text{C}\), \(c_{2}=0.943\), \(c_{3}=0.028\ ^{\circ}\text{C}\text{m}^{2}\text{W}^{-1}\) and \(c_{4}=-1.528\ ^{\circ}\text{C}\text{s}\text{m}^{-1}\) are coefficients stated empirically. Considering now the PV module efficiency, and its variation with respect to reference conditions STC (\(G_{STC}=1000\) (\(\text{W}/\text{m}^{2}\)), \(T_{cell}=25\ ^{\circ}\text{C}\), AM = 1.5), it can be expressed by an equation in which the dependency on \(G\) and \(T_{cell}\) is expressed. In this case the effect of other losses (IAM optical losses, and the Joule losses) are neglected [19]. \[\eta_{\text{el,PV}}=\gamma_{PV}\cdot\eta_{PV,STC}\cdot(1+\alpha_{PV}\cdot(T_{ cell}-T_{STC}))\cdot\Big{(}1+\beta_{PV}^{II}\cdot(G-G_{STC})\Big{)}=\gamma_{PV}\cdot \eta_{PV,STC}\cdot P_{R} \tag{2}\]  
where:  
\(\eta_{\text{el,PV}}\) is the electrical efficiency of the PV module (1);  
\(\gamma_{PV}\) is the degradation rate (1), i.e., considers the reduction of the rated power during the designed life of the PV module;  
\(\eta_{PV,STC}\) is the electrical efficiency in STC (1);  
\(\alpha_{PV}\) is the power temperature coefficient (1/\({}^{\circ}\)C);  
\(T_{cell}\) is the cell temperature (\({}^{\circ}\)C);  
\(T_{STC}\) is the temperature in standard test conditions (\({}^{\circ}\)C);  
\(\beta_{PV}^{II}\) is the solar radiation coefficient of the power at maximum power point (MPP) (1/W/m\({}^{2}\));  
\(G\) is the surface downwelling solar radiation (W/m\({}^{2}\));  
\(G_{STC}\) is the surface downwelling solar radiation at standard test conditions (W/m\({}^{2}\));  
\(P_{R}\) is the performance ratio (1). Another aspect that modifies the solar radiation is the concentration of aerosols in the atmosphere. Indeed, aerosols scatter and absorb solar radiation, modifying the shortwave radiation that reaches the PV modules [18]. Moreover, concentrations of aerosols could have a relation with climate change [20]. Therefore, climate change will also affect the absorption of solar radiation from the atmosphere, so it is worth citing another efficiency expression where the air mass (AM) is considered [19]:  
\[\eta_{\text{el,PV}}=p\cdot\bigg{(}q\cdot\frac{G}{G_{STC}}+\bigg{(}\frac{G}{G_{ STC}}\bigg{)}^{m}\bigg{)}\cdot\bigg{(}1+r\cdot\frac{T_{cell}}{T_{STC}}+s\cdot \frac{AM}{AM_{STC}}+\bigg{(}\frac{AM}{AM_{STC}}\bigg{)}^{u}\bigg{)}. \tag{3}\]  
where:  
\(p\), \(q\), \(m\), \(r\), \(s\) and \(u\) are parameters that must be determined for each type of module from a specific set of outdoor measurements;  
\(AM\) is the air mass (1);  
\(AM_{STC}\) is the air mass at STC (1). In climate change studies, future variations in PV electricity production are calculated as a function of installed capacity.