# Assessment of the Impacts of Climate Change on Power Systems: The Italian Case Study
## 1 Introduction
### Generation and Demand Models
#### 2.2.3 Thermoelectric Power Modelling  
Several studies have demonstrated that droughts and hotter water and air temperatures caused by climate warming will reduce thermoelectric plant efficiency by 0.12\(-\)0.45% for each 1 \({}^{\circ}\)C of warming [24]. The reasons of this strong impact are several, and change depending on the cooling system technology selected. Figure 1 shows two main cooling system technologies of power plants: the once-through system and the recirculating system. Both simple steam Rankine cycle and the combined Rankine/Brayton cycles of steam cycle can have either type of cooling system. The efficiency and useful power output of gas turbines depend on the ambient temperature. Considering that average air temperatures are expected to increase due to global warming, it is reasonable to consider the effects of air temperature on efficiency and useful power output of the gas turbine. The International Standards Organization (ISO) sets the reference conditions for air temperature and pressure at 15 \({}^{\circ}\)C and 1.013 bar. Considering the efficiency of the gas turbine at ISO conditions \(\eta_{GT,X}\) and the useful power of the gas turbine at ISO conditions \(P_{GT,X}\), two empirical relationships can be given [25]:  
\[\eta_{GT}=\eta_{GT,X}-(0.1)\Delta T_{a} \tag{7}\]  
where:  
\(\eta_{GT}\) is the predicted efficiency of the gas turbine at an ambient temperature that differs from the ISO conditions by \(\Delta T_{a}\) (1);  
\(\eta_{GT,X}\) is the efficiency of the gas turbine at ISO conditions (1);  
\(\Delta T_{a}\) indicates the temperature difference from the ISO condition of 15 \({}^{\circ}\)C (\({}^{\circ}\)C). \[P_{GT}=P_{GT,X}-(1.47)\Delta T_{a} \tag{8}\]  
where:  
\(P_{GT}\) is the predicted power output of the gas turbine at an ambient temperature that differs by \(\Delta T_{a}\) from the condition ISO (W);  
\(P_{GT,X}\) is the useful power of the gas turbine at ISO conditions (W). Considering these equations, it can be said that for every 1 \({}^{\circ}\)C increase in ambient temperature from the temperature specified in the standards of ISO, the gas turbine efficiency decreased by 0.1%, while the useful power output decreased by 1.47 MW [25]. To evaluate the impact of climate change on steam gas turbine, a model of the power plant efficiency as a function of ambient variables must be used. In [24], a least squares model (GLS), based on numerical regression, for the hourly efficiency was used where the variables were: hourly plant capacity factor \(C_{f}\) (%), ramp rate \(\Delta C_{f}\) (%), and either water temperature \(T_{w}\) (\({}^{\circ}\)C) and dry-bulb air temperature \(T_{db}\) (\({}^{\circ}\)C) for once-through plants, or simply wet-bulb air temperature \(T_{wb}\) (\({}^{\circ}\)C) for recirculating plants. Air temperature was included too, due to the potential impacts from ambient air drawn into the boiler. The error term \(\varepsilon\) contained the autocorrelation and white noise error of the model. For open-loop thermoelectric plants, the increase in temperature due to global warming will lead to a reduction of cooling water availability and an increase in coolant temperatures. The latter effect impacts the open-loop power plant efficiencies because hotter waters remove less heat from the plants' steam cycle. Wet-bulb air temperature has not been included in the open-loop model because research suggests that the effect of humidity on boiler efficiency is minimal [26]. Figure 1: Cooling system technology of power plants: (**a**) the once-through cooling system, (**b**) the recirculating cooling system. Either type of steam cycle can have either type of cooling system. Blue arrows indicate cold fluid flow and red hot/warm fluid flow. The hourly efficiency of a once-through plant is expressed as:  
\[\eta_{\text{open}}=a+b\Big{(}C_{f}\Big{)}^{\text{f}}+c\Delta C_{f}+dT_{w}+ \varepsilon T_{db}+\varepsilon \tag{9}\]  
where \(a\) [%], \(b\) [%], \(c\) [h], \(d\) [%/\({}^{\circ}\)C], \(e\) [%/\({}^{\circ}\)C],\(f\) (unitless) are constant coefficients.