# 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
For closed-loop thermoelectric plants, the efficiency is more impacted by elevated ambient air temperature and humidity (characterized both by wet-bulb temperature). Both effects, indeed, reduce the condensation in cooling towers and thus the system's cooling capacity. The hourly efficiency of closed-loop plant is expressed as:  
\[\eta_{\text{closed}}=m+n\Big{(}C_{f}\Big{)}^{\text{q}}+o\Delta C_{f}+pT_{\text{ wb}}+\varepsilon \tag{10}\]  
where \(m\) [%]: \(n\) [%], \(o\) [h], \(p\) [%/\({}^{\circ}\)C], \(q\) (unitless) are constant coefficients. For closed-loop (or recirculating) plants, the temperature of the coolant is determined principally by the cooling tower, whose performance is a function of both humidity and dry-bulb air temperature. For this reason, the authors used \(T_{wb}\) for this kind of plants. Moreover, the boiler of these plants can be affected by \(T_{wb}\). Equations (9) and (10) depend on capacity factor \(C_{f}\) in turn, the capacity factor is proportional to the usable capacity. Therefore, another crucial model expresses the \(P_{usable}\) as not only a function of the \(T_{W}\) but also of the water availability \(Q\) (kg/m\({}^{3}\)), the latter depending on the actual environment and climate conditions. In [27], in order to represent the actual conditions, a cooling water scarcity factor \(\varphi\) was assumed to be the ratio of \(Q\) and \(q\), where \(q\) is the amount of cooling water required (m\({}^{3}\)/h). As \(T_{w}\) is the inlet cooling water temperature, two temperature thresholds \(T_{health}\) and \(T_{shut\_down}\) have been defined. If \(T_{w}<T_{health}\), the usable capacity \(P_{usable}\) would be determined only by \(\varphi\):  
\[P_{usable}=\min(\varphi,\ 1),\ T_{W}\leq T_{health} \tag{11}\]  
This means that \(Q\) dominates the impact on the usable capacity, until \(T_{w}\) reaches \(T_{health}\). When \(T_{w}>T_{shut\_down}\) the \(P_{usable}\) is zero. \[P_{usable}=0,\ T_{shut-down}\leq T_{W} \tag{12}\]  
When \(T_{health}<T_{w}<T_{shut\_down}\), both \(Q\) and \(T_{w}\) have an impact on usable capacity. When \(T_{out\_max}-T_{w}>\Delta T_{max}\) (where \(\Delta T_{max}\) is the allowance of the maximum temperature difference between the inlet and outlet cooling water (\({}^{\circ}\)C)), \(q\) is constant. In this way, \(P_{usable}\) depends on the relation between \(Q\) and \(q\). In order to evaluate the decrease in the usable capacity with the increase of \(T_{w}\), a linear function was proposed with a coefficient \(\lambda_{D}\), as shown below:  
\[P_{usable}=\min(\varphi,1)\cdot(1-\lambda_{D}(T_{W}-T_{health})),\ T_{health} \leq T_{W}\leq T_{outlet\_max}-\Delta T_{max} \tag{13}\]  
The impact of \(Q\) was considered by introducing the coefficient min(\(\varphi\),1) in the previous equation. If \(T_{w}\) continued to increase, \(T_{outlet\_max}-T_{w}\) would become less than \(\Delta T_{max}\), causing a significant increase of \(q\). In this situation it is assumed that \(P_{usable}\) would be affected only by an increase of \(q\). For this reason, a de-rating factor is introduced in the following equation:  
\[P_{usable}=\frac{T_{outlet\_max}-T_{W}}{\Delta T_{max}}\cdot\min(\varphi,1) \cdot(1-\lambda_{D}(T_{outlet\_max}-\Delta T_{max}-T_{health})), \tag{14}\]  
For open-loop cooling systems, the models in (11) and (14) are more appropriate because they properly consider the inlet cooling water temperature and water availability. For closed-loop/hybrid cooling systems, since the cooling water circulates in a closed loop, the loss of this water is about 2-4% of the inlet cooling water used in the open-loop cooling systems. In this sense, the water availability has negligible effect on closed-loop/hybrid cooling systems. Due to these considerations, it is possible to say that the models in (11) and (13) can be used to represent closed-loop cooling systems, assuming \(\varphi=1\), and a very high \(T_{outlet\_max}\).