## 3 Chance-Constraint Two-Stage Stochastic Unit Commitment  
### Uncertainty of Renewables  
In this section, renewable energy scenarios are generated for the stochastic UC program. In this paper, s represents the index of second-stage scenario from 1 to \(N_{s}\). The time interval \(t\) is set a 1 h. Wind generation fluctuation (\(w_{w,t,s}^{WIND,fore}\)), PV generation fluctuation (\(v_{v,t,s}^{PV,fore}\)) and solar power fluctuation in SF of CSP station (\(q_{c,t,s}^{SF,fore}\)) are considered as random functions. In this paper, the point forecast of load is generally hypothesized to be accurate, in other words, the uncertainty of load is ignored. The point forecast of load is \(L_{n,t}^{0}\). Probabilistic forecasting is the widely used method to provide the inherent uncertainty of renewables [29]. For a given point forecast of renewable energy, probability distribution functions are necessary to gain the future realization of renewables [30]. Currently, much previous research concerns the probability distribution functions, involving Gaussian distribution function [31], Beta distribution function [32; 33] and truncated normal distribution function [34]. In this paper, network constraints are not involved in the proposed model. Therefore, because of the central limit theorem, the wind and PV production random functions could be simply described by Gaussian distributions with zero-mean Gaussian distributed errors within each time interval [21; 35]. The wind power distribution function is described as Equation (24). \[w_{w,t,s}^{WIND,fore}\sim\mathrm{N}(w_{w,t}^{WIND,0},\sigma_{w,t}^{WIND,p})=w_ {w,t}^{WIND,0}+e_{w,t,s}^{WIND,e},\ \forall t,\forall w,\forall s \tag{24}\]  
where, \(w_{w,t}^{WIND,0}\) represents the point forecast of wind power; \(e_{w,t,s}^{WIND,e}\) denotes the zero-mean Gaussian distributed forecast errors. The PV distribution function is described as Equation (25). \[v_{v,t,s}^{PV,fore}\sim\mathrm{N}(v_{v,t}^{PV,0},o_{v,t}^{PV,v})=v_{v,t}^{PV,0 }+e_{v,t,s}^{PV,e},\ \forall t,\forall v,\forall s \tag{25}\]  
where, \(v_{v,t}^{PV}\) represents the point forecast of PV station; \(e_{v,t,s}^{PV,e}\) denotes the zero-mean Gaussian distributed forecast errors. As for the CSP station, it is acknowledged that CSP is a partially dispatchable resource, however, in order to guarantee the credibility and stability of the results, the uncertainty of solar power in the \(SF\) section could not be simply ignored. More specifically, although the power output of the CSP station has no direct relationship with the instantaneous irritation owing to the large-capacity TES system, problems would come because the SOC of the TES system should restore to the initial state at the end of the day [3]. The storage level of TES would be affected by the uncertain DNI absorbed from the SF capsule, and would influence the power output of CSP. Therefore, it is necessary to take into account the uncertainty of solar energy received by SF in the stochastic scenarios. The CSP distribution function is described as Equation (26). \[q_{c,t,s}^{SF,fore}\sim\mathrm{N}(q_{c,t}^{SF,0},o_{c,t}^{SF,v})=q_{c,t}^{SF,0}+e_{c,t,s}^{SF,e},\ \forall t,\forall c,\forall s \tag{26}\]  
where, \(q_{c,t}^{SF,0}\) is the point forecast of thermal energy converted from solar power; \(e_{c,t,s}^{SF,e}\) denotes the zero-mean Gaussian distributed forecast errors. The net equivalent load is defined as the difference between load and the power output of wind power and PV power described in Equation (27). Equation (28) describes the mean and variance of the net equivalent load. CSP is assumed to be the controllable resource as a thermal unit. \[ \begin{array}{ll}L_{t,s}^{EQ,fore}&=\sum_{n=1}^{N_{N}}L_{n,t}^{0}-(\sum_{w=1}^{N_{ W}}w_{w,t,s}^{WIND,fore}+\sum_{v=1}^{N_{V}}v_{v,t,s}^{PV,fore}),\ \forall t,\forall s\\ &\sim\text{N}(L_{t}^{EQ,0},\sigma_{t})\end{array}  \tag{27}\]  
\[