## 1 Introduction
The detailed configuration of grid-connected CSP station is illustrated in Figure 1.  
From the aspect of the power dispatching system, the model of CSP station could ignore the short-time dynamic process of energy exchange, and concentrate on the power flow and operation constraints among different modules [28]. Based on the operation mechanism of CSP, this paper proposes a linear steady-state dispatch model of a CSP station which is applicable for the incorporation into the dispatching system. The operating state of a grid-connected CSP station with TES and EH equipment could be reflected by mixed integer linear constraints. The simplified energy flow is illustrated in Figure 2.  
Figure 1: Configuration of a two-tank concentrating solar power (CSP) station with electrical heater (EH) equipment. From the perspective of \(HTF\), the energy flowing into a CSP station involves two main parts: thermal energy from \(SF\) (\(q_{c,t}^{SF\_HTF}\)) and thermal energy from EH (\(q_{c,t}^{ET\_HTF}\)). Correspondingly, the energy consumed by a CSP station includes thermal energy exchange of TES (\(q_{c,t}^{HTF\_TES}-q_{c,t}^{TES\_HTF}\)) and thermal energy consumption by \(PB\) (\(q_{c,t}^{HTF\_PB}\)). The possible thermal energy dissipation is the solar power curtailment in \(SF\) and the loss in charging and discharging process, which is embodied in the efficiency parameters. The power balance can be expressed by Equations (1)-(4). \[q_{c,t}^{SF\_HTF}+q_{c,t}^{EH\_HTF}=\ (q_{c,t}^{HTF\_TES}-q_{c,t}^{TES\_HTF})+q_{c,t }^{HTF\_PB}\,\forall t,\forall c \tag{1}\]  
\[q_{c,t}^{SF\_HTF}=q_{c,t}^{SF,0}-p_{c,t}^{CSP,cur}/\eta_{c}^{PB}\,\forall t,\forall c \tag{2}\]  
\[q_{c,t}^{TES\_chu}=\eta_{c,t}^{TES\_chu}q_{c,t}^{HTF\_TES}\,\forall t,\forall c \tag{3}\]  
\[q_{c,t}^{TES\_dis}=q_{c,t}^{TES\_HTF}/\eta_{c}^{TES\_dis}\,\forall t,\forall c \tag{4}\]  
where, \(q_{c,t}^{SF}\) is the point forecast of thermal power converted from solar power; \(p_{c,t}^{CSP,cur}\) represents the possible power spillage of CSP station; \(\eta_{c}^{PB}\) means the efficiency of \(PB\); \(q_{c,t}^{TES\_chu},q_{c,t}^{TES\_dis}\) stand for the actual charging and discharging thermal power of the TES system respectively; \(\eta_{c}^{TES\_chu}\), \(\eta_{c}^{TES\_dis}\) represent the charging and discharging efficiency of the TES system respectively. The TES system possesses three operating states: charging, discharging and thermal equilibrium. The thermal power balance and the upper-lower limits are given by Equations (5) and (6). Besides, during the operation day, the state of charge (SOC) of the TES system is assumed to restore to the initial state at the end of the day which is shown in Equation (7). \[E_{c,t}^{TES}=(1-\gamma_{c}^{TES})E_{c,t-1}^{TES}+(q_{c,t}^{TES\_chu}-q_{c,t} ^{TES\_dis})\Delta t\,\forall t>1\,\forall c \tag{5}\]  
\[E_{c}^{TES,+}\leq E_{c,t}^{TES}\leq E_{c}^{TES,-}\,\forall t,\forall c \tag{6}\]  
\[E_{c,t}^{TES}=E_{c,t+23}^{TES}\,t=1,\ \forall c \tag{7}\]  
where, \(E_{c,t}^{TES}\), \(E_{c,t-1}^{TES}\) represent the SOC of TES at time \(t\) and \(t-1\); Thermal energy loss is represented by parameter \(\gamma_{c}^{TES}\); \(\Delta t\) stands for the time interval; \(E_{+c}^{TES}\), \(E_{c}^{TES,-}\) show the upper-lower limits of the SOC of TES. Equations (8) and (9) set the charging and discharging rate of the TES system. When the on/off state variables of charging function (\(o_{c,t}^{TES,chu}\)) and discharging function (\(o_{c,t}^{TES,dis}\)) are equal to 1, the feasible interval of charging and discharging rate of TES system is [0, \(q_{c}^{TES,max}\)]. Figure 2.0  
Figure 2.1 Simplified energy flow in CSP station with thermal energy storage (TES) and EH. Figure 2.2  
Equations (10)-(12) describe the relationship between the on/off state variable and the starting-up variable. The charging and discharging state could not happen simultaneously, and the TES discharging would arise only if the PB on/off state variable (\(o_{c,t}^{PB}\)) is equal to 1.