*3.1. Energy Balance*

.

The net rate of heat input to the ISCC ( *QISCC*,*in*) is given by

.

$$
\dot{Q}\_{l\text{SCC},in} = \dot{Q}\_{fuel} + \dot{Q}\_{inc} \tag{1}
$$

.

where *Qf uel* is the rate of heat addition to the ISCC from the fuel combustion and *Qinc* is the absorbed incident solar radiation. The heat from the fuel combustion ( . *Qf uel*) as a function of the fuel flow rate ( .*mf uel*) and the fuel heating value (*Hv*) is given by

$$Q\_{fuel} = \dot{m}\_{fuel} \ast H\_v \tag{2}$$

and the heat from the absorbed incident solar radiation ( *Qinc*) as a function of the direct normal insolation (*DNI*), incidence angle (θ), incidence angle modifier (*IAM*), and solar collectors' aperture area (*Amirrors*) is given by

$$Q\_{\rm inc} = DNI \* \cos\theta \* IAM \* A\_{\rm micror}.\tag{3}$$

.

Here, the incidence angle modifier (*IAM*) is the correlation of the losses from the collectors due to additional reflection and absorption by the glass envelope, and it can be calculated as follows:

$$IAM = 1 + \frac{0.000884 \ast \theta}{\cos \theta} - \frac{0.00005369 \ast \theta^2}{\cos \theta} \tag{4}$$

and the solar collectors' aperture area (*Amirrors*) is calculated from the number of solar field collectors (*Ncollectors*) and the width (*Wcollector*) and length (*Lcollector*) of the collectors as follows:

$$A\_{\rm micro} = N\_{\rm collector} \ast \mathcal{W}\_{\rm collector} \ast L\_{\rm collector} \tag{5}$$

The electric power output of the ISCC ( *Welec*,*ISCC*) is equal to the sum of the electric power outputs of the gas turbine ( . *Welec*,*GT*) and the steam turbine ( . *Welec*,*ST*) as follows:

.

.

$$
\dot{\mathcal{W}}\_{\text{clc,JSCC}} = \dot{\mathcal{W}}\_{\text{clc,GT}} + \dot{\mathcal{W}}\_{\text{clc,ST}} \tag{6}
$$

As a result, the overall first law efficiency of the ISCC power plant is

$$\eta\_{I,cylc\&} = \frac{\mathcal{W}\_{\text{clear},ISCC}}{\dot{Q}\_{ISCC,in}} \tag{7}$$
