*5.2. Constraints for the Utility System*

The utility system consists of a boiler, turbine and deaerator. Steam at different pressure levels is extracted from the turbine as a utility. Equation (44) presents the required heat load of steam *n*, *qsteamn*, equaling to that consumed in inter-stage steam-steam exchanges and inner-stage steam-steam exchanges. The mass flow is deduced from Equation (45), wherein *lheatn* is the latent heat of saturated steam *n*:

$$qsteam\_n = \sum\_j qhn\_{j,0,n} + \sum\_j \sum\_k qhn\_{j,k,n} + \sum\_j \sum\_k qhus\_{j,k,n} \tag{44}$$

$$
gamma m\_n = \text{\textit{qstear}}\_n \times \text{ahour} \times \text{\textit{3600/lleat}\_n} \tag{45}
$$

Superheated steam extracted from the turbine is desuperheated by boiler feedwater from the deaerator. Equations (46)–(48) give the mass and heat balances for this process, according to the model of Luo et al. [18]. Saturated steam is obtained after mixing superheated steam and the boiler feed water which comes from the deaerator. Equations (46) and (47) describe the mass and heat balances of this desuperheating process, wherein *enth* denotes the enthalpy of each involved stream/steam. As all condensate water of saturated steam is mixed with exhaust steam in the deaerator at the specified operating temperature of the device, the flow rate of the exhaust steam must be constrained by the balance of the deaerator as indicated in Equation (48), wherein *mext* denotes the mass flow of exhaust steam from turbine.

$$msteam\_{n} = msteam\_{suprhated,n} + mw\_{deacartor,n} \tag{46}$$

$$m\text{stam}\_n \times \text{enth}\_n = m w\_{\text{denerator},n} \times \text{enth}\_{\text{denerator},n} + m \text{stam}\_{\text{superheated},n} \times \text{enth}\_{\text{superheated},n} \tag{47}$$

$$\sum\_{n} m \text{steam}\_{n} \times \text{enth}\_{\text{condensate},n} + m\_{\text{czt}} \times \text{enth}\_{\text{czt}} = \left(\sum\_{n} m \text{steam}\_{n} + m\_{\text{czt}}\right) \times \text{enth}\_{\text{dcertator}}\tag{48}$$

Equations (49)–(52) are used to calculate economy-related factors. Equation (49) gives the power generation model of the steam turbine, wherein *msteamz* is the total mass flow through subsection *z* of the turbine, equaling the sum of the steam at lower pressure level. As shown, the quantity of generated power is determined by the enthalpy difference of the inlet and outlet superheated steam as well as the steam flow rate through each section. The costs of fuel, turbine and boiler, which are highly-related to steam distribution and power generation, are obtained through Equations (50)–(52) [15], respectively. Fuel cost is calculated in Equation (50), wherein the required heat load for generating steam from condensate to superheated state is determined by steam flow rate, *n msteam*sup*erheated*,*n*, and unit enthalpy

difference of the material in and out the boiler, *enthboil*,*out* <sup>−</sup> *enthboil*,*in* . Accordingly, the consumption of fuel can be calculated based on the heat content of fuel, *heatcap*, and boiler efficiency, *e f f boil*. As shown in Equations (51)–(52), the capital cost of the turbine is determined by the quantity of generated power and the capital cost of the boiler depends on the amount of steam generated:

$$wt^{\text{total}} = \sum\_{z} m \text{stamm}\_{z} \times (enth^{\text{in}}\_{\text{superheated},z} - enth^{\text{out}}\_{\text{superheated},z}) \times effturb/3600 \tag{49}$$

$$C\_{fuel} = \left( \left( \varepsilon \text{t} \mathbf{t}\_{\text{bvil},nt} - \varepsilon \text{t} \mathbf{t}\_{\text{bvil},in} \right) \times \sum\_{\mathbf{n}} \text{msteam}\_{\text{superhantel},\mathbf{n}} \right) \times \varepsilon \,\text{fuel} / \left( \varepsilon \text{ff} \,\text{bvil} \times \text{heatcap} \right) \tag{50}$$

$$C\_{\rm tur} = a\_{\rm tur} + b\_{\rm tur} \times wt^{\rm total} / ahour \tag{51}$$

$$C\_{b\text{oil}} = a\_{b\text{oil}} + \left(b\_{b\text{oil}} \times \left(\sum\_{n} msteam\_{\text{superheated},n} + m\_{\text{ext}}\right)\right) / ahour \tag{52}$$
