*5.3. Objective Function*

The aim the study is to obtain an integrated system with the minimum total annual cost (TAC). As presented in the objective function of Equation (53), the TAC equals the total economic cost minus the profit from selling power. Economic cost is composed by the capital cost for exchangers, turbine, boiler, and the operating cost for fuel and cold utility consumption. The exchangers are assessed in general form *CF* + *CE* <sup>×</sup> *A*β, in which *CF*, *CE* and <sup>β</sup> denote the fixed charge of heat exchanger, coefficient of area cost and exponent for area cost, respectively. *lheatcondenser* is latent heat of exhaust steam from turbine end. The costs of turbine, boiler and fuel are obtained according to Equations (50)–(52). The quantities of consumed cold utility and generated power are determined by Equations (38) and (49), then the corresponding cost and profit are calculated by multiplying the unit prices *Ccu* and *Cpow*:

$$\begin{split} \text{minTAC} &= \sum\_{i} \left( \text{CF}\_{\text{LU},i} \times \text{zcu}\_{i} \right) + \sum\_{i} \sum\_{j} \sum\_{k} \left( \text{CF}\_{i,j,k} \times \text{z}\_{i,j,k} \right) + \sum\_{j} \sum\_{n} \left( \text{CF}\_{\text{bus},j} \times \text{zdu}\_{j,0,n} \right) \\ &+ \sum\_{j} \sum\_{k} \sum\_{n} \left( \text{CF}\_{\text{bus},j} \times \left( \text{zbus}\_{j,k,n} + \text{zbu}\_{j,k,n} \right) \right) + \sum\_{i} \left( \text{CE}\_{\text{coll},i} \times \text{Acu}\_{i}^{\text{\\$}} \right) \\ &+ \sum\_{i} \sum\_{j} \sum\_{k} \left( \text{CE}\_{i,j,k} \times \text{A}\_{i,j,k}^{\text{\\$}} \right) + \sum\_{j} \sum\_{u} \left( \text{CE}\_{\text{lu},j} \times \text{Adu}\_{j,0,u}^{\text{\\$}} \right) + \sum\_{j} \sum\_{u} \left( \text{CE}\_{\text{lu},j} \times \left( \text{Adu}\_{j,k}^{\text{\\$}} + \text{Adu}\_{j,k,u}^{\text{\\$}} \right) \right) \\ &+ \mathbb{C}\_{uu} \times \left( \sum\_{j} \text{q} c\_{j} + m\_{\text{cell}} \times \text{heat}\_{\text{condenser}} \right) + \mathbb{C}\_{fud} + \text{C}\_{\text{tor}} + \text{C}\_{\text{bol}} - \text{C}\_{\text{pw}} \times \text{w}^{\text{total}} \end{split} \tag{53}$$
