# Economic Energy Allocation of Conventional and Large-Scale PV Power Plants
## 2 Research Method  
Low economic efficiency is one of the main arguments against renewable energy sources. Therefore, economic efficiency is a crucial aspect of renewable energy project planning. Electricity distribution companies seek to reduce the total cost and achieve the highest profit through the optimal electricity allocation between the different power plants, as shown in the following objective Function (1):  
Minimize the total energy purchase cost (C),  
\[\sum_{\text{p}=1}^{\text{CP}}\text{CC}_{\text{p}}\text{EC}_{\text{p}}+\sum_{ \text{v}=1}^{\text{PV}}\text{CV}_{\text{v}}\text{EV}_{\text{v}} \tag{1}\]  
where:  
\(\text{CC}_{\text{p}}\): the unit cost of purchased energy from conventional plant p, \(\forall\text{p}\in\text{CP}\)  
\(\text{EC}_{\text{p}}\): purchased energy from conventional plant p, \(\forall\text{p}\in\text{CP}\)  
\(\text{CV}_{\text{v}}\): unit cost of purchased energy from PV plant v, \(\forall\text{v}\in\text{PV}\)  
\(\text{EV}_{\text{v}}\): purchased energy from PV plant p, \(\forall\text{v}\in\text{PV}\)  
\(\text{CP}\): a set of conventional power plants, indexed by p  
\(\text{PV}\): a set of PV power plants, indexed by v  
The unit cost is the summation of capital recovery, operation and maintenance (O & M), and gas consumption costs. The constraints are:  
1. Annual energy demand (D) has to be met by the generation from the different power plants during the whole year. \[\sum_{\text{p}=1}^{\text{CP}}\text{EC}_{\text{p}}+\sum_{\text{v}=1}^{\text{PV} }\text{EV}_{\text{v}}\ \geq\ \text{D}\] (2) This constraint will be an input to the proposed model. 2. Transmission lines (TL) limits: Each network consists of many transmission lines to transfer the generated energy from the power plants to consumers. Sometimes, maintenance activities or tripping incidents will restrict the power flow, and not all power will be evacuated. The power transfer on the transmission lines must not exceed the transmission lines' maximum power transfer limits. \[\text{PF}_{1}\ \leq\ \text{CPF}_{\text{1}}\ \forall\ \mathbb{I}\ \in\ \text{TL}\] (3) where: \(\text{PF}_{\text{i}}\): load on the transmission line l, \(\forall\mathbb{I}\in\text{TL}\)  
\(\text{CPF}_{\text{i}}\): maximum load the transmission line l can carry, \(\forall\mathbb{I}\in\text{TL}\)  
\(\text{TL}\): a set of transmission lines, indexed by l  
Therefore, transmission lines-limit affect the power stations' evacuation. As a result, this constraint will be used as a percentage of the power stations' maximum capacities, as shown in (4) and (5). \[\text{EC}_{\text{p}}\ \leq\ \text{EP}.\ \text{ECP}_{\text{p}}\ \ \ \ \ \forall\text{p}\ \in\ \text{CP} \tag{4}\]  
\[\text{EV}_{\text{v}}\ \leq\ \text{EP}.\ \text{ECV}_{\text{v}}\ \ \ \ \ \ \forall\text{v}\ \in\ \text{PV} \tag{5}\]  
where:  
EP: evacuation factor: a factor that defines the maximum evacuation energy  
\(\text{ECP}_{\text{p}}\): maximum annual energy capacity of conventional plant p, \(\forall\text{p}\in\text{CP}\)  
\(\text{ECV}_{\text{v}}\): maximum annual energy capacity of PV plant v, \(\forall\text{v}\in\text{PV}\)
3. Water demand (WD): cogeneration (combined-cycle or combined heat and power) is the concept of generating electricity and heat or steam for water desalination. Conventional power plants have both turbines and water distillers. The turbines and distillers are connected in a combined cycle. In order to produce water, it is required to generate steam amount from the side of the turbine. However, due to the country's requirements, sometimes the power companies require electricity only. In this case, there will be no water distillers. As a result, the electricity distributors attempt to meet the consumers' water demand with the best energy allocation to the power plants. Usually, power plants need a minimum amount of energy to produce the requiredheat in order to meet the water demand. Therefore, this constraint will be expressed as a percentage from the power stations' maximum capacities, as shown in (6) and (7).