# Economic Energy Allocation of Conventional and Large-Scale PV Power Plants
## 2 Research Method
\[\text{EC}_{\text{P}}\;\geq\;\text{WP.}\;\text{EC}_{\text{P}}\qquad \forall\text{p}\;\in\;\text{CP} \tag{6}\] \[\text{EV}_{\text{v}}\;\geq\;\text{WP.}\;\text{ECV}_{\text{v}}\qquad \forall\text{v}\;\in\;\text{PV} \tag{7}\]  
WP: water factor: a factor that defines the minimum energy needed to meet water demand  
The minimum amount of energy required for water production is considered a must-run generation. * Maximum energy generation from the conventional or PV power plants: the maximum energy generation from a power plant can be considered to run with its full capacity throughout the year, as shown in (8) and (9). \[\text{EC}_{\text{P}}\;\leq\text{EC}_{\text{P}}\qquad\qquad\forall\text{p}\;\in \;\text{CP}\] (8) \[\text{EV}_{\text{v}}\;\leq\text{ECV}_{\text{v}}\qquad\qquad \forall\text{v}\;\in\;\text{PV}\] (9)  
For example, if the power plant capacity is 500 MW, then the maximum energy generated is expressed as follows:  
\[\text{Maximum energy}=(\text{Full Capacity}\;(\text{FC}))*(\text{hours in a year})=(500)*(8760)=4380\;\text{GWHr}\]
* Minimum-take energy (MTE): the power plant investors pay much money to build and operate the plants and take many operating risks. Therefore, to ensure they can profit from these projects, they add a minimum-take energy concept to the contracts. This amount also is called a take-or-pay (TOP) amount. A take-or-pay contract is common in the energy sector, where the overhead costs are high. The buyers guarantee to take an agreed minimum portion of goods during a specific period. In this type of contract, the risk is shared between the buyers and sellers. \[\sum_{\text{p}=1}^{\text{CP}}\text{EC}_{\text{p}}+\sum_{\text{v}=1}^{\text{PV} }\text{EV}_{\text{v}}\ \geq\ \text{D}\]0 (10) \[\sum_{\text{p}=1}^{\text{CP}}\text{EC}_{\text{p}}+\sum_{\text{v}=1}^{\text{PV} }\text{EV}_{\text{v}}\ \geq\ \text{D}\]1 (11) \[\sum_{\text{p}=1}^{\text{CP}}\text{EC}_{\text{p}}+\sum_{\text{v}=1}^{\text{PV} }\text{EV}_{\text{v}}\ \geq\ \text{D}\]2 \[\sum_{\text{p}=1}^{\text{CP}}\text{EC}_{\text{p}}+\sum_{\text{v}=1}^{\text{PV} }\text{EV}_{\text{v}}\ \geq\ \text{D}\]3  
Many optimization methods such as linear programming (LP), stochastic programming, genetic algorithms, and neural networks [18; 19] can solve the aforementioned problem. LP is a commonly-used optimization method where the objective function is linear, and the constraints are specified using only linear equalities and inequalities [20; 21]. If the electricity distributor did not reach the MTE amount through the specific period, the cost of the minimum-take energy would be paid to the power plant. As a result, it is a loss for the electricity distributor, and it has to be avoided. Figure 1 is an example to demonstrate the MTE concept for eight power plants (A to H). The blue part represents the MTE amount for each power plant as a percentage of the total generated energy. The orange bars represent the remaining amount of the total generated energy. The percentages are different based on the contracts between the power distributor and power plants. The first four constraints will be considered hard constraints, whereas the last constraint will be considered the soft one. The decision variables are the energy amounts allocated to the conventional and PV power plants. Moreover, there are two essential parameters: unit rate and heat rate, which need to be considered. The electricity distributors purchase the energy from different power plants with different cost rates as per the contracts. As a result, the electricity distributors aim to meet their consumers' demands at the cheapest cost. The energy rate includes capital recovery, operation and maintenance (O & M), and gas consumption costs. In addition, heat rate is the amount of fuel required to generate one unit of electricity. It is a term commonly used in power stations to indicate power plant efficiency. The heat rate is the inverse of the efficiency, and a lower heat rate is better.