# A Hybridized Flower Pollination Algorithm and Its Application on Microgrid Operations Planning
## 4 Application of the HSFPA for Microgrid Operations Planning
### Multiobjective Model Construction  
The proposed HSFPA would process in the objective function of the optimization based on finding out the feasible optimization area in the problem search space. In optimization processing, the objective function is critical in moving fitness ahead to the best global result produced from mathematical modeling. The variable electricity prices for active microgrid power are optimized by the HSFPA algorithm as the period changes synchronously. We construct the optimization problem with a mathematical multi-object model based on the relevant economic costs and environmental profits of a power activities microgrid system with a scheduling cycle. The goal function of microgrid optimization operations is a mathematical model developed using the microgrid's minimum economic costs and the environmental pollution control's minimum costs as follows:  
\[min\ F=\sum_{t=1}^{T}(F_{1}(t),F_{2}(t)), \tag{24}\]  
where \(F\) is the multiobjective function for relevant total costs of microgrid-connected operations; \(F_{1}\) and \(F_{2}\) are the economic and environmental costs of power generation, and \(T\) is the scheduling period \(t\), the multiobjective function subject to the constraints as  
Figure 4: Comparative curves of the evaluated performance of the proposed HSFPA with the FPA, MFPA, and PSO algorithms for the testing function of F3, F4, F5, F7, F11, F12 as in subfigures: (a–f), respectively. mentioned in Section 2.1. Time interval and period use can be a year, month, day, or hour determined by the power supply outputs. The daily load curve's unit and the generating plants' output curve's period, such as 24 h, are used, and the same with 12 months for a year and four seasons. The economic costs of the microgrid power generation are, e.g., operation and maintenance costs of micropower sources for gas, wind, solar turbines, and generators connected to the main grid power. The first objective function is modeled by calculating summarized economic costs of the ES, WT, FC, MT, PV, and EX operations. Each power source component's expense, as mentioned in Section 2.1, is subject to its constraints. For example, the cost of WT is shown in Equation (3) is subject to Equation (4) constraints, and the other expenses of FC, MT, PV, and EX are subject to Equations (8)-(10) constraints. The first objective function \(F_{1}\) is formulated as follows:  
\[F_{1}(t)=\sum_{t=1}^{T}[\alpha_{ES}C_{ES}(t)+\alpha_{WT}C_{WT}(t)+\alpha_{FC}C_ {FC}(t)+\alpha_{MT}C_{MT}(t)+\alpha_{PV}C_{PV}(t)+\mu\alpha_{EX}C_{EX}(t)], \tag{25}\]  
where \(C_{i}(t)\) are relevant operations costs of (\(i\)-th is set of the \(ES\), \(WT\), \(FC\), \(MT\), \(PV\), \(EX\)); \(\alpha_{i}\) are the unit prices of some kinds of operations, e.g., maintaining, investing, depreciating, and interactive power with the grid in the period \(t\), respectively; \(\mu\) is a parameter if it is set 1, it means a state of grid-connected operation; otherwise, it is an off-grid operation. The variables, sets, and the bounds of the optimization constrained are set specified in the experimental section  
Another function of the object is the environmental costs that are a conversion processing development effected around envirement. The related costs operation parameters are considered with each treatment and the emission coefficients of various pollutants at using period point prices. The cost of treating pollutants discharged \(F_{2}\) with expression is calculated as follows:  
\[F_{2}=\sum_{t=1}^{T}\sum_{k=1}^{K}b_{k}\left(\sum_{i=1}^{N}a_{i,k}\cdot P_{i} \right), \tag{26}\]  
where \(b_{k}\) and \(a_{i,k}\) are the treatment cost and coefficient of class \(K\) pollutants discharged, \(\$/\)kg; \(P_{i}\) is the \(i\)-th distributed power source, g/KWh; \(K\) is the serial number of pollutants [7]. The variable \(P_{i}\) is the distributed power source that is an influential factor for optimal results.