# A Hybridized Flower Pollination Algorithm and Its Application on Microgrid Operations Planning
## 2 Related Work
### Microgrid Operation Planning Statement  
The grid operation planning model is one of the most effective alternative ways can generate the service-consuming power with better quality power supply, as demand for improved power supply quality in isolated or distant places grows [2; 42]. Figure 1 displays a typical structure of a microgrid with power sources distribution. The expression balance of the system power load in period \(t\) is figured out as an equality constraint:  
\[P_{total}(t)=P_{ES}(t)+P_{WT}(t)+P_{FC}(t)+P_{MT}(t)+P_{PV}(t)+u\cdot P_{EX}(t) \tag{1}\]  
where \(P_{t}(t)\) are the components power outcomes of the energy supply system; \(i=1.2\dots\)\(n\): corresponds to the following characters: ES--Energy storage batteries; WT--Wind turbines; FC--Fuel cells; MT--Micro-gas turbines; PV--Photovoltaic power, EX--Extra grid; \(P_{total}(t)\) is the power load of the system for the period of \(t\) as times [43]. The generated operation cost of ES is assumed as charging and discharging power with a constant variable at the end of the period (\(t\)) connected to the next period at the end of the period (\(t-1\)) that allows for brief dispatching interval characteristics. The link  
Figure 1: A typical structure of a microgrid with power sources distribution. between energy storage capacity and charge-discharge power in the electric energy storage model is expressed as follows:  
\[C_{ES}(t)=(1-\tau)P_{ES}(t-1)+\left[P_{ES,dh}(t)\eta_{ES,dh}-\frac{P_{ES,dis}(t)}{ \eta_{ES,dis}}\right]\times\Delta t, \tag{2}\]  
where \(C_{ES}(t)\) is a relevant operation cost of the ES in period \(t\); \(P_{ES}(t)\), \(P_{ES,dh}(t)\), and \(P_{ES,dis}(t)\) are the power of storage capacity, charge, and discharge of the ES in period \(t\), respectively; \(\eta_{ES,dh}\), \(\eta_{ES,dis}\) are coefficients of the ES efficiency adjustment, respectively, \(t\) time; \(\tau\) is a variable rate of the energy self-discharge. The operations relevant economic costs of the WT are related to the power outcome determined [15] by the natural wind speed, primarily the output of wind turbines:  
\[C_{WT}(t)=\frac{1}{\eta_{WT}(t)}\times P_{WT}(t), \tag{3}\]  
where \(C_{WT}(t)\) and \(P_{WT}(t)\) are relevant operation costs and output power capacity of the \(WT\) in period \(t\); \(\eta_{WT}(t)\) is a converted coeffic parameter that is related to unit prices of some kinds of operations, e.g., investment, depreciation, maintenance. \(\eta_{WT}\) is set to as expression of \(0.057+0.34\left(\frac{P_{WT}(t)}{35}\right)-0.3095\left(\frac{P_{WT}(t)}{33} \right)^{2}+0.033\left(\frac{P_{WT}(t)}{33}\right)^{3}\) in the experiment section [2,44]. The output power comprises numerous factors of the wind turbine's power output connected to wind speed:  
\[P_{WT}(t)=\left\{ \begin{array}{c}0,\;0\leq v(t)<v_{ci}\\ A+B\times v(t)+C\times v(t)^{2},\;\;v_{ci}\leq v(t)\leq v_{r}\\ P_{v(t)},\;\;v_{r}\leq\;v(t)\leq v_{co}\\ 0,\;\;v_{co}<v(t)\end{array} \right., \tag{4}\]  
where \(v(t)\) is \(v_{ci}\), \(v_{r}\), and \(v_{co}\) are the wind-cut, wind-rated, and wind-cutting velocities; the \(WT\) parameters of \(A,B,C\) are coeffective of the power characteristic curve; \(P_{v(t)}\) is the rated power of the fan. The energy FC operating cost for consumption generated power during the operation [16] is expressed as follows:  
\[C_{FC}(t)=\frac{G_{price}}{L_{gas}}\times\frac{P_{FC}(t)\Delta t}{\eta_{FC}(t)}, \tag{5}\]  
where \(P_{FC}(t)\) is the output power of the fuel cell and \(\eta_{FC}(t)\) is the efficiency in the period of \(t\)[17]; \(L_{gas}\) is natural gas's low calorific value. A relationship between \(P_{FC}(t)\) and \(\eta_{FC}(t)\) of the FC power generation efficiency and outcome power is expressed as the following function of \(\eta_{FC}(t)=0.6735-0.0023\times P_{FC}(t)\)[2,44].