## 2 System Description
### Fuzzy Logic System Description  
#### 2.4.1 Fuzzy Logic MPPT  
The fuzzy logic method is widely used in PV systems because can track changing conditions more rapidly than the perturb and observe or incremental conductance algorithm. The flow chart of the fuzzy MPPT method is illustrated in Figure 6. The main elements that construct an FLC system are the fuzzifier unit at the input terminal, the inference engine with rule base, and defuzzifier at the output terminal [20].  
The input parameters to the FLC are the voltage (\(Vpv\)) and current (\(Ipv\)) supplied by the solar panel. The output is represented by the inverter reference voltage (\(Vmpt\)). Based on the input signals in the MPPT block, the power is calculated, which is one of the input parameters of the fuzzy logic controller. To determine the second input of the block, namely the voltage variation (\(\Delta V\)), we need the current value of the voltage and its previous value. This requires the use of a delay block [21].  
The next two equations give the fuzzy logic controller inputs:  
\[Ppv=\text{I\_panel}\,\times\,\text{V\_panel}, \tag{17}\]  
\[\Delta Vpv=V(k)-V(k-1) \tag{18}\]  
Figure 7 shows the implementation of the MPPT algorithm with fuzzy logic using the components provided by the Simulink (Figure 7a) and the fuzzy designer functions [22].  
Figure 5: Simple PLL grid synchronization.  
Figure 6: The flow chart of Fuzzy Logic MPPT method.  
Figure 7: Implementation of the MPPT fuzzy: (**a**) Simulink implementation, (**b**) Fuzzy logic designer  
function, (**c**) The membership functions of input variable \(\Delta Vpv\), (**d**) The membership functions of input variable \(Ppv\), (**e**) The membership functions of output variable \(Vmppt\).  
To implement the MPPT algorithm, the fuzzy logic designer function from Figure 7b is used. The fuzzy inference technique used is [PERSON]'s approach, which is based on the max-min composition. The fuzzy database includes 49 rules expressed in terms: _\"If...Then\"_ presented in Table 1. Fuzzy block output (\(Vmppt\)) will be determined based on this table, and the composition of the rules will be as follows: the maximum power is reached at the output of the solar panel [22].  
For example, we take a given control rule from Table 1; if \(Ppv\) is PB and \(\Delta Vpv\) is ZE, then \(Vmpp\) is PM. This implies that if the operating point is far from the point (MPP) to the right and the voltage change is zero, the controller should decrease the operating ratio to reach MPP [22].  
Figure 7c,d show the membership functions of the input variables \(\Delta Vpv\) and \(Ppv\) and Figure 7e of the output variable \(Vmppt\), each having seven fuzzy subsets [22].  
The input variables \(\Delta Vpv\) and \(Ppv\) are normalized to correspond to the ranges \([-1,1]\) and \([0,150]\), and the output variable \(Vmppt\) has values in the range [34; 35][22].  
Any input value that does not correspond to the range is perceived as too high and causes signal errors. For convenience, triangular and trapezoidal membership functions are used, through which the fuzzy controller allows a rapid minimization of signal errors, ameliorating the system's transient response [23].