# Methods Improving Energy Efficiency of Photovoltaic Systems Operating under Partial Shading
## 3 Efficiency Estimation of PV Installation
### PV Installation with Individual Matching Converters and Micro-Inverters  
In order to solve the first and partly the second problem, recently, individual matching converters and micro-inverters installed on each (in some cases up to two) PV module have begun to be widely used [31; 32; 33; 34]. These devices set the selection of electrical energy to the point of maximum power for each module individually, which allows you to receive more energy from solar installations operating in uneven lighting conditions. Their use makes it possible to install modules on almost any plane or site, making the most of the entire available area. The advantages of such devices can also be attributed to the fact that most of them have a remote monitoring function, which allows you to monitor the performance of each module, as well as to analyze the main electrical parameters. The outputs of individual matching converters are connected in a series (Figure 5a), which makes it possible to easily implement them in already built solar power plants. Switching of micro-inverters is carried out by means of their parallel connection (Figure 5b), which complicates their implementation at the constructed stations. The world leader in the production and implementation of individual matching converters (IMC) is the company \"Tigo Energy.\" The principle of their operation is based on the use of DC/DC SEPIC converters with an automatic control system that sets the mode of taking electrical energy from the module at the maximum power point, with a current value equal to the current of the entire battery at the maximum power point. This means that in the event of shadowing of one of the modules, the converter reduces the value of the output voltage, increasing the output current. Thus, the module is not switched off by shunt diodes, and it continues to generate electrical energy, albeit at a reduced power in comparison with other series-connected non-shaded modules. As a result, \(P_{d}\) is excluded from the calculation of losses, and \(P_{sh}\) is reduced by the amount of power \(P_{IMC}\). Thus, the power loss of a PV installation will be equal to:  
\[P_{loss}=P_{sh}-P_{IMC}. \tag{13}\]  
Figure 5: Switching of individual matching converters (**a**) and micro-inverters (**b**). Power \(P_{IMC}\) will be equal to:  
\[P_{IMC}=I\sum_{i=1}^{p}U_{IMC\ i}, \tag{14}\]  
where \(U_{IMC}\) is the voltage at the output of an individual matching converter, (V), equal to:  
\[U_{IMC}=\frac{U_{IMC}^{in}I_{IMC}^{in}}{I}\eta_{IMC}, \tag{15}\]  
where \(U_{IMC}^{in}\) is the voltage at the input of an individual matching converter (V); \(I_{IMC}^{in}\) is the input current of the individual matching converter (A); \(\eta_{IMC}\) is the efficiency of an individual matching converter. From relations (14) and (15) it follows that for any values of the current \(I\) array, the output power of the individual matching converter is constant, which is confirmed by its output current-voltage characteristic \(U_{IMC}(I)\), shown in Figure 6:  
\[P_{IMC}=\sum_{i}^{p}\left(U_{IMC}^{in}I_{IMC}^{in}\eta_{IMC}\right)_{i}=I\cdot \sum_{i=1}^{p}U_{IMC\ i}=const. \tag{16}\]  
From the characteristics, it is seen that the current (\(I\)) can take values both above and below the current value at the point of maximum power of the characteristic of a group of solar cells connected to the input of an individual matching converter. Thus, at any value of the array current, the current at the output of the individual matching converter (\(I_{IMC}\)) is able to take on the same meaning \(I\)=\(I_{IMC}\). Hence, when the solar cells group with such a converter, it is capable of transmitting electrical energy under any illumination, whether it be shading, pollution, or increased illumination (for example, when working in conjunction with solar concentrators).