# Methods Improving Energy Efficiency of Photovoltaic Systems Operating under Partial Shading
## 3 Efficiency Estimation of PV Installation
### PV Installation with Shunt Diodes
Wherein, that with the greatest power is the global extremum, or the point of the absolute maximum (AMP), determining the maximum power take-off from PV  
Figure 3: Current-voltage characteristic of an unevenly illuminated array of solar cells (**a**) and its structural diagram (**b**) (1—solar cell; 2—shunt diode; 3—load). installations. MPP on the power characteristic of the solar cell array P(U) will be defined as the extremum of the curve \(S_{p}(U)\) drawn along the points LMP shown in Figure 4.  
\[P_{AMP}=\frac{dS_{p}(U)}{dU}=0. \tag{7}\]  
It can be seen from the figure that MPP can fall on the characteristic of any group of solar cells included in the array, depending on the radiation intensity in the shaded areas and the number of shaded elements. It follows from this that most of the algorithms for determining MPP (disturbance and observation, constant voltage (current), augmented conductivity, and others) are not able to determine the AMP in such conditions, setting the mode of electrical energy extraction located near, or the corresponding LMP, which leads to significant electrical energy losses--algorithmic losses equal to:  
\[P_{loss}^{A}=P_{AMP}-P_{LMP}, \tag{8}\]  
where \(P_{AMP}\) is the power at the point of absolute maximum (W); \(P_{LMP}\) is the local maximum power (W). The total losses of the PV array, in this case, will be equal to:  
\[P_{loss}=P_{sh}+P_{loss}^{A}+P_{d}=P_{sh}+P_{AMP}-P_{LMP}+P_{d}, \tag{9}\]  
where \(P_{sh}\) is the power of a group of solar cells, switched off by shunt diodes, under uniform illumination, given by the Equation (7), (W); \(P_{d}\) is the power dissipated by the shunt diodes, given by the Equation (11), (W). \[P_{sh}=IU_{sh}=I\bigg{[}\frac{(n_{m}-n_{x})(\mathrm{A}kT)}{q}In\bigg{(}\frac{I _{ph}}{I_{0}}-\frac{I}{I_{0}}+1\bigg{)}-(n_{m}-n_{x})IR_{s}\bigg{]}, \tag{10}\]  
\[P_{d}=IU_{d}p=IU_{d}\bigg{(}\frac{n_{m}-n_{1}}{z}\bigg{)}. \tag{11}\]  
If the MPPT is correctly determined by the controller of the maximum power point, the losses will be equal to:  
\[P_{loss}=P_{sh}+P_{d}. \tag{12}\]  
It should also be noted that the shunting of partially shaded PV modules with diodes can lead to an even more significant limitation of the power generation of a PV installation. The reason for this is that the input voltage range of the inverter may be higher than the voltage range near the point of maximum power of the PV installation, as a result of which  
Figure 4: Power characteristic of an unevenly illuminated array of solar cells. the energy extraction from them will be carried out in a sub-optimal mode or not at all due to the impossibility of turning on the inverter. Based on this, it can be summarized that the use of shunt diodes is a prerequisite for the reliable operation of PV installations, but they are not able to solve all the problems that arise in conditions of uneven illumination. Such problems include:  
* shutdown of a sufficiently large group of solar cells (having partial or complete shading), despite the fact that they are almost always still capable of generating electrical energy;
* decreasing the voltage at the point of maximum power of the entire array of solar cells, which leads to a significant decrease in its energy efficiency when arrays are connected in parallel or when using an inverter with an input voltage range value exceeding this value.