According to the PV output volt-ampere characteristic curve, there must be dP/dV=0 at the maximum power point, where P is the PV output power and V is the output voltage. As a solar energy battery, its output power P=IV, where I is the output current. Through derivation, it can be considered that at the maximum power point, the following formula holds:

Therefore, the increment of admittance can determine whether the maximum power point has been reached, at which point the perturbation of the operating point is stopped. This avoids oscillations around the maximum power point (MPP) and enables fast tracking. If the condition does not hold, the direction of MPPT operating point disturbance can be calculated by the relationship between dI/dV and -I/V. There are two situations when photovoltaic cell output changes:

(1) assuming that external conditions such as light and heat do not change, the relationship between photovoltaic output voltage and current changes on the same characteristic curve due to the change of load impedance, and both voltage and current change at this time;

(2) When the external conditions change, the relationship between photovoltaic output voltage and current changes to another characteristic curve, photovoltaic output voltage (or current) may be unchanged, but only the current (or voltage) changes. Therefore, V (k) -V (k-1) is first used to judge. If its value is equal to zero, it means that the output characteristic is unchanged or has been transferred to another characteristic curve. At this time, as the voltage remains unchanged, the direction of power change can be determined only by detecting the current change. If the current is unchanged, the output characteristics of the system are unchanged. At this time, the duty cycle remains unchanged. If the current increases, the operating point of the system moves toward the maximum power point. At this time, the duty cycle should be increased to further increase the current. Otherwise, the duty cycle will be reduced if the current decreases. When V (k) -V (k-1) is not equal to zero, the conditions of the above formula can be used to determine whether the operating point falls on the left or right side of the maximum power point, and then the value of duty cycle can be adjusted accordingly.Theoretically, the proposed method can finally run stably at the maximum power point, but in digital processing, due to the existence of sampling time, the operating point may fluctuate around the maximum power point. The shorter the sampling time, the smaller the fluctuation. However, due to the problem of digital processing data accuracy, the fluctuation caused by sampling time is offset in a certain range of data accuracy, and the conditions of the above formula may still be satisfied numerically, and the system works stably at the maximum power point.

Because the external conditions and load conditions often change, DC/DC converter is usually used to balance the power and load impedance in order to achieve the maximum power output of photovoltaic cells. Although BUCK circuit is more efficient than BOOST circuit, the output voltage of photovoltaic cells is generally low (12V or 24V), and most loads need to work at higher voltage levels, so the BOOST circuit with voltage boosting function is more often used as the maximum power tracker of photovoltaic power generation system. When the photovoltaic cell is connected to the BOOST conversion circuit, considering that the output load of the BOOST circuit is still pure resistance, and according to the conversion principle of the BOOST circuit to the impedance, the equivalent input impedance of the BOOST circuit can be expressed as (8-2) :

Where, RB is equivalent input impedance of BOOST circuit; D is the duty cycle of switch; R ‘l is the load impedance. In this equation, the resistance of the BOOST inductor itself is not considered, and the polarity of the equivalent resistance is not considered.

According to Equation (8-2), the larger the switching duty cycle, the smaller the input impedance of the BOOST circuit. When the switching duty cycle of the BOOST circuit is changed so that its equivalent input impedance matches the photovoltaic output impedance, the photovoltaic cell will output the maximum power, which is also the theoretical basis for using the BOOST circuit to realize the maximum power tracking.