 # Maximum Power Transfer Theorem

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According to maximum power transfer theorem, power delivered by the source to the load is maximum when the internal source impedance is approximately equal to the load impedance . The output power of the PV panel is variable according to the solar irradiance and temperature as shown in Figure 4.7. Therefore, internal impedance of the PV panel is also variable according to variation in solar irradiance and temperature.

Figure 4.7 Characteristic of PV panel at variable solar irradiance
According to maximum power transfer theorem, to obtain maximum external power from a source with a finite internal resistance, the resistance of the load must equal the resistance of the source as viewed from its output terminals. In order to achieve the maximum power from the PV panels, the PV
The power consumption by the load is given as
The VPV and Ri are constant, then Consider = 0, then . Hence load can achieve maximum power when Ri = Ro.
The above explained simple method cannot be used to get the maximum power. To achieve the goal boost converter is used, which is shown in the Figure 4.9.

Figure 4.9 Circuit diagram of boost converter employed in PV system
The analysis is performed under the ideal condition. It is assumed that the load is pure resistive and impedance of the boost converter is neglected. The time period and duty cycle of the boost converter are denoted as D and T respectively.
When the IGBT switch is in ON state, the output voltage is: Vpv. D.T;
When the IGBT switch is in OFF state, the output voltage is: —(Vo- V p v). (1 — D). T;
As it is assumed that LB is pure inductor, the voltage across the inductor is zero. Therefore, the total output voltage is zero. Hence, (4.12)
The eq. (4.12) can also be written as: (4.13)
Eq. (4.13) gives the relation between output and input as Under the ideal condition, the boost converter will be lossless. Therefore, input power is equal to output power:
PPV = Po