Internal Resistance of a Source

Definition:

The resistance within a battery, or other voltage source, that causes a drop in the source voltage

when there is a current .

Lecture 3

The battery internal resistance

=

𝑉 𝐿=𝑉 𝑡=𝑉 𝑛𝑙− ( 𝐼𝐿×𝑟 )= 𝐼𝐿×𝑅𝐿

Maximum Power Transfer Theorem

𝜀=𝑉 𝑛𝑙

𝑅𝑖𝑛𝑡

𝑻𝒉𝒆𝒎𝒂𝒙𝒊𝒎𝒖𝒎𝒑𝒐𝒘𝒆𝒓 𝒕𝒓𝒂𝒏𝒔𝒇𝒆𝒓 𝒕𝒉𝒆𝒐𝒓𝒆𝒎 𝒔𝒕𝒂𝒕𝒆𝒔𝒕𝒉𝒂𝒕 :

𝜀=𝑉 𝑛𝑙

𝑅𝑖𝑛𝑡

𝜀=𝑉 𝑛𝑙

𝑅𝑖𝑛𝑡

It is clear that . If the load power calculated for a range of variation of load resistance from 0.1 Ω to 30 Ω, and plotted as shown in the figure , then this will lead to a certain conclusion.

This table represents the values of the output power, the load current and load voltage

This plot shows the load power as a function of load resistance

This plot shows the variation of load voltage and current with load resistance

The plotted results shows that the maximum load power occurs when the load resistance equal to the internal resistance. Also, it shows that the variation in power is very steep when . This can be verified due to the steep change in load voltage and load current in the same region. Since:

=Where is the power dissipated inside the source due to its internal resistance, then:

This equation means when , tends to . But in this case the power in the circuit will be very small, as shown in the proceeding slide.

This plot shows the truth that when , tends to , While the following relation show the reduction in output power at this case.

𝑃𝑠=𝑉 𝑛𝑙× 𝐼 𝐿

𝑃 (W )

𝑅𝐿=𝑅 𝑖𝑛𝑡=9Ω

𝑃 𝐿𝑚𝑎𝑥

𝑃 𝐿

𝑅𝐿 (Ω )𝑅𝐿=𝑅 𝑖𝑛𝑡=9Ω

This leads to the fact that the best operating condition is that, when the load resistance equal to the internal resistance of the source, form the view point of maximum power transfer from source to load.

New and Renewable Energy Sources

Photovoltaic Panel(PV) Panel

And Wind Energy

The Solar Energy• The Photovoltaic Panel is no more than an energy transducer. It has an ability

to generate electric energy from solar energy. It is one of the renewable energy sources. It is cheap, clean and available.

• The most important property to be considered, is that “it has a non-linear internal resistance”. This property is shown in the figures below:

• The V/I characteristics shows that this source has a nonlinear internal resistance as compared with that of the battery. Then its output power has a maximum value at one point only as shown in the P/V characteristics shown above.

PV Array characteristics at different irradiation levels

Note: Such a source needs special arrangements in order to achieve the maximum power point. This is done by changing the value of the input load resistance continuously in order to follow the source internal resistance.