Does Thevenin’s theorem apply in power plants

powerthevenin

I know when we analyze a circuit's Thevenin equivalent, the best we can ever get is 50% power transfer to the load. I would assume that this holds true for power plants (source) and the rest of the grid (load). I realize this is a fairly simplified view.

Anyway, I'm taking a thermodynamics class in mechanical engineering this summer and we toured a cogeneration plant on campus. I asked about this at the plant, but neither the plant manager nor my thermo professor seemed to know what I was talking about.

This graphic below was produced from data collected by the DOE at LBL. The 62 units lost in the power plant could mean imply the efficiency of a typical power plant, or be half of the current maximum of about 60% efficiency divided in half due to Thevenin. Any way, this is just speculation. I'm hoping a power engineer can weigh in?

Here's a silly graphic.

Best Answer

I know when we analyze a circuit's Thevenin equivalent, the best we can ever get is 50% power transfer to the load.

That's a misunderstanding of the maximum power transfer theorem according to which the maximum power that can be delivered to the load is 50% of the maximum power available from the source.

But that doesn't mean that the best power ratio is 50%.

For a Thevenin voltage \$V_{th}\$, Thevenin resistance \$R_{th}\$ and load resistance \$R_L\$, the power delivered to the load is

$$P_L = \frac{V^2_{th}}{\left(R_{th} + R_L \right)}\frac{R_L}{\left(R_{th} + R_L \right)}$$

which is indeed maximum when \$R_L = R_{th}\$.

However, the power developed by the Thevenin source is

$$P_{th} = \frac{V^2_{th}}{\left(R_{th} + R_L \right)}$$

and so the fraction of the source power delivered to the load is thus

$$\frac{P_L}{P_{th}} = \frac{R_L}{\left(R_{th} + R_L \right)}$$

So, for \$R_L >> R_{th}\$, almost all of the power supplied by the source is delivered to the load (though this power is much less than the maximum power available from the source).

I don't have the expertise to address the reasons for 62 units of energy lost in the power plant so this answer is just to address the proper interpretation of the maximum power transfer theorem.