Can loads absorb more power than needed/requested?

Question

I was designing the governor of a generator, implementing in Digsilent Powerfactory a 1 bus grid like that in the picture.

The generator delivers 350 MW and the 3 loads withdraw respectively 25 MW, 25 MW, and 300 MW (from left to right). All the components have a PF=0,95.

During the simulation, I simulated an opening of one load (the 25 MW one) and, at steady-state, the loads absorb more power than they need. The 300 MW absorbs 322 MW and the 25 MW absorbs 26,8 MW at steady state.

I designed the regulator to keep the output power to 350 MW as far as possible. It's silly but done more to understand the behaviour of the system and how to design properly the regulator.

My question is: if, in reality, I force a generator (whatever it is) to produce 350 MW, is it possible that loads absorb more power than they really need?

If yes, what happens to them? It is like I'm forcing to do that in my simulation but does it also happen in reality?

Answer 1

Well, it kind of depends of your generator.

The same reasoning applies to AC and DC. For simplification, let's use DC and pure resistive loads. Let's use only two of them: R1 and R2.

^{simulate this circuit – Schematic created using CircuitLab}

Case 1

Consider your generator is a Voltage source, with voltage U1, and a maximum output power P1_max (so a maximum current I1=P1_max/U1).

Then, provided the generator can supply enough power, the power consumed by R2 will be P2=U1^2/R2 and the power consumed by R3 will be P3=U1^2/R3. The power provided by the generator will be P1=P2+P3 <= P1_max.

In this case, if you disconnect one load, it will have no influence on the other load. And the generator will just generate less power. This is the desired behaviour on most electrical networks. When you turn off your oven, you don't want the radio to get the power no longer used by the oven, or you would destroy the radio.

Case 2

The generator is a power generator that generates power P1 (=P1_max) all the time, independently of the load.

Let's suppose that when everything is connected, the voltage U1 of the generator matches the rated voltage for the loads.

We have P1=U1_nomxI1_nom=U1_nom²/R2 + U1_nom²/R3.

So P1=U1_nom²x(1/R2 + 1/R3)

Now suppose we disconnect R2, while keeping the power constant. We now have P1=U1xI1=U1²/R3, therefore U1=sqrt(R3xP1).

If we reuse the previous equations, it gives us

U1 = sqrt(R3xP1) = sqrt(R3xU1_nom²x(1/R2 + 1/R3)) = U1_nom x sqrt(1+R3/R2)

So if you disconnect R2, the voltage will increase above the nominal one (by a factor sqrt(1+R3/R2)>1, and the power consumed by R3 will increase with the square of this factor (i.e. by 1+R3/R2).

So in this second case, you are indeed forcing more power into the remaining load (by increasing voltage), which might lead to the destruction of the load.

So, to summarise:

• If you have a voltage generator then it only has a maximum power. As long as that is not exceeded, the voltage remains constant. That way, you can plug/unplug loads and a load always draws the same power: its nominal power. This is what you want in most cases e.g. in household devices.

• If you have a constant power generator then remove one load, the power it uses will split among the other devices, by increasing the voltage. That might damage those other devices if the voltage rises too high. This is useful to harvest the maximal power out of a generator, for example with a wind turbine or a solar panel. However, the equipment at the other side must be able to absorb that extra power. For example, it is often fine to charge batteries but try to do the same with something more sensitive, like a computer, and you will destroy it.

On real-world electrical networks like the mains, it's a bit of a mix. When some few electrical devices are switched off, the voltages rises a tiny bit but household devices can handle the mains tolerance without problems. When the voltage rises too high, the network operator has to regulate it, by turning down one electrical generator or by starting pumping water up dams to store energy for later use. If the network operator doesn't do this then when power consumption is at its lowest (middle of the night), the voltage would be far too high and destroy equipment.

On a smaller scale, if you use a fuel generator, it varies the power it produces by consuming more or less fuel, in order to ensure a stable output voltage.