Superposition Principle for two Voltage Sources (confusions about....)

[The Tortoise-Man]

I have a question about natural limitations when the superposition principle for circuits is applicable. Possibly there is a quite elementary reason why the problem I'm going to present next fails, but up to now I haven't a precise reason why that's exactly the case. Could somebody help?

Consider the following situation which rather confuses me:

The voltage sources $S_1$ and $S_2$ with voltages $V_1$ and $V_2$ which we assume to be equal: $V_1= V_2 (=V)$

We want to calculate the current $I$ across the resistor $R$ using two methods: 1) usual standard way we learn to add up two parallel voltages and 2) aplication of superposition prinicple.For 1): Due to basic calucation rules for two parallel voltage sources with SAME voltage $V_1= V_2$ we can make a replacement:

Now if we set $I_1$ to be the current in

then $I= 2I_1$.

For 2): On the other hand if we try to apply the superposition principle to this circuit and short out say $S_2$ then we
obtain

with $I_{\infty}= \infty$ and $I^1_R=0$ since we have shorted $S_2$. From symmetrical
reasons in the same game shorting out $S_1$ we obtain $I^2_R=0$ and therefore $I= I^1_R + I^2_R =0$ and that
contradicts to the considerations above.

So seemingly in this situation the superposition principle fails because 2) make no sense at experience level. But on the other hand I read that the only obstruction to use superposition principle is the requirement that the circuit/network should be linear, that's all as far I know.
This one is linear. But seemingly the application of superposition here gives absurd results.

Where is the error in my reasonings?

 

[alan123hk]

The second method is not allowed, because if an ideal voltage source with zero internal resistance is connected to a zero-resistance circuit, the final voltage or current cannot be determined. Since the result of multiplying zero by infinity is in an indeterminate form, this contradicts the constant voltage of an ideal voltage source.

 

[Baluncore]

In the first case, the resistor obeys Ohms law. I = V / R.
Half the current comes from each battery.

 

[Svein]

In practice, the two voltages are not exactly the same. There will be a high current (slight voltage difference divided by zero ohms) going from one battery to another.

Two basic rules for voltage sources:

1. Never connect voltage sources in parallel
2. If you must connect them in parallel, insert resistors between the voltage sources and the voltage summing point.

Take a look into one of your battery-powered devices. The batteries are always connected in series, never in parallel.

 

[DaveE]

Any network that contains a loop of only voltage sources and/or capacitors is not solvable, not realistic. The same is true of any circuit node that has only current sources and/or inductors connected to it.

So, while you will get a bunch of answers from people, this is, by definition, not a solvable circuit. I suppose there is the trivial case where the sources are equal*, in which case, why not just delete one?

So let's just pause for a moment and ponder, what does it really mean to have two ideal voltage sources connected in parallel? Why would you pose this problem?

* In the general case with either capacitors or inductors, you would need the initial conditions to match perfectly. Otherwise you will have infinite solutions for some of the currents or voltages.

 

[Borek]

Never connect voltage sources in parallel

Actually I do that all the time with LiPo batteries in RC models, but the rule is: connect them only when they are charged 100% (sure, that's an approximation, it is never perfect 4.2V per cell, but the differences and leveling currents are negligible in such a case).

 

[DaveE]

Actually I do that all the time with LiPo batteries in RC models, but the rule is: connect them only when they are charged 100% (sure, that's an approximation, it is never perfect 4.2V per cell, but the differences and leveling currents are negligible in such a case).

Those voltage sources are networks in the circuit modeling world. You can parallel them because of their series resistance. Once you start drawing equivalent circuits and writing equations, you've entered into the modelling world, where it never makes sense to have voltage sources in parallel. So, yes, you can parallel batteries, but not ideal voltage sources.

 

[Averagesupernova]

Take a look into one of your battery-powered devices. The batteries are always connected in series, never in parallel.

You mean like batteries in diesel trucks, tractors, stationary equipment, etc.? Sorry, you're just plain wrong.

 

[anorlunda]

The standard way to create a house battery bank.

 

[sophiecentaur]

Actually I do that all the time with LiPo batteries in RC models, but the rule is: connect them only when they are charged 100% (sure, that's an approximation, it is never perfect 4.2V per cell, but the differences and leveling currents are negligible in such a case).

A diode in series with each battery will isolate the two from each other and they will both discharge in a well behaved way. Only problem could be the loss of half a volt or so. Not a good idea to try charging them that way because the charger reads the wrong volts for optimum charging.

 

[sophiecentaur]

The standard way to create a house battery bank.

That's ok if all the batteries are the same make, type number and age. That way they are near enough to each family member not to misbehave. An old and a new battery connected like that will discharge the newer battery into the old one. Only justified with two different batteries when you happen to need a lot of current. It's common in boats to have two batteries. There is a four position breaker switch; Off, No1,No2, Nos 1 + 2. Only use 1+2 for starting a tired engine. Even charging may not charge both batteries fully.

 

[Baluncore]

High current batteries are usually designed so that if a cell fails internally as a short-circuit, the resulting stored energy release will be contained to that one cell. The cell has been designed to survive and contain such a failure.
When you parallel several batteries, the failure of one cell will discharge all those in parallel through the one failed cell. That may exceed the containment and cause a major incident.

 

[DaveE]

High current batteries are usually designed so that if a cell fails internally as a short-circuit, the resulting stored energy release will be contained to that one cell. The cell has been designed to survive and contain such a failure.
When you parallel several batteries, the failure of one cell will discharge all those in parallel through the one failed cell. That may exceed the containment and cause a major incident.

Which is why it's much better to buy a battery pack than build your own. Manufacturers can take steps in design, assembly, and test to improve safety (ANSI/CAN/UL 2734, for example). We can't.

 

[The Tortoise-Man]

Any network that contains a loop of only voltage sources and/or capacitors is not solvable, not realistic. The same is true of any circuit node that has only current sources and/or inductors connected to it.

So, while you will get a bunch of answers from people, this is, by definition, not a solvable circuit. I suppose there is the trivial case where the sources are equal*, in which case, why not just delete one?

So let's just pause for a moment and ponder, what does it really mean to have two ideal voltage sources connected in parallel? Why would you pose this problem?

* In the general case with either capacitors or inductors, you would need the initial conditions to match perfectly. Otherwise you will have infinite solutions for some of the currents or voltages.

Ok, so in summary the point is just that the superposition principle always subliminally assumes that we work with solvable circuits in the sense that there is nowhere loop with short circuit in the given circuit.

 

[DaveE]

Ok, so in summary the point is just that the superposition principle always subliminally assumes that we work with solvable circuits in the sense that there is nowhere loop with short circuit in the given circuit.

Your network needs some rules about what the voltage is across each branch. You just can't have rules that conflict. Rules that agree and provide identical information (the trivial case) are redundant and one can be immediately eliminated at no cost.

The algebraic equivalent is this:
x=2 and x=3, find the value of x.
Or, x=2 and x=2, find the value of x.

It's not rocket science, don't dwell on the obvious, it's not worth your time.

 

[Borek]

A diode in series with each battery will isolate the two from each other and they will both discharge in a well behaved way. Only problem could be the loss of half a volt or so. Not a good idea to try charging them that way because the charger reads the wrong volts for optimum charging.

In the past I though about making a special connector with built in diodes, but two things threw me off. Voltage loss was the first. Second: in my models we are talking about currents in the 40A+ range, which means diodes will be bulky.

As the charger pumps them up to 4.2V per cell, the voltage difference between batteries fresh after charging is in mV range and I connect them immediately after charging.

 

[sophiecentaur]

Second: in my models we are talking about currents in the 40A+ range, which means diodes will be bulky.

Those types of battery are "bulky" too. But TO-220AC is not a big package.
Voltage loss can be a problem, of course.
On my boat, I ended up with a VSR (Voltage sensitive relay) which charged the start battery preferentially and switched in the domestic battery when the start battery was charged. That meant that the standard regulator on the alternator was working with the optimum voltage. The system worked very well and needed no constant nursing, as the original system did. But this is a bit of a red herring if two batteries need to work together.

 

[anorlunda]

Don't forget EV battery packs. They necessarily have series and parallel connections.

 

[sophiecentaur]

Don't forget EV battery packs. They necessarily have series and parallel connections.

Wouldn't all the batteries be same batch, same age, same use? Also, in an expensive setup like an EV, wouldn't there be a lot of monitoring to spot potential problems?
This thread has morphed from the theoretical to the very practical.

 

[Baluncore]

In the past I though about making a special connector with built in diodes, but two things threw me off. Voltage loss was the first. Second: in my models we are talking about currents in the 40A+ range, which means diodes will be bulky.

When I am faced with that situation I use the bulk substrate diode of a mosfet. When the voltage becomes positive, so current begins to flow, I turn on the mosfet. That reduces resistance which reduces the voltage drop and the power dissipated in the diode. There are a couple of handy components designed for automotive applications that cost less than $5 each. They are very handy when controlling multiple parallel battery sysetms.
IRF1405 IR Power MOSFET; TO-220AB, N-Channel, 55V, 169A.
IRF4905PBF Power MOSFET; TO-22DD, P-Channel, 55V, 74A.

 

[rude man]

I have a question about natural limitations when the superposition principle for circuits is applicable. Possibly there is a quite elementary reason why the problem I'm going to present next fails, but up to now I haven't a precise reason why that's exactly the case. Could somebody help?

Consider the following situation which rather confuses me:View attachment 294570

The voltage sources $S_1$ and $S_2$ with voltages $V_1$ and $V_2$ which we assume to be equal: $V_1= V_2 (=V)$

We want to calculate the current $I$ across the resistor $R$ using two methods: 1) usual standard way we learn to add up two parallel voltages and 2) aplication of superposition prinicple.For 1): Due to basic calucation rules for two parallel voltage sources with SAME voltage $V_1= V_2$ we can make a replacement:

View attachment 294571
Now if we set $I_1$ to be the current in

View attachment 294572then $I= 2I_1$.

For 2): On the other hand if we try to apply the superposition principle to this circuit and short out say $S_2$ then we
obtain

View attachment 294573with $I_{\infty}= \infty$ and $I^1_R=0$ since we have shorted $S_2$. From symmetrical
reasons in the same game shorting out $S_1$ we obtain $I^2_R=0$ and therefore $I= I^1_R + I^2_R =0$ and that
contradicts to the considerations above.

So seemingly in this situation the superposition principle fails because 2) make no sense at experience level. But on the other hand I read that the only obstruction to use superposition principle is the requirement that the circuit/network should be linear, that's all as far I know.
This one is linear. But seemingly the application of superposition here gives absurd results.

Where is the error in my reasonings?

You cannot short one source (V1=0) while the other is at V2 = V'. You have contradicted yourself.