In theory, if the national grid operated with a non-sinusoidal waveform, like a triangular or square wave, a grid-following inverter would try to produce a matching non-sinusoidal output current containing the same harmonics. However, in practice, most grid-following inverters are designed only for clean, sinusoidal operation. Their power electronics and output filters cannot properly handle or reproduce significant low-order harmonics, and their control systems may fail to track highly distorted waveforms. Severe distortion can confuse the phase-locked loop, causing loss of synchronization and triggering protective shutdowns. As a result, instead of delivering a distorted current, the inverter would most likely disconnect automatically to prevent damage and maintain grid safety, since such abnormal conditions violate standard power quality requirements.

If the national grid operates with non-sinusoidal waveforms like square or triangular waves, a Grid-Following Inverter will attempt to synchronize with the fundamental frequency (e.g., 50 Hz) using its Phase-Locked Loop (PLL). The inverter does not control the grid voltage waveform; it simply injects current in phase with the grid voltage. Ideally, it tries to inject clean sinusoidal current, but severe voltage distortion may affect synchronization accuracy. If the harmonic content is too high, the inverter’s output current may become distorted as well. In extreme cases, the inverter may reduce its power output or disconnect for safety. It cannot correct or clean the grid waveform only follow it. The control system is designed to operate under typical grid conditions, which assume nearly sinusoidal voltage. Excessive distortion can therefore trigger protective responses. In short, a Grid-Following Inverter adapts to the grid waveform but cannot improve it.

Actually it depends on how the controls are designed. Clearly the voltage will just follow what the inverter is being supplied, however the format of the current would be different depending on the control scheme used.

I have designed grid following inverters that used a PFC control ASIC to generate the control PWM - this is a very simple an effective way of implementing control and in this case the output current would 'follow' the shape of the applied voltage. The problem with this simple control method is that the output current THD is dependent on the applied voltage THD so this might be the source of undesirable compliance testing failure.

Most sophisticated grid following inverters will use some form of PLL to synchronize to the grid and then this PLL will generate a pure sinewave that is used to modulate the AC output current and hence with this control design (which is by far the most common design approach) the output current will be a low distortion sinewave output despite the voltage waveform.

Beyond this it is permissible within the specified current harmonic limits for a grid tied inverter to respond to a distorted grid waveform in a 'smart' way - this is not typical with what you find in most grid following inverters, but there are inverters out there that would look at the applied voltage distortion and then manipulate the individual output current harmonics within the allowable compliance limits to try and correct the voltage distortion. With this type of control scheme the output current would appear to be an approximation of a sinewave but would include deliberate harmonic distortion to try and force the voltage waveform to better approximate a sinewave.

Also within the permissible harmonic limits a really sophisticated inverter might/could be attempting other control schemes such as sequence related response in a bid to implement functions such a anti-islanding.

Interesting hypothetical. Not very practical, but interesting.

Square waves won't work with transformers and the whole concept of shipping energy on the grid is high AC voltage from a source to a sink with a large distance between them. Hook up DC to a transformer...... no energy is moved.

Triangle waves at least have constantly changing potential. Voltage, that is constantly changing. The jump in continuity is likely a concern. Current has moment and you are going to have transient effects twice a cycle. Are there efficient differences in triangle energy transmission?

Probably. Could we do it?

Probably. Inverters with no spinning motor loads. Batteries, to inverters, to transformers, to transmission, to transformers, to rectification, to a capacitor, to a computer. That part of /transformers, to transmission, to transformers/..... a high voltage grid.... could that be triangle waves? Yes.

Sine waves don't have transients in steady state operation. Sine is created by circular motion. a repeated motion. Sine creation doesn't have an abrupt change of energy. No jumps in continuity, smooth. No transients. When you spin on a ferris wheel, or a merry go round, the forces you experience are constant, not abrupt. Consider doing circles in a car versus driving and making an abrupt change of direction 20 degrees right, or a right turn. Forces and potentials are both manifestations of energy. Triangle waves are changing directions twice a cycle.

How would a high voltage grid to with triangle waves to move energy?

I imagine efficiency and harmonics become big topics like it is when discussing electronic loads.

Not consider cutting out the HV system. Battery to computer. Then Battery to DC bridge (capacitor) to computer. The rectifier has a DC bridge and an electronic device is choosing to charge twice each cycle. It could be don't otherwise, that is just how the actual design is set up.

Chris Cockrell - your comment that square wave don't work with transformers is simply wrong. So long you stay within the volt-second (flux) limit of the transformer a transformer works perfectly OK being fed with a square-wave. Also if the current draw is a square-wave then the power being transferred through the transformer will be constant. If you take a look at some EE textbooks that explain how multi-megawatt utility scale inverters operate then you will discover that what I am describing here isn't just some hypothetical concept but rather this describes the reality of what has been considered conventional EE design concepts that been employed in inverter designs going back over 100 years.

See: Hazeltine, Louis. 1933. “Method and Apparatus for Converting Electric Power.” US Patent 1,904,455, filed July 5, 1923, and issued April 18, 1933.

Is your point that square waves (inverters using PWM) can drive AC high voltage transmission systems? Right? Is that an accurate stealman?

I assume that because you wrote:

/a transformer works perfectly OK being fed with a square-wave/

And what does the HV system's voltage in that look like? A square wave?

An electric valve converter. That is the patent, right? That is validation of using duty cycles (square waves) with energy storage elements (like capacitors and inductors) to use on and off switching. AKA filtering PWM.

A lot of my point, which I admit is not clearly articulated, and I could very well be wrong about, is that you won't create a HV square wave since the transformer operates on changes in voltage and you constantly have to be changing voltages on a transformer to get an input and output relationships.

As you pointed out, volt-second limits exist. At very high frequency voltage doesn't get to the output of a transformer because of the saturation. CTs and PTs (transformers) can saturate if not properly design and that you can miss the transient fault event. Yes, there are transformer voltage - current limits that get filtered or lost if voltage changes are too fast. Protective relay operations using transformer sensing for breaker operations.

The example is that if you input a 60Hz 2Vrms sine wave with a +5V DC off set, does the 5Vdc get through the transformer?

I'd say the 5Vdc is filtered. The flux isn't changing. But the 2Vac rms will get reflected across the transformer.

What else would you point me at?

I think this is a very interesting question. This whole sine, vs triangle, vs square.

Go to Amazon and type in "Modified Squarewave Inverter" - I found one for $15 - buy this and then observe the transformer primary and secondary waveforms with an oscilloscope. I think this might teach you some details regarding Maxwell's Equations that you seem to have got confused. But don't feel bad about this - I have corrected several EE university professors who seem to echo the same understanding that you seem to have picked up.

/What would happen if the national grid suddenly operated with a non-sinusoidal waveform, like a triangular or square wave?/

This is his question, right?

/then observe the transformer primary and secondary waveforms with an oscilloscope/

/Modified Squarewave Inverter/

Inverters by definition produce AC. I've never heard of a modified squarewave. A modified sinewave is a deformed sinewave. A sine wave that is not smoothed. The rougher modified sinewave look like square waves due to the step functions it uses. So it has a high harmonic component until it gets filtered. I can see why someone would call it a modified squarewave as it is unsmoothed. A bad sine wave.

If I observe the secondary waveform, I see an AC waveform on the secondary, not a square waveform. A transformer secondary requires a changing voltage on the input. Producing a square wave on the secondary of a transformer is just not feasible. I don't see any 230kV or 13kV lines operating with square waves. Ever. The national grid will not see square waves any time soon.

I'm not saying that an inverter's power electronics doesn't produce a square wave composed signals. It does. I just don't see the national grid operating with square waves, instead of sine waves.

HVDC is a different discussion, but I don't think that is actually in question here. Even though that is the closest to a square wave as power transmission gets.

Maxwell's Equations. Yeah, they aren't as intuitive as they seem.

Chris Cockrell - using a squarewave for power transmission would certainly result in higher losses than what occurs with using sinewaves, however the transformers are able to work with a squarewave (albeit the losses will increase).

However your assertion that "A transformer secondary requires a changing voltage on the input" is just plain wrong. If you drive the input of a transformer with a zero-average squarewave such that it changes polarity to avoid saturation of the core then you will find that the secondary voltage will also be a squarewave following the shape of the applied primary voltage.

What I suspect that you are getting confused about is the need for a transformer to have a changing magnetic flux (not changing voltage) in order to generate a voltage on a winding. Applying a constant voltage across the primary winding results in a changing flux based on the equation B = int(V.dt)/N.Ae where B is the magnetic flux density, N is the number of turns, and Ae is the magnetic core area. This changing magnetic flux then generates a voltage on the secondary winding also defined by the above equation - basically you can derive the relationship the Vp/Vs = Np/Ns which holds true so long as the value of B is kept below the saturation limit for the core.

What is the intention motivating this hyper-hypothetical question ?

It would be more pragmatic/rigorous to refer to specific examples of national grids which have been deliberately specifically designed to operate with triangular or square waveforms before positing the hypothetical behaviour of equipment most likely designed to work with sinusoidal waveforms...

Is this a "gotcha" setup ?

"Aha, gizmo XX is not REALLY a Grid-Following Inverter!!"

It is quite clear that this scenario is unlikely to have any definitive answer.

GFI's will do their best to match the Grid waveform, and will likely have limits beyond which they will likely disengage for self-protection

Kurt Klingbeil - that is a really great question that maybe Bipu Alam Emon should elaborate on. I have thrown in some comments here on the basis that I have been involved in designing grid-following and grid-forming inverters as well as creating grid connection standards. I don't see any real practical application for a square-wave or triangular-wave grid voltage, however I have corrected the misconception that a square-wave would not work due to the use of utility transformers. I am guessing (but it is based on my assumptions) that the reason someone might be interested in understanding on how a grid-following inverter might respond to a non-sinusoidal voltage waveform is to understand the response of a grid connected inverter to distortion on the grid - I.E., will the inverter be constructive, destructive, or neutral in mitigating the grid distortion.

@Michael

Seems to me a generic question like this implicitly refers to residential / commercial solar inverters which, like fleas on a dog, have no chance to modify/mitigate the grid waveform ...

Best case scenario is for the devices to self-protect and eject under adverse conditions

The scenario of specialized high power industrial / utility inverters is beyond the scope of generic public questions

Kurt Klingbeil - I would challenge your assertion there. Back in the 1970's 'bridge-cap' electronic loads started getting connected to the grid. These loads had really terrible harmonics but the argument was that a few of these loads scattered across the grid can't do any real harm, but a few decades later it was obvious that these bridge-cap loads were causing a major problem - this was solved through legislations such as EN 61000-3-2 etc.

It is true that one small PV inverter alone on the grid has no chance at impacting the overall grid voltage quality, however if you project forward in time based on where technology is going it doesn't take much imagination to realize that in the very near future the vast majority of grid connected devices will take the form of an IBR (Inverter Based Resource). Also there is no practical reason stopping even the smallest IBR from being able to operate in a grid-forming mode of operation and implement a full utility control stack with primary control responses and secondary control scheduling - and even inertia with frequency and voltage ride-through capability. I work for Enphase Energy and even their smallest 300W microinverter is capable of all this functionality.

@Michael

I contend that the context of inverters failing to track bad, off-spec, malformed grid waveforms is substantially different from inverters doing their best to track / create solid in-spec grid waveforms.

I'll engage in a metaphorical reference:

It is not a sign of sanity to be well adapted / conformant to a pathologically sick society...

Or conversely, it may be a sign of sanity to be maladaptive to such a society.

Kurt Klingbeil - that is an enlightened perspective.

Michael Harrison

Yes, that is my claim. "A transformer secondary requires a changing voltage on the input." The input being a primary coil that you use to drive the other coil's voltages. Only when you first apply a 5Vdc to the primary coil will you see a spike of voltage on the secondary. If you are alternating between + and - 5V. You will see voltage spikes + and - linked to the changing input voltage, the rising and falling edges of the average 0 volt square wave, on the secondary voltage.

I find it interesting that you keep pointing at changing flux. I don't get a changing flux if there is no changing voltage. When discussing magnetic circuits, I can understand discussing the changing flux but the changing voltage and changing flux are linked phenomena.

https://youtu.be/y0WrKT45ZZU?si=brTg679VPEPFfKG8&t=127

Chris Cockrell - check out my credentials - ask any leading magnetics expert in academia if I know what I am talking about with regard to magnetics. Probably the two leading magnetics experts in the USA in academia would be David Perrault (MIT) or Charlie Sullivan (Dartmouth). Magnetics research is a topic that I financially sponsor within several US universities, and I act as a subject matter expert advising agencies such as the National Science Foundation regarding the establishment of government funding in magnetics research within the US.

I agree with your assertion that you need a changing magnetic flux being created in the core in order to create a voltage in a transformer winding. The bit you seem to be missing (and a really common misconception out there) is in what is needed in order to establish a changing magnetic flux in the transformer core. The magnetic flux in the units of a Tesla is defined as the volt-second integral per cross sectional area per winding turn.

If you apply a constant voltage across a given winding and plot the volt-second integral as a function of time then you find that the volt-second integral increases linearly in time. It is hence the simple passage of time that creates the changing magnetic flux.

I suspect that your confusion might be coming from applying a DC voltage for too long a time across a transformer winding and simply driving the transformer core into saturation.

Michael Harrison I don't doubt your credentials. I just don't understand your claim.

I don't consider myself an expert on magnetics or transformers. The older I get, the dumber I realize I am. lol.

I'm happy to be wrong about my claim and my understanding. I'm happy any time I improve my understanding of reality. I don't see what is incorrect in my understanding here.

The volt-sec integral concept is the same lumped parameter tools in circuit theory that we use to model an inductor's current. We integrate the voltage a crossed time to get the momentary current in an inductor.

/If you apply a constant voltage across a given winding and plot the volt-second integral as a function of time then you find that the volt-second integral increases linearly in time./

The linear increase makes sense, integrate a constant and you get a sloped line. That is exactly how the inductor current works.

As shown in the video provided, you can see that he turns on the potential to the input of the transformer. 0V to 5V. (I have no clue what the actual voltage is, could be 2V or otherwise).

Then he turns it off. 5V to 0V. The primary to secondary induced linkage only occurs during the rising edge and the falling edge of the input voltage. Rising and Falling edges are the voltages changing. If the voltage is not changing, the secondary or tertiary voltages will not manifest on the coils. This is a causal relationship.

I'm going back to basics here. Faraday's Law (1831), the law of electromagnetic induction, says that if the magnetic flux lines linking a closed electric coil change, then an emf is induced in the coils.

That is why I am pointing to changing voltage as being so critical.

Appearantly, I don't understand ...

/what is needed in order to establish a changing magnetic flux in the transformer core/

Are you saying it is the volt-seconds that change the magnetic flux?

Is changing voltage not a part of that idea? Changing voltage is not part of changing a magnetic flux in a core?

If I apply a DC voltage to the coil of a transformer, I create an electromagnetic but the magnetic flux only changes when I hook up the 5V and disconnect the 5V supply. The 5V creates a magnetic flux, hence the electromagnet but it creates no changing magnetic flux in the transformer's core while connected with 5V.

Can you link a video that explains what I'm missing here? If I really have no clue, I'd like to see what videos are out there which might help.

Chris Cockrell - magnetic flux IS the the volt-second integral. Sure there is a scale factor that comes into the equation based on the number of turns - but this should be easy to understand why the number of turns increases the magnetic flux due to a simple super-position of the individual flux generated by each individual turn (I.E., it is a linear system). You also need to factor in the core area if you want to determine the magnetic flux density. The SI unit for magnetic flux is the Tesla which has the base unit kg.s^-2.A^-1. If you consider that the Volt has the base unit kg.s^-3.A^-1 then it should be apparent that a Tesla is simply a volt-second.

Applying a constant voltage across a winding results in a linearly increasing volt-second integral which is exactly the same as saying a linearly increasing magnetic flux. In reality there are a couple of factors that come into play - the magnetic core can only support a given maximum flux density before it saturates (typically 300mT for ferrite and over 2T for some high permeability iron alloys). In addition to the magnetic core reaching a saturation limit the resistance of the winding will also ultimately limit voltage being applied across the inductive element - this results when the current rises to a value determined by the applied winding voltage divided by the winding DC resistance - when this occurs the effective voltage being applied to generate magnetic flux drops to zero and hence the magnetic flux no longer increases.

If you consider a super-conductor air cored transformer there is in theory nothing to stop the magnetic flux increasing indefinitely, however in practice the non-zero resistance of a super-conducting winding will lead to Joule heating in the winding that if sustained long enough with heat the winding to a point where the super-conducting property will be lost.

In practical transformer applications the above limits based on reaching a winding resistance current limit and a magnetic flux density limit in the transformer core are avoided by ensuring the volt-second integral never exceeds a practical limit and by ensuring what is known as volt-second balancing - basically ensuring an AC voltage is applied across the windings such that the long term volt-second integral is kept centered at zero.

Chris Cockrell - I have been quite vocal within academia in the US regarding how magnetic theory is taught in universities. I don't know where or when it started but many of the academics in the US teach that magnetic flux is proportional to the current density in line with the Ampere-Maxwell law - although this is technically correct, I believe that it obfuscates the underlying physics which is much better portrayed by the Maxwell-Faraday equation. At a very fundamental level the current that is established in the winding is the result of the voltage applied across that winding. Hence explaining that the established magnetic flux is a direct result of the winding current is actually getting the cause and effect back to front. It is the magnetic flux generated by the applied volt-second integral that causes the current to flow through the winding.

Michael Harrison Thanks for all the explanation and energy. I love being wrong and appreciate your effort. It gives me so much more to think about and revisit. Maybe I need to revisit EM. lol.

I ran a 1 Hz signal and my secondary died off like I was thinking. But there was more inertia in the magnetic flux(?), in the volt-second integration, than I realized. Like an inductor's current has inertia, and takes some time to decay/reach a steady state, same with the magnetic flux, or the voltage on a capacitor. Just by running an 10Hz signal, the square wave passes beautifully and has no time to decay. Not exactly what I was thinking of.

Are you familiar with why the decay has two time constants (in the image)? I assume that the first is the time for the straggling domains to align, the high energy of the rising edge alignment. And the second is the time for the domains to lose alignment. So to create the field and then to lose the field.

The square wave did exactly what I was thinking it would.

Your education concerns are interesting. I know I feel similarly with circuit theory. Are we teaching in a way that they understand it well? Capacitors are like springs and inductors are flywheels. One is an electric storage, it is a potential energy, while the other is a kinetic energy or a magnetic storage. One is tied to voltage and the other is current. I suppose that is why I view superconductors as odd. When considering electric circuits, I can't have a current without a voltage. But I can have a voltage without a current. OC. However, superconductors are kind of an exception to that, right?

Chris Cockrell - it looks from that waveform that you are saturating the transformer. You are applying a 1Hz, 15V square-wave to the CH1 winding. I am guessing that you are using a 60Hz line frequency transformer here that is designed for a 120Vac sinewave voltage? The volt-second integral for a 120Vac 60Hz sinewave works out to being 2.8 volt-seconds per half cycle. Based on this calculated assumption, then that would mean that rather than applying a 15V square-wave at 1Hz, you should drop the magnitude of the square-wave down to about 5V and then I would expect to see less evidence of any saturation. You mention that at 10Hz the square-wave is transformed without any distortion - assuming that you are also using a 15V drive in this case then the volt-second integral would be 0.75 volt-seconds - clearly less than the saturation limit of the transformer.

Regarding your thoughts about electrical and mechanical analogies - these are useful for helping introduce a student to electrical theory if they are already well versed in the ideas behind mechanical systems and kinematic equations etc. however these analogies only hold true up to a point and serve no real value if your student is not fully versed with an understanding of the underlying physics of mechanical systems. There are some people (myself included) who became well versed with Maxwell's equations years before learning about the physics of mechanical systems.