Crazy Transformer Setup Efficiency Calculation

[CaptKarnage]

Hopefully I can describe this sufficiently for someone to understand. At a job I'm working, I found they had an absolutely bonkers (IMO) setup for some heaters. I know this setup is horribly inefficient and I believe this setup will likely cause equipment to breakdown sooner than expected. I also know this system is costing them a lot of money. However, I have been unable to convince anyone of this, or to invest in different equipment. I'm trying to do calculations to PROVE it, but they have become very intense, and any little error I make could throw the whole thing off. I also have to make some assumptions - some of which I know aren't right. Last thing I want to do is present something that's incorrect, so if anyone could check my assumptions and maybe see if I'm missing anything. I'm sparing some of the details, but here is a summary.

Here is the general setup:
480V, 3 phase power feed into a 150 kVA 1:1 isolation transformer
The 150 kVA transformer feeds 5 VFDs - set to constant frequency (60 Hz), variable voltage mode
Each VFD then in turn feeds a 30 kVA Delta-Wye step down transformer (to 208/120V)
Then, the A and B phases of the Wye sides are each connected to a 6.6 kW heater (tied to neutral)
The C phases of the step down transformer secondaries are all open

There is a PLC controlling the VFDs, using PID control to increase or decrease the voltage output of the VFD to adjust the heaters. I don't want to get into the control details here - the controls work, they do the job. My concern is on the power feed.

Most of my calcs use "ideal transformer" equations - so they are wrong. However, I'm not sure how to account for ALL losses. That is what is important to me, what are ALL my losses.

I have logged data from the VFDs which show an average current over 30 days (running 24 hours a day) of approximately 7A, with a minimum of 0.7A and a max of 13.45 A. My calculations at least agree that these recordings are within the expected range.

The 30 kVA transformers are all Sola HD T2H30S, all made before 2006 - so before DOE 2016 and even before NEMA TP-1 took effect. I have the data sheet, it has no efficiency data. If I try to take power out over power in based on the spec sheet, I get a value over 100%, so they have rounded the values in such a way they are useless to any efficiency calculations. If anyone has efficiency data on this transformer (rated efficiency, what the test load was used [NEMA/DOE use 35% but back then it was likely near 80%], or no-load losses, even coil impedance, etc...) anything at all that could help me calculate efficiency, it would be great.

I'm trying to show how many kWhs (and therefore how much $$$) are wasted by this setup. I have a couple of proposed improvements, and I can easily calculate efficiency and losses on my proposed changes, so I don't need suggestions on that. I just need help figuring out the efficiency of the existing system.

If I ASSUME:
1. These transformers were rated at 80% load, and (Likely in the ballpark, but could be different)
2. Have maximum efficiency of 97.5% (NEMA TP-1 level) and (Likely Higher than actual due to age)
3. The maximum efficiency also applies at 80% load, and (Really don't know if this is accurate or not)
4. I ASSUME purely resistive loading / unity pf (Close enough to true for the secondary load, but could appear reactive due to other factors)

... and I ignore stray losses and ignore dielectric losses (this is air cooled, dry type transformer - so likely negligible).

I can then calculate the total losses at 80% load, which would be 80% * 30000 kW * .025 = 600 W. Again, with the assumption that 97.5% is maximum efficiency and that occurs at 80% load, this means at 300 W would be no load / iron losses and 300 W would be loaded / copper losses. I'm sure this estimate is low but I don't have any reliable information to go higher.

This portion of the loss of 300 W, being no load / "iron" losses, would be lost 24/7. In particular, one phase, 1/3 * 300 = 100W of this is on an open phase on the secondary that never provides any useful power and has 0% efficiency. That's 72 kWh per month per phase, including the unloaded phase.

From the other half, knowing the copper losses are proportional to the square of the current, I can come up with a constant (I'll call kp, or primary side constant) of 0.1200292 which I can multiply times the square of a given current to get a close approximation the copper losses.

Given 7A average (~19.4% loading), my average copper loss is then 5.88 W per phase for the loaded phases. Over 30 days, 24 hours a day, that's 605 kWh per transformer in copper loss. So for loaded losses in two phases and no load loss in all three phases, we get 2x605 + 3x72 = 1,426 kWh per transformer, 7,130 kWh per system (5 VFD/transformer set) per month or 85,560 kWh per system per year. There are 7 systems (49,910 kWh per month / 598,920 kWh per year total).

So, that's the MINIMUM being lost from this crazy setup - I believe the real number to be much higher. As big as this would be to a residential customer, this is a huge company that pays between 3 to 5 cents per kWh and it's a drop in the bucket to them so far, but I think if I could get a reasonable estimate of the real losses, it might be enough drive them to replace this ridiculous setup.

This doesn't yet account for other losses due to the open phase and the current imbalance. I can get the losses in the lines, including in the neutral, which will be high due to the imbalance. It will take me a bit to find the wire sizes and lengths used to get that number but I can get it. I also haven't factored in VFD losses yet, but that will be easy enough as well as I have all those specs.

What I'm not sure how to calculate is the current through the primary C phase with the secondary C phase being open. Ideal equation says 0, but I know there's a voltage difference and there would be some leakage current (though purely reactive) in the C phase on the primary and I'm not sure how to best calculate that (first thing that comes to mind is to reflect the impedance - but then I have to assume it's not an infinite impedance, either). I know the phase angles will be out of whack. There's normally a 30 degree shift in the line current due to the delta wye transform, but the open leg is making the primary phase angles -120 and 60 degrees (180 degrees out of phase) which I believe means a good chunk of the line current is reactive current to flowing in line C adding to the losses. I need to vet that out yet, though. I also don't know the internal calculation of the VFD and how it reports current. I'm suspecting it's only reporting phase A current and assuming balance. If it were averaging the 3 phases, I would expect the logged values to be lower by 1/3.

Also, I'm not sure if the imbalance on the load side of the VFDs is passed to the line side. I was originally thinking that at least swapping which phases each pair was on (Say AB, BC, CA, AB, BC or something like that) would lessen the imbalance the overall system sees, and therefore the isolation transformer as well and make some improvement. However, Since most VFDs do an AC to DC conversion and back to AC, wouldn't the current pulled by the VFD still be balanced even if the output is imbalanced? If that's the case, that won't actually affect the isolation transformer at all.

 

[winnie]

Too much for me to dive into without being on contract but a couple of points:

Before even looking at numbers you need to take a Dale Carnegie style course. It doesn't matter how right you are on the physics; this is a sales job.

On the numbers:
The VFDs are presumably reducing the output voltage to control the heaters. When this happens I would expect transformer core losses to change...but the PWM switching will also impact core losses. I don't think you are correct to assume fixed core losses.

You are correct, the VFDs are going ACC:AC thus the supply to the VFD is balanced even when feeding a single phase load.

You might get improved efficiency with minimal changes if you connect the heaters 'open delta' at the tail end of the system, operating the transformers at lower voltage and using all the coils.

You need to understand exactly the basis for using this seemingly crazy system before pushing hard to change it. It seems nutso to me as well, but perhaps there is an underlying rationale that makes the nutso worth it.

Jon

 

[CaptKarnage]

@winnie yeah, I know it's a bit much. I have no one here that I can bounce this off of as there are very few knowledgeable people on it, and those who are simply don't want to upset the apple cart and they don't really know the history either. I'd be happy if someone could find efficiency data on that transformer - or, even pre-2007 transformers in general so I could get a better estimate.

Thank you, though, for some very excellent points, I'll be sure to look into them. I'm not sure how much the PWM will play into this, as the VFDs were upgraded and are very new and likely have a lot of filtering that should mitigate those issues, but I will double check that in the VFD specs now, as I could be wrong. The voltage is definitely a very good point. As I stated they were set to fixed frequency, variable voltage mode - so the voltage is definitely varied, and I know a 480 V transformer only getting, say 100V into it to begin with (it is running at 20% load, on average, with a nearly fixed resistance load) it is going to be much less efficient than at rated voltage.

Also, I'll look at open delta as you suggested. Would still be somewhat unbalanced but less so and would possibly eliminate the neutral return current. I'd have to check NEC on this setup though, too, to see if that's allowed in this situation.

No one here can tell me the original rationale behind it. Every outside contractor that has come in has agreed it's nuts and have seen other similar facilities that do not do it this way. As best I can tell, that rationale at the time it was designed was they were the cheapest set of parts available to do the job, and it's been maintained in order to reduce the different spare parts they had to keep on hand and save money there as well. Not a good reason IMO.

My report, when I issue it, will include some caveats including potential rationale for the existing setup. I'm not going to spend the time now to design the exact replacement system, just to get the justification for someone to pursue and design an alternate system, with some suggestions as to direction.

 

[winnie]

As I stated they were set to fixed frequency, variable voltage mode - so the voltage is definitely varied, and I know a 480 V transformer only getting, say 100V into it to begin with (it is running at 20% load, on average, with a nearly fixed resistance load) it is going to be much less efficient than at rated voltage.

Also, I'll look at open delta as you suggested. Would still be somewhat unbalanced but less so and would possibly eliminate the neutral return current. I'd have to check NEC on this setup though, too, to see if that's allowed in this situation.

I'd expect the transformer to get _more_ efficient as voltage goes down. Conduction losses scale as the square of current flow. Core losses scale non-linearly with voltage. As voltage goes down core losses will go down.

The NEC is equally happy with L-N and L-L loads; with the exception of disconnect switches.

-Jon

 

[wwhitney]

Is it feasible to measure the actual power in and power out? E.g. log the 480V 3 phase supply and each of the 10 heaters, simultaneously? That would certainly let you measure the efficiency directly.

Or if you know that the control system frequently adjusts the heaters one at a time, then I think it would be enough to instrument the 480V 3 phase supply plus the heaters, one at a time (if the heaters are plausibly different in their characteristics). That will let you see the delta P in and out for each heater, and you can come up with a linear model for P_in vs P_out.

Cheers, Wayne