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How to Calculate Current on a 3-phase, 208V Rack PDU (Power Strip)

Posted on March 14, 2011 by Henry Hsu  |  Comments (20)

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Problem Statement

In recent years, extending 3-phase power distribution all the way to server cabinets and racks has become extremely popular in new data center builds—for many good reasons. Principally, for cabinet power capacities above 5kVA, utilizing 3-phase rack power strips can significantly reduce the copper required to supply such dense loads.

But unfortunately, many users (rightly) find it cumbersome to provision and calculate current (amperage) for 3-phase power in the rack—for example, a typical question would be:

If I plug in a 250W power supply (about 1.2 amps) on this receptacle right here, how will that affect the current that flows through each of the three phases of this rack power strip? Which one will be closest to tripping a circuit breaker?

In North America, where 3-phase, 208V power distribution is wired “line-to-line”, the answer to this question is particularly counter-intuitive. I was astonished to find that the almighty Internet offers virtually no good tools to help answer this question, and so created one together with my colleagues at Raritan (link follows).

Why 3-Phase (208V) Power Strip Loading Is Difficult

With single-phase power strips, loading and provisioning is straightforward: if you add a device to the rack that draws 10 amps—in turn, 10 amps of additional load is drawn from the input line of the power strip.

But with 3-phase power strips, when you add the same 10 amp device to a server cabinet, it is unclear what results. From which of the three lines will additional current flow? How much of the 10 amps flows from which of the three lines? etc.

As we shall see, the answer is not always obvious.

1. In North America, a 208v, 3-phase power strip is divided, well, into 3 sections:

  • L1/L2:  outlets that are wired to draw current from lines L1 and L2 (aka, XY);
  • L2/L3:  outlets that are wired to draw current from lines L2 and L3 (aka, YZ);
  • L3/L1:  outlets that are wired to draw current from lines L1 and L3 (aka, XZ);

2. One would intuitively expect the following to occur when a load is applied:

  • Start with a completely empty rack / power strip;
  • Add a 10A load onto an outlet that is supplied from L1/L2;
  • In turn, 10A of current flows from L1; and 10A of current flows from L2.

This is intuitive, and indeed, it does happen exactly as you would expect.

3. But next, let us apply another load:

  • Start with the above cabinet (where 10A is already flowing on both L1 and L2);
  • Now, add another (second) 10A load to the cabinet, but plug it into an outlet that is supplied from L2/L3;
  • You would expect an additional 10A load to flow on L2; and 10A on L3;

In fact, this does not happen!

  • Indeed, 10A flows from L1 (no change);
  • As you would expect, 10A flows from L3—a result of the new load;
  • But on L2, the current becomes 17.3A—NOT 20A (10A + 10A).

On the surface, 17.3A on L2 appears to be a completely random number. There are two 10A loads that are wired to L2, but the current is not 10A, not 20A, not 15A, but… 17.3A !?!?

I asked one of our senior power engineers to explain this in laymen’s terms. He sent me the following diagram:

Absolutely true story. Obviously, the moral of the story here is: don’t ask an engineer to explain things in laymen’s terms.

In all seriousness, the essential truth illustrated by the diagram is that the amount of current on a given line (L1, L2, and L3) depends on the amount of current on the other two lines. Calculating each line value requires vector addition (a.k.a. “complex” arithmetic), which really cannot be done in your head—or even with simple Excel formulae.

These calculations simply require more than straightforward arithmetic. And therefore, are neither intuitive nor simple to execute “back-of-the-envelope” calculations. This issue comes up so often with my clients that, for your convenience and reference, I have created the following…

3-Phase Rack Power Strip Current + Power Capacity Calculation Tool

Download Now

This 3-phase current and power capacity tool, which you can download by clicking on the button above, is completely vendor agnostic. Regardless of the manufacturer of your rack power strip, this tool will be applicable.

Generally-speaking, 3-phase rack power strips can be purchased most commonly in the following 208V electrical configurations:

  • 30A (24A derated) : NEMA L21-30P or NEMA L15-30P input plugs;
  • 50A (35A derated) : Hubbell CS8365C “California-style” input plug, but with only three branch circuit breakers [or, less desirably, fuses] on the unit.
  • 50A (40A derated) : Hubbell CS8365C “California-style” input plug, but with six branch circuit breakers [or, less desirably, fuses] on the unit.
  • 60A (45A derated) : IEC 60309 60A, 3-pole / 4-wire, “pin-and-sleeve” input plug, but with smaller, 6# AWG gauge input conductors. Check your manufacturer’s spec sheet closely. If it states that: (a) the rated current is 45A; or (b) the rated power capacity is 16.2kVA [not 17.3kVA], then you have this type of power strip.
  • 60A (48A derated) : IEC 60309 60A, 3-pole / 4-wire, “pin-and-sleeve” input plug, but with larger, 4# AWG gauge input conductors. Check your manufacturer’s spec sheet closely. If you have this type of power strip, the spec sheet will explicitly state either: (a) the rated current is 48A; or (b) the rated power capacity is 17.3kVA [not 16.2kVA].

Simply download the 3-phase Capacity Planning Tool, and select the correct worksheet among the five tabs along the bottom. Enter in the expected amperages per outlet, being careful to enter loads underneath the correct corresponding circuit breaker heading. (That is, look at your power strip physically [or on engineering submittal drawings], to determine whether a given outlet is on the L1/L2, L2/L3, or L3/L1 branches—also known as XY, YZ, and XZ).

The tool will automatically calculate the resulting current (in amps) on each of the three lines, and highlight any possible error. If you do not see any red warnings (“OVERLOAD” or “ERROR”) on your spreadsheet, then you are good to go!

Note that, if you have a fully-redundant environment (Tier IV), wherein each server cabinet uses two rack power strips originating from two redundant UPS feeds, you should enter loads into this tool assuming that one of the two rack power strips is offline. This ensures that you have enough power capacity on the rack power strip, in case such a power loss does occur.

Download Now

Fine Print Required By Law

  • If you find this tool useful, please consider linking to this blog post;
  • If you find this tool useful, please consider Raritan’s extensive line of 3-phase rack power strips—among the most comprehensive in the market;
  • This tool is provided only for your guidance and convenience. Its calculations are not warranted by me or by Raritan (i.e., check your work with actual measurements).

Finally, as it is relevant: allow me to plug the real-time energy metering provided by Raritan’s portfolio of rack power distribution units. Our devices provide billing-grade accurate power information (amps, kWh, voltage, power factor, kVA, kW) for every cabinet—and in many models, for every power supply in every cabinet.

Such information perfectly complements the provisioning task which this 3-phase capacity tool enables. Also, your purchase helps fund my children’s future college educations.

Hope you find this helpful. Comments welcome, as always.

 

Learn about Raritan Power or request a call from a Data Center Power expert. 

All Recent Comments

Dave Clark wrote on 03/21/11:

Henry,

  This is very useful.  Any possibility you can do same thing for 415/240v 3-phase strips?

paula wrote on 03/21/11:

Thank you!!  This clear language explanation was just what I needed & had been unable to find anywhere.  Expecting the 3-phase calculator to be equally helpful.  And the non-pushy plug for Raritan is well-written & effective grin

Henry Hsu wrote on 04/07/11:

Hi Dave,

The reason I didn’t create a 415V version—even though we have an extensive line of 415V power strips both in the U.S. and internationally—is because unlike the 208V 3-phase strips, 415V 3-phase arithmetic is straightforward. This is because 415V power strips are wired “line-to-neutral”, otherwise known as “3-phase WYE”.

What that means in English is that any given outlet only affects a single line. Each circuit will be one of the following:

L1 to Neutral: Servers on these outlets place their load directly on L1
L2 to Neutral: Servers on these outlets place their load directly on L2
L3 to Neutral: Servers on these outlets place their load directly on L3


So to find out how much current is on L1, you just add up the current from all the servers on the one circuit. Unlike a 208V 3-phase power strip, the rest of the servers on the power strip do not affect L1 at all. This is a remarkably convenient truth about 415V power distribution, and one of the reasons some of my biggest clients are using 400V 3-phase distribution to the cabinet.

Let me know if that is unclear in any way.

3-Phase Balancing Act « Virtually From Scrat wrote on 06/07/11:

[...] happen to like the Raritan 3Ø Rack PDU Calculator and Henry Hsu does a great job of explaining the understanding problem on their blog. The Excel spreadsheet they provide is straightforward to use and does all the pertinent math for [...]

Wish to remain anonymous wrote on 07/11/11:

This spreadsheet incorrectly utilizes what seems to becoming known as the Oregon Fudge Factor. This factor is in reality the power that could become available to us in a reactive load is as a result of the phase angle difference between the phases in a 3 phase system. In a 3 phase system, the additional power that becomes available to us is 1.732, the square root of 3. In a 208v single phase (polyphase) circuit, the additional power that could become available to us in a reactive load (not resistive load) is 2/square root of 3 or 1.15470054. So you are incorrectly subtracting it from the sum of single phase load and not adding it to the 208v polyphase circuit.

Walt Stevens wrote on 09/01/11:

Hello, wonderful calculator.  It is helping with my project with a 60 amp(48 amp) 17.3 KVA PDU.  I have one twist in that this PDU also has and additional 120v NEMA 5-15 receptacle which uses Phase X to Neutral. 

Any suggestions on how to get a better estimate of Phase X amperage with this additional outlet on the PDU. ?

How would this 115V output on Phase X upset the phase balance. 

Thanks

Bob wrote on 09/26/11:

The calculation for the L1 “Capacity Remaining” for the two 60A sheets are using the incorrect breaker values. They are using 40, but should be 45 and 48. Is it possible to add a sheet for a 100A feed?

chris wrote on 09/27/11:

Hi

I wonder if you can help ?

 

We are doing some rough non invasive monititoring in factory.

 

We can calibrate the monitor units for UK single phase power, but will only be putting a clamp on one of the phases on the 3 phase - I know there are inaccuracies but what would be an appropriate multiplier factor for the power in a 415V 3 phase system top give teh power in this?

 

Thanks

 

Chris

Larry wrote on 07/13/12:

If I am told I have a 50amp three phase circuit feeding my rack, does that mean I can have up to 50 amps on each of the three phases for a total of 150 amps?
Also if my 50amp circuit is connected to a three phase PDU with three banks and a 20amp circuit breaker in each bank, I assume that the most current I can draw is 20 amps in each bank regardless of how the current adds up on the three phase lines(l1,l2, and l3).

don wrote on 09/01/12:

How do I calculate the total amporage on a exesting 3 phase 120/208 panel?

shmuel kochavi wrote on 10/10/12:

dear

thanks very much

 

what are the z1-z6?

 

can it be altered for 115v?

Henry Hsu wrote on 03/03/13:

Sorry it took 2 years to reply to this post! Yes, the spreadsheet I created is specifically created for data centers—the main target audience of this blog. In this environment, the resistive load assumption is both standard and realistic.

Appreciate your eagle-eyed review!!

Masawudu Abdul Mugeez. wrote on 03/07/13:

It is altered to 113v.

Henry Hsu wrote on 03/26/13:

Hi Bob, Sorry it took 1.5 years to reply to this. Thanks for catching the typo; I have updated it appropriately.

Henry Hsu wrote on 03/26/13:

Hi Chris,

In a 3-phase unit at 415V, the complications discussed in this blog post don’t apply. 415V/3-phase power is very simple, because the lines are not interconnected. Rather, each line is connected directly to neutral.

 

Thus, clamping any one of the lines gives you the exact current (at single-phase, 230V) you need to know. Clamping each of the three lines, multiplying by 230V, will give you a pretty accurate nominal reading of apparent power.

Henry Hsu wrote on 03/26/13:

The easiest way to understand this is to click on the “50A (35A rated)” tab of the spreadsheet linked on this page.

In short, no, you cannot assume that there is a “total of 150amps”. Such a statement is a confusion of how 3-phase power works.

 

The power strip you describe would actually be rated as 35A, so—and this is for Larry, nobody else copy/paste this answer, please—the best way to think of your particular power strip in single-phase terms is that no one bank can exceed 20amps.

 

If and when you loaded such a power strip (full 20a on each of the three banks), you would see that the actual current flowing in each of the three lines is actually 35A each ... for the reasons I explained on this blog entry.

 

It is confusing, but true, that putting 20A on each of three circuits, results in 35A flowing on each of three lines. Completely counter-intuitive, and hence the need for a tool like this one.

3-phase, 208V Power Strips (Rack PDUs) Demystified wrote on 04/09/13:

[...] you think is reasonable in your head is, in fact, not actually the way it works. In a previous post, I attempted to explain at a lower-level the reasons why this is true — including a link to a [...]

Ted Mittelstaedt wrote on 10/21/13:

Hmm I wonder if this spreadsheet’s real intent is to convince you to buy metered PDUs? wink

The only problem I have with this article is the following:

 

“Principally, for cabinet power capacities above 5kVA, utilizing 3-phase rack power strips can significantly reduce the copper required to supply such dense loads….If I plug in a 250W power supply (about 1.2 amps) on this receptacle right here…”

 

For starters, 3 phase only reduces copper in the PDU feeds but the majority of copper is the connections from the PDU outlets to the servers, so really the big benefit is going to 208v power instead of 120v power.  Higher voltages reduce copper more so than the phase. Your example of a 250W supply drawing 1.2A is only valid for 208v power, not 120v power.

 

Of course, I will take the opportunity to complain about the brain-dead manufacturers who continue to supply big, thick power cables with their servers - come on people, we do not need #14 GA stranded power cables to carry 2A - we do not need conductors so thick that your minimum bend radius is 3 inches - do you really think I like stuffing that into my server cabinets?  Ironically they are all competing with each other over who makes the servers that are the “greenest” and take the least power - but the image is that the thicker and heavier the power cord is the more powerful the server - go figure!

SP wrote on 03/13/14:

Reference to “3-Phase Rack Power Strip Current + Power Capacity Calculation Tool” can someone please explain to me how do you calculate the Line currents (L1, L2 and L3), here are some figures to reference:
L1/L2 = 8.1
L2/L3 = 10.6
L3/L1 = 11.5

L1 = 17.1
L2 = 16.2
L3 = 19.1
Total Power (kVA) = 6.3

sf wrote on 08/14/14:

Is there a way to edit the spreadsheet, or do you have another one that includes a tab for
3phase 208V-16A @ 5.8kVa ?


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