Voltage Drop Formulas

This week we will take a break from Grounding and Bonding to talk about Voltage Drop formulas. Voltage Drop calculations are arguably the most complicated, yet one of the most important items an individual electrician must perform. Total impedances and resistances of conductors may cause a substantial variation of voltages between the service supply and the voltages present at the point of utilization. Overly excessive VD's can severely impair starting and the operational running of equipment. Voltages that are too small for their nominal ratings cause substantially high inefficiencies in equipments, lighting, and heating. Even a small drop of only 10% of the rated voltage causes decreases of 15% for fluorescent lighting, and as much as 30% for incandescent lighting! Motors will run with less torque and operate at higher temperatures. Given the same 10% VD, the Full Load Amperage increases by 11%, the operating temperature rises by 12%, and the torque produced would DROP by 19%!



These figures showcase the field electrician's ability to help (or harm) the overall efficiency of an electrical system's installation. In today's climate, conserving energy is now a MAJOR consideration. Many electricians hate math and granted, voltage drop formulas seem only a step down from an engineer's level of calculation. Few, maybe as small as 10% of us, even remember the formulas off hand, much less apply them on a daily basis. However, the electrical engineer isn't present during an installation, YOU are! The EE has no way of knowing the actual routing or footage a particular circuit conductor may take. Thus the installer MUST be the person responsible for these calculations!



There are essentially five types of voltage drop formulas. These are,



(1):Direct Current VD (the most commonly used and the simplest one) that uses a "constant value" for "k" (specific resistivity),

(2): Direct Current VD that use individual resistance values from Chapter 9, Table 8 of the NEC,

(3): A/C resistance VD using an 85% Power Factor and multiplying factors from Chapter 9, Table 9,

(4): A/C resistance VD using the "Neher-McGrath" method for specific Power Factors other than 85% (the single most difficult formula to use), and finally,

(5): The "Mid-Point" calculation, used for multiple loads over a distance but on a single circuit. Here are the formulas written out:



(1) VD = 2*(K)*I*D

-----------

CM



(2) VD = 2*D*R*I

----------

1000



(3) VD (line to neutral) = Table Value * D * I

--------------------

1000' (Multiply times 2 for 2 pole circuits such as 240V etc...)



(4) Zc = (Rx * cos0) + (XL * sin0)





(5) Includes steps from 1 and 2 with averages (more about this formula next week)...



While none of these are NEC code requirements, they are listed as FPN's in 210.19(A)(1) FPN(4), and 215.2(A)(2) FPN(2). VD calculations are simply good and smart practices to include in your day to day work. The use of any of these formulas will give, in most cases, fairly close values, therefore, many use the simplist of them for ease of daily use. Formula 1 has, for the most part, become the "de facto" one to use in the field. All you must remember is that "k" is a constant value of 12.9 for copper and 21.2 for aluminum. The circular mils value is a quick reference in Table 8 and you're all set. (The 12.9 ohms value is derived by using the ohms per 1,000' of a given stranded wire, divided by 1000 to get the per foot values, then multiplied by the circular mils of the wire size. Interestingly, solid wire has a smaller "k" value of 12.6 ohms. However, use of the 12.9 value will give you the more conservative value.)



One final note to always consider is that all of these formulas and values are based on a temperature rating of 75 degrees C (167 degrees F). Any higher temperature would greatly increase the VD percentages. Temperature increases would use R1 [1 + .00323 (T2 - 75)], where T2 is your higher temp value in degrees and R1 would be the ohms value from Chapter 9, Table 8. (Use this formula for copper only).



All of this being said, VD calculations can be quite the time consuming, confusing, pain in the rear for the field electrician. Electrician Testing has created some very unique and very useful/helpful charts for VD. These charts virtually eliminate the need to remember any of the above formulas, values, and math! Contact us, via email, for a copy of them. Next week we should be back to grounding and bonding! Hope you have a great week, and let us know, as usual, if you have any specific questions....

Wire Ampacity and Conduit Fill Calculation

Wire Ampacity and Conduit Fill Calculation

This week I want to take a minute to review our wire ampacity and conduit fill (wire fill) calculation.

There seems to be a lot of common confusion out there when it comes to wire fill. Annex "C" in the back of the 2208 NEC © is a good tool, but it can be very dangerous to use it without considering the impact of de-rating factors found in Chapter 3.

We normally use a 20 amp circuit breaker to protect #12 AWG cu wire. Annex C tables show that we can safely place a total of 16 of this size (Type THHN, THWN, or THWN-2) in a 3/4" EMT conduit. this is only for the protection of the wire from a physical stand point. Annex C is only concerned with the protection of the wire during installation. It does NOT take the ampacity of the wire into consideration!

When de-rating wire, we begin with table 310.16 (page 147, 2008 NEC ©) and de-rate for our ambient temperature AS WELL AS the number of current carrying conductors. The de-rating table T310.15(b)(2)(a) on page 145 shows us:

"Adjustment Factors for more than Three Current carrying conductors in a Raceway or Cable"

Number of C.C.C.	% of 310.16 Values
4-6 Conductors	80%
7-9 Conductors	70%
10-20 Conductors	50%
21-30 Conductors	45%
31-40 Conductors	40%
41+ Conductors	35%

You can quickly see that in our earlier example, if we put 16, #12 THHN conductors in that 3/4" conduit, we would have to drop the circuit breaker to a 15 ampere size! Now seriously, how many electricians in the field really do that? You understand now how dangerous the casual use of Annex "C" can be.

For all practical purposes, only 9 current carrying conductors could be placed in that conduit without having to drop the OCPD (circuit breaker) size: [T310.16 value for #12 THHW=25 Amps. 25 Amps X 70% (the de-rating for 7-9 conductors) would equal 17.5 Amps, and due to 240.3(B) we are allowed to round up to a 20A breaker.]

The grounded conductor (neutral) can also cause confusion sometimes. It counts as a "current carrying conductor" in some cases, but not in others. If it is shared between two different phases in a multi-wire circuit, it usually does not count as a current carrier , as it only carries the unbalanced load in the circuit. [For example, a "full boat with circuits #3, #5, #7 in a 30 panel, would not usually have their neutral counted.]

Where non-linear loads are supplied however the neutrals DO count. If you have electronic fluorescent ballasts or heavy computer loads (etc...) on a shared branch circuit neutral, it will have harmonic distortions that will disrupt the cancellation of loads between phases and can actually cause larger loads on a neutral that are found on any single ungrounded phase conductor in the circuit.

If the (neutral) grounded conductor is NOT shared between phases, i.e. a single 120V single phase branch circuit, such as a general purpose receptacle outlet circuit conductor, it counts as a current carrying conductor. In this installation it carries the full load on it back to the distribution point. Two other common issues with Annex C are considerations for different sized EGC/GEC conductors, and differences between Annex C values and manual fill calculations using Chapter 9, tables 4 and 5.

The value of Annex C is a "staff it full" value. Therefore you would have to keep in mind your additional ground wire, which is usually a smaller size than that of the phase conductors. The only way to use Annex C in this case is to always consider your EGC or GEC as a full size conductor count. A manual calculation is more accurate than Annex C and it has been this author's observation that Annex C values sometimes vary quite a bit from a manually calculated fill based on Chapter 9 tables.

All of that considered, going back to our 3/4" raceway, we could put 3 "full boats" in this raceway (3 neutrals not counted, 9 phase conductors, and 1 equipment ground) for a total of 13 conductors. This results in 3 less than our "fill amount" according to our Annex C tables. Thus, our advice is to always carefully consider your ampacity de-rating factors as required by 310.15.

(Author's Note: As evidenced by the above, an electrician would have to refer to several different tables in order to correctly and safely calculate the correct fill and ampacity values for watch and every pipe run. we are excited to provide and industry first for all our members. Electrician Testing has painstakingly prepared a custom table; available only through us, that considers ALL required factors. Everything is brought together in one quick and easy to follow chart. Contact us today to get yours, and look for our upcoming publication that will include this chart along with many, many more custom time saving tables!)