## Sunday, July 25, 2010

### 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

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1000

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

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

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

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....