Series voltage drop is the progressive loss of voltage that occurs when feeding a string of parallel-connected loads. It's of particular concern when feeding a string of roadway, walkway, or parking lot lamps (Photo). These situations definitely call for calculations to determine the voltage drop at the last luminaire.
The NEC does not consider voltage drop to be a safety concern. Thus, it provides only Fine Print Notes (FPNs) in Sec. 210.19 for branch circuits and Sec. 215.2 for feeders. The combined branch and feeder voltage drops recommended are 5%.
Many designers prefer to limit the voltage drop to 3% on the basis that the difference in illumination due to voltage drop would then be negligible. Many utilities, cities, states, and federal projects have their own specifications for maximum allowed voltage drop for street and area lighting, which can vary from a low of 3% to a high of 8%.
Aside from the negative effect on lighting illumination, excessive voltage drop can result in a reduction of equipment life, reliability, and performance. Line losses, resulting from undersized conductors, will result in increased utility costs, while simply over-sizing conductors to limit voltage drop will result in increased project construction costs.
Because the current varies from wire segment to wire segment along roadway, walkway, or parking lot lighting circuits, the procedure for calculating series voltage drop can be very tedious. Although you may apply rules-of-thumb, they don't usually give the desired confidence and are not usable for more complex lighting layouts.
Because the first segment of a string of loads carries the most current (and the last segment carries the least), it doesn't make economic sense to necessarily size all segments the same. By selectively increasing the size of the first few segments, you can obtain the desired overall voltage drop without oversizing the entire circuit. This approach results in the most economical solution, but also requires the most time-consuming analysis.
Consider a simple example, with five luminaires equally spaced, as shown in Fig. 1 (click here to see Fig. 1). Each luminaire contains one 250W HID lamp fed by a 240V, 2-wire source and No. 10 AWG copper wires in PVC conduit. The spacing from the power source to the first pole is 200 feet. For simplicity, the subsequent spacing between segments is also 200 feet. What is the percent voltage drop at the last pole?
For manual voltage drop calculations, the easiest and most common equation is as follows:
VD = (2 × R × L × I) ÷ 1,000 (Ref: “American Electricians' Handbook,” 14th Edition)
VD = Voltage drop in volts across the serving conductor,
R = Wire resistance in ohms per 1,000 feet at 75°C (available from Table 9 of the NEC),
L = One way length in feet, and
I = Current being drawn
A 250W HID lamp would typically have a Type S-50 HPF ballast and would represent a load on the line of 325VA. You would calculate the current draw per luminaire on the 240V source as follows:
I = VA ÷ V = 325VA ÷ 240V = 1.354A
From Table 9 of the NEC, the wire resistance (R) for 10 AWG copper wire for alternating current is 1.2 ohms per 1,000 feet. So, the voltage drop for each 200-foot segment is as follows:
VD = (2 × R × L × I) ÷ 1,000 = (2 × 1.2 × 200 × 1.354) ÷ 1,000 = 0.650V
The first segment will carry the total current, which is five times 1.354A or 6.770A. The current decreases for each subsequent segment down to 1.354A for the last segment.
The % VD equals 100 × (VD × 240). The % VD for each segment is equal to (0.650V ÷ 240V) × 100 = 0.271%. The respective currents for the five segments are 6.770A, 5.416A, 4.062A, 2.708A, and 1.354A. The respective cumulative % VD for the five segments are 1.354%, 2.437%, 3.250%, 3.792%, and 4.063% for the final luminaire position. A 4.063% total voltage drop at the last pole would be excessive for some specifications but acceptable for others.
As you can see, calculating a series of voltage drops is tedious work — even when the situation is a simple series string, and you're using simple equations.
Frequently, a series of luminaires is not all in a string. At some poles or junction boxes, there will be side laterals to other poles. This can be thought of as a “tree” distribution (Fig. 2). Series voltage drop calculations are most tedious, time consuming, and error prone for “tree” distributions. The procedure is to select the poles that represent the longest path through the tree. Where laterals (other poles) connect to this main path, you insert the total load from the side lateral(s).
Let's consider the example shown in Fig. 2. Assume that the longest path is the combination P1-P3-P5-P7-P8-P9 path. At position P3, you would include the loads P2 and P4. Correspondingly at position P5, you would include the load for P6. The resulting calculation, by either manual or computer means, will give the voltage drop at P1, P3, P5, P7, P8 and, most importantly, at P9.
Figure 3 shows the computer solution to the above tree problem. The problem is entered, solved, and documented in a matter of minutes. Notice how simply changing the size of the first two conductor segments from 10 AWG to 4 AWG lowered the end-of-circuit voltage drop to less than 5% without changing the size of the downstream conductors.