Ecmweb 7300 Voltage Drop 1 Pr
Ecmweb 7300 Voltage Drop 1 Pr
Ecmweb 7300 Voltage Drop 1 Pr
Ecmweb 7300 Voltage Drop 1 Pr
Ecmweb 7300 Voltage Drop 1 Pr

Uncovering the Cost Benefits of a Good Lighting Circuit Design

April 20, 2015
Why you should beware of simplistic voltage drop calculations.

Iterative voltage drop calculations are some of the most tedious and time-consuming components of an electrical design process. This is especially true for large lighting installations, such as those found in parks and parking lots as well as roads and highways. As a result, it is common for designers to oversimplify voltage drop calculations in a lighting design. With the lighting industry trending toward LED use, it is becoming increasingly common to string large quantities of luminaires on a single circuit due to the decreased load per luminaire. Now more than ever, detailed voltage drop calculations can avoid over engineering of lighting systems and substantially decrease project costs.

Parks such as Spokane, Wash.’s recently renovated Huntington Park on the Spokane River extends down the hillside, which places lighting poles along a meandering path — far from the source of electricity. In cases like this, precise voltage drop calculations are critical.

Guides and online calculators are readily available for little or no cost, many of which are based on IEEE Standard 141-1993, Recommended Practice for Electric Power Distribution for Industrial Plants. In Chapter 3.11 of this standard, voltage drop calculations and formulas are outlined in great detail. This standard, however, does not address voltage drop over long strings of loads. It is written primarily for a situation where a single load is energized at the end of a long feeder. However, this standard and the tools based on it are often inappropriately applied to voltage drop calculations of lighting systems.

Although the actual mathematics of the voltage drop calculation are beyond the scope of this article, it’s important to keep in mind these calculations will reveal some complexities beyond Ohm’s law. For example, voltage drop depends on the reactance of the conductor, the type of conduit surrounding the conductor, the power factor of the served load, and the temperature of the conductors during operation.

Lighting project example

On many projects, it often becomes necessary to branch out perpendicularly from a single string of luminaires rather than run along a fairly straight and long line. The lighting layout in Spokane’s Huntington Park (see Photo) is a good example of this type of arrangement. The one-line diagram for this specific project (Fig. 1) resembles a tree shape. However, not all designers will approach sizing the required conductors in the same way. If the designer is still using traditional rules of thumb, the result could add significant cost to the project. Let’s assume the following with regard to this particular project:

Fig. 1. Shown is a simplified one-line diagram of light pole connections in a Spokane, Wash., park.

• The average distance between luminaires is 50 ft.

• Each pole-mounted LED luminaire consumes 178VA.

• The power factor is 1.00.

• The feeder uses Schedule 40 PVC.

• I2R losses in the conductors are ignored.

• The available voltage at the source panel is 277VAC.

The one-line diagram in Fig. 1 is often mistakenly modeled as shown in Fig. 2. To quickly size the required conductor in this example, a designer might perform the following calculation:

Fig. 2. Here, the one-line diagram from Fig. 1 is being modeled as a single-point load.

• Determine the total load on the circuit.

• Determine the branch with the longest distance from the source.

• Determine the design characteristics of the installation (such as those in Table 1).

Table 1. Design characteristics of conductor run serving the park luminaires.

Using the findings from the above steps, determine the required conductor size.

Running through this exercise will yield a result of two 4 AWG conductors and a 4 AWG ground in a 1 in. Schedule 40 PVC conduit. Note that the equipment grounding conductor increases are proportionate to the phase conductors per the requirements of Sec. 250.122(B) of the NEC. With a calculated voltage drop of approximately 2.3%, this installation will be Code compliant, meet desired design requirements, and adhere to IEEE Standard 141-1993 requirements.

This calculation can be performed in under an hour and doesn’t require expensive software to yield an acceptable result. There are, however, numerous flaws with this approach, and more sophisticated approaches to this calculation will save the owner of this installation a substantial amount of money during construction.

Sizing with precision: the “nodal” model

The above method was sufficiently accurate in situations where only a few luminaires are placed on a single circuit. But as the number of luminaires on the circuit increases, the result of such a simplistic calculation deviates increasingly from reality. This is primarily due to the fact that the load on a segment increases as you approach the source — a factor ignored by this model. The first segment out to the first luminaire carries substantially more load than the segment near the end of the string.

In order to properly model the example above, the designer must treat each load as a “node” and run a voltage drop calculation for each segment between nodes. Where a node has multiple branches, the longest branch should be selected first, and that node should be treated as a single node with the sum of all the loads on the unused branches. This can be seen in Fig. 3. The longest string (ending with load 12) was selected, and all the loads at nodes 4 and 6 were consolidated into single large loads.

Fig. 3. This one-line diagram models the lighting load on the circuit using a “node” approach.

In Fig. 3, the string of luminaires can be separated into 11 segments. This will require 11 voltage drop calculations. The starting voltage for each segment will be the end voltage of the previous voltage drop calculation. Table 2 summarizes the cumulative loads found in each segment and the resulting voltage drop.

Table 3. Here is a cost summary of the three different design approaches outlined in this article.

The simplest approach to sizing the wiring at this point is the guess-and-check method. Assume a conductor size, run through the voltage drop calculations, adjust the wire size (as necessary), and repeat. The overall voltage drop for the feeder will be the total of all voltage drops calculated. It can be assumed that the consolidated unused branches, such as the branches on nodes 4 and 6, will have a voltage drop less than the calculated voltage drop due to the decreased distance and load.

Some designers choose to build complicated spreadsheets or use expensive modeling software. Regardless of the method, it becomes clear early in the process that this will require substantially more effort than the simple method outlined in the previous section. However, as you’ll see, it’s well worth the effort.

Using this approach will yield a result of two 8 AWG phase conductors and an 8 AWG ground conductor in a ¾-in. Schedule 40 PVC conduit. Again, with a calculated voltage drop of approximately 2.79%, the design achieved the same design goals and meets the same Code requirements as the previously described method.

Stepped conductor sizes

The previous two approaches make the assumption that a single conductor size will be used for the entire installation. To take the nodal method one-step further, a designer may wish to size each segment separately in order to achieve even greater cost savings to the project. However, it is important to keep in mind that for some projects, requiring many different wire sizes may cost more than choosing two or three. For example, in smaller installations, it may be less cost effective for a contractor to bring many wire sizes on-site — each with a minimum ordering quantity that is much greater than the required length.

Therefore, a reasonable balance must be found. Using the example from above, consider finding what appears to be the “trunk” of the system. This will be the area where the majority of the current will be carried. The most effective place to have an altered conductor size will be in this area. Leaving that conductor large and decreasing the conductor size in the less heavily loaded branches will allow for the most effective gains. Node 6 in Fig. 1 is the last node with branches and could represent the end of the “trunk”. For example, 8 AWG wire could remain in segments 1 through 6, and 10 AWG wire could be used for all the remaining branches. The resulting voltage drop over the branch circuit will approach 2.98% but still remain within recommended design limits and Code requirements.

Cost benefit

The cost benefit of this detailed approach outweighs the cost of the designer’s time by a significant margin. Estimating the cost of each installation provides some surprising results. Note that cost estimates were performed using the recently published conductor pricing, conduit, and labor pricing from the latest edition of RS Means, industry standard contractor overhead and profit, and a 10% margin of error.

Using the simple method of sizing conductors (Method 1), the installation would cost approximately $24,088. Using the “nodal” model (Method 2), and using a single conductor size, the installation would cost approximately $17,353. Using the “nodal” model with a stepped conductor sizing scheme (Method 3), the cost of the installation would be $13,424. The percent of cost savings of Methods 2 and 3 as compared to Method 1 is summarized in Table 3.

Table 2. Here’s a summary of the cumulative voltage drop calculations for each segment of the lighting system shown in Fig. 3.

As you can see from these findings, the cost of the additional design effort is well worth the savings. In a large park, road, or highway lighting project — where branches of these type can be found numerous times throughout the design — the savings to the overall project add up quickly.                                                                                             

Hesse, P.E., is an electrical engineer with Coffman Engineers, Spokane, Wash. He can be reached at [email protected].

About the Author

Aaron Hesse, P.E. | Electrical Engineer

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