Voltage Drop Calculation in an Electrical Circuit

 Wires used in electrical installations must be suitable for carrying current and avoiding excessive voltage drops. With a few exceptions, NEC has no voltage drop requirement as it is not considered unsafe. However, it wastes energy, so it's up to you to investigate. 

Voltage drop is the total amount of voltage loss experienced by all or part of a circuit due to impedance and other factors. The higher the voltage drop in the system, the more likely adverse effects will occur. Voltage drops are considered system losses and inefficiencies as they can lead to malfunctions and poor performance of the entire system.

Due to the fact that voltage and current are transmitted through cables and wires, resistance or impedance will develop based on the cable's size(cross-sectional area) or length. Consequently, after doing the voltage drop calculations, the final cable and conductor size for every project is required.

Voltage drop occurs when the total expected voltage from the source is not been delivered to the load. Example -  An electric motor that was supplied with a single phase 220V from source when measured at the motor terminal with a multimeter might be reading let say 150V.

Causes of Voltage Drop

1. From the Conductor Side

3 major factor contributes to the amount of voltage drop in a conductor - 

1. Resistivity - Type of Conductor (Aluminum or Copper)

The two major conductor metal used for electrical system are copper and aluminum. Copper has a resistivity of 1.62 x 10^8Ω while aluminum has a resistitvy of 2.63 x 10^8Ω. The higher the resistivity of a material the lesser will be the conductivity of that material. So, copper has lower resistivity and higher conductivity as compare to aluminum. Also, the higher the resistitivty that higher will be the voltage drop

2. Cross Sectional Area of the conductor 

The higher the cross sectional area of cable (cable diameter in mm^2) the higher will be its conductivity and the lesser will be its resistivity. Conductors with larger diameters will result in less voltage drop than conductors with smaller diameters of the same length

3. Length of cable

The length if a conductor is a very important factor in cable selection as the longer the length of a cable the higher will be its resistivity and the higher will be its voltage drop. 

So, shorter conductors will have less voltage drop than longer conductors for the same conductor size and type

Other factors to consider are - 

Loose Connections - 

Poor cable termination (on cable lugs, terminal blocks etc) or cable joint will produce more resistance, heat loss and invariably lead to voltage drop.

Temperature - 

as a general rule, most conductive materials will increase their resistance with an increase in temperature.

Reducing Voltage Drop

It’s not possible to have zero voltage drop — because some voltage loss is going to occur naturally from the resistance of the conductors themselves — simply because it takes effort (voltage) to push current through a conductor. However, the goal is to minimize the voltage drop as much as possible. Besides wasting electricity that you are paying for, there are other reasons to keep voltage drop to a minimum when performing electrical wiring. These reasons include: 

1. System efficiency. If a circuit has much of a load, a larger conductor (that allows less voltage drop) pays for itself many times over in energy savings alone. 

2. System performance. As stated before, excessive voltage drop in a circuit can cause lights to flicker and/or burn dimly; heaters to heat poorly; and can cause overheating, inefficiency, and shorter life span of motors. 

3. Troubleshooting. When one follows the Code voltage drop recommendations, the electrician doing troubleshooting does not have to guess whether his low voltage field measurements indicate (1) a problem or (2) that voltage drop was not accounted for in the design.

 

Voltage Drop Calculation

As a summary : NEC (National Electrical Code) and CSA (Canadian Electrical Code) recommends the voltage drop in a circuit should not be more than 5% of the supply voltage while BS (British Standard) recommend 4% of the supply voltage.

According to NEC 2011 article

• The maximum allowable voltage across branch circuit is 3 percent, measured between the corresponding electrical panel and the farthest outlet delivering power, heating, lighting or any combination of such loads.
• The maximum combined voltage drop across main feeders and branch circuits is 5 percent, measured from the service connection to the farthest power outlet.

These voltage drop levels are considered to provide reasonable operational efficiency. It is important to note that, when circuit conductors are increased in size to compensate voltage drop, the equipment grounding conductor must be increased accordingly.

Hence, based on this rules, design engineer should ensure there installation is such that it meet this standard to avoid post installation problem.

To calculate the voltage drop in your installation, you can use the formula below - 

where:

I = Load current (amps)

L = Length of cable

K = ohms-cmil per ft

cmil = circular mil area of the conductor

K factor explained

K is the “electrical resistivity” of the type of conductor being used. The K value is a constant and can be found in most physics tables that provide resistivity of various materials. This electrical resistivity is calculated by (electrical resistance x cross-sectional area/ longitudinal length) and is expressed as (ohms x cmil/ft) or simply (ohms-cmil/ft.) Copper has a K value of 12.9 ohms-cmil/ft and aluminum has a K value of 21.2 ohms-cmil/ft. Other reference materials may show slightly different values, but for the purposes of this discussion, these values are acceptable. These two values are derived from the data found in Chapter 9, Table 8 of the Code. The K factor is found by multiplying the conductor’s resistance (ohm/kFT) by the conductor’s circular mil area and then dividing by 1000.

cmil explained

The circular mil or cmil is a unit of area that’s used when denoting the cross sectional size of something circular in shape — such as a wire. Wire size can be measured in several ways such as its diameter. We could say this wire has a diameter of ½ inch. Calculating the area of the cross-section with the common formula of Area = πr2 or Area = [(π)(d/2)^ 2] — would give us [(3.14) x (0.50 inches/2) 2] for an answer of 0.1963 square inches. As you can see, that is an extremely small number to work with and would be hard to express the wire size to others using this method. Since it’s the cross-sectional area that matters most when regarding current fl ow, we are better off designating wire size in terms of its cross-sectional area. So, another expression of wire diameter called circular mils is used. The formula for calculating the circular mil area of a circular wire is as follows:

cmil = (wire diameter in decimal inches x 1000)^ 2

You could also use this online mm2 to convert cable mm^2 to cmil to make it easier

Example 1 - 

A single-phase motor is located 250 feet(76.2 meters) from its power source and is supplied with 10 AWG copper (5.26mm^2). The motor has a full load current draw of 24 amps and voltage of 230V. What is the voltage drop when the motor is in operation? (Please note that for motors or continuous loads, the total current of the load in question is at 100%, not at 125%).

 Answer: Applying the single-phase formula for voltage drop, where: 

K = 12.9 ohms-cmil/ft for copper; 

I = 24 amps; 

D = 250 ft; 

cmil for 10 AWG = 10,380 cmil. 

Example 2 - 

A three-phase, 100 ampere load rated 208V is wired to the panelboard with 80ft lengths of #1 AWG  THHN aluminum. What is the approximate voltage drop of the feeder circuit conductors?

Answer: 

Applying the three-phase formula for voltage drop, where: 

K = 21.2 ohms-cmil/ft for aluminum; 

I = 100 amps; 

D = 80 ft; 

cmil = 83,690 cmil. 

How to correct Voltage Drop

In other to correct voltage drop during the design stage of an installation project. I will recommend two different approach.

1. Increase the calculated cross sectional area of the cable

2. Reduce the length of the cable

Conclusion

Most voltage drops mentioned by the National Electrical Code are recommendations. Beware that figures in some sections are requirements.

Voltage drop must be as low as possible, balancing technical and economic factors.

Where significant distance and power are involved, it is advantageous to use higher voltages to reduce conductor size and copper loss.

Approximate voltage drop calculations are frequently acceptable. However, it is essential to understand the fundamental limitations of different types of voltage drop computation procedures.