How to Calculate Voltage Drop Over Long Wiring Runs

Introduction

Voltage drop is an important consideration when running long wiring lengths. Excessive voltage drop can cause problems like reduced equipment performance, overheating of conductors, and nuisance tripping of circuit breakers or blown fuses. As an electrical engineer, I need to be able to accurately calculate expected voltage drop to ensure proper system operation.

In this article, I will provide a step-by-step guide on how to calculate voltage drop over long wiring runs. I will cover the basic formulas, discuss the key factors that affect voltage drop, and provide examples to demonstrate the voltage drop calculation process. Properly accounting for voltage drop is crucial for any electrical design, so being able to accurately determine expected voltage losses is an essential skill for engineers.

What is Voltage Drop?

Voltage drop refers to the reduction in voltage that occurs as power flows through a conductor. It is essentially the loss of voltage between the power source and the electrical load. This voltage reduction happens due to the electrical resistance of the conductors.

As current flows through a conductor, the resistance causes some energy to be lost in the form of heat. This energy loss causes a slight drop in voltage along the length of the conductor. The longer the conductor, the more resistance it has and the larger the voltage drop.

Excessive voltage drop is undesirable because it can lead to:

• Diminished performance of electrical equipment due to lower operating voltage
• Overheating of conductors as more current is drawn to compensate for the voltage drop
• Nuisance tripping of circuit breakers or blown fuses if voltage at load end drops too far
• Damage to sensitive electronic equipment that requires steady voltage input

By calculating the expected voltage drop for a particular wiring run, I can predict if these issues might occur and take steps to avoid them through wiring sizing or other methods.

Basic Voltage Drop Formula

The basic formula for calculating voltage drop is:

Voltage Drop = (2 × Resistance of Conductor × Load Current)

Where:

• Resistance of Conductor is in ohms (Ω)
• Load Current is in amps (A)
• Voltage Drop is measured in volts (V)

This simple formula gives me the voltage drop over the entire length of the conductor, accounting for the out and return paths. The (2 × Resistance × Current) portion covers the total voltage drop over the complete circuit loop.

To determine the resistance of the conductor, I need to know:

• The conductor length (in feet)
• Conductor size (cross-sectional area in circular mils)
• Conductor material resistivity (in ohm-circular mil/ft)

The resistance is calculated as:

Resistance (Ω) = (Conductor Length × Material Resistivity) / Conductor Area

I'll demonstrate how to use these formulas with some examples in the next sections. But first, let's look at the key factors that affect voltage drop.

Key Factors Affecting Voltage Drop

The amount of voltage drop depends on several important factors:

• Length of the conductor - The longer the run, the higher the resistance and voltage drop. Doubling the length doubles the drop.

• Conductor size - Larger conductors have less resistance, resulting in lower voltage drops. Doubling the conductor area (e.g. going from #12 to #10 AWG) halves the resistance.

• Load current - Higher current draw causes larger voltage drops across a conductor. Doubling the current doubles the drop.

• Conductor material - Materials like copper have lower resistivity than steel or aluminum, so copper wiring has lower voltage drop.

• Power source voltage - For a given load, a higher voltage system will have a lower percentage drop than low voltage.

• Power factor - Loads with a poor power factor draw more current, increasing voltage drop.

As you can see, the conductor length, size, and load current have the biggest impact on voltage drop. Understanding this allows me to minimize voltage drop through proper conductor and overcurrent device sizing.

Voltage Drop Examples

Let's walk through some examples to demonstrate calculating voltage drop using the basic formula:

Example 1

A 10 AWG copper conductor feeds a 200A load drawing 20A of current, over a 75ft circuit length. Calculate the voltage drop if the power system is 120V.

• Conductor size: 10 AWG copper
• Area: 10,380 circular mils
• Length: 75ft
• Load current: 20A
• Copper resistivity: 10.4 ohm-circular mil/ft

First, calculate the conductor resistance:

Resistance = (Length x Resistivity) / Area
= (75ft x 10.4 Ω-cmil/ft) / 10,380 cmil
= 0.072 Ω

Now use the voltage drop formula:

Voltage Drop = (2 x Resistance x Current)
= (2 x 0.072Ω x 20A)
= **2.88V**

For a 120V system, this 2.88V drop represents 2.4% loss. This is an acceptable voltage drop.

Example 2

A residential bathroom circuit uses #14 AWG copper wiring to feed a 20A load at 120V. If the total circuit length is 65ft, what is the expected voltage drop?

• Conductor: #14 AWG copper
• Area: 4,110 cmil
• Length: 65ft
• Current: 20A
• Resistivity: 10.4 Ω-cmil/ft

The resistance is:

Resistance = (Length x Resistivity) / Area
= (65ft x 10.4 Ω-cmil/ft) / 4,110 cmil
= 0.166 Ω

The voltage drop is:

Voltage Drop = (2 x Resistance x Current)
= (2 x 0.166Ω x 20A)
= **6.64V**

For a 120V circuit, this represents a 5.5% drop. This exceeds the recommended 3% limit, so a larger conductor size is required.

Recommended Voltage Drop Limits

For proper system performance, voltage drop should be limited to:

• Feeders - 3% maximum
• Branch circuits - 5% maximum

For low voltage systems like 12V or 24V DC, even smaller drop limits may be required, sometimes 1% or less.

As the examples show, calculating the expected voltage drop during design allows corrective actions to be taken early to avoid problems.

Tips for Minimizing Voltage Drop

Here are some tips to minimize voltage drop in electrical systems:

• Increase conductor size - Larger wires reduce resistance and drop

• Use copper wiring instead of aluminum - Copper has lower resistivity

• Specify higher system voltage - Eg. 480V instead of 120V

• Locate panelboards and loads close together - Shorter wire runs

• Use separate neutral conductors - Eliminates neutral return drops

• Use voltage drop calculators - Quickly evaluate alternatives

• Follow code requirements - NEC Article 210.19 lists maximum drop values

• Test under fully loaded conditions - Identify unacceptable drops

Carefully calculating and limiting voltage drop is crucial for maintaining proper equipment operation and power quality in electrical systems.

Conclusion

Voltage drop is a critical electrical design consideration, especially for long wiring runs. In this article, I've explained the key factors that contribute to voltage drop and demonstrated how to use the basic formulas to calculate expected voltage loss in different scenarios.

The examples illustrate how conductor length, size, and load current impact the drop. By limiting drop to recommended values, issues like overheating, poor performance, and nuisance tripping can be avoided. Proper calculation and minimizing of voltage drop ensures electrical systems will operate safely and efficiently.