Voltage Drop Calculations

Voltage Drop Calculations are an important part of electrical system design to ensure that the voltage at the load end of a circuit does not drop below the acceptable level due to the resistance and reactance of conductors over the distance the electricity is transmitted. Excessive voltage drop can lead to inefficient operation of electrical equipment, overheating, and potential failure.

Key Concepts:

1.      Voltage Drop: The reduction in voltage in the electrical circuit between the source and the load due to the resistance and reactance of the conductors.

2.      Acceptable Voltage Drop: Most electrical codes, including the National Electrical Code (NEC), typically limit the acceptable voltage drop to 3% for the branch circuits and 5% for the total feeder and branch circuits combined.

3.      Components Influencing Voltage Drop:

• Conductor resistance (R): Resistance of the conductor material (typically copper or aluminum).

• Conductor reactance (X): Impedance due to inductive reactance, especially for alternating current (AC) circuits.

• Current (I): The amount of current being drawn by the load.

• Conductor length (L): The distance between the power source and the load.

Voltage Drop Formula

The basic formula for calculating voltage drop in a single-phase circuit is:

Vd=2×I×R×L1000V_d = \frac{2 \times I \times R \times L}{1000}

Where:

• VdV_d is the voltage drop (in volts).

• II is the current (in amperes).

• RR is the resistance of the conductor (in ohms per unit length).

• LL is the one-way length of the wire (in meters or feet).

• 10001000 is used to convert the units to volts if current is in amperes and resistance is in ohms.

• 3≈1.732\sqrt{3} \approx 1.732 is a constant for three-phase circuits.

• ZZ is the total impedance (in ohms), and Z=R2+X2Z = \sqrt{R^2 + X^2}.

For a three-phase system, the voltage drop formula is:

Vd=3×I×R×L1000V_d = \frac{\sqrt{3} \times I \times R \times L}{1000}

Where:

In three-phase systems, the resistance (R) and reactance (X) are combined into the impedance (Z) of the wire.

For AC circuits, the impedance (Z) combines both resistance (R) and reactance (X), and the formula becomes:

Vd=3×I×Z×L1000V_d = \frac{\sqrt{3} \times I \times Z \times L}{1000}

Where:

Factors That Affect Voltage Drop:

1.      Conductor Material:

• Copper has lower resistance than aluminum, so it will result in a smaller voltage drop for the same current and length.

2.      Wire Size (Gauge):

• Larger wires (with lower resistance) will cause less voltage drop than smaller wires. For example, 10 AWG wire will have more resistance than 6 AWG wire, resulting in a larger voltage drop.

3.      Conductor Length:

• The longer the wire, the greater the voltage drop. Therefore, circuits that run long distances will require larger wire sizes or will need to use a higher voltage to compensate for the drop.

4.      Current Flow (Amperage):

• The higher the current, the higher the voltage drop. For example, a motor running at full load will cause a higher voltage drop than one running at idle.

5.      Phase Type:

• Voltage drop is lower in three-phase systems compared to single-phase systems due to the nature of three-phase power.

Example of Voltage Drop Calculation:

Example 1: Single-Phase Circuit

• Current (II) = 20 A

• Conductor resistance (RR) = 0.5 Ω/km

• Conductor length (LL) = 100 meters (one way)

Suppose you have a single-phase circuit with the following parameters:

Using the formula for voltage drop:

Vd=2×20×0.5×1001000V_d = \frac{2 \times 20 \times 0.5 \times 100}{1000} Vd=20001000=2 voltsV_d = \frac{2000}{1000} = 2 \, \text{volts}

So, the voltage drop in this circuit is 2 volts.

Example 2: Three-Phase Circuit

• Current (II) = 30 A

• Impedance (ZZ) = 0.6 Ω/km

• Conductor length (LL) = 150 meters (one way)

For a three-phase system with the following parameters:

Using the formula for voltage drop in a three-phase system:

Vd=3×30×0.6×1501000V_d = \frac{\sqrt{3} \times 30 \times 0.6 \times 150}{1000} Vd=1.732×30×0.6×1501000V_d = \frac{1.732 \times 30 \times 0.6 \times 150}{1000} Vd=46.741000=0.047 volts=47 mVV_d = \frac{46.74}{1000} = 0.047 \, \text{volts} = 47 \, \text{mV}

So, the voltage drop in this three-phase circuit is 47 millivolts.

Example 3: Voltage Drop and Wire Gauge
Voltage Drop and NEC Code:

• Branch circuits: Maximum 3% voltage drop.

• Feeder circuits: Maximum 5% total voltage drop (including branch circuits).

If you want to reduce the voltage drop in a circuit, you can use a larger wire size. For instance, if a 12 AWG wire is resulting in too much voltage drop, upgrading to 10 AWG or 8 AWG wire will decrease the resistance and, thus, the voltage drop.

The NEC (National Electrical Code) typically recommends a maximum of 3% voltage drop for branch circuits and 5% for total feeders and branch circuits combined to ensure efficient operation of electrical systems.

If a voltage drop exceeds these values, equipment may not function properly, especially motors and sensitive electronics. To meet code, you may need to increase the conductor size (decreasing resistance) or reduce the load on the circuit.

How to Mitigate Excessive Voltage Drop:

1.      Increase Conductor Size:

• Choose a larger wire size to reduce the resistance and, thus, the voltage drop. Larger wires cost more but reduce the overall energy loss.

2.      Reduce Circuit Length:

• If possible, reduce the distance from the power source to the load. This can be done by relocating equipment or using a more direct path for wiring.

3.      Use Higher Voltage:

• If feasible, increasing the system voltage will reduce the voltage drop since the voltage drop is proportional to the voltage. For example, use 400V for longer circuits instead of 230V.

4.      Use a Higher Current Rating Transformer:

• A transformer with a higher current rating can be used to supply the required power while minimizing the effect of voltage drop over distance.

5.      Install Voltage Drop Compensators:

• Certain devices, like boosters or voltage regulators, can help mitigate voltage drop by maintaining a stable voltage at the load end.

Attention 

Voltage drop calculations are essential to ensure that electrical circuits are designed to maintain an acceptable level of voltage at the load end. The key factors influencing voltage drop include conductor material, wire size, circuit length, current, and whether the system is single-phase or three-phase. By calculating the voltage drop and taking corrective measures, you can ensure the efficiency, safety, and reliability of the electrical system.