Voltage drop calculation using TVD, cable size, current, route length, power factor and conductor arrangement.

A correct voltage drop calculation is essential when selecting electrical cables. A cable may have sufficient current-carrying capacity, but it can still be unsuitable if the voltage reaching the load is too low. This guide explains TVD, cable sizing, power factor, conductor arrangement, temperature correction and practical worked examples for electrical engineers.

Table of Contents

1. What Is Voltage Drop?
2. Why Voltage Drop Must Be Checked
3. Understanding Tabulated Voltage Drop
4. Single-Phase Voltage Drop
5. Three-Phase Voltage Drop
6. How to Read TVD From a Cable Table
7. Worked Example: Three-Phase Motor
8. Effect of Conductor Temperature
9. Common Calculation Mistakes
10. Frequently Asked Questions

What Is Voltage Drop?

Voltage drop is the reduction in voltage between the source and the load terminal. When current flows through a cable, the cable impedance causes part of the supply voltage to be lost along the route.

For a simple resistive circuit:

V_drop = I × R

where:

• V_drop is the voltage drop in volts.
• I is the load current in amperes.
• R is the circuit resistance in ohms.

In an AC circuit, the cable has both resistance and inductive reactance. For a lagging power-factor load, the approximate voltage-magnitude drop is:

V_drop = I(R cos θ + X sin θ)

The resistance component is affected by conductor material, cross-sectional area, length and temperature. The reactance component is influenced mainly by cable geometry, spacing, formation and system frequency.

Why Voltage Drop Must Be Checked

Cable selection cannot be based on ampacity alone. A complete cable-sizing process normally requires both a thermal check and a voltage-drop check.

I_z ≥ I_n ≥ I_b

where:

• I_b is the design current.
• I_n is the protective-device rating.
• I_z is the corrected current-carrying capacity of the cable.

The cable must also satisfy:

V_drop ≤ V_drop,max

Excessive voltage drop can cause:

• Low motor starting torque.
• Contactor dropout during starting.
• Dim lighting and unstable electronic equipment.
• Reduced heater output.
• Higher cable losses.
• Poor equipment performance and reduced reliability.

Engineering reminder A cable may pass the current-carrying-capacity requirement and still fail the voltage-drop requirement. The final cable size must satisfy both conditions.

Steady-State Voltage Drop

Steady-state voltage drop occurs while equipment operates under its normal continuous load. Examples include a motor running at full load, a distribution board supplying its normal demand or a lighting circuit operating continuously.

Transient Voltage Drop

Transient voltage drop occurs for a short period during high-current events such as direct-on-line motor starting, transformer energisation, compressor starting and welding operations.

Because voltage drop is approximately proportional to current, a motor drawing six times its full-load current during starting may produce a temporary voltage drop several times greater than its normal running voltage drop.

Understanding Tabulated Voltage Drop

Cable tables often provide voltage-drop values in millivolts per ampere per metre:

mV/A/m

This is commonly known as the Tabulated Voltage Drop, or TVD. The basic TVD formula is:

V_drop = (TVD × I_b × L) ÷ 1000

where:

• TVD is the tabulated voltage drop in mV/A/m.
• I_b is the design current in amperes.
• L is the one-way cable-route length in metres.
• The division by 1000 converts millivolts to volts.

Simple TVD Example

Assume:

• TVD = 2.8 mV/A/m
• Current = 50 A
• Route length = 100 m

V_drop = (2.8 × 50 × 100) ÷ 1000 = 14 V

V_load = 230 − 14 = 216 V

Voltage drop % = (14 ÷ 230) × 100 = 6.09%

Single-Phase Voltage Drop

In a single-phase circuit, current travels to the load through the live conductor and returns through the neutral conductor. Both conductors contribute to the total voltage drop.

TVD_r = 2r

TVD_x = 2x

The single-phase voltage-drop formula becomes:

V_drop,LN = [(TVD_r cos θ + TVD_x sin θ) × I_b × L] ÷ 1000

Important When using a tabulated single-phase TVD value, the live-and-neutral return path has already been included. Use the one-way route length and do not multiply the result by two again.

Three-Phase Voltage Drop

For a balanced three-phase system:

V_LL = √3 × V_LN

The conventional formula using per-phase resistance and reactance is:

V_drop,LL = √3 × I(R cos θ + X sin θ)

However, most three-phase cable tables provide TVD values that already include the three-phase relationship. When separate three-phase TVD_r and TVD_x values are given, use:

V_drop,LL = [(TVD_r cos θ + TVD_x sin θ) × I_b × L] ÷ 1000

Do not add another √3 If the table already provides three-phase mV/A/m values, the √3 factor is normally already included.

Cable data used	Formula approach
Resistance and reactance per phase in Ω	Include √3 for a balanced three-phase circuit.
Three-phase TVD values in mV/A/m	Do not add another √3.

How to Read TVD From a Cable Table

The correct TVD value depends on more than conductor size. The designer must identify the actual cable system and installation arrangement.

1. Select the conductor cross-sectional area.
2. Select single-phase or three-phase AC.
3. Select the correct reference installation method.
4. Select whether the cables are enclosed, clipped direct, on tray or in free air.
5. Select whether the conductors are touching or spaced.
6. Select trefoil or flat formation for single-core three-phase cables.
7. Read the corresponding r, x and z values.

How TVD_r = 1.50 mV/A/m Is Obtained

For the worked example, the selected system is:

• 25 mm² single-core copper/PVC cable.
• Three-phase AC circuit.
• Reference Method C or F.
• Cables clipped direct, on tray or in free air.
• Cables touching in trefoil formation.

At the intersection of the 25 mm² row and the three-phase trefoil column, the table gives:

TVD_r = 1.50 mV/A/m

TVD_x = 0.175 mV/A/m

The value 1.50 mV/A/m is read directly from the cable table. It is not calculated separately in the worked example.

Why Cable Arrangement Changes Reactance

Cable resistance depends mainly on conductor material, cross-sectional area, temperature and length. Cable reactance is more sensitive to conductor spacing and geometry.

Three-phase arrangement for 25 mm² cable	TVDr	TVDx
Enclosed in conduit or trunking	1.50	0.29
Touching, trefoil	1.50	0.175
Touching, flat	1.50	0.25
Spaced, flat	1.50	0.32

All TVD values in the table above are expressed in mV/A/m.

Trefoil formation usually produces lower reactance because the three phase conductors are placed close together in a compact and symmetrical arrangement.

Worked Example: Three-Phase Motor Cable Sizing

Design parameter	Value
Full-load current, Ib	102 A
Power factor, cos θ	0.8 lagging
sin θ	0.6
Cable route length	75 m
Supply voltage, VLL	400 V
Maximum permissible voltage drop	2%

V_drop,max = 0.02 × 400 = 8 V

Initial Selection: 25 mm² Cable

Assume the cable has a current-carrying capacity of 104 A.

104 A > 102 A

The cable initially passes the ampacity requirement. From the three-phase cable table for touching trefoil formation:

TVD_r = 1.50 mV/A/m

TVD_x = 0.175 mV/A/m

V_drop,LL = [(1.50 × 0.8 + 0.175 × 0.6) × 102 × 75] ÷ 1000

1.50 × 0.8 = 1.20

0.175 × 0.6 = 0.105

1.20 + 0.105 = 1.305 mV/A/m

V_drop,LL = (1.305 × 102 × 75) ÷ 1000 = 9.983 V

Voltage drop % = (9.983 ÷ 400) × 100 = 2.496%

Result: Fail The calculated voltage drop is 2.496%, which exceeds the permitted limit of 2%. The 25 mm² cable passes the ampacity check but fails the voltage-drop check.

Revised Selection: 35 mm² Cable

TVD_r = 1.10 mV/A/m

TVD_x = 0.17 mV/A/m

V_drop,LL = [(1.10 × 0.8 + 0.17 × 0.6) × 102 × 75] ÷ 1000

1.10 × 0.8 = 0.88

0.17 × 0.6 = 0.102

0.88 + 0.102 = 0.982

V_drop,LL = (0.982 × 102 × 75) ÷ 1000 = 7.512 V

Voltage drop % = (7.512 ÷ 400) × 100 = 1.878%

Result: Pass The 35 mm² cable produces a voltage drop of approximately 1.88%, which is below the 2% project limit.

This example demonstrates an important engineering principle: cable size may be determined by voltage drop rather than current-carrying capacity.

Effect of Power Factor on Voltage Drop

V_drop ≈ I(R cos θ + X sin θ)

cos θ = 0.8

sin θ = √(1 − 0.8²) = 0.6

The resistive contribution is represented by IR cos θ, while the reactive contribution is represented by IX sin θ. For small conductors, resistance normally dominates. For larger conductors, resistance becomes lower and the reactive contribution becomes relatively more important.

Example Using a 10 mm² Cable

• Three-phase current = 50 A
• Power factor = 0.8
• Cable size = 10 mm²
• Cable length = 30 m
• TVD_r = 3.8 mV/A/m
• TVD_x = 0

V_drop,LL = [(3.8 × 0.8) × 50 × 30] ÷ 1000 = 4.56 V

Voltage drop % = (4.56 ÷ 400) × 100 = 1.14%

V_drop = (3.8 × 50 × 30) ÷ 1000 = 5.7 V

The simplified result is more conservative but less accurate for a motor operating at a power factor of 0.8.

How Conductor Temperature Affects Voltage Drop

The resistance of a metallic conductor increases as its temperature rises. Higher conductor resistance produces a larger voltage drop.

R_T = R₂₀[1 + α(T − 20)]

α ≈ 0.004 per °C

Cable tables may provide resistive TVD values at the cable's maximum normal operating temperature, such as 70°C for a PVC-insulated conductor. A lightly loaded cable may operate below this temperature, so its actual resistance and voltage drop will be slightly lower.

R_T2 = R_T1 × [(230 + T₂) ÷ (230 + T₁)]

Temperature correction Temperature correction applies to the resistive component of voltage drop. Cable reactance is normally treated as unaffected by conductor temperature.

Why Tabulated TVD Can Be Conservative

A cable reaches its maximum conductor temperature only when it operates close to its rated current under the applicable reference conditions. When the actual current is lower, the conductor is cooler, its resistance is lower and the actual voltage drop is lower than the full tabulated-temperature result.

P_loss = I²R

A cable operating at 50% of rated current has approximately 25% of the rated temperature rise because heating is related to the square of current.

Common Voltage-Drop Calculation Mistakes

1. Doubling the Single-Phase Length Twice

A single-phase mV/A/m value normally already includes the live and neutral conductors.

2. Adding Another √3 to Three-Phase TVD

Three-phase TVD values normally already include the three-phase relationship.

3. Selecting the Wrong Installation Column

The TVD depends on conduit, trunking, clipped-direct, tray, trefoil, flat, touching and spaced arrangements.

4. Ignoring Power Factor

A motor at 0.8 power factor does not produce the same result as a unity-power-factor resistive load.

5. Checking Ampacity Only

A cable can safely carry the load current and still produce excessive voltage drop.

6. Using the Wrong System Voltage

Use line-to-neutral voltage for a single-phase line-neutral load and line-to-line voltage for a three-phase load.

Practical Cable-Sizing Procedure

1. Calculate the design current, I_b.
2. Select the protective-device rating, I_n.
3. Apply the relevant correction factors.
4. Select a preliminary conductor size from the current-rating table.
5. Confirm that the corrected cable capacity satisfies the design current.
6. Select the correct TVD table and installation column.
7. Calculate the voltage drop in volts and percentage.
8. Compare the result with the permitted project limit.
9. Increase the cable size when the voltage drop is excessive.
10. Check motor starting, fault current, protection coordination and short-circuit withstand.

Frequently Asked Questions

What does mV/A/m mean?

It means millivolts of voltage drop for every ampere of current and every metre of one-way cable route.

Is cable length doubled for a single-phase circuit?

Not when a tabulated single-phase mV/A/m value already includes the live and neutral return path.

Why is √3 not shown in the three-phase TVD formula?

The √3 factor is normally already included in the three-phase tabulated mV/A/m value.

Where does TVD_r = 1.50 mV/A/m come from?

It is read directly from the cable table at the intersection of the 25 mm² row and the selected three-phase installation column, such as cables touching in trefoil formation.

Why does trefoil formation have lower reactance?

Trefoil formation places the three phase conductors close together in a compact and symmetrical arrangement, reducing magnetic-loop area and cable reactance.

Can voltage drop require a larger cable size?

Yes. A cable may pass the current-rating requirement but fail the voltage-drop limit, requiring the next larger conductor size.

Conclusion

A reliable voltage drop calculation requires the correct cable size, design current, route length, power factor, installation method, conductor arrangement and TVD value.

In the three-phase motor example, the 25 mm² cable could carry the required 102 A but produced a voltage drop of 2.496%, exceeding the 2% project limit. Increasing the cable size to 35 mm² reduced the voltage drop to approximately 1.88%.

The key engineering lesson is that a cable should never be selected based on ampacity alone. The final design must also satisfy voltage drop, protection, installation and equipment-performance requirements.

Engineering note: Confirm final cable data and permissible voltage-drop limits against the applicable local regulations, current standards, manufacturer information and project specifications.