In an AC cable the voltage drops because the conductor has both resistance and reactance. The drop grows with current and length and depends on the load power factor. In large cross-sections reactance dominates, so a bigger conductor helps less and less. The result is compared with the limit set by the applicable code or the equipment specification.
Short answer
An AC cable is not an ideal conductor: it has resistance (R) and reactance (X). When current flows, part of the voltage stays in the cable and the load receives less than the source delivers. That difference is the voltage drop. It depends on the current, the length, R, X and the power factor of the load. It is calculated to confirm that the connected equipment receives a voltage within its allowed range and, on long runs, it often decides the cable size.
What causes it
The current flowing through the cable produces two effects:
- Resistive drop. It is the product of the current and the conductor resistance. It is in phase with the current and turns energy into heat.
- Reactive drop. Alternating current creates a magnetic field around the cable. That field opposes changes in current and shows up as reactance. This drop is 90° out of phase with the current and does not cause losses by itself.
The line-to-line voltage drop of a three-phase circuit is estimated with:
ΔV = √3 · I · L · (R · cos φ + X · sin φ)
where I is the line current in amperes, L the length in kilometers, R and X the resistance and reactance per kilometer of each conductor, and φ the angle between the load voltage and current. In a single-phase circuit the factor √3 is replaced by 2, because the current flows out and back. You can try it with the cable voltage drop tool. This is the approximate method used by IEC 60364-5-52, Annex G, for low-voltage installations.
When several conductors run in parallel per phase, the current is shared and R and X are divided by the number of conductors.
Why power factor matters
The power factor (cos φ) sets how much each part contributes to the drop. With a purely resistive load (cos φ = 1) only resistance counts. With an inductive load, such as a motor, reactance also adds and the drop is larger for the same current. With a capacitive load the reactive term subtracts, and in extreme cases the voltage at the end of the cable can be higher than at the start.
The angle between voltage and current is easy to see in a phasor diagram; the guide Phasor diagram explains it step by step.
Cable resistance and reactance
Resistance depends on the material (copper or aluminum), the cross-section and the temperature. Aluminum has more resistance than copper for the same cross-section. When the conductor heats up under load its resistance rises, so the drop is calculated with the resistance at operating temperature rather than at 20 °C. The DC resistance values of conductors are standardized in IEC 60228.
Reactance depends on the spacing and arrangement of the conductors, not on the cross-section. A multicore cable has its conductors very close together and low reactance. Three separated single-core cables have higher reactance. Manufacturers publish it per kilometer for each cable type.
The practical consequence lies in the ratio between R and X. In small cross-sections R is much larger than X and the calculation reduces almost to resistance alone. In large cross-sections R falls and X stays almost the same: doubling the cross-section no longer halves the drop.
How the result is used
The voltage drop is compared with a limit. That limit is set by the code that applies to the installation, the utility or the equipment manufacturer, and it is not the same for every circuit. Check which one governs before accepting a cross-section.
Cable size is set by at least three criteria, and the most demanding one is adopted:
- Current-carrying capacity (ampacity): the cable must not heat above the temperature rating of its insulation. It is covered in the guide on power cables.
- Voltage drop: the load must receive an adequate voltage. This is the criterion of this guide.
- Short circuit: the conductor must withstand the fault current for as long as it takes to clear.
On short runs ampacity usually governs. On long runs or with high-current loads, voltage drop governs.
What to do when the drop is excessive
You can act on each term of the formula:
- Increase the cross-section, useful as long as resistance dominates.
- Use parallel conductors, which share the current.
- Shorten the route or bring the source closer to the load.
- Raise the supply voltage: for the same power, the current falls in proportion.
- Improve the power factor with reactive compensation, which reduces the reactive current and the X · sin φ term.
- Use a transformer with a tap changer to raise the output voltage, when the problem affects a whole circuit.
Approximate versus exact calculation
The formula above is an approximation that adds the drops as if they were along the direction of the voltage. It is sufficient for the vast majority of circuits. The exact calculation solves the full phasor triangle: it starts from the source voltage and obtains the real voltage at the load. It matters more when the drop is large, for example on long medium-voltage feeders. The difference between the two methods grows with the drop.
Cases calculated separately
- Motor starting. The starting current is several times the rated current and the power factor is low, so the momentary drop can be high and affect other equipment on the bus. It is covered in starting large motors and voltage drop.
- Direct current. Reactance plays no part and only the resistance of the outgoing and return path counts. See DC voltage drop in solar.
- Transformers. Their internal drop is calculated from the short-circuit impedance, as described in transformer voltage drop under load.
Calculate it here
To check a circuit with its material, length, resistance and reactance, use our free cable voltage drop tool.
We can help with the engineering of your installation
At Tiza Group we prepare the primary engineering of substations and plants, including cable selection and verification of the voltage at the loads. If you have a long circuit or a sensitive load, we will quote the review.
Related guides
- Power cables
- DC and AC cable sizing and raceways in photovoltaic systems
- Starting large motors and voltage drop
- DC voltage drop in solar
- Phasor diagram
References
- IEC 60364-5-52, Low-voltage electrical installations - Selection and erection of electrical equipment - Wiring systems, Annex G (voltage drop).
- IEC 60228, Conductors of insulated cables.
- The local electrical code and the utility’s requirements that apply to the installation.
Frequently asked questions
Why does a larger cable barely improve voltage drop in big cross-sections?
Resistance falls as the cross-section grows, but reactance hardly changes: it depends on the spacing between conductors, not on their area. Once reactance dominates, a larger cross-section adds little. It is better to shorten the route, use parallel conductors or raise the voltage.
What is the difference between arithmetic and vector voltage drop?
The vector drop is the real difference between the sending-end and receiving-end voltages, which are not in phase. The arithmetic drop is an approximation that adds the resistive and reactive drops along the direction of the voltage. In ordinary circuits the two almost coincide; they separate when the drop is large.
Is voltage drop calculated with the load current or the starting current?
Normal service is checked with the load current. For a motor, starting is checked separately because the current is several times higher and the power factor is different; that case has its own analysis.