A GIF below shows the working of simple bulb operating through a switch. When switch get closed, bulb starts glowing.
Another GIF is shown below with a bit more elaboration. A source with potential difference V is connected across the bulb through a switch. When switch get closed, A potential difference V get available across the bulb. Current I starts flowing and bulb starts glowing.
When a circuit is “small“. The input voltage can be equal to output voltage. But when circuit length is “large “and “complex “than there can be a differences in between input voltage and output voltage. Input voltage can be greater than or equal to output voltage.
Another GIF is shown below, This time circuit has much larger cable. Source having a voltage V1. When switch get closed, Voltage V2 get available across the bulb. Current I flows through the circuit. (V1>V2) . The potential difference is knows as “Voltage drop“.
“Voltage drop“ is big concern in distribution and transmission of Electrical power. In this post, We are going to discuss the voltage drop in long cables.
What does voltage drop actually means ?
“Voltage drop” appear across the circuit; When a power get drop across the line & Voltage get reduced at load side.
In Distribution design, Voltage drop plays a very important role. All the important parameters related to voltage drop must be considered.
Reasons of voltage drop
There are four major reasons of voltage drop :
- Resistive heating (I²R)
- Skin effect and proximity effect
- Current leakage
- Power factor
1. Resistive heating (I²R)
Resistive heating also known as I²R loss appears in heat form across the line. There are 2 main parameters; Current and Resistance. Higher the parameter, higher will be the loss.
- Current depend on load which is connected across the cable. Higher the current, higher will the loss. That’s the reason in power transmission, Voltage is been stepped up to reduce the line current.
- Resistance further depend upon conductor’s material type(resistivity), Its Length and cross section area.
Resistance of a conductor
R=ρ(L/A)
Where R is resistance, ρ is constant of proportionality, L is length of conductor, A is area of conductor
- Resistance is directly proportional to length of conductor. Higher the length, Higher will be the Resistance.
- Resistance is inversely proportional to Area. Higher the area, Lower will be the Resistance.
- Constant of proportionality, ρ , known as resistivity. Entirely depend upon the material type such as “copper “or “aluminum”. Copper have lower resistivity as compare to aluminum.
2. Skin effect and proximity effect
Skin effect, which appear across the cable. In this effect, current flows at outer surface; rather than even distribution through the cable. Skin effect leads to less area for current flow which increases the overall resistance of the line. Higher the Resistance, Higher power drop.
Proximity effect, This effect appears when multiple lines running parallelly. Due to magnetic field interaction, eddy current get generated in the cable. Eddy current further increases the power loss in line.
| Phenomenon | Effect | Definition | Reason |
| Skin effect | Self generated phenomenon, Increases overall resistance | Current has tendency to flows at outer surface(skin) of conductor rather than ever distribution. That effect is known as skin effect. | Due to eddy current generation at core of the conductor. |
| Proximity effect | Mutually generated phenomenon, Increases overall Resistance | Current flows at outer side of conductor due to magnetic field interaction from near by conductor . | Eddy current generation from the magnetic effect of near by conductor |
3. Current leakage
Over the time due to insulation deterioration or wrong insulation selection, Current leaks through the cable insulation . That current leakage increases the power loss across the line. At output load side, voltage get reduced.
4. Power factor
Power factor indicates how efficiently electrical power is being utilized by a load. This value ranges from 0 to 1(maximum). Low power factor leads to higher current which further leads to higher power drop.
For example, approximately:
P= V*I*cos(φ) Where V→ Voltage, I→ Current, cos(φ)→ Power factor
- 10 kW load at PF = 1 → 43.5 A at 230 V
- 10 kW load at PF = 0.8 → 54.3 A at 230 V
Since cable voltage drop depends on current, the higher current at 0.8 PF produces more voltage drop.
Cables and their specifications
Cable has multiple specifications such as voltage level, cross sectional area, number of cores, material type and with or without armour. Next, some of the specifications of the cables are discussed in a tabular form.
Both the cable types “copper “and “aluminum “having same cable size, are specified in a table below :
| Cable Size (mm Sq.) | Working voltage level (V) | Cable type | Conductor material | Max. DC resistance at 20°C | Approx. AC Resistance of conductor at 90°C (ohm/Km) | Approx. Reactance (ohm/Km) | Approx. Capacitance (uF/km) | Ampere (in air at 40°C) |
| 185 | 1100 | Armoured 3 Core | Aluminum | 0.164 | 0.210 | 0.072 | 1.31 | 329 |
| 185 | 1100 | Armoured 3 Core | Copper | 0.0991 | 0.127 | 0.072 | 0.63 | 422 |
| Cable size (mm Sq.) | Working voltage level (V) | Cable type | Conductor material | Max. DC resistance at 20°C | Approx. AC resistance of conductor at 90°C (ohm/km) | Approx. Reactance (ohm/Km) | Approx. Capacitance (uF/Km) | Ampere in air (at 40°C) |
| 10 | 1100 | Armoured,3 Core | Aluminum | 3.08 | 3.94 | 0.0837 | 0.31 | 54 |
| 10 | 1100 | Armoured,3 Core | Copper | 1.83 | 2.34 | 0.0837 | 0.31 | 70 |
Ampere Vs Cable size Vs Conductor material
- Copper conductor has more current carrying capacity in comparison to Aluminum conductor; same cable size. 10mm Sq. aluminum cable has rated current of 54 Amps. While 10mm Sq. copper cable has rated current of 70 Amps. (Source : KEI)
- As cable size increases; current carrying capacity increases. 10mm Sq. copper has rated current 70 Amps while 185mm Sq. copper has rated current 422 amps. (Source : KEI)
Tabular data explained in a graph below.
Graph- Resistance Vs Cable size Vs conductor material
- Aluminum conductor has more resistance in comparison to copper conductor; same cable size. 10mm Sq. aluminum cable has Max. DC resistance at 20°C; is 3.08 ohm/km. While 10mm Sq. copper cable has Max. Dc resistance at 20°C; is 1.83 ohm/km. (Source : KEI)
- As cable size increases, Conductor resistance decreases. 10mm Sq. copper cable has max. DC resistance at 20°C, is 1.83 ohm/Km. While 185mm Sq. copper cable has Max. DC resistance at 20°C; is 0.0991 ohm/Km. (Source : KEI)
Voltage drop Calculations
For Single phase, Voltage drop across the cable → Vd=2IL(Rcosϕ+Xsinϕ)
Where ,
- L= Length
- I= current
- R= Resistance per unit length
- X= reactance per unit length
- cos= Power factor
- Sinϕ= related to reactive component of current
For a 3-phase AC cable, the commonly used approximate voltage-drop formula → Vd=3IL(Rcosϕ+Xsinϕ)
Next, Voltage drop calculated on 3.5 Core 185 mm Sq. Aluminum armoured cable.
- Approx. AC Resistance of conductor at 90°C = 0.197 ohm/Km ((Source : KEI))
- Approx. Reactance = 0.087 ohm/km ((Source : KEI))
- Length = 160m (considered)
- Resistance per 160m = 0.03152
- Reactance per 160m= 0.01392
- cos(phi) 0.995 (considered)
- Sin(phi) 0.0999
After Adding the total data in a formula; Vd=3IL(Rcosϕ+Xsinϕ)
It is clearly seen in a graph, As line current increases voltage drop increases across the line.
| Line current | Voltage drop |
| 35 | 1.9 |
| 50 | 2.71 |
| 100 | 5.43 |
| 150 | 8.14 |
| 200 | 10.86 |
How to troubleshoot excessive voltage drop
As discussed, Voltage drop is happening due to 4 major reasons. That are :
- Resistive heating (I²R)
- Skin effect and proximity effect
- Current leakage
- Power factor
Next, All the reasons are discussed one by one !
Reducing the voltage drop by reducing the current
| Particulars | Definition |
| Balancing the three phase system | Balancing the current across the 3 phases. reduces the current at neutral side. |
| Improved power factor | Improved power factor reduces the line current |
| Reducing the line current by reducing the load | Better distribution, Reducing the load, reduces the line current |
| Stable system voltage | Reduced voltage increases the line current. Stable system voltage prevent the rise in line current. |
| Increasing the system voltage | To reduce the line current in transmission, Voltage is been stepped. |
Reducing the voltage drop by reducing the resistance
| Particulars | Definition |
| Changing the conductor material | Different conductive materials have different resistivity. For example copper has low resistivity in comparison to aluminum. |
| Reducing the conductor length | Reduced conductor length reduces the resistance. |
| Increasing conductor diameter | Increased diameter reduces the overall resistance of conductor and current carrying capacity is get increased. |
| Parallel conductors instead of individual single conductor | Parallel conductors reduces the overall resistance of the line. |
| Avoiding the cable joints | Cable joints, Increasing the voltage drop by adding the extra resistance value. |
| Adjust conductor temperature | lower temperature lower the resistance of the conductor. |
Reducing the voltage drop by reducing skin effect
- Hollow pipe conductor
- Avoiding Single solid conductor
- Bundled multiple conductors
- Use of foil conductors
- Choose non-magnetic low resistive material
Reducing the voltage drop by reducing the proximity effect
- Optimize strand twisting and lay length
- Increase spacing between conductors
- Use of inter-strand and inter-winding insulation
- Use foil with proper spacing
Reducing the voltage drop by reducing the current leakages
- Right selection of insulation material
- Right selection of Ingress protection of cable
- Use of armoured or shield cables
- Limit cable length
Reducing the voltage drop by Improving the power factor
- Use of shunt capacitors
- Use of Automatic power factor controllers
- Addressing the cable charging current (leading power factor); By shunt reactors
Frequently Asked Questions (FAQs)
1. Why does voltage drop increase with cable length?
Voltage drop increases with cable length because a longer conductor has greater resistance. At the same current, a longer cable generally produces a greater voltage drop.
2. How do you calculate voltage drop in a cable?
For a single-phase AC circuit, voltage drop can be calculated using:
Voltage Drop = 2 × I × L × (R cos φ + X sin φ)
For a balanced three-phase AC circuit:
Voltage Drop = √3 × I × L × (R cos φ + X sin φ)
Here, I is the current, L is the one-way cable length, R is the conductor resistance per unit length, X is the reactance per unit length, and φ is the load power-factor angle.
3. Does increasing cable size reduce voltage drop?
Yes. Increasing the conductor cross-sectional area generally reduces resistance and voltage drop for the same current and cable length. The selected cable must also meet current-carrying capacity and applicable installation requirements.
4. Which cable has less voltage drop: copper or aluminium?
Copper generally has lower electrical resistance than aluminium for the same cross-sectional area. However, a suitably sized aluminium conductor can also provide an economical solution for power distribution.
5. Does an unbalanced three-phase load increase voltage drop?
Yes. When one phase carries more current than the others, its conductor can experience greater voltage drop. Balancing the loads can reduce excessive voltage drop in the heavily loaded phase, depending on the system configuration and operating conditions.
6. What happens when voltage drop is too high?
Excessive voltage drop can cause motors to experience reduced starting torque, electrical equipment to malfunction, and energy losses to increase. The actual effects depend on the equipment, load, and severity of the voltage drop.
7. How can voltage drop in long cables be reduced?
Voltage drop can be reduced by increasing conductor size, shortening the cable route where practical, improving power factor where appropriate, and balancing three-phase loads. Cable selection must also consider current-carrying capacity, installation conditions, and applicable electrical standards.