Voltage loss refers to the numerical voltage difference across the ends of impedance components in a circuit.. In engineering calculations, the voltage loss approximates the longitudinal component of the voltage drop.
Voltage losses in a circuit can be divided into two parts:
First part: It is caused by the active power in the resistance R of the circuit, expressed as PR/U.
Second part: It is caused by the reactive current induced by the reactance of the circuit, expressed as QX/U. For lines of 110 kilovolts or more, The relationship between X and R is approximately 4 a 10, so voltage losses caused by reactance are predominant.
Calculation of voltage losses in general circuits (for the longest supply circuit)
From B2F Substation to SOHO General Lighting Distribution Box
Input parameters: Circuit operating voltage U = 0.38 (kV), Densely populated busbar 1600A, Calculated working current Ig = 850 (A), Circuit length L = 0.200 (km), Power factor cosφ = 0.85.
Circuit material: Copper.
Intermediate parameters: Resistance r = 0.033 (Oh/km), Reactance x = 0.020 (Oh/km).
Calculation formula and result: 0.38KV circuit voltage loss – ΔU1% = (173/U) * Ig * L * (r * cosφ + x * sinφ) = (173/(0.38*1000)) * 850 * 0.2 * (0.033 * 0.85 + 0.020 * 0.53) = 2.99.
From General Lighting Distribution Box to SOHO Office Distribution Box
Input parameters: Circuit operating voltage U = 0.22 (kV).
Type of cable: Wire; Cable Cross Section S = 10 (mm2); Calculated working current Ig = 16 (A); Circuit length L = 0.050 (km). Power factor cosφ = 0.85.
Circuit material: Copper.
Intermediate parameters: Resistance r = 2.25 (Oh/km), Reactance x = 0.087 (Oh/km).
Calculation formula and result: 0.38KV circuit voltage loss – ΔU2% = (173/U) * Ig * L * (r * cosφ + x * sinφ) = (173/(0.38*1000)) * 16 * 0.050 * (2.25 * 0.85 + 0.087 * 0.53) = 0.72.
From the SOHO office distribution box to the farthest light fixture
Input parameters: Circuit operating voltage U = 0.22 (kV).
Type of cable: Wire, Cable cross section S = 2.5 (mm2); Calculated working current Ig = 4.5 (A); Circuit length L = 0.020 (km); Power factor cosφ = 0.85.
Circuit material: Copper.
Intermediate parameters: Resistance r = 8.97 (Oh/km), Reactance x = 0.1 (Oh/km).
Calculation formula and result: 0.22KV circuit voltage loss – ΔU3% = (200/U) * Ig * L * (r * cosφ + x * sinφ) = (200/(0.22*1000)) * 4.5 * 0.020 * (8.97 * 0.85 + 0.1 * 0.53) = 0.59.
Calculation of voltage losses in public lighting (for the longest supply circuit)
From B2F Substation to SOHO Street Lighting Distribution Box
Input parameters: Circuit operating voltage U = 0.38 (kV)
Type of cable: Pre-branch cable, Cable cross section S = 95 (mm2); Calculated working current Ig = 129 (A); Circuit length L = 0.200 (km); Power factor cosφ = 0.85.
Circuit material: Copper.
Intermediate parameters: Resistance r = 0.229 (Oh/km), Reactance x = 0.077 (Oh/km).
Calculation formula and result: 0.38KV circuit voltage loss – ΔU% = (173/U) * Ig * L * (r * cosφ + x * sinφ) = (173/(0.38*1000)) * 129 * 0.2 * (0.229 * 0.85 + 0.077 * 0.526783) = 2.76
From the street lighting distribution box to the farthest light fixture
Input parameters: Circuit operating voltage U = 0.22 (kV)
Type of cable: Cable conductor, Cable cross section S = 2.5 (mm2); Calculated working current Ig = 4.5 (A); Circuit length L = 0.030 (km); Power factor cosφ = 0.85.
Circuit material: Copper.
Intermediate parameters: Resistance r = 8.97 (Oh/km), Reactance x = 0.1 (Oh/km)
Calculation formula and result: 0.22KV circuit voltage loss – ΔU3% = (200/U) * Ig * L * (r * cosφ + x * sinφ) = (200/(0.22*1000)) * 4.5 * 0.030 * (8.97 * 0.85 + 0.1 * 0.526783) = 0.88
Total voltage loss from B2F substation to farthest light fixture from SOHO office
Namely: ΔU% = ΔU1% + ΔU2% = 2.76 + 0.88 = 3.64
Voltage losses are less than 5%, which meets the requirements of the regulations.
Cable tension loss table
Table of voltage loss per kilowatt per kilometer of load for 660V copper cables
| COSΦ | 4 | 6 | 10 | 16 | 25 | 35 | 50 | 70 |
|---|---|---|---|---|---|---|---|---|
| 0.6 | 1.295 | 0.876 | 0.524 | 0.342 | 0.225 | 0.167 | 0.128 | 0.096 |
| 0.65 | 1.290 | 0.873 | 0.521 | 0.319 | 0.222 | 0.164 | 0.125 | 0.093 |
| 0.7 | 1.286 | 0.869 | 0.517 | 0.336 | 0.219 | 0.161 | 0.122 | 0.091 |
| 0.75 | 1.283 | 0.866 | 0.514 | 0.333 | 0.216 | 0.158 | 0.119 | 0.088 |
| 0.8 | 1.280 | 0.863 | 0.512 | 0.330 | 0.214 | 0.156 | 0.117 | 0.086 |
| 0.85 | 1.277 | 0.861 | 0.509 | 0.327 | 0.211 | 0.152 | 0.114 | 0.083 |
| 0.9 | 1.219 | 0.858 | 0.506 | 0.325 | 0.208 | 0.151 | 0.112 | 0.081 |
| R0(Oh/km) | 5.500 | 3.690 | 2.160 | 1.370 | 0.864 | 0.616 | 0.448 | 0.315 |
| X0(Oh/km) | 0.101 | 0.095 | 0.092 | 0.090 | 0.088 | 0.084 | 0.081 | 0.078 |
Voltage Loss Calculation for 660V Rubber-Sheathed Copper Cables
| Cable Section | Voltage Loss per kW·km | Calculated Power (kW) | Cable length (km) | Power and Length Product (kW·km) | Voltage Loss |
|---|---|---|---|---|---|
| 50 | 0.119 | P=20 | L=1.5 | PL=30 | ΔU=3.57 |
| 16 | 0.333 | P=37 | L=0.01 | PL=0.37 | ΔU=0.12321 |
| 16 | 0.333 | P=22 | L=0.01 | PL=0.22 | ΔU=0.07326 |
| 25 | 0.216 | P=10 | L=0.5 | PL=5 | ΔU=1.08 |
| 35 | 0.158 | P=59 | L=0.48 | PL=28.32 | ΔU=4.47456 |
| 70 | 0.088 | P=13 | L=0.5 | PL=6.5 | ΔU=0.572 |
Conclusion
Calculating voltage drop on power lines is essential to ensure a reliable and efficient power supply. This measurement allows evaluating the voltage loss throughout the electrical network, which helps prevent system failures and maintain service quality. Besides, Knowing the voltage drop facilitates proper planning of the electrical infrastructure, allowing the necessary conductors and equipment to be correctly sized to minimize losses and optimize energy efficiency.