English
Deutsch
Português
Español
- Electrical engineering
- Voltage Current Resistance
- Star Delta Transformation
- Practical Voltage and Current Sources, equivalent circuit diagram
- Capacitor to DC voltage
- Inductors in DC Circuits
- Alternating current
- AC Inductive Circuits
- Three-phase Current
- Transformer
- Complex numbers
- Locus Diagram in AC circuits
- Measurement error
- Videos electrical engineering
- Index electrical engineering
Home ⇒ Overview Courses ⇒ Electrical engineering ⇒ Three-phase Current ⇒ Unbalanced load
3 Phase Unbalanced Load
Table of Contents
ToggleAn unbalanced load in a three-phase system occurs when the current or voltage in each phase of a three-phase power supply system is unequal. This is the case if the loads connected to each phase have different power ratings, different power factors or faults occur in the system, e.g. in case of a phase loss.
3 phase unbalanced star connection

3 phase unbalanced star connection
If the resistors R1, R2 and R3 do not have the same value, the phase currents are different. As a result, the neutral carries current, which we can determine by the vector diagram of the currents.
The vectors are added mathematically by adding the XY-values of the polar coordinates:

Calculation Unbalanced load
Example: The resistors R1 = 100 Ω, R2 = 80 Ω and R3 = 50 Ω are connected to a star with neutral wire (3-Phase 4 Wire). Calculate the current INeutral and the total power and sketch the current vectors.
I1 = 230 V = 2,3 A
. 100 Ω
I2 = 230 V e-j120° = 2,875 A e-j120°
. 80 Ω
I2 = 230 V e-j240° = 4,6 A e-j240°
. 50 Ω

Calculation Unbalanced load x and y values
Thus IN = - 1,438 A + j1,49 A = 2,07 A e-j226°
The vector image not true scaled:

Calculation Unsymmetrical load Vector image
The total power as the addition of the single phase power:
Ptot = P1 + P2 + P3 = I1 R12 + I2 R22 + I3 R32
Ptot = 2,3 A (100 Ω)2 + 2,875 A (80 Ω)2 +4,6 A (50 Ω)2 = 2248,25 W