Equivalent Circuit and Phasor Diagram of a No-Load Transformer

Overview

• Discuss the behavior of a transformer when there is no load on the secondary side
• Draw equivalent circuit and phasor diagram for this no-load condition

Transformer Structure

• Primary Winding: Receives supply voltage (V1), resulting in primary current (I1)
• Secondary Winding: Open-circuited, hence secondary current (I2) is zero
• Core: Magnetic flux generated by primary current passes through the core
• Leakage Flux: Some flux completes its path outside the core

Primary Winding Behavior

• Primary Voltage (V1) creates Primary Current (I1)
• I1 induces magnetic flux in the core, which generates EMF (E1) in primary winding
• Some flux leaks outside the core as Leakage Flux

Secondary Winding Behavior

• Flux links with secondary winding inducing EMF (E2) but no current flows as it's open-circuited (I2=0)
• Terminal Voltage (V2) equals induced EMF (E2)

No-Load Primary Current (I0)

• I0 is very small and has two components:
  • Magnetizing Component (Iµ): Responsible for generating magnetic flux
  • Core Loss Component (Ic): Accounts for core losses (hysteresis and eddy current) and primary side copper losses

Equivalent Circuit Representation

• Primary Side:
  • Resistance (R1): Primary winding resistance
  • Leakage Reactance (X1): Represents primary leakage flux
  • Core Loss Resistance (Rc): Represents core losses
  • Magnetizing Reactance (Xm): Represents magnetizing characteristics
• Secondary Side (open):
  • Resistance (R2): Secondary winding resistance
  • Leakage Reactance (X2): Represents secondary leakage flux
• Primary Induced EMF (E1) and Secondary Induced EMF (E2) are linked through the core

No-Load Equivalent Circuit Elements

• V1: Primary voltage
• R1: Primary winding resistance
• X1: Primary leakage reactance
• I0: No-load primary current
• Ic: Core loss component of I0
• Iµ: Magnetizing component of I0
• Rc: Core loss resistance
• Xm: Magnetizing reactance
• E1: Primary induced EMF
• E2: Secondary induced EMF
• V2: Secondary (terminal) voltage, equal to E2
• N1: Number of primary winding turns
• N2: Number of secondary winding turns
• I2: Secondary current (zero in no-load condition)

Phasor Diagram at No-Load

• Flux (Φ): Represents the magnetic flux
• Induced EMF (E1, E2): Lag the flux by 90 degrees
• Magnetizing Current (Iµ): In phase with flux, responsible for production of Φ
• Core Loss Component (Ic): In-phase with -E1, accounts for core losses
• No-Load Primary Current (I0): Phasor addition of Ic and Iµ
• Voltage Drops:
  • I0R1: In phase with I0
  • I0X1: 90-degree leading with respect to I0
• Resultant Primary Voltage (V1): Phasor addition of -E1, I0R1, and I0X1
• No-Load Phase Angle (Φ0): Angle between V1 and I0

Conclusion

• The core loss and magnetizing components always exist, whether loaded or not
• Understanding no-load condition is crucial for analyzing loaded conditions
• Visual representation helps in understanding interdependencies between voltages, currents, and magnetic flux in the transformer