Voltage and Current Relationships
The transformer operates on the principle of electromagnetic induction and changes the voltage and current levels between its primary and secondary windings.
Key Formulas
Voltage Transformation Ratio (
Where:
: Transformation ratio. : Voltage in the primary (Volts) : Voltage in the secondary (Volts) : Number of turns in the primary. : Number of turns in the secondary.
Current Relationship
Where:
: Current in the primary (Amperes) : Current in the secondary (Amperes)
Impedance Transformation Ratio (
Where:
: Impedance reflected to the primary side. : Impedance reflected to the secondary side.
Power in the Transformer
The power in an ideal transformer (without losses) is the same in both the primary and secondary.
Key Formulas
Apparent Power
Where:
: Apparent power in the primary (Volt-Amperes, VA) : Apparent power in the secondary (Volt-Amperes, VA)
Active Power (
Where:
: Active power (Watts) : Voltage (Volts) : Current (Amperes) : Power factor.
Reactive Power (
Where:
: Reactive power (Volt-Amperes Reactive, VAR)
Losses in the Transformer
In real transformers, there are losses due to winding resistance and losses in the magnetic core.
Key Formulas
Copper Losses (
Where:
: Losses in the primary and secondary windings (Watts) : Resistance of the primary winding (Ohms) : Resistance of the secondary winding (Ohms) , : Currents in the primary and secondary (Amperes)
Core Losses (
Where:
: Core losses (Watts) : Hysteresis losses (Watts) : Eddy current losses (Watts)
Total Losses
Efficiency of the Transformer
The efficiency of a transformer is defined as the ratio of output power to input power.
Key Formulas
Efficiency (
Where:
: Output power (Watts) : Input power (Watts) : Total losses (Watts)
Efficiency in Terms of Losses
Where:
: Apparent power in the secondary (Volt-Amperes) : Phase angle between current and voltage.
Voltage Regulation
The voltage regulation of a transformer indicates the change in secondary voltage when transitioning from full load to no load.
Key Formulas
Voltage Regulation (
Where:
: No-load voltage (without load) : Voltage at full load.
Reactances and Admittance
In the equivalent model of the transformer, reactances and admittances play an important role.
Key Formulas
Impedance Referred to Primary (
Where:
, : Resistances of the primary and secondary. , : Leakage reactances of the primary and secondary. : Transformation ratio.
Impedance Referred to Secondary (
Excitation Current (
Where:
: No-load or excitation current. : Active component of the current (related to core losses) : Reactive component of the current (related to core magnetization)
Transformer Tests
There are two basic tests to calculate the losses and parameters of the transformer: Open Circuit Test and Short Circuit Test.
Tests
Open Circuit Test (measures
Short Circuit Test (measures
Where:
: Voltage applied in the short circuit test. : Short circuit current.