A current transformer (CT) is a crucial instrument transformer widely used in power systems for measuring, protecting, and controlling electrical circuits. Its operation is based on Faraday's law of electromagnetic induction. This paper aims to elucidate the electromagnetic induction principle of CTs and conduct an in - depth analysis of their equivalent circuits.
Faraday's law of electromagnetic induction states that an electromotive force (EMF) is induced in a closed - loop conductor when the magnetic flux linking the loop changes with time. Mathematically, it is expressed as:
e=−NdtdΦ
where e is the induced EMF, N is the number of turns in the coil, and dtdΦ is the rate of change of magnetic flux.
In a current transformer, there are two coils: the primary coil and the secondary coil. The primary coil, usually having a small number of turns (N1), is connected in series with the high - current circuit to be measured. The secondary coil, with a larger number of turns (N2), is connected to measuring instruments, relays, or other low - power devices.
When an alternating current I1 flows through the primary coil, it generates a time - varying magnetic flux Φ in the core. According to Ampere's circuital law, Hl=N1I1, where H is the magnetic field intensity and l is the mean magnetic path length in the core.
The magnetic flux Φ links both the primary and secondary coils. Due to the change in Φ over time, an EMF e2 is induced in the secondary coil according to Faraday's law. The induced current I2 in the secondary coil can be calculated by I2=Z2e2, where Z2 is the impedance of the secondary circuit.
The relationship between the primary and secondary currents is approximately given by the turns - ratio principle:
I2I1≈N1N2
This relationship allows for the transformation of high primary currents into measurable low - level secondary currents.
In an ideal current transformer, there is no magnetic leakage, no core losses (hysteresis and eddy - current losses), and the magnetizing current Im=0. The equivalent circuit of an ideal CT simply shows a current - controlled current source, where the secondary current I2 is directly proportional to the primary current I1 based on the turns ratio (I2=N2N1I1).
In practical applications, a current transformer has several non - ideal characteristics that need to be considered in the equivalent circuit:
Magnetizing Branch: A magnetizing current Im is required to establish the magnetic flux in the core. This current lags the primary voltage by 90° and is responsible for core magnetization. The magnetizing impedance Zm=Rm+jXm, where Rm represents the core loss resistance (accounting for hysteresis and eddy - current losses) and Xm is the magnetizing reactance.
Leakage Reactance: There is magnetic leakage in the transformer, which is represented by leakage reactances Xl1 and Xl2 in the primary and secondary circuits respectively. These leakage reactances cause a voltage drop in the windings.
Winding Resistance: The primary and secondary windings have resistances R1 and R2 due to the resistivity of the conductor material.
The equivalent circuit of a real - world current transformer is shown as follows:
The primary current I1 can be divided into two components: the magnetizing current Im and the component that is transformed to the secondary side I2t. The secondary current I2 is related to I2t by the turns ratio.
I1=Im+I2t
The secondary voltage V2 can be expressed as:
V2=I2(Zload+R2+jXl2)
where Zload is the impedance of the load connected to the secondary side of the CT.
The presence of the magnetizing current Im and leakage reactances in the equivalent circuit leads to two types of errors in CTs:
Ratio Error: It is defined as the difference between the actual turns ratio and the nominal turns ratio. Mathematically, Ratio Error=N2I2N1I1−N2I2×100%. The ratio error is mainly caused by the magnetizing current Im and winding resistances.
Phase Error: It is the phase difference between the primary current I1 and the secondary current I2 referred to the primary side. The phase error is affected by the magnetizing reactance Xm and leakage reactances Xl1, Xl2.
The operation of current transformers is fundamentally based on the principle of electromagnetic induction. By understanding this principle, engineers can design and apply CTs effectively in power systems. The equivalent circuit analysis provides a quantitative method to study the non - ideal behavior of CTs, including ratio and phase errors. This knowledge is essential for ensuring the accuracy of current measurement, reliable operation of protection relays, and efficient control of electrical power systems. Further research can focus on optimizing CT design to minimize errors and improve the overall performance of power system instrumentation.
