25-08-2017, 09:32 PM
CURRENT TRANSFORMER CONCEPTS
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ABSTRACT
This paper reviews the C and K bushing relay accuracy ratings for current transformers (cts) and
their implications in relay application. The paper relates the concept of knee-point and the 10
ampere excitation voltage of a conventional excitation curve to the actual secondary waveforms
produced at and above the ANSI voltage rating. The paper uses the volt-time area concept to
introduce ct saturation and the voltage rating using an idealized B-H curve. Computer simulation
using the actual shape of the B-H curve is then introduced and used to analyze specific ct
applications in transformer and generator differential relays.
INTRODUCTION
A ct appears to be the simplest of electrical devices. For example, the bushing type ct is simply a
winding on an insulated core which becomes a transformer only when placed over the primary
conductor. The opening paragraph of Moreton's classic paper [1] states that the art of calculating
current transformer characteristics from excitation curve data has been known for some time.
Moreton wrote this paper in 1943 and referred to papers written two years earlier. Today, nearly
50 years later, there is still a vital interest in this seemingly simplest of electrical devices. For
example, the IEEE/PES Instrument Transformer Subcommittee is voting on a revision of C57.13
(Project No. P546/D7a), which includes a K rating in addition to the C and T rating, and the
Power System Relay Committee (PSRC) Working Group F7 is completing a publication titled:
"Guide for the Application of Current Transformers for Relaying" (PC37.110/D9). PSRC
Working Group F5 is also completing a paper dealing with the problems of applying low ratio cts
and the adverse effect of saturation on relay performance due to extremely high fault currents. At
the same time Electric Power Research Institute (EPRI) is funding a project to study models used
to determine ct transient performance for relay testing using the Electromagnetics Transient
Program (EMTP) [2].
CT EQUIVALENT CIRCUITS
A current transformer can be modeled as a constant current source where ratio current is injected
into a magnetizing impedance in parallel with the burdens shown in Figure 1. Using a reactance
to represent the magnetizing leg of a ct, as shown in Figure 1, is a useful visual concept.
However, magnetization is a non-linear phenomenon, and different values of reactance must be
used for each level of excitation. For example, the three B-H diagrams, shown in Figure 1, as
flux φ versus magnetizing current IM, represent low, medium and high levels of excitation.
At low excitation, the slope dφ/dI representing the inductance is low. This low slope indicates a
disproportionate amount of magnetizing current compared to the burden current at low excitation.
At medium excitation, the dφ/dI is relatively high and the magnetizing current is small compared
to the current in the burden. At high excitation, the B-H curve exhibits the maximum slope in
transition between saturated states. The fact that magnetizing current is so small compared to the
ratio current during the transition suggests that it can be ignored. Consequently the core can be
viewed simply as a volt-time switch as shown in Figure 1 which opens during a rate of flux
change and closes during saturation.
The Excitation Curve
The volt-time concept assumes the magnetic core is a volt-time switch. This concept assumes no
magnetizing current when there is rate of change of flux and all the ratio current flows to the
burden. When saturation flux is reached, as indicated by volt-time area, and there is no longer a
change of flux, the switch closes shunting all the ratio current away from the burden until a
reversal of current and integration becomes negative to reduce the flux. Here saturation occurs at
a well defined point indicated by a specific value flux and turns.
However, finite ampere-turns are required to establish flux in the core, which can be expressed as
magnetizing current measured at the secondary terminals. The excitation current, which is
subtracted from the ratio current, has definite values for each voltage as shown by the excitation
curve in Figure 4. This figure depicts steady-state voltage versus excitation current where voltage
is measured with an average reading voltmeter calibrated in rms. It is actually a plot of flux
versus magnetizing current since the average voltage is the volt-time integral averaged over the
period of the sine wave.
COMPUTER SIMULATION
Because cts are subject to saturation during the dc transient of fault current, there is a growing
interest in computer simulations like the EMTP program which produce detailed plots of current
corresponding to an oscillograph obtained from a full-scale system test. A primary aim of the
simulation is to obtain digitized records which can be reconstituted as secondary analog signals
using D/A conversion and amplification for the purpose of relay testing.
The simple equivalent circuit for the simulation is shown in Figure 5. In Figure 5 the primary
current referred to the secondary is a constant current feeding a non-linear magnetizing
inductance and the resistance and inductance of the burden.