31-08-2016, 03:01 PM
Current Transformer Errors and Transformer Inrush as Measured by
Magnetic, Optical and Other Unconventional CTs
1451823950-CurrentTransformerErrorsandTransformerInrush.pdf (Size: 992.62 KB / Downloads: 7)
Classical magnetic current transformers are prone to error during a variety of conditions.
The first part of this paper will identify some of those conditions and will provide a means
of analyzing the resulting CT performance level. One situation of particular interest is
transformer inrush current. Transformer inrush may be among the worst types of current
for a magnetic CT to reproduce, because it has a combination of effects that put CT performance
most at risk. Inrush may be high in magnitude, may contain a heavy DC offset with
a long time constant, and it may have a unipolar half-wave nature. The paper will review
the errors in secondary current that will be seen for these various primary current conditions,
will provide means of determining when CTs are at risk of saturation and will show,
using numerical analysis results, what the output of a saturated CT is like.
A viable alternative to magnetic CTs is the use of optical CTs that eliminate the errors commonly
associated with magnetic CTs. These errors can be highly objectionable in some
applications. The second part of this paper will review the various types of current sensors
available on the market, including conventional, hybrid, and optical sensors. Focusing on
"pure" optical sensors, the techniques used to sense current optically will also be examined,
as manufacturers can use fundamentally different methods. Optical CT signals are
interfaced with commercially available relays using low level analog signals and, in the
near future, digital signals. These signal levels, as outlined in IEEE and IEC standards, will
be examined. Finally, the future of optical sensors with respect to relaying will be examined.
Magnetic CT Performance Analysis Techniques
Steady State Circuit Analysis
The first approach to determine if a CT is under risk of CT saturation is to calculate whether
the AC voltage that will be impressed on its secondary during a fault will exceed the voltage
that the CT can support. This is typically done using RMS values of AC current with no
DC offset.
Equivalent Electric Circuit
Most engineers have worked with CT equivalent circuits, with various modifications. The
derivation and analysis is available in many references [e.g.,1]. One fairly complete version
is shown in Figure 1.
2
Figure 1: Simplified CT Equivalent Circuit
Note that Xm in the figure is labeled as negligible or 100-10,000 ohms (higher impedance
for higher ratio CTs). The impedance of the excitation branch varies tremendously from
one CT design to the next, the tap ratio used, and the Vexc seen by the CT. However, it is
the negligible impedance during CT saturation that will most affect relay settings. This low
impedance occurs when all the steel is magnetized at the steel’s maximum, yet the primary
current flow is oriented toward deeper magnetization. It is not until the primary current
wave form decreases and eventually reverses direction that the flux level begins to
reduce and saturation is removed.
CT, Line, and Relay Impedances
In Figure 1 the CT primary impedances and secondary reactance are shown but are commonly
negligible. This reasonably accurate representation is used herein. However, only
when a CT has “fully distributed” windings can the CT secondary reactance be considered
as negligible without research. Not all CTs have fully distributed windings, but relaying
class bushing CTs typically have fully distributed windings when the full ratio is used. The
partial tap windings may or may not be fully distributed in old CTs.
Secondary line impedances are typically highly resistive compared to their reactance for
the wire size used in CT circuits. In modern low impedance solid state relays, the burden
of the relay on the CT circuit is typically negligible.
CT Secondary Voltage Rating
The impedance of the magnetizing branch is non-linear. Its approximate fundamental
impedance varies with applied voltage to the CT secondary, but will typically be in the
several hundred to several thousand ohms range until the saturation voltage level is
reached. Note in the CT excitation curve in Figure 2 that at the indicated ANSI knee point
the magnetizing impedance is 5000Ω (= 200V/0.04A). The ANSI knee point corresponds
approximately to the highest magnetizing impedance of the CT. Above the knee point,
small Vexc increases cause large Iexc increases, which corresponds to a low Xm