Electromagnetic Transient Studies

Transformer Modelling in EMTP® — Instrument Transformers

Instrument transformers reuse the non-ideal-unit and nonlinear-core idea of the power transformers, with a measurement burden added — and, for the CVT, a capacitive divider, tuning reactor, stray capacitances and a ferroresonance-suppression circuit. This part covers the EMTP® CT, VT and CVT devices and how to choose between them by study type.

Reading time ≈ 10 min · Part Five of the series

Instrument transformers are not modelled to represent power transfer. They are modelled to reproduce the voltage or current signal delivered to protection, control and measurement equipment. The outputs that matter are therefore secondary current, secondary voltage, saturation behaviour, transient error, burden effect and relay-input response.

Key takeaway

CT models study secondary-current accuracy, saturation, remanent flux and relay performance.
VT models study secondary-voltage response, burden effect and ferroresonance risk.
CVT models need special care — the capacitive divider, tuning reactor and ferroresonance-suppression circuit strongly affect transient response.
For protection studies, the burden and the initial magnetic condition can matter as much as the transformer ratio.

Instrument transformers — the voltage transformer (VT), current transformer (CT) and capacitive voltage transformer (CVT) — are EMTP® library devices that share a common modelling philosophy with the nameplate power-transformer units described in the device catalogue page: each is a masked subnetwork built from a non-ideal unit (series winding \(R\)/\(X\) branches around an ideal-unit ratio) plus a nonlinear magnetisation branch (a nonlinear inductance in parallel with a loss resistance \(R_{mag}\)) carrying optional remanent (initial) flux. On top of this core, each instrument-transformer model adds the features that matter for measurement studies: a burden representing the connected metering/relay load, and — for the CVT — a capacitive divider, a tuning reactor, stray capacitances and a ferroresonance-suppression circuit. All three are available in 1-phase and 3-phase versions; the phase count switches automatically when a 3-phase signal is connected to (or routed through) the device power pin. The subcircuit of each can be inspected by entering it with Alt+double-click. Magnetisation data is always entered as a secondary-side current–voltage excitation curve, which EMTP® converts internally to instantaneous current–flux point vectors (\(\texttt{ILnonl}\), \(\texttt{PhiLnonl}\)) using the "L nonlinear data function" service, accounting for the current drawn by \(R_{mag}\) during the open-circuit test. Steady-state, frequency-scan and time-domain solutions are all derived directly from the subnetwork contents; automatic initial conditions come from the steady-state solution, or per-phase fluxes may be set manually on the IC tab.

The three devices are modelled for different reasons, summarised below before the detailed sections.

Table 1 — Practical comparison of CT, VT and CVT models in EMTP®.

Instrument Transformer	Main Purpose in EMTP® Studies	Key Effects to Model	Typical Output of Interest
CT	Current signal to protection and metering	Saturation, remanent flux, burden, fault-current offset	Secondary current and relay input current
VT	Voltage signal to protection and metering	Magnetisation, burden, possible ferroresonance	Secondary voltage
CVT	Voltage signal through a capacitive divider	Capacitive divider, tuning reactor, burden, ferroresonance suppression	Transient secondary voltage and relay input voltage

Burden

The burden is the impedance connected to the secondary circuit of the instrument transformer — relay input impedance, meters, test links, wiring resistance and any connected devices. It affects secondary voltage, secondary current, accuracy and saturation behaviour.

The instrument transformer is one link in a measurement chain

In a protection study the instrument transformer sits inside a chain: the network transient produces the primary current or voltage; the CT, VT or CVT converts it to a secondary signal; the burden and secondary wiring modify that signal; and only then does the relay interpret it. Each link can introduce error, so a correct primary transient does not by itself guarantee a correct relay input. If the instrument-transformer model is reduced to an ideal ratio — no saturation, no remanence, no burden — the waveform the relay actually sees can differ in magnitude, shape and timing from the true secondary quantity, and the relay decision is then judged on that distorted input rather than on the primary fault.

Section 1

Voltage transformer (VT) — `VoltageTransformer`

Concept / role. A VT is a wound, two-winding transformer connected in shunt across the line to step a primary voltage down to a low secondary voltage for metering and protection. In EMTP® the device output is a control-signal bundle giving the secondary voltage(s): breakout "a" (1-phase) or "a", "b", "c" (3-phase). Because the subcircuit retains a nonlinear magnetisation branch with remanent flux, the VT model reproduces saturation and the resulting low-frequency nonlinear phenomena rather than acting as an ideal ratio.

A VT model represents the voltage supplied to protection, control and measurement equipment — not power transfer. For most studies the quantities of interest are the secondary-voltage magnitude, phase angle, transient response and the effect of the connected burden.

Parameters and what they represent.

Nominal frequency \(f\) — the surrounding-network frequency, used when reactances are entered in ohms and when computing the flux points of the magnetisation branch.
Ratio — primary rated voltage / secondary rated voltage, both in volts (e.g. \(230000/115\)).
Connection — the 3-phase winding connection type.
Winding 1 \(R_{1}\), \(X_{1}\) and Winding 2 \(R_{2}\), \(X_{2}\) — primary and secondary series resistance and (leakage) reactance of the non-ideal-unit branches around the ideal ratio. (In the data mask the \(X\) field is labelled the inductance of the winding.)
Standard / \(Z_{burden}\) / Power Factor — the connected burden. Selecting an IEEE C57.13 (ANSI) standard burden auto-populates the burden impedance magnitude \(Z_{burden}\) and power factor PF; leaving the Standard field blank lets the user enter \(Z_{burden}\) and PF directly.
Magnetization data — secondary current–voltage excitation curve, converted to instantaneous current–flux as above.
Magnetization resistance \(R_{mag}\) — the loss resistance in parallel with the nonlinear inductance.
Initial flux (0) phase A/B/C (IC tab) — remanent flux per phase. For the open-delta variant, "phase A" is the flux of the winding between A–B and "phase C" the flux of the winding between B–C (phase B is not considered).

IEEE C57.13 (ANSI) voltage-transformer burdens. Selecting a standard designation populates \(Z_{burden}\) and PF. The standard burdens are specified as VA at a stated power factor:

Table 2 — IEEE C57.13 standard voltage-transformer burdens.

Designation	Burden VA	Power Factor
W	12.5	0.10
X	25	0.70
M	35	0.20
Y	75	0.85
Z	200	0.85
ZZ	400	0.85

(Note: the source PDF table is column-shifted by OCR; the designations and VA/PF pairs are reconstructed to the IEEE C57.13 standard voltage-transformer burden set. Confirm against the live EMTP® dropdown when populating a model.)

Study uses. Voltage measurement for control diagrams; VT ferroresonance and saturation studies (where the nonlinear core and remanent flux govern the onset and sustainment of ferroresonant modes); and transferred transients to the secondary, i.e. evaluating the voltage stress and waveform that reach metering/protection circuits.

VT ferroresonance can occur when the VT’s nonlinear magnetising branch interacts with system capacitance, especially in lightly loaded or unearthed systems. If ferroresonance is being studied, the VT magnetisation curve, losses and connected burden must be represented carefully. The risk is highest on isolated-neutral, resonant-earthed or otherwise capacitance-dominated systems, and is influenced by the switching sequence that initiates it and by the residual flux left in the core.

Section 2

Current transformer (CT) — `CurrentTransformer`

Concept / role. A CT is inserted in series with the conductor (1-phase or 3-phase wye-connected) and steps the primary current down to a standard secondary current (typically 5 A or 1 A) feeding a relay or meter. It carries two power pins ("k" and "m") and a control bundle that outputs the secondary current(s). The subcircuit again uses a non-ideal unit with a nonlinear magnetisation branch (∥ \(R_{mag}\)) and remanent flux — here the remanent (residual) flux is critical, because a CT that has not been demagnetised can drive deeply into saturation on the next fault, collapsing the secondary current and delaying or mis-operating protection.

CT saturation occurs when the core can no longer reproduce the primary current accurately on the secondary side. During faults, the DC offset in the primary current and any residual flux in the core can drive it into saturation; the secondary current then becomes distorted and may no longer represent the actual primary fault current.

Remanent flux (a critical CT initial condition)

A CT with residual flux may saturate much earlier during a fault than one starting from zero flux. CT studies should therefore consider credible remanence assumptions, especially for protection-performance assessment.

Parameters and what they represent.

Nominal frequency \(f\) — as for the VT.
Ratio — primary rated current / secondary rated current in amperes (e.g. \(200/5\)). For a multiratio CT this is the currently selected operating tap.
Winding 1 \(R_{1}\), \(X_{1}\) and Winding 2 \(R_{2}\), \(X_{2}\) — primary and secondary series resistance and reactance (the \(X\) fields are entered as winding inductance). A representative secondary resistance \(R_{2}\) can be loaded with "Load typical R", whose value depends on the Class, Ratio and Secondary voltage inputs.
Standard / Class / Secondary voltage / \(Z_{burden}\) / Power Factor — the burden. For IEEE C57.13 (ANSI) the Standard selection populates \(Z_{burden}\), PF and the rated secondary voltage from the B-class table below.
IEC 185 inputs — for the IEC standard: Rated power (VA), Precision, and precision-limit factor \(K_{p}\), together with the Class.
Multiratio CT / Maximum ratio — enable tapped operation and set the maximum ratio.
Excitation Curve — secondary current–voltage curve; "Load typical Excitation Curve" generates a representative curve from the Class and Ratio data, respecting the specified precision limits, again converted to current–flux internally.
Magnetization resistance \(R_{mag}\) — parallel loss resistance.
Initial flux (0) phase A/B/C (IC tab) — per-phase remanent flux.

IEEE C57.13 (ANSI) B-class burdens. Selecting a B-class fills the burden impedance, power factor and rated secondary voltage:

Table 3 — IEEE C57.13 standard current-transformer (B-class) burdens.

B-Class	\(Z_{burden}\) (Ω)	Power Factor	Secondary Voltage (V RMS)
B-0.1	0.1	0.9	10
B-0.2	0.2	0.9	20
B-0.5	0.5	0.9	50
B-0.9	0.9	0.9	90
B-1.8	1.8	0.9	180
B-1	1	0.5	100
B-2	2	0.5	200
B-4	4	0.5	400
B-8	8	0.5	800

Note the power-factor convention: PF = 0.9 for the low-impedance metering-class burdens up to B-1.8, and PF = 0.5 for the relaying-class burdens B-1 … B-8 (the higher reactive content reflecting electromechanical-relay loads). The rated secondary voltage of each class is consistent with the standard CT secondary saturation-voltage definition.

Study uses. Protection and relay modelling (the canonical EMTP® example is a 3-phase CT feeding a relay element); CT saturation during faults and asymmetrical (DC-offset) currents; residual-flux effects on re-energisation and auto-reclose; and secondary burden effects — a heavier \(Z_{burden}\) raises the secondary EMF demand and pushes the core into saturation sooner.

One fault magnitude is not enough

CT saturation is not set by the fault-current magnitude alone. It depends jointly on the DC offset and X/R ratio of the primary fault current (which fix how long the flux keeps building), the remanent flux already in the core, the connected burden and the chosen CT class. Checking one symmetrical fault magnitude is therefore not enough to judge CT performance — the onerous case is typically a fully offset fault on a high-X/R source combined with unfavourable remanent flux, which can drive the core into saturation within the first cycle.

Important modelling note

For CT studies, the burden should include the full secondary circuit, not only the relay burden. Secondary cable resistance can be significant and raises the voltage the CT must produce — making saturation more likely during high fault currents.

Section 3

Capacitive voltage transformer (CVT) — `CapacitiveVoltageTransformer`

Concept / role. A CVT measures EHV/HV bus voltage by first dropping it across a capacitive voltage divider and then transforming the reduced voltage down through an intermediate (electromagnetic) VT. A series tuning reactor cancels the divider capacitance at power frequency so the secondary voltage tracks the primary in magnitude and phase. The EMTP® Ratio includes both the capacitive divider and the ideal transformer, so it is entered as primary/secondary rated voltage directly (e.g. \(230000/115\)). The intermediate transformer carries a nonlinear magnetisation branch (∥ \(R_{mag}\)) with remanent flux, exactly as the VT — which is why CVTs are prone to ferroresonance and need a suppression circuit. The stray capacitances and the ferroresonance-suppression circuit are optional and can be included when their effects matter.

A CVT is not simply a voltage transformer with a different ratio. It includes a capacitive voltage divider, an intermediate transformer, a tuning reactor, a burden and usually a ferroresonance-suppression circuit — and these elements can significantly affect the transient secondary voltage.

Components and parameters.

Capacitive divider — \(C_{1}\) (top) and \(C_{2}\) (bottom). The divider scales the primary voltage by \(C_{1}/(C_{1}+C_{2})\), and its Thévenin capacitance \(C_{1}+C_{2}\) sets the value of the tuning reactor.
Tuning inductor branch — series \(R\), \(L\), \(C\); the inductance \(L\) is chosen to resonate with the divider at nominal frequency, ideally satisfying

\[ \omega L \;=\; \frac{1}{\omega\,(C_{1}+C_{2})}, \qquad \omega = 2\pi f, \]

\(\omega L\): reactance of the CVT tuning reactor
\(C_{1},\,C_{2}\): top and bottom capacitances of the capacitive divider
\(\omega = 2\pi f\): angular frequency at the nominal frequency \(f\)

so the divider’s capacitive reactance is compensated and the secondary follows the primary; \(R\) represents the reactor loss and \(C\) is the branch’s own capacitance term.

Intermediate transformer — winding 1 \(R_{1}\)/\(X_{1}\), winding 2 \(R_{2}\)/\(X_{2}\), nonlinear magnetisation (∥ \(R_{mag}\)) and remanent flux; the Magnetization data is the secondary current–voltage excitation curve of the voltage transformer behind the capacitor bridge.
Stray capacitances — must be included when fast transients are studied, in particular to capture travelling-wave propagation from the CVT primary to the secondary:
- \(C_{stray0}\) — tuning-inductor stray capacitance;
- \(C_{stray1}\) — winding-1-to-ground;
- \(C_{stray2}\) — winding-2-to-ground;
- \(C_{stray12}\) — winding-1-to-winding-2 (the inter-winding path responsible for capacitive — not turns-ratio — transfer of steep fronts).
Ferroresonance-suppression circuit — RLC branches designated (0-1-2), each with its own \(R\), \(L\), \(C\); damps the low-frequency ferroresonant oscillation between the divider/tuning capacitance and the saturable magnetising inductance of the intermediate VT.
Standard / \(Z_{burden}\) / Power Factor — burden per IEEE C57.13 (ANSI) (same voltage-transformer burden set as the VT section above), auto-populated or entered manually.
Initial flux (0) phase A/B/C (IC tab) — remanent flux of the intermediate-transformer magnetisation branch.

Study uses. CVT transient response — the divider, tuning reactor and burden form a resonant network whose ringing produces measurement errors during faults (the secondary voltage does not collapse instantaneously with the primary), which directly affects distance- and directional-relay performance; CVT ferroresonance (interaction of the capacitances with the saturable VT core, and the effectiveness of the suppression branches); and fast-front transfer, where \(C_{stray1}\), \(C_{stray2}\), \(C_{stray12}\) and \(C_{stray0}\) govern how steep primary surges couple capacitively to the secondary.

During fast voltage changes the CVT secondary voltage may not follow the primary instantly: the capacitive divider, tuning reactor and damping circuit introduce oscillations, delay and transient error. This matters for distance protection, voltage-based protection, synchronising, power-quality assessment and post-fault voltage recovery studies.

The CVT stray capacitances are not cosmetic detail: a model that omits them can match the real CVT exactly at power frequency yet behave incorrectly for steep-front transients, because the dominant transfer path at those frequencies is capacitive rather than through the turns ratio.

Section 4

Selecting an instrument-transformer model

Because all three devices reuse the same non-ideal-unit + nonlinear-core foundation, the model is chosen less by which instrument transformer and more by which physical effect the study must capture — principally the treatment of remanent flux, the burden, and (for the CVT) the stray capacitances:

Do not use an ideal ratio model when

CT saturation is important; remanent flux may affect the result; relay performance is being assessed; VT or CVT ferroresonance is possible; CVT transient response or voltage delay is important; or the connected burden may influence the secondary signal.

Table 4 — Recommended instrument-transformer modelling emphasis by study focus.

Study Focus	Remanent Flux	Burden (\(Z_{burden}\), PF)	CVT Stray Capacitances
Steady-state / metering accuracy	Not critical	Important (loads the secondary)	Not needed
CT saturation, relay operation, asymmetric faults	Essential (residual flux sets the saturation margin)	Important (drives the secondary EMF)	n/a
VT / CVT ferroresonance	Essential (nonlinear core + remanent flux)	Important (damping)	Usually not needed (low-frequency)
CVT transient response (relay errors during faults)	Secondary	Important (tunes the resonant response)	Helpful, not always essential
Fast-front / travelling-wave transfer to secondary	Negligible (core does not penetrate)	Secondary	Essential — include \(C_{stray0}\), \(C_{stray1}\), \(C_{stray2}\), \(C_{stray12}\)

In short: enter a realistic excitation curve and \(R_{mag}\) and set remanent flux whenever core saturation can occur (CT relaying, VT/CVT ferroresonance); always represent the standard burden matching the connected load (IEEE C57.13 for the VT and CVT, IEEE C57.13 B-classes or IEC 185 with \(K_{p}\) for the CT); and switch on the CVT stray capacitances and ferroresonance-suppression branches only when the study reaches into the fast-transient range or specifically targets ferroresonance — for steady-state and low-frequency work they can be omitted to keep the model simple. As with the power-transformer devices in the device catalogue page, none of these models is intended for very-fast-front internal-winding stress; for that a detailed winding model (see the high-frequency modelling page) is required.

On standard class data. Standards such as IEEE C57.13 and IEC 185 are useful because they define burden, accuracy and performance class. For transient simulations, however, class information may not be enough — detailed excitation data, burden data and secondary-circuit details may still be required.

Before modelling an instrument transformer — checklist

Ratio and rated primary/secondary quantities.
Accuracy class and protection class.
Burden and secondary cable resistance.
Magnetisation / excitation curve.
Knee-point voltage, where applicable.
Winding resistance.
Remanent-flux assumption.
Connected relay or meter impedance.
CVT capacitance values, tuning reactor and damping-circuit data.
Grounding arrangement and secondary-circuit connection.
Primary-system X/R ratio and fault-current waveform (DC offset and duration).
Switching sequence / energisation conditions, where ferroresonance or remanence is relevant.

Common modelling mistakes to avoid:

using only the relay burden and ignoring cable resistance;
assuming zero remanent flux for all CT faults;
using an ideal CT where saturation is important;
representing a CVT as a simple VT;
ignoring the ferroresonance-suppression circuit;
assuming the secondary signal follows the primary waveform perfectly during fast transients.

The same principle as the rest of the series applies: the model must match the study objective. For steady-state ratio checks a simple model may be enough; for protection transients, saturation, burden, remanence and CVT dynamic response may dominate the result. Framed another way, instrument-transformer modelling for transients is a protection-performance problem: the engineer must decide whether only a nominal secondary value is needed, or whether transient error, CT saturation, remanence, burden interaction, CVT recovery or ferroresonance must be reproduced — and for relay studies the CT, VT or CVT model should be validated as part of the complete measurement chain, not in isolation.

Part Five Reading now

Instrument Transformers (CT, VT, CVT)

The EMTP® current, voltage and capacitive-voltage transformers — the non-ideal unit with a nonlinear core and remanent flux, standard IEEE C57.13 / IEC 185 burdens, and the CVT divider, tuning reactor, stray capacitances and ferroresonance-suppression circuit.

Series progress 5 of 5

Part Four

Power-Transformer Device Catalogue

A working catalogue of the EMTP® power-transformer library devices — the ideal unit and m-winding ideal unit, the 2- and 3-winding nameplate-input transformers, and the BCTRAN matrix model — with formulas, input data and limitations.