Description

The inductance matrix transformer (IMT) model reproduces the behavior of a three-phase linear transformer at power frequency. This model works with the Transformer data Tab. Based on excitation and short-circuit tests in positive and zero sequences, the tool computes two matrices [R] and [L] modeling the transformer. The R_i and L_i are the resistance and self inductance of each coil. M_ij are the mutual inductances between coils. HYPERSIM simulates the transformer as mutually-coupled R-L branches. All computing details of matrices [R] and [L] can be found in the Transformer data Tab documentation.

Supports

A three-limb core representation
A five-limb core representation
Internal faults simulation

Does not support

A three single-phase cores representation
Saturation

Table of Contents

Mask and Parameters

General Parameters

The base parameters are computed in the Transformer data Tab.

Description	Use this field to add information and pertinent details about the component
Base primary/secondary/tertiary winding voltage (rmsLL)	Base value for PU conversion (kV); defined in Transformer data Tab (kV). Voltage expressed in kV rms LL This base voltage and nominal voltage will change, if the corresponding winding connection switches between delta and Y.
Base power (total)	Base value for PU conversion (MVA)
Base frequency	Base value for PU conversion (Hz)

Winding Parameters

The R and L matrices as well as the positive- and zero-sequence parameters are computed in the Transformer data Tab.

Primary/secondary/tertiary connection	Winding type Y ground: Grounded Y connection (can use the internal neutral impedance specified in the other tab) Y floating: Floating Y connection Y neutral: Y connection with impedance connected at the input pin N1 or N2 Delta lead: Delta connection with lead of 30° Delta ground: Grounded delta connection (Phase C is grounded) Delta lag: Delta connection with lag of 30°
Rm - positive sequence	Defined in Transformer data Tab (Ω)
Rm - zero sequence	Defined in Transformer data Tab (Ω)
[R]	Leakage resistance matrix (Ω)
[L]	Leakage inductance matrix (H)

Fault Parameters

Faulted winding	(primary or secondary)
Leg of faulted winding	(A, B, or C)
Fault type	When a fault is enabled, new [L] and [R] matrices are computed but are not displayed in the mask (none, turn-to-ground or turn-to-turn)
Fault resistance	(Ω)
Fault inductance	(H)
Fault turns A	Determines the position of the faulty connection for turn-to-ground faults or turn-to-turn faults in combination with the parameter Fault turns B (% total turns)
Fault turns B	Determines the position of the faulty connection for turn-to-turn faults in combination with the parameter Fault turns A (% total turns)
Sigma AB	Leakage factor between the two turns A and B of the faulty connection Sigma AB = 1 - M_AB² / (L_A * L_B)
Epsilon	Ratio of leakage factor between faulted winding and other windings Epsilon = Sigma Ai / Sigma fi Sigma Ai: Leakage factor between subwinding A and i Sigma fi: Leakage factor between faulted winding (A+B) and i

Neutral Impedance Parameters

The neutral impedance parameters are computed in the Transformer data Tab.

R1, R2, R3	Neutral resistance of the winding; only applies to Y ground (Ω)
L1, L2, L3	Neutral inductance of the winding; only applies to Y ground (H)
C1, C2, C3	Neutral capacitance of the winding; only applies to Y ground (F)

Transformer Data

To Learn How to Generate Transformer Parameters See:

- How to Generate [Z]-Based Transformer Parameters

Ports, Inputs, Outputs and Signals Available for Monitoring

Ports

Net_1	Primary winding connection (supports only 3-phase connections)
Net_2	Secondary winding connection (supports only 3-phase connections)
Net_3	Tertiary winding connection (supports only 3-phase connections)
Net_N1	Neutral connection for primary winding (supports only 1-phase connections)
Net_N2	Neutral connection for secondary winding (supports only 1-phase connections)
Net_N3	Neutral connection for tertiary winding (supports only 1-phase connections)
Net_TG	Used for turn-to-ground faults by connecting a 1-phase fault-to-ground component
Net_TT	Used for turn-to-turn faults by connecting a 1-phase circuit breaker component between Net_TG and Net_TT

Inputs

None

Outputs

None

Sensors

IPRIM(a,b,c,n)	Primary current for each phase (A)
ISEC2(a,b,c,n)	Secondary current for each phase (A)
ISEC3(a,b,c,n)	Tertiary current for each phase (A)

Fault Modeling

The development and validation of the method is based on [2].

Without any faults, matrices [R] and [L] are 9 x 9.

To modelize a faulted coil between turn and ground or between any two turns, the faulted coil must be divided.

For a turn-to-ground fault, the faulted coil is divided into na and nb.

na: from top to fault location T1 (in % of nf)
nb: from fault location T1 to bottom of nf

→ Fault position T1 in % = nb / (na + nb) * 100

Matrices [R] and [L] hence become 10 x 10.

For a turn-to-turn fault, the faulted coil is divided into na, nb and nc.

na: from top to fault location T1 (in % of nf)
nb: from fault location T1 to fault location T2 (in % of nf)
nc: from fault location T2 to bottom of nf
→ Fault position T1 in % = na / (na + nb + nc) * 100
→ Fault position T2 in % = (na + nb) / (na + nb + nc) * 100

Matrices [R] and [L] hence become 11 x 11.

References

[1] Dommel, H., et al., Electromagnetic Transients Program Reference Manual (EMTP Theory Book), 1986
[2] A transformer model for winding fault studies, Patrick Bastard, Pierre Bertrand, Michel Meunier, IEEE, Vol 9, No 2, April 1994

See also:

- Transformer data Tab | Inductance Matrix Transformer Programming Interface

HYPERSIM Documentation

3-Winding Impedance-Matrix-Based Transformer with Internal Fault