Description

In three-limb transformers, the magnetic flux associated with quasi DC Geomagnetic Induced Currents (GICs) passes through the high reluctance path of the transformer tank and air. Therefore. three-limb transformers are less sensitive to GICs. To consider the impact of the core structure in GIC studies, a fictitious winding (delta grounded) is added to the basic autotransformer model.

Table of Contents

Mask and Parameters

General Parameters

Tertiary connection	Select whether the delta-connected winding voltage will lead or lag the star-connected winding voltage or ground C-phase
Flux-Current characteristic model	Model saturation only or saturation with hysteresis
Iteration in saturation model	Enable or disable iteration to achieve more accurate results at the expense of computation time when the saturation segment changes
Base serial/common/tertiary winding voltage (rmsLL)	Base value for PU conversion (kV)
Rm	Equivalent resistance of iron losses of the magnetic circuit (Ω)
Base primary/secondary winding voltage (rmsLL)	Base value for PU conversion (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)
R12	Primary to secondary resistance (pu)
R13	Primary to tertiary resistance (pu)
R23	Secondary to tertiary resistance (pu)
L12	Primary to secondary inductance (pu)
L13	Primary to tertiary inductance(pu)
L23	Secondary to tertiary inductance (pu)
Parameter calculation method	Equal R1 R2: Resistance of the series winding is set equal to the common winding Classic: R1, R2, and R3 are calculated using between winding resistances R12, R13 and R23
3-limb magnetic circuit	Enables/disables the modeling of the three-legged magnetic circuit
Air and tank leakage inductance	Inductance of the fictitious winding (pu) [uses the same base as tertiary winding]
Air and tank leakage resistance	Resistance of the fictitious winding (pu) [uses the same base as tertiary winding]

Neutral Impedance Parameters

R1, R2, R3, R4	Neutral resistance of the winding; only applies to Y ground (Ω)
L1, L2, L3, L4	Neutral inductance of the winding; only applies to Y ground (H)
C1, C2, C3, C4	Neutral capacitance of the winding; only applies to Y ground (F)

Saturation Parameters

Number of data points	Number of segments of the current-flux saturation curve; only the positive part of the curve must be specified, the negative part being completed by symmetry
Saturation current	Current for each segment of the saturation curve; the origin (0,0) is implied (A)
Saturation flux	Flux for each segment of the saturation curve; the origin (0.0,0.0) is implied (V.s)

Hysteresis Parameters

Saturation data type	Determines if the saturation curve is calculated by the model or defined by a series of segments (Equation, Curve)
Air core inductance	Value of the saturation inductance that the curve approaches asymptotically (H)
Slope at Ic:	Flux slope at coercive current (H)
Coercive current - Ic	Positive coercive current at null flux (A)
Saturation current - Is	Current value of the first point in the saturation zone (A)
Current tolerance	Special parameter limiting the generation of minor nested loops. When the magnetizing current values at the last inversion point and the preceding inversion point are closer than the specified tolerance (in % of Ic), it is assumed that there is a displacement on a trajectory represented by a straight line segment.
Remanent flux - Φr	Positive remanent flux at null current (V.s)
Saturation flux - Φs	Flux value of the first point in the saturation zone (V.s)
Flux tolerance	Special parameter limiting the generation of minor nested loops. When the flux values at the last inversion point and the preceding inversion point are closer than the specified tolerance (in % of Φs), it is assumed that there is a displacement on the current loop.
Initial flux (peak)	Initial flux determining initial trajectory which is calculated by supposing that it has an inversion point on the main cycle (V.s)
Number of data points	Number of segments of the current-flux saturation curve; only the positive part of the curve must be specified, the negative part being completed by symmetry
Saturation current	Current for each segment of the saturation curve; the first value must be equal to Is (A)
Saturation flux	Flux for each segment of the saturation curve; the first value must be equal to Φs (V.s)

Ports, Inputs, Outputs and Signals Available for Monitoring

Ports

Name	Description

Name	Description
Net_1	Primary winding connection (supports only 3-phase connections)
Net_2	Secondary winding connection (supports only 3-phase connections)
Net_N1	Neutral connection for primary winding (supports only 1-phase connections)
Net_3	Tertiary winding connection (supports only 3-phase connections)

Inputs

None

Outputs

None

Sensors

Name	Description	Unit

Name	Description	Unit
FLUX(a,b,c)	Magnetization flux for each phase	V.s
IMAG(a,b,c)	Magnetization current for each phase	A
IPRIM(a,b,c)	Primary current for each phase	A
ISEC2(a,b,c)	Secondary current for each phase	A
ISEC3(a,b,c)	Tertiary current for each phase	A
ISEC4(a,b,c)	Fictitious winding current for each phase ( only available when the "3 limb magnetic circuit" setting is "yes."	A
SEG(a,b,c)	Segment number of the saturation curve In the saturation model, the numbering is always positive starting at 1 for the last segment in the negative saturation zone. In the hysteresis model, the numbering is positive/negative starting at 1/-1 in the positive/negative saturation zone. In the hysteresis zone, it takes a null value.

Internal Connection and Parameters

The internal connection of the autotransformer is shown below. Note that it is the phase C's terminal of tertiary and fictitious windings which are grounded. The neutral point of the autotransformer is accessible via the single-phase "N" terminal.

The main parameters (R₁₂, R₁₃, R₂₃, X₁₂, X₁₃, X₂₃) are entered in "per unit" only. They are then used to determine the parameters of windings (R₁, R₂, R₃, X₁, X₂ and X₃) as a function of the nominal voltages of the windings (N₁ and N₂) according to the expressions below, N₁ and N₂corresponds to the series winding and common winding, respectively.

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The values obtained are referenced to the primary nominal voltages (VbasePrimary = VnomSeries + VnomCommon), secondary (VbaseSecondary = VnomCommon) and tertiary (VbaseTertiary = VnomTertiary).

V base primary	Base primary winding voltage of the auto-transformer in kV rms LL
V base secondary	Base secondary winding voltage of the auto-transformer in kV rms LL
V base tertiary	Base tertiary winding voltage of the auto-transformer in kV rms LL
V nom	Rated voltage of winding (kV rms) as defined in General Parameters

All other parameters are entered in the same way as for other HYPERSIM transformer models. The saturation is placed at the series winding and uses the nominal voltage of this winding for the "per unit" conversion.

Load Flow and Initialization

The autotransformer sends the parameters of a standard equivalent transformer to the power flow algorithm.