Three-Phase Transformer Inductance Matrix Type (Two Windings)
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Transcript Three-Phase Transformer Inductance Matrix Type (Two Windings)
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Basic transformer model
L11 and L22 are the self-inductance of winding 1 and 2 respectively, and L12 and
L21 are the mutual inductance between the windings.
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Basic transformer model
Example: Consider a transformer with a 10% leakage reactance
equally divided between the two windings and a magnetising current
of 0.01 p.u.
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Basic transformer model
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Numerical implementation
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Numerical implementation
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Numerical implementation
Transformer equivalent after discretisation
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Modelling of non-linearities
Typical studies requiring the modelling of saturation are: Inrush
current on energising a transformer, steady-state overvoltage
studies, core-saturation instabilities and ferro-resonance.
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Modelling of non-linearities
to impose a decay time on the inrush currents, as would occur on
energisation or fault recovery:
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Three-Phase Transformer Inductance Matrix Type
(Two Windings)
The phase windings of the transformer are numbered as
follows:
1 and 4 on phase A
2 and 5 on phase B
3 and 6 on phase C
other phase (This core geometry implies that phase winding 1 is coupled to all
windings (2 to 6)
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Three-Phase Transformer Inductance Matrix Type
(Two Windings)
Transformer Model
The Three-Phase Transformer Inductance Matrix Type:
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Three-Phase Transformer Inductance Matrix Type
(Two Windings)
R1 to R6 represent the winding resistances.
The self inductance terms Lii and the mutual inductance terms Lij
are computed from the voltage ratios, the inductive component of the
no load excitation currents and the short-circuit reactances at nominal
frequency.
Two sets of values in positive-sequence and in zero-sequence allow
calculation of the 6 diagonal terms and 15 off-diagonal terms of the
symmetrical inductance matrix.
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Three-Phase Transformer Inductance Matrix Type
(Two Windings)
The self and mutual terms of the (6x6) L matrix are obtained from
excitation currents (one three-phase winding is excited and the other
three-phase winding is left open) and from positive- and zerosequence short-circuit reactances X112 and X012 measured with threephase winding 1 excited and three-phase winding 2 short-circuited.
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Three-Phase Transformer Inductance Matrix Type
(Two Windings)
Q11= Three-phase reactive power absorbed by winding 1 at no load when
winding 1 is excited by a positive-sequence voltage Vnom1 with winding 2
open
Q12= Three-phase reactive power absorbed by winding 2 at no load when
winding 2 is excited by a positive-sequence voltage Vnom2 with winding 1
open
X112= Positive-sequence short-circuit reactance seen from winding 1
when winding 2 is short-circuited
Vnom1, Vnom2= Nominal line-line voltages of windings 1 and 2
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Three-Phase Transformer Inductance Matrix Type
(Two Windings)
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Three-Phase Transformer Inductance Matrix Type
(Two Windings)
Extension from the following two (2x2) reactance matrices in positive-sequence
and in zero-sequence
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Three-Phase Transformer Inductance Matrix Type
(Two Windings)
In order to model the core losses (active power P1 and P0 in positive- and zerosequences), additional shunt resistances are also connected to terminals of one of
the three-phase windings. If winding 1 is selected, the resistances are computed as:
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Three-Phase Transformer Inductance Matrix Type
(Two Windings)
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Three-Phase Transformer Inductance Matrix Type
(Two Windings)
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Three-Phase Transformer Inductance Matrix Type
(Two Windings)
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UMEC (Unified Magnetic Equivalent Circuit) model
Single-phase UMEC model
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UMEC (Unified Magnetic Equivalent Circuit) model
Single-phase UMEC model
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UMEC (Unified Magnetic Equivalent Circuit) model
Three-limb three-phase UMEC
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UMEC (Unified Magnetic Equivalent Circuit) model
Three-limb three-phase UMEC
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