Component 155: Transformer

Specification

Line Connection
1	Power Inlet
2	Power Outlet
3	Power Loss

General User Input Values Physics Used Displays Example

General

Component 155 (Transformer) represents an electrical device used to change the voltage of a single or three-phase alternating current at constant frequency. The underlying physical model accounts for the iron losses (representing the losses due to eddy currents and hysteresis in the core of the transformer) and the copper losses (representing losses due to the resistance of the windings of the transformer). Using the approximation that the ratio of outlet voltage to inlet voltage is equal to the ratio of windings of the two circuits (i.e. neglecting the magnetizing current, which is a valid approach for power plant transformers), the respective exit current and power factor cos phi at the transformer outlet are determined.
For adapting the model to measured performance of a specific transformer, the physical model for off-design performance can be refined with a correction factor defined in a characteristic based on the ratio of apparent power under current and design conditions.

User Input Values

FMODE	Flag to set the calculation mode Design / Off-design Like in Parent Profile (Sub profile option only) Expression =0: Global =1: Local off-design (i.e. always off-design mode, even when a design calculation has been done globally) =-1: Local design (i.e. always design mode, even when a off-design calculation has been done globally)
FVOLT	Method for specification of outlet voltage Like in Parent Profile (Sub profile option only) Expression =0: Defined by specification value VOLT =1: Set externally
U2	Outlet voltage
EFF	Efficiency
LFFE	Iron loss fraction (proportion of total losses)
FEFFOD	Off-design efficiency method Like in Parent Profile (Sub profile option only) Expression =0: QLOSS = LOSSFE + LOSSCU =1: QLOSS = (LOSSFE + LOSSCU) * CFLOSSES(QAPP/QAPPN)
QAPP1N	Nominal apparent power
LOSSN	Nominal total losses
LOSSFEN	Nominal iron losses
COSPHI2N	Nominal outlet power factor

Result values

RLOAD	Apparent load fraction
REFF	Calculated efficiency
QLOSS	Calculated losses
LOSSFE	Iron losses
LOSSCU	Copper losses
QAPP1	Apparent power at inlet
QAPP2	Apparent power at outlet
QREAL2	Calculated outlet power
QREACT2	Calculated reactive outlet power
COSPHI1	Calculated inlet power factor (cos phi1)
COSPHI2	Outlet power factor (cos phi2

Physics Used

In the transformer model of component 155, the voltages U1 and U2 are assumed to be constant and independent of load. The model is also simplified in terms of neglecting the magnetizing current of the transformer. The underlying energy balances are shown in the section Equations below.

Design Calculations

In design mode, the user has to specify

the exit voltage U2,
the overall efficiency of the transformer with the parameter EFF,
and the parameter LFFE for fraction of the iron losses relative to the total losses.

For the current input to the transformer will be

Real power,
type of current (NPHAS - number of phases, NPHAS is transferred in the direction of the flow. When connecting lines with different NPHAS,
the value of the main inlet is used. )
and
voltage at the transformer inlet
determined by components upstream of the transformer, and

exit power factor cos phi
is defined by components downstream.

If data from the manufacturer are available, the component can also be sized by defining the nominal values for

apparent power QAPP1N,
total losses LOSSN
iron losses LOSSFEN,
and power factor cos(phi) at the outlet COSPHI2N

In this case, the calculation mode FMODE must be set to the value of 1: "Local off-design".

Off-Design Correlations

The losses of the transformer are composed of iron losses and copper losses. Iron losses are assumed to be constant and independent of load, whereas the copper losses are related to the resistance in the copper windings and therefore have a quadratic correlation with the inlet current.

With the setting FEFFOD = 1, a correction term can be activated that uses the characteristic CFLOSSES for a correction factor as a function of the ratio of current inlet apparent power to nominal inlet apparent power.

Equations

All cases
	Energy balance: Q1 = Q2 + QLOSS = Q2 + LOSSFE + LOSSCU Q1 = I1 * U1 * COSPHI1 * SQRT(NPHAS) Q2 = I2 * U2 * COSPHI2 * SQRT(NPHAS)
Design
	Loss calculation based on user input: LOSSN = (1-EFF )* Q1 LOSSFEN = LFFE * LOSSN LOSSCU = (1 - LFFE) * LOSSN I2 = (Q1 - LOSSN) / (U2 * COSPHI2 * SQRT(NPHAS)) QAPP2 = U2 * I2 * SQRT(NPHAS) I1 = I2 * (U2/U1) + LOSSFE / (U1 * SQRT(NPHAS)) QAPP1N = U1 * I1 COSPHI1 = (U2 * I2 + LOSSFEN) / (QAPP1N * SQRT(NPHAS))
Off-Design
	Losses depending on inlet current and apparent power at the inlet: LOSSFE = LOSSFEN (constant) LOSSCU = LOSSCUN * (I1/I1N)^2 QLOSS = (LOSSFE + LOSSCU) * CFLOSSES(QAPP1/QAPP1N); if FEFFOD=0 then CFLOSSES=1 COSPHI1 = (U2I2 + LOSSFE) / (U1I1 * SQRT(NPHAS))

Characteristics Lines

Characteristic line 1 (CFLOSSES): loss correction factor = f (QAPP1/QAPP1N)

Characteristic line 1: power loss

     X-Axis        1          QAPP1/QAPP1N                     1^st point
                        2          QAPP1/QAPP1N                     2^nd point
                        .
                      N         QAPP1/QAPP1N                     last point

Y-Axis 1 loss correction factor (CFLOSSES) 1^st point
2 loss correction factor (CFLOSSES) 2^nd point

.
N loss correction factor (CFLOSSES) last point

Literature References

W. Plaßmann, D. Schulz (Hrsg.), Handbuch Elektrotechnik, Springer Fachmedien, Wiesbaden 2013

W. Weißgerber, Elektrotechnik für Ingenieure, Springer Fachmedien, Wiesbaden 2015

Component Displays

Display Option 1

Example

Click here >> Component 155 Demo << to load an example.

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