Transformers Transformers The simple transformer law relates output

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Transformers

Transformers

Transformers • The "simple transformer law" relates output voltage to input voltage and turns

Transformers • The "simple transformer law" relates output voltage to input voltage and turns ratio. Investigate the importance of frequency and other parameters in determining the nonideal behaviour of transformers.

The "simple transformer law"

The "simple transformer law"

Using the Kirchhoff's and Faraday’s laws

Using the Kirchhoff's and Faraday’s laws

Neglects No magnetic hysteresis We also need to separate running with load and free

Neglects No magnetic hysteresis We also need to separate running with load and free running, as it’s particular case.

Dependence of coefficient against frequency (with load) (

Dependence of coefficient against frequency (with load) (

Dependence of coefficient against frequency (free running) (

Dependence of coefficient against frequency (free running) (

Dependence of coefficient against voltage

Dependence of coefficient against voltage

Dependence of coefficient against resistance

Dependence of coefficient against resistance

Part 1 • Measuring parameters of our transformer

Part 1 • Measuring parameters of our transformer

1 st experiment: VAC Ohm’s law: A V We used small DC voltages to

1 st experiment: VAC Ohm’s law: A V We used small DC voltages to measure the resistance of the winding

Plot VAC, 1 st winding

Plot VAC, 1 st winding

Plot VAC, 2 nd winding

Plot VAC, 2 nd winding

Theory We will seek the solution of this equations in form:

Theory We will seek the solution of this equations in form:

Vector diagram

Vector diagram

Inductance. Current fading V

Inductance. Current fading V

Measures by current fading

Measures by current fading

Linearization

Linearization

Calculation from graph of inductance

Calculation from graph of inductance

Theory and practice, dependence on frequency(with load) theory experiment

Theory and practice, dependence on frequency(with load) theory experiment

Dependence M against frequency M(mutual inductance factor) depends on frequency because of depending µ

Dependence M against frequency M(mutual inductance factor) depends on frequency because of depending µ on it

Dependence on frequency(with load) after addition M dependence

Dependence on frequency(with load) after addition M dependence

Diffusion flux Inside flux

Diffusion flux Inside flux

Demonstration. Flux.

Demonstration. Flux.

Without core

Without core

Rotation

Rotation

Dependence of coefficient against angle

Dependence of coefficient against angle

Linearization

Linearization

Part 2 • Describing all looses in the transformer

Part 2 • Describing all looses in the transformer

Losses We measured steel losses using the chain (right). A ~ V V

Losses We measured steel losses using the chain (right). A ~ V V

Steel looses. Foucault currents r h

Steel looses. Foucault currents r h

Dependence of full losses in the 1 st winding against voltage

Dependence of full losses in the 1 st winding against voltage

Dependence of temperature losses in the 1 st winding against voltage

Dependence of temperature losses in the 1 st winding against voltage

Dependence of steel losses against voltage

Dependence of steel losses against voltage

Dependence of diffusion flux against voltage

Dependence of diffusion flux against voltage

Rebuilding a chain We can rebuild our chain using diffusion inductance

Rebuilding a chain We can rebuild our chain using diffusion inductance

Including diffusion flux

Including diffusion flux

Demonstration Ferromagnetic erromagnet

Demonstration Ferromagnetic erromagnet

Part 3 • Measuring and modeling hysteresis

Part 3 • Measuring and modeling hysteresis

Hysteresis

Hysteresis

Changing U 0

Changing U 0

Modeling hysteresis loop If we know all the coefficients, we can have as a

Modeling hysteresis loop If we know all the coefficients, we can have as a result of our model real hysteresis loop

Modeling changing signal

Modeling changing signal

Changing w

Changing w

Changing n • We are changing numbers of coil turns A ~ V V

Changing n • We are changing numbers of coil turns A ~ V V

Dependence of coefficient against number of turns

Dependence of coefficient against number of turns

Theory

Theory

Resonance mode We can imagine a real winding as system of coils, resistances and

Resonance mode We can imagine a real winding as system of coils, resistances and capacitors.

Conclusions • Transformer coefficient depends on 1. frequency because of the resistances of windings

Conclusions • Transformer coefficient depends on 1. frequency because of the resistances of windings and the dependence of induction on frequency 2. the load because of the resistance of the 2 nd winding 3. input voltage because of hysteresis mode 4. turns number of the windings because of dependence M on it

Thanks for your attention

Thanks for your attention

Dependence of steel losses in the 2 nd winding of voltage

Dependence of steel losses in the 2 nd winding of voltage

Dependence of coefficient against frequency (with load) (

Dependence of coefficient against frequency (with load) (

Changing amplitude of U 0

Changing amplitude of U 0

Unideal transformer Resistance of the winding Losses of the flux Losses in the core

Unideal transformer Resistance of the winding Losses of the flux Losses in the core

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