 # Transformers Transformers The simple transformer law relates output

• Slides: 57 Transformers 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" Using the Kirchhoff's and Faraday’s laws 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 (free running) ( Dependence of coefficient against voltage Dependence of coefficient against resistance Part 1 • Measuring parameters of our transformer 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, 2 nd winding Theory We will seek the solution of this equations in form:   Vector diagram   Linearization Calculation from graph of inductance 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 on it  Diffusion flux Inside flux Demonstration. Flux. Without core Rotation Dependence of coefficient against angle Linearization Part 2 • Describing all looses in the transformer Losses We measured steel losses using the chain (right). A ~ V V Steel looses. Foucault currents r h Dependence of full 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 diffusion flux against voltage Rebuilding a chain We can rebuild our chain using diffusion inductance Including diffusion flux Demonstration Ferromagnetic erromagnet Part 3 • Measuring and modeling hysteresis Hysteresis Changing U 0 Modeling hysteresis loop If we know all the coefficients, we can have as a result of our model real hysteresis loop Modeling changing signal Changing w Changing n • We are changing numbers of coil turns A ~ V V Dependence of coefficient against number of turns Theory 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 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   Dependence of steel losses in the 2 nd winding of voltage Dependence of coefficient against frequency (with load) ( Changing amplitude of U 0 Unideal transformer Resistance of the winding Losses of the flux Losses in the core