Transformer: Load Factor

Transcription

1 Transformer Introduction Construction Theory of Operation Ideal Transformer Transformer Rating Equivalent Circuit Per-Unit System oltage Regulation Efficiency Tests No-Load Current and In-rush Current Special Transformers Three Phase Transformers Parallel Operation Practical Aspects for transformers

2 Transformer: Load Factor Load factor It s the ratio between the apparent power (current) drawn by the load at a certain condition and the full load power (current) of the transformer. k S S L FL k I I FL k I I FL Z L

3 Transformer: oltage Regulation oltage Regulation It s the difference between the load voltage (secondary voltage) at no-load and the load voltage at a certain loading condition as a percentage of the no-load voltage. (i.e. the percentage voltage drop) R - NL e NL 00 Z L

4 Transformer: oltage Regulation R NL e - NL 00 e NL - 00 NL NL NL e - 00 Z L

5 Transformer: oltage Regulation I ( R + jx ) + eq eq Z Z f L L - X L f tan R L q sc tan - X R eq eq I Z cos( q -f ) eq sc E I Z eq negligible ery small phase shift f I q sc IReq qsc IXeq -f

6 Transformer: oltage Regulation e - e 00 IZ eq cos( q sc -f) 00 f I E q sc IR eq IZ eq qsc IX eq -f e IZeq cos( qsc -f) 00 NL q sc tan - X R eq eq

7 Transformer: oltage Regulation e ( I / IFL ) Zeq cos( qsc -f) 00 ( / I ) NL FL Load Factor k I I FL Zeq Zeq Zeq ( / I ) ( / I ) Z NL FL b b b Z eq pu e cos( q - f ) 00 kz eq pu sc

8 Transformer: oltage Regulation In general: e cos( q f ) 00 kz eq pu sc -ve for lagging, +ve for leading Maximum regulations happens when: cos( q f ) sc Zero regulation happens when: f q sc lagging cos( q f ) sc zero qsc f + f 90 o -q leading 90 o sc

9 Transformer: oltage Regulation f q sc at k k f -q 90 o sc

10 Transformer: Tapping The transformer voltage at the load side desired to be constant or as close to the nominal value. But the load voltage may vary according to current drawn by the load or supply voltage. Taps are provided on a transformer winding for selecting/cutting out a certain number of turns on the transformer winding thus obtaining a variable turns ratio. This allows adjustments of the output voltage. Typically, transformers are provided with four tapes allowing ±5% adjustments above or below the nominal voltage. The taps are usually on the high voltage side. The taps are connected to a tap-changer. Tap changers are either on-load type or off-load type.

11 Transformer: Tapping

12 Transformer: Efficiency Pout h 00 P in h Pout 00 P + P out losses h Pin -Plosses 00 P in

13 Transformer: Efficiency Transformer Losses. Copper losses: Winding losses due to winding resistances. P I R + I R cu P I R cu eq P cu I R eq ariable losses Z Z f L L

14 Transformer: Efficiency Transformer Losses. Iron (core) losses: Eddy loss + Hysteresis loss P iron R Constant losses c Z Z f L L

15 Transformer: Efficiency Transformer Losses 3. Stray losses: Not all flux flow in the iron core, some leakage flux may induce eddy currents in the metal structures supporting the core or the transformer housing, producing power loss. (5-0% of the transformer losses) 4. Dielectric losses: happens in the insulating materials in the transformer and in the transformer oil. ery small and often neglected.

16 Transformer: Efficiency P out h P S cosf out L P out P P + P in out losses h Pout S L cosf P S cosf + P + P in L iron cu k I I FL S S L FL P ks cosf out FL

17 Transformer: Efficiency P I R cu eq k I S L I P cu k IFL Req FL SFL P cu kpcufl h ks cosf ks P k P FL FL cosf + iron + cufl

18 Transformer: Efficiency h ks cosf ks P k P FL FL cosf + iron + cufl h k f k cosf P P + + k iron cufl cos SFL SFL P Z S R R Z R P iron b * b c b c / b c pu I R R R CuFL FL eq eq Sb Sb Sb / IFL eqpu h k cosf k cosf + + R c pu k Reqpu

19 Transformer: Efficiency Maximum Efficiency h ks cosf ks P k P FL FL cosf + iron + cufl k m P P iron cufl h m k S k S m FL cosf cosf + P m FL iron

20 Transformer: Efficiency All Day Efficiency h Output Energy during the day AllDay 00 Output Energy during the day + Energy losses h h Eout AllDay 00 E + E out n å losses ( ks cos f) T i FL i i AllDay n n å ( ks i FL cos f) Ti + Piron Ttotal + åki PcuFL Ti i i

21 Transformer: Tests The equivalent circuit parameters are determined using two standard experiments.. Open Circuit Test: - Performed by supplying the rated voltage to one side while keeping the other side open circuit. - Preferably done by low voltage side with the rated voltage while keeping the high voltage side open. - The H and L sides voltages, the input current and the input power are measured.

22 Transformer: Tests. Open Circuit test: Po I o Rated oltage o P P I cosf o iron o o o o R c o o o X m Iocosfo Iosinfo o N N R cl X ml N N

23 Transformer: Tests. Short Circuit Test: - Performed by short-circuiting one side while supplying a reduced voltage to the other side. - Preferably done by supplying the reduced voltage to the high voltage side while the low voltage side is short-circuited. - The reduced voltage is usually adjusted so that the current equals the full load current. - The supply voltage, the input current and the input power are measured.

24 Transformer: Tests. Short Circuit Test: Psc I sc Reduced oltage sc R & X >> m R, X C eq eq P I R sc sc eq ( sc ) R P Z R + X sc eq( sc) eq( sc) eq( sc) Isc sc eq( sc) X eq ( sc ) Zeq ( sc )-Req ( sc ) I R eqh X eqh

25 Transformer: No-load Current Nature of the No-load Current. Magnetizing Current (I m ) df sin( w t) N dt m f m p sin( wt - ) wn Ni fâ l mc  ma c N L  i m m p sin( wt - ) w L m I m jx m

26 Transformer: No-load Current Nature of the No-load Current. Magnetizing Current (I m ) The magnetizing current is nonsinusoidal due to the non-linear effect of saturation and hysteresis of the core material. The third harmonics is about 40% of the magnetizing current. Â l mc ma c

27 Transformer: No-load Current Nature of the No-load Current:. Core loss current (I c ) Core-loss current is also non-sinusoidal due to the nonlinear effect of hysteresis.

28 Transformer: In-rush Current Switching transient current When switching on a transformer, the initial transient magnetizing current is much higher than the steady state value. It may be up to 6-0 times the full load current. This current is called in-rush current. Problems associated with high in-rush current:. Winding deformation due to high mechanical stresses associated with high current levels, shortens the life span of the transformer.. Differential protection mal-function. 3. Non-sinusoidal current with high DC component and harmonic content.

29 Transformer: In-rush Current Switching transient current The magnitude and duration of the in-rush current depends on:. The value of the voltage at the instant of switching.. The value and sign of the residual flux in the transformer core (remnant flux due to previous operation) 3. The magnetic characteristics of the core material.

30 Transformer: In-rush Current Switching transient current If the transformer is switched on at the instant of voltage zero, the flux wave is initiated from the same origin as voltage waveform, the value of flux at the end of first half cycle of the voltage waveform will be, d f N dt f N ò dt p m ò m sin( t) d( t) wn 0 f w w f wn m

31 Transformer: In-rush Current Switching transient current But if the transformer is switched on at the instant of maximum voltage, the value of flux at the end of first quarter cycle of the voltage waveform will be, p/ m ò m sin( t / ) d( t) wn 0 f w + p w f wn m

32 Transformer: In-rush Current Switching transient current The only way to avoid high in-rush current is to select the proper instant of switching and eliminate any residual flux in the core prior to switching