ECE 3600 Transformers b

Transcription

1 Transformer basics and ratings A Transformer is two coils of wire that are magnetically coupled. Transformers b Transformers are only useful for AC, which is one of the big reasons electrical power is generated and distributed as AC. Transformer turns and turns ratios are rarely given, V p /V s is much more common where V p /V s is the rated primary over rated secondary voltages. You may take this to be the same as / although in reality is usually a little bit bigger to make up for losses. Also common: V p : V s. Transformers are rated in VA Both RMS Transformer Rating (VA) = (rated V) x (rated ), on either side. Don't allow voltages over the rated V, regardless of the actual current. Don't allow currents over the rated, regardless of the actual voltage. deal Transformers ron-core transformer primary secondary V V Z L deal: P = P power in = power out Transformation of voltage and current Turns ratio Turns ratio as defined in Chapman text: a = = V V =, same as N = (Ryff, Fig.7.) Note: some other texts N define the turns ratio as: Be careful how you and others use this term Transformation of impedance V V Z You can replace the entire transformer and load with (Z eq ). This "impedance transformation" can be very handy. V Z eq Z eq = N. Z =. Z Transformers can be used for "impedance matching" This also works the opposite way, to move an impedance from the primary to the secondary, multiply by: Transformer notes p

2 Model of non-ideal Transformer Transformer notes p. deal transformer R s X s R N V m X. m V V Z L R m - Core losses Eddy-current losses - minimized by laminating the core and adding silicon to raise the resistivity Hysteresis losses - caused by the B-H hysteresis curve (Ryff, Fig.7.) X m - basic inductance caused by the need to magnetize the core R s - Winding resistance (copper) losses X s - Reactance caused by flux leakage (leakage reactance) Move the load impedance to simplification the analysis. R s X s R m X N V m Z. eq Z L Typical calculations V no_load V full_load. Voltage regulation %VR = 00.% V full_load P out. Efficiency η = 00.% P in Transformer notes p

3 Tests to find parameters Transformer notes p3 Open-circuit test P wattmeter ==> V R m X m Short-circuit test Vari-AC (Ryff, Fig.7.6) P wattmeter S =. V Q = S P R m = V P V = rated voltage rated X m = V Q V ==> V R s X s (Ryff, Fig.7.7) Other Transformers Multi-tap transformers: S =. V Q = S P = rated current R s = P X s = Q Many transformers have more than two connections to primary and/or the secondary. The extra connections are called "taps" and may allow you to select from several different voltages or get more than one voltage at the same time. solation Transformers: All transformers but auto transformers isolate the primary from the secondary. An solation transformer has a : turns ratio and is just for isolation. Special Sensing Transformers (Ryff, Fig.7.7) "Potential" transformer, for voltage monitoring (Ryff, Fig.7.6) VT or PT CT The secondary must always be shorted or nearly shorted! Transformer notes p3

4 V V = V V = Regular winding connections Transformer notes p4 P = = V = S V = Auto Transformer Connections 4 basic possibilities = S P = V V = = V V V Rating: _rated. _rated P = = S = V V V = Rating: _rated. _rated Subtraction connections Actual currents are in the reverse directions P = = S = S P = = V = V Rating:. _rated _rated Power Flow Through Transformer = S = V V V = Rating:. _rated _rated Transformer notes p4 Primary and Secondary could be swapped on any of these connections for an additional 4 possibilities

5 Vari-AC type autotransformer Transformer notes p5 This adjustable autotransformer is wound on a toroidal core. moveable tap showing only a few windings Side view, A B step down Top view B f you cut the toroid open and straightened it out, you would get the views below. step up B P = moveable tap P V = P V S moveable tap = V V = A A Vari-AC type autotransformer "Rating", Based or the maximum winding current: max = max = max = max = max.5. max. S max. max.. max 0.5 step down <-- --> step up Transformer notes p5

6 3-phase Transformer Connections Y - Y Connection Multiple cores Transformer notes p6 Single-core (3-phase) transformer Advantages: cheaper, less core loss (Elgerd, Fig.5.8) Symbol Disadvantage: ndividual transformers can limp along even if one winding fails, this cannot. (Elgerd, Fig.5.0) (Ryff, Fig.7.8) Third-harmonic currents (due to B - H non-linearity) add up to a significant neutral current. Any winding will allow the third-harmonic current to flow in a loop. Transformer notes p6 (Elgerd, Fig.5.)

7 - Y Connections, Y - are the opposite Transformer notes p7 Symbol - Y is usually step-up Y - is usually step-down (Elgerd, Fig.5.) - Y and -Y always introduce a 30 o phase shift, + or - depending on how they are wired. - Y is usually step-up phase shift Different connections - 30 o phase shift (Elgerd, Fig.5.4) Y - (usually step-down) would also give a -30 o phase shift Single-core 3-phase transformers can also be used this way Transformer notes p7

8 Phase-Shifting Transformers Transformer notes p8 Windings drawn in parallel are on the same core Used to control the direction of power flow on the network (Stevenson, Fig.9.5) (Stevenson, Fig.9.4) Voltage Regulating Transformers (Stevenson, Fig.9.3) Off-Nominal Turns Ratio Note the weird direction Z s V : t V Z s = f there is a phase shift, t will be complex Transformer notes p8 Y s Y s t Y =. s Y s Y s t t ( t ) V V = complex conjugate of t