Lab 4: The transformer

Transcription

1 Lab 4: The tranformer ELEC 305 July 8 05 Read thi lab before your lab eriod and anwer the quetion marked a relaboratory. You mut how your re-laboratory anwer to the TA rior to tarting the lab. It i a long lab and require the full 3 hour to omlete. Divide into grou of (or more if neeary). Someone mut have the following role: Exerimentalit: Taking meaurement off the oillooe Theorit: Doing alulation and organizing exerimental data Hint: If uing exel, enure all angle are in radian for trig funtion NOTE: Eah grou member mut reare hi own lab reort. Lab reort i to inlude re-lab quetion anwer. Introdution The objetive of thi lab are to invetigate: a) The relationhi between urrent and voltage in the rimary and eondary winding of a tranformer. b) Imedane tranformation with a tranformer. ) How well a widely-ued equivalent iruit deribe the behavior of a real tranformer. d) How real tranformer have a limited frequeny range of ueful oeration. e) A egment of a ower tranmiion line for home delivery. Pre-lab quetion: ) Baed on the theory etion rovided derive equation (4) tarting from equation et (.A) and (.B). ) Uing the voltage and urrent tranformation equation, (4) and (6), obtain the imedane tranformation (5). 3) Define leakage indutane. 4) Define magnetization indutane. 5) Deribe Eddy urrent and how they lead to ower lo in a real tranformer 6) Deribe hyterei loe and how they lead to ower lo in a tranformer. 7) What te are taken to minimize Eddy urrent loe and hyterei loe in real tranformer? 8) Draw a hemati of a large ale ower ditribution network tarting from the megawatt generator and branhing out to different onumer load (reidential, indutrial, ).

2 . Theory The tarting oint for analyzing the tranformer i the bai equivalent iruit of figure. In thi iruit, L the indutane of the eondary, and M the mutual indutane between the two oil. Current and voltage in the tranformer are deribed by ~ ~ v~ L di M di = (.A) dt dt ~ ~ v~ M di L di = dt (.B) dt In the following we will ue the ymbol v ~ to rereent a omlex voltage, and v to rereent the voltage amlitude. M i related to L and L by: M = k L L () where k i the fration of the flux in eah turn of oil whih alo thread eah turn of oil. Alo, if there are N turn in the rimary and N turn in the eondary: L N a N L = = (3) where a = N i the turn ratio of the tranformer. In a well-deigned iron ore tranformer, N k i loe to. In an ideal tranformer it i aumed that k =. In thi ae: v = N = a (4) v N If a load reitane, R L i onneted aro the eondary of the tranformer, it an alo be hown v that the inut imedane, Z i, een "looking into" the rimary i given aroximately by in = (ideal tranformer exreion): i Z in R L = a (5) The tranformer an therefore rovide a very valuable imedane tranformation funtion. It hould be noted that (5) i an aroximation whih i only valid if ω L >> a RL. In other word, for imedane tranformation to work it i vital that the magnitude of the reatane aoiated with the tranformer rimary winding be muh larger than the tranformed load reitane. Under thi ondition, it an alo be hown that the urrent in the rimary and eondary are related by:

3 i = a (6) i Figure : Bai tranformer equivalent iruit. It i often onvenient to redraw the equivalent iruit of figure in the form hown in figure below. The ideal tranformer in the enter of thi iruit ha the ame turn ratio a a the real tranformer, but ha erfet flux ouling and infinite indutane in the rimary and eondary oil. The indutane ( k) L i ometime alled the leakage indutane, while kl i the magnetizing indutane. You hould be able to how that thi iruit give exatly the ame relationhi between voltage and urrent at the terminal a the iruit of figure. Figure : Alternative tranformer equivalent iruit. Loe in real tranformer are often aroximately modeled by adding to reitane to the equivalent iruit of figure, giving the iruit of figure 3. The reitor R rereent the reitane of the rimary winding, and R the reitane of the eondary winding. Reitane R aroximately rereent loe due to hyterei and Eddy urrent in the ore.

4 Figure 3 Tranformer equivalent iruit allowing for loe Figure 3 i till an aroximate derition of the real tranformer. It make no allowane for the aaitane between the winding in the rimary and the eondary, for the fat that the reitane of the winding i ditributed throughout the oil and annot be rereented by a ingle lumed reitor, nor for the deendene of ore loe and ore ermeability on frequeny. When the eondary winding are horted, the equivalent iruit for the rimary redue to that of figure 4. Thi iruit how that by meauring the inut imedane with the eondary horted it i oible to determine the winding reitane and the leakage indutane. Figure 3: Equivalent iruit with eondary horted. Uually we will have R and ωkl both muh greater than the erie ombination of R + a R ω k L in whih ae the equivalent iruit redue to that of figure 5. and ( )

5 Figure 4: Simlified equivalent iruit with eondary horted. When the eondary i oen iruit, the equivalent iruit beome that of figure 6.. Equiment and Proedure Figure 5: Equivalent iruit with eondary oen. The tranformer onidered in thi lab i a tyial low ot audio tranformer deigned to imedane math all 8 Ω eaker to a tranitor amlifier outut tage over the frequeny range from aroximately 0 Hz to 0 khz. The ore of thi tranformer onit of "oft" iron late laminated to redue Eddy urrent loe. To omlete the lab, it will be neeary to meaure the urrent flowing in the rimary of the tranformer. Thi will be done by onneting a mall reitor in erie with the rimary, and meauring the voltage dro aro thi reitor.

6 Figure 7: Exerimental etu. One ide of the tranformer rimary i onneted to the lug marked "Outut" on the funtion generator. There i a able on eah ide of the rimary onneted to the oillooe. A wire i ued to onnet the 0 Ω reitor in erie (ee figure 7). The outut labeled CH on the board give v, while the outut labeled CH i the voltage aro the reitor, whih an be ued to find i. In your lab book draw the equivalent iruit. Are the ground ide of the oe inut onneted together? How to ue the Oillooe: To meaure the voltage, re Meaure, then re more otion until you find amlitude Pk to Pk To meaure the hae angle, re Meaure, then roll down to a above and re Phae (make ure the hae differene i being alulated from CH to CH otherwie your angle will be negative) If the angle i the omlementary angle (for examle 0 ο intead of 60 ο ), then move the urve horizontally) To ale roerly, uually the Auto Sale will be enough but make ure when taking meaurement that you ee to 4 yle. (Not too zoomed in or zoomed out)

7 To find the inut imedane of the tranformer, we will need to meaure the hae angle φ between v and i. Thi an be done by dilaying both the voltage and urrent waveform on the oillooe and etting the time bae to the longet value for whih a half-eriod T/ of both waveform i viible. Letting t ο be the time differene between the zero roing of the voltage waveform and the zero roing of the urrent waveform, we have: t φ 360 T Traditionally we would meaure the time differene, to, to find the angle, but newer oillooe are able to diretly meaure the hae angle. Thi tehnique i illutrated in figure 8. ο ο = (7) Figure 8: Meauring hae differene between v and i ; voltage lead urrent in thi ae. In an ideal indutor, urrent lag voltage by 90 o. We will define thi to be a oitive hae angle. If urrent lead voltage (the ae in a aaitor), the hae angle i negative. Throughout thi lab, it i imortant to note whether urrent lead voltage or vie vera.

8 Figure 9: Side-by-ide examle of maximizing dilay etting to imrove auray of reult. 3. Meaurement and Calulation Carry out the following meaurement on the audio tranformer. To do thi, onnet the yn of the generator to CH4 of the oillooe. The yn will hel in getting a table wave on the oillooe a it will ue CH4 a a trigger for ynhronizing both mahine. One the deired voltage ha been et on the generator, you are then ready to onnet the outut to the rimary oil. a) Uing a digital multimeter, meaure the tranformer rimary and eondary oil reitane, R and R. Make ure the tranformer i not onneted to anything. Additionally, verify the value of both reitor uing the multimeter. ( mark) b) In thi exeriment, we meaure the turn ratio, a, of the audio tranformer, auming it ideal. Set the funtion generator frequeny to khz. Set the voltage to be 4 V eak to eak. To omute the turn ratio, a v, ue the oillooe to meaure the voltage aro the v rimary oil ( v ) and aro the eondary oil ( v ). Comare your value to the turn ratio of the tranformer eified by the manufaturer, whih i 7.9 :. ( mark) ) Introdution to thi quetion: In thi exeriment you will omute the inut imedane and it omonent (reitane and reatane) with the eondary oil hort iruited. Uing the et-u hown in figure 7, you will meaure the urrent and voltage in the rimary to alulate the ratio v, whih give the inut imedane. Note that thi will be omlex a we have the effet i of a reitane and an indutane onneted in erie, a hown in figure 5. The reitane i R + Ra and the indutane i ( k) L. Proedure: Connet the tranformer a hown in figure 7, hort iruit the eondary oil, add a 0 Ω reitor to the rimary oil and meaure the urrent flowing in the rimary. Set f = khz

9 on the funtion generator. Meaure v, i and the hae angle φ between them. Remember that the outut onneted to "CH " give v, while the outut onneted to "CH " give the voltage aro the reitor. See figure 8 for intrution on how to meaure the hae angle. Given true: Z in i rereented a a reitane R in erie with an indutane L the following i v i R = o( φ) and ω = in( φ) L v (8) i Ra Comute R and L. From figure 5, we hould have R = R + and L = ( k) L. Comute R + Ra from the reult of art (a) and (b) and omare with the meaured value of R. Comute ( k) L. Don t forget to how all of your alulation! (5 mark) d) Introdution to thi quetion: The uroe of thi exeriment i to meaure the Eddy urrent loe R and kl. For thi we oen iruit the eondary and hene, figure 6 ome into effet. A in the reviou exeriment, you hall meaure v and i. From that you an etimate the effetive erie reitane and the indutane of the iruit in figure 6, R and L a before. From figure 6 you will ee that thee value deend uon R, ( k) L, R and kl. But we already know the value of R (art a) and ( k) L (half the value of the indutane found in (art )), o to find the remaining unknown, ( R and kl ), you mut ue relationhi (0) given below and then ue the value of R, L, R and ( k) L to omute R and kl. Proedure: Oen iruit the eondary, and et f = khz and the eak to eak voltage to 4 V. Reord v, i and φ re-alulate R and L from equation (8). To determine R and kl in the equivalent iruit 9 of figure 6, we need to aount for the winding reitane R and leakage indutane ( k) L. R' and L' are defined a R ' R R = and ( ) L ' = L k L (9) Additionally, R = o( θ ) and ω Z ' in( θ ) ' Z kl = (0) where Z ' ( R ') + ( ωl ') = () and ωl ' tan θ = () ( ) R '

10 Comute R and kl. Uing kl determined here, and ( k) L found in art ), etimate k. You have equation and unknown. Don t forget to how all of your alulation! (6 mark) e) Reeat the meaurement deribed in art d) at frequenie of 00 Hz, 500 Hz and 5 khz, uing a eak to eak voltage of V. Remember to kee trak if the voltage i lagging or leading the urrent, whih tell you if the reatane of the rimary i aaitive or indutive (ee the Exeriment and Proedure etion). Ue the table format given below to reord your data (whih inlude R and kl ). Comment on the ability of the equivalent iruit of figure 3 to aurately rereent the behavior of the tranformer over thi frequeny range. Seulate on why R and kl aear to deend on frequeny. (4 mark) f(hz) v (V) i (A) φ ( ) R (Ω) kl (H) f) Reeat the meaurement of v, i and φ at f = 00 khz. I the reatane een looking into the rimary now indutive or aaitive? Sugget an exlanation for your obervation. (3 mark) F (Hz) v (V) i (A) φ ( ) g) Connet a 0 Ω load reitor aro the eondary of the tranformer. Kee the eak to eak voltage to V and meaure v, i and φ at frequenie of 00 Hz, khz, 0 khz and 00 khz. Rereenting Z in a a reitor R in arallel with an indutane L the following i true. v i L = v (3) i R = o( φ) and ω in( φ) Contrut a table howing R and L a funtion of frequeny. For an ideal tranformer we would have R = a RL (ee equation (5)) and L would be infinite. Note that exeriment (g) (and (h) to follow) i a reetition of the reviou exeriment, with hange:. The 0 ohm load on the eondary winding.. The reulting equivalent iruit looking into the oure v i a reitane and an indutane in arallel, a ooed to in erie, a ha been the ae in reviou exeriment.

11 With v and i, you will meaure the reitane and indutane onneted in arallel. Ue relationhi (3) to meaure the value of R and L. Comare the behavior of the real tranformer at different frequenie with the ideal model deribed in (5) and eulate why your reult do not atify the imle model, eeially at low frequenie. The urrent and the voltage ditort at ome value of v a you inreae it. Note that oint and exlain why. Hint: What do you remember of indutor, when it ome to DC urrent and very high frequeny AC urrent? (8 mark) f (Hz) v (V) i (A) φ ( ) R (Ω) L (H) h) Leave the 0 Ω load reitor in lae aro the eondary and et f = 0 Hz. Inreae v toward 0 V, until the i waveform tart to ditort. Note the aroximate value of v and i at whih the ditortion begin. Make a keth of the urrent waveform. Alo make a keth of the v waveform under thee ondition. Give a brief exlanation for the ditortion. ( mark) Tranmiion Line In thi art of the exeriment you will make ue of the two tranformer on the board. The objetive i to examine the voltage along the line (relative to ground) of a mall ale ower tranmiion ytem. The tranformer ued in art a) to h) i to be onfigure a a te u tranformer. The other tranformer ha a enter ta on one ide and will be ued a the te down tranformer. The enter ta ide will be onneted to the reidential load made u of two 0 Ω reitor. The tranmiion line loe are rereented by a 0 Ω reitor onneted between the two tranformer. The eletrial iruit i hown in figure 0. Setu the iruit. Figure 0: Small ale tranmiion ytem.

12 Set u the tranmiion line a hown in the figure below. Set the frequeny to khz and the eak to eak voltage to 4 V. a) Meaure the inut voltage, a well a the voltage aro eah of the oil in the tranmiion line. When meauring the voltage aro the oil with 3 outut, do meaurement. Take eah meaurement from the ground to the other outut. Exlain the hange in the voltage throughout the line a well a it hae. ( mark)