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Symmetrical components

Hello everyone

I hope this isn't the wrong place to ask, but I'm having a bit of a problem= . I am trying to build an abc to positive/negative/zero components transfor= mation block (in LTspice), I did it, but sometimes I get erroneous behaviou= r: DC levels seem to be "omitted" at the output for an 'abc > 120 > abc' ch= ain.

The schematic I'm using is this: i45.tinypic.com/2hwhaqh.png (hopefully the= link won't get deleted)

and the waveforms are these: i50.tinypic.com/21o4fpk.png

You can see that all are identical, but b/b* and c/c* have a DC difference = between them. Here are the differences: i50.tinypic.com/juy1pv.png (in1, in2 and in3 are the a, b and c in the previous screenshots)

The signals from the generator are these:

- all three phases have unity fundamental + 3rd/3, 5th/5 and 7th/7 all posi= tive harmonics;

- phase a has twice the amplitude;

- phase b has 0.1Vdc;

- phase c has 0.3rad phase lead.

If only b or c phase have offset, the output seems to swap it, for example = (this case): b phase has 0.1Vdc, but b* has zero, while c* has 0.1Vdc. The = same happens for c with DC and b normal. But if both b and c have the same = offset, all the three phase's wafeforms match! For a phase, everything work= s.

Is this normal? Are DC bias levels "left behind"?=20

Thank you in advance, Vlad

PS: In order to build the schematic for a practical use, I had to maneuver = a bit through the equations to avoid the [+/-]2*pi/3 delay, and so I transf= ormed exp([+/-]j*2*pi/3)=3D-1/2[+/-]j*sqrt(3)/2, which left only j to take = care of, a minor leap for SPICE-kind. That's why the delays used are "0.25/= f", not "0.666/f".

Reply to
Vlad
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Maybe someone can suggest another group or forum for a possible answer? I have tried a few but, so far, no answer. Could I hope I stumbled across some forbidden art? :)

Vlad

Reply to
Vlad

am trying to build an abc to positive/negative/zero components transformation block (in LTspice), I did it, but sometimes I get erroneous behaviour: DC levels seem to be "omitted" at the output for an 'abc > 120 > abc' chain.

link won't get deleted)

--
If you could post the circuit list here, then we could all run the sim 
and maybe offer some help without having to do a lot of roadwork. 

In order to do that, go to the folder where the circuit's .asc file is 
stored, copy it with, say, notepad, and paste it into one of your next 
posts.
Reply to
John Fields

tried a few but, so far, no answer. Could I hope I stumbled across some forbidden art? :)

--
You're home. :-)
Reply to
John Fields

If you are doing sequence transformations, remember that they are defined as phasor operations, so they are only truly valid when presented with static, single frequency inputs. DC is certainly a different frequency than the 50 Hz you are using in your delay circuits (to emulate multiplication by 'a'), so don't expect it to work.

Reply to
Ralph Barone

Hello

And thank you for the replies. Actually, thank goodnes. :)

an

I was counting on the fact that the tline delays the DC, as well but, since it isn't phasor math, this explains why the DC levels appeared "swapped": before the delay, 1+0.1, after, -j0.9. I was wondering why wxMaxima gave go od results for even the slightest of DC, while LTspice didn't. My intention was to make this block for instantaneous values so the thing that puzzled me most was that it works flawlessly up until DC enters the scene.

Now, for the reverse transformation I could do (a+b+c) and use a moving ave rage for 1/(3*f), then add the DC to b* and subtract it from c* but, while it works, it's not a solution because, since the delays are the problems, t he errors start right within the abc/120 block. A Clarke matrix gives the p ossibility of angle=atan2(B,A) + DC, but how to go on from there, it's a mistery, since further on there's only sum/difference, how do you do that i n polar? I would have to change to cartesian, then do the math, then back t o polar, but then I'm back at the beginning. I am very confused.

The only reasonable way to do this, (LT)spice wise, is an FFT. Unless any o f you can suggest me another path, I'm afraid I'll have to point my neuron to this direction.

Well, if it helps, here it is (one symbol from the picture does more than o ne thing, so I gave up the harmonics):

Version 4 SHEET 1 3180 1024 WIRE -112 -720 -208 -720 WIRE -80 -720 -112 -720 WIRE 224 -720 144 -720 WIRE 288 -720 224 -720 WIRE 368 -720 288 -720 WIRE 656 -720 560 -720 WIRE 688 -720 656 -720 WIRE -208 -704 -208 -720 WIRE -112 -704 -112 -720 WIRE 144 -704 144 -720 WIRE 224 -704 224 -720 WIRE 288 -704 288 -720 WIRE 560 -704 560 -720 WIRE 656 -704 656 -720 WIRE -208 -608 -208 -624 WIRE -112 -608 -112 -624 WIRE -112 -608 -208 -608 WIRE 144 -608 144 -624 WIRE 224 -608 224 -624 WIRE 224 -608 144 -608 WIRE 288 -608 288 -624 WIRE 288 -608 224 -608 WIRE 560 -608 560 -624 WIRE 656 -608 656 -624 WIRE 656 -608 560 -608 WIRE -112 -592 -112 -608 WIRE 224 -592 224 -608 WIRE 656 -592 656 -608 WIRE 0 -464 -64 -464 WIRE 48 -464 0 -464 WIRE 96 -464 48 -464 WIRE 784 -464 736 -464 WIRE 848 -464 784 -464 WIRE 944 -464 848 -464 WIRE -304 -448 -336 -448 WIRE 688 -448 624 -448 WIRE -304 -416 -336 -416 WIRE -304 -384 -336 -384 WIRE 784 -352 784 -464 WIRE 784 -352 736 -352 WIRE 848 -352 784 -352 WIRE 0 -336 0 -464 WIRE 0 -336 -48 -336 WIRE 48 -336 0 -336 WIRE 688 -336 672 -336 WIRE 912 -336 896 -336 WIRE 0 -176 -64 -176 WIRE 48 -176 0 -176 WIRE 96 -176 48 -176 WIRE 800 -176 736 -176 WIRE 848 -176 800 -176 WIRE 944 -176 848 -176 WIRE -112 -160 -416 -160 WIRE 688 -160 400 -160 WIRE -304 -112 -368 -112 WIRE -160 -112 -208 -112 WIRE -112 -112 -160 -112 WIRE 496 -112 448 -112 WIRE 640 -112 592 -112 WIRE 688 -112 640 -112 WIRE 0 -48 0 -176 WIRE 0 -48 -48 -48 WIRE 48 -48 0 -48 WIRE 800 -32 800 -176 WIRE 800 -32 752 -32 WIRE 848 -32 800 -32 WIRE 0 144 -64 144 WIRE 48 144 0 144 WIRE 96 144 48 144 WIRE 800 144 736 144 WIRE 848 144 800 144 WIRE 944 144 848 144 WIRE -112 160 -416 160 WIRE 688 160 400 160 WIRE -304 208 -368 208 WIRE -160 208 -208 208 WIRE -112 208 -160 208 WIRE 496 208 448 208 WIRE 640 208 592 208 WIRE 688 208 640 208 WIRE 0 272 0 144 WIRE 0 272 -48 272 WIRE 48 272 0 272 WIRE 800 288 800 144 WIRE 800 288 752 288 WIRE 848 288 800 288 FLAG -304 -448 in1 FLAG -64 -96 0 FLAG 48 -96 0 FLAG 96 -176 out1 IOPIN 96 -176 Out FLAG -96 16 0 FLAG -48 32 0 FLAG -368 -32 0 FLAG -160 -32 0 FLAG -64 224 0 FLAG 48 224 0 FLAG 96 144 out2 IOPIN 96 144 Out FLAG -368 288 0 FLAG 736 224 0 FLAG 848 224 0 FLAG 448 288 0 FLAG 944 144 c* IOPIN 944 144 Out FLAG 736 -384 0 FLAG 848 -384 0 FLAG 736 -272 0 FLAG 688 -288 0 FLAG 848 -272 0 FLAG 896 -288 0 FLAG 944 -464 a* IOPIN 944 -464 Out FLAG 688 -400 0 FLAG 48 32 0 FLAG 96 16 0 FLAG -96 336 0 FLAG -48 352 0 FLAG 48 352 0 FLAG 96 336 0 FLAG 704 352 0 FLAG 752 368 0 FLAG 848 368 0 FLAG 896 352 0 FLAG 736 -96 0 FLAG 848 -96 0 FLAG 448 -32 0 FLAG 944 -176 b* IOPIN 944 -176 Out FLAG 704 32 0 FLAG 752 48 0 FLAG 848 48 0 FLAG 896 32 0 FLAG -48 -256 0 FLAG 48 -384 0 FLAG 96 -464 out3 IOPIN 96 -464 Out FLAG 48 -256 0 FLAG -64 -384 0 FLAG 96 -272 0 FLAG -112 -400 0 FLAG -96 -272 0 FLAG -304 -80 0 FLAG -208 -80 0 FLAG -160 288 0 FLAG -304 240 0 FLAG -208 240 0 FLAG 640 -32 0 FLAG 496 -80 0 FLAG 592 -80 0 FLAG 640 288 0 FLAG 496 240 0 FLAG 592 240 0 FLAG -304 -416 in2 FLAG -304 -384 in3 FLAG -112 -448 in1 FLAG -96 -320 in2 FLAG 96 -320 in3 FLAG -416 -96 in2 FLAG -416 -48 in3 FLAG -416 -160 in1 FLAG -96 -32 in2 FLAG 96 -32 in3 FLAG -96 288 in2 FLAG 96 288 in3 FLAG -416 224 in2 FLAG -416 272 in3 FLAG -416 160 in1 FLAG 624 -448 out3 FLAG 912 -336 out2 FLAG 672 -336 out1 FLAG 400 -160 out3 FLAG 400 -96 out1 FLAG 400 -48 out2 FLAG 400 160 out3 FLAG 400 224 out1 FLAG 400 272 out2 FLAG 896 -16 out2 FLAG 704 -16 out1 FLAG 896 304 out2 FLAG 704 304 out1 FLAG -80 -720 in1 FLAG 368 -720 in2 FLAG 688 -720 in3 FLAG -112 -592 0 FLAG 224 -592 0 FLAG 656 -592 0 SYMBOL g -64 -192 R0 WINDOW 3 -7 121 Left 2 WINDOW 0 23 100 Left 2 SYMATTR Value {1/3} SYMATTR InstName Ga2 SYMBOL res -176 -128 R0 SYMATTR InstName Rbc1 SYMATTR Value 1 SYMBOL g -48 -64 R0 WINDOW 3 -51 127 Left 2 WINDOW 0 -50 106 Left 2 SYMATTR Value {-1/6} SYMATTR InstName Gb2 SYMBOL g 736 128 R0 WINDOW 3 25 92 Left 2 WINDOW 0 9 114 Left 2 SYMATTR Value 1 SYMATTR InstName G17 SYMBOL res 832 128 R0 SYMATTR InstName R15 SYMATTR Value 1 SYMBOL g -368 -128 R0 WINDOW 3 -17 122 Left 2 WINDOW 0 18 99 Left 2 SYMATTR Value {sqrt(3)/2} SYMATTR InstName Gbc1 SYMBOL g 736 -480 R0 WINDOW 3 27 88 Left 2 WINDOW 0 14 109 Left 2 SYMATTR Value 1 SYMATTR InstName G22 SYMBOL res 832 -480 R0 SYMATTR InstName R17 SYMATTR Value 1 SYMBOL g 736 -368 R0 WINDOW 3 19 92 Left 2 WINDOW 0 8 118 Left 2 SYMATTR Value 1 SYMATTR InstName G23 SYMBOL g 848 -368 M0 WINDOW 3 25 93 Left 2 WINDOW 0 15 115 Left 2 SYMATTR Value 1 SYMATTR InstName G24 SYMBOL g 752 272 R0 WINDOW 3 -3 119 Left 2 WINDOW 0 17 94 Left 2 SYMATTR Value -0.5 SYMATTR InstName G15 SYMBOL g 848 272 M0 WINDOW 3 5 118 Left 2 WINDOW 0 19 96 Left 2 SYMATTR Value -0.5 SYMATTR InstName G16 SYMBOL res 832 -192 R0 SYMATTR InstName R18 SYMATTR Value 1 SYMBOL g 752 -48 R0 WINDOW 3 1 122 Left 2 WINDOW 0 16 103 Left 2 SYMATTR Value -0.5 SYMATTR InstName G21 SYMBOL g 848 -48 M0 WINDOW 3 4 120 Left 2 WINDOW 0 17 101 Left 2 SYMATTR Value -0.5 SYMATTR InstName G25 SYMBOL res 32 -480 R0 SYMATTR InstName Rabc1 SYMATTR Value 1 SYMBOL g 48 -352 M0 WINDOW 3 -55 126 Left 2 WINDOW 0 -53 107 Left 2 SYMATTR Value {1/3} SYMATTR InstName Gc1 SYMBOL g -64 -480 R0 WINDOW 3 -55 121 Left 2 WINDOW 0 -51 102 Left 2 SYMATTR Value {1/3} SYMATTR InstName Ga1 SYMBOL g -48 -352 R0 WINDOW 3 -54 128 Left 2 WINDOW 0 -53 106 Left 2 SYMATTR Value {1/3} SYMATTR InstName Gb1 SYMBOL tline -256 -96 R0 WINDOW 3 -7 -41 Top 2 WINDOW 0 -2 43 Bottom 2 SYMATTR Value Td={1/4/f} Z0=1 SYMATTR InstName Tbc1 SYMBOL tline -256 224 R0 WINDOW 3 3 -41 Top 2 WINDOW 0 -3 41 Bottom 2 SYMATTR Value Td={1/4/f} Z0=1 SYMATTR InstName Tbc2 SYMBOL res 624 -128 R0 SYMATTR InstName R3 SYMATTR Value 1 SYMBOL tline 544 -96 R0 WINDOW 3 -8 -40 Top 2 WINDOW 0 0 41 Bottom 2 SYMATTR Value Td={1/4/f} Z0=1 SYMATTR InstName T3 SYMBOL res 624 192 R0 SYMATTR InstName R4 SYMATTR Value 1 SYMBOL tline 544 224 R0 WINDOW 3 -11 -41 Top 2 WINDOW 0 -1 43 Bottom 2 SYMATTR Value Td={1/4/f} Z0=1 SYMATTR InstName T4 SYMBOL g 48 -64 M0 WINDOW 3 -53 126 Left 2 WINDOW 0 -51 104 Left 2 SYMATTR Value {-1/6} SYMATTR InstName Gc2 SYMBOL g -48 256 R0 WINDOW 3 -65 128 Left 2 WINDOW 0 -58 105 Left 2 SYMATTR Value {-1/6} SYMATTR InstName Gb3 SYMBOL g 48 256 M0 WINDOW 3 -62 125 Left 2 WINDOW 0 -53 104 Left 2 SYMATTR Value {-1/6} SYMATTR InstName Gc3 SYMBOL g -64 128 R0 WINDOW 3 -12 120 Left 2 WINDOW 0 21 94 Left 2 SYMATTR Value {1/3} SYMATTR InstName Ga3 SYMBOL g -368 192 R0 WINDOW 3 -24 128 Left 2 WINDOW 0 17 102 Left 2 SYMATTR Value {-sqrt(3)/2} SYMATTR InstName Gbc2 SYMBOL g 448 -128 R0 WINDOW 3 -15 125 Left 2 WINDOW 0 22 105 Left 2 SYMATTR Value {-sqrt(3)/2} SYMATTR InstName G13 SYMBOL g 448 192 R0 WINDOW 3 -13 124 Left 2 WINDOW 0 22 101 Left 2 SYMATTR Value {sqrt(3)/2} SYMATTR InstName G12 SYMBOL g 736 -192 R0 WINDOW 3 -7 121 Left 2 WINDOW 0 23 100 Left 2 SYMATTR Value 1 SYMATTR InstName G14 SYMBOL res 32 -192 R0 SYMATTR InstName Rabc2 SYMATTR Value 1 SYMBOL res 32 128 R0 SYMATTR InstName Rabc3 SYMATTR Value 1 SYMBOL res -176 192 R0 SYMATTR InstName Rbc2 SYMATTR Value 1 SYMBOL current -208 -624 R180 WINDOW 0 24 80 Left 2 WINDOW 3 24 0 Left 2 SYMATTR InstName I1 SYMATTR Value sine 0 1 {f} SYMBOL res -128 -720 R0 SYMATTR InstName R1 SYMATTR Value 2 SYMBOL current 144 -624 R180 WINDOW 0 24 80 Left 2 WINDOW 3 24 0 Left 2 SYMATTR InstName I5 SYMATTR Value sine 0 1 {f} 0 0 -120 SYMBOL res 208 -720 R0 SYMATTR InstName R2 SYMATTR Value 1 SYMBOL current 560 -624 R180 WINDOW 0 24 80 Left 2 WINDOW 3 24 0 Left 2 SYMATTR InstName I9 SYMATTR Value sine 0 1 {f} 0 0 137.2 SYMBOL res 640 -720 R0 SYMATTR InstName R5 SYMATTR Value 1 SYMBOL current 288 -624 M180 WINDOW 0 24 80 Left 2 WINDOW 3 35 53 Left 2 SYMATTR InstName I13 SYMATTR Value 0.1 TEXT -544 -440 Left 2 !.tran 0 .1 0.02 TEXT -544 -400 Left 2 !.param f=50

Thank you for the trouble, Vlad

Reply to
Vlad

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