Prof. Pekarek:
Please elaborate on the requirement for phasor diagrams as stated in text (p.
120, item 3.). I have calculated the AC response of vAB, vab, iA, ia using
phasor calculations. I wrote complex-math phasor expressions for supply voltages
and transformer impedance and did the math (using Matlab) to solve for vAB, vab,
iA, ia. My results agree with my simulation (and Prof. Ong's simulation.)
Need I only show this work along with a polar diagram of the resulting vAB, vab,
iA, ia?
Thanks.
Xxx
xxx,
Yes, your work is answering the question posed. You do not need anything further.
Steve
Professor,
Let me tack onto the last question (fig 4.18):in problem 2, i think I am having
issues getting matlab to recognize my simulink outputs. I used a simout block
for v1, v2p, i1, lambda1, and lambda2p. But I am wondering, does this just mean
I can use them with my integration routine as is? Or do I need to do something in
matlab to 'notice' them? Like simout(v2p)= etc. I made sure to name my variables
i.e. v1, v2p, etc.
when you go back into the simulink workspace, these variables should be present.
Type ‘whos’ and you will see that they are.
This is a fundamental question that you might want to shoot me for, I know it's like a rip in the music, but
what is actually causing the saturation? That wasn't entirely clear in class, and from this project, all I can
really see is at certain phases the signals get clipped or distorted. But it's hard to really see what's going on.
thanks,
As current increases, the magnetic flux does so too – but only to a limit. The amount of flux that the
material can handle is kind of like the amount of water a sponge can handle.
Professor Pekarek,
Thanks. I should have realized that. One quick clarification. For problem 3, I
have so far used the model provided by the book (i.e. M4 and S4). Did you want
us to create a different model, more in line with what we discussed in class
(i.e. no neutral ground resistor), or were you expecting us to use the book
model?
Thanks,
xxx
xxx,
I prefer using the method discussed in class over the book, but if time
constraints do not permit, I am ok with book model. Just to clarify, it should be
your model from problem 1, adapted to 3-phase.
Steve
Professor Pekarek,
For problem 2, part 2, you ask us to create a numerical integration routine to
take the time-domain current data to obtain lambda1 and lambda'2. I am having
some difficulty understanding what needs to be done. In session 6 you stated
that lambda1 = int(v1-r1*i1)dt. Considering I am using a dc voltage source, and
i1 = Vdc/r1, when I plot dlambda1/dt , the plot trends to 0, as i1 becomes
constant. When I use matlab's existing function, trapz, it takes the area under
this decaying curve, providing one data point, the area, and I am not sure how I
would obtain a series of lambda1 values over time.
Xxx
Xxx,
From your simulink model, you will have v1 and i1 versus time following a step dc
input. Send these to the Matlab workspace.
In matlab, you will need to calculate the integral to obtain labmda1. I use a
foward euler algorithm. So
lambda1(k+1) = lambda1(k) + h*(v1(k) - r1*i1(k))
t(k+1) = t(k) + h
the v1(k) and i1(k) are your simulink data.
Steve
Professor Pekarek,
I plugged in the reactance given for Xl1 directly in for Ll1 (and for the other
two). Thinking about this more, the reluctance is w*Ll1. Do I need to take
solve for Ll1 by dividing by 2*pi*60? Also, I am using the ode45 variable step
solver, maybe this is not the correct one to use?
Reactance is w*L, so you need to put L in your model (if you are following class
notes). The book does use reactance, but then they use psi instead of lambda for
a state variable.
When i connect this for the open circuit analysis, I will have to derive the R
and L/C component depening upon the given power factor and S=1.5kVA, right?
For open circuit, you will not have a load. For the case in which you have power
delivered to a load you will use a parallel R/L.
*
Going back to freshman circuit class, I'm alittle fuzzy on the analytical
steady state response I should be expecting for problem 1. I took the T
equivalent circuit and re-represented the components using impedances, after some
phasor and complex manipulations, I have an expression for i2'=3.33<theta-98.4.
I left this in terms of theta since we have to do this for theta at two
different values. Can you refresh my memory on how i get the steady state
response from this expression? Is is just the magnitude of the current so 3.3 A?
I'm thinking this isn't right because then it wouldn't be theta dependent...
The t-circuit can be solved from a phasor analysis. Replace all inductors with
j*w*L. The input voltage is
V<angle
then you use complex (real/imaginary) algebra to solve.
*
For problem 2, what parameter values from problem 1 can i use. You mention
in the problem to find the transformer inductances, so does this mean i should
not be using Ll1, Lm1, and Lm2' from the orignal problem, since I need to
calculate these? To calculate Lambda 1 using numerical integration, i was going
to start with the function that Lambda1=int((v1-r1)*i1 dt) in which case i'd need
to use at least the r1 and v1 values, from that i can back calulate the
transformer inductances and get the graphs you are looking for...
No - you use your model from problem 1, but you are using this to 'test' the
method of determining inductances. So, take the model from problem 1. You will
have the secondary voltage open-circuited. Apply a dc voltage to the primary, and
'measure' both input voltage, input current, and secondary voltage. You will use
these in a Matlab script that calculates
lambda1 = integ(v1-r1*i1)
lambda2p = integ(v2p)
Use a forward Euler or backward euler algorithm to solve the integrals.
*
For problem 3, (once i get the problem 1 to operate correctly) i understand
that i should replicate problem 1 as a subsystem and then replicate it three
times. I'm having a hard time following how they did this in the book versus how
we did it in class for the single transformer. Does the model we did in class
(and for problem 1) plop into the figure 4.18 model where they have the
subsystems noted "an_units" and "ref load"? and then the rest of the model in Fig
4.18 is the same?
Yes, in reality this is book keeping. You now have 3 transformers and are thus
determining the a-phase quantities, b-phase quantities, and c-phase quantities.
Professor,
1) When calculating my load parameters (L and R) there ends up being one equation with two
unknowns...Z= parallel combination of L and R. Z was found from S and V2rms. One thought I had was
to solve for R in terms of real power, then use this value of R into the Z=L//R equation. Is this correct? My
hesitation here is well then in theory the reactive power could be used to solve for L in a similar way and
then there are 3 equations and two unknowns. Not sure how to address this imbalance and solve correctly.
When I did it this way (this way being R found from real power) I got R to be 24 and L to have a real and
imaginary term. For S conjugate in my calculation for Z I used P-jQ, so that gave me a Z term that was
both real and imaginary, and thus L that way too. I feel like R is too small and will be a problem for
compatibility when I get to the open circuit case, but I'm getting ahead of myself.
Z = (N1/N2)^2*Vrated^2/S*
Z = R||(jwL) = R*jwL/(R +jwL) =
R*jw*(R-jwL)/(R^2 + w^2L^2)
(equation 1)
This has a real and imaginary part that both depend on R and L.
S = Sreal + jSimag
So (N1/N2)^2*Vrated^2/S*
= (N1/N2)^2*Vrated^2*(Sreal – jSimag)/(Sreal^2 + Simag^2)
(equation 2)
Equate the real and imaginary parts of equation 1 and equation 2 and you will have 2 equations and 2
unknowns to solve for R and L.
2) When we are asked to plot v1, i1, lamdam, etc do you want these all on the same plot? Actually I'm
making an assumption here that when you told us to do it the way we did in class, that it is in terms of
lamd_ m, not the total flux linkages given in the book (I can't remember what the pitch fork looking greek
letter is).
No, these should be on different plots. When you open a Scope block, you can choose the number of
plots by opening the scope parameters and setting the number of axis. The default is 1 (meaning you
just have 1 plot). If you want to plot v1, i1, and lambdam, you would set this to 3.
I want you to do the way we did in class – not in terms of psi (pitch fork).
3) I was putting all my signals into one scope to show on one plot but I can't seem to figure out how to distinguish
which signal is which. Is there a tie somewhere in the scope to the signal it actually is? For instance I added another
gain to get r1 out of the way so I can get to i1 and see it on the scope. I have all my signals going to one scope, and
v1 is obvious and v2p is obvious (since it is zero) but the others I can't tell which is what. Do you mind looking at
this for me and letting me know if there is a trick I'm missing?
I think my answer to question 2 will solve this. Put each one on a different axis.
4) The book tells us to "energize the transformer at the following" points of the wave of v1...first the peak with a
phase of 90, then the zero at a phase of zero. What does this mean in simulation space? I can change my phases for
v1 but I don't notice a difference in my scope. I'm not sure how to pull the peak value to "energize" this
transformer. I know the peak, it will always be 120sqrt(2) due to the input. Is zero here meaning the zero crossing,
and then if so what does that really mean or tell us. I'm more inclined to think it means the minimum or negative
peak if-you-will.
It means that you change the phase of your input voltage. When you open the Sine wave, it allows you
to put a different phase. This just means putting in either a sine = cos(we*t – pi/2), or a cos(we*t).
5) The very large ficticious resistor that is used to simulate an open circuit, is this in addition to the resistor that is
part of the load (figure 4.7 made me question) or is making the load resistor already added there very large the same
effect?
If you can, try avoiding using a fictitious resistor for the open circuit – use the technique I showed in class on page 5
of lecture 6. You can set the load resistor to a very large value – yes. The load inductor needs to be removed prior to
doing
so.
6) also in problem 2, do we actually need to change the v1 input to be DC in this case? You only mention the
modification to make it open circuit.
Yes, v1 needs to be DC in this test.
7) when you say obtain i1 and v2p versus time data (in problem 2), what is meant by that? I'm assuming not plots,
but not sure in simulation space what you mean. It could just be a wording issue.
It means you need to output these values to the matlab workspace so you can use them to do the
integrations
Lambda1 = integ(v1-r1*i1)
Lambda2p = integ(v2p)
You can use the simout block or the ‘to file’ blocks.
8) I'm trying to create my 3 phase simulation model in Simulink, however I am lost in making my two winding
model into a subsystem to include in my 3-phase model. In figure 4.18 in the text, are those ABan-Unit blocks their
2 winding models? If so, would my i1 current become my iap current? And then what about i2p what would this
be? It looks like they put Vasp into this block, and they get iAB out (which I believe is equivalent to my iap
maybe?), they also put van into this block which would replace my v2p i believe. Can you confirm? Basically I got
lost with my currents from the 2 winding case to the 3 winding case.
Yes, the ABan-Unit block is the single winding block. I1 will become Iap. I2p will be the secondary current
Ias.
You will have 3 transformers in the 3-phase case – 1 for each phase. Each will be your single phase
transformer from Problem 1 with the respective phase assigned (a, b, or c).
The issue with breaking out the signals to see them better is key. Without it I can't really "see" what is going on let
alone the differences from the loaded case versus shorted case. I don't see saturation, I see almost identical plots on
my scope. But I can't get a clear view of the signals. This was one of the original issues I had emailed you about
when we went through chapter 2. I know the matlab plots are better than merely using the scope but I cannot seem to
get matlab to plot my simulink. I do not have the CD with the book (didn't realize it didn't have it from Amazon
order) so I can't trouble shoot the plot issue. I have a colleague I can discuss this with next week but if you have any
insight I'd appreciate it. Is there a way to obtain the CD or critical files, maybe from your course website?
The simulink plots can look better by storing more data – open the scope gui and increase the number
of saved points.