Mitch, phasors can simply be represented as complex numbers, and the Wolfram Language primitives deal just fine with manipulating complex numbers and then extracting the phase/magnitude after doing those manipulations. I asked ChatGPT (4o) your question, and it returned a completely competent answer:

https://chatgpt.com/share/2d90bf49-19af-43f7-8d7c-18c935d35a88 .

In general, ChatGPT is great for generating little code fragments of Wolfram Language code for questions just like this. Just keep in mind that all of the LLMs will create slightly or completely wonky answers from time to time. Trust, but verify.

Hey Ankit,

Did you see my previous post?

Here is the thing. The learning curve for learning how to use System Modeler is steep. It doesn't really follow the paradigm of Wolfram Language. I start to think I am getting the hang of it, but then I get these weird curve balls. My purpose for following this class is not so much to learn circuit design, but it's to learn how to use System Modeler effectively in circuit design. That's not the emphasis for this class as it turns out, but still, a little help might convince me to buy the too or convince me to convince my corner of Boeing to buy the tool.

Wolfram U prefers that students not discuss quiz answers in the DSG for a course. You should e-mail wolfram-u@wolfram.com or you can put info in the feedback form that pops up at the end of each lecture.

FWIW, I'll also be providing them feedback to the quizzes.

I have checked the questions you mention and it seems that the answer key is incorrect, so the options we took as correct are wrong. I will update the quiz to reflect the correct answers.

Leo, I just had my score on Quiz 1 re-checked. I refreshed the course framework (in my Safari browser). The suspect question is still getting flagged as incorrect. As far as I can tell, the quiz answer sheet has never been updated with the correct answer. It's been almost 3 days since the errors on Quiz 1 and Quiz 2 were reported and over 2 days since you said that they would be fixed. Please fix them promptly. There's some in-course joke I should say about hysteresis at this point, but I can't quite figure out what it is. :)

I apologize for sending this message to the public forum, but this is the only means we're given to contact the instruction staff. If this were in an in-person class, I would speak directly with the teacher or the TAs.

Can you try to switch the Modelica Version to 3.2.3 and simulate again?

Right-click on Modelica library, go to version and switch to 3.2.3, and try to simulate? Let me know if that works else I will troubleshoot further.

In version 14, we made version 4.0.0 as the default. I am currently updating the Wolfram U videos to use this new version.

In today's class, somebody asked:

why are frequencies represented with imaginary numbers?

I highly recommend ChatGPT for this kind of question. That exact question yields a comprhensive answer in the AI. Since ChatGPT 4o is available freely for anyone who requests an account; I highly recommend using that tool. OpenAI even provides an app for MacOS to help keep things uncluttered on your desktop.

In class today, our instructors were discussing the variety of sinusoidal behaviors associated with electronics and signal processing. I believe they were searching for a particular word. There is a pertinent list of such terms available online in the Electromagnetic Terms section of the Wikipedia entry for Oliver Heaviside. The terms are admittance, elastance, conductance, electret, impedance, inductance, permeability, permittance, and permittivity. Two other terms were coined by Heaviside's peers around the same time: susceptance and reactance. These terms were coined from 1885 to 1894. Some are widely used today in physics and engineering; others have withered into obscurity. Some terms deal with real values; others deal with imaginary values. The Wikipedia article contains links defining each of these terms.

Anyone who thoroughly understands these eleven concepts is a signal processing wizard.

The capacitor model in the Electrical and the Spice library looks the same to me. Unfortunately, we do not support it yet. For this course, you can create all the models using the Modelica.Electrical library.

class Modelica.Electrical.Analog.Basic.Capacitor
  Real v(quantity = "ElectricPotential", unit = "V", start = 0.0) "Voltage drop of the two pins (= p.v - n.v)";
  Real p.v(quantity = "ElectricPotential", unit = "V") "Potential at the pin";
  Real p.i(quantity = "ElectricCurrent", unit = "A") "Current flowing into the pin";
  Real n.v(quantity = "ElectricPotential", unit = "V") "Potential at the pin";
  Real n.i(quantity = "ElectricCurrent", unit = "A") "Current flowing into the pin";
  Real i(quantity = "ElectricCurrent", unit = "A") "Current flowing from pin p to pin n";
  parameter Real C(quantity = "Capacitance", unit = "F", min = 0.0, start = 1.0) = 1.0 "Capacitance";
equation
  n.i = 0.0;
  p.i = 0.0;
  v = p.v - n.v;
  0.0 = n.i + p.i;
  i = p.i;
  i = C * der(v);
end Modelica.Electrical.Analog.Basic.Capacitor;

class Spice3.Basic.C_Capacitor
  Real v(quantity = "ElectricPotential", unit = "V") "Voltage drop of the two pins (= p.v - n.v)";
  Real p.v(quantity = "ElectricPotential", unit = "V") "Potential at the pin";
  Real p.i(quantity = "ElectricCurrent", unit = "A") "Current flowing into the pin";
  Real n.v(quantity = "ElectricPotential", unit = "V") "Potential at the pin";
  Real n.i(quantity = "ElectricCurrent", unit = "A") "Current flowing into the pin";
  Real i(quantity = "ElectricCurrent", unit = "A") "Current flowing from pin p to pin n";
  parameter Real C(quantity = "Capacitance", unit = "F", min = -1.7976931348623157e+308, start = 0.0) = 0.0 "Capacitance";
  final constant Real WSMServices.Machine.Real_MAX = 1.7976931348623157e+308 "Maximum finite Real number.";
  parameter Real IC(quantity = "ElectricPotential", unit = "V") = 0.0 "Initial value of voltage";
  final constant Real ModelicaServices.Machine.inf = 1.7976931348623157e+308 "Biggest Real number such that inf and -inf are representable on the machine";
  evaluated parameter Boolean UIC = false "Use initial conditions: true, if initial condition is used";
  protected Real vinternal(quantity = "ElectricPotential", unit = "V") "Capacitor voltage";
  final constant Real Modelica.Constants.inf = 1.7976931348623157e+308 "Biggest Real number such that inf and -inf are representable on the machine";
equation
  n.i = 0.0;
  p.i = 0.0;
  v = p.v - n.v;
  0.0 = n.i + p.i;
  i = p.i;
  vinternal = p.v - n.v;
  i = C * der(vinternal);
end Spice3.Basic.C_Capacitor;

Hi Leonardo,

I can see how it can be a real advantage to take a more simplistic approach. For example, system modeler is probably never going to be as accurate as a dedicated multi-physics FEA but it will get reasonable ballpark answers very quickly for complex multi-physics system-level problems (which is a big advantage). Accurate simulation for electronics can be very complex, System Modeler seems to be taking a more high-level simpler approach which is nice.

Is there any strategy for automatically taking outputs from software like Ansys, Comsol, LTSpice or other simulation programs and integrate the outputs as part of a system-level multi-physics simulation that System Modeler could model?

This would help solve scaling issues with the packages I mentioned above; they are so computationally intensive that doing large systems are not really feasible. It would be interesting to see some System Modeler examples doing this.

Another application where I'd love to see what System Modeler can do is as a tool something like LangChain where LLM outputs can be chained together to action complex tasks.

Apologies, my question maybe a little off-base, just a few general thoughts/questions.

Just thinking out loud here: From what you quoted, the imbalance appears to have been in the generator frequencies to start with? I imagine they need to stay synchronized in frequency if they are sharing loads. Otherwise you set up a beat frequency at the difference frequency between the two generating systems, and their voltages will move from being in phase to being out of phase, back to being in phase again at the rate of the beat frequency. I don't know how power grids really work, but I imagine this will cause intolerable voltage variations as they sum in phase and out of phase. Did that happen? It's a simple graph to add two sine waves of equal amplitude but with a slight difference in phase to show what happens.

But upon closer inspection of the article you mentioned it looks like the real complaint was simply that having a slightly lower frequency than the assumed 50 Hz, kitchen equipment that assumes 50 Hz and some kind of zero crossing counter as a clock reference will get a long term clock drift.

As an aside, when we talk about load impedances being a function of frequency, unless the load has a very high Q (lossless resonance), they don't change very much in the vicinity of the frequency of the stimulus. Bio-mechanical systems (a cool topic) are inherently lossy and must have low Qs. To a first order it would be surprising to see much sensitivity to the frequency of the stimulus. But I can see additions and cancellations of multiple stimulus playing a role. And our internal body clocks seem to get reset every day according to the motion of the sun.