I appreciate your response, but fail to have the background to understand much of it ...
Ah... well suffice it to say, this is the study of dynamical systems: differential equations, difference equations (used in DSP and computer models), polynomial roots, stuff like that. Numerical analysis in particular, using Newton's method (aka trapezoidal approximation), higher order (Runge-Kutta) methods, and more advanced things (that SPICE uses).
You should also have a background in circuit analysis: what it means to have current flowing between components, and voltages around them; and how to solve an AC circuit including transformers, dependent sources and all that.
In particular, nodal analysis is most often used. This turns the schematic graph into a matrix, and matrix inversion is used to solve A*x = b.
(SPICE uses a number of methods to compute this, so that rather than brute-forcing the matrix inversion -- an expensive and numerically unstable operation -- it's done incrementally, to as much accuracy as is required. And if it can't complete the step, it adjusts parameters and tries again: source stepping, GMIN stepping, variable timestep and so on. Advanced topics!)
A dominant loss attached; I have no comprehension of what that means.
Some kind of damping -- a resistor causes an oscillating LC circuit to decay towards zero, over time. (This can be
proven, using calculus to solve the differential equation exactly. You can then use the proper solution, of simple problems like this, to assess the accuracy and stability of numerical solvers.)
Without loss, trapezoidal approximation tends to exhibit growing oscillation over time. (It also tends to produce alternating results:
http://www.ece.uidaho.edu/ee/power/ECE524/Lectures/L18/numerosc.pdf )
On the other hand, RK2 tends to exhibit slight damping (even when the system is ideal).
Real circuits always have resistance, so it's also more realistic to build a model with resistance.
My focus was to study fringe cases exhibiting this particular characteristic of escalation; what may be reasonable in assuming is the rarely studied, electrical equivalent contributing to spontaneous combustion of pole transformers, very large loudspeakers at rock concerts, and humans.
Well you've chosen a pretty terrible simulator to try and prove the existence of such phenomena.
Trying to "prove" such a thing, through such means, is rather ponderous to begin with. If you're searching for suspicious (oscillating, diverging) behavior, in a simulated system, you are massively predisposed to finding exactly the unstable edge-cases of the simulator itself -- and absolutely nothing to do with the thing you thought you were searching for in the first place!
Does this mean that the simulation is creating an unrealistically large surge? Since I would expect, and encourage, the creation of surges for the purposes of this study, any surge - no matter how small - would be welcome since I also expect these surges to buildup sooner or later within the confines of the two ultra-low capacitors bounded by the two transformers.
No, none of that happens, nor can happen -- and you've simply found an example of the above.
The underlying reasons why those things happen (the things you listed above), is largely to do with thermal overload of materials. To even begin to test that, in a representative way -- you need to build a model that has some representation of temperature, and its effects on the materials used in the circuit. And you need the circuit to be representative of the real system.
Pole transformers are connected to the mains supply, so under fault conditions, they can draw megawatts, no sweat. There is absolutely no need to even suspect an exponential divergence here! What's more, the phenomenon fundamentally doesn't exhibit an exponential divergence: the transformer fails internally (usually something like insulationg breakdown, resulting in shorted turns, further heating, and arcing), then consumes power from the supply, limited by resistance and inductance in the path. The consumed power level increases,
then levels off. After some cooking, the transformer finally arcs over and blows out, drawing enough current to blow a fuse. The transformer goes out with a bang, and the line voltage stops, returning things to a safe condition.
To model this with circuit components, you need a number of state variables (which might be represented by the voltage across a capacitor), and a selection of dependent sources, which are controlled by those variables. The variables, in turn, are affected by the conditions during the event: ambient temperature and heat dissipation, for example.
Tim
Home
Help
Search
Login
Register
