Calculating Nonlinear Power: Fill & Download for Free

This question is about eight months old and no one has answered it yet. So I'll offer an answer.Short circuit ratio (SCR) in a power system can have different definitions depending on what is being studied or measured.For synchronous machines, it is the ratio of field currents: The field current necessary to produce rated terminal voltage at no load divided by the field current necessary to produce rated current into a short circuit. It is used to measure the difference between the nonlinear open circuit characteristic curve and linear short circuit charactersitc. A large SCR will be an indication of a greater degree of nonlinearity.For distributed generation applications, the SCR gives an indication of the system strength at the connection point of a generator. It is defined to be the three-phase short circuit level (symmetrical current) without the generator connected divided by the rated current of the generator. The greater the SCR is, the better (lower) the voltage regulation will be for a given generator.For nonlinear power converter loads like motor drives and inverters, the SCR is used to determine how well the power system grid can absorb harmonic distortion produced by the power converter. A larger SCR means that the grid can absorb more harmonic distortion without exceeding a certain voltage distortion level.There are likely other definitions of SCR in use around the world. In general, it provides a way to assess the degree on nonlinearity in a rotating machine or a way to measure the relative strength of the power grid at the connection point of some kind of generator or other type of load.

Here are three. I wouldn’t call these systems, but… close enough?My first exam in college was differential equations. The professor was new to the school, and apparently misjudged the talents of his class. The scores were, shall we say… bad.He chastised us all, but acknowledged to us that he couldn’t just fail everyone. So he decided to curve the scores. But he didn’t want the two or three people who actually did well to either break the curve, or somehow be given too great a grade. (He was a control theorist, not a statistician… something in his soul prevented him from just dealing with outliers separately.)The curve he came up with was as follows. If [math]r[/math] is your raw score, then your curved score was [math]10\sqrt{r}[/math]. (And grades were then assigned traditionally: an A was 90–100, a B was 80–89, etc.)In other words, a deeply-failing 36 is now a barely-passing D. But [my] 80 became… damn it… an 89. B’s got curved to B’s. Screw you, Dr. Ding!(I say “screw you” with some affection. I ended up liking him and his class very much.)I was fortunate not to take this class, but my friend took a nonlinear dynamics class. The final exam was, in its entirety: “Come up with a problem and solve it. You will be graded on the accuracy of the solution and the difficulty of the problem.”Pure torture.As a young arrogant student with poor judgment, I would occasionally play “exam chicken.” The classic, (non-exam) chicken is played with two players driving towards each other in cars, on bikes, or whatever. The first person to swerve away loses. He’s the chicken.Exam chicken applies that concept to exams. There are variations, but generally the first person to make some agreed “move” on the exam loses. Maybe the move is looking at the exam. Maybe it’s first putting pen to paper. (This was my preferred version, because I was pretty good at mental calculations.)Anyways, as a graduate student I was now, for the first time, in a position of power! My friends and I considered announcing an unusual grading policy that promotes exam chicken. Before the exam, we’d describe how exam chicken is played, and then add the incentive that if exactly one person turns in a blank test, they’d get an automatic A. If two or more people turned in blank tests, they’d of course get F’s.We chickened out (ha!) and never announced that policy. But I was thiiiis close I tell ya!

For an optical fiber there are actually 2 limits on power level for it to be useful.The first and more obvious one is the damage threshold. Light is a form of electromagnetic power, and some of the power is lost to heat inside the optical fiber. At a certain high power level, you start to do damage to the fiber. Usually the damage threshold is specified by the fiber manufacturer and included in the datasheet. Here's an example of how it is calculated:Laser Damage Threshold(It specifies a laser, but it also holds for fiber and any other things intended for use with lasers).The second and much less obvious one has to do with optical nonlinearity. Under ideal conditions, you would think that the optical signals just add. But the response of a material to electromagnetic fields comes from the electrons and protons or the anions and cations in the material stretching apart from the electric and magnetic fields, and it is idealized as a spring (restoring force proportional to displacement). But if you look at the electromagnetic force equations, you find that the restoring force is actually not linear for large enough separations -- that is, strong enough fields. In other words, for high intensity, the fields don't simply add.Because they don't simply add, you get things like harmonic generation (put in red light, get green light out), sum and difference frequency generation (actually how an AM radio works).Nonlinear opticsWhen you hit the limit where nonlinear effects start to occur, the wavelengths start interfering with each other and you no longer have a valid signal.