reflected wave

[cvirgil]

After seeing a few post on this board about VFDs and the problems with refelcted wave I've though about our utility lines here in the States. How does the utility line keep the refelcted waves at 60HZ from being a problem. In addition, what about the reflected waves on an applinace branch circuit in our homes?

 

[Warpspeed]

Another factor with reflections is that the ideal mathematical model usually assumes minimal circuit losses. The surge travels back and forth slowly fading away.

But a power grid is not like that, there is power being consumed all along its length, so it is a very "lossy" or "heavily damped" circuit. Any surge or sag will not go far, especially if the system is heavily loaded as it usually is.

 

[bacon4life]

There are apparently two different issues to consider here. The first is the length of the line, approaching 1250km would have wave effects such as standing waves and reflections. The second issue is how to model the line. In order to model it as simply an inductor, product of the propogation velocity and the line length has to be WAY smaller than 1. When it is much smaller than 1, it can be modeled as simple pi circuit. As it gets closer to 1, a more complicated analysis has to be done using either wave equations or correction factors based on the wave equations.

K = 2*pi*f*sqrt(L*C)*length

Using values from a typical 2 bundle 345 kV line of:
L = 9.83x10-7H/m
C =11.59x10-12F/m
R~=0
length K
50km 0.063
100km 0.127
300km 0.382

I need to correct myself that cables do not see an increase in wave behavior such as reflections and standing waves, but rather just must be modeled at shorter distances. For example a theoretical cable with:
L = 9.83x10-7H/m
C = 190x10-12F/m
R~=0
length K
10km 0.052
50km 0.258
100km 0.515
200km 1.030

The cable length would instead be limited by the shunt capacitance causing large charging currents to flow and causing the voltage at the midpoint end to change drastically depending upon the load flowing through the line.

 

[Bung]

The Cahorra Bassa hydro station line to South Africa is about a 1/4 wavelength at 50Hz. It is a dc link (two pole, =/- 500kV, 3600MW total capacity), partly for that reason. There are several dc lines in Russia of similar lengths. There are some large expanses of very little in some parts of the world beyond the borders of the good ole US of A!


Bung
Life is non-linear...

 

[Bung]

Back to the "electromechanical wave" question, we shouldn't forget the effects of power system resonances against the mechanical devices connected to them. For example, Hoover Dam and other SSR events. I can recall one event in Durban where the lights dimmed and brightened at about a 1 hertz rate when the Drakensberg Pump Storage scheme machines (4*250MW) had a disagreement with the rest of the system. The generators were connected by a 400kV line around 250km long into the grid at a point also several hundred km from the nearest substantial (but very stiff) generation.

The mechanical analogy would be a lump of concrete (Durban)bouncing at the connection of two springs, one that is connected at the other end to a solid base (infinite bus) and the other to another lump of concrete (the generators). Give the "generators" a kick, and the whole thing bounces around.

In fact, all power systems are continually oscillating ever so slightly- its just not normally noticable. It's really quite extraordinary (to my simple mind) that power systems remain as stable as they do.

Bung
Life is non-linear...

 

[jraef]

Some of these towers are spectacular. Most complex I have ever seen!

itsmoked,
Have you ever seen the power line pylon near Orlando Florida as you approach Disneyworld? It is sculpted to look like Mickey Mouse!

http://www.hiddenmickeys.org/WDW/Property/Celebration.html

 

[itsmoked]

jraef Yes!

I just saw it in the last week... A picture.

That really takes the cake..

Nice analogies Bung.

 

[lengould]

{bung}It's really quite extraordinary (to my simple mind) that power systems remain as stable as they do.

Absolutely agreed, provided you qualify with "A/C power systems". Notwithstanding my enormous admiration for the skills of those engineers who are capable of keeping a system like the North American grid even operating, I often wonder if they've just gotten too busy or too specialized to have noticed the current progress of modern electronics and DC transmission.


Pechez les vaches.

 

[rempman]

I see that we have had a wonderful discussion on theory and transmission lines.

The simplist method of limiting the amplitude of reflected wave is the installation of arrestors on the end of terminal lines. This would apply to both transmission and distribution.

I might suggest that the area that you need to address first is your underground distribution. Reflected waves that occur at the end of lines may overstress the insulation medium that is being used. Generally you would use an arrestor elbow installed on a junction box, transformer, or LRTP on a 600A non-load break elbow.

 

[Bung]

lengould, dc transmission is fine up to a point, but all you are doing is moving the stability problems from the lines into the control electronics. And my understanding is that a 10 foot power arc on the Cahorra Bassa lines cannot be extinguished except by ramping back the electronics.

But you need ac (or some incredible switch mode PSUs!) to convert voltage levels. If the electronics is so good, maybe we should use ac (simplest for generation), and then just do all the rest with electronics. No need for dc versus ac at all - just do whatever is simplest from a field operations (=users) switching, etc point of view.

And the reflected wave problems would be pretty mind boggling too, with all those harmonics etc!

Bung
Life is non-linear...

 

[lengould]

Bung: Why might "ramping back the electronics" be, as you seem to imply, so much less desireable than having a huge A/C breaker throw a 25 ft arc into the air to interrupt a fault?

The last true arguments in favour of AC over DC for any significant amount of power any distance were 1) that DC could only go point-to-point, no intermediate tapping, and 2) DC-to-AC converters needed working AC on the load side before they could work.

Both those problems have long ago been overcome, and the "economic crossover distance" has been steadily dropping, now dropping under 250 miles.

Also I'd suggest any engineer who wants to work on future superconductor transmission had better start learning their DC now.


Pechez les vaches.