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# reflected wave

## reflected wave

(OP)
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?

### RE: reflected wave

Wave behavior is not apparent at low frequencies like 60hz since the waveleng is so long.

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### RE: reflected wave

Yes, the wavelength would be something like 60 000 km and the critical length 15 000 km. That is not likely to exist anywhere in this world. Actually, the length is even more since the speed of an electric signel is lower in a cable than in air.

### RE: reflected wave

The wave length of a wave with frequency of 60Hz and speed of light 'c' is c/f or 3x10^8/60 or about 5000km, quarter wave length is 1,250km and there are lines that long.  As speed goes down wave length goes down.

### RE: reflected wave

cvirgil the wavelength of 60Hz IS short enough to require design changes to power grids, (as apposed to "just run wires from here to there Joe-bob").  The power grid is designed with some aspects as a "distributed system". This is just like how worry about impedance matching on a circuit board running at 100's of MegaHertz.

If you look at high tension lines as you drive around you will often see that inexplicably at some tower two of the wires will go thru a strange re-routing then continue until it happens again.  This is because of the distributed nature of the system.  These wires get swapped around to keep the distributed impedances balanced.

Someone correct me if I'm off on this.

### RE: reflected wave

I have never seen the transposition you mentioned.  It occurs to me it may be required to balance inductance since the center phase sees just a little different environment than the end phases.  If that were the cases, in my terminology I would call that a field effect rather than a wave effect  (we can model an inductor without resorting to wave effects).

Going back to reflection in power systems, I think that reflection effects may be important in study of switching transients.

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### RE: reflected wave

Transpositions on overhead lines are common, but as Pete says, they are done more for purpose of balancing out the inductance of the three conductors, not because of any wavelength effects.

### RE: reflected wave

That's the inductance between the lower phases and the ground right?

### RE: reflected wave

I was looking for a picture of a transposition.  Didn't find one but I was surprised to find a site with hundreds of picture by the Power Pylon Appreciation Society.

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

Lotta pictures of infrared scans with obvious problems.

Check it out.

http://www.gorge.org/pylons/page1.shtml

### RE: reflected wave

Another possibility besides transposition among phases would be transposition among parallel conductors in a single phase, again to equalize inductance.  Balancing inductance among parallel condutors in a phase would be important to ensure the parallel conductors share load similarly.

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### RE: reflected wave

For short transmission lines, the wave effects at 60 Hz are ignored.  However, for medium length lines(50-150 miles) a pi model is used to approximate wave behavior. For even longer lines, they are modeled using hyperbolic sines and cosines.  Also, the ratio of inductance to capacitance of the line has a significant effect on whether it is considered a short or long line.  The length of AC high voltage cables is partially limited by the higher shunt capacitance causing wave effects at less than 50 miles.

DC transmission lines are popular partially because there are no wave effects at zero frequency.

I knew it!  :)

### RE: reflected wave

I have to begrudgingly admit I was 100% wrong.  I have learned the transmission line theory but I guess my brain was not engaged.

Using the distributed model of series of infinitessimal shunt capacitances and series inductances we come up with the Pi equivalent circuit.

How does that relate to voltage reflection causing increased voltage at an impedance discontinuity? Worst case increase occurs on an open circuit.  Think about a pi equivalent circuit tranmission line open on one end and connected to a system at the other end.  All of the vars generated by the capacitance modeled at the open end have to flow through the series inductance element to reach the connected end, in the process creating a voltage drop going from the open end to the connected end.  In other words the open end will have higher voltage than the connected end. The equivalent circuit has predicted the voltage increase at the open end.  I suspect that with more detailed analysis of reflected waves we could come up with the same conclusion.

My apologies for mudding the thread and thanks to bacon and itsmoked for straightening me out.

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### RE: reflected wave

One thing to note, the voltage increase is not a doubling. We could calculate the voltage increase as Vopen_end = Vconnected_end * (Zc/[Zc+ZL])  where Zc is impedance of the shunt capacitve element and Zl is impedance of the series element.  Since Zc and Zl are opportite signs, the quantity in [ ] is less than Zc and the quantity in ( )  is greater than 1.

I know that part of what tripped me up was thinking about the smith chart, which gives periodically varying characteristics (neglecting losses) as we increase lenght of the line (the anlge of the offset vector on the smith chart rotates as we increase length).  The thing about 60hz power lines is the  length is very short compared to the wavelength so we don't get anywhere near one rotation. And in fact as someone pointed out we don't get anywhere near the 1/4 wavelength where I think maximum voltage amplification occurs. A line of several hundreds of mils represent only a very small rotation on the Smith chart which is approxiamtely modeled by the pi circuit model.

I suspect in practical terms the most important impact to system operators is that the associated vars from distributed capacitance affect their voltage profile.  Voltage increase from power frequency at an open end I suspect is small only a few percent (could be calculated as above). However the voltage at the open end of a line may have much greater amplification of transient switching surges than of low frequency 60hz power.

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### RE: reflected wave

electripete,

The quarter wave length for 60 Hz is only about 1250km.  Given the makeup of the North American grid, it isn't that difficult to find lines that long.  BPA has east-west and north-south lines that long or longer.  Power flowing from the Grand Coulee area to San Diego could approach a phase shift of 180 degrees, although it would take several lines end-to-end to make that journey.

### RE: reflected wave

electricpete you've probably forgotten more than I'll ever know on the subject.

I suspect you are right about the voltage profiles being the biggest concern.

### RE: reflected wave

A line 1250 km long with no taps would be useless because  inductance would be very high and ability to transfer real power would be tiny.  If you have such a line the people who built it wasted their money.  More likely you will find substations every 20 - 100 miles or so where there are interconnections to other lines, loads and generation. It no longer acts like one long line.  You have a transmission network. Phase differences are primarily determined by real power flow through series inductances as well as interconnections to other systems possibly other voltage with transformer induced phase shifts.

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### RE: reflected wave

#### Quote (electricpete):

More likely you will find substations every 20 - 100 miles or so where there are interconnections to other lines, loads and generation.

Are you familiar with the inter-mountain west?  A 500kV line can go hundreds of miles without anything else to connect to.  Lines between western Montana and the Pacific Coast, or between Salt Lake City and southern Oregon pass through large expanses of very sparse territory.  Long line models are quite necessary.  I don't know the details of these lines, but the maps I've seen certainly suggest that the lines run very long distances without significant connections.

### RE: reflected wave

A few hundred miles I can buy. You said 1250km or longer.

"...1250km.  Given the makeup of the North American grid, it isn't that difficult to find lines that long.  BPA has east-west and north-south lines that long or longer."

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### RE: reflected wave

Ok, for the purposes of seeing wave length related phenomenon I suppose you are right that there are enough things along these very long transmission corridors that would alter the electrical parameters enough that one could not consider the line as simply running from point A to point B, very far a part from each other.  All it would take would be a series capacitor to cancel out some of the inductive reactance, or some other form of var support.

### RE: reflected wave

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.

### RE: reflected wave

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.

### RE: reflected wave

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...

### RE: reflected wave

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...

### RE: reflected wave

#### Quote:

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

### RE: reflected wave

jraef Yes!

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

That really takes the cake..

Nice analogies Bung.

### RE: reflected wave

#### Quote:

{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.

### RE: reflected wave

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.

### RE: reflected wave

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...

### RE: reflected wave

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.

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