3rd harmonic

(1)

The 3

rd

_{Harmonic Problem}

and how Delta configurations help

reduce its affects.

(2)

Harmonics are multiples of the fundamental

frequency of a wave. They cause waveform

distortions like the one seen below.

(3)

What causes harmonics?

• Non-linear components

• Diodes

• Transistors

• Electric motors

• SMPSs (switch-mode power supply)

(4)

Harmonics can be modeled in a system separately as a source with a frequency an integer multiple of the fundamental frequency (60 Hz in our case). So a model

including harmonics can be seen as a source sending a 60 Hz sine wave to a load (and since the load generates the harmonics) and a source bank at the load with each source sending an integer multiple of 60 Hz sine wave.

So we see how the harmonics can be modeled as sources in the system.

Now we can examine why using a wye delta transformer can help us with

the 3rd harmonic problem.

(5)

In a balanced 3-phase wye system, the currents going into the neutral node are

supposed to cancel, so that there is no current on the neutral wire. Harmonic waves may not behave this way, so we should investigate…

Harmonics can be modeled as current sources as we have seen, but equivalently, they can be modeled as voltage sources. Lets look at the 2nd _Harmonic…

The system will still be balanced in the presence of the 2nd _{harmonic (except negative}

sequence) and the current from the 2nd _{harmonic sources will still cancel in the neutral}

wire! It can be shown that this is true with ANY even harmonic. Now lets examine the 3rd _harmonic… ) 120 2 cos( ) 240 2 cos( ) 120 ( 2 cos 2 ) 120 2 cos( ) 240 2 cos( ) 120 ( 2 cos 2 ) 2 cos( ) 0 2 cos( ) 0 ( 2 cos 2 ° − = ° + = ° + = ° + = ° − = ° − = = ° + = ° + = wt E wt E wt E Vcn wt E wt E wt E Vbn wt E wt E wt E Van ) 3 cos( ) 360 3 cos( ) 120 ( 3 cos 3 ) 3 cos( ) 360 3 cos( ) 120 ( 3 cos 3 ) 3 cos( ) 0 3 cos( ) 0 ( 3 cos 3 wt E wt E wt E Vcn wt E wt E wt E Vbn wt E wt E wt E Van = ° + = ° + = = ° − = ° − = = ° + = ° + =

(6)

There is something interesting that is immediately visible about the third harmonic voltage equations we just found. All the waves are in phase with each other. This is well

illustrated in the following figure.

In a similar derivation as the previous slide, with current instead of voltage we can get in the neutral wire:

In the 2nd _{harmonic, the current still cancels in the neutral wire, but the 3}rd _harmonic

current adds, producing a very large neutral current.

) 3 cos( 3 3 3 3 Ibn Icn I wt Ian In= + + = ⇒

Figure 2: phase waves and their 3rd_Harmonic 3rd_{harmonic wave} 3 3 3 Ibn Icn Ian = = ) 3 cos( 3 3 3 Ibn Icn I wt Ian In= + + = ⇒ * VI S =

(7)

So we need to get rid of the neutral wire. By using a delta configuration, we can trap the current in the delta loop and also take advantage of one useful property. We all know that when going from line-to neutral voltage, to line-to-line voltage:

And since

we can easily see that the power across the load in a delta loop due to the third harmonic is zero. Vbn Van Vab= − 3 3 3 Vbn Vcn Van = = * VI S = 0 )* )]( 3 cos( ) 3 cos( [ )* )( 3 3 ( )* 3 )( 3 (

3= Vab Iab = Van −Vbn Iab = E wt − E wt Iab =

(8)

How does a delta configuration

help with the triplen harmonics?

When you use a delta

configuration, with the delta on

the load side, there is no

neutral wire for the harmonic

currents to travel in. The the

harmonics travel around the

load loop and get trapped in it.

As seen in the figure, the

triplen currents are not

traveling into the rest of the

sytem. Thus, they do not add

together and cause the wave

distortion that they do in a wye

connected system.

(9)

Harmonics still a problem

Because the delta loop traps the triplen harmonic currents

in itself, the problem stays in the load. Therefore the delta

configuration is the best configuration to use when the load

is non-linear, but harmonics still cause us to lose monetary

efficiency even when delta transformers are used. Even

though we can isolate the effects of the triplen harmonics to

the load, transformers must be derated to use a low

percentage of their capacity because of the high currents in

the secondary windings. With all the harmonic current

confined to the delta loop, the conductors would overheat if

we did not use a derated transformer.

(10)

Works Cited

1. IAEI, “The 3

rd

_{Harmonic Blocking Filter”, Jan-Feb 2003, 2 Mar 2006,}

http://www.iaei.org/subscriber/magazine/03_a/magazine_03_lowens

tein.htm

2. C. Sankaran, “The Basics of Delta-Wye Transformers”, 1 Dec 2000,

2 Mar 2006,

http://www.ecmweb.com/mag/electric_basics_

deltawye_transformers/index.html

3. John Dedad, “Trouble Comes in Threes”, 1 Jul 2004, 2 Mar 2006,

http://www.ecmweb.com/mag/electric_trouble_comes_threes/

4. All About Circuits, “Harmonics in Polyphase Power Systems”, post

date unknown, 2 Mar 2006,

http://www.allaboutcircuits.com/vol_2/

chpt_10/7.html

– Figure 1, Figure 2

5. Pacific Gas and Electric Company, “Power System Harmonics”, Jan

1993, 2 Mar 2006,

http://www.pge.com/docs/pdfs/biz/

power_quality/power_quality_notes/harmonics.pdf

(11)