# LC Filter for three phase inverter

#### Prithvi10

Joined Apr 1, 2019
31
Hi Prithvi10

Below is a mathcad display showing the calculations for any Ott filter , but of course the example is for the filter
you need to transform a square wave of 400 hertz into a fairly cleans sinusoid with less than 4% total harmonic
distortion. The equations are algebraic and can be executed with just about any program.

View attachment 207948

Below is the Ltspice program that used the numbers above to calculate the filter performance:

View attachment 207949

And below is the performance calculated using the LTspice program:
The red plot is the square wave into the OTT filter. The Green plot is the sinusoidal waveform across the load
resistor at a power level of 20kw. Total harmonic distortion is 3.54 percent as noted above on the schematic.

Note that with a driving waveform duty cycle of 33.34% the total harmonic distortion would drop to below
1% and that is how I have driven the OTT filter in the past using a phase shift power stage.

View attachment 207950

The current through the each inductor is a quasi-resonant shape with few harmonics so copper wire losses will
be at the fundamental frequency of 400 hz for all practical purposes. What I usually do is measure the flux
density of each coil for 100 turns and 1cm squared core area. Then scale both of those values to design the
real hardware. I did not do it here though. Due to the inductance values being in the microhenrys, perhaps
ferrite material could be used for the inductor cores. By comparison, steel is very expensive.

I hope this material will help. The I will try to post the LTspice program itself in this communication.

Best regards, keep well away from the Corona virus.

Wendell Boucher
Hi Mr.Wendel,

I tried the filter design you gave me, I simulated my design in Simulink and the waveform is not exactly clean.
and the THD is also quite high with 9%. I am sorry that I didn't tell you that I am using a Sine PWM inverter with a Switching frequency of 10000kHz.

#### Prithvi10

Joined Apr 1, 2019
31
Hi Marc,

Thanks for the filter values. It will be very helpful if you can share the design method of the R,L and C values.

I got the exact output as yours, but when i connect the inverter with the rectifier ouput the Dc waveform is not the same.
This is how the waveform and there is no change in the inverter output current waveform.
Above is the Inverter output waveform, the voltage waveform looks neat but the current waveform still looks distorted. The inverter i use is an sinepwm inverter with 10000kHz switching frequency

Thank you

#### Marc Sugrue

Joined Jan 19, 2018
222
Hi Mr.Wendel,

I tried the filter design you gave me, I simulated my design in Simulink and the waveform is not exactly clean.View attachment 207961
and the THD is also quite high with 9%. I am sorry that I didn't tell you that I am using a Sine PWM inverter with a Switching frequency of 10000kHz.
Hi Marc,

Thanks for the filter values. It will be very helpful if you can share the design method of the R,L and C values.

I got the exact output as yours, but when i connect the inverter with the rectifier ouput the Dc waveform is not the same.
View attachment 207962This is how the waveform and there is no change in the inverter output current waveform.View attachment 207963
Above is the Inverter output waveform, the voltage waveform looks neat but the current waveform still looks distorted. The inverter i use is an sinepwm inverter with 10000kHz switching frequency

Thank you
Hi Prithvi,
What is the makeup of your 3 Phase R Load? Is it just resistors?

Could you also clarify how are you measuring the output current ? The ouput current should be the current in your resistors not the current in the inverter. The odd waveform looks like your seeing the phase currents as one phase comes down from the crest and the other phase going up.

If your voltage is Sine Wave on each phase and you have a Resistive Load on each phase then the current each resistor should also be sine wave (ohms law). Your waveforms suggests thats not whats been measured.

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#### Prithvi10

Joined Apr 1, 2019
31
Hi Prithvi,
What is the makeup of your 3 Phase R Load? Is it just resistors?

Could you also clarify how are you measuring the output current ? The ouput current should be the current in your resistors not the current in the inverter. The odd waveform looks like your seeing the phase currents as one phase comes down from the crest and the other phase going up.

If your voltage is Sine Wave on each phase and you have a Resistive Load on each phase then the current each resistor should also be sine wave (ohms law). Your waveforms suggests thats not whats been measured.
Hi Mr.Wendel,

Actually Matlab has a three phase measurement block which gives us the peak value of both volatge and current for both phase and line. Yes sir the load is resistor.

This is my Inverter output when I use DC source as an input.
But when i connect the inverter inputs to the rectifier output, then the waveform of the current is distorted
This is the output of my inverter after i connect the rectifiers output to inverter input terminal

#### MrAl

Joined Jun 17, 2014
9,751
Hi ,

I am designing a closed-loop sine pwm three-phase inverter with an output power of 60kVA with a phase RMS voltage of 115. I am struggling to design the LC filter for the system to convert the square wave output into a sine wave. Please help with the design of the filter.

Thank you.

Regards,
Prithvi
Question: why are you using a square wave why not a sine synthesized PWM?
Even back in the 1980's we did this so it is definitely possible now.
The extra pulses relaxe the filter requirements by a ton.

#### Prithvi10

Joined Apr 1, 2019
31
Question: why are you using a square wave why not a sine synthesized PWM?
Even back in the 1980's we did this so it is definitely possible now.
The extra pulses relaxe the filter requirements by a ton.
Hi MrAl,

I am not using Square PWM, I am using a Sine PWM with Switching frequency of 10kHz

Thank you

#### Marc Sugrue

Joined Jan 19, 2018
222
Hi Mr.Wendel,

Actually Matlab has a three phase measurement block which gives us the peak value of both volatge and current for both phase and line. Yes sir the load is resistor.

View attachment 207980This is my Inverter output when I use DC source as an input.
But when i connect the inverter inputs to the rectifier output, then the waveform of the current is distortedView attachment 207981
This is the output of my inverter after i connect the rectifiers output to inverter input terminal
Can you post
Hi MrAl,

I am not using Square PWM, I am using a Sine PWM with Switching frequency of 10kHz

Thank you
Could
Hi Mr.Wendel,

Actually Matlab has a three phase measurement block which gives us the peak value of both volatge and current for both phase and line. Yes sir the load is resistor.

View attachment 207980This is my Inverter output when I use DC source as an input.
But when i connect the inverter inputs to the rectifier output, then the waveform of the current is distortedView attachment 207981
This is the output of my inverter after i connect the rectifiers output to inverter input terminal
Sorry i'm not familiar with MATLAB but the Iabc output of your far right block on your block diagram i'm strugging with. If you have a Sinousiodal Voltage on a resistor the current is also Sinousoid, its Ohms Law. As that far right block only has a single Iac output for 3 phases whats it measuring?
As per my previous post if you measure the current in a single resistor at any point in time from one of the phases the instantanous current at any point should be I = V/R, as your voltage is Sine the current also has to be.

#### WendellB

Joined Feb 14, 2020
22
Hi Mr.Wendel,

I tried the filter design you gave me, I simulated my design in Simulink and the waveform is not exactly clean.View attachment 207961
and the THD is also quite high with 9%. I am sorry that I didn't tell you that I am using a Sine PWM inverter with a Switching frequency of 10000kHz.
Hi Prithvi10,

I will withdraw from contributing further for I really cannot design hardware with confidence that connects to a circuit I have not seen nor, in my opinion, has been defined enough to accurately test any proposed solution I might suggest.

So Good luck with your project. Stay healthy.

Best regards

Wendell

#### Marc Sugrue

Joined Jan 19, 2018
222
Just did a little bit of Research here https://www.mathworks.com/help/physmod/sps/powersys/ref/threephasevimeasurement.html

I think your using the wrong measurement tool. You probably need to look at the 3 single phases independently as opposed to raw 3 phase measurement as you are currently. What you should be interested in is the voltage accross each resistor on each phase, the voltage phase relationship between phases, and the single phase current through each resistor with respect to Voltage.

Each Voltage Phase should be 120 Degrees out of phase with the other.

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#### schmitt trigger

Joined Jul 12, 2010
515
Wendell;
thanks for bringing back some fond memories of my time as a power electronics engineer back in the early 1980s.

Back then.......We also used an Ott filter in conjunction with an SCR based inverter.

In my experience, obtaining the actual real world L and C components was the most significant challenge. For the inductors is was very critical not reach core saturation as the inductance drops quite quickly. And the capacitors sustain large ripple currents and thus the capacitor type must be selected carefully. Otherwise they will burst.

#### WendellB

Joined Feb 14, 2020
22
I agree with you, in fact my next task was to look at the quality caps that could be used. Probably made by Electronic Associates, for the have a great line of low ESL and ESR caps, not electrolytic but film with real specifications. Also it occured to me looking at
the inductor values that they might be possible in air, perhaps a torroidal shape to contain the stray field.

But now I am going no further for lack of a real schematic to connect to.

I didn't realize that the Ott filter was still being used as late at the 80s, yes it is a very good filter. I did propose it for a military
application for the Navy in 2014. And used it for a 1mhz task in 1998, worked great in both applications.

Goodby and Best regards, Wendell

#### Prithvi10

Joined Apr 1, 2019
31
Just did a little bit of Research here https://www.mathworks.com/help/physmod/sps/powersys/ref/threephasevimeasurement.html

I think your using the wrong measurement tool. You probably need to look at the 3 single phases independently as opposed to raw 3 phase measurement as you are currently. What you should be interested in is the voltage accross each resistor on each phase, the voltage phase relationship between phases, and the single phase current through each resistor with respect to Voltage.

Each Voltage Phase should be 120 Degrees out of phase with the other.

View attachment 207986
Hi Marc,

I tried the other method of voltage and current measurement. I get the same clean wave for the voltage for both phase and line. The current waveform is still the same.

#### Prithvi10

Joined Apr 1, 2019
31
I agree with you, in fact my next task was to look at the quality caps that could be used. Probably made by Electronic Associates, for the have a great line of low ESL and ESR caps, not electrolytic but film with real specifications. Also it occured to me looking at
the inductor values that they might be possible in air, perhaps a torroidal shape to contain the stray field.

But now I am going no further for lack of a real schematic to connect to.

I didn't realize that the Ott filter was still being used as late at the 80s, yes it is a very good filter. I did propose it for a military
application for the Navy in 2014. And used it for a 1mhz task in 1998, worked great in both applications.

Goodby and Best regards, Wendell
Hi Mr.Wendel,

Thank you for all your effort. If you dont mind could you please take a look at the doc i have attached. I have tried the circuit in different software and tried to put it as a schematic. Will that be helpful

#### Attachments

• 20.9 KB Views: 15

#### Prithvi10

Joined Apr 1, 2019
31
Just did a little bit of Research here https://www.mathworks.com/help/physmod/sps/powersys/ref/threephasevimeasurement.html

I think your using the wrong measurement tool. You probably need to look at the 3 single phases independently as opposed to raw 3 phase measurement as you are currently. What you should be interested in is the voltage accross each resistor on each phase, the voltage phase relationship between phases, and the single phase current through each resistor with respect to Voltage.

Each Voltage Phase should be 120 Degrees out of phase with the other.

View attachment 207986
Hi Marc,

I simulated the system and measured the phase voltage of the output, and it looks the same distorted way the current wave looks. All this time i have been measuring the line voltage and did not care to check the phase voltage.
I apologize for that.
Now, how to make the phase wave a pure sine. Kindly help me.

Thank you.

this is the waveform of the phase voltage and the current wave.

#### MrAl

Joined Jun 17, 2014
9,751
Hi MrAl,

I am not using Square PWM, I am using a Sine PWM with Switching frequency of 10kHz

Thank you
Oh well you said square in your original post.
What are you using then, a multi pulse PWM or just one pulse per half cycle?

#### Marc Sugrue

Joined Jan 19, 2018
222
Hi Marc,

I simulated the system and measured the phase voltage of the output, and it looks the same distorted way the current wave looks. All this time i have been measuring the line voltage and did not care to check the phase voltage.
I apologize for that.
Now, how to make the phase wave a pure sine. Kindly help me.

Thank you.

View attachment 208008this is the waveform of the phase voltage and the current wave.
That now makes much more sense. You have a distorted voltage, hence the distorted current.

I've no idea what the blocks are in MATLAB for the inverter stages or what the control methodologies are for them. As others have pointer out previously you'll need a modulated PWM to your chosen frequency see http://www.ti.com/lit/an/slaa602a/slaa602a.pdf?ts=1590351389984 as a start point.

Whats it like under DC conditions now? Still distorted?

If i were you i'd try to determine what type of control you have currently implemented for the inverter, remove all the blocks outside of the inverter & resistive loads (no filter etc), power it from DC and get some waveforms of what unfiltered signals your currently generating. People will be able to support better once there some facts about what you've got under DC input conditions.

#### Papabravo

Joined Feb 24, 2006
19,822
IMHO you are asking for something which is not possible. A filter can be designed to affect magnitude, phase, and group delay. AFAIK there are no filters which reduce distortion, at least not one that I am familiar with. If you require low distortion that has to be an initial design requirement. You can put lipstick on a pig, but in the end it will still be a pig.

#### Prithvi10

Joined Apr 1, 2019
31
Oh well you said square in your original post.
What are you using then, a multi pulse PWM or just one pulse per half cycle?
I am using multiple pulse pwm , sine wave is my reference with a freq of 400 and triangle as carrier with freq of 10kHz

#### Prithvi10

Joined Apr 1, 2019
31
That now makes much more sense. You have a distorted voltage, hence the distorted current.

I've no idea what the blocks are in MATLAB for the inverter stages or what the control methodologies are for them. As others have pointer out previously you'll need a modulated PWM to your chosen frequency see http://www.ti.com/lit/an/slaa602a/slaa602a.pdf?ts=1590351389984 as a start point.

Whats it like under DC conditions now? Still distorted?

If i were you i'd try to determine what type of control you have currently implemented for the inverter, remove all the blocks outside of the inverter & resistive loads (no filter etc), power it from DC and get some waveforms of what unfiltered signals your currently generating. People will be able to support better once there some facts about what you've got under DC input conditions.
Hi Marc,
When I use the DC source instead of the rectifiers output the waves are clean from both the current and the voltage.Does this mean the problem is with the rectifier ?
I have not connected any control elements so far, all I was trying is to connect the rectifiers output to inverter and get clean waveform.

#### MrAl

Joined Jun 17, 2014
9,751
I am using multiple pulse pwm , sine wave is my reference with a freq of 400 and triangle as carrier with freq of 10kHz
Ok good, then you should sim with that also.
Your pattern should be checked for harmonics too.