Archive for the ‘Numeric Precision’ Category

Power Electronics Digital Control Webinar Schedule for 2018-2019

Tuesday, May 8th, 2018

We are pleased to announce the 2018 power electronics digital control webinar schedule for ELMG Digital Power.

These free webinars are the best chance to be among the best digital power electronics control engineers in the world.

The sessions cover the need to know details of Digital Control of Power Electronics and include a question and answer session after the webinar.

Power Electronics Digital Control Webinar Schedule

Make a note of the dates.

Tuesday May 1 Digital Control of Power Electronics using Zynq …[sign up here]
Tuesday June 5 What you need in a development platform for Digital Power Electronics…[Sign up here]
Tuesday July 3 Designing and Implementing Digital Integrators
Tuesday August 7 Using Simulation Tools effectively in Digital Power Electronics Development.. [Sign up here]
Tuesday September 4 Measuring Power Converter Control Transfers
Tuesday October 2 Basics of Digital Power Electronics Control – Where to Start
Tuesday November 6 How to choose your control processor for Digital Power Electronics
Tuesday December 4 Frequency Domain Control Design for Digital Power Using SciLab
Tuesday January 8 2019 Precision Correction in Digital PWM Modulators
Tuesday February 5 2019 Filter Structures for Digital Power Electronics Control
Tuesday March 5 2019 Fractional Step Digital Filters
Tuesday April 2 2019 Development Structures for Firmware and Software in Digital Power Electronics
Tuesday May 7 2019 Grid Synchronization with PLLs

We’ll remind you of the time, dates and where to sign up by e-mail.

The webinars will be presented by ELMG Digital Power CTO, Dr Hamish Laird.

Power Electronics Digital Control Webinar Schedule

Dr. Hamish Laird at the ELMG Digital Power Camarillo Office

Three Day Digital Control Course August 22-24 California

Friday, July 22nd, 2016

The ELMG Digital Power Electronics Control Course

Three days of focused unique training in digital control of power electronics!

Our Digital Power Electronics Control Course overs the essential knowledge and know-how for engineers to implement digital power electronic control!

Come to the Three Day Digital Control Course in Camarillo, California August 22-24, 2016.  Register here.

How did the course came about?

Essentially the course came about because we were asked by one of our customer’s to provide one. The story is we were in the middle of a “fix up” job where the power supply had shown some control instability at its final release testing. The testing that showed the problem was passing a short circuit test of parallel connected power supplies. When the short circuit was removed the supplies came out of current limit, however they did not come out of the limit at exactly the same time. This created an oscillation where individual power supplies came out of current limit and then returned to current limit.  It was possible for the oscillation to continue indefinitely.  This was an unacceptable and embarrassing problem.

Six months of expertise in a three day course

During the six month project to rework the control code we spent lots of time teaching the team about the underlying issues that had been missed when the controller had been designed, coded and tested.  And part way through the “fix-up” the R and D manager suggested we could put a course together covering all that the team needed to know.

And so the digital control course was born

The first course covered exactly what we had discovered during the fix up job.  This included lots of digital expertise targeted for power electronics.  The areas we covered were diverse from;

  • Numeric precision loss in filters
  • Improvement of modulation spectral performance
  • Stability
  • The effect of numeric precision on stability
  • Best filter forms
  • Direct digital control design
  • Linearising control loops

What is covered in our course?

The course was created at the request of a Power Electronics Research  and Development manager.  He asked that we make it specific his team’s needs.  And this is why the course has the unique structure that it has.  We have been through the pain and heartbreak of having digital control development go wrong and have seen clearly where the repeated problems lie; our course addresses those areas.

Digital PWM and VPO modulators

One of the big differences between digital power electronics control and conventional analog control is the timer precision in digital modulators. This difference can be corrected or made negligible and in some cases can be made an advantage.  Spectral control in digital modulators is a focus area in the course as it is so effective.

Digital Precision in control blocks

It is possible to use a digital system and adjust the coefficients of the filters so that small inputs result in no output from the filter. Such scaling issues often lead to a loss of precision in the digital control system. The resulting slip-strike behavior can create limit cycle oscillations in the power converter output.

Direct Digital design of controllers

The “design then translation” approach of taking analog controllers to digital form can be avoided by using the direct digital design approach. This simple but powerful method of digital control loop design is covered in the course.

Converter non-linearity correction

Certain converter topologies are non-linear either in the control input to the output or the conversion ration.  Dealing with the converter non-linearity to achieve high bandwidth is key to stable parallel connected converters.


The course covers the fundamentals of stability from a physical basis with a focus on measurements of power converter transfers.  This along with a simple framework for managing margins and robustness is an integral part of the course.

Why we offer the course?

Understanding and implementing digital control of power electronics offers great advantages for configuration and flexibility. However, this is not without road blocks and issues that need to be designed around. This course provides the know how to get digital control working robustly and reliably.

How do I get on the course?

The course is next being run in Camarillo, California USA August 22-24.  To register for the course, click and visit the information page here. Press the ‘Register’ button on the page and this will take you to the shopping cart for the course. Complete the purchase to register for the course.

Next course

The next course is being held August 22-24 in Camarillo, California, USA.



There are several hotels a short distance from the Ridley Engineering Design Center. The prices below reflect their current prices for August 2016. The last hotel listed is a nice beachfront resort if you do not mind the 25-minute commute to the office. Regardless of your selection, we recommend arriving on Sunday evening and departing Wednesday evening or Thursday.


Best Western Inn

295 E Daily Drive, Camarillo

0.3 mi.



Residence Inn by Marriott

2912 Petit Street, Camarillo

2.8 mi.



Courtyard by Marriott

4994 Verdugo Way, Camarillo

4.3 mi.



Hampton Inn & Suites

50 W Daily Drive, Camarillo

1.1   mi.



Hilton Garden Inn

200 Solar Dr., Oxnard

5.6 mi.



Embassy Suites Mandalay Beach Resort

2101 Mandalay Beach Rd., Oxnard

15.4 mi.



Travelling to the course


Airports: There are three options for airports. Bob Hope Airport in Burbank will be the least congested and is serviced by American, United, Delta, Southwest and JetBlue:

Bob Hope Airport (BUR)

Los Angeles International Airport (LAX)

Santa Barbara Airport (SBA)

Shuttle: The Roadrunner Shuttle is a Camarillo-based service that provides door-to-door service from the airport.


Bob Hope Burbank Airport (BUR) via US 101

Los Angeles International Airport (LAX) via US 101

Los Angeles International Airport (LAX) via Pacific Coast Highway (PCH)

Santa Barbara Airport (SBA) via US 101

About the presenter

3 Day Digital Control Course

Dr. Hamish Laird

Dr. Hamish Laird is a well regarded digital power electronics control engineer, researcher, lecturer and teacher.  Hamish is Chief Technology Officer at ELMG Digital Pwoer and holds a visiting academic position at the University of Canterbury in Christchurch, New Zealand.

During his career Dr Laird has worked on the control for;

  • High Voltage Direct Current Transmission
  • Reactive Power Compensators
  • AC and DC Motor Drives
  • DC to DC converters including LLC and phase shifted bridges
  • Medium and low voltage AC motor starters

Dr. Laird has worked for;

  • Alstom Grid (GEC Alsthom)
  • Eurotherm Drives
  • University of Canterbury
  • Aucom

Through ELMG Digital Power Dr. Laird  has provided advice, services and products to;

  • ABB
  • Enphase
  • Comsys
  • Evashred
  • TNEI
  • Eaton

Dr Laird says

“In designing and presenting the course we aim to have engineers able to use digital control in power electronics to achieve robust and reliable results.  See you in Camarillo”.


How to Register

Click here to register.  

P.S. Please note that the ELMG Digital Power course is being hosted at the Ridley Engineering Centre in Camarillo, California.  Ridley Engineering are processing all course registrations viatheir webstore.  Click here to register.  

Congratulations to Dr. Rabia Nazir on completing her PhD in fractional delays in repetitive control

Friday, December 18th, 2015

Over the last two years ELMG Digital Power CTO, Dr. Hamish Laird, has helped supervise (the now Dr.) Rabia Nazir in the pursuit of her Doctoral studies.

Hamish Laird says

“The research that Rabia has completed in the area of fractional delays in recursive filters for current control in grid tied inverters gives great control tools in the implementation of control for GTIs in grids where the AC system frequency is varying. It is always great to help with PhD research as I learn so much so thanks to Rabia for letting me help.”

Congratulations to Dr. Rabia Nazir on her successful oral defense of here work.  Dr Laird again

“It was fantastic to attend Rabia’s defense.  I am so proud of and pleased with the work she did in analysing, simulating and building power converter hardware to show her findings. It was a great learning experience for me.”

Recently (now Dr.) Rabia Nazir presented a paper at a conference in Sicily on the use of Taylor Series expansion based fractional delay filters for recursive control of grid inverter currents.

Contact us for a copy of the paper.



Power Electronics Digital Control – Free Report on Three Key Issues

Monday, September 14th, 2015

Three Key Issues

People often ask us what are the key advantages in Digital Control of Power Electronics that make it such a good solution to modern power converter control.

The advantages of Power Electronics Digital Control are

  • Flexibility
  • A common control platform technology across different converters
  • The repeat cost on code is zero
  • The digital controller can deal with the non-linearity and mode changes the power converter
  • Digital control allows control systems that are not possible with analogue including dead beat, recursive or model predictive control.
  • Increased efficiency through switching instant control.
  • Increased efficiency through converter topology change that brings new control challenges that are best met digitally.

With all these advantages digital control is a great choice for your next power converter development.

A microprocessor used in digital power control.

Digital Control of Power Electronics dominates the solar inverter and motor drives industries.

Murphy’s law

Those of you who are aware of Murphy’s or Sod’s law will know that there has to be some downside to power electronics digital control.  As we have been working with digital control of power since 1992 we often get asked to help out with problems that people have in their digitally controlled power converters.

We see the same issues regularly and so have put together a report that covers the three most important issues to take care of in digital power electronic control development.

The report is available for download for free by clicking here.

Get the free ELMG Digital Power report on the Three Key Issues in Digital Control of Power Converters

Download report



Fixed Point Numerical Systems for Digital Control

Saturday, August 29th, 2015

One question which is commonly asked is “how do I represent fractional numbers on my fixed-point MCU, DSP or FPGA?” One of the best solutions to this is use of the Q number system.

The Q number system is a fixed point system where the available bits are divided amongst the integer bits (those to the left of the decimal point), fractional bits (those to the right of the decimal point) and a sign bit. You may ask “I know how integers are represented in binary but not fractions?” The answer is that just like integers, fractional bits are just multiplied by powers of two, except the powers are negative. For example:

  • 0.011B = 0*2-1+1*2-2+1*2-3 = 0.375

Q numbers can take on multiple forms with different numbers of fractional and integer bits. They are commonly written mQn or Qm.n where m is the number of integer bits and n is the number of fractional bits. Note m+n+1 = total number of bits available.



Q numbers of the same form can be added together with no issue. The only thing to consider here is overflow.

If you have different forms they need to be converted before the arithmetic. This can be done by shifting. For example:

  • 2Q13 << 1 is now 1Q14 (lose an integer bit and gain a fractional bit) and
  • 3Q12 >> 1 is now 4Q11 (lose an fractional bit and gain an integer bit)


  • The rule when multiplying two Q numbers together is:
  • m1Qn1 * m2Qn2 = (m1+m2)Q(n1+n2)

Once the multiplication is complete, then a shift is needed to get it into the Q format the system needs.

The big issue with multiplication is overflow and precision loss. When there exists m > 0, then scaling back to your original system is difficult. For example:

  • 2Q13 * 2Q13 = 4Q26

In order to scale this back to the original 16 bits you either have to sacrifice integer bits (you have to be very careful that the top integer bits don’t contain information – limit the overflow) or lose precision by discarding fractional bits. The solution to this is to try and use systems where m=0.

Digital Control

Choosing the Q number system for digital control is important. The general rule of thumb is you want as much precision as possible and you want to avoid overflows in multiplication. Therefore the best solution is to make all your bits fractional (i.e. m=0). This gives as much precision as your system allows and makes sure there are no overflows (<1 x <1 = <1). In a 16-bit system this is 0Q15 (referred to as Q15).

Once you have your system then you need to make sure that all inputs and outputs fit this system and falls within the range -1 <= x < 1. This is as simple as setting your inputs and outputs to be +1 = full scale positive and -1 = full scale negative.

The key for this to work in a digital control system is to remember the gains on the inputs and outputs. This means remembering what +1 and -1 stand for. For example a voltage input may be -230V to +230V and an output maybe -400V to 400V. The input gain is therefore 1/230 and the output gain 400. Once you have these gains you need to include them in your design of the control system, whether it be through calculation or simulation. Failing to include them leads to incorrect margins and possibly instability.

One potential pitfall of the m=0 approach is how to deal with numbers greater than one. In digital control these can come up quite often generally in biquad filters. The trick is to this is to scale the coefficients by ½, perform the multiplies and then scale back by 2 (shift left 1). This does lose one bit of precision in this particular calculation however it is better than losing one fractional bit in all calculations.


Q number systems allow the designer to use a reliable fixed point system to represent fractional numbers. This allows the use of less expensive fixed point processors instead of the more complex and generally more expensive floating point alternatives.

Download the report ‘Your Digital Power Future – Roadblocks to Avoid’ to learn about the three key issues to watch out for in the Digital Control of Power electronics.

Download report now

Is digital control of power electronics the best way forward?

Monday, May 12th, 2014

Digital Control of Power Electronics

The main and key reason that digital control of power electronics and power converters is a good way forward is that it provides flexibility.  And flexibility is useful for a number of reasons.  The first is that the function of the product can be changed by changing the firmware or the software.  There is always verification and validation effort associated with flexibility but this effort is often worth bearing for a digital controller running in a programmable processor or FPGA.  The second reason is the use of common processor parts across a number of products giving purchasing advantage.  A third reason is that effectively the production repeat cost of firmware and software is zero.  This is because typically the BOM cost of the software or firmware is usually zero rather than the code’s amortized development cost.

There is also flexibility in the control approach.  Software or firmware allows switching strategies to be changed for different converter operating conditions.  Alongside this the switching instants themselves can be adjusted to minimise the switching loss.

For applications where flexibility is not required then analogue control may be what is required.  In these cases digital control may not be the best.  Traditional analogue control has many strengths.

So back to digital.  There are specific advantages that digital control of power electronics provides when compared to traditional analogue control.  These include

  • Configurability
  • Re-tuning the loop for component variation such as Electrolytic capacitor freeze out at low temperatures
  • Management of the non-linearity of the converter
  • Self measurement of the loop response in closed and open loop.
  • The ability to tune the switching times precisely to minimize the power loss and maximize the efficiency.
  • Flexibility

These have proved very useful for power converter control.

There are some differences with a digital controlled converter when compared to analogue control.  These differences can be problematic if you are not ready for them.

So what should the digital control of power electronics be implemented with?

This is a good question that does not have one answer.  Many microprocessors are able to control power electronics.  Other options are digital signal processors (DSP) and field programmable gate arrays (FPGA).  Choosing an appropriate solution means assessing the processing power against the allowable control loop delay for the power converter and the target bandwidth.  For increasing loop bandwidth the solution order is microprocessor, DSP and the FPGA.  The FPGA can provide the least loop delay as it can process the signals very quickly in parallel.

And what issues are key to take care of to go digital?

It is great idea to use digital control for power electronics.  Hopefully it will allow the power electronic converter to be more efficient and more flexible.  One key issue is numeric precision.

1. Numeric precision – limited number of bits

The digital controller is made up from an analogue to digital converter (ADC), some digital filters which implement the controller and then a digital to analogue converter typically in the form of the pulse width modulator (PWM) or a variable frequency/period oscillator (VFO/VPO).  Each of these has a limited number of bits and has an effect on the precision and noise performance of the entire system.   The analogue to digital converter has a limited number of bits.  Typically analogue to digital converters have eight, ten, twelve, fourteen, sixteen, eighteen or twenty bits.  The increasing number of bits means increasing cost.  Determining how many bits are required for the ADC is the first step in designing the digital controller.

The limited number of bits means that the measured output voltage or current is quantized and the dynamic range is limited.  This means that the precision to which the output can be controlled is limited to the step size in the ADC.  If the precision is not accurate enough then the feedback loop will not be able to measure the difference from the required output value.  Effectively the precision of the output control will be limited to the least significant bit step of the ADC.  Typically there is a trade-off between dynamic range and precision in the ADC.  It is useful to use some precision extension techniques on ten and twelve bit ADC inputs to get both a high dynamic range and accurate output control.  Precision extension techniques can include only sampling the error signal created with an analogue summing amplifier or using two ADC channels together to provide the precision and the range.

2. Digital filter coefficients – numeric precision

The internal calculations for the filters involve multiplications and additions.  These are the typical MAC (multiply and accumulate) instructions in a DSP.  These MACs realize the digital filters that provide the integrators, phase lift networks, differentiators and low pass filters that are used in closing the control loops.  Each multiplication by a filter coefficient effectively reduces the precision of the signal.  This reduction in precision is especially noticeable in digital integrators and digital filters with narrow bandwidth.  This loss of precision can, if it is large, lead to the digital filter failing to operate on small inputs.

Managing the digital precision of the digital filter is done by ensuring that as many bits as possible are retain in all the calculations by using coefficients that are chosen to maximize the retained signal level without clipping in large transients.  Another precision extension system is the retention of extra result bits in the internal filter accumulators.  This has a remarkably useful effect on reducing digital power control system noise.

Other Issues

Other issues that arise in the digital control of power electronics are

  • Timer Precision for PWM
  • Converter Non-linearity effects on the digital control
  • Bandwidth limits from sampling
  • Anti-aliasing filter effects
  • Processing delays

First step toward Digital Control of Power Electronics

Taking the first step toward going digital can involve a leap of faith.  Alternately it can involve understanding the issues, the disadvantages and the advantages.  The primary first choice of processor or controller technology involves determining how much processing power and the number of bits the power converter controller requires.