Hybrid Filter for High-Power Converter Systems

Guilherme H. K. MartiniProgress Rail Services

Curitiba, Brazil

gmartini@progressrail.com

Joao Alberto FabroDepartment of Informatics

Graduate School of Applied Computing (PPGCA)

Federal University of Technology - Parana

Curitiba, Brazil

fabro@utfpr.edu.br

Abstract---This paper presents a digital hybrid filter whichcan be applied to power electronics control systems. The filtersuppresses high-frequency noises while still providing a faststep response, its weighting algorithm is based on an open-loopcriteria that analyses the discrepancy between an Infinite ImpulseResponse (IIR) and a Moving Average (MA) filter. The filterperformance is compared to classical implementations througha step response and a Signal-to-Noise Ratio (SNR) analysis. Thecomputational cost is also evaluated to verify its use on hard real-time systems. To evaluate the proposed filter, experiments weremade on a microcontroller-based high-power frequency inverterwith hard-time constraints, ensuring its applicability.

Index Terms---Hybrid Filters, Embedded Software, DigitalSignal Processing, Power Electronics, Switching converters.

I. INTRODUCTION

Control systems that make use of high-power switching

drivers are very dependent on continuous voltage signals.

Those signals usually inform to the controller the conditions of

currents, voltages and temperatures of the operating equipment.

The information carried by the signals is critical to the correct

operation of the system and due to various noise sources those

signals are usually degraded. This degradation can be caused

by the driver switching output itself, by its switching power

supply, by its proximity to the load, and many other factors

that, depending on the application, are inevitable.

In order to keep the system operation adequate to its needs,

a filtering method is required. The ideal filter would attenuate

all high-frequency components while still having a good step

response. This would allow the system to respond quickly

to changes and to work with stability on its steady-state.

Frequency-domain based filters would give an exceptional

attenuation by using a Fast-Fourier Transform (FFT) to easily

detect the noise components but wouldn’t fit the tight time

requirements of the switching converters control loops, hence

the use of a time-domain based filter is required.

The direct use of moving average (MA) filters would give

a good white noise suppression, but, when the order of the

filter increases in an attempt to get a better attenuation, the

step response delay becomes larger. The MA filter is also

problematic when the signal contains narrowband noise, which

is exactly the one generated by the switching components.

Finite impulse response (FIR) filters would also need to have

too many delay stages to attenuate narrowband noise, thus

having the same disadvantage.

A low-pass infinite impulse response (IIR) filter would

deliver an even better noise attenuation but the step response

would be a drawback. As the step response time and the

filtering attenuation are trade-offs, a change on its frequency

response is needed to allow the system to have a better step

response.

Time constraints and the previous knowledge of the noise

characteristics are the main bottlenecks to the development

of such hybrid methods. Recent papers show that hybrid and

adaptive filtering methods are being used in a wide range

of applications. For example, an adaptive weighted moving

average (WMA) algorithm is proposed in [1] to clean the

channel noise generated in a wireless sensor network. Statistical

filters are applied allowing the change of the filter coefficients

depending on the noise spectrum in [2]. Warm-up periods of

MA filters are evaluated in [3], indicating that certain time-

critical applications must be developed with special care. In

the same area of application, [4] presents a FIR filter for delay-

constrained applications showing that a flexible filter can have

a better step response than the traditional moving average filter.

Hybrid filters can be used to suppress the noise generated

by non-linear loads on power applications, as presented in

[5], that uses passive and active elements that form a hybrid

filter to damp undesired harmonics in a shunt compensation

application. Harmonics elimination over voltage signals on

power applications using adaptive and hybrid filters can also

be verified on [6] and [7]. Examples of adaptive filtering being

applied in high-power applications can also be found in [8], [9]

and [10]. Implementations that have a prediction step phase

such as the Kalman filter are also common [11] but those

are not suited for this work because of time constraints of

the application. Predictive filters have a higher computational

cost generated by the mathematical models which attempts to

reproduce the plant behavior.

The development of a simple hybrid filter that has a good

step response while still attenuating high-frequency noises

is the main purpose of this work. Every stage of the filter

is presented in a general structure allowing its use in any

application that has the same requirements. The computational

cost is shown and compared to traditional techniques to allow

its applicability in hard real-time applications. Empirical data is

retrieved from an application of the filter in a microcontroller-

based AC-AC (alternate current) frequency inverter to analyze

978-1-4799-1132-5/13/$31.00 c© 2013 IEEE

978-1-4799-1132-5/13/$31.00 ©2013 IEEE

3ϕ

Input

Full Bridge

Diode

Rectifier

μC-Based

Control

Board

IGBT-Based

3ϕ Source

Inverter

DC Bus

Output

toLoad

System

Set-Points

Output to

Actuator

Feedback

Sensor Data

Feedback Sensor Data

Fig. 1. 3-phase AC-AC frequency inverter structure.

its final performance. Those frequency-inverters are already

being used on a locomotive fleet running on the southeastern

part of the United States. They drive traction motor blowers

and air compressors, generate 220V AC to peripherals on

each locomotive and produce power to the cabin heater/air

conditioning system.

The second section of this paper provides a brief description

of the equipment in which the filter was applied and the filter

design structure along with every limiting factor that affected

its conception. The third section describes the implementation

of the filter and presents its results when applied to the

frequency inverter. A comparison with other classical filter

implementations is also made in this section. The fourth section

concludes the paper.

II. FILTER DESIGN REQUIREMENTS EVALUATION AND

CONCEPTION

The filter design method was defined to meet the application

constraints. Those constraints are usually the same or very

similar for every power converter equipment: fast control loops

that make complex algorithms very cumbersome; inevitable

noise generated by the equipment itself; the need to have a good

steady-state regulation to increase the equipment efficiency;

and a good step response to allow the control to respond well to

unexpected plant variations, increasing the equipment lifetime,

security and reliability.

The testing equipment is a 3-phase AC-AC frequency

inverter consisting of a full rectifying bridge, a microcontroller-

based control board and a IGBT-based (Insulated Gate Bipolar

Transistor) three-phase voltage source inverter as seen in figure

1. A group of sensors and transducers are also included in the

equipment allowing a closed loop control that is performed by

a RISC (Reduced Instruction Set Computer) microcontroller

running at 88Mhz.

The process control block consists of a plant, that in most

applications of the equipment is an AC induction motor, a

control transfer-function and a filter transfer-function. The filter

transfer-function samples analog signals from the plant, filters

them and sends its information to the control transfer-function.

The main scope of this work is to deliver a reliable feedback to

the control by developing this filter transfer-function. The filter

block is evaluated only by its inputs and outputs, verifying

the gain that this block provides to the whole process. The

filter’s transfer-function is easily modifiable because it can

be developed by software after the analog-to-digital converter

(ADC) acquisition in the microcontroller, allowing progressive

improvements without any change on its physical structure

(which is not possible to the equipments that are already running

on field).

The control-loop time is constant and set to 1 millisecond

allowing its actuation to meet the equipment application

requirements. Every new control loop requires new information

from five different sensors to verify the actual output state and

calculate the new system actuator output. The five cited sensors

measure the following signals: The DC input voltage after the

rectifying bridge, the three AC output currents and the IGBTs

heat sink temperature. Besides the heat sink temperature, all

measurements are time-critical and need to be updated before

the execution of every new control iteration. Knowing this

constraint, it is set that the time window given to the filter

stage to produce the sensor outputs is up to a quarter of the

control-loop time, i.e. 250 microseconds, thus 50 microseconds

per sensor. The temperature sensor is sampled with the same

frequency of the other sensors for a better measurement as it is

a low-power input. The remaining time of the loop is used to

perform the control loop, update the actuators outputs, sample

the analog inputs, receive its set-points through industrial

communications protocols and inform its actual state through

the same industrial network.

A common method used to reduce white noise from analog

inputs is to oversample them. Using a moving average stage

before the actual filter with an oversampled input would fit

easily in the time constraints cited above and would result

in a very good final result if not for one shortcoming: The

ADC conversion must be done when the output IGBTs are

not switching states to avoid spurious samples caused by

electromagnetic interference. The switching pattern used for

switching the output allows the microcontroller to sample

all analog inputs every 1 millisecond in noise-free moments,

this would be enough to change the control loop input in

every iteration but it wouldn’t be enough to oversample the

inputs. Changing the switching pattern would provide a larger

sampling time but would also result in a poorer output quality

and controllability. This leads to the conclusion that changing

the sampling time would not be a good approach to the problem.

The step response time is another constraint that must be

observed. Differently from the time constraint, it is hard to

estimate what is the maximum allowable settling time. The

closer that the filter responds to the step, the better would be

the control adaption. On the other hand, a fast step response

filter would probably have a poor noise attenuation. The same

happens to the noise attenuation criteria, there is no optimal

or desired value for it. With that defined, it was stipulated that

the evaluation of the filter step response and noise attenuation

would be made by comparing its values with a moving average

filter of order 20. From previous experiments it is possible to

know that the MA filter of order 20 provides a satisfactory

Stage IIIStage IIStage I

ADC

Spurious

Samples

Rejection

20th order

MA Filter

5th order

Chebyshev

Filter

Weighting

Stage

ADCSampleInput

OutputtoControl

Fig. 2. Block Diagram of the proposed filter.

step response but poor noise attenuation, specially narrowband

noise.

After defining every limitation of the filter application, it

is possible to describe the filter structure. The block diagram

of the filter is shown in figure 2. It is composed of three

consecutive stages, where the first one requests ADC samples

of every analog input of the system. The main function of the

first stage is to reject spurious samples from the ADC that are

caused by electromagnetic interference. This type of noise is

present even when sampling is synchronized with the switching

instants. The first step of this stage is to double-sample every

input, meaning that whenever a sample is requested, two

instantly consecutive ADC conversions of the same signal

are made. For example, when sampling an input at 1KHz,

two ADC conversions are made one right after another. The

time between those two samples is determined only by the

ADC conversion delay, that is around 8μs. After around 1

millisecond, two consecutive ADC conversions are once again

performed. After this sampling step, both samples are compared

and their difference is calculated. If the difference is below a

stipulated value, the mean value of the two samples is directed

to the stage output. If the difference is above that value, the last

valid conversion is placed as the stage output. This mechanism

can be seen as a high-frequency narrowband noise attenuator

that works between the two samples that were acquired, being

a simplified oversampling method that performs well due to

the low probability of occurrence of two consecutive spurious

samples. The output results can be seen in the next section

where this stage has been proven useful while still fitting the

time requirements.

The second stage consists of two parallel classical filters

with different transfer functions. One of them is a moving-

average filter that has 20 delay stages. The other one is a

Chebyshev-IIR low-pass filter of the 5th order. The purpose

of the two filters is to provide the third stage two different

inputs with different characteristics of the same signal. The

moving average filter responds better to step responses while

still benefits from the narrowband attenuation of the first filter.

The IIR filter provides a very slow step response but provides a

very good noise attenuation when the signal is steady. The 20-

delay MA filter was chosen due to its previous implementation

at the same application. By inspection of data retrieved from

the frequency inverter, its was possible to verify that its step

response was adequate. Its noise suppression capability was

not optimal, but still significant while on transients. The IIR

filter was designed to deliver the largest possible attenuation at

stopband frequencies, because of that the Chebyshev topology

was chosen. The order was determined by its execution delays:

Bigger orders increased execution time but did not deliver a

much better noise attenuation.

The third and last stage is the weighting part of the filter.

Using both filters from the second stage as inputs, a weighted

average of both is provided in its output. The weighting method

varies depending on the difference of the two inputs. If the

MA filter is providing a value that is too different from the IIR

filter, the weights favors the moving average aiming to deliver

a better step response. If not, the filter favors the IIR filter

to maximize noise attenuation. Besides the weighting process,

the triggering of the change of weights can only happen when

some threshold values are surpassed. This trigger mechanism

prevents MA filter from being favored over the IIR filter when

the output of the MA filter is noisy, allowing the weighting

algorithm to differ a step from random noise. The fine tuning

of the third stage is done empirically to ensure its applicability

on the frequency inverter.

With the requirements described and the filter design

structure defined, simulations and practical tests were realized

to verify its performance. The evaluation metrics and its

results are shown in the next section. Also, details about every

parameter used in the whole process along with simulations of

frequency responses, timings and empirical results are given.

III. FILTER IMPLEMENTATION AND RESULTS

For the implementation of the filter, a simulation step was

made previous to its application to allow a faster tuning of

every stage of the filter and to grant its stability before applying

it to the equipment. Three different filters were developed: a

20 delay stages MA, a 32 delay stages low-pass FIR with the

Blackman window function (for comparative purposes) and a

low-pass 5th order Chebyshev IIR filter. As the hybrid filter

uses the MA filter and the IIR in its second stage, no further

development in the simulation step is needed for its validation.

The trade-off between passband ripple and stopband gain of

the Chebyshev topology is assumed to be well suited to this

application. The criteria used to determine the zero and pole

placing of the IIR filter was to minimize the gain in stopband

frequencies.

The MA filter discrete-time transfer function 1 indicates that

that its output gain is always set to 1, exactly like the FIR

filter transfer function 2, that uses the normalized Blackman

window function 3 to produce the same gain.

F (z) =

20∑

n=0

1

21z−n (1)

F (z) =

32∑

n=0

w(n)z−n (2)

TABLE IIIR FILTER COEFFICIENTS

n/p Feedforward (bn) Feedback (ap)

0 3.35×10−8 1

1 1.68×10−7 -4.95

2 3.35×10−7 9.84

3 3.35×10−7 -9.80

4 1.68×10−7 4.90

5 3.35×10−8 -0.98

0 100 200 300 400 500-450

-400

-350

-300

-250

-200

-150

-100

-50

0

Frequency [Hz]

Mag

nit

ud

e [

dB

]

(a)

(b)

(c)

Fig. 3. Frequency response of the modeled filters. (a) IIR response. (b) FIRresponse. (c) MA response.

w(n) =7938

18608−

9240

18608cos(

2πn

31) +

1430

18608sin(

4πn

31) (3)

The IIR filter discrete-time transfer function 4 uses the

feedforward an feedback gains that are described in table I.

By looking at the feedforward gain values it is possible to

conclude that the step response is very slow due to the very

small input gains.

F (z) =

5∑n=0

bnz−n

5∑p=0

apz−p

(4)

With the discrete-time transfer functions modeled it was

possible to determine the filters frequency responses, phase

delays and stability. The frequency response can be seen in

figure 3. All responses are plotted in the same graph so the

magnitude response of every filter for a same frequency can

be easily compared. It is clear that the IIR response is much

more adequate for noise suppression purposes while the MA

would still provide the best step response.

The phase delay of the filters were not evaluated at the

simulation step as their temporal responses are much more

important and are examined further in the development process.

The FIR and MA filters are inherently stable and a pole-zero

plot of the IIR filter would show that every pole is inside

the unit circle of the Z plane, being also stable. The stability

was tested after the truncation of the filter coefficients for

fixed-point use.

0 100 200 300 400 500-450

-400

-350

-300

-250

-200

-150

-100

-50

0

Frequency [Hz]

Mag

nit

ud

e [d

B] (a)

(b)

Fig. 4. Variable frequency response of the proposed filter. (a) IIR filterthreshold. (b) MA filter threshold.

TABLE IIFILTERS ITERATION TIME

Filter Iteration Time

Moving Average 2μs

FIR 9μs

IIR 28μs

Hybrid 48μs

The spurious samples rejection stage of the hybrid filter is

directly validated with empirical data due to its implementation

simplicity. The weighting stage, which is also validated

empirically, has a final output gain that is always 1, so if

the input filters of this stage are stable, the final output is

also stable. The weighted average between both inputs always

calculates the gain of the MA filter that is between 0 and 1. The

IIR gain receives the remainder, 1 minus MA gain. That hybrid

filter algorithm leads to a final frequency response which is

between the MA response and the IIR response, the variation

is represented by the gray area in figure 4. The threshold value

for triggering the weighted average calculation was determined

empirically, it was based on the noise magnitude observation

and is set to permit calculations only when the inputs differ in

more than 5% of the sensor range in 25 consecutive samples.

If this does not happen, the MA input receives gain 0 and the

IIR input receives gain 1, producing a good noise attenuation

output.

After simulating, the filters were implemented in C, de-

bugged with a random noise generator code, and ported to

the application. With the filters running at the microcontroller,

their iteration times could be verified, being then possible to

evaluate if they fit in the time constraint, which was previously

determined to be 50μs. Table II shows the time consumed by

every filter to calculate its outputs.

The timing verification was made with an oscilloscope.

It measured one microcontroller digital output which was

switched at the beginning and end of every filter execution,

resulting in a square wave. The table data shows that the MA

filter is very time efficient because it can be implemented with

3 operations. The FIR filter needs to recalculate every new filter

gain when a new input is received thus having an increased

Computer

Delta-Connected

Inductive Load

Frequency

Inverter

Human

Interface

3ϕ

Input

3ϕ Output

Set-Point Filtering Data

Fig. 5. Hardware test bench set to acquire empirical data.

iteration time. The IIR filter would have the same iteration time

of a 12th order FIR (being faster than the implemented FIR

filter) if their input/output gain ratio was not so small. That

difference requires some extra operations to keep its precision

when implemented in fixed-point architectures, which is the

case. The hybrid filter iteration time is the sum of all processes

involved in all filter stages: 8μs used to take a second sample

from an analog input, 2μs to calculate the first filter stage,

28μs to iterate the IIR filter of the second stage, 2μs to iterate

the MA filter of the second stage and 8μs to calculate the third

stage. That extra sample time could have been removed from

the calculation as it is not part of the filter. It was decided to

add this time to the hybrid filter because its first stage requires

more data than the other filters, thus this extra-sampling is a

requirement of the filter, being only executed because of the

filter needs.

The timing constraints were met by every filter implementa-

tion. The next step in the development was to retrieve empirical

results of the noise filtering. To perform that task, a test bench

was set both in software and hardware. The software test bench

removed the control loop from the equipment, leaving only all

the filter implementations working in parallel so the filters can

produce a different output from the same input, making it easier

to generate benchmark data. A simple communication protocol

was also left in the code so an external computer could acquire

data from the equipment and control its outputs. The hardware

test bench consists of a computer used to retrieve data and

command the equipment output, the frequency inverter, a 220V

AC voltage source and inductors connected in delta as the load.

Figure 5 shows the set-up built.

The first test evaluated the input and output of the first stage

of the hybrid filter. The data acquisition refers to the voltage

input of the equipment which was sampled when the system

was producing 300A, 200V AC in every phase output. It is

known that the system produces more noise when the output

power is higher, justifying the need to excite the load. Figure

6 shows the gain of the first stage of the filter. It is possible

to determine graphically that the first stage produces a very

good result suppressing spurious samples.

A second test evaluated the final performance of all filters in

terms of step response and noise attenuation. Using the same

2900

2910

2920

2930

2940

2950

2960

2970

2980

2990

3000

0.00 100.00 200.00 300.00 400.00 500.00 600.00 700.00

Volt

age

[dV

]

Time [ms]

(a)

(b)

Fig. 6. Results of the first stage of the hybrid filter narrowband noise rejection.(a) Filter input. (b) Output of the first stage of the filter. The stage outputindicates that the proposed method suppresses most of the undesired samples,providing a better input signal for the next stage.

analog input as reference for the comparison, the step was

generated by changing the input voltage with a contactor that

opens and closes the power input line of the equipment. The

noise attenuation test was made with the same conditions of

the previous tests, 300A and 200V AC in every phase output.

The results are shown in figures 7 and 8.

The step response chart shows that the hybrid filter takes a

little longer than the MA filter to start converging to its new set-

point, this happens because of the decision process of changing

the weights, which expects the difference between the MA

input and the IIR input to be bigger than 5% in 25 consecutive

samples. This mechanism is used to certify that random noise

won’t make the third stage detect an input step spuriously,

after the step is detected, the hybrid filter reproduces the MA

output just before it reaches the new set-point. As the MA is

a 20-delay filter, it is convenient to use all its settling time to

certify that a step really occurred.

The FIR filter takes a little longer to converge, which is

justified by its bigger amount of delay stages and for its smaller

gains on the most recent samples that run through the filter. The

IIR filter is slower that the others, taking around 500ms to settle.

It is noticeable that the Chebyshev signal has a ripple during

its settling time, this is due to its 8dB passband attenuation

and is not considered an issue to this application. After the

step, the third stage of the filter gradually returns the gain of

the weighted average to the IIR filter. This happens linearly

on time and only when the difference between the inputs is

smaller than 5%, ensuring that the step phase is over.

The steady state of the filter worked as expected, the gain

of the weighting stage is completely bound to the IIR filter

input, making their responses identical. It is also possible to

verify the problems caused by narrowband noise in the FIR

and MA filters outputs.

Table III quantifies the results shown in figures 7 and 8. The

0

500

1000

1500

2000

2500

3000

3500

10 30 50 70 90 110 130 150 170

Vo

lta

ge [d

V]

Time [ms]

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 7. Step response the filters. (a) Input voltage of the equipment, inputsignal for all filters. (b) MA filter response. (c) FIR filter response. (d) IIRfilter response, reached its new set-point on 500ms. (e) Hybrid filter response.(f) IIR gain at the third stage of the hybrid filter, the range is from 0 to 1000,meaning a weight multiplier that varies from 0 to 1.000. The MA gain is1000-IIR gain.

2860

2870

2880

2890

2900

2910

2920

0.00 200.00 400.00 600.00 800.00 1000.00 1200.00

Vo

lta

ge

[dV

]

Time [ms] (a)2860

2870

2880

2890

2900

2910

2920

0.00 200.00 400.00 600.00 800.00 1000.00 1200.00

Vo

lta

ge

[dV

]

Time [ms] (b)

2860

2870

2880

2890

2900

2910

2920

0.00 200.00 400.00 600.00 800.00 1000.00 1200.00

Vo

lta

ge

[dV

]

Time [ms] (c)2860

2870

2880

2890

2900

2910

2920

0.00 200.00 400.00 600.00 800.00 1000.00 1200.00

Vo

lta

ge

[dV

]

Time [ms] (d)

Fig. 8. Noise attenuation results in a noisy environment. The frequencyinverter was producing 100kW in its output. (a) Steady state voltage inputsampled by the equipment. (b) MA filter output. (c) FIR filter output. (d)IIR/Hybrid filters identical outputs.

signal to noise ratio was calculated by dividing the mean signal

value by its standard deviation (5). This is a good approach

to calculate the noise over a DC signal because it provides a

very accurate dispersion measurement, which is dimensionless.

SNR =μ

σ(5)

The step response time was calculated from the moment

that the step occurred until the moment that the signal reaches

97% of its set-point.

IV. CONCLUSION

Simulations and empirical data show that the proposed

hybrid filter is capable of yielding a good noise attenuation

while still providing a satisfactory step response, even in

noisy environments. The proposed approach is suitable for

applications that operate with very strict time limits. Its basic

TABLE IIIFILTERS STEP RESPONSE TIME AND STEADY STATE NOISE ATTENUATION

Filter Step Response Time SNR

Input Signal ---- 140.83

Moving Average 16ms 343.69

FIR 28ms 304.82

IIR 496ms 704.01

Hybrid 16ms 704.01

topology relies on the fact that the weighting stage of the filter

receives an input that responds well to steps and another that

has a good noise attenuation.

The filter was tested on a frequency inverter that already runs

on 6 American locomotives. Each one provides up to 100kW

of AC power (every locomotive has 3 inverters installed)

that drives blower/air compressor motors, generates 200V

AC to auxiliary systems and produces power to the cabin

heater/air conditioning system. They also provide power to

the battery charging equipment that together with the blowers

and compressors are critical to the locomotive operation. It is

expected that this filter will make the inverters safer and more

energy-efficient.

Some further development can be made to improve noise

attenuation depending on the IIR filter used, other applications

can use this filter topology and adapt it to solve problems

related to electromagnetic interference caused by its switching

converters and rotating loads.

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