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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 22, NO. 1, JANUARY 2007 223

A Novel Method for Selective Harmonic Eliminationin Power Electronic Equipment

Vladimir Blasko, Senior Member, IEEE

AbstractThe algorithms for adaptive canceling of selected har-monic components have been well developed in digital signal pro-cessing. In those applications, filtering is a primary objective.However, in power electronic applications control, with objectiveslike fast responseof systemon reference and disturbance change, isof primary importance. This paper provides a novel and a system-atic design approach for applying signal processing methods (likemodified adaptive selective harmonic elimination algorithms) asan addition to conventional control. Thus, both control objectiveslike fast transient response and efficient harmonic (disturbance) fil-tering are achieved. The filtering algorithm does not interfere andhas minimal impact on the stability of the primary control loop. Itssole function is to eliminate undesirable higher harmonic compo-

nents from selected variable (current or voltage) and it requiresonly knowledge of the frequency of the component to be elimi-nated. The methodology is applicable for a wide range of equip-ment like uninterrupted power systems, regenerative converters,active power filters, etc. The application of the proposed methodin a regenerative voltage source converter for dead time compen-sation is used as an example for illustrating its effectiveness anddesign procedure.

I. INTRODUCTION

PLANTS like three phase regenerative converters, uninter-ruptible power supplies, motor drives, etc. are often im-

plemented with proportionalintegral (PI) or similar regulatorsfor control. The controllers are designed to provide the neces-sary dynamics required by the system in terms of bandwidth andstep response.However, there are disturbancesin the system thatcreate harmonic distortion of control variables. The examplesof sources of disturbances are: a) blanking time of pulsewidthmodulation (PWM), b) distortion of the utility voltage due tonotching created by silicon-controlled rectifier (SCR) bridges,and c) nonlinearities in the system like saturation of reactors,nonlinear loads etc. The bandwidths of regulators when imple-mented in a discrete domain/microprocessor are limited by thesampling rate and are usually not sufficiently high enough toprovide satisfactory rejection of such a high frequency of peri-

odic disturbances (above 300 Hz).One way to cope with the limited bandwidth of regulators isto use predictive regulators[1]which are able to reach the de-sired value in one or two sampling intervals. However, usage ofpredictive and dead bit regulators requires knowledge of plantparameters. Additionally, predictive regulators lack the robust-ness to disturbances that are often random in nature and hard toincorporate in the model. The alternative to fast regulators is to

Manuscript received February 6, 2006; revised April 16, 2006. Recom-mended for publication by Associate Editor J. Enslin.

The author is with the Otis Elevator Company, Farmington, CT 06032 USA(e-mail: [email protected])

Digital Object Identifier 10.1109/TPEL.2006.886599

use synchronous regulators working in the reference frame ro-tating with the circular frequency of the harmonic componentthat should be eliminated,[2],[3],[4]. For practical purposessynchronous reference frame regulators can be transformed andimplemented in a stationary frame of reference preserving theiroriginal features from synchronous reference frame. Thus, har-monic components can be selectively eliminated. The genericsynchronousreference frame regulators generally, when appliedfor selective harmonic elimination, require low pass filteringwith associated delay and are more suited for three then forsingle-phase applications.

In [5], a generic adaptive noise-canceling algorithm forelimination/filtering of single frequency from signal, as usedin digital signal processing (DSP) [6], was introduced. Thealgorithm was modified to take plant characteristics into ac-count. The methodology was developed for combining the filterwith the already existing regular proportionalintegral (PI)controls of the plant.

In this paper, the additional theoretical treatment and furtherimprovements to increase speed of convergence and simplifyuse of the method from[5]are provided. The method is appli-cable to the broad class of single and three phase power elec-tronics equipment like active power filters, uninterrupted power

systems (UPS), active front end converters in drives etc. Nomodifications are required for the method to be used in syn-chronous or stationary reference frame.

A three-phase regenerative front-end voltage source converterwas used for the simulation to verify the effectives of the de-veloped adaptive selective harmonic elimination (ASHE) algo-rithm. The effectiveness was investigated by simulation to elim-inate the fifth and seventh harmonics in line currents. The har-monics in the current were created by dead time and distortionof utility voltage.

II. SINGLEFREQUENCYADAPTIVE SELECTIVE

HARMONICELIMINATIONFILTERThe task of eliminating an undesirable harmonic component

from a signal in DSP can be done by the ASHE algorithm orfilter. The filter, shown inFig. 1, consists of a combiner, a leastmean square (LMS) adaptation algorithm, and a summing point.It operates in the following way[6].

a) The reference signal with two orthogonal components co-sine and sine ( and ) is sampled. It has the frequency

2 . The frequency 2 should be elimi-nated fromprimaryinputsignal . isa samplingperiodand is a discrete time index.

b) The reference input (vector with and components)

is multiplied by corresponding weights ( and ). The0885-8993/$25.00 2007 IEEE


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224 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 22, NO. 1, JANUARY 2007

Fig. 1. Structure of a singlefrequencyadaptive selective harmonic elimination/cancelingfilter.

Fig. 2. Block diagram of LMS algorithm(5).

weighted sine and cosine components of reference signal

are combined/added together to match amplitude and

phase angle of interfering sinusoid in the primary input

. Adaptation process adjusts weights to exactly match

amplitude and phase of the interference[6].

c) The signal , created by a combiner, is subtracted from

the primary input (signal to befiltered) and eliminatedfrom the output of the filter . Signal inFig. 1 hasa dual meaning: a) it is the output of the filter, and atthe same time it is also b) an error signal for adaptation

process because it contains harmonic-error component to

be eliminated.

The LMS adaptation algorithm as developed in[6] will be

briefly reviewed. The error estimate follows fromFig. 1

(1)

The reference and weight vectors are defined as

(2)

(3)

If is used as an estimate of then in each iteration

step the gradient can be estimated as

(4)

With an estimated gradient as in(3),the steepest-decent type of

algorithms can be used for weight adaptation

(5)

where is the adaptation gain constant, it regulates speed and

stability of adaptation. Without averaging, by using as an esti-mate of , the gradient estimate(4)contains a substan-

Fig. 3. Integration of ASHE and regular plant control.

tial amount of noise which is attenuated by the adaptive process

(5). To quantify noise attenuation(5)can be viewed as discrete

implementation of the integrator with product as an input.

The salient features of the LMS algorithm(5) with block dia-

gram inFig. 2are its elegance, efficiency, and simplicity.

III. INTEGRATION OFASHE FILTERINTOPLANTCONTROL

To integrate/combine ASHE with existing control of the plant

the following assumptions are made.

a) The adaptation process of ASHE is slow. Therefore, the

ASHE does not interfere with dynamics and does not alter

the transfer function of the plant and associated control.

The signal generated by the ASHE and injected into the

plant from the regular plant control looks like disturbance.

b) The harmonic component to be eliminated by the ASHE

has a high frequency highly above the bandwidth of reg-

ular control.

The consequence of the above assumptions is that there are

no interactions between regular control and ASHE. Therefore,

both ASHE and plant control can be analyzed separately.

The ASHE algorithm combined with plant control is shown

inFig. 3. The configuration inFig. 3 differs fromFig. 1, andprimary input

(6)

consists of the control input created by regular plant con-

trol and harmonic distortion component with known fre-

quency. The plant output is connected to the error input

of the ASHE. The objective is to eliminate undesired harmonic

component from plant output which is created by . The

elimination is accomplished when output of the ASHE multi-

plied with an inverse transfer function of the plant matches the

harmonic component in the signal .

It is important to note that reference in regular control

should not have harmonic component content . Such a com-

ponent can be created in the case of cascaded control by the

outer control loop whose output is reference input into innercontrol . In this case, the separation principle between regular


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BLASKO: NOVEL METHOD FOR SELECTIVE HARMONIC ELIMINATION 225

and harmonic control will be violated. The harmonic controller

in inner loop will work to eliminate harmonic component gener-

ated by controller in outer loop, which will evidently be needed

for achieving objective of outer control loop.

A. Incorporation of Inverse Transfer Function of the Plant in

ASHE

The propertythat gains and changes muchmore slowly

then the variables in the system is intrinsic to the adaptive algo-

rithms [7]. The rateof change/adaptation of gains and can

be made arbitrarily slow by choosing an adaptation gain that

is sufficiently small. In practical terms, it means that the adap-tive gain should be selected low to takefive or more periodsof harmonic component for the gains and to reach the

final value. One of the results of slow adaptation is attenuationof high frequency components from the input to propagate

to the output of the LMS algorithm(5).

In thefirst approximation, the slowly changing gains and

can be assumed to be constants. With this assumption, theplant transfer function in output signal from ASHE

(7)

acts as a linear operator on sine and cosine inputs into the com-

biner. Therefore, can be implemented as linear combina-

tion of sine and cosine functions from reference input. Thus,

the need for the direct implementation of the dynamic inverse

model of the plant is avoided.

The example of a resistanceinductance ( ) plant with in-verse transfer function estimate will be used to

illustrate the process. For an plant the output of the ASHEis

(8)

or linear combination of sine and cosine functions from the ref-

erence input. Note that allows the term with resis-

tance to be neglected. Also, there is no need for explicit knowl-

edge of the inductance, the LMS algorithm will incorporate it in

the weights through adaptation process namely

(9)

The block diagram of ASHE derived based on the above as-

sumptions with incorporated inverse transfer function of the

plant is shown inFig. 4. Note a change in polarity at the sum-

ming point. Also, weights and multiply sine and cosine

inputs, respectively (opposite than in the original combiner in

Fig. 1). For this particular case, the complexity of the struc-

ture of combiner plant inverse did not increase and is compa-

rable with complexity of combiner only. Using(7) and proce-

dure as described any other plant transfer function can be easily

integrated with combiner and only knowledge about plant (ortransfer function) type, not plant parameters is required.

Fig. 4. ASHE with incorporated inverse transfer function of the plant

.

Fig. 5. Elimination offifth and seventh harmonics from the controlled plant(single phase) output

by multiple frequency ASHE block (MF ASHE).

B. Selective Elimination of Multiple Harmonics

Selective elimination of multiple harmonics is illustrated in

Fig. 5. Thefifth and seventh harmonics are eliminated from theoutput variable of the plant . The expansion to eliminate theother harmonic components can be done by adding blocks like

fifth and seventh. Additional blocks will have the same errorinput , frequency of the reference signal will be equal to the

harmonic component to be eliminated and the output will be

added to the outputs of the previous blocks (5 and 7).

Using the block 1, which contains ASHE from Fig. 1, the

first harmonic is taken out of the primary input . This step,although not necessary, considerably reduces noise in gradient

estimation in blocks 5 and 7 (for elimination offifth and seventhharmonics) and makes adaptation process faster. The output of

the block 1, withfiltered outfirst harmonic and withfifth andseventh harmonic components still present, is introduced to theerror inputs of the blocks 5 and 7. Those blocks have ASHE


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Fig. 6. Integration of two ASHE blocks fromFig. 5in the control of regener-

ative converter for selective elimination offifth and seventh harmonics.

with built in inverse transfer functions of the plant. In the case

of the plant these blocks will look like the one inFig. 4.

IV. APPLICATION EXAMPLE ON A THREE-PHASE

REGENERATIVE CONVERTER

The application of ASHE in the regenerative front-end

voltage source converter as a representative of three-phase

equipment is illustrated in Fig. 6. The converter had PI con-

troller U reg for dc bus voltage control and two PI regulators,

Iq reg and Id reg implemented in synchronous reference frame

for current control. Reference angle for generation of sine and

cosine functions with frequency of fundamental component

and frequencies offifth and seventh harmonics is created by aphase look loop (PLL) block. Sine and cosine components with

fundamental frequency are phase locked with utility voltage

and are used for stationary to synchronous (and vice versa)

reference frames transformations. Sine and cosine components

with five and seven times higher frequencies are used forselective harmonic elimination. Sampled currents from

the stationary (a,b,c) reference frame were transformed into

two phase stationary reference frame (block 3/2) and

then into synchronous reference frame (block s/e).

The conventional part of control works as follows: voltage

regulator U reg depending on dc bus voltage error creates an

active current reference . For unity power factor reactive cur-rent reference is kept at zero. PI current regulators maintain

an average value of feedback currents and equal to the

average values of corresponding references. Outputs of current

regulators are transformedfirst from synchronous to stationaryreference frame (block e/s) and then from two-phase ( ) to

three-phase (a,b,c) system and written into PWM to control con-

verter insulated gate bipolar transistor (IGBT) bridge. Due to the

limited bandwidth, PI regulators are not able to suppress high

frequency components from current feedback.

To eliminate harmonic components from three phase-load

currents, a similar approach to the single-phase generic solu-

tion inFig. 5was adopted. The elimination was done in the sta-

tionary two-phase rather then the three-phase a,b,c system.Two separate MF ASHE ware added around existing current

Fig. 7. Waveforms of input-line currents of (a) a regenerative converter and (b)

spectrum of current showingfifth, seventh, 11th, and 13th harmonic compo-nents.

control loops, gray block in Fig. 6. Currents and wereintro-

duced into associated MF ASHE blocks, each with a diagram as

inFig. 5. The outputs MF ASHEs were added (with minus po-

larity) to the transformed signals from PI regulators. Summed

signals were after 2/3 transformations introduced into PWM.

The components contributed to PWM from ASHE blocks will

create voltage at the output of the inverter with amplitudes and

phase angles as needed to cancel harmonic components from

the load currents.

V. RESULTS OF SIMULATION

To illustrate the effectiveness, the operation of a three-phase

regenerative voltage source converter was simulated with un-

compensated dead time without and with ASHE algorithms. The

PWM frequency was 10 kHz and dead time was 4 s. Sam-

pling rate was 5 kHz. The dead time creates current distortion

as shown inFig. 6with the most significantfifth and seventhand smaller 11th and 13th harmonicsFig. 7. Although used forelimination of harmonics created by dead time, the algorithm


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BLASKO: NOVEL METHOD FOR SELECTIVE HARMONIC ELIMINATION 227

Fig. 8. Improved waveforms (a) of input-line currents and (b) spectrum of linecurrent

after applications of MF ASHE.

willfilter out distortion created by any other source (like dis-tortion of input line voltage) with the harmonic components for

which thefilter is designed for.The improved waveforms of line currents after applications

of MF ASHE for elimination of onlyfifth and seventh compo-nents are shown inFig. 8. Note that practically complete elim-

ination offifth and seventh harmonics. The 11th and 13th har-monics remained unchanged. For further improvement of wave-

form and elimination of 11th and 13th harmonics the extensionof MF ASHA filter is a straightforward task and can be deductedfromFig. 5.

Fig. 9shows coefficients of the adaptivefilters andfor the first, fifth, and seventh harmonics for current as a func-tion of time. Note fast convergence, the coefficients reached thefinal value practically after 0.1 s. Note that for the (heuristically)selected adaptation gain thenoise from harmonic weightcoefficients (Wc5, Ws5, Wc7, and Ws7) was substantially re-duced when the weights of fundamental components (Wc1 and

Ws1) reachedfinal value. After that, fundamental componentwas reconstructed and removed from input/error signal usedin further adaptation processes for weights (Wc5, Ws5, Wc7,

and Ws7). It shows usefulness to filter out the fundamental com-ponentfirst and then use only remaining signal as the input for

Fig. 9. Coefficients of the adaptivefilters and for thefirst,fifth, andseventh harmonics for current as a function of time.

adaptation in higher harmonic blocks. Alternatively, without use

of block 1, the noise in weight coefficient can be reduced by fur-ther reduction of adaptation gain , however with consequence

of slower convergence.

VI. CONCLUSION

The disturbances in power electronics equipment are often

periodic and rich in higher harmonics. They have known fre-

quencies and are often above the bandwidth of regulators used to

control fundamental components. Therefore, theregularcon-trol can only partially reduce their effects on the distortion of

control variables.The ASHE method was developed to be used as an addition

to the regular (primary) control for elimination of selected har-

monic components from control variables. The ASHE takes as

the input the control variable with undesirable higher harmonic

component. Through an adaptive process it creates harmonic

signal, which is injected into the system in order to the cancel

harmonic component in the control variable. The speed of adap-

tation of an ASHE algorithm is assumed to be well below the

bandwidth of the primary control and thus it has negligible im-

pact on the dynamics of the primary control loop. Therefore,

both ASHE and plant control can be analyzed separately. Only

knowledge of the frequency of components to be eliminated and

character (not parameters) of the plant are required for the de-sign. The extension of cancellation of single to cancellation of

multiple higher harmonic components is illustrated in the paper.

The effectiveness of the ASHE was verified by simulationof a regenerative converter with a distorted current by uncom-

pensated dead time in PWM. The algorithm was able to effi-ciently eliminatefifth and seventh harmonics form line current.For the fast convergence it was found useful tofilter out funda-mental components and use only the remaining signal (higher

harmonic-distorted currents) for adaptation as shown inFig. 5.

REFERENCES

[1] S.-G. Jeong and M.-H. Woo,DSPBased active power filter withpredictive current control,IEEE Trans. Ind. Electron., vol. 44, no. 3,pp. 329336, Jun. 1997.


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[2] P. Mattavelli, A closed-loop selectiveharmonic compensationsfor ac-tivefilters,IEEE Trans. Ind. Appl., vol. 37, no. 1, pp. 8189, Jan./Feb.2001.

[3] M.J. Newman and D.G. Holmes, Delta operator digital filters for highperformance inverter applications,IEEE Trans. Power Electron., vol.18, no. 1, pp. 447454, Jan. 2003.

[4] X. Yuan, W. Merk, H. Stemmler, and J. Allmeling,Stationary framegeneralized integrators for current control of active power filters with

zero steady-state error for current harmonics of concern under unbal-anced and distorted conditions,IEEE Trans. Ind. Appl., vol. 38, no. 2,pp. 523532, Mar./Apr. 2002.

[5] V. Blasko,Adaptivefiltering for selective elimination of higher har-monics from line currents of a voltage source converter, inProc. IEEE

Ind. Appl. Society Annu. Meeting, St. Louis,MO, Oct.1215,1998, pp.12221228.

[6] B. Widrow and S. D. Stearns, Adaptive Signal Processing. Engle-wood Cliffs, NJ: Prentice-Hall, 1985.

[7] K. J.strm and B. Wittenmark, Adaptive Control, 2nd ed. Reading,MA: Addison-Wesley Publ. Co., 1995.

Vladimir Blasko(M89SM97) received the B.Sc.,M.S., and Ph.D. degrees from the University of Za-greb, Croatia, in 1976, 1982, and 1986, respectively,all in electrical engineering.

From 1976 to 1988, he was with the Elec-trotech-nical Institute of Koncar Company, Zagreb,in the Power Electronics and Automatic ControlDepartment. From 1989 to 1992, he was with the

Research and Development Center of Otis ElevatorCompany, Farmington, CT. From 1992 to 2000, heworked for Rockwell Automation Allen Bradley

Company, Mequon, WI. Currently, he is with the Drives and Motion Depart-ment of Otis Elevator Company Farmington, CT. During the academic year

19881989, he was a Postdoctoral Fellow at the University of Wisconsin(UW), Madison. His primary areas of interest are modern ac drives, powerelectronics, intelligent power management, and applied modern control theoryand technology.

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A_Novel_Method_for_Selective_Harmonic_Elimination.pdf