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Review of Current Regulation Techniques For Three-phasePWM InvertersMarian P. Kaunierkowski*, Maciej A. Dzieniakowslu**

Warsaw University of Technology, Institute of Control and Industrial Electronics,00-662 Warsaws, ul. Koszykowa 75, Polandphone:+48+2+6280665; fax:+48+2+6256633; e-mail: [email protected]*, [email protected]*

Abstrocr - This paper presents a review of recently usedcurrent regulation techniques for Voltage Sourced Pulse WidthModulated (VS-PWM) inverters. A variety of techniques,different in concept, are described , as follows: On-Offhysteresis free running and fued frequency regulators (phaseindependent, look-up table based, space vector based), linearregulators (carrier based, working in stationary and rotatingcoordinates, PI and state feedback), predictive (minimum andconstant switching frequency) and dead beat regulators. Also,nowadays trends in the current regulations - neural networksand fuzzy logic based regulators - are presented Someoscillograms which illustrate properties of the presentedregulator groups are shown. The references include 96 actualpapers and conference contributions.INTRODUCTION

Current regulation technique plays the most important role inCurrent Regulated PWM (CR-PWM) inverters which are widelyapplied in ac motor drives, ac power supply and active filters. TheCR-PWM inverters, also known as current mode PWM hverters,implement an on line current feedback (closed loop) type of P W M[34]. In comparison to a conventional f eedfomd (open loop)voltage controlled PWM inverters they shows following advantages:- control of instantaneous peak current (this is of particularimportance for tramistor-type power semiconductor devices,which arepeak current sensitive),- overload problem is avoided,- pulse droppii problem does not occur,- extremelygood dynamics,- nearly sinusoidal current waveforms, expect for the hannonics- small c m t also torque in ac drives) ripple in the wide output- compensation of the effect of load parameter changes (resistance

andreactance).The basic problem involved in the implementation of CR-PWMinverters is the choice of suitable current regulation strategy, whichaffects both the parameters obtained and the fmal configuration ofthe entire control system. Lastly, the performance and cost criteriaare desired factors when designing CR-PWM inverters.

which are basicallylinked o the switching Erequency,f r e s U e n C Y

BASICEQUIREMENTSNDFERFOWCE CRITERIAThe main task of the control system in CR-PWM inverter is toforce the current vector in the three phase load according to thereference trajectory. The basic requirement are as follows:

- no phase and amplitude mors (ideal tracking) in wide output- fast response to provide high dyndmic of the system,-limited or constant switching Erequency to guarantee safe- good dolink voltage utilisation.

Erequencv range,operation of power semiconductor switches,

The applied performance criteria can be divided in tw o groups(see able):- criteria specific for CR-PWM inverters e), based on current errordefition- criteria which are also valid for open loop voltage PWM (see .g.

[34,72,731) Performance CriteriaI Criteria definition I Comments I

h,(k-f,) -discretecurrent spectrah&f) - density current spectraON-OFFCURRENTEGULATORS

Variable switching frequency hysteresis regulatorsThe simplest current regulation scheme is based on a nonlinearfeedback loop with two-level hysteresis comparators (Fig.1) [82].However, this class of the systems, also known as fke-runninghysteresis regulators [73], has he following disadvantages:

- the inverter switchmg fiequency depends largely on the load- the operation is somewhat rough due to the inherent randomnessis

parameters and comparator hysteresis band,caused by limit cycle, therefore protection of the inverterdifficult [65].

1C

Fig. 1. Free-running hysteresis regulator: block scheme (a),switching rajectory (b)

a

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It is characteristic for the hysteresis regulators that the instau-taneous current is kept exact in tolerance band except systemswithout zero loaders, where the instantaneous emx can reachdouble value of the hysteresis band [12,61] (Fig.2).

1 I

-0.151 I-0.15 E a 01 5

0 m 20 -0.6 i, 0.6

Fig. 2. Free-running hysteresis regulator (Ah4.05):output currents(a), phase current error (b), vector current area (c), output vectorcurrent loci (d)This is due to the interaction in the system with three independentcontrollers. The comparator state change in one phase influencesthe voltage applied to the load in tw o other phases (couphg). How-ever, if al l three CuITent are considered as the space vector[80], the interaction effect can be compenwed, nd many variantsof regulators known as space vector based, can be created[28,44,91,94]. Moreover, if a look-up table with three-levelcomparators will be applied, a d d e r a b l e &creasing of theinverter Switching 6qu ency can be achieved [1,44,45,47,94]. Thisis thanks to appropriate selection of zero voltage vectors [44](Fig.3).

" 0 m 40Fig. 3.Number of inverter sw i t chs N of three different types ofcurrent regulators: three two-level hysteresis comparators (a), spacevector based regulator with three-level comparatos and look-up tableworking in the stationary@) and otating (c) coordinatesIn the synchronous rotating coordinate systems, the hysteresisregulators offer additionally the - of independent har-monic selection by choosing different hysteresis values [45,47,83].This can be used for the torque ripple minimisation in the vectorcontrolled ac motor drives (hysterese for torque current componentis set lower then for flux current component) [45].The main advantages: simplicity, load parameter changesindependence, lack of tracking errors, and extremely good dynamicsmake the hysteresebased regulators stillattractive to researchesanddesigners.The nowadays works enable limit cycle suppression by introducinga suitable offset signal to either current references or hysteresis

band [87,92]. Also systems with variable hysteresis width to keepthe switching fiquencyin very l imted variation range areproposed[6,10,61,62].Limited switchingfrequency regulators

A special class of On-off current regulators are systems based onthe delta modulation principle [sa]. The basic scheme, known asDelta regulator [SO], is shown in Figure 4.

Fig. 4. Delta modulation current regulator - basic block schemeThanks to a S&H block applied after ideal comparator, thes w i t c h fi-equency is l imted to the sampling fresuency f,. Theamplitude of current hamoNcs isnot constantbut is determined byload parameters, b l i n k voltage and sampling frequency. If thesampling signal in the three-phase system is shifted 120"el. in eachS&H block (FigSa), only one of the inverter legs will change itsstate during sampling period l/fs This guarantees only neighbourvoltage vectors selection and collsequentlybetter quality of currentformation (lower RMS, J) at this same sampling 6quency fs(FigSb) [18].

b ) o . l ~ o . l ~ - -

0 0 T O TFig. 5. Delta modulation current regulator: sampling techniques (a)and quality factors (b)This type of the discrete cutTent regulators have found a wideapplication in the three-phase resonant b l i n k converters with zerovoltage switchmg technique where the sampling signal is deliveredfiomzerocrossingdc ink voltage [27,46,50,79,93].It is noteworthy, that the delta modulation technique can also beapplied in the space vector based regulators working in the sta-tionary or the rotating coordinate systems [93,95].

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The main advantages are an extremely simple and h fadjustment hardware implementation and good dynamics.Fixed switching requency regulators

A serious drawback of the fiee-running hysteresis and deltamodulation based regulators is the variable switchmg fkquency,which produces an unpleasant Bcousfic noise. For that reason incommercial applications only fmed-kqwcy based regulatm areapplied. This is achieved by using carrier signal which may bedeliveredto the comparator input as shown in Fig. 6.

41

Fig. 6. Fixed kquency hysteresis regulatorIn this way one obtains asynchronous sinetriangle PWM in whichthe current error constitutes a modulatingsignal [12]. Conseqwtly,the inverter becomes switched with the triangular wave frequencyand produces well4ehed harmonic spectrum [73]. This is theessentiaI advantage of this technique. Its disadvantage is inherenttraclung error [12,61,80]. The constant mean switchmg kquencycan be achieved by approPriate reduction of the inverter phaseinteraction and PLL control of the hysteresis width [61,62]. Thisclass of regulators guarantee fast response without traclung errors,but the umtrol algorithm is m m omplex and the main advantageof the hysteresis umtrol -namely the simplicity- is lost.

Lmm REGULATORSIn addition to nonlinear On- regulators, there are linearregulators which operate in association of conventional voltage typePWM modulators. Therefore, in contrast to the hysteresisregulators, this class of the systems have clearly separated currenterror compensation and voltage modulation parts. This conceptallows to take such advantages of feedforwad modulator(sinusoidal PWM, space vector modulator, optimal PWM) as:constant switching frequency, welldehed harmonic spectrum,

optimum switch pattern, &bus utilisation, etc. Also, fidlindependent design of the overall umtrol structure as well as openloop test of the inverter and load can be easy perfmed.Three PI regu lators

The regulation principle is shown in Fig. 7 [14]. In each phasethere is a linear PI regulator which, by comparing the command iAc(i%, k c ) and measured iA (iB,k) alues, generates the commandvoltage U A ~U&, wC). n keepingwith the sinusoidal modulationprinciple, there followscomparisonwith the triangular carrier signalin the comparators, which generate the inverter switches controlsignals SA(SB,Sc).

I

Fig. 7. Current regulator with threePIcontrollersThe properties of this regulator are similar to regulator typepresented on Fig. 6. However, the use of PI regulator makes itpossible, in a definite fieqwcy band, to minimise the tracking

errors of the output currents. To achieve compensation of the phaseerrors,use is alsomade of additional P U ircuits [20].Sp ce Vec torBased SynchronousRegulators

In many industrial applications the ideally impressed current isrequired, because even small phase. or amplitude errors causesi n m t ystem operation (e.g. vector controlled ac motors). In suchcases the regulation schemes based on space vector approach areapplied.

Fig. 8. Vector current regulator working in synchronous coordinateswith dc componentsFigure 8 illustrates the control principle involving the use of tw o PIregulators of current vector components defined in rotatingsynchronous rectangular coofdinates [14,49,57]. Practicalimplementationof this technique in ac drive systems involves theuse of field oriented umtml, and is based on idonnation about thefluxvector position - ys A characteristicfeatureof such control sys-tem s that, thanksto applied coordinate transformations, i and isyare dcunnponents, and the use of linear PI regulators makes itpossible to attain very high accuracy n the steady states.Based on work [88] (where it has been demonstrated that ispossible to perform current regulation in an arbitrary coordinates),in [85] a synchronous regulator working in the stationaryCOoTdinafes with accomponents is presented.As shown in Fig.9 by dashed line, the inner loop of theregulation system (consisting two integrators and multipliers) is avariablekquencygenerator, which alwaysproduces reference volt-age%,upc for PWM modulator, even when in the steady state thecurrent ermr signals arem.

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iL ll a I

Fig. 9. Vector current regulator woriung with ac componentsIn general, thanks to use of PWM modulators, the linearregulators make well defined harmonic spectrumavailable, but theirdynamicproperties are inferior to those of On-Off regulators.

1 . . . : . .'TA. . . ...: . . . . . . . . . . . . . . . . .r. :-.:j ...:...... :i

1. . . . . . . . . . . . . . . . . .: . I

I."

. n

Fig. 10. The overmodulation operation of the vector currentregulator working with ac components: output current ia (a), outputcment ip (b), output voltageU,(c), output voltage up (d), currentamplitude command signal (e)If the PWM modulator operation region is overstepped, the systemloses its stability and high peak current can occur [85] Fig.10).Therefore the system has o be appropriately protected.State Feedback Regulators

The conventionalPI regulators in the current error compensationpart canbe replaced by state feedback regulator (Fig.11) [22,53,71].This regulator works in synchronous rotating coordinates and issynthesised on the base of linear multivariable state feedback

A feedbackgainmatrix k=B~,kk]s derived by utilising the poleassignment technique to guarantee sufficient damping. While withintegral part (k~)he static error can be made zero, the transienterror may be unacceptable large. Therefore, feedforward signals for

theory.

reference @f) and disturbance(&)nputs are addedto the feedbackcontrol law.

I

Fig. 11. State feedback current regulatorBecause of more complex control algorithm the performances ofthe state feedback regulator &e Superior to conventional PIregulators [53], but the absolute criterion on pole placement is notyet established.

PREDICTIVEEGULATORSIn contrast to the above presented on-off and linear regulators,

which canbe implemented in both hardware or software way, thegroup of modern predictive regulators performs real-timeoptimisation algorithm and, therefore, can be realised by usingmicroprocessor technique only.Minimum switching fmquency algorithm

The concept of this algorithm [31] is based on space vectoranalysis of the hysteresis regulators.errorarea actual

0Fig. 12. The exampleof error area in the predictive algorithm

The boundary delimiting the current error area in the case ofindependent regulators with equal tolerance band +H n each ofthree phases d e s regular symmetrical hexagon (Fig. 1b). Suppose only one hysteresis regulator, but one acting on the currenterror vector, could substitute the set of three. In such case, heboundary of the error area (also calls as switching or error curve)might have any form (Fig. 12). The location of the error curve is&terminated by the current command vector i,. When he currentvector is reachesa point on the error curve, seven Merent trajecto-ries of the current are pmhcted, one for each of seven possible (sixactive and zero) inverter output voltage vectors. Finally, based onoptimisation procedure, the voltage vector which minimises themean inverter switching fieqwcy is selected. For fast transientstates the strategy which min im i s es the response time is applied.

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Note that the shape of the error curve is independent of the choiceof particular coordinates and, therefore, the regulator can be imple-mented in any rotating or stationary coordinates.m p h g error 'd

Fig. 13. Minimum switching frequency predictive current regulatorSimilarly to the three level hysteresis regulator working in fieldoriented coordinates x-y [45], a further switching frequencyreduction can be achieved by selection a rectangular error curvewith higher length along rotor flux direction. In practice, the timeneeded for prediction and optimisation procedure limits theachieved switching frequency. Therefore, in more recentlydeveloped algorithms a reduced set of voltage vectors consisting ofthe two active vectors adjacent to the EMF vector and the zerovoltage vector are considered for optimisation without loss ofquality [32].

Constant switching requency algorithmIn this case he predictive algorithm [64,81], once every samplinginterval T, alculates the voltage vector commands usc(T); whichwill force the current vector according to its command i, (Fig. 14).The inverter voltage us(T)and EMF voltage e(T) of the load is as-sumed to be constant over the sampling interval T. The calculatedvoltage vector usc(T) s then implemented in the PWM modulatoralgorithm, e.g. space vector modulator [28,80,81]. Thus, the errorcompensation and modulation parts - similarly as in linearregulators (see Section IV) - is separated. Note that while thecurrent ripple cannot be explicitly detenninated, the inverter

switching fresuency is fixed as 1/2T. The disadvantage of thisalgorithm is that does not guarantee the inverter peak current limit.'d..

b

Fig. 14. Constant switching frequency predictive current regulatorAlso algorithms based on dead-beat control approach andpredictive state observers of the whole control plant (e.g. vectorcontrolled ac motor or U P S systems [4,40]) as well as hybridregulators combined hysteresis with predictive technique are

proposed [55].

Optimal discrete modulation algorithm fo r Resonant DC LinkConverters (RDLC)For the RDLC converters, where only discrete type of modulationcan be used, optimal algorithm selects voltage vector whichminimalise RMS current error for each resonant pulse [27]. Asshown in [go] this is equivalent to selection the nearest availablevoltage vector commands usc(T). So, instead of PWM modulatoralgorithm (Fig.14)only voltage vector selector is required (Fig. 15).

-I load~ model

UFig.15 . Optimal discrete modulation regulator for RDLC

The typical waveforms for discrete delta modulation and optimal(minimumRMS error) current regulation are shown in Fig.16a andFig. 16b respectively.A modulation (a) optimal modulation (b)

2.3

-2.5

2.3

? C

....... ...: ..I.-..

I . -

0.0

0 ms 20 0 ms 20Fig. 16.Current regulation in RDLC, based on discrete modulationI - up, II- i,,ip, ITI - (ca2+cp2)1n, IV - RMS& J of e(t)

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Ifparameter perhubation or model uncertainty exists, however,the p e r f i i c e of the predictive regulators +.rapidly deterioratedbecause it does not involve integral part. Therefore, the ~ccuracyand robustnessof the controller can be improved by introducing anintegral compensation [56].NEW NETWORKNDFUZZYOGICBASEDEGULATORS

The problem of exact knowledge of the load parameters neededfor implementing the predictive regulators can be avoided by usingnew class regulatorsbased on fkzy logic and neural network theory.Neuml Netwonk based regulators

An example, in which the optimal discrete current regulator forRDLC (Fig.15) is replaced by off line trained neural network isshown n Fig.17. The three layer feedforward neural network, usedas egulator, is trainedbyback propagation algorithm [13].

UFig. 17.N e d Network discrete modulation regulator forRDLC

As trai ni ng signal, random selected data b m he output pattern ofthe simulated optimal regulator of Fig.15 are applied. Thewaveform obtained in the system with NN egulator are shown inFig.18. Note that NN can regulate the output cutTent very wellwithout on line calculation needed in the case of the optimalregulator.

2.5 1.5

-2.5 -1.50.5

0.00 ms 20Fig.18. Typical waveforms in the NN current regulator (comparewith Fig. 16b)

I -up, II- ia,ip III - E ~ ~ + E & ~ Q ,N RMS8t J ofgt)The robustness, very fast operation, insensitivity to loadparameter changes and 1 ability are the main advantages ofneural network based regulators. However, because of high

nonlinearity of the system, the design (learning) procedure is timeconsuming-FuayLogic based current regulators

Typically the power electronic plants are nonlinear, havecomplexity coupled parameters and it is generally difficult to applyany known analytic technique o design regulator structure. Fuzzylogic application solves this problem because fuzzvfication,delkq&ation and fuzzy rules need not be describedon he basis ofknowledge of exact mathematical modelling of the controlledsy--In basic applimtionsthe fkzy controller is used as he substituteof typical cutrent regulator (Fig. 19) [69]. The block scheme ofcurrent regulation structure is similar o the conventionalsystem.

I .i

"dJ=L

UFig. 19. Fuzzy current controllerThe currenterror and its derivative are regulator input crisp values.States of PWM modulator inputs are fkzy current regulator crispoutput commands.In suchapplications FL is used for improving properties of classical(e.g. PI) regulators.The basic block scheme of FLC, including fuzzyinference mechanism, is shown on Fig.20.

a> INFERENCE MECHWISMI

-I J

Ve r r o r

Fig.20. Fuzzy Logic Controller: auto-tuned PIcontrollera) block scheme of FLCb) control surf- of classicalPI controllerc) controlsurface of FLcontrollerThe contents structure of all blocks largely depend on expertisingknowledge base. Its gives possibility to form static and dynamicregulator properties (Fig.2Oa and Fig.ZOb), ac"g to p i t i cneeds of whole regulation structure, n whole control range.Figure 21 presents one phase VSI output current in the case of usingclassicalPIandFL based regulators.

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Fig.21. One phase VSI output current waveforms (a) and currenttrajectory (b) in the c ~ s e f step change of command signalamplitude.However, advantages of f t m y controllers pdaspose thisregulator type to application in more complex systems, in whichexcept culTeat regulation there are another system tasks - flux andtorque (701,speed and position 1781 regulations.

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