Bust Control Pwm

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Control Strategies for Voltage Control of a Boost T ype PW M C onverterR. S. Pens''),R. J. Cardenas('), J.C.Clare'2), G.M.Asher(*)(1) Electrical Engineering DepartmentUniversity of Magallanes.Punta Arenas. [email protected]

Abstrad This paper addresses the non-linear problem ofregulating the DC link voltage, in a vector controlled three-phase boost type PWM converter with particular emphasis onapplications in wind energy systems. The AC side currentcontrol is performed in a synchronously rotating referenceframe. An analysis of the system is provided and severalalternative DC link voltage controller designs are investigatedand compared. Fuzzy controllers augmented using a feed-forward compensation technique are found to provide excellentperformance. A 3kW experimental set up has been built andexperimental results are provided to validate the controldesigns.

I. INTRODUCTIONBoost type PWM converters provide a bi-directional DC-AC interface with high quality currents on the AC side andcontrollable displacement factor [1-41. The converter findsmost use as the "front end" in AC drive applications where itallows non dissipative regeneration capability and nearlysinusoidal input currents. This paper, however, concentrates

on Wind Energy Conversion Systems (WECS), where theboost converter is used as the interface to the AC grid system.When induction machines are used for grid connectedvariable speed WECS, for example, two back to backconverters are required for squirrel cage m achines [4,6,7] aswell as for doubly fed induction machines [5-81. Control ofthe AC side currents is usually carried out in a d-qsynchronously rotating reference frame [1,2]. Highbandwidth current response is then achieved and furthermorede-coupled control of the active and reactive power flowbetween the converter and the grid is possible. In a WECS,there may be a number of generation sources/loads connectedto the DC link in general as shown in Fig. 1. The converterpower flow must be controlled in order to regylate the DClink voltage E d c according to a reference value E dc .This paper concentrates on control strategies to regulate

the DC link voltage. The problems created by non-linearimpedance on the DC side are addressed particularly whenthe characteristics of the DC side generation/load areunknown. A PI type fuzzy logic controller is proposed andfeed-forward or load compensation is used to improve theperformance of the controller to load disturbance rejection.State observers are used to estimate the load current needed

(2 ) School Electrical & Electronic Engineering.The U niversity of NottinghamNottingham. [email protected]

for the feed-forward compensation. Experimental resultsobtained from a 3kW prototype are discussed and theperformances of the control strategies are compared.

storage

Fig.1. Boost type PWM Rectifier11. SYSTEM MODELLING

The equivalent circuit of a three-phase boost converter in ad-q synchronous reference frame, rotating at we, aligned withthe supply voltage vector can be derived as shown in Fig. 2[21.

I

E d c i o = V d l i d + V q l i q -%ssFig. 2. Boost converter equivalent circuit in d-q co-ordinates

According to this figure, the energy balance can be w rittenas :

0-7803-7067-8/01/$10.00 200 1 IEEE 730
mailto:[email protected]:[email protected]


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Where vd, v,, id. iq, vd] , vqI are the supply voltages, supplycurrents and converter voltages respectively, referred to thesynchronous frames and k s a constant which depends on thetransformation used. R an d L are the input filter resistanceand inductance respectively. Plossepresents the losses in theconverter and iL , ic represent the load and generationconnected to the DC link capacitor respectively.In order to regulate Edc it is necessary to control the realpower flow via id . The quadrature current iq is normally closeto zero implying close-to-unity displacement factoroperation. Using (l), neglecting the inverter losses andassuming iq=O, a small signal transfer function can beobtained between Edc and id for an operating point (Edd),ia,( i L + J 0 ) s follows:

Equation (2) may be used to design a linearised controller.However, the transfer function is dependent on the operatingpoint. Moreover, the pole of ( 2 ) is strongly dependent on thedisturbance current (iL-iG). n general either iG or iLmay be afunction of Edc. For example, a static load could be placedacross the DC link andor ic may be supplied from agenerator operating a constant power. Given the variation of(2 ) over the operational range and the generally unknownload an d generating conditions, a fixed classical controller isinappropriate.

The approach taken in this paper to account for the non-linearity and uncertainty in ( 2 ) is to derive a PI type fuzzycontroller augmented by a feed-forward compensationtechnique [9].111. DC LINK VOLTAGE CONTROLLER

A . PI Type Fuzzy Con troller.The scheme for the fuzzy logic controller is shown in Fig.3. The inputs to the controller are the DC voltage error, e@ )

and the change of voltage error, Ae(k). The output of thefuzzy controller is the change in the d-axis reference currentAid. The updated d-axis reference current is then calculatedfrom:i: ( k )= i: ( k -1)+Ai: ( k ) (3)

Ed c Iuzzy LogicController i[; k - 1)Fig. 3. Fuzzy logic controller scheme.

For the fwzification process, seven fuzzy levels areselected with the following fuzzy-set values for e(k) andAe(k): NB (negative big), NM (negative medium), NS(negative small), ZE (zero), PS(positive small), PM (positivemedium), and PB (positive big). Triangular-type fuzzy-setvalues are used with 50% overlap. The control rules areshown in Table I. The inferred output of each rule is obtainedusing Mamdani's min fuzzy implication [ l o ] .

TABLE I.CONTROLULES.Change in Voltage Error Ae(k)

\ NB NM NS ZE PS PM PBgNE3: N MNSZE'-d PMa PB* PS

For the defuzzification process, seven triangularmembership fimctions are also used, again with 50% overlap.A crisp value for Aid is calculated using the high - weightedmethod [lo]. Tuning of the fuzzy controller was initiallydone off-line using a guided-search algorithm [ 1 11. Minoradjustments of the controller parameters were subsequentlydone on-line to improve the response to step changes in DClink voltage reference.B . Feed-forward Compensation.

In order to improve the DC link voltage regulation feed-forward sompensation is used. This is based on theparametric model of the system and relates the disturbancecurrent (i&) to id. Neglecting the energy variation in Lbecause the input filter inductance is small and consideringthat the energy variation in C is also negligible because thevoltage is kept relatively constant by the controller actionthen the steady state equation may be used to derive the feedforward com pensation term. From (1) the sieady state powerbalance for unity-power factor operation, i, = 0 , is then givenby :

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Edc( iL i c ) + & o , = k ( v d i , - R i j ) (4)From which the feed-forward term is given by:

=[a b cl

The current supplied by the converter to the DC link isotta ine dp y using the signals from the PWM and the currentsid and iq . This is obtained as:

31 1 cos i l - s inA id-51 1 [ cosill[i ] (9)Equation (5) can be calculated in real time using a look uptable. However, a simpler expression can be obtained byneglecting the inductor cop per losses which yields:

Either (5 ) or (6) can be used to implement feed-forwardcompensation, but in any case, knowledge of the current (iL-ic ) is necessary. This can be obtained either through directmeasurement or an observer can be used. Both techniqueshave been implemented, although an observer is preferable,since it avoids the need for a transducer and the associatedelectronics. Finally, the d-axis reference currentid,ref including the feed-forward compen sation term is givenby:

id,ref = ii i d , c o m p (7 )IV LO AD OBSERVER FOR FEED-FORWARD COMPENSATIONThe discrete state eq uation for the observer, assuming thatthe load current does not chang e during one sampling period,is given by:

Where io is the current supplied by the converter into theDC link and A i, ( k )= (iL (k)-ic ( k ) ) is the estimation ofdisturbance or load current in the DC link. T is the samplingtime, C is the DC link voltage capacitor and 11, 12 are theobserver coefficients.

Where h is the voltage vector position in the synchronousreference frame. The values [So, S,, S are the duty cy cl y ofthe three top switches of the converter. By using the i d , currents in (9 ) the switching noise of the io, ib, zmeasurem ents is avoided. 4

When the PW M signals are not available, the load observercan still be implemented using a parametric model of theconverter. Neglecting the losses and the variation of theenergy stored in the filter inductance, i,, can derived from ( 1 )as :

d i d ,c o m pio = k -

Equation (9) gives a better estimation of io than (10)which ismore sensitive to variation in the param eters and noise on thesignals. Moreov er, it requires the determination of Theobserver gains are obtained from classical observer designand for the system parameter of the Appendix, gain values of11=0.45218 an d I F -0.17028 give and observer dynamicnatural frequency of about 4OOrads.A schematic of the overall control scheme employing thefuzzy PI with feed-forward compensation is show n in Fig. 4 .The block labelled Non linear gain can implement eitherequation (5) or (6).

v. EXPERIMENTALET-UP AND RESULTSA schematic of the experimental rig used to validate thecontrol strategy is shown in Fig. 5. A commercial 7.5kWPW M inverter is used which is connected to the grid via three12mH line inductors. The DC link voltage Edc is regulated at550V with a supp ly voltage that has been set to 2 5 0 V using athree-phase variac. This gives a nominal modulation depthfor the converter of about 0 . 7 5 , which provides enough

latitude during transients to avoid o vermodulation problems.A chopper controlled resistive load has been used to extractcurrent transients from the DC link to study the performanceof the DC link voltage controllers to step load impacts. APWM switching frequency of 1kHz (regular samplingasymmetric PWM) is used. A 0.5ms sampling period is usedfor voltage and current measurement and for calculation of

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the d-q axis current controllers and load observer. DC linkvoltage control is carried out every 5ms. The experime ntal riguses two T800 floating point Transputers, although thecomputational burden is not great and could be met by mostDSP devices.F u z z v control ler( i L - i G) '

I - I bd

- upplyFig. 4. Schematicof the proposed control system.

3-phaseUariac

Figure 5 . Experimentalset-up.Fig. 6 illustrates the performance of the controller,showing the response of Ed, and id for step chang es in the DClink voltage reference from 500V to 550V. A voltageresponse with no overshoot is obtained with minor on-lineadjustment of the fuzzy controller.

d0

-20 0.1 0.2 0.3 0.4 0.5Time($Fig. 6. Controller performance for step change in the reference voltage.

Figure 7 (a)+(d) shows the results for load disturbance(a) Fuzzy controller.(b) Fuzzy controller with feed-forward compensa tion and

(iL-iG) easured using a hall effect current transducer.(c) Fuzzy controller with feed-forward cornpensftion with(i&) estimated using the currents id , iq and thePWM signals [So,Sb,S,].(d) Fuzzy controller with feed-forward compensation. Thecurrent (i&) is observed with a parametric model ofthe power converter.

rejection for the following controllers:

In each figure a load step impact of 2.5kW is applied att=25ms and removed at e275ms. The performance of thecontrollers is summarised in Table I1TABLE 11.CONTROLLERERFORMANCEORDISTURBANCEEJECTION

29ms54msTaking the performance of the fuzzy controller alone as thebasis for comparison (Fig 7a), Fig. 7b demonstrates theeffectiveness of the feed-forward compensation term whenthe current is measured directly. The settling time is reducedby 60% and dip and the oversh oot are reduced by 80%.Usinga current observer for (iL-iG)with io estimated from the PW Msignals (Fig 7c) still yields significant improvement, with areduction in settling time of 60% and diplovershoot of 64%Finally, the response when ( i L - iG ) is observed using aparametric model of the converter (Fig 7d) shows a reductionin settling time of 25% and diplovershoot of 58%. Whilst the

performance is not as good when an observer is used in placeof direct current measurement, there is still a very worthw hileimprovement over the case without feed-forwardcompensation.

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I " " " " ' 112 56 0

5001 ' . . ' . ' ' I0 0. 1 0. 2 0 . 3 0.4 0.5T i m e (s )

0 0.1 0.2 0.3 0.4 0. 5Time (s)

0 0.1 0.2 0 .3 0.4 0. 5Time (s)

S

500 ' " " " " I0 0.1 0.2 0.3 0.4 0.5Time (s)Fig.7. Performance of various controllers for load disturbance rejectionFinally, the proposed DC link voltage control scheme hasbeen verified on a variable speed wind energy systememulation [12]. Tw o back-to-back PW M converters are usedto interface a cage induction generator to the grid supply. Theinduction generator is driven with a DC drive that emulatesthe wind turbine characteristic and is controlled using vectorcontrol [8]. Figure 8shows the AC side converter current, theassociated phase voltage and the DC link voltage for steadystate operation. The system is operating at the optimum

operating speed with the wind turbine $mulation systemsetting a w ind velocity of 8 m/s. Because iq is set to zero thephase displacement between the phase voltage and current is180' as expected.

0 0.02 0.04 0.06 0.08 0.1Time(s)Fig. 8. Steady state performance in a wind energy system emulation

VI. CONCLUSIONSIn this paper a new improved control structure forregulating the DC link voltage of a boost type front-endconverter in wind energy systems has been presented.Because of the non-linear and variable DC sidecharacteristics, a PI type fuzzy logic controller has beenproposed. An improvement in regulation has been obtainedusing feed-forward mapping of the net dc-link disturbancecurrent with the direct axis (real power) cu rrent component ofthe power converter. To avoid the need to measure thecurrent, a loaddisturbance estimator has been used to obtainthe feed-forwa rd compensation term.The experimental results show that excellent regulationcan be achieved even without direct measurement of the DCside current. Finally, the sche me has also bee n validated in a n

experimental system emulating a wind turbine driveninduction generator with a back to back converter interface tothe grid.ACKNOWLEDGMENTS

The financial support provided by Fondecyt, throughprojects 1980688 and 7980077, is gratefully acknowledged.The financial support provided by the British Councilthrough the Academic Link Programme (SAN/984/) is alsoacknowledged.REFERENCES

N. R. Zargary and G. Joos, "Performance Investigationof a Current-controlled Voltage-regulated PWMRectifier Rotating and Stationary Frames", IEEEtransactions on Industry Electronics, Vol. 42, No. 4,1995, pp. 396-401

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[2] C.T. Rim, N.S. Choi, G.C. Cho and G.H. Cho, Acomplete DC and AC A nalysis of Three-phase CurrentPWM Rectifier Using d-q Transformation, IEEETransactions on Power Electronics, Vol. 9, No. 4,[3] J. Jung J., et al, A feedback linearizing controlscheme for PWM converter-inverter having a verysmall DC-link capacitor. IEEE Transactions. onIndustry. Application, Vol 35, No 5, pp.1124-1131,1999.[4] R. Jones and I. Gilmore, Benefits of SinusoidalRectifiers on Variable Speed Wind Turbines. HighQuality Mains Power from Variable Speed WindTurbines. 17h British Wind Energy AssociationConference, pp.339-345, 1995.S. Muller, M. Deicke, R. De Donker, Ajustable SpeedGenerator for Wind Turbine Based on Doubly-fedInduction Machines and 4 Quadrant IGBT ConvertersLinked to the Rotor. IEEE Industry Application Ann ualMeeting, IAS-2000, October 2000, Rome, Italy.

S.A. Papathanassiou and M.P. Papadopoulos, DynamicBehaviour of Variable Speed Wind Turbines underStochastic Wins. IEEE Transactions on E nergyConversion, Vol. 14, No. 4, pp.1617-1623, December1999.R. Peiia, R. Cardenas, G.M. Asher and J.C: Clare, Vector Controlled Induction Machine for Stand-AloneWind Energy Applications, IEEE Industry ApplicationAnnual Meeting,US-2000,October2000,Rome, Italy.

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[8] R. Peiia, J.C. Clare, G.M. Asher, A doubly fedinduction generator using back to back PWMconverters and its application to variable speed windenergy generation, IEE-Proceeding part B (ElectricPowe r and Applications), pp. 23 1-24 1. Ma y 1996.R. C ardenas, R. Peiia R., G.M. Asher G and J.C. Clare, Control Strategies for Energy Recovery fi-om a FlywheelUsing a Vector Controlled Induction Machine, IEEEPower Electronics Specialists Conference, PESCOO,June 2000, Galway, Ireland, pp. 454-459.[ I O] D. Driankov, H. Hellendoorn, M. Reinsrank, AnIntroduction to Fuzzy Control, S pringer-Verlag, 1993.[113 M.E. El-Hawary, Electric po we r applications of fuzzysystems, IEEE Press, ISBN 0-78 03-1 197-3, 1998[121 D. Sbarbaro, R. Peiia, R. Cardenas, A Robust VariableStructure PI Controller for Small Wind EnergySystems. Proceedings of the dh IEEE InternationalWorkhop on Variable Structure Controller pp.480-489. Queensland, Australia, December 2000.

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APPENDIX.System parameters:AC Filter inductance L=12mHAC filter resistance R=O. 1SZDC link filter capacitance C=12OOpF

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