00178359 imp vcontrol of parallel connected inverters in stand-alone ac supply systems

8/6/2019 00178359 Imp VControl of Parallel Connected Inverters in Stand-Alone AC Supply Systems

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Control of Parallel Connected Inverters in Stand-Alone AC Supply SystemsM. C. Chandorkar D. M. DivanDepartment of Electrical and Computer EngineeringUniversity of W isconsin-Madison1415 Johnson Drive

Madison, WI 53706Abs l r u c l - A scheme for c ont ro l l ing pnra l le i c onnc c tc dinv e r te rs In a stand-alone AC supply system i s prcsentcd inthis paper. A key feature of this schcme I s that it uses onlythose variables which can be measured locally at the lnvertcr,and docs not need communicat ion of control signals betweenthe inverters . This feature i s im por ta nt In high re l ia b i l i t yUninte r rupt ib ie P ow e r S upply ( U P S ) systems, and in largeD C power sources conncctcd to an AC distr ibut ion system.Real and react ive power sharing between inverters can bea c hie v e d by c ont ro l l ing t w o independent quant it ies at theinv e r te rs - the power angle, an d the fundamen tal inver tervoltage magnitude.

I. INTRODUCTIONAs DC to AC power converters feeding power to ACsupply systems become m ore numerous, the issues relating totheir control need to be addressed in greater detail. Examplesof such inverters feeding power to AC supply systems includelarge , d is t r ibuted Uninterrupt ib le Power Supply (UPS)systems and Photovoltaic systcms. In addition, over the pastseveral years, there has been considerable interest in applyinginverter technology to low voltage DC (LVDC) meshedpower transmission systems. Th e feasibility from the conlrolview-point of an LVDC mesh has been demonstrated in [l].The transmission system could typically consist of invertersconnected at several points on the LVDC mesh, and providingpower to AC systems which could be interconnected as well.Multiple inverters connected to a common AC sys temessentially operate in parallel, and need to be controlled in amanner w hich ensures stable o peration and prevents inverteroverloads. Although inverter topologies used for power

transmission have traditionally been currcnt sourced, inrecent years Voltage Source Inverters (V S I ) have beenincreasingly used for high power applications like electrictraction and mill drives, photovoltaic power systems andbattery storage systems. Control schem es for VSI's in powersystem environments have formed the topic of reccnt work[2]. Further, with inverter topologies like the Neutral-PointClamped (NPC) inverter [3], i t i s poss ible to achievesubstantial harmonic reduction at reasonably low Pulse WidthModulation (PWM) switching frequcncics.A stand-alone AC system may be described as one inwhich the entire AC power is delivered to the system throughinverters. Thus, there are n o synchronous alternators presentin the system which would provide a refcrence for the systemfrequency and voltage. All invertcrs in the systcm necd to beoperated to provide a stable frequency and voltage in the

prcscnce of arbitrarily varying loads. This paper firs tdcvclops a control nicthod for an invcrtcr fccding rcal andreactive power into a stiff AC system with a defined voltage,as shown in Figure 1. This forms the basis of a control

@7803-O453-5/91$1o@991IEEE

R. AdapaElectric Power Research InstitutePalo Alto, CA

method suitable for stand alone operation. The invcrtcr is aVSI with Gate Turn-off thyristor (GTO) switches, andoperating from a DC power source and feeding into the ACsystem through a filter inductor. In a stand-alone system, afilter capacitor is needed to suppress the voltage harmonics ofthe inverter. The requirements for controlling such aninterface are described in the next section. Later sectionsdescribe the development of an effective control scheme tomeet these requirements, and present simulation resultsobtained from the study of a po wer distribution system withparallel connected inverters.

11 REQUIREMENTS O F THE CONTROL SYSTEMThe control of inverters used to supply power to an ACsystem in a distributed environment should be bascd oninformation available locally at the invertcr. In typicalpower-systems, large distances between inverters may makecommunication of information between inverters impractical.Communication of information may be used to enhancesystem performance, but must not be critical for systcmoperation. This essentially implies that inverter controlshould be based on terminal quantities.

Inverter- Stiff ACLf-V T System

Figure 1: Inverter Co nnected to Stiff AC SystemIt is well known that stable operation of a power systemneeds good control of the real power flow (P) and thereactive power flow (Q). The P and Q flows in an AC systemare decoupled to a good extent [4]. P depends prcdominantlyon the power angle, and Q depends predominantly on thevoltage magnitude. This is il lustrated in Figure 2. It isessential to have good control of the power angle and thevolhage level by means of the inverter. Contro l of frequencydynamically controls the power anglc, and thus thc realpower f low. To avoid overloading the inverters , i t isimportant to ensure that changes in load are takcn up by thei n v e r t e r s i n a p r c d c t c r m i n c d m a n n e r , w i t h o u tcommunication. This is achicvcd in conventional powersystems with multiple generators by introducing a droop inthe frequency of each generator with the real power P

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delivered by the generator [4]. This permits each generator totake up changes in total load in a manner determined by itsfrequency droop characteristics, and essentially utilizes thesystem frequency as a communication link between thegenerator control systems. The same philosophy is used inthis paper to ensure reasonable distribution of total powerbctween parallel-connected inverters in a stand-alone ACsystem. Similarly, a droop in th e voltage with reactive poweris used to ensure reactive power sharing.-V

p = = s i n s0 Lf0 L f 0 LfQ =2 Y-E- cos6

Figure 2 Real and Reactive Power Flows

111. CONTROL OF SINGLE INVERTER FEEDING INTOA STIFF SYSTEMThe power schematic of Figure 1 shows a singleinverter connected to a stiff AC system through a filterinductor. Th e inverter is assumed to be a six-pulse GTO VSI.This section details the control of the inverter based onfeedback of quantities measured locally at the inverter. Thereal and reactive power fed into the AC system are the twovariables that are controlled by the inverter. Given set pointsfor the real and reactive power, P* and Q*. the real andreactive power, P and Q , fed by the inverter into the ACsystem can be controlled by a method that controls the time-integral of the inverter output voltage space vector. Thisconcept has previously been applied extensively to AC motordrives [5 , 61. The entire control of the inverter is performed

in the stationary d-q reference fram e, and is essentially vectorcontrol. T he t rans form at ion from the phys ica l a -b-creference frame to the stationary d-q-n reference frame isdescribed by the following equations [7]....(1)

...(3)In these equations, the quantity 'fgenerically denotes aphysical quantity, such as a voltage or a curre nt. In theabsence of a neutral connection, the quantity 'fn ' is of no

interest. For a six-pulse VSI, the inverter output voltagespace vector can take any of seven positions in the planespecified by the d-q coordinates. These a re shown in Figure 3as the vectors 0 - 6. Th e time-integral of the inverter output

1 2 3 4

Figure 3b : Inverter Sw itch Positio nsI

I 2I3

5 6

d1 : Invater Voltage Vector I0:ector I For Choice of Inverter Voltage Vector

Figure 3a: Inverter Output Voltage Vectors

voltage space vector is called the 'Inverter Flux Vector' forshort. The flux vector does not have the same significance asin motor applications. Rather it is a fictitious quantity relatedto the volt-seconds in the filter inductor. The d and q axiscomponents of the inverter flux vector YV re formallydefined as:

-The m agnitude of '+'vis:

...(4)

...(5 )

...(6 )

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-


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P IRegulator -Lhoicaof

V, i e.

Vc 1 ecFEEDBACK

vb eb

Po& Q* Set Points or Real& Reactive Power

Figure 4: Inverte~ on~rol cheme-The angle of W V with respect to the q -axis is:6, =w-l(w-)

vgv ...(7)The d ann q axis components of the AC system voltage fluxvector, ye, its magnitude anAangle ,are defined in a similarmanner. The angle between y v an d w e s defined as:

$ = S , -6e ...(8)Control of the flux vector has been shown to havegood dynamic and steady-state performance [5 . 61. It alsoprovides a convenient means to define the power angle, since

the inverter voltage vector switches position in the d-q plane,while there is no discontinuity in the inverter flux vector. Itis useful to develop the power transfer relationships in termsof the flux vectors. The basic real power transfer relationshipfor the system of Figure 1 in the d-q reference frame is:...9)

In (9). eq and ed are the q and d axis componentsrespectively of the AC system voltage vector E.Also, iq andid are the components of the current vector i.When iq and idare expressed in terms of the fluxes, the equation is expressedas:

Taking into account the spatial relationships bctwecnthe two flux vectors and assuming the AC system voltage tobe sinusoidal, (10) can be expressed as:

..(1 )In this expression, we and WV are the magnitudes of theAC system and the inverter flux vectors respectively, and S,is the spatial angle between the two flux vectors. o s thefrequency of rotation of the two flux vectors. The expressionfor reactive power transfer for Figure 1 can be derived in asimilar manner. This is:

...(12)Equations (11) and (12) indicate that P can becontrolled by controlling 6, , which can be defined as the

power angle, and Q can be controlled by controlling y v .Th ecross-coupling between the control of P and Q is alsoapparent from these equations.The control system for the inverter is given in Figure

4. The two variables that are controlled directly by theinverter are '+v an d S, . The vector y v is controlled so as tohave a specified magn itude and? specified position relative tothe AC system flux vector '4%. This control forms theinnermost control loop, and is very fast. It is noted that boththe inverter and the AC system voltage space vectors areobtained by me asuring instantaneous voltage values which arcavailable locally. The set points for the controller are P* andQ*, and the set points for the innermost control loop, y; an dare derived from these. The actual values of P and Qcalculated from the feedback are compared with the setvalues. The error drivcs a Proportional-Integral (P-I)regulator, which generates the sct points d nd 6*, for the


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innermost control loop. The control of the invertcr togenerate the specified Vv and 6p is detailed in the next sub-section.A. Control of vvand 6,

The control of Vvand 6p forms the firs t level ofcontrol, and directly controls the inverter switching. Thechoice of the inverter switching vector is made on the basis ofthe deviations of w v and 6p from the set values 'Y an d ,and the position of the inverter flux vector in the d-q plane.given by & . f the deviation of 6p from 6*p is more than aspecified limit, a zero switching vector is chosen. If thisdeviation is less than a specified limit, or if YV eviates from'46 by more than a specified amount, a switching vector ischosen which increases 6, and changes yrv in the correctdirection. This is essentially accomplished by hysteresiscomparators for the set values, and then using a look-up tableto choose the correct inverter output voltage vector . T heconsiderations for developing the look-up table are dealt within [5].Th e choice of inverter switching vector is dictated bythe value of 6v .The d-q plane is divided into six sectors for6~ s shown in Figure 3a, which also shows the inverterswitching vectors. The inverter switch positions for thevectors are shown in Figure 3b. The value of 6v determinesthe choice of two possible inverter switching vectors, apartfrom the zero vector. One vector increases the magnitude Vvand the other decreases it, while both tend to increase 6,.Thus, to decrease S, , he zero switching vector is chosen. Tocorrect the value of vv, one of the two active switchingvectors is chosen depending on the sign of the correctionrequired. Table-1 gives the choice of active vectors for givenpositions of the inverter flux vector, specified by 6v . n thismanner , Vv and 6 p are tightly controlled to lie withinspecified hysteresis bands by means of inverter switching.The tip of the inverter flux vector is guided along an almostcircular path. Control of Yv an d S, in this manner results in aPWM voltage waveform at the inverter output.Table-1: Choice of Switchine Vector

Sector NO . (Location of WV

(The zero vector is chosen to decrease Ep)B . Sitnulalion Results

Simulation results of the control scheme of Figure 4applied to the power system of Figure 1 are presented inFigures 5 .6 , an d 7. The DC bus voltage is taken to bc 10 kVand the line-to-line voltage of the AC system is taken to be3.3 kV rms. Figure 5 gives the plot of the locus of the

-inverter flux vector YV. he locus is sccn to be close to acircle, since the m agnitude v v very tightly controlled. Figure6shows the inverter line-to-line voltage v& and the invcrtcrline current ia for P* = 1 MW and Q* = 500 kVAR. Figure7 shows the response of the inverter to step changes in Q*and P* successiv ely. It is noted that there is a distu rbance in Pwhen Q* is changed and a disturbance in Q when P* ischanged. In each case, the P-I regulators modify the setvalu es of 6*, and $ to maintain the P and the Q at thc setvalues. Also, the tight control of P and Q within limits isapparent from Figure 7.

- ,L10.O -6 .00 -i,oo i 00 6.00 10 0

Figure. 5 : InvcrterRUX ectorYCP

IV . CONTROL OF INVERTERS IN A STAND-ALONESYSTEMThe control of a single inverter feeding a stiff AC

system based only on instantaneous mcasurement of terminalquantities now forms the basis of the control scheme formultiple inverters in stand-alone system environments. Theessential difference in the control scheme is that in the stand-alone system, there is no AC side voltage available forreference. The inverters themselves produce the AC systemvoltage, which is fcd back to control the inverters. There isthus a possibility of controlling the voltage and the frequcncyof the AC system by inverter control. Figure 8 shows twoinverters feeding into a stand-alone AC system. The invertcrsare interfaced to the AC systcm through LC filters. The twoinverters are connccted by a tie line, and each invertcr has alocal load. The DC power source rcprescnts a 10 kV DCpower transmission mcsh. The nominal voltage on the ACsystcm is 3.6 kV rms linc-to-line, and the nominal frcqucncyis 60 Hz. Each inverter is a six pulse VSI made up of GTOswitches.As in the single inverter case, the two variables that are

directly controlled are YV nd 6p for each invertcr. Outcr


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U0

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Figure 6 InverterVoltageand Cunent Waveformscontrol loops are then used to control the magnitude andangular frequency of the AC system voltage vector E. Thhe se tpoints for the magnitude and angular frequency of E a r eobtained from the outermost loop, which implementsspecified droo p characteristics for the frequency w ith P andmagnitude with Q, s mentioned in Section 11 and detailed inSection IV . The e ntire control is thus a three level structure.The innermost control level controls '4% and 6p , and is thesame as that described in the previous section. The secondlevel controls the AC side frequency and the voltage at eachinverter, and provides set points 6*p and v': for the innermostlevel. The third level computes the set points for frequencyand voltage for each inverter. The two outer control levelsare described below.

Ra iInverter 1

Figure 8: Stand-AloneAC SystemA. Control of Frequency and Voltage

The frequency controller determines the sctpoint 6*pthat is needed to attain the specified frequency. The structure

Figure 7: Inverter Real and Reactive Powerof the frequency controller is given in Figure 9. Thefrequency setting, a*,s integrated to obtain a reference forthe position &*=of the AC system voltage vector E across thefilter capacitor. This is compared with the actual position 6~of E. The error is used to drive a P-I regulator, whichproduces the setpoint 6*p which is given to the innermostcontrol loop described previously. This scheme achievcs avery tight control of the output frequency since the regulatorattempts to control the output voltage vcctor angle at cvcryinstant.

The voltage controller determines the setpoint y v ha tis needed to attain the specified A C system voltage magnitudc.The voltage controller needs to take care of the filtcrdynamics to determine the exact value of d . he structureof the voltage controller is given in Figure 10. The controller-ommand input is E*, the specified value of the magnitude ofE. Th e controller consists of a command feed-forward tcrmand a voltage magnitude feedback term. The command feed-forward term is given by

*

E* [I d f c f ]aThe command fccd-forward gives the value of dneeded to achieve the spccified E* with an unloadcd filter,and is intcndcd to speed up the voltage control loop. Thcvoltage magnitude feedback term is used to generate an errorsi nal which actuates a P-I controller. The resultant value of

YV is used as a sctpoint for the innermost control loopdescribed in the previously. The A C system frequency o scomputed six times in one cycle. For this purpose, six axesare defined in the d-q plane. The time taken by the vector Eto cross from one axis to the next consecutive axis is used tocompute the frequency. For parallel operation of multipleinverter units, the setpoints O* nd E* need to be chosen to

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*K*+%

IFrom FilterOutputToInverterController

To. nverterController

Figuro 9:FrcqucncyController forStand-hloncSystcmensure the correct P an d Q sharing bctwcen the inverters inresponse to arbitrary load changes. This has to be donewithout communication of the setpoints between the twoinverter systems. Th e next sub-section describes theoutermost control loop, which determines the setpoints o*an d E* for each inverter system independently without anysignal communication. This is done on the basis of the realand reactive power loading of' the inverter systems.B . Computing a* nd E* fo r parallel operation

The outermost loop determines the setpoints for o*an d E* to ensure correct real and reactive power sharingbetween the parallel connected inverters. This action issimilar to that used in conventional power systems to ensurethe correct load sharing between generators feeding to acommon A C system [4]. For the frequency set point, a droopis defined for the P-o* characteristic of each inverter. Thefrequency set point is thus made to decrease with increasingreal power supplied by the inverter. The P-a* roopcharacteristic c an be described by:4 =O.Q mi oi -pi) ...(13)

In this expression, i = 1 for inverter 1 and i = 2 orinverter 2 Figure 8). 6%is the nominal operating frequencyof the AC system, and is taken to be 377 radians/second (60Hz). a is the power rating of the 'i 'th inverter, and P i is itsactual loading. The slope of the droop characteristic is mi ,and is numerically negative. The values of mi for differentinverters determine the relative power sharing between theinverters. In typical systems, the P-o* haracteristics arestiff, and the frequency change from no load to full load isextremely small. If the slopes mi for different inverters arechosen such that

m l Pol =m2P02 = ...=mnPOn ...(14)then for a total power P, he load distribution between theinverters satisfies the relationships:

ml P1 = m 2 P 2 = ...= m n P n ...(15 )Pi +P2 + ...+Pn= F ...(16)By choosing the slopes according to (14), it can beensured that load changes are taken up by the inverters in

proportion to their power ratings. The power sharingmechanism can be best understood by considering the twoinverter system shown in Figure 8. An increase in powerdrawn by the load near Inverter 2 esults in increased powerfrom both inverters. If the magnitude of m2 s larger than

figurc 10:Voltage Conirollcr for Simid-hlonc ystcm *that of gl,% would tend to dfpp lower than O1. Hence, thevector E2 would lag the vector E l , and the power flow in thetie-line from Inverter 1 to Inverter 2 would increase. Thus,Inverter 1 would take up a larger proportion of the load. It ispossible to define a com posite power-frequency curve for allthe inverters in the system. The composite load curve islikewise defined. At the steady-state operating point on thecomposite load-frequency curve, the total power delivered bythe inverters matches the power consumed by the loads.Depending on the stiffness of the comp osite power-frequencycurve, the steady-state system frequency will change onchanging loads. The frequency may then be restored to itsnominal value by a slowcr outer loop. To restore thefrequency, the value of Poi , 13) has to be modified for theinverters. This is equivalent to shifting the power-frcqucncycurve vertically up or down.

In a similar manner, the sctpoints %* for the AC systemvoltages at the inverter systems can be determined fromdrooping reactive p ower-voltage characteristics ( Q- E) for theinverters . This droop ensures the desired reactive powcrsharing between the inverter systems, and is described by:...(17 )

The scheme described in this paper uses P-I egulatorsto determine the set points for 6*, and $ . Howcver, thedynamic performance of the system can bc substantiallyimproved if an observer structure is used to determine thefrequency. Th e position of the A C system voltage vector canbe determined very accurately at any time. This informationcan be used to set up a frequency obscrvcr, the output ofwhich would be an estimated frequency. The time-integral ofthe estimated frcquency can be compared to the actualposition of the voltage vector, and the estimated frequencycan be modified accordingly. Feedback of the observer statesresults in a system with very good dynamic response anddisturbance rejection properties.

The control system dcscribcd above has bccn applicd tothe stand-alone system of Figure 8.Th e results of simulationstudies are presented below.C . Simulation Results

For the simulation studies, the droops of the twoinverter systems are characterized by the followingparameters:Pol = 0.75 MWm l = -1.4 x 10-5 P02= 0.6 MWm2 = -1.75 x 10-5


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0 00 lrl

0 00 In

1' Figure 11: Inverter Real and Rea aive Power (Stand-Alone System) IQ o l = 0 . 2 M V A R Q02 = 0.1 MVARn i =-1.0 x 10-4 n2 =-2.0 x 10-4The nominal voltage is 3.6 kV rms line-to-line and thenominal frequency is 60 Hz . The filter components for thetwo invcrter systems are identical. Figure 11 shows thercsponse of the inverters when the resistance RE2 (Figure 8 )is decreased suddenly to half its value. Figure 11 shows thercal and reactive powers supplicd by the two invericr systemsto the load. Figure 11 shows that Inverter 1 carries a largershare of the real power, since it has a stiffer slope. Figure 12shows the line-to-line voltage across the filter capacitor ofInverter 1. Th e plot for the reactive powers in Figure 11shows oscillations. These oscillations occur in the absence ofactive damping of the loop formed by the tw o filtercapacitors and the tie-line inductance.

Figure 1 2 Voltage across Inverter 1 Filta Capacitor

V. CONCLUSIONSThis paper has dcscribcd a method to effectivelycontrol inverters in a stand-alone AC supply system, withoutany form of signal communication. The simulation results

presented indicate that the scheme effectively achieves thegoals of power sharing in the presence of arbitrarilychanging loads. Active damping in the loop formed by thefilter capacitors and the tie line, and the use of a frcqucncyobserver would enhance the performance further. Thcseform the goals of a later paper.

VI. ACKNOWLEDGEMENTSThis project is currcntly funded by grant #8818339 ofthe National Science Foundation and AgreementRP79 1- 12 ofthe Electric Power Research Institute.

VU. REFERENCES[ l ] B . K. Johnson, R. 11. Lasseter . R. Adapa. "Power ControlA plications on a Superconducting LV dc Mes h', 90 S M 335-0 PWKD.&E/lJES 1990 Summ er Meeting. July 1990 (to appear in IEEE Trans. onPowcx Delivery).[2] L. Angquist, L . Lindbcrg. "I nner'Phas e Angle Control of VoltageSource Converter in High Power Applications", T o be presented at th eE E E Power Electronics Specialists Confercnce, 1991.[3] A. Nabae, I. Takahashi, 11. Akagi. "A Neutral-Point-Clamped PW MInverter", IEEE Trans. Ind. Appl., vol. IA-17, pp. 518-523. Sept/Oct1981.[4] A. R. Uergcn, "Power System Analysis". Prcntice-IId, Inc., 1986.[SI 1. Takahashi and T. Noguchi, "A New Quick-Response and Iligh-Elficiency Control Strategy of an Induction Motor", ICEE Trans. lnd.[6] M. Dcpcnbrock. "Direct Self-Control (DSC) of Inverter-Fed InductionMachine", IECE Trans. Power Electronics, vol. 3, pp . 420-429. Oc t1988.[7 ] T. A. Lipo, "Analysis of Synchronous Machines", Course Notes,Univcrsity of Wisconsin-Madison, 1990.

Appl., vol. IA-22, pp. 820-827. Sep/Oct 1986.

00178359 imp vcontrol of parallel connected inverters in stand-alone ac supply systems

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