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with load. Ooi and David[8] used a synchronous condenser asan adjustable reactive power source for voltage control.However, a synchronous machine is expensive and requires a DC supply for its excitation, and that overrides theadvantages of using an induction generator. A static VAR compensator (SVC) [9, 10] and static compensator (STATCOM) [7, 11] can also be used to provide adjustablereactive power. However, both the SVC and STATCOM areexpensive and sophisticated power electronic-based devices

and, thus, their use in a small power plant in remote areasmay not be justiable. For such an application, it is very important to have a simple, robust and less expensive systemthat requires minimum maintenance because such facility islikely to be managed by unskilled operators. In addition, theloads in remote areas are usually not very sensitive to small voltage deviation (VD). Thus, a voltage controller that canmaintain voltage within an acceptable range is possibly moreappropriate. Singhet al. [6, 12] used switched capacitors tocontrol voltage in a discrete manner. By selecting appropriate values of xed and switched capacitors, it is possible tomaintain voltage within the lower and upper acceptable limitsfor the entire operating range (from no-load to full load). Theuse of such a voltage controller in a small power plant inremote areas is more appropriate.

As mentioned earlier, for constant voltage operation, thereactive power demand of an induction generator increases with its active power delivery. Thus, the use of a seriescapacitor to supply a part of additional reactive power demand would denitely improve the voltage prole. To utilise thisfeature, short- and long-shunt congurations of inductiongenerators are proposed by some researchers[1316]. In boththe short- and the long-shunt congurations, two sets of capacitors (series and shunt), as shown inFig. 2, are used. Inthe short-shunt conguration, the shunt capacitor is directly connected across the machine terminals. The load is thenconnected to the machine terminals through the series

capacitor. In the case of the long-shunt conguration, thestator windings of the machine are connected in series withthe series capacitors. The load, in parallel with the shunt capacitor, is then connected across the series combination of stator windings and series capacitors. Comparative studiesrevealed that the short-shunt conguration can provide better results than its counterpart long-shunt conguration[13, 14].Even for the short-shunt conguration, the voltage prole inthe entire operating range (form no-load to full load) may exceed the upper and lower acceptable limits. However, the voltage prole can be improved by using additional shunt switched capacitors. The number of switched capacitorsneeded in this case would be much less than that in theconventional shunt generator of Fig. 1 (where only the shunt capacitor is used).

This paper describes a method of determining the values of series and shunt capacitors needed in a short-shunt induction

generator to maintain the load voltage within the upper andlower acceptable limits. The effectiveness of the proposedmethod is then evaluated on a three-phase, 1.5 kW short-shunt induction generator. The simulation results obtainedby the proposed method are also compared with thecorresponding experimental values.

2 Mathematical model The per-phase equivalent circuit of a three-phase short-shunt induction generator with its excitation capacitors and anR-Lload is shown inFig. 3, where R 1 , X 1 , R 2 , X 2 , R c and X mrepresent the stator resistance, stator leakage reactance,rotor resistance, rotor leakage reactance, core loss resistanceand magnetising reactance, respectively.F and v represent the per unit (pu) frequency and speed, respectively. Thereactance of the series and shunt capacitors is representedby X se and X sh , respectively. The load impedance isrepresented by Z L / u (R L jX L). The pu frequency F and the pu speedv are dened as

F f f b

and v N N s

(1)

Here, f and N are the actual operating frequency (Hz) androtor speed (rpm), respectively, of the generator, andf b and N s are the base or rated frequency (Hz) and thecorresponding synchronous speed (rpm), respectively, of the

Figure 2 Schematic diagram of:a Short-shunt generatorb Long-shunt generator

Figure 1 Schematic diagram of a SEIG

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machine. When the generator operates at a frequency other than the base frequency, all reactances (inductive andcapacitive) are to be adjusted accordingly. In a generic way,

the inductive reactances are to be multiplied by the pufrequency F and the capacitive reactances are to be dividedby F . The circuit shown inFig. 3 represents a genericequivalent circuit of the generator where all parameters(resistances and reactances) and voltages are divided by thepu frequency F , whereas the currents remain the same[3]. The above circuit is used in[1719] for both xed and variable speed operations of the generator.

All parameters of the generator, except the magnetising reactance, are considered as constant. The variation of magnetising reactance X m is the main factor in theprocess of the voltage build-up and stabilisation of theoperating point of an SEIG. The value of X m dependson magnetic saturation or air-gap ux, which in turndepends on the ratio of the air-gap voltage to frequency (V g / F ). The relationship betweenV g / F and X m can beestablished from the synchronous speed test results[7].Mathematically, the above relationship can be expressedin many ways such as a linear function[12, 20], piece- wise linear function[9, 14], an exponential function[3]or a higher-order polynomial [7, 17, 21]. In thisstudy, V g / F is expressed by the following third-order polynomial of X m

V g F

k0 k1 X m k2 X 2m k3 X

3m (2)

The coefcients of the above polynomial can easily beobtained by applying any standard curve tting technique to the synchronous speed test results.

3 Analysis The steady-state performance of an induction generator is

usually determined from its equivalent circuit. To simplify the analysis, the circuit of Fig. 3 is represented by threeseries impedances as shown inFig. 4. The impedances are

given by

Z 1 (R 1=F jX 1) (3a)

Z 2 1

R c=F

1 jX m

1

R 2=(F v ) jX 2 1

(3b)

Z 3 1 jX sh=F 2 1

R L=F jX L jX se=F 2 1

(3c)

The loop equation inFig. 4 is

I 1 Z 1 Z 2 Z 3 0 (4)Under normal operating conditions, the stator current I 1 isnot zero and thus

Z 1 Z 2 Z 3 0 (5)

Note that the above equation must be satised for alloperating conditions of the generator. By separating thereal and imaginary parts of (5), the following two scalar equations can be obtained

g 1 real(Z 1 Z 2 Z 3) 0 (6)

g 2 imag(Z 1 Z 2 Z 3) 0 (7)

Note that (6) and (7) can provide the values of only the twounknowns. However, the circuit of Fig. 3 has six unknownsor adjustable parameters: magnetising reactanceX m , pu speedv , pu frequency

F , series capacitive reactance

X se, shunt

capacitive reactanceX sh and load impedanceZ L (for a givenpower factor). In general, (6) and (7) are simultaneously solved to obtain the values of X m and F for given values of v , X se, X sh and Z L . The above equations, in a general form, canbe written as

G ( X ) 0 (8)

Here, G [ g 1 g 2] T and X [ X m F ] T. Once the value of X mand F are known, V g can be evaluated through (2). Theterminal voltageV t of thegenerator (inFig. 4) can bewritten as

V t V g Z 3

Z 1 Z 3(9)

Figure 4 Simplied representation of the equivalent circuit of Fig. 3

Figure 3 Per-phase equivalent circuit of a three-phaseshort-shunt induction generator

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Here, V g is considered as the reference (i.e.V g V g / 08). The load current I L (in Fig. 3) can be written as

I L V t

R L j (FX L X se=F )(10)

The active power (P L) and the reactive power (Q L) absorbed by the load are given by

P L 3 I L2R L and Q L 3 I L

2FX L (11)

Thereactive power supplied by theseries capacitor (Q se)andtheshunt capacitor (Q sh) are given by

Q se 3 I L2 X se

F and Q sh

3 V t 2

X sh=F (12)

The total reactive power (Q T) supplied by the series and shunt capacitors is

Q T Q se Q sh (13)

As mentioned earlier, an induction generator absorbs reactivepower for its excitation. Thus, for a stand-alone operation, thereactive power demand of the generator as well as the loadmust be supplied by the external capacitors.

The load voltageV L in Fig. 3 can be expressed as

V L V t R L jFX L

R L j (FX L X se=F )(14)

When the magnitude of the load voltage is kept constant at a pre-specied value of V spL , the above equation becomes

g 3 V t (R L jFX L)

R L j (FX L X se=F ) V spL 0 (15)

At no-load, I L 0 and, thus, the series capacitor does not supply reactive power. In this case, the voltage of the circuit is determined by the shunt capacitor alone. Under loadconditions, I L = 0 and, thus, both the series and shunt capacitors supply the reactive power and control voltage of the circuit. For given values of v , X se and Z L , the value of X sh needed to maintain the load voltage at a pre-specied value can be determined by embedding (15) into (8).Under this case, the system of equations becomes

G V ( X ) 0 (16)

Here, G V [ g 1 g 2 g 3] T and X [ X m F X sh] T. Insolving (16),v , X se and Z L are considered as xed parameters.Generator characteristics obtained through repeated solutionsof (16), for various values of Z L , can be used in selecting thecapacitor sizes and is discussed in Section 4.

When the generator is driven by an unregulated primemover, the operating speed v cannot be considered as

constant but depends on the load. Determination of generator characteristics for such an operation requiresequating the torque speed characteristics of the generator and the prime mover and embedding it into the system of (8) or (16). This would simply increase the dimension of theproblem by one. Alghuwainem, Chen and Haque[1719]investigated the generator characteristics for such anoperation. It may be mentioned here that, for a givenfeasible set of capacitors, there is a minimum or criticalspeed below which the generator would fail to build up voltage. Al-Jabri and Alolah[22] determined the criticalspeed of a shunt generator for both no-load and full-loadconditions. For a short-shunt generator, (8) can also be usedto determine the critical speed at no-load condition, but that requires considering v (instead of X m) as an unknown or independent parameter and assigning the value of X m as thecorresponding unsaturated value.

In terms of load voltage and current, the terminal voltageV t of the generator can be written as

V t V L ( jX se=F ) I L (17)

For a constant load voltageV L , the terminal voltageV t dependsnot only on load power (or current) but also on the load power factor as can be seen in the phasor diagram of Fig. 5. Theabove phasor diagram clearly demonstrates that the terminal voltage for the leading power factor is much higher than that for the lagging power factor. Thus, for the leading power factor, the generator operates at a higher saturation level and,

hence, needs more reactive power for its excitation. In thiscase, the shunt capacitor also provides more reactive power because of a higher terminal voltage. The opposite is also truefor the lagging power factor.

In this study, (8) and (16) are solved using a numericalbased routine fsolve given in the optimisation toolbox of MATLAB [23]. It uses a nonlinear least-squares algorithmthat employs the Gauss Newton or the LavenbergMarquardt method. A least-squares-based method usually converges to a point where the residual is the minimum.However, if the formulated problem (8) or (16) does not have a zero (numerically) because of the selection of unrealistic values of some parameters, the routine may stillconverge to a point where the residual is the minimum but not necessarily zero. Such a solution cannot be consideredas acceptable and it can easily be identied by evaluating the residual at the solution point and comparing it with a very small tolerance (say, 102 6).

4 Results and discussions The proposed method of selecting the capacitor valuesis tested on a 1.5 kW, 4-pole, 50 Hz, three-phase,

Y -connected (with a phase voltage of 220 V) IM operatedas a short-shunt induction generator. The xed parametersof the generator are R 1 5.033 V, R 2 4.667 V,


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R c 5.0147 k V and X 1 X 2 5.606 V . From thesynchronous speed test results, the coefcients of (2) arefound as k0 596.03, k1 2 12.035, k2 0.1374 andk3 2 5.636 10

2 4. It is considered that the generator isdriven by a regulated turbine at a constant speed of 1.0 pu(or 1500 rpm). The simulation and experimental results

found for this generator are briey described in the following.

First, the machine is operated as a shunt generator and thecorresponding characteristics can be obtained from the sameequations (as derived in Section 3) by setting X se 0. For a shunt capacitor (C sh) of 35mF, the no-load voltage of thegenerator is found as 231.5 V per phase (about 105% of rated value). The generator is then loaded gradually at a unity power factor (by decreasing the load impedance) and the variation of load voltage against load power is shown inFig. 6. The gureindicates that the voltage initially decreases with the load, andthat represents the normal operation[24]. The above pattern

continues until the maximum power point is reached. For thiscase, the generator can deliver a maximum power of 744.6 W at which the voltage drops to 178.6 V / phase (Fig. 6). Further reduction of the load impedance decreases both the voltageand the power, and such a situation represents an abnormaloperation [24]. The experimental results are also shown in thegure and are observed to be very close to the simulationresults. During simulation, the residual at the solution point isalso evaluated and its distribution is shown inFig. 7. Themaximum residual is found to be only 1.84 102 13,indicating that the fsolve routine successfully converged tothe numerical zero point.

During the experiment, it was found that the generator canmaintain a sustainable voltage in the abnormal operating

region until the power is reduced to about 600 W. When theload impedance is decreased further, a voltage collapse occursindicating that the generator cannot maintain a right saturation level to provide a sustainable voltage. However, theoperation in the normal operating region or upper part of theP V (powervoltage) curve is always stable, indicating that the respective magnetising reactance can maintain the right level of saturation. In general, a generator operates in thenormal operating region and, thus, the characteristic in theabnormal operating region is not so important.

The machine is then operated as a short-shunt generator by adding the series capacitor (C se). Fig. 8 shows the

Figure 6 Variation of load phase voltage against load power of a shunt generator

simulation results; o experimental results

Figure 5 Phasor diagram of a constant load voltage operation:a Lagging pf b Leading pf c Unity pf


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gure is plotted from repeated solutions of (16) for different values of Z L and is used to determine the values of xed andswitched capacitors needed to satisfy the above voltagecriterion. It can be noticed inFig. 10 that an initial shunt capacitor of C o 33.43 mF (point a) is needed to obtainthe maximum acceptable voltage of 1.03 pu at no-load. The above capacitor can maintain the load voltage withinthe acceptable limits (0.971.03 pu) until the load power isincreased to P 1 ( 405 W) at point b, where the voltagedecreases to the lower acceptable limit of 0.97 pu. Toincrease the voltage to the upper limit of 1.03 pu at P 1 , it isnecessary to increase the shunt capacitor toC 1 ( 37.44 mF at point c). Now,C 1 can maintain the voltage within theacceptable limits until the power is increased toP 2( 882 W) at point d, where the shunt capacitor is againincreased toC 2 ( 43.03 mF at point e). Similarly,C 2 canmaintain the voltage within the limits up to a power of P 3( 1353 W) at point f , where the shunt capacitor is

further increased toC 3 (

45.00 mF) so that the minimum voltage of 0.97 pu can be maintained at the full load of 1.5 kW.

The above discussion clearly indicates that four steps of shunt capacitors (C 0, C 1 , C 2 and C 3) are needed to maintainthe load voltage in between 0.97 and 1.03 pu for the entireoperating range.Table 1 summarises the number of steps as well as the value of the shunt capacitor in each step for various values of VD, and it indicates that only two steps of the shunt capacitor are required when a VD of + 5% isconsidered. That is, an initial xed capacitor of

C 0

34.85 mF and an additional switched capacitor of 8mF ( 42.85 2 34.85 mF) are needed ( Table 1). However, if themachine is operated as a shunt generator, four steps of theshunt capacitor are needed for the same VD of + 5% [25]. Thus, in the case of short-shunt, the number of switchedcapacitors is reduced (from three to one) by using a xedseries capacitor, and that would signicantly reduce the cost and complexity of the voltage regulator. It is worth

mentioning here that a shunt capacitor branch usually have a large current surge at switching when connected to an ideal voltage source with zero impedance. However, for aninduction generator, the current surge would not be so largebecause of the stator impedance (especially reactance) andthe smaller size of capacitors. The current surge can further be reduced by using a small surge current limiting reactor inseries with the capacitor [26].

Fig. 11 shows the variation of load voltage against loadpower with two steps of the shunt capacitor (as describedabove for a VD of + 5%), and it clearly indicates that theload voltage is always maintained in between the lower andupper acceptable limits (0.95 1.05 pu or 209231 V) inthe entire operating range. The experimental results are alsoshown in the gure and are observed to be slightly higher but very close to the corresponding simulation results. It may be mentioned here that the nearest capacitor values

(i.e. 35 and 43mF instead of 34.85 and 42.85mF,respectively) were used in the experiment. In addition, theseries and shunt capacitors used in the experiment had a tolerance level of + 5%. The author believes that the abovefactors are the main reasons for having slight discrepanciesin simulation and experimental results. The variations of the stator current ( I 1), load current ( I L) and shunt capacitor current ( I C) against the load power are shown inFig. 12,and it again indicates that the experimental results are closeto the corresponding simulation results. Note that thegenerator was loaded only up to 1.2 kW because of thepower limitation of the prime mover used in the experiment.

The characteristics of the generator for a VD of + 3% arealso evaluated for three different load power factors (0.98lagging, 0.98 leading and unity). A summary of steppedcapacitors needed for this purpose is given inTable 2. Asmentioned earlier that, for a constant load voltage, thegenerator operates at a higher saturation level for the

Table 1 Number and values of stepped capacitors neededfor various values of VD

Voltagedeviation No. of steps Capacitor value in mF in eachstep (Power in W at thetransition point)

2% 6 32.81, 35.18, 38.19, 41.93,46.01, 46.06 (258, 553, 873,

1189, 1465)

3% 4 33.43, 37.44, 43.03, 45.0 (405,882, 1353)

4% 3 34.11, 40.16, 43.93 (569, 1212)

5% 2 34.85, 42.85 (750)

6% 2 35.64, 41.75 (944)7% 2 36.48, 40.64 (1138)

Figure 11 Variation of load phase voltage against power for a maximum VD of + 5% simulation results; o experimental results


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leading power factor. The similar situation can also beexpected when the load voltage is maintained in betweenthe upper and lower limits. The variation of the terminal voltage and the total capacitive reactive power against theload power for various power factors is shown inFigs. 13and 14, respectively. The above gures clearly indicate that both the terminal voltage and the capacitive reactive power are usually higher for the leading power factor compared with the cases of the lagging or unity power factors, asexpected.

5 Conclusions A simple method of selecting the values of xed and switchedcapacitors needed in a short-shunt induction generator tosatisfy a desired voltage criterion is described. First, the value of the xed shunt capacitor is selected in such a manner that the no-load voltage does not exceed the upper limit. The size of the series capacitor is then selected toobtain the minimum VD at the full-load condition. If theminimum VD is beyond the lower acceptable limit,switched shunt capacitors can be used to improve the voltage prole. The number and the values of the switchedshunt capacitors are then determined from the capacitor against the power characteristics of the generator under constant voltage (at upper and lower limits) operations. Theequations required to obtain such characteristics are alsoderived and solved using the fsolve routine given inMATLAB. The effectiveness of the proposed method isthen evaluated on a three-phase, 1.5 kW inductiongenerator. The simulation results obtained by the proposedmethod are also compared with the corresponding actual values found through an experimental setup and areobserved to be in very good agreement. It is also found that the number of switched shunt capacitors needed in a short-

shunt generator is much less than that of a simple shunt generator, and that would denitely reduce the cost andcomplexity of the voltage regulator.

Figure 12 Variation of various currents against power for a

maximum VD of + 5% simulation results; o experimental results

Table 2 Number and values of stepped capacitors neededfor various power factors with a VD of + 3%

Powerfactor

No. of steps

Capacitor value in mF in eachstep (Power in W at the

transition point)

0.98(lagging)

5 33.43, 36.59, 40.19, 44.78, 45.24(294, 620, 1012, 1467)

0.98(leading)

4 33.43, 38.67, 44.73, 45.34 (525,1003, 1456)

unity 4 33.43, 37.44, 43.03, 45.0 (405,882, 1353)

Figure 13 Variation of terminal voltage for various power factors

Figure 14 Variation of total capacitive reactive power for various power factors


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6 References

[1] BASSET E.D., POTTER F.M.: Capacitive excitation of induction generators, AIEE Trans. Electr. Eng. , 1935, 54 ,pp. 540545

[2] BARKLE J.E., FERGUSON R.W.: Induction generator theoryand application, AIEE Trans. Electr. Eng. , 1954, 73 ,pp. 1219

[3] SIMOES M.G., FARRET F.A.: Renewable energy systems design and analysis with induction generators (CRC Press,2004)

[4] BANSAL R.C.: Three-phase self-excited inductiongenerators: an overview, IEEE Trans. Energy Convers. ,2005, 20 , (2), pp. 292299

[5] BANSAL R.C., BHATTI T.S., KOTHARI D.P.: Bibliography on theapplication of induction generators in nonconventionalenergy systems, IEEE Trans. Energy Convers. , 2003, 18 ,(3), pp. 433439

[6] SINGH S.P., SINGH B.P., JAIN M.P.: Comparative study on theperformance of a commercially designed inductiongenerator with inductor motors operating as self excitedinduction generators, IEE Proc. C , 1993, 140 , (5) ,pp. 374380

[7] SINGH B., MURTHY S.S., GUPTA S.: Analysis and design of

STATCOM-based voltage regulator for self-excitedinduction generators, IEEE Trans. Energy Convers. , 2004,19 , (4), pp. 783790

[8] OOI B.T., DAVID R.A.: Induction-generator / synchronous-condenser system for wind-turbine power, IEE Proc. C ,1979, 126 , (1), pp. 6974

[9] AHMED T., NORO O., HIRAKI E., NAKAOKA M.: Terminal voltageregulation characteristics by static var compensator for athree-phase self-excited induction generator, IEEE Trans.Ind. Appl. , 2004, 40 , (4), pp. 978988

[10] AHMED T., NISHIDA K., SOUSHIN K., NAKAOKA M.: Static VARcompensator-based voltage control implementation of single-phase self-excited induction generator, IEE Proc. C ,2005, 152 , (2), pp. 145156

[11] SINGH B., SHILPAKAR L.B.: Analysis of a novel solid statevoltage regulator for a self-excited induction generator,IEE Proc. C , 1998, 145 , (6), pp. 647655

[12] SINGH S.P., SINGH B., JAIN M.P.: Performance characteristicsand optimal utilization of a cage machine as capacitorexcited induction generator, IEEE Trans. Energy Convers. ,

1990, 5, (4), pp. 679685

[13] SHRIDHAR L., SINGH B., JHA C.S., SINGH B.P., MURTHY S.S.:Selection of capacitors for the self regulated short shuntself excited induction generator, IEEE Trans. Energy Convers. , 1995, 10 , (1), pp. 1016

[14] WANG L., SU J.Y.: Effects of long-shunt and short-shuntconnections on voltage variations of a self-excited inductiongenerator, IEEE Trans. EC , 1997, 12 , (4), pp. 368374

[15] SINGH B., SRIDHAR L., JHA C.S.: Improvements in theperformance of self-excited induction generator throughseries compensation, IEE Proc. C , 1999, 146 , (6), pp. 602 608

[16] BIM E., SZAJNER J., BURIAN Y.: Voltage compensation of aninduction generator with long-shunt connection, IEEE Trans. Energy Convers. , 1989, 4 , (3), pp. 526530

[17] ALGHUWAINEM S.M.: Steady-state analysis of an isolated

self-excited induction generator driven by regulated andunregulated turbines, IEEE Trans. Energy Convers. , 1999,14 , (3), pp. 718723

[18] CHEN T.F.: Self-excited induction generator driven byregulated and unregulated turbines, IEEE Trans. Energy Convers. , 1996, 11 , (2), pp. 338343

[19] HAQUE M.H.: Characteristics of a stand-alone inductiongenerator in small hydroelectric plants. AustralasianUniversities Power Engineering Conf., Sydney, Australia,1417 December 2008

[20] MURTHY S.S., MALIK O.P., TANDOR A.K.: Analysis of self-excitedinduction generators, IEE Proc. C , 1982, 129 , (6) ,pp. 260265

[21] ALOLAHA.L., ALKANHALM.A.: Optimization-based steady stateanalysis of three phase self-excited induction generator, IEEE Trans. Energy Convers. , 2000, 15 , (1), pp. 61 65

[22] AL-JABRI A.K., ALOLAH A.I.: Capacitance requirement forisolated self-excited induction generator, IEE Proc. B,1990, 137 , (3), pp. 154159

[23] Matlab R2007a and Simulink, 2007

[24] KUNDUR P.: Power system stability and control(McGraw-Hill, New York, USA, 1993)

[25] HAQUE M.H.: Voltage regulation of a stand-aloneinduction generator using thyristor-switched capacitors.IEEE Int. Conf. Sustainable Energy Technologies,Singapore, 2427 November 2008

[26] MAHAN N., UNDELAND T.M., ROBBINS W.P.: Power electronics converters, applications, and design (John Wiley, 1995, 2nd

edn.)


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