IEEE Transactions on Energy Conversion, Vol. 5, No. 1, March 1990
ANALYSIS OF GRID CONNECTED INDUCTION GENERATORS DRIVEN BY HYDRO/WIND TURBINES UNDER REALISTIC SYSTEM CONSTRAINTS
S.S.MURTHY and C.S.JHA
Department of Electrical Engineering Indian Institute of Technology, Delhi
NEW DELHI 110 016 (India)
P.S.NAGENDRA RAO
Department of Electrical Engineering Indian Institute of Science
BANGALORE 560 012 (India) Abstract
Results of an investigation dealing with the behaviour of grid connecfod induction generators (GCIG) driven by typical prime movers such as mini- hydro/wind turbines are presented. Certain practical operational ..problems of such systems are identified. Analytical techniques are developed to study the behaviour of such systems . The system consists of the induction generator (IG) feeding a 11 kV grid through a step up transformer and a transmission line. Terminal capacitors to compensate for the lagging VAR are included in the study. Computer simulation is carried out to predict the system performance at the given input power from the turbine. Effects of variations in grid voltage, frequency, input power and terminal capacitance on the machine and system performance are studied. Analysis of self excitation conditions on disconnection of supply has • been carried out. Behaviour of a 220 kW hydel system and 55/11 kW & 22 kW wind driven system corresponding to actual field conditions are presented and discussed.
1_^ INTRODUCTION
In recent years considerable attention is focussed on Induction Generators (IG) for low and medium power generation, as they have certain inherent advantages over conventional alternators; low unit cost, less maintenance, rugged and brushless rotor (squirrel cage type), asynchronous operation etc. The energy crisis has necessitated the tapping of the vast mini-hydro and wind energy potential available in isolated locations. Since these generating units have to operate at remote unattended sites, a maintenance free system is desirable and the IG is highly suitable in such cases. Inductive VAR required by both the generator and the load has to be supplied by the grid, though connecting suitable shunt capacitors considerably reduces the VAR drain. Utilities have . often shown some reservations in such schemes due to the lack of data on the effects o£ frequent system disturbances in terms of voltage and/or frequency variations or grid failure. Therefore a study was undertaken to investigate the effects of variation of system conditions on the performance of the generator connected to the grid so that the suitability of the GCIG can be evaluated.
^ -f o l l o w i? 9 practical aspects encountered in the
GCIG operation have been identified for the study.
a) The
Even the grid failure/disconnection is not uncommon!
b) The input power to the generator can be normally
^ P ' c o[ ;s t a"t "i t h hVd r o turbines. The wind turbine o n the other hand provides varying power input dependent on the wind speed. Hence studies with both constant and varying input powers are required.
89 SM 630-5 EC A paper recommended and approved by the IEEE Energy Development and Power Generation Committee of the IEEE Power Engineering Society for presentation at the IEEE/PES 1989 Summer Meeting, Long Beach, California, July 9 - 14, 1989. Manuscript submitted February 1, 1989; made available for printing May 23, 1989.
c) Capacitors are connected to the generator terminals to improve the system power factor and to reduce the VAR drain from the grid . Effect of capacitor sizes will have to be assessed to arrive at a suitable rating.
d) The terminal capacitor may cause 'self excitation' and result in high voltages under disconnection from the grid and subsequent overspeeding of the turbine.
If self excitation has to be avoided capacitor should either be below a certain value (which may compromise with (c) above) or should be automatically disconnected under grid failure. Thus the knowledge of the minimum capacitor to cause self excitation at different speeds should be known to check whether the power factor improving capacitor is larger than this value. Alternative-ly, with the connected capacitor the variation of self excited voltage with speed should be assessed.
Analytical techniques to study the above problems are presented in the paper and appropriate computer algorithms are developed. Cafe has been taken to choose realistic system parameters so that the data presented is reliable for use by system designers.
Typical power ratings of induction generators used in mini-hydro and wind power units are chosen for study.
As a study of mini-hydro system details of a 220 kW IG unit planned for installation in India have been considered. For wind energy systems horizontal axis wind turbines driving 55/11 kW sets are considered.
This configuration consists of two IGs 55 kW and 11 kW; the 55 kW unit is coupled to the main shaft connecting the turbine through a gear (typical ratio 1:22). Speed of the 11 kW set is made higher than the 55 kW set by a factor of around 1.25. 11 kW unit operates at low wind speeds (around 3 to 5 m / s e c ) , while the 55 kW unit operates at high wind speeds
(upto about 20 m/sec).
Since standard Induction motors are preferred to be used as IGs, choice of the appropriate motor is important as there are different designs of motors for . each rating, e.g. NEMA A, B, C, D designs. Criteria for the right choice of motor is discussed in the paper.
2^ ANALYTICAL TECHNIQUES
Fig.l shows the schematic diagram of the system considered. The induction generator is driven by a prime mover which is a hydro or a wind turbine. It feeds power to the 11 kV grid through a step-up transformer (415 V/ 11 kV) and an 11 kV tranmission line. For generality terminal capacitors are shown on both LV and HV sides of the transformer though only, one of them would be present in a given situation.
2.1 Effftot' of wv«t.ftm paramwt.f.r.i:
In this the system is considered to be in steady state and the equivalent circuit approach is used wherein the generator and the associated network are represented by the circuit of Fig.2(a), (drawn fox the base frequency referring all quantities to LV side) using the/ollowing symbols: V, I, R, X, E, Y and S represent per phase voltage, current, resistance, reactance, impedance, admittance and p.u. slip respectively. Subscripts S, L, T, CL, CH, G, s, r, m correspond to System (grid), transmission line, transformer, LV capacitor, HV capacitor, generator, stator, rotor and magnetising branch respectively.
The model as shown in Fig. 2(a) has been made realistic by including the core loss (Rm ) HV and LV capacitors (YG t_, Y C M) , Transformer impedance (R-T- X--) line impedance CR^, X |_ ) and short circuit reactance of the grid (Xg ). The performance analysis of the ' IG system using the above equivalent circuit would have been a very straight-forward problem, if the slip could be considered as a known control variable. However, this is not so here. For the
normal induction generator, the problem centers around determining the responses such as current, slip, etc.
for the given value of power input P and system voltage V . Though one may estimate P for different S and fix S corresponding to the given P the procedure is obviously cumbersome and direct estimation of S from P is preferred, especially when we are interested to know the effects of variation in grid voltage, frequency, terminal capacitance and power input. Such a direct computation method is explained here.
The power input to the generator is taken to be the turbine output minus the friction and windage losses and is given by
2
Pin = - 3 Ir Rr (1 - S)/S (D (Since S is negative Pin is positive)
To find the response at constant P / « and V^ , a simplified 'Thevenin1 equivalent circuit as given in Fig 2(b) can be used where Z ^ ( = Rtfi + Jx th\ a n d
VM. correspond to the Thevenin equivalent impedance affti voltage looking from the terminals of Rr/S. From Fig.2(b)
Vth +(Rth + Rr /S + j Xth) Ir =0 (2) Knowing V« and system parameters Vth and Zth can be
estimated. We no« have two eqns . (1) >' (2). w" ' \t u o
unknowns Ir and S to be determined. From Fitf. ~(b) - 2 2 "'*•
I r = V t h ^ t R t h + R r / S ] + XtlA . . . . ( 3 ) S u h s t.i t u t i n g f o r I r f r o m ( 3 ) i n ( 1 ) a n d s i m p l i f y i n g , w e g e t a q u a d r a t i c e q u a t i o n ' i n S ( i n t e r m s o f P ) o f t h e f o r m
415V: 11 kV Transformer
< Transmission
Ind
Prime ' Btntrator
rotor ^Capacitor i P i g . l . Schematic of the System
11 kV grid
i!!L i ! k Rs
Pig.2(a) Equivalent Circuit
A S + BS + C = 0 . ( 4 )
where A - R
v /p
t h i B = 2 R R
th r
3 V /P
th i = R
Eqn.(4) can be easily solved for S. Knowing the p.u.
slip S, the active power, reactive power, power factor, efficiency at the generator and the grid can be easily obtained based on the equivalent circuit of Fig'. 2(a) .
2+Z Analysis under self iSEA
The analysis under self excitation is aimed at (a) determining the minimum capacitor size to cause self excitation at different, speeds and (b) estimating the self excited voltage and current due to the connected capacitor during overspeed; these two aspects are no doubt interlinked.
A technique to estimate minimum capacitance for SE [1]
using the operational equivalent circuit of the motor is employed here. With no supply source the operational loop impedance when equated to zero yields a characteristic polynomial in the time derivative operator p with complex coefficients which are functions of machine parameters, capacitance and speed. SE is ensured if one of the roots of this polynomial lias a positive real part, v.'hich tends to zero at minimum capacitance at that, speed. Thus the minimum capacitance for any speed to cause self-excit- ation can be estimated by a computer a.1 gorithin based on this principle.
The steady state equivalent circuit of Fig.3 can be used to estimate the self excited voltage and current for the given capacitive reactance xc (at base frequency) and p.u. speed •'d. Here F, the p.u frequency, and x^are the unknowns. Equating the loop impedance, corresponding to the loop current Id to zero and separating real and imaginary parts, two non linear equations in x_and F are obtained, which can be solved by Newton-Raphson method [3], taking suitable initial values. Corresponding to this saturated x airgap voltage ^«of Fig.3. is obtained using the saturation charac-Ceristics of the IG. Knowing Vy, F
Fig.2(t>) Theveniii Jiquivalent Circuit
J*lr
j xls
Stats ai Circuit under SE and x yrt the self excited terminal voltage V^.
currents I and I are obtained using Fig.3.
different speeds.
and for
iu COMPUTER SIMHLA1IQH
The models presented for the steady state and the self excitation behaviour can be directly simulated on a computer by developing suitable algorithms. The computer program developed to analyse the steady state behaviour has four segments. The first segment computes the equivalent circuit parameters at base frequency. The second optional segment is used when the p.u, frequency f ^ 1 , as it computes the circuit parameters of Fig.2 for non base frequencies. The third segment determines the slip for the specified power input. Here V-fy and Z fcfcf Fig.2(b)are determined using circuit parameters. Then (4) is used to find S. The fourth segment is used to determine all the performance quantities of interest with slip and Vs being known.
As already mentioned the computer algorithm for performance analysis under self excitation would (a) estimate minimum capacitance to cause 8E at- different speeds, say from 0.6 to 2 p.u and (b) estimate the self excited voltage and current with the connected capacitor at the above speed range.
For (a) above the roots of the characteristic polynomial resulting from the operational equivalent circuit [1] are determined using a subroutine, to ensure that one of the roots has a positive, real part.
Value of C is iterated till that real part becomes, zero yielding minimum C for that speed. The computation is carried out for different speeds For Cb) above with C fixed, the saturated xm and F for the given speed are obtained using the Newton-Raphson method to solve the two equations derived from Fig.3.
Using the simulated saturation curve, the airgap voltage V is obtained for the above x . By simulating the volt-ampere equations derived from Fig.3 the self excited voltages and currents are estimated.The process is repeated for different speeds
Analysis has bee generating schemes
!, RESULTS fiND DISCUSSION
I carried out on three practical listed below.
Scheme I Hydro t u r b i n e driven 220 kW Induction
£el~.< rno 11 : Wind t u r b i n e ( h o r i z o n t a l
55/11 kW Induction g e n e r a t o r . axis) driven Scheme III : Wind turbino (vertical axis) driven 22 kW Induction generator.
Normal Induction motors of the same rnt.infl nrp.
employed as generators. Details of the generators and associated systems are listed in Appendix I.
In 11 kV grids, voltage and frequency may vary over a wide range. A series of curves
showing the effects of variation of grid voltage and frequency at constant power input and capacitance need to be generated. By obtaining data on system response under varying power input, we can determine the maximum possible power input to the generator, which is limited by the winding currents and heating. Study of variation of input power i-s of great importance specially in the case of wind turbines to assess the power delivered to the grid at different wind speeds, and to specify the optimum rating of the generator to be used. Results obtained at different values of terminal capacitors would indicate the optimum value of capacitor to be. chosen to achieve the desired power factor at the grid. Effect of these capacitors on other system responses is also of interest. Results are presented in this paper keeping the above points in view. All quantities are represented in p.u. of corresponding machine ratings, as it is felt that such a representation would make the results more meaningful and useful in studying other similar systems.
4.1 Results with Hzdxo. z scheme
Results are presented in Figs.4(a - c) for the 220 kW set where the following response quantities are plotted taking grid voltage, grid frequency, power input and capacitance as variables, considered one at a time. From a perusal of these results the following observations can be made.
Ef£est sf variatisn in Sxid V_oli.age and Freouencv To deliver rated power at generator terminals, input power had to be fixed at 1.055 p.u. (232 kW), which results in nominal generator current at nominal voltage and frequency jtnd this current is 0.95 times the motor full load current. Current drops with voltage and rises with frequency, highest value occuring at the lowest voltage and highest frequency, a situation unlikely to occur as both grid voltage and frequency rise or fall simultaneously depending on the load on the system. Range of current variation is 0.9 3 to 1.12 times generator nominal current or 0.89 to 1.14 times motor nominal current. This band would be narrowed if simultaneous drop or rise of voltage and frequency is considered. System current decreases by G% due to capacitor.
Copper loss decreases in stator and increases in rotor under generating mode when compared to motoring mode.
Since, the squirrel cage rotor has higher thermal withstand capability this is acceptable. Further, there is a decrease in copper loss when terminal capacitors (75 kVAR) are used. The sum of stator copper loss and core loss can be taken to be the main source of heating. For the cosidered range of variation of voltage and frequency, this total loss is given in Table.1.- This sum remains almost constant since under the condition of high copper loss (low voltage, high frequency), core loss is low due to decreased flux and vice versa. Thus one need not take on alarmist view of the machine heating under these grid fluctuations as similar variation in losses are observable even in motoring mode under identical grid disturbance and a normal thermal relay can protect the machine.
SDM OF
TABLE z 1
STATOR COPPER LOSS AND CORE LOSS DIFFERENT VOLTAGE AND FREQUENCY
(kW) AT
Freq.
p.u. 0.9 1.0 1.05
0.85 1.0 1.05
6.68 6 . 5 5 6 . 6 3
6 6 6
. 9 4 . 6 5 .715
7 . 6 . 6 . 2 7 76
Power fed to the grid varies from 0.94 to 0.97 p.u.
due to variations in line losses, while generator output almost remains constant. With the terminal capacitor, there is a marginal increase (2%) in power fed to the grid resulting in improved efficiency.
Efficiency variation follows the same pattern as power variation . Variation of Reactive VAR and power factor given in Fig.4 are explicit and need no comment.
Generator requires more VAR than a motor due to increased airgap voltage and flux. For machine considered VAR required was 0.623 p.u. as generator against 0.56 p.u. as motor. By connecting a capacitor of 75 kVAR (0.34 p.u), grid PF. raised from 0.81 to 0.95 as the VAR demand dropped from 0.69 to 0.32 p.u.
A capacitive VAR equal to 35% of the machine power rating can be recommended for these ratings.
Effect of variation in i
These resuitr, as given in Figs.4(b) though more relevant to wind generator applications, nonetheless provide guidelines on optimum power of operation for hydro sets. Obviously output current and power increase with input power. Maximum system efficiency is at a power input of about 0.92 p.u. It is interesting to note that there i3 a wide band of power input at which the efficiency, both of the system and the machine, is fairly high. It is observed that by connecting a capacitor of 100 kVAR (0.455 p.u), a significant improvement in system efficiency, which remains almost constant ovel' the power range can be achieved.Further,the system PF is considerably improved resulting even in leading PF at low power ranges. UPF condition is observed at 0.7 p.u. of input power. It is significant to note that under varying input conditions the terminal capacitor improves the system performance (both efficiency and power factor). The PF which is in the range 0.22 to 0.81 without capacitor improves to a range 0.9 to 1.0.
Effect of variation of Terminal Cap.aciior.
When the terminal capacitor is varied from 0 to 200 kVAR, the generator terminal voltage raises by 5%, while current falls. Power and Efficiency vary as shown in Fig.4(c). Obviously reactive VAR and power factor are affected by capacitance. UPF condition is observed at a VAR of above 0.63 p.u. beyond which leading VARs are drawn from the grid at full load.
Internal performance of the generator is unaffected by capacitor.
ITT
4. 2 Results wiih wind generating scheme
Results pertaining to IG's used in wind energy schemes II and III mentioned above are presented in Figs. 5(a - d) indicating the variation of performance quantities with power input. These normalised curves would be very useful in designing such systems.
Knowing the power input to the generator at different wind speeds the power fed to the grid, system current, efficiency, power factor, VAR drawn etc, can be estimated using these characteristics. It is found that the p.u. capacitive kVAR required for improving the system PF is not the same as it increases at lower ratings. For the 55, 11 and 22 kW sets 20, 8 and 10 (or 15) kVAR capacitors respectively were found to be suitable.
4.3 Criiaria far. cheesing tha mcier. fox operating as It is desirable to chose a normally available Induction motor for generator operation, as no changes in design and manufacturing strategies would be called for. However, different types of motor designs are available. These are broadly classified as NEMA A, B, C & D, designs depending on their starting and running perf oruTJnce. Different characteristics are achieved by employing different types of squirrel cage rotors such as die cast, brazed, single cage/ double cage, deep bar or sash bar configurations. We have to chose one of these designs for generator operation.
Good criteria would be minimum VAR requirement and higher output and efficiency at rated current. Thus
'running' performance of the motor gets preference over 'starting' performance. Studies were made using different designs under generating mode to check the 3bove criteria. It is found that class A designs normally meet these requirements, though in some cases class B designs were also found suitable. Results presented for 220, 55, 11 and 22 kW sets in Figs.4 & 5 except 5(c) pertain to class A design. Results of a class B design of the 22 kW set employing a double cage rotor is presented in Fig. 5(c).In this case it is seen that class B design results in reduced VAR drain.
NoJ:e_: (1) A^ll y - a x i s q u a n t i t i e s are in per unit in F i g . 4 T a ) .
( 2 ) Th_e quantity represented i s _^n<H ~ cated in the
4.4 Results under- self excited condition
Fig.6 shows the minimum capacitor (expressed in p.u.
kVAR) required for self excitation for the above machines at different speeds, indicating a decrease in capacitance as speed increases. At increased • IG rating the p.u. capacitor decreases. Obviously during turbine overspeed due to load 'throw off there is a high probability of self excitation due to the connected capacitor. Self excitation occurs for speeds above that at which minimum C corresponds to the connected capacitance. These capacitor values are 0.34, 0.364, 0.46 and 0.73 p.u. for the 220, 55, 22 and 11 kW sets respectively to obtain a grid PF of 0.95. Fig.7 shows the variation of self excited voltage and current with speed with these capacitors.
Alarmingly high voltages and currents are induced if the speed is allowed to reach near 2.0 p.u.
The curves presented in Figs.6 & 7 are useful in the choice of capacitors and are helpful in assessing their impact under self excitation.
0 - 96 -
rreqtp.u}
1-2
1-0
0 - 8
0 - 6
0-4
0 - 2
0 - 0 - -
— Current (p.u.) -- •/• Slip x 0-2
-
" ^ ^ " ^ " - ^
\ *0-95
i 1 i
Freq (p.u.)
Freq (p.u.) 1-051
1 • 00 1 K
«t 1
" i
0-9 ;i 1 0 - 9 3
0 - 9 4
0 - 9 0
0-85 0-9 0-95 1-0 1-0S I GRID VOLTAGE ( p.uj —•
( i ) p . u . ouTrerxt& s l i p . L 0 8 8
c - Power output at generator d - Power output at grfd
0. 90
0 8 6
0-84
0-82 /
0 8 0
0-78
0 7 6
— RF. at the grid (no capacitor) RF at generator ( - d o — ) RF. at the grid (with 75kVAR
capacitor freq. = 1-Op.u) __ Freq.(pu)
""" " """^ 0-9 - - - ' " ~ ~ "r~ ~ — 0-95
er input = 1-055p.ut
0-45 0-95 1-0 1-05 I -10
GRID VOLTAGE (p.uj
power output at generator « ^
( i i l )""££«£
a*
Fig.4(a). Effect of variation £D Grid voltage and frequency.
0 - 8 5 0 - 9 0 0 - 9 5 1 0 1-05 n GRID VOLTAGE ( p u . ) — « -
&
' • o h
t - O l -
0-2 Without capac'tor
With capacitor (lOOkVAR) J.
0-2
Lead
0-6 0-8 1-0 1-2 POWER INPUT ( p . u . ) - »
0-4 0-6 0-8 1-0 POWER INPUT (p.u.) „
1-2 0 - 0
0-0
). Effect of variation in input power.(all <iuantities in p.u.) a:current(p.tt.),e:power at generator^ dspovier at the grid,
e,ftefficiency of generator-,systesi.g,litreactive power at generator, grid i, it power- factor at generator,grid.
N c>_t e_: A ^ _ J ^ J
0-2 0-4 0-6 0 8 CAPACITOR kVAR ( p.u.)
Fig.4(c) Effect of variation of terminal capacitor.
5- CQNCLUSIQHS
Behaviour of normal Induction Motors operating as generators driven by Hydro/Wind Turbines feeding a 11 kV grid through a step up transformer is studied, System representation has been made realistic by taking into account actual operating parameters of the machine, transformer and line impedance and short circuit reactance of the grid. A simple computer algorithm has been developed to determine the system response at constant power input. Studies are made considering variations in grid voltage, grid frequency, power input and VAR compensation level.
Typical results are graphically presented using p.u.
notation so as to provide useful guidelines to generator manufacturers and utilities. Analysis of self excitation during grid disconnection has been carried out both with respect to the capacitance values causing self excitation and the expected range of induced voltages and currents.
Following are the major observations based on this analysis:
i) A normally designed Induction motor can perform well as a generator feeding power to a 11 kV grid ii) Deterioration in performance due to fluctuations in grid voltage and frequency is not very appreciable, forthe range of variations considered
iii) Connecting a terminal capacitor of suitable value the system power facctor can be improved to about.0.95 at nominal power output. This also results in marginal improvement in system efficiency, with reduced losses.
iv) Induction generator can be effectively used with varying power input (as with a wind turbine), maximum power being limited by machine capacity. Terminal capacitor considerably improves system efficiency.
v) With connected capacitor as in (iv), there is a possibility of self excitation on disconnection of grid coupled with overspeeding of turbine, causing the voltages to reach upto 2 - 3 p.u. with associated high currents at a speed of 2.0 p.u., needing appropriate precaution.
S+ ACKNOWLEDGEMENT
This project was undertaken on behalf of M/S. Kirloskar Electric Company Limited, (KEC), Bangalore. The authors express their sincere thanks to the Management of KEC, for supporting this study and for the permission to publish the results. Authors thank their affiliating Institutions I.I.T, Delhi and I.I.Sc..Bangalore, respectively for providing the necessary support.
1+ REFERENCES
1. S.S.Murthy, G.J. Berg, C.S.Jha and A.K.Tandon, "A Novel Method of Multistage Dynamic Braking of Three Phase Induction Motors", IEEE Trans on IA, Vol.IA-20, March/April 1984, pp 328 - 334.
2. S.S.Murthy and P.S.Nagendra Rao, "Behaviour of Grid Connected Induction Generators under Realistic Power System Constraints", Paper No.C5-l, Fourth National Power System Conference, EHU, Varanasi, Feb.
1986.
3. S.S.Murthy, O.P.Malik and A.K.Tandon, "Analysis of Self Excited Induction Generators", Proc. IEE, Part C, Nov. 1982, pp 260 - 2R5.
1 '86) wa
I n He M , f r I n T e
< 1 ( 1 .
s d i a T e e oni d i a c h n 9 6 9 9 7 4
DO o r h . B g n o l
) )
r n n De ecei a n d incfal osiy
an r e s p
i
<::• e
v e P o r I n Bo d e c
Insti Joine and 1973.
P r o f e D u r in E l e c t u p o n h i s
mber 6t 1.946 • d t h e B . E J h.D. • decjr ees e University?
s t i t u t e of rribly (I IT ) I I T J Delhi t:i. vely ,
After teaching a year gt the Sir la tute of Techno lossy and Science* Pilani» he d I IT Delhi in 1.970 as A s s o c i a t e Lecturer was promoted to the post of Lecturer in A s s i s t a n t Professor in 1975* A s s o c i a t e ssor in 1980> and Professor in 1.983.
i<3 1975 -76 he was at the D e p a r t m e n t of rical Engineering* U n i v e r s i t y of N e w c a s t l e Tyne ( E n g l a n d ) as V i s i t i n g s t a f f ' Using s a b b a t i c a l leave he worked as a V i s i t i n g
0-8
0 - 4
0 - 0
Without capacitor
With capacitor 20WAR (0-364p.u.)
0-0 0-2 0-4 0-6 0-8 1-0
POWER INPUT (p.u.) — . -
(a) 55 Jew. 6-pol
€generator.
-With capacitor lOkvAR (0-455p.u.)
0 - 8 _
0-6 -
5- 0 - 4 -
0-2 -
0 - 0 0-0 0-2
POWER INPUT (p.u.) —fc-
(c) 22 kW. 4-pole generator (Class-a design)
Without c a p a c i t o r
w;t h C Q pa c i ' t o r SkVAR (0-73 p.u.)
0-0 0-2 0-4 0-6 0-8 1-0
POWER INPUT ( p . u ) — »
(T>) 11 kw. 6-pole generator
-Without capacitor
1.0 -
0-8 -
0-4 -
With capacitor !5kVAR
0-0 0-2 0-4 0-6 0-8 1-0 1-2
POWER INPUT (p.u.) —to
d 1-6 -
ig^.5« Characteristic of Wind driven Induct ion Generator at varying power input.
atmachlne CTtrrent, iMmachine efficiency, ctpower fed to grid, d:p.u.slipxlO etsystem current, fsViR drawn from grid, gtPF at grid
a- 22 kW, 4 pole II k W , 6 pot*
0-4 -
1-0 1-2 S P E E D ( p u ) »
Pig. 6. MinimaB capacitance for self-excitation
at different speeds.
SPEED ( D . U . ) —m-Pig.7.Variation of self-excited current &
voltage with speed.
APPENDIX z 1
DATA REGARDING THE GCIG SYSTEM STUDIED
Common Data: Generator - 415 V, 5- Hz, Grid - 11 kV, 50 Hz, Transformer impedance - (0.0165 + j 0.0428)p.u.
H.V. Transmission line impeedance - (1.021 + j 0.382) ohm/Km.
Short circuit MVA of the grid = 250
Length of. HV line = 10 km (Hydro) and 2 km (Wind)
Equivalent circuit parameters in p.u.
IG Typical Transformer Class of Rated/
Rating Prime Rating Design Base
(kW) Mover (kVA) Curren R R x x x R (A) s r Is lr m m 2 2 0 M i n i 2 5 0 A 3 6 0 0 . 0 1 3 5 0 . 0 2 4 0 . 1 0 5 0 . 1 6 9 3 . 3 4 7 2 . 2 ( 6 P o l e ) H y d r o ( Y d l l )
T u r b i n e
5 5 w i n d 6 3 A 9 3 0 . 0 1 9 0 . 0 1 6 4 0 . 0 6 9 0 . 0 8 7 3 . 0 4 7 . 8 5 ( 6 P o l e ) T u r b i n e
(Horizontal axis)
11 » A 21 0.0504 0.0493 0.076 0.132 2.35 32.8 (6 Pole)
22 Wind Turbine A 42 0.031 0.0256 0.0657 0.094 2.08 42.5 (4 Pole) (Vertical axis)
22 " B " 0.0492 0.031 0.0933 0.179 3.19 52.42 (4 Pole)
'
S c i e n t i s t / F e l l o w at the U n i v e r s i t y of C a l g a r y E l e c t r i c a l M a c h i n e T h e o r y grid aPPl least i o n s and (Canada.) f r o m N o v e m b e r 1.980 to May 1 9 8 2 . He p u b l i s h e d a l a r g e n u m b e r of r e s e a r c h p a p e r s in w o r k e d a t the R&D d e p a r t m e n t o f Kirlosk.gr n a t i o n a l and i n t e r n a t i o n a l J o u r n a l s . H a s b e e n E l e c t r i c Co.? Bans) a lore as a v i s i t i n g i n - h o u s e i n v o l v e d in p l a n n i n g and a d m i n i s t r a t e i o n of C o n s u l t a n t d u r i n g 1 9 8 5 - 8 6 aod e x e c u t e d s e v e r a l t e c h n i c a l e d u c a t i o n i n India s i n c e the e a r l y p r o j e c t s r e l e v a n t to the I n d u s t r y . He w a s 1 9 7 0 s . He w a s D i r e c t o r of the p r e s t i g i o u s I IT a l s o a.n a d j u n c t P r o f e s s o r of the I n d i a n at K h a r a S p u r d u r i n g 1 9 7 4 - 7 8 and w a s i n c h a r g e of I n s t i t u t e o f S c i e n c e * B a n g a l o r e ? d u r i n g t h i s T e c h n i c a l E d u c a t i o n p l a n n i n g a t the N a t i o n a l year> level a s E d u c a t i o n a l A d v i s e r t o t h e G o v e r n m e n t of India ( 1 9 7 9 - 8 4 ) . He h a s b e e n a f o u n d e r He h g s p u b l i s h e d a n u m b e r of p a p e r s and member- of t h e I n d i a n S o c i e t y for T e c h n i c a l h a s e d i t e d and p u b l i s h e d two l a b o r a t o r y E d u c a t i o n and h a s t a k e n a c t i v e p a r t i n m a n u a l s . H e h a s c o m p l e t e d many i n d u s t r i a l l y C u r r i c u l u m p l a n n i n g and d e v e l o p m e n t o f s p o n s o r e d p r o j e c t s . H i s c u r r e n t i n t e r e s t a r e a s e n g i n e e r i n g e d u c a t i o n i n I n d i a . H e h a s w o r k e d i n c l u d e e l e c t r i c a l m a c h i n e s ! e l e c t r i c drives? a s V i s i t i n g P r o f e s s o r i n nany u n i v e r s i t i e s i n t h y r i s t o r a p p l i c a t i o n s ? e f f i c i e n t e l e c t r i c the Uest? h i s l a t e s t a t t a c h m e n t w a s a s e n e r g y u t i l i s a t i o n ? i s o l a t e d power g e n e r a t o r s ? P r o f e s s o r o f E l e c t r i c a l E n g i n e e r i n g a t the w i n d ? w a v e and ra i c r o hy d r o p o wer g e n e ra. t i o n ? P e n n s y1v ani a St a te Un i ve r s i t y i n U . S . A . (19 8 5- encfineering e d u c a t i o n . 8 7 ) . W a s a m e m b e r o f t h e B o a r d o f T r u s t e e s o f t h e A s i a n I n s t i t u t e o f T e c h n o l o g y ? B a n g k o k He is a F e l l o w of t h e I n s t i t u t i o n of ( 1 9 / 4 - 8 6 ) and w a s C h a i r m a n of its E d u c a t i o n a l E n g i n e e r s ( I n d i a ) and a L i f e M e m b e r of the P o l i c y C o m m i t t e e ( 1 9 8 2 - 3 6 ) . He is a m e m b e r s of I n d i a n S o c i e t y for T e c h n i c a l E d u c a t i o n . I n t h e U N E S C O i n t e r n a t i o n a l w o r k i n g g r o u p o n 1 9 7 6 h e r e c e i v e d the P r e s i d e n t o f India A w a r d C o n t i n u i n g E d u c a t i o n o f E n g i n e e r s ? s i n c e 1 9 7 5 . for t h e b e s t r e s e a r c h paper p u b l i s h e d in the He is a F e l l o w and C h a i r m a n ? E l e c t r i c a l J o u r n a l s of the I . E . ( I ) . E n g i n e e r i n g D i v i s i o n of the I n s t i t u t i o n of
E n g i n e e r s .
I n d i. a n 1.964.
V.L±. QhMUltM. Shekh^r.
J I "i a ? b o r n a t V i J a y a n a g a r ( B i h a r ) on 1.7.1934 and e d u c a t e d a t P a t n a U n i v e r s i t y ? I n d i at n 1 n s t i t u t e o f S c i e n c e ? B a n g a 1 o r e ? H e r i o t - W a 11 C o 11 e 9 e ? E d i n b u r g h ( U . K . ) a n d B r i s t o 1 U n i v e r s i ty (U.K.)? h a s b e e n a P r o f e s s o r o f E l e c t r i - cal E n g i n e e r i n g at the technology Delhi (I. IT) s i n c e
- i g n i f i c a n t c o n t r i b u t i o n i n
P.S. Na/jendra, Rao was born in Periyapatna*
Karnataks? India in 1950. He received his BE ( E1 e c t. ) a n d M E ( P o w e r S y s t e m s > f r o m t h e University of Mysore? Mysore in 1.971. and 1.973 respectively. In 1.981 he obtained his Ph.D.
degree from the Indian Institute of Technology?
Delhi .
From 1.973 to 1.984? he was on the faculty of the Electrical Engineering Department of the National Institute of Engineering* Mysore. In 1984? he Joined the Electrical Engineering Deptt. of the Indian Institute of Science?
Bangalore? a.s ^n Assistant Professor. His field of interest are Load Flow Studies? Design of Distribution Systems and Application of Parallel Processing for Power System P r o b l e m s .
