33rd Power Electronics Specialists Conference 23 - 27 June 2002 Cairns Convention Centre, Queensland, Australia
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Paper 2-4-2 A Nonlinear Control Method of Dynamic Voltage Restorers 1 2 1 1 1 2 S. Chen , G. Jóos , L. Lopes , W.N. Guo , Concordia University, CANADA, McGill University, CANADA Paper 2-4-3 A Novel Control Strategy for Unified Power Quality Conditioner (UPQC) 1 2 1 1 2 M. Tarafdar Haque , T. Ise , S.H. Hosseini , Tabriz University, IRAN, Osaka University, JAPAN
SESSION 2-5:W IND GENERATION SYSTEMS Session Chair: Zhe Chen, Aalborg University, DENMARK Paper 2-5-1 A New Fuzzy Logic Controller to Improve the Captured Wind Energy in a Real 800 kW Variable Speed - Variable Pitch Wind Turbine 1 1 1 1 1 2 2 M.M. Prats , J.M. Carrasco , E. Galván , J.A. Sánchez , L.G. Franquelo , C. Batista , Á. González , S. 2 1 2 Hurtado , Universidad de Sevilla, SPAIN, MADE Tecnologías Renovables SA, SPAIN Paper 2-5-2 New Formula to Determine the Minimum Capacitance Required for Self-Excited Induction Generator A.M. Eltamaly, Elminia University, EGYPT Paper 2-5-3 A Reliable and Efficient New Generator System for Offshore Wind Farms with DC Farm Grid M. Henschel, T. Hartkopf, H. Schneider, E. Troester, Darmstadt University of Technology, GERMANY
SESSION 2-6:PASSIVE COMPONENTS Session Chair: Roberto Prieto, Universidad Politecnica de Madrid, SPAIN Paper 2-6-1 Embedded Capacitance in the PCB of Switchmode Converters 1 2 3 3 1 J.A. Ferreira , E. Waffenschmidt , J.T. Strydom , J.D. van Wyk , Delft University of Technology, THE 2 3 NETHERLANDS, Philips Research Laboratories, GERMANY, CPES, Virginia Polytechnic Institute and State University, USA Paper 2-6-2 Using Supercapacitors to Improve Battery Performance T.A. Smith, J.P. Mars, G.A. Turner, cap-XX Pty. Ltd., AUSTRALIA Paper 2-6-3 A Passive Soft-Switching Snubber for PWM Inverters 1 2 3 1 2 F.Z. Peng , G-J. Su , L.M. Tolbert , Michigan State University,USA, Oak Ridge National 3 Laboratory, USA, University of Tennessee, USA
SESSION 3-1:CONTROL OF DC CONVERTERS Session Chair: Fang Lin Luo, Nanyang Technological University, SINGAPORE Paper 3-1-1 Control Bandwidth and Transient Response of Buck Converters K. Yao, Y. Meng, F.C. Lee, CPES, Virginia Polytechnic Institute and State University, USA Paper 3-1-2 A Novel Synchronous Rectification Circuit Using a Saturable Current Transformer 1 1 2 2 2 1 K. Kuwabara , H. Matsuo , K. Kobayashi , K. Nishimura , Nagasaki University, JAPAN, Fujitsu Denso Ltd., JAPAN Paper 3-1-3 New Driving Scheme for High-Efficiency Synchronous Rectification in Wide-Input-VoltageRange DC/DC Converter has Output Current Always Flowing Through a Low-Resistance Switch 1 2 1 1 1 1 P. Zumel , N.O. Sokal , P. Alou , J.A. Cobos , J. Uceda , Universidad Politécnica de Madrid, 2 SPAIN, Design Automation, Inc., SPAIN Paper 3-1-4 Modeling and Simulation of New Digital Control for Power Conversion Systems 1 1 1 2 1 G. Capponi , P. Livreri , M. Minieri , F. Marino , Università di Palermo, ITALY, 2 STMicroelectronics, ITALY Paper 3-1-5 Small Signal Modelling of a Half Bridge Converter with an Active Input Current Shaper A. Fernández, J. Sebastián, M.M. Hernando, P. Villegas, Universidad de Oviedo, SPAIN Paper 3-1-6 Analysis of DC-DC Converters with Current-Mode Control and Resistive Load when using Load Current Measurements for Control B. Johansson, University of Kalmar, SWEDEN Paper 3-1-7 A Simple Low-Loss Linear Negative Resistor Emulator J.S. Glaser, General Electric Global Research Center, USA
New Formula to Determine the Minimum Capacitance Required for Self-Excited Induction Generator ALI M. ELTAMALY, PhD Electrical Engineering Department, Faculty of Engineering Elminia University, Elminia, Egypt E-mail: eltamalv@,vahoo.com Abstract- Induction generator is the most common generator in wind energy systems because of its simplicity, ruggedness, little maintenance, price and etc. The main drawbacks in induction generator is its need of reactive power means to build up the terminal voltage. But this drawback is not an obstacle today where PWM inverters can accurately supplies the induction generator with its need from reactive power. The minimum terminal capacitor required for induction generator to build up is the main concern. Most of previous work uses numerical iterative method to determine this minimum capacitor. But the numerical iteration takes long time and divergence may be occurs. For this reason it cannot be used online. A new simple formula for the minimum selfexcited capacitor required for induction generator is presented here. By using this formula there is no need for iteration and it can be used to obtain the minimum capacitor required online. Complete mathematical analysis for induction generator to drive this new formula is presented. The result from this new formula is typical as the results from iterative processes.
I. INTRODUCTION Induction generator has a widely acceptance in using with wind energy conversion systems for many reasons. Induction generator is very simple, very rugged, reliable, cheap, lightweight, long lifetime (more than 50 years), produces high power per unite mass of materials and requires very little maintenance. All above advantages are very important especially in wind energy conversion systems where the generator is in the top of the tower where the weight, maintenance and life time are very important aspects. Induction generator can be used with stand alone as well as grid connected wind energy conversion systems. Also, induction generator works with constant speed constant frequency systems as well as variable speed constant frequency systems. The main drawback of induction generator in wind energy conversion systems applications is its need for leading reactive power to build up the terminal voltage and to generate electric power. Using terminal capacitor across generator terminals can generate this leading reactive power. The capacitance value of the terminal capacitor is not constant but it is varying with many system parameters like shaft speed, load power and its power factor. If the proper value of capacitance is selected, the generator will operate in self-excited mode. The capacitance of the excitation capacitor can be changed by many techniques like switching capacitor bank [l], [2], thyristor controlled reactor [3] and thyristor controlled DC voltage regulator [4]. In last decade many researches uses PWM technique to provide the desired excitation by controlling the modulation index and the delay angle of the
0-7803-7262-X/02/$10.00 Q 2002 IEEE.
control waveform [ 5 ] . All previous techniques require an accurate capacitance value for the terminal capacitor with changing the system parameters. Many researches have been done to determine the minimum capacitor for self excited Induction generator [6,7,8,9,10]. Most of these researches use loop equations in the analysis of induction generator equivalent circuiit [7], [8]. Most of these researches have much difkulty and it needs numerical iterative techniques to obtain the minimum capacitance required. Some of these researches require several minutes of computation by computer to obtain accurate value for the minimum capacitor required for this reason it is impossible to uses these methods online [9].
11. INDUCTION GENERATOR EQUIVALENT CIRCUIT The structure of squirrel cage induction generator is same as induction motor have alurrunum bar winding laid into the slots of the rotor core and short-circuited at both ends. Single-phase equivalent circuit of three-phase cage generator is similar to three-phase transformer equivalent circuit with one winding is short-circuited, and the same circuit models apply as shovm in Fig.1 (all reactances are refereed to rated frequency, 5 and the stator side). The terminal capacitor shown in Fig.1 is to feed the induction generator with the required reactive power. The circuit shown in Fig.1 can be used in steady state operation. But, in case of v,arying operating frequency of the generator, this circuit can be modified to be as'the circuit shown in Fig.2 [ll]. 'The elements of this circuit is corresponding on the rated fiequency. In this circuit, the machine core losses have been ignored. In fact, for minimum capacitance requined, the machine must operate at threshold of saturation. Therefore, ignoring such losses will result in no serious errors in estimating C,,, [6]. The successfully build up in sellf-excited induction generator occurs when X , have a value in saturation such as shown in Fig.3 (i.e. X, should be less thanX,,)
Fig. 1 The equivalent circuit of one phase of three-phase induction generator.
106
P(X,,a) = (4X,+ 4 ) a 3+ (AJ,
+ A4)a2
+(4X,+%>a +(4X,+ $1 = 0
-I
Q(X,,u) = (BIX, + B2)a4+ (B3X, + B4)a3
(5)
(6)
+(B,X, +B,)aZ + ( B , X m + B * ) a + B , = o The values of coefficientsAl to A8 and Bl to B9are
I Rr
given in [7].
__.____I
Knowing the relationship between X, and (Via) (It can be experimentally determined [7]) it is possible to compute C,, by using the following iterative procedure: (i) Assume initial value of terminal capacitor C and solve ( 5 ) and (6) for X , and a. The initial value of C should be large enough to cause self-excitation of self-excited induction generator; X, has a value that lies in the saturation region. (ii) Gradually decrease the value of C in steps and compute X, corresponding to each value of C. A plot of X, versus C is thus obtained. (iii) C,, is obtained from such a plot as the intersection of X , versus C curve and the line X,=X,, where X,, is the maximum saturated reactance of the machine.
,....._.____________________.~.~.,
Fig.2 Modified equivalent circuit of induction generator.
Where the slip S is shown in equation (1)
Divided (1) by Nsp Then; S=- a - b a
In this method the variation of X, with VJfis taken into account.
I
The magnetizing reactance X, decreases with increasing saturation as shown in Fig.4. The value of X, corresponds to an operating point tangent to the magnetizing curve is X,, that can be experimentally determined [7]. The value of X, of the machine varies with operating conditions; the assumption of single value of X, in the analysis is acceptable [6] and [lo].
Im Fig.3 The saturation characteristicsfor induction generator.
III. CALCULATING C ,, BY USINGLOOPANALYSIS The calculation of C,, by using loop analysis technique has been presented in many researches [6], [7], [8] and [lo]. This technique is listed in this section to explain its drawbacks. The loop equation for Is of Fig.2 can be written as :I,Z=O (3) Where Z is the loop impedance seen by the current, Is and can be obtained as in (4) z=z, +ZLC+ZS (4) Where
Z ,,
=(+]Il[$+
If we use the value of X, in.the calculation of C,, then the result is the minimum the minimum capacitance required (Cmifl)for successful build up in self-excited induction generator. According to this assumption (X, = constant) reference [6] modifies ( 5 ) and (6) to be as shown in (7) and (8) are function in a and Xc. - ala3+ a2a2+ (a3X , + a4>a- a, X, = o (7) -b1a4+b2a3+(b3X , + b 4 ) a 2 +(b, X , +b,)a-b, X , = O Then by separation of Xc in (7) and (8) we can get the following two equations: X, =
j X L ) And Z,
=S+ R jX,
ala3-a2a2- a4a a3a-a5
(9)
x, = b1a4- b2a3- b4a2- b,a
a
b, a' - b5a- b,
In steady state operation IS f 0 otherwise there is no generated voltage. Then; from (3); Z has to be equal to zero. By equating both the real and imaginary parts of (3) by zero we get two nonlinear equations ((5) and (6)) in function of X , and a. Solving ( 5 ) and (6) together yields the values of X, and a.
The Coefficients al to a5and bl to b7 are positive real constants given in [61. By equating the right hand sides in (9) and (10) then we have the following equations:-
107
ala3- a2a2- U,U
b1a4- b,a3 - b4a2- b6a -
a3a-a,
b 3 a 2-b,a-b,
(11)
(a,b3 -a3 b,)a4-(a, b 3 + a ,b, - a 3 b, - a 5 b,)a3
+ (U, b5 + a3b, - a, b, - a, b, - a, b, )aZ
(12)
-(a3b, + a , b, - a 4 b, - a 2 b,)a+ (a, b, + a , b7)= 0
From (12) the frequency can be calculated and then substitute this ftequency in (9) or (10) to calculate Xc and C,;,,. Then [6] can eliminate the iteration process and numerical solution in [7] and [8].
IV.NEW FORMULA TO CALCULATE C M ~BY, USING NODALANALYSIS The proposed technique uses nodal analysis instead of loop analysis to obtain just one formula for the minimum capacitance required for induction generator operation at different load and speed conditions. In this technique, the operating frequency can be obtained directly from equating the real part of admittance with zero where the real part does not function in &, then use the imaginary part to calculate the value of XC. The new proposed method is explained in the following:Applying the nodal analysis at the terminal voltage V, of the circuit shown in Fig.3 we get the following equation:-
-Y,=o v, U
Where Y, = Kn +Y, +Y, shown in Fig.2)
(all these admittances are
Then, Real of Y, = 0 And Imaginary of
(14)
=0
(15)
After some algebraic operations we can get the following:1-
From real part we get the following equation:-
c, a4+ C3a3+ C2a2+ C p + CO= 0
(16)
The Coefficients C,,,n=O, 1, 2, 3, 4 are shown in Appendix 1. The coefficients of this equation do not contain Xi. The frequency can be obtained directly by solving (16) to get the operating frequency. There are four roots; the positive real roots only have the physical meaning. If there is no any positive real root, then there is no self-excitation.
The coefficients MI,MI, h43 and M4 of (17) are shown in Appendix I . In this method we used the real part of Y,=O to determine the frequency due to the resultant equation does not contains Xc and substituting this frequency in imaginary part to calculate C,;,, in a simple form as shown in (17). This new formula can be used on line to calculate the minimum capacitor required for induction generator to build up. This new formula does not require any numerical analysis iteration.
v. APPLICATION AND RESULTS To validate the above formula (17) we can use the same machine in [6] and [8]. The data are: X, =3.23 pu, R, ~ 0 . 017PU,R, =0.088 1 PU, X, = X, =O. 1813 PU,2b343.3 N= 1800 revlmin,f6=60Hz, R,:=1 pu, XL=2pu, b = 1 pu. Applying these data to (16) and solve it for the frequency we get only two positive real roots which are (~)~=0.5191 and (~)~=0.9937. Applying these frequencies to (17) we get the corresponding capacitors C1=:200pF and C2=42.95 pF. Then, the minimum capacitor is Cmi,,=42.95pF. The same results are obtained in the two methods loop and nodal analysis. Also it is the same results as shown in the two references [6] and [8]. The consistence in the results from (17) and results of (3) can prove the accuracy of the new formula (17). The variation of the minimum capacitance required with rotational speed in the same generator [6] and [8] at RL=l pu, XL=Opu is shlown in Fig.4. It is clear that the required capacitance is inversely proportional with the speed. Fig.5 shows the variation of the minimum capacitance required with rotational speed in the same generator for at no load. It is clear also the steady state operation of induction generator at no loads requires a terminal capacitor inversely proportional with the shaft speed. Fig.6 shows the variation of reactive power required for the induction generator and the output power with rotational speed at RL=lpu and unity power factor. It is clear fiom Fig.6 that the active and reactive power is increasing with speed.
Fig.7 shows the variation of reactive power required for the induction generator and the output power with rotational speed at different values of load resistance (RL=0.7,1and 2pu) and unity power factor. It is clear from Fig.7 that the active and reactive power is increasing with speed.
2- From the imaginary part we can drive a simple formula for the minimum value of terminal capacitor as shown in (17).
The variation of the stator frequency with rotational speed is shown in Fig.8.
108
-
,uF
C,
I
: Active powbr
100
80
60 40
20 0
50
100
150
50
200
% speed Fig.4 variation of
c,,
100 %speed
200
150
Fig.6 Variation of reactive power and output power with rotational speed at RL=lpu and unity power factor.
with rotational speed at RL=lpu and unity power factor.
3
I
:
I
Active pcjwer
80 60 40
20 50 I
100
50
150
I 200
,c,
150
%Speed Fig.7 Variation of reactive power and output power with rotational speed at different values of load resistance (R~=0.7,1and 2pu) and unity power factor.
%Speed Fig.5 Variation of
100
with rotational speed at no load.
109
REFERENCES
4
I 1.8
[ 11 R. M Hilloowala, A. M. Sharaf“ Modeling, simulation and analysis of variable speed constant frequ.ency wind energy conversion scheme using self excited induction generator”, 1991. Proceedings, TwentyThird Southeastern Symposium on System Theory, Page(s): 33 -38. [2] E. Muljadi and J. Sallan, M. Sam and C. P. Butterfield “Investigation of Self-Excited Induction Generators for Wind Turbine Applications”, LPS conference, IEEE, 3-7 October 1999, Phoenix, Arizona USA. [3] A. A. Shaltout and M. A. Abdel-Halim, “ Solid-state control of a wind driven self-excited induction generator ”,International Journal on Electric machines andpower .systems,vol. 23, 1995, pp. 571-582. [4] N. Ammasaigounden, M. Subbiah “Chopper-controlled wind-driven self-excited induction generators” IEEE Transactions on Aerospace and Electronic Systems, 1989 Volume: 252, Page@): 268 -276. [5] S. Wekhande V. Agarw “Wind Driven Self-Excited Induction Generator with Simple De-Coupled Excitation Control” US conference, IEEE, 3-7 October 1999, Phoenix, Arizona USA. [6] A. K. Al. Jabri and A. L. Alolah “ Capacitor requirement for isolated self-excited induction generator“,ZEE proceedings, Vol. 137, pt. B, No. 3, May 1990 [7] N. H. Mal& and S. E. Haque “ Steady state analysis and perfomance of an isolated self excited induction generator” IEEE Trans., ~ 1986,EC-1, “ ~ ~ 2 (3).~ pp. 134-139. [8]N. H. Malik and A. A. Mazi “ Capacitance requirements for isolated excited induction generators”, IEEE Trans., 1987, EC-2 (I), pp. 6269. [9] M. Orabi “design of wind energy conversion system”, MSc. Electrical Engineering Department, Faculty of Engineering, Elminia University, Elminia, Egvpt, 2000. [lo] S. S. Murthy and N. H. Malilc and A. K. Tandon ”Analysis of self excited induction generators”, ZEEproceedings, Vol. 129, pt. C, No. 6, November 1982. [ 113 Say, M. G. “Alternating Current Machines”, book, pitman, 1976.
/A
A No load
4:’
1.4
L=lpu
0
~ N
*
W
O
a
O
C
-
x
p
~
E
~
Fig.8 Stator frequency with rotational speed is for different loads.
VI CONCLUSIONS In this paper a new formula for the m i n i ” capacitance required for self-excited induction generator is presented. This new formula is simple and it does not need numerical iteration. For this reason this new formula helps to determine the minimum capacitance required for self excited induction generator on line. The new formula gives typical results as the results obtained fiom iterative technique without any iteration or divergence problem.
Appendix 1
LISTOF SYMBOLS Actual or (generated) fiequency, P*N&20. Actual or (generated) rational speed, 120 fJP. Rated fiequency of induction generator , P*N,420. Rated speed of induction generator, 120f/P. Synchronous speed corresponding to actual fiequency. Synchronous speed corresponding to rated fiequency. Pu fiequencyfdfr Pu speed NJNsr. Slip of induction generator. Load resistance. Load inductance. Inductance of terminal capacitor. Stator resistance. Stator inductance. Magnetizing inductance. Rotor resistance. Rotor inductance. Terminal voltage. Maximum value of magnetizing inductance. Magnetizing current. Loop impedance. Output real power. Reactive power required for induction generator. Capacitance of the terminal capacitor. Minimum capacitance of the terminal capacitor.
110
The coefficientsof equation (: 16)
c4= X;R, ( L L,~ - L , ) + X ; R , L: + R, L;, C, =X;R,v(L, - L , L , ) - 2 v ( X ~ R , L : + R L L ~ ) ,
c, = R;(R,
r: - RJ,+R ~ L+,;Y;R, ~ (R; + g v z )
+ 2 * RLR, R,(L, L, - 4 ) +RLL(L&’ + R:L,
C, = RZR, v(L, - L, L 3 ) - 2v R, R,L: (R,
+ L’, v 2 ) R , R, (R, t.R , )
CO=(R:
The coefficientsof equation (17) M,=R,R,-f~f-v)L, Y
M2
=Rrf
M3 = R i
L3
+ R, (f
+ X: f
9
and
M4 =R, * M 2- L2f (f- v)A4, Where, L1= x,( X , + X,)
+ x,x,,
L2 = X , + X , and, L3=X,
+x,
+ R:c ,
+ R, )
and,
‘
