This paper presents an induction generator model that can be used for simulations to investigate and evaluate the control strategies for variable speed operation of doubly fed induction generators driven by wind turbines in transient conditions. The model makes use of rotor reference frame

Chellapilla, Srinivasa R.

Chowdhury, Badrul H.

English

Missouri University of Science and Technology (Missouri S&T): Scholars' Mine

Missouri University of Science and Technology Scholars' Mine Electrical and Computer Engineering Faculty Research & Creative Works Electrical and Computer Engineering 01 Jan 2003 A Dynamic Model of Induction Generators for Wind Power Studies Badrul H. Chowdhury Missouri University of Science and Technology, bchow@mst.edu Srinivasa R. Chellapilla Follow this and additional works at: https://scholarsmine.mst.edu/ele_comeng_facwork  Part of the Electrical and Computer Engineering Commons Recommended Citation B. H. Chowdhury and S. R. Chellapilla, "A Dynamic Model of Induction Generators for Wind Power Studies," Proceedings of the IEEE Power Engineering Society General Meeting, 2003, Institute of Electrical and Electronics Engineers (IEEE), Jan 2003. The definitive version is available at https://doi.org/10.1109/PES.2003.1270995 This Article - Conference proceedings is brought to you for free and open access by Scholars' Mine. It has been accepted for inclusion in Electrical and Computer Engineering Faculty Research & Creative Works by an authorized administrator of Scholars' Mine. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact scholarsmine@mst.edu. A Dynamic Srinivas R. Chellapilla model of Induction Generators for Wind Power Studies Abstract: This paper presents an induction generator model that can be used for simulations to investigate and evaluate the contml strategies for variable speed operation of doubly fed induction generators driven by wind turbines in transient conditions. The model makes use of mtor reference frame. Keywords: Induction generator, refemnce frame theory, variable speed operation, wind machine. I. INTRODUCTION n the US, a total of 1,700 MW of wind power were added Association. The rest of the world received more than 1. in the year 2001, according to the American Wind Energy Badml H. Chowdhury, Senior Member, IEEE C,= Coefficient of performance (typically 0.35) The relationship between rotor speed and wind speed can be given by: /2=O"R ( 2 )  I' where R = wind machine rotor radius, w, = rotor speed in radlsec, and h = tip speed ratio = ratio between the linear speed of the tip of the blade with respect to the wind speed. Thus Q. (1) becomes: (3) 4,800 MW of wind power capacity in the same year. So whv is wind getting so much attention where c,, is the value of C, at a specific value of h. Wind-generated electricity has become more economical to produce in the past 10 years, dropping from as much as 30 cents per kilowatt-hour to 4 to 6 cents, making it more competitive with other energy sources. The cost to develop and build a wind energy facility is approximately $1 million per megawatt, compared to a cost for gas-fired energy generation of $550,000 to $700,000 per MW. Also with tax credits and other state and federal incentives, wind can become major players in the future energy delivery infrastructure. The federally sponsored wind production tax credit provides 1.8 cents per kilowatt-hour generated for the first 10 years of a wind turbine's output. So, turbines built by the end of 2003 will qualify for the tax credit for 10 years. The wind energy sector is expected to grow about 20 percent B year, with an emphasis on Europe, the US. and Latin America. With increasing penetration of wind-derived power in interconnected power systems, it has become necessary to model the complete wind'energy systems in order to study their impact and also to study wind plant control. This paper presents a model of the induction generator written in There are two basic options for wind power conversion ~ fixed speed and variable speed operation. In fixed speed operation, the aeroturbine can be operated at a constant speed by blade-pitch control of the wind turbine even under varying wind speeds. This option was very common because of the cost involved with the power converter needed in the variable speed generation to convert the variable frequency to match the constant grid frequency. In variable speed operation, the aeroturbine rotational speed can be allowed to vary with wind to maintain a constant and optimum tip speed ratio. A constant speed wind turbine is designed to obtain a maximum efficiency at one wind speed that will give the optimum tip speed to wind speed ratio for the rotor airfoil. The variable-speed operation by active pitch angle control allows optimum efficiency operation of the turbine over a wide range of wind speeds, resulting in increased power outputs [3].  Fig. 1 shows how variable speed operation will allow a wind turbine to capture more energy from the wind [4,5]. 2500 I I I I - appropriate d-q reference frame to facilitate investigation of control strategies. Wind turbine power depends on both rotor speed and wind speed [ 1, 21. Aerodynamic power available in the 2000 5 1500 a .B 1000 wind can he calculated using Eq. (1). - P =0.5p AC,v' (1) 5 500 where, P = power in watts 0 400 600, 800 1000 Shaft speed(r/mn) p = air density (about 1.225 Kg/m3 at sea level) 0 Fig. 1. Wind turbine power characteristics A = rotor swept area; v = wind speed in Wsec 0-7803-7989-6/03/$17.00 02003 IEEE 2340 As one can see, the maximum powcr follows a cubic relationship. For variable speed generation, an induction generator is considered attractive duc to its flexible rotor speed characteristic in  contrast to the constant speed characteristic of synchronous generator .Doubly fed induction generator conliguration is best suited lor variable speed generation since i t  can he controlled from rotor sidc as well as stator side [6J. This is possible since rotor circuit is capable of bidirectional power flow .The doubly fed machine can he operated in generating mode in both sub-synchronous and super-synchronous modes [7]. The rotor will absorb slip power from the grid in sub synchronous operation and can feed slip power back to grid in super synchronous operation. The cost of power converter can be reduced greatly by employing doubly fed conliguration such as a wound rotor machine[X], since power converter can be designed to be partially rated as is needs to carry only slip power. All these advantages make the doubly fed induction generator a favorable candidate for variable speed generation. A commonly used model for induction generator converting power from the wind to serve the electric grid is shown in Fig. 2. Utility connection Wound rolor Slip energy control in rotor circuit Fig. 2. Simplified model of a doubly-fed induction generator In this paper, an attempt is made to develop a dynamic model of induction generator which can be simulated as a doubly fed generator when testing control strategies. Though the model developed in this paper can be used for simulating all types of induction generator configurations, the choice of rotor reference frame makes it particularly favorable for the simulation of doubly fed configuration in transient conditions [XI. 11. LIST OF SYMBOLS v ~ , v ~ , , v ~ , , v ~ ~  = d - q  axis machine voltages. ids, iqr, idr , i9, = d - q axis machine voltages Y = flux linkage q, =base electrical frequency (rated) U=angular velocity of reference frame U, =angular frequency of rotor T,, = electromagnetic torque Tmech =externally applied mechanical torque (from wind turbine shaft) Td,,,p =damping torque r = resistance x = reactance H = inertia constant Subscripts: d ,  q = d-q axes s, r =stator, rotoi 1 = leakage managnetking Superscripts: ' = referred value 11. DYNAMIC MODEL The equations (1)-(4) can be found in literature[X] and 191. Using the rotor reference frame: w= w, and v9, = vd, = 0 Substituting these conditions the above equations boil down to: The currents can now be calculated as: Ymq and Yd in the above four equations are calculated by: 2341 1 Where = (1 / X", + 1 / X I >  + I  / X l i )  Now that we knowYq,,  iq,,  Y&and id, the electromagnetic torque can be calculated by: The equation that govems the motion of rotor is obtained by equating the inertia torque to the accelerating torque: Expressed in per unit values the above equation becomes 111. METHODOLOGY For maintaining proper flow of variables and for convenience of simulating, the above equations are separated into the q-axis, the d-axis and the rotor circuits. In the q-axis circuit, the Eq. ( 5 ) .  (7), (9), (11)  and (13) are used to calculatey',,% , Y'qr,  i , ,  , i',,.and Y,,,, respectively and yqA and i, arc used in the calculation of electromagnetic torque. In the d-axis circuit, the Eq. (6), (8), (10). (12) and (14) are used to calculatey', , y'd,, id,, i',,and yd respectively and Yd,  and are used in the calculation of electromagnetic torque. The rotor circuit makes use of the yqS and i,, obtained from the q-axis circuit and yd., and i, obtained from the d- axis circuit and calculates the electromagnetic torque using Eq. (15).The rotor circuit also takes the input mechanical torque values supplied to it and computes -from Eq. (17). Sirnulink@ U, Ua Fig. 3 shows an implementation of the above model on Fig. 3. Implementation of the induction generator model in Sitnulink@ operated with variable speed so that it will operate in the peak power tracking mode. A varying wind speed profile is applied to the generator to investigate its performance. The wind speeds were changed at t=0.6, 0.8, 1.2 and 1.6 seconds to 5 d s ,  7 d s  and 11 d s  respectively. The peak powers corresponding to wind spceds of 5 m / s ,  7 m / s  and 11 d s  were 180 W, 480 Iv. RESULTS The Simulink model is simulated with parameters as shown in Table 1. Vaz, vh,, vcg are the applied voltages to the stator from the grid. The wind turbine is assumed to be 2342 Induction Generator Characteristic Stator winding resistance 3.35 ohm 2.616 ohm Value resistance as refcrred to Time (Sec) 0 0.6 0.8 I .2 1.6 Rotor leakage reactance 1 2.616ohm Rotor inertia 1 0.1 Kg-m2 TABLE 11.  MECHANICAL POW:R CORRESFUNOLNGTOTHE OPI~MUY w m  SPEED AND ROTOR SPEED Wind Speed Mechanical (&sec) (W) 0 0 5 180 7 480 9 1060 11 1980 Power V. CONCLUSIONS The choice of the reference frame will affect the waveforms of all dq variables. It will also affect the simulation speed and in certain cases the accuracy of the results. Generally the conditions of operation will determine the most convenient reference frame for analysis. The following guidelines are adopted for choosing the reference frame [8]: Case I :  Stationary reference frame should be used if the stator voltages are unbalanced and the rotor voltages are balanced. Case 2:  Rotor rcference frame should be used if the rotor voltages are unbalanced and the stator voltages are balanced. Case? Either the stationary or synchronous reference frame can be used if all voltages are balanced and continuous. Since our objective is to develop a dynamic model of induction generator for rotor side control studies, Case 2 applies to our model and rotor reference frame is chosen accordingly with acceptable results. References G.L. Johnson. Wind Energy Syrremr. Prentice~Hall. 1985. C.G. Justus. Windr arid Wind Sysrerri Pefhnance,  The Franklin Institute Press, 1978. R.D. Richardson. G.M. McNemey. "Wind Energy Systems," I'rocredingr o/.the IEEE. Vol. 81, No. 3. March 1993, pp 378 - 389. P.W. Carlin, A.S. Laxson, E.B. Muljadi. "The History and State of the An of Vanable-Spd Wind Turbine Technology." Nurionol R e w w b l e  E n q y  Labs. NREW-500-28607, February 2001. Available from: l ~ t t p : i i r r w u . . n ~ l . ~ o ~ ~ i ~ ~ ~ i ~ d ~ l i ~ ~ ~ ~ ~ . h t ~ ~ ~ l  C.S. Bwne. R. S p ,  A.K. Wallace. "Experimntal Evaluation of a Variable-Speed Doubly-fed Wind Power Generation System" IEEE Transactions on Industry Application. Vol. 30. No. 3. 648-655. MayNune 1994. S. Muller, M. Deicke. R.W. De Doncker, "Doubly Fed induction Generator System for Wind Turbines." IEEE Industry Applications Magazine. Vol. 8. No. 3, 26-33, MayIJune 2002. W.L Kling. H. Polinder. J.G. Slwtweg. "Dymmic modeling of a wind turbine with doubly fed induction senerator." Power Engineering Society Su,nnwr Meering. Vancouver, Canada. July 2001. P. C. Krause. 0. Wasynczuk. S. D. Sudhoff.. Ana1ysi.s "f electric muchineq and drise swem.~, IEEE Press Power Engineering Series. pp l41-l87.2002 Chre-Mun Ong. D.vnomic simulorion of elccrric mochinr!y, Prentice Hall PTR, pp 167-258, 1998 Bioaraphies Srinivas Chellapilla received his BTech degree in Electrical and Electronics Engineering from Jawaharlal Nehru Technological University, Kakinada, India in 2000. He is presently an MS student at the Department of Electrical Engineering, University of Missouri-Rolla. Badrul H. Chowdhnry obtained his M.S. and Ph.D. degrees in Electrical Engineering from Virginia Tech, Blacksburg, VA in 1983 and 1987 respectively. He is currently a Professor in  the Electrical & Computer Engineering department of the University of Missouri- Rolla. From 1987 to 1998 be was with the University of Wyoming's Electrical Engineering department where he reached the rank of Professor. Dr. Chowdhury's research interests are in power system modeling, analysis and control; power electronics and drives. 2343 stator phase t o  neutral voltage 200 > .5 m m > -200 0.7 0.75 0.8 stator current 0.6 20 .c 0 4 In m .- -20 1.2 1.4 1.6 1.8 2 o.2 0.4 o.6 od!&elopeld toraue 20 I. I I I E z: -40 I I I I I I I I I I I 0 0.2 0.4 0.6 0.Fu speeJ.2 1.4 1.6 1.8 2 I I I I I I I I I ..+ ..-.. -----,---.---~------ I I I 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 time in sec Fig. 4. Dynamic responsc of the induction generator to variable wind speeds 2344 

A Dynamic Model of Induction Generators for Wind Power Studies

https://scholarsmine.mst.edu/cgi/viewcontent.cgi?article=2351&amp;context=ele_comeng_facwork

A Dynamic Model of Induction Generators for Wind Power Studies

Abstract

Similar works

Full text

Available Versions

Missouri University of Science and Technology (Missouri S&T): Scholars' Mine