MATLAB Based Steady State Analysis of Self Excited Induction Generator

Transcription

1 MATLAB Based Steady State Analysis of Self Excited Induction Generator S S Murthy, Sandeep Acharya Department of Electrical Engineering, Indian Institute of Technology, Delhi Hauz Khas, New Delhi -006 Abstract - This paper presents a MATLAB based technology to predict the steady state behaviour of Self Excited Induction Generator. Taking into consideration the fact of rapid growing popularity of Self Excited Induction Generator research has been centered on analysis, control and design of the same for standalone applications. In this paper to obtain relevant performance equations, symmetrical component theory is used to obtain performance equations. Steady state analysis is carried. To suit the computer simulation manageable equations were derived by incorporating some valid simplifications from the analysis. Non linear parameters were chosen corresponding to appropriate saturation levels. Results of this simulation help us in realizing the usage of 3-phase self induction generator in standalone power generation. Efficiency of MATLAB softwares is demonstrated for this application in contrast to earlier reported work. ABBREVIATIONS AND SYMBOLS The list of symbols used in this paper are as follows List of Symbols A operator e I(2lI/3) B C G F,v I R V w r X Y Z impedance Subscripts A,b and c; Susceptance Capacitance Conductance p.u. frequency and speed Current Resistance Voltage Rotor Speed Reactance of Load Admittance of load phases L G,2 and 0 sequence s andr and m Load airgap positive, negative and zero stator and rotor leakage and magnetising I. INTRODUCTION In the last 2 decades Self Excited Induction Generator has attracted considerable attention due to its application as a standalone generator using conventional and non conventional energy sources. While extensive literature is now available reflecting studies on SEIG, only a few are cited in references here. Induction machine modeling has continuously attracted the attention of researchers not only because such machines are made and used in largest numbers but also due to their varied modes of operation both under steady and dynamic states. Induction machines operate both in motoring and generation modes. Till recently motoring operation was almost universal. But recent exploitation of renewable energy systems such as wind and small hydro has led to use of grid connected and self excited induction generators. Out of these, self-excited induction generators are growing in popularity due to their advantages over the conventional synchronous generators and ease of use under standalone mode. The essence of simulation of such complex machines such as Self Excited Induction generator involves solving of complex equations of high order. In the method repeated so far, specific In the method reported so far, specific familiar procedures were evolved to obtain saturated magnetizing reactance and generated frequency under different operating conditions. In a recent paper[l] a general steady state analysis was presented under any unbalanced conditions. Operational equivalent circuit of induction machine was used in [2] to obtain unknown parameters, while Newton Raphson method was used in [3]. Steady state and transient analysis 749

2 dealt in [4] used the d-q transformation fixed to stator frame. Analysis of a novel -phase SEIG is using approximate equivalent circuit is explained in [5]. Optimization method is used to analyse unbalanced systems in [6]. However none of the work repeated so far exploits the advantages of recent software packages such as MATLAB to predict the performance of SEIG. This paper is an attempt in this direction to provide a user friendly software package. Thereby it is imperative to have a special user and batch oriented language, which can handle the complex equations with equal ease to handle the equivalent circuit equations. Thus the need arose to choose some advanced language which can assist in handling matrices etc to make the job of simulation much more easier for the programmer and the user as well. As a result of this, MATLAB/Octave was chosen as the language for the simulation. Now the availability of para MATLAB softwares, toolboxes can be created to estimate the performance of SEIG. This paper is a step in that direction to develop a complete toolbox of SEIG in MATLAB to make the numerical computations easier. II. PERFORMANCE EQUATIONS As a general case a 3-phase symmetrical induction machine(a,b,c phases) connected to unbalanced 3-phase capacitors and resistive load is considered as in Fig.l. Capacitor and load in parallel for each phase form unbalanced admittances Y ai, Y,L,Y CL. Symmetrical component concepts can be used to analyze such unbalanced systems using positive and negative sequence equivalent circuits. Certain simplifying assumptions can be made to evolve more manageable equations without much loss in accuracy.. All the equivalent circuit parameters except the magnetizing reactance are considered constant the latter being affected by saturation. 2. Core loss in the machine is neglected although it can be easily incorporated in the program. 3. MMF space harmonics and time harmonics in the induced voltage and current waveform are neglected. 4. Stator and rotor leakage reactance are taken to be equal. 5. Per Unit Frequency 'F' is taken to be equal to the per unit speed V except in the term (F-v) 6. In the negative sequence equivalent circuit the magnetizing reactance X m2 is taken as unsaturated whose value is very high compared to the rotor resistance branch in parallel. 7. The rotor rotates in a direction such that the phase sequence is a-b-c. Simplified Positive and negative equivalent circuits are as Fig.l Schematic Diagram of Self Excited Induction Generator Fig 2(a) Simplified Positive sequence equivalent circuit Fig 2(b) Simplified Negative Sequence circuit 750

3 j * ISO- As is very clearly seen from the above figures, to keep the voltage constant we have to increase the value of capacitance with the increase in load and vice versa. III.EQUATIONS By solving the equivalent circuits, Z, = R s + jvx, + jx ml * [vry(f-v) l] =40-20 JlOO -80 i r <S JO I' 5 nil in U 20 n u 0 Capacitance V Fig. 3 Magnetization characteristics CapacJance (Sm) Capacitance (Bp) S 6 7 Power(kW) Power to Keep Terminal Voltage Constant lor Three-Phase Balanced Load Fig 4. Capacitance v/w Power to keep the voltage constant for a 3-phase balanced load '- ^» ^ * y f M&p] j ^ ^ b(bcp) b**(snj b(6p) Power (kw) Winding Current Vs Pow lira-phase Balanced Load Fig. 5 Winding current v/s Power for a 3- phasc 55\fter separating the real and imaginary parts of the above equations can be simplified into two non linear equations in the unknown F and Xm as []. F(D,X ml + D 2 ) + (D 3 X nl,+d 4 ) =0 F(D 5 X ml + D 5 ) + (D 7 X ml +D 8 ) =0 Where, D! = 2*G,*X, - 4*G L * X, + B 5 * R s - B 4 P 2 (4) D 2 = X,[G X - 3G L Xr +B 5 R S - B 4 P 2 ] (5) D 3 = vr r [B 5 -B 4 ] - vd, (6) D 4 = P 3 - vd 2 (7) D 5 = 2*B 5 *X, - 4B 4 X, + G L P 2 - G^ + 3 (8) D^X.fBjX! - 3B 4 X, +G L P 2 - G,R S ] +3X, (9) D 7 = vr r (G L -G,) (0) D 8= P 4 -vd 6 () In equations 4- the defined constants are, P, = R s +R,/2 P 2 = P, + R s G, = K P,+ 2K 2 X B5- -K.2Hi+2iC[X[ P 3 = vr r [3+G L P 2 - G,R S - SBaX^BsX,] P 4 = vr r [B 4 P 2 - B 5 R S + 3G L X! - G,X,] K = - (Y al + a * Y bl +a 2 * Y cl ) /(3 Y 2 +Y al +Y b,+y cl ) By solving the above equations p.u. generated frequency F and saturated magnetizing reactance X m [ are obtained. The next step is to determine normalised airgap voltage Vg/F corresponding to this saturated X m,. As explained in [], the relevant magnetizing characteristics relating Vg/F 75

4 with X m i can be obtained by a synchronous speed test. Performance equations can now be written by using the equivalent circuit modified to generating connection, in which the current direction of I[,I 2 and I r i reverses. Since F is known now, the earlier assumption made i.e. F=v can be ignored. Thus after re-substituting we get, I, = VgAjFXm) + Vg/[(FR/F-v) + jfx,] V, = V g - (Rs+jFX,)I, V 2 = KV, I, = V 2 /Z, From these sequence quantities, phase voltages and currents in the machine can be computed using the following sequence equations, needed to stress on the fact that we can not use other toolboxes for implementing the same. Thus, many user-defined functions were made in the program so as to help the reader in assessing and/or modifying the same. Thus, the above set of equations were used and a flowchart was designed for its implementation. The flowchart can be written as under: Start Enter the values of Equivalent Circuit parameters, Capacitance, speed V b = V o + a 2 V, + a V 2 V c = V o + a V, + a 2 V 2 V a +V b + V c = 0 Calculation of sequence voltages, current and equivalent circuit Impedance Thus, Currents in the external network would be IaL=V a /(R a,+jfx al ) Similar equations can be written for It,L and I cl. Power output from the SEIG can be expressed as Calculation of Xm and f IV. PROPOSED METHODOLOGY USING MATLAB The task of simulating Self Excited Induction generator was not simple due to it involving solving of higher order equations, handling of complex numbers etc. Thus a suitable language had to be found to do the same. Due to the inherent capability of MATLAB, the abovementioned tasks become a lot simpler. This simulation is a step in the direction to make a complete toolbox for the performance estimation of SEIG under steady state conditions. Thus, by using the command line interface, suitable performance equations were entered in a file and executed using the batch level orientation of MATLAB. Also since this toolbox is a step towards achieving a complete toolbox, there Calculation of Performance of SEIG Using the performance ennatinns Stop V MACHINE DETAILS AND EXPERIMENTATION Relevant experimentation was carried out on a 3 phase 45/240V, 4.6/26.2A, 7.5KW 4- pole, Y/A connected squirrel cage induction machine driven by Thyristor fed DC motor to check the validity of the method of 752

5 S.No analysis. Fixed and saturation dependent parameters are determined as mentioned in []. R s = lqr r = 0.77ft X ls = X lr =0.77 Q. To measure the performance of the above machine as SEIG, necessary variable capacitor banks and loads are used with a controllable DC motor drive used as a prime mover. RESULTS A. Figures and Tables Fig.6 Voltage v/s Power for No V 0 L T T xo ISO :- Wilted ^_ compensation e '^c ftwr Cliaraoteil C4Q; a ao 2 3 * S Voltage KwerCKW ofs-ph.vt S T S Power(kW) As the above figure clearly show, the voltage v/s power characteristics of an Self Excited Induction generator feeding 3-phase R-Load. As, is very clearly observed from the equivalent circuit of an SEIG, the terminal voltage of an Self Excited Induction generator has to decrease with the increase in load under fixed value of capacitance, due to the lack of capacitive VAR compensation of the SEIG. As seen from the experimental results, the simulation of Self excited induction generator has a high accuracy due to the realistic assumptions made. Thus the simulation can be used in estimating the performance of Self-Excited Induction Generator. REFERENCES [I] S S Murthy, B Singh, S Gupta, B M Gulati : "General steady-state analysis of three-phase self-excited induction generator feeding three-phase unbalanced load/single-phase load for stand-alone applications", Generation, Transmission and Distribution, IEE Proceedings, Volume: 50 Issue:, Jan Page(s): [2] A.K.Tandon, S S Murthy and G J Berg : "Steady State analysis of capacitor self excited induction generators", IEEE Transactions on Power Apparatus Systems, 984, 03, pp62-68 [3] S S Murthy, B P Singh, C Nagmani and Satyanarayan: "Studies on the use of induction generators as self excited induction generators", IEEE Transaction Energy Conversion, 988, pp [4] L B Shilpakar: "Steady State and transient analysis of self excited induction generators", PhD Thesis, IIT Delhi, Department of Electrical Engineering, IIT Delhi, 998 [5] J E Brown, C S Jha: "Generalised Rotating Field Theory of polyphase induction motors and its relationship to symmetrical component theory", Proc Inst. Electr Engg, 962, 09(43), pp [6] P L Alger: "Induction Machines" (Gordon and Breach Science, New York, 2 nd Edition) [7] Murthy S S : " A novel self excited self regulated single phase induction generator part -basic system theory", IEEE Transaction Energy conversion 993,8(3), pp [8] Bhattacharya J L and Woodward J L :"Excitation balancing of a self excited induction generator for maximum power output" IEE Proc C- Gener. Trans. Distrib. 988,:35(2),pp88-97 [9] Jose R : "Investigations on standalone microhydel systems employing self excited induction generator and electronic load controller" M.S.(Research) dissertation, Department of Electrical Engineering, IIT Delhi, 999 [0] Murthy S S, Singh B : " A novel microhydel power generation system for single phase supply", Indian Patent 2000 [II] Mishra H N: "Analysis of three winding self excited induction generator for single phase load", M Tech Dissertation, Department of Electrical Engg, IIT Delhi, 996 [2] Smith NPA :"Induction generator for standalone micro hydro systems",proceedings of IEEE International conference on Power electronics, drives and energy systems for industrial growth, PEDES, New Delhi, India, January 996, pp [3] Murthy, S.S.; Rai, H.C.; Tandon, A.K.: "A novel selfexited self-regulated single phase induction generator. II. Experimental investigation" Energy Conversion, IEEE Transactions on, Volume: 8 Issue: 3, Sept. 993 Page(s):