Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 3 (4): 729-733 Scholarlink Research Institute Journals, 2012 (ISSN: 2141-7016) jeteas.scholarlinkresearch.org Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 3(4) 729-733 (ISSN: 2141-7016) Modeling of a Stand-Alone Induction Generator on Load Using MATLAB Simulink Tilak Thakur and Shailendra Kumar Gupta Punjab Engineering College, Chandigarh. Corresponding Author: Shailendra Kumar Gupta Abstract The work in this paper had been motivated by the increased role of renewable source based energy generating systems in today s world of power deficit and increased complexity in power generation. Also, it gives a simulated platform to study the physical system before making it operational. This paper proposes a MATLAB simulink model of a stand-alone induction generator used in renewable source based power generation on load. Rotor and stator d-q axis current has been chosen as state variable in the mathematical model with an aim of developing a simple stand-alone induction generator simulink model. The proposed simulink model was then used to study the electrical and mechanical dynamics of the generator on varying the load across the machine also, the operating phenomenon is analyzed and the discussion is verified by referred papers. This paper also put forward the increased role played by induction generator in the field of stand-alone generation. Keywords: renewable source, matlab simulink, microgeneration, self excitation, single phase induction generator (SEIG) INTRODUCTION In present scenario due to increased power demand, limited fuel supply, emission of green house gases and increase in the complexity of system need for a standalone non-conventional renewable source based generating system has increased. These generating units are helpful in lighting remote areas where transmission is not only difficult but also not cost effective. Among distinct stand alone generation alternative, small hydro power station using synchronous generator (SG) can be considered the most efficient one.sg has many technical advantage such as good voltage control, stability, frequency control and thus, its complexity and it s demand of skilled labour force for maintenance and operation make it sometime, economical unviable[guiliani and Figueiredo 2011]. Thus, self excited induction generator (SEIG) comes into picture. SEIG use induction machine that are low cost, robust, easily available in market and also needs low skilled labour force for its maintenance and operation [Bhim Murthy, and Gupta, (2005) [Grantham, D. Sutanto and B. Mismail, 1989]. As far as operation of SEIG is considered it is an induction generator that is governed by self excitation phenomenon to generate a steady voltage across its terminal. The initiation of the self-excitation process is a transient phenomenon and is better understood if the process is analyzed using the transient model for both the voltages and currents. Granthum et al. have demonstrated the initiation of the voltage build-up process by discussing the transient phenomenon in the RLC circuits. In this case the stator of the self-excited induction generator may be represented by an RLC 729 circuit in which the transient voltage and current have terms of the form k*exp(st). The root s is often a complex quantity and its real part, which is adjusted by the saturation of the magnetic circuit. In this paper the simulink model, to simulate the SEIG, is developed [Dawit, Colin, and Muhammed 2003]. MATHEMATICAL MODEL For the modeling of the self-excited induction generators, the main flux path saturation is accounted for while the saturation in the leakage flux path, the iron and rotational losses are neglected [Dawit, Colin, and Muhammed 2003]. Therefore in the following analysis the parameters of the induction generator are assumed constant except the magnetizing inductance which varies with saturation [Dawit, Colin, and Muhammed 2003]. In the proposed simulink model d-q current of rotor,idr and Iqr, and stator,ids and Iqs, are taken as state variable. Current Equations The current equation in the stationary reference frame for squirrel cage or wound rotor induction machine in the generating mode are [4] piqs = a1iqs +a2ids +a3iqr +a4idr +a5kq+ b6vcq (1) pids = b1iqs +b2ids +b3iqr +b4idr +b5kd + b6vcd (2) piqr = c1iqs +c2ids +c3iqr +c4idr +c5kq + c6vc (3) pidr = d1iqs +d2ids +d3iqr +d4idr +d5kd + d6vcd (4) Where a1, a2, a3, a4. are variables and there values are given in appendix. Here, Kq and Vcq0 are initial voltage across q-axis rotor winding and stator winding respectively and Kd and Vcd0 are initial voltage across d-axis rotor winding and stator winding respectively.
Voltage Equation Voltage across the terminal of the SEIG are given by [Dawit, Colin, and Muhammed 2003] Vcq= (1/C)*ʃIqs dt +Vcq0 (5) Vcd= (1/C)*ʃIds dt +Vcd0 (6) C. Mechanical dynamic equation Governing mechanical equation of SEIG are [4] Tsh =Te + J*(2/P)*pωr Thus, Pωr = (P/2J)*(Tsh-Te) (7) here, Te is taken as Te = (3/2)*(P/2)*Lm*(Ids*Iqr Iqs*Idr) (8) The model consist of 3 subsystem accommodating varying inductance (subsystem 1), machine internal behavior (subsystem 2) and mechanical dynamics of machine (subsystem 3) respectively. The machine subsystem models the equation of induction machine on load in d-q axis in stationary reference frame that has been shown in figure 2. Here, Te is the electromagnetic torque generated by machine, Tsh is the turbine input torque, J is inertia of the machine plus turbine, P is the no. of pole, pis the derivative, wr is the rotor speed of machine in radian per second and Lm is the magnetizing inductance. Magnetizing Characteristic Since the operation of the SEIG takes place in the nonlinear region of the magnetization characteristics, therefore the magnetization current should be calculated in each step of integration in terms of both stator and rotor currents using the following formula. Im =sqrt(imq^2+imd^2) (9) Where, Imq= Iqr + Iqs (10) Imd= Idr +Ids (11) Accounting the saturation of magnetic circuit, on experimental basis, the saturated magnetizing inductance is varied in terms of magnetizing current which is given by [Dawit, Colin, and Muhammed, 2003] Lm=a+bIm+cIm 2 +dim (12) a, b, c, d are constants whose values are given in appendix II The above set of equation is then modeled by using MATLAB simulink model as shown in figure1 Fig 2. Machine subsystem simulink model In varying magnetizing system the inductance is varied in accordance to magnetizing current by equation 12. This varied inductance is then feed to machine governing equation that is governed by equation 1-6 and mechanical dynamics governing equation 7 and 8 that produces new set of stator and rotor current which is then feed back to the subsystem 1 and accordingly inductance of the magnetic circuit is changed. This cycle continues until steady state condition is reached where current generated by capacitor is equal to the magnetizing current. MODELING OF LOADED MACHINE Modeling of a Loaded induction generator takes into the effect of load into equation 5 and 6. The equation can be rewritten as Icq= Iqs + ILq (13) Icd= Ids + ILd And as per capacitor equation Vcq= (1/C)*ʃIcq dt +Vcq0 - Vcd= (1/C)*ʃIcd dt +Vcd0 Putting Icq and Icd values in above equation we get, Vcq= (1/C)*ʃ(Iqs+IqL) dt +Vcq0 (14) Vcd= (1/C)*ʃ(Ids+IdL) dt +Vcd0 (15) Where, IqL=Vqs/RL and IdL=Vds/RL; Fig 1. System simulink model Here IqL and IdL are quadrature axis and direct axis current component of load current, Vqs and Vds are quadrature axis and direct axis stator voltage component and RL is the load applied to the generator in ohms. Equation 13 and 14 implementation has been shown in machine model (fig.2) [Dawit, Colin, and Muhammed, 2003] [Ekanayake, 2002] [Fathy, 2006] 730
RESULTS The parameters of the machine used in the simulation are 230 V, 26.2 A, 7.5 kw three phase squirrel cage induction machine whose stator resistance is 1 Ω, a rotor resistance referred to the rotor side of 0.77 Ω, a stator leakage reactance of 1 Ω, rotor leakage reactance referred to the rotor side of 1 Ω, The moment of inertia of the drive system is 0.1384 kg.m^2 [8]. Load taken is in the form of resistance applied to the machine and the load variation is given in fig 8.The result are analytically justified and compared to the paper referred In this paper at time t=2.5 sec the machine is loaded by a load of RL=120 ohm, the load is then varied and at time t=5 sec it is decreased to RL=240 ohm then at time t=7.5 sec the machine is loaded by RL=360 ohm and at t=10 sec it is loaded by RL=480 ohm. The results are given below Fig 5. c phase voltage curve Fig 3, 4 and 5 shows the voltage variation generated by generator when varying load is connected across it. These transients can be clearly seen in the fig where, at t=2.5 sec the voltage rms value dips to 92 volts from its no load rms voltage of 108V it can also be seen that voltage increases as the load is decreased from RL=120 ohm to RL=240 ohm at time t=5 sec which again varies at t=7.5 second at t=10 sec. The transient at t=2.5 second in the generated voltage is due to the decreased rotor speed to produce required slip and electromagnetic torque to supply the instantaneous load[9].the transients at t=5 sec, t=7.5 sec and t=10 sec is due to the increase in rotor speed to supply reduced torque on reduced load. Fig 3 a phase Voltage curve Fig 6. Magnetizing current curve Figure 6 shows the magnetizing current Vs time graph which shows the behavior of SEIG whose magnetizing current decreases on loading. The decrease in magnetizing current can be justified by the decreases in generating frequency on load which in turn decreases the reactance of machine that demands reduced magnetizing current. Fig 4 b phase Voltage curve 731
Fig 7. Magnetising inductance Vs time curve Figure 7 shows the magnetizing inductance curve which varies as per magnetizing characteristic of SEIG as per equation 12. Figure 6 and 7 shows the obvious relation between operating flux (magnetizing current) and generated voltage. Fig 10. Rotor speed Vs time curve Fig 11. Input torque,electromagnetic torque Vs time curve Fig 8. Stator phase current Figure 10 and 11 shows the mechanical dynamics of the machine. Rotor speed decreases as the machine is loaded to supply required electromagnetic torque which is then fed by increasing the input torque from turbine coupled to the rotor of the machine. Figure 11 clearly shows the transients in electromagnetic torque (Te) and the way input turbine torque tracks Te. Fig 9. Phase load current Figure 8 and 9 shows the stator and load current curve respectively. Stor current curve clearly shows the obvious effect on variation of load on stator and load current as per equation 13 and 14. Load current is zero till machine is loaded at time t=2.5 sec and thereafter starts building up and decreases as the load is decreased at time t=5, 7.5 and 10 sec. Fig 12. Output power generated Vs time curve Fig 12 shows the output power generated as per loading of the machine. 732
CONCLUSION A sophisticated mathematical model has been chosen for simulating self excited induction generator on load which uses d-q axis current as state variable. A detailed analysis of the variation in SEIG upon loading has been done which is then compared with reference papers The study done in this thesis is based on resistive load and further study is to be done on inductive load on which the performance of SEIG is poorer. APPENDIX I a1= -Lr*Rs/L; a2= -Lm^2*ωr/L; a3=lm*rr/l; a4= - Lm*ωr*Lr/L; a5=lm/l; a6=-lr/l b1=lm^2*ωr/l; b2=-ls*rs/l; b3=lm*ωr*lr/l; b4=lm*rr/l b5=lm/l; b6=-lr/l c1=lm*rs/l; c2=ls*ωr*lm/l; c3=-ls*rr/l; c4=ls*ωr*lr/l c5=-ls/l; c6=lm/l d1=-ls*ωr*lm/l; d2=lm*rs/l; d3=-ls*ωr*lr/l; d4=-ls*rr/l d5=-ls/l; d6=lm/l where, L=Ls*Lr-Lm^2 Ls= Lls+Lm Lr=Llr+Lm Fathy M. M. bassiouny, (2006): Dynamic Performance of Isolated Asynchronous Generators Under Different Loading Conditions Using Matlab Simulink, the eleventhinternational middle eastpom (er systems conference (mepcon'2oo6) Ofualagba, G and Ubeku, E.U, The Analysis and Modelling of a Self-excited Induction Generator Driven by a Variable Speed Wind Turbine, Federal University of Petroleum Resources, Effurun Nigeria Smith, N.P.A, (1996): Induction generators for stand - alone micro - hydrosystems, Power Electronics, Drives and Energy Systems for Industrial Growth, 1996., Proceedings of the 1996 International Conference on Volume: 2,Pp: 669-673 vol.2. Yaser N. Anagreh and Imadden M. Al- Refae e, Teaching the self-excited inductiongenerator using Matlab, Department of Electrical Power Engineering, Yarmouk University, Irbid, Jordan APPENDIX II a=0.1407, b=0.0014, c=-0.0012, d=0.0005 REFERENCES Guiliani Scherer, Lucas; Figueiredo de Camargo, Robinson, (2011):advances in modeling and control of micro hydropower stations wit h induction generators, Energy Conversion Congress and Exposition (ECCE), 2011 IEEE, Pp: 997 1004 Bhim Singh, S. S. Murthy, Sushma Gupta, (september/october 2005): Transient Analysis of Self-Excited Induction Generator With Electronic Load Controller (ELC) Supplying Static and Dynamic Loads IEEE trans. on industry applications, vol. 41, no. 5, C.Grantham, D. Sutanto and B. Mismail, "(March 1989): Steady-state and transient analysis of selfexcited induction generators", proceedings of lee,. Vol. 136, Part B, No.2, pp.61-68, Dawit Seyoum, Colin Grantham, Muhammed Fazlur Rahman, (july/august 2003): The Dynamic Characteristics of an Isolated Self-Excited Induction Generator Driven by a Wind Turbine, IEEE trans. on industry applications, vol. 39, no. 4,. Ekanayake.J.B, (2002): induction generators for small hydro schemes, Power Engineering Journal, Volume: 16, Issue: 2, Pp: 61 67 733