Intenational Jounal of Recent Tends in Engineeing, Vol, No., May 9 Steady State and Tansient Pefomance Analysis of Thee Phase Induction Machine using MATAB Simulations Pof. Himanshu K. Patel Assistant Pofesso, Instumentation & Contol Engineeing Depatment, Institute of Technology, Nima Univesity of Science & Technology. India. E-mail : hkpatel@nimauni.ac.in, hkpatel@hkpatel.com,himu@yahoo.com Abstact: DC dives have hitheto been widely used in vaious Industial applications but ecent device technology and high speed micopocessos have tilted the balance and the induction machine is becoming the wokhose of the electical powe industy. Compute based modeling and simulation of induction machine has cetainly opened new hoizons fo the pefomance analysis. A good mathematical model can help in pedicting the behavio of an induction machine unde diffeent opeating conditions and in selecting the appopiate machine fo a specific application. This pape pesents a quality mathematical model of induction machine based on the steady state and dynamic equations and D-Q tansfomation technique. This model can be used fo steady state as well as tansient analysis of squiel cage o wound oto stuctue. The model is used to investigate the effects of vaiations in the machine size and paamete values on the dynamic pefomance of induction machine. Diffeent opeating conditions ae simulated using Matab code. Also, the behavio of the induction machine is obseved with and without supply hamonics. used to excite the induction moto ae ich in hamonics. These time hamonics poduce espective oto cuent hamonics, which in tun inteact with the fundamental ai gap flux, geneating hamonic toque pulsations. The toque pulsations ae undesiable: they geneate audible noise, speed pulsations, and losses thus deceasing the themal capabilities of the moto and eventually deating the moto. In this pape the induction moto pefomance is analyzed fo the effects of the d, 5 th & 7 th hamonics at the supply side. MATAB is used to solve the diffeential equations. MATAB is a pominent softwae package fo compute simulation []. II. MODEING OF THE -PHASE INDUCTION MACHINE: Fig.- shows the detailed single-line diagam of a theephase induction machine with all the components efeed to the stato side [], [4], [6]. Index Tems -- -φ Induction Moto, Steady state & Tansient Response, Supply Hamonics, Synchonous speed. I. INTRODUCTION The dynamic model of induction machine and its simulation plays a vital ole in the validation of design pocess of the moto-dive systems, eliminating inadvetent design mistakes and the esulting eos in the pototype constuctions and testing. The dynamic model of the Induction machine in d-q-o axes is deived fom fundamentals. This pape pesents a compute pogam, which is developed to analyze the pefomance of induction moto []. The powe of the poposed tool lies in the ability to study the dynamic behavio of the induction machine in the absence of complicated mathematics. The pogam was designed to illustate clealy the effects of the Pak s tansfomation. This concept is nomally vey difficult to lean, but by epesenting the model of the induction moto in a geneic efeence fame otating with an angula speed ω, and simulating some tansients, with diffeent opeating conditions, one can lean quite well this concept. Nomally the invete voltage wavefoms Pof. Himanshu K. Patel, Assistant Pofesso, Institute of Technology, Nima Univesity of Science & Technology, Ahmedabad, Gujaat, INDIA. (e-mail : hkpatel@nimauni.ac.in, himu@yahoo.com). Fig.. Single line diagam of a phase induction machine. The induction machine equations ae deived fom basic pinciples [6] and applied to induction motos [] and the elationship between the induction machine stato and oto quantities can be pesented as: Vabcs si abcs + pλ abcs V abc i abc + p λ abc () V abcs Vas ias V, bs i abcs i, bs Vcs ics v abc v i a a v, i b abc i b v c i c () λ abcs λ abc s s s i abcs i abc () 66 9 ACADEMY PUBISHER
Intenational Jounal of Recent Tends in Engineeing, Vol, No., May 9 ls + ms.5 ms.5 m s.5 ms ls + ms.5 ms.5 ms.5ms ls + ms l + m.5 m.5 m (4).5 m l + m.5 m.5 m.5m l + m and, π π cos θ cos( θ + ) cos( θ ) (5) π π s ls cos( θ ) cos θ cos( θ + ) π π cos( θ + ) cos( θ ) cos( θ ) d In ()-(5) p denotes the opeato, and λ,, m, dt and s, denote the flux, leakage inductance, mutual inductance and oto-stato inductance espectively. Afte applying d-q tansfomation, a set of non-linea fist-ode diffeential equations will esult. Thee is one moe equation that elates the input and output toques to the speed of the oto: T e J ρω + T (6) P d ' i' d ( ω ω ) λ' q + ρλ' d o ' i' o + pλ' o (7) Whee, λ qs ls iqs + M (iqs + i' q ) λ ds lsi ds + M(i ds + i' d ), λ os ls i os λ ' q ' l i' q + M (i qs + λ ' d ' lc i' d + M(ids + i' d ) λ ' o ' l i ' o (8) Also, the developed electical toque can be witten as: P (9) i' q ( i i ' i i ' ) T e M qs d ds d Solving (6), (7) and (9), simultaneously, gives the stato and oto cuents, as well as the oto speed. Fig. shows the flow chat of the Matlab pogam developed fo the analysis of induction machine pefomance using equations () to (9). III. EXPERIMENTA DATA: The poposed model of the machine is used to study the pefomance of two induction machines of diffeent sizes. One of the machines is much bigge than the othe one. Simulation esults ae obtained fo both machines and compaed to illustate the effects of the machine paametes on the outputs, as well as the steady state and tansient behavios. Futhemoe, the effects of changing the load on the machine s pefomance ae shown. The paametes of the two -phase, 4-pole, 6Hz machines, ae as follows: Machine : hp, V, 7 pm, s.45 Ω, X ls.754 Ω X M 6. Ω, X l.754 Ω.86 Ω J.89 kg.m Machine : 5 hp, V, 786 pm, s.9 Ω X ls.6 Ω, X M.4 Ω X l.6 Ω. Ω J 6.87 kg.m. Hee, X M has been assumed to be constant due to the fact that the machine is diectly connected to the gid and thus the output voltage of the machine is equal to the gid voltage. IV. SIMUATION RESUTS: This section pesents the simulation esults fo the machines intoduced in the pevious section and compaed to investigate the effects of machine s size & diffeent opeating conditions on its pefomance. ) Fig. : Flow Chat The dynamic equations of the machine in d-q fame ae: V qs s i qs + ωλ ds + ρλ qs Vds si ds ωλ qs + ρλ ds V os s i os + p λ os q ' i' q + ( ω ω ) λ' d + ρλ' q 9 ACADEMY PUBISHER 67 Some of the cuves ae shown just to pove the accuacy and dependability of the simulations. Fist, the lage machine 5 hp has been simulated.
Intenational Jounal of Recent Tends in Engineeing, Vol, No., May 9.4. 5 Roto speed(p.u).8.6.4 Toque(Nm) 5. Toque(Nm) - - 4 6 8 x 4 Fig.. Roto speed (p.u.) 4 6 8 Fig. 4. Toque (Nm) Fig. and Fig.4 coespond to the case whee the machine uns at no-load. Fig.4 clealy shows that the developed toque goes to zeo afte the initial tansition. Fig. shows that the machine otates at a speed vey close to the synchonous speed when opeating at no-load. Now, same cuves fo the hp induction machine will be pesented. It can be seen that the oscillatoy behavio of the smalle machine is much moe acceptable than that of the lage machine. In fact, the best cuves fo compaison ae those fo the no-load machine fom standstill to synchonous speed. -5.5.5 Fig. 6. Toque (Nm) Again compaison between Fig. and Fig.5 clealy poves that the smalle machine has almost no oveshoot while the lage one has a consideable oveshoot and a tansient peiod of almost times longe than that of the smalle machine. The tansient behavio of the machine can be elated to its inetia. The lage the machine is, o the lage its inetia (J) is, the lage is the toque equied duing the stat-up peiod to speed it up. Afte eaching the synchonous speed (in the case of no-load machine) the lage machine s speed will oveshoot, taking some time to stabilize at aound the synchonous speed. This implies the possibility of instability in big machines if connected diectly to the gid. Futhemoe, the vey lage inush cuents at stat-up of lage machines can damage the wiing of the machine. Roto speed(p.u).4..8.6.4 Roto speed(p.u).5.5. 4 6 8 x 4 Fig. 7. Roto speed (p.u.).5.5 Fig. 5. Roto speed (p.u.) Toque(Nm) - - 4 6 8 Fig. 8. Toque (Nm) 9 ACADEMY PUBISHER 68
Intenational Jounal of Recent Tends in Engineeing, Vol, No., May 9.5 x 4 Roto speed(p.u).5 Toque(Nm) - - 5.5.5 Fig. 9. Roto speed (p.u.).4. 4 6 8 Fig.: Toque (Nm) Toque(Nm) 5 Roto speed(p.u).8.6.4. -5.5.5 Fig.. Toque (Nm).5.5 Fig.. Roto speed (p.u.) 5 Fig. 7 and Fig. 9 illustate the behavios of the two machines due to the same amount of change in the p.u. applied toque. The change in the p.u. oto speed fo the smalle machine is much lage than that of the lage machine. The behavio of the 5-hp and -hp machines in esponse to a step change in the applied toque can be confimed by examining the oto speed to toque sensitivities of the two machines. Toque(Nm) 5 The oto speed to toque sensitivity, i.e., evaluated at the opeating point fo the 5-hp and -hp machines wee found to be. and.4, espectively. As seen, the speed of the smalle machine is much moe sensitive to a change in toque. Roto speed(p.u).4..8.6.4. 4 6 8 Fig.. Roto speed (p.u.) -5.5.5 Fig. 4. Toque (Nm) Fig. to Fig.4 illustates the behavio of the two machines due to the same amount of hamonics pesent in the stato supply. The hamonics injected in the stato supply ae d, 5 th & 7 th. Hee it is clealy obseved that thee will be pulsations in the developed toque due to pesence of supply hamonics. CONCUSIONS This pape pesents a compehensive model fo Induction machine which can be used fo studying the behavio unde diffeent opeating conditions. The model is based on the d-q tansfomation and coves the steady-state and tansient behavios of the machine. The model is quite vesatile and capable of simulating the machine duing a sudden change in load toque, with and without supply hamonics. Two induction machines of diffeent sizes wee simulated to illustate the diffeences in machines' behavios due to simila changes in the applied toque and supply hamonics to the induction moto. 9 ACADEMY PUBISHER 69
Intenational Jounal of Recent Tends in Engineeing, Vol, No., May 9 The geneal conclusion based on the compaison between the 5-hp and -hp machines can be summaized as follows: (a) The smalle machine has smalle inetia and shows shote tansient peiod and less oveshoot duing stat-up o following any changes in the inputs. Geneally speaking, it has bette tansient behavio compaed to the lage machine. (b)the 5-hp induction machine is moe stable afte eaching the steady-state, since sudden changes in input toque can not acceleate o deceleate the machine as easily as in the case of the -hp machine. REFERENCES [] Paul C. Kause, Analysis of electic machiney, McGaw- Hill, New Yok, 986. [] Chales V. Jones, The Unified Theoy of Electical Machines, Plenum Pess 967. [] Matlab Uses Guide. Mathwoks, 99 [4] R. Kishnan, Electic Moto Dives: Modelling, Analysis and Contol, Pentice-Hall of India Pivate td-. [5] i wang, Ching-Huei ee, "A novel analysis on the pefomance of an isolated self- excited induction geneato", IEEE Tans. On Enegy Convesion, vol., No., June 99. [6] Ion Boldea and Syed A. Nasa, The Induction machine Handbook, CRC Pess New-Yok. 9 ACADEMY PUBISHER 7