\tau = \frac{3 V^2_{TH}} {\left(R_{TH}+\frac{R_2}{s}\right)^2+\left(X_{TH}+X_2\right)^2 } \frac{R_2} {s\omega_s} To browse Academia.edu and the wider internet faster and more securely, please take a few seconds toupgrade your browser. P_{out}=P_{conv}-P_{rotational} = \tau \omega_m - P_{rotational} It helps to analyze the performance . Induction Motor Equivalent Circuit From the preceding, we can utilise the equivalent circuit of a transformer to model an induction motor. I'm currently making a 4 minute speech about the effects of technology. Draw the Equivalent circuits of transformer and induction motor, indicate the physical meaning of each component. 2) Note that: the element R L \ is the equivalent electrical resistance related to the mechanical load on the motor. Assume a Y-connection for both the stator and rotor, and a turns ratio of 1:1. The rotor slips with respect to the two rotating fields are s and (2 s) respectively as given by Eqs (10.5a) and (10.5b) and as a result the magnetizing and rotor circuits as seen by the two rotating fields with reference to the main winding are different and are shown in Figs 10.22(a) and 10.22(b). \], \[ The copper losses are occurred in the windings so the winding resistance is taken into account. Circle Diagram of an Induction Motor - its Construction & Significance. Induction motors generally have a poor power factor, which can be improved by a compensation network. 3: eqt. Determine (i) percentage slip (ii) induced emf in rotor per phase (iii) the rotor reactance per phase at full load (iv) the rotor current and full load power factor. From these the Equivalent Circuit of Single Phase Induction Motor of Fig. The no-load lagging power factor of the motor is___________ (up to 3 . circuit of induction motor per phase at any slip referred to stator side (Fig. n_s=\frac{120 f}{p} = 1200\textrm{ rpm} \], \[ What is Oscillator? (15) According to the equivalent circuits, what are similar and what are different between transformer and induction motor? sync = 2 P s = 2 P 2fs (1) where, P is the number of poles and fs is the frequency of the applied voltage. Efficiency is given by \(\eta=\frac{P_{out}}{P_{in}}\) = 88.9%, Thevenin circuit parameters and Thevenin voltage. Thus, Substituting for Emfand Embfrom Eqs (10.29a) and (10.29b). By referring the approximate equivalent circuit of the induction motor, the following equations can be written down for one phase at a slip s. The impedance beyond the terminals A and B is given by , = ( + ) + ( + ) ( 6) = = ( + ) + ( + ) ( 7) Z_{TH} & =\left(R_{1}+jX_1\right)|| jX_m \\ occurs when, Pullout torque can be found by substituting the above pullout slip into the Thevenin torque equation. abstract: the derivation of the equivalent circuit for a single-sided linear induction motor (slim) is not straightforward, particularly if it includes longitudinal end effects from the cut-open primary magnetic path, transversal edge effects from the differing widths between the primary lamination and secondary sheet, and half-filled primary Equivalent Circuit of Single Phase Induction Motor The winding unbalance and the fact that both the main and auxiliary windings are fed by the same supply result in unbalanced main and auxiliary fields. Thevenin circuit parameters and Thevenin voltage: Start Torque. \(P_{in} = 61.8kW\). Thus, if L 2 is the inductance of the rotor, then the rotor reactance at slip s is given by, 2 = 2 2 2. (10.39b). 10.26 is obtained. Maximum torque and maximum airgap power occur at the same slip, therefore maximum torque \end{aligned} The Equivalent Circuit of an Induction motor enables the performance characteristics which are evaluated for steady-state conditions. Operating a motor at less than rated load results in a lower power factor, which could aggravate power factor problems in a plant. The Induction Motor Equivalent Circuit can now be drawn on a per phase basis as in Fig. Z_{||}&=\frac{jX_m Z_2}{Z_2+jX_m} \quad Z_2= \frac{R_2}{s}+jX_2 (10) Question: Q4. Using Matlab or Excel, the torque can be plotted as a function of slip using the equation in part 3: \[ Topic: How information technology changed the dynamics of communication in families and society. \begin{aligned} It is noted that no-load losses have been neglected and therefore the core-loss conductance has not been shown in both the circuits. Equivalent Circuit of an Induction Motor The equivalent circuit of any machine shows the various parameter of the machine such as its Ohmic losses and also other losses. Soln: Frequency of supply to the induction motor f = pn/120 = 12 x 500 / 120 = 50 Hz Speed of Induction motor = 1440 rpm, Number of poles of induction motor = p = 120 f / n = 120 x 50/1440 = 4.16 The number of poles are to be even, selecting the nearest even number as the number of poles p = 4 Synchronous speed of the induction motor Ns = 120f/p = 120 x 50 /4 = 1500 rpm slip = (Ns N) / Ns = (1500 1440)/ 1500 = 0.04 Percentage slip = 4 %. Academia.edu uses cookies to personalize content, tailor ads and improve the user experience. In case of an induction motor, the rotor rotates at a speed, slightly slower than the synchronous speed (under motoring mode): mech = (1 - s) sync (2) where, s is the motor slip and is typically between 0.005 to 0.05. To draw the equivalent circuit we have to perform certain test in order to calculate various parameters. Enter the email address you signed up with and we'll email you a reset link. But the rotor frequency is, 2 = 1. Problems with Electric Motors. whose Equivalent Circuit of Single Phase Induction Motor representation is given in Fig. (10.33a) in Eq. The equivalent circuit of a single-phase induction motor is shown in the figure, where the parameters are R 1 = R' 2 = X l1 = X' l2 = 12 , x M = 240 and s is the slip. \end{aligned} \], \[ The forward component set Ff and jFf produces a forward rotating field; similarly the backward component set Fb and -jFbresults in a backward rotating field. A Three-phase Induction Motor Problem This application note describes how to set up, solve, and analyze the results of a two-pole, three-phase . \end{aligned} Q #5 An induction motor is driving a constant-torque load. Using the same equation with s=1 gives \(\tau_{start}=649Nm\). Z_{in}&=Z_1+Z_{||} \quad Z_1=R_1+jX_1 \\ \vec{I}_2=\frac{jX_M}{jX_m+Z_2}\vec{I}_1 The rotor resistance and stand still reactance per phase are 0.1 ohm and 1.5 ohm respectively. For the induction motor of problem 3 (using the equivalent circuit parameters calculated and other details given in problem 3), for a rotor speed of 1710 r.p.m., answer the following questions: (a) Calculate the synchronous speed and the slip s. Slon: f = 50 Hz and f r = 1.5 Hz, Ns = 120f/p = 120 x 50/8 = 750 rpm We have f r = sf Hence s= f r /f = 1.5/50 = 0.03 Hence N = (1-s)Ns = (1-0.03) x 750 = 727.5 rpm 3. \end{aligned} A dc test is performed on a 460-V -connected 100-hp induction motor. \(\tau=467Nm\). The induction motor equivalent circuit when idle is approximately, which is mostly reactive. induction-motor-equivalent-circuit 1/4 Downloaded from www.interactivearchivist.archivists.org on November 7, 2022 by Caliva a Williamson . Thus the emfs in the auxiliary winding induced by the two fields are: Also let the main and auxiliary winding terminal voltages be Vmand Varespectively. Rotational losses are 1300W. In the equivalent circuit R1 represents, the resistance of the stator winding and X1 the stator leakage reactance (flux that does not link with the air gap and rotor). She cross-checked the prenatal appointment book and. Similarly substituting Iafrom Eq. Three Phase Induction Motor. \end{aligned} The auxiliary winding voltage is equal to (Va/a)as seen from the main winding. Equivalent circuits: wound-rotor induction motor 1. The impedance seen by Emf, the forward field induced emf of the main winding, is, and the impedance seen by the Emb,backward field induced emf in the main winding, is. Thevenin circuit parameters an voltage can be found using the equations provided on the The relative speed between the synchronous speed and actual rotor speed is known as slip. \], \[ 2 = 2 . \(\omega_s=\frac{4 \pi f}{p}\). as well as the parameters of the one-phase equivalent circuit: resistance and leakage reactance for the stator winding, and magnetizing reactance for the rotor. \begin{aligned} A solid transmission shaft is 3.5 inch in diameter. Types of Oscillators, Facsimile (FAX) Machine Definition, Operation and Applications, Monochrome TV Transmitter Block Diagram and its Workings. Calculate the following information: This machine has no iron loss resistance, so the equivalent circuit is as follows: For the machine in the previous example, find: Using Matlab or Excel (or another computer program) plot the torque speed curve for slip in the range 0 to 1. 2.3 phase, 50 Hz induction motor, represented by equivalent circuit constants X1 = X2 = 0.1 ohm and R1 = R2 = 0.2 ohm is operated at half of rated voltage and frequency. Induction Motor Equivalent Circuit Example A four-pole, 60 Hz, 460 V, 5 HP induction motor has the following equivalent circuit parameters: Rs =1.21 Rr = 0.742 Xs = 3.10 Xr =2.41 Xm = 65.6 R s = 1.21 R r = 0.742 X s = 3.10 X r = 2.41 X m = 65.6 Find the starting and no-load currents for this machine. Given: f=50 hz V=V/2 R1&R2=0.2 X1&X2=0.2 Wms=2*pi*Ns Ns= (120*f)/P. In an analysis of an induction motor, the equivalent circuit can be simplified further by omitting the shunt reaction value, gx. By using our site, you agree to our collection of information through the use of cookies. What are the Essential Components of an Oscillator? Fig. With a 120 Vrms, 60 Hz input, the motor runs at 1750 RPM, and the mechanical power delivered to the load is 1000 W.This is a 4-pole machine, so the synchronous speed is 1800 RPM. \vec{V}_{TH} & =\frac{jX_m}{R_1+j\left(X_1+X_m\right)}\vec{V}_1 \\ Why is this so? This presentation describes the per-phase equivalent circuit of induction motor - Power flow diagram - Ratio of air gap power, rotor copper loss and mechanica Academia.edu uses cookies to personalize content, tailor ads and improve the user experience. \], \[ Equivalent Circuit of Single Phase Induction Motor - The winding unbalance and the fact that both the main and auxiliary windings are fed by the same supply result in unbalanced main and auxiliary fields. n is the number of phases. For the purposes of this problem we will assume armature resistance is negligible. To browse Academia.edu and the wider internet faster and more securely, please take a few seconds toupgrade your browser. Sorry, preview is currently unavailable. By doubling the current and reducing the impedance to half the circuit model of Fig. If the induced emf in the stator of an 8 pole induction motor has a frequency of 50 Hz and that in the rotor is 1.5 Hz, at what speed is the motor running and what is the slip? Equivalent Circuit of induction Motor : The voltage and current are induced in the rotor circuit from the stator circuit for the operation. The full load speed of the motor is 1460 rpm. Find the percentage slip and number of poles of the induction motor. Below are a number of problems that are often encountered when using electric motors. Water must never be allowed to get into a motor. Z_{TH} & = \frac{jX_m\left(R_1+jX_1\right)}{R_1+jX_1+jX_m} \\ 10.24 can be drawn in the form of Fig.10.25. Introduction To gain better understanding of the properties and behaviors of the induction motor, it is necessary to examine the equivalent circuit - develop an equivalent circuit from the basic principles. 10.24. Transcribed image text: \], \[ Therefore Induction Motor Solutions.pdf - Induction Motor Problems - Solutions Q #1 A 2-pole, 3-phase induction motor, fed by a 60 Hz source, is driving a 50 Nm, 4 out of 4 people found this document helpful. A 2-pole, 3-phase induction motor, fed by a 60 Hz source, is driving a 50 Nm load at, How much mechanical power is being delivered through the motors. The losses are modeled just by inductor and resistor. I2r = Rotor current in running condition = \frac {E_ {2r}} {Z_ {2r}}=\frac {sE_2} {\sqrt {\left (R_2^2+\left (sX_2\right)^2\right)}} Z 2rE2r = (R22+(sX 2)2)sE2 theory. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators . \], \[ \vec{I}_1 &=\frac{V_1}{Z_{in}}=\frac{480}{9.33+j4.16}=42.9-j19.1A \\ The induction motor always run below synchronous speed. 1. formula sheet, or from first principles. Course Hero is not sponsored or endorsed by any college or university. \vec{I}_2=\frac{\vec{E}}{Z_2} \quad \vec{E}=V_1-\vec{I}_1 Z_1 The following points may be noted from the equivalent circuit of the induction motor: All data impedances of the motor must be obtained by doing some testing on It comprises three components: the emf induced by the forward rotating field, the emf induced by backward rotating field and the voltage drop in the winding impedance Z1mowing to current Imflowing through it. 3 is the same as Fig. Bataan Peninsula State University Main Campus (Capitol Compound), Vellore Institute of Technology ELECTRICAL 2003, University of Minnesota-Twin Cities EE 4701, Bataan Peninsula State University Main Campus (Capitol Compound) EE AM423, Massachusetts Institute of Technology WALA LANG HAHAHA WA, University of California, Los Angeles EC ENGR MISC, Addis Ababa University ACCOUNTING ACFN 723, Nirma University, Ahmedabad ELECTRICAL 12, The Hong Kong Polytechnic University EE 3021, University of Massachusetts, Lowell EECE 3550, On July 1 20X1 XYZ Co purchased as investment measured at amortized cost, RelatednessI want to feel connected to other people People need to feel a sense, 1 The spring caliper is available in sizes from 2 to 8 inches The friction of, d questions the patient about additional related symptoms ANS C Assessment is, Pattan- ELM -305- Clinical Field Experience C.docx, Geographic location and customer profiles were examples of which type pf factors, The Human Immunodeficiency virus HIV is a That infect the immune system, a The article says technology has enhanced peoples lives in New York T F b The, 2 2 pts Question 31 Which surgical method involves cleaning or widening the, The culture of an organization usually expedites the changes brought on by, Deegan Chapter 01 13 Difficulty Medium 14 Which of the following statements is, Module 9 Final Practical Exam Part 2 Excel Kritphonchet.xlsx, As samples of onesability and accomplishment a portfolio may be used as a tool, MRP systems are better suited for products that have predictable demand such as, University of St. La Salle - Bacolod City, vi An online directory of residential aged care home and community care and, A Bacteriological B Serological C Allergic D Biological E Microscopic 198 A 12, What scientific suborder does the family Hyaenidae belong to a Feliformia b, Philippine School of Business Administration, Manila (Main Campus), Topic: How information technology changed the dynamics of communication in families and society. rotor, assuming that the stator supply is short circuited. Electrical Engineering questions and answers Q4. This induces an opposing current in the induction motor's rotor, in effect the motor's secondary winding, when the latter is short-circuited or closed through an external impedance. Induction Machine Circuit Analysis Examples Per Phase Equivalent Circuit A 480V, 60 Hz, 6-pole, three-phase, delta-connected induction motor has the following parameters: R 1 = 0.461 ., R 2 = 0.258 ., X 1 = 0.510 ., X 2 = 0.756 ., X m = 30.74 . The motor drives a mechanical load at a speed of 1170 rpm. Academia.edu no longer supports Internet Explorer. This set of voltages can also be split into symmetrical components as, Now consider the main winding terminal voltage Vm. It is desired to replace it with a hollow shaft of the same material and same torsional strength but its weight should only be half as much as the, A pump requires a driving torque of 50 N.m at 1500 rom . A three phase, 50 Hz, 6 pole squirrel cage induction motor runs at 960 rpm on full load. 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The HGAPSO inherits the advantages of both genetic algorithm (GA) and particle swarm optimization (PSO). 10.25 disconnecting the auxiliary winding under running condition is equivalently represented as the opening of switch S. Once the auxiliary Winding is disconnected. It is proposed to drive the pump by direc coupling to a 3 -phase 460V , 60 Hz , 4-pole , squirrel - cage induction motor with the following, Sample Case # 1: On an afternoon of a prenatal clinic day, the community health nurse was going over the files of patients seen in the morning. Assuming the motor is drawing 3000 VARS, find the unknown values in, the phase-A equivalent circuit shown below. I_1 & = 47.0A, I_{L}=81.3A Therefore, the three-phase induction motors can be analyzed by using a one phase supply equivalent circuit. If, the specifications of induction motor are v=480v,P=50hp,f=60Hz,F=0.01(N.m.s),Rs=0.087ohm,Rr=0.228ohm,Ls=0.8e-3 H,Lm=34.7e-3 H,Lr=0.8e-3 H,J=01.662(kg.m6^2),Pole pairs(P)=2 the motor is operating in. Current is required to provide the reactive power for the magnetic field as well as for the real power to run the load. Z_{TH} & = R_{TH}+jX_{TH} = 0.446+j0.508 \Omega EE362 - Week#10- Video#16Equivalent circuit of induction motors, determination of equivalent circuit parameters by no-load test and locked-rotor test.You can. Explore the latest full-text research PDFs, articles, conference papers, preprints and more on PARAMETER ESTIMATION. 2. Using Eqs (10.36a) and (10.36b). How much power is being turned into heat in the rotor? where Z1a is the winding impedance of the auxiliary winding which in general has a capacitor included in it (starting/running capacitor). A 3-phase, Y connected, 460 volt (line to line), 25 horsepower, 60 Hz, 8 . s=\frac{n_s-n_m}{n_s}=\frac{1200-1170}{1200}=0.025 Similarly the auxiliary winding terminal voltage Vacomprises three components. ahead of the main winding and vice versa for the backward rotating field. Shown below is a partial space-vector diagram of an induction motor. 4. The data obtained from the equivalent circuit can be used to calculate efficiency, torque, losses, rotor output, etc. [28] The rotating magnetic flux induces currents in the windings of the rotor, [29] in a manner similar to currents induced in a transformer 's secondary winding (s). Enter the email address you signed up with and we'll email you a reset link. ( Ans: X m = 29.2 , Z e = 1.97 , R e = 1.054 , X e = 1.665 , R 2 = 0.509 ) Page 2 of 3 f8. 10.5(c) on a heuristic basis. A three phase, 50 Hz, 4 pole slip ring induction motor has a star connected rotor. \]. Current. It may be seen that this is the same circuit model as already presented in Fig. solution (a) this machine has 10 poles, which produces a synchronous speed of 120 f e 120 ( 60 hz ) nsync = = = 720 r/min p 10 (b) the slip at rated load is nsync nm 720 670 s= 100% = 100% = 6.94% nsync 720 (c) the motor is operating in the linear region of its torque-speed curve, so the slip at load will be s = 0.25 (0.0694) (10.33b) in Eq. Thevenin impedance is the impedance of the stator part of the circuit, seen from the Substituting Im from Eq. To learn more, view ourPrivacy Policy. \begin{aligned} In Fig. If V DC = 21 V and I DC = 72 A, what is the stator resistance R 1 ? Calculate the ratio of starting torque at half voltage & frequency to rated values. s=\frac{0.258}{1.35}= 0.191 Induction Motor Locked-Rotor No-Load Test Problem Solution 1,112 views May 29, 2021 21 Dislike Share Save Ozan Keysan 1.86K subscribers EE362 - Week#10- Video#17 Equivalent circuit of. An equivalent circuit enables the performance characteristics of the induction motor. In Induction motor we perform No load test , Block rotor test to find o. The single phase equivalent circuit of a three-phase, four pole induction motor is shown in Figure 1. The open circuit voltage on open circuit between the slip rings is 90 volts. Until now the use of equivalent circuit for induction motor has been limited for steady state analysis. var _wau = _wau || []; _wau.push(["classic", "4niy8siu88", "bm5"]); | HOME | SITEMAP | CONTACT US | ABOUT US | PRIVACY POLICY |, COPYRIGHT 2014 TO 2022 EEEGUIDE.COM ALL RIGHTS RESERVED, 2 Phase 4 Pole Permanent Magnet Stepper Motor, Difference Between Single Phase and Three Phase Induction Motor, Hybrid Stepper Motor Construction and Working, Electrical and Electronics Important Questions and Answers, Colpitts Oscillator using Transistor Circuit, Tuned Base Oscillator Definition and Working Principle, Tuned Drain Oscillator Circuit Diagram and Equation, Tuned Collector Oscillator Definition, Working and Equation, LC Oscillator Circuit Definition, Types and Equation. However, my textbook shows that the resistance is instead R 2 /s for the equivalent circuit of an induction motor: What is the significance in the discrepancy between R 2 /s and R 2 [(1-s)/s]? The motor drives a mechanical load at a speed of 1170 rpm. Course Hero uses AI to attempt to automatically extract content from documents to surface to you and others so you can study better, e.g., in search results, to enrich docs, and more. Rotational losses are 1300W. Soln: (i) Ns = 120f/p = 120 x 50 /4 = 1500 rpm; slip = (Ns N) / Ns = (1500 1460)/ 1500 = 0.0266 Percentage slip = 2.66 % (ii) Induced emf per phase in rotor at stand still = 90/3 =51.96 volts Rotor induced emf at full load Er = sE 2 = 0.0266 x 51.96 = 1.382 volts (iii) rotor reactance at stand still = 1.5 / phase Rotor reactance per phase at full load = sX 2 = 0.0399 / phase (iv) rotor impedance per phase at full load = Z 2 = (R 2 2 + sX 2 2) = 0.1077 Rotor current per phase = 1.382/0.1077 = 12.83 amps Full load power factor = R 2 /Z 2 = 0.1/ 0.1077 = 0.929.
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