Its equivalent circuit components are R 1 R 2 XM X 1 X 2 P mech = 300 W P misc 0 core = 200 W For a slip of 0.05, find (a) The line current IL (b) The stator copper losses P SCL (c) The air-gap power P AG (d) The power converted from electrical to mechanical . In order to obtain the complete per-phase equivalent circuit of an induction motor, it is required to refer the rotor part to the stator side frequency and voltage level. Notify me of follow-up comments by email. The input power to the stator is given by, $$\mathrm{_{} = 3__ cos \varphi_s = 3_'_ cos \varphi_{r} + _= 3_{}^{2}( +\frac{_}{}) + _ (15)}$$. 2. A pure inductive reactance X0 carries magnetizing current I and non-inductive resistance carries core-loss current I. Neglect shunt branch in the equivalent circuit. The equivalent circuit of a single-phase single winding induction motor with the standstill rotor is shown below. As shown in the above figure, one resistance depends on the slip s. This resister represents the developed mechanical power by the rotor. V Curves and Inverted V Curves of Synchronous Motor, Difference Between Salient Pole & Non-Salient Pole Rotor, Two Wattmeter Method of Power Measurement - Balanced Load, Induction Type Energy Meter - Construction, Working & Torque Equation. Using the per phase Approximate equivalent circuit of the induction motor, find: All currents, input, airgap and output powers, the torque and efficiency for a slip of 2% then find maximum torque and slip at which this torque occurs from the plot of torque/slip characteristics. Introduction Three-phase induction motors are the most common and frequently encountered machines in industry - simple design, rugged, low-price, easy maintenance - wide range of power ratings: fractional horsepower to 10 MW - run essentially as constant speed from no-load to full load - Its speed depends on the frequency . A 208-V four-pole 60-Hz Y-connected wound-rotor induction motor is rated at 15 hp. These are used for domestic purposes. The simulation results are compared with practical . This is very similar to that of transformer equivalent circuit when its secondary is shorted. Losses in a Motor - Power Stages in an Induction Motor . Again, when slip s = 0, r2[ (1-s)/s)] = . The stator consists of the stator winding and stator core. What happens if You Connect a 3- Induction Motor to 1-Phase Supply? 3) Reading of voltmeter V scl = Line voltage on the short circuit P sc = 3V scl cos? sc Where cos? The stator circuit model of the induction motor consists of a stator phase winding resistance R1, a stator phase winding leakage reactance X 1. Motor Protection Types of Faults and Protection Devices. The double revolving field theory can be effectively used to obtain the equivalent circuit of a single phase induction motor. Induction Motor Equivalent Circuit Here, we assume a stationary rotor that carries the same current as the actual rotating rotor and produces the same MMF. = \frac{E_{2r}}{Z_{2r}}=\frac{sE_2}{\sqrt{\left(R_2^2+\left(sX_2\right)^2\right)}}. Both parts have different circuit model. An induction motor or asynchronous motor is an AC electric motor in which the electric current in the rotor needed to produce torque is obtained by electromagnetic induction from the magnetic field of the stator winding. R c is the core loss component. The data obtained from the equivalent circuit can be used to calculate efficiency, torque, losses, rotor output, etc. 1. The rotor reactance is given by; The relation between supply frequency f1 and rotor frequency f2 is given by; The circuit diagram of the rotor circuit model is shown in the figure below. The method consists of determining the values of both the fields clockwise and anticlockwise at any given slip. An induction motor works on the principle of electromagnetic induction. The proposed equivalent circuit of Figure 1 is simulated in the Matlab/Simulink model of induction machine used as an induction motor to calculate the iron core loss accurately at no load and at full load to show the effect of temperature, skin, and saturation on the motor core loss and hence on the motor efficiency. I'_{2r}=KI_{2r}\frac{KsE_2}{\sqrt{\left(R_2^2+\left(sX_2^{ }\right)^2\right)}}, X'_2=\frac{X_2\ }{K^2} = reflected rotor reactance, R'_2=\frac{R_2\ }{K^2} = reflected rotor resistance, R'_L=\frac{R_L\ }{K^2}=\frac{R_2}{K^2}\left(\frac{1-s}{s}\right)=R'_2\left(\frac{1-s}{s}\right). Let the stator impedance be Z . Three Phase Motor Power & Control Wiring Diagrams. reactance X 01 referred to the stator. To derive the exact per-phase equivalent circuit of an induction motor, we need to calculate the rotor part of a model over to the stator circuits frequency and voltage level. This test is the equivalent of short-circuit test in a transformer. All other components are constant. In the analysis, all components in the motor equivalent circuit are referred to the stator. The equation of slip and synchronous speed is shown in the below equation. The greatest relative motion occurs when the rotor is stationary. The rotor current I2r has reflected component on the stator side which is I2r. rotor electricaltechnology wiring windings stator. Stator Circuit Model By using this website, you agree with our Cookies Policy. The equivalent circuit of an induction motor is similar to a transformer equivalent circuit because the energy is transferred from stator to rotor is essential as a transformer operation from primary to the secondary winding. What is the Role of Capacitor in a Ceiling Fan Motors? Solution I_{2r}=\frac{sE_2}{\sqrt{\left(R_2^2+\left(sX_2^{ }\right)^2\right)}}=\frac{sE_2}{\sqrt{\left(\left(\frac{R_2^{ }}{s}\right)^2+X_2^2\right)}}. An induction motor can therefore be made without electrical connections to the rotor. What is Motor Starter? 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 The approximate equivalent circuit of the induction motor is obtained by shifting the shunt branches R0 and X0 in the equivalent circuit. What happens to the 3-Phase Motor When 1 Out of 3 Phases is Lost? There are three basic insulator materials available. In equation-2, I2s is produced by constant line frequency voltage E20 and the rotor circuit has an impedance of (R2/s)+ jX20. Also, in fig-2, the rotor circuit model has a constant resistance R2 and variable leakage reactance sX20. Transformer works on the principle of electromagnetic induction. An induction motor is based on the principle of induction of voltages and currents. The working of an induction motor is similar to the transformer. $$\mathrm{_{}= Effective\:turns\: ratio \:of \:induction \:motor}$$, $$\mathrm{_{} = Resistance \:of \:the \:rotor\: winding\: per\: phase\: referred \:to \:stator}$$, $$\mathrm{_{0} = Standstill \:rotor \:reactance \:per \:phase\: referred\: to \:stator}$$. 2) Reading of ammeter I scl = line current on short circuit. In general, the higher the relative motion of the rotor and the stator magnetic fields, the higher is the resulting rotor voltage. Therefore, I2s in equation-2 is a line frequency current and I2s in equation-1 is a slip-frequency current. We know that, transformation ratio, k = E 2 /E 1 All the rotor parameters are transferred to the stator side as follows: E 2r ' = E 2r /k I' 2 r = kI 2r X' 2 = X 2 /k 2 and R' 2 = R 2 /k 2 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). A pure inductive reactance X0 represents the magnetising reactance of the induction motor which has a much higher value. Conventional equivalent circuit of the three-phase induction motor per phase[9]. The figure shows the complete equivalent circuit of the induction motor. Equivalent Circuit of Induction Motor Referred to Stator Side Fig. When the rotor parameters are shifted they can be represented as. This voltage is induced in a rotor containing both resistance and reactance. The energy transfers in an induction motor from stator to rotor is a quite similar operation as energy transfers in the transformer from primary to secondary. The equivalent circuit of an induction motor is drawn only for one phase. The equivalent circuit of a single phase single winding induction motor with the standstill rotor is shown below. \frac{R_2}{s}=R_2+R_2\left(\frac{1-s}{s}\right). X 1 is the inductance of the stator winding. EE-Tools, Instruments, Devices, Components & Measurements, Equivalent Circuit of Electrical Transformer, Power, Voltage and EMF Equation of a DC Motor Formulas, Exact Equivalent Circuit of Induction Motor, Single-Phase Induction Motor Construction, Working, Types & Applications, Three-Phase Induction Motor Construction, Working, Types & Applications, Difference Between Single Phase & Three Phase Induction Motor. We depends on ad revenue to keep creating quality content for you to learn and enjoy for free. There are two types of equivalent circuits in case of a three-phase induction motor- Exact Equivalent Circuit Here, R 1 is the winding resistance of the stator. The voltage and current are induced in the rotor circuit from the stator circuit for the operation. 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. In an induction motor, the no-load current is 25 to 40% of the rated current and in a transformer, the no-load current is 2 to 5% of the rated current. E m is the resultant induced voltage in the main winding. The Induction Motor Equivalent Circuit can now be drawn on a per phase basis as in Fig. What is the Equivalent Circuit of Induction Motor? To develop the equivalent circuit, let us assume initially that the core loss is absent. What the stator sees in the air gap is the equivalent of putting an impedance (equal to R2/s + jX2) across E2. X 1 = Stator reactance. Rotor's Equivalent Circuit: It an induction motor, when a 3 supply is applied to the stator windings, a voltage is induced in the rotor windings of the machine. If we divide the above equation by slip s, we get; The representation of this equation is shown in the figure below. R 2 = rotor resistance referred to stator. Induction Motor Equivalent Circuit From the preceding, we can utilise the equivalent circuit of a transformer to model an induction motor. Thus, if L2 is the inductance of the rotor, then the rotor reactance at slip s is given by, $$\mathrm{\therefore\: _2 = 2_1_2 = (2_1_2) = _{20} (3)}$$. Therefore, the rotor EMF referred to stator side is given by, $$\mathrm{\frac{_}{_{}}=\frac{_}{_{}} (1)}$$, $$\mathrm{_ =\frac{_{}}{_{}}_ = _{} . Where, s is the fractional slip of the rotor. By using this website, you agree with our Cookies Policy. The induction motor can be treated as generalized transformer. The loss produced in the stator winding is represented by the stator resistance R1 and the loss produced in the stator core is represented by the stator reactance X1. Where, X20 is the standstill rotor reactance. If you are facing with any issues or want to request any article please feel free to contact us, and also check out our privacy policy. Induction Machine Circuit Analysis Examples Per Phase Equivalent Circuit A 480V, 60 Hz, 6-pole, three-phase, delta-connected induction motor has the following parameters: R 1 = 0.461 ., R 2 = 0.258 ., X 1 = 0.510 ., X 2 = 0.756 ., X m = 30.74 . The transformation of the rotor circuit of the induction motor can be done by the means of effective turns ratio of the induction motor. When a 3-phase supply voltage is applied to the stator windings of an induction motor, a voltage is induced in the rotor windings of the induction motor. So the variable rotor resistance R2/s has two parts. 2) Note that: the element R L \ is the equivalent electrical resistance related to the mechanical load on the motor. In the case of induction motor, when the rotor current and voltages are referred to stator side, their frequency is also changed to stator frequency. In the literature [4], equations (1) - (4) are commonly used to establish an equivalent circuit of the machine in steady-state as presented in the figure below. When a three-phase supply is given to the stator winding, the EMF is induced in the rotor winding. In an approximate equivalent circuit, we need to assume that; The approximate equivalent circuit of the induction motor is shown in the figure below. The induction motor is an asynchronous motor. Rotor impedance referred to stator side is given by, $$\mathrm{_{0} = _{}^{2}(\frac{}{}+ _{0}) (4)}$$. When induction motor is on no load, it draws a current from the supply to produce the flux in air gap and to supply iron loss. At the standstill condition E mf = E mb In order to obtain the complete per-phase equivalent circuit of an induction motor, it is required to refer the rotor part to the stator side frequency and voltage level. C - Exact equivalent circuit The stator impedance, z1= r1 + j x1 The rotor impedance, z2s' =r2'/s + j x2' The admittance of the shunt branch, ym= 1/rc - j (1/xm) = gc -j bm The impedance of the shunt branch, zm = 1/ ym Here z1, z2s' and zm are complex quantities. Let suffixes "s" and "r" be used for stator and rotor quantities respectively. And the speed of a motor depends on the loading condition. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); Our website is made possible by displaying online advertisements to our visitors. In the transformer equivalent circuit, the voltage, current, and impedance on the secondary side are transferred to the primary side with the help of the turns ratio (a). Thus if V1 is the supply voltage per phase to stator, it produces the flux which links with both stator and rotor. Electric Power Single and Three Phase Power Active All per phase quantities are used in representing the equivalent circuit. Induction Motors. Reactances shown in the figure correspond to the fixed stator frequency f1. Transferring all the rotor parameters to stator, K=\frac{E_2\ \ \ }{E_1}\ =transformation\ ratio. The equivalent circuit of an induction motor is similar to a transformer equivalent circuit because the energy is transferred from stator to rotor is essential as a transformer operation from primary to the secondary winding. Why We Need to Install a Starter with a Motor? b-) Power flow of induction generator. Your email address will not be published. Our articles are written by the electrical engineers in a simple and easy way. This current I0 has two components. E m is the resultant induced voltage in the main winding. R1 = 0.78, R2 =4.2, X1=X2=5.3, Xm=93 (a) The voltage applied to phase a is 220V at 0 degrees and that applied to phase b is 220 V at 65 . The reactance of an induction motor rotor depends on the inductance of the rotor and the frequency of the voltage and current . This means the secondary is shorted. Solving for the Rotor Impedance in parallel with the Air Gap Impedance will yield the following simplified equivalent circuit: Here, we can see that the magnitude and phase angle of I2s remains unchanged by this modification. Without core loss Let the stator impedance be Z Z = R 1 + j X 1 Where R 1 = Stator resistance X 1 = Stator reactance And X 2 = rotor reactance referred to stator R 2 = rotor resistance referred to stator From this equation, it is noted that I2s is a slip-frequency current produced by slip-frequency voltage sE20 and rotor circuit having an impedance of R2 + jX2s. All other quantities are constant and the reactances correspond to those quantities at the fixed stator frequency (fs). Hence an induction motor acts like a transformer with stator forming primary and rotor forming the secondary. If the induced rotor voltage at standstill condition is E20, then the induced rotor voltage at any slip value is given by. Simple Project on Hydroelectric Power Station with Turbine. The induction motor is an asynchronous motor. In running condition, the induced emf in rotor becomes E2, which is sE2. The line impedance is modeled as a lumped parameter impedance Z = R + jL. Without core loss. Also, an equivalent circuit of an induction motor is similar to the equivalent circuit of a transformer. Thus RL is reflected mechanical load on stator. The rotor voltage depends on the relative motion of the rotor and stator magnetic field. a-) Power flow of induction motor. They are. The resistance R2(1-s)/s = RL is fictitious resistance representing the mechanical load on the motor. The Equivalent Circuit of an Induction Motor 5 R 1 = Stator resistance/phase X 1 = Stator leakage reactance/phase R 2 = Rotor resistance referred to stator/phase X 2 = Rotor leakage reactance referred to stator/phase Figure 6-12 The per-phase equivalent circuit of an induction motor. Where R 1 = Stator resistance. This imaginary stationary rotor makes it possible to transfer secondary (rotor) impedance to the primary (stator) side. Induction Motor Equivalent Circuit. The equivalent circuit of an induction motor is drawn only for one phase. fr = sfe. Parameters And Equivalent Circuit Of Induction Motor In induction motor the transfer of energy from stator to rotor takes place entirely inductively. Then also there is a huge difference between both equations. It is important to note that as load on the motor changes, the motor speed changes. Your email address will not be published. A star-connected, 12.5 kW, 208 V (line), 3-phase, 60 Hz squirrel cage induction motor has following equivalent circuit parameters per phase referred to the stator: R 1 = 0.3 , R 2 = 0.3 , X 1 = 0.41 , X 2 = 0.41 . It has got two parts one main winding and one auxiliary winding. The relative speed between the synchronous speed and actual rotor speed is known as slip. 1. a. The stator consists of the stator winding and stator core. Therefore, the per phase rotor current of the induction motor is given by, $$\mathrm{_2 =\frac{_2}{_2}=\frac{_{20}}{_2 + _{20}} (5)}$$. At the standstill condition E mf = E mb (Modal), 2 Speeds 1 Direction 3 Phase Motor Power and Control Diagrams, Three Phase Motor Connection Star/Delta (Y-) Reverse / Forward with Timer Power & Control Diagram. The transformation of the rotor circuit of the induction motor can be done by the means of effective turns ratio of the induction motor. As explain in the construction of induction motor, there are two main parts; stator and rotor.
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