Documentation
The 3 HP machine is connected to a constant load of nominal value 11. Because the machine windings are connected in a three-wire Y configuration, there is no homopolar 0 component.
INTRODUCTION The Permanent capacitor single-phase induction motors SPCIMs are commonly found in the drive systems of fans, compressors and pumps etc. Because the stator is fed by a PWM inverter, a noisy torque is observed. Chaos can be defined as an a-periodic long term behaviour in a deterministic system that exhibits sensitive dependence on initial condition.
Documentation - This parameter is only visible when you select By motor ratings for the Model parameterization parameter and Use measured stator resistance R1 for the R1 parameterization parameter. However, if you choose to simulate a delta source connection, you must use only two sources connected in series.
The electrical part of the machine is represented by a fourth-order or sixth-order for the double squirrel-cage machine state-space model, and the mechanical part by a second-order system. All electrical variables and parameters are referred to the stator, indicated by the prime signs in the following machine equations. All stator and rotor quantities are in the arbitrary two-axis reference frame dq frame. The subscripts used are defined in this table. Set to infinite to simulate locked rotor. H Combined rotor and load inertia constant. Set to infinite to simulate locked rotor. F Combined rotor and load viscous friction coefficient Parameters Specific to Double-Cage Rotor Definition R' r1, L' lr1 Rotor resistance and leakage inductance of cage 1 R' r2, L' lr2 Rotor resistance and leakage inductance of cage 2 L' r1, L' r2 Total rotor inductances of cage 1 and 2 i' qr1, i' qr2 q axis rotor current of cage 1 and 2 i' dr1, i' dr2 d axis rotor current of cage 1 and 2 ϕ' qr1, ϕ' dr1 q and d axis rotor fluxes of cage 1 ϕ' qr2, ϕ' dr2 q and d axis rotor fluxes of cage 2 Rotor type Specifies the type of rotor: Wound default for SI units , Squirrel-cage default for pu units , or Double squirrel-cage. Squirrel-cage preset model For single squirrel-cage machines, provides a set of predetermined electrical and mechanical parameters for various asynchronous machine ratings of power HP , phase-to-phase voltage V , frequency Hz , and rated speed rpm. To make this parameter available, set the Rotor type parameter to Squirrel-cage and click Apply. Select one of the preset models to load the corresponding electrical and mechanical parameters in the entries of the dialog box. The preset models do not include predetermined saturation parameters. Select No default if you do not want to use a preset model, or if you want to modify some of the parameters of a preset model. When you select a preset model, the electrical and mechanical parameters in the Parameters tab of the dialog box become nonmodifiable unavailable. This does not change the machine parameters. By doing so, you just break the connection with the particular preset model. Select Torque Tm default to specify a torque input, in N. The machine speed is determined by the machine Inertia J or inertia constant H for the pu machine and by the difference between the applied mechanical torque Tm and the internal electromagnetic torque Te. The sign convention for the mechanical torque is: when the speed is positive, a positive torque signal indicates motor mode and a negative signal indicates generator mode. The machine speed is imposed and the mechanical part of the model Inertia J is ignored. Using the speed as the mechanical input allows modeling a mechanical coupling between two machines. The next figure indicates how to model a stiff shaft interconnection in a motor-generator set when friction torque is ignored in machine 2. The speed output of machine 1 motor is connected to the speed input of machine 2 generator , while machine 2 electromagnetic torque output Te is applied to the mechanical torque input Tm of machine 1. The KT factor takes into account torque units of both machines pu or N. Also, as the inertia J2 is ignored in machine 2, J2 referred to machine 1 speed must be added to machine 1 inertia J1. Select Mechanical rotational port to add to the block a Simscape mechanical rotational port that allows connection of the machine shaft with other Simscape blocks having mechanical rotational ports. The Simulink input representing the mechanical torque Tm or the speed w of the machine is then removed from the block. The next figure indicates how to connect an Ideal Torque Source block from the Simscape library to the machine shaft to represent the machine in motor mode, or in generator mode, when the rotor speed is positive. Because the machine windings are connected in a three-wire Y configuration, there is no homopolar 0 component. This configuration also justifies that two line-to-line input voltages are used inside the model instead of three line-to-neutral voltages. The following relationships describe the dq-to-abc reference frame transformations applied to the Asynchronous Machine phase currents. The following table shows the values taken by Θ and β in each reference frame Θ e is the position of the synchronously rotating reference frame. Use signal names to identify bus labels When this check box is selected, the measurement output uses the signal names to identify the bus labels. Select this option for applications that require bus signal labels to have only alphanumeric characters. When this check box is cleared default , the measurement output uses the signal definition to identify the bus labels. The labels contain nonalphanumeric characters that are incompatible with some Simulink applications. Nominal power, voltage line-line , and frequency The nominal apparent power Pn VA , RMS line-to-line voltage Vn V , and frequency fn Hz. Stator resistance and inductance The stator resistance Rs Ω or pu and leakage inductance Lls H or pu. Rotor resistance and inductance The rotor resistance Rr' Ω or pu and leakage inductance Llr' H or pu , both referred to the stator. This parameter is visible only when the Rotor type parameter on the Configuration tab is set to Wound or Squirrel-cage. Cage 1 resistance and inductance The rotor resistance Rr1' Ω or pu and leakage inductance Llr1' H or pu , both referred to the stator. This parameter is visible only when the Rotor type parameter on the Configuration tab is set to Double squirrel-cage. Cage 2 resistance and inductance The rotor resistance Rr2' Ω or pu and leakage inductance Llr2' H or pu , both referred to the stator. This parameter is visible only when the Rotor type parameter on the Configuration tab is set to Double squirrel-cage. Mutual inductance The magnetizing inductance Lm H or pu. Inertia constant, friction factor, and pole pairs For the SI units dialog box: the combined machine and load inertia coefficient J kg. For the pu units dialog box: the inertia constant H s , combined viscous friction coefficient F pu , and pole pairs p. Simulate saturation Specifies whether magnetic saturation of the rotor and stator iron is simulated or not. Magnetic saturation of the stator and rotor iron saturation of the mutual flux is modeled by a piecewise linear relationship specifying points of the no-load saturation curve. The first row of this matrix contains the values of stator currents. The second row contains values of corresponding terminal voltages stator voltages. This point corresponds to the point where the effect of saturation begins. You must select the Simulate saturation check box to simulate saturation. If you do not select the Simulate saturation check box, the relationship between the stator current and the stator voltage is linear. Click Plot to view the specified no-load saturation curve. To inherit the sample time specified in the Powergui block, set this parameter to —1 default. Discrete solver model Specifies the integration method used by the block when the Solver type parameter of the Powergui block is set to Discrete. The choices are: Trapezoidal non iterative default and Trapezoidal iterative alg. The Forward Euler option is no longer recommended for discretizing machine models because it requires you to add non-negligible shunt load at the machine terminals to guarantee simulation stability. For more information on what method you should use in your application, see. Tm The Simulink input of the block is the mechanical torque at the machine's shaft. When the input is a positive Simulink signal, the asynchronous machine behaves as a motor. When the input is a negative signal, the asynchronous machine behaves as a generator. When you use the SI parameters mask, the input is a signal in N. You can demultiplex these signals by using the Bus Selector block provided in the Simulink library. Depending on the type of mask that you use, the units are in SI or in pu. The cage 2 rotor signals return null signal when the Rotor type parameter on the Configuration tab is set to Wound or Squirrel-cage. You must be careful when you connect ideal sources to the machine's stator. If you choose to supply the stator via a three-phase Y-connected infinite voltage source, you must use three sources connected in Y. However, if you choose to simulate a delta source connection, you must use only two sources connected in series. Large sample times require larger loads. The optimum resistive load is proportional to the sample time. Remember that with a 25 μs time step on a 60 Hz system, the minimum load is approximately 2. For example, a 200 MVA asynchronous machine in a power system discretized with a 50 μs sample time requires approximately 5% of resistive load or 10 MW. If the sample time is reduced to 20 μs, a resistive load of 4 MW is sufficient. Example 1: Use of the Asynchronous Machine Block in Motor Mode The example illustrates the use of the Asynchronous Machine block in motor mode. It consists of an asynchronous machine in an open-loop speed control system. The machine rotor is short-circuited, and the stator is fed by a PWM inverter, built with Simulink blocks and interfaced to the Asynchronous Machine block through the Controlled Voltage Source block. The inverter uses sinusoidal pulse-width modulation. The base frequency of the sinusoidal reference wave is set at 60 Hz and the triangular carrier wave frequency is set at 1980 Hz. The 3 HP machine is connected to a constant load of nominal value 11. It is started and reaches the set point speed of 1. The parameters of the machine are those found in the preceding SI Units dialog box above, except for the stator leakage inductance, which is set to twice its normal value to simulate a smoothing inductor placed between the inverter and the machine. Also, the stationary reference frame was used to obtain the results shown. In the simulation parameters, a small relative tolerance is required because of the high switching rate of the inverter. The first graph shows the machine's speed going from 0 to 1725 rpm 1. The second graph shows the electromagnetic torque developed by the machine. Because the stator is fed by a PWM inverter, a noisy torque is observed. However, this noise is not visible in the speed because it is filtered out by the machine's inertia, but it can be seen in the stator and rotor currents. Two identical three-phase motors 50 HP, 460 V, 1800 rpm are simulated, with and without saturation, to observe the saturation effects on the stator currents. Two different simulations are realized in the example. The first simulation is the no-load steady-state test. This table contains the values of the Saturation Parameters and the measurements obtained by simulating different operating points on the saturated motor no-load and in steady-state. The measured operating points fit well the curve that is plotted from the Saturation Parameters data.
Simulate an AC Motor Drive To use the AC drive models of the Electric Drives library, you first specify the types of motors, converters, and controllers used in the six AC drive models modelling of single phase induction motor in simulink the library designated AC1 to AC6. Simulation of the servile sided linear induction machine is well documented in computer hardware and software, new simulation packages which are faster and more user friendly are now available. Remember that with a 25 μs time step on a 60 Hz system, the minimum load is approximately 2. The circuit is now north for simulation. Closed-Loop Speed Control with Slip Compensation In this type of control, a slip speed command is added to the measured rotor speed to produce the desired inverter frequency. Vector control is applicable to both induction and synchronous motors. In order to have torque regulation, you must la the regulation mode in the Controller section of the user interface. F Combined rotor and load viscous friction coefficient Parameters Specific to Double-Cage Rotor Definition R' r1, L' lr1 Rotor resistance and leakage inductance of cage 1 R' r2, L' lr2 Rotor resistance and leakage inductance of ring 2 L' r1, L' r2 Total rotor inductances of cage 1 and 2 i' qr1, i' qr2 q axis rotor current of cage 1 and 2 i' dr1, i' dr2 d axis rotor current of cage 1 and 2 ϕ' qr1, ϕ' dr1 q and d axis rotor fluxes of cage 1 ϕ' qr2, ϕ' dr2 q and d sin rotor fluxes of cage 2 Rotor type Specifies the type of rotor: Wound default for SI unitsSquirrel-cage default for pu unitsor Double squirrel-cage. Initially the speed of the motor rises from zero and increases above the nominal speed; it experiences some transients and then settles to a la level within few milliseconds. Description This machine has two windings: main and auxiliary.