Project 2 - Modeling of 3 phase Induction Motor Drive
This project is focused towards electric vehicle application using an Induction Motor. Student will have to take following steps for a successful model:
- Model 3 Phase Inverter using Simulink (model the parasitic as well) with a switching frequency of 10Khz using 3 phase Squirrel Cage Induction motor, using V/F method, open loop
Design Parameters:
- Power = 100 HP
- DC Voltage = 800 V
- Output Voltage = 460 VRMS – line to line
- Initial Speed = 1500 RPM
- Final Speed = 1000 RPM
- Initial Load Torque = 10 Nm
- Final Torque=20 Nm
- Torque Step Time = 0.1 secs
For Induction Motor model – use Asynchronous Machine from Simulink with Squirrel Cage Preset Model – 05 , for 100HP Motor
For back emf to speed relation, assume a linear rate from 0.25 to 1, with speed changing from 500 RPM to 2000 RPM
Plot speed, stator voltage (line to line) and frequency.
Plot stator line voltage, phase current
2. Use the 3 phase inductor motor theory to derive the transfer function of 3 phase Induction Motor
3. Model 3 phase induction motor with a 3 phase inverter using Direct Torque control using an Average Model, Implement both torque and flux control to achieve desired power.
Design Parameters:
- Initial Speed = 0 RPM
- Flux Target = 2.5 webers
- DC Voltage = 500 V;
- Fundamental Frequency = 60 Hz
- Speed Step Time = 0.01 secs
- Determine fundamental speed based upon fundamental frequency
- Determine the switching sequence for direct torque control
- Moment of Inertia = 0.1 Kgm^2
- Load Torque Initial = 0 Nm
- Final Load Torque = 50 Nm
- Torque Step Time = 0.03 secs
Motor Parameters: (Create an Average Model)
- Stator Resistance = 0.5 Ohms
- Rotor Resistance = 0.2 Ohms
- Stator Leakage Inductance = 20 mH
- Rotor Leakage Inductance = 10 mH
- Magnetizing Inductance = 200 mH
- Number of Poles = 4
- Torque to Speed
- Model 3 Phase Inverter using Simulink (model the parasitic as well) with a switching frequency of 10Khz using 3 phase Squirrel Cage Induction motor, using V/F method, open loop
Design Parameters:
- Power = 100 HP
- DC Voltage = 800 V
- Output Voltage = 460 VRMS – line to line
- Initial Speed = 1500 RPM
- Final Speed = 1000 RPM
- Initial Load Torque = 10 Nm
- Final Torque=20 Nm
- Torque Step Time = 0.1 secs
For Induction Motor model – use Asynchronous Machine from Simulink with Squirrel Cage Preset Model – 05 , for 100HP Motor
For back emf to speed relation, assume a linear rate from 0.25 to 1, with speed changing from 500 RPM to 2000 RPM
Plot speed, stator voltage (line to line) and frequency.
Plot stator line voltage, phase current
Open Loop V/F Control:
The open loop V/F control of an induction motor is the most common method of speed control because of its simplicity and these types of motors are widely used in industry. Traditionally, induction motors have been used with open loop 50Hz power supplies for constant speed applications. For adjustable speed drive applications, frequency control is natural. However, voltage is required to be proportional to frequency so that the stator flux
Ѱs=Ѵs/ωs
Remains constant if the stator resistance is neglected. The power circuit consists of a diode rectifier with a single or three-phase ac supply, filter and PWM voltage-fed inverter. Ideally no feedback signals are required for this control scheme.
The PWM converter is merged with the inverter block. Some problems encountered in the operation of this open loop drive are the following:
The speed of the motor cannot be controlled precisely, because the rotor speed will be slightly less than the synchronous speed and that in this scheme the stator frequency and hence the synchronous speed is the only control variable.
The slip speed, being the difference between the synchronous speed and the electrical rotor speed, cannot be maintained, as the rotor speed is not measured in this scheme. This can lead to operation in the unstable region of the torque-speed characteristics.
The effect of the above can make the stator currents exceed the rated current by a large amount thus endangering the inverter-converter combination
These problems are to be suppressed by having an outer loop in the induction motor drive, in which the actual rotor speed is compared with its commanded value, and the error is processed through a controller usually a PI controller and a limiter is used to obtain the slip-speed command
I am modelling a three phase inverter with a 10khz switching frequency for three phase squirrel cage induction motor using V/F open loop speed control method by using below design parameters
- Power = 100 HP
- DC Voltage = 800 V
- Output Voltage = 460 VRMS – line to line
- Initial Speed = 1500 RPM
- Final Speed = 1000 RPM
- Initial Load Torque = 10 Nm
- Final Torque=20 Nm
- Torque Step Time = 0.1 secs
The model is shown below
inside spwm is shown below
In v/f control method we can control the speed by varying the voltage and frequency so in the requirement the intial speed is 1500 and final speed of the motor is 1000 so i vary the frequency and voltage of three phases by using step and Vm as shown above are connected to three phases and are comparing with the repeating sequence by using relational operator and generating the three gate signal and another three gate signals are generating by using NOT gate.
For speed i am taken step as shown below
three phases are shown below
For gate signals generation as shown below
Inside inverter subsystem is shown below
induction motor is shown below
For torque i am taken step for reference as shown below
the block parameters are shown below
The line voltages are shown below
the speed and torque characteristics are shown below
First plot indicates the stator current of three phases.
Second plot indicates torque of the motor.
the speed is controlled from 1500 to 1000rpm as above shown third plot.
2. Use the 3 phase inductor motor theory to derive the transfer function of 3 phase Induction Motor
The transfer function of an Induction motor will be determined as follows
Mathematical modeling of induction motor can be obtained by taking all the basic equations
r1=resistance of Stator
X1=Stator leakage reactance
I1=stator current
Rc=shunt branch resistance
Xm=magnetizing reactance
Ie=per phase no-load current
I2=Rotor current
I2'=Rotor Current per phase referred to stator
X2'=standstill rotor reactance referred to stator
r2'=rotor resistance referred to stator
V1=Stator Voltage
E1=stator induced emf
s=slip
The electrical equation of the machine is
Va=IaRa+JXsIa+Eb
where Eb∝dθdt
Applying Laplace transforms,
Va(s)=Ia(s)(Ra+jXs)+Eb(s)
we know that
Eb=Ktsθ(s)
substituting, we get
Va(s)=Ia(s)Z(s)+Ktsθ(s)
⇒Va(s)−Kt(s)sθ(s)Z(s)=Ia(s)
Electrical Torque is given by
Te=E2sinθ
Mechanical Torque is given by
Tm=J..θ+Bθ
Taking Laplace Transforms,
Tm(s)=(Js2+Bs)θ(s)
Tm=Te⇒E2θ(s)=Js2+Bs(θ(s))
⇒(Js2+Bs−E2)θ(s)=Tm
⇒Js2+Bs−E2=Tmθ(s)
⇒θ(s)Tm(s)=1Js2+Bs−E2
we know that T∝ϕIacosθ(takeθ=0)
T=KϕIa
⇒T=Kϕ(s)Ia(s)
From above we know Ka[Va(s)−Ktsθ(s)]Z(s)=(Js2+Bs−E2)θ(s)
⇒KaVa(s)=(Js2+Bs−E2)θ(s)Z(s)+Ktsθ(s)
⇒Va(s)θ(s)=(Js2+Bs−E2)Z(s)+KaKtsKa
⇒θ(s)Va(s)=Ka(Js2+Bs−E2)Z(s)+KaKts
⇒θ(s)Va(s)=Ka(Js2+Bs−E2)(Ra+Las)+KaKts
The transfer function of the induction motor is given as
⇒θ(s)Va(s)=KaJLas3+(RaJ+BLa)s2+(BRa+KaKt)s
3. Model 3 phase induction motor with a 3 phase inverter using Direct Torque control using an Average Model, Implement both torque and flux control to achieve desired power.
Design Parameters:
- Initial Speed = 0 RPM
- Flux Target = 2.5 webers
- DC Voltage = 500 V;
- Fundamental Frequency = 60 Hz
- Speed Step Time = 0.01 secs
- Determine fundamental speed based upon fundamental frequency
- Determine the switching sequence for direct torque control
- Moment of Inertia = 0.1 Kgm^2
- Load Torque Initial = 0 Nm
- Final Load Torque = 50 Nm
- Torque Step Time = 0.03 secs
Motor Parameters: (Create an Average Model)
- Stator Resistance = 0.5 Ohms
- Rotor Resistance = 0.2 Ohms
- Stator Leakage Inductance = 20 mH
- Rotor Leakage Inductance = 10 mH
- Magnetizing Inductance = 200 mH
- Number of Poles = 4
- Torque to Speed
Aim: Model 3 phase induction motor with a 3 phase inverter using Direct Torque control using an Average Model, Implement both torque and flux control to achieve desired power.
I am taking a matlab example model in that i am implemented the design parameters.the design parameters are shown below
Design Parameters:
- Initial Speed = 0 RPM
- Flux Target = 2.5 webers
- DC Voltage = 500 V;
- Fundamental Frequency = 60 Hz
- Speed Step Time = 0.01 secs
- Determine fundamental speed based upon fundamental frequency
- Determine the switching sequence for direct torque control
- Moment of Inertia = 0.1 Kgm^2
- Load Torque Initial = 0 Nm
- Final Load Torque = 50 Nm
- Torque Step Time = 0.03 secs
Motor Parameters: (Create an Average Model)
- Stator Resistance = 0.5 Ohms
- Rotor Resistance = 0.2 Ohms
- Stator Leakage Inductance = 20 mH
- Rotor Leakage Inductance = 10 mH
- Magnetizing Inductance = 200 mH
- Number of Poles = 4
- Torque to Speed
theory:
Electrical Model
The DC bus is connected to a three-phase, two-level converter. This converter generates the variable voltage and frequency required for variable-speed operation of the 150 HP induction motor. In addition, a braking chopper is connected to the DC bus in order to dissipate the kinetic energy of the motor during deceleration.
An inverter-fed induction motor drive can be controlled through various techniques depending on application, desired performance, and controller design complexity. Commonly used schemes are scalar control (V/Hz control or open loop flux control) or vector control (field-oriented control or direct torque control). This is a hysteresis-based direct torque control (DTC) technique.
Direct Torque Controller
Direct torque control (DTC) is a technique that allows you to instantaneously control the motor magnetic flux and its electromagnetic torque in a decoupled way. Controlling the torque directly permits accurate static and dynamic speed regulation. The main components of the DTC subsystem are:
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Flux and Torque Calculation — The stator flux linkage is estimated by integrating the stator voltages, and torque is calculated based on the estimated flux and the motor currents.
-
Speed Regulator — The regulator compares the actual motor speed with the speed reference and generates the torque reference.
-
Hysteresis Control — The calculated flux magnitude and torque are compared with the reference values. When the resulting flux or torque error crosses either the positive or negative hysteresis band value, a control signal is activated in order to correct the error.
-
Optimal Switching — Pulses to the motor inverter are produced based on the control signals generated by the hysteresis control and the stator flux linkage position.
The figure below illustrates the strategy used to determine the best voltage vector when the flux linkage is located in sector 0.
The image shows four cases:
-
V3 is selected when the electromagnetic torque should be increased and the flux should stay unchanged. Selecting the V3 voltage vector speeds up the flux and thus applies an acceleration torque to the rotor while slightly decreasing the flux magnitude.
-
V2 is selected when the electromagnetic torque should be increased and the flux should be increased. Selecting the V2 voltage vector slightly speeds up the flux and increases its magnitude.
-
V6 is selected when the electromagnetic torque should be reduced and the flux should be increased. Selecting the V6 voltage vector slows down the flux and thus applies a deceleration torque to the rotor while increasing the flux magnitude.
-
V5 is selected when the electromagnetic torque should be reduced and the flux should stay unchanged. Selecting V5 the voltage vector applies a deceleration torque to the rotor and slightly decreases the flux magnitude. Note that voltage vectors V1 and V4 are not selected in sector 0. Using these two vectors would have too much negative impact on the desired flux value. Finally, to keep the torque and the flux unchanged, the null voltage vectors V0 or V7 are selected.
When the flux linkage vector moves to sector 1, the selected voltage vectors become V4 for case 1, V3 for case 2, V1 for case 3, and V6 for case 4, and vectors V2 and V5 are not used. This 60 degree shift in the voltage vectors happens each time the flux linkage vector enters a new sector.
The simulation model is shown below
Block parameters are shown below
Subsytem of direct torque control is shown below
Flux and torque calculation is shown below
Speed regulation is shown below
The block parameters are shown below
Determining fundamental speed based upon fundamental frequency:
speed Ns = 120 * f / P
fundamental frequency (F) = 60Hz
number of poles P = 4
Fundamental speed Ns = 120 * 60 / 4
Fundamental speed N = 1800
Simulation results
The Induction motor speed, current, and power are measured and shown in the below plots.
