Project 2 - Modeling of 3 phase Induction Motor Drive

Aim:

• To 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.
• Use the 3 phase inductor motor theory to derive the transfer function of 3 phase Induction Motor
• To 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.

1.

Design Parameters:

1. Power = 100 HP
2. DC Voltage = 800 V
3. Output Voltage = 460 VRMS – line to line
4. Initial Speed = 1500 RPM
5. Final Speed = 1000 RPM
6. Initial Load Torque = 10 Nm
7. Final Torque=20 Nm
8. Torque Step Time = 0.1 secs

Simulink Model:

V/f control is a method to control a ratio between primary voltage (V) to be applied to the induction motor and
inverter output frequency (f) to be constant. This control enables to obtain satisfactory torque characteristics in a wide
frequency range by maintaining the magnitude of the rotating magnetic field vector independently from the inverter
output frequency when voltage drop due to a primary winding resistance is ignored.
However, as the frequency declines, the voltage drop due to the primary winding resistance becoming too large to be
ignored, and consequently, it becomes impossible to obtain sufficient torque. In such a case, applying a higher voltage
than the voltage calculated from the V/f ratio which was used for a high frequency makes it possible to secure enough
torque even at a low frequency.

Whenever three phase supply is given to three phases induction motor rotating magnetic field is produced which rotates at a synchronous speed given by

In three phase induction motor emf is induced by induction similar to that of a transformer which is given by

Where,

K is the winding constant

T is the number of turns per phase

f is frequency.

Now, synchronous speed varies as frequency is changed, but when frequency is decreased, flux increases. This change in flux value results in saturation of the rotor and stator cores, which further raises the motor's no-load current. Hence, maintaining flux at a consistent value is crucial, and doing so requires changing the voltage. In other words, if we lower the frequency, the flux will increase, but if we lower the voltage, the flux will drop as well, creating no change in flux and keeping it constant. Hence, we are maintaining a constant V/f ratio here. As a result, it is called the V/f approach.

Simulation Results:

Rotor speed

Electromagnetic Torque

Rotor currents

Stator currents

• When we alter the V/f ratio from one value to another, using a multilayer inverter for speed control of the induction motor will be smooth, flexible, and also significantly minimize transients.
• The fundamental disadvantage of multilayer inverters is the enormous quantity of flying capacitors and clamping diodes needed for high-speed switching power electronics.

2. 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 = Stator resistance

X1 is the stagger leakage reactance

I1 equals stator current

Shunt branch resistance is Rc.

Magnetizing reactance: Xm

Ie is the unitary no-load current.

Rotor current = I2.

I2'= Rotor Current Per Phase As Shown By Stator

X2'= stator-referenced stationary rotor reactance

r2' is the stator's rotor resistance.

Stator Voltage, V1,

E1 = emf caused by a stator

s= slip

The machine's electrical equation is

Va=IaRa+JXsIa+Eb

in which Ebddt

Laplace transformations are used,

Va(s)=Ia(s)(Ra+jXs)+Eb(s)

we know that

Eb=Ktsθ(s)

replacing, we obtain

Va(s)=Ia(s)Z(s)+Ktsθ(s)

⇒Va(s)−Kt(s)sθ(s)Z(s)=Ia(s)

The source of electrical torque is

Te=E2sinθ

The source of mechanical torque is

Tm=J..θ+Bθ

Laplace Transforms are used,

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 are aware that TIacos (take = 0)

T=KϕIa

⇒T=Kϕ(s)Ia(s)

From above, we may determine Ka[Va(s)Kts(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 induction motor's transfer function is provided as

⇒θ(s)Va(s)=Ka*J*La*s^3+(RaJ+BLa)s^2+(BRa+KaKt)s

3.

Design Parameters:

1. Initial Speed = 0 RPM
2. Flux Target = 2.5 webers
3. DC Voltage = 500 V;
4. Fundamental Frequency = 60 Hz
5. Speed Step Time = 0.01 secs
6. Determine fundamental speed based upon fundamental frequency
7. Determine the switching sequence for direct torque control
8. Moment of Inertia = 0.1 Kgm^2
9. Load Torque Initial = 0 Nm
10. Final Load Torque = 50 Nm
11. Torque Step Time = 0.03 secs

Motor Parameters:

1. Stator Resistance = 0.5 Ohms
2. Rotor Resistance = 0.2 Ohms
3. Stator Leakage Inductance = 20 mH
4. Rotor Leakage Inductance = 10 mH
5. Magnetizing Inductance = 200 mH
6. Number of Poles = 4

• The three-phase voltage source is fed to the diode rectifier to convert 3 phase to a DC Voltage Source.
• Three-phase two-level inverter is connected to the dc voltage source and then connected to the induction motor.
• The DC source is charged from the grid equivalent and then discharged by the 3 phase inverter.
• To achieve this, a breaking chopper is added.