Project 2 - Modeling of 3 phase Induction Motor Drive

Project 2 - EV Application of Induction Motor

___Q1___

AIM : Open Loop speed control of 3 phase Induction Motor using V/F method.

THEORY :

- Three phase Induction Motor (IM) produces Rotating Magnetic Field (RMF) rotating at Synchronous Speed (`N_s`).

- `N_s = (120*f)/P`

- EMF induced in IM is given by, `V\ \=\ \4.44*f*phi*K*T`.

- Where f = Fundamental Frequency; P = Number of Poles; T = number of turns per phase;

- Flux induced is given by, `phi\ \=\ \V/(4.44*f*K*T)`

- Now if frequency is changes, synchronous speed also changes; but with decrease in frequency flux will increase .

- This change in flux causes saturation or rotor and stator core which causes increase in NL current of motor.

- So, to maintain the flux constant, applied voltage (V) needs to be changed.

- Thus, decrease in frequency causes flux to increase but at the same time if voltage is decreased flux decreases, causing no change in flux.

- Hence by keeping V/F constant, speed is changed.

DESIGN PARAMETER :

- 3 phase squirrel cage IM.

- Power = 100 HP.

- DC Voltage = 800 V.

- Switching Frequency = 10 kHz.

- 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.

SIMULINK MODEL :

Each block is explained below :-

1 - V/F Control :

- Matlab Function Block It is used to create sine waves depending upon the input given to this block. It has three inputs f (frequency); Ma(Modulation Index) t (time). It has 3 sine waves at 120 phase shift.

- Frequency input is taken by converting Input Speed using formula`f = (N_s*P)/120` - This model uses 4 pole motor. - Speed Reference is simulated by Step block. - Step/speed changes from 1200 to 1000 at 1 second. - Modulation Index represents V/F i.e. 1/F

2 - SPWM

- Sine Pulse Width Modulation Sine wave inputs from V/F control subsystem are compared with 10 kHz carrier wave. Carrier wave is simulated by Sawtooth generator. Not gate is used to prevent the trigerring of same switch of a single leg. Hence upper switches are trigerred with 1,3,5 and lower switches are trigerred with 4,6,2 gate pulses.

3 - Inverter

-	DC Voltage Source with 800 V as input is given to Inverter.
-	6 IGBT switches are used to create a 3 phase inverter. Each is triggered by gate pulses from SPWM taken via from block.
-	Three phase VI Measurement block is used to measure inverter phase to phase voltage.
-	Filter Design : `L < (0.03*V_(i\n))/(2*pi*f*I_(Lmax))` `C = 1/((2*pi*f)^2 *L)` `L = 80\ \muH` `C = 11.9\ \mF`

4 - Three Phase Induction Motor.

- Asynchronous Machine block set as model : 05 100 HP 460V 60Hz 1780 RPM with Squirrel Cage.

- Torque reference is modelled using a step block, wherein at 0.1 second torque changes from 10 Nm to 20 Nm.

RESULTS :

- Plot below shows Frequency, Speed and Torque of the IM.

- As seen frequency changes from 50 Hz to 33 Hz at 1 second.

- Speed first settles at 1500 rpm from 1800 rpm after intial ringing, at 1 second the speed changes to 1000 rpm and thus to keep the flux constant, frequency also steps downs.

Plot below shows Stator Voltages

Plot below shows Phase currents.

After initial transients the current settles to nomial value.

___Q2___

AIM : To derive the Transfer Function of 3 phase Induction Motor.

THEORY :

Circuit Diagram below shows the equivalent model of IM where rotor referred to stator side.

where,

`V_1 =`Stator Voltage

`R_1 =`Stator Resistance

`X_1 =`Stator Leakage Reactance

`I_1 =`Stator Current

`R_c =`Shunt Branch Resistance

`X_m =`Magnetising Reactance

`I_o =`Per phase NL current

`R_2' =`Rotor Resistance referred to Stator

`X_2' =`Standstill Rotor Reactance referred to Stator

`I_2' =`Rotor Current per phase referred to Stator

s = Slip

Equation of Electrical Machine is given by,

`V_a = I_aR_a\ \+\ \jX_sI_a\ \+\ \E_b`

Taking Laplace Transform

`V_a(s) = I_a(s)(R_a\ \+\ \jX_s)\ \+\ \E_b(s)`

Back EMF `E_b = K_tstheta(s)`

putting in equation above

`V_a(s) = I_a(s)(R_a\ \+\ \jX_s)\ \+\ \K_tstheta(s)`

rearranging,

`I_a(s) = (V_a(s)\ \-\ \K_tstheta(s)) / (Z(s))`

Electrical Torque is givne by,

`T_e = (KE^2R)/(R^2+X^2)`

Taking Laplace Transform

`T_e = E^2sintheta`

Similarly, Mechanical Torque is given by,

`T_m = Jddottheta\ \+\ \Btheta`

Taking Laplace Transform

`T_m(s) = (Js^2\ \+\ \Bs)theta(s)`

`T_m = T_e`

`E^2theta(s) = Js^2\ \+\ \Bs(theta(s))`

`(Js^2\ \+\ \Bs\ \-\ \E^2)theta(s)\ \=\ \T_m`

rearranging,

`(Js^2\ \+\ \Bs\ \-\ \E^2)\ \=\ \T_m/(theta(s))`

`(theta(s))/T_m = 1/ ((Js^2\ \+\ \Bs\ \-\ \E^2))`

`T\ \prop\ \phiI_acostheta`

putting `theta = 0`

`T = KphiI_a`

Taking Laplace Transform

`T = Kphi(s)I_a(s)`

Equating both T and putting value of `I_a`

`K_aV_a(s) = (Js^2\ \+\ \Bs\ \-\ \E^2)theta(s)Z(s)\ \+\ \K_tstheta(s)`

Rearranging,

`(Output)/(Input) = (theta(s))/(V_a(s)) = (K_a)/((Js^2\ \+\ \Bs\ \-\ \E^2)Z(s)\ \+\ \K_aK_ts)`

Transfer Function = `(Output)/(Input)`

`(theta(s))/(V_a(s)) = (K_a)/(JL_as^3\ \+\ \(R_aJ\ \+\ \BL_a)s^2\ \+\ \(BR_a\ \+\ \K_aK_t)s)`

___Q3___

AIM : To Model 3 phase induction motor with a 3 phase inverter using Direct Torque control using an Average Model.

THEORY :

Variable frequency drives control AC induction motors through one of several control schemes. Scalar control (V/f control) varies both the voltage and frequency of power supplied to the motor to maintain a fixed ratio between the two. This keeps the strength of the magnetic field at a constant level so that torque production remains stable. Scalar control is a simple, inexpensive control method, but it doesn’t allow precise control of motor speed.

Vector control (FOC) controls the magnetizing and the torque-producing components of the stator current independently to control both motor speed and torque.

Another control method, known as direct torque control (DTC), is similar to field oriented control, in that it decouples torque and flux and controls them independently. But DTC controls motor torque directly, without a modulator, so torque response is much faster.

The principle of DTC is based on the direct application of a control sequence to the switches of the voltage inverter .

The choice of this sequence is made by the use of a switching table and two hysteresis regulators whose role is to control and regulate the electromagnetic torque and the flux of the machine in a decoupled manner.

The electromagnetic torque is controlled using a three level hysteresis comparator.

While the stator flux is controlled using a two level hysteresis comparator.

The outputs of these comparators, as well as the flux vector information, are used to determine the switching table.

SIMULINK MODEL :

Electrical Model

The electrical energy is supplied by DC Voltage Source. 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 example uses 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: