Project 1
Problem Statement :
Simulate the starting behaviour of a 5 horsepower(3.75kW), 3-phase 3-wire, 230V, 60Hz, 4-pole squirrel cage induction machine with parameters:
rs=0.531Ω,rs=0.531Ω, Lls=Llr=2.52mHLls=Llr=2.52mH
rf=0.408Ωrf=0.408Ω, Lm=84.7mHLm=84.7mH
J=0.1kgm2J=0.1kgm2
The machine is suddenly connected to a balanced three-phase 230V rms sinusoidal supply voltage at frequency 60Hz. After reaching rated speed the motor is loaded to 0.83 times rated torque at 0.7secs. The load is removed after 0.1sec.
Solution:
Below is the Simulink Model based on given parameter -
a)Start up behaviour of induction motor represented in stationary d-q frame where w=0.
In that case rotor speed reaches approx. 377 rad/s on appying load speed decreases by some value and after removal of load it again increases.
In stationary reference frame, Vds and Vqs are having constant frequency of 60 Hz. THis does not change when the load is applied.
In stationary reference frame, Idr and Iqr are dependent on load. If there is no load the value is 0. Ids and Iqs have the frequency of 60 Hz.
The electromagnetic torque and load torque are shown. below for stationary reference frame.
b) Start up behaviour of induction motor represented in synchronous reference frame where w=wsyn (wsyn = 120f/p= (120*60)/4 = 1800 rpm = ((2*3.14)/60)*1800 = 188.5 rad/s.
In synchronous reference frame, Vds and Vqs are having constant frequency of 30 Hz.
In synchronous reference frame, Idr and Iqr are dependent on load. If there is no load the value is 0. Ids and Iqs have the frequency of 30 Hz.
The angle Theta required for abc-dq transformation can be seen below.
Steady state values of idr, iqr, ids and iqs can be seen below. They all are AC values.
Idr, Iqr, Ids and Iqs plot is seen below during the starting.
c) Start up behaviour of induction motor represented in rotor reference frame where w=wr or the rotor speed.
In rotor reference frame, Vds and Vqs are having constant value in steady state. Vds has a value of -187.35 V and Vqs has a value of 12.73 V in steady state
The angle Theta required for abc-dq transformation can be seen below.
In rotor reference frame, Idr, Iqr,Ids and Iqs are having constant value in steady state. Without load, Idr and Iqr remain zero in steady state. Ids is 0.295 A and Iqs is 5.7 A in steady state. Iqs increases when load torque is applied.
d) Start up behaviour of induction motor represented in rotor flux reference frame where wslip is calculated and based on it wr is recalculated.
Rotor Flux Reference Speed = slip*wr = ((ws - wr)/ws ) * wr
In rotor flux reference frame, Vds and Vqs are having variable frequency.
The reference speed is negative here.