Induction Machine Model for Start-Up Simulation

     This article is about the basic modelling of induction machine using the delta equivalent circuit parameters. With this model, we can easily observe how input voltage, stator current, electromechanical torque and shaft speed changes with time during start-up. Basic mathematical model of an induction machine is formed using the mathematical equations of current,torque and mechanical motion equation. The mathematical model is simulated for 1 second to observe the start-up situation. The MATLAB model for this purpose is as stated below;

% Induction Motor Model

t = 0:0.001:1; % 1sec simulation with time step of 0.001 sec

dt = 0.001;

% Motor Parameters

R1 = 0.205; % Ohm

R2 = 1.408; % Referred value, Ohm

X1 = 1.507; % Ohm

X2 = 1.507; % Ohm

Rc = 315.6; % Shunt branch, Ohm

Xm = 42.5; % Shunt branch, Ohm

Vin = 537.4*cos(2*pi*50*t); % Input voltage,50 Hz, Vphase 220 V

I = zeros(1,1001);

s = 1; % slip=1 at the beginning

w = zeros(1,1001); % rotor speed

Pe = 0; % Electromechanical power output

Te = zeros(1,1001); % Electromechanical torque

Jm = 0.1285; % kg/m2 , Inertia of machine

% Load parameters

Tl = 0; % Load Torque

Jl = 0; % Load Inertia

Xeq = X1 + X2;

Leq = Xeq / 100 / pi;

    

for n=2:1001

   Vth = abs(1i*Xm/(R1 + 1i*(X1 + Xm))*Vin(1,n)); 

   I(1,n) = (Vin(1,n) + I(1,n-1)*Leq/dt) / (R1 + R2/s + Leq/dt); % Motor Current 

   Te(1,n) = 3*Vth^2*R2/((R1 + R2/s)^2 + (X1 + X2)^2)/s/100/pi; % Electromechanical Torque

   

   % Torque balance equation

   w(1,n) = w(1,n-1) + (Te(1,n) - Tl)/(Jm + Jl)*dt; % new speed value 

   s = (100*pi-w(1,n))/100/pi ; % new slip value

end

     After we run this code, w, Te and I vectors against time is created at the workspace. We can plot them to see their variation in time during start-up.

     Simulation Results (NO-LOAD Start-Up)

 Simulation Results (LOAD with only inertia no torque Start-Up , inertia Jload = 3xJmotor)

     Summary

     

     Note that the in rush current of the motor start-up is easily observed in current graphs. 

     Note that the results are for 2 pole machine

     When a load of only inertia that is 3 times larger than motor inertia, the start-up time is increased.

     Please investigate the torque graphs, the mean of the torque values shows a typical torque-speed curve, which is expected.

     Since there is no load torque and friction&windage torque is neglected, the motor current reduced to zero after rated speed is reached. 

     What if the motor is suddenly loaded with a constant torque of 40 Nm during 1.5 < t < 1.7 sec ?

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