Mathematical Analysis

The simulation program is based on the pseudo-code displayed below.

Start block:
    Set the values of load reactance, line reactance, capacitor, load fraction.
    Set the desired output voltage, PI controller parameters
    Set the current firing angle to be 120^o.
    Set base reference angle to 60^o.
    Set Commute = 0.   ( Indicates no commutation overlap exists at start. )
    Go to Loop Routine.
    Set theta to zero.

Loop Routine
    Call Compute routine.
    Increment theta.
    If {(theta + base reference angle) = (next firing angle) }
       [
        current firing angle = next firing angle.
        base reference angle = next firing angle - 60^o.
        Set Commute = 1 .  ( Indicates next SCR is triggered)
      ]
    Execute Loop Routine

Compute Routine:
    If  (Commute == 0)
        [
         compute next value of link inductor current.
       ]
    else
        [
         compute next value of triggered SCR current.
         compute next value of link inductor current.
         if (SCR current link inductor current) Reset Commute to 0.
        ]
    Compute next value of capacitor voltage.
    Compute next value of PI controller's output.
    Compute next firing angle.

The equations used in the Compute Routine are obtained as follows.

When there is commutation overlap, the output voltage behind the source inductance is expressed by equation (1). In equation (1), m is the overlap angle and U is the amplitude of line voltage. If the output voltage be v_o(q) during this period, the differential equation for the current through the dc link inductance is presented as equation (2). During commutation overlap, the current in the SCR just triggered on is described by equation (3). The commutation overlap ends when the current through this SCR equals the dc link inductor current. When there is no overlap, the bridge output voltage is described by equation (4).

The differential equation that describes the dc link inductor current is then described by equation (5). The differential equation for the capacitor voltage is easily obtained and it is expressed as equation (6). Next the equations relating to closed-loop control are described. Let the output of PI controller be v_C(q) and it is expressed by equation (7). In equation (7), A is a constant to be evaluated, K is the proportional gain of the controller and T is its time constant. The above equation is represented as equation (8) , which is more convenient for use in simulation. In equation (8), V_ref is the desired output voltage. The output of the controller is normally checked to ensure that it is within the set limits. From the output of the controller, the firing angle, a can be obtained. The maximum output voltage of the controller should correspond to zero degree firing angle and the minimum to 120^o firing angle. Hence we get the following equation for firing angle. This means that the range for v_C(q) is from 0 to V_Cmax.

The simulation program uses the above equations and displays the results in a graphical format.

 
TO THE TOP