The RMS value of thyristor current can be calculated using the following formula:

Irms = Idc / sqrt(2)

where Idc is the average value of the thyristor current.

To find the average value of thyristor current, we need to first consider the circuit operation. A 3-, 3 pulse converter is a type of AC to DC converter that uses three thyristors to control the output voltage. In this case, the converter is fed from a delta star transformer, which means that the input voltage is a three-phase AC voltage.

At firing angle 60°, one of the thyristors is turned on for each phase of the input voltage. The thyristor conducts for a certain portion of the input waveform, which results in a pulsating DC output voltage. The freewheeling diode is connected across the load to provide a path for current when the thyristor is turned off.

To calculate the average value of thyristor current, we need to consider the waveform of the output current. At firing angle 60°, the output current waveform has a triangular shape, with a peak value occurring when the thyristor is turned on and a zero value occurring when the thyristor is turned off. The average value of this waveform can be calculated as:

Idc = (1/2) * Imax * (1 - cos(alpha))

where Imax is the peak value of the output current waveform and alpha is the firing angle (in radians).

In this case, Imax can be calculated as the maximum value of the load current. Since the load requires ripple free current, we can assume that the load current is constant and equal to the DC output current. Therefore, Imax is equal to the DC load current.

The DC load current can be calculated as the output voltage divided by the load resistance. Since the output voltage is a pulsating DC voltage, we need to use the formula for the average value of a triangular waveform:

Vdc = (3/π) * Vm * (1 - cos(alpha))

where Vm is the peak value of the input voltage waveform.

In this case, Vm can be calculated as the line-to-line voltage of the input voltage divided by sqrt(3). Therefore:

Vm = Vll / sqrt(3) = 230 / sqrt(3) = 132.7 V

Plugging in the values, we get:

Vdc = (3/π) * 132.7 * (1 - cos(60°)) = 89.9 V

The load resistance is not given, so let's assume it is 10 ohms. Therefore, the DC load current is:

Idc = Vdc / Rload = 8.99 A

Finally, we can calculate the RMS value of thyristor current as:

Irms = Idc / sqrt(2) = 8.99 / sqrt(2) = 6.36 A (rounded to two decimal places)