In a three-phase half-wave cycloconverter, both inverting and converting actions take place.

Explanation:
A cycloconverter is a type of power electronic device that converts AC power at one frequency to AC power at another frequency. It is commonly used in applications where the frequency needs to be changed, such as in motor drives, induction heating, and power supplies.

A three-phase cycloconverter can be either a full-wave or a half-wave cycloconverter. In a half-wave cycloconverter, only one-half of each input cycle is converted. This means that the output waveform will have a lower frequency compared to the input waveform.

Inverting Action:
The inverting action of a cycloconverter refers to the conversion of positive half-cycles of the input waveform to negative half-cycles of the output waveform. In other words, it changes the direction of current flow in the load. This is achieved by controlling the triggering of the thyristors in the cycloconverter.

During the positive half-cycle of the input waveform, the thyristors are triggered to conduct and the load current flows in the forward direction. However, during the negative half-cycle of the input waveform, the thyristors are triggered in reverse to allow the load current to flow in the opposite direction. This results in the inverting action of the cycloconverter.

Converting Action:
The converting action of a cycloconverter refers to the conversion of the input frequency to a lower frequency in the output waveform. In a half-wave cycloconverter, only one-half of the input cycle is converted, which means that the output frequency will be half of the input frequency.

During each positive half-cycle of the input waveform, the thyristors are triggered to conduct and the load current flows in the forward direction. This results in the conversion of the positive half-cycle of the input waveform to the positive half-cycle of the output waveform. However, during the negative half-cycle of the input waveform, the thyristors are not triggered, and no conversion takes place.

Conclusion:
In a three-phase half-wave cycloconverter, both the inverting action and the converting action take place. The inverting action changes the direction of current flow in the load, while the converting action reduces the frequency of the input waveform.