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How do I operate a star delta starter with 2 wire control?

First it is necessary to understand the difference between 2 and 3 wire control.
Most motor systems, that require operator action to start a motor, use 3 wire control. This is a method by which a pulse of control voltage is applied, usually through a momentary pushbutton or spring return selector etc, to the control circuit. The pulse will bring in a contactor or relay which will electrically latch through one its own normally open contacts to hold itself in once the start button is released and the pulse removed.
The stop button is usually a normally closed contact in series with the supply to start button and coil of the latching relay, so that when pressed the contact will open, break the supply to the coil and the relay/contactor will drop out, and remain out, until the start device is again operated.
Below is a simple diagram illustrating the principle of three wire control.
Two wire control is much simpler, a straightforward on/off switch will do the job. Applying power to the control circuit starts the motor, removing the control voltage stops it.
Below is a schematic of how a star delta starter can be operated in two wire control.
96 is the terminal for the NC contact on the overload relay, the run signal will be applied to terminal 95 to enable the overload to switch off the motor in the event of a motor fault.
KM1 is the Star contactor, KM2 is the Line contactor and KM3 is the Delta. Timer is most commonly a pneumatic timer fitted to KM2 and will normally operate a few seconds (typically 5-30 seconds) after KM2 has energised.

This type of operation will usually be found where a star delta is to be operated by a PLC, a pressure or temperature switch or some other device which is going to provide a simple on/off signal.
Although 2 wire operation is theoretically simple, it does introduce some problems.
Where possibility of physical interaction between people and a piece of driven machinery exists it is necessary to prevent unexpected re-starts after an overload reset,  power resumption after a power cut, emergency stop reset etc. 3 Wire control achieves this automatically as the latching contactor will drop out after a supply or control interruption and will not restart until another start signal is given. With two wire control the machine will restart immediately power is restored unless the control signal has first been removed.
This may not be an issue on an enclosed system, perhaps a ventilation system with enclosed fans etc but on something like a machine tool, saw, conveyor etc, it essential that an opportunity is given for an operator to ensure everything is clear before initiating a restart.
If control is by PLC or similar it may be possible to build into the software to detect an unintended stop and then require a reset input to the PLC before the PLC can restart the motor.
Alternatively an electromechanical system of de-energise and reset of control voltages could be applied. This may a suitable solution where motors are controlled by a pressure or temperature switch etc. Attached is an example diagram of how such a circuit might be applied to a pressure switch. In this case, once a start signal has been applied the motor will be under the control of the pressure switch, but after a supply or control circuit interruption it will be necessary to press the start button again to reset the control circuit. Any emergency stop application must be upstream of the overload to ensure that in the event of an emergency stop the control circuit will be de-energised requiring a “Start” signal to reset the control supply.
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