No, the power to the SSR comes from the AC lines. The PID only provides a low voltage, low current DC control signal to the SSR. Also, SSR's are designed to handle inductive loads (motors, etc.), and have built in snubber circuits to absorb voltage spikes, and resistive loads don't spike when switched. Like
@augiedoggy , I recommend putting the element contactors on the power input side of the SSR's rather than on the load side of the SSR's. This way you can electrically isolate (disconnect) the SSR completely from the lines voltage in case of failure. All my designs are done this way.
Brew on