What is the minimum power that needs to be produced by the solar panels?

Your solar panels need to be exporting more than 1400W to the grid for your car to charge (or in the case of the software-based solution, the predicted output of the panels must be above 1400W). If they are producing less, then no charge will go into your car. This means that the total power produced minus the household load needs to be greater than 1400W.