I think there are two things you need to investigate more fully here
1/ what will be the shape of the power delivery curve each day considering the location of your panels, this will also show you what peak installed power you will need to maintain 1.5Kw for the number of hours you want and the months you want. There are many websites for this.
2/ Determine the characteristics of your AC, for example is it an old capacitor start motor, then you will have trouble due to the very heavy inrush and no protection against frequent starts. Or is it a more modern inverter type, these have a lower inrush and can sustain frequent starts as they have inbuilt timers etc.
Also not all inverters you might use for supply are the same when it comes to motor start so depending on your AC characteristics be careful what you buy. I am with you on the battery front BUT for this application it depends if the PV costs for the extra peak power required without a battery is cheaper than the alternatives (battery and charge controller).
I just saw your latest reply, it's a capacitor start motor.......well I think the only practical way to avoid batteries is to use the grid to start it (as you have a grid), in other words invest in a GTI. Yes I understand that means investigating the regulatory requirements but that may be time well spent. There are a lot of "plug in" GTI's that are normally acceptable up to 1kW and there's nothing stopping you using multiples
The only problem is sometimes there input range is a bit restricted meaning you have to use expensive 12V leisure panels but again a bit of research can pay dividends.
Another thing I forgot to mention is check your electric meter specification on the web and make sure its not going to do anything nasty with export power, some of them treat it as fraud or charge you for it but a quick word with your local company normally gets this sorted out (meter change etc).