How to explain in PhD interview about leaving current PhD due to lack of funding? I am invited to interview for a PhD position.  I am very afraid about the questions which will be asked. However I have a big fear, and it is that I am currently PhD student, started 1.5 year ago. I was the only PhD student in the group who was not paid, so I needed to work extra for an international research project to finance myself. Some months ago I again spoke with my supervisor and he told me he has no budget and I am free to leave the group whenever I like! 

Due to all this, I decided to change my group. Now I am invited to interview for a competitive PhD position ( in another university but the same city). I would like to get this fully paid position which also fits well to my experiences, however I do not know how to tell the new professor about my current PhD? 

I did not mention my current PhD in CV, and just wrote about my working experience in the last 1.5 year. 

How shall I explain this issue to new professor?  Can this issue be a reason that he does not accept me?
You don't have the degree, but you were registered as a graduate student for 1.5 years, and that should be on your CV. If you had listed it, there would be no problem at all: "Unfortunately, my current program was unable to fund me. I would prefer to give my full attention to my PhD studies and research, without the need for an outside job."