My research was plagiarised and won best paper of a conference. How to proceed? I am a PhD student in electrical engineering, and I recently found out a published paper from another research group which I am collaborating through a joint project using exactly my idea and the data that I collected.

I don't have any public evidence that I was working on it, but since it is a joint project, the other research group was aware of my research and my ideas.

On their paper, they don't mention my work, they don't acknowledge and they didn't ask permission to use the data that I collected. They had access to my data because I needed to use their equipment to collect the data.

The paper that they published won the best overall paper of the conference and they got a prize of €2000.

I contacted the head of the research group to make them withdraw their paper, but they don't agree, they claim they are doing something different, but they suggested to add myself as one of the authors (even after the paper was published), which I don't agree at all since I didn't work on this paper.

I have evidences through emails, meetings and presentations that they were aware of my research. I would like advice on how to proceed.
Talk to your advisor. If you have compelling evidence they may be willing to stake their reputation and research collaboration with this group in order to get them to at least acknowledge your contribution after the fact. Again, you need to be prepared to hear that your advisor will be very limited in what they can do apart from trying to straighten things out informally. Given that papers usually take several months to write, I’m curious to know why no one knew about this happening. 

Ownership of the idea is going to be hard to argue at this point given that the paper has already been published (and has won an award!). It won’t be withdrawn, it probably can’t be withdrawn since it’s already been published, not a reversible action in most cases. The authors could say that you misunderstood, that they independently came up with the idea, or any number of plausible sounding defenses.

Your best plan forward is perhaps to be involved in follow up work, and be more careful with this group who’s acted in an unethical and mean way. 

Finally, if you really feel like you would like to escalate it further, reach out to your university's ombudsperson, vice-dean for research matters, or department head (depending on your university's structure the point of contact differs). Again, since you say you don't have public evidence of precedence, I doubt there's much they could do, but at the very least that would be the correct order of doing things. 

In particular, I would most definitely not go to the conference chairs, publicly post something online, or escalate this further before consulting with the appropriate people. You would be burning serious bridges by doing something like that, and chairs/editors are very much averse to getting involved in such things if they don't have to. You may end up looking like some bitter person who sees a colleague's best paper and wants in on the action after the fact.