Question: I'm an undergraduate electrical engineer. I have studied up to 80 percent of a masters in electrical engineering program and have two IEEE published papers. Is there such a thing as a PhD entrance exam that I can take to prove my ability to pass advanced electrical courses and get admitted directly into a PhD in a university in Europe?

Answer: 
Admission and funding in European PhD programs depends a lot on the university and the country's regulations. You should search for the programs you are interested in applying to and read their specific requirements.
The Dutch (eg. Eindhoven) situation is that a PhD is normally funded (or done as an external PhD with a company). As such anyone will have to go through what amounts to a "job" interview. Within the system a masters is normally expected, but exceptions can be made, especially for candidates from countries where a masters would not be required to start a PhD.

A PhD in The Netherlands will always have a full professor who will function as promotor (under whom's responsibility you would work). You may in addition have a daily supervisor with less experience. You will basically need to convince your interviewers that you can do the research. A common question would be for you to present your Msc thesis (or bsc thesis) as an example of your ability to write, the papers you published could be a good alternative, especially if you were the main (or only author). Be prepared to answer the question why you didn't finish the masters (in this case time can be in your benefit)