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.
In Spain it is in general necessary to have an "Oficial" Master's degree to enter a PhD program. The "official" qualifier means that some master's programs are formally recognized as conduits to doctoral programs, whereas others are not. In general a foreign degree would have to be recognized as equivalent to a Spanish degree, usually by the administration of the university offering the doctoral degree. Although there are lots of qualifications to this general statement, applicable in special cases, basically you need to have a master's degree already. [Here](https://www.ucm.es/requisitos-de-acceso-doctorado) and [here](http://www.ucm.es/informacion-adicional-para-alumnos-con-estudios-extranjeros-1) is information (in Spanish) about the requirements at the Universidad Complutense de Madrid, which is probably typical. For someone who does not have an official Spanish master's degree or a foreign degree recognized ("homologado") as such, there is a process to apply for admission, but the details probably depend on the particularities of the applicant.

Admission and funding are generally separate matters. The summary with respect to funding is that there isn't much, what there is pays poorly by the standards of northern Europe or the US, and it's competitive to get what little there is.