I think you'll experience some difficulty in defining the "study of electricity" as anything other than electrical engineering although I appreciate that the subject no longer confines itself strictly to electricity alone nowadays. It's certainly not an "-ology".
According to Merriam-Websters Collegiate Dictionary an "electrologist" is defined as:
"noun [blend of electrolysis and -logist (from -logy + -ist)] (circa 1902) : a person who removes hair, warts, moles, and birthmarks by means of an electric current applied to the body with a needle-shaped electrode. - electrology"
There even seems to be a medical diploma called a DMRE which stands for Diploma in Medical Radiology and Electrology.