How can electrons (with a negative charge) be the particles in electricity?
I think you have misunderstood the concept of a negative charge. A negative charge does not mean that the particle has negative energy. The terms “positive” and “negative” are used to explain charges simply because they are opposites. The term negative is just a matter of convention. We could have, for example, said that electrons had a “left” charge and that protons have a “right” charge because this is where their charges fall on the number line. (The charge of an electron is to the left of zero, whereas the charge of a proton is to the right of zero.) Conversely, we could have said that electrons have a positive charge and protons a negative charge, and it would not change any of the math. We only use positive and negative to explain that the charges oppose each other, and that if you have a system with one electron and one proton (i.e. a Hydrogen atom) the charge of the entire atom would be neutral.
