This is a question we come across often. The speed of any electromagnetic wave depends on the medium. In Vacuum, the speed of an electromagnetic wave will almost approach the speed of light. However, in actual power transmission, the speed of electricity is lesser than the speed of light. The speed depends on what is known as the velocity constant. This depends on the resistance, inductance and the capacitance of the transmission line. Of these, the capacitance is the primary quantity which determines the speed of electricity through the system.
For instance, in cables, the speed of electricity is dependant on the capacitance of the cables.
The velocity constant of a transmission line is given by VF = 1/k where k is the dielectric constant of the material through which the electromagnetic signal passes.