I though it was only slight slower than the speed of light
Electricity "flows" at the speed of light in the dielectric medium surrounding the conductors. For ordinary insulated cables like twisted pairs and coax that is around 0.66*c. For power lines, I guess it would be closer to c. However, that is not what is important. What matters is the phase accumulation along the path. The transmission lines themselves accumulate phase based on their propagation velocity, but other components like transformers and loads introduce phase shifts.