The discovery and understanding of electricity were one of the most important drivers of the second industrial revolution (1870 onwards) and the rapid progress in humanity’s quality of life and engineering in the past 150 years.

The process of delivering electric power from power stations to people’s homes required a number of engineering innovations to solve the associated challenges, which were possible based on the scientific understanding of electricity as provided by the experiments of Michael Faraday and the 4 equations of electromagnetism derived by James Maxwell.

The first challenge, how to transfer power over long distances in an efficient way? The cables have a finite resistance resulting in heat dissipation and loss of energy. One option is increasing the input energy, which of course makes the price of electricity much more expensive. Another other option is to reduce the resistance of the cables, either by using different metals, which again is more expensive, or using a thicker cable, which however results in heavier cables. The power dissipated in a given load is $P=IV$, and using Ohm’s law $V=IR$, we can also write $P=I^2R=V^2/R$. As a result, we can provide the same power to a load (for example a home appliance requiring a 100W) using a higher voltage and a lower current, which as a result gives a lower heat dissipation ($I^2R$). Indeed this is the chosen way, in which the power lines going from the power plant carry very high voltages (order of few $10^5 \rm{V}$), to reduce the losses due to the cables’ resistance.

Using a high voltage results in a new challenge, the appliances and wires in our homes cannot withstand such high voltages (they operate typically at 240V in Europe for example), as these high voltage additionally require significant insulation to not discharge into the air. The way to reduce the voltage in the wires is achieved using a device called a transformer, which directly utilizes Faraday’s law of induction, which relates the electro-motive force (emf or voltage) in a circuit to the rate of change of magnetic flux through the circuit: $V = - N \frac{d\Phi}{dt}$, where $N$ is the number of turns or windings around the flux source, and $\Phi$ is the magnetic flux through one turn. A transformer achieves the step down in voltage by coupling two circuits using a magnetic material as the conductor of the magnetic flux. By using a lower number of turns in the secondary (output) circuit a reduction in voltage is achieved. Since the flux is the same in each turn in both circuits as they are coupled, we get for the step-down in voltage $\frac{V_p}{V_s} = \frac{N_p}{N_s}$, where $p$ stands for primary and $s$ for secondary, i.e. the reduction in voltage is proportional to the ratio of turns in both circuits.

A crucial point in the transformer’s description is the fact that there is a a changing magnetic flux ($\frac{d\Phi}{dt}\ne 0$). To achieve that requires the current current generated at the source (the power plant) be an AC (Alternative Current) as opposed to DC (Direct Current) resulting in a changing magnetic flux.

The AC power generated by the power plant has another technicality, which involves the generation of three phases of AC each (sin wave) offset by 120 degrees. The advantage of three phases is in the fact that there is no point at which all phases are at zero voltage, resulting in a more efficient power supply. As a result there are 3 wires carrying the three phases and an additional ground wire.

Reference: power grid