# The Power Flow Crux

The electrical power grid operates in equilibrium. The power supply from the generator matches the demand levied by the end-users. The flow of power to enable this demand-supply equilibrium over the transmission lines (T-lines) is governed by the following conditions.

• Thermal limitation of T-lines
• Voltage drop limitation

### Thermal Limitation of T-lines

Current carrying conductors are designed to carry a limited amount of current. When it is operated beyond its design rating, it starts to sag. Excessive sagging of T-lines leads to the infringement of safe electrical clearances.

Power flow over short lines (less than 80km) are limited by their thermal ratings.

### Voltage Drop Limitation

On long T-lines (greater than 300km), voltage drop is an issue. Unless compensated for, power flow should be monitored and regulated to minimize the drop in voltage.

In AC systems, the power delivered from point a to point b is given by:

P = \frac{3*V_a*V_b}{X_s}\sin\delta Watts

Although it makes sense to use \delta=90^{\circ} to maximize the power flow, it is never done, however. This is because the generators connected to the grid may fall out of sync and may trip for a small disturbance in the system. \delta at the generation is typically maintained between 30 to 45deg.

Steady-state stability limitation too, like voltage drop, does not allow loading of long T-lines (greater than 300km) to approach the thermal rating of the conductor.

In the modern power systems, Flexible AC Transmission devices and High Voltage DC systems are playing a crucial role in controlling and maximizing the power flow over the transmission lines. In the near future, it is possible to have the power system operate close to its limitations while operating reliably.