Synchronous phase modifiers are installed at the sending end of the transmission line.

Explanation:
Synchronous phase modifiers, also known as synchronous condensers, are devices used in electrical power systems to regulate voltage and improve power factor. They are typically installed at the sending end of a transmission line.

- Importance of Power Factor Correction:
Power factor is a measure of how effectively electrical power is being utilized in a system. It is the ratio of real power (useful power) to apparent power (total power). A low power factor can result in inefficient use of electrical energy, increased line losses, and reduced system capacity. Power factor correction is necessary to improve the power factor and optimize the performance of the power system.

- Operation of Synchronous Phase Modifiers:
Synchronous phase modifiers are rotating electrical machines that are similar in construction to synchronous motors. They are typically operated in an over-excited mode, meaning that they consume reactive power from the system and provide capacitive reactive power. By injecting reactive power into the system, synchronous phase modifiers help to balance the reactive power demand and improve the power factor.

- Placement of Synchronous Phase Modifiers:
Synchronous phase modifiers are installed at the sending end of the transmission line for several reasons:
1. Voltage Regulation: By injecting or absorbing reactive power, synchronous phase modifiers can help regulate the voltage at the sending end of the transmission line. This ensures that the voltage remains within acceptable limits and avoids voltage drops or surges.
2. Power Factor Improvement: Installing synchronous phase modifiers at the sending end allows for better control of the power factor at the point of generation. This helps to minimize transmission losses and maintain a high power factor throughout the system.
3. System Stability: Synchronous phase modifiers contribute to the stability of the power system by providing reactive power support during disturbances or sudden changes in load. Placing them at the sending end ensures that their impact is felt throughout the system.

- Conclusion:
In summary, synchronous phase modifiers are installed at the sending end of the transmission line to regulate voltage, improve power factor, and enhance overall system stability. Their placement at this location allows for better control and coordination of reactive power injection, leading to efficient power transmission and distribution.