**Back-to-back HVDC and its purpose:**

Back-to-back HVDC refers to a configuration where two HVDC converters are interconnected without any transmission line between them. This configuration is used to provide stable interconnection between two AC systems that have different frequencies, voltages, or phase angles. It essentially acts as a translator between the two systems, allowing power to be transferred between them.

**Explanation of the correct answer:**

The correct answer for this question is option 'D', which states that back-to-back HVDC is used to provide stable interconnection. This means that the main purpose of using back-to-back HVDC is to ensure a reliable and stable connection between two AC systems with different characteristics.

**Detailed explanation:**

1. **Stable interconnection:** Back-to-back HVDC provides stable interconnection between two AC systems. It can handle the differences in frequency, voltage, and phase angle between the two systems, allowing power to be transferred smoothly and efficiently. This stability is crucial for the overall performance and reliability of the interconnected systems.

2. **Frequency conversion:** In some cases, the AC systems connected through back-to-back HVDC may have different frequencies. The HVDC converters in the back-to-back configuration can perform frequency conversion, allowing power to be transferred between the systems despite the frequency differences. This enables the interconnection of power systems operating at different frequencies, such as those found in different countries or regions.

3. **Voltage transformation:** Back-to-back HVDC can also be used to connect AC systems with different voltage levels. The HVDC converters can perform voltage transformation, allowing power to be transferred between systems with different voltage magnitudes. This is particularly useful when integrating renewable energy sources, as they often operate at different voltage levels than the existing grid.

4. **Phase angle compensation:** Another important feature of back-to-back HVDC is the ability to compensate for phase angle differences between the interconnected AC systems. This ensures a smooth and stable power transfer between the systems, minimizing any disturbances or voltage fluctuations.

5. **Enhancing system stability:** By providing stable interconnection, back-to-back HVDC helps enhance the overall stability of the interconnected systems. It allows for efficient power flow control, reduces the risk of voltage instability, and helps maintain system frequency within acceptable limits.

In summary, back-to-back HVDC is used to provide stable interconnection between AC systems with different characteristics, such as frequency, voltage, and phase angle. It enables seamless power transfer, enhances system stability, and allows for the integration of different power systems.