## 4 Commutation Failure (CF) in a Multi-Infeed LCC-HVDC System
The absolute sum of the current in all phases of a transformer becomes less than double of the DC current. This indicates commutation failure in an HVDC converter. For the CIGRE benchmark model, the normal extinction angle is \(15^{\circ}\). An extinction angle of \(7^{\circ}\) is considered to be a critical extinction angle. Below \(7^{\circ}\), commutation failure occurs. The fault level that reduces the extinction angle to \(7^{\circ}\) is named critical fault. The fault above the critical level causes commutation failure. The ideal critical value for commutation failure is \(0^{\circ}\), but for practical projects, it is calculated to be \(7^{\circ}\), providing a sufficient voltage time area to remove charges. The extinction angle method for detecting commutation failure only estimates the critical fault level. It ignores transient affects, such as phase shift, harmonics, and DC current change. These transient phenomena influence the commutation failure probability [33]. The steady-state method results in optimistic values of the voltage level, which cause commutation failure, while the transient technique yields an accurate value of voltage, which is higher than the steady-state value for commutation failure. This means that a steady-state value indicates that commutation failure will occur for a very low value of voltage, but in actuality, it is not the case. Commutation failure, in the transient technique, occurs for a higher value of voltage than the value that the steady state predicted. The difference is due to the aforementioned facts. Commutation failure analysis using an electromagnetic transient program needs a term (index) to find a critical fault value that does not cause commutation failure. This leads to the introduction of the commutation failure immunity index (CFII). The CFII is based on the minimum value of inductance that does not cause commutation failure. This corresponds to the ratio of the worst critical fault MVA level to the rated DC power of a converter. Similar to local and concurrent commutation failure, a local CFII determines the immunity of a local converter, and a concurrent CFII estimates the immunity of a remote converter to a local fault. The MIIF plays a vital role in the occurrence of concurrent commutation failure. The MIIF is influenced by the AC system strength of each converter in a multi-infeed configuration. Thus, concurrent commutation failure indirectly depends on the AC system strength of converters in proximity. The concurrent CFII is inversely proportional to the MIIF. This means that a low value of the MIIF corresponds to a higher value of the concurrent CFII. It is discussed in [14] that if the MIIF is less than 0.3, concurrent commutation failure would not be a serious issue. Similar to single infeed, in multi-infeed HVDC systems, recovery from commutation failure depends on the MIESCR. The higher is the MIESCR, the faster is the recovery. A single commutation failure does not have a destructive nature. Although a single commutation failure disturbs power quality, it does not have too much effect on system stability. If commutation failure occurs more frequently, it will definitely be a challenge for system planners and a great threat to system stability. Frequent commutation failure in a single infeed HVDC system is a most harmful event. Similarly, frequent commutation failure in a multi-infeed HVDC system is a great reason for system instability and energy loss. The impact of frequent commutation failure in multi-infeed DC systems is much more destructive than in a single infeed system. Several precautions are described to reduce the commutation failure frequency, such as reducing the interaction factor, using a large smoothing reactor, and increasing the extinction angle. In ref. [34], a detailed analysis of commutation failure in multi-infeed HVDC is presented. The AC system is modeled as an equivalent Thevenin impedance and a corresponding voltage source.