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The commutation failure vulnerability of single and multi-infeed HVDC converters to AC side faults is analysed. A new indicator of the susceptibility of the converter to commutation failures the "commutation failure immunity index" (CFII) is proposed. Faults in multi-infeed systems can cause commutation failure events in the nearby local converter or concurrently in both converters. The immunity of the system to both these events is investigated and suitably parameterized.