## 2 Multi-Infeed LCC-HVDC System
### Fundamental Indices Developed for a Multi-Infeed LCC-HVDC System  
The multi-infeed interaction factor (MIIF) is an important quantitative index to determine the closeness between two converters in a multi-infeed scenario. The MIIF was first reported in [12] and later in [13]. It estimates the degree of voltage interaction between converters' AC buses. The MIIF\({}_{21}\) from converter 1 to converter 2 is actually the ratio of voltage change at converter 2 to voltage change at converter 1 caused by an injection of reactive power at converter 1. A 1% voltage change is recommended to calculate the MIIF. It is suggested in [14] that an MIIF of less than 0.15 between two converters means that the interaction is quite small, and the multiple DC systems can be considered a single infeed. Furthermore, if the MIIF ranges between 0.15 and 0.40, then the interaction is moderate, and if the MIIF is greater than 0.4, then the multi-infeed system has strong interaction between converters' AC bus voltages. Converters with high power rating affect more compared with low-rating converters, and converters with low power rating influences less compared with high-power-rating converters in a multi-infeed configuration. The CIGRE report [14] discusses the multi-infeed HVDC systems in detail. The report discusses the MIIF between converters. It provides bases to cop various transient and steady-state phenomena of multi-infeed HVDC systems. It is given that if the MIIF is zero, then all HVDC systems in close proximity will behave as a single infeed HVDC system, and if the MIIF is 1, then the all HVDC systems in a multi-infeed scenario will operate as they are connected to the same AC bus. Single-infeed HVDC systems use a fundamental indicator to assess the strength of an AC system to which the HVDC is connected. This index is called short circuit ratio (SCR). It is basically the ratio of the short circuit level of the HVDC link at the commutation bus to the power rating of the HVDC link. The installed reactive power support at the HVDC commutating bus disturbs the system strength at the fundamental frequency. Consequently, the effective short circuit ratio (ESCR) index is introduced to overcome the filter's response at a fundamental frequency. This index is actually calculated by subtracting the total reactive power at the commutation bus from the short circuit level of the HVDC link and then taking the ratio to the rated power of the HVDC. The stronger the AC system is, the higher is the short circuit level, and subsequently, the better is the performance of the HVDC link. Mostly the HVDC link is planned for an ESCR higher than 2.0. Multi-infeed scenarios have led to a new index called multi-infeed effective short circuit ratio (MIESCR). The traditional index was not sufficient enough to measure the strength of the multi-infeed configuration because it was unable to incorporate the nearby HVDC links in the system strength. The concept of multi-infeed short circuit ratio was first proposed in [15]. The concept then extended to various versions to incorporate all converters in proximity. This new index helped to investigate multi-infeed configurations because it results in actual system strength compared with previous indices, which produce optimistic results. In single infeed HVDC systems, the power and voltage stability are characterized on the ESCR. If the effective short circuit ratio (ESCR) is less than critical value, then the voltage collapses. Similar concepts are being extended for multi-infeed configuration, but they are more complex because the MIESCR is always less than the ESCR of a single infeed HVDC system. The practical AC network between two converters of a multi-infeed HVDC system can be simplified as one impedance. It is also important to mention that a multi-infeed scenario with multiple converters has multiple MIIFs (as the MIIF exists in between any two converters). Transient overvoltage occurs when a converter stops absorbing reactive power; temporarily, the converter fails to transfer active power.