## 1 Introduction  
Recent trends/researches show that a multi-terminal high voltage direct current (MT-HVdc) system is an emerging and encouraging option to meet the growing demands of future transmission networks. MT-HVdc systems not only offer substantial benefits, but have developed some promising applications [1; 2; 3]. Integration of offshore wind farms and solar power plants to ac main lands is remarkable feature. This feature leads towards the proposal of European super grid and promising interconnection of North Sea wind farms to Scandinavian hydropower and Mediterranean solar plants [4; 5; 6]. Absence of capacitive current in MT-HVdc system makes it the best replacement of long cable ac transmission. In the forthcoming years, robustness and intelligently controlled infrastructures of MT-HVdc grids [7; 8; 9; 10] will bring new challenges for power system engineers. Voltage source converter (VSC) based HVdc is a practical/effective option for multi-terminal HVdc (M-HVdc) as compared to line commutated converter (LCC) based HVdc technology, as VSC offer small filter sizes, black start capability, reactive power support, and soft bidirectional dc power flow [11; 12; 13; 14; 15]. An MT-HVdc system is composed of a number of offshore and onshore VSCs. Therefore, operation, control, and protection of MT-HVdc systems are complex and challenging. VSC based MT-HVdc systems offer benefits like redundancy, flexibility, and reliability for power transmission [2; 3]. An appropriate protection scheme ensures the reliability of dc grid and apposite actions are activated in case of abnormalities for averting shutdown of dc grids [7]. However,the challenging task is the relatively low impedance of MT-HVdc grid in the event of dc faults. Hence, the dc fault currents build up enormously and rapidly. Thus, reliable and prompt relaying mechanism is required along with HVdc circuit breakers to mitigate the effects of sudden building up of large fault currents and to ensure the continuity of the supply [16]. However, the prototypes of existing dc circuit breakers (DCCB) have limited current interruption capability or are slow in operation [17; 18; 19; 20]. A number of relaying algorithms are proposed for prompt response against dc faults [21; 22; 23; 24]. These algorithms are based on either selective or non-selective fault clearance strategies. In the selective fault clearance strategy, HVdc breakers operate exactly at the instant of fault, while HVdc breakers are installed at the ends of the transmission lines (TL) [18]. Non-selective fault clearance strategy is based on the joint action of multiple components, like converters with current limiting or interrupting components [25; 26; 27; 28; 29]. Typically, an MT-HVdc grid is divided into various zones of protection to enhance reliability, speed, selectivity, sensitivity, and security [30]. Primary protection (PP) responds to the fault immediately after occurrence. Backup protection (BP) waits unless the primary protection fault clearance time is completed. Backup protection operates after the failure of primary protection. PP may fail due to malfunctioning of DCCB or primary relay. Therefore, it is always necessary to provide BP to enhance security and reliability. A speedy response from backup protection is always expected in case of PP failure [31]. However, a time delay is added between PP and BP operations to avoid incoordination and selectivity issues [32]. Estimation of fault location (FL) is a core constituent of MT-HVdc grid protection. Without it, relaying strategies and circuit breaker technology cannot be developed and there would be a question mark over the reliability of MT-HVdc systems. Different traveling waves (TW) based fault location estimation methods are developed and are available in literature [4; 23; 33; 34; 35; 36; 37; 38; 39]. In this paper, different methods of fault classification and location (FCL) in MT-HVdc systems are critically and mathematically analyzed.