## 1 Introduction  
In recent years, multi-terminal high voltage direct current (MT-HVdc) systems topologies have attracted great attention for the integration of offshore wind farms to ac grids [1]. In this emerged paradigm, the main objectives are improving the stability and reducing the cost of multi-terminal HVdc grid as a whole and particularly the cost of dc circuits, control systems, the number of offshore substations, and HVdc circuit breakers (DCCB), respectively. Currently, more than 200 point-to-point HVdc transmission systems have been launched around the world. Actually, the parallel connection of HVdc systems was investigated in 1963 [2], while series HVdc was discussed in 1965 [3]. However, in order to get the first working parallel MT-HVdc system,some existing HVdc applications have been extended with more than two terminals over the last two decades [4; 5]. Provision of the MT-HVdc grid, comprised of multiple voltage-source converters (VSCs), has become an encouraging choice with the increased advancements and rapid availability of high-power VSCs from multiple vendors [5]. In this regard, MT-HVdc grid applications and its significant advantages have been identified and proposed in [6; 7; 8; 9; 10; 11]. Moreover, MT-HVdc systems are derivers of the developments of European super-grid [12; 13; 14; 15; 16], in order to interconnect North Sea wind farms with the Scandinavian hydropower and Mediterranean solar power plants. Predominantly, MT-HVdc grids emerged as a strong contender that can meet the future needs of electrical power systems. Therefore, the topological evaluation of MT-HVdc grid circuits is the need of time. [PERSON] et al. studied the impacts of HVdc grid topology on transient stability on the HVdc segmented electric grid [17; 18]. HVdc grid converter topologies are discussed in [19]. Connection schemes for integration of offshore wind farms with mainland grids via VSC-HVdc grid are discussed in [20] but lack protection and control strategy. [PERSON] et al. worked on the connection of HVdc link with different circuit topologies [21]. Examination of different communication topologies for distributed control of multi-terminal HVdc grids is carried out in [22]. [PERSON] studied the impact of dc-link voltage drop on the power flow of the MT-HVdc grid using droop control [23]. Therefore, in this paper, the tolerance limit of \(\pm 10\%\) of dc-link voltage has been selected as a stability evaluation criterion for the topologies [24]. [PERSON] et al. studied the impacts of HVdc grid topology on MT-HVdc grid fault, but this study is limited to star connection topology [25]. The dc transmission circuit topology affects the protective operations in MT-HVdc networks [26]. Thus, it is important to lay out a detailed techno-economic comparison of HVdc grid topologies to address the shortcomings. Finally, a solution is proposed in terms of more dynamic MT-HVdc grid topology to cope with shortcomings. Various topologies for MT-HVdc grids are proposed in [27; 28; 29; 30], namely: point-to-point topology (PPT), star topology (ST), general ring topology (GRT), the star with central switching topology (SGRT), substation ring topology (SSRT), and wind farm ring topology (WFRT). However, these topologies lose their flexibility, stability, and redundancy in the event of an ac network fault [29; 30]. In [30], WFRT and SSRT are analyzed and compared in detail and, based on that, a more efficient 2 WF-ISST topology is proposed. However, 2 WF-ISST of [30] also loses its flexibility, redundancy, and does not follow the maximum power loss criterion of the Great Britain's security and quality of supply standards (GBSQSS) [31] during (i) mainland ac grid fault (grid side VSC) and (ii) dc-link fault on either of the extreme ends (end sectioned lines), simulations proved these drawbacks in Section 6. Thus, a new better circuit topology/variant is needed.