1 Modeling and Stability Analysis of MTDC Grids for Offshore Wind Farms: A Case Study on the North Sea Benchmark System Nilanjan Ray Chaudhuri, Member, IEEE, Rajat Majumder, Member, IEEE, Balarko Chaudhuri, Member, IEEE, Jiuping Pan, Senior Member, IEEE, Reynaldo Nuqui, Senior Member, IEEE Abstract—Modeling of VSC-based multi-terminal DC (MTDC) grids for modal analysis and stability studies is reported consider- ing bipolar converters and DC cable network with metallic return path. The proposed model is flexible enough to accommodate different converter grounding options and unbalance on the DC side due to cable and/or converter outage. A simplified version of the benchmark test system for the envisioned offshore MTDC grid in the North Sea is studied. Modal participation factor analysis under nominal and converter outage conditions is used to ascertain the nature and root cause of the dynamic responses. Comparison of the time-domain simulation results using the pro- posed averaged model in Matlab/SIMULINK against a detailed switched model in EMTDC/PSCAD confirm the accuracy of the modeling approach. Index Terms—Multi-terminal DC (MTDC), Wind, Voltage source converter (VSC), Stability, Modal analysis, Participation factor I. I NTRODUCTION A S large offshore wind farms move deeper into the sea the case for a multi-terminal DC (MTDC) grid rather than individual point-to-point connections to shore is getting stronger to effectively share the wind resources among the European countries. An MTDC grid has been envisioned around the North sea to tap the rich wind resource of the region and also interconnect the UK and Nordic pool with continental Europe in future [1], [2]. VSC-based MTDC has received relatively less attention until recent past when modeling [3], control [4], [5], [6] and protection [7] issues were studied. Major challenges in operation of an MTDC grid includes appropriate primary control of converter stations to ensure autonomous sharing of power imbalance following a converter and/or cable outage. Interaction of primary controls with the neighboring AC net- works including possible provision for AC system support like frequency control [8] etc. are critical from the point of view of operators. To study these issues a proper modeling and analysis framework for MTDC grids is essential which is presented in this paper through a case study on the simplified version of the benchmark test system for the envisioned offshore MTDC grid in the North Sea. Support from EPSRC,UK under grant EESC P11121 is acknowledged. N.R. Chaudhuri and B. Chaudhuri are with Imperial College London, Lon- don, UK (e-mail: n.chaudhuri@imperial.ac.uk, b.chaudhuri@imperial.ac.uk). R. Majumder, J. Pan, R. Nuqui are with the ABB Corporate Re- search, Raleigh, NC, USA (e-mail: rajat.majumder@us.abb.com, jiup- ing.pan@us.abb.com, reynaldo.nuqui@us.abb.com). A general asymmetric bipole 1 MTDC grid with the provi- sion of metallic return network is considered here. The model- ing framework is generic enough to accommodate a detailed pi section approximation of DC side cables and simulate different types of DC cable/converter faults followed by their outages. The proposed averaged model in Matlab/SIMULINK is vali- dated against a detailed switched model in EMTDC/PSCAD software enabling easy integration of the MTDC grid with the multi-machine AC system models for stability studies. II. MODELING A. Converter Modeling The converters were represented by their averaged model [9] in a synchronously rotating reference frame d ′ -q ′ where the d ′ - axis is locked with the voltage E ac at the point of common coupling (PCC) on the AC side of the converters (Fig. 1(a)) to ensure decoupled control of the active and reactive power. All notations in the modified reference frame are henceforth denoted with a prime. The AC system connected to the MTDC Fig. 1. (a) modified reference frame for decoupled control (b) converter P - Q control (c) converter V DC - Q control grid is modeled in d - q reference frame shown in Fig. 1(a) which needs to be transformed to d ′ -q ′ frame and back while interfacing the MTDC grid variables with those of the AC system. From Fig. 2 the dynamics of the converter transformer 1 unlike symmetric bipole, an asymmetric bipole has the metallic return circuit to carry the current due to unbalance