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With the expansion of distributed power systems and renewable energy worldwide, the use of synchronous condensers (SC) has been gradually increasing to maintain the power quality of an electric grid. Because SC generates fewer harmonics and has the advantage of strengthening system inertia, it is considered as a primary option in Korea over other options such as Static Var Compensator (SVC) and STATic synchronous COMpensator (STATCOM). If superconductor synchronous condenser (SSC) is applied instead of SC, it brings more advantages: (1) it can minimize the adverse impact on the power system due to lower synchronous reactance, and (2) the higher power density can lead to many advantages in a limited area of substation. With these backgrounds, we report a design study on 40 MVAr SSC with no-insulation high-temperature superconductor (NI-HTS) field coil. Firstly, design criteria and procedures for electromagnetic design were set. Secondly, with the design procedure, the electromagnetic design having the minimum HTS conductor usage was obtained among the designs satisfying design criteria. Based on the final design, key characteristics of SSC including no-load voltage, the maximum flux density under the rated-load condition, V-curve characteristic, synchronous reactance, zero sequence reactance, negative sequence reactance, critical current, and NI-HTS characteristics were calculated by using finite element method. Lastly, the design comparison between SSC and SC was presented. • The use of synchronous condensers has been gradually increasing. • Superconductor synchronous condenser is a promising alternative option. • It has not only a much lower synchronous reactance but also a higher power density. • The advantages were confirmed through the electromagnetic design study. [ABSTRACT FROM AUTHOR]