High efficiency, flexibility and competitive capital costs make supercritical CO2 (sCO2) systems a promising technology for renewable power generation in a low carbon energy scenario. Recently, innovative supercritical systems have been studied in the literature and proposed by DOE-NETL (STEP project) and by a few projects in the EU Horizon 2020 (H2020) program aiming to demonstrate supercritical CO2 Brayton power plants, promising superior techno-economic features than steam cycles particularly at high temperatures. The H2020 SOLARSCO2OL project, which started in 2020, is building the first European MW-scale sCO2 demonstration plant and has been specifically tailored for Concentrating Solar Power (CSP) applications. After a detailed explanation of the modelling approach for steady and unsteady cycle simulations, this paper presents the off-design and dynamic analysis of such plant layout, which is based on a simply recuperated sCO2 cycle. The entire system model has been developed in TRANSEO environment. The part-load analysis ranged from 50% of nominal up to a 105% peak load, discussing the impact on compressor and turbine operating conditions. Full operational envelop has been determined considering cycle main constraints, such as maximum turbine inlet temperature and minimum pressure at compressor inlet. The off-design performance analysis highlights the most relevant relationships among the main part-load regulating parameters, namely molten salt mass flow rate, CO2 mass flow rate, total CO2 mass in the loop, and shaft line speed. The results show specific features of different control approaches, discussing the pros and cons of each solution, considering also its upscale towards commercial applications. In particular, the analysis shows that at 51% of load an efficiency decrease of 20% is expected. Finally, the dynamic characterization of the closed loop shows the relatively fast responsiveness of the plant to compressor speed variations, causing quick changes in CO2 mass flow rate, together with longer time scale phenomena related to the plant heat exchangers. In this respect, sCO2 plants demonstrate to have the potential to provide primary reserve for the electrical grid, as far as thermal stresses on main plant components are kept under acceptable limits.