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This paper proposes a comprehensive methodology for determining the converter droop settings to ensure the voltage security in a multi-terminal direct current (MTDC) grid. The novelty lies in the introduction of the concept of over- and under-voltage containment reserves in analogy to the frequency containment reserves in AC systems. This not only gives a distinction of the contribution between the converters in rectifying and inverting modes, but also significantly facilitates the sizing of the necessary amount of reserves within their available headroom capacity of power. In particular, the constraints of converter outages, converter rating, and DC voltage deviations are all taken into account in the design of reserves. The effectiveness of the proposed approach is demonstrated by a contingency power flow analysis algorithm and EMT simulations of a four-terminal MTDC grid. [ABSTRACT FROM AUTHOR]

• Reserve capacity activation is explicitly modelled for hydropower plants. • A new hybrid stochastic-robust optimization model is formulated. • The column-and-constraint generation technique is used to create extreme scenarios. • The new hybrid model is compared to the standard stochastic and robust formulations. As the penetration of variable renewable power generation increases in power systems around the world, system security is challenged. It is crucial to coordinate the available flexible generating resources, such as hydropower, to meet the need for system balancing. However, reserved capacity on hydropower plants should only be activated if there is sufficient energy or storage capacity to either increase or decrease production. The potential change in production will also affect all reservoirs and plants connected by the cascaded topology. These issues are largely ignored or simplified in hydropower reserve scheduling models. To properly account for the possible activation of reserved capacity, several two-stage model formulations based on stochastic and robust optimization are presented and compared in this paper. The uncertainty in net load deviations due to forecasting errors in renewable power generation is considered the source of reserve capacity activation. The case study based on a real Norwegian watercourse clearly shows the benefit of using any of the two-stage model solutions over the standard deterministic reserve procurement. A novel hybrid stochastic-robust model formulation is presented and shown to efficiently increase the robustness of the solution without notably increasing the reserve procurement cost compared to the stochastic and robust models. [ABSTRACT FROM AUTHOR]