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The future power grid is gradually transitioning towards a greater utilization of inverter-based resources (IBRs) to integrate renewable energy in generation portfolio. The existing synchronous generator (SG)-dominated power system is evolving into a grid, where both SGs and IBRs coexist. Since SGs are sources of mechanical inertia, their gradual replacement is resulting in a low-inertia power grid. One of the main challenges faced by such systems incorporating SGs and IBRs is the primary frequency response following a loss of generation or sudden large change in loads, which may lead to underfrequency load shedding (UFLS). Broadly, bulk power systems connected to SGs and a significant number of IBRs are the subject matter of this dissertation, with a focus on modeling, stability analysis, and control for providing frequency support from the perspective of primary frequency response. Although IBRs can be of different types depending on the control strategy, grid-forming converter (GFC) technology with a direct control over its frequency is much less understood, and is a major focus of research in this dissertation. These GFC-interfaced renewable resources in future low-inertia grids are expected to provide primary frequency support so that underfrequency load shedding is averted. The GFCs can be divided into two classes based on the control strategy: (a) class-A: droop control, dispatchable virtual oscillator control, and virtual synchronous machine, and (b) class-B: matching control. It is observed that while providing frequency support, the class-A GFCs may undergo dc-voltage collapse under current limitations during underfrequency events. On the contrary, class-B GFCs are more robust in this context. In the first part of the dissertation, we perform a stability analysis of both classes of GFCs following such events. To that end, first, the averaged phasor models of these GFC classes are developed, which can be seamlessly integrated with traditional positive sequence fundamental frequency planning models of grids. Building on this, simplified averaged models are derived to study the stability of the dc-link voltage of the GFCs under current limitations in a generic multimachine system. Using these models, the sufficiency conditions for stability for both the classes and that of instability for class-A GFCs are established. As a logical next step, a decentralized supplementary control for the droop-based class-A GFC is proposed to solve the dc-link voltage instability issue under the current limitations. This sliding mode control-based approach also aims to provide primary frequency support after the contingency. The proposed method leads to quantifiable frequency support irrespective of frequency deviation, which in turn can incentivize the plants through market participation. This approach requires the communication of frequency measurements of GFCs from adjacent buses. The proposed controller guarantees asymptotic stability of power grids with generic configurations that include multiple SGs and GFCs under dc power flow approximation and a mild assumption on the center-of-inertia based frequency dynamics model. The sliding mode controller design is challenging for a grid with multiple GFCs, as the sliding surface for each GFC requires iterative experiments for refinement. Moreover, for sliding mode control we could not establish the stability guarantee in the reduced-order system in presence of the constraints on the control input. To solve this problem, a nonlinear model predictive control (NMPC) strategy is proposed for frequency support from the GFCs, which ensures dc-link voltage stability. The NMPC approach considers a multitude of constraints including those on control input and tracks the dc-link voltage reference to indirectly regulates active power output. The controller also ensures finite-time practical stability of the close-loop system. The above-mentioned analyses and control strategies are primarily evaluated in positive sequence fundamental frequency phasor models of multiple modified IEEE benchmark systems with IBRs. Finally, the detailed electromagnetic transient (EMT) models of the IBRs are used to closely replicate the behavior of the GFCs in a real-world power grid. An EMT-TS co-simulation platform is developed for integrating the EMT models of IBRs to the phasor-based planning models of bulk power systems. This platform is used to integrate the planning model of the Western Electricity Coordinating Council (WECC) grid with an EMT-based GFC model. The proposed sliding mode control is validated in this co-simulation model to ensure the dc-link voltage stability of the GFC and provide frequency support following a contingency.
