Large-scale integration of renewable generation, usually interfaced to the network through power electronics, has led to drastic changes in power system dynamics. This paper presents novel insights into stability properties of such systems. For that purpose, a high-fidelity dynamic model of a generic low-inertia power system has been developed. The full-order, state-of-the-art control schemes of both synchronous and converter-based generators are included, with the latter differentiating between grid-forming and grid-following mode of operation. Furthermore, the dynamics of transmission lines and loads are captured in the model. Using modal analysis techniques such as participation factors and parameter sensitivity, the most vulnerable segments of the system are determined and the adverse effects of timescale coupling and control interference are investigated. More precisely, this work characterizes the maximum permissible penetration levels of inverter-based generation as well as the nature of the associated unstable modes and the underlying dynamics. Finally, potential directions for improving the system stability margin under different generation portfolios are proposed for several benchmark systems.

In this paper, the Unit Commitment (UC) problem in a power network with low levels of rotational inertia is studied. Frequency-related constraints, namely the limitation on Rate-of-Change-of-Frequency (RoCoF), frequency nadir and steady-state frequency error, are derived from a uniform system frequency response model that incorporates dynamics and controls of both synchronous generators and grid-forming inverters. These constraints are then included into a stochastic UC formulation that accounts for wind power and equipment contingency uncertainties using a scenario-tree approach. In contrast to the linear RoCoF and steady-state frequency error constraints, the nadir constraint is highly nonlinear. To preserve the mixed-integer linear formulation of the stochastic UC model, we propose a computationally efficient approach that allows to recast the nadir constraint by introducing appropriate bounds on relevant decision variables of the UC model. This method is shown to be generally more accurate and computationally more efficient for medium-sized networks than a piece-wise linearization method adapted from the literature. Simulation results for a modified IEEE RTS-96 system revealed that the inclusion of inertia-related constraints significantly influences the UC decisions and increases total costs, as more synchronous machines are forced to be online to provide inertial response.

The undergoing transition from conventional to converter-interfaced renewable generation leads to significant challenges in maintaining frequency stability due to declining system inertia. In this paper, a novel control framework for Synthetic Inertia (SI) provision from Wind Turbines (WTs) is proposed, which eliminates the secondary frequency dip and allows the dynamics of SI from WTs to be analytically integrated into the system frequency dynamics. Furthermore, analytical system frequency constraints with SI provision from WTs are developed and incorporated into a stochastic system scheduling model, which enables the provision of SI from WTs to be dynamically optimized on a system level. Several case studies are carried out on a Great Britain 2030 power system with different penetration levels of wind generation and inclusion of frequency response requirements in order to assess the performance of the proposed model and analyze the influence of the improved SI control scheme on the potential secondary frequency dip. The results demonstrate that the inclusion of SI provision from WTs into Unit Commitment (UC) can drastically impact the overall system costs.

Autonomous optimization refers to the design of feedback controllers that steer a physical system to a steady state that solves a predefined, possibly constrained, optimization problem. As such, no exogenous control inputs such as setpoints or trajectories are required. Instead, these controllers are modeled after optimization algorithms that take the form of dynamical systems. The interconnection of this type of optimization dynamics with a physical system is however not guaranteed to be stable unless both dynamics act on sufficiently different timescales. In this paper, we quantify the required timescale separation and give prescriptions that can be directly used in the design of this type of feedback controllers. Using ideas from singular perturbation analysis, we derive stability bounds for different feedback laws that are based on common continuous-time optimization schemes. In particular, we consider gradient descent and its variations, including projected gradient, and Newton gradient. We further give stability bounds for momentum methods and saddle-point flows. Finally, we discuss how optimization algorithms like subgradient and accelerated gradient descent, while well-behaved in offline settings, are unsuitable for autonomous optimization due to their general lack of robustness.

High penetration of renewable energy sources and the increasing share of stochastic loads require the explicit representation of uncertainty in tools such as the optimal power flow (OPF). Current approaches follow either a linearized approach or an iterative approximation of non-linearities. This paper proposes a semidefinite relaxation of a chance constrained AC-OPF which is able to provide guarantees for global optimality. Using a piecewise affine policy, we can ensure tractability, accurately model large power deviations, and determine suitable corrective control policies for active power, reactive power, and voltage. We state a tractable formulation for two types of uncertainty sets. Using a scenario-based approach and making no prior assumptions about the probability distribution of the forecast errors, we obtain a robust formulation for a rectangular uncertainty set. Alternatively, assuming a Gaussian distribution of the forecast errors, we propose an analytical reformulation of the chance constraints suitable for semidefinite programming. We demonstrate the performance of our approach on the IEEE 24 and 118 bus system using realistic day-ahead forecast data and obtain tight near-global optimality guarantees.

A rapid deployment of renewable generation has led to significant reduction in the rotational system inertia and damping, thus making frequency control in power systems more challenging. This paper proposes a novel control scheme based on Model Predictive Control (MPC) for converter-interfaced generators operating in a grid-forming mode, with the goal of exploiting their fast response capabilities to provide fast frequency control service to the system. The controller manipulates converter power injections to limit the frequency nadir and rate-of-change-of-frequency after a disturbance. Both centralized and decentralized MPC approaches are considered and compared in terms of performance and practical implementation. Special attention is given to the decentralized controller by generating an explicit MPC solution to enhance computational efficiency and reduce hardware requirements. Simulation results obtained from a detailed dynamic model of the IEEE 39-bus system demonstrate the effectiveness of the proposed control schemes.