The modern power grid features the high penetration of power converters, which widely employ a phase-locked loop (PLL) for grid synchronization. However, it has been pointed out that PLL can give rise to small-signal instabilities under weak grid conditions. This problem can be potentially resolved by operating the converters in grid-forming mode, namely, without using a PLL. Nonetheless, it has not been theoretically revealed how the placement of grid-forming converters enhances the small-signal stability of power systems integrated with large-scale PLL-based converters. This paper aims at filling this gap. Based on matrix perturbation theory, we explicitly demonstrate that the placement of grid-forming converters is equivalent to increasing the power grid strength and thus improving the small-signal stability of PLL-based converters. Furthermore, we investigate the optimal locations to place grid-forming converters by increasing the smallest eigenvalue of the weighted and Kron-reduced Laplacian matrix of the power network. The analysis in this paper is validated through high-fidelity simulation studies on a modified two-area test system and a modified 39-bus test system. This paper potentially lays the foundation for understanding the interaction between PLL-based (i.e., grid-following) converters and grid-forming converters, and coordinating their placements in future converter-dominated power systems.

Power converters may lose synchronization with the remaining network when integrated in a weak power grid. Such an instability phenomenon [known as grid-synchronization instability (GSI)] features the frequency divergence of phase-locked loop (PLL) and oscillations of the converter's power output. In this paper, we focus on the influences of reactive power control (RPC) methods on GSI. We develop a single-input-single-output model to explicitly reveal how the PLL interacts with the other parts of the converter system in terms of grid synchronization. Then, after deriving the open-loop transfer function and sensitivity function of the entire converter system, we compare the stability margins for different RPC methods. Furthermore, we elaborate on the interactions among RPC, PLL, and voltage feedforward (VFF), and then demonstrate that different design methods of RPC and VFF will lead to different stability margins. The subsequent stability analysis provides insightful guidelines for coordinating the design of multiple control loops, i.e., RPC, VFF and PLL. In particular, we demonstrate how the loop shaping of PLL takes effect in increasing the stability margin and eventually preventing the converter from GSI. The validity of the stability analysis is verified through simulations in MATLAB/Simulink.

Because failures in distribution systems caused by extreme weather events directly result in consumers’ outages, this paper proposes a state-based decision-making model with the objective of mitigating loss of load to improve the distribution system resilience throughout the unfolding events. The system topologies including on/off states of feeder lines are modeled as Markov states, and the probabilities from one Markov state to another Markov state throughout the unfolding events are determined by the component failure caused by the unfolding events. A recursive optimization model based on Markov decision processes (MDP) is developed to make state-based actions, i.e., system reconfiguration, at each decision time. To overcome the curse of dimensionality caused by enormous states and actions, an approximate dynamic programming (ADP) approach based on post-decision states and iteration is used to solve the proposed MDP-based model. IEEE 33-bus system and IEEE 123-bus system are used to validate the proposed model.

The increasing penetration of renewable generation presents challenges for system frequency regulation due to short-term power fluctuations and system inertia reductions. This paper presents a coordinated control strategy for frequency regulation in which inverter air-conditioning (IAC) units are used to perform primary frequency regulation (PFR) and fixed frequency air-conditioning (FFAC) units are used to perform secondary frequency regulation (SFR). In PFR, the regulation power is provided by adjusting the setpoints of the IAC units. A random number generation method is proposed to stochastically trigger IAC units based on the frequency deviation in real time. Furthermore, a recovery method is presented to stably restore the IAC units to their initial operating states after regulation. In SFR, a constant equivalent duty ratio method is raised to keep the regulation power stable over a long instruction interval. Based on this, the transforming time interval method is presented to determine the ON/OFF status of FFAC units to provide the required regulation power. Additionally, a recovery method for FFAC units is proposed to mitigate the power rebound after regulation. The proposed control strategy achieves an improved frequency regulation effect with fewer communication demands. Dynamic simulations in a six-machine two-area system and an isolated microgrid with wind power verify the effectiveness of the proposed control strategy.

Virtual synchronous machines (VSMs) emulate the swing equation for grid synchronization and inertia provision. Usually, a large damping coefficient is necessary in VSMs to provide equivalent damper winding effect, which is, however, not aligned with the fact that the physical swing equation of synchronous generators (SGs) contains only a small mechanical friction factor. This large damping coefficient could result in undesired droop characteristics. In this letter, we use damping torque analysis to reveal the damping mechanism of SGs, and show that the damping effect actually comes from the dynamics of the transient/subtransient reactances aggregated as a dynamical impedance. Based on this finding, we elaborate on how to get rid of the large damping coefficient in VSMs by using a dynamical virtual impedance (DVI) to emulate SG's damping mechanism.