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Synchronous condensers (SynCons) have been deployed in power grids penetrated by inverter-based resources (IBRs) worldwide to strengthen and stabilize the grids. This paper examines which machine parameters influence IBR weak grid stability and whether excitation systems also play a role. Four types of stability scenarios are examined, including transient stability, oscillations of a few Hz, oscillations near 9 Hz, and dynamic voltage stability. It is shown that the most influential machine parameter varies for the different types of stability issues. While minimization of field winding inductance (typically the major component of the machine transient reactance, X′d) can significantly improve transient stability, voltage stability, and low-frequency oscillatory stability, this parameter has no influence on relatively rapid oscillations. On the other hand, minimizing rotor damper winding inductance (typically the major component of the machine subtransient reactance, X′′d) improves the 9-Hz oscillation stability, but with insignificant influence on the other three types of stability. Furthermore, the excitation system characteristics show negligible influence for any of the scenarios. In addition to the simulation studies, we show how the operational reactances are associated with the machine's dq impedance viewed from the terminal bus and how a SynCon reduces the equivalent grid impedance, thereby improving weak grid stability. Finally, it is concluded that minimization of both transient and subtransient direct-axis reactances should help in a range of stability scenarios, while cautions should be taken when dealing with quadrature-axis transient reactances. 

Voltage control is often time provided at the plant-level control of inverter-based resources (IBR). Addition of energy storage systems in an IBR power plant makes it feasible to have frequency control at the power plant level. While frequency control appears as a simple frequency-power droop control to adjust real power commands to inverter-level controls with measured frequency as an input, care must be taken to avoid interactions among the plant frequency control with communication delays, inverter-level control effects, and the frequency sensor, usually a phase-locked-loop (PLL). This paper present two types of interaction scenarios that makes frequency control design challenging. The first interaction scenario may occur if the frequency control's gain is large, while the second interaction scenario may occur at a small control gain if the plant-level PLL lacks sufficient damping. We contribute to the fundamental understanding of the causation of stability issues due to plant frequency control through the derivation of a simplified feedback system focusing on the frequency and power relationship, and the follow-up frequency-domain analysis for gaining insights. For validation, we also design a data-driven approach to obtain models from data generated from an electromagnetic transient (EMT) simulation testbed. The findings from analysis have all been validated by EMT simulation. Finally, we contribute to mitigating strategies and also the understanding of the role of additional proportional integration power feedback control. This addition has been demonstrated as an efficient stability enhancement strategy to mitigate the effect of communication delay. 

In this paper, we demonstrate methods to extract dq admittance for a solar photovoltaic (PV) farm from its black-box model used for electromagnetic transient (EMT) simulation. Each dq admittance corresponds to a certain operating condition. Based on the dq admittance, analysis is carried out to evaluate how grid strength and solar irradiance may influence stability. Two types of stability analysis methods (open-loop system based and closed-loop system based) are examined and both can deal with dq admittance's frequency-domain measurements directly and produce graphics for stability analysis. The findings based on dq admittance-based analysis are shown to corroborate EMT simulation results. 

In system-level dynamic studies, grid-following inverter-based resources (IBRs) have been treated as current sources synchronized to the main grid via phase-locked-loops (PLL), while the interconnected transmission line is usually treated as a constant complex impedance. In this letter, we present the derivation of transient algebraic impedance of the transmission line and demonstrate its superiority over constant impedance. We show significant accuracy improvement in predicting transient stability and oscillations when the constant impedance is replaced by a transient algebraic impedance. Furthermore, we derive a small-signal model by use of the transient algebraic impedance and this model is successful in explaining the interaction between the PLL and the grid. On the other hand, if constant impedance is assumed, such stability issues cannot be predicted. 

While dq admittance models have shown to be very useful for stability analysis, extracting admittance models of inverter-based resources (IBRs) from the electromagnetic transient (EMT) simulation environment using frequency scans takes time. In this letter, a new perturbation method based on Gaussian pulses in combination with the system identification algorithms shows great promise for parametric dq admittance model extraction. We present the dq admittance model extracting method for a type-4 wind turbine. Challenges in implementing Gaussian pulse excitation are also pointed out. The extracted dq admittance model via the new method shows to have a high matching degree with the measurements obtained from frequency scans. 

Electromagnetic transient simulation of parallel-connected 4-MW type-3 wind turbines based on original equipment manufacturer's real-code turbine model shows 1.2-Hz turbine–turbine oscillations in reactive power. This letter reveals why such oscillations occur in the individual var measurement while being insignificant in the total var measurement, regardless of the varying grid impedance. We adopt two analysis approaches, i.e., open-loop single-input single-output analysis and network decomposition. These two approaches differ in their treatment of turbine–network interaction. The open-loop analysis shows that the turbine–turbine oscillation mode is due to an open-loop system pole being attracted to an open-loop system zero. Furthermore, we use a network decomposition method to explain why this mode is observable in individual vars, while not observable in the total var. The entire system of n turbines can be viewed as n decoupled circuits. For the two-turbine case, the system has an aggregated mode and a turbine–turbine oscillation mode. The aggregated mode is associated with a circuit associated with the total var, while the turbine–turbine oscillation mode is associated with the var difference and is insensitive to the grid parameters. 

Hitting control limits changes the behavior of the control systems and invalidates commonly adopted assumptions made when calculating the operating point of doubly fed induction generator (DFIG)-based wind turbines (WTs). The current computing methods rely on trials and errors and iterations. This paper proposes an optimization-based algorithm with control limits integrated into the problem formulation. Hitting or not hitting a control limit is modeled as a binary variable. Both rotor-side converter (RSC) current order limits and grid-side converter (GSC) current order limits are modeled in the proposed mixed-integer programming (MIP) formulation. For a WT with given terminal voltage and wind speed, the electrical and mechanical variables of the system can be computed directly from the optimization problem. The proposed formulation has included losses in the back-to-back converters and nonzero reactive power support through GSC. The computing results have been validated with the electromagnetic transient (EMT) simulation results. This formulation can help accurately detect whether control limits are hit for low voltage conditions and facilitate Type-III wind turbine fault ride through analysis.