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This paper presents a dynamic event data-based stability risk assessment method for power grids with high penetrations of inverter-based resources (IBRs). This method relies on obtaining the IBRs’ DQ admittance through dynamic event data and computing the system’s eigenvalues based on the admittance models. Two critical technologies are employed in this research, including time-domain and frequency-domain data fitting and $dq$ -frame voltage and current signal derivation. The first technology is key to obtaining the $s$ -domain expressions from the transient response data, and the $s$ -domain DQ admittance model from the frequency-domain measurements. The second technology is key to obtaining the $dq$ -frame voltage and current signals from either the three-phase instantaneous measurements or the phasor measurement unit (PMU) data. The method is illustrated using data generated from a Type-4 wind power plant modeled in PSCAD. This paper demonstrates the technical feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]

The paper introduces the concept of complex frequency. The imaginary part of the complex frequency is the variation with respect of a synchronous reference of the local bus frequency as commonly defined in power system studies. The real part is defined based on the variation of the voltage magnitude. The latter term is crucial for the correct interpretation and analysis of the variation of the frequency at each bus of the network. The paper also develops a set of differential equations that describe the link between complex powers and complex frequencies at network buses in transient conditions. No simplifications are assumed except for the usual approximations of the models utilized for the transient stability analysis of power systems. A variety of analytical and numerical examples show the applications and potentials of the proposed concept. [ABSTRACT FROM AUTHOR]

The advantages of operating selected transmission lines at frequencies other than the standard 50 or 60 Hz are numerous, encompassing increased power transfer capacity and better utilization of existing infrastructure. While high voltage DC (HVDC) is by far the most well-established example, there has been an emerging interest low frequency AC (LFAC) transmission in applications ranging from offshore wind to railway systems and mining. In this paper, we investigate the use of LFAC as a transmission upgrade and propose models and analysis methods to determine the optimal choice of frequency. The paper first presents an optimal power flow model with frequency as a variable, assuming modular multilevel converters for frequency conversion. Using this model, we analyze LFAC as an embedded upgrade in a transmission system using existing lines. We quantify the system-wide advantages from improved power flow control and frequency reduction and find that an LFAC upgrade achieves similar and sometimes better results compared with HVDC upgrades. Finally, we analyze the factors which determine the optimal frequency for these upgraded transmission lines, and we demonstrate the benefits of changing the frequency in response to different system topologies and operating conditions. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the existence and stability of equilibrium of dc micro-grids under the master-slave control (where some distributed generations (DGs) are under droop control with dual-loop (Droop-DGs) and some DGs are under MPPT control (MPPT-DGs)). Firstly, the power-flow equation of the dc micro-grids under master-slave control with CPLs is obtained. Then, we transform the solvability of the power-flow equation into the existence of a fixed point for a contraction mapping. Based on Banach's fixed point theorem, a sufficient condition to guarantee the existence of the power-flow solution in dc micro-grids is derived. The condition derived in this paper is not only useful for master-slave control but also for droop control. Besides, to calculate the power-flow solution, an iterative algorithm with exponential convergence rate is proposed. Secondly, we use a singular perturbation model to predict the qualitative behavior of the system near the equilibrium point. By analyzing eigenvalues of the boundary layer system and reduced-order system Jacobian matrix, the robust stable analytic conditions of the system are obtained. The effect of the sampling delay on the system stability is analyzed, the robust stability condition is obtained by using linear matrix inequality. The simulation results verify the correctness of the proposed conditions. The obtained conditions provide a reference for establishing a reliable dc micro-grid. [ABSTRACT FROM AUTHOR]

The continuous-time model is widely used to design load frequency control (LFC) schemes for power systems with delays and demand response (DR). In practice, however, the LFC system works in a sampled-data manner. The plant operates continuously while the control updates every few seconds. This paper focuses on the sampled-data LFC system with DR and the delay. Based on the linear quadratic regulator (LQR) theory, an optimal control scheme is designed to regulate the DR and generation units in a sampled-data manner. The LQR controller can be applied to the LFC system with constant and time-varying delays, regardless of DR. An observer is also designed to make the state-feedback control law feasible. The observer is efficient in that its gain is delay independent. Case studies on the one-area and multi-area LFC systems are conducted to verify the effectiveness of the proposed LFC controller. Simulation results also demonstrate the excellent stability and performance of the proposed LQR controller in the sampled-data LFC-DR system. [ABSTRACT FROM AUTHOR]

This paper investigates the effects of the dynamic properties of a photovoltaic generator (PVG) on the stability of a grid-connected current-source inverter (CSI)-based photovoltaic system and presents a simple yet effective active compensator to ensure system stability. A detailed equivalent model of the PVG that considers the dynamic resistance, diffusion capacitance, series inductance, and dc cable resistance and inductance is used, and the effects of these parameters are assessed. It has been found that when the PVG operates in the constant-current region (CCR), the phase margin becomes negative in the control-to-input dynamics, which alters the stability of the dc-link current control. The change in the system dynamics when the operating point of the PVG shifts from the constant-voltage region (CVR) to CCR is verified through a detailed small-signal state-space model of the complete system. Furthermore, an active compensator is proposed to ensure stable dc-link current control operation at all operating points of the PVG. The influence of different control parameters on the integrated system dynamics is examined to determine the range of the control parameters required for stable operation. The performance of the proposed system under utility-grid fault, grid voltage parameter variation, weak grid, and changes in insolation level is also evaluated. Detailed nonlinear time-domain simulation results, using a typical utility-scale CSI-based PV system, validate the analytical results and the effectiveness of the proposed active stabilization under different operating conditions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The existing research on voltage-source converter HVDC (VSC-HVDC) system stability mostly focuses on small-signal stability analysis methods. However, when large-signal disturbances occur, the intrinsic nonlinearity of the VSC-HVDC system becomes inevitable so that the small-signal studies are no longer valid. In this paper, a large-signal stability analysis method of the VSC-HVDC system is proposed based on the estimation of domain of attraction (DOA). This method can not only analyze the asymptotic stability of the operating point, but also answer the question of how large deviations from the operating point can be tolerated by the system. By using Takagi-Sugeno (T-S) fuzzy model and Lyapunov stability theorem, the DOA of the VSC-HVDC System at the operating point is estimated, and the large-signal stability of VSC-HVDC System is analyzed. On this foundation, the influence of system parameters on the large-signal stability is studied. The results can be used to guide the adjustment of system parameters to solve the problem of system instability. The time-domain simulations conducted in Matlab/Simulink are used to test the stability of the system under large-signal disturbance in the range of DOA. The simulation results verify the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamic voltage support (DVS) from inverter-based resources (IBRs) under voltage sags to enhance the low-voltage ride-through performance. The DVS problem is formulated as a nonconvex optimization program that maximizes the positive-sequence voltage magnitude at the point of common coupling (PCC) subject to the current, active power, and synchronization stability constraints. Then, we perform the optimality analysis to explore the global optimum analytically. It is found that the unique global optimum has three scenarios/stages (S1–S3), which depends on the specific relationship among grid voltage, grid strength, and physical limits of IBRs. The explicit closed-form solutions in S1 and S3 are derived, and the optimality conditions (an implicit solution) of S2 are provided, which guarantees the global optimality and enables the compatibility with fast real-time control. Finally, we implement the optimum with a grid-connected single-stage photovoltaic (PV) power plant by integrating a DVS controller. Dynamic simulations are carried out under different scenarios to test our proposal. The robustness against model errors is also discussed. [ABSTRACT FROM AUTHOR]

Fast frequency response (FFR) is an option in maintaining system security under low inertia conditions. Power electronics interfaced energy resources such as wind and photovoltaics have the capability to deliver FFR. At present, almost all installed power electronics interfaced energy resources are connected to the grid by the phase locked loop (PLL)-synchronized voltage source converter (VSC) and they usually implement inertial response by measuring the rate of change of frequency (RoCoF). However, RoCoF measurements are highly susceptible to disturbances in the grid. In this paper, a novel inertia controller is developed for PLL-synchronized VSC interfaced energy resources to implement natural inertial response without measuring RoCoF. A thorough stability analysis is performed to study the impact of proposed inertia controller on the VSC in weak grid. The proposed inertia controller makes the deviation of DC voltage proportional to the deviation of system frequency. Further, a method of primary frequency control is proposed by measuring DC voltage rather than grid frequency. The proposed FFR scheme of inertia and primary frequency control is applied to a direct-drive windfarm connected to a grid, and its correctness and advantages are verified by simulation. [ABSTRACT FROM AUTHOR]

In view of the increasing levels of renewable generation across the world, the operational dynamics of power systems are changing. One of the dimensions of this transformational change is the nature of fault ride through behavior of renewable technologies such as wind and the associated differences compared to conventional generation. This paper investigates the impacts of fault ride through behavior of wind farms on the system stability in detail, using full dynamic model of a low inertia island power system. Recorded PMU measurements are used to establish the variations in wind farm behavior during and after a fault. A detailed sensitivity analysis on the active and reactive power injection behavior of wind farms is carried out to establish the component of fault ride through behavior that is most critical to system stability, using the full model of the Ireland and Northern Ireland Power system (All island power system). Detailed investigation of the mechanics of a fault in a low inertia, wind generation dominated system is carried out to reveal potential technical scarcities. Finally, mitigations for identified scarcities arising from non-ideal fault ride through behavior of wind farms are presented in terms of Transmission System Operator led novel system services. [ABSTRACT FROM AUTHOR]

This paper proposes a Transient Stability Constrained Optimal Power Flow (TSCOPF) formulation that models non-synchronous renewable generation equipped with synthetic inertia. The proposed optimization problem calculates the optimal operating point of the system, accommodating high shares of non-synchronous renewable generation while ensuring transient stability in the event of critical incidents. Synthetic inertia controllers are used to improve the dynamic stability of the system in cases of very high share of renewable generation. The proposed tool is tested in the North-West Spanish system, a network with a high penetration of wind energy that causes a reduction in the total system inertia. The results of the study show that 1) synthetic inertia in renewable power plants can diminish electromechanical oscillations after a severe contingency, reducing the cost of ensuring transient stability; 2) using synthetic inertia the system becomes more stable when conventional generation is decommissioned following de-carbonization and renewable promotion policies; and 3) the proposed model can be used to calculate the parameters of the synthetic inertia control. [ABSTRACT FROM AUTHOR]

Since the wide application of virtual synchronous generators (VSGs), the power grid faces great challenges in the safe and stable operation due to their limited thermal capacity and weak anti-disturbance ability. During transient period, for example, a fault occurs in the transmission line, the VSG may lose the transient angle stability and provoke the current hard limit. Even if the fault is cleared by tripping of line, it still faces the problem of instability and voltage dips. To address this problem, in this paper, the post-fault large-signal model of VSG is derived first via the travelling waves based fault information acquisition. Subsequently, with the effect of both active and reactive power loops taken into account, a two-stage simultaneous control scheme is proposed for improving the transient stability of VSG, while considering the current limitation during fault state and voltage support after fault clearance. This method is fulfilled by mode switching and an additional feedback control based on the fault signal. Finally, the effectiveness of the proposed method under both symmetrical and asymmetrical faults is verified. Moreover, the application of the proposed method in a multiple VSGs system is also verified. Besides, the robustness to parameter mismatch and the feasible operating region for the method are discussed. [ABSTRACT FROM AUTHOR]

The power oscillation damper (POD) in the doubly-fed induction generator (DFIG) is to damp the low- frequency oscillation (LFO) in the power systems. But the POD will introduce the LFO to the DFIG and intensify the oscillation of the latter. In this paper, open-loop subsystems of the DFIG with the POD and the rest part of power system are derived to describe the interaction between them. The balanced truncation method is used to reduce the transfer function of the DFIG and derive the analytical description to the oscillation of the DFIG. Considering the impact of the POD on the DFIG, the constraint to the DFIG is newly incorporated in the optimization model to the POD parameters, with the aim to alleviate the oscillation of both the DFIG and power system. The simulation verifies the accuracy of the reduced model of the DFIG, and validates the effectiveness of the improved optimization to the POD of the DFIG. [ABSTRACT FROM AUTHOR]

In this paper, a Frequency Stability Constrained Unit Commitment (FSCUC) model is presented. The on/off status of generating units, generation levels and operating reserves are optimized to minimize the operational daily costs. The frequency stability constraints are included in the proposed FSCUC model to guarantee the safety of System Frequency Response (SFR) under sudden generation outages. A new multi-area SFR model is proposed to capture the regional dynamics of system frequency with considering the impacts of transmission network. An SFR model is developed for each electric region and then the resulted regional SFRs are coupled via a set of constraints. In order to enhance the primary SFR and keep the daily operating point at its economic schedule, Flywheel Energy Storage (FES) devices are utilized in the proposed FSCUC model. The proposed multi-area SFR model allows the optimal allocation of operating reserve and the accurate modeling of FESs in FSCUC model. The proposed FSCUC model is formulated as a Mixed Integer Linear Programming (MILP) problem and is applied over the IEEE 118-bus test system to show the accuracy of the proposed multi-region SFR and the impact of FES in frequency support. The developed MILP model is solved using CPLEX in GAMS. [ABSTRACT FROM AUTHOR]

This paper presents some results on the accuracy of normal form analysis for large deviations from the stable equilibrium point (SEP) in a power system. The results of studies on the region of convergence of Neumann series, which is required for normal form analysis, are presented. A polynomial function approximation is proposed to model the generator exciter limiter. Studies on the accuracy of higher order normal form analysis for large deviations from SEP are presented. Use of Prony analysis in addition to simulation is proposed for the verification of accuracy. [ABSTRACT FROM AUTHOR]

The impedance of the virtual synchronous generator (VSG) is an effective method to analyze the dynamic interactions between the VSG and the grid. For the existence of power controllers and asymmetric inner-loop controllers in the d- and q-axis, there are couplings in the output sequence impedance of VSG. Although the couplings are relatively small, they still have a significant impact on the stability performance. However, there is no result published on this aspect up to now. To bridge this gap, a sequence impedance model based on harmonic linearization is established in this paper, which explicitly reveals the mirror frequency effect (MFE) in VSG. Subsequently, the relationships between the power controllers and the MFE are demonstrated. Finally, simulation results verify the feasibility and correctness of the theoretical analysis presented above. [ABSTRACT FROM AUTHOR]