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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 low-frequency oscillations (LFOs) inherent in power systems will be impacted by the increasing penetration of renewable energy sources (RESs). This paper investigates the impact of virtual synchronous machine (VSM) based RESs on the LFOs in power systems. A detailed two-machine test-bed has been developed to analyze the LFOs which exists when VSMs replace synchronous generators. The characteristics of the LFO modes, and the dominant states have been comprehensively analyzed. Furthermore, this study analyzes the LFO modes which exists in an all-VSM grid. The role of the power system stabilizers in the all-VSM grid has been comprehensively evaluated. The IEEE benchmark two-area four-machine system has been employed to corroborate the results of the small-signal analysis, and observe the transient performance. The analysis in this paper have been performed in MATLAB/SIMULINK environment. [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 paper presents the theoretical foundation and practical implementation aspects of Fractional Order Controllers (FOCs) for power system applications. With this aim, the paper provides a comprehensive mathematical background on the stability analysis of dynamic systems with inclusion of fractional order derivatives and discusses their software implementation based on the Oustaloup's Recursive Approximation (ORA) method. Then the paper illustrates a variety of examples of ORA-based FOCs, namely, automatic generation control of synchronous machines; frequency control of a converter-interfaced energy storage system; and voltage control through a static synchronous compensator. The WSCC 9-bus test system and a realistic 1,479-bus model of the Irish transmission system are employed to test and compare the examined FOCs with their integer-order versions. [ABSTRACT FROM AUTHOR]

This paper proposes a novel unified prediction approach for both small-signal and transient rotor angle stability as opposed to other studies that have only addressed transient rotor angle stability. Deep learning techniques are employed in this paper to train an online prediction model for rotor angle stability (RAS) using the voltage phasor measurements which are collected across the entire system. As a result, the trained model provides a fast yet accurate prediction of the transient stability status when a power system is subjected to a disturbance. Also, if the system is transiently stable, the prediction model updates the power system operator concerning the damping of low-frequency local and inter-area modes of oscillations. Therefore, the presented approach provides information concerning the transient stability and oscillatory dynamic response of the system such that proper control actions are taken. To achieve these objectives, advanced deep learning techniques are employed to train the online prediction model using a dataset which is generated through extensive time domain simulations for wide range of operating conditions. A convolutional neural network (CNN) transient stability classifier is trained to operate on the transient response of the phasor voltages across the entire system and provide a binary stability label. In tandem, a long-short term memory (LSTM) network is trained to learn the oscillatory response of a predicted stable system to capture the step-by-step dynamic evolution of the critical poorly damped low-frequency oscillations. The superior performance of the proposed model is tested using the New-England 10-machine, 39-bus, IEEE 16-machine, 68-bus, 5-area and IEEE 50-machine, 145-bus test systems and is verified with time domain simulation. [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]

This paper presents a novel distributed voltage control method for multi-terminal direct current (MTDC) systems based on the average consensus algorithm. The proposed method combines the idea of secondary integral voltage control and regulator synchronization problem. It realizes adjustable tradeoff between two conflicting control objectives, that is, voltage regulation and power sharing. The proposed control algorithm only needs a low-bandwidth communication between two adjacent voltage source converters (VSCs) and local information to work effectively. Moreover, regarding the system dynamic response, a parameter tuning method for the proposed controller is provided to achieve the fastest convergence of the distributed control algorithm. This paper also develops a small-signal dynamic model for VSC-MTDC systems with distributed controllers to evaluate the system dynamic performance. The proposed method is validated by time-domain simulation of a 4-terminal VSC-MTDC system. The simulation results show that flexible tradeoff between voltage regulation and power sharing can be achieved under necessary constraints on the DC bus voltages and power sharing ratio. [ABSTRACT FROM AUTHOR]

This paper proposes an approach to determine the participation of algebraic variables in power system modes. The approach is based on a new interpretation of the classical participation factors, as well as on the definition of adequate output variables of the system's state-space representation. The paper considers both the linear and generalized eigenvalue problems for the calculation of the participation factors and presents a theorem to cope with eigenvalue multiplicities. An illustrative example on the two-area system, as well as a study on a 1479-bus dynamic model of the all-Irish transmission system are carried out to support the theory and illustrate the features of the proposed approach. [ABSTRACT FROM AUTHOR]

The reduction in bus voltage magnitudes as the load demand grows may lead to sudden disconnection of loads and/or distributed generation units, in distribution grids, caused by undervoltage protection schemes. As proposed in this paper, this discontinuous behavior of distribution grids can be modeled as a sudden load variation in traditional static voltage stability assessment methods, such as the continuation power flow (CPFLOW). A discussion on the impacts of these discontinuities on the equilibrium diagram of the system is presented in this paper, as well as a set of numerical simulations showing that the traditional CPFLOW algorithm presents convergence problems caused by the discontinuities under analysis. From this perspective, this paper proposes an algorithm based on novel predictor/corrector and identification schemes, which are capable of successively calculating the discontinuities that exist in the equilibrium loci of the system under analysis, as well as the maximum loadability point and the type of bifurcation. A simplified modeling approach that eliminates the need for a complex (and computationally expensive), detailed description of distribution grids is also elaborated and incorporated into the proposed algorithm. The simulated examples show that the proposed algorithm adequately handles the problem, yelding more accurate results than the traditional CPFLOW algorithm. [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]

This paper proposes a method for the optimal deployment of Corrective Control Measures (CCMs) for the improvement of transient stability in uncertain power systems. First, the critical oscillation patterns of the disturbed system are identified using Hierarchical Clustering (HC) with statistically defined algorithm parameters. This is followed by the identification of critical generators where the application of CCMs will have maximum impact. The results show that a significant reduction in multi-machine unstable events can be achieved by the strategic deployment of CCMs. The proposed method is demonstrated on a modified IEEE 68 bus NETS-NYPS test network with Renewable Energy Sources (RES) and realistically modelled system uncertainties. [ABSTRACT FROM AUTHOR]

Reachable power flow (ReachFlow) is a newly developed formal method for enclosing the complete set of uncertain power flow states. To enable ReachFlow's transition from theory to practice, the paper makes three major contributions: (1) both small- and large- signal stability proofs for the ordinary differential equation (ODE)-based power flow are devised to theoretically ensure the robustness of ReachFlow; (2) a model-order-reduction-empowered ReachFlow(ReachFlowR) algorithm is created for analyzing interested regions in large power systems; and (3) a parallel ReachFlow(ReachFlowP) algorithm is established to scale up ReachFlow for the accurate analysis of very large power systems. Extensive case studies are performed on a series of test systems, ranging from a 33-bus microgrid to a 2,000-bus power system, to thoroughly verify the correctness, efficacy and practicality of ReachFlow in formally verifying microgrid and macrogrid power flows as well as power flow control strategies. [ABSTRACT FROM AUTHOR]

Power system stability is widely assessed based on tools that rely on the representation of voltages and currents through quasi-static phasor calculus, implying that the network itself and the synchronous machine stators are modeled by algebraic equations. Accordingly, the associated fast transients are neglected, assuming those decay rapidly. However, with the increasing penetration of converter interfaced generation in power systems, the reliance on quasi-static phasor calculus is to be questioned. In this paper, the validity of quasi-static phasor calculus models is verified, and dynamic phasor calculus is considered as the alternative. A methodology to systematically compare quasi-static and dynamic phasor calculus is developed. It includes frequency response, modal, and sensitivity analyses. The methodology is applied to an IEEE test network considering penetrations of converter interfaced generation of up to 100%. The models are implemented in MATLAB. The H-infinity norm is proposed as an indicator to identify differences in the applicability of the models. The results show that the quasi-static phasor calculus is suitable for stability analysis only if low bandwidths of converter controls are given. Dynamic phasor calculus instead is suitable and applicable to generic stability studies of integrated power electric and electronic systems with high penetration of renewables. [ABSTRACT FROM AUTHOR]

This paper investigates systemwide short-term voltage stability concerns of power systems due to the multiple parametric uncertainties in the dynamic load model. The impact of regional load model uncertainty can be widespread and may mislead the whole system analysis and subsequent measures, if not properly addressed. This research discloses that the systemwide impact is related to the voltage weak areas through voltage stability modal analysis, and suggests that the impact of uncertain parameters needs to be assessed from a systems perspective, which has rarely been done in the existing practices. We thus present a three-step methodology for evaluating the systemwide uncertainty impacts: Firstly, it screens possible trajectories of all buses. The second step verifies whether the screened trajectories comply with the defined criteria, and determines the necessity of the final step. The final detailed analysis is conducted for those selected scenarios. Comprehensive studies for both the IEEE test and real Korea power systems consistently confirm the observations and demonstrate the efficacy and validity of the proposed method. [ABSTRACT FROM AUTHOR]

The connection of distributed energy resources (DERs) to distribution feeders can significantly increase the operational flexibility of system operators. Local feedback control schemes (such as Volt/VAr droop curves) are a cheap, scalable, and communication-free solution to control DERs in active distribution grids. However, these controllers can interfere detrimentally with each other when they act on multiple DERs connected to the same grid. We show that even the standardized curves recommended in the most recent grid codes may exhibit an unstable behavior. In this paper, we investigate the stability of local incremental DER control laws in three-phase active distribution grids with balanced, and unbalanced loading, and we bound the resulting rate of convergence. The use of low-pass filters on the DER set-points allows us to achieve closed-loop stability even for high-gain local control laws that would otherwise destabilize the grid. This feature is particularly relevant in data-driven approaches that yield optimal DER local control schemes, often in the form of steep customized piece-wise linear Volt/VAr curves. [ABSTRACT FROM AUTHOR]

Homotopy analysis method (HAM) is a popular semi-analytical method used widely in applied sciences. It stands out from the rest of the semi-analytical methods as it provides a family of solutions to nonlinear equations, including ordinary differential equations (ODEs), partial differential equations, etc. The convergence characteristics of the solutions can be varied by changing an auxiliary parameter ($\hbar$) in HAM. The convergence region of solution of ODEs using HAM can be improved by applying it over multiple intervals of time, which is referred to as multi-stage HAM (MHAM). In this paper, MHAM models for the IEEE Model 2.2 synchronous machine, IEEE Type-1 excitation system, first-order governor and first-order turbine models have been developed. The applicability of MHAM for power system dynamic simulations has been investigated in this paper using seven widely used test systems ranging from 10 generators 39 bus systems to 4092 generators 13 659 bus systems. The effect of number of terms, $\hbar$ and the time step on the accuracy and stability of the solution has been studied. The effectiveness of MHAM has been compared with the modified Euler (ME) and midpoint Trapezoidal (TrapZ) methods. The accuracy of MHAM has been found to be comparable with ME and TrapZ methods for the values of $\hbar$ between $-$ 1.05 and $-$ 0.95. The best accuracy is obtained for $\hbar$ = $-$ 1.0, which is a special case of MHAM called multi-stage homotopy perturbation method (MHPM). In this paper, it is also shown that MHPM is equivalent to multi-stage adomian decomposition method, which has been recently explored for large power system simulations. [ABSTRACT FROM AUTHOR]

Load characteristics have substantial influence on the voltage stability of power systems. The self-restorative characteristic and stalling of induction motor loads can deteriorate the voltage stability, so it is necessary to develop accurate and efficient dynamic analysis methods for voltage stability analysis of systems with induction motor loads. In this paper, a set of methods based on holomorphic embedding is proposed, which is able to solve steady states and dynamics of a power system with induction motors. The paper is the first work that applies holomorphic embedding to dynamic problems of power systems. The test cases on the IEEE 14-bus system, the NPCC 140-bus system, and the Polish 2383-bus system verify both accuracy and efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

High intermittency in today's renewable-rich distribution systems, and the prohibitive cost of upgrading the system infrastructure, has rendered voltage instability a real concern for heavily loaded systems. The voltage instability of distribution systems can spread to the corresponding transmission grid, as proven by real-life incidents. Recent advances in energy storage systems (ESSs), however, have offered a viable means of enhancing the reliability and robustness of power systems. In this paper, the optimal placement, sizing, and operation of ESS devices in wind-intensive distribution power systems are studied. The objectives of this paper are to minimize the ESS size (power and energy), required to ensure a desired voltage stability margin (VSM), and to minimize the reactive power loss and reactive power import from the upstream network. Wind uncertainty has been accounted for through a risk-based stochastic optimization framework. Besides, active network management (ANM) tools, such as the tap position of on-load tap changers, modelled by using a new method, and reactive power capabilities of both ESS devices and wind farms, are used as additional means to reduce the required ESS size. The results show that the required ESS significantly increases with increase in the desired VSM. Nevertheless, the increase can be considerably curtailed by using risk-based VS constraints and ANM tools. [ABSTRACT FROM AUTHOR]

A robust adaptive backstepping approach is considered in this paper to design excitation controllers for synchronous generators in power systems. The higher-order dynamical models of synchronous generators are considered to design the proposed excitation controller. Since the parameters appearing within these dynamical models (especially the parameters related to the synchronous generators and excitation systems) significantly affect the stability of power systems, these parameters are considered as completely unknown during the proposed controller design process. The parameter adaptation laws are used in this paper to estimate the unknown parameters while maintaining the overall stability of power systems. The effects of external disturbances are also considered in this paper to incorporate the model accuracies and measurement noises, which in turn ensure the robustness of the proposed control scheme. The control Lyapunov functions are used to analyze the stability of the whole system through the negative semi-definiteness of their derivatives. Simulation studies are carried out on an IEEE standard power system, the New England 10-machine 39-bus power system, to further validate the performance of the proposed scheme under different operating conditions. Comparisons are also made with different existing nonlinear excitation controllers sliding mode controller and robust partial feedback linearizing controller, which are designed based on the higher order models as well as with the robust adaptive controller, which is designed based on the traditional one-axis model. Simulations results, under different operating conditions, demonstrate the superiority of the proposed control scheme over all these existing nonlinear excitation controllers. [ABSTRACT FROM AUTHOR]

This paper studies the impact of realistic wide-area measurement system (WAMS) time-varying delays on the dynamic behavior of power systems. A detailed model of WAMS delays including quasi-periodic, stochastic, and constant components is presented. Then, this paper discusses numerical methods to evaluate the small-signal stability as well as the time-domain simulation of power systems with inclusion of such delays. The small-signal stability analysis is shown to be able to capture the dominant modes through the combination of a characteristic matrix approximation and a Newton correction technique. A case study based on the IEEE 14-bus system compares the accuracy of the small-signal stability analysis with Monte Carlo time-domain simulations. Finally, the numerical efficiency of the proposed technique is tested through a real-world dynamic model of the all-island Irish system. [ABSTRACT FROM AUTHOR]

This paper analyzes the robust stability of a mixed source microgrid comprised of a synchronous generator-based distributed energy resource (DER) and an inverter-based DER. Few studies conducted recently indicated that power system stabilizers (PSSs) are advantageous for damping local oscillations of synchronous generator-based DERs. However, stability issues may arise due to interaction of the parameters of PSS and system. This paper proposes a method to determine the stability region for the system when any two parameters are considered uncertain based on robust control theory. A sufficient condition for robust stability is presented using bialternate sum matrix of the system with uncertain parameters. The bialternate sum matrix approach is compared with a branch and bound approach presented in earlier studies. These two methods are shown to yield identical results for a single machine infinite bus system. However, the proposed bialternate sum matrix approach requires far less computational effort. Therefore, it is applied to determine the stability region for the operation of mixed source microgrid in both grid-connected and islanded modes. [ABSTRACT FROM AUTHOR]

This paper discusses the implementation of a transient stability model of Compressed Air Energy Storage (CAES) systems in a power system analysis package. A block-diagram based model of a two-machine CAES system is proposed, including specific controls for active power, reactive power, and State of Charge (SoC), which consider limits associated with the cavern pressure. As an application, the model is implemented in Powertech's TSAT software connected to the 9-bus WSCC benchmark power system, which is then used to study the impact of a CAES facility in the transient and frequency stability of the system. Several contingencies are simulated comparing the CAES performance to a gas turbine and a base-case without storage, demonstrating that the CAES system improves the system transient stability due to its charging stage, controls, and additional inertia. Finally, the CAES model is used to study the effects of cavern sizes in the frequency of the system. It is shown that CAES systems have certain special characteristics that make them attractive as a storage technology to provide stability and regulation services, besides their energy arbitrage capabilities. [ABSTRACT FROM AUTHOR]

Energy storage systems (ESSs) have been applied in power systems for a long time. It participates in the grid frequency control at two levels, the primary frequency control and the secondary frequency control. In this paper, a control strategy that integrates one synchronous generator (SG) and ESS as one single generation unit named flexible generator (FG) is proposed, allowing ESS to participate in primary frequency control. The main trick is that the proposed control strategy not only adopts SG's frequency as the ESS control input but also feeds back FG's total output power to control the ESS. FGs have more substantial damping and stability than SGs. The proposed control strategy has a superior performance compared to traditional PID control and fuzzy control strategies of ESSs. The flexible control parameters are determined by the linear quadratic regulator (LQR) with disturbance suppression. The ESS's capacity is discussed and determined. Simulation results of the New England 39-bus system verify the advantages of FGs both in load changes and faults. The HIL experiment results also illustrate the applicability and effectiveness of the flexible control. [ABSTRACT FROM AUTHOR]

Wide-area damping controller (WADC) is a very effective tool to damp out the low-frequency oscillation in wide-area power systems. However, the WADC needs communication networks to transmit remote signals; hence, the network-induced delay and packet dropout are inevitably introduced in the communication of wide-area measurement systems (WAMS). In order to effectively compensate delay and packet dropout, in this paper, a new wide-area dynamic damping controller (WADDC) is designed. Firstl the discrete-time model of power system with random delay, packet dropout, and external disturbance is established. Then, the WADDC based on robust H∞ control is designed and the sufficient condition about stability of the closed-loop system is given. Finally, the controller designed in this paper is tested on the two-area four-machine power system and the 16-machine 68-bus system. Simulation results demonstrate the effectiveness the proposed methods for damping out the low-frequency oscillation and compensating the network-induced delay and packet dropout. [ABSTRACT FROM AUTHOR]

This paper introduces a new approach, based on faster-than-real-time (FTRT) analysis, to predict out-of-step (OOS) condition of a turbine-generator (T-G) unit subsequent to a fault scenario. The proposed FTRT analysis is based on 1) solving a state-space model of the T-G electromechanical system and corresponding controllers without the need for online measurements, and 2) an estimated Thevenin equivalent of the rest of the power system. The measurement-free FTRT analysis is carried out after the Thevenin parameters are estimated subsequent to the fault clearance instant. Equal area criterion is applied on the predicated variables to detect OOS condition. A reliable decision can be made based on this approach, since it does not involve simplifying assumptions contrary to the existing approaches. The FTRT approach accurately considers the impacts of the detailed model of the generator, automatic voltage regulator, prime mover, governor system, and the host power system. This paper provides detailed mathematical formulation for the proposed OOS detection method and verifies its feasibility and accuracy based on single machine and large test systems. The proposed approach is also implemented on an industrial platform and evaluated. The results confirm that the proposed approach can accurately identify OOS conditions, earlier than the rotor angle noticeably increases. [ABSTRACT FROM AUTHOR]

This paper presents a fundamental study of voltage collapses that occur on a post-fault trajectory of a stressed power system in seconds after large disturbances. The focus of the study are voltage collapses that are induced by certain load models. Using an n-machine-N-bus power system model, the paper explicitly shows that the voltage collapse is caused by the non-existence of a real, positive solution for a load voltage magnitude in different areas of a relative rotor angle space when the load is of non-linear type. These “areas without voltage solution” are denoted as Voltage Impasse Regions (VIR) and are mathematically characterized as trigonometric functions of (n -1) relative rotor angles. Once the post-fault trajectory enters a VIR, voltage magnitude solutions become complex or negative, the algebraic Jacobian becomes singular, and the behaviour of a system becomes undefined. The case study has been carried out using a simple 3-machine-1-load system with static load models. In the study, VIR appeared and enlarged as the non-linear (constant power and constant current) load increased. Furthermore, the non-convergence of time-domain solution occurred exactly at VIR, thereby confirming that the problem is of structural nature. [ABSTRACT FROM PUBLISHER]

This paper examines the impact of dynamic interactions between the voltage source converters (VSCs) on the small-signal stability of an AC/MTDC (multiterminal dc) power system. The examination is carried out based on a closed-loop interconnected model consisted of an open-loop VSC subsystem and an open-loop subsystem of the rest of MTDC network (RDCN). Open-loop modal coupling is the modal condition that an oscillation mode of open-loop VSC subsystem is close to an oscillation mode of open-loop subsystem of the RDCN on the complex plane. Analysis indicates that the open-loop modal coupling may very likely degrade the small-signal stability of the AC/MTDC power system. If a VSC uses the active power control, the open-loop VSC subsystem is of no oscillation mode. Hence, open-loop modal coupling between the VSCs cannot occur in the MTDC network implementing the master–slave control. Whilst the open-loop modal coupling may introduce instability risk to the MTDC network using the dc voltage droop control. Therefore, the paper reveals the mechanism about how and why the dynamic interactions between the VSCs may degrade the small-signal stability of the AC/MTDC power system from the perspective of the system modal condition—the open-loop modal coupling. [ABSTRACT FROM PUBLISHER]

This paper examines distribution systems that have a high integration level of distributed energy resources (DERs), and addresses the design of local control methods for real-time voltage regulation. Particularly, the paper focuses on proportional control strategies wherein the active and reactive power output of DERs are adjusted in response to (and proportionally to) local changes in voltage levels. The design of the voltage-active power and voltage-reactive power characteristics leverages suitable linear approximations of the ac power flow equations and is network-cognizant; that is, the coefficients of the controllers embed information on the location of the DERs and forecasted noncontrollable loads/injections and, consequently, on the effect of DERs power adjustments on the overall voltage profile. A robust approach is pursued to cope with uncertainty in the forecasted noncontrollable loads/power injections. The stability of the proposed local controllers is analytically assessed and numerically corroborated. [ABSTRACT FROM AUTHOR]

The paper presents a comprehensive study of small-signal stability analysis of power systems based on matrix pencils and the generalized eigenvalue problem. Both primal and dual formulations of the generalized eigenvalue problem are considered and solved through a variety of state-of-the-art solvers. The paper also discusses the impact on the performance of the solvers of two formulations of the equations modelling the power systems, namely, the explicit and semi-implicit form of differential-algebraic equations. The case study illustrates the theoretical aspects and numerical features of these formulations and solvers through two real-world systems, namely, a 1,479-bus model of the all-island Irish system, and a 21,177-bus model of the ENTSO-E network. [ABSTRACT FROM PUBLISHER]

This paper establishes a closed-loop interconnected dynamic model of a power system with a doubly fed induction generator (DFIG) for wind power generation, wherein, the DFIG and power system are modeled as two open-loop interconnected subsystems. The established model indicates that the impact of the dynamic interactions introduced by the DFIG on the power system's small-signal angular stability is the difference between the closed-loop and open-loop electromechanical oscillation modes (EOMs). The analysis conducted in this study reveals that when an open-loop DFIG oscillation mode (DOM) is close to an open-loop EOM on the complex plane, the modal coupling of the open-loop EOM and DOM can cause strong dynamic interactions between the DFIG and the power system; thus, the DFIG has a significant impact on the power system's small-signal angular stability. An example multimachine power system with grid-connected DFIGs is presented to demonstrate and validate the analysis and conclusions made in the paper. [ABSTRACT FROM PUBLISHER]

The proliferation of inverter-based generation and advanced sensing, controls, and communication infrastructure have facilitated the accelerated deployment of microgrids. A coordinated network of microgrids can maintain reliable power delivery to critical facilities during extreme events. Low-inertia offered by the power-electronics interfaced energy resources, however, can present significant challenges to ensuring stable operation of the microgrids. In this work, distributed small-signal stability conditions for inverter-based microgrids are developed that involve the droop-controller parameters and the network parameters (e.g. line impedances, loads). The distributed closed-form parametric stability conditions derived in this paper can be verified in a computationally efficient manner, facilitating the reliable design and operations of networks of microgrids. Dynamic phasor models have been used to capture the effects of electromagnetic transients. Numerical results are presented, along with PSCAD simulations, to validate the analytical stability conditions. Effects of design choices, such as the conductor types, and inverter sizes, on the small-signal stability of inverter-based microgrids are investigated to identify interpretable stable/unstable region estimates. [ABSTRACT FROM AUTHOR]

Voltage stability assessment on a deterministic direction of loading variation may provide misleadingly high values of voltage stability margin due to uncertainties in load forecast. On the other hand, by disregarding loading forecast information and computing the worst case scenario, we may obtain unrealistic and very conservative margin values. This paper proposes a new voltage stability index that takes place between these two approaches. In this proposal, a set of credible loading variation directions is considered and the closest bifurcation point is determined within this set. A fast method for computation of this index is also proposed. The method is able to detect both saddle-node and limit-induced bifurcations. The efficiency of the proposed method is confirmed by means of numerical simulation on different power systems. [ABSTRACT FROM AUTHOR]

Based on the knowledge accumulated off-line and feature extractions, a novel data-based learning and control method is proposed for the long-term voltage stability problem in this paper. All the spatial-temporal data is considered and the features of different emergency events are extracted by principle component analysis which can reduce the dimension and reveal the significant internal structure of the data. An artificial neural network is used to build a classifier to reinforce the relationship directly between the system dynamics and optimal control actions. With the prepared control knowledge, it is faster to find an optimal control action online with a good system performance. Simulation results on the 6-bus system, New England 39-bus system and Iceland 189-bus system are given to show the potential of this method for on-line control. [ABSTRACT FROM AUTHOR]

Recently, the low-frequency oscillation (LFO) frequently happens in the vehicle-grid system of high-speed railways when electric multiple units (EMUs) are put into operation. As a possible solution, a single-phase cascaded H-bridge static synchronous compensator (CHB-STATCOM) directly connected to the traction network is applied to dynamically compensate the reactive power of vehicle-grid system. This paper focuses on the impedance modeling and stability analysis in the vehicle-grid system with CHB-STATCOM. Firstly, the vehicle-grid system is simplified to a single-phase rectifier with large grid inductance. The accurate dq-frame impedance of the rectifier system with CHB-STATCOM is derived in detail. Secondly, through the generalized Nyquist stability criterion (GNSC), the influence of CHB-STATCOM and its different control parameters on the stability of rectifier system is revealed. Thirdly, the excellent performance of CHB-STATCOM in suppressing the LFO and the accuracy of theoretical analysis are verified via time-domain simulations. Finally, to further verify the effectiveness of CHB-STATCOM in real applications, a dSPACE based controller hardware-in-the-loop (HIL) simulation platform is established, which includes the physical control circuits of eight EMUs. The experimental results show that the CHB-STATCOM has a good dynamic compensation effect and can efficiently suppress the LFO. [ABSTRACT FROM AUTHOR]

Retaining frequency stability is becoming increasingly challenging as the power system incorporates more non-synchronous generation. Assessing the frequency stability in a system has been predominantly completed by focusing on the quantity of connected synchronous kinetic energy in the system, or inertia. This traditionally was considered a function of generator construction – network factors typically were not considered. The research in this paper investigates how network topology, power flow, droop gain distribution, and inertia distribution all impact frequency stability. A generic four-area model has been created that allows discrete system setups. This research has shown that certain topologies lead to a more severe rate of change of frequency. A key finding is that the frequency drop is further increased when there is greater power flow into the area that experiences the disturbance. The extent to which the rate of change of frequency and frequency drop are influenced differently is emphasized, highlighting the need to procure different services depending on which metric is of primary significance at a specific location. [ABSTRACT FROM AUTHOR]

This paper develops a hierarchical deep learning machine (HDLM) to efficiently achieve both quantitative and qualitative online transient stability prediction (TSP). For the sake of improving its online efficiency, multiple generators’ fault-on trajectories as well as the two closest data-points in pre-/post-fault stages are acquired by PMUs to form its raw inputs. An anti-noise graphical transient characterization technique is tactfully designed to transform multiplex trajectories into 2-D images, within which system-wide transients are concisely described. Then, following the divide-and-conquer philosophy, the HDLM trains a two-level convolutional neural network (CNN) based regression model. With stability margin regressions hierarchically refined, it manages to perform reliable and adaptive online TSP almost immediately after fault clearance. Test results on the IEEE 39-bus test system and the real-world Guangdong Power Grid in South China demonstrate the HDLM's superior performances on both stability status and stability margin predictions. [ABSTRACT FROM AUTHOR]

This paper proposes an interconnection and damping assignment passivity-based control (IDA-PBC) for multimachine power systems including hydro-turbine governing systems (HTGS) with surge tank. The main objective is to stabilize the rotor speed and regulate the terminal voltage of each synchronous machine in a power system. The proposed control is decentralized, thus avoiding challenges of communication between generators. Passivity theory is used since the open-loop of the HTGS presents a port-Hamiltonian structure. IDA-PBC allows a control law that maintains the passive structure in closed-loop, guaranteeing its asymptotic stability using Lyapunov's theory. The dynamics of each HTGS are described by an eleventh-order model, which can be reduced to a tenth-order. The proposed control is tested in a 12-bus test system and compared to a standard control, which considers a voltage regulator and exciter based on the IEEE type ST1A excitation system model and power system stabilizer IEEE-PSS1A. The governing system based on a PID control with static and transient droop is also employed. Additionally, the proposed controller is compared to a sliding mode controller. Time-domain simulations demonstrate the robustness and appropriate performance of the proposed decentralized control under different large disturbances. [ABSTRACT FROM AUTHOR]