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Time-domain indirect methods based on Lyapunov stability theory and linear matrix inequality techniques (LMIs) have been applied for delay-dependent stability analysis of large-scale load frequency control (LFC) schemes. This paper aims to enhance the numerical tractability of large-scale LMIs by exploiting the special characteristics of the LFC loops. First, in the typical LFC model, only a few delayed states that are directly influenced by transmission delays are distinguished from other normal system states. Hence, an improved reconstruction model is formed, based on which the delay-dependent stability condition is established with the decreased order of the LMIs and decision variables. Then, to further improve the numerical tractability of the developed stability criterion, all weighting matrices required in the augmented Lyapunov functional are enforced to have structural restrictions by proposing an extended symmetry-exploiting technique. Case studies show that the method proposed in this paper significantly improves the calculation efficiency of stability criterion established for multi-area power systems at the cost of only a minor reduction in computational accuracy. [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]

This paper proposes a method to design power system stabilizers (PSSs) based on single-machine infinite-bus system models to mitigate the risk of low-frequency electro- mechanical power oscillations in an N-machine power system. First, models of N fabricated identical-machine power systems are established for the N-machine power system. Analysis in the paper indicates that the electromechanical oscillation mode of fabricated identical-machine power systems with the least damping is of less damping than the electromechanical oscillation modes of N-machine power system. Second, it is proved that models of fabricated identical-machine power systems are dynamically equivalent to the single-machine infinite-bus system models. Finally, it is suggested that the PSSs are designed using single-machine infinite-bus system models to enhance the least damped electromechanical oscillation mode of fabricated identical-machine power systems. This eventually improves the damping of electromechanical oscillation modes of N-machine power system, thus mitigating the risk of low-frequency electromechanical power oscillations. In the paper, the proposed method is demonstrated and evaluated by using three well-known example multi-machine power systems. Effectiveness of PSSs is confirmed by the results of modal computation and simulation. [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]

Aggregated loads of induction motors are often used in the study of power system dynamic stability. This paper reports the finding that aggregation of the same or similar induction motors may likely cause the dynamic instability. Theoretical analysis is presented in the paper to show that a group of N same induction motors in parallel connection is equivalent to N dynamic independent subsystems. Oscillation modes of one of the equivalent subsystems are affected by the number of induction motors. Hence, when the number of induction motors increases, it is possible that the oscillation modes of the group of induction motors may move toward the right on the complex plane, leading to the dynamic instability in the worst case. The analysis explains why aggregation of induction motors may possibly bring about the risk of power system dynamic instability. In this paper, case studies of an example power system with a cluster of induction motors are presented. Results of modal computation and simulation demonstrate that when the number of induction motors increases, aggregation of the same or similar induction motors leads to the dynamic voltage instability and growing low-frequency electromechanical power oscillations in the test case. [ABSTRACT FROM AUTHOR]

This paper discusses a recent event in the western American power system when a forced oscillation was observed at a frequency that was close to a well-known 0.38-Hz inter-area electromechanical mode frequency of the western system. The event motivates a systematic investigation in this paper on the possibility of resonant interactions between forced oscillations and electromechanical inter-area oscillatory modes in power systems. When the natural oscillatory mode of a power system is poorly damped, and the forced oscillation occurs at a frequency close to system mode frequency at critical locations for the mode, resonance is observed in simulation test cases of the paper. It is shown that the MW oscillations on tie-lines can be as high as 477 MW from a 10-MW forced oscillation in Kundur test system because of resonance. This paper discusses the underlying system conditions and effects as related to resonance in power systems caused by forced oscillations and discusses ways to detect such scenarios using synchrophasors. Simulated data from Kundur two-area test power system as well as measurement data from western American power system are used to study the effect of forced oscillations in power systems. [ABSTRACT FROM AUTHOR]

Transient stability of a power system can be significantly affected by wind power generators due to their stochastic power output and complex dynamic characteristics. This paper proposes a robust optimization approach for coordinating generation dispatch and emergency load shedding against transient instability under uncertain wind power output. The problem is modelled as a two-stage robust optimization (TSRO) model considering transient stability constraints, where the first-stage is to optimize the generation dispatch (preventive control) before a contingency and the second-stage decision is the emergency load shedding (emergency control) after the contingency occurrence under the worst case of wind power variation. To solve this TSRO problem, this paper also proposes a solution algorithm which integrates transient stability assessment and transient stability constraint construction in a column and constraint generation framework. The proposed method is validated on the New-England 39-bus system and the Nordic32 system, which shows high computational efficiency and stability robustness against uncertain wind power. [ABSTRACT FROM AUTHOR]

Phase angle measurements from synchrophasors show discontinuities when they roll over from +180 to -180 degrees or vice versa. This paper proposes efficient strategies for unwrapping of the angles in real-time data streams. Examples presented in this paper first show that the phase angle differences across bus voltage phasors can go over 360 degrees in a synchronized power system under stressed conditions. Unwrapped phase angles are shown to be useful in fast reliable islanding detection methodology, and for phase angle arithmetic such as for averaging of phase angles and for phase angle difference calculations. Strategies for handling missing phase angle data in real-time data streams are also discussed. [ABSTRACT FROM PUBLISHER]

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]

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 proposes a control scheme to improve the dynamic response of power systems through the automatic regulators of converter-based Distributed Energy Resources (DERs). In this scheme, both active and reactive power control of DERs are varied to regulate both frequency and voltage, as opposed to current practice where frequency and voltage controllers are decoupled. To assess the proposed control against the current state-of-art, the paper also defines a metric that captures the combined effect of frequency/voltage response at any given bus of the network. Results indicate that the proposed control strategy leads to a significant improvement in the stability and performance of the overall power system. These results are based on a comprehensive case study carried out by employing a modified version of the IEEE 39-bus benchmark system, where a portion of the synchronous machines is substituted by converter-interfaced DERs. The impact on the proposed control of load models, the $R/X$ ratio of network lines, as well as the level of DER penetration to the grid, are properly evaluated and conclusions are duly drawn. [ABSTRACT FROM AUTHOR]

Microgrid's voltage regulation is of particular importance during both grid-connected and islanded modes of operation. Especially, during the islanded mode, when the support from the upstream grid is lost, stable voltage regulation is vital for the reliable operation of critical loads. This paper proposes a robust and data-driven control approach for secondary voltage control of AC microgrids in the presence of uncertainties. To this end, unfalsified adaptive control (UAC) is utilized to select the best stabilizing controller from a set of pre-designed controllers with the minimum knowledge required from the microgrid. Two microgrid test systems are simulated in MATLAB to verify the effectiveness of the proposed method under different scenarios like load change and communication link failure. [ABSTRACT FROM AUTHOR]

Extreme events can cause severe power system damage. Resilience-driven operation of networked microgrids (MGs) has been heavily studied in literature. There is, though, little research considering the influence of resilience on decision making for planning. In this paper, a three-level model is suggested to solve the optimal sizing problem of networked MGs considering both resilience and cost. In the first level, a meta-heuristic technique based on an adaptive genetic algorithm (AGA) is utilized to tackle the normal sizing problem, while a time-coupled AC OPF is utilized to capture stability properties for accurate decision-making. The second and third levels are combined as a defender-attacker-defender model. In the former, the suggested AGA is utilized to generate attacking plans capturing load profile uncertainty and contingencies for load shedding maximization, while a multi-objective optimization problem is suggested for the latter to obtain a trade-off between cost and resilience. Simulations considering meshed networks and load distinction into critical and non-critical are developed to demonstrate algorithm effectiveness on capturing resilience at the planning stage and optimally sizing multiple parameters. The results indicate that higher resilience levels lead to higher investment cost, while sizing networked MGs leads to decreased investment in comparison with standalone MGs sizing. [ABSTRACT FROM AUTHOR]

This paper discusses the impact of discrete secondary controllers on the dynamic response of power systems. The idea of the paper originates from the observation that there is a range of values, from few tens of seconds to few minutes, of the execution cycles of conventional automatic generation control (AGC) that leads to a limit cycle. Below and above this range the system is stable. This is certainly not a problem in practice as the AGC updates the power set points of generating units every few seconds. However, this phenomenon has interesting consequences if one considers real-time electricity markets with short dispatch periods (i.e., 5 minutes) as these markets can be modeled as a sort of AGC. The paper first provides a formal analogy between conventional AGC and real-time electricity markets. Then it shows that the discretization-driven instability exists if the system includes a real-time electricity market modeled as secondary frequency controller. Finally, the paper discusses the impact of the combined effect of high wind generation shares and discrete secondary controllers on power system dynamics. [ABSTRACT FROM AUTHOR]

This paper examines the dynamic aggregation of a group of M same wind turbine generators (WTGs) in a parallel connection. The group of WTGs could either be a part of a grid-connected wind farm or constitute the entire wind farm. Analytical derivation in this paper indicates that the group of M same WTGs is equivalent to M dynamically independent subsystems. Each of the subsystems is comprised of a single WTG. Hence, the dynamic aggregation of a grid-connected group of same WTGs in a parallel connection can be represented by grid-connected single-WTG subsystems for studying the oscillation stability. Further analysis in this paper reveals that when the number of WTGs in a parallel connection increases, it is possible that oscillation modes of the group of WTGs may move into the right half of a complex plane. Thus, the dynamic coupling of the increasing number of WTGs in a parallel connection may likely cause growing oscillations in the wind farm. An example grid-connected DFIG wind farm is used to demonstrate and evaluate the analysis and conclusions made in this paper. The oscillation stability of the example wind farm was examined when the dynamic models of a group of DFIGs in a parallel connection in the example wind farm were identical and different. [ABSTRACT FROM AUTHOR]

In this paper, an expression for the Cramér–Rao bound (CRB) on the frequency and damping of electromechanical modes is derived. This provides an invaluable tool when documenting the performance capabilities of mode meter algorithms, as the CRB is used as a benchmark to which mode meter variance may be compared. It is shown that the derived CRB expression is supported by several well-known mode estimation phenomena, and it is numerically validated using the asymptotically efficient Prediction Error Method (PEM) on Monte Carlo simulations of an autoregressive moving average (ARMA) model. Finally, a practical use case is given, in which the CRB on the frequency and damping of an inter-area mode from the miniWECC system is used to compare the performance of several well-known mode meters in a study of how sample size affects accuracy. [ABSTRACT FROM AUTHOR]

This paper proposes a Principal Component Analysis (PCA)-based method to construct composite indices to rapidly assess power system transient stability. By assigning appropriate weights to a few selected sub-indicators, a composite index can be constructed to guarantee a better coverage of worst-case stability scenarios of the power system. This paper provides an automatic method to construct a composite index with four sub-indicators calculated by the integral of acceleration, speed deviation and rotor angle of generators over a certain integration period using PCA. The effectiveness of the sub-indicators is validated first, followed by a comprehensive example of process of composite index construction, and the assessment of the influence of the effect of integration period on the performance of the composite index. High accuracy of classification has been demonstrated using composite index with appropriate settings of the integration periods of the sub-indicators. [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 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]

This paper proposes a direct damping feedback control method against power system oscillations under small or large disturbances. For a targeted oscillation mode, this control method continuously minimizes the difference between the real-time estimated damping ratio and a desired value by changing power outputs of selected inverter-based resources. The method adopts a proportional-integral controller whose parameters are tuned using a nonlinear single-input-single-output model on damping estimation and control with a single-oscillator equivalent regarding the targeted power system mode. Also, optimization of these controller parameters considers both robustness and time performance in damping control. The paper also proposes utilizing a “zero-th order” parametric resonance phenomenon to simplify the controller design. Tests on a small power system and a 140-bus 48-machine Northeast Power Coordinating Council system validate the effectiveness of the proposed damping controller utilizing battery-based energy storage systems. [ABSTRACT FROM AUTHOR]

A large number of non-linear hardware and control units exists in power electronic system used in grid connected devices. The analytical transient stability analysis of grid-connected converters presents numerous difficulties. A common method to tackle this problem is the stability analysis using Lyapunov’s method. By applying this method, difficulties arise not only from finding a suitable Lyapunov function, but also from checking the constraint of Lyapunov stability. If the appropriate Lyapunov function is a high-order polynomial, it is very challenging to test if it meets the constraints of Lyapunov stability in certain regions. In this paper, the sum-of-squares programming method is used to obtain the estimation of a converter’s domain of attraction with a relatively small number of iterations compared to classically applied methods, such as the Monte Carlo method. The estimation of the domain of attraction are verified by time-domain simulations and StarSim’s controller hardware-in-the-loop tests in this paper. [ABSTRACT FROM AUTHOR]

This paper proposes a control-oriented energy function (COEF) based on passivity for transient stability control (TSC) of power systems and investigates the feasibility of an iterative process using the COEF for determining generation shedding (GS) requirements for real-time TSC, in particular, for severe cases when autoreclosing fails due to permanent faults. The COEF for TSC set up in this paper gives directly the GS requirement without calculations of stability region and Critical Clearing Time, and exempts all modeling assumptions except for nonnegative damping the generator models. The simulation with the full planning model of Western Electricity Coordinating Council system shows that the passivity-based COEF for TSC offers a concise, practical, and effective index for GS determination for transient stability control of power systems, which is particularly suitable for the Remedial Action Schemes that BC Hydro has been using. [ABSTRACT FROM AUTHOR]

In this paper, detectability analysis is studied and extended to guide selection of measurements for the dynamic state estimation (DSE) of a synchronous machine. To make sure that the DSE converges, past studies suggested that enough measurements must be available to make the system observable. In this paper, the convergence condition is relaxed via detectability analysis to reduce the number of required measurements. Because the objective of the DSE is to estimate the current states as time progresses, it is shown that a DSE observer can converge not only for an observable system but also for an unobservable system if the eigenvalues corresponding to the unobservable states are stable. Simulation results using the IEEE 10-machine, 39-bus system show that the unscented-Kalman-filter-based DSE can converge when measurements are chosen such that the unobservable states have stable eigenvalues. In comparison with observability analysis, the proposed application of detectability analysis can reduce the number of measurements required for the existence of a DSE observer. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach for power system dynamic simulation based on the differential transformation (DT). The DT is introduced to study power systems as high-dimensional nonlinear dynamical systems for the first time, and is able to avoid computations of high-order derivatives with nonlinear differential equations by its transform rules. This paper, first, proposes and proves several new transform rules for generic nonlinear functions that often appear in power system models, and then uses these rules to transform representative power system models such as the synchronous machine model with trigonometric functions and the exciter model with exponential and square root functions. This paper also designs a DT-based simulation scheme that allows significantly prolonged time steps to reduce simulation time compared to a traditional numerical approach. The numerical stability, accuracy, and time performance of the proposed new DT-based simulation approach are compared with widely used numerical methods on the IEEE 39-bus system and Polish 2383-bus system. [ABSTRACT FROM AUTHOR]

Case-by-case study in the literature has found from the results of numerical computation and simulation that a grid-connected virtual synchronous generator (VSG) can maintain the stability under the condition of extremely weak grid connection. This paper presents the theoretical proof to the finding and thus, generally concludes that the grid-connected VSG is immune to the instability risk under the condition of weak grid connection. In addition, the paper extends the theoretical proof to the case of a grid-connected PMSG wind farm with multiple VSGs. An example grid-connected PMSG wind farm with twenty VSGs is presented to demonstrate and evaluate the theoretical analysis and conclusion made in the paper. [ABSTRACT FROM AUTHOR]

Co-simulation of heterogeneous systems allows for in-depth analysis of various aspects of power systems’ operation while staying within the environments of the simulation tools that are best fit to represent their respective domains. Equipped with a proprietary co-simulation platform, the paper focuses on the issue of power-conjugate coupling between parts of power grids modeled in transient stability and electromagnetic transient simulation tools. The problems of co-simulation stability and precision in presence of delays are tackled by means of designing a proper coupling interface. It is shown that two established interface methods – the V-I method and the Transmission Line Interface – are special cases of a generalized interface framework proposed in the paper. Moreover, a new interface algorithm is described by parametrizing the generalized framework. Analytical tools are also formulated to aid in the analysis of interface stability and precision via the concepts of passivity and transparency. Simulation results of benchmark systems of various complexity demonstrate the application of the developed power coupling interface. [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]

This paper proposes a systematic and general approach to model correlated stochastic processes in power systems by means of stochastic differential-algebraic equations. The paper discusses the theoretical background of stochastic differential-algebraic equations and provides a variety of examples of correlated stochastic models for power system applications. With this aim, stochastic processes with Normal and Weibull distributions are considered. The case study utilizes the well-known two-area system to demonstrate that the presence of correlation between the stochastic processes can cause instability, despite the fact that the same system is stable if the same processes are uncorrelated. The case study also considers a 1479-bus dynamic model of the all-island Irish transmission system to show the scalability of the proposed technique, and to compare scenarios with different levels of correlation among stochastic processes. Results indicate that correlation has a non-negligible impact on short-term dynamics. A high level of correlation among the processes, in fact, can give raise to instability. [ABSTRACT FROM AUTHOR]

As power systems are undergoing a significant transformation with more uncertainties, less inertia and closer to operation limits, there is increasing risk of large outages. Thus, there is an imperative need to enhance grid emergency control to maintain system reliability and security. Towards this end, great progress has been made in developing deep reinforcement learning (DRL) based grid control solutions in recent years. However, existing DRL-based solutions have two main limitations: 1) they cannot handle well with a wide range of grid operation conditions, system parameters, and contingencies; 2) they generally lack the ability to fast adapt to new grid operation conditions, system parameters, and contingencies, limiting their applicability for real-world applications. In this paper, we mitigate these limitations by developing a novel deep meta-reinforcement learning (DMRL) algorithm. The DMRL combines the meta strategy optimization together with DRL, and trains policies modulated by a latent space that can quickly adapt to new scenarios. We test the developed DMRL algorithm on the IEEE 300-bus system. We demonstrate fast adaptation of the meta-trained DRL polices with latent variables to new operating conditions and scenarios using the proposed method, which achieves superior performance compared to the state-of-the-art DRL and model predictive control (MPC) methods. [ABSTRACT FROM AUTHOR]

Ensuring long-term voltage stability is critical for reliable operations of power grids. High share of distributed energy resources (DERs) can create complicated system operation modes that may invalidate the traditional long-term voltage stability analysis based on typical operation modes. To address this challenge, this paper investigates how to compute the shortest path to the voltage stability boundary in the DER aggregated load space with large dispersion. Instead of working in the Euclidean space, we establish the analysis and computations on the algebraic power flow manifold to better capture the curvature change of the shortest path along the direction of losing stability. A modified optimal control framework is presented for obtaining the ground-truth of the smooth shortest path on the manifold. To efficiently and accurately solve for the shortest path, we further leverage the geometric features of the power flow manifold and propose a tri-sectional approximation model that is scalable for large-scale systems. Several numerical examples, up to the 1354-bus system, with different DER penetration levels and high dimensional renewable power injection variations are evaluated. The simulation results demonstrate that the tri-sectional approximation achieves high accuracy and efficiency to approximate the shortest path to the voltage stability boundary. [ABSTRACT FROM AUTHOR]

In many power systems, the increased penetration of inverter-based renewable generation will cause a decrease in kinetic energy storage, leading to higher frequency excursions after a power disturbance. This is the case of the future Nordic Power System (NPS). The look-ahead study reported in this paper shows that the chosen units participating in Frequency Containment Reserves (FCR) cannot keep the frequency above the prescribed threshold following the outage of the largest plant. This analysis relies on a detailed model of the Northern European grid. The latter is compared to the classical single-mass equivalent, and the impact of voltage-dependent loads is assessed in some detail. Next, the paper focuses on emergency power control of the HVDC links that connect the NPS to the rest of the European grid, which can supplement or even replace part of the FCR. The proper tuning of that control is discussed. Finally, the analysis is extended to the HVDC links connecting the future North Sea Wind Power Hub under two configurations, namely low and zero inertia. The impact of outages in the latter sub-system is also assessed. The material to simulate the system with industrial software is made publicly available. [ABSTRACT FROM AUTHOR]

The high penetration of renewables has sparked new oscillatory concerns in hybrid AC/DC grids. Knowledge of the oscillation regarding its source and propagation mechanism, is crucial to system operation. In this respect, the frequency-domain modal analysis (FMA) provides a way (e.g., participation factor) to extract these oscillation properties, and has been widely applied in converter-based AC grids. Compared to AC grids, oscillation properties of hybrid AC/DC grids are much more complex. Such complexity mainly originates from the diversity of oscillation propagation behaviors in hybrid AC/DC grids, where a distinctive local-area oscillation will emerge. Therefore, a dedicated oscillation propagation analysis for hybrid AC/DC grids is desired, which is the main focus of this paper. First, the mechanism of the distinctive local-area oscillation is analyzed considering AC/DC coupled dynamics of converters. Then, a systematic method for the oscillation propagation analysis is presented, where indices for characterizing the local-area oscillation and its impact area are established. Finally, some propagation properties are discussed, by which a strategy for the online oscillation source locating is designed. Case studies are carried out in a typical hybrid AC/DC grid to validate the propagation analysis in this paper. [ABSTRACT FROM AUTHOR]

Online transient analysis plays an increasingly important role in dynamic power grids as the renewable generation continues growing. Traditional numerical methods for transient analysis not only are computationally intensive but also require precise contingency information as input, and therefore, are not suitable for online applications. Existing online transient assessment studies focus on the determination of post-contingency system stability or stability margin. This paper develops a novel graph-learning framework, Deep-learning Neural Representation or DNR, for online prediction, of the time-series trajectories of the system states using initial system responses that can be measured by phasor measurement units (PMUs). The proposed DNR framework consists of two sequential modules: a Network Constructor that captures network dependencies among generators, and a Dynamics Predictor that predicts the system trajectories. The key to improved prediction performance is the introduction of the spatio-temporal message-passing operations into graph neural networks with structural knowledge. Its effectiveness and scalability are validated through comparative studies, demonstrating the prediction performance under different contingency scenarios for systems of different sizes. This framework provides a solution to online predicting post-fault system dynamics based on real-time PMU measurements. Additionally, it can also be applied to facilitate the offline transient simulation without simulating the entire trajectories. [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 loss of small signal stability under parameter variation (e.g., fluctuation of loads and wind powers) can be ascribed to local bifurcations, i.e., saddle-node, Hopf, singularity-induced, and limit-induced bifurcations. Classic bifurcation calculation methods like the direct method and continuation method can only provide a bifurcation point or two-parameter bifurcation curve. Based on Galerkin method and the implicit function theorem, this paper proposes accurate polynomial approximations of bifurcation hypersurfaces in the multi-dimensional parameter space of interest. The proposed method can ensure high accuracy in this parameter space, and thus is preferable to the existing Taylor expansion-based local approximation method, given the intrinsic large-variation characteristic of wind powers. Acquired bifurcation hypersurfaces are immediately used to construct the small signal stability region of the continuous system, and then compute the stability margin for the operating point subjected to uncertainty of wind generation. Besides, the validity scope of the proposed method is analyzed, and the handling of limit-triggered equation switching as well as its computational difficulty is discussed. Computational results on the two-parameter 11-bus two-area and six-parameter IEEE 145-bus test systems validate the high accuracy and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The paper provides a novel framework to study the accuracy and stability of numerical integration schemes when employed for the time domain simulation of power systems. A matrix pencil-based approach is adopted to evaluate the error between the dynamic modes of the power system and the modes of the approximated discrete-time system arising from the application of the numerical method. The proposed approach can provide meaningful insights on how different methods compare to each other when applied to a power system, while being general enough to be systematically utilized for, in principle, any numerical method. The framework is illustrated for a handful of well-known explicit and implicit methods, while simulation results are presented based on the WSCC 9-bus system, as well as on a 1,479-bus dynamic model of the All-Island Irish Transmission System. [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]

Voltage regulation and proper load-sharing are two main control objectives of DC microgrids which the consensus-based secondary control can be regarded as a feasible approach to achieve them. Using this approach, in addition to the stable voltage regulation, the load is shared according to the nominal potential of the distributed generation units. Nevertheless, the conventional consensus-based secondary control uses the time-triggered communication paradigm that leads to a high communication burden due to transmitting and receiving unnecessary data. In this paper, to prevent excessive data-exchanging, the mentioned approach is upgraded with a novel event-triggered scheme. The system stability analysis under the suggested event-triggered secondary controller is assessed using the Lyapunov theorem. Furthermore, the Zeno-freeness feature of the proposed solution is mathematically proved after assessing uniformly ultimately bounded stability and extracting the current per-unit and voltage derivatives dynamic as the consensus algorithm’s external inputs. The proposed approach is applied to a DC microgrid, and its performance is validated under different scenarios using Simulink/MATLAB environment. Moreover, the experimental tests prove the merits of the suggested method. [ABSTRACT FROM AUTHOR]

This paper proposes a data-driven small-signal stability constrained optimal power flow (SSSC-OPF) method with high computational efficiency. Instead of repeating the computational expense small-signal stability analysis via differential and algebraic equations during the iterative OPF process, a computationally cheap surrogate constraint for small-signal stability is developed. To reduce the learning difficulty for small-signal stability boundaries, an efficient sample generation strategy is proposed with sampling space compression. This allows us to use the support vector machine (SVM) with a kernel function to derive the explicit data-driven surrogate constraint for small-signal stability. Penalty factor optimization is proposed to compensate for the error caused by SVM. The learned small-signal stability constraint is embedded into the OPF model for generator control. An examination strategy is also developed to avoid the small-signal instability of re-dispatch caused by the error of the data-driven surrogate model. Comparison results with other model-based and data-driven methods on the IEEE 39-bus and 118-bus systems demonstrate the high computational efficiency and economic benefits of the proposed method. [ABSTRACT FROM AUTHOR]

Penetration of renewable energy resources (RERs) in the power grid continues to increase as we strive toward a greener environment for the future. While they have many advantages, most RERs possess little or no rotational kinetic energy, thereby threatening the frequency stability of future power grids. Energy storage systems (ESSs) can be used to mitigate this problem, as they are capable of providing virtual inertia to the system. This paper proposes a novel analytical approach for sizing ESSs to provide inertial support to the grid and maintain frequency stability in presence of RERs. This method analytically estimates the total inertia of the system using probability distributions of the outage states of conventional generators and RERs. RERs are modeled as multi-state units, considering the variability of their output power due to changes in weather conditions and also the forced outages of their equipment. The ESS is utilized to provide virtual inertia to the grid in the form of active power once the estimated system inertia falls below the minimum required during a disturbance. The efficacy of the proposed approach is tested on the IEEE 39 bus system and the results obtained by the analytical approach are validated using Monte Carlo simulation. [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]

Deep learning (DL) techniques have shown promising performance for designing data-driven power system transient stability assessment (TSA) models. However, due to the deep structure of the DL, the resulting model is always a black-box and hard to explain, which hinders its practical adoption by the industry. This paper proposes an interpretable DL-based TSA model to balance the TSA accuracy and transparency. The proposed method combines the strong nonlinear modelling capability of a deep neural network and the interpretability of a decision tree (DT). Through regularizing DL-based model with the average DT path length in the training process, the proposed interpretable DL-based TSA method can visually explain the TSA decision-making process. Simulation results have shown that the proposed method can deliver highly accurate TSA results and interpretable TSA decision-making rules, which can be used for designing preventive control actions. [ABSTRACT FROM AUTHOR]

This paper investigates a procedure of coordinated tuning of power system decentralized damping controllers based on reduced-order model (ROM). In the paper, the cross-gramian technique is applied to obtain an equivalent ROM for power systems. Once the controllers' locations are selected appropriately, the critical modes are approximated well in the reduced model. The controllers are designed on ROM using search algorithm and then tested on the unreduced system to demonstrate their availability. The benefit of adopting ROM is to decrease the complexity of objective function computation. The proposed method is tested on power systems with 4-machine and 156-machine to validate its efficiency. [ABSTRACT FROM AUTHOR]

Prior research has shown that autocorrelation and variance in voltage measurements tend to increase as power systems approach instability. This paper seeks to identify the conditions under which these statistical indicators provide reliable early warning of instability in power systems. First, the paper derives and validates a semi-analytical method for quickly calculating the expected variance and autocorrelation of all voltages and currents in an arbitrary power system model. Building on this approach, the paper describes the conditions under which filtering can be used to detect these signs in the presence of measurement noise. Finally, several experiments show which types of measurements are good indicators of proximity to instability for particular types of state changes. For example, increased variance in voltages can reliably indicate both proximity to a bifurcation and the location of increased stress. On the other hand, growth of autocorrelation in certain line currents is related less to a specific location of stress but, rather, is a reliable indicator of stress occurring somewhere in the system; in particular, it would be a clear indicator of approaching instability when many nodes in an area are under stress. [ABSTRACT FROM AUTHOR]

Convex hull pricing has been introduced recently to increase transparency and reduce uplift payments for the U.S. wholesale markets. A convex primal formulation approach is one of the most efficient methods to obtain a high-quality convex hull price. Even though significant progress has been made, the co-optimization of energy and ancillary services is much more challenging due to the discrete nature in formulating ancillary services, for example, the regulating reserve commitment variables, which are binary introduced by some Independent System Operators (ISOs), such as Midcontinent ISO (MISO), to capture the special characteristics of certain generators, such as combined-cycle units. In this paper, we propose convex primal formulations for convex hull pricing considering regulating, spinning, and online/offline-supplemental reserves, in which the regulating reserve commitment variables are considered. Accordingly, we can solve a linear program, instead of a mixed-integer program, which is much harder to solve, to derive the minimum uplift payments and exact convex hull price for the case without general ramping constraints. For the case with general ramping constraints, an upper bound of the minimum uplift payment can also be derived. The final computational experiments on MISO cases verify the effectiveness of our approach in solution quality and computational time. [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]

Emergency frequency control is one of the most critical approaches to maintain power system stability after major disturbances. With the increasing number of grid-connected renewable energy sources, existing model-based methods of frequency control are facing up with challenges of computational speed and scalability for large-scale systems. In this paper, the emergency frequency control problem is formulated as a Markov Decision Process and solved through a novel distributional deep reinforcement learning (DRL) method, namely the distributional soft actor critic (DSAC) method. Compared with other reinforcement learning methods that only estimate the mean value, the proposed DSAC model estimates the distribution of value function over returns. This advancement can lead to more insights and knowledge for the agent, with the benefit of a much faster and more stable learning process, and the improved frequency control performance. The simulation results on IEEE 39-bus and IEEE 118-bus systems demonstrate the effectiveness and robustness of proposed models, as well as the advantage compared to other state-of-the-art DRL algorithms. [ABSTRACT FROM AUTHOR]

The paper proposes a technique for the on-line estimation of Thévenin equivalent (TE) which only needs the present phasor measurements. The technique is based on the wide-area measurements including voltage and current phasors of the system loads and synchronous generators, so that it can simultaneously estimate TE of the system seen from the interested buses. The technique has two main steps. In the first step, the conventional impedance matrix $\bar{Z}_{\rm bus}$ is modified to be suitable for TE estimation. In the second step, a correction coefficient based on the sensitivity theory calculated by using two consecutive phasor measurements is applied to correct the diagonal terms of the $\bar{Z}_{\rm bus}$ matrix. Simulation results carried on the IEEE 39-bus and 118-bus test systems show that the proposed technique can accurately estimate the TE for both generation and consumption buses under any load-increase scenario. The comparison scenarios verify the superiority of the proposed technique over others. [ABSTRACT FROM AUTHOR]

This paper presents a methodology for the design of over-frequency containment schemes in low inertia, high renewable systems. This methodology is demonstrated through the comprehensive redesign of the containment scheme for significant over-frequency events (e.g., the loss of an exporting HVDC interconnector) in the Ireland and Northern Ireland power system (All-Island System). The new scheme allows an existing synchronous generator runback system integrity protection scheme to be replaced with fixed wind tripping and dynamic response from wind. This exploits the capabilities of renewable generation to create effective protection and control resources. The methodology provides the steps required to determine the key parameters of the scheme (e.g., maximum allowable frequency, required volume of tripping, lowest trip frequency). A key consideration of the methodology is the volume of dynamic response from wind that can be deployed before frequency limits are violated (e.g., inertia and wind penetration). Dynamic simulations are performed in DSE Tools for the All-Island system considering a 2020 operational scenario. These simulations support the application of the methodology and demonstrate the effectiveness of the scheme designed for the All-Island system. [ABSTRACT FROM AUTHOR]

The fast development of renewable energies leads to an increase in the power electronics penetration in transmission systems. This is particularly true if one considers a 100% renewable energies power system, where wind and solar photovoltaic energies, which make most of the renewable energies connections today, are connected to the grid through power electronics converters. Because power electronics-based generators and synchronous machines-based generators have very different dynamic behaviours, some approximations usually used to run transient simulations of transmission systems might not be optimal for future grids. The systematic use of the phasor approximation applied to the power lines, implemented in most of the Transient Simulation Programs, is indeed not relevant any more. To avoid the use of Electromagnetic Transient simulations, that are resource-demanding and time-consuming, this paper presents a novel Model Order Reduction technique for large grids with a high penetration of power electronic devices. Compared to the classical phasor approximation, this event-based state residualization approximation allows accurate transient simulations and at the same time an optimal reduction of the number of the system’s state variables depending on the observed variables, the considered events and the tolerated approximation error. [ABSTRACT FROM AUTHOR]