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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]

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 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]

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]

Voltage source inverters (VSIs) with vector control based on phase-locked loop (PLL) suffer instability when connecting to a very weak AC grid (short circuit ratio (SCR) $ < $ 1.3). The conventional inductive grid impedance compensation for the PLL by virtually reducing the grid impedance can stabilize this connection. However, the analysis in this paper indicates that its stabilization effectiveness is sensitive to grid impedance variance and, indeed, overcompensation causes the PLL instability. Therefore, in this paper, an improved grid impedance compensation for the PLL is proposed to achieve the same stabilization for very-weak-grid connection and possess a good tolerance of grid impedance variance and overcompensation. A comprehensive small-signal model of the VSI using the proposed PLL’s grid impedance compensation is derived for stability analysis and parameter design. The time-domain simulation for this VSI is built to validate the stability analysis. Comparison studies for both proposed and conventional PLL’s grid impedance compensation are conducted including the stability effectiveness, VSI performance and grid impedance variance. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive self-tuned current controller design for an LCL-filtered LC-tuned single-phase shunt hybrid active power filter (HAPF), which offers adaptability and flexibility of the control system to filter parameters changes. System modelling and online identification of parameters are presented. Then, a systematic self-tuned controller (STC) design is proposed to calculate the controller parameters and obtain the final control law adaptively. The exact HAPF parameters design is described and the overall closed-loop stability evaluation with considering digital control delay is discussed in this paper. To confirm the theoretical achievements, simulations and experimental tests on a real prototype system are performed. The results are in good accordance and demonstrate the effectiveness and superior performance of the suggested control technique. Furthermore, a comprehensive comparison between the proposed control technique and other controllers is provided to show the superiority of the proposed system from different aspects. [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]

Multi-terminal modular multilevel converter (MMC) power transmission is the current development trend in DC transmission. However, owing to its fast control and dynamic characteristics, it may interact with the other inductive devices or the grid and cause stability issues. This paper describes the use of the impedance analysis method in the frequency domain to analyze system stability. First, the multi-harmonic linearization method is used to model the impedance of a three-terminal MMC system. To make the model more accurate, the modeling considers the effect of frequency coupling caused by an asymmetric controller and the AC sampling site position. This paper then proposes an equivalent method of the grid impedance for the three-terminal system that can accurately judge the stability of the grid-connected system when the AC side is coupled. This work provides a theoretical basis for the prediction and suppression of the oscillation of MMC grid-connected system with coupling on the AC side. Finally, a three-terminal MMC model is built in Matlab/Simulink and the Nyquist stability criterion is used to verify the correctness of the analysis. [ABSTRACT FROM AUTHOR]

This paper addresses the interactions among the control loops of voltage-sourced converters (VSCs) embedded in high-voltage direct current (HVDC) systems and the impact of these interactions on the performance of individual control loops. Furthermore, this paper proposes a method to design the individual control loops, rather than the interconnected control system, such that the overall system stability is ensured in the presence of interactions. This paper addresses three aspects of the impact of control loop interactions on the overall control system of the VSC including stability, transient response, and steady-state response. To illustrate the impact of interactions on the VSC small-signal stability, stability regions of the interconnected control loops are obtained and compared against those of the various individual control loops. Then, a novel formulation of the VSC stability criterion is presented, and the small-gain theorem is utilized to determine a range of stabilizing gains for the interconnected control system. Moreover, new indices using the infinity norm are introduced to evaluate the impact of interactions on the transient response of the VSC. Finally, the DC gain of a certain set of transfer functions is used to assess the impact of control loops interactions on the set-point tracking capability of the VSC. The introduced indices along with time-domain simulations show that the transient response of the d-axis control loops is not impacted by the interactions, whereas that of the q-axis control loops is significantly impacted by the interactions. The set-point tracking capability is proved to be independent of interactions. [ABSTRACT FROM AUTHOR]

This paper investigates the transient stability of power systems co-dominated by different types of grid-forming (GFM) devices. Synchronous generators (SGs and VSGs) and droop-controlled inverters are typical GFM devices in modern power systems. SGs/VSGs are able to provide inertia while droop-controlled inverters are generally inertialess. The transient stability of power systems dominated by homogeneous GFM devices has been extensively studied. Regarding the hybrid system jointly dominated by heterogeneous GFM devices, the transient stability is rarely reported. This paper aims to fill this gap. It is found that the synchronization behavior of the hybrid system can be described by a second-order motion equation, resembling the swing equation of SGs. Moreover, two significant differences from conventional power systems are discovered. The first is that the droop control dramatically enhances the damping effect, greatly affecting the transient stability region. The second is that the frequency state variable exhibits a jump at the moment of fault disturbances, thus impacting the post-fault initial-state location and stability assessment. The underlying mechanism behind the two new characteristics is clarified and the impact on the transient stability performance is analyzed and verified. The findings provide new insights into transient stability of power systems hosting heterogeneous devices. [ABSTRACT FROM AUTHOR]

The stability of power systems can largely limit the power transfer capability limit of transmission lines. The PV generator control is different from synchronous generator control. The impact of PV generator dynamics on the power transfer limit constrained by stability is not well explored in the literature. This paper focuses on improving the stability constrained power transfer capability limit of transmission lines emanating from PV generators. The PV generator is provided with dc link voltage and reactive power control and is equipped with low voltage ride through capability, voltage and frequency support functionalities. In this paper, Lyapunov function analysis based adaptive tuning laws are proposed for PV control parameters to improve the power transfer capability limit (constrained by stability) of transmission lines connecting PV generators to grid. The tuning laws are proposed for Phase Locked Loop (PLL), outer and inner control loop parameters. The proposed tuning laws have inherent robustness towards faults, changes in solar irradiation, changes in grid topology, network impedances, generation and loads in the system. The effectiveness of the proposed method is validated on a Single PV-Synchronous Machine system, modified IEEE-39 and IEEE-118 bus system. The performance of the proposed method is investigated considering various disturbances such as symmetrical and asymmetrical faults on transmission line, switching of a transmission line and change in solar irradiation of PV. Comparison with existing method shows that the proposed tuning method can achieve higher power transfer capability limit considering stability. [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]

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]

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]

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 analyzes high-frequency interactions between a Modular Multilevel Converter (MMC) and High Voltage Direct Current (HVDC) grid resonances by studying their effect on the system stability. The recent appearance of converter-related instabilities due to high-frequency oscillations at the converter's ac side raises concerns about whether similar interactions can also take place at its dc side. To determine the risks imposed by such interactions within an HVDC grid, this paper assesses the impact of the MMC internal dynamics and dc system resonances on the stability using an analytical impedance-based method. The effect of fault current-limiting inductors, grid topology changes and transmission line length is investigated, indicating that these parameters considerably influence the electromagnetic characteristics of the HVDC grid and consequently the system stability. Furthermore, a sensitivity analysis of the MMC internal controller dynamics on the converter's non-passivity, causing the instability, is performed. [ABSTRACT FROM AUTHOR]

Autonomous power systems with a single power station and a high-voltage (HV) network may be susceptible to overvoltage instability, especially during light-load conditions. Moreover, in low inertia systems, considerable frequency excursions may be observed after disturbances. To deal with voltage and frequency stability problems in such isolated power systems, several measures should be taken, such as rules for adequate automatic voltage control of the synchronous generators and load-tap-changers (LTCs), and/or adequate design of actions applied during emergency system conditions such as reactors switching, and redesigning underfrequency load shedding taking into account overvoltage problems. The effectiveness of the proposed countermeasures against overvoltage instability in autonomous power systems is illustrated in this paper. In 2016, the autonomous power system of the Greek island of Rhodes experienced similar voltage/frequency problems leading to a blackout. This event has been accurately reconstructed in this paper. The application of the suggested countermeasures during the simulation of the 2016 blackout event in Rhodes, further highlighted the effectiveness of these measures, providing a guideline for similar cases. [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 analytically derives oscillatory stability criteria of a grid-connected PMSG based on the block diagram model. The derivation reveals the general mechanism about how the condition of grid connection, loading and converter control parameters setting of the PMSG jointly affect the oscillatory stability of the PMSG. It logically explains why the condition of weak grid connection and heavy loading may cause destabilization. In addition, computationally simple and modal-computation free indices are proposed to identify the instability risk caused by the “improper parameters setting” of the control system of grid side converter (GSC) and the phase locked loop (PLL). Following analytical conclusions are obtained: (1) When the PLL is of high-frequency bandwidth, high-frequency oscillations are mainly caused by the PLL or the open-loop modal resonance between the PLL and current control of the GSC. In addition, the low-frequency oscillations may also occur as caused by the power control of the GSC. (2) When the PLL is of low-frequency bandwidth, low-frequency oscillations may be caused jointly by the power control of GSC and the PLL. An example grid-connected wind farm with eighteen similar PMSGs is presented to demonstrate and evaluate the stability criteria derived and analytical conclusions obtained in the paper. [ABSTRACT FROM AUTHOR]

With the increase of photovoltaic penetration, the power-electronic converter (PEC)-interfaced generators with traditional control strategy may cause severe power oscillations after being disturbed due to lack of inertia and damping. The photovoltaic power plant controlled by virtual synchronous generator (VSG) technology, while introducing virtual inertia and virtual damping to improve the stability of the system, will also inherit its oscillation characteristics and cause a new oscillation mode. Aiming at this problem, this paper analyzes the difference between the system low-frequency oscillation (LFO) modes before and after the VSG is connected to the two-area system by the modal analysis. It is pointed out that the PEC-interfaced renewable energy generators based on VSG control technology could change the oscillation mode of the original system. The influence of VSG's main parameters and capacity on system dynamics is analyzed. Finally, a synchrophasor-based inter-area oscillation suppressed comprehensive control strategy is proposed to suppress the LFO of active power on the tie line, and the superiority of the strategy is verified by DIgSILENT /PowerFactory. [ABSTRACT FROM AUTHOR]

The decarbonization plans are leading to the decommissioning of conventional power plants, resulting in a deep transformation of power systems. Balearic Islands are not an exception and, in order to compensate this generation reduction and increase the security of supply, a second HVDC link is planned to interconnect the Balearic power system to the Spanish mainland. In this application paper, Modular Multilevel Converters (MMCs) have been assumed as the preferred technology for this HVDC link. A transient analysis has been presented to evaluate the system performance after the introduction of this new HVDC link. Grid-following and grid-forming control strategies have been implemented, comparing their impact on the system performance and stability. The transient events considered are the disconnections of the main synchronous generators of the islands and AC faults in several locations of the Balearic power system. A final case based on a penetration of 100% of converter-based resources has been also simulated to study the islanded operation of the MMC-HVDC link. [ABSTRACT FROM AUTHOR]

Concerns about the cybersecurity and resilience of power systems have heightened in electric utilities and regulatory agencies over the past decade mainly because of the unpredictable target, location and scale of cyberattacks and the potential severity of consequences. The cybersecurity of pilot protection is paramount in bulk power systems considering their prevalence and the crucial role they play in protecting critical assets and preventing large system disturbances and major blackouts. This paper investigates the resilience of pilot protection using a co-simulation platform based on OPAL-RT simulator and Riverbed Modeler. It is demonstrated that software-defined networking for operational technology (OT SDN) significantly improves the resilience of pilot protection to false data injection (FDI) attacks compared to traditional networks. Moreover, the resilience of OT SDN based pilot protection to denial of service (DoS) attack against the SDN controller is investigated both in the proactive and reactive modes of operation. The simulation results verified the resilience of OT SDN controller in OT SDN based pilot protection to DoS attacks in the proactive mode of operation. [ABSTRACT FROM AUTHOR]

The risk of unstable subsynchronous oscillations (SSO) in DFIG-based wind parks radially connected to transmission lines with series capacitive compensation is typically assessed with numerous electromagnetic transient (EMT) simulations, which is a time-consuming process. However, not all operating scenarios present risk of SSO and require such a detailed investigation. This paper proposes two charts based on impedance equivalents of wind generators obtained through frequency scans to quickly map which combinations of parameters can create unstable SSOs and which combinations are risk-free. With the information, engineers can immediately filter out scenarios with no risk of instability and conduct detailed studies on fewer scenarios that are truly critical. These charts can be obtained with simple equations that use only information readily available in practice to engineers, without the need to run any computer simulation. The charts also reveal the key operating conditions that can increase the risk of an unstable SSO and provide real-time quantitative insights into how close a wind park is to an instability. Application examples are provided to illustrate how this approach can help engineers speed up studies to identify the risk of SSO. [ABSTRACT FROM AUTHOR]

The increasing penetration of distributed renewable energy sources drastically alters the dynamic characteristics of distribution networks (DNs). Therefore, several equivalent models have been recently proposed, to analyze more accurately the complex behavior of modern DNs. However, relatively simple models are still commonly used in practice for dynamic power system studies. In addition, dynamic equivalent models for DNs are sensitive to different operating conditions and there is lack of systematic understanding of their performance. Scope of this paper is to propose a methodology for identifying the applicability range in terms of accuracy and generalization capability of several conventional and newly developed equivalent models for the dynamic analysis of modern DNs. A set of metrics is used for the modelling accuracy assessment and a sensitivity analysis framework is introduced to fully quantify the generalization capabilities of DN equivalent models. Based on the above, guidelines and recommendations for the development of robust equivalent models for DN analysis are proposed. [ABSTRACT FROM AUTHOR]

Geomagneticallyinduced current (GIC) studies usually focus on transformer response to dc but seldom analyze generator excitation systems. A GIC is driven by an electric field which is induced by a very low-frequency geomagnetic field. It is widely acceptable to model GICs with dc, mostly suitable for static voltage stability analysis, but this does not adequately characterize a power system's dynamic response. Considering this, we studied a multi-machine power system on an OPAL-RT digital real-time simulator (DRTS)-MATLAB/Simulink system. We used real GIC measurement data from high and mid-latitude regions. Wavelet analysis related the frequency components of the GIC to the power system's response. A dynamic generator model with excitation voltage control modelled the source. Our main finding is that excitation system control contributes to reducing the voltage drop caused by increased var demand in saturated transformers with GICs. Measured GICs revealed non-negligible short-term dynamics affecting bus voltages that are not captured with dc-modelling assumptions, yet they are important for voltage stability analysis. This study implies that excitation control creates a buffer for high GICs to flow without violating the grid codes for minimum operating voltages and this paper demonstrates the optimization of this novel approach. [ABSTRACT FROM AUTHOR]

The major concern for the single-phase grid-connected inverter system is the phase and frequency error of the phase-locked loop (PLL) under various grid disturbances. This paper employs an effective cascaded band pass filter (CBPF) to eliminate the effects of the DC offset and harmonics present in the grid voltage. However, the presence of a prefilter slowed the dynamic performance of all-pass filter (APF) based PLL, implied to generate the orthogonal signal in the single-phase system. To improve the dynamic performance along with the harmonics filtering capability, a nonlinear loop filter (LF) based PLL with CBPF is proposed. The nonlinear LF contains a nonlinear function applied in proportional-integral control to improve the dynamic response of the PLL. Under various grid disturbances, the proposed controller has a faster dynamic response with less overshoot. Furthermore, the proposed PLL is capable of eliminating the effects of DC offset and subharmonics. The proposed PLL is compared with different state-of-the-art PLLs to assess the performance under various grid disturbances. The efficacy is validated experimentally as well as through simulation results. [ABSTRACT FROM AUTHOR]

Phase–locked loop (PLL) is commonly used for the grid-connected voltage-source converter (VSC) to synchronize with the grid. Under weak grid conditions, it has been found that the frequency-dependent characteristic of the network impedance inherently introduces a positive feedback loop into PLL. Previous studies focused on the PLL analysis intuitively believe that the positive feedback loop will deteriorate the dynamic performance of the PLL. However, this conclusion is not rigorous since only the dynamic of the PLL is considered and the theoretical analysis is insufficiency to reveal the influence of the positive feedback loop on system stability. In this paper, the impact of the frequency-dependent network on VSC stability is quantified in terms of the overall system based on the damping torque analysis. It is found that the influence of the positive feedback loop on stability depends on the parameters of the PLL and the damping of the dominant eigenvalues. Besides, an angular frequency feedback scheme is proposed to eliminate the adverse effect of the frequency-dependent network and enhance the stability of the VSC under weak grid conditions. Time-domain numerical simulations and reduced-scale experiments are performed to validate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper develops a supervised learning of overcomplete dictionaries (SLOD) to efficiently perform online analysis and prediction of dynamic stability (DSP) in large power systems. To this end, multiple post-contingency signals with varying faults, load and generator switching are acquired by phasor measurement units (PMUs) based monitoring of all generators to form the training dataset. The SLOD approach then jointly learns a sparse feature dictionary and a stability status classifier using dynamic singular value decomposition (D-KSVD) and orthogonal matching pursuit (OMP). The aim is to learn features of the signals while adding a stability status term to the optimization problem. This enabled stable/unstable classes to be represented. The proposed SLOD manages to improve online DSP shortly after a contingency. It does this without any prior assumptions or signal preprocessing except for dynamic state estimation to get rotor speed from generator terminal PMU data. Test results on the IEEE 2-area 4 machines, 39 and 68 -bus test systems demonstrate that the SLOD gives more than satisfactory performance in all cases (i.e., ∼99.99% accuracy, ∼99.99% reliability, and 100% security) compared to Statistics and Machine Learning Toolbox™ -MATLAB that use time-series-based high-dimensional stability indices as input for DSP. [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]

The increasing complexity of modern AC/DC power systems poses a significant challenge to a fast solution of large-scale transient stability simulation problems. This paper proposes the hybrid parallel-in-time-and-space (PiT+PiS) transient simulation on the CPU-GPU platform to thoroughly exploit the parallelism from time and spatial perspectives, thereby fully utilizing parallel processing hardware. The respective electromechanical and electromagnetic aspects of the AC and DC grids demand a combination of transient stability (TS) simulation and electromagnetic transient (EMT) simulation to reflect both system-level and equipment-level transients. The TS simulation is performed on GPUs in the co-simulation, while the Parareal parallel-in-time (PiT) scheduling and EMT simulation are conducted on CPUs. Therefore, the heterogeneous CPU-GPU scheme can utilize asynchronous computing features to offset the data transfer latency between different processors. Higher scalability and extensibility than GPU-only dynamic parallelism design is achieved by utilizing concurrent GPU streams for coarse-grid and fine-grid computation. A synthetic AC/DC grid based on IEEE-118 Bus and CIGRÉ DCS2 systems showed a good accuracy compared to commercial TSAT software, and a speedup of 165 is achieved with 48 IEEE-118 Bus systems and 192 201-Level detail-modeled MMCs. Furthermore, the proposed method is also applicable to multi-GPU implementation where it demonstrates decent efficacy. [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]

In traditional power systems, the load consumption inside the distribution networks has a relatively passive behavior. Consequently, transmission system operators have commonly aggregated the load centers using static loads such as exponential load models. This is a practical approach for bulk power system stability studies. In modern systems, the impact of distributed generation units on the system dynamics can no longer be neglected. Static load models fall short to represent the highly dynamic behavior of active distribution networks. This paper proposes a methodology for equivalencing such networks while conserving the dynamics of interest for long-term stability studies. The methodology is based on Hammerstein-Wiener models that use only boundary variables measured at the distribution network point of common coupling. Therefore, unlike gray-box models, no previous knowledge about the system is required. Furthermore, the proposed methodology has a transparent relationship to linear systems and a convenient block representation that can be implemented in commercial power system analysis software using only standard elements. This allows for easy implementation, overcoming a barrier for a rather conservative sector such as power systems planning and operation. The conclusions are derived from time-domain simulations on the IEEE test system for voltage stability assessment. [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]

As synchronous generators (SGs) are extensively replaced by converter-based generators (CBGs), modern power systems are facing complicated frequency stability problems. Conventionally, the frequency nadir and the rate of change of frequency (RoCoF) are the two main factors concerned by power system operators. However, these two factors heavily rely on simulations or experiments, especially in a power system with high-penetration CBGs, which offer limited theoretical insight into how the frequency response characteristics are affected by the devices. This paper aims at filling this gap. Firstly, we derive a formulation of the global frequency for a CBG-integrated power system, referred to as common-mode frequency (CMF). The derived CMF is demonstrated to be more accurate than existing frequency definitions, e.g., the average system frequency (ASF). Then, a unified transfer function structure (UTFS) is proposed to approximate the frequency responses of different types of devices by focusing on three key parameters, which dramatically reduces the complexity of frequency analysis. On this basis, we introduce two evaluation indices, i.e., frequency drop depth coefficient (FDDC) and frequency drop slope coefficient (FDSC), to theoretically quantify the frequency nadir and the average RoCoF, respectively. Instead of relying on simulations or experiments, our method rigorously links the system's frequency characteristics to the characteristics of heterogeneous devices, which enables an in-depth understanding regarding how devices affect the system frequency. Finally, the proposed indices are verified through simulations on a modified IEEE 39-bus test system. [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]

In this paper, a detailed qualitative & quantitative comparative analysis of measurement based centralized voltage stability monitoring approaches using Thevenin equivalent is presented. These methods typically utilize the state estimation output, making them easily implementable at the control centers. The metrics for comparison are defined in terms of computation resources required, accuracy of identifying the critical loading point, critical contingency screening, and robustness to noise. These performance metrics are relevant for practical implementation and are presented on the IEEE 300 bus system and the MATPOWER 2383-bus system. To the best of our knowledge, this is the first systematic qualitative & quantitative comparison between various measurement based voltage stability methods using these performance metrics. The results will guide the utilities and operators about possible trade-offs between the various methods for large systems, enabling them to make an informed decision on the specific method to use for their needs. [ABSTRACT FROM AUTHOR]

A new smooth model is proposed in this paper to eliminate the non-differentiability of several types of limits in power flow models. The proposed smooth model accurately represents power system static models with limits as a continuously differentiable function. Analytic results are developed to show that each solution of the proposed smooth model is arbitrarily close to a solution of the corresponding original power flow model with limits. The proposed smooth model includes a wide range of devices with physical limits, such as generators, transformers, HVDCs, phase shifters, and shunts. In addition, it is shown that every generic static bifurcation in the original model is transformed into a saddle-node bifurcation in the smoothed model. Hence, the search for bifurcations in voltage stability assessment can be greatly simplified. Several numerical studies of the proposed smooth model on a 9241-bus power system and on a 13659-bus power system have shown promising results. [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]

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]

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]

Low-inertia microgrids are prone to large frequency fluctuations due to high penetration of inverter-fed renewable sources. A virtual synchronous machine (VSM) is capable of handling these frequency fluctuations. VSM imparts inertial behaviour in grid-connected inverters with the help of an electric storage device. Most of the reported VSM control schemes use a constant inertia parameter that leads to an inadequate dynamic frequency response. In this paper, a fuzzy controller-based self-adaptive VSM control scheme is proposed. Here, the value of the inertia parameter is decided using fuzzy rules which take the penetration index of renewable energy, frequency deviation and rate-of-change-of-frequency as the input parameters. These rules are formulated with the help of the sample data obtained from simulations done in MATLAB/Simulink, where the inertial parameter is optimized using a genetic algorithm for various cases. The proposed method is validated for solar photovoltaic-fed microgrid test systems using power–hardware-in-the loop and the results indicate a reduction in maximum frequency deviation compared to the constant inertia parameter based VSM schemes. The introduction of renewable energy penetration level and fuzzy expert system in modifying the inertia parameter are the novel contributions in this paper. [ABSTRACT FROM AUTHOR]