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• This paper proposes a fault location method based on composite traveling wave, which can easily eliminate the traveling wave from adjacent lines. • The traveling wave from other adjacent lines, which is never detailed discussed in previous research, hinders the accurate identification of wavefront. • The refraction coefficient of busbar with multiple transmission lines is negative for current traveling wave, but positive for reflection coefficient. • The time–frequency matrix is able to present the energy of traveling wave in wideband. As the speedy expansion of power gird, the traveling wave fault locator in substation may not always connect to newly added transmission lines in time, which reduces the effectiveness of fault locator. In this paper, an adjacent fault-free line based fault location scheme for newly additional line is proposed. Since the traveling wave from adjacent fault-free line results in severe difficulty for identification of traveling waves from faulty line, the time–frequency matrix is performed to screen traveling waves. Firstly, in order to remove the influence of waves from remote terminals of adjacent fault-free line, the current refraction coefficient is theoretically analyzed. Due to the negative refraction coefficient, traveling waves from remote terminals of adjacent fault-free line can be reduced by the proposed composite traveling wave. Secondly, the time–frequency matrices of composite traveling wave and original traveling wave is obtained by S-transform. Then, these matrices are applied to form ratio matrix which thoroughly eliminated waves from remote terminals of fault-free lines. Moreover, the robustness of the proposed fault location scheme is thoroughly validated by the simulation of PSCAD/EMTDC. Finally, the proposed fault location method has the great accuracy in simulation tests and field data test. [ABSTRACT FROM AUTHOR]

• This paper proposes a fast non-unit traveling wave protection scheme for multi-terminal HVDC system. • The new method has a clear theoretical calculation method in setting values and a strong robustness to high-resistance fault. • The time-domain expressions of the backward line-mode voltage traveling wave after different line faults occur are derived respectively. The rapid and accurate dc line protection scheme is of great value in isolating dc line faults and improving the reliability of multi-terminal HVDC systems. Nowadays, the traveling wave (TW) protection is widely used as the primary protection in HVDC transmission systems. However, the traditional TW protection has the problems of poor resistance to high impedance faults and the setting value depends on simulation. For the hybrid three-terminal LCC/MMC HVDC system, this paper provides a fast non-unit protection scheme. Firstly, the time-domain expressions of the backward line-mode voltage TW after different line faults occur are derived respectively. Based on the expressions, a non-unit protection scheme depending on the difference value of the line-mode backward TW is proposed. Finally, the scheme is verified by simulation. The method only needs single-ended data to realize the rapid dc line protection without converter station communication which has a clear theoretical calculation method in setting values and a strong robustness to high-resistance fault. [ABSTRACT FROM AUTHOR]

• Linearized HVDC Link model implemented, which is applicable to dynamic performance studies of power electronic equipment considering electromagnetic transients of electrical network; • Using of generalized switching functions and dynamic phasors in the proposed model; • Mitigation of poorly damped oscillation problems due converter interactions with network; • Model validation and application using PSCAD as benchmark; • Simulation of a large-scale model of Brazilian system with HVDC Multi-infeed configuration. This paper presents a linearized HVDC link model, which was implemented in PacDyn software and is applicable to dynamic performance studies of power electronic equipment considering electrical network electromagnetic transients, differently from electromechanical studies where the network dynamics is usually neglected. The proposed HVDC model was developed employing equivalent switching functions concepts and dynamic phasors. Simulations and results for small and large-scale test systems are presented. Model validation is performed through comparisons between results obtained by PacDyn and PSCAD. In sequence, there are practical examples of controller tunning considering adverse dynamic interaction mitigation between HVDC Link and electrical grid. The final results on a large-scale model of the Brazilian power system demonstrate that the proposed HVDC model can be used in actual engineering studies. [ABSTRACT FROM AUTHOR]

• Developing a comprehensive model of a transformer winding which incorporates skin effect, proximity effect, and eddy current losses in the core, • Studying the effects of the core at high frequencies using simulations and measurements, • Investigating the skin and proximity effects on the frequency response and impedance characteristics of transformers, • Performing empirical measurements to validate the reduced influence of the core at high frequencies. This paper investigates the high-frequency transformer losses attributed to eddy currents in both conductors and the core. A comprehensive model of a transformer winding is presented, meticulously incorporating skin and proximity effects. The winding resistance increase due to these effects is determined by applying analytical and finite element methods. The investigation highlights that eddy current losses in the magnetic core notably increase the resistance of each winding section in low frequencies. However, the impact of these losses diminishes as the winding length approaches the voltage wavelength at high frequencies. Consequently, the net magnetomotive force and flux in the core become negligible. As a result, the high-frequency impedance characteristics are remarkably similar for windings with and without a magnetic core. These findings are substantiated through rigorous simulations and empirical measurements. [ABSTRACT FROM AUTHOR]

In this paper we present a scalable approach based on the latency-based linear multistep compound method to use graphic processing unit (GPU) to accelerate the power system simulations with electromagnetic transients. To balance between the computational load and accuracy, we modeled the power system using shifted frequency analysis. Then, to efficiently exploit the hardware, our computational approach is designed to utilize both data-parallel and task-parallel execution. In addition, a graph-based thread safety design is introduced to achieve high scalability in the paralleled component computations. Furthermore, our implementation introduces a translation layer for different heterogeneous computing frameworks during compile time, so that a wide range of GPU devices can be supported without losing performance. Finally, benchmark results show that our approach achieves faster-than-real-time capability for systems with hundreds to thousands of nodes. [Display omitted] • Exploits data- and task-parallelism together in an automated way. • A graph-based approach to ensure thread safety to increase scalability. • A compile-time translation layer to allow execution on various platforms. • Faster-than-real-time for system with more than 10,000 dynamic components. • 82 × faster compared to an optimized sequential simulation. [ABSTRACT FROM AUTHOR]

Grid forming control applied to power converters termed as grid forming converters (GFC) interfacing storage and renewable generation has been identified as a potential solution to facilitate a more significant penetration of converter-based renewable generation in the power system. The emulated electromechanical model in the GFC is also the synchronization unit which typically utilizes measured output active power from the GFC as the feedback variable. However, this feature has opened up a concern on the transient stability due to loss of synchronism under significant transient events in the power systems, which include frequency change, phase jump, and voltage dips. This paper presents a quantitative and illustrative analysis of the impact of the current limit in GFC on the transient stability of a system comprising of GFC. Furthermore, a solution based on virtual active power is proposed to improve the transient stability margin of the GFC when the GFC enters the current limit. Finally, the analysis and the proposed method to enhance the transient stability are verified by Power hardware in the loop (PHIL) experimental tests. • Outlined the challenges for grid forming converters when current limit is present. • Provided clarification to the transient stability for grid forming converters. • Provided a quantitative analysis of transient stability for grid forming converters. • Introduced virtual power in control design to extend the transient stability margin. • Conducted Power-HiL evaluation on a modified low inertia IEEE 9-bus system. [ABSTRACT FROM AUTHOR]

• Efficient dynamic modelling framework for the analysis of fair-sized DC microgrids. • Nodal formulation combined with Newton–Raphson and implicit trapezoidal methods. • BESS, CHP units, PV plants and series connected DC/DC converters can be studied. • Results are validated versus EMT simulation conducted in Simscape Electrical. • Small errors are obtained with a small fraction of time taken by the EMT simulation. This paper introduces a novel modelling framework for conducting dynamic analysis of DC microgrids (MG), considering components such as battery energy storage systems (BESS), combined heat and power (CHP) cogeneration, photovoltaic (PV) plants and DC/DC converters. The MG dynamics are accurately captured using well-founded modelling practices of the power system transient analysis field. Firstly, the power device models are derived based on fundamental operating principles using a lumped-type parameter modelling approach. Secondly, the DC microgrid is formulated using nodal power injections, which is combined with Newton–Raphson and implicit trapezoidal methods to efficiently solve fair-sized networks of arbitrary topology. The dynamic outcomes of a 13-bus MG were compared with those of an electromagnetic transient (EMT) simulation conducted in Simscape Electrical for load and solar irradiance changes and for a DC/DC converter outage. For these events, errors smaller than 2.5% were yielded by the new approach, only requiring 3.1% of the computing time employed by the EMT simulation. The method's applicability was also showcased by assessing the dynamic performance of a larger DC microgrid containing 118 buses, twelve distributed generators and five BESS, which was subjected to typical contingencies such as load increases and distribution line disconnections. [ABSTRACT FROM AUTHOR]

• Truely on-site measurements of the transient voltage in a 220 kV substation; • Statistical analysis on the difference between on-site measured transient voltage waveforms and standard impulse waveforms; The electromagnetic transient overvoltage in the substation is an important factor that affects the life of insulation equipment. For evaluate the economy and reliability of the insulation design of substation equipment, it is necessary to study and analyze the actual measured overvoltage waveforms in the substation. In this paper, firstly, the 3018 pieces of overvoltage data monitored in the 220 kV substation from 2018 to 2019 are preprocessed to obtain the required overvoltage waveform. Next, by analyzing and classifying the overvoltage data, four typical overvoltage waveforms suffered by the insulation equipment in the substation are extracted. Combined with the IEC60060 standard, the time parameters of the overvoltage waveform are selected and defined: wave-front time (T f), half-value time (T half), main oscillation frequency (f), and attenuation constant (α). Further, statistical analysis is performed on the parameters of each waveform. The distribution law, distribution characteristics and distribution range of the parameters are obtained. Finally, the parameters of four typical overvoltage waveforms are summarized and compared, the cumulative distribution functions are obtained. This results can guide and optimize the insulation design of the insulation equipment in the substation, reduce design errors. It provide data support for the economy and reliability of insulation design. [ABSTRACT FROM AUTHOR]

• The virtual inertia hidden in the energy storage device is explored to obtain the synchronous operation capability. • A novel virtual shaft is added to the VSG to capture more transient energy from synchronous generators to energy storage devices. • The virtual shaft control strategy of the hybrid energy storage device is proposed for both frequency support and oscillation suppression. • The proposed control strategy is tested on a controller hardware-in-the-loop platform. If the hybrid energy storage device (HESD) with virtual inertia is coupled with synchronous generators (SGs) by a virtual shaft, the stronger transient stability of the power system can be achieved if more transient energy is captured by renewable power generation. In this paper, the conversion relationships between the static energy of the HESD and the kinetic energy of the SG are established. The virtual inertia hidden in the HESD is then explored to obtain the synchronous operation capability. To capture more transient energy from SGs to HESD, a novel virtual shaft is added to the VSG, and moreover, the impacts of HESD coupled with the virtual shaft on system transient stability are analyzed. Using the Hamiltonian energy function, the necessary conditions for improving the transient energy capture efficiency of the HESD are presented, and thus the virtual shaft control strategy of the HESD is proposed to integrate the power support functions for system frequency regulation and power oscillation damping. Finally, a typical test system with high penetration of photovoltaic arrays and HESDs is implemented on a hardware-in-the-loop platform. The results demonstrate that under the proposed control strategy, the transient stability of system frequency and rotor angle can be both significantly improved. [ABSTRACT FROM AUTHOR]

This paper proposes a methodology for modeling and simulating electromagnetic transients in power transmission cables with arbitrary cross-sections, usually applied in offshore power transmission and variable speed machine drive. This way, a sector-shaped cable is modeled taken into account its frequency-dependent parameters. Both impedance and admittance parameters are calculated by using the Finite Element Method, without analytic formulations based on the approach by an equivalent cylindrical cross-section, which leads to several inaccuracies. In sequence, the cable is decoupled into its four propagation modes by using an approximate modal transformation matrix with real and constant terms. Finally, each mode is modeled directly in the time domain by equivalent electric circuits, in which the lumped circuit elements are obtained from the rational function approach and fitting techniques. • Electrical parameters of submarine cables based on geometric characteristics and finite elements method. • Frequency-dependent equivalent circuit in the time domain by using the Vector Fitting algorithm. • Determining the modal transformation matrix with more than three propagation modes. • Modeling and simulation methodology applied to cables with arbitrary cross section and multiple modes. [ABSTRACT FROM AUTHOR]

• Supervisory control of CIRs improves transient stability of synchronous generators. • CIRs are allowed to participate in dynamic grid support during abnormal conditions. • Control of CIRs can be performed during fault and post-fault periods. • The increasing penetration of CIRs can help improve the transient stability margins. Power-electronic converters are increasingly utilized to integrate renewable and distributed energy resources (DERs) with conventional power grids. The increasing penetration of converter-interfaced resources (CIRs) could, in turn, influence the transient stability of traditional synchronous generators (SGs) in power systems due to their fast response and low inertia nature. This paper evaluates the transient stability of power systems containing SGs and grid-following CIRs under various control schemes and penetration of CIRs. The critical clearing time (CCT) of the SGs is used as the criterion for assessing transient stability following a fault. It is demonstrated that stability margins can be improved by actively controlling the grid-following CIRs during fault and post-fault periods. The proposed method is shown to increase the CCT compared to the conventional/alternative approaches, particularly the common practice that requires CIRs to inject only reactive power to support/regulate voltage during the fault period. It is also shown that with increased penetration of CIRs, if controlled appropriately, the transient stability of SGs can be improved, which is not commonly expected in low-inertia systems. [ABSTRACT FROM AUTHOR]

The high penetration of photovoltaic (PV) in power grids typically leads to the displacement of traditional synchronous generators (SGs). However, with a high penetration of PV, fewer SGs are running, and the sharing of responsibility to control the system frequency is reduced and easily exacerbates the problem of reduced inertia response in the power system. This can increase frequency deviation when there is a load-generation imbalance or unexpected disturbances. The limited amount of inertial response from the PV generation means that it cannot provide the same frequency support as SGs. Therefore, this paper suggests a fast frequency control (FFC) technique for the battery energy storage system (BESS) to reduce the instantaneous frequency deviation (IFD) in the Ethiopian grid. The authors specifically provide knowledge of the modeling of droop-type controlled BESS, which can provide additional damping, enhance the inertial ability of the system, and reduce IFD. The simulation results indicate the effectiveness of BESS in mitigating the adverse inertial impact of PV and meeting the necessary grid requirement. The proposed method was tested on the Ethiopian power system model through simulations by using DIgSILENT simulation software. To validate the model, transient frequency simulation studies are performed for various fault conditions, and comparisons are made with and without BESS for different levels of PV penetration. • A model of the Ethiopia–Kenya LCC HVDC interconnection is developed. • The study examines the integration of large and small-scale grid-connected PV systems into the power grid at varying penetration levels. • Frequency responses are analyzed for PV penetration levels (15%–45%) with load or generation contingency. • BESS modeled and controlled using droop control with PI-lead and lead–lag algorithms, considering frequency deviation input. [ABSTRACT FROM AUTHOR]

• This paper establishes a small signal model of variable speed pumped storage unit with full size converter. • The oscillation modes and key influencing factors are clarified. • A coordinated control strategy for suppressing the ultra-low frequency oscillation is proposed. The research on control strategies of the variable speed pumped storage unit with full size converter (FSC-VSPSU), mainly focuses on the rapidity of power regulation. But the speed oscillation and slow speed regulation performance caused by fast power regulation are ignored, which is not conducive to the safe and efficient operation of the unit. This article investigates the dynamic stability characteristics of the FSC-VSPSU in detail. In turn, the stability risks are clarified and serve for the design of its control strategy and the improvement of operational efficiency. The small-signal model of FSC-VSPSU considering the variation of water head and load in fast power mode is established. The dominant instability control link and key parameters are revealed based on the eigenvalue analysis. Oscillation mode analysis shows that the unit has a wide-band oscillation characteristic. The dominant oscillation mode is the ultra-low frequency oscillation (ULFO) caused by the governor control system. To suppress the ULFO and improve the optimal speed tracking performance of the unit to the greatest extent, a coordinated control strategy of governor variable parameter control and governor power system stabilizer (GPSS) is proposed. The electromagnetic transient simulation based on PSCAD verifies the effectiveness of the proposed measures. [ABSTRACT FROM AUTHOR]

• An electromagnetic transient model of the Sen Transformer (ST) with inter-turn fault (ITF) is proposed. • The hysteresis effects are considered as it affect the accuracy of the analytical results of the proposed model. • The current variation of the ST in the event of an ITF is analyzed. • The effects of number of fault turns and fault locations on the current of the ST with ITF are presented. In order to analyze the electromagnetic characteristics of the Sen Transformer (ST) in the event of an inter-turn fault (ITF), an electromagnetic transient model of the ST with ITF based on reluctance is proposed in this paper. Firstly, the magnetic equivalent circuit model of the ST with ITF is established based on the magnetic coupling relationship among the internal windings of the ST with ITF. Secondly, the electrical analytical model for the current in each winding of the ST with ITF is derived from the electrical connection established the ST with ITF and the external system. Finally, the electromagnetic transient model of the ST with ITF can be obtained by combining the magnetic equivalent circuit model with the electrical analytical model. The J-A hysteresis model is employed for representing the saturation characteristics of the iron core and the hysteresis effects. Meanwhile, an energy method is used to calculate the leakage reluctance between the windings. Three case studies have been conducted with the assistance of MATLAB and ANSYS/Maxwell. The results of the analytical calculations are compared with the time-domain simulation to verify the validity of the model. Furthermore, the growth of the current in the fault phase is significant after an ITF occurs in the ST, while the growths of the currents in the non-fault phases are very small. Moreover, the effects of the number of fault turns and the fault location on the current in the ST with ITF are further analyzed. [ABSTRACT FROM AUTHOR]

• The vulnerable branches which affect the transient voltage security are identified. • Image-form samples combine grid structure and power flow information visually. • Knowledge visualization makes CNN-based transient voltage stability assessment model more understandable and reliable. • A comprehensive vulnerability indicator integrates the knowledge in CNN, grid topology and branch state. • The proposed method is demonstrated on a real-life provincial grid with renewable energy integration. Because of the increasing proportion of grid-connected converters, the transient voltage problem has increased the risk of the secure and stable operation of power systems. As the extension of transient voltage stability assessment (TVSA), transient voltage vulnerability assessment is the key technique to detect the crucial elements which can cause the insecurity risk of power system transient voltage. Although deep learning-based TVSA models have demonstrated the high accuracy, it is more important to display the knowledge learnt by the models and utilize it to recognize the weakness of transient voltage. This paper presents a transient voltage vulnerability assessment method by knowledge visualization of convolutional neural network (CNN). First, the image-form sample construction method is proposed to characterize the power system operating condition, which prepares for training CNN-based TVSA model. Then, the knowledge in TVSA model is visualized based on Gradient-weighted Class Activation Mapping (Grad-CAM) and Activation Maximization (AM) algorithms, which is analyzed from the perspective of power system stability. Finally, a comprehensive vulnerability indicator is proposed for identify the weakness of transient voltage, which combines the knowledge inside the TVSA model and the indicators with clear physical meaning. Simulation results of the New England 39-bus test system and the real Shandong provincial power grid in China demonstrate that the visualization makes the model more reliable and the proposed method can accurately identify the vulnerable branches. [ABSTRACT FROM AUTHOR]

The deployment of sophisticated and costly large-capacity wind turbines continues to rise. It is urgent for precise real-time simulation to accurately identify and address potential problems. However, the existing solutions, which joint various simulation platforms, suffer from the disadvantages of complex architecture and high cost. This paper proposes a CPU-FPGA heterogeneous computing-based real-time simulation platform for detailed wind turbine model (DWTM). DWTM encompasses the turbine model (covering the inflow wind, aerodynamic, and mechanical dynamic), the electrical model (covering the electromagnetic transient), and the control system. The real-time operating system is introduced to guarantee the real-time performance of the turbine model and control system in the CPU. FPGA is used to perform real-time electrical model calculation. Furthermore, a general FPGA solver for electromagnetic transients is designed. It can accommodate various circuit topologies without the need for recompiling the FPGA code. Finally, the real-time simulation performance and accuracy are verified. The coupled dynamics between the turbine and electrical models are investigated under multiple power grid and wind conditions. • The CPU-FPGA heterogeneous computing platform for the real-time simulation of detailed wind turbine model is developed. • A general FPGA solver is designed and developed for various circuit topologies. • The coupling phenomena between power grid faults and mechanical component vibrations are analyzed comprehensively under multiple power grid conditions and wind conditions. [ABSTRACT FROM AUTHOR]

• An end-to-end fault situation identification framework for distribution networks. • A high-precision digital twin agent with parallel and ultra-real-time computing and identifying. • Skip-connected dilated convolutional networks and knowledge sharing via multi-task learning. • An automated hyper-parameter tuning strategy. • Case studies validate the effectiveness and robustness of the approach. The gradual integration of distributed wind power into distribution networks presents significant challenges for identifying faults, as it requires accurate and timely fault identification based on large-scale data. This paper proposes a novel fault situation identification framework driven by digital twins to overcome the existing bottleneck of asynchronous online fault identification and offline post-event analysis. The framework employs a high-precision digital twin avatar with parallel strategies of fully electromagnetic transient calculation to obtain the real-time operation status of distribution networks connected with distributed wind power. Furthermore, the framework employs skip-connected dilated causal convolution to mine meaningful multi-time-scale features from massive data, while using an automatic hyper-parameter tuning strategy. A case study based on IEEE 33-node standard distribution network and a real-world distribution network demonstrates the effectiveness of this framework, achieving ultra-real-time and high-precision simulation and effective fault identification even under noise or missing data, accelerating traditional post-fault analysis to microsecond-level situation identification. [ABSTRACT FROM AUTHOR]

The uneven distribution of renewable energy supply and demand promotes the development of high-voltage direct current transmission. As the critical reactive power compensation equipment for high voltage direct current transmission, the synchronous condenser must have a strong overload capability. One of the critical factors limiting the improvement of its overload capacity is the reliability of the end winding, which depends on the magnitude of the force on end windings during dynamic large reactive power output. Therefore, this paper proposes a coupling model of transient electromagnetic force for the high voltage direct current transmission system and the end zone of the synchronous condenser. The transient response of the synchronous condenser under different fault degrees is calculated, analyzed, and verified by experiments. Based on the current response of the synchronous condenser, the transient electromagnetic force on end windings is calculated. The distribution law of the force on end windings of the synchronous condenser under different degrees of dynamic reactive power compensation process is revealed. Further, the regions on end windings with larger force during strong overload are indicated. The optimizing fixation scheme for end windings is proposed according to the distribution features of the force, which can improve the operational reliability of end windings. • Force on end windings under dynamic large reactive power output is important. • Propose transient force coupling model of end winding under large reactive power. • Reveal the law of the force on end winding during dynamic reactive power process. • Indicate the regions with a larger force under large reactive power. • Propose an optimized fixing scheme to enhance the reliability of the end windings. [ABSTRACT FROM AUTHOR]

The resilience of power systems is critical in mitigating faults caused by the impending effects of climate change. Typical operational methods, such as network reconfiguration, may be insufficient to mitigate faults in the event of a contingency. On the other hand, reducing system demand may help increase the number of restored loads. As a result, this paper proposes a novel self-healing optimization approach based on a power grid concept known as conservative voltage reduction (CVR), which results in system demand reduction. The proposed optimization model is formulated as a mixed integer non-linear (MINLP) problem to fulfill an objective of minimizing unserved loads within the system. Voltage, thermal capacity, system radiality, and several more constraints have been taken into consideration while formulating the proposed model to handle both grid-connected and isolated modes of operation. Both dispatchable and non-dispatchable distributed generators (DGs) are taken into consideration. Dispatchable DGs are assumed to be capable of switching back and forth between constant power (PQ) and droop controls for the purpose of grid following and grid forming in grid-connected and isolated modes of operation, respectively. The proposed optimization approach is coded and solved using the General Algebraic Modeling System (GAMS) software. The IEEE 69-bus power distribution test system is utilized to test the validity and superiority of the proposed model. The results show that the proposed model effectively increases the system resilience by reducing the unserved power/energy within the system following a contingency. • Optimized MINLP fuses Reconfiguration with Conservative Voltage Reduction (CVR). • Increased system resilience against climactic faults using the proposed fusion. • Proposed approach was tested on grid connected &isolated systems following a fault. • Deterministic and probabilistic analysis was explored alongside proposed approach. • The proposed fusion recovered up to 6% more load than reconfiguration without CVR. [ABSTRACT FROM AUTHOR]

• An analytical criterion to investigate the transient angle stability of the grid-forming controlled type-4 wind turbine during the fault is proposed. • Various key factors on the transient stability of the system are jointly and comprehensively revealed by using the criterion. • Impacts of the reactive power control and time-delay of power references switching on the transient stability are studied by utilizing phase portrait of the derived third-order large-signal model. Thanks to the ability of the inertia provision and the voltage support, the virtual synchronous generator with reactive power control (RPC) is a promising solution among various grid-forming control schemes. This paper analyzes the transient angle stability of the grid-connected type-4 wind turbine with virtual synchronous generator and reactive power control strategy during the fault. By deriving the analytical criterion with the transient energy function, various key factors on the transient stability of the system can be revealed comprehensively and jointly. Additionally, the impacts of the integral coefficient of the RPC and the power reference switching delay on the transient stability are also analyzed by plotting the phase portraits of the derived third-order large-signal model of the grid-connected wind turbine system. The analytical result can be helpful for the determination of the parameters of the grid-connected wind turbine in order to keep transient stable and keep connected with the grid during the fault. Finally, the robustness and the effectiveness of the theoretical analysis results are validated by the electromagnetic transient simulation in MATLAB/Simulink under various conditions. [ABSTRACT FROM AUTHOR]

• The state-of-the-art research advances in power system restoration with large renewable penetration are reviewed from different system levels, i.e., transmission system, distribution system, and coordinated transmission and distribution system. • The methods of handling renewable power uncertainty during system restoration are summarized. • The laboratory validations and practical applications of the renewable power system restoration strategies are reviewed. • Promising research directions for renewable system restoration are provided, including uncertainty handling, artificial intelligence techniques, transient stability issues, cyber-physical interlinking, and multi-energy coupling. The catastrophic blackout events and ever-increasing penetration of renewable power generation highlight an advanced restoration strategy to effectively and reliably employ renewable power generation to contribute to renewable power system restoration. This paper reviews the research advances of power system restoration involving large renewable penetration, and the methods of handling renewable power uncertainty during restoration are also summarized. First, the transmission system restoration processes are divided into three sequential stages: a) black-start, b) network reconfiguration and c) load restoration, and the research advances of these three restoration stages involving large renewable generation are presented. Then, the distribution system restoration assisted by multiple flexible resources, such as renewable distributed generators, remotely-controlled switches, energy storage systems, and soft open points, are reviewed with emerging techniques, including micro-grids, multi-agent systems, repair crews, and mobile power sources. Furthermore, with the growing activeness and flexibility of the distribution system, the coordinated transmission and distribution system restoration and their information interactions are also discussed. Finally, for practical applications, the laboratory validations of restoration strategies using realistic power grid data, real-world restoration strategies, decision support systems, and field tests of black-start procedures are introduced to complete this literature review. Effectively deploying renewable power sources can significantly improve the power system restoration efficiency, and their inherent uncertainty should be carefully handled. Moreover, promising research trends are provided to improve the power system restoration with large renewable penetration. [ABSTRACT FROM AUTHOR]

• A robust optimization for small-signal stability constrained optimal power flow (SSSCOPF-RO) model of a power system considering the dynamic characteristics and uncertain power output of DFIGs is established. • The SSSCOPF-RO model is transformed into an SDP model using the semi-definite relaxation (SDR) and McCormick envelop relaxation (MER) techniques to improve the convergence and computational efficiency. • The bilayer robust optimization model is transformed into a single-layer optimization model based on dual programming theory to be directly solved by commercial solvers. • Results show the high efficiency, accuracy and robustness of the proposed method. When substantial wind power generation is integrated into the power system, the low rotational inertia and uncertain power output of wind turbines pose a great challenge to the small-signal stability (SSS) of power system operation. In this paper, considering the dynamic model of a doubly fed induction generator (DFIG) and the uncertainty of wind power, we establish a bilayer robust optimization of the SSS constrained optimal power flow (SSSCOPF-RO) model for a power system with DFIGs. It uses Lyapunov's second theorem to describe the SSS constraint. By the semi-definite relaxation and McCormick envelope relaxation techniques, we transform the inner-layer optimization of the SSSCOPF-RO model into a semi-definite program (SDP) model to improve the convergence reliability and computational efficiency of solving the model. Based on the dual optimization theory, the inner-layer SDP model is converted into its dual SDP model, and the bilayer robust optimization model is transformed into a single-layer optimization model, which can be solved using the solver MOSEK in the software CVX. Finally, case studies were conducted on IEEE 9-, 39-, and 118-bus systems to validate the proposed method. The obtained optimal solution of the transformed single-layer optimization model could ensure the SSS of the system under the uncertain fluctuation of DFIGs' active power output and effectively reduce the network loss cost, and the results indicate the effectiveness and robustness of the proposed model. [ABSTRACT FROM AUTHOR]

• For dc fault diagnosis in MMC-MT-HVdc grids, improved features are collected using DWT-based MRA and Parseval's theorem. • An optimal ANN architecture is used to classify fault patterns based on transient features. The proposed protection scheme is robust against severe noise conditions and high impedance faults. Bayesian optimization is a well-suited technique to optimize ANN hyperparameters. • The Bayesian optimization method also significantly reduces the time required to evaluate and select ANN models. • It is further finding an efficient autonomous solution to tune excessive multiple hyperparameters with the help of Bayesian optimization and providing a basic understanding of it. • This algorithm is implemented in a single-end main and coordinated secondary unit containing control logic. By detecting internal dc faults as soon as possible, the proposed scheme covers the failure of the main unit with expedited backup. This paper proposes a fault detection and classification scheme for multi-terminal high voltage direct current (MT-HVdc) lines by integrating discrete wavelet transform (DWT) multi-resolution analysis with artificial neural networks (ANNs). Previously, such intelligent protection schemes used manual approaches or arbitrary rules of thumb to optimize a set of hyperparameters of the neural networks without applying any optimization algorithm. In order to improve accuracy, this work proposes an efficient Bayesian Optimization (BO) approach for evaluating and establishing the regulated hyperparameters for ANNs. The DWT multi-resolution analysis (MRA) and Parseval's theorem are used to extract energy variation for various faults. The energy variation of fault signals at different scales is fed into a multi-stage model to optimize the hyperparameters of neural networks with minimal training setup time and compute effort. After training, the data-based algorithm is implemented in a single-end main and coordinated secondary unit with control logic. The proposed scheme intends to detect internal short-circuit dc faults as quickly as possible and cover the failure of the main unit with expedited backup action. The findings of the study reveal that the proposed scheme can accurately detect internal faults in a variety of testing conditions and remain stable against external faults or disturbances with an average recognition accuracy of 99.38%. [ABSTRACT FROM AUTHOR]

• Propose an error-and-hold algorithm for the SOGI-FLL that can quickly detect faults and give a response that consists in holding the previous to the fault estimated frequency value during these perturbations. • Develop the algorithm using the absolute value of the SOGI's error, its average, and the average of the FLL's estimated frequency to operate, to reduce induced errors in the SOGI-FLL's quadrature outputs, improves the FLL's transient response, hold the estimated frequency, and restores the phase to its previous value before the fault. • Using the LTP model of the SOGI-FLL, to demonstrate how voltage sags and swells affect the amplitude voltage and frequency via an asymmetrical-gain mutual interaction between the SOGI-FLL estimates and a sinusoidal gain that relies on the grid voltage phase. • Demonstrate the practicality of the proposed algorithm, using MATLAB/Simulink software simulations and experimental results, illustrating how it can enhance the SOGI-FLL's response to these disturbances. The Second Order Generalized Integrator–Frequency Locked Loop (SOGI-FLL) is a widely used and popular adaptive filter for estimating grid voltage parameters with minimal computational burden. However, it is vulnerable to voltage sag and swell faults, especially voltage sags that can significantly distort the estimated frequency. In this paper, we propose an error-and-hold algorithm for the SOGI-FLL that can quickly detect faults and hold the estimated frequency during these perturbations. The algorithm uses the absolute value of the SOGI's error, its average, and the average of the FLL's estimated frequency to operate. It reduces induced errors in the SOGI-FLL's quadrature outputs, improves the FLL's transient response, holds the estimated frequency, and restores the phase to its previous value before the fault. The proposed algorithm is a straightforward and low computational burden algorithm that can be executed on a low-cost processor. We validate the effectiveness of the proposed error-and-hold algorithm through simulations and experimental results. [ABSTRACT FROM AUTHOR]

• Robust nonlinear control technique for enhancing LVRT capability of DFIG Wind Turbines. • Easy implementation with no additional hardware or energy storage and less computational complexity. • Adaptable to any existing wind farm without additional cost. • Superior electrical and mechanical performance, which limits high current and torque oscillation. This paper proposes a nonlinear controller for doubly fed induction generator (DFIG) wind turbines using partial feedback linearization (PFL) technique. The controller generates switching signals for driving both the rotor side converter and grid side converter simultaneously enhancing the low voltage ride through (LVRT) capability over a wide range of operating conditions. The proposed PFL method has been implemented into a partially linearized form of a nonlinear system, where the transformed system has been made autonomous and reduced in order. All calculations in the proposed method except for the control laws have been carried out offline resulting in reduced design and implementation complexity, small computational burden, and offline control tuning with fast tracking performances. The step-by-step approach of control design and implementation includes system modeling and partial linearization, control law derivation, software implementation, and controller tuning. The effectiveness of the proposed controller has been evaluated through electromagnetic transient simulations. The simulations have demonstrated that the controller has successfully augmented the LVRT capability of DFIG wind turbines and has remained robust against diverse wind conditions and voltage sags. [ABSTRACT FROM AUTHOR]

This paper presents the stability augmentation of pitch angle control for a permanent magnet synchronous generator (PMSG)-based wind turbine system (WTS) with pitch actuator uncertainty via L 1 adaptive scheme. To do this, a novel L 1 adaptive scheme is firstly proposed to regulate the pitch angle at above-rated wind speed conditions and maintain the rated rotor speed in the presence of pitch actuator uncertainties in the obtained pitch system. Next, a non-affine PMSG system with uncertainties is utilized to represent the pitch regulated variable-speed WTS. Then, the L 1 adaptive scheme is proposed as a stability augmentation system. At this time, the bound conditions are presented to prove the stability and performance evaluation of the proposed L 1 adaptive scheme. Finally, through the simulation of the 20 − MW PMSG-based WTS, the proposed algorithm proves its efficiency and applicability compared to the existing control methods. • This study is to effectively regulate the pitch angle and extract the maximum power from the 20MW WTS. • The proposed adaptive control scheme introduces the SAS method to improve the transient and steady-state performance of the system. • The proposed stability augmentation scheme minimizes the frequency of adaptation estimations and gain values required. • The proposed scheme is evaluated under various environmental conditions, such as gust wind, step wind, and varying wind speed. • The proposed algorithm is provided to prove its efficiency and applicability compared to existing control methods through MATLAB/SIMULINK simulation of the 20 − MW PMSG-based WTS. [ABSTRACT FROM AUTHOR]

• Protection issues of TCSC compensated line integrated with DFIG based Wind Farm. • A novel protection algorithm is proposed to detect the faulty phase in a TCSC compensated line connected with DFIG based Wind Farm. • This proposed method is also validated in a real time platform using dSPACE DS-1104 based prototype processor. • Use of the ITD based technique for detecting faulty phase in TCSC compensated line connected to DFIG based wind farm. • This ITD based algorithm is sensitive for close in fault and high resistance fault in TCSC line with wind farm. Nowadays there is a trend for offshore wind farms to be connected with power grids through a TCSC series controlled compensating device employed in transmission lines for the improvement of large power flows. In such transmission lines, faulty phase identification and ground detection create a challenge for conventional distance relaying schemes because of non-linear output power fluctuation due to variations in wind speed and different firing angle operations of TCSC. Therefore, to overcome the problem of such transmission lines relaying, a novel time-frequency analysis-based intrinsic time scale decomposition (ITD) method is proposed in this paper. The proposed intrinsic time scale decomposition method uses only a three-phase grid side current from relaying end for faulty phase and ground detection and ITD supported random forest classifier for fault classification accuracy approach. The evaluation of the proposed scheme is tested on several fault cases with varying system parameters and non-fault transient events through the EMTDC/PSCAD platform during different wind speeds and varying firing angle operations of TCSC. The performance of the proposed scheme is also verified through a real-time interface dSPACE DS 1104 control prototype hardware. Finally, a comparison analysis with existing techniques demonstrated the effectiveness of the presented method to assess the mentioned problem of the conventional protective relaying schemes. The proposed method demonstrated a 100% accuracy for faulty phase selection and a 99.99% accuracy for fault classification. [ABSTRACT FROM AUTHOR]

• The characteristic function of the grid-connected VSC is established. • The impacts of the system resistances on the system stability are studied analytically. • An analytical stability criterion for the grid-connected VSC is derived by neglecting the system resistances. • The power transmission limitation of the converter is obtained from the derived stability criterion. This paper provides an analytical investigation of the small-signal stability of the grid-connected voltage source converter (VSC) as well as the impacts of the system resistances. The dynamic model of the studied system is first established, and the characteristic function is derived from the linearized model. Based on the characteristic function, the analytical relationships between the system resistances and the dominated pole are obtained utilizing the analytical sensitivity approach. It is found that the line resistance can provide positive damping for the oscillation mode, improving the system stability, while the converter resistance will worsen the system stability. Generally, the line resistance has an evident more substantial impact on the stability of the grid-connected VSC than the converter resistance. The stability analysis results of the grid-connected VSC conducted by ignoring the system resistances are conservative. Ulteriorly, the characteristic function is simplified by neglecting the system resistances, and a sufficient and analytical stability criterion is established from the simplified characteristic function using the Routh Judgement. It exhibits the constraint condition among controller parameters, electrical distance and operation conditions for ensuring system stability. Moreover, the power transmission limitation of the converter affected by the controller parameters and electrical distance is obtained from the derived stability criterion. The small perturbation analysis and electromagnetic transient simulation give a demonstration to the analysis. [ABSTRACT FROM AUTHOR]

High-frequency oscillation is one of the critical issues threatening the stability of modular multilevel converter (MMC) based high-voltage direct current (HVDC) system. A new 2 kHz high-frequency oscillation has occurred in the wind farm-side MMC station of Rudong wind farm integrated MMC-HVDC project of China during no-load charging process. The mechanism of this high-frequency oscillation is different to previous ones. Apart from the time delay of MMC, the stray capacitance of converter transformer makes a significant contribution to the high-frequency oscillation. This paper investigates the high-frequency oscillation mechanism of wind farm-side MMC station during no-load charging process. First, the harmonic state space (HSS) model of a wind farm-side MMC station is established. In addition to the leakage inductance, the stray capacitance is considered in the converter transformer model. To reveal the significance of the converter transformer stray capacitance in this new high-frequency oscillation, the root loci of the system are calculated with varying stray capacitance. Then, the state variables with high degree of participation in the high-frequency oscillation modes are determined by the participation factor analysis. A reduced-order model suitable for the high-frequency oscillation analysis is further established based on the participation factor analysis results. Next, the high-frequency oscillation mechanism is revealed by impedance analysis. Finally, the effects of system parameters are analyzed by the combination of eigenvalue analysis and impedance analysis. The analysis results are validated by electromagnetic transient simulations. • High-frequency oscillation mechanism of MMC charging with transformer is revealed. • The transformer stray capacitance must be considered in the oscillation analysis. • Participation factor analysis is carried out to determine main influencing factors. • A reduced-order model suitable for high-frequency oscillation analysis is proposed. • AC voltage control of MMC has significant effects on the high-frequency oscillation. [ABSTRACT FROM AUTHOR]

The existing ultra-fast non-unit protection methods for modular multilevel converter (MMC) HVDC grids based on the protection boundary have shortcomings, such as a lack of adaptive ability and difficulties in threshold setting. The key point is that it is hard to obtain the status of the fault point, which makes the method that uses a fixed threshold value difficult to adapt to various fault conditions. In this paper, the fault voltage which is composed of many sub-components is analyzed based on the built equivalent circuit of MMC-HVDC grids after DC line faults. A fault resistance estimation method is proposed by utilizing the ratio of the second module maximum to the initial module maximum after filtering by a multi-resolution morphological gradient algorithm, and the approximate difference in propagation distance is obtained by using the time difference and the change directions of the initial two surges to correct the influence of distance. A self-adaptation non-unit protection scheme is proposed based on the estimated fault resistance, which consists of the start-up unit, identification of fault types, fault resistance estimation, and self-adaptation main protection. A four-terminal ring-topology MMC-HVDC grid built in PSCAD/EMTDC demonstrates the higher performance of the proposed scheme under various fault conditions. • The expressions of fault voltages at various positions in MMC-HVDC grids are derived. • A fault resistance estimation method is proposed by using the ratio of two surges. • The propagation distance is obtained by using time difference and change direction. • A self-adaptation protection is proposed based on the estimated fault resistance. [ABSTRACT FROM AUTHOR]

• Developing impedance models of IBR and SM considering detailed control for stability analysis of severe grid conditions. • Adverse control interaction of SM/SC and GFL IBR may occur by high IBR penetration during system-split situations. • The low-frequency non-passivity of GFL IBR and SM/SC can adversely participate their control interaction. • Oscillation risk in SM and GFL IBR system can be mitigated by retuning their control, but may induce other stability issue. • Through changing part of the IBRs from GFL to GFM, both grid-support services and oscillatory stability can be ensured. Motivated by the potential transient oscillation risks in inverter based resource (IBR) dominated power systems, the paper is to identify the unwanted control interactions between traditional synchronous machines (SMs) and IBRs during system-split situations. Modal impedance analysis method is applied to reveal oscillation risk and the underlying mechanism, while electromagnetic transient (EMT) simulation analysis is used to observe reliable oscillation phenomenon. Impedance models of IBRs considering both grid-following (GFL) and grid-forming (GFM) control schemes and SMs equipped with automatic voltage regulator (AVR) and power system stabilizer (PSS) are developed for grid conditions with large frequency and/or voltage deviations, and validated by EMT simulations. Potential adverse control interactions within an exemplary test system are analyzed taking into account the impacts of: 1) renewable penetration level; 2) converter control scheme (GFL or GFM); 3) converter control tuning; 4) SM control setting; 5) grid-support capabilities of converter-interfaced loads. It has been observed that oscillation instability at around several Hz can occur by high penetration of GFL controlled IBRs after system-splits, which can be mitigated by redesigning the AVR & PSS control, or retuning the power/voltage control loops and phase-locked loop (PLL) of GFL converter. However, such measures might inevitably induce other stability issues, e.g. synchronization instability. From the oscillation analysis, it has also been revealed, through replacing part of the GFL converters with GFM converter(s), the oscillation mode at several Hz can disappear, owning to the varied impedance including better damping of GFM than GFL for the frequencies between 1 and 10 Hz. [ABSTRACT FROM AUTHOR]