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This paper presents a novel methodology for the construction of a transient stability boundary (TSB) that overcomes the lack of TSB analytical description for multiple operating states and contingencies in power systems. The proposed approach models the TSB as a nonlinear mapping between the system parameters of interest and the corresponding critical clearing time (CCT). This compact mathematical expression is built based on an efficient discriminative network, broad learning system (BLS). While keeping a high accuracy and generalization ability, the newly introduced construction method provides an efficient update strategy that does not require an entire retraining cycle. These properties make this method suitable for online transient stability assessment (TSA). The prospects of the developed method are verified via case studies by employing the IEEE 9-bus, IEEE 39-bus (New England) test systems and a real system of China Southern Power Grid. In comparison with existing methods, the newly introduced algorithm has a higher prediction accuracy and improved robustness. The demonstrated characteristics indicate that the proposed method may serve as a valuable tool in the framework of online TSA. [ABSTRACT FROM AUTHOR]

The real-time simulation based on the field programmable gate array (FPGA) is receiving more and more attention. However, up to now, the simulation scale for the power electronic system is not so satisfactory due to the real-time requirement and the FPGA resource limitation. This paper proposes a sub-microsecond level real-time simulation method for microgrids. The power converters are modeled with fixed-admittance models and simulated with a compact electromagnetic transients program (EMTP) algorithm. In the meanwhile, the distribution lines/cables are modeled with π-circuit models and simulated with a distributed circuit solution method, called the latency insertion method (LIM). As a result, the distribution generation (DG) systems are decoupled with each other and can be simulated in parallel. The case study shows that the proposed simulation method consumes much fewer FPGA resources compared with the traditional one. Besides, the time step can be much smaller and doesn't need to increase with the simulation scale. With these advantages, the real-time simulation of a microgrid consisting of three three-phase converters, three boost circuits and 21 three-phase lines can be achieved on the Xilinx Kintex-7 410T FPGA with a minmum time-step of 380 ns. [ABSTRACT FROM AUTHOR]

Power converters in the system-level real-time simulation are usually emulated by L/C-based associated discrete circuit (L/C-ADC). However, the L/C-ADC approaches may suffer from two issues: How to mitigate the unacceptable virtual power loss especially in high-frequency applications, and how to tune LC parameters setting which is affected by the external circuit. This paper proposes a novel generalized associated discrete circuit (G-ADC) model with parameterized history current sources. By utilizing the stability region of the feasible parameter space, the optimized G-ADC models with the best damping characteristic are developed for both two-level and three-level converters. The analytical results also guarantee that the parameters of the optimized G-ADC model are independent of the external circuit for most power grid applications. Furthermore, an field programmable gate array (FPGA)-based real-time simulation platform is built to verify the feasibility of the proposed scheme. Extensive simulation and hardware-in-loop experiment results demonstrate the effectiveness and superiority of best-damped models as well as the modeling flexibility corresponding to insensitivity to operating conditions and external system parameters. [ABSTRACT FROM AUTHOR]

This study develops a system‐level dynamic phasor (DP) model of a hybrid AC/DC microgrid. A new definition of DP, based on the multiple frequency shift transformation, is proposed to extend the models of a variety of AC/DC and DC/DC converters. The comprehensive control system is considered in developing the DP model of microgrid. Furthermore, a computational framework for applying this DP model into system‐level simulation and small signal analysis (SSA) is given. The DP‐based simulation is tested under conditions of environmental disturbances and unbalanced supply voltages. The SSA is performed on the developed DP model to evaluate the voltage stability and harmonic modes of the microgrid. Besides, this DP model shows high potential when implemented in the real‐time simulation with larger scale system. [ABSTRACT FROM AUTHOR]

The rising penetration of renewable generation as a result of environmental concerns generates increased uncertainties in power systems. This necessitates probabilistic analyses of the system performance, which include probabilistic power flow (PPF). The PPF suffers from the curse of dimensionality due to a large number of random loads. To address this issue, a multivariate dimension-reduction (MDR) method is proposed for PPF studies in this paper. The MDR decomposes the PPF problem into lower dimensional PPF subproblems which are further solved with promising accuracy. The computation time of the proposed method is proportional to the number of wind farms, which noticeably facilitates computation. The proposed method is applied to the IEEE 118-bus system and 2383-bus system. Simulation results demonstrate the accuracy and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Probabilistic load flow (PLF) is a powerful and widely used tool to address the random nature of renewable energy resources for the planning and operation of power systems. In this study, a new approach using a combination of the multiple integral method (MIM) and the cumulant method (CM) is proposed for PLF studies. The PLF problem with high dimensionality is decomposed into a bi‐level problem and solved by MIM and CM to reduce the computational burden significantly while achieving satisfactory accuracy. The proposed method is applied to the IEEE 118‐bus system and is compared with CM and point estimate method. Simulation results show that the proposed method achieves great computational efficiency and accuracy. [ABSTRACT FROM AUTHOR]

This paper presents an analysis of the evolution of the probability density function of the dynamic trajectories of a single machine infinite bus power system. The probability density function can be used to determine the impact of random (stochastic) load perturbations on system stability. The evolution of the state probability density function over time leads to several interesting observations regarding stability regions as a function of damping parameter. The Fokker-Planck equation (FPE) is used to describe the evolution of the probability density of the states. The FPE is solved numerically using PDE solvers (such as finite difference method). Based on the results, the qualitative changes of the stationary density produce peak-like, ridge-like and other complicated shapes. Lastly, the numerical FPE solution combined with SMIB equivalent techniques lay the framework extended to the multimachine system. [ABSTRACT FROM PUBLISHER]

This article presents a feedback linearization based controller design methodology for a unified power flow controller to achieve rapid reference signal tracking in the internal control level. Feedback linearization is a non-linear control technique based on the differential geometry theory and overcomes the drawback of traditional linear proportional-integral control, which is typically tuned for one specific operating condition. In this article, feedback linearization control is developed for the unified power flow controller dynamic model via an appropriate coordinate transformation, and linear quadratic regulator control is then applied on the transformed linear system. The proposed control is validated via a detailed device-level simulation on an 11-bus system and a large scale simulation on the IEEE 118-bus and 300-bus systems. The proposed control is benchmarked against proportional-integral control. [ABSTRACT FROM PUBLISHER]

A new internal STATCOM control based on feedback linearization is proposed. The feedback linearization controller is developed without any simplifying assumptions to the STATCOM model. The proposed control is validated on the IEEE 118-bus system with full-order generator and network models as opposed to a small test system. Furthermore, the proposed control is benchmarked against published results. Lastly controllability issues associated with a singularity in the feedback linearization control (FBLC) coordinate transformation is identified, and a solution is provided to avoid instability. [ABSTRACT FROM AUTHOR]

This paper presents the development of a real-time hardware/software laboratory to interface a soft real-time power system simulator with multiple unified power flow controllers (UPFC) via hardware-in-the-loop (HIL) to study their dynamic responses and validate control and placement approaches. This paper describes a unique laboratory facility that enables large-scale, soft real-time power system simulation coupled with the true physical behavior of a UPFC as opposed to the controller response captured by many other real-time simulators. The HIL line includes a synchronous machine, a UPFC, and a programmable load to reproduce the physical dynamics of the UPFC sub-network. [ABSTRACT FROM PUBLISHER]

The L/C-based fixed-admittance model (L/C model) is usually used in the real-time simulation for power electronic converters. However, the L/C switch model suffers from the problems of virtual power loss and complicated optimal parameter settings. This article proposes a small-step synthesis real-time simulation method suitable for power electronic converters. By modeling the power electronic converter with a small (nanosecond) time-step and simulating with a normal (microsecond) time-step, the issue of virtual power loss of the L/C model caused by the transient process after the switching action is solved. The real-time simulation experiments with different type converters based on one set of simulation parameters are carried out on field-programmable gate array separately to verify the insensitivity to converter topologies. Furthermore, the real-time simulation results of the small-step synthesis method using the L/C model are compared with those of the traditional electromagnetic transient program (EMTP) method using the L/C model and the Ron/Roff model. The simulation results provide verification of the effectiveness of the small-step synthesis method as well as the insensitivity to carrier frequencies, and L/C model parameters. [ABSTRACT FROM AUTHOR]

Charging behaviours of electric vehicles (EVs) exhibit substantial randomness, making accurate prediction or modelling challenging. Furthermore, as the number of EVs continues to increase, charging stations are diversifying their offerings to accommodate distinct charging characteristics, addressing a wide spectrum of EV charging needs. Previous research mostly focused on the randomness of EVs while neglecting the heterogeneity in charging infrastructure. Therefore, this paper introduces a decentralized collaborative optimal method for EV charging stations, taking into account the varying facility types and the power limitations. First, a decentralized collaborative framework is proposed. The energy boundary model and the average laxity of EVs contribute to transforming the optimization problem into a Markov Decision Process (MDP) with uncertain transitions. Then, multi‐agent deep deterministic policy gradient multi‐individuals (MADDPG‐MI) algorithm is developed to train several heterogeneous agents presenting different types of charging facilities. Each agent makes decisions for multiple homogenous charging piles. Numerous simulation studies validate that the proposed method can effectively reduce charging costs and manages in scenarios involving either homogeneous or multiple heterogeneous charging facilities. Moreover, the MADDPG‐MI algorithm demonstrates performance consistency among multiple decision‐making units while consuming lower training resources offering enhanced scalability. [ABSTRACT FROM AUTHOR]

This study proposes a novel robust transmission‐constrained unit commitment model with adjustable conservatism (denoted as RAC‐TCUC). Ellipsoidal uncertainty set (EUS) is adopted in this model to well fit the spatial–temporal correlated wind power. The affine policy is utilised in the generation dispatch process of the model for the sake of computational tractability. To reduce the conservatism, a novel criterion for budget value selection of the EUS is presented. Moreover, this study discusses a crucial, yet barely addressed issue in the literature: the feasibility of the solution against the realisation of uncertainties beyond the prescribed EUS. To prove the validity of the criterion, an analytical relationship between the budget value of the EUS and the actual probability of solution's feasibility against all possible scenarios of uncertainties is presented. Finally, the testing results demonstrate the effectiveness and economic benefits of the proposed method. [ABSTRACT FROM AUTHOR]

Modern power systems are experiencing an escalation in the penetration of wind power sources which have both positive and negative impact on small signal stability. Wind power being stochastic in nature introduces uncertainties which make it necessary to account for such uncertainties during power system modeling and analysis. Probabilistic methodologies are appropriate choices in accounting for such uncertainties. These methodologies have recently developed concerns with regard to the probabilistic small signal stability analysis of power system integrated with wind power generation. Accounting for the dependence existing between wind power sources is considered as an important option to aid in simulating the impact of the wind power integration towards small signal stability. Numerous dependence modeling methods exist, each with its strengths and weaknesses. This paper presents an overview of the probabilistic methods applied in small signal stability analysis and methodologies used to model dependence or correlation in the probabilistic stability analysis. A comparative analysis of different dependence models is performed. The model accuracy is compared under different scenarios and the efficiency is discussed. [ABSTRACT FROM AUTHOR]

Transient control performance of power systems is extremely important, especially during the recovery stage from a system temporary fault. A large power angle error or generator relative speed could result in unrecoverable failure or system damage. In this study, a class of novel excitation controllers is proposed for power systems to place user‐defined time‐varying constraints on the system errors. First, the direct feedback linearisation technique is employed to transfer the original non‐linear system to a linear one. An error transformation method is introduced to generate a new non‐linear system, whose stability ensures that the time‐varying constraints on the original system are satisfied. Thus, a backstepping‐based excitation control methodology is designed for ideal case by assuming all system parameters are known. Thereafter, the uncertainties of system dynamics are also considered and compensated by designing an adaptive excitation controller. By utilising the standard Lyapunov synthesis, the closed‐loop system is proved to be asymptotically stable, and all the other signals are bounded for the two control schemes. Furthermore, the system transient performance can be shaped arbitrarily with predefined trajectories, in the sense that the system errors never cross certain boundaries during transient phase. Eventually, extensive simulation studies demonstrate the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

In the integrated energy system with small samples, insufficient data limits the accuracy of energy load forecasting and thereafter affects the system's economic operation and optimal dispatch. For this specific environment, this paper proposes a multi-energy load forecasting method based on the neural network model and transfer learning to meet the demand of enterprises for forecasting accuracy. The method improves forecasting accuracy through three stages including data analysis and processing, a combined model built and load forecasting. More specifically, the Pearson correlation coefficient is used to filter out meteorological variables with strong correlation based on energy load and meteorological data. A combined model is developed based on the convolutional neural network and gated recurrent unit. A model structure adjustment strategy based on the maximum mean difference is proposed to dynamize the structure to cope with the complex prediction environment. The synergy between source and target domain data is realized based on transfer learning. In addition, the model performance is further optimized through model training, transfer learning, and parameter fine-tuning, which lays the foundation for improving the forecasting accuracy of electricity, gas, cooling, and heating loads. The simulation results show that the proposed method can achieve satisfactory predictions for integrated energy systems with small sample data. • A multi-energy load forecasting method based on transfer learning is proposed. • A combined model is proposed to extract the coupled features. • An optimization strategy of the model structure is designed. • The proposed method can handle the small sample forecasting problem. [ABSTRACT FROM AUTHOR]

With the increment of scale of power system, the accuracy and efficiency requirements of N-1 static security analysis (SSA) keep increasing. In order to satisfy these requirements, this paper proposed a GPU-accelerated N-1 SSA method to reduce computation burden and ensure the accuracy of alternating current power flow (ACPF) and connectivity test simultaneously. First, in the algorithm, ACPF is performed by holomorphic embedding load flow method (HELM). The construction and solution of sparse linear system both adopts fine-grained parallelism. According to the mathematical lemma of combining linear equations, this paper performs fine-grained parallelism Padé approximation of HELM. Second, considering the high time complexity of the original search-based algorithm and adjacency matrix method which is not suitable for sparse graph, this paper proposes a GPU-accelerated Union Set algorithm. Its main advantage is lower time complexity compared to other graph theory methods. And most importantly, it is very suitable for parallelization. Shared memory can be used in this algorithm well. Therefore, it is not complicated to perform a block-level parallelism in GPU-accelerated Union Set. Finally, the overall framework of GPU-accelerated N-1 SSA method is shown in this paper. It has been tested on large-scale power systems of up to 2869 buses. The computation results are compared with MATPOWER and the execution times are compared with other mainstream method to show the improvement in performance. • Significant improvement in accuracy for power system N-1 static security analysis. • GPU-based sparse linear system equations solver • Fine-grained parallelism HELM to accelerated ACPF for N-1 static security analysis • A block-level parallelism GPU-based Union Set algorithm to accelerate connectivity test. [ABSTRACT FROM AUTHOR]

With growing complexity and uncertainty from distributed generations and active customers, distribution networks are facing more unexpected events and topology changes; while very limited measurements may degrade the observability of distribution system states and endanger the security of the system. Meanwhile, massive data from various types of users (if they can be used), can be valuable for power utilities. This makes privacy and data security a more critical issue, while being endowed with operation and market flexibilities. Thus, we propose a blockchain-based privacy-protecting approach for Dynamic Topology Awareness (DTA) to distinguish topology changes from cyber anomalies, including physical, cyber and business layers. At the bottom layer (physical layer), the distribution network is partitioned into subareas and tie-line areas, coping with local data from measurement devices or users. Estimated border values from parallel local estimations would be examined through data consistency checking. And DTA consensus algorithm might be triggered, querying historical status stored as blockchain contracts for anomalies detections and new block formations. Voting mechanism is then adopted to verify new blocks from data tampering. The performance of the proposed DTA approach is validated through simulations to identify topology changes and cyber anomalies, with additional discussions on the trade-off between DTA sensitivity and estimation accuracy. [ABSTRACT FROM AUTHOR]

To effectively capture interactions of large-scale ac–dc systems integrating line commutated converter (LCC) and modular multilevel converter (MMC) based multiterminal dc grids, a numerically accurate and efficient simulation method is desirable. To achieve this objective, a cosimulation method is proposed in this article, where the target system is decoupled into the shifted-frequency phasor (SFP) subsystem, the dynamic phasor (DP) subsystem, and electromagnetic transient (EMT) subsystem, respectively. The MMCs are included in the SFP subsystem and implemented on massively paralleled graphics processing units (GPUs). Thus, the simulation efficiency is greatly improved by adopting a much larger time step, the model order reduction technique, and GPU acceleration. The LCCs are represented by DPs and are included in the DP subsystem. The majority of ac grids are covered in the EMT subsystem. Further, the interactions between SFP and EMT subsystems are reflected by the proposed multidomain transmission line model, which can produce instantaneous and phasor values simultaneously. The interface model between DP and EMT subsystems is modeled as a special controlled voltage and current circuit. Finally, the overall cosimulation method is realized by the respective SFP/DP and EMT models, among which their interactions are reflected by the proposed interface models and the time sequences of simulations. The performance of the proposed method has been fully validated on a practical large-scale ac–dc system. [ABSTRACT FROM AUTHOR]

As a clean energy, wind power has been extensively exploited in the past few years. However, oscillations in wind turbines, particularly those from controllers, could severely affect the stability of power systems. Therefore, oscillation suppression is a recent research focus. Based on the small-signal model eigenvalues and participation factors, this paper detects the sub-synchronous interactions (SSI) mainly determined by converters’ PI parameters in a grid-connected doubly fed induction generator (DFIG). With the aim of oscillation restraint, a novel optimization model with the reference-point based non-dominated sorting genetic algorithm (NSGA-III) and the t-distributed stochastic neighbour embedding (t-SNE) is developed to explore and visualize optimal ranges of PI parameters, facilitating the selection of the appropriate PI parameters to augment the damping. Additionally, to study the adaptability of the optimal PI parameters, interactions performance of the system that uses optimal parameters is studied with different output levels of the wind turbine. Finally, a time domain simulation and a practical experiment are conducted to demonstrate the effectiveness of the proposed approach. Results illustrate that the SSI of a grid-connected DFIG is suppressed by the optimization model. This study is highly beneficial to power system operators in integrating wind power and maintaining system stability. [ABSTRACT FROM AUTHOR]

• A decentralized framework for large-scale EV scheduling. • A DEB model discretizing use's charging demand and the charging capacity of the CS. • RDDPG method to train one agent model to schedule multi charging piles. • Significant improvement in scalability for large-scale EVs scenario. The rapid growth of electric vehicles (EVs) is an unstoppable worldwide development trend. An optimal charging strategy for large-scale EVs is able to deal with the randomness of EVs charging and satisfy charging demands of users while ensuring safe and economic operation of the power system. The current centralized and model-based methods failed to overcome the randomness charging problem of the large-scale EVs. Thus, the paper proposes a decentralized approach based on model-free deep reinforcement learning (DRL) to determine the optimal strategy for reducing EVs charging cost considering power limit of the charging station (CS), users' charging demands and fair charging fees. First, a decentralized framework and a dynamic energy boundary (DEB) model of single EV which discretizes the charging demand are proposed. Second, the problem as a Markov Decision Process (MDP) with unknown transition probability is formulated. Moreover, the recurrent deep deterministic policy gradient (RDDPG) based approach is proposed to determine the charging strategy for all charging piles in the CS. Finally, digital simulation studies are conducted to demonstrate the effectiveness of the proposed approach in charging cost reduction and fair charging fees. In addition, the RDDPG-based approach has great scalability which can apply a small-scale model to solve a large-scale problem without being retrained. [ABSTRACT FROM AUTHOR]

• Mechanical mapping model is used to evaluate resilience enhancement in distribution networks with SOPs. • Both normal operations and power restoration are considered to maximize resilience enhancement. • A bi-level programming algorithm is proposed to determine the siting and sizing of SOPs to boost resilience. Disturbances such as natural disasters or man-made attacks exert serious influences on power system, resulting in an increasing awareness of resilience enhancement strategies. As the integration of microgrids, distributed generators (DGs) and power electronic devices adds to the vulnerability of power distribution network to disruptions, it is highly required to enhance the resilience against failure. Soft open points (SOPs) are flexible power electronic devices, which can balance power distribution under normal operation, and supply restoration under abnormal conditions. Thus, the application of SOPs can boost resilience both in pre-failure prevention and post-failure recovery. In this paper, to maximize the effect of SOPs on the boost of resilience of distribution network, a mixed integer non-linear optimization problem is proposed to schedule the siting and sizing of SOPs based on multi-stage elastic mechanical model. A bi-level algorithm is used to tackle the SOP planning problem. The selection of location and capacity is solved by genetic algorithm, after which the control strategies of SOP are optimized by particle swarm algorithm with given planning scheme to obtain the maximum resilience. Finally, case studies on the IEEE 33-bus system and IEEE 123-node test feeder are used to verify the effectiveness and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Differentiation of resilience from reliability has been a heated topic ever since the emergence of the former upon the limitation, and as a complement, of the latter, while finding the common ground for both has been scarce. This study first picks out the steady-state performance of both to be the common ground, while differentiating their typical causes, namely, the extreme weather for the resilience threats and the component ageing for the reliability challenges. An original evaluation framework developed earlier for the sole reliability is then extended here towards this common ground to accommodate resilience, becoming the joint reliability and resilience evaluation framework. The joint evaluation framework is built upon the Monte Carlo simulation, which embeds the rolling unit commitment as the system operation module to balance the optimality of operation strategy and the punctuality of condition update, and the forecast module with the machine learning technique for generate varied operation conditions. The proposed evaluation framework that joins resilience with reliability not only has its efficacy validated on the 39-bus system, but also deepens the evaluation by analyzing scenarios created with variating the values of key factors that impact resilience, including the typhoon speed, load factor, restoration time, and typhoon direction. Such a joint reliability and resilience evaluation pioneers as an integrated approach to conduct both evaluations in three aspects, namely, differentiating the causes of reliability and resilience harms and paralleling the challenges of both on system performance, upgrading the existing evaluation methods by applying the rolling mechanism to the operation strategy, and offering an open framework to embed complex functions, such as forecast tools enabled by machine learning and proactive responses for resilience enhancement. • Research gap of common ground of resilience and reliability spotted from literature. • A joint resilience and reliability evaluation framework with the Monte Carlo simulation. • Rolling unit commitment as the embedded operation module of the evaluation. • An open framework extensible for more complex strategies of resilience enhancement. • Proven convenience of the framework for application to real systems. [ABSTRACT FROM AUTHOR]

The Tongling district is one of the most important non-ferrous metal producers in China. The origin of Cu-Au deposits in the region is closely related to Late Mesozoic intermediate intrusions, which are mainly high-K calc-alkaline and shoshonitic series. Geochemical characteristics indicate that these granitic rocks are mixtures of more than two compositional end-members, i.e. mantle-derived melts and crust components incorporated through assimilation. Three important magmatic intrusions related to the Cu-Au deposits in the Tongling region - the Jiguanshi quartz monzodiorite, the Xishizishan quartz diorite and the Miaojia diorite porphyry - were selected for this study. Zircon U-Pb dating by LA ICP-MS yielded two groups of ages (∼130-132 and 138-140 Ma) for these intrusions. Pyrite Re-Os age for the Xinqiao Cu-Fe-S deposit in the Tongling region is 126±11 Ma. Trace elements of zircon grains show that the earlier Cu-Au mineralization event was associated with adakitic rocks characterized by high positive Ce anomalies, produced at an elevated oxygen fugacity range. In contrast, later iron-sulphur mineralization was closely related to low positive Ce anomalies, reflecting low oxygen fugacities. Considering that Pacific lithospheric subduction was the dominant factor that controlled major tectonic evolution in eastern China during the Early Cretaceous, the geochemical characteristics of these coeval ore-forming intermediate intrusive rocks in the Tongling district were likely the result of Pacific plate underflow. [ABSTRACT FROM AUTHOR]