In this study, by using generator electrical output power and rotor speed, a new algorithm for out-of-step prediction is proposed. In this online method, after fault clearance, the trend of generator output power will be predicted using sinusoidal variable frequency function curve fitting. Finally, time-domain equal area criterion (TDEAC) is used to evaluate the transient stability. The mathematical proofing of TDEAC and its validity in large-scale systems are presented too. Real-time prediction, fast calculation, using only local parameters and estimation of the remaining time until instability are some of the proposed method's advantages. The performance of this algorithm is examined on IEEE 39-bus New England and Iran electrical power network systems. The results show that the proposed method represents a valuable alternative for out-of-step protection possessing fast and high-efficiency performance. The simulations are carried out using the Power Factory^® software and the proposed algorithm has been developed in MATLAB.

Microgrids experience significantly different fault currents in different operating scenarios, which make microgrid protection challenging. Existing intelligent protection schemes rely on the extraction of appropriate fault features using statistical parameters. The selection of these features is difficult in a microgrid because of its various operating scenarios. This study develops a convolutional neural network-based intelligent fault protection strategy (CNNBIPS) for microgrids that inherently integrates the feature extraction and classification process. The proposed strategy is directly applicable to three-phase (TP) current signals; thus, it does not require any separate feature extractor. In the proposed CNNBIPS, TP current signals sampled by the protective relays are used as an input to three different CNNs. The CNNs apply convolution and pooling operations to extract the features from the input signals. Then, fully connected layers of the CNNs employ the features to develop fault-type, phase, and location information. To analyse the efficacy of the proposed design, we execute exhaustive simulations on a standard microgrid test system. The results confirm the effectiveness of the proposed strategy in terms of detection accuracy, security, and dependability. Moreover, comparisons with previous methods show that the proposed approach outperforms the existing microgrid protection schemes.

An extra transient block (ETB) for virtual synchronous machine (VSM) that is able to provide extra transient damping and adjust transient inertial to better stabilise the frequency of the VSM in a shorter time during transient period without altering the steady-state performance is proposed in this study. The ETB uses extra parallel series lead-lag blocks to get the transient frequency output to make the stability of the VSM less intensive to the parameter design of the virtual inertial and damping coefficient so that an easier parameter design method can be used. In other words, this method helps to solve the contradiction between dynamic response and stable performance, especially when the damping coefficient cannot be freely modified to increase damping for a large inertial value because of the mutual dependence between damping coefficient and droop coefficient caused by the use of inner reference frequency. Moreover, a simplified method for the parameter design of the ETB is proposed and the small-signal model of the ETB-based VSM is also derived. After that, the power coupling situation is analysed and comparisons with other control strategies are presented. Furthermore, time-domain simulation results are demonstrated to verify the effectiveness of the proposed method.

In cyber-physical power systems, tiny failure occurring in the communication network could propagate to affect the operation of the physical power grid through inter-links and even cause catastrophic blackouts. The authors propose a partial random coupling systems model to study the vulnerability of nodes and connectivity of systems in a cascading failure. In terms of traffic loads generated in systems, they employ load spill index to analyse dynamic states of nodes in cascading failure. In cascading failure, considering the effect from a communication network, vulnerability matrices are established to study the vulnerability of nodes in the physical power grid. Furthermore, an efficiency index is defined to analyse connectivity of systems. In the numerical simulation, they verify the accuracy of the proposed evaluation approach and test its scalability and universality in different power systems.

A transactive energy coordination mechanism is proposed in this study where community microgrids are supplying power to multi-dwelling residential apartments. The proposed transactive energy coordination mechanism coordinates the energy sharing among apartments based on the energy profile of the community microgrid where the excess energy is traded with non-contributing apartments. The proposed coordination mechanism is embedded within an energy management controller which uses the energy profile and determines the valuation of energy. A choice factor along with the bound on electricity prices is also incorporated to calculate the bidding price and a double-sided auction mechanism is considered for the bidding purpose. The utility maximisation approach is used to clear the market. Different scenarios based on the flexibility in the pricing strategy are considered to evaluate the performance of the proposed transactive energy coordination mechanism. The potential economic benefits of the proposed scheme are also analysed which clearly demonstrate that it is beneficial for all participants.

Mechanical malfunction is a main failure mode for circuit breakers (CBs). Vibrations generated from CB switching operations contain rich information of its mechanical condition. However, the vibrations are highly time-varying and non-stationary, which makes it very difficult to precisely extract effective features for machinery fault diagnosis. This study presents a methodology to obtain the CB vibration characteristics based on time–frequency and chaotic analysis. A new method, called adaptive chirp mode decomposition (ACMD), is introduced to extract the fast fluctuating instantaneous frequency and catch each signal component individually from the CB's vibration signal. A high resolution adaptive time–frequency spectrum which can clearly represent the mechanical condition alteration in CB is obtained by the ACMD. The component with the most significant time–frequency fluctuation is reconstructed into a high-dimensional phase space to recover and extract the dynamic variation characteristics of the CB. Based on the reconstructed phase space, a new set of features, namely RST (ratio of major–minor axis, shape complexity and trajectory compactness), is proposed for realising the stability and accurate diagnosis of CB faults. Experimental study and practical application cases are presented showing the efficiency of the methodology proposed here.

Thyrist or controlled series compensator (TCSC) configuration in power system comprises of controlled reactors in parallel with sections of a capacitor bank. This combination offers smooth control of basic frequency capacitive reactance over a wide range. Its benefits include eradication of resonance risks, stability improvements and so on, offering dynamic power flow control. However, the TCSC controllers face issues, while determining their optimal locations and parameter settings (sizing). Hence, this study intends to solve these problems by considering three objectives, namely, congestion minimisation, investment cost minimisation and increased transient stability. The objectives are achieved by optimising various locations of the bus system, where the TCSC has to be placed, and its sizing. From the optimised results, the best solution is chosen to attain the abovementioned objectives. The presented scheme obtains the best solution by a hybridised model, exploiting the dragonfly algorithm (DA) and the particle swarm optimisation (PSO), called PSO-dependent step vector for DA. Finally, the proposed approach is compared with the conventional schemes by analysing the outcomes for two benchmark systems, namely, IEEE 24 and IEEE 9 test bus systems.

Thermal conditions of power transformers in abnormal operating conditions such as harmonic loads can be considered as a critical case. In this study, thermal analysis of transformer and additional imposed heat on it, caused by non-linear loads, are addressed. For this purpose, an appropriate thermal equivalent circuit is used in which temperature of different parts of oil-immersed power transformers are obtained for harmonic loads. The losses of various components of transformer as heat-generating sources are estimated. At this end, an appropriate three-dimensional finite element method is applied to estimate the losses of different parts of transformer. To keep the transformer temperature rise around the permissible value, the transformer is derated. Transformer derating based on the IEEE Std C57.110–2008 recommendation considerably reduces the transformer loading capability. Therefore, this study introduces a new technique for derating of transformer for harmonic loads. This enhances the transformer thermal limits and transformer loading capacity.

Cable incipient fault is an intermittent arc fault, and may evolve into a permanent fault. Due to the short duration of the fault, the conventional overcurrent protection device cannot detect it. A cable incipient fault identification method is proposed in this study, using restricted Boltzmann machine (RBM) and stacked autoencoder (SAE). Firstly, disturbance current waveforms data is effectively compressed by RBM, which can improve analysis efficiency and obtain the shallow features of the data. Then, the compressed data is used as the input of SAE, and the optimal network parameters are obtained through layer-by-layer pre-training and fine-tuning. Finally, a well-trained SAE network is used to learn deep features from the input data to identify cable incipient fault, and softmax outputs identification result. In addition, the performance of the proposed method is compared with other methods. The accuracy of the proposed method is 98.33/95.62% for simulated data/measured data, and is 1.66/1.09%, 3.33/1.76%, 17.31/28.48% and 40.17/46.1% higher than the accuracies of convolutional neural network, deep belief network, random forest and back propagation neural network, respectively. The results show that the proposed method has high identification accuracy and feasibility.

In this study, a simple, fast, and adaptive network reduction procedure is presented for long-term voltage stability analyses, to speed up the simulation time. The proposed procedure consists of two parts including disturbance detection based on data from synchronised measurement devices; and the rest, up to the final estimated values, based on simulations and calculations. In turn, simulations and calculations result in an adaptive dynamic-oriented determination of external sub-network (according to the disturbance occurred) and substituting an appropriate equivalent for that subsystem. The external subsystem is determined without any need to measure post-disturbance data, while the detection criteria are calculated by simulations at 0.8 s after disturbance occurrence. The results have shown considerable reduction in the simulation time while providing acceptable accuracy in delivering the time of voltage instability occurrences, especially when applying the proposed error compensation procedure.

Voltage sag frequency estimation is necessary for understanding the voltage sag severity in power system and offering full information for the interested parties to mitigate voltage sag. The high penetration of wind power in the power system and the uncertainty of the fault distribution raise new challenges to accurate voltage sag frequency estimation. This study presents a systematic voltage sag frequency estimation method, considering the fault distribution density, fault ride-through (FRT) process of wind turbines during voltage sag and the interval characteristic of voltage sag frequency. First, this study proposes a fault distribution estimation model based on adaptive kernel density. Second, this study proposes a method for calculating the residual voltage and duration of voltage sag during FRT and combines the common distance protection action to analyse the effect on voltage sag by FRT process of wind turbines. Lastly, this study proposes an interval-valued voltage sag estimation method considering the interval characteristics of fault rate in the power system. IEEE 30-bus test system is used to verify the proposed method, the estimation results show better performance of the proposed method compared with the typical estimation methods.

Air gap discharge voltage is the key parameter to determine the minimum approach distance for live working. In this study, a mathematical–physical model for predicting 50% discharge voltage of the transmission line air gaps considering the effect of live line worker is developed based on the continuous leader inception criterion. Also, the tower structure coefficient S _T is proposed to represent the influence of various tower structures and S _T is calculated by finite element method. Finally, the switching impulse discharge tests of the equipotential worker-tower structure gaps are carried out on 750 kV transmission lines to verify the proposed model. The research results show that the errors between the calculation and experimental data are within ±4.03% which demonstrates the feasibility of discharge voltage prediction for complicated live working gaps. This model offers a possible way to determine the safety air gap distance for live working by analytical and numerical calculation rather than costly and time-consuming experiments.

Tidal power plant (TPP) is an emerging and fast-growing addition to clean energy technologies. Potentially, it may bridge the gap of energy scarcity and lower environmental impacts. Therefore, a meticulous study on it in providing support to various ancillary services, especially, in load frequency control (LFC), need to be carried out. Penetration of the intermittent unit like TPPs into the power system causes capacity addition but at the cost of a decrease in inertia and primary frequency response owing to the power electronic interface. Due to this, following disturbance, both the maximum frequency nadir and the rate of change of frequency deviation deteriorate, which poses a threat to LFC service. So, in this study, the contribution of the deloaded TPPs, with different level of penetration, in frequency regulation employing control strategies such as inertia control and droop control is analysed. Performance of these control strategies has been successfully demonstrated through a series of simulation-based experiments. Further, the impact of virtual inertia contribution from capacitive energy storage systems (CESSs), in case of insufficient inertia support from TPPs on LFC performance of the system is investigated. Lastly, the impact of a combined response of inertia and droop control strategies with CESSs on frequency nadir is also explored.

This paper proposes a novel approach for modeling and revealing the competitors' behavior from perspective of an intended player (IP). To this end, from perspective of IP, we define an Equivalent Rival (ER) whose behavior in the electricity market reflects the aggregation of behaviors of all individual competitors. It is assumed that IP and its ER participate in an equivalent market which its outcomes are approximately equal to those of the real market. The revealing procedure is designed as a two-stage Artificial Neural Network-based approach to estimate and predict the bids of ER after each run of the real market. Predicted bids of ER are used for the bidding strategy of IP. The proposed approach has been examined on two different case studies. In the first case study the aggregate supply curve of a market with 12 players has been obtained using the proposed approach and the result has been compared with a Bayesian inference approach. In the second case study a six-player electricity market is considered. The competitors' behavior has been revealed from perspective of an intended player using proposed approach and an optimal bidding strategy based on the proposed approach has been constructed.

In this study, coordination mechanisms are designed for price anticipatory transactive microgrids. The mechanisms are designed by considering the neighbourhood energy transactions among different consumers in a residential microgrid as well as energy trading among several microgrids within an area. The energy trading framework among different consumers in a microgrid is developed based on a non-cooperative leader–follower game theoretic approach to maximise the utilities of both sellers and buyers. The energy transactions among different parties within a microgrid are defined, in this study, as intra-microgrid energy trading. A double-auction mechanism is used for energy trading among different microgrids where energy shortage and excess information from each microgrid are coordinated. The proposed mechanisms are developed by considering the physical properties of microgrids, e.g. power flow and voltage variations. The performance of the proposed mechanism is evaluated through the investigation of different properties, e.g. individual rationality of participants, budget balance, operational efficiencies in terms of cost saving, and optimality to achieve the grid independency.

A new type of non-linear adaptive phase-locked loop (PLL) has been proposed here, which is based on spline interpolation. The study discusses the method of cubic spline, which is used to extract the fundamental voltage component, its phase angle and frequency. Test results under varying grid conditions viz. normal and distorted conditions such as the presence of harmonics, noise, phase and frequency variations etc. are presented for the developed PLL. An application of the proposed PLL to power quality improvement of grid current using shunt active power filter is further discussed here. The study demonstrates that the spline-based controller can be effectively employed as a PLL and to achieve improvement in the power quality of a three-phase, three-wire power distribution system.

This study validates an alternative restoration of a critical load area using remote black-start units. Using the conventional restoration, switching actions on a nominal system voltage create switching transients, especially when energising a transformer. The transients maybe close to the resonance frequencies of a weak island system, which may induce high voltages, delay the restoration and damage the equipment in the grid. This study proposes an alternative restoration procedure where, to avoid switching transients, hundreds of kilometres of transmission lines and several transformers are energised using a gradually increasing voltage, which is controlled by the synchronous generator exciter. This study presents detailed procedure flowcharts, a proof of concept for the proposed procedure using a Finnish and an Austrian field tests and theoretical analyses of the tests. The results show that with the gradually increased voltage, harmonic resonances and switching transients during the initial system energisation maybe avoided. In addition, the study shows that variations in the system frequency may cause voltage problems in a weak system during restoration since the system reactance is dependent on the system frequency. Thus, large frequency variations and the unstable operation regions of turbine governors should be avoided during the restoration.

State estimation affords real-time network modelling facilitating distribution network (DN) operation and control, and is an indispensable component of distribution management systems. However, given the lack of real-time measurements of DN, its observability relies heavily on pseudo-measurements, which are associated with relatively large errors. So the pseudo-measurements can be expressed as interval numbers. In such cases, interval state estimation models maybe useful. Using interval analysis methods, interval state estimations yield the upper and lower bounds of system state variables, but such conventional methods ignore correlations among interval numbers; the estimations are very conservative. Here, the authors develop an improved interval analysis method by combining the interval constraint-propagation (ICP) algorithm with the Krawczyk–Moore test. Numerical tests of IEEE distribution systems at different scales showed that their method outperformed conventional ICP methods.

Power-grid partitioning is an important prerequisite for power systems security analysis and control. In this study, a novel recursive grid bipartitioning strategy is proposed. First, two analytical expressions are derived from Kirchhoff's equations to represent coupling relationships between nodes. Then, generator nodes under study are divided into two groups by recursively applying the coupling relationships between generator nodes. Finally, the coupling relationships between generator and load nodes are used to merge relevant load nodes to the corresponding groups of generators. The stopping criterion of the grid bipartitioning process is also discussed. The proposed bipartitioning strategy is implemented on the IEEE 118-bus system and a practical provincial power grid in China to demonstrate its effectiveness.

In this study, a new kind of hybrid high-voltage direct current (HVDC) system is proposed. Each terminal of the proposed system consists of one line commutated converter (LCC) and one full-bridge modular multilevel converter (FB-MMC). The LCC and FB-MMC are connected in parallel so that they can share the same transmission line. The active–reactive power capability of the hybrid HVDC system is extended compared with the conventional LCC-HVDC system, and power reversal control without power interruption can be achieved by the coordination control of LCC and FB-MMC. Besides, the proposed hybrid HVDC system is capable of handling DC fault, because both LCC and FB-MMC have DC fault blocking capability. Moreover, the power rating of FB-MMC can be designed to low value while keeping the bulk-power transmission capability of LCC. A two-terminal bipolar hybrid HVDC system is built in PSCAD/EMTDC. The simulation results verify the effectiveness and feasibility of the proposed hybrid topology and corresponding control strategies.

Fault detection and location is a challenging issue in microgrid protection, which is increasingly more complex in the presence of distributed generators based on renewable energy, due to their inherent intermittency. In this context, a novel data-driven approach for fault detection and location in microgrids is proposed, by using graph theory representation and micro-synchrophasors also known as PMUs. This proposal adopts the conviction to provide an accurate fault location even under variations in short-circuit levels caused by the intermittency of distributed generators. This is in sharp contrast with traditional short-circuit rating-based methods, which are not always advisable due to the intermittent nature of power sources. This work proposes the use of a modelling specification in terms of equilibrium equations, that can reveal not only the underlying physical laws of the netowork, but also the occurrence and location of short circuits based on phasor data. The intermittency of distributed generation is modelled in the proposed approach, which permits to yield trustworthy information either distributed generators are involved in a fault or not. As a consequence, the fault location errors are significantly reduced during the fault location process. The theoretical findings of this proposal are validated via simulation results and experiments using commercial micro-synchrophasors and hardware-in-the-loop emulation of a realistic microgrid.

Decentralised droop-like control method is the most favourable control system for power converter-based microgrids (MGs). In conventional V–Q droop loops, reactive power sharing is used as a means of voltage regulation to prevent currents from circulating among distributed generation units. However, since the voltage is not a global variable, reactive power sharing is not implemented precisely, and thus converters may be exposed to overcurrent conditions and the stability of the MGs is put at risk. Besides, the droop-like reactive power sharing causes voltage deviations and power quality issues. This study proposes a novel control method which is able to implement accurate reactive power sharing and voltage regulation to its nominal band in a networked MG. Both the control targets are achieved, fast and simultaneously, by only one control signal. So the requirement of a secondary controller for voltage restoration is obviated. A novel power flow-based method is proposed to estimate the voltage at the MG main bus, which is adopted as a common variable, thus making the proposed method decentralised. The presented method is fast, effective and applicable to networked MGs with arbitrary topology. Simulation results prove the effectiveness and superiority of the proposed method over existing methods.

During the current transformer (CT) saturation, the secondary current waveform of a CT is notably different from the primary current's waveform. When the discrete Fourier transform (DFT) is applied to such a distorted secondary current of a CT, the obtained root mean square (RMS) value is significantly lower than it actually is, which can lead to the malfunctioning of the relay protection devices. The operation of some relay protection algorithms (such as certain algorithms for electric arc detection on overhead lines) is conditioned by higher fault current harmonics. Obviously, due to the secondary current's distortion, the higher current harmonics cannot be accurately estimated. On the other hand, even when there is no CT saturation, the RMS value can be incorrectly estimated under DFT due to the fault current's direct component. This study presents a new algorithm which enables an accurate RMS value estimation regardless of the CT saturation and/or presence of the direct fault current component. What is more, the algorithm also enables the estimation of higher fault current harmonics under CT saturation. Various tests have indicated a high precision and robustness of the proposed algorithm and the possibility of combining this algorithm with the algorithm for electric arc detection on overhead lines.

Frequency stability control in multiple asynchronous grids is a challenging and complex issue. An adaptive droop control strategy to improve the frequency regulation of asynchronous AC areas connected by a multi-terminal DC grid is proposed here. The droop coefficients are adjusted to share the active power adaptively among multiple asynchronous AC grids based on the characteristics of frequency deviation and rate of change of frequency. This results in a cogent allocation of imbalance power in multiple asynchronous grids from the frequency variation perspective. The performance of the proposed scheme is evaluated in a modified multi-machine power system using DIgSILENT Power Factory. Simulation results under significant frequency disturbances caused by credible contingencies are presented to demonstrate the effectiveness of the proposed approach. It is found that the proposed adaptive control ensures an excellent and robust frequency response under different operative conditions.