In this study, a comprehensive approach for model order reduction based on a Fourier series of a discrete system representation is proposed. The developed method represents an alternative to model reduction of large-scale dynamical systems and can be used for the analysis of unstable dynamic systems and the study of interactions among power system controls. Drawing on the principle of conformal mapping, the linearised system model is first transformed into its discrete equivalent. Then, the Fourier series of the discrete-time transfer function is used to obtain a reduced-order model (ROM). Using this model, approximate Hankel-based interaction measures are proposed to efficiently analyse large, unstable linear system representations and determine pairs of input outputs to design controller. The high degree of applicability and accuracy offered by the method, and its ability to extract ROMs from stable and unstable systems is demonstrated on three test systems.

Generation units connected to the grid are currently required to meet low-voltage ride-through (LVRT) requirements. In most developed countries, these requirements also apply to renewable sources, mainly wind power plants and photovoltaic installations connected to the grid. This study proposes an alternative characterisation solution to classify and visualise a large number of collected events in light of current limits and requirements. The authors’ approach is based on linearised root-mean-square-(RMS)-voltage trajectories, taking into account LRVT requirements, and a clustering process to identify the most likely pattern trajectories. The proposed solution gives extensive information on an event's severity by providing a simple but complete visualisation of the linearised RMS-voltage patterns. In addition, these patterns are compared to current LVRT requirements to determine similarities or discrepancies. A large number of collected events can then be automatically classified and visualised for comparative purposes. Real disturbances collected from renewable sources in Spain are used to assess the proposed solution. Extensive results and discussions are also included in this study.

The potential impacts of data integrity attacks on multi-settlement electricity markets have been recently investigated and have sent a strong message to power grids independent system operators (ISOs) that adversaries could launch profitable cyber attacks by casting an incorrect image of transmission lines congestion pattern. However, these cautionary messages may be underestimated due to the adversaries unrealistic requirements (e.g. having access to real-time measurements) to launch a successful stealthy and profitable attack. This study examines the potential of the aforementioned risk by demonstrating how a malicious power market participant could disturb the electricity market operation, using a pre-designed false data injection attack along with bogus electricity trades in both day-ahead and real-time markets. The proposed attack design is robust against market uncertainties and the adversary can guarantee the success of the attack in advance. Hence, the existence of such cyber attacks against electricity markets can make the adversaries more aggressive. The numerical results on the IEEE 14-bus test system confirm the vulnerability of multi-settlement electricity markets to such financial cyber attacks. The results obtained from investigating such an attack design can be employed by ISOs in order to provide appropriate countermeasures.

Reconfiguration and smart control of remote-controlled sectionalising switches in distribution networks are considered as the major solutions for loss mitigation, interruption time reduction and reliability improvement after events. That is because these automation tools bring about changes in the topology of the network, isolate the faulted regions, operate distributed generators for local load satisfaction and restore the un-faulted regions as rapidly as possible. Thus, a new solution methodology for solving the simultaneous optimal wind turbines (WTs)/switches placement as well as network reconfiguration is developed to enhance the distribution network's efficiency and reliability. Power losses, voltage deviation index, switch cost and reliability cost based on expected customer interruption cost are considered as the objective functions. The approach profits from a new multi-objective algorithm based on modified artificial bee colony for providing the best compromise solution. The presented framework is shown to provide superior results when applied to the IEEE 69-node test feeder. Finally, different scenarios based on feeder reconfiguration, switch placement and WT placement problems are constructed and presented in Section 5.

It is important to search voltage stability margin (VSM) of an interconnected power system in order to determine secure operation constraints. Traditionally, centralised continuation power flow (CPF) is used, which may fail to model the varied load growth directions of different regional power grids. In this study, a distributed VSM searching method is proposed grounding on a coordinated CPF (CCPF) performed by neighbouring dispatch centres. First, a distributed power flow model for VSM is established, which considers the automatic allocation of network loss. Then, a critical bus of the power system is used to indicate the system-level voltage stability. It is chosen according to the sensitivity of the minimum singular value of Jacobi matrix to nodal voltage amplitudes, and the sensitivity of boundary power injection to nodal voltage amplitudes. Moreover, the gradient of critical bus voltage amplitude to regional loading parameters is computed, which is set as the load growth direction for the current step. The severest VSM is obtained by solving the CCPF iteratively along the worst load growth direction. Tests on IEEE 118 bus system and a real power grid of China validate the proposed method in the enhancement of the security for interconnected power systems.

This study describes a new class of system identification procedures, tailored to electric power systems with renewable resources. The procedure described here builds on computational advances in differential geometry, and offers a new, global, and intrinsic characterisation of challenges in data-derived identification of electric power systems. The approach benefits from increased availability of high-quality measurements. The procedure is illustrated on the multi-machine benchmark example of IEEE 14-bus system with renewable resources, but it is equally applicable to identification of other components and systems (e.g. dynamic loads). The authors consider doubly-fed induction generators (DFIG) operating in a wind farm with system level proportional–integral controllers.

This study presents a loss formula-based simultaneous reconfiguration and distributed generation (DG) sizing algorithm for active power loss minimisation in distribution networks. A new heuristic technique based on the exact loss formula for reconfiguration is proposed. The exact loss formula-based analytical approach is used for DG sizing and siting. The proposed algorithm is tested on 33-, 69-, 84- and 136-bus distribution systems. The simulation results demonstrate the effectiveness of the proposed approach to obtain the best solution. The impact of the initial voltage selection on this approach is analysed. The results are suggesting that it requires no load flow solution and it is the unique feature of this approach. The proposed approach can be used as a primary analysis tool for active distribution network real-time operation and planning. The proposed method further extended to the multi-objective approach using the weighted sum technique.

The fault location in transmission systems remains a challenging problem, primarily due to the fault location near the substation ends or the weak fault signals. In this study, an adaptive extended Kalman filter (EKF) based on the maximum likelihood (ML) is proposed to estimate the instantaneous amplitudes of the travelling waves. In this method, the EKF algorithm is used to estimate the optimal states (the clean travelling waves) with additive white noise while ML is used to adaptively optimise the error covariance matrices and the initial conditions of the EKF algorithm. Using the proposed method, the singularity points of travelling waves can be detected, and the exact arrival time of the initial wave head at the substations M and N can be easily yielded. Thus the fault distance can be calculated precisely. The effectiveness of exacting mutation feature using the proposed method has been demonstrated by a simulated instantaneous pulse. Also, the proposed method has been tested with different types of faults, such as different fault locations, different fault resistances and different fault inception angles using ATP simulation. The accuracy of fault location using the proposed method has been compared with conventional wavelet transformation scheme.

The transformer losses can usually be classified into two basic categories: losses in the transformer core (voltage-dependent losses) and losses in the transformer winding copper (current-dependent losses). By increasing the number of active transformers in the transformer substation the authors reduce the total losses in the transformer copper but on the other hand increase the total losses in the transformer iron core. Considering this, it can be concluded that it is possible to determine the optimum number of active transformers in the substation for each operating condition together with the way they are connected. In this study, the authors propose a novel optimisation algorithm which can be used to determine the optimal operating conditions of the transformer substation to minimise annual energy losses while avoiding frequent transformer switching and assuring provision of sufficient transformation power in order to supply distribution load. The algorithms which are outlined are applicable for substations 110/x kV and 35/10(20) kV which have more than one transformer installed with different levels of substation topology complexity (flexibility).

This study proposes an optimal control scheme based on linear quadratic regulator (LQR) to control of the oscillatory behaviour of the doubly-fed induction generator (DFIG) connected to the grid and improve the stability. The control approach integrates a non-linear dynamic state estimation by means of unscented Kalman filter to estimate the unobservable internal states, to be used by the LQR. The only measurements required to achieve the control objective are terminal voltage and stator current of the DFIG which may have measurement-noise to some extent. The detailed model of the DFIG-based wind turbine with two-mass drive-train model has been described first and then its linearised state model has been obtained to identify the oscillatory modes, which have further been used to decide the weight matrices for LQR. The performance of the proposed LQR-based damping controller has been compared with the power system stabiliser incorporated with the DFIG. The efficacy of the proposed scheme of the DFIG has also been tested in WSCC 3-machine 9-bus power system by integrating the DFIG in it.

An innovative system restoration strategy using doubly-fed induction generator-based wind farms is proposed. The strategy involves retention of charge in the DC bus following a blackout and ‘Hot-Swapping’ between direct flux control mode and conventional grid-connected mode, which does not require resetting of any controller dynamic states and avoids the need for energy storage. An autonomous synchronisation mechanism enabled by remote synchrophasors is also proposed. A blacked-out system, which includes a wind farm and a voltage source converter (VSC)-HVDC connected to a network unaffected by blackout, is used as the study system. Transmission line charging and load pickup is performed using the wind farm in flux control mode while the VSC-HVDC system conducts the same process for another portion of the system. The proposed ‘Hot-Swapping’ and autonomous synchronisation approach is applied to connect the two parts of the grid and switch the wind farm to grid connected mode of operation. The results are demonstrated in a hybrid co-simulation platform where the aforementioned system is modelled in EMT-type software and the rest of the network is represented in a phasor framework.

Estimation of energy savings in distribution network through smart grid-enabled conservation of voltage reduction (CVR) approach has been investigated in this study. To achieve higher-energy savings, CVR operation has been carried out with deeper voltage reduction in association with photovoltaic (PV) system while keeping the node voltages within acceptable limits. The additional reactive power support has been injected by PV inverters. The injected reactive power has been controlled by droop characteristics method. Besides, the moving cloud transient effect has been incorporated in PV power output. To evaluate the energy savings, the volt-VAR control operation has been carried out in three different modes such as without CVR, only CVR, and CVR with PV system on the modified unbalanced IEEE 123 node test system. The test system and control algorithms have been developed and simulated in open distribution system simulator interfaced with MATLAB. From simulation results, it has been demonstrated that higher-energy savings and peak load demand reduction can be achieved through smart grid-enabled CVR and PV system in comparison with the only CVR with proper voltage regulation.

Reliability has become a key design aspect in modern energy system's planning. Owing to the higher fault rate in power distribution systems (PDSs), comparing with generation and transmission systems, considering reliability in PDSs’ planning is very crucial. This study presents a novel robust approach to cluster the existing PDSs with intermittent distributed generators (DGs) into a set of reliable microgrids (MGs). For this purpose, first, a new reliability index is defined to evaluate the reliability of MGs in terms of real and reactive power adequacy as well as frequency and duration of interruptions. Then, the k-means algorithm, based on weighted graph partitioning method, is proposed for changing the system into a multi-MG system. Furthermore, a modified version of particle swarm optimisation approach is proposed and the Silhouette technique is used to determine the optimal location and sizes of DGs as well as the number of MGs. The design and sensitivity analysis performed by the proposed multi-objective optimisation algorithm on the well known IEEE 69-bus distribution system show the effectiveness and robustness of the proposed algorithms for constructing reliable MGs in modern PDSs.

In this study, an adaptive continuous wavelet transform (CWT)-based overcurrent protection for smart grids is proposed to enhance the overcurrent protection performance encountering high-impedance fault (HIF) and current transformer (CT) saturation, which are extremely complex phenomena and their impacts often cause mis-coordination or mal-operation. The proposed algorithm samples three phase current waveforms and imports them to CWT to extract high frequency coefficients. Afterwards, the sum of absolute values of the coefficients, S _coef, is calculated for each sample during the last cycle. Meanwhile, several simulations related to HIFs with different impedances and CT saturations with different severities are executed and the fault currents and the sum of absolute values of the coefficients are achieved and saved in the relay memory as (X, Y) coordinates of points (I_{L- fault}, S_{L- coef}), named ‘learning data’. Thereafter, each S _coef is imported to the X−Y plane and, consequently, the occurrence of HIF or CT saturation is detected and the real-fault current is estimated by both non-linear interpolation and extreme learning machine approaches. Subsequently, new time dial setting and I _pickup of the relays are computed and reloaded. Security, dependability, and sensitivity of the proposed adaptive protection method are confirmed by numerous simulation studies.

Electric load variation results from a variety of factors. This study discusses the inner mechanism of load variation and presents a load forecasting method based on multi-source data and day-to-day topological network. Multi-source data including weather data, seasonal attributes, calendar attributes, holiday attributes and load growth rate are considered to be the dominant factors that cause the load variation. Initially, a day-to-day topological network is generated that reflects the similarity between any 2 days. Additionally, the random walk with restart (RWR) algorithm is applied to the topological network to construct the training set. The support vector regression model is then adopted. With case studies using the data of Guangzhou, the authors obtain a decrease of the mean absolute percentage errors of 19.5 and 25.7% over the SV machine method and a neural network ensemble model. Their research reveals three points: (i) weather elements, especially temperature, air pressure and water vapour pressure, have a dominant influence on load variation besides historical load; (ii) multi-source data improves the accuracy, meanwhile the applying of RWR algorithm maximises its effect; and (iii) since some of the factors that cause a constant error remains unknown, they can use the feedforward correction to decrease the affects.

Due to the increasing penetration of the uncertain single-phase distributed generations (DGs), the current distribution networks are becoming more uncertain, unbalanced, and complicated than ever before, which brings great challenges for distribution network operators. This study proposes an adaptive robust optimal reactive power dispatch approach for the unbalanced distribution networks (U-DNs) considering uncertainty caused by DGs. Leveraging the reactive power compensation from inverters of DGs, the purpose of the proposed method is to minimise power losses and maintain the voltage within regulatory limits. The feasible region of DGs is estimated and considered as a new constraint, aiming to guarantee the reliable operation of U-DNs. The optimal reactive power dispatch problem is then formulated as an adaptive robust optimisation problem based on semidefinite programming. The adaptive function, which derives the relationship between reactive power and active power outputs of DGs, is utilised to make the method more flexible and less conservative. The cutting plane algorithm is introduced to solve the proposed adaptive robust reactive power dispatch model efficiently. Moreover, case studies are separately conducted on the modified IEEE 13-bus and 123-bus test systems to demonstrate the effectiveness of the proposed method.

Optimal transmission switching (OTS) has been introduced as a persuasive approach for cost minimisation and the improvement of power system flexibility by utilising the lines’ existing conditions. Ordinary OTS based on optimal power flow (OPF) equations used in the previous studies may expose system security in some cases. This study proposes a novel sequential method to investigate the security of the system in post-OTS circumstances by considering N − 1 contingency criteria. The proposed method ranks the candidate lines as an operational strategy to reach the maximum reduction of the total operational cost by considering the security roles of transmission lines. The formulation of OTS and security assessment programs is based on alternating current OPF. The proposed approach provides more accurate solutions to a mixed integer non-linear programming model of the OTS program with N − 1 security criteria within a reasonable computation time. The obtained simulation results of the proposed method have been presented on IEEE 57-bus and IEEE 118-bus standard test systems. It is shown that the results of the ordinary OTS for lines’ outage ranking change because of system security consideration.

A decentralised load frequency control (LFC) for multi-area power systems with communication delays is studied. Active disturbance rejection control (ADRC) method is adopted to handle the communication delays. First the conventional ADRC is tuned via the bandwidth method and it is shown that the achievable performance for delayed systems is no better than proportional-integral-derivative (PID) controllers. Then a modified ADRC structure is discussed and it is shown that the achievable performance is limited by the controller bandwidth. In order to improve the performance, a method to tune the parameters of ADRC is proposed via the internal model control method. Simulation results show that the proposed method is easy to apply and can achieve good damping performance.

The Cooray–Rubinstein formula has been widely used for evaluating the horizontal component of the electric field generated by a lightning return stroke over a lossy ground. An accurate and efficient time domain method is presented in this study, by means of piecewise recursive convolution. The recursive convolution is achieved by expressing the kernel function of the ground surface impedance by a piecewise exponential function, in which the integral form of the modified Bessel function of the first kind is evaluated using the trapezoidal numerical integration. Since the time-domain analytical expression of the ground surface impedance kernel function has been adopted, the computational error can be directly controlled within a reasonable tolerance. The validity and efficiency of the proposed method are demonstrated by the extensive comparisons with the method in other literature.

A new analytical solution for the self- and mutual inductances of arbitrary triangular coils with rectangular cross-section is presented. Firstly, the electromagnetic field problem of a filamentary triangular coil is solved based on second-order vector potential. Then, the solution is effectively extended to the arbitrary triangular coil with different track widths by changing the radius of its inscribed circle. A series of new formulae are given for calculating electromagnetic field, self- and mutual inductances of triangular coils with different shapes, separation distances, lateral misalignments or angular misalignments. Finally, the verification experiments are carried out on a series of irregular and regular triangular coils. Also, the experimental results show that the measured values are in good accordance with the calculated ones.

The acquisition of discharges data is usually affected by external interference leading to erroneous interpretations. In the viewpoint of improving computation accuracy, the discrete wavelet transform (DWT) has been used as an effective tool for de-noising purposes. In this study, creeping discharges waveforms have been investigated under the positive lightning impulse voltage over various materials. The used polymers belong to three distinct families (i) thermoplastics (namely polyamide 6 and polyamide 66), (ii) one filled cycloaliphatic epoxy resin and (iii) one unfilled ethylene propylene diene monomer (EPDM). Two approaches namely one-dimensional (1D) and 2D DWT algorithms have been adopted for de-noising signals and images, respectively. Both techniques were applied for simulated and laboratory data using various wavelet families (Daubechies, Symlet and Coiflet). The comparison of de-noising performance for signals has been achieved through the calculation of signal-to-noise ratio, normalised correlation coefficient (Norm_corr) and root mean squared errors. Moreover, the computation of power spectral density of lightning current transients using a periodogram estimator is also analysed. For images, mean square error and peak-signal-to-noise ratio assess the quality of filtering regarding the visualisation of discharges patterns. Results show that Coiflet wavelets demonstrate their effectiveness to reduce background noise and preserve the signals shape and images edges.

In this paper, the propagation mechanism of creeping discharges up to flashover for short air gaps is examined and described on various materials based on laboratory de-noised data (namely current, voltage and captured images). The main parameters considered for investigating the development of creeping discharges and their characteristics deal with the measurement, modelling and calculation of (i) their final/stopping length and morphology, (ii) their propagation velocity and (iii) the electric field distribution including the maximal magnitude (E _max) and the geometric coefficient (β) estimation. The obtained results evidenced that both length and velocity of discharges are emphasised for polyamide-based materials (namely PA6/50 and PA66/50) whereas their ignition remains inhibited for filled cycloaliphatic epoxy resin (FCEP) and ethylene propylene diene monomere (EPDM) surfaces. As the electric field is concerned, both analytical and numerical models are developed and their results are compared and discussed. It has been shown that the presence of a polymer acts as a barrier when being incorporated between an electrodes gap whose dielectric strength depends strongly on the used material. Moreover, the FCEP barrier, in comparison to other materials, exhibits a marked dielectric reinforcement and an enhanced stability of the system making it suitable to provide a better protection to high-voltage equipment against discharges effects.

With the development of power electronics technology, numerous studies have been conducted on voltage-source converter-based high-voltage DC (VSC-HVDC) transmission technology and low-voltage DC micro-grids. However, DC power distribution networks are more sophisticated than HVDC transmission networks with respect to the complex topology, changeable operation modes and use of diverse power electronic devices. Research on voltage-source converter-based medium-voltage DC (VSC-MVDC) distribution networks is still in its infancy stage, and whether or not some of the existing control and protection schemes used in VSC-HVDC can be applicable to the distribution networks remains a question. In this study, a dynamic simulation platform with DC circuit breakers is initially established. This platform is based on the first dual-terminal VSC-MVDC distribution network constructed in China. Second, a complete overall control scheme is proposed for VSC-MVDC distribution networks. The control scheme is proposed with an array of control strategies, including controls for system startup/shutdown, voltage coordination, operation mode transition, single-station integration, system fault isolation, and recovery. Finally, the proposed scheme is validated through experiments using the dynamic simulation platform. Experimental results indicate the effectiveness of the proposed overall control scheme for VSC-MVDC power distribution networks. Thus, the proposed scheme can be used in the design and operation of future VSC-MVDC distribution networks.

Changing dynamics of power systems caused by the migration from conventional to distributed energy sources increase the risk of blackouts due to voltage instability, especially in case of unforeseen network conditions (e.g. (N-k)-cases). To enable both secure and efficient power supply, novel monitoring and emergency control systems for the identification of voltage emergency situations as well as the execution of control actions are required that react reliably in due time and adaptively in the case of changing network situations. This study presents a distributed agent-based approach to counteract voltage instability that is based solely on local measurements and limited inter-agent communication. Distributed agents located at substations in the (sub-)transmission network monitor distribution and transmission voltages, as well as, load tap changer positions and are able to autonomously curtail load in case system stability is endangered. The applicability of the approach is demonstrated in a co-simulation environment interfacing the multi-agent system with a dynamic power system simulation. The presented approach allows for an early detection of voltage instability as well as a coordinated execution of available control actions.