This study proposes a new approach to determine harmonic contributions in distribution networks. The approach effectively combines underdetermined blind source separation (UBSS) and form similarity distance (FSD), and it aims to minimise the negative impacts of harmonic source coupling and background harmonic fluctuations. Considering the underdetermined measurement, UBSS is introduced to estimate the harmonic emission current in the light of the sparsity of source signals. Through analysing the form variation features of harmonic time series, FSD is applied to identify the relatively stable background harmonics for utility equivalent harmonic impedance calculation. Furthermore, a complete procedure of harmonic contribution assessment is presented. To verify the high performance of the proposed approach, the simulation study and field test are both conducted, and a detailed comparative analysis of different approaches is carried out. The results show that the proposed approach is able to more accurately determine harmonic contributions than the existing methods, and has better robustness against significant harmonic source coupling and drastic background harmonic fluctuations.

Modular multilevel matrix converter (M3C) is a competitive option in the fractional frequency transmission system (FFTS) application. Focusing on stability and power quality issues, this study firstly proposes a new mathematical model and control strategy. Different from the previous research, this control scheme is based on the frequency decoupling model of double dq coordinate transformation and the control of the sub-converter, which implements the frequency decoupling control and solves the frequency leakage problem. Subsequently, a complete state-space model and small-signal model of M3C are built for analysing small disturbance stability. On this basis, the optimisation of M3C in FFTS is studied, and an optimisation method based on particle swarm algorithm is proposed. This method can directly design the adaptive objective function according to the optimisation requirements of system control performance to simultaneously optimise all controller parameters of the system. After optimisation, the stability and dynamic performance of the system have been significantly improved. Finally, the effectiveness of the proposed control and optimisation is verified by the simulation results in MATLAB/ Simulink.

This study discusses a control algorithm for dynamic voltage restorer (DVR) based on sliding mode observer (SMO) with an optimisation-based proportional integrator (PI) tuning to compensate the voltage related power quality problems. In this work, a three-phase VSC-based topology of DVR is selected with a self-supported capacitor. This DVR configuration using the proposed control algorithm has been used for mitigation of unbalance, sag, and swells in the supply voltage. The estimation of grid parameters in undesirable situations based on the exosystemic model are the advantages proposed control. New nature-inspired optimisation algorithm named as Harris hawks optimiser (HHO) has been applied to obtain the PI gains in the control algorithm to eliminate the time required for the tuning process. The main advantage of HHO is the avoidance of local minima and exploration and exploitation features of the algorithm. DVR system with a combination of SMO-based control algorithm along with HHO optimised PI controllers have been developed in MATLAB/Simulink and tested for above said voltage-based disturbances mitigation in the supply voltage.

Load frequency control in modern-complex-uncertain power systems (PSs) assumes significance due to their challenging nature of the operation and hence utilisation of robust controllers is indispensable. In the industry, conventional single-loop controllers may not offer robust behaviour under changed operating conditions. Alternatively, two-loop cascade fuzzy structured controllers can show significant robust performance in dynamic conditions and best suited in systems having non-linearities. Hence, a novel optimal cascade fuzzy-fractional order integral derivative with filter (CF-FOIDF) controller is utilised for 2-area thermal and hydrothermal PSs considering various physical constraints from a practical point of view. As physical constraints mandate an energy storage system, hence in this study, batteries of electric vehicles (EVs) are employed to assist power plants to swiftly arrest oscillations in the system frequency following load demands. A combined model of EV fleets is incorporated in the control areas of PSs. Numerous simulations are conducted to authenticate the robustness and excellence of EVs and the suggested control strategy over existing methods.

Wind power application in producing electrical energy is an integral part of the increased eco-friendly generation. Accordingly, wind power producers may have a dominant position in some electricity markets. This study mainly concerns a strategic wind power investor who owns a number of units and seeks to optimise its expansion plans on sizes and sites of new generation capacities in a horizon year. Here, the investor is a price-maker in both day-ahead (DA) and intraday (ID) markets, while acts as a deviator in the balancing market. A stochastic bi-level model is proposed wherein the upper-level, the investor maximises the expected profit. Both DA and ID market clearings are considered in the lower-level (LL). The model is formulated as a mathematical program with equilibrium constraints (MPEC) by replacing the LL problem with its Karush–Kuhn–Tucker (KKT) conditions. The MPEC model is then converted to a mixed-integer linear programming model. A three-bus illustrative example and IEEE 24-bus reliability test system are used to demonstrate the effectiveness of the proposed model. The results confirm that the presence of the ID market in the investment model has increased the expected profits of the investor and also increases invested wind capacity.

Presenting an accurate and cost-effective solution to tackle static load encroachment issues in backup protection of transmission networks stand as a challenging task. Therefore, this study aims at devising a new backup protection scheme via GPS-based distance relays (GBDRs) against this issue. In this scheme, each GBDR calculates the vulnerability index locally, which helps to find out the vulnerable situation. When these indices exceeded their threshold, the protection centre is allowed for real-time monitoring in the corresponding area. In this regard, after calculating superimposed components, they are sent to the protection centre for discriminating faults from stressed conditions. Deployment of GPS-based relay in each bus brings higher costs and entails sharing large amounts of data. Therefore, a new techno-economic approach helps for the optimal deployment of these relays. To this end, zone-3 in some buses are eliminated, and the rest are equipped with GBDRs while each line at least is protected by two existing zones-3. By doing so, the network is divided into different areas that are protected with the minimum number of these relays. Whereby, coupled with the vulnerability indices, minimising the number of GBDRs alleviates the exchanged data.

A multi-microgrid (MMG) system comprises of a group of self-sufficient microgrids capable of operating in grid-connected, islanded, or interconnected modes. A three-microgrid-based MMG system consisting of a solar photovoltaic system, doubly-fed induction generator-based wind generation, and static synchronous compensator as distributed energy sources are considered. Each microgrid includes a battery interfaced with a bidirectional DC–DC converter. As there are multiple battery units in the MMG system, different states-of-charge (SoC) are evident in the batteries. Hence, there is a need to charge/discharge by following the SoC of the batteries. In this study, an intelligent scheme employing fuzzy logic is applied to monitor the SoC of the batteries and determine the reference current for current control through the bidirectional DC–DC converter in an MMG system. Microgrid frequency control in the MMG system is carried out using the proposed five-membership function-based fuzzy logic control. During sudden transient events, the proposed intelligent frequency control strategy shows an improved transient response as compared to conventional PI control. A multi-input and multi-output fuzzy logic-based power management algorithm is proposed to handle multiple sources, batteries, and loads in the system. The MMG system with the proposed control is simulated using real-time digital simulator OP4510 from OPAL-RT.

This study does research on resonance and harmonic transmission problems in a new continuous cable traction power supply system (CCTPSS), CCTPSS can realise long-distance co-phase power supply and effectively reduce phase separation and is applicable for extended power supply in areas with the weak power grid. Firstly, the system structure is introduced, a cable traction network is divided into three kinds of subnets for its complicated topology and huge system scale. The equivalent circuit model and mathematical model of each subnet are established with distribution parameters, especially the cable capacitance effect be considered. Then, according to the two-port network analysis theory, the system equivalent circuit is constructed by considering the electrical connection relationship, system harmonic impedance expression is calculated. Resonance influence factors and harmonic transmission mechanisms are analysed. Finally, theoretical analysis validity is verified in simulation; harmonic transmission characteristics CCTPSS including traction cable and overhead catenary, are studied. The new system shows better resonance performance compared with the existing AT traction power supply system.

Due to increasing complexity of power systems the task of ensuring adequate operation of relay protection becomes more urgent. Detailed mathematical models of relay protection together with modern power system simulators are proposed to be used as a solution of this problem. At the same time, the adequate simulation of instrumental transformers, in particular the magnetization process of the core, is very important because the waveform of signals controlled by relay protection largely determined by transducers' errors. The developed mathematical model of current transformer reproducing the magnetic hysteresis in accordance with the Preisach theory is presented in the paper. Unlike other similar models, the Preisach' particle distribution function in the developed model is based not on the reference typical magnetizing curves, but on the volt–ampere characteristic of current transformer. This approach is better applicable in practice, since typical magnetization curves are not always available and become less relevant during transformer operation. There are presented the results of impact assessment of different types and values of burden on current transformer operation and comparison of the implemented model with existing methods of magnetization and hysteresis modeling. The adequate behavior of the developed model has been confirmed by the research.

This study presents a structured pattern-recognition framework for fault pattern recognition in large power systems. The main novelty of the study is in the efficient use of techniques to reduce data acquisition and administration requirements and limiting the computational overhead without sacrificing fault recognition accuracy and reliability. Optimal fault recorder placement based on the criterion of ‘network observability’ has been suggested for real-time monitoring of voltage and current at strategic network locations. An efficient feature-screening method has been adopted to select only the recorders whose data are assessed to be critical for fault recognition. ‘Wavelet’-based multi-resolution decomposition facilitated the extraction of important fault features from recorded waveforms and feature-screening was leveraged, once more, to eliminate irrelevant features to ensure that the data presented to the fault classifier is precise and feature-enriched. Random forest ensemble classifier was used for final class prediction and location of faults through voting of several individual learners to achieve high prediction accuracy. The proposed approach proved to be computationally efficient and consistent when tested on IEEE 118-bus system.

With the increasing penetration rate of renewable energy sources, variability impacts, aside from uncertainty, will increase the need for operational flexibility resources in power systems. Accordingly, in this study, flexibility provision from both generation and demand sides are considered in a day-ahead scheduling problem. Fast start gas-fired units, due to their agility in starting-up and high ramping capabilities are considered as generation side flexibility providers. However, the normal operation of these units strictly depends on a secure gas supply through connected gas pipelines. Thus, gas-supply uncertainty is considered in the proposed model to mimic the impacts of deviations in gas volume through pipelines. On the other hand, demand response programs (DRPs) with their specific characteristics are among powerful demand side flexibility providers. However, unlike the existing literature that considers a supplementary role for DRPs, this study introduces the main role for DRPs as flexibility providers through comprehensive modelling of versatile DRPs. The proposed day-ahead scheduling problem is a multi-resolution robust security constrained unit commitment that the robustness comes from the decision making against sub-hourly gas-supply uncertainty and wind power variability. The applicability of the proposed model is tested on both an 8-bus and IEEE-118-bus standard test systems.

In this study, a maiden application of cascade proportional–integral–derivative with filter (PIDF) and one plus fractional-order derivative (1+FOD), i.e. PIDF(1+FOD) controller is proposed for the load frequency control mechanism. The main purpose of the cascade and fractional order controller is to increase the degree of freedom and reject the disturbances faster. A novel attempt has also been made to model a static synchronous series compensator (SSSC) with AC tie-line and HVDC tie-line. Here SSSC and HVDC tie-line are used to regulate and increase the power transfer capabilities between interconnected areas. Furthermore stored energy in the HVDC tie-line is utilised to improve the system dynamics by inertia emulation control strategy. An evolutionary salp swarm algorithm-based optimisation technique is adopted to optimise control parameters. The performance of the proposed controller is tested on a two-area hydro-thermal interconnected power system in deregulated environment. First, the effectiveness AC–DC-SSSC tie line is shown over AC-SSSC and alone AC tie-line with proposed PIDF(1+FOD) controller followed by the supremacy of proposed PIDF(1+FOD) over classical controllers. Finally, sensitivity is analysed by variation in system parameters, which shows the robustness of the proposed controller.

Existing active arc suppression methods compensate fault current through controlling busbar voltage to zero. However, it may boost the fault point voltage in the case of considering load and feeder impedance, and fail to suppress arc. This study proposes a fault current suppression method by controlling the faulted terminal open-circuit voltage (FTOCV) and harmonic impedance of neutral-point. The effect of load and feeder impedance are taken into account. Depending on this, a faulted terminal open-circuit voltage controller (FTOCVC) is proposed for arc suppression, which consists of a reference voltage calculation module (RVCM) and a reference voltage tracking controller (RVTC). RVTC utilises a dual-loop voltage control method to adjust the neutral voltage for reducing FTOCV and providing a very low harmonic impedance for neutral-point. A reference voltage needed by RVTC can be figured out using RVCM accurately considering load impedance and fault distance. Thus, the proposed method can restrain the fault current to almost zero without influence by the load and feeder impedance. Comparison of several arc suppression methods was performed by simulation, and the results indicated the proposed method is more beneficial to extinguish fault arc.

Accurately identifying the key links in active distribution network (ADN) that affect the system's safety and stability is of great significance to improve the efficiency of operation and maintenance and risk early warning for distribution network (DN). In this study, the node resilience (NR) is first proposed as an indicator for structural stability identification of DN. Then, a critical node identification method considering the security, economy and structure stability in ADN is proposed, which uses the NR, the utility risks of branch load change, node voltage deviation and line loss variation as the identification indicators. Also, combining with subjective experience and objective data, the comprehensive evaluation method of critical nodes is improved, and the multilevel and multidimensional evaluation model of critical nodes is constructed. Furthermore, the time sequence of load change and photovoltaic output is considered. Finally, the rationality and effectiveness of the proposed method are proved by taking IEEE 33-bus system and an actual ADN as examples.

Phasor measurement unit can monitor the variation of phase angle of power grid in real time, which is of great significance to ensure the safe and stable operation of power grid. Among them, the virtual phasor measurement algorithm based on discrete Fourier transform (DFT) has been widely used because of its simple principle and relatively easy implementation. However, the existing virtual phasor measurement algorithm only gives the dynamic error reduction effect under the fixed offset angle, and does not give the rule of the reduction effect with the different offset angle. The relationship between anti-harmonic interference capability and response speed with the different offset angles is not analysed. Therefore, this study deduces the pattern of dynamic error reduction effect, anti-harmonic interference ability and response speed with the different offset angles. The dynamic error reduction effect of the algorithm is the best when the offset angle is π/2, and the anti-harmonic interference ability of the algorithm is the strongest when the offset angle is π/3. The response speed of the algorithm increases linearly with the increase of the offset angle. On this basis, the correctness of the algorithm is verified by numerical simulation experiments.

A new islanding detection method based on image classification with support vector machine is proposed in this study. Histogram of oriented gradient features is extracted from the image for classifying non-islanding and islanding events. In the proposed technique, the time-series signal acquired from the point of common coupling is first converted into an image. Histogram of oriented gradient features is extracted from the image, which is used as an input feature vector for training and testing multiple support vector machine classifiers. Parameters such as voltage, rate of change of voltage, and rate of change of negative sequence voltage are used. Furthermore, a feature for early islanding detection is also presented to detect an islanding event even before it has occurred. The detection accuracy of the proposed method is tested with different kernels. The performance of all the classifiers is tested with 5-fold cross-validation. The classification results show that islanding detection with image classification based on the histogram of oriented gradient feature and multiple support vector machine classifiers can achieve excellent results.

Power distribution networks are in a transformation active distribution networks with distributed energy resources. However, the widely adopted distribution test networks were established many years ago, which are untimely and cannot reflect the characteristics of high penetration renewable energy. Therefore, in this study, a distribution network with high penetration renewable energy is established based on the real data of a renewable-energy-rich radial rural distribution network in China. The proposed radial distribution network includes three types of loads and two types of renewable energy distributed generations. The evaluation indexes are designed to assess the proposed system and compare with the existing distribution networks. In addition, the topical high/low voltage problem of distribution network caused by high penetration of renewables is discussed. Furthermore, based on the measured time series characteristics of load and renewable resources, the effectiveness of the proposed system is validated by power flow analysis and dynamic characteristic criterion.

In recent years, there has been an increasing interest in using AC power flow equations for the transmission expansion planning (TEP) studies. The AC power flow equations are quadratic and hence the TEP problem can be formulated as a mixed-integer quadratically constrained programme. Therefore, the complexity of the TEP problem lies in the non-convexity of AC power flow equations in which the global optimal solution is not guaranteed to be found. This study aims at proposing a tight convex relaxation for the TEP problem. In this context, first, the TEP problem is formulated as a mixed-integer bilinear problem by representing the complex bus voltage in its rectangular coordinates. Second, the multiparametric disaggregation technique (MDT) and piecewise McCormick relaxation are employed to generate a mixed-integer linear relaxation. MDT is based on the discretisation of the domain of one of the variables in every bilinear term. The method presented is much more precise compared with the DC or other linearisation approaches, while the optimal solution is of high quality. The results of the case studies show the tractability and exactness of the proposed model as well as its superiority over the state-of-the-art schemes.

The operation of multiple microgrids (MGs) with distribution system enhances reliability and resiliency of the power supply significantly by enabling high penetration of locally available distributed energy resources (DERs). However, there are several issues in the proper operation of multiple MGs that need to be addressed. Providing proper protection coordination is one of the most important issues in the coordinated operation of networked MGs (NMGs). In this study, an efficient protection coordination scheme for NMGs is proposed by utilising the commonly used numerical directional overcurrent relays (DOCRs) with single and dual settings. Issues related to the operation of NMGs such as the change in network topology, connection status of the point of common coupling and low voltage fault ride through of DERs have been considered. The protection coordination problem has been formulated as an optimisation problem and solved using the interior point method. The proposed protection coordination scheme of NMGs has been tested on the 69-bus radial distribution system with the integration of three MGs, which is not reported in earlier literature. The suitability and effectiveness of the proposed DOCRs coordination scheme have been demonstrated.

In this study, algorithm for a directional earth-fault relay is modified to work properly without voltage inputs. The presented modification of the algorithm implies that only current inputs are required, and the algorithm is used in isolated neutral networks. The main modification of this algorithm is that only one phase current is used as a reference quantity instead of the zero sequence voltage or three phase currents. The algorithm is further upgraded by using the phase current of the supply feeder as a reference signal for all relays of outgoing feeders. This way the reference quantity becomes more stable and the number of measurements per feeder is reduced to only one. The introduction of simple communication between relays on feeders, a wide operation range is achieved. With this algorithm detection of earth-fault is ensured regardless of the network load: purely capacitive, predominantly resistive or purely inductive. The algorithm successfully detects the faulted line and phase containing a phase-to-earth fault. The aim of this study is to design low-cost directional relays with no voltage inputs, a small number of current measurements and a wide range of possible network loads.

The expansion planning of a distribution network (DN) is studied separately and independently from the behaviour of the transmission network (TN) as well as other DNs. However, DNs are being converted from passive to active mode by extensively integrating distributed generations (DGs) into them. Hence, an uncoordinated expansion planning may lead to redundant investment cost and suboptimal solutions. Accordingly, the main motivation of this study is to propose a coordinated expansion scheme among distribution companies (DISCOs). In doing so, a novel bilevel game-based framework is presented to coordinate the decisions of DISCOs for distribution expansion planning problem. Primal–dual formulation is used to convert the bilevel problem into a single level one resulting in a discretely-constrained generalised Nash equilibrium problem. The generalised Nash equilibrium problem is further formulated as a mixed-integer linear program using Karush–Kuhn–Tucker conditions. The methodology proposed is applied to the IEEE 24-bus RTS with several 24-bus DNs. The results show that ignoring the action of other DISCOs may lead to the over- or under-investment in DG sector which consequently decreases the DISCOs’ profit. The results also show that congestion in transmission lines can considerably affect the strategic decisions of DISCOs on DG investment.

This article studies a hybrid AC/DC microgrid with bidirectional Γ-Z-source inverter as an interlinking converter (IC). The Γ-Z-source inverter is capable of providing high-voltage gainand it does not have the drawbacks of the conventional inverters. In this hybrid microgrid, DC-type energy sources and loads are connected in DC sub-grid and AC-type energy sources and loads are connected in AC sub-grid to reduce the extra power conversion stages in both AC and DC sub-grids. Therefore system volume and cost decreases and system reliability and efficiency increases. In DC sub-grid, the advantages of multi-port power electronic interface (MPEI) are utilised. The individual DC–DC power converter, a MPEI, is used for interconnecting DC distributed generators. Photovoltaic system and battery unit are used as DC distributed generators. The article presents the control of three operation modes including grid-connected mode, islanded mode and islanded mode with power flow management and the IC and distributed generators. For power sharing management, droop strategy is used. The performance of the proposed IC in all three operation modes is evaluated by time domain simulations in MATLAB/Simulink.

With the development of renewable energy market, Renewable Portfolio Standard (RPS) has become the targeted renewable energy incentive mechanism in China and it is under a government's long-term plan that RPS overtakes feed-in tariff gradually in recent years. Given this background, the decision-making model of electricity retailers to accomplish the obligation under RPS is constructed as a bi-layer portfolio selection model. In the inner-layer, both capital allocation of the retailers to purchase various kinds of renewable energy capacity as well as RECs are optimised. In the outer-layer, the capital investment portfolio of each risky and risk-free strategy is determined based on the Behavioural Portfolio Theory, with different mental accounts (MAs) with different aspiration points and threshold levels built to describe the investor philosophy of retailers during the decision-making process. The simulation results of a provincial electricity market in China demonstrate that the presented model can effectively assist electricity retailers in making their capital investment strategies under RPS with relevant market factors. In addition, the proposed model provides insights for policy makers to set key parameters involving the design of RPS by analysing behaviours of retailers, including required quota ratio and value of fines.

Superconducting current limiters (SFCLs) can limit short-circuit fault current and provide sufficient time for DC circuit breakers (DCCBs) to isolate faults. An SF₆ passive resonance DCCB combined with a superconducting current-limiting module and a DC interruption module is proposed due to the high current interruption properties and the low on-state loss. However, experimental investigations of SF₆ passive resonance DCCBs combined with SFCLs using DC source are currently lacking. The objective of this paper is to obtain the interruption characteristics and modeling design methods of the proposed SF₆ passive resonance DCCB. This paper designs a 10 kV SF₆ passive resonance DCCB and tests the DCCB in a 10 kV/10 kA circuit. Quenching resistance and arc models are established based on experimental results. Experimental results show that the superconducting current-limiting module responds fast at 0.3 ms and limits the DC fault current of 10 kA to a peak of 816 A. Then the DC interruption module interrupts the limited current successfully. Besides, there is no overvoltage afterward in all the tests because the superconducting current-limiting module absorbs much of the energy during the interruption. The proposed DCCB would be an effective method for interrupting short-circuit faults in high voltage DC systems.