In order to manage the charging behaviour of electric vehicles (EVs), this study for the first time develops a set of EV charging load profiles: EV templates. EV charging profiles have unique waveforms similar to a rectangular pulse train. This characteristics significantly limits the performance of clustering analysis in that traditional distance calculation, such as Euclidean distance, which cannot reflect the morphological dissimilarities. This study proposes a novel clustering method using rough set theory to accurately measure the dissimilarity between the EV profiles. The pulse train waves are firstly extracted as mixed data features, which are partitioned by an improved K-prototypes method based on rough set distance. The proposed method is implemented on the real charging load profiles and compared with K-means and traditional K-prototypes. Their clustering performances are evaluated by diverse validity indices. The results show that the proposed method outperforms other comparison methods.

Widespread use of electric vehicles (EVs) requires investigating impacts of vehicles’ charging on power systems. This study focuses on the design of a new DC fast-charging station (DCFCS) for EVs combined with local battery energy storages (BESs). Owing to the BESs, the DCFCS is able to decouple the peak load demand caused by multiple EVs and decrease the installation costs as well as the connection fees. The charging system is equipped with a bidirectional alternating current/direct current (DC) converter, two lithium-ion batteries and a DC/DC converter. The introduction of BES within the DCFCSs is investigated with regard to operational costs of the CSs as well as the ability of a BES to mitigate negative impacts on the power grid during congestion hours. The proposed solution is shown to reduce not only the installation costs, but also the charging time and it facilitates the integration of fast chargers in existing low-voltage grids. A cost–benefit analysis is performed to evaluate the financial feasibility of BES within the DCFCSs by considering the installation costs, grid connection costs and battery life cycle costs.

The location of public electric vehicle charging stations (PEVCSs) has a great influence on the operational efficiency of charging stations, charging behaviours of EVs and the power quality of grids. To optimise the PEVCS locations for plug-in electric taxis (PETs), this study proposes to utilise the multi-agent system (MAS) and evidential reasoning (ER) approach. First, an MAS simulation framework for PET operation is proposed to dynamically simulate the PETs’ daily operation and estimate the charging demands of PETs, where a variety of agents are built to simulate not only the operation related players but also the operational environments. To accelerate the convergence rate and provide better operational strategies for PETs, a multi-step learning is developed to make decisions for PET agents whether to find passengers or to charge under various situations. Moreover, a multi-objective model for optimising the location of PEVCSs is developed considering the benefits of PETs and the power grid. Finally, an ER approach is applied to determine the final optimal siting considering the uncertainties of the assessor's cognition. Simulation results have demonstrated that the proposed MAS simulation framework and ER approach can effectively optimise the PEVCS locations.

Fast charging stations are critical infrastructures to enable a high penetration level of plug-in electric vehicles (PEVs) into future distribution networks. The fast charging stations need to be carefully planned to meet the PEV charging demand as well as reduce costs. This study addresses this technical challenge and proposes a hierarchical planning solution for both sitting and sizing of PEV fast charging stations based on a temporal-SoC (state-of-charge) characterisation and modelling of PEV fast charging demand. The optimal sitting of fast charging stations is firstly determined to ensure minimising the total number of stations and meeting the PEV fast charging demand considering the constraints of transportation networks and the expected PEV remaining mileage. Then the sizing (number of chargers and waiting spaces) of fast charging station is optimised by the use of M/M/s/N queuing model, so as to maximise the expected profit of the operator. The proposed solution is evaluated through a set of case studies for a range of scenarios, and numerical simulation results have confirmed the effectiveness of the proposed solution.

To stimulate the participation of electric vehicles (EVs) in vehicle-to-grid (V2G) activities, some economic incentives should be offered to the EV owners and the discharging price is negotiated by EV aggregator and electricity grid. Here, this study proposes a negotiation strategy between EV aggregator and electricity grid which focuses on how to develop a reasonable mechanism for discharging price, and then the bilateral negotiation function models of discharging price based on fuzzy Bayesian learning are established. In the models, the certain parameters are calculated according to the profits and cost of the EV aggregator and electricity grid; and the fuzzy probability calculation method is formulated to estimate and calculate the uncertain parameters of the functions of both sides, respectively. Additionally, the negotiation function models based on fuzzy Bayesian learning is utilised for updating and correcting the deviation of estimates and the discharging price is finally found out by the parameters above. Through numerical cases, the negotiation strategy proposed in this study is verified to be effective in the early promotion of V2G.

The node voltage profile is more likely to be violated as the electric vehicles (EVs) charging load spreads in distribution network. Due to the stochastic nature of EV charging load spatially, more flexible reactive power compensation in different locations becomes important. However, the conventional reactive power compensation equipment has no flexibility spatially. Therefore, two kinds of reactive power compensation strategies using EVs considering drivers’ reasons are proposed. Drivers’ reasons contain charging demand, charging opportunity loss (time) and profit. In Strategy 1, EV chargers are used to fully compensate reactive power after finishing the unregulated charging. Thus, drivers’ charging behaviour is not influenced at all. In Strategy 2, the operating power factors of EV chargers are treated as variables for the optimisation. The constraint of operating power factors is derived from analysing the charging demand and the charging opportunity loss (time) for drivers. Then, in order to motivate drivers, an incentive method is introduced based on the quantification of each driver's contribution to the voltage. The case study shows that Strategy 1 performs well at nodes having the non-significant voltage deviation without any constraint on driver's charging behaviour, while Strategy 2 performs well at nodes where the voltages deviation is significant.

The integration of demand flexibility in distributed generation (DG) planning either lacks accuracy or ignores the potential of the behaviour of consumers in promoting the integration of renewables. This study proposes a DG planning model coordinating demand flexibility, in which the DG expansion plan and the behaviour of consumers in demand response (DR) programmes are co-optimised for the highest social welfare and the optimal utilisation of renewable generation. Consequently, the supply cost is reduced by utilising higher renewable generation instead of buying electricity from the grid. A share of the cost savings is allocated to the consumers to encourage their participation in DR programmes. Simulation results show that the expansion capacity of renewable generation is increased by 7.4% compared with no demand flexibility incorporation, and the social welfare is increased by up to 13.5% compared with no DG installation and 3.1% compared with no demand flexibility incorporation. Besides, the DR programmes carried out in the distribution system interact with the DG expansion plan, and higher subsidy rates in DR programmes could further promote the integration of renewables.

This paper presented a scenario-based robust distributed generation investment planning (DGIP) model, which considered the uncertainties of wind turbine (WT) generation, photovoltaic (PV) generation and load demand. The robust economic model aims to maximize the net present value (NPV) from the distribution network operator's (DNO's) perspective. The uncertainties are described by an uncertainty matrix based on a heuristic moment matching (HMM) method that captures the stochastic features, i.e. expectation, standard deviation, skewness and kurtosis. The notable feature of the HMM method is that it diminishes the computational burden considerably by representing the uncertainties through a reduced number of representative scenarios. The uncertainty matrix is integrated with deterministic power flow equations to formulate a cost-benefit analysis based robust DGIP model with the objective of maximizing the DNO's net present value. The effectiveness of the proposed DGIP model is firstly verified in a 53-bus distribution test feeder, and then its scalability is further validated in a 138-bus distribution network. The numerical results confirm that the proposed DGIP solution is more robust for all representative network scenarios against the deterministic solution.

Battery energy storage systems (BESSs) are incorporated into wind farms to gain more profits by shifting energy over time and to track predetermined power schedules. In operations, charging/discharging power of the BESS is adjusted flexibly to follow the power schedules of the wind-BESS hybrid systems (W-BESS-HS), which are set to be the sum of short-term predicted wind powers and charging/discharging schedules of the BESS. In order to extend lifetime of batteries, the BESS operation is subject to a sequential charging/discharging state sequence, which is predetermined according to time-of-use (ToU) pricing schemes. An iteration scheme is presented to update scheduled charging/discharging rates of the BESS according to simulation results based on sequential Monte-Carlo simulation (SMCS) technology so that the W-BESS-HS can not only meet a probabilistic requirement on generation schedule tracking but also gain further economic benefits by achieving a trade-off between punishments resulted from power deviations and wind power curtailment losses. In the SMCS simulation, a series of real-time indices are presented to evaluate performances of the W-BESS-HS at every dispatching interval and provide updating directions of the iteration scheme. The research work can provide theoretical support when operating the W-BESS-HS in ToU pricing schemes.

Owing to the recent power outages caused by extreme events, installing battery energy storage and backup generators is important to improve resiliency for a grid-tied microgrid. In the design stage, the event occurrence time and duration, which are highly uncertain and cannot be effectively predicted, may affect the needed battery and backup generator capacity but are usually assumed to be pre-determined in utility planning tools. This study investigates the optimal battery and backup generator sizing problem considering the stochastic event occurrence time and duration for the grid-tied microgrid under islanded operation. The reliability requirement is quantified by the mean value of the critical customer interruption time in each stochastic islanding time window (ITW), whose length is the duration and the centre is the occurrence time. The stochastic ITW constraint is then transformed to a probability-weighted expression to derive an equivalent Mixed Integer Linear Programming model. Numerical simulations on a realistic grid-tied PV-based microgrid demonstrate that the total cost is reduced by 11.5% considering the stochastic ITW, compared with the deterministic ITW under the same reliability requirement.

For off-grid microgrids in remote areas (e.g. sea islands), proper configuring the battery energy storage system (BESS) is of great significance to enhance the power-supply reliability and operational feasibility. This study presents a life cycle planning methodology for BESS in microgrids, where the dynamic factors such as demand growth, battery capacity fading and components’ contingencies are modelled under a multi-timescale decision framework. Under a yearly timescale, the optimal DER capacity allocation is carried out to meet the demand growth, while the investment decisions of BESS are made periodically to yield the optimal sizing, type selection and replacement plans of BESS during the entire lifetime of the microgrid. Then, under an hourly timescale, the long-term probabilistic sequential simulation is adopted to comprehensively evaluate the investment decisions and derive detailed operation indicators. Moreover, a decomposition–coordination algorithm is developed to address the presented planning model, which iteratively strengthens the feasible space of investment-decision model by substituting the operation indicators until an acceptable sub-optimal solution is obtained. Case studies on a wind–solar–diesel microgrid in Kythnos Island, Greece illustrate the effectiveness of the proposed method. This study provides a practical and meaningful reference for BESS planning in off-grid microgrids.

This paper presents a planning approach for improving the rooftop photovoltaic (PV) hosting capacity and energy efficiency of distribution networks with the placement of voltage-sourced converters (VSCs). The PV hosting capacity (PVHC) is the maximum amount of PV generation that a distribution network can accommodate without deteriorating the operational performance of the network. The PVHC is derived under the constraint of a maximum allowable network power loss. Two different types of VSCs are modelled for the placement in distribution networks to improve the PVHC. These are series and shunt VSCs. The series VSC is designed to inject a series voltage in quadrature with the line current to maintain a constant bus voltage. The shunt VSC is designed to improve the load power factor to unity by injecting a shunt compensating current in quadrature with the bus voltage. The objective function is to maximise the PVHC to obtain the maximum PV generation capacity to be integrated in each bus. The particle swarm optimisation is used as a solution approach. The results show that the placements of VSCs improve the PVHC. This also reduces energy loss when there is no PV generation available.

Although the wide integration of advanced metering infrastructure on distribution network facilitates the application of volt/var optimisation (VVO) in real-time circumstance, the contradiction between heavy computation load and low solution efficiency is still a big challenge, thus the system scales investigated in the literature are limited. In this study, the full AC real-time VVO is formulated based on particle swarm optimisation (PSO) framework and direct approach (DA) power flow method, where all components, such as distributed generator and on-load tap changer transformer, are formulated and integrated into the iterative DA process. Since both PSO and DA are suitable for parallel implementation, the graphics processing unit (GPU) is introduced for acceleration in order to achieve the possibility for real-time application. All the solution process is executed by GPU with the well-established data structure and thread organisation pattern, resulting in high efficiency by guaranteeing coalesced access within each warp. Case studies are conducted on four systems with sizes ranging from 136-bus to 1760-bus. Solution accuracy and convergence property are validated by the popular open source package Matpower. Based on the results from solution efficiency comparison between CPU sequential, CPU parallel, and GPU parallel programs, the promise of the proposed parallel implementation scheme for practical application is established.

With recent development on renewable energy and distributed generation (DG), distribution system expansion planning (DSEP) problem is facing more challenges. This study proposed a multistage coordinate planning model to minimise the present value of construction cost and operating cost over the planning horizon. Installation of DGs, static var generators, and expansion of distribution network were considered simultaneously. The proposed model is a large-scale mixed-integer second-order conic programming (MISOCP) problem containing large amounts of constraints and variables. The MISOCP can be decomposed into: (i) the master problem which determines the construction plan, (ii) and many subproblems which optimise the operating states under different network configurations and different load levels. A modified Benders decomposition method was applied to generate valid cuts from subproblems with integer variables. Results of the proposed decomposition method were compared with those obtained by commercial software on a 24-node distribution system. Numerical experiments showed that the proposed method can solve the integrated DSEP problem efficiently.

In this article, a new concept of flexible distribution network (FDN) is proposed for the power grid with increasing distributed energy resources (DERs) and power electronic devices. First, the authors define FDN as a flexible closed-loop operation smart distribution network with the capability of wide-area energy exchange. In FDNs, flexible networking devices are the key facilities, which upgrade traditional networking devices by soft open point (SOP). Second, several typical network configurations of FDN are presented, which facilitate smooth upgrades from traditional networks to FDNs. Third, the normal operation mode, N − 1 mode, and the related analysis methods of FDN are presented. Finally, the world's first three-terminal SOP-based FDN pilot project is introduced and analysed to demonstrate the advantages of FDN in controlling power flow and integrating DERs.

Existing AC medium-voltage distribution networks are facing challenges on handling increasing loads and renewable energy integrations. However, it is very difficult to build new distribution lines in urban areas. This study proposes a configuration method of hybrid AC/DC medium-voltage distribution networks, in which some existing AC lines are converted to DC operation. Existing topologies and dispatching scenarios are considered during configuration because the overall power flow can be rescheduled in the hybrid AC/DC distribution network. Therefore, transfer capacities of the lines are fully utilised, and more renewable energies are accommodated. A bi-level programming model is established embedding chance constraint programming to consider the intermittent output of renewable energy. In the upper level, a multiple objective optimal model is proposed in order to balance investments, power losses, and the maximum load level and renewable energy capacity. In the lower level, daily operations of the newly installed VSCs are optimised by a chance constraint programming. The influences of energy storage systems on the configuration are also analysed. Simulation studies are performed to verify the proposed method.

As a core of energy internet, the energy router (ER) controlled by information flows can better realise the large scale utilisation of renewable energy. In order to build a cost-effective energy internet, a modified minimum spanning tree algorithm is proposed to optimise the cable layout among ERs, i.e. topology design. Considering the real-time and the asynchrony of power transmission in the above topology determined energy internet, an energy routing control method based on Dijkstra algorithm is put forward for source-and-load pairs to find a no-congestion minimum loss path. Besides, the loss allocation and congestion managements are realised at the same time. Finally, the simulation results prove the feasibility and effectiveness of proposed optimisation algorithms.

Distribution system reconfiguration (DSR) is a critical process that improves the power transfer efficiency and reduces the over-all operational cost. There have been various methods for addressing the DSR problems. Recently, DSR problems formulated in mixed-integer linear programming (MILP) has gained popularity as they generally can be solved by the state-of-the-art commercially accessible linear programming solvers, and is able to solve the system with thousands of unknown variables within a reasonable time. However, in some MILP formulations, the distribution line losses are omitted in the nodal power injections for the sake of simplicity. This compromises the accuracy of the linearised model and contributes to the disparity between the MILP and the true non-linear model. Hence, in this study, new formulations are introduced for embedding the expressions of line losses inside load flow equations so that the deviations between the modelled and exact losses notably reduce. Moreover, other novel formulations have also been presented for simultaneously optimising distributed generation (DG) locations and sizes, while at the same time considering various DG's modes of connection to the distribution grid. The validity and effectiveness of the proposed MILP model is tested on standard IEEE systems and actual distribution network.

This study presents a reconfiguration methodology based on a multi-objective modified flower pollination algorithm (MO-MFPA) that aims to achieve the power loss reduction, minimum load balancing index, and maximum voltage profile in radial distribution networks with photovoltaic (PV) arrays and distribution static compensator (D-STATCOM). Here, PV array is considered as distributed generation and D-STATCOM acts as a distribution flexible AC transmission system. The MO-MFPA is a meta-heuristic technique based on the combination of flower pollination algorithm and cloning selection algorithm. A reconfiguration is done through changing the tie and sectional line positions in the distribution system. At the time of reconfiguration, movement of load node to a set of power nodes secures the radial structure of the network. Voltage stability index is used to pre-identify the most candidate buses for placing PV arrays and D-STATCOM. Then the proposed MO-MFPA is employed to deduce the size and locations of PV arrays and D-STATCOM from the elected buses. For more practical applications, different cases of reconfiguration, PV, and D-STATCOM installation are considered to evaluate the performance approach at different load factors. The proposed method has been effectively tested on IEEE 33, 69, and 118-bus distribution systems and encouraging results have been obtained.

Planning the distribution network of the future involves forecasting the most likely scenario to make appropriate investment decisions. Many uncertainties concerning, e.g. the evolution of conventional loads, renewable production and electric vehicles (EVs) make it difficult to predict the location of the distribution network's weaknesses (overvoltages, undervoltages and overcurrents) and their occurrence. In some cases, alternative solutions such as demand response (DR) and reconfiguration can remove the constraints and prevent expensive network investment. This study proposes a two-stage algorithm that is able to give the probability that no technical constraints will appear as a function of the reinforcement cost with and without using DR and/or reconfiguration. The first stage of the algorithm consists in running Monte Carlo simulations based on realistic scenarios for loads, EVs and renewable production development provided by French governmental roadmaps. The cost of reinforcement per line and per hour of constraints enables selection of the feeders, where DR (solved with linear programming) and/or reconfiguration (exhaustive research) will be implemented in the second stage of the algorithm to remove these constraints. The methodology is applied to a real part of a French distribution network.

With an increasing number of renewable energy integrated into the power system, the impact of intermittent and random wind power and photovoltaic power on the power system is becoming larger and larger. To study the probabilistic correlation between wind power and photovoltaic power on different temporal and spatial scale, a joint probability model needs to be established. On the basis of the third-order Gaussian mixture model, a photovoltaic–wind joint power probability model is proposed in this study. By analysing the statistical probability characteristics of the measured power output data, this method avoids the error accumulation caused by the individual modelling of the wind and photovoltaic generators and considers the joint correlation between wind power and photovoltaic power. On the basis of this model, the corresponding time series of wind power and photovoltaic power is calculated. The results indicated that the coastal joint power probability model and the inland joint power probability model are quite different on the same time scale, the parameters of joint probability model on different time scales are close to each other. The effectiveness of the proposed method is verified by the measured data.

A larger integration worldwide of renewable energy sources (RESs) in the electricity distribution system is certainly desirable, to reduce CO₂ emissions and to contribute to a sustainable development. However, the increasing penetration of renewable energy is a challenge for the system performance, because it affects the power quality and the load management, forecasting, and scheduling. To reduce the impact of intermittent energy sources on network security, it is mandatory to predict with reasonable accuracy the renewable energy variations. The study is mainly focused on solar energy and its integration with distribution network. The technical issues and the economic impact of more accurate weather forecasts are discussed with particular reference to the results of the absolutely first field tests on a new forecast system implemented in the Italian distribution network by the most important Italian distribution system operator. The fundamental role of land weather stations as a new essential component of the distribution network is highlighted.

Photovoltaic (PV) electric power has been widely employed to satisfy rising energy demands because inexhaustible renewable energy is environmentally friendly. In order to mitigate the impact caused by the uncertainty of solar radiation in grid-connected PV systems, a hybrid method based on a deep convolutional neural network (CNN) is introduced for short-term PV power forecasting. In the proposed method, different frequency components are first decomposed from the historical time series of PV power through variational mode decomposition (VMD). Then, they are constructed into a two-dimensional data form with correlations in both daily and hourly timescales that can be extracted by convolution kernels. Moreover, the time series of residue from VMD is refined into advanced features by a CNN, which could reduce the data size and be easier for further model training along with meteorological elements. The hybrid model has been verified by forecasting the output power of PV arrays with diverse capacities in various hourly timescales, which demonstrates its superiority over commonly used methods.

The electric power output of the wind energy conversion system (WECS) fluctuates owing to the inherent feature of the wind speed, which do harm not only to the power grid it connected into, but also to the lifetime of power converters. The electric power fluctuation characteristic of WECS is analysed in frequency domain under overall wind speed to facilitate the planning of distribution grids and to reveal the key factors influencing power fluctuation under different operation modes. The analysis results are well-validated by detailed simulations. On the basis of power fluctuation characteristic analysis, the power-smoothing schemes are carried out in different operation modes. In variable-speed mode, an enhanced optimal torque control is proposed for power smoothing. In constant-speed mode, the control bandwidth of speed loop or the slope of look-up table is decreased to smooth the electric power, and a feed-forward pitch control is proposed to prevent the wind turbine from exceeding safe speed. In constant-power mode, the suggested power-smoothing scheme is worked out. The analysis results and the proposed control schemes are verified by refined co-simulation platform based on GH bladed and real-time digital simulator.

The division of urban power supply district is an essential issue in the medium voltage distribution network plan. This study develops a method for division of an urban load power supply district, integrating the open source data into the distribution network planning, at first, raw georeferenced point of information data is crawled by crawler program based on location retrieval service interface (Place API), the buildings’ data of the planned urban district is extracted and power load estimation are introduced in detail, the dataset of the low-voltage load spatial distribution is set-up; secondly, the clustering algorithm selects both the local density of samples and the distance between samples as criteria to form the clusters, cluster centres are recognised from the binary pair in ‘decision map’, as load density peaks. Thirdly, the spatial distribution dataset of the low-voltage users is taken as the data points in the clustering algorithm; the result of clusters corresponds to division in the power distribution with certain capability. Consequently, the methodologies proposed are verified on one example district of ∼71.7587 hectares, the division scheme can provide theoretical guidance for the location and sizing of power distributors in the urban distribution network.

Due to the intermittent power generation, wind farms integrated into the grid may cause a problem of large frequency fluctuation, when the capacity of load frequency control (LFC) is not enough to compensate the unbalance between the generation and the load demand. In this study, a new robust LFC strategy against load disturbance and wind power fluctuation is proposed to improve the disturbance-resistant performance of the power system with wind farms. First, a simplified model of the power system with wind farms is established without considering the accurate model information. Then, a control scheme based on the compensation of equivalent input disturbance (EID) is introduced, and a method of EID estimation is presented. The robust LFC design addresses various disturbances and internal/external uncertainties of power systems. Finally, to evaluate the effectiveness of the proposed method, two case studies are carried out and the performance comparisons with the classical proportional–integral–derivative control scheme are used to confirm the proposed method.

This work presents the first comprehensive study of active anti-islanding techniques suitable for module integrated converters (MICs), which considers the high penetration level of photovoltaics (or other distributed energy resources) at low-voltage distribution networks. As such, the state of the art in anti-islanding methods are presented and the most appealing solutions compatible with MICs are selected and experimentally evaluated, reaching to some valuable conclusions from the perspective of MICs. In order to compare these methods under the same operating conditions and specifications, a benchmark is set based on zero non-detection zone, reduced false-detection zone, and power-quality requirements compliance. Based on comparative results, the most suitable methods for wide MICs penetration in low-voltage distribution networks are suggested.

Control mode switching strategy of droop controlled inverter can effectively avoid overcurrent during grid fault, but it is easy to cause inrush voltage and current during grid fault clearance, which leads to the failure of fault ride through process of the distribution network. In this study, a new control mode re-switching method is proposed on the basis of restricting the outputs of the off-line controllers, which can make sure that the inrush voltage and current are suppressed and return to the normal condition quickly. First, the dynamic characteristics of fault current of droop controlled inverter are analysed. Then, the instantaneous inrush voltage and current caused by the output saturations of voltage controller and power controller before the re-switching process are mainly discussed. This method takes full advantage of integration of the existing off-line controllers to limit the output saturations, which can make the inrush problems well solved, and reduce the influence on grid connected inverters and the distribution network. Simulation results verify the validity of the theoretical analysis.

In this study, a multi-stage long-term expansion planning model for an active distribution network (ADN) is presented, with the aim of minimising the investment and operation cost in a coordinated manner over an established horizon. The planning model optimises the following alternatives: upgrading the capacities of substations, reinforcing and/or constructing cable circuits, placing voltage regulators (VRs) and/or static VAR generators, and determining the connection points for distributed generators (DGs). The investment decisions are optimised over the entire planning horizon which can be further divided into multiple periods, and the operation strategies, e.g. active management of DG as well as ADN topology reconfiguration, are determined according to the profiles of representative scenarios. To relieve the computational burden, the original model is properly simplified as a mixed-integer quadratic constrained programming problem through linearisation and approximation techniques, and the solution optimality is guaranteed after invoking the off-the-shell solver. A 24-node test system is employed to validate the effectiveness of the proposed model.

In the smart-grid paradigm, since distribution systems are controlled by various independent operators, it becomes inevitable for all dispatchers to have a wide-area view of the network for situational awareness and protection. This visualisation is accomplished with the aid of protection (p) type micro-phasor measurement unit (μPMU) installed at the bus of the respective distributed generation (DG). One of the pressing issues with DG's is the concern of inadvertent islanding that disrupts orderly reconnection besides posing hazards to utility workers. In view of this, this study proposes a real-time inadvertent islanding detection by μPMU. The voltage and current phasors obtained from these μPMUs by discrete Fourier transform are further processed by Fortescue transform to compute the angle of sequence components. The absolute angle difference between positive and zero components is used to initiate signal for accomplishing intelligent islanding under islanded condition. The simulation results prove the method to be robust, computationally efficient, non-detection zone free and feasible. Most significantly, as measuring equipment and relay are already present in p type μPMU, therefore unlike other detection methods, no extra arrangements are required in this method making it economically viable and easy to implement.