One of the most intricate optimisation problems in power systems is generation scheduling. It determines the schedule and dispatch of electrical power generation to meet the load demand under various technical and operating constraints. Generation scheduling is a vivid problem, particularly in recent years, due to the aggressive integration of renewable energy, with stochastic nature, into power grids. As the literature size has swollen substantially in the past several years, this study critically looks into uncertainty modelling and the formulation of various techniques that were implemented in stochastic optimisation-based generation scheduling. The strengths and weaknesses of existing methods are fully exposed. Market operation policies that significantly affect the scheduling of renewable energy generation in different timescales are elaborated. Potential applications and future trends in terms of modelling, computational performance, and incorporation of flexibility and resilience notions are thoroughly discussed.

The microgrid concept has gained enormous popularity in the power industry due to recent advances in the power electronic converter (PEC) technology and environmental concerns over green-house gas emissions from power generation. Among microgrids, the hybrid AC/DC microgrid concept has been promoted as a viable concept to reduce energy conversion losses. However, hybrid AC/DC microgrids are susceptible to stability issues during high penetration of dynamic loads (e.g. induction machines). The non-linear dynamics of induction machines result in sustained voltage/frequency oscillations following disturbances in the microgrid, which is a major challenge for stable operation of the hybrid AC/DC microgrid. The PEC-based energy storage systems (ESSs) are used as an effective solution for power balancing in the microgrid; hence with the fast response of the PEC, microgrid voltage/frequency could be stabilised rapidly. Thus, a supplementary power oscillation damping (POD) controller is proposed in this paper for the ESS to damp low-frequency oscillations (LFOs) in the hybrid AC/DC microgrid. The effectiveness of the proposed damping controller is verified using non-linear simulations considering different penetration levels of dynamic loads and disturbances in a hybrid AC/DC microgrid. Results indicate that the proposed supplementary POD controller can significantly damp the LFOs in the hybrid AC/DC microgrid.

Current feed-in-tariff (FIT) schemes for photovoltaic (PV) generators are set in the long term, thus they do not provide optimal dynamic price signals on the operational state of the distribution system. This work presents a transactive energy scheme to jointly optimise the operation of smart distribution networks, residential flexible loads and distributed PV-battery systems. With this aim, a day-ahead dynamic pricing (DADP) is proposed, which results in the economic social welfare maximisation of both distribution system operator (DSO) and prosumers in a 24 h time window, considering AC network constraints. DADP consists of distribution locational marginal prices that quantify DSO power delivery costs over time and across distribution network buses. To enable the participation of PV batteries in the DADP settlement scheme, and to consider the value of stored energy, a preference model is proposed on the willingness of prosumers to charge or discharge active power from batteries. The social welfare maximisation problem is proposed within the context of Latin American distribution networks and solved using the alternating direction method of multipliers, which is tested via simulations on a radial test feeder. Results indicate that DADP outperforms FIT scheme in terms of social welfare, and volume of exchanges among prosumers, DSO and wholesale market.

Several international standards have suggested to detect the unintentional island formation to safeguard the working personnel and protect the electrical equipment in the system. An active islanding detection technique, which employs the q-axis current disturbance injection, has been utilised and an analysing technique is proposed in this work based on a combination of band pass filter and mean of absolute frequency variation (AFVmean) to detect and differentiate the island formation from other transient events. The proposed analysing technique (PAT) detects island formation within 180 ms, which is less than the prescribed time of various international standards, applicable to dynamic loading conditions without the need of adaptive threshold and communication, and offers zero non-detection zone (NDZ). The disturbance injection makes significant variation in the frequency of voltage signal on post-islanding condition even for zero-power mismatch condition, therefore, the NDZ is zero. The PAT is corroborated for various islanding and non-islanding events and the simulations are performed in MATLAB/Simulink tool.

Reliability is one of the most important factors to judge a power system. So, assessing reliability is an important task in power system planning. Many techniques have been developed to enhance the reliability of a power system. Some of those techniques depend on integrating new components and other techniques depend on changing some characteristics of existing components. One of the techniques depending on integrating new components is to integrate an energy storage system (ESS) with a power system. If the ESS is optimally sized to minimise the investment and operating cost, it enhances the reliability of the power system with a notable difference. This paper illustrates how to optimally size an ESS to be integrated with a grid-connected microgrid using the mixed-integer linear programming method. Moreover, load uncertainty is considered and the optimisation problem is solved using two different approaches to optimally size the ESS. Reliability indices of the microgrid are calculated before integrating it with the ESS and after integrating it to illustrate the enhancement of the reliability indices. Simulation results depict the effectiveness of the proposed approach.

Curtailable loads (CLs) are regarded as one of the last lines of defence to maintain the security and stability of power systems. Nevertheless, if organised carefully, they can also be exploited as preventive security procurement measures for power systems. This is especially true for heavily loaded power systems in which the normal control schemes are already exhausted. In this study, a new power market approach is proposed to utilise CLs’ potential in ensuring voltage stability margin (VSM) for heavily-loaded power systems. The proposed method aims to provide a mechanism to engage CLs as active players in the power market, and hence, minimise the disruptive effect of the load curtailment. Next, CLs participation in the power market is utilised to minimise the cost of achieving a desired level of VSM, at normal and N − 1 contingency conditions, in a preventive manner. The most efficient load curtailment and power generation pattern are determined, using a modified particle swarm optimisation algorithm, to minimise the system's total cost, while meeting grid's VSM requirements. The simulation results verify that the desired level of VSM can be effectively obtained using the proposed approach, with much less operational cost compared to the established methods.

This study presents a thorough analysis of the effect of load models on frequency response, small and large disturbance stability of the power system, in order to identify the type of stability exhibiting most sensitivity to load models, and for each type of studied stability to pinpoint the load model that has the worst effect. The presented analysis shows clearly that transient stability is the most sensitive to load models. The number of unstable cases varies considerably with each type of studied load model. The effect of the load model magnifies with the reduction in headroom of synchronous generators. The results of frequency response of the system following an active power disturbance demonstrate that the influence of constant power loads can be significant if the system is operating with reduced primary frequency response at high load. High integration of renewable energy sources (RES) increases the variation in the damping of electromechanical modes due to increased uncertainties, and a high proportion of induction machines can reduce the damping of inter-area modes considerably, making a well stable mode unstable for certain operating points. The influence of load models has been illustrated using a 68-bus system with 30% and 52% penetration of RES.

The analysis of dielectric response function obtained from the power transformer is a well-accepted technique in insulation diagnosis. A convenient way of analysing time-domain dielectric response φ(t) is the formulation of simple resistance−capacitance-based circuits like the conventional Debye model (CDM) or the modified Debye model (MDM) that are capable of modelling φ(t). However, available techniques do not guarantee unique branch parameters of such circuits for a given φ(t). In fact, the branch parameters are known to depend on the curve-fitting procedure opted during model formulation. This makes accuracy of CDM and MDM parameter-based diagnosis techniques less reliable. Furthermore, it seems logical to analyse the time-domain dielectric response of oil-paper insulation using a model containing time-varying parameters. In this study, a methodology is proposed using which such an insulation model (containing time-varying parameters) is formulated using time-domain insulation response. Related analysis presented suggests that the proposed model is immune to problems associated with available insulation models (containing time-invariant parameters). The performance of the proposed model in indicating insulation condition is tested on data obtained from several real-life power transformers.

Power-to-gas (P2G) technology opens up another perspective for effective, long-term, large-scale energy storage, so that it can promote large-scale wind power integration. Under this background, this study introduces P2G technology into the economic dispatch model of wind power integrated systems. First, an uncertainty interval model of wind power is built based on the probability distribution of wind power prediction error. Then, considering P2G's function of absorbing surplus wind power and undertaking downward spinning reserve, the factors that influence P2G's ability in enhancing the accommodation of wind power are analysed through theoretical derivation. Consequently, the relationship between the maximum wind power integration and the power delivered to the P2G facilities under a given capacity of P2G can be further understood. Moreover, an economic dispatch model incorporating wind power, P2G facilities and battery energy storage systems is established and a feasible region relaxation algorithm is proposed to deal with the non-smooth functions in the proposed model. Case studies are conducted on a modified IEEE 39-bus system. The results verify the correctness of theoretic analysis and show that the proposed model can help to reduce wind power curtailment and enhance the security and economy of the power system.

In this study, a method for detecting misjudgements in customer harmonic responsibility determination is proposed. The method is based on waveform correlation analysis. The quantitative relationship between waveform correlation coefficients and equivalent harmonic current injections is studied and discussed through theoretical derivations. The complete harmonic responsibility misjudgement detection method is then proposed on the basis of quantitative analysis and validated by means of simulation studies and field tests. The method has the ability of detecting harmonic responsibility misjudgements made on linear inductive loads using direct harmonic current measurement indices. On-line detection of misjudgements made by power quality monitoring systems in harmonic responsibility incentive management can be achieved by the proposed method.

In this paper, a new kind of coupling mechanical high-voltage direct current (HVDC) circuit breaker topology based on pulse transformer is proposed and its working principle is analysed in detail. On the basis of the requirement of 160 kV rated voltage, and 9 kA breaking current, the varying trend and design principle of parameters are given by the theoretical calculation. The prototype design of 160 kV HVDC circuit breaker is completed and type test passes. Results prove that the prototype of 160 kV HVDC circuit breaker has natural bi-directional breaking capacity. It can interrupt the current below 9 kA and withstand transient interruption voltage 272 kV. The breaking time is <5 ms.

This study proposes a comprehensive model to investigate winding vibration characteristics. The radial vibration model is firstly established based on the Euler–Bernoulli beam theory, and the radial acceleration is found to be the second derivative of deflection under the quasi-static load. The fluid-loading effect of oil on winding vibration is then investigated through experimental modal analysis and finite element method. This effect leads to the decrease of natural frequencies and the increase of damping ratios. The harmonic response of axial winding vibration at 100 Hz shows the symmetry distribution that vibration on the one quarter and three-quarters of the winding height are larger than other positions. The radial acceleration is not affected by the clamping pressure, whereas the axial acceleration is in a reciprocal relationship with it.

Conventional distribution network is a radial network with a single power source. Usually, overcurrent protection schemes are employed for such system protection for their simplicity and low cost. With the introduction of renewable generations, the existing protection coordination needs to be upgraded. Provision of directional feature and the requirement of high capacity circuit-breakers at certain points for the protection scheme demands considerable investment. The renovation cost required for upgrading the protection scheme will significantly impact the network cost requirement and consequently distribution use of system (DUoS) charges. This study aims to investigate the impact of renewable generations on the DUoS charges considering the cost associated in revamping the protection scheme. A power flow based MW + MVAr-miles DUoS charging method, that considers used capacity of the network, is proposed to carry out the DUoS charging calculations. The proposed charging mechanism appraise/penalise the users in accordance they are affecting system power factor. Accordingly, the proposed pricing algorithm may encourage users to act based on the economic signal generated at each location. The proposed charging algorithm has been tested on IEEE-33 and IEEE-69 bus distribution systems to examine the impact of renewable generations on the use of network costs.

This study proposes a decentralised robust fuzzy control strategy for islanded operation of an AC microgrid with voltage source inverters. The objective is to design a robust controller for regulating the load voltage and sharing power among distributed generators (DGs) in the presence of uncertainties in the system and non-linear loads. The AC microgrid consists of parallel DGs connected to a main AC bus. A Takagi-Sugeno fuzzy approach is developed in this article to achieve stability and desired performance in dealing with non-linearities in the islanded microgrid and H _∞ criterion is used to obtain a robust control strategy in presence of uncertainties raised by unmodelled and high frequency dynamics. Therefore, a non-convex condition in H _∞ optimisation problem is converted to a convex linear matrix inequality (LMI) condition and is solved by MATLAB LMI toolbox. In order to develop a decentralized system, P–f and Q–V droop controllers are used to specify set-points for local inverter controllers in each DG. The effectiveness of the proposed control strategy in presence of constant power load and DG accidental outage is validated by the simulation of a microgrid test system in MATLAB SimPowerSystems toolbox. Comparison with cascaded proportional integral controller shows advantages of robust T-S controller.

This study presents a novel faulted line identification method that is applicable in power systems with only sparse synchronised measurements, and at the same time, with significantly reduced computational burden so that it can be a competitive choice for wide-area backup protection schemes. By revealing the behaviour pattern of bus voltages from the perspective of high-dimensional unitary space, the method is enabled to avoid unnecessary computation and thus to remarkably improve its efficiency. Analysis in high-dimensional unitary space also gives a direct and feasible guideline for phasor measurement unit (PMU) placement, from which a PMU optimal placement strategy is developed. Performed on the IEEE benchmark systems of 39 and 118 buses, the proposed method gives encouraging results.

In this study, a distributed energy management for community microgrids considering phase balancing and peak shaving is proposed. In each iteration, the house energy management system (HEMS) installed in each house minimises its electricity costs and the costs associated with the discomfort of customers due to deviations in indoor temperature from customers’ set points. At the community level, the microgrid central controller (MCC) schedules the distributed energy resources (DERs) and energy storage based on the received load profiles from customers and the forecast energy price at the point of common coupling. The MCC updates the energy price for each phase based on the amount of unbalanced power between generation and consumption. The updated energy price and unbalanced power for each phase are distributed to the HEMSs on corresponding phases. When the optimisation converges, the unbalanced power of each phase is close to zero. Meanwhile, the schedules of DERs, energy storage systems and the energy consumption of each house are determined by the MCC and HEMSs, separately. In particular, the phase balancing and peak shaving are considered in the proposed distributed energy management model. The effectiveness of the proposed distributed energy management has been demonstrated by case studies.

Voltage/VAR regulation (VVR) implemented by capacitor banks (CBs), on-load tap changers (OLTCs), and photovoltaic (PV)-associated inverters is effective to enhance voltage stability and reduce power loss. On the other hand, conservation voltage reduction (CVR) has been widely adopted in distribution networks to reduce load demand. Existing works mainly focus on each of them. This paper proposes a VVR method with CVR, forming a multi-objective optimisation problem which minimises (i) voltage collapse proximity indicator (VCPI), (ii) load demand, and (iii) power loss. Besides, PV power generation as uncertainty significantly impairs the VVR results. To deal with the uncertainty issue, this paper proposes a rolling-horizon framework to determine VVR and applies Taguchi's orthogonal array testing (TOAT) to model the uncertain PV power generation, achieving rolling-horizon-based multi-objective robust VVR. The proposed model is tested and demonstrated on the IEEE 33-bus and 69-bus systems, and simulation results verify that the proposed method can support robust solutions of the multi-objective VVR problem for decision-making.

Electricity generation's planning and operation have been key factors for any economic development in the power industries but it can only be achieved if the generation was accurately forecasted. This made forecasting systems essential to planning and operation in the electricity market. In this study, a novel system called multi-GRU (gated recurrent unit) prediction system was developed based on GRU models. It has four level of prediction process which consists of data collection and pre-processed module, multi-features input model, multi-GRU forecast model and mean absolute percentage error. The data collection and pre-processed module collect and reorganise the real-time data using the window method. Multi-features input model uses single input feeding method, double input feeding method, and multiple feeding method for features input to the multi-GRU forecast model. Multi-GRU forecast model integrates GRU variation such as regression model, regression with time steps model, memory between batches model, and stacked model to predict the future electricity generation and uses mean absolute percentage error to evaluate the prediction accuracy. The proposed systems achieved high accuracy prediction results for electricity generation.

This study explains the underlying concepts and implementation details of using an open source distribution analysis tool – OpenDSS to conduct dynamic simulations of converter interfaced generation (CIG) in large, realistic power distribution systems. The dynamic models of different types of CIGs are derived and written into the dynamic-link library (DLL) to be called by OpenDSS during simulation. The DLL development is illustrated in detail with the programme structure and the model derivation of CIG. A phasor domain modelling method is adopted to derive single-phase CIG models in order to make the DLL models compatible with OpenDSS. The conversion between phasor and natural waveform data when simulating single-phase systems is discussed. The DLLs are derived based on the equations of the power stage circuit including the filters and the specific controllers. Applications of developed DLLs are illustrated with test cases, where volt-VAR control and microgrid mode control of CIGs are tested in a large-scale distribution system. This study can be used as a tutorial for performing the dynamic analysis for single-phase converters in OpenDSS.

Degradation of the electrical insulation within power transformers by partial discharge (PD) may lead to catastrophic failure of the apparatus, hence PD should be detected at an early stage. Ultra-high frequency (UHF) measurement method, i.e. detecting electromagnetic (EM) waves in the UHF range radiated from PD, has recently received attention for its various advantages, such as the robustness against external noises and its capability of localisation of the PD position. However, the EM waves suffer attenuation while propagating within transformers, in some cases, which results in undesirable low detection sensitivity. To evaluate the propagation and attenuation characteristics of the EM waves quantitatively, the simulation technique of the EM wave propagation is of importance. In this study, at first, the EM waveforms as well as attenuation properties of their amplitudes and cumulative energies while propagating through transformer windings in an oil-filled tank were experimentally investigated. Next, the detailed conditions for simulating the EM wave propagation based on time-domain finite integration technique were described. Then, the simulated results were compared with the experimentally obtained ones. These simulation and measurement results showed good agreement with each other, therefore the authors have successfully validated the newly developed simulation of the EM wave propagation.

This work demonstrates a grid-supportive photovoltaic (PV) system with an adaptive pseudo-linear control. The proposed PV system utilises a boost converter and a voltage source converter (VSC). The VSC performs multitasks such as load balancing, harmonics suppression and enhancing active power penetration to the grid. Wherein, a perturb and observe based technique serves the function of maximum power point tracking through the control of a boost converter. However, an adaptive pseudo-linear control is used for control of VSC. The adaptive pseudo-linear algorithm is used for the evaluation of fundamental components of load currents and it estimates the reference grid currents. The grid currents are controlled to generate the insulated gate bipolar transistors firing signals for VSC. A prototype of PV system is developed in the laboratory and implemented under different loads and solar insolation levels. The total harmonic distortions of grid currents are preserved within the limits in accordance with the IEEE-519 standard.

In order to solve the problem of noise interference in power quality disturbance identification, a new method of multiresolution hyperbolic S-transform for noise abatement based on energy density is proposed. First, multiresolution hyperbolic S-transform is performed on the power quality disturbance signal. This method combines suitable time-frequency resolution with good noise suppression performances. Second, the transient disturbance time-frequency domain is determined according to the fluctuation energy density. By using a mean time-frequency filter, the interference of the noise in the non-transient disturbance time-frequency domain with signals is eliminated, and the noise in the non-signal time-frequency domain is suppressed. Then, the signal time-frequency domain is determined according to the energy density, and the noise in the non-signal time-frequency domain is further suppressed by the denoising time-frequency filter. The characteristic curve is extracted from the complex matrix module after the noise abatement. Finally, a time-frequency database of tree structure is established. The dynamic time warping distance query classification method is used for quick classification according to the relationship of membership degree, which reduces the number of queries and improves the recognition accuracy. The classification result shows the effectiveness of the algorithm in high noise background and the applicability in actual fields.

In allusion to the prediction for the failure rate of transmission lines under multiple external environmental factors, a comprehensive prediction method for the failure rate of transmission lines based on an multi-dimensional cloud model and Cholesky decomposition was proposed in this study. According to the historical data in meteorological early warning system and icing forecasting system, the mutual correlation degrees of these multiple external environmental factors are got by the grey relational algorithm and the comprehensive prediction model for the failure rate of transmission lines was established based on an multi-dimensional cloud model and Cholesky decomposition. In light with the external environmental factors in the next year, the failure rate of transmission lines was predicted by this proposed method. The test results based on actual data in Guizhou Power Grid show that this proposed comprehensive prediction method for the failure rate of transmission lines has high accuracy as the prediction error is about 2.05% and a much low computational burden as it only takes 30.25 s which is highly suitable for practical applications.

This study, based on a novel control strategy, proposes a sizing method for battery energy storage systems (ESSs), which makes the wind power system more dispatchable. The main objective of the proposed control-based sizing method is to facilitate robust unit commitment by smoothing the output power of wind according to a desired reference. Owing to the energy conversion loss, the controller closely monitors the battery state of charge (SOC) to prevent the battery from being fully discharged during the smoothing procedure. The proposed controller can automatically revise the battery dispatching reference maintaining the SOC constant. In each dispatch interval, model predictive control is used in real time to ensure that the output power follows the generated reference. The ESS is sized according to the simulation results solved by the proposed control strategy. Meanwhile, the performance of the proposed control strategy is validated over actual wind power data.

To utilise load-side control for frequency regulation in transmission networks, the designed control schemes need to be granulated down to the subtransmission level as only aggregate loads are used on the transmission level. Moreover, due to a higher R/X ratio in subtransmission networks, the active power changes caused by frequency control will influence bus voltages. To achieve the required active power response and regulate bus voltages, a control scheme is proposed for subtransmission networks by adopting electric spring (ES) aggregators consisting of ESs and non-critical loads. To implement the dual goals, the ES voltage of each ES aggregator is decoupled into d and q components. A distributed leader-following consensus algorithm is adopted for ES aggregators to control its active power consumption by sharing information with neighbouring aggregators. The d component of the ES voltage is adjusted accordingly to provide the required active power cooperatively. To avoid the consequent voltage variation, decentralised proportional–integral (PI) control is adopted for ES aggregators to adjust the q component of the ES voltage accordingly. Simulation results show that ES aggregators manage to achieve the required coordinated active power response to regulate frequency and keep bus voltages within the acceptable region under the proposed control method.

Helical coils in different forms find applications in various areas of electrical engineering. While power engineers use close-pitched coils in inductors, reactors and transformer windings, communication engineers use large-pitched helical coils as antennas. In classical power engineering, coils are represented as lumped inductors for power frequency applications and switch-over to distributed circuit models while dealing with switching and lightning transients. Even for very fast rising excitations such as very fast transient overvoltages, chopped lightning waves and propagation of partial discharge pulses, multi-conductor transmission-line-based models have been employed, which appears to be an over-simplification. It would be very useful if an upper-frequency limit for the circuit-based models is quantified, which requires an extensive solution of the electromagnetic fields. After realising the inherent late-time instability of marching-on-in-time methods, a relatively new method called the marching-on-in-degree-based scheme is adopted for the solution of the associated electric field integral equation. A deeper insight is first obtained by analysing the helical antennas. Subsequently, based on the extensive simulation results for the single-layer helical coils, an empirical relation relating the upper-frequency bound for the circuit-based modelling has been deduced.

Series capacitor compensation technology has been widely used in long-distance wind power transmission, which can improve the power transmission capacity and enhance the static stability of the power system. However, adding a series capacitor in the line may present a potential risk of subsynchronous resonance (SSR) to the system. This study focuses on the SSR caused by induction generator effect of the doubly-fed induction generator-based wind farms. The SSR phenomenon of wind power system is researched by the impedance analysis method. A mitigation strategy of adding a virtual inductance based on integral control is proposed for enhancing the system stability and alleviating the SSR. It has clear and intuitive physical concept, which is beneficial to system integration and provides a simpler and more economic method for mitigating SSR. Moreover, the principle and process of controller design are elaborated. Moreover, the time-domain simulation is carried out to prove the effectiveness of the proposed control strategy under different operating conditions considering various compensation levels and wind speeds. Finally, the suppression effects of the virtual inductance in rotor-side converter and grid-side converter are compared.

Reductions in system inertia due to increasing penetration levels of wind power may result in frequency stability issues. Thus, it is necessary to provide a comprehensive method to estimate the maximum level of wind power that can maintain a system's frequency within allowable security limits following a major disturbance. Here, a fast method to estimate maximum wind power penetration level (WPPL) that considers frequency cumulative effect is proposed. The method first establishes an average system frequency response (ASFR) model of integrated wind power and then calculates the corresponding frequency response trajectory characteristics. Subsequently, a new transient frequency security index (TFSI) based on the frequency cumulative effect is expressed. The physical basis for the TFSI is that it can objectively reflect the dynamic security state of the system frequency. The quantitative functional relationship between the WPPL and the TFSI can be obtained by combining the frequency response characteristics and the TFSI definition. A numerical expression for the maximum WPPL integrated into the grid can be obtained, and the maximum WPPL of the integrated wind power system can be instantaneously and quantitatively estimated. Finally, the feasibility and effectiveness of the proposed analytical method is demonstrated on a 10-machine 39-bus system.

Fast load restoration based on network reconfiguration is a key step to enhance the resilience of distribution systems (DSs). For DSs equipped with remote-controlled switches (RCSs), the reconfiguration can be completed promptly. However, when the branch is equipped with manual switches only, it cannot be operated immediately, and its post-event state is determined by its pre-event state. Considering these facts, this study proposes a unified two-stage reconfiguration method for the resilience enhancement of DSs. In the pre-event stage, the allocation of RCSs and the reconfiguration of the network are determined to prepare the system for a set of possible fault scenarios caused by upcoming extreme weather. In the post-event stage, network reconfiguration based on the placed RCSs is performed for fast load restoration to minimise the loss of load expectation (LOLE). A new mathematical expression is proposed to ensure the radial operation of DSs with islanded DSs and islanded microgrids. To improve the computational efficiency, the scenario decomposition algorithm is employed to decompose the proposed model into several subproblems, which can be solved in parallel. The results show that the proposed method can significantly reduce the LOLE caused by extreme weather events, thus enhancing the resilience of DSs.

A method to estimate frequency domain soil parameters of horizontally multilayered earth is developed. Cole–Cole model of complex conductivity form is adopted to describe the frequency dependence of soil parameters. The estimation of frequency domain soil parameters includes two stages. In the first stage, soil-layered structure is determined under the DC field by the interpretation of resistivity sounding data. The obtained model parameters in this stage include the DC soil conductivity and thickness of soil layers. In the second stage, Cole–Cole model parameters are estimated based on the soil-layered model obtained in the first stage. The theoretical formula of complex apparent resistivity is derived from Green's function with considering dynamic-state field theory. Since dynamic-state field is considered in the inversion algorithm, this method can be extended into high-frequency domain. Discrete complex image method is used to calculate Sommerfeld integral quickly. In order to remove electromagnetic (EM) coupling between cables at high frequencies, a new electrode configuration method is proposed. Genetic algorithm is improved by combining with parallel computing. The parallel genetic algorithm is applied to the optimisation of model parameters.