In development of electric power products, aspects related to thermal phenomena are becoming very important due to the fact that they guarantee the correct operation of product. The temperature limits specified by the standards cannot be exceeded which makes the knowledge of the temperature behaviour an important factor in order to predict reliability and performance of the product component in its working environment. In this study, thermal network method (TNM) is used for modelling of temperature conditions in typical geographical information system (GIS) compartment arrangements. Models implemented in ATP–EMTP software were validated with OrCAD Capture simulation environment and with high-current measurement results. On the bases of the TNM presented as the network approach composed of heat sources, thermal resistances and capacitances which can be easily represented and calculated by means of ATP–EMTP simulation software and also with the OrCAD Capture environment. This study addresses the thermal behaviour of a standard ELK-3 GIS compartment. Modelling in application to design rating calculations of the typical GIS compartment arrangements are presented and analysed. These analyses can serve as a base for development of more advanced ATP–EMTP models using the TNM approach.

In this study, a multi objective method for optimal network reconfiguration as well as reactive power dispatches of distributed generations (DGs) has been proposed to improve the network performances by using non-dominated sorting particle swarm optimisation. The various network performances in terms of multi objective function include minimisation of system power loss, voltage deviation and energy wastage from solar and wind generation system. The effectiveness of the proposed method has been tested on the IEEE 33-bus radial distribution system for different combinations of network reconfiguration and reactive power output of DGs or its varying power factor. The obtained results also compared and indicated that better network performances achieved with both network reconfiguration and power factor optimisation over other cases. In addition, this strategy also results in lesser energy wastage from distributed renewable generation over without network reconfiguration option; hence, this approach is also suitable for saving and utilising maximum capacity of available renewable sources.

Automatic load transfer (ALT) on the 11 kV network is the process by which circuit breakers on the network are switched to form open points in order to feed load from different primary substations. Some of the potential benefits that may be gained from dynamically using ALT include maximising utilisation of existing assets, voltage regulation and reduced losses. One of the key issues, that has yet to be properly addressed in published research, is how to validate that the modelled benefits really exist. On an 11 kV distribution network where the load is continually changing and the load on each distribution substation is unlikely to be monitored – reduction in losses from moving the normally open point is particularly difficult to prove. This study proposes a method to overcome this problem and uses measured primary feeder data from two parts of the Western Power Distribution 11 kV Network under different configurations. The process of choosing the different configurations is based on a heuristic modelling method of locating minimum voltages to help reduce losses.

This study addresses some issues related to reactive power support in electric power systems. This study considers the QV curve as a tool for indicating the robustness of generators in terms of their reactive power margin (RPM). The QV curve yields information that is then considered for contingency studies. Then, the dynamic behaviour of a system with respect to the RPM is investigated. A positive margin, the study shows, may drive a system to instability. To move the system to a secure region, fuzzy logic is proposed and the effects are dynamically analysed. To simulate the proposed methodology, the study employs a sample system of five buses and a real Brazilian system.

In this study, a new algorithm for discrimination between internal faults and inrush current conditions in power transformers is presented. First, the proposed algorithm removes the pre-fault conditions of the fault currents. Then, those currents are processed using the discrete wavelet transform to obtain the wavelet matrix. The correlation matrix is computed from wavelet matrix to know the eigenvalues associated with each frequency scale and to reduce the analysed information. This algorithm, which the authors are going to call wavelet correlation modes, is used to identify inrush and internal fault currents in power transformer. To validate the proposed algorithm, simulations are carried out in power systems computer-aided design software, and the obtained signals are analysed in order to evaluate its performance and sensitivity.

This study proposes a hierarchical hybrid control strategy to ensure stabilisation performance during the micro-grid operating mode conversion. Designing the hierarchical hybrid control strategy is divided into two stages. In the first stage, the research focuses on constructing a hybrid control scheme, where besides that the storage I unit needs to implement switching control strategy by means of an upper-level switching controller, the storage II unit that acts as a master unit also needs to be switched between two kinds of control modes including voltage–frequency droop control and PQ control in response to different micro-grid operating modes, and other slave distributed generation (DG) units operate in PQ control mode all the time. Moreover, during the operation mode conversion, according to the assessment indexes regarding voltage and frequency, the upper-level switching controller determines whether and when to send switching commands to the master DG unit. In the second stage, the research focuses on designing the hierarchical control strategies in the PQ control mode and the voltage–frequency droop control mode, as well as designing the upper-level switching controller to guarantee the stabilisation performance of the micro-grid during operation mode conversion. In the PQ control mode, all controllers are designed as a fractional order proportional–integral–derivative (FOPID) controller. Finally, the validity of the proposed hybrid control strategy is demonstrated by means of simulation results.

With the development of power grid interconnection, the disturbances propagation behave as a sort of electromechanical waves. The study of the disturbance propagation mechanism in the interconnected power networks is of great importance for controlling the spreading of disturbance and improving the security level of power systems. In this study, the electromechanical wave equation is built based on the discrete inertia model of power networks. In order to describe the phase and amplitude variations, the wave transfer function is derived. Then, the propagation characteristics of different frequency disturbances are analysed. The corner frequency of the discrete inertia model is proposed. Furthermore, the frequency dispersion and local oscillation are revealed as well as their relationships with corner frequency. Computer simulations for a 50-generator chain network are used to verify the propagation characteristics of disturbances with different frequencies. The research work is beneficial to analyse the influence of disturbance and develop countermeasures for disturbance based on electromechanical wave theory.

In low-voltage autonomous micro-grids, preserving both frequency and voltage stabilities at event of severe contingencies is an unsolved technical challenge. The conventional control algorithms are designed based on either one of frequency and voltage stabilities and do not bring satisfactory performance for real world practices. As per experiences in the transmission level, load shedding (LS) can be an effective countermeasure to overcome this challenge. This study introduces an under voltage-frequency LS (UVFLS) scheme to achieve proper load shed amounts (LSAs). The voltage effect is accounted for in two online and real-time mode stages. A quick computational algorithm is proposed in the online stage to obtain ‘nose’ curves of the network as a linearised piecewise function of voltage/load level. Then in the real-time operation stage, according to these curves and the present operating points of the system, optimum LSA is calculated. The frequency droop characteristics of distributed generation units are employed to incorporate the effect of frequency on the LSA. Simulation studies are carried out on two distribution systems, a 5-bus autonomous micro-grid and the modified standard IEEE 37-bus system. Validation of the proposed method shows that frequency and voltages are restored to their desired ranges using the novel UVFLS algorithm.

Concerning the difficulty in quantitatively describing the influence of different disturbances on power system stability, a novel composite energy stability region (ESR) is proposed in this study based on the dynamic damping theory. First, considering the influence of time-variant factors in the oscillation process on the dynamic characteristics of the system, the dynamic damping is energized. Thus power system dynamic stability criteria considering both the disturbance magnitude and system operation state is obtained. Then, the energy boundary of ESR is determined in the energy space according to the criteria, and the parameter boundary of ESR is determined in the parameter space combining the small signal stability region. On this basis, in the parameter-energy multi-dimensional space, the ESR which could reflect the dynamic stability and transient stability of power system under different disturbances is established. Finally, the ESR of IEEE 4-machine 11-bus system is drafted based on the dynamic damping theory. Simulation analysis of different parameter-energy pairs inside and outside the ESR verifies the correctness of the ESR drafted. The research in this study is of significant value in guiding system dispatch, predicting potential risks, formulating control strategies, and guaranteeing the safe and stable operation of power system.

Load frequency control is among the most important control tasks in power systems operation. Many researchers have focused on tuning the load frequency controllers using single-objective evolutionary algorithms. To avoid the drawbacks of single-objective optimisation algorithms, in this paper, tuning the load frequency controllers is modelled as a many-objective (MO) minimization problem. This MO optimisation problem is solved using an MO optimisation algorithm with clustering-based selection. Considering the maximum value of each objective among the non-dominated solutions found by the MO optimisation algorithm, the worst solution is determined. To select one of the obtained non-dominated solutions as the controllers’ parameters, a strategy based on the maximum distance from the worst solution is proposed. In order to measure the effectiveness of the proposed MO technique against several recently proposed single-objective optimisation algorithms, for tuning load frequency controllers, comparative simulation studies are carried out on two different test systems. Simulation results show that, in terms of different performance indices, the controllers designed by the proposed MO method are far superior to the controllers designed with the single-objective optimisation algorithms. Also, the presented results confirm the robustness of the controllers designed by the proposed method in case of power system parameters variations.

Cascaded static synchronous compensator (STATCOM) with delta-connected configuration is an effective solution to compensate reactive and negative-sequence currents. This study focuses on the circulating current and compensation method of delta-connected STATCOM under asymmetrical voltage conditions. According to the phasor analysis, constrains of voltage phasors and current phasors under reactive current compensation mode, negative-sequence current compensation mode and comprehensive compensation mode are deduced. On the basis of this, the analytical expressions of circulating current under the three modes are derived. Furthermore, a comprehensive compensation method for delta-connected STATCOM is proposed. In the proposed method, phase current references are calculated directly with the instantaneous voltage and current signals, which could enhance the dynamic behaviour and cluster-balancing control performance especially under asymmetrical voltage conditions. Finally, simulation and experiment results have been given to verify the effectiveness and feasibility of the proposed control method.

State estimation (SE) has been considered the fulcrum of advanced computer-aided tools used to monitor, control, and optimise the performance of power grids. It is destined for the provision of a consistent real-time dataset, free of compromising errors. To the SE eye, observability is the faculty of seeing the actual system operating state. As such, it is vital to evaluate this faculty, especially in quantitative terms. Drawing a parallel between the financial market (in which investment grades – intended to signal the suitability of an investment – are assigned by credit rating agencies) and SE arena, this study proposes the establishment of observation grades. With a view to performing a reliable SE, these are defined as ratings capable of indicating that a measurement system (devoted to observing the state of a power grid under many different conditions), has a seal of approval, i.e. relatively low risk of being unsuccessful. The methodology proposed to express observation grades is based on the Monte Carlo simulation approach. The availability of measurement units and grid branches are adequately considered. Numerical results of a proof of concept study performed on the 24- and 118-bus benchmark systems illustrate the application and expected benefits of the proposed methodology.

With the rapid evolution of electricity markets and the need for higher economic efficiency of power industry, attempts for lowering down the maintenance costs as a large portion of system operation expenses seem imperative. Recognised as a crucial step in practical implementation of modern maintenance paradigms, e.g. reliability-centred maintenance, this study proposes an efficient method to quantify the generating units’ criticality on the bulk power system reliability performance. The proposed approach utilises a solution concept of game theory and evaluates the contribution of each generating unit on the overall system reliability when a higher-order contingency occurs. The suggested framework would lead to a fair identification of critical units in restructured power systems for more focused maintenance activities and also helps in recognising where investments should be made to improve the system reliability. The effectiveness of the proposed approach is confirmed through implementation on the IEEE 24-bus reliability test system.

When an extreme weather event strikes a distribution system, the utility power may not be available for days or even weeks. As a result, a microgrid in the affected area will be operated in the islanded mode during that period. To continuously serve critical load with available generation resources, which are usually limited, load shedding actions can be performed to gradually disconnect load with low priority. This study proposes a method to obtain the dynamic load shedding strategy for an islanded microgrid with limited generation resources. First, dynamic load shedding is formulated as a stochastic optimisation problem, where the uncertainties induced by intermittent energy sources and load are incorporated. The objective is to maximise the economic performance of the microgrid. Limits on the generation resources and operational constraints are considered. Then, a model based on Markov decision process (MDP) is developed for the problem. A solution method for the MDP model is proposed to obtain the optimal load shedding strategy. Finally, numerical simulations are performed to validate the effectiveness of the proposed method. Impacts of available generation resources, uncertainties of wind power prediction, and load shedding time period on the load shedding strategy are discussed.

This study is concerned with the problem of computing the maximum loading point (MLP) in large-scale power systems. A modified asymptotic numerical method (ANM) with λ-parameterisation is used to fast approximate the MLP, which needs to solve a successive of power flows with adaptive load and generation increments. The ANM with Newton corrections is used to deal with the problem of reactive limits violations. The saddle-node bifurcation is identified by the accumulation of small step-lengths. The proposed algorithm has been tested on the IEEE-300, 9241-bus and a real 35,000-bus power system in China. Some comparisons with other algorithms have been performed. Numerical results reveal that a lower number of the Jacobian matrix factorisations are needed with the proposed method, which significantly reduces the computational costs.

The manuscript addresses the problem of finding all solutions of power flow equations or other similar non-linear system of algebraic equations. This problem arises naturally in a number of power systems contexts, most importantly the direct methods for transient stability analysis and voltage stability assessment. Here, the authors introduce a novel form of homotopy continuation method called the numerical polynomial homotopy continuation method that is mathematically guaranteed to find all the solutions without ever encountering a bifurcation. Since finding real solutions is much more challenging, first the authors embed the real form of power flow equation in complex space, and then track the generally unphysical solutions with complex values of real and imaginary parts of the voltages. The solutions converge to physical real form in the end of the homotopy. The so-called gamma-trick mathematically rigorously ensures that all the paths are well-behaved along the paths, so unlike other continuation approaches, no special handling of bifurcations is necessary. The method is embarrassingly parallelisable. The authors demonstrate the technique performance by solving several test cases up to the 14 buses. Finally, they discuss possible strategies for scaling the method to large size systems, and propose several applications for security assessments.

Transmission expansion planning (TEP) is an important and computationally expensive decision-making process in power systems. Expression of the power flows using power transfer distribution factors (PTDFs) could potentially reduce the size and computational cost of the TEP. However, this formulation does not lend itself easily for this problem as the system topology changes in the course of the optimisation procedure. This study presents a PTDF-based TEP model devoid of voltage angles and nodal power balances, while producing the same solution as angle-based TEP models. The proposed model is capable of monitoring a limited number of transmission lines that have significant impact on the system's reliable and optimal operation. It thus considerably reduces the number of constraints and results in a scalable optimisation problem. The proposed model is highly advantageous especially for the TEP of large-scale power systems. The numerical results provide an indication for the effectiveness of the proposed model.

High impedance fault (HIF) has long been a challenging problem in network protection due to its random behaviour and low magnitude. The conventional protection devices cannot be utilised since the HIF does not draw enough current to cause tripping. The feature of wavelet transform (WT) which decomposes a signal into different frequency bands and locations in time can be utilised to extract HIF features and detect its occurrence. In the study, HIF arcing currents associated with different types of contact surface are produced by experiments set up in the laboratory. Features of the fault currents are extracted and a new detection criterion is developed based on WT coefficients. Transformer magnetising inrush currents and capacitor switching transients are also produced by experiment and simulation, respectively, to represent transient disturbances commonly occurred in the distribution network. The detection criterion is used to discriminate the HIF from other normal non-fault transient events. Three different types of wavelet are tested and the Daubechies wavelet Db4 gives the best performance based on its detection and discrimination rates. The efficacy of utilising existing conventional current transformers for HIF application is also tested and verified by experiment.

In this study, a general framework for implementing a retail energy market based on the Nikaido–Isoda/relaxation algorithm is proposed as an electricity market structure with large distributed energy resources (DERs) penetration and demand side management of consumers. Moreover, the consumers are able to participate in the market as prosumers (i.e. producer and consumer at the same time). By considering the related uncertainties, the DERs can maximise their expected payoff or profit by undertaking strategies through the price bidding strategy, based on the proposed structure, considering Nash equilibrium. The results show the effectiveness and accuracy of the proposed framework in determining the optimal power set-points of players participating in the market to achieve the objectives.

As advanced metering infrastructure (AMI) is deployed, the AMI data is used to detect an energy fraud. Along with context analysis of AMI data such as detection of an unreasonably low consumption AMI data mining is a primary solution for detecting abnormalities that cannot be detected using simple context analysis. Traditionally, abnormality detection based on AMI data mining compares a load profile with predefined normal prototypes. However, since a load profile can be normal in one condition and abnormal in another, the condition associated with the load profile should be considered as determining the normality. However, existing methods do not connect the normality of a prototype and a specific condition. In this study, the authors propose a mechanism that incorporates the conditional probability into determination of the normality of the prototype for comparison. The novelty of their study is its generating a two-dimensional space using similarity and conditional probability, so that several multi-dimensional classification methods can be applied. They compare the proposed mechanism with best-fit and average prototype-based abnormality detection methods. In conclusion, the proposed mechanism can distinguish fraud data with a higher precision than the traditional methods. They also explore the accuracy of the mechanism with various parameters.

In an ill-conditioned power system, the Jacobian matrix is singular or near singular and solving the power flow equations by the traditional methods such as Newton method may lead to divergence. In this paper, we have applied a high-order Levenberg–Marquardt approach for solving the power flow problems in the ill-conditioned power systems. High reliability and high speed are the main characteristics of the proposed method. Using the controlling parameters of this method (σ and μ) can decrease the number of iterations and the computation time in solving the power flow problem of the ill-conditioned power systems. The proposed formulations and algorithm are tested on the 11-bus, 57-bus, 118-bus and 2383-bus ill-conditioned test systems. The simulation results show that the proposed method can significantly reduce the computation time and the number of iterations.

This study presents a mixed-integer linear programming (MILP) model to solve the simultaneous transmission network expansion planning (TNEP) and reactive power planning (RPP) problem. The proposed model considers reactive power, off-nominal bus voltage magnitudes, power losses, multistage expansion, and security constraints. The use of an MILP model guarantees convergence to optimality by using existing classical optimisation methods. In order to validate the approximation performed, the steady-state operation points were compared with those obtained using an AC load flow method. Garver's 6-bus system and a modified IEEE 118-bus system were used to show the precision and efficiency of the methodology. The results indicate that better expansion and generation plans are found by considering RPP simultaneously with the AC TNEP, when the solutions were compared with the plans of the TNEP using the AC model without RPP and the TNEP considering the DC model, with RPP conducted at a subsequent stage.

The need to increase power transmission capability in electrical power systems led to the proposal of possible alternatives to the traditional three-phase (3P) AC overhead transmission lines (OHLs). In addition to high-voltage DC connections, the alternatives include non-conventional solutions such as 4P AC lines and combined AC–DC lines. All these solutions have been examined in recent works where, however, the technical and economic aspects are usually separately analysed. On the contrary, a proper comparison among different solutions requires a combined technical–economic evaluation and, therefore, a systematic methodology based on a multi-criteria approach. This study compares the various possible OHL solutions resorting to an original methodology that joins technical and economic aspects. The former are taken into account by means of the loadability curves (properly computed for each solution). The latter include various cost items (for investment, energy losses, reliability and land occupation) computed for each solution. The different aspects are joined by computing the per-unit-of-transportable-power cost of each solution. This parameter provides, for any given line length, a total cost normalised in terms of the theoretical transmission capability of each solution and, thus, an interesting comparison tool among different solutions.

A novel output feedback dynamic excitation control scheme is proposed for efficient load angle trajectory tracking tasks for synchronous generators. In this way, effective tracking of reference trajectories for the state variables and electric power is also guaranteed. The introduced control design approach is robust against parametric uncertainty, unmodelled dynamics, and variable mechanical power input commonly present in practical electric power systems. The control scheme only requires measurements of the load angle variable, and state and disturbance estimation is properly avoided. Computer simulation results are included to show the controller robustness and the satisfactory reference trajectory tracking specified for the machine operation for both continuous and switched control voltage signals.

This study puts forward a probabilistic power flow calculation method based on the Johnson system and Sobol's quasi-random numbers. The Johnson system is utilised to simulate the distribution function of one dimensional variable and model the correlation of multiple uncertainties with historical data of the uncertainties. The improved Sobol's quasi-random number generator is adopted to produce the low-discrepancy samples in Monte Carlo simulation. The accuracy of the Johnson system is compared with other modelling methods of uncertainties and the comparison of Sobol's quasi-random numbers and other techniques, such as Latin hypercube sampling and simple random sampling are presented for the cases of IEEE 30-bus system and IEEE 118-bus system.

The paper proposes a new method for optimal allocation of shunt capacitors in distribution network with renewable distributed generation units such as wind turbines and/or solar power plants. The proposed method, based on application of the Monte Carlo simulation methods, respects the uncertainties associated with load demand and renewable sources power production. The optimisation problem is modelled by two criterion functions with the aim of improving voltage profile in a network by optimal selection of the locations and installed powers of the shunt capacitors. The suggested criterion functions have been optimised simultaneously by applying the non-dominated sorting genetic algorithm. On the basis of the measured data on wind speed and solar radiation, the method has been tested by the example of a real distribution network.

Decentralised control methods of voltage-source inverters-based multi-distributed energy resource (DER) microgrids and microgrids hierarchical control scheme studied in earlier researches limited to primary and secondary control levels while the proposed control scheme is completely analysed so that the three hierarchical control levels modelled for both grid-connected mode and islanded modes. In this study, the proposed hierarchical control scheme adds new control loop to control the reactive power reference by a fuzzy logic controller to have the benefit of increasing the system stability margins. In addition to the small-signal events, it maintains the stability of microgrids faced with large-signal disturbances such as short circuits, line outage, heavy motor starting etc., and improves fault ride through capability. However, power sharing to loads and network is sufficiently done. To demonstrate the effectiveness of the proposed hierarchical controller, simulation studies have been performed on a microgrid consisting of four units of distributed generation with local loads and in presence of main grid using MATLAB/SIMULINK software (offline simulations) and OPAL-RT real time digital simulator for verification.

This study introduces power quality (PQ) state space representation to describe continuous PQ disturbances. A tolerance boundary is designed to represent the integrated disturbance tolerance of all equipment connected to electric power network, and the uncertainty of integrated disturbance tolerance is described with the cloud model. Electromagnetic compatibility and incompatibility degree indices are proposed to reflect the severity of PQ disturbances affecting the equipment. The influence degree index is defined to quantify the severity and impact scope of PQ disturbances. The uncertainty of equipment fault state is expressed by a fuzzy membership function. Subsequently, PQ performance is assessed according to equipment compatibility/incompatibility degree to PQ disturbances. Case studies on a 14-bus distribution system are performed and analysed. Results reveal the effectiveness and reasonableness of the proposed indices in assessing equipment compatibility/incompatibility degree to PQ disturbances, influence of PQ disturbances on the equipment, and PQ performance.

In order to evaluate impact of different uncertainty, such as the intermittent behaviour of wind power and photovoltaic (PV) generation and bus load, and adjacent wind farms or PV resources on performance of power system, a new three-phase probabilistic load flow (PLF) algorithm with asymmetric line parameter and unbalanced load of distribution system is proposed. Correlation among input random variables is considered, especially the joint correlation of wind power and PV generation and bus loads is considered, and then joint probabilistic model of wind power, PV generation and bus load is established. Then a joint cumulants method and Gram–Charlier expansion are applied to obtain the cumulative distribution function of desired random variables, and PLF results based on joint cumulants method are compared with the ones of Monte Carlo simulations. Proposed method allows evaluating potential impact of different correlation and renewable energy generation penetration on the PLF of power system. The effectiveness of proposed method is demonstrated with a typical structure of 25-bus distribution system.

The recently proposed parallel hybrid modular multilevel converter is considered to be a low loss, low component count converter with soft switching capability of the ‘main’ H-bridge. The converter has similar advantages to other emerging modular multilevel converter circuits being considered for high-voltage, direct current power transmission and can be made compact which is desirable for offshore application. However, during ac network unbalance the individual ‘chain-links’ (CL) exchange unequal amounts of power with the grid which requires appropriate remedial action. This study presents research into the performance of the converter and proposes a suitable control method that enables the converter to operate during grid voltage unbalance. The proposed control concept involves the use of asymmetric third harmonic voltage generation in the ‘CL’ of the converter to redistribute the power exchanged between the individual ‘CL’ and the grid. Mathematical analysis and simulation modelling with results are presented to support the work described.