This study proposes the concept, calculation and application of dimension of distribution system security region (DSSR). Two forms of DSSR dimension are presented: one is named binary dimension; the other is called unary dimension. First, the binary dimension is defined as the number of security boundaries and the number of variables in them. A method based on main transformers connection vector can obtain binary dimension without listing model expressions of DSSR. Second, the unary dimension is proposed, which uses a single value in the form of N_e   ×  N_e to describe the scale. This form is convenient to compare the scale of different DSSRs. Moreover, a method based on association matrix is also presented. Third, a case is used to illustrate proposed definitions and methods. The relationship between distribution network and its DSSR dimension is analysed separately. Finally, the application of DSSR dimension is discussed. The unary dimension is applied to solve the problem of large-scale combinations for two-dimensional observation on DSSR. Any two feeders are possible to be combined, but many combinations are unnecessary. By the proposed method, the combinations that are really needed can be accurately obtained, and the use of DSSR is simplified.

It is necessary to design an economic dispatch mechanism to ensure the stability of the electricity market and the equilibrium of pricing strategy in a smart grid with real-time pricing. In this study, the pricing strategy in the smart grid is analysed by modelling the economic dispatch problem as a bi-level game in the electricity market, including the wholesale market and the retail market. In the wholesale market, the negotiation of the wholesale price between the generation company and multiple utility companies is formulated as a Nash bargaining problem. In order to guarantee the profit of the generation company and the social welfare of the utility companies simultaneously, the Nash bargaining solution is adopted to find an optimal wholesale price. In the retail market, the Shapley value is utilised to achieve profit distribution among the utility companies, and then a distributed gradient algorithm is proposed to search for the optimal retail price. Numerical results demonstrate the effectiveness of the proposed algorithm and the superiority of the economic dispatch strategy.

Renewable energy sources, particularly wind power, are being increasingly deployed in power systems to reduce environmental contamination. However, the uncertainty of wind power significantly influences power system economy. Therefore, this study presents Wiesemann–Kuhn–Sim (WKS)-type distributionally robust optimisation for performing an optimal two-stage sub-hourly look-ahead economic dispatch considering uncertain wind power. The dispatch considers the scheduling of thermal generators, wind power generators, and fast-response resources. The optimisation aims at minimising the expected total operational cost, including the costs of generation, generation shedding, and wind power curtailment. The hourly stage determines the thermal generation that can withstand the worst-case wind power distribution. The sub-hourly stage schedules the fast-response operations to correct the hourly dispatch. To characterise the uncertainty, a novel WKS-format ambiguity set that can obtain wind power distribution from historical data is constructed using the lifting theorem. Based on the ambiguity set and linear decision rule, a general lemma is employed to convert the model into a tractable conic optimisation that can be directly solved. Experimental results demonstrate the effectiveness of the presented approach compared to adjustable robust optimisation and sample-based stochastic optimisation.

With the increase in power rating of electric vehicle chargers, concerns regarding their integration to the grid have likewise grown. This paper investigates a novel technique for start-up of high-power fast electric vehicle (EV) charger using a solid-state inrush current limiter (SSICL). The circuit consists of three similar sets of bidirectional switch and limiting resistor that utilizes a control strategy based on a simple Kalman filter (KF) to suppress the converter start-up current and transient over-voltages. In fact, the built-up profile of the inrush current is dictated in accordance with the estimated current by the slow dynamic KF. Compared to alternatives, such as start-up resistors, the presented SSICL achieves faster start-up with comparable peak current, tends to provide lower distortion, and provides a good balance between speed and efficiency. Simulation and experimental results confirm that the proposed method can considerably suppress inrush currents, while improving the total harmonic distortion. Comparing the behaviour of the SSICL to other relevant techniques underlines the advantages of the proposed solution. Furthermore, although the focus of this paper is start-up of the fast EV chargers, the proposed circuit can act as an inrush-current limiter in most AC to DC converter structures.

The real-time transient stability assessment (TSA) is critical for emergency control of power systems. Accurate and fast TSA can provide an important basis for post-fault control of power systems. At present, the accuracy of the evaluation model based on machine learning is very high, but there are still some misjudgements in the results. In order to build a high-accuracy evaluation model, a novel frame based on the cost-sensitive method is proposed. Firstly, a deep belief network (DBN) is applied to build a TSA frame. The DBN is effectively trained by means of pre-training and fine tuning. Secondly, two models with the opposite preference are constructed based on the cost-sensitive method. Based on the output results of the two models, the deterministic or uncertain evaluation results are obtained. The samples that may be misclassified are divided into uncertain evaluation results. Thus, the accuracy of the deterministic evaluation results can be improved greatly. Through this design, the practicability of the evaluation model based on machine learning is greatly improved. The effectiveness of the proposed scheme is verified by the simulation results in the IEEE-39 bus system and a realistic regional system.

High voltage dc (HVDC) transmission, especially voltage source converter (VSC)-based HVDC transmission requires high-speed operation for relay protection. However, traditional derivative-based non-unit travelling wave-based protection (TWP) methods are sensitive to the fault impedance, resulting in low protection sensitivity in case of the high-impedance fault. First, the fault information containing in the fault travelling wavefront is analysed based on the frequency-dependent parameters of the dc transmission line and the broadband characteristic of the fault-point initial travelling wave. It can be concluded that the distortion of the fault travelling wavefront depends on the fault distance and the amplitude of the fault travelling wavefront depends on the fault impedance. Then, a principle of non-unit TWP for dc transmission line based on waveform correlation calculation is proposed. The proposed method is verified in both thyristor-based HVDC and VSC HVDC PSCAD test systems. The simulation results verify the high-speed, high fault-impedance tolerability and correctness of the proposed protection method.

The characteristics of pulsed power loads (PPLs), which contain several power electronic components, are different from the conventional RLC loads. If a PPL is directly connected to a sole power supply that has limited generation and small inertia (e.g. diesel generator), the sudden increase of energy demand could cause the huge voltage sags and the significant frequency drop upon the power supply. For this reason, this study proposes a large-signal model of PPL for analysing the dynamic voltage and frequency during PPL deployment. The proposed model can be described by non-linear differential-algebraic equations and established based on the equivalent circuit of PPL and the corresponding switching functions. According to the case study, the proposed model is compared with the conventional state-space averaged model and the time-domain simulation, by analysing the dynamic voltage and frequency. Finally, the test results verify the effectiveness of the proposed model and demonstrate that the proposed large-signal model would help for the study on the stability of the case-study system as well as the interaction between the diesel generators and the PPLs.

Reliability evaluation of power distribution systems is a well-studied and understood problem, but topology analysis efficiency and failure feature description are still limiting the practical application of reliability evaluation in distribution systems. One approach the authors proposed in this study is to incorporate the machine-learning technique into the simulation-based reliability evaluation method, and assess the system reliability in an empirical fashion. In this study, a framework for performing the machine-learning-based reliability evaluation, and corresponding modelling processes are first established. Then, by inducing a supervised learning algorithm named perceptron, a state-space classification-based (SSC) method for system state assessment, the core procedure of reliability evaluation, is proposed. On this basis, a reliability evaluation algorithm combining the SSC-based system state assessment and sequential Monte Carlo simulation is proposed, where the workload of topology analysis required in conventional reliability evaluation methods can be released. Furthermore, extensive case studies are conducted on the Roy Billinton Test System (RBTS) bus 2 system and an actual distribution system to verify the proposed models and algorithms. Results show that the proposed framework supports a more efficient reliability evaluation pattern while ensuring the evaluation accuracy.

This study presents a probabilistic approach to calculate locational marginal price (LMP) at distributed generation (DG) buses in an electric power distribution system to ensure that the network operates at reduced active power losses (APLs). The proportional nucleolus theory-based iterative method is proposed as a deterministic approach to compute LMP based on APLs. Uncertainties in load and market price were captured by using a scheme of the point estimation method. To compute the contribution of the reactive and active power of the DG on the APL of the network, loss sensitivity factors have been developed. The proposed method provides an active power price in terms of LMP and reactive power price to each DG as per its contribution to loss reduction. To verify the performance of the proposed method, it was implemented on the Taiwan Power Company distribution system. The proposed method can be utilised by a distribution company to operate the network at reduced APL and improve the benefit of DG owners.

To solve the negative sequence (NS) problem and enhance the regenerative braking energy (RBE) utilisation in an electrified railway, a novel energy storage traction power supply system (ESTPSS) is proposed in this study. In the new system, a power flow controller is adopted to compensate for the NS, and a super-capacitor energy storage system is applied to absorb and release the RBE. In addition, through the cooperation of each part, the proposed power supply system can provide continuous power without neutral sections. The NS compensation principle of the new system is illustrated. Depending on the operational state of the traction load, the control model is presented for different working patterns, including a regenerative braking pattern, a peak clipping pattern and a valley filling pattern. Moreover, a hierarchical control strategy including upper energy management and low-layer converter control is proposed, which effectively coordinate switches between the different working patterns. Finally, the validity of the control method and the excellent performance of the system are demonstrated by a case study. The results indicate that compared to a conventional TPSS, the ESTPSS increases the RBE utilisation of the system by 83%.

This study focuses on the selection of the most effective location of direct current power system stabiliser (DC-PSS) in multi-terminal high-voltage direct current (MT-HVDC) grids that is applied to voltage source converter (VSC) to voltage stability enhancement and oscillation damping. Due to the adverse interaction between having multiple number of DC-PSS, it is necessary to select the best location for installing DC-PSS in MT-HVDC grid. In this study, the participation factor (PF) method is used. This method assists to find which power converters are more sensitive and have a major impact on the instability of the entire system. In this approach, the whole of the system is modelled as a multi-input multi-output (MIMO) dynamic system. PFs related to each power converter are intended by the oscillatory mode sensitivity analysis against the components of the MIMO matrix of the system. The PF analysis determines which VSC station is more participating in the small-signal instability of the system. In order to endorse the efficiency of the proposed method, time-domain MATLAB simulations are conducted in Cigré MT- HVDC grid benchmark.

Voltage droop control is considered as a reliable control approach for multi-terminal DC (MTDC) grid system. A low value of droop constant may result in a high dynamic variation associated with oscillations for power and DC voltage deviation. Thus, the stability of the MTDC grid is at risk. This study presents a linear quadratic regulator (LQR) control design with an adaptive droop to achieve appropriate power sharing among the converter terminals. A control strategy with the combination of adaptive droop and LQR is designed in this study. The weights of LQR are tuned using the Gramian analysis. The closed-loop stability analysis is carried out using Lyapunov's stability approach. The proposed control scheme improves the closed-loop system dynamics by reducing the overshoots/undershoots and time to reach steady-state condition. In addition, power sharing according to converter rating is appropriately achieved. The performance of the proposed control scheme is validated on five terminal MTDC grid system simulated in MATLAB^®.

In order to reduce the voltage unbalancing, the delta reactances connected to the single-phase load, known as the Steinmetz circuit, are utilised. In this study, the design of passive filters in presence of the Steinmetz circuit is presented to balance the unbalanced networks including single-phase load. Voltage distortion and resonance phenomenon are very serious problems in power systems. Some methods have been proposed to provide the solution to this problem, among which passive filters are used as the most economical and efficient way to reduce harmonics. In this research, in addition to a brief review of the passive filters and their common types, the objective functions of the issue are discussed. The optimised functions for this issue are total harmonic distortion,voltage deviation value, total filters cost, frequency response and the critical bus power factor of the network. To solve the problem of the suggested multi-objective optimisation, NSGA-II is presented, and finally, the best solution is proposed with the normalised method from among the Pareto front. To verify the effectiveness of the proposed method, two networks of 13-buses industrial test network and modified 33-buses IEEE network are evaluated. These networks are included non-linear loads and Steinmetz circuit.

To achieve comprehensive insulation deterioration monitoring of power equipment and fault early warning in air-insulated substations, the detection and localisation of partial discharge (PD) using ultra-high frequency (UHF) antennas were widely studied. The existing UHF PD localisation system is mainly based on time-difference of electromagnetic wave signal, which requires very high time synchronisation accuracy and sampling rate. This study proposes a received signal strength indicator (RSSI)-based angle of arrival (AoA) method using the monopole UHF wireless sensor array. Multiple antennas are evenly placed in a circle frame and form an antenna array. Then an AoA estimation scheme is derived from the radiation pattern of designed UHF antenna. RSSI difference data, interpolation, and clustering are applied to improve the AoA resolution. A field test is performed to verify the effectiveness of the proposed PD localisation system. The results show that the estimated error on average is below 3.5°. Compared to the time-difference-based method, the accuracy of the designed system is more feasible for practical application of fault early warning considering its significant low-cost feature.

By means of advanced information and communication technology, cyber-physical power systems can attain real-time monitor and control but have to suffer the damage caused by a cyber attack. In this study, the authors' define attack efficiency to evaluate attack paths that attacker may adopt to intrude systems, to find the most efficient attack paths (i.e. the most vulnerable paths). Based on the actual power grid and security stability control system, the coupling model of cyber-physical power systems is established to analyse the propagation of cascading failure within and across the physical power grid and communication network. In the attack model, the attack cost matrix is built to describe the cost between directly connected nodes in a communication network. Furthermore, considering the probability that control commands are successfully transmitted from router nodes to generator/substation nodes, the total attack cost from the communication network to the physical power grid is figured out. To search for the most vulnerable attack paths in systems, the attack efficiency is proposed to quantify the relation between attack cost and attack gain, wherein the attack gain is the damage on systems caused by the cyber attack.

Atmospheric snow accretion along the insulators can eventually bridge adjacent shed spacing, which pose severe risks to the security of power networks. Aiming to investigate the influence of snow accumulation on the electrical performance of various types of insulators, the flashover tests of snow-accreted insulators were conducted. The effects of various factors on the electrical characteristics of insulators were analysed based on the experimental data. Results show that AC arc flashover gradient of the insulator covered with nonuniform snow accumulation is lower than that of the uniform snow-covered insulator. The former is as low as 22.5% lower than the latter. Moreover, the AC arc flashover gradient of the porcelain and glass insulators is 0.27–6.27% higher than that of the DC. For a silicone rubber insulator, this gap is greater than 20%. The flashover gradient of the glass insulator is the minimum at the snow thickness of 10 mm. The flashover process of snow-covered insulator is neither similar to that of the contaminated insulator nor different from that of the iced insulator but a combination of the two. The presented work helps to better understand the flashover mechanism of snow-covered insulators, and take efforts to mitigate its effects.

The lack of comprehensive monitoring equipment in low voltage (LV) residential feeders, impedes a near-term deployment of centralised schemes for the integration of domestic-scale distributed generation (DG). In this context, this study introduces a technique that generates a set of fitted polynomials, derived from offline simulations and regression analysis, that characterise the magnitude of representative network variables (i.e. key for network operation) as a direct analytical expression of the controllable local conditions of any DG unit (i.e. active and reactive power injections). Crucially, the coefficients of these polynomials can be estimated, autonomously at the location of each DG unit, without the need for remote monitoring (i.e. using only locally available measurements). During online implementation, the method only consists of direct calculations (i.e. non-iterative), facilitating real-time operation. The accuracy of the polynomials to estimate the magnitude of the network variables is assessed under multiple scenarios on a representative radial LV feeder. Furthermore, the robustness of the method is demonstrated under the presence of new generation and electric vehicles.

AC transmission expansion planning (TEP) is a complex problem to solve due to its large scale, mixed-integer, non-linear and non-convex characteristics. This paper presents an efficient sensitivity based approach which employs the primal-dual interior point method (PDIPM), for tackling integer variables in AC TEP. PDIPM's Hessian is used to evaluate the sensitivities of the objective function with respect to the line candidates, which are then used to find a feasible AC TEP solution. The proposed approach solves this non-convex mixed integer non-linear programming problem, without resorting to any use of relaxations/approximations in the AC TEP model. Also, the need and superiority of the AC TEP over the conventional DC TEP is established by comparing both using the proposed approach. Solutions of AC TEP with reactive power planning and an integrated multistage AC TEP are also obtained to demonstrate the performance of the proposed approach. Superior solution quality and lesser computation time of the proposed approach are confirmed by comparing the same with that of the branch and bound/cut approach, constructive heuristic algorithm, merit function-based approach, conic programming and particle swarm optimisation. The studies performed for the various test cases prove the efficacy and computational efficiency of the proposed approach.

Apparently, battery energy storage (BES), intelligent protection and power quality are considered as independent issues. These three factors can be interlinked effectively for control of microgrid through automated demand side management (ADSM). In this context, the proposed approach may change the conventional way for microgrid operation and control giving priority to the power quality issues considering protection and BES systems. The control algorithm is implemented through fuzzy inference system based power quality monitoring index and ADSM. As a part of intelligent protection, logic table for circuit breaker (CB) coordination has been developed without/with backup for relay devices to provide ADSM. The model has been simulated using Matlab-software and validated experimentally using OPAL-RT OP4510 real-time simulator through the assessment of power quality-related parameters such as voltage, frequency, total harmonic distortion and power factor. The results are found satisfactory showing the feasibility of the proposed microgrid model.

Optimal capacitor placement for radial distribution systems (RDSs) considers minimising the total cost of new fixed capacitors, switchable capacitors, and losses, while satisfying power balance equations, limits on bus voltages and capacitor limits. It is a non-convex mixed-integer non-linear programming (MINLP) challenge. In this study, the authors propose a solution method using a line-wise model (LWM) of power balance equations. First, equations for LWM are presented with their Jacobian for solving the power flow problem using Newton–Raphson method. Then, an optimal non-convex MINLP capacitor placement formulation with LWM power balance equations is presented. Thereafter, it is transformed into a convex mixed-integer conic programming formulation using second-order conic relaxation. Both the non-convex and convex optimal capacitor placement formulations are used to study 69-bus and 136-bus RDS. The results are compared with a formulation that uses the branch flow model (BFM) for power balance equations. Results show that the non-convex LWM-based formulation is twice as fast when compared with the BFM-based formulation. The convex LWM-based formulation is from 4 to 30 times as fast when compared with the BFM-based formulation, demonstrating the benefits of the use of the LWM-based formulation for enhancing the solution space of the optimisation problem.