Due to the non-linear power flow equality constraints and uncertain injected power of renewable generation, the reactive power optimisation problem is stochastic and non-convex, which is hard to be solved efficiently. Therefore, the discrete probability model of renewable generation is utilised to build the multi-scenario deterministic formulation of the stochastic problem, which is further changed to a conic optimisation model via the second-order conic relaxation. By using the skill of splitting buses and the augmented Lagrangian decomposition, the problem is separated into several smaller manageable sub-problems. Moreover, on the basis of the accelerated local augmented Lagrangian, a fully distributed conic optimisation algorithm is developed and the global optimal solution can be obtained iteratively in a parallel fashion. During the iterative procedure of the algorithm, only partial local message, without central coordination, need to be exchanged between the neighbouring subsystems. Each subsystem is interested in knowing only some components rather than the entire information, which improves communication efficiency. Simulations verify the effectiveness of the proposed algorithm.

The surface pollution layer of polluted insulator absorbs fog water and gets damp in salt fog. Meanwhile, the salts in the salt fog deposit on insulator surface, which increases the surface conductivity and degrades the flashover performance of insulators. At present, the effects of fog water conductivity (γ ₂₀) and equivalent salt deposit density (ESDD) are analysed separately, which does not reveal the essence of the flashover in salt fog. In this study, a plenty of experiments on porcelain, glass and composite insulators are carried out in salt fog conditions, and the 50% flashover voltage stress, leakage current and variation of ESDD during the wetting process are studied. The concept of additional salt deposit density (ASDD) is proposed to quantitatively analyse the additional ESDD caused by salt fog. The test results indicate that the ac flashover voltage stress decreases with the increase of both ESDD and fog-water conductivity. Both the ESDD and leakage current become larger in salt fog compared with those in clean fog. The ASDD can be applied to analyse the combined effect of ESDD and fog-water conductivity and be expressed as ASDD = k × γ ₂₀ × ESDD. Then the flashover voltage stress is E = A × (ESDD + ASDD)^−a . The values of k for the porcelain, glass and composite insulators are 0.179, 0.191 and 0.230, respectively. The flashover in salt fog environment is a special kind of pollution flashover in essence.

This study deals with an approach for photovoltaic (PV) panel monitoring based on extended Kalman filter (EKF). For detection of anomalous condition, I–V and P–V characteristics derived by the PV model in normal condition (named reference model) are compared with the corresponding ones extracted from the PV model in the test condition (named test model). Parameters of the reference model are obtained from the standard test condition. Generally, maximum power point (MPP) tracking algorithms deviate operating point of PV systems to find the global MPP. In the proposed approach, the measured operating points of the PV system are passed through the EKF. In fact, the EKF is an adaptive low-pass filter for estimation of the operating MPP dictated by the MPP tracker. During a predefined inspection time interval, parameters of the test model are derived from the estimated MPP. The performance of the proposed method is evaluated using some simulations and experiments in different normal and anomalous conditions. The results confirm desirable accuracy and reliability of the proposed method for detection of the PV panels’ anomalous condition.

Time–frequency-based differential scheme is proposed for microgrid protection using non-stationary signal analysis. The non-stationary signal processing algorithm Hilbert–Huang Transform (HHT) have been implemented for the protection objective and the comparative assessment with that of S-transform, differential current is carried out in order to demonstrate the reliability of the proposed protection scheme with different case studies. The series of simulation results demonstrates the efficacy of HHT, than that of S-transform in some critical cases such as high impedance fault where accurate detection is a challenge. The configuration of the microgrid test model has been developed in PSCAD with different distributed generation such as photovoltaic and wind generation system penetrated at different buses. Thus, it is found that the HHT scheme is quite reliable and efficient for fault detection objective.

A new transient stability-constrained optimal power flow (TSCOPF) model for power system optimal operations is presented in this study. The proposed model is a non-linear, non-convex, discrete, and non-differentiable optimisation problem, and very difficult to be solved by classic programming algorithms. In this study, an effective optimisation framework is developed to address the TSCOPF problem. The self-adaptive differential evolution (SaDE) algorithm is employed in the framework, which can effectively eliminate the needs for the strategy selection process and at the same time improve the robustness of the DE search process. The benchmark New England 10-generator, 39-bus system is used to verify the efficacy of this algorithm. The simulation result obtained using SaDE is compared with both conventional mathematical method and the recently published heuristic methods for OPF problems. The simulation results reveal that the SaDE optimisation technique outperforms other algorithms in both terms of robustness and solution quality.

This study presents a new parallel algorithm for power system transient stability computation based on symplectic Gauss method. The s-stage 2s-order symplectic Gauss method is used to convert the differential-algebraic system simultaneously at s time points into a set of non-linear algebraic equations, and the algebraic system is then solved by Newton method. Based on the block matrix characteristics, the solution of the linear equations involved in Newton method's process can be divided into two parts: the first part is fully parallelisable in time, and the second part is solved by preconditioned GMRES method while an efficient preconditioner has been proposed based on the V -transformation. For test, the proposed algorithm is implemented on three programming models, the first is the traditional central processing unit (CPU) computing, the second is CPU-single graphics processing unit (GPU) cooperative computing, and the last one is CPU-multiple GPUs cooperative computing. The results show that, the proposed parallel algorithm is accurate, has good convergence, and has good scalability both in the problem size and in the number of used GPU.

Uncertain reactive power optimisation incorporating wind power (RPOWP) is mainly solved by chance constrained programming (CCP) and robust programming (RP) at present. However, it is well-known that CCP is a time-consuming method due to usage of Monte Carlo simulation (MCS), and RP always gives conservative solutions with poor economy, for it conducts optimisation on the box sets without using the available distribution information. To overcome these merits, this study proposes a method called optimal scenario method (OSM), and it can deal with the uncertainties incorporated in RPOWP without using MCS, as well as utilise the distributions of wind power. It is implemented in two stages by using the interior point method (IPM) and genetic algorithm (GA). First, IPM is used to find the optimal wind power scenario by controlling continuous control variables, where the number of voltage overrun is the smallest in all scenarios and the average real power losses is also reduced. Second, GA is employed to reduce the times of constraints violation further by coordinating discrete control variables. Two test systems are analysed in case study, with results of IEEE14 system compared with CCP method, and IEEE57 system is tested to show the applicability of OSM to larger systems. It is concluded that the proposed OSM performs better than conventional method and holds ability to apply to larger grid.

This study addresses the vulnerability analysis of power systems over a time horizon. The authors introduce a model which could be used by system operators to assess where and when, over a specific time horizon, their power systems are most vulnerable to intentional attacks. This new time-phased vulnerability analysis is modelled as a bilevel programming problem in which in the upper level, an attacker determines the best attack plan, including the best locations and the best times over the time horizon, for launching attacks. In the lower level, the system operator minimises the system operation and load shedding costs. Using duality theory, the bilevel optimisation problem is converted into a mathematical programming with equilibrium constraints which is subsequently converted to a single-level mixed integer linear programming problem by means of linearisation techniques. This model is tested on modified Garver 6-bus test system, modified IEEE 24-bus reliability test system, and IEEE 300-bus test system. The results appreciate the capability of the proposed model and show that it is indispensable to consider the time in analysing the vulnerability of power systems.

In a competitive electricity market, suppliers seek the optimal bidding strategy, maximising their individual profit. Due to the uncertainties, unknown parameters and dynamics of electricity market, the optimal bidding strategies cannot be attained through straightforward optimisation methods. In this study, the supply function equilibrium model is considered together with uniform price market clearing mechanism. The interaction among suppliers is modelled as an incomplete information game problem and multi-agent reinforcement learning (MARL) is utilised to find the optimal bidding strategy of the suppliers in a non-cooperative game. The proposed framework is an extension, from single agent Markov decision process to Markov game process, which is suitable for studying multi-agent decision making problems in stochastic environments. In this study, a Markov game model of the electricity market is proposed and a new state-action and Markov model of electricity market is proposed to built up the MARL environment. In addition, a learning-based non-cooperative MARL method is utilised for learning the optimal bidding strategies of the suppliers in a day-ahead electricity market. The proposed method is successfully applied to IEEE-30-bus power system. To examine the statistical significance of the results, the T-test method is applied to compare the competitive behaviour of the players in both multi- and single-agent frameworks.

This study presents a comprehensive analytical study of a fuzzy proportional-integral-derivative (fuzzy-PID) controller with derivative filter (fuzzy-PIDF) for automatic generation control (AGC) in multi-area power system tuned by a novel hybrid local unimodal sampling-teaching learning based optimisation (LUS-TLBO) algorithm. The relevant advantage of this recommended controller is its high sensitivity to load perturbation. Initially a two area non-reheat type thermal system is considered and the gains of PIDF controller are tuned employing hybrid LUS-TLBO algorithm. The supremacy of PIDF controller is shown by comparing the results with some recently published articles. The study is further extended to design fuzzy logic based PID controller with derivative filter (fuzzy-PIDF) for AGC of the same power system employing hybrid LUS-TLBO algorithm. Supremacy of the proposed approach is shown by comparing the results with another recently published article. In addition, the work is also extended to deal with AGC issues in two area multi source hydro thermal power system using the proposed controller. Finally, it is seen that fuzzy-PIDF controller retains its supremacy over PID/PIDF/fuzzy-PID controllers. In addition to it, robustness analysis is carried out for the non-reheat two area thermal power systems by varying different parameters within the range of ±50%.

This study analyses the effect of replacing existing synchronous generators (SGs) equipped with power system stabilisers (PSS) by doubly fed induction generator (DFIG) based wind farms on the damping of power system oscillations in a multi-machine power system. A power system stabiliser was designed to enhance the capability of DFIG to damp power systems oscillations. The validity and effectiveness of the proposed controller are demonstrated on the widely used New England 10-machine 39-bus test system that combines conventional SGs and DFIG based wind farms using eigenvalue analysis and non-linear simulation. The non-linear simulation is used to demonstrate how the damping contribution of DFIG based wind farms is affected by different operating conditions within the same wind farm and stochastic wind speed behaviour. The results show that installing conventional fixed parameters PSS within reactive power control loop of DFIG rotor side converter has a positive damping contribution for a wide range of operating conditions. Furthermore, the results clearly show that DFIG based wind farms equipped with the proposed farm level PSS can damp power system oscillations more effectively than SGs PSS.

Partial discharge (PD) is the most important factor in gradual insulation deterioration of high-voltage (HV) power equipment, and then PD trend monitoring is a great issue for their condition assessment. Impulsive high-frequency PD current/voltage signals can be detected by using electrical sensors, e.g. inductive/capacitive sensors. A comprehensive feasibility study is carried out to use the power frequency current transformers (CTs) that are already installed in medium voltage and HV electrical power systems instead of high-frequency CTs. To achieve this aim, frequency response of a sample protection CT is extracted experimentally and it is fitted to appropriate transfer functions to access the related frequency characteristics. Regarding improper CT frequency response and its extreme variations in different frequencies, reversed transfer function is obtained to apply to CT secondary signals for reconstructing CT input PD pulses. Two types of artificial PD pulses are examined to validate the proposed method and the experimental results show that power frequency CTs can be used for PD detection and measurement in some frequency bands.

This study presents a novel methodology for evaluating customer and energy based reliability indices for distribution systems in the presence of distributed generations, considering the effect of omission of random tolerable interruption durations at load points. Bootstrapping technique along with Monte Carlo simulation has been employed to evaluate the impact of omission of random interruption durations on the customer and energy based indices. These indices have been evaluated with and without omission of interruption durations. Results have been obtained for a standard RBTS distribution system.

This study presents an advanced technique provided with adaptive differential relay characteristics for avoiding current transformer (CT) saturation effects. The proposed technique uses the alienation and differential protection principles to make adaptive logic; if no CT saturation is detected, the differential principle alone is capable of tripping the busbar. If CT saturation is detected, both the alienation and differential principles must pickup in order to trip. The alienation coefficient is useful in CT saturation detection, evaluation of CT saturation degree and adapting the differential relay characteristics during saturation period of CTs to avoid false operation in the event of external faults. The differential current and alienation coefficient are calculated from two terminal currents of the busbar. The proposed protective scheme has several attractive features, including the simplicity of on-line implementation, not affected by the remanent flux in the CT core, and it is independent of the CT parameters/characteristics and secondary burden. A real 19.57 kV busbar is simulated using Alternate Transients Program/Electro-Magnetic Transient Program and MATLAB packages to examine the suggested scheme under different types of faults. Under normal operating conditions and external faults, the scheme remains stable and it operates only for the case of internal faults. Moreover, it is unaffected by CT saturation.

Steady-state voltage levels will be a significant problem in the future distribution network due to a high penetration of new technologies, particularly photovoltaics. A smart transformer which incorporates a fixed tap transformer with a power electronic voltage regulator has the potential to mitigate this problem by varying the line voltage automatically in response to changes in loading. This study considers various control strategies for the voltage regulator and looks at the potential impact that a smart transformer could have on reducing system voltage violations. These impact studies are performed on a computer model of an entire utility's distribution system in New Zealand.

In this study, a fast learning method of back-propagation (BP) multilayer perceptron neural network-based control algorithm for shunt compensator in three-phase distribution systems is presented. The proposed method comprises of quadratic linear and non-linear errors to determine optimisation criterion error function to train the BP algorithm while the existing methods have used only linear quadratic error term. The newly developed optimisation criterion error function accelerates the convergence efficiency of BP algorithm for performance improvement of shunt compensator at point of common coupling under non-linear loading conditions. With the help of the proposed algorithm, the weighted amplitude of fundamental active and reactive current components of the load current are extracted from which the reference source currents are estimated. The performance analysis of the proposed algorithm has been evaluated using two case studies for zero-voltage regulation and power factor correction. The total harmonic distortions are improved in comparison with standard BP algorithm which has been validated in above-mentioned two case studies. This is the quite important advantage of the proposed control algorithm to improve the power quality over existing control algorithms for shunt compensator.

Owing to the increasing penetration of single-phase small generation units and electric vehicles connected to distribution grids, system operators are facing challenges related to local unbalanced voltage rise or drop issues, which may lead to a violation of the allowed voltage band. To address this problem, distribution transformers with on-load tapping capability are under development. This study presents model and experimental validation of a 35 kVA three-phase power distribution transformer with independent on-load tap-changer control capability on each phase. With the purpose of investigating and evaluating its effectiveness under different operative conditions, appropriate scenarios are defined and tested considering both balanced and unbalanced situations, also in case of reverse power flow. The experimental setup is built starting from an analysis of a Danish distribution network, in order to reproduce the main feature of an unbalanced grid. The experimental activities are recreated in by carrying out dynamics simulation studies, aiming at validating the implemented models of both the transformer as well as the other grid components. Phase–neutral voltages’ deviations are limited, proving the effectiveness of the phase-independent tap operations. Furthermore, minor deviations of the results from simulations and experiments confirm that all the system components have been properly modelled.

This study presents an adaptive differential evolution (DE) algorithm to allocate the thyristor-controlled series compensator (TCSC) incorporated with the reactive power management problem. In addition, a dynamic updating is applied for scaling and penalty factors to enhance the performance of the multi-objective DE algorithm. During the selection of the best candidate lines for efficient allocation of TCSC devices, three situations are considered for excluded transmission lines. These situations are the lines connected between two generating units; lines connected through transformers and the lines of low losses. The considered multi-objective function compromises between reducing power losses, improving voltage profile, reducing reactive power losses, reducing TCSC cost and reducing number of flexible alternating current transmission systems units. The optimal siting and sizing of TCSC is defined for normal and emergency operating conditions. The proposed procedure is employed for IEEE 9-bus and IEEE 30-bus test systems in addition to western delta network as a real part of the Egyptian network. Four case studies are considered for each test system to represent normal and abnormal operating conditions. Results clearly indicate the effectiveness of the adaptive DE algorithm to allocate perfectly the TCSC to enhance the system performance.

Power transformers are of vital importance for the stable operation of power system. Hence, to grasp transformers’ health condition is of imminent importance. However, the evaluation of transformers’ health condition is bound with fuzzy, uncertainty, and even conflict information. To address these problems, a novel evaluation model for transformer, by integrating the merits of fuzzy set theory, fuzzy analytical hierarchical process (AHP), and modified weighted averaging combination, is proposed in this study. The evaluation model contains four factors: dissolved gas analysis, electrical testing, oil testing, and miscellaneous factors, as well as 20 indices. The evaluation process consists of three steps. First, the fuzzy set theory is used to obtain assessment grades for each quantified indices. Second, the fuzzy AHP using fuzzy preference programming, which extends classical AHP and can better tackle the uncertainty existed in the comparison matrix given by experts, is introduced to calculate the weights of indices. Finally, the assessment is processed through the modified weighted averaging combination, which is able to handle the conflicts among evidences. The proposed method is verified by evaluating a realistic transformer, and the results of field examples indicate that the method can evaluate the transformer health condition effectively.

Due to the severe damages to transmission systems caused by ice storms, reasonable de-icing work becomes pressingly significant for power systems. This study proposes a transmission line de-icing outage optimal scheduling framework based on DC de-icing method. First, an ice thickness prediction model and a time-varying forced outage rate model are introduced to delineate the ice accretion and the reliability of lines. Then, a multi-objective de-icing outage optimal problem is formulated to minimise the ice thickness peak value of icing lines and the expected energy not supplied of the system during the decision period. Finally, non-dominated sorting genetic algorithm-II optimisation approach is used to determine the Pareto optimal solutions, and a decision making method is utilised to choose the final de-icing scheme. Simulation results on IEEE 24-bus reliability tests system show the effectiveness of the proposed de-icing strategy.

The integration of multiple renewable energy resources to meet the energy needs of the consumers in remote locations with better reliability is a major challenge due to inherent characteristics of available renewable sources namely unpredictability and variability. This requires development of effective micro-grid controllers to manage power balance between load and generation. In this study, a micro-grid controller integrating the output from multiple types of renewable energy conversion systems, namely, wind and solar along with diesel generator as well as battery storage has been developed with source and load control features using field programmable gate arrays (FPGAs). The load controller facilitates load management (switching ON/OFF non-critical loads) based on the generation availability and energy storage capacity. The source controller facilitates source management based on the load requirement and battery status. The various parameters of these different power generation sources and loads are displayed on visual screen using FPGA for online condition monitoring of the micro-grid. It also includes the communication between source and load controllers using Ethernet for exchange of monitored data for a suitable control action. This innovative work has been developed in such a manner that it will be replicable in the field to bring it on the large scale.

Power transformers are some of the most valuable and critical elements of power systems. Therefore, accurate and detailed assessment of technical and economical (techno-economical) condition of the transformers is absolutely important to ensure its reliable operation. In this study, in order to assess the overall condition of the power transformers, an overall condition index (OI) obtained from technical lifetime index (TI) and economical lifetime index (EI) will be defined. The OI index, which provides a practical tool to assess the overall condition of the asset, combines the results of operating observations, field inspections, site and laboratory testing, and analysis of investment and operating and maintenance costs into an overall index. An adaptive neuro-fuzzy inference system model is used to assess the TI, and a fuzzy logic model is used for EI evaluation. Large power transformers rated over 50 MVA, which are more critical and important in the network, are investigated. The models are developed using 170 experimental field datasets of transformer oil characteristics and dissolved gas analysis, and economical data such as operating and maintenance costs. The results prove that the models can be used to effectively assess the techno-economical lifetime of power transformers.

Conventional approaches for measurement-based load modelling uses measured voltage (V) as the input to calculate the load model output – P and Q powers. This assumes that the P and Q response is a function of V. In fact, there is an inherent interaction among the three variables (P, Q, and V) especially when motor load occupies a large proportion. With increased penetration of wind power, the fault-induced dynamic voltage response is becoming a serious concern given the low-voltage-ride-through (LVRT) requirement of wind turbines. This paper firstly shows that given different load model parameters, the V responses can vary significantly. Then, an improved method is proposed for more accurate measurement-based load modelling. The proposed method incorporates the V response into the load model output, therefore is able to accurately reflect the dynamic voltage trajectories. Given the load model parameters, the system responses of P, Q, and V are all simulated via time-domain simulations using industry-grade software, and problem is to search the load model parameters to minimise the fitting error between the simulated and measured system responses. A trajectory sensitivity index is used to identify the well-conditioned parameters, and a parallel-differential evolutionary algorithm is designed to solve the model.

Short-term voltage stability (STVS) issue poses a significant threat to receiving-end power systems with high penetration of induction motors. To improve STVS of a receiving-end system in a limited geographic area, this study proposes a local-area STVS control system (LVCS). LVCS consists of phasor measurement units (PMUs), a local-area centralised controller (LCC), generator-level actuators (GLAs) and high-speed communication networks. The PMUs or GLAs are pre-deployed according to the observability or controllability of STVS. LCC receives and processes voltage measurements from PMUs to generate supplementary excitation control signals (SECSs). The SECSs are next forwarded to and executed by GLAs. Simulation studies on a practical receiving-end system in China Southern Power Grid demonstrate that: once the target system suffers a serious fault, LVCS can ‘feel’ the voltage sag at critical buses and enforce the excitation control of generators to inject more dynamic var into the receiving-end system. As a result, the increasing var demand is met locally and STVS can be improved considerably. Time delay caused by synchrophasor transmission has also been considered in the design of LVCS to make it feasible in practice. Thus, the proposed LVCS offers a new and effective solution to the STVS problem.

Power flow (PF) problem need to be further studied when confronted with uncertainties brought in by the increasing use of renewable energy. This study proposes a new solution method based on linear approximation of the affine arithmetic (AA) based PF model and optimal solution technique incorporated with boundary load flow framework under generation and load data uncertainties. In each iteration solution step, non-linear interval PF problem is modelled by the approximation technique with AA. Boundaries of state variables are explored by solving linear programming models with constraints reformed at given operating points. After optimisation process, new operating point is obtained and updated for further iteration solution step. Application of the proposed methodology is implemented in several IEEE benchmark test systems and results are demonstrated in details. Comparisons between the previous interval method and Monte Carlo simulations verify the effectiveness and better performance of the proposed method.

Integration of distributed energy resources in power networks make them interconnected and active. Depending upon the type, short circuit capability and location of distributed energy resource in transmission and distribution systems, design of protection coordination schemes becomes very challenging. Complexity further increases in the design of protection coordination schemes, when penetration effect of these resources reaches to upstream transmission lines and coordination among the distance and over current relays requires a review. The protection coordination scheme discussed in this article monitors the state of power network continuously. Depending upon the operational topology of the network, time dial settings as well as plug settings of over current relays and zone-2 setting of distance relays are selected from pre-optimsed relay group settings. Whenever there is any change in the network fault level either due to change in line parameters or incoming of new distributed energy resource, new relay group settings are communicated to corresponding relays. The proposed protection coordination scheme is implemented in RSCAD software for modified eight bus test bus and modified IEEE14 bus system. It is observed that the proposed protection approach is highly flexible to maintain the coordination among the over current and distance relays.

Electric load forecasting is essential to economic operation and power system control in the electric power industry. Modelling and forecasts for different time horizons are of increasingly importance for different operations. Discrete cosine transform (DCT) is one Fourier-related computational technique. It is widely used in signal and image processing for its remarkable characteristics on optimal decorrelation and energy compaction. From time-series analysis perspective, this study proposes a DCT-based predictive model for forecasting hourly load movement. Based on finite hourly load observations, the proposed DCT-based predictive model combines with the least-squares approach to get the optimum DCT coefficients, which are approximated in the least-squares sense. Then the obtained least-squares-optimum DCT coefficients are employed for forecast modelling to predict the load future movement. Experimental results and analysis show workability of the proposed forecast modelling. It is indicated that the DCT-based least-squares predictive model predicts hourly load movement most fitting with about 12-term DCT coefficients.

The massive power flow transferring triggers the node overload cascade, which further activates the protection system hidden failures. In this study, we propose a cascading failure model based on complex network theory by combining the node overload failures and hidden failures of transmission lines in blackouts together. The model concerns the electrical characteristics, which has not been involved in the existed cascading failure model when modelling node loads. The cascading failure simulations on the 500 kV Center China power grid and the IEEE-300-bus test system demonstrate that the proposed cascading failure model with node load built on electrical characteristics can bring better network invulnerability than the model with that constructed on pure structure topology. Meanwhile, the proposed model can better exhibit the negative aspects of hidden failures in the blackouts. The deliberate attacks based on high-risk nodes can decrease the invulnerability of power grids more seriously compared with those based on high-degree and high-load nodes. The results provide a new way to analyse the power grid cascading failure mechanism based on the complex network theory.

This study addresses proportional–integral–derivative (PID) optimal fine tuning of load frequency controllers for multi-area interconnected power systems. For realistic study, generation rate constraints are considered to increase system non-linearity. The proposed method is applied to equal and unequal multi-area interconnected power systems. A methodology based on water cycle algorithm (WCA) is proposed. WCA is applied to generate optimal fine settings for the four parameters of the PID. A constrained optimisation problem with relevant integral of time multiplied by summation of absolute errors as an objective function is established. The time-domain dynamic performances using the generated optimal PID parameters are demonstrated under disturbed load conditions. At this moment, to show the robustness of the cropped optimised PID parameters, sensitivity analysis under uncertainty conditions is made by varying the system parameters from their nominal values. Specifications of time-domain dynamic performances are compared with other competing and Ziegler–Nichols PID tuning techniques which attest the significance of the proposed WCA-based LFC. Finally, the proposed WCA-based PID controllers are verified against random step load perturbations with different sampling times.

This study proposes a new time-domain fault location method based on the impulse response (image) of a power system. The proposed algorithm captures an electrical image of the power system in normal operation by injecting a train of impulses. Following fault detection, an updated electrical image is acquired and compared with the normal operating image. The comparison between both images, in time domain, permits the estimation of the distance to the fault. The performance of the proposed method has been evaluated in a 20 kV distribution system modelled in power systems computer-aided design/electro-magnetic transient design and control (PSCAD/EMTDC). Moreover, laboratory and field tests in a 15 kV overhead line have been carried out to verify and validate model accuracy and performance. Results show a considerable improvement in the accuracy of fault distance estimation compared with existing algorithms. A relevant advantage of the proposed method is its high immunity to ground resistivity, fault resistance and fault type and location in the distribution system.