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This paper presents a Super-Twisting Algorithm (STA) sliding mode control technique as an alternative to the conventional Proportional-Integral (PI) control system. This application is specifically in the context of a nonlinear Archimedes Wave Swing (AWS) device, which functions as a wave energy converter system (WECS) connected to the power grid. The main goal is dynamic performance enhancement of such wave energy systems under network disturbances. Two STA controllers are essential for the rectifier control system in the grid-connected system to capture the most power from waves while limiting losses in the AWS linear generator. In addition, four STA controllers are incorporated into the inverter control loop to preserve the DC link and common coupling voltages at the preset values. The Honey-Badger Algorithm (HBA) is applied for the optimization of gain parameters of the STA controllers, which are compared to the PI gains adjusted using the coot, the hybrid augmented grey wolf optimizer and cuckoo, and PSO search techniques to assess the worthiness of adopting this new control approach. The grid-connected AWS experiences a variety of faults, including symmetrical and unsymmetrical faults with successful and unsuccessful breaker reclosures. Finally, the system is experimentally validated using the OP4510 real-time simulator. The experimental results reveal that the HBA-STA controllers outperform PI controllers in omitting fluctuations in the regulated variables, making the STA a strong contender as a control method.

Hydrogen provides the greatest performance in conditions of capacity and duration when related to other energy storage techniques. Renewable energy sources including solar, geothermal, wind, wave and tidal energy, and hydropower, are used to create green hydrogen. However, biogas is converted into renewable hydrogen via chemical procedures. A comparison of several water Electrolyzer types is provided by this research. All kinds of Electrolyzers have an impact on how well a green hydrogen production system works were discussed. This review gives a broad review of environmentally friendly hydrogen generation techniques based on renewable energy sources. These sources incorporate solar energy, hydropower, wind energy, tidal and wave energy, biogas systems, geothermal energy, and hybrid systems of these sources. The method used to obtain the hydrogen and its effects on the environment is the primary distinction between green hydrogen and other colors. Climate, control, management systems, and tracking systems. The innovations and difficulties that green hydrogen systems encounter are highlighted. In the final section, the costs associated with manufacturing hydrogen are explained through an economic study of the understudied production systems LCOE and LCOH. Furthermore, the advantages and disadvantages of all electrolyzers are discussed.

Electric mobility (E-Mobility) has expedited transportation decarbonization worldwide. Lithium-ion batteries (LIBs) could help transition gasoline-powered cars to electric vehicles (EVs). However, several factors affect Li-ion battery technology in EVs’ short-term and long-term reliability. Li-ion batteries’ sensitivity and non-linearity may make traditional dependability models unreliable. This state-of-the-art article investigated power fade (PF) and capacity fade (CF) as leading reliability indicators that help analyze battery reliability under various ambient temperatures and discharge C-rates. Trends in LIBs applications for EVs and E-mobility are discussed. Furthermore, qualitative analysis and risk management were conducted to identify the reliable and unreliable zones of battery operation based on these indicators and the degradation circumstances implemented in recent publications. Besides, the influence of degrading circumstances on reliability indicators over the battery’s lifespan, such as a high C-rate at a low temperature throughout the battery's lifetime, has been presented in a comprehensive investigated case study in this work.

Introduction: At the present time, much attention has been focused on new types of solar cells, called perovskite solar cells. They are highly efficient devices with more than 25% power conversion efficiency. However, perovskite solar cell performance has not yet been fully explored. Objectives: We aimed to mathematically investigate the analytical modeling of current–voltage curves of planar heterojunction perovskite solar cells using Perovich Special Trans Function Theory (STFT). Furthermore, we proposed novel analytical closed-form solutions for short-circuit current and open-circuit voltage of these cells in terms of STFT. We evaluated the safety for laying the theoretical foundation by comparing the accuracy of the proposed expressions by the known methods. Methods: A novel hybrid metaheuristic algorithm, called particle swarm optimization (PSO) – evaporation rate water cycle algorithm (ERWCA), is proposed to determine equivalent circuit parameters of the perovskite solar cell. A novel objective function is introduced for estimating the parameters for that purpose too. Results: It was shown that STFT is very applicable and efficient for representing current–voltage expressions of perovskite solar cells. STFT provides a more accurate solution and requires fewer order members than the solutions provided by the conventional Taylor series. Based on these expressions and numerical calculations, it is verified that the characteristic values ​​of variables (short-circuit current, no-load voltage, efficiency, and fill factor) were not accurately calculated in the literature. Also, parameters of equivalent circuits of these cells were not accurately estimated. The equivalent circuit parameters were determined using the algorithm proposed in this work, which fit the verified values ​​of characteristic quantities much better than the literature. Conclusion: This work lays the foundation for developing the planar-structured perovskite solar cell models, in which the proposed estimation method and expressions are highly effective and provide excellent results.

Harmonic distortion levels in current power systems have increased due to technical advancements in industrial and renewable energy applications. So far, passive power filters have been widely employed to minimize harmonics and lessen their adverse effects. In this regard, this paper presents a novel bi-level design of damped double-tuned passive filters operating in a non-sinusoidal power system with nonlinearities at both the source and the load. A modern metaheuristic optimization technique known as wild horse optimization is applied to acquire the parameters of the used filters. Several objective functions, such as voltage total harmonic distortion, current total demand distortion, active power losses, and resonance-based metric minimization, were researched to improve the analyzed system's overall power quality performance. The mathematical derivations of the filter design expressions are given in detail. In the literature, there are several schemes for damped double-tuned filters. This paper investigates and analyses four schemes of this filter. The results are compared to those obtained from other metaheuristic optimization algorithms to ensure that the proposed algorithm produces the most effective outcomes. Statistical analysis is performed using many criteria to ensure the superiority of the proposed algorithm. Furthermore, depending on several assessment criteria, the analytical hierarchy process is employed to find the most effective candidate scheme. One of the schemes tested (scheme B) outperformed the others.

Harmonic pollution is one of the challenging problems facing power networks recently due to the widespread non-linear loads and inverter-based renewables. In this regard, this work presents the optimal design of damped and undamped passive filters using a solver called Mixed-Integer Distributed Ant Colony Optimisation (MIDACO). This solver is employed to obtain an optimal design strategy for single-tuned passive power filters by investigating three primary criteria – minimisation of active power losses of the Thevenin’s resistor, maximisation of the true power factor, and maximisation of the transmission efficiency. Several constrictions associated with the designed filters have been considered, in which the global maximum or minimum criterion was attained by retaining the quality factors of the designed filters within a particular range, damping harmonic resonance, achieving a permissible range of the power factor, limiting voltage harmonic distortion by complying with IEEE Std. 519–2014 restrictions. Besides, the performance limits of capacitors operating in distorted systems have been met while complying with IEEE Std. 18–2012. Further, the results obtained using the MIDACO solver in four different case studies are compared to those obtained using particle swarm optimisation and genetic algorithm. In addition, this work depicts the damping resistor of the inductance in the single-tuned filters. The benefits and drawbacks of damping over an undamped filter are discussed. Finally, the results validate the effectiveness of the MIDACO solver employed in this paper.

This paper presents an integrated generation and transmission expansion planning (G&TEP) model embedding with energy storage systems (ESSs) to reduce G&TEP projects’ cost, enhance power system’s reliability, decrease carbon emission, and increase the penetration of renewable energy systems. ESSs are a key component of modern power grids for their ability to solve many challenges and problems. Electrical system operators and planners often resort to ESSs, which are considered promising technology and are sometimes the only economically viable way to address deficiencies in the planning phase, specifically in the presence of renewable energy sources. However, choosing the right ESS type to solve a problem is still a challenge and essential to cost-effectively integrating ESSs into power systems. In this work, a techno-economic planning model is formulated to decide on a suitable ESS type for the optimal configuration of two power systems, taking into account the technical and economic aspects of ESSs. Three long-term and seven medium-term types of ESSs were tested for this purpose. A hybrid scheme of Runge Kutta optimizer and gradient-based optimizer is applied to solve the problem. The proposed planning model is implemented on the known Garver system and a real system in Egypt (Egyptian west delta network). The numerical results found that pumped hydroelectric storage is the most effective type in achieving N-1 reliability constraints, increasing the use of RESs, and reducing the planning cost. ESSs enhanced systems’ security and reduced the total planning cost by 0.86%–2.35% for the Garver network. The results showed that using ESSs is necessary for some power systems, like the west delta network, to avoid rolling blackouts. The investment and operating costs of ESSs, in the presence of RESs, reach more than 50 % of the total planning cost in some case studies. However, ESSs, in the absence of RESs and reliability constraints, increase the planning cost by 5%–50%. Finally, the hybrid scheme proved its superiority in solving the proposed problem.

This paper introduces fault type identification, fault section selection, and fault phase selectivity using a Karen Bell Transformation matrix in earthed distribution grids coupled with Doubly Fed Induction Generator (DFIG). Rogowski Coil’s (RC) model is estimated using a system identification toolbox to obtain the precise terminal voltage. This model is calculated and verified using experimental results for the RC’s primary input current and output voltage. Then, the estimated voltage relies on the current signals in the measuring point. The transient slope of the ground and aerial modes voltages is extracted during the fault to classify the fault type, discriminate the fault section and identify the faulted phase in every cycle. Further, earth faults are detected using ground and phase faults using aerial modes. The relative polarity of the front slopes at the terminals of each section created by the fault voltage is extracted to perform faulty section discrimination. The value of aerial modes is used to identify the defective phase selectivity. The overall protection selectivity function’s integration procedure with modified autonomous control is proposed for earthed distribution systems. The Transient Selectivity Function (TSF) was presented in unearthed and compensated grids in the literature. After estimating the RC voltage output at each agent, the discrete Fourier transform (DFT) phasor extraction is done. Different standard fault cases and system conditions are investigated to evaluate the proposed scheme’s behavior. Simulation results are designed using the ATP-EMTP program. The simulation results obtained validate the effectiveness of the scheme proposed in this work.

The broad spread of renewable energy sources (RESs) and storage systems increases modern power systems’ challenges and may conflict with system operation requirements. Determination of the maximum hosting capacity (HC) is crucial for utilities to estimate the maximum capacity of RESs and storage units that a network can accommodate efficiently. Several models were developed in the literature that lacks studying the impact of reliability requirements and the size of other network components on the HC levels. This paper proposes a framework to effectively maximize the hosting of RESs and storage systems in power systems. An AC optimal power flow is used to formulate the problem and consider the networks’ real operation. The objective function is formulated to expand transmission lines, allocate fault current limiters (FCLs), and ensure HC enhancement. The AC models are always complex and non-convex, and finding optimal solutions is critical. A hybrid artificial rabbits sine–cosine algorithm is developed to solve the problem, and its performance is compared to some well-known metaheuristics. The numerical studies on the Garver network and the IEE 24-bus system demonstrated that the size of different power technologies directly impacted the amount of RESs deployed. The penetration of RESs and storage systems was maximized by increasing the number of candidate circuits. The results revealed a 22 % increase in the size of RESs installed in the Garver network. Also, a 25.7 % increase in the size of RESs for the 24-bus system was obtained due to the increased candidate transmission lines. Further, an increase of 49 % was noticed in the size of storage systems built for the 24-bus system. The use of FCLs was necessary to maintain the short-circuit current below the required values. For both systems, the size of FCLs required was increased by 24.3 % and 28 %, respectively. The results also showed that the hybrid artificial rabbits sine–cosine optimizer was more efficient than other algorithms in solving the investigated problem.

Abstract In this paper, the amount of microgrid frequency deviation in the dynamic state can be reduced by improving the frequency controller and implementing a new method. The proposed controller is designed for a microgrid including renewable resources, and the proposed control strategy is such that the controller coefficients are adjusted and optimised at all times by the model predictive control (MPC). The weight parameters of the MPC controller have been optimised by the particle swarm optimisation (PSO) algorithm. The proposed controller is located in the secondary frequency control loop, and by applying a control signal to the sources, the frequency perturbations following the power changes in the microgrid are reduced. The simulation results show that the proposed controller performs better than the Ziegler–Nichols PI controller (PI‐ZN) method, PI‐based controllers that rely on fuzzy logic (PI‐Fuzzy), the fractional‐order proportional‐integral‐derivative (FOPID) controller that is based on chaos particle swarm optimisation (FOPID‐CPSO) algorithm and the PID controllers based on CPSO algorithm (PID‐CPSO). It has been able to effectively reduce the frequency fluctuations in terms of amplitude and number of oscillations is also more resistant to the uncertainty of microgrid parameters and shows better performance when changing parameters than other methods.

This article comprehensively reviews recent Electric Vehicle (EV) charging infrastructure, technology, and issues related to charging station identification. A literature study on the above key areas shows an increasing consideration of EVs over the past decade. Further, the recommendations for user-friendly selection of the Charging Station (CS) are discussed. The transport sector is one of the leading contributors to global warming. It has a high dependence on fossil fuels such as petrol and diesel, which are expected to be scarce shortly. Therefore, EVs have attracted considerable attention as they can minimize fuel consumption and emissions. For the last few years, studies related to Plug-in-Hybrid Vehicles (PHEVs)/EVs have drawn the researcher’s attention. Moreover, several technical articles associated with charging technologies with available infrastructures are discussed, and we highlighted their pros and cons, particularly in charging infrastructure, and the charging power and power transfer between EV and grid are broadly discussed. From a customer perspective, the selection of charging stations and associated problems are presented. Finally, the suggestions for the user-friendly selection of charging stations are discussed.

There is a common misconception that at least 95% of Egypt’s potential hydropower has already been used, which does not reflect reality. Currently, only five hydropower plants operate along the river Nile, from Aswan high dam to Assiut barrage. The total installed capacity is around 2840 MW. However, Egypt has many main canals and Rayahat and an irrigation network system, including barrages, head regulators, and navigation locks, which enable 120 MW of clean electricity (equivalent to 4 times of Assiut power station generation) if used to generate electricity. This paper aims to assess mini and micro hydropower’s potential in Egypt for the main grid areas. Eight sites have been selected and ranked as an application sample in this work based on their hydraulic data availability. The rank of the most suitable energy generation sites is determined with spatial maps’ aid based on the flow duration curves, capacity factor, and multi-criteria analysis. The decision matrix developed to rank the selected locations, and the turbine efficiency curve is proposed in terms of the available flow to decide the suitable turbines. Also, the spatial maps give a clear vision to decision-makers of the possibility of exploiting different resources and the priority of implementation. The results obtained show a promising prospect of mini and micro hydropower in Egypt. The annual energy from the eight studied sites is estimated by 200 GWh according to the daily hydraulic data of the year 2017. Damietta barrage takes priority as the weight value of criteria is the highest value by 2.85, and its annual energy is estimated by 78.5 GWh. The eight sites are more suitable for peak load plants, but Damietta and Zefta are appropriate by less priority for baseload plants.

Today’s power systems are characterized by a considerable penetration of electricity production from renewable energy sources. However, renewable energy sources are characterized by intermittent non-stationary output, which leads to more complicated regulation of voltage, power flows, and frequency in power systems. Energy storage systems (ESSs) have been identified as one of the more efficient solutions to overcome some of these problems. In the literature, ESSs have been predominantly viewed as producers (in discharging) or consumers (in charging) of active power. Using bi-directional converters (BDCs), ESSs can regulate the connection point’s reactive power. Therefore, this paper aims to consider the effects of the coordination of BDCs and ESSs on modern power systems. The CONOPT solver embedded in the general algebraic modeling system (GAMS) was used to analyze this problem and find the optimal location of ESSs in the system. All calculations were performed on both IEEE 39- and IEEE 30-test networks, while the objective function was minimizing the power loss. The presented results show that losses in the power system can be reduced by correctly allocating ESSs. Furthermore, the simultaneous allocation of ESSs and BDCs efficiently reduce power system losses using the CONOPT solver.

This paper presents an economical-technical-environmental dispatch (ETED) model for an adapted IEEE 30-bus system incorporated with thermal and a mix of renewable energy sources (RESs). Total fuel costs, active power losses, and emissions level minimization is the main aim. Different equality and inequality limits involving prohibited operating zones (POZs) are considered as system restrictions. Metaheuristic optimization techniques – moth-flame optimization, salp swarm algorithm, improved grey wolf optimizer, and multi-verse optimizer – are employed to find the best solution for the generation cost, losses, and emissions. Various scenarios are examined to approve the ability of the formulated optimization model in solving the problem. A weighted sum strategy using the analytic hierarchy process (AHP) is used to convert the multi-objective problem into a normalized single-objective one. The AHP-ETED model presented in this work can significantly minimize fuel costs to 902.4951 $/h, lower emission levels as 0.09785 t/h, and achieve a lower power loss of 2.4110 MW. The results attained validate that the IGWO outperforms the other considered algorithms in finding the best solution to the ETED problem.

Hosting capacity (HC) is the mathematical interpretation for the maximum aggregated distributed generations (DGs) penetration among the distribution networks. DGs integration has been adopted as a cleaner energy resource, but it has major operational issues like overvoltage, harmonics, and others. In this work, a novel mathematical optimization algorithm is adopted for HC maximization via sequential network reconfiguration followed by soft open points (SOPs) placement. Besides, a novel SOPs allocation index is proposed to reduce the computational burden taken by the optimization techniques while controlling the discrete allocation variables. Thus, to ensure maximum penetration of DG units and optimum operation scheme, HC maximization is formulated as multi-objective optimization approach, while considering system performance indices as a portion of the objective function. The proposed optimization algorithm succeeded in maximizing the HC of the IEEE 33- node distribution network, the IEEE 69- node network, the 59-node Egyptian distribution network and the 135-node Brazilian distribution network efficiently while improving system performance indices. Further analysis is conducted on the studied distribution systems to assess the effect of load growth on system’s HC after allocating both SOPs and DGs.

The problems of increasing electricity consumption and atmospheric pollutants emissions are targeted as critical challenges for power transfer in modern distribution networks. In order to tackle this issue, many researchers have proposed the incorporation of Distributed Generator (DG) units, as well as different types of reactive power compensation devices, which will contribute to the increase of networks efficiency through loss minimization, voltage profile improvement, or even increasing transmission line’s capacity. This paper addresses the optimal allocation/coordination of DG, Distributed Static VAR Compensator (D-SVC), and Distributed Thyristor-Controlled Series Compensator (D-TCSC) to reduce total power loss in the distribution network. The allocation problem is formulated as a mixed-integer nonlinear programming (MINLP) and is solved using a basic open-source MINLP (BONMIN) solver embedded in GAMS. The proposed method was tested in IEEE 16-bus and 33-bus distribution test systems, where two cases were considered. Firstly, BONMIN solver is used for allocation of D-SVC, and D-TCSC, respectively, where the results showed that incorporation of these devices leads to reduction of the active power losses, while the minimal losses and highest efficiency increase for both test networks occurred in the case where 3 D-TCSCs allocated. Secondly, a coordinated allocation of DGs and D-SVCs, as well as DGs and D-TCSCs, is presented, where it was shown that coordination of these devices leads to even greater loss reduction, i.e. increased efficiency. Also, it was concluded that DG and D-TCSC coordination is better suited for loss reduction in the 16-bus system, while DG and D-SVC coordination leads to greater loss reduction for the 33-bus system. Furthermore, the comparison between BONMIN and metaheuristic methods was performed for DG allocation and DG and D-TCSC coordination in IEEE 33-bus system, where it was concluded that BONMIN performs better in terms of minimal power loss, compared to the results which were presented in the available literature. Finally, the BONMIN solver’s performance is evaluated using three parameters: number of nodes, number of iterations, and total execution time, where the numerical analysis showed that BONMIN is efficient in solving the addressed problems.

Mathematical design of a new fourth-order harmonic passive filter is presented and its optimal strategy is proposed with regards to various design scenarios. The considered objective function is total demand distortion minimization of the supply current. The crow spiral-based search algorithm (CSSA) is applied to solve the design problem formulated. This CSSA relies on a spiral search mechanism that improves the convergence and balances the exploration and exploitation abilities of the conventional crow search algorithm. Various power quality indices are taken into consideration like the individual and total harmonic voltage distortion values, individual and total current harmonic distortion values, active power loss, actual and displacement power factor percentages, and resonance damping capabilities. These indices were handled as non-linear constraints in the design. Additionally, a comparative investigation of the different damped filters is presented to assess the planned filter performance. The results obtained confirm the success of the filter design proposed in this paper.

This paper presents a hybrid metaheuristic method for optimal tuning of four different types of proportional-integral-derivative (PID) controller for an automatic voltage regulator (AVR) system. The method is based on the manta ray foraging optimization algorithm which is merged with the simulated annealing algorithm. Additionally, novel objective functions for the optimization of the controller’s parameters are proposed. The performance of the obtained ideal PID, real PID, fractional-order PID, and PID with second-order derivative controllers is verified by carrying out a comparison with the controllers tuned by different algorithms presented in the literature. Results of the simulations validate that each type of controller tuned with the proposed SA–MRFO algorithm outperforms the controllers tuned by other algorithms. Further, a comparative analysis is carried out to determine the most suitable controller for application in AVR systems. The main advantage of the proposed algorithm is the significant increase in the convergence speed.

Usually, electric vehicle systems are based on various modules that should ensure the high power and stability of the vehicle on the track. The majority of these components are linked to the charging mechanism. In this regard, dynamic wireless power transfer is a practical method to solve electric vehicle range anxiety and reduce the cost of onboard batteries. Wireless recharging has long been common with pure electric vehicles and is designed to allow charging even when the vehicle is in motion. However, it is difficult to analyze this method since its operating philosophy is complex, particularly with the existence of several variables and parameters. Also, the state of the vehicle, whether it is in motion or not, defines several parameters such as the vehicle speed as well as the sizes and dimensions of the coil receivers. This paper presents a novel method to improve the performance of the dynamic wireless recharge system. In the proposed system, receiver coils have been added to maximize charging power by offering a dynamic mathematical model that can describe and measure source-to-vehicle power transmission even though it is in motion. In the proposed mathematical model, all physical parameters describing the model were presented and discussed. The results showed the effectiveness of the proposed model. Also, the experimental tests confirmed the validity of the simulation results obtained by providing two coil receivers under the vehicle.

Nowadays, the continuous increase of power demand leads to various challenges for distribution system operators (DSOs) such as power quality, system stability and reliability. Microgrids (MGs) and hybrid power generation systems (HPGSs) can play a significant role in solving these issues while improving the performance of electrical power systems. In this paper, an optimal multi-criteria design of a grid-connected HPGS is introduced, taking into consideration involvement of a natural gas distribution network (NGDN) in the proposed configuration, where the NGDN supplies natural gas to a gas turbine. The HPGS system consists of wind turbines (WT), photovoltaic (PV) arrays, battery banks (BBs), gas turbines (GTs), in addition to a utility grid (UG). Two different meta-heuristic optimization algorithms, namely whale, and sine cosine, are employed to find the optimal design of the system for minimizing the total annual cost and system emissions. A detailed comparative study of the results with results of the cuckoo search and firefly optimization algorithms is presented to show the robustness of the used techniques. Keywords: Distributed generation, Power generation systems, Natural gas, Optimization algorithms

There has been an increase in the potential use of wireless devices in healthcare domain for a variety of reasons. The most commonly used device is the cellular phone, which emits strong electromagnetic energy affecting thereby the functionality of the vital medical equipment such as ventilators, ECG monitors, cardiac monitors, and defibrillators. This prompted the healthcare concerns to restrict the use of these phones in the proximity of critical and non-critical care medical equipment. Due to the developments made in the design of medical equipment to comply with the EMC standards, the restriction had been slowly laid off. Still, the researchers are concerned about the electromagnetic interference with medical devices by cellular phones in the healthcare domain and recommend for conducting continuous research to study their interaction with medical equipment. This paper overviews the certain investigations carried out in the recent years to study the electromagnetic interference between medical devices and 2G/3G/4G LTE cellular phones. During the initial development of cellular phones, the 2G cellular phones had caused more interference that affects the function and operation of some medical devices. The possibility of interference from 3G cellular phones with medical devices was considerably lower than the 2G phones, but still exists. Furthermore, almost all of the 4G phones have little to no interference with the medical devices. Currently, with the development of the medical devices industry, the current medical devices are designed to operate safely under any conditions of usage. Finally, a careful analysis would require statistics on the frequency of adverse events across the healthcare system, which apparently do not exist.

Voltage sags can be symmetrical or unsymmetrical depending on the causes of the sag. At the present time, one of the most common procedures for mitigating voltage sags is by the use of dynamic voltage restorers (DVRs). By definition, a DVR is a controlled voltage source inserted between the network and a sensitive load through a booster transformer injecting voltage into the network in order to correct any disturbance affecting a sensitive load voltage. In this paper, modelling of DVR for voltage correction using MatLab software is presented. The performance of the device under different voltage sag types is described, where the voltage sag types are introduced using the different types of short-circuit faults included in the environment of the MatLab/Simulink package. The robustness of the proposed device is evaluated using the common voltage sag indices, while taking into account voltage and current unbalance percentages, where maintaining the total harmonic distortion percentage of the load voltage within a specified range is desired. Finally, several simulation results are shown in order to highlight that the DVR is capable of effective correction of the voltage sag while minimizing the grid voltage unbalance and distortion, regardless of the fault type.

This paper presents a mathematical linear expansion model for the probabilistic Multistage Phasor Measurement Unit (PMU) Placement (MPP) in which zero-injection buses (ZIBs), as well as communication channel limitations, are taken into consideration. From the linearization perspective, presenting a model formulizing the probabilistic concept of observability while modelling the ZIB is of great significance, and has been done in this paper for the first time. More importantly, the proposed probabilistic MPP utilizes a technique disregarding the prevalent subsidiary optimizations for each planning stage. Although this technique, in turn, increases the problem complexity with manifold variables, it guarantees the global optimal solution in a wider and thorough search space; while in the prevalent methods, some parts of the search space might be missed. Furthermore, the proposed model indicates more realistic aspects of the MPP where system operators are allowed to follow their intention about the importance of buses such as strategic ones based on monitoring the priority principles. In addition, the model is capable of considering the network topology changes due to long-term expansions over the planning horizon. Finally, in order to demonstrate the effectiveness of the proposed formulation, the model is conducted on the IEEE 57-bus standard test system and the large scale 2383-bus Polish power system.