Electrical Circuit Research Articles

Integration of photovoltaic systems in Algeria's building electrical network: technical and financial analysis

Integration of photovoltaic systems in Algeria's building electrical network: technical and financial analysis

Fuzzy-fractional modeling and simulation of electric circuits using extended He-Laplace-Carson algorithm

In literature, most of the electric circuits are found to be at integer order, which are unable to capture the involved uncertainties and memory effects. To understand these effects, the current study is focused on modeling and analysis of fuzzy-fractional L˜C˜ circuit, R˜C˜ circuit, R˜L˜ circuit, and R˜L˜C˜ circuit. Triangular fuzzy numbers (TFNs) are utilized to introduce uncertainties in circuits. The memory effect is considered through fractional derivative in Caputo sense. A hybrid homotopy perturbation method (HPM) is established for solution purpose, in which standard HPM is combined with Laplace-Carson transformation in fuzzy-Caputo sense. This leads to an excellent and well-organized approach to calculate numerical solutions in the aspect of fuzzy logic and fractional calculus. The results obtained through proposed approach are validated by comparing them with already existing results in literature. Residual errors are also calculated across the domain of r at fractional order to determine the convergence and stability of electric circuit models. To study the dynamics of inductor, resistor, and capacitor on current along with fractional and fuzzy parameters involved in the electric circuits, contour and three-dimensional plots are constructed. Several plots specifying the fuzzy membership function of models across various parameter values are also demonstrated. The results achieved through this study indicate that He-Laplace-Carson method can assist engineers and researchers when dealing with electric circuits characterized by fuzzy and fractional dynamics.

Fractional-Order Equivalent-Circuit Model Identification of Commercial Lithium-Ion Batteries

Abstract The precise identification of electrical model parameters of Li-ion batteries is essential for efficient usage and better prediction of the battery performance. In this work, the model identification performance of two metaheuristic optimization algorithms is compared. The algorithms in comparison are the Marine Predator Algorithm (MPA) and the Partial Reinforcement Optimizer (PRO) to find the optimal. Three fractional-order (FO) electrical equivalent circuit models (ECMs) of Li-ion batteries with different levels of complexity are used to fit the electrochemical impedance spectroscopy (EIS) data operating under different states of charge (SOC) and different operating temperatures. It is found that there is a tradeoff between ECM complexity, identification accuracy, and precision.

Design of Radial Distribution System to Study Load-Flow and Short Circuit Analysis Using ETAP Software

This work's analysis provides information on fault analysis and load flow studies, which help to understand how radial distribution networks operate both in normal and emergency circumstances. The research explores optimization methods, describing capacitor placement, transformer size, and feeder reconfiguration in order to lower losses and increase system efficacy. Moreover, the work looks at reliability-focused maintenance techniques, stressing the need of predictive maintenance and condition monitoring in raising the dependability of radial distribution networks. Modern electrical power networks depend heavily on their radial distribution system, which effectively and dependable distributes electricity to customers. Many radial distribution system-related topics are covered in detail on this website, including analytical methods, optimization processes, and dependability enhancement strategies. Power flow, voltage control, and losses in radial networks are investigated in this paper under a range of operational situations. The last and crucial stage of a power system, the electrical distribution system makes sure that customers have a steady supply of electricity. Regretfully, because it is often neglected and exposed to environmental risks, our distribution network has a number of problems. Our distribution feeder is rigorously analyzed for load flow and short-circuits in order to overcome these challenges and find and fix problems. The main topics of this study are the load flow and short-circuit analysis of a radial distribution feeder, which is mostly constructed with (ETAP). The final and crucial part of a power system, the electrical distribution system ensures that consumers receive an uninterrupted and steady supply of electricity. Our distribution feeder undergoes a rigorous and cautious process to address these issues front on because of the uncontrollable nature and susceptibility of our network to environmental hazards. This paper delves deeply into the issues of short-circuiting and load flow in radial distribution feeders. Both symmetrical and asymmetrical faults are thoroughly investigated by mathematical computations and ETAP simulations; the results of the software simulations are contrasted with those of the mathematical analysis. These discoveries will definitely influence the development and management of our system and point us in the direction of workable and practical solutions.

Hybrid optimization schemes for solving the piezoresistive inversion problem in self-sensing materials

Abstract Materials with electrically conductive nanofillers have the ability to 'sense' changes to their mechanical state. When these materials are subjected to deformation, the electrical networks formed by the nanofillers are disturbed causing a measurable change in the electrical conductivity of the material. This self-sensing property, known as piezoresistivity, has been leveraged in numerous engineering venues. Although this property has been thoroughly explored, prevailing self-sensing techniques are limited in that they provide little-to-no information about the underlying mechanical state of the material, such as the displacement and strain. This information must be indirectly obtained from the conductivity change. This limitation exists because obtaining mechanics from conductivity is an under-determined inverse problem with many possible mathematically feasible solutions. Previous work in this area used metaheuristic algorithms integrated with mechanics-based conditions to solve the piezoresistive inversion problem. Although these approaches were successful, they were computationally inefficient due to the stochastic search process and the need to perform multiple searches to find a converged solution. To overcome this limitation, we herein propose a hybrid optimization scheme for solving the piezoresistive inversion problem. This scheme is implemented in two steps. In the first step, a metaheuristic algorithm performs a single search for a suitable solution to the inverse problem. In the second step, a gradient descent algorithm searches for the final solution using the solution from the previous step as the starting point. We explore different norms for the fitness function of the metaheuristic search and demonstrate using experimental results that the proposed hybrid optimization scheme can accurately and efficiently solve the piezoresistive inversion problem. This exploration significantly advances the state of the art by enabling computationally efficient and highly accurate predictions of full-field mechanical condition in self-sensing materials for the first time, thereby paving the way for greater use of these principles in practice.

Temperature Fluctuations in Power conductors: Analysis and Overcurrent Relay Adaptation Strategies for Mitigation

In electrical networks, the efficient flow of energy faces constraints primarily associated with the conductor’s temperature. By assessing transmission infrastructure, identifying critical geographical and climatic zones, one can compute the line’s temperature. Focusing on the importance of maintaining optimal conductor temperature for efficient power transmission, this paper evaluates the critical role of conductor temperature in overhead transmission lines and explores its dynamic variations influenced by various ambient conditions. Emphasizing the significance of maintaining optimal conductor temperature, the study delves into mitigation strategies and adaptive protection mechanism, with a focus on overcurrent relays, with specific emphasis on the efficacy of current-time graphs. By addressing these factors, the research aims to enhance the reliability and efficiency of power transmission systems, ensuring sustained performance under diverse environmental scenarios. Overall, the paper contributes valuable insights to optimize the flow of energy in overhead transmission lines, thereby enhance the robustness also, improving the resilience and functionality of electrical networks.

Electrorheological and magnetorheological properties of liquid composites based on polypyrrole nanotubes/magnetite nanoparticles

This research presents an in-depth exploration of the electrical and magnetic properties of a polypyrrole nanotubes/magnetite nanoparticles (PPyM) material embedded in a silicone oil matrix. A key finding of our study is the dual nature of the composite, i.e. it exhibits a behaviour akin to both electro- and magnetorheological suspensions. This unique duality is evident in its response to varying electric and magnetic field intensities. Our study focuses on examining the electrical properties of the composite, including its dielectric permittivity and dielectric loss factor. Additionally, we conduct an extensive analysis of its rheological behavior, with a particular emphasis on how its viscosity changes in response to electromagnetic stimuli. This property notably underscores the material’s dual-responsive nature. Employing a custom experimental design, we integrate the composite into a passive electrical circuit element subjected to alternating electric fields. This methodological approach allows us to precisely measure the material’s response in terms of resistance, capacitance, and charge under different field conditions. Our findings reveal substantial changes in the material’s electrical conductivity and rheological characteristics, which are significantly influenced by the intensity of the applied fields. These results enhance the understanding of electro-magnetorheological properties of PPyM-based magnetic composites, and also highlight their potential in applications involving smart materials. The distinct electrical, magnetic and rheological modulation capabilities demonstrated by this composite render it as promising candidate for advanced applications. These include sensory technology, actuation systems, and energy storage solutions.

EDUPERES and GAMERES: A smart interactive education platform and digital gamification for basic circuit analysis

AbstractThis paper introduces Education Platform for Equivalent Resistance (EDUPERES) and Gamification of Equivalent Resistance (GAMERES), two different parts of a new computer aided education platform with interactive and imaginative design and game elements, which have been created during 4 years. In Vocational School of Transportation of Eskişehir Technical University, electrical circuit analysis is a compact course which exhaustively yet quickly covers all the DC and AC circuit concepts. During the course, it is observed that some students have difficulties in some basic capabilities such as calculation of equivalent resistance of either a standard or a compact circuit, dividing currents, and so on. More sadly, this inability spreads to the rest of the semester. This study aims to overcome this issue through a smart interactive education platform and gamification. The first part, that is, EDUPERES visualizes and animates the solutions of electrical circuits. To make the students exercise circuit questions, it provides an interface which simulates the comfort of using paper and pencil. This platform is powered by a smart algorithm to watch almost all of the actions of the students and to give prompt warnings. It allows students to transform the shapes of compact circuits during circuit reduction. The second part, that is, GAMERES imaginatively converts the circuit questions into action, competition, shooter, puzzle, and maze games. Via box plots and Mann–Whitney–Wilcoxon nonparametric tests, it is shown that EDUPERES and GAMERES can significantly increase students' learning. The success of EDUPERES and GAMERES is discussed with regard to previous studies and gamers' motivations.

A logic device based on memristor-diode crossbar and CMOS periphery as spike router for hardware neural network

A programmable logic device based on a memristor-diode crossbar and CMOS logic has been developed. The crossbar implements NAND logic gates using memristor ratioed logic and CMOS inverters. The digitally controlled peripheral circuit provides digital signals transmission and allows modification and evaluation memristor states in the crossbar. The proposed logic device circuit requires fewer transistors than known analogues and less area on the chip.The maximum size of the crossbar in a logic device is estimated by numerical simulation at the level of electrical circuits. The limited size is caused by the degradation of the logic levels voltages in the memristor-diode crossbar. The operability of peripheral circuits as part of a complete electrical circuit of a logic device is demonstrated during the simulation of the execution of logical operations, the processes of modification and evaluation states of individual memristors.

A multi-objective energy scheduling of the reconfigurable off-grid microgrid with electric vehicles using demand response program

Microgrids are essential in ensuring responsible energy consumption and production patterns to support and advance the United Nations’ sustainable development goals. However, due to the limited supply in the off-grid microgrids, an increase in the integration of electric vehicles (EVs) into electrical networks for their charging operation is expected to create a void between the energy supply and demand. Demand response (DR) programs provide a better solution to the energy management problem of microgrids. However, the difference in the objectives of the stakeholders of the off-grid microgrid can create an issue in providing optimal solutions to its energy scheduling problem. This paper focuses on the multi-objective energy scheduling strategy of the off-grid microgrid to manage its limited energy supply optimally using an incentive-based DR program. A fast heuristic approach is also presented in this work to reconfigure off-grid microgrid optimally during its hourly operations. Furthermore, Hong’s (2m+1) point estimation method is used in this work to consider the uncertainties in the EVs and other DR participants. The proposed work is analyzed on the 33-bus and 69-bus off-grid microgrid consisting of droop-controlled distributed generations, EV charging stations, and consumers with curtailable loads. For the day-ahead operation of the off-grid microgrids, the analysis shows that the proposed work reduces the operational cost of the two off-grid microgrids by 2.3% and 4.56%, respectively.

A Review on the Recent Advances in Battery Development and Energy Storage Technologies

Energy storage is a more sustainable choice to meet net-zero carbon foot print and decarbonization of the environment in the pursuit of an energy independent future, green energy transition, and uptake. The journey to reduced greenhouse gas emissions, increased grid stability and reliability, and improved green energy access and security are the result of innovation in energy storage systems. Renewable energy sources are fundamentally intermittent, which means they rely on the availability of natural resources like the sun and wind rather than continuously producing energy. Due to its ability to address the inherent intermittency of renewable energy sources, manage peak demand, enhance grid stability and reliability, and make it possible to integrate small-scale renewable energy systems into the grid, energy storage is essential for the continued development of renewable energy sources and the decentralization of energy generation. Accordingly, the development of an effective energy storage system has been prompted by the demand for unlimited supply of energy, primarily through harnessing of solar, chemical, and mechanical energy. Nonetheless, in order to achieve green energy transition and mitigate climate risks resulting from the use of fossil-based fuels, robust energy storage systems are necessary. Herein, the need for better, more effective energy storage devices such as batteries, supercapacitors, and bio-batteries is critically reviewed. Due to their low maintenance needs, supercapacitors are the devices of choice for energy storage in renewable energy producing facilities, most notably in harnessing wind energy. Moreover, supercapacitors possess robust charging and discharging cycles, high power density, low maintenance requirements, extended lifespan, and are environmentally friendly. On the other hand, combining aluminum with nonaqueous charge storage materials such as conductive polymers to make use of each material’s unique capabilities could be crucial for continued development of robust storage batteries. In general, energy density is a key component in battery development, and scientists are constantly developing new methods and technologies to make existing batteries more energy proficient and safe. This will make it possible to design energy storage devices that are more powerful and lighter for a range of applications. When there is an imbalance between supply and demand, energy storage systems (ESS) offer a way of increasing the effectiveness of electrical systems. They also play a central role in enhancing the reliability and excellence of electrical networks that can also be deployed in off-grid localities.

Identification of Prospective Physics Teacher’s Problem Solving Skills: A Study on Simple Electrical Circuits Topic

Problem-solving is one of the essential and crucial skills for physical learning. This study describes the problem-solving skills of college students taking physics education programs and their incorrect answers on simple electrical circuits topic. We used four essay questions representing the series, parallel, combined series-parallel, and double-loop electrical circuits concepts to measure their problem-solving skills. Meanwhile, for describing their problem-solving skills, we used five categories of problem-solving processes, consisting of useful description (UD), physics approach (PA), specific application of physics (SAP), mathematical procedures (MP), and logical progression (LP). Further, to identify their mistakes, we examined the general mistakes in each problem-solving process. Our analysis results suggested that the college students taking the physics education program have relatively high problem-solving skills in the UD and PA categories. Still, they have low skills in SAP and MP categories, with poor ability in the LP category. Their mistakes were mostly observed in drawing complete electrical circuits and the circuits with missing and changing components (UD category), the correlation between each physic concept, law, and principle with the simple electrical circuits topic (PA category), confusion and inconsistency to correctly determine the + or – symbols for every source of voltage and difficulty in using the Kirchoff’s second law following the loop direction. Besides, the participants also frequently used incorrect V, and I value on the problem being reviewed (SAP category), did not re-evaluate the order and completeness of their answer, as well as the logical reasoning for the obtained V and I from their problem-solving process based on the scientific and physic concepts and characteristics (LP category).

Influence of the magnetic flux on the dynamics of a self-sustaining System: Analytical, numerical and analogical investigations

Abstract This paper investigates the nonlinear dynamics of a ferroelectric enzyme-substrate
reaction modeled by \textcolor{red}{the} bi-rhythmic \emph{van der Pol} oscillator coupled to \textcolor{red}{the} magnetic
flux. We derive the equilibrium points and study their stability.
We analyze some bifurcation structures and the variation of the Lyapunov exponents.
The phenomena of symmetric attractors and the
 anti-monotonicity are observed. \textcolor{red}{By} increasing the magnetic flux,
 \textcolor{red}{we find that the equilibrium points are stable},
 tends to control chaotic regimes, and affects regular and quasi-regular ones.
 As the magnetic flux increases, the amplitude of the oscillations around the equilibrium
 points decreases and the \textcolor{red}{amplitude of the}
 limit cycles at the Hopf bifurcation \textcolor{red}{tends} to disappear.
 Further \textcolor{red}{increasing the magnetic flux gives} rise to chaotic dynamics.
 The electrical circuit and analogical simulations are \textcolor{red}{derived} using the PSpice software.
\textcolor{red}{The agreement between analogical and numerical results is acceptable}.

Development of an electric drive for personal light electric vehicles

Problem. The article addresses the challenge of enhancing inclusive mobility and environmental cleanliness by developing a traction electric drive for personal light electric vehicles. A study was conducted on modern electric drive systems for personal light electric vehicles. Goal. The aim is to boost inclusive mobility and environmental cleanliness through the development of a traction electric drive for a personal light electric vehicle, specifically based on a tricycle. Methodology. The methodology involves scientific analysis and synthesis of traction electric drives for electric vehicles. An assessment of the nominal capacity of the battery module from the Nissan Leaf electric car was conducted using both partial discharge procedures and the Leaf Spy Pro program. Results. Based on an analysis of existing electric drive systems, a traction electric drive for a tricycle was developed. A functional diagram of the electric bicycle drive was generated. A control system for a sensorless brushless motor was developed, determining rotor position by measuring EMF in the free phase. This led to the creation of a stable voltage electrical circuit with a virtual midpoint. The tricycle's electric drive utilizes two 10-inch motor wheels on the rear wheels, enabling high speed and efficiency. Controllers specifically designed for electric wheel motors with a power of 350 W were selected to control the traction electric drive. Modules from the 2015 Nissan Leaf electric car's battery, which had depleted 20% of their capacity, were chosen to power the electric drive. The battery health status is 77.95%. A model of the battery's electrical equivalent circuit was constructed, and partial discharge graphs of the Nissan Leaf battery module were analyzed. Originality. The results provide a comprehensive insight into the development of a traction electric drive for personal light electric vehicles, using a tricycle as an example. Practical value. The research led to the development of an electric drive for a three-wheeled vehicle, with two motor wheels of 350 W nominal power each. The power supply voltage ranges from 36 V to 48 V, powered by six battery modules from the Nissan Leaf electric car, totaling 48 V. The energy capacity of one battery module is 0.3898 kWh, resulting in a total energy capacity of 2.3388 kWh for the vehicle's battery. However, the realizable capacity does not exceed 1.871 kWh, providing a travel distance of approximately 75 km on one battery charge. These findings demonstrate the feasibility of reusing batteries from electric cars with diminished capacity to power light electric vehicles. The results are relevant for scientific and technical professionals involved in electric vehicle development.

A pareto strategy based on multi-objective optimal integration of distributed generation and compensation devices regarding weather and load fluctuations

In this study, we present a comprehensive optimization framework employing the Multi-Objective Multi-Verse Optimization (MOMVO) algorithm for the optimal integration of Distributed Generations (DGs) and Capacitor Banks (CBs) into electrical distribution networks. Designed with the dual objectives of minimizing energy losses and voltage deviations, this framework significantly enhances the operational efficiency and reliability of the network. Rigorous simulations on the standard IEEE 33-bus and IEEE 69-bus test systems underscore the effectiveness of the MOMVO algorithm, demonstrating up to a 47% reduction in energy losses and up to a 55% improvement in voltage stability. Comparative analysis highlights MOMVO's superiority in terms of convergence speed and solution quality over leading algorithms such as the Multi-Objective Jellyfish Search (MOJS), Multi-Objective Flower Pollination Algorithm (MOFPA), and Multi-Objective Lichtenberg Algorithm (MOLA). The efficacy of the study is particularly evident in the identification of the best compromise solutions using MOMVO. For the IEEE 33 network, the application of MOMVO led to a significant 47.58% reduction in daily energy loss and enhanced voltage profile stability from 0.89 to 0.94 pu. Additionally, it realized a 36.97% decrease in the annual cost of energy losses, highlighting substantial economic benefits. For the larger IEEE 69 network, MOMVO achieved a remarkable 50.15% reduction in energy loss and improved voltage profiles from 0.89 to 0.93 pu, accompanied by a 47.59% reduction in the annual cost of energy losses. These results not only confirm the robustness of the MOMVO algorithm in optimizing technical and economic efficiencies but also underline the potential of advanced optimization techniques in facilitating the sustainable integration of renewable energy resources into existing power infrastructures. This research significantly contributes to the field of electrical distribution network optimization, paving the way for future advancements in renewable energy integration and optimization techniques for enhanced system efficiency, reliability, and sustainability.

Joint energy management with integration of renewable energy sources considering energy and reserve minimization

In light of electric vehicles (EVs) and demand-side management, a combined optimization paradigm for microgrid (MG) resource scheduling is proposed in this study. Renewable energy sources, including wind and solar power, fulfill a fraction of the consumption demand, while the MG maintains a connection to the electrical network to facilitate power transactions. By utilizing EVs, we can mitigate the inherent volatility of renewable energy production with manageable loads and level out the system's demand profile. The proposed system employs a bi-level programming strategy, wherein the initial level is dedicated to the minimization of aggregate costs, encompassing those related to energy and reserves. Additionally, costs associated with resource redistribution due to the uncertainty of solar and wind power output are minimized at the second level. Subsequently, the objective function is addressed using the enhanced adapted approach of modified marine predators algorithm (MMPA), chosen for its robustness and effectiveness as an optimization technique. The outcomes obtained for a microgrid underscore the superior performance of the results achieved through the application of the MMPA algorithm when contrasted with alternative established methodologies. The outcomes have demonstrated that integrating EVs and adaptable loads contributes to a decrease in operational expenses and emissions. Furthermore, the uncertainties associated with WT and PV are effectively counterbalanced. Additionally, the results garnered from the simulations indicate that the recommended MMPA technique has the capacity to yield superior solutions compared to several other widely recognized optimization algorithms. Scheduling with both DR and EVs with three cost components are considered, generation cost, reserve cost, and initial unit cost, amounting to $740.11, $9.61, and $6.07, correspondingly and it can lead to decreased emission levels and increased incentives for proprietors of EVs, responsive load participants, and RES.

A Design and Construction of the Vibration Perception Threshold Measurement Device for Diabetes

The purpose of this study was to design and build a mechanical vibration assessment tool for diabetic patients’ peripheral nervous systems. There is a substantial correlation between peripheral sensory neuropathy and vibration perception threshold (VPT). Peripheral sensory neuropathy has been identified by VPT determination utilizing the VPT measurement instrument built for that purpose. The designed device can assist in determining the threshold and tracking any progressive changes or trends. This designed device consists of two main components: hardware and software. The hardware part includes a DC power supply circuit, an Arduino NANO, a display, an isolation MOSFET driver for the electrical isolation circuit, a transducer driver, and a transducer head. The software part uses C programming on the Arduino to generate signals and display the transducer supply voltage. The testing results consist of 1) the voltage settings results (5–30 volts) comparing the voltage values on the display between the designed device and a digital multimeter, which has an average error of 0.75%, 2) According to the transducer head pressing test results, the Vibrotest Digital Biothesiometer and the proposed device had different pressing weights of ±0.02 g, and 3) the electrical safety testing results of the designed device is in the standard of IEC60601-1. (IEC: International Electrotechnical Commission).

Solid-Emission-Tunable Squaraine with Thermal-Promoted Aggregate-State Transitions for Fast Thermal History Sensing.

Determining thermal history is crucial in many industrial processes, but reliable and sensitive organic thermal history indicators are currently absent. Herein, we report on the development of a squaraine-based fluorescent molecule, DPEA-SQ, for the detection of thermal exposure histories up to 436 K. DPEA-SQ forms multiple single crystals (DPEA-SQ-I, DPEA-SQ-II, and DPEA-SQ-III) with different conformations and aggregate-state packing modes, contributing to their different fluorescence wavelengths, lifetimes, and efficiencies. Interestingly, DPEA-SQ-I and DPEA-SQ-III undergo aggregate-state structural transitions to form the thermodynamically more stable DPEA-SQ-II, which are accompanied by changes in their fluorescence. By taking advantage of similar aggregate-state structural transformations during heating, a high-temperature thermal exposure history of up to 436 K is recorded and reflected by their fluorescence. To demonstrate the potential practical applications of DPEA-SQ, a DPEA-SQ-Powder/PDMS film is prepared and coated on an electric circuit board, which enables real-time monitoring of localized overheating by the naked eye. Additionally, the fluorescence peaks of DPEA-SQ-Powder and DPEA-SQ-Powder/PDMS films remain unchanged after storage at 373 K for 52 days, demonstrating high aggregate-state stability. The fast and reliable responses of this system make it an excellent candidate for the detection of overtemperature traces in electronic components and circuit diagnosis.

Convex Relaxations of Maximal Load Delivery for Multi-Contingency Analysis of Joint Electric Power and Natural Gas Transmission Networks

Recent increases in gas-fired power generation have engendered increased interdependencies between natural gas and power transmission systems. These interdependencies have amplified existing vulnerabilities in gas and power grids, where disruptions can require the curtailment of load in one or both systems. Although typically operated independently, coordination of these systems during severe disruptions can allow for targeted delivery to lifeline services, including gas delivery for residential heating and power delivery for critical facilities. To address the challenge of estimating maximum joint network capacities under such disruptions, we consider the task of determining feasible steady-state operating points for severely damaged systems while ensuring the maximal delivery of gas and power loads simultaneously, represented mathematically as the nonconvex joint Maximal Load Delivery (MLD) problem. To increase its tractability, we present a mixed-integer convex relaxation of the MLD problem. Then, to demonstrate the relaxation’s effectiveness in determining bounds on network capacities, exact and relaxed MLD formulations are compared across various multi-contingency scenarios on nine joint networks ranging in size from 25 to 1191 nodes. The relaxation-based methodology is observed to accurately and efficiently estimate the impacts of severe joint network disruptions, often converging to the relaxed MLD problem’s globally optimal solution within ten seconds.

Mathematical improvisation of electrical equivalent circuit model for commercial dye-sensitized solar module with Gauss–Seidel, curve fit and theoretical approach

Mathematical improvisation of electrical equivalent circuit model for commercial dye-sensitized solar module with Gauss–Seidel, curve fit and theoretical approach