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With the growing adoption of renewable energy resources, microgrids (MGs) are increasingly relying on these sources to meet their electrical load demands. To ensure efficient operation, these units must be scheduled in a coordinated manner. This paper introduces a stochastic model for the joint scheduling of renewable and thermal energy units. The study focuses on integrating proton exchange membrane fuel cell-based combined heat and power (PEMFC-CHP) units, wind turbines (WTs), and photovoltaic (PV) systems within the scheduling framework. Additionally, hydrogen storage strategies are incorporated into the PEMFC-CHP operations. The model addresses uncertainties such as wind speed, solar irradiance, and market price fluctuations using a scenario-based approach. The proposed method formulates the scheduling problem as a mixed-integer nonlinear programming (MINP) model, incorporating hydrogen storage strategies. The inherent uncertainties in these parameters further transform the problem into a stochastic MINP. Coordinated scheduling of renewable and thermal units within microgrids not only optimizes resource utilization but also enhances the overall objective function value. These advancements align with current energy policy objectives aimed at improving the efficiency and sustainability of energy systems. To solve the complex scheduling problem, this research employs an Improved Salp Swarm Algorithm (ISSA), which has been tested on a modified 33-bus distribution network. Simulation results indicate that the ISSA achieves over 5% higher revenue compared to other optimization methods. Furthermore, incorporating combined heat and power (CHP) operations increases the total system profit by more than 15%. The algorithm achieved the optimal result in 28 out of 30 attempts. The ISSA algorithm, with a remarkable success rate of 95.28%, demonstrates its effectiveness in minimizing MG operating costs, a critical component of energy policy goals. • A stochastic model is created for coordinated scheduling of renewable energy. • Including uncertainties in the model improves overall profitability. • The role of combined heat and power systems is analyzed in the model. • Hydrogen storage supports fuel cell operation in the proposed framework. • Profit maximization of the microgrid is the main objective. [ABSTRACT FROM AUTHOR]

The integration of a distributed generator (DG) into the distribution network alters the topology structure and power flow distribution, subsequently causing changes in network loss. Moreover, existing distribution network optimization methods face high computational complexity, low efficiency, and susceptibility to local optima. This article proposes a scenario generation method using a generative adversarial network (GAN) to handle the uncertainty associated with DGs and constructs a two-layer optimization model for the distribution network. The upper layer model determines the installation location and capacity of distributed power and energy storage systems with the lowest economic cost. The lower layer model establishes an optimization model, including wind, solar, and storage, with active power network loss and voltage deviation as objective functions. Both layers are solved using the Improved Whale Optimization algorithm (IWOA). Then, the IEEE-33 node distribution system was taken as a simulation example to verify the effectiveness and superiority of the proposed model and algorithm. [ABSTRACT FROM AUTHOR]

The optimal power flow (OPF) is an important technique for optimizing the control parameters of modern power systems by taking into account the desired objective functions considering system constraints. This paper provides a developed particle swarm optimization (PSO) method for solving the OPF problem with a rigorous objective function of minimizing generation fuel costs for the utility and industrial companies while satisfying a set of system limitations. By reviewing previous OPF investigations, the developed PSO is used in the IEEE 30-bus test system to reduce overall fuel cost, active/reactive power losses, and exhaust. The obtained results are compared to those obtained using a typical PSO technique and other algorithms. In the IEEE 30-bus test system, one of the paper's key findings is that the cost of fuel is computed as 800.41 $/h, 830.7779 $/h, 825.6922 $/h, 826.54 $/h, 826.3176 $/h, 823.3999 $/h, 786.03 $/h with the conventional PSO, backtracking search algorithm (BSA), hybrid SFLA-SA, differential evolution (DE), enhanced GA (EGA), monarch butterfly optimization (MBO), proposed algorithm, respectively. Moreover, there is a great reduction in the fuel cost by 4.358% compared with the robust MBO algorithm. MATLAB software is used to demonstrate the effectiveness and accuracy of the proposed technique. [ABSTRACT FROM AUTHOR]

Motivated by the change of effective electrical properties grain or phase boundaries, a computational multiscale framework for continua with interfaces at the microscale is proposed. Cohesive-type interfaces are considered at the microscale, such that displacement and electrical potential jumps are accounted for. The governing equations for materials with interfaces under mechanical and electrical loads are provided. Based on these, a computational multiscale formulation is proposed. The coupling between the electrical and mechanical subproblem is established by the constitutive equations at the material interface. In order to investigate deformation-induced property changes at the microscale, the evolution of interface damage is elaborated. The proposed multiscale framework is further examined through various representative boundary value problems so as to identify its key properties. [ABSTRACT FROM AUTHOR]

The stochasticity of power flow of distributed generations (DGs) and load in the microgrid has great influence on power flow distribution and voltage quality of the distribution network. For improving the voltage quality of the distribution network, the questions need to be further studied, which include the description of the stochasticity of the power flow in the microgrid and the impact of the microgrid into the distribution network on the power flow. Therefore, a novel stochastic power flow calculation and optimal control method for the microgrid based on multivariate stochastic factors fusion-sensitivity (MSFF-sensitivity) is proposed in this paper. Firstly, the multivariate stochastic factors fusion (MSFF) function is developed by using the probability density function to extract the stochasticity and correlation of power flow among different stochastic factors in the microgrid, which are effectively unified. Furthermore, the fusion-sensitivity (F-sensitivity) of the power flow in the microgrid integrated into the distribution network is constructed to accurately characterize the influence degree of various stochastic factors in the microgrid on the power flow of the distribution network. Based on this, the output power of the stochastic factor is adjusted to optimally control the power flow of the distribution network. Finally, the algorithm verification suggests that, compared with the conventional power flow methods, the method proposed in this paper is more suitable for the microgrid. The influence of stochastic power flow on the distribution network can be effectively reduced and the voltage quality of the distribution network can be improved by optimizing control of the power flow in the microgrid integrated into the distribution network. [ABSTRACT FROM AUTHOR]

As the proportion of new energy increases, the traditional cumulant method (CM) produces significant errors when performing probabilistic load flow (PLF) calculations with large-scale wind power integrated. Considering the wind speed correlation, a multi-scenario PLF calculation method that combines random sampling and segmented discrete wind farm power was proposed. Firstly, based on constructing discrete scenes of wind farms, the Nataf transform is used to handle the correlation between wind speeds. Then, the random sampling method determines the output probability of discrete wind power scenarios when wind speed exhibits correlation. Finally, the PLF calculation results of each scenario are weighted and superimposed following the total probability formula to obtain the final power flow calculation result. Verified in the IEEE standard node system, the absolute percent error (APE) for the mean and standard deviation (SD) of the node voltages and branch active power are all within 1%, and the average root mean square (AMSR) values of the probability curves are all less than 1%. [ABSTRACT FROM AUTHOR]

Many developing countries, including Indonesia, are progressing poorly in residential rooftop photovoltaic (PV) adoption, including on-grid systems. On the customer side, the decision to implement on-grid rooftop PV or rely only on power from the utility grid has often been made without appropriate knowledge of techno-economic considerations. This includes the impression of high system costs. This paper introduces KawanSurya: PV calculator, a solar rooftop PV techno-economic application for Android mobile phones, designed to help residential customers assess the potential of installing ongrid rooftop PV systems. The tool allows users to select a specific geographic location, calculate daily load profiles, and determine available roof areas. It uses irradiance data from the PVGIS API and HOMER's solar PV output equation to determine hourly PV output power. Simulation results for a typical 2,200 VA household show a payback period of 9.44 years or beyond, significantly influenced by electrical load profiles and bill reduction factors. A 65% bill reduction factor and similar load profile prolong the payback period, while a 0% billing reduction factor or uncompensated electricity sales may exceed the project's lifetime. [ABSTRACT FROM AUTHOR]

This study focuses on reactive power planning in the IEEE30-bus test system, specifically involving the integration of flexible AC transmission systems (FACTS) within the utility system. The primary objective is to minimize power loss and voltage deviation. To address this, a recently developed optimization algorithm called modified ant-lion optimizer (MALO) is applied to solve the optimal reactive power dispatch (ORPD) problem on the IEEE 30-bus system. A comparative analysis is conducted between the results obtained with and without FACTS devices. The findings reveal that the utilization of FACTS devices leads to significantly improved outcomes compared to scenarios without FACTS devices. Among the FACTS devices studied, the unified power flow controller (UPFC) demonstrates superior performance compared to the static synchronous compensator (STATCOM) and interline power flow controller (IPFC). [ABSTRACT FROM AUTHOR]

Load frequency control is necessary for power system management. The power system must maintain a frequency range to ensure power supply stability. System faults and demand fluctuations may cause frequencies to change quickly. System stability and integrity suffer. We are optimizing the two-degree-of-freedom (2-DOF) proportional-integral-derivative (PID) controllers chess algorithm. This article addresses electrical load frequency regulation. We employ classical control theory and current adjustment. It aims for electrical system efficiency and dependability. It checks for errors using integral absolute error (IAE), integral squared error (ISE), integral of time multiply absolute error (ITAE), and integral time squared error (ITSE). Particle swarm algorithm (PSO) compares performance. The IAE of 0.03364, nearly identical to it, shows that chess trumps other algorithms in many scenarios. The chess algorithm's ISE was 0.00035, like PSO's 0.03363. The ISE was 0.00036, indicating PSO's error-reduction capabilities. For the chess algorithm, PSO is 0.07929, and ITAE is 0.07647. This indicates the PSO responds faster to system breakdowns and load changes. Finally, the chess algorithm's ITSE is 0.00072, below the PSO 0.00076. The chess algorithm is better at managing long-term load frequency. [ABSTRACT FROM AUTHOR]

The increasing adaption of Plug-in Electric Vehicles (PEVs) has increased the power demand for charging. Renewable generation can significantly help to meet this demand. The uncertainty of renewable generation and randomness in PEV charging makes the demand management of charging stations challenging. To address these challenges, this study proposes a novel demand management pricing strategy for renewable integrated charging stations. The proposed strategy uses reinforcement learning for charging coordination of PEVs. The renewable generation is estimated using weather data and accordingly PEVs are scheduled for demand management. The strategy decides the PEV power price based on real-time price, renewable tariff and PEV load. The strategy uses the bidirectional power flow with battery degradation cost. The distribution transformer operating cost and loading constraints are included to resemble the real-time environment. The PEV randomness and uncertainty of renewable generations are incorporated in the study. The results of the numerical case study show that the proposed strategy can manage the charging station load efficiently. The proposed strategy has optimized the cost of charging, discharging and charging station profit and increased the service capability of the charging station. [ABSTRACT FROM AUTHOR]

The stochastic volatility of the rail transit load brings greater uncertainty to the vulnerability of the power grid. To solve the problem of the inaccurate results caused by the incomplete time-domain simulation model of the power system with rail transit load integration, this paper proposes a vulnerability analysis method for the power system with rail transit load integration based on the random matrix theory. In this paper, we first constructed a rail transit load model based on Deep Convolutional Generative Adversarial Networks (DCGAN) to simulate the situation that massive rail transit load merged into the Grid Scenario. Then, we generate a high-dimensional random matrix based on the power flow of the grid-connected system under different rail transit loads. Then, we construct a vulnerability analysis model combining the random matrix theory and the real-time separation window. Finally, we take the IEEE-39 bus system and a regional power grid in China as examples to evaluate the vulnerability of the grid-connected system. The results show that our method quantifies not only the impact of the rail transit load volatility on the system vulnerability, but the system endurance under different capacities of the rail transit load connected to grid. Moreover, it also provides a new way for system planning and safety monitoring in the power system with rail transit load integration. [ABSTRACT FROM AUTHOR]

Battery and hydrogen-based energy storages play a crucial role in mitigating the intermittency of wind and solar power sources. In this paper, we propose a mixed-integer second order cone program (MISOCP) to jointly optimize the dimensioning and energy management of a grid-connected wind-PV-hydrogen-battery system. With the proposed optimization formulation, we comparatively investigate the impacts of the hybrid combination of battery and hydrogen storages on an IEEE 33-bus network in 4 different scenarios. The simulation results show that, the systems with hydrogen storage renders a remarkable profit raise, up to 43.6 %, compared to those systems without hydrogen production. The power consumed by the electrolyzer far surpasses the grid power and accounts for up to 99.5 % of the renewable energies. Additionally, the power losses in the network with hydrogen storage are also reduced due to the onsite consumption. • A MISOCP formulation to optimize a wind-solar-hydrogen-battery system is presented. • Both power flow and nonlinear modeling of the grid-connected system are considered. • The approach simultaneously optimizes the storage sizes and energy management. • The impacts of different energy storages on the grid-connected system are analyzed. [ABSTRACT FROM AUTHOR]

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Multi-port DC power electronic transformer (PET) is a core equipment for achieving transformation of different voltage levels and flexible interconnection of different DC buses in a DC distribution system. It is capable of bidirectional energy flow, flexible regulation of power flow, port fault isolation, and other functions. A new five-port DC transformer topology based on soft switching technology is proposed in this paper. In this topology, different DC voltage levels can be interconnected efficiently, such as 20 kV, 750 V, ±375 V, and 300 to 500 V adjustable. The control of each port is simple and flexible. The output voltage is stable, and they are independent of each other, which can improve the system reliability. The topology of the proposed multi-port DC transformer is introduced in detail. The working principle, control strategy, and parameter design method of the transformer are analyzed. Simulations and experimental results are provided to validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

A growing interest in offshore wind energy in the Mediterranean Sea has been recently observed thanks to the potential for scale-up and recent advances in floating technologies and dynamic cables: in the Italian panorama, the offshore wind connection requests to the National Transmission Grid (NTG) reached almost 84 GW at the end of September 2024. Starting from a realistic estimate of the offshore wind power plants (OWPPs) to be realized off the southern coasts in a very long-term scenario, this paper presents a novel optimization procedure for meshed AC offshore network configuration, aiming at minimizing the offshore wind generation curtailment based on the DC optimal power flow approximation, assessing the security condition of the whole onshore and offshore networks. The reactive power compensation aspects are also considered in the optimization procedure: the optimal compensation sizing for export cables and collecting stations is evaluated via the AC optimal power flow (OPF) approach, considering a combined voltage profile and minimum short circuit power constraint for the onshore extra-high voltage (EHV) nodes. The simulation results demonstrate that the obtained meshed network configuration and attendant re-active compensation allow most of the offshore wind generation to be evacuated even in the worst-case scenario, i.e., the N1 network, full offshore wind generation output, and summer line rating, testifying to the relevance of the proposed methodology for real applications. [ABSTRACT FROM AUTHOR]

The rising energy demand, coupled with increased integration of distributed energy resources (DERs) and fluctuating renewable generation, underscores the need for effective load management within energy communities. This paper addresses these challenges by implementing effective, constraint-aware load shifting within microgrid-based energy communities. Specifically, the goal of this study is to flatten the electrical load profile of a High-Voltage (HV)/Medium-Voltage (MV) power transformer. The load of a central power transformer includes (a) the diverse, fluctuating electrical and thermal demands of buildings within the energy community and (b) the load of the area supplied by the substation excluding the energy community loads. To achieve a flattened load profile, we apply time shifting to both electrical and heating, ventilation, and air conditioning (HVAC) loads of the energy community, allowing for a redistribution of energy consumption over time. This approach entails shifting non-critical loads, particularly those related to HVAC and other building operations, to off-peak periods. The methodology considers critical operational constraints, such as maintaining occupant thermal comfort, ensuring compliance with building codes, and adhering to technical specifications of HVAC and electrical systems and microgrid organized energy communities. Detailed simulations were conducted to prove the effectiveness of this constraint-aware load-shifting approach. [ABSTRACT FROM AUTHOR]

The process of establishing relay protection and automation (RPA) settings for electric power systems (EPSs) entails complex calculations of operating modes. Traditionally, these calculations are based on symmetrical components, which require the building of equivalent circuits of various sequences. This approach can lead to errors both when identifying the operating modes and when modeling the RPA devices. Proper modeling of measuring transformers (MTs), symmetrical component filters (SCFs), and circuits connected to them effectively solves this problem, enabling the configuration of relay protection and automation systems. The methods of modeling the EPS in phase coordinates are proposed to simultaneously determine the operating modes of high-voltage networks and secondary circuits connected to the current and voltage transformers. The MT and SCF models are developed to concurrently identify the operating modes of secondary wiring circuits and calculate the power flow in the controlled EPS segments. This method is effective in addressing practical problems related to the configuration of the relay protection and automation systems. It can also be used when establishing cyber–physical power systems. For a comprehensive check of the adequacy of the MT models, 140 modes of the electric power system were determined which corresponded to time-varying traction loads. Based on the results of calculating the complexes of currents and voltages at the MT terminals, parametric identification of the power transmission line was performed. Based on this, the model of this transmission line was adjusted; repeated modeling was carried out, and errors were calculated. The modeling results showed a high accuracy when calculating the modules and phases of voltages using the identified model. The average error value for current modules was 0.6%, and for angles, it was 0.26°. [ABSTRACT FROM AUTHOR]

The nuclear energy development strategy in Russia involves the construction and commissioning of a number of new nuclear power plants, which will lead to an increase in the share of nuclear power plants in the country's energy systems. Based on the information presented in the energy development strategy of Russia for the period until 2035, it is planned to involve nuclear power plants with generation «3+» reactors in regulating the unevenness of daily electrical load schedules. In these circumstances, unloading of the nuclear power plant is inevitable, which is ineffective for a number of reasons. Combining a nuclear power plant with a hydrogen complex makes it possible to achieve the goals set by the government of the Russian Federation, starting from the need to introduce a third-party energy complex that adapts the nuclear power plant to an alternating operating mode without changing the thermal load on the reactor and steam generators. There is a known option for combining a nuclear power plant with a hydrogen complex using piston compressor units, but the introduction of this type of equipment negatively affects the probability of failure-free operation of the hydrogen complex as a whole due to the high failure rate. The new concept of combining a nuclear power station with a hydrogen complex implies the exclusion of gas compressors by organizing excess pressure in a capacitive storage system due to the electrolysis of high-pressure water. In this case, the compressors are replaced with pressure reduction units that meet a higher level of reliability. The main results of the work carried out are a probabilistic assessment of reliability and an analytical comparison of capital investments in the reserve of the hydrogen complex, which allows us to collectively reflect the impact of changes in the number of reserves in terms of the probability of failure-free operation and the economic side of the study. As the assessments performed have shown, a hydrogen complex based on the use of high-pressure water electrolysis has a higher level of reliability, as well as, in the considered pressure range, lower capital costs for reserve. [ABSTRACT FROM AUTHOR]

The integration of hybrid alternating current (AC) and direct current (DC) networks has gained relevance due to the growing demand for more flexible, efficient, and reliable electrical systems. A key aspect of this integration is the parallelization of power converters, which presents several technical challenges, such as current sharing imbalances, circulating currents, and control complexity. This paper proposes a distributed control architecture for parallel resonant CLLC dual active bridge (DAB) converters to address these issues in hybrid AC–DC networks and microgrids. The approach includes a master voltage controller to regulate the output voltage and distributed local current controllers to ensure load balance. The approach minimizes the difference between the output and input voltages, allowing for independent control of power flow. Simulation and experimental results show significant improvements. The system stability has been demonstrated experimentally. Transient response has been improved with response time 80% lower using the feed-forward term. The system maintained stability with current sharing deviations below 3% under full and low load conditions. Finally, scalability is ensured by the proposed distributed controller because the central power controller is not affected by the number of units in parallel used in the application. This solution is suitable for advanced hybrid networks and microgrid applications. [ABSTRACT FROM AUTHOR]

Nowadays, the proliferation of distributed renewable energy sources is a fact. A microgrid is a good solution to self-manage the energy generation and consumption of electrical loads and sources from the point of view of the consumer as well as the power system operator. To make a microgrid as versatile as necessary to carry that out, a flexible inverter is necessary. In this paper, an algorithm is presented to control an inverter and make it complete and versatile to work in grid-connected and in isolated modes, injecting or receiving power from the grid and always compensating the harmonics generated by the loads in the microgrid. With this inverter, the microgrid can work while optimizing its energy consumption or according to the power system operator instructions. The inverter proposed is tested in a designed Matlab/Simulink simulation platform. After that, an experimental platform designed and built ad hoc, including a DC source, AC linear and non-linear loads, and a Semikron power inverter, is used to test the proposed control strategies. The results corroborate the good system performance. The replicability of the system is guaranteed by the use of low-cost devices in the implementation of the control. [ABSTRACT FROM AUTHOR]

The independent DC bus structure multiport power electronic transformer (IDBS-MPET) is a novel power electronic transformer designed to integrate multiple DC sources and DC loads. Due to the configuration of DC ports, which are directly constructed by the parallel connection of dual active bridge (DAB) converters, the distribution of DC sources and DC loads among the three phases becomes unbalanced. In cases where the load power at certain ports is too high, this imbalance may lead to the over-modulation of the front-end H-bridge (HB). Since the output power at a certain port in the IDBS-MPET is constrained by the loads at other ports, this paper proposes a multiport steady-state power flow allocation method. This method establishes the load sensitivity correlation factor to enable all the ports to adjust power cooperatively based on it. By applying the proposed steady-state power flow allocation method, iterative calculations continuously update the priority of all the ports and their load sensitivity correlation factors. This process ensures that the power flow converges to a steady-state solution. Simulation results for two different IDBS-MPETs demonstrate that the power flow at all the ports effectively meets load requirements, while the front-end HB avoids over-modulation, ensuring the safe and stable operation of the IDBS-MPET. The results validate the effectiveness of the proposed steady-state power flow allocation method. [ABSTRACT FROM AUTHOR]

A power factor corrector (PFC) is a device whose job is to improve the power factor of a device. Several connections of semiconductor converters are used for this purpose; one of them is the bridgeless totem-pole power factor correction converter (BLTP-PFC). The bridgeless totem-pole power factor correction converter (BLTP-PFC) is known for its advantages, including its simple topology, low interference capability, high efficiency, and environmental friendliness. Initially, this article focuses on a single-phase PFC, precisely the principle of operation of the BLTP-PFC converter and its simulation verification. Finally, an experimental prototype of an interlaced totem-pole bridgeless PFC converter is designed to verify the correctness and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Accurate load forecasting is of vital importance for improving the energy utilization efficiency and economic profitability of intelligent buildings. However, load forecasting is restricted in the popularization and application of conventional load forecasting techniques due to the great difficulty in obtaining numerical weather prediction data at the hourly level and the requirement to conduct predictions on multiple time scales. Under the condition of lacking meteorological forecast data, this paper proposes to utilize a temporal convolutional network (TCN) to extract the coupled spatial features among multivariate loads. The reconstructed features are then input into the long short-term memory (LSTM) neural network to achieve the extraction of load time features. Subsequently, the self-attention mechanism is employed to strengthen the model's ability to extract feature information. Finally, load forecasting is carried out through a fully connected network, and a multi-time scale prediction model for building multivariate loads based on TCN–LSTM–self-attention is constructed. Taking a hospital building as an example, this paper predicts the cooling, heating, and electrical loads of the hospital for the next 1 h, 1 day, and 1 week. The experimental results show that on multiple time scales, the TCN–LSTM–self-attention prediction model proposed in this paper is more accurate than the LSTM, CNN-LSTM, and TCN-LSTM models. Especially in the task of predicting cooling, heating, and electrical loads on a 1-week scale, the model proposed in this paper achieves improvements of 16.58%, 6.77%, and 3.87%, respectively, in the RMSE indicator compared with the TCN-LSTM model. [ABSTRACT FROM AUTHOR]

The typical bistable energy harvester (TBEH) systems usually have a limited working frequency bandwidth and low performance in energy conversion. This paper proposed a unilateral vibro-impact piezoelectric cantilever beam energy harvester. The novel vibro-impact bistable energy harvester (VIBEH) improves the drawbacks of a TBEH system. Despite previous research, in this paper, the collision process is modeled by nonlinear Hertzian contact theory. Nonlinear contact law adds strong nonlinearity to the harvester. By using the extended Hamilton principle and Euler-Lagrange equation, the governing equations of the energy harvester are derived and solved numerically. The existing nonlinearities cause frequency leaks and affect the type of motion (inter-well or intra-well motion) by changing the equilibrium points of the system. By applying nonlinear tools like Poincare diagrams, bifurcation plots, and phase portraits, the effects of periodic or chaotic oscillations will be studied on the performance of the VIBEH system. Finally, the effects of barrier stiffness, initial gap, barrier location, and electrical load are determined on the performance of the VIBEH system. The obtained results showed that using the VIBEH system could broaden the working frequency bandwidth by about 71.9%. Furthermore, the optimized values of impacting properties and electrical load are examined. [ABSTRACT FROM AUTHOR]

ABSTRACT Electric buses are introduced toward achieving carbon neutrality by 2050, and there is a movement to utilize their storage batteries. On the other hand, the electric power system, where distributed energy resources are rapidly spreading, is becoming increasingly complex, and the impact of charging by electric buses on power system is an issue. In this study, we propose an optimization method for electric bus charge/discharge schedule that considers sector coupling between transportation system and power system. Then, we evaluate the effectiveness of the proposed method from the viewpoints of both the distribution system operator and the electric bus operator by performing power flow calculations using a distribution system model. The results show that the proposed method can contribute to power demand shifting and smoothing power flow in distribution network by charging and discharging, and that multiple evaluation indices, for example, peak‐cutting of power flow, line occupation rate, distribution loss, reverse power flow utilization rate, renewable energy rate and CO2 emissions, are improved compared to the conventional charging scheduling method. [ABSTRACT FROM AUTHOR]

ABSTRACT This paper proposes a new three‐port bidirectional DC–DC converter designed for integration into photovoltaic systems with battery energy storage. The proposed topology features three ports: two for power supply (one powered by batteries and the other by photovoltaic panels) and a third for the load. Due to its bidirectional characteristics, this converter facilitates power flow both from the batteries and/or photovoltaic panels to the load, as well as from the photovoltaic panels to the batteries. The converter operates in open loop, and this paper presents qualitative and quantitative analyses of the converter operating in continuous conduction mode (CCM) for two power flow scenarios. Additionally, an illustrative design is detailed for a nominal power of 1.5 kW, a switching frequency of 30 kHz, a battery voltage of 48 V, a photovoltaic panel voltage of 142 V, and a load bus voltage of 250 V. The theoretical analysis is validated through experimental results. Some of the main highlights include operating the inductor at twice the switching frequency, significantly reducing both the inductor's size and the input current ripple. Furthermore, the optimal battery current ripple occurs at a duty cycle close to 50%, where it is practically zero. The converter efficiency was analyzed in all power flow scenarios at various operating points, reaching up to 97.33%. Furthermore, a supplementary video showcasing its functionality is included with this manuscript. [ABSTRACT FROM AUTHOR]

The increasing demand for renewable energy sources necessitates the development of sophisticated control systems that can seamlessly integrate and manage multiple power sources. This research introduces an advanced intelligent adaptive neuro fuzzy-based control (IANFC) for multiport DC-AC converters with differential power processing (DPP) converters, tailored for customized hybrid renewable power generation systems (HRPGS). The system aims to optimize HRPGS performance and efficiency through neuro-fuzzy control techniques. When integrating different DC power sources, such solar panels and wind turbines, into AC loads or the grid, multiport DC-AC converters are essential. These converters reduce the amount of power conversion steps, which improves the system's overall efficiency and scalability. Complementary DPP converters process only the differential power, thereby significantly reducing total power consumption and conversion losses. The IANFC framework combines fuzzy logic reasoning, based on rules, with neural network adaptive learning capabilities. This hybrid control method effectively manages the nonlinear and dynamic behavior of HRPGS, ensuring reliable performance under varying load demands and environmental conditions. The controller dynamically adjusts the converter's operating point to ensure optimal power flow and system stability. Simulation findings using MATLAB/Simulink verify the efficacy of the suggested IANFC system. Under various operational situations, key performance measures like response time, stability, and system efficiency are examined. As evidenced by the data, system performance has significantly improved as compared to traditional control techniques. The proposed system demonstrates an efficiency of 99.45% and achieves stability in just 0.02 s. Compared to conventional algorithms, this approach shows superior performance across multiple metrics. [ABSTRACT FROM AUTHOR]

The erosion characteristics of high sand flow fields are essential to the durability and performance of double jet pumps in oil and gas production. Using solid–liquid two-phase flow theory and an erosion model, this study evaluated how particle size, mass flow rate, and power fluid flow rate affect the erosion of double jet pumps. The findings reveal that erosion mainly occurs on the inner wall at the throat inlet, throat outlet, and diffuser inlet. With an increase in power fluid flow rate from 11 to 15 L/s, the maximum erosion rate at the throat's inlet cone escalates by a factor of 14.2. The throat inlet's service life is estimated at 275 hours. These insights provide valuable guidance for optimizing double jet pump design and application. [ABSTRACT FROM AUTHOR]

We demonstrate that fundamental nonlinear localized modes can exist in the Chen–Lee–Liu equation modified by several parity-time (P T) symmetric complex potentials. The explicit formula of analytical solitons is derived from the physically interesting Scarf-II potential, and families of spatial solitons in internal modes are numerically captured under the optical lattice potential. By the spectral analysis of linear stability, we observe that these bright solitons can remain stable across a broad scope of potential parameters, despite the breaking of the corresponding linear P T -symmetric phases. When these bright spatial solitons interact with external incident waves, they can always maintain their original shape, while the external incident wave may remain unchanged or may generate a reflected wave after the interaction. Then, the adiabatic switching of potential parameters is carried out in a way that allows these bright solitons to be excited from one unstable bound state to another alternative stable bound state. Many other intriguing properties associated with these nonlinear localized modes including the lateral power flow are further analyzed meticulously. Various high-order rogue waves induced by modulation instability in these P T -symmetric systems are generated too. These results may be useful to construct novel optical soliton communication schemes or design related optical materials. [ABSTRACT FROM AUTHOR]

The optimization of the symmetry of MTDC systems after a contingency is crucial for the stable and economic operation of the MTDC systems. In this paper, a multi-objective optimal control method for the power flow symmetry of MTDC systems for the large-scale integration of offshore wind farms is proposed. A mirror relationship between the available headroom of DC lines and VSCs and their actual power flow distribution performance is established. A corresponding symmetry index is established for the MTDC network, and the multi-objective optimization problem is converted into a series of single-objective problems by the normal boundary intersection method, and solved by the original dyadic interior point method, so as to obtain the Pareto optimal solution with uniform distribution. The compromise optimal solution is decided according to the entropy weight double-basis point method, which provides decision-making guidance for the operators. The simulation results show that the normal boundary intersection method can solve the multi-objective dynamic optimal control problem of the VSC-HVDC system quickly and efficiently, and improve the symmetry of the power flow in an MTDC network. [ABSTRACT FROM AUTHOR]

In the past, providing an online and real-time response to cyber–physical attacks in large-scale power microgrids was considered a fundamental challenge by operators and managers of power distribution networks. To address this issue, an innovative framework is proposed in this paper, enabling real-time responsiveness to cyberattacks while focusing on the techno-economic energy management of large-scale power microgrids. This framework leverages the large change sensitivity (LCS) method to receive immediate updates to the system's optimal state under disturbances, eliminating the need for the full recalculation of power flow equations. This significantly reduces computational complexity and enhances real-time adaptability compared to traditional approaches. Additionally, this framework optimizes operational points, including resource generation and network reconfiguration, by simultaneously considering technical, economic, and reliability parameters—a comprehensive integration often overlooked in recent studies. Performance evaluation on large-scale systems, such as IEEE 33-bus, 69-bus, and 118-bus networks, demonstrates that the proposed method achieves optimization in less than 2 s, ensuring superior computational efficiency, scalability, and resilience. The results highlight significant improvements over state-of-the-art methods, establishing the proposed framework as a robust solution for real-time, cost-effective, and resilient energy management in large-scale power microgrids under cyber–physical disturbances. [ABSTRACT FROM AUTHOR]

A matrix converter (MC) converts an AC source voltage into a variable-voltage variable-frequency AC output voltage (direct AC-AC) without an intermediate DC-link capacitance. By eliminating the traditional DC-link capacitor, MCs can achieve higher power densities and reliability when compared to conventional AC-DC-AC converters. MCs also offer the following characteristics: total semiconductor solution, sinusoidal input and output currents, bidirectional power flow and controllable input power factor. This paper reviews the history, recent developments and commercialization of MCs and discusses several technical requirements and challenges, including bidirectional switches, wide bandgap (WBG) opportunities using GaN and SiC, overvoltage protection, electromagnetic interference (EMI) and ride-through in motor drive applications. MC design solutions and operation are discussed, including a comparison of control and modulation techniques as well as the detailed development of space vector modulation (SVM) to provide a deep insight into the control implementation and results. The paper concludes with compelling motor drive innovation opportunities made possible by advanced MCs including fully integrated and multiphase systems. For conventional MCs, size reductions of 30% are reported, as well as efficiencies of 98% and low input current total harmonic distortion of 3–5%. [ABSTRACT FROM AUTHOR]

Research in renewable energy sources and microgrid systems is critical for the evolving power industry. This paper examines the operational behavior of both pico- and nano-grids during transitions between grid-connected and islanded modes. Simulation results demonstrate that both grids effectively balance the power flow, regulate the state of charge (SOC), and stabilize the voltage during dynamic operational changes. Specific scenarios, including grid disconnection, load sharing, and weather-based energy fluctuations, were tested and validated. This paper models both pico-grids and nano-grids at the Singapore Institute of Technology Punggol Campus, incorporating solar PVs, energy storage systems (ESSs), power electronic converters, and both DC and AC loads, along with utility grid connections. The pico-grid includes a battery storage system, a single-phase inverter linked to a single-phase grid, and DC and AC loads. The nano-grid comprises solar PV panels, a boost converter, a battery storage system, a three-phase inverter connected to a three-phase grid, and AC loads. Both the pico-grid and nano-grid are configurable in standalone or grid-connected modes. This configuration flexibility allows for a detailed operational analysis under various conditions. This study conducted subsystem-level modelling before integrating all components into a simulation environment. MATLAB/Simulink version R2024b was utilized to model, simulate, and analyze the power flow in both the pico-grid and nano-grid under different operating conditions. [ABSTRACT FROM AUTHOR]

The utilization of Harris Hawks Optimization (HHO) for Multi-Objective Optimal Power Flow (MaO-OPF) challenges presented in this paper is both novel and compelling, as this approach has not been previously applied to these types of optimization problems. HHO, which shares characteristics with ant behavior, demonstrates significant strength in addressing high-dimensional, nonlinear optimization issues within power systems. In this study, HHO is implemented on an IEEE 30-bus power system, optimizing six competing objectives: minimizing total fuel cost, emissions, active power loss, reactive power loss, reducing voltage deviation, and enhancing voltage steady state. The effectiveness of HHO is assessed by comparing its performance to two alternative methods, MOEA/D-DRA and NSGA-III. Experimental results reveal that solutions derived from HHO exhibit superior convergence, enhanced diversity maintenance, and higher quality Pareto-optimal solutions compared to the MOEA/D trail algorithms. The research breaks new ground in the application of the Harris Hawks Optimization (HHO) algorithm to the Multi-Objective Optimal Power Flow (MaO-OPF) problem. The restructuring not only incorporates self-adaptive constraint-handling techniques and dynamic exploration exploitation strategies, but also addresses the more pressing requirements of modern power systems with even better convergence, and both sequential and global computational efficiency than existing skill. This approach proves to be a powerful and effective solution for addressing the complex challenges associated with MaO, enabling power systems to manage multiple conflicting objectives more efficiently. [ABSTRACT FROM AUTHOR]

In this paper, the voltage regulation in power systems is addressed from the perspective of the modern paradigm of control logic supported by phasor measurement units. The information available from measurements is used to better adapt the regulation actions to the actual operation point of the system. The use of the online measurement data allows for identifying the sensitivity matrix and for improving the regulation performances with respect to the fast load variations that increasingly affect modern power systems. With the aim of estimating the sensitivity matrices, a preliminary action is necessary to reconstruct the phases of the network voltages, which are assumed not to be provided by the phasor measurement units. This allows for obtaining a model-free adaptive control method. It is then shown how the regulation problem can be formulated in terms of a linear quadratic Gaussian problem, properly considering the load modeling in terms of the stochastic Ornstein–Uhlenbeck process. This control strategy has the advantage of avoiding dangerous oscillations of power flows, as demonstrated through the results of some simulations on a classical test network. Particularly, the advantage of the proposed approach is shown in the presence of different levels of load disturbances. [ABSTRACT FROM AUTHOR]

The Optimal Power Flow (OPF) problem, as a critical component of power system operations, becomes increasingly difficult to solve due to the variability, intermittency, and unpredictability of renewable energy brought to the power system. Although traditional optimization techniques, such as stochastic and robust optimization approaches, can be leveraged to address the OPF problem, in the face of renewable energy uncertainty, i.e., the dynamic coefficients in the optimization model, their effectiveness in dealing with large-scale problems remains limited. As a result, deep learning techniques, such as neural networks, have recently been developed to improve computational efficiency in solving OPF problems with the utilization of data. However, the feasibility and optimality of the solution may not be guaranteed, and the system dynamics cannot be properly addressed as well. In this article we propose an optimization Model-Informed Generative Adversarial Network (MI-GAN) framework to solve OPF under uncertainty. The main contributions are summarized into three aspects: (i) to ensure feasibility and improve optimality of generated solutions, three important layers are proposed: feasibility filter layer, comparison layer, and gradient-guided layer; (ii) in the GAN-based framework, an efficient model-informed selector incorporating these three new layers is established; and (iii) a new recursive iteration algorithm is also proposed to improve solution optimality and handle the system dynamics. The numerical results on IEEE test systems show that the proposed method is very effective and promising. [ABSTRACT FROM AUTHOR]

Australia's National Electricity Market (NEM) has amongst the highest take-up rates of rooftop solar PV in the world. As with California, this has produced a distinctive load shape termed the "duck curve." The Queensland version is being principally driven by non-scheduled (i.e., uncontrolled) rooftop solar PV. When combined with inflexible coal plant, it leads to a "minimum load problem." In this article, we examine the feasibility of dispatch with ever-expanding rooftop solar PV resources in the NEM's Queensland region and minimal demand elasticity. We find episodes of intractable dispatch throughout the year with rising intensity in the winter and spring months. Furthermore, we find no ability to "export your way out of the problem" via larger interstate interconnectors because the same problem is emerging in the adjacent region at the same time. Resolution ultimately requires inflexible coal plant exit, and entry of flexible plant. JEL Classification: D25, D80, G32, L51, Q41 [ABSTRACT FROM AUTHOR]

Model of theoretical description of a change in optical properties in near-surface layers due lightwave propagation along a parabolic graded-index film waveguide structure is proposed. Exact analytical solution of the value boundary problem formulated, which describe the stationary eigenmodes of the waveguide structure, are found. The modes correspond to a discrete spectrum of values of the effective refractive index determined by the optical and geometrical parameters of the waveguide system. The field amplitude enlarges and the penetration depth of the field decreases with an increase in the longitudinal wave numbed. The intensity of the light flux in thicker films in the center of the film is higher than near its surfaces. The equation is derived, the use of which makes it possible to establish the adequacy of the choice of a parabolic profile for real semiconductor crystals for a given film thickness and wavelength. Analytical expressions of the total power flow of the lightwave along the waveguide structure are obtained. The total power flow enlarges with an increase in the film thickness for modes of all orders. The minimum of dependence of the flow on the wave number is observed. The value of the power flow minimum decreases with increasing order of the mode and goes into saturation. Possibility to choose a thickness of the parabolic graded-index film is shown, at which the power of the transferred light flux will be concentrated in a certain region of the waveguide structure. [ABSTRACT FROM AUTHOR]

In order to improve energy efficiency, reduce dependence on fossil fuels, and enhance the sustainable development capability of the power system, this paper proposes a virtual grid and thermal power joint peak shaving optimization model based on the power Internet of Things. Establish an objective function to optimize the charging and discharging loss cost of energy storage equipment, the interruption compensation cost of interruptible loads, and the operating cost of thermal power units, in order to improve the optimization scheduling effect of the power system. Set power balance constraints, interruptible load constraints, energy storage constraints, and power constraints for thermal power units to maximize their operational efficiency, and construct a virtual grid and thermal power joint peak shaving optimization model. Using ant colony algorithm to solve the model and obtain the optimal peak shaving value that meets the development needs of the power system. The simulation results show that the mean r2 of our method is 0.97, and the average RMSE is 0.17. It has been proven that the model has good joint shaving optimization ability and high optimization accuracy. It can ensure the output of thermal power units and lower the peak shaving pressure of the power system, thereby promoting the sustainable development and stable operation of the power system. [ABSTRACT FROM AUTHOR]

Due to increased energy consumption in upcoming years, the power system needs to be expanded to meet suitable technical conditions. The primary requirement is to gain accurate information about consumption growth in the planning horizon, which can be obtained via forecast studies. Since renewable sources can grow beside the demand, the accurate prediction should consider simultaneous changes in supply and demand in the future. In this paper, a reliability-constrained transmission expansion planning (RCTEP) is proposed. It simultaneously is based on the load forecasting and renewable sources production, named the net power demand forecasting technique (NPDFT). NPDFT consists of a time series-based logistic method, which forecasts loads at planning years. RES generation forecasting forecasts the following year's generation by an estimated coefficient. RCTEP minimizes the summation of the planning, operation, and reliability cost so that it is limited to the AC optimal power flow equations, planning constraints, and reliability limitations for N – 1 contingency. Then, the stochastic programming based on the Monte Carlo Simulation and the simultaneous backward approach models the uncertainties of the load, RES power, and availability of network equipment. This problem is solved by the hybrid algorithm of grey wolf optimization and training and learning optimization algorithm to achieve the securable optimal solution with a low standard deviation. Generally, this paper contributes to predicting the net power demand, simultaneous modeling of operation, reliability, and economic indices, besides using hybrid algorithms to solve the defined problem. Finally, this strategy is implemented on the 3-bus, 30-bus, and 118-bus transmission networks in MATLAB software. The numerical results confirm the capabilities of the proposed method in improving network operation and reliability indices. Higher reliability can be found for the network by defining a desirable penalty price. Also, operation indices, such as voltage profile and power loss, increase more than 10% under these conditions. [ABSTRACT FROM AUTHOR]

Penetration of distributed generators (DGs) to the grid is transcending because of the importance given to green energy. Microgrids are gaining attention because of DGs and local control to reduce peak demand on the grid. Power flow analysis in microgrids must be considered while expanding the microgrids. Even though the conventional methods for power flow analysis apply to grid-connected mode, they cannot be used for an islanded mode of microgrid operation. Many modifications to the existing approach were proposed in the literature such as no slack bus, variable system frequency, and droop-controlled generators. A low-voltage microgrid of short distance which is for small communities is considered in the work. For such transmission lines, the resistance will be more than the line reactance. This paper focuses on modifying the conventional Gauss–Seidel method for the power flow analysis in low-voltage short transmission islanded microgrid. The power flow equations are modified considering there is no slack bus, and DG models are formulated for low-voltage, short transmission networks with droop control. The effectiveness of these considerations is illustrated by conducting simulation studies on a six-bus network and its effect on system frequency, real, and reactive power losses are also analyzed. The results obtained are compared with the existing results in the latest literature in which optimization techniques were used for droop coefficients calculation, and it is found that in the proposed approach, the real power losses are reduced by 2 kW without using any optimization algorithm for calculating the droop coefficients. Hence, the proposed approach is a good choice for power flow analysis in low-voltage microgrids for smaller communities. [ABSTRACT FROM AUTHOR]

Researching cluster partitioning and adjustment methods is essential for effectively implementing cluster control strategies and ensuring the safe operation of power grids amid challenges like reverse power flow and voltage violations resulting from large-scale distributed photovoltaic grid integration. The paper comprehensively evaluates factors including electrical distance, supply-demand balance, and power transmission. It introduces a method for partitioning and dynamically adjusting distributed photovoltaic clusters, based on an improved adaptive genetic algorithm (AGA). Firstly, a comprehensive performance index is introduced based on modularity, incorporating intra-cluster power supply rate and inter-cluster power transmission. Next, an unweighted adjacency matrix is employed to encode chromosomes, and an adaptive optimization parameter adjustment strategy is introduced to enhance the AGA, ensuring both direct node connectivity within clusters and improved global solution performance during optimization. By integrating these comprehensive indicators with AGA, a cluster partitioning optimization model is formulated based on the comprehensive indicator system. The IEEE 33-node system is utilized for cluster partitioning simulation analysis with this model. The outcomes demonstrate that, in contrast to the single modularity index-based cluster partitioning approach, the proposed comprehensive indicator method enhances the intra-cluster active and reactive power supply rates by approximately 20.34% and 28.61%, respectively, while decreasing inter-cluster power transmission by roughly 24.98%. Furthermore, in scenarios of insufficient photovoltaic power output, the cluster scheme, after dynamic strategy adjustment, notably mitigates system voltage fluctuations and network losses. [ABSTRACT FROM AUTHOR]

This study uses advanced metaheuristic algorithms to solve energy-saving problems in the loop distribution network. An initiative energy management system (EMS) is suggested to deliver optimal commands to the loop power controller (LPC) whose operation is optimized by combining a metaheuristic algorithm with a ladder iterative technique. Here, the performance of state-of-the-art metaheuristic algorithms applied in the proposed EMS–LPC solution is compared and evaluated by simulation in a real-world case study. Simulation results show that all metaheuristic algorithms meet the optimization objective of reducing distribution loss in which the artificial ecosystem-based optimization (AEO) algorithm outperforms with both the lowest optimum value and the fastest convergence time. Consequently, the proposed EMS–LPC method results in a daily energy savings of 18% in comparison with the base case. Then, the proposed solution has potential for real-time applications to save grid power and reduce operating expenses due to the perfect performance of the suggested EMS–LPC approach. [ABSTRACT FROM AUTHOR]

The power system outlook has been going through a swift transition with the growing demand and expansion of infrastructure making the overall system more vulnerable to load changes. The sensitivity of electrical quantities varies in a direct proportion to the network size and affects the system performance determined by voltage levels, power factor (PF) and losses. This paper deals with tuning bus PF using STATCOM by partial reactive power injection based on new schemes of phase modulation and amplitude modulation for a standalone and interconnected network. For a standalone network, tuning of PF has been demonstrated as a test case using both open-loop and closed-loop designs followed by comprehensive mathematical model and an analogical correlation. Based on the benchmark set for the standalone network with both modulation schemes, PF control is extended at bus level using multiple closed-loop STATCOMs in IEEE 9 Bus system. The primary objective of this research is the voltage correction by maintaining specific PFs at PQ buses whose values are evaluated by particle swarm optimization algorithm. It is concluded that STATCOM-controlled PF tuning at PQ buses has indirectly corrected under and overvoltages leading to an improvement in objective function from 0.9849 to 0.9915. [ABSTRACT FROM AUTHOR]

Inserting interline dc power flow controllers (IDC-PFCs) promote the control flexibility of the DC power flow in meshed voltage source converter (VSC)-based high voltage direct current (HVDC) grids. Moreover, the steady-state security of the VSC-HVDC grids can be enhanced significantly when the IDC-PFCs are optimally placed and tuned. Therefore, it is proposed to apply minimum spanning tree graph theory to specify safe subgraph and unsafe subgraphs (which are prone to getting overloaded) of the VSC-HVDC grids and provide graphical insights on the static security conditions. The concept of the current variation index (CVI) is introduced to find the optimal locations of the IDC-PFCs within the identified unsafe subgraphs with maximized current alteration capability. The location with the highest value of CVI is considered the optimal placement scenario. As the focus would be on unsafe subgraphs, the optimal placement process would be done with the minimum computational burden. Then, static mixed-integer power injection models are proposed to model multiple optimally-placed IDC-PFCs and develop mixed-integer security-constraint dc optimal power flow (MI-SC DC-OPF) formulations. The proposed MI-SC DC-OPF would simultaneously activate the minimum required number of most effective optimally-placed IDC-PFCs and specify optimum references for them according to the operating point of the VSC-HVDC grid. The effective performances of the proposed placement strategy and selective/optimal operation method are evaluated on CIGRE B4 and IEEE 57-bus VSC-HVDC girds by performing static analysis. [ABSTRACT FROM AUTHOR]

The paper presents a semiempirical method to estimate the rate of scour of earth materials, supplementing existing empirical and semiempirical methods that only quantify maximum scour depth. The premise is that the rate of scour equals the rate of removal of earth material that has already been dislodged by flowing water. A universal relationship between effective energy and the amount of dislodged material removed over a certain period is explored. Energy is defined as the product of stream power and flow duration and effective energy is the energy remaining after the energy required to dislodge the earth material has been consumed. An energy-based equation based on fundamental principles of physics is derived and its potential universality illustrated using laboratory and case study data. Analysis of volumes of gneiss scoured from the Kariba Dam plunge pool over a period of 20 years and analysis of experimental rate of scour data of soils occurring within minutes confirm the essential character of the equation. The ease by which the equation can be applied is demonstrated by an example calculation estimating the rate of scour at a bridge pier. Practical Applications: Designing hydraulic structures to withstand the maximum scour depth can be unnecessarily costly if the time required to reach that depth exceeds the design life of the structure. Most of the empirical methods available to practicing engineers only estimate maximum scour depth and not the rate of scour, thereby hampering efforts to optimize designs. Implementing the energy-based equation presented in this paper offers a solution to this problem by following a two-step procedure. The first step is to estimate the maximum scour depth and the associated volume of material to be removed. This is done using existing empirical methods. Once the volume of material to be removed is known, the second step entails quantifying the rate of removal of the dislodged material. The principal objective of this paper is to enable the second step by offering an equation for calculating the rate of scour. The ease of application of this two-step procedure is illustrated by presenting an example calculation of scour at a bridge pier. [ABSTRACT FROM AUTHOR]

• An off-grid photovoltaic power generation energy storage refrigerator system was designed and constructed. • The system's cooling performance and off-grid operation were tested. • Daily power generation was found to be affected by irradiance, photovoltaic module cleanliness, ambient temperature, sunlight hours, and battery voltage. • Daily power generation is significantly affected by irradiance(r = 0.49) and battery voltage(r = 0.64). • The refrigerator's BCR is 1.629, LCOE is 0.495 CNY/kWh, NPV is 3,709.954 CNY, and IRR is 8.66 %. With the rapid advancement of photovoltaic and energy storage technologies, photovoltaic energy storage refrigerator systems have gained significant attention as an innovative energy solution. This paper designs and constructs an off-grid photovoltaic power generation energy storage refrigerator system, and evaluates its economic viability in practical environments. By measuring indoor temperature, refrigerator internal temperature, irradiance, and daily power generation, the paper analyzes system operating parameters such as refrigerator cooling rate and power supply mode, and studies the system's refrigeration performance, off-grid operation capability, and factors affecting daily power generation. Utilizing economic indicators such as benefit-cost ratio, levelized cost of electricity, investment dynamic payback process, net present value, and internal rate of return, the economic viability of the system is assessed. Results indicate that the system meets refrigeration performance requirements, maintaining a uniform temperature distribution and extended off-grid operation capability. Daily power generation is influenced by weather conditions, seasons, and all electrical loads in the system. In the Dalian region of China, the system demonstrates good economic viability, enabling investment recovery and profitability in a relatively short period. This system has broad market prospects in areas with abundant solar resources or high demand for refrigerator usage. [ABSTRACT FROM AUTHOR]