Forward-backward Sweep Research Articles

Three‐phase four‐wire power flow solution for multi‐grounded distribution networks with non‐bolted grounding

AbstractThis study proposes a direct three‐phase four‐wire power flow method to accurately analyse the neutral line and multiple grounding characteristics. In particular, the proposed grounding impedance building‐based solution method was used to analyse the neutral grounding impedance in power flow studies based on the slack bus grounding impedance. The accuracy of the proposed method was verified using a neutral‐to‐earth voltage test system. IEEE 13‐bus and 123‐bus test systems were used to compare the advantages and disadvantages of the proposed method. Compared to the current injection full Newton and forward–backward sweep methods, the proposed method achieves a significant reduction in iteration numbers of up to 76.92% and 77.78%, respectively. For different grounding scenarios, stable convergence characteristics were exhibited by the proposed method after six to seven iterations.

Voltage enhancement and loss minimization in a radial network through optimal capacitor sizing and placement based on Crow Search Algorithm

In power systems, the distribution network is crucial as it serves as the final stage in delivering energy from generation plants to end users. However, reactive power demand from consumers can create challenges such as low power factor, voltage drops, and increased power losses depending on the distribution system used. This study aims to enhance the performance of radial distribution networks (RDNs) by optimizing capacitor placement and sizing based on the Crow Search Algorithm (CSA). Additionally, the study addresses the Optimal Power Flow (OPF) within the network by employing the Backward/Forward Sweep (BFS) method. The study accesses CSA’s effectiveness compared to other metaheuristic optimization techniques through simulation. The simulation results showed that the Voltage Stability Index improved from 0.61 for base case to 0.68 pu with CSA, compared to 0.66 for Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), Genetic Algorithm (GA), and Teacher Learner Based Optimization (TLBO and 0.67 for Invasive Weed Optimization (IWO). CSA also achieved a 30.41 % reduction in active power losses, outperforming PSO, ABC, GA, and TLBO having 26.61 %, and IWO at 24.92 %. Additionally, application of CSA led to a 29.33 % reduction in reactive power losses, compared to 21.91 % for PSO, ABC, GA, and TLBO, 18.2 % for IWO. In the simulated IEEE 33 bus Radial Distribution Network (RDN) topology, the lowest bus voltage at bus 18 increased from 0.8820 in the base case to 0.9080 with CSA, indicating a 32.9 % improvement in voltage deviation. Furthermore, the optimization resulted in a significant reduction of 3.841 pu in capacitor cost, demonstrating CSA’s efficiency in both technical and economic aspects. CSA not only showed favorable results in minimizing power losses and improving voltage profiles but also provided substantial cost savings in capacitor implementation, making it a robust and cost-effective solution for enhancing RDN performance.

Cost-effective and optimal control analysis for mitigation strategy to chocolate spot disease of faba bean

Faba bean is one of the most important grown plants worldwide for human and animal. Despite its various importance, the productivity of faba bean has been constrained by several biotic and abiotic factors. Many faba bean pathogens have been reported so far, of which the most important yield limiting disease is Chocolate Spot Disease (Botrytis fabae). The dynamics of disease transmission and decision-making processes for intervention programs for disease control are now better understood through the use of mathematical modeling. In this paper a deterministic mathematical model for Chocolate Spot disease (CSD) on faba bean plant with an optimal control model was developed and analyzed to examine the best strategy in controlling CSD. The optimal control model is developed with three control interventions, namely prevention (u1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u_{1}$$\\end{document}), quarantine (u2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u_{2}$$\\end{document}) and chemical control (u3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u_{3}$$\\end{document}). The Pontryagin’€™s maximum principle isused to derive the Hamiltonian, the adjoint variables, the characterization of the controls and the optimality system. A cost-effective approach is chosen from a set of possible integrated strategies using the incremental cost-effectiveness ratio (ICER). The forward-backward sweep iterative approach is used to run numerical simulations. We obtained the Hamiltonian, the adjoint variables, the characterization of the controls and the optimality system. The numerical results demonstrate that each integrated strategy can reduce the diseases within the specified period. However due to limited resources, an integrated strategy prevention and uprooting was found to be a best cost-effective strategy to combat CSD. Therefore, attention should be given for the integrated cost-effective and environmentally eco-friendly strategy by stake holders and policy makers to control CSD and disseminate the integrated intervention to the farmers in order to fight the spread of CSD in the Faba bean population and produce the expected yield from the field.

Modeling environmental-born melioidosis dynamics with recurrence: An application of optimal control

Melioidosis is a significant health problem in tropical and subtropical regions, especially in Southeast Asia and Northern Australia. Recurrent melioidosis is a major obstacle to eliminating the disease from the community in these nations. This work aims to propose and analyze a human melioidosis model with recurrent phenomena and an optimal control model by incorporating time-dependent control functions. The basic reproduction number (R0) of the uncontrolled model is derived using the method of the next-generation matrix. Using the construction of a Lyapunov functional, we present the global asymptotic dynamics of the autonomous model in the presence of recurrent for both disease-free and endemic equilibria. The global asymptotic stability of the model’s equilibria shows the absence of a backward bifurcation for the model in both cases, whether in the absence or presence of relapse. The sensitivity analysis aims to identify the parameters that have the most significant impact on the model’s dynamics. Furthermore, qualitative analysis of the model’s global dynamics and the changing effect of the most influential parameters on R0 are supported by numerical experiments, with the results being illustrated graphically. The model with time-dependent controls is analyzed using optimal control theory to assess the impact of various intervention strategies on the spread of the epidemic. The numerical results of the optimality system are carried out using the Forward–Backward Sweep method in Matlab. We also conducted a cost-effectiveness analysis using two approaches: the average cost-effectiveness ratio and the incremental cost-effectiveness ratio.

Fast power flow calculation for distribution networks based on graph models and hierarchical forward-backward sweep parallel algorithm

IntroductionIn response to the issues of complexity and low efficiency in line loss calculations for actual distribution networks, this paper proposes a fast power flow calculation method for distribution networks based on Neo4j graph models and a hierarchical forward-backward sweep parallel algorithm.MethodsFirstly, Neo4j is used to describe the distribution network structure as a simple graph model composed of nodes and edges. Secondly, a hierarchical forward-backward sweep method is adopted to perform power flow calculations on the graph model network. Finally, during the computation of distribution network subgraphs, the method is combined with the Bulk Synchronous Parallel (BSP) computing model to quickly complete the line loss analysis.Results and DiscussionResults from the IEEE 33-node test system demonstrate that the proposed method can calculate network losses quickly and accurately, with a computation time of only 0.175s, which is lower than the MySQL and Neo4j graph methods that do not consider hierarchical parallel computing.

Strategic DG placement and sizing in developing nations' power systems using ISNT and modified forward-backward sweep

The power sector in many developing nations faces challenges in meeting consumers’ demands for a reliable electricity supply due to increased load demand, primarily driven by population growth. Urban areas receive 24 h power, while extensive losses within the system limit coverage. Setting up centralised stations offers a temporary solution, but the capacity of the ageing transmission lines is uncertain. This study proposes integrating distributed generators (DG) into the power system, using Inherent Structural Network Topology (ISNT) for DG siting and a modified Forward-Backward Sweep model for sizing. Voltage Stability Index (VPI) assesses network stability. The model considers voltage profile and line losses, optimizing DG sites and sizes. Results demonstrate the model’s efficacy, offering insights for optimal DG planning to minimize losses and enhance voltage profiles. The study informs power system engineers for future planning, aiding decisions on DG location and size, potentially reducing line losses and improving voltage profiles, thus assisting in network upgrades or expansions.

Nonstandard finite difference schemes for some epidemic optimal control problems

We construct and analyse nonstandard finite difference (NSFD) schemes for two epidemic optimal control problems. Firstly, we consider the well-known MSEIR system that can be used to model childhood diseases such as the measles, with the vaccination as a control intervention. The second optimal control problem is related to the 2014–2016 West Africa Ebola Virus Disease (EVD) outbreak, that came with the unprecedented challenge of the disease spreading simultaneously in three different countries, namely Guinea, Liberia and Sierra Leone, where it was difficult to control the considerable migrations and travels of people inbound and outbound. We develop an extended SEIRD metapopulation model modified by the addition of compartments of quarantined and isolated individuals. The control parameters are the exit screening of travelers and the vaccination of the susceptible individuals. For the two optimal control problems, we provide the results on: (i) the (global) stability of the disease-free and/or endemic equilibria of the state variable systems; (ii) the positivity and boundedness of solutions of the state variables systems; (iii) the existence, uniqueness and characterization of the optimal control solutions that minimizes the cost functional. On the other hand: (iv) we design Euler-based nonstandard finite difference versions of the Forward-Backward Sweep Method (NSFD-FBSM) that are dynamically consistent with the state variable systems; (v) we provide numerical simulations that support the theory and show the superiority of the nonstandard approach over the classical FBSM. The numerical simulations suggest that significantly increasing the coverage of the vaccine with its implementation for adults as well is essential if the recurrence of measles outbreaks is to be stopped in South Africa. They also show that the optimal control vaccination for the 2014-2016 EVD is more efficient than the exit screening intervention.

Sensitivity assessment of optimal control strategies and cost-effectiveness analysis of a novel Candida Auris environmental transmission model in intensive care facilities

Candida Auris is an emerging fungal pathogen flagged by CDC as a serious global health threat among nosocomial infections in the recent times. As an evolving pathogen that often goes misidentified or unidentified under standard laboratory tests, it has the ability to cause fatal infections among the target population involving patients with serious medical conditions admitted to intensive care facilities, due to its capacity to resist anti-fungal treatment and the ability to persist in the hospital environment for long periods. The subject of this paper is to develop a deterministic model to study the transmission nature of Candida Auris wherein measures like apt admission screening methods with weekly screening follow-ups, transmission prevention, proper treatment protocols and environmental disinfection procedures are introduced as constant mitigating controls into the model initially which are later redefined as variable control functions during the optimal control analysis. The theory of optimal control implemented into the model helps us to understand the sensitivity of each control strategy upon the behaviour of each state variable. Further, cost-effectiveness analysis is rigorously conducted using incremental cost-effectiveness ratio (ICER) to identify and rank the control strategies involved based on their economic efficiency. Numerical simulation for the optimal control analysis is performed in MATLAB using the Forward–Backward Sweep Method and the findings are illustrated graphically.

Low-carbon oriented planning of shared photovoltaics and energy storage systems in distribution networks via carbon emission flow tracing

With the targets of carbon peaking and carbon neutrality, carbon emission reduction measures have become significant issues in new-type power systems. Distribution networks (DNs), which multiple power sources and flexible loads access to, play an essential role in exploiting the potential of reducing carbon emissions on the demand side. To achieve a global carbon emission reduction considering the carbon quota of each customer, shared photovoltaics (PVs) and energy storage systems (ESSs) are allocated with a centralized calculation and optimization conducted by DNs. To solve two key points in demand-side planning of shared PVs and ESSs in distribution networks, i.e., the accuracy of carbon emission flow (CEF) calculation and carbon quota-oriented optimization planning, this paper proposes a low-carbon oriented planning method for shared PVs and ESSs via CEF tracing. Firstly, a novel CEF calculation method is proposed based on the forward current sweep and backward voltage sweep algorithm, which considers the tracing of reactive power and power losses. Next, carbon emission index and economic index of allocating shared PVs and ESSs are defined. Subsequently, a bi-level optimization model is presented, considering the excess carbon emissions of each load based on carbon accounting and carbon quotas. Finally, the superiority of the proposed method is verified through a modified IEEE 33-node distribution network, and the effects of various investment constraints and carbon quotas are discussed.

Modeling the transmission dynamics of the co-infection of COVID-19 and Monkeypox diseases with optimal control strategies and cost–benefit analysis

This study explores a mathematical model in continuous time, elucidating the transmission dynamics of the co-infection of COVID-19 and Monkeypox. We implemented an optimal control strategy that includes adherence to wearing nose/face masks, practicing social distancing, employing rodenticides, and getting vaccinated against these lethal illnesses. The goal is to reduce their spread among people, consequently lessening their impact on the human population. Utilizing the discrete-time Pontryagin maximum principle, we determined optimal control strategies through an iterative approach to solve the optimal system. By utilizing the MATLAB optimization toolbox with the Runge–Kutta forward–backward sweep technique, we performed numerical simulations to demonstrate how these control parameters impact different sections of the human population, including both infected and uninfected compartments. We conducted a comprehensive cost–benefit analysis to identify the control measures that would produce the best outcome in minimizing both the expenses and the incidence of co-infection cases involving COVID-19 and Monkeypox diseases. Our analyses indicated that intensifying the utilization of nose/facemasks, rodenticides, personal protective equipments (PPEs) in Monkeypox treatment facilities, immunization, and implementing social distancing measures can notably diminish the prevalence of COVID-19, Monkeypox, and their concurrent infections among the human populace.

Backward–forward sweep inverse power flow for distribution line parameters estimation with metering data

AbstractThe transition towards the smart grid requires better information on the electrical networks at the distribution system level. Information about electrical line parameters is a critical part of such information. An algorithm for estimating electric line parameters of medium‐voltage distribution networks is proposed. The algorithm relies upon active/reactive power and nodal voltage magnitude data from advanced metering infrastructure and combines an Ordinary Least Squares estimator with the classical Backward–Forward Sweep load‐flow method to iteratively estimate the admittance parameters of the electrical network components. The algorithm is proposed to be applied to balanced loading situations of networks where zero‐injection non‐monitored nodes may exist. Simulations using the IEEE 33‐bus system are used to demonstrate the effectiveness of the method under different loading situations and measurement noise levels.

Optimal control and bifurcation analysis of a delayed fractional-order epidemic model for the COVID-19 pandemic

In this paper, a delayed fractional-order epidemic model with general incidence rate and incubation period is proposed for the Corona Virus Disease 2019 (COVID-19) pandemic. The corresponding sufficient conditions are established to analyze the existence and stability of disease-free equilibrium and endemic equilibrium of the proposed model. The conditions for the existence of Hopf bifurcation are obtained by selecting the time delay as the bifurcation parameter. The control strategies for the COVID-19 pandemic are designed, and the corresponding delay fractional order optimal control problem (DFOCP) is analyzed based on the generalized Euler–Lagrange equation. The parameters of the model are identified based on the data of multiple types of the COVID-19 pandemic. Further, the effectiveness of the model in describing the trend of the COVID-19 pandemic is verified. Based on the results of parameter identification, the influence of incubation period on the COVID-19 pandemic is discussed. The forward–backward sweep method (FBSM) is adopted to numerically solve DFOCP, and the control effects under different control measures are analyzed.

RUNGE–KUTTA LIKE METHOD FOR THE SOLUTION OF OPTIMAL CONTROL MODEL OF REAL INVESTMENT AND FISH MANAGEMENT

This study develops the Runge-Kutta Like Method (RKLM), which uses Pontryagin's principle to solve optimal control problems numerically using forward-backward sweep methods. It is based on the Patade and Bhalekar methodology. The RKLM's stability properties and its convergence are examined. The Forward-backward sweep algorithm and the RKLM algorithm are implemented using MATLAB code. Physical optimum control problems are solved with the RKLM. The first problem's conclusion demonstrates that, when investment declines, the capital first grow to boost production before it depreciates. The outcome of the second problem demonstrates that a larger weight parameter causes the harvesting rate to reach zero more quickly and the total fish mass to reach its maximum level more quickly. The findings obtained demonstrate the effectiveness of using RKLM in conjunction with forward-backward sweep methods to solve optimal control problems.

Iterative method for the numerical solution of optimal control model for mosquito and insecticide

A linear multistep method is transformed into an iterative method based on Patade and Bhalekar's technique for the numerical solution of the optimal control problem modeled for mosquito and insecticide management using forward-backward sweep methods via Pontryagin's principle. Stability and convergence analysis of the iterative method are carried out, and it is found to be stable, convergent, and of order four. Results obtained by the method clearly show that the population of mosquitoes can be minimized to a large extent using the new iterative method while reducing the harmful effects of the insecticide, subsequently reducing the spread of malaria.

Optimal Control of Transmission Dynamics of Meningitis Disease with Vaccination, Campaign, and Treatment Factors

Meningitis disease is an inflammation of the membranes that protect the brain and spinal cord. This disease can be fatal to life-threatening because symptoms can appear suddenly. Meningitis is also common in infants and young children and can cause complications if not treated promptly. To prevent infection of susceptible compartment and to speed recovery of infected compartments, vaccination, campaign, and treatment are needed to prevent the spread of the disease or at least reduce the number of carrier and infected individuals. Therefore, we propose a model of meningitis disease spread consisting of five compartments, namely susceptible, carrier, infected with and without symptoms, and recovered. Vaccination, campaign and treatment are included in the model mechanism as controls. This study aims to observe the effectiveness of vaccination, campaign, and treatment in inhibiting the spread of the disease and accelerating the recovery of infected individuals. The Pontryagin minimum principle is followed to derive the optimal control problem. Numerical simulation using Runge-Kutta of order four scheme with the forward-backward sweep approach is applied to visualize the curves of state and control variables. From the numerical simulations, it is found that vaccination, campaign, and treatment are reasonable to apply in order to bridle meningitis disease from the population.

Optimal Rotation Age in Fast Growing Plantations: A Dynamical Optimization Problem.

Forest plantations are economically and environmentally relevant, as they play a key role in timber production and carbon capture. It is expected that the future climate change scenario affects forest growth and modify the rotation age for timber production. However, mathematical models on the effect of climate change on the rotation age for timber production remain still limited. We aim to determine the optimal rotation age that maximizes the net economic benefit of timber volume in a negative scenario from the climatic point of view. For this purpose, a bioeconomic optimal control problem was formulated from a system of Ordinary Differential Equations (ODEs) governed by the state variables live biomass volume, intrinsic growth rate, and area affected by fire. Then, four control variables were associated to the system, representing forest management activities, which are felling, thinning, reforestation, and fire prevention. The existence of optimal control solutions was demonstrated, and the solutions of the optimal control problem were also characterized using Pontryagin's Maximum Principle. The solutions of the model were approximated numerically by the Forward-Backward Sweep method. To validate the model, two scenarios were considered: a realistic scenario that represents current forestry activities for the exotic species Pinus radiata D. Don, and a pessimistic scenario, which considers environmental conditions conducive to a higher occurrence of forest fires. The optimal solution that maximizes the net benefit of timber volume consists of a strategy that considers all four control variables simultaneously. For felling and thinning, regardless of the scenario considered, the optimal strategy is to spend on both activities depending on the amount of biomass in the field. Similarly, for reforestation, the optimal strategy is to spend as the forest is harvested. In the case of fire prevention, in the realistic scenario, the optimal strategy consists of reducing the expenses in fire prevention because the incidence of fires is lower, whereas in the pessimistic scenario, the opposite is true. It is concluded that the optimal rotation age that maximizes the net economic benefit of timber volume in P. radiata plantations is 24 and 19 years for the realistic and pessimistic scenarios, respectively. This corroborates that the presence of fires influences the determination of the optimal rotation age, and as a consequence, the net economic benefit.

Optimal Social and Vaccination Control in the SVIR Epidemic Model

In this paper, we introduce an approach to the management of infectious disease diffusion through the formulation of a controlled compartmental SVIR (susceptible–vaccinated–infected–recovered) model. We consider a cost functional encompassing three distinct yet interconnected dimensions: the social cost, the disease cost, and the vaccination cost. The proposed model addresses the pressing need for optimized strategies in disease containment, incorporating both social control measures and vaccination campaigns. Through the utilization of advanced control theory, we identify optimal control strategies that mitigate disease proliferation while considering the inherent trade-offs among social interventions and vaccination efforts. Finally, we present the results from a simulation-based study employing a numerical implementation of the optimally controlled system through the forward–backward sweep algorithm. The baseline model considered incorporates parameters representative of typical values observed during the recent pandemic outbreak.

Bi-Basis Function Second Derivative Block Method for the Solution of Optimal Control Problems

This paper determines the state trajectory of a dynamic system over a period to optimize a given performance index. A one-step second derivative hybrid method based on the combination of Lucas and first Boubaker polynomials as basis functions is formulated for the solution of optimal control problems via the forward-backward sweep method. The technique is used to generate a set of hybrid schemes at selected grid and off-grid points with implementation in block form. The stability and convergence of the new method is discussed and the accuracy of the method is tested on some numerical examples. The results obtained correspond to a large extent with the results obtained by the exact solution. Bi-bases function, Block method, First Boubaker polynomials, Lucas polynomial, Optimal control problem

Impact of infectious density-induced additional screening and treatment saturation on COVID-19: Modeling and cost-effective optimal control

This study introduces a novel SI2HR model, where “I2” denotes two infectious classes representing asymptomatic and symptomatic infections, aiming to investigate and analyze the cost-effective optimal control measures for managing COVID-19. The model incorporates a novel concept of infectious density-induced additional screening (IDIAS) and accounts for treatment saturation. Furthermore, the model considers the possibility of reinfection and the loss of immunity in individuals who have previously recovered. To validate and calibrate the proposed model, real data from November–December 2022 in Hong Kong are utilized. The estimated parameters obtained from this calibration process are valuable for prediction purposes and facilitate further numerical simulations. An analysis of the model reveals that delays in screening, treatment, and quarantine contribute to an increase in the basic reproduction number R0, indicating a tendency towards endemicity. In particular, from the elasticity of R0, we deduce that normalized sensitivity indices of baseline screening rate (θ), quarantine rates (γ, αs), and treatment rate (α) are negative, which shows that delaying any of these may cause huge surge in R0, ultimately increases the disease burden. Further, by the contour plots, we note the two-parameter behavior of the infectives (both symptomatic and asymptomatic). Expanding upon the model analysis, an optimal control problem (OCP) is formulated, incorporating three control measures: precautionary interventions, boosted IDIAS, and boosted treatment. The Pontryagin's maximum principle and the forward-backward sweep method are employed to solve the OCP. The numerical simulations highlight that enhanced screening and treatment, coupled with preventive interventions, can effectively contribute to sustainable disease control. However, the cost-effectiveness analysis (CEA) conducted in this study suggests that boosting IDIAS alone is the most economically efficient and cost-effective approach compared to other strategies. The CEA results provide valuable insights into identifying specific strategies based on their cost-efficacy ranking, which can be implemented to maximize impact while minimizing costs. Overall, this research offers significant insights for policymakers and healthcare professionals, providing a framework to optimize control efforts for COVID-19 or similar epidemics in the future.

Optimal control of red palm weevil model incorporating sterile insect technique, mechanical injection, and pheromone traps

The red palm weevil is one of the most dangerous pests affecting date palm trees in the Gulf region and the Middle East. This paper investigates the control of the red palm weevil (RPW) in date palms using several techniques, namely stem injection, sex pheromone traps, and the Sterile Insect Technique. A mathematical model describing the spread of the red palm weevil is presented, and the boundedness of the solution for the RPW system is studied. The conditions for local stability, forward bifurcation, and Hopf bifurcation are also obtained. Additionally, this research highlights the significance of optimal control in managing RPW and simulates the model using the Forward-Backward Sweep numerical method. It is observed that the parameters of the sterile insect technique, the pheromone trap, and the mechanical injection play important roles in controlling the RPW. Mechanical Injection may be more effective in controlling the palm weevil compared to the other two methods.