Forward-backward Sweep Research Articles

An improved wild horse optimization algorithm for reliability based optimal DG planning of radial distribution networks

This paper introduces a novel technique for optimal distribution system (DS) planning with distributed generation (DG) systems. It is being done to see how active and reactive power injections affect the system’s voltage profile and energy losses. DG penetration in the power systems is one approach that has several advantages such as peak savings, loss lessening, voltage profile amelioration. It also intends to increase system reliability, stability, and security. The main goal of optimal distributed generation (ODG) is a guarantee to achieve the benefits mentioned previously to increase the overall system efficiency. For extremely vast and complicated systems, analytical approaches are not suitable and insufficient. Therefore, several meta-heuristic techniques are favored to obtain better performance from were convergence and accuracy for large systems. In this paper, an Improved Wild Horse Optimization algorithm (IWHO) is proposed as a novel metaheuristic method for solving optimization issues in electrical power systems. IWHO is devised with inspirations from the social life behavior of wild horses. The suggested method is based on the horse’s decency. To assess the efficacy of the IWHO, it is implemented on the 23 benchmark functions Reliability amelioration is the most things superb as a result of DGs incorporation. Thus, in this research, a customer-side reliability appraisal in the DS that having a DG unit was carried out by a Monte Carlo Simulation (MCS) approach to construct an artificial history for each ingredient across simulation duration. For load flow calculations, the backward Forward Sweep (BFS) technique has been employed as a simulation tool to assess the network performance considering the power handling restrictions. The proposed IWHO method has been measured on IEEE 33 69 and 119 buses to ascertain the network performing in the presence of the optimal DG and the potential benefits of the suggested technique for enhancing the tools used by operators and planners to maintain the system reliability and efficiency. The results proved that IWHO is an optimization method with lofty performance regarding the exploration–exploitation balance and convergence speed, as it successfully handles complicated problems.

On Characterization of Optimal Control Model of Whooping Cough

Whooping cough is a vaccine avoidable public health problem which is caused by bacterium Bordetella Pertussis and it is a highly contagious disease of the respiratory system. In this paper, an SIR epidemiological model of whooping cough with optimal control strategy was formulated to control the transmission. The model was characterized to obtain the disease free and the endemic equilibrium points. Finally, the simulation was carried out using the Forward-backward sweep method by incorporating the Runge Kutta method to check the validity and the result obtained was an improvement over the existing results.

A two-stage method for optimal placement of distributed generation units and capacitors in distribution systems

This paper proposes a two-stage procedure to enhance the distribution system performance by determining the optimal sizes and locations of distributed generations (DGs) and capacitors considering single and multi-objective functions. In stage-1, two voltage sensitivity factors (VSFs) based on voltage deviation (VD), and voltage stability index (VSI) are proposed to reduce the search space (SS) by selecting the candidate buses for DGs and capacitors placement. In stage-2, the chaotic bat algorithm (CBA) is applied to find the optimal sizes and locations of DGs and capacitors, according to different objective functions (OFs) and system constraints. The considered OFs are real power loss reduction, total VD minimization, and total VSI maximization. The multi-OF, which aims to optimize these objectives simultaneously, is also considered. The load flow calculations are carried out using the backward/forward sweep (BFS) algorithm. The proposed methodology is evaluated and tested on small and large-scale standard test systems, namely 34-bus and 118-bus radial distribution systems, through different case studies. The numerical results obtained by the proposed procedure are compared with other methods in the literature to show the superiority of the proposed procedure for reducing the total real power loss and improving the voltage profile, especially at increasing the power system sizing.

Optimal Control of an HIV Model with Gene Therapy and Latency Reversing Agents

In this paper, we study the dynamics of HIV under gene therapy and latency reversing agents. While previous works modeled either the use of gene therapy or latency reversing agents, we consider the effects of a combination treatment strategy. For constant treatment controls, we establish global stability of the disease-free equilibrium and endemic equilibrium based on the value of R0. We then consider time-dependent controls and formulate an associated optimal control problem that emphasizes reduction of the latent reservoir. Characterizations for the optimal control profiles are found using Pontryagin’s Maximum Principle. We perform numerical simulations of the optimal control model using the fourth-order Runge–Kutta forward-backward sweep method. We find that a combination treatment of gene therapy with latency reversing agents provides better remission times than gene therapy alone. We conclude with a discussion of our findings and future work.

Modelling Infectiology of Bursal Disease in Chicks with Control Measures

This paper focuses on mathematical control of infectious bursal disease in chicks. The model boundedness and the control measures to reduce the spreads of the disease have well analytically examined. The theory of Pontryagin’s maximum principle used in analysing necessary conditions to combat the disease. Numerically, forward backward sweep method and fourth-order Runge-Kutta scheme using the forward solution of the state equations was applied. The outcome indicates that the combination of vaccination of chicks and environmental sanitation as the most cost-effectiveness strategy to combat the spread of IBD with limited resources. Therefore, IBD can be controlled if the poultry farmers will effectively apply vaccination of chicks and environmental sanitation.

Mobile Emergency Power Source Configuration Scheme considering Dynamic Characteristics of a Transportation Network

Recently, with the large scale of power grids and the increase in frequency of extreme weather, the safe and stable operation of power systems is facing great challenges. Therefore, mobile emergency power source (MEPS) are a promising and feasible way to deal with extreme weather and reduce economic losses. However, the current urban power grid and transportation network are closely coupled, and the congested traffic hinders the rapid configuration of MEPSs. Therefore, this paper proposes an MEPS configuration scheme considering real-time traffic conditions. Firstly, the dynamic road traffic index (DRTI) is defined, which can fully describe the dynamic characteristics of traffic. The wavelet neural network (WNN) is used to predict the traffic flow. Then, combined with the knowledge of graph theory, an A-Star algorithm (AS) is used to determine the optimal path. Secondly, the optimal installation location of MEPSs is determined by forward–backward sweep method in distribution network. Finally, the feasibility, accuracy, and time cost of the proposed method are verified by numerical simulations, which can meet the requirements of online application.

Pressure Retarded Osmosis Power Units Modelling for Power Flow Analysis of Electric Distribution Networks

Pressure retarded osmosis (PRO) power units, which produce electrical energy from salinity gradient sources located at coastlines, are a technology still in the process of maturation; however, there is an expectation that this technology will need to be integrated into electrical distribution networks. Such integration will drive changes in the electric response of the distribution systems which may lead to harmful operating conditions. Power flow analysis is a tool used to reveal the steady-state operating condition of distribution systems and which could be extended to study and address the integration of PRO power units. To the best of the authors’ knowledge, such extension of power flow analysis has not yet been addressed in the literature. Accordingly, this paper comprehensively provides a model to evaluate the electric current and complex power produced by PRO power units. This model is directly embedded in the forward-backward sweep (FBS) method, extending the power flow analysis of electric distribution systems in this way so as to consider the integration of PRO power units. The resulting approach permits revealing of the steady-state operating response of distribution systems and the effects that may be driven by the integration of PRO power units, as corroborated through numerical results on a 14-node test distribution system.

Stability and Hopf bifurcation analysis of multi-lingual rumor spreading model with nonlinear inhibition mechanism

The stability and hopf bifurcation of the multi-lingual rumor spreading model are mainly studied in this paper. A nonlinear inhibition mechanism is introduced to formulate an IS2R2 model with concerning the cross propagation in the multi-lingual environment. Next, the existence and stability of equilibrium points are analyzed systematically here. Meanwhile, choosing the key parameter and time delay of inhibition functions as bifurcation parameters, the characteristics of Hopf bifurcation are further displayed through certain critical values. Besides, an optimal control strategy involving inhibition functions is designed, and simulated via forward-backward sweep algorithm. Finally, the comparative analysis of various parameters in the numerical simulation is presented to justify our theoretical results.

Limiting current and voltage unbalances in distribution systems: A metaheuristic-based decision support system

Voltage and current unbalances are highly harmful to electrical power systems and the equipment connected to them. Thus, the development of a method that enables the quantification and limitation of unbalances is of great interest, especially in the analysis of distribution systems that are intrinsically unbalanced. In this work, a method for limiting unbalances through the insertion of capacitors based on the iterated local search (ILS) metaheuristic is presented. This method can identify how many capacitors are required, which bus they should be connected to, and the power of each capacitor. A power flow based on the backward forward sweep (BFS) method and three-phase modeling of the system equipment is used, and the symmetrical component method is used to calculate the unbalance index. The following IEEE test feeders are used in the experiments: 4-bus, 13-bus, 34-bus, and 123-bus. The results demonstrate the robustness of the method even when applied to large systems, enabling the limitation of unbalances with a computational time that is compatible with studies on the planning, operation, and expansion of electrical systems.

Optimal Control of a Mathematical Model of Smoking with Temporary Quitters and Permanent Quitters

Abstract This article discusses the optimal control of a mathematical model on smoking. This model consists of six population classes, namely potential to become smoker snuffing class irregular smokers regular smokers temporary quitters and permanent quitters The completion of this research uses the Pontryagin minimum principle and numerically using the forward-backward Sweep method. Numerical simulations of the optimal problem show that with the implementation of education campaigns and anti-nicotine medicine, the smokers can be decreased more quickly and the smoking population who quit permanently can be increased. The implementation of both through large amounts needs to be done from the beginning. The use of control in the form of education campaigns is of great value until the end of the research period means that it needs to be done continuously to reduce the number of smokers in the population.

A new method to incorporate three-phase power transformer model into distribution system load flow analysis

This paper proposes a new and simple method to incorporate three-phase power transformer model into distribution system load flow (DSLF) analysis. The objective of the present work is to find a robust and efficient technique for modeling and integrating power transformer in the DSLF analysis. The proposed transformer model is derived based on nodal admittance matrix and formulated by using the symmetrical component theory. Load flow formulation in terms of branch currents and nodal voltages is also proposed in this paper to enable integrating the model into the DSLF analysis. Singularity that makes the calculations in forward/backward sweep (FBS) algorithm is difficult to be carried out. It can be avoided in the method. The proposed model is verified by using the standard IEEE test system.

New class of hybrid explicit methods for numerical solution of optimal control problems

Forward-backward sweep method (FBSM) is an indirect numerical method used for solving optimal control problems, in which the differential equation arising from this method is solved by the Pontryagin’s maximum principle. In this paper, a set of hybrid methods based on explicit 6th-order RungeKutta method is presented for the FBSM solution of optimal control problems. Order of truncation error, stability region, and numerical results of the new hybrid methods were compared with those of the 6th-order Runge Kutta method. Numerical results show that new hybrid methods are more accurate than the 6th-order Runge–Kutta method and that their stability regions are also wider than that of the 6th-order Runge–Kutta method.

Forward-Backward Sweep Method를 활용한 분산전원 연계 가능 여부 평가 Tool 개발에 관한 연구

Reducing greenhouse gas emissions is essential to deal with climate change and the Paris Climate Change Accord was adopted in 2015. Net-Zero means that the actual carbon emissions will be zero by equalizing emissions and absorption, and South Korea has declared that it will achieve Net-Zero by 2050. To achieve Net-Zero, renewable energy sources are increasing, and Photo Voltaic(PV) accounts for a high proportion. However, in order to interconnect PV to the power system, there should be no adverse effects such as reverse power and overvoltage. The capacity of PV that can be connected without adversely affecting the power system is called Hosting Capacity(HC). In this paper, we check for reverse power flow, overvoltage, steady-state voltage fluctuation rate and calculate HC through Forward-Backward Sweep method.

An Optimal Control Analysis of the MERS-CoV Outbreak in South Korea

MERS-CoV is a respiratory disease that originated in the Middle East. This disease is caused by a novel coronavirus which transmits from Dromedary camels to humans, then passed on to other humans through direct contact or droplets. Said to be the biggest to occur outside of Middle East with 186 cases, the outbreak in South Korea should be discussed further. By going through the chain of transmission, it was found that 44\% of the infected individuals were exposed to the virus in the healthcare facilities' environment. To reduce the risk of exposure to the virus, several efforts have been made such as restricting healthcare facilities visitors and increasing the number of isolated individuals in hospitals. The previous study has developed a mathematical model for the outbreak in South Korea and estimated transmission rates from the data provided by the government. In this study, both efforts will be added as control variables to form an optimal control problem to minimize the number of infected individuals and the costs incurred. The optimal control will be obtained using the Pontryagin maximum principle, then simulated using the fourth-order Runge-Kutta forward-backward sweep method for two scenarios to see the effectiveness of both controls. The simulation showed that restricting health facilities visitors to limit the chance of exposure was the most effective strategy to control the MERS-CoV outbreak in South Korea.

Implementation and acceleration of optimal control for systems biology.

Optimal control theory provides insight into complex resource allocation decisions. The forward–backward sweep method (FBSM) is an iterative technique commonly implemented to solve two-point boundary value problems arising from the application of Pontryagin’s maximum principle (PMP) in optimal control. The FBSM is popular in systems biology as it scales well with system size and is straightforward to implement. In this review, we discuss the PMP approach to optimal control and the implementation of the FBSM. By conceptualizing the FBSM as a fixed point iteration process, we leverage and adapt existing acceleration techniques to improve its rate of convergence. We show that convergence improvement is attainable without prohibitively costly tuning of the acceleration techniques. Furthermore, we demonstrate that these methods can induce convergence where the underlying FBSM fails to converge. All code used in this work to implement the FBSM and acceleration techniques is available on GitHub at https://github.com/Jesse-Sharp/Sharp2021.

A time-delay model of diabetic population: Dynamics analysis, sensitivity, and optimal control

Diabetes, also known as diabetes mellitus, is a chronic degenerative disease with a variety of adverse complications. Due to its slow progression, a mathematical model of the diabetic population with time lag is developed. This novel study aims to analyze the stability of the diabetic equilibrium and also formulate an optimal control problem with lags. We show that under some values of parameters, a limit cycle arises through Hopf bifurcation. Sensitivity analysis, which used the direct differential method, reveals which parameters have a major impact on the model dynamics. An optimal control strategy is developed with two control variables for the description of the control strategy. A suitable objective function is formulated to minimize the total number of diabetics and the relative cost of implementing the controls. The resulting optimality system is solved numerically by using the Forward-Backward Sweep Method. Graphical results are examined with different parameter values and are compared with and without controls. The total number of diabetics continued to increase without controls, but the number of these individuals decreased after control. The optimal controls prevent the progression of diabetes complications by awareness, education, and medical care at the least cost.

Stochastic security-constrained optimal power flow for a microgrid considering tie-line switching

With the rapid development of microgrid, its tie-line switching from grid-connected to islanded mode is a topic worth discussing for considering both main grid resilience and microgrid security. In this paper, a stochastic security-constrained optimal power flow (OPF) method is proposed to deal with these conditions under high uncertainties. Firstly, a linear load flow model and a backward forward sweep algorithm are applied to present microgrid power flow with reduced computing burdens. Secondly, with consideration of tie-line switching from grid-connected to islanded operation mode, a security-constrained OPF problem for a microgrid is proposed to minimize operating cost and by optimizing microturbine setpoints and load shedding coefficient. To promise stable islanded operation after disconnection from the main grid, a Benders decomposition method is developed to decouple the OPF problem into a grid-connected master problem and an islanded sub-problem and then solve them iteratively with Benders cuts to guarantee microgrid security after tie-line switching. Last, a stochastic optimization method with probabilistic modelling is adopted to address the uncertainty issue caused by renewable energy sources and loads. The proposed stochastic security-constrained OPF method has been verified with high computing efficiency and robust security via comprehensive numerical simulations.

Analysis of optimal control strategy on transmission dynamics of HPV-HSV-II coinfection model

In this paper, optimal control problem is applied to Human Papillomavirus (HPV) and Herpes simplex virus type 2 (HSV-2) coinfection model formulated by a system of ordinary differential equations. Optimal control strategy is employed to study the effect of combining different intervention strategy on the transmission dynamics of HPV-HSV-II coinfection diseases. The necessary conditions for the existence of the optimal controls are established using Pontryagin’s Maximum Principle. Optimal control systems were performed with help of Runge-Kutta forward-backward sweep numerical approximation method. Finally, numerical simulation illustrated that a combination of all controls is the most effective strategy to minimize the disease from the community. The results shows that the size of infectious population are minimized by using different control strategies.

A Multiregion Discrete-Time Epidemic Model of Mycobacterium tuberculosis Infections: An Optimal Control Approach

The main goal of this article is to devise the spatial-temporal spread of TB, in multiple neighboring domains, taking into account the epidemiological diversity of their populations. However, since both the environment and any population are spatially heterogeneous, it is obviously desirable to include spatial structure into an epidemic model. Individuals with tuberculosis can spread the disease by moving from one area to another. In addition, people travel by air between cities, so diseases can be spread quickly between very distant places (as was the case with the COVID-19). In our model, each region’s studied population is divided into five compartments S, L1, I, L2, and R. Further, we introduce in our discrete systems three control variables which represent the effectiveness rates of vaccination, travel-blocking operation, and treatment. We focus in our study to control the outbreaks of an epidemic that affects a hypothetical population belonging to a specific region. Firstly, we analyze the epidemic model when the control strategy is based on the vaccination control only, and secondly, when the travel-blocking control is added, we finish with the introduction of the treatment control. The optimal control theory, based on Pontryagin’s maximum principle, is applied thrice in this paper, for the characterizations of the vaccination, travel-blocking, and treatment controls. The numerical results associated with the multipoint boundary value problems are obtained based on the forward-backward sweep method combined with progressive-regressive Runge–Kutta fourth-order schemes.

Mathematical modeling of HIV/AIDS with optimal control: A case study in Ethiopia

In this paper, we developed HIV/AIDS mathematical model which comprises important compartments such as individuals with aware and unaware susceptible, undiagnosed HIV infections, diagnosed HIV infectious with and without AIDS symptom, and treated from the disease. This model considers the rate of becoming aware and unaware as a function of media campaign, whereas screening and treatments rates are constants. The effective reproduction number, equilibria and their nature of stability were formulated. The bifurcation also occurred when the effective reproduction number is equal to unity. This model extended to a new model which incorporates interventions such as preventive, screening, and treatment strategies. In this model the optimal control problem is formulated and solved analytically. In addition to this the optimality system is derived and solved numerically using the forward-backward sweep method (FBSM). Finally the cost-effectiveness of these combination controlling strategies is derived.