Forward-backward Sweep Research Articles

Optimal capacitor bank placement and sizing using particle swarm optimization for power loss minimization in distribution network

This study delves into the issues concerning power quality in distribution systems, which commonly experience substantial losses, voltage fluctuations, and instability in bus voltages. More specifically, this paper centered on optimizing the Distribution Static Compensator (DSTATCOM) to tackle these challenges. To achieve this objective, we employ the Backward/Forward Sweep (BFS) method for load flow analysis and the Particle Swarm Optimization (PSO) algorithm to determine the ideal size and placement of the DSTATCOM. The study evaluates three different scenarios: the first scenario considers a 50-bus system without DSTATCOM, while the second and third scenarios incorporate the use of PSO to identify the optimal location and size of fixed and switched DSTATCOM. The aim is to reduce active and reactive power losses, enhance the voltage profile, and minimize system costs. The DSTATCOM integration significantly improved the distribution system by raising the minimum bus voltage from 0.817 p.u. to 0.95 p.u. Case 1 and Case 2 experienced notable reductions in active and reactive power losses, with percentages ranging from 58.72% to an impressive 96.69%. Economically, both cases demonstrated substantial net savings of 58.85% and 58.71%. The results demonstrate that employing PSO to allocate and size DSTATCOM can significantly decrease distribution system losses.

The effect of curative and preventive optimal control measures on a fractional order plant disease model

In this paper, we present a novel mathematical model of fractional order for epidemic dynamics in plants, this fractional order model (FOM) in the sense of Caputo derivatives governing fractional differential equations (FDEs), introducing modified parameters to coincide both sides dimensions for FOM that means enhancing its accuracy in representing the real-life scenarios to control the spread of the epidemic. Our contributions include a comprehensive qualitative analysis of the proposed FOM, such as proving the existence and uniqueness of the projected solution by transforming our problem into a fixed point problem and applying a Banach contraction principle and Schauder’s fixed-point theorem. The positivity and boundedness of this solution are also demonstrated. We precisely evaluate all equilibrium points (EPs), examine their local and global stability by using Routh–Hurwitz conditions and fractional LaSalle’s invariance principle (LIP), respectively and shed light on the dynamic behavior of the FOM. Furthermore, we discuss the sensitivity analysis for parameters of the control reproduction number (CRN), with insightful plots to illustrate the model’s response to parameter changes (replanting and roguing parameters). From this foundation, we formulate a fractional optimal control problem (FOCP) by incorporating preventive u1 and curative u2 controls to effectively eliminate the propagation of the epidemic in plants. The fractional necessary optimality conditions (FNOCs) are derived attribution to Pontryagin’s maximum principle (PMP). We employ the forward–backward sweep method (FBSM) based on fractional Euler method (FEM) in order to facilitate control implementation and show the different suggested strategies. By enhancing this method, optimal control efforts are projected onto the FOM and yield three various strategies to impact the epidemic’s trajectory. For each strategy, we explain how the presence (i.e. with control cases) and absence (without control cases) of the proposed controls affected the susceptible, protected and infected plants. Some attractive figures with various values of the weight factor and fractional order α for the CRN are also presented, allowing a visual assessment of their impact on the dynamics of the epidemic in plants. In addition, we calculate the objective function for controlled and uncontrolled cases to provide a quantitative measure of its effectiveness in containing the outbreak in the plants. The results gained from our analyses and simulations provide valuable guidance for the management and elimination of epidemics in plants by offering various scenarios to implement the proposed controls.

Distribution State Estimation and Its Impact of Load Modeling

To maintain system security and other essential parameters like reliability and quality, continuous monitoring of the system is very important. Considering the distribution network, state estimation (SE) methods can be adopted. The purpose of the method is to identify and estimate unknown variables based on the online measurements of test data. The primary objectives considered in this paper are: To choose the exact SE method and the artificial neural network (back propagation algorithm), which can be used for determination in the islanding mode of distribution network states, the composite load model is considered for the estimation of states and further enhancement. By adopting the system, state variables in terms of error are measured in the 12-bus distribution network with precise measurements and compared with practical values. The SE proposed includes results with the load flow backward-forward sweep method to satisfy the system state variables. Numerical results indicate that the model performs better for error measurement data with states and in the case of state forecasting.

An Aerodynamic Investigation of the Last-Stage Turbine in an Upgraded Gas Turbine

Abstract Due to the lengthy certification process for newly designed turbine blades, product upgrading of industrial gas turbine units is often performed solely on compressor and combustor. Since their inlet conditions are significantly changed, the entire four-stage turbine operates far away from its original design point, leading to decreased efficiency, and increased flutter risk. This investigation first performs numerical simulations to study the flow field change of the last-stage turbine in a gas turbine before and after product upgrading. To reduce the load of the last-stage turbine without reducing the power output of the whole turbine, the enthalpy drops of turbine are reallocated to the front three stages. After modifying the blade profile based on S1 stream surface analysis, a CFD simulation is carried out on the modified three-dimensional blade passage. It is shown that the modified blade design greatly reduces the Mach number at the tip outlet of the last-stage blade, thus possibly reducing flutter risk and improving the aerodynamic efficiency of the turbine. This paper also attempts to redesign the blade geometry by different radial blade stacking of both forward sweep and backward sweep. It is found that the backward-swept blade modification can effectively reduce the endwall flow loss. This work presents the improvements of the aerodynamic efficiency of last-stage through a series of improvement methods and provides a reference for future detailed optimization of this last-stage turbine.

OPTIMAL CONTROL ON FRACTIONAL ENZYME KINETICS WITH INHIBITORS

In enzyme kinetic chemical reaction, inhibitors are working as a regulators of the metabolism of the systems and the biochemical activities as well. The main focus of this study is to explore the fractional dynamics of enzyme kinetic biochemical reactions with competitive and uncompetitive inhibitors. Further, the analysis continuous with the optimal controls on the system which accelerate biochemical reactions and maximize product generation. Eventually, the numerical analysis have been done by the Adams predictor–corrector method and the forward–backward sweep method for the dynamics and optimal control study, respectively.

Optimal control and cost-effectiveness analysis for the human melioidosis model

In this work, we formulated and investigated an optimal control problem of the melioidosis epidemic to explain the effectiveness of time-dependent control functions in controlling the spread of the epidemic. The basic reproduction number (R0c) with control measures is obtained, using the next-generation matrix approach and the impact of the controls on R0c is illustrated numerically. The optimal control problem is analyzed using Pontryagin's maximum principle to derive the optimality system. The optimality system is simulated using the forward-backward sweep method based on the fourth-order Runge-Kutta method in the MATLAB program to illustrate the impact of all the possible combinations of the control interventions on the transmission dynamics of the disease. The numerical results indicate that among strategies considered, strategy C is shown to be the most effective in reducing the number of infectious classes compared to both strategy A and strategy B. Furthermore, we carried out a cost-effectiveness analysis to determine the most cost-effective strategy and the result indicated that the strategy B (treatment control strategy) should be recommended to mitigate the spread and impact of the disease regarding the costs of the strategies.

A Comparative Study of Optimal PV Allocation in a Distribution Network Using Evolutionary Algorithms

The growing distributed energy resource (DER) penetration into distribution networks, such as through residential and commercial photovoltaics (PV), has emerged through a transition from passive to active networks, which takes the complexity of planning and operations to the next level. Optimal PV allocation (sizing and location) is challenging because it involves mixed-integer non-linear programming with three-phase non-linear unbalanced power flow equations. Meta-heuristic algorithms have proven their effectiveness in many complex engineering problems. Thus, in this study, we propose to achieve optimal PV allocation by using several basic evolutionary algorithms (EAs), particle swarm optimization (PSO), artificial bee colony (ABC), differential evolution (DE), and their variants, all of which are applied for a study of their performance levels. Two modified unbalanced IEEE test feeders (13 and 37 bus) are developed to evaluate these performance levels, with two objectives: one is to maximize PV penetration, and the other is to minimize the voltage deviation from 1.0 p.u. To handle the computational burden of the sequential power flow and unbalanced network, we adopt an efficient iterative load flow algorithm instead of the commonly used and yet highly simplified forward–backward sweep method. A comparative study of these basic EAs shows their general success in finding a near-optimal solution, except in the case of the DE, which is known for solving continuous optimization problems efficiently. From experiments run 30 times, it is observed that PSO-related algorithms are more efficient and robust in the maximum PV penetration case, while ABC-related algorithms are more efficient and robust in the minimum voltage deviation case.

Game-theoretic modeling and analysis of cyberbullying spreading on OSNs

The rapid development of online social networks (OSNs) has enabled seamless cyberbullying activities, which not only cause psychological harm to victims but also bring disharmony to society. From the perspective of OSN platform administrators, strategic decision making towards when/how to launch an anti-cyberbullying campaign is the key to mitigating its negative impact. Hence, this paper develops a dynamic anti-cyberbullying investment solution to mitigate the adverse impact of strategic cyberbullying phenomena cost-effectively. Specifically, this paper first quantifies the payoffs of the attacker/bullying instigator and the defender/platform administrator based on a newly proposed propagation model. Then, considering the budget-constrained factor for both sides, a differential game-theoretical model is proposed to simulate each party's optimal trade-off between cost and benefit. Next, by utilizing Pontryagin Maximum/Minimum Principle, a set of necessary conditions for a Nash equilibrium strategy profile have been proposed. Based on the forward-backward sweep method, an iterative algorithm (SCR optimization algorithm) is tailored to solve the conditions numerically. Through experiments conducted under Facebook, Youtube and Twitter sub-networks, the algorithm's performance has been evaluated by inspecting its convergence speed and payoff compared with randomized profiles. Consequently, the resulting strategies are verified to exhibit superior performance in dealing with cyberbullying spreading.

A deterministic transmission model for analytics-driven optimization of COVID-19 post-pandemic vaccination and quarantine strategies.

This study developed a deterministic transmission model for the coronavirus disease of 2019 (COVID-19), considering various factors such as vaccination, awareness, quarantine, and treatment resource limitations for infected individuals in quarantine facilities. The proposed model comprised five compartments: susceptible, vaccinated, quarantined, infected, and recovery. It also considered awareness and limited resources by using a saturated function. Dynamic analyses, including equilibrium points, control reproduction numbers, and bifurcation analyses, were conducted in this research, employing analytics to derive insights. Our results indicated the possibility of an endemic equilibrium even if the reproduction number for control was less than one. Using incidence data from West Java, Indonesia, we estimated our model parameter values to calibrate them with the real situation in the field. Elasticity analysis highlighted the crucial role of contact restrictions in reducing the spread of COVID-19, especially when combined with community awareness. This emphasized the analytics-driven nature of our approach. We transformed our model into an optimal control framework due to budget constraints. Leveraging Pontriagin's maximum principle, we meticulously formulated and solved our optimal control problem using the forward-backward sweep method. Our experiments underscored the pivotal role of vaccination in infection containment. Vaccination effectively reduces the risk of infection among vaccinated individuals, leading to a lower overall infection rate. However, combining vaccination and quarantine measures yields even more promising results than vaccination alone. A second crucial finding emphasized the need for early intervention during outbreaks rather than delayed responses. Early interventions significantly reduce the number of preventable infections, underscoring their importance.

Adjoint-based optimal control of contractile elastic bodies. Application to limbless locomotion on frictional substrates

In nature, limbless locomotion is adopted by a wide range of organisms at various length scales. Interestingly, undulatory, crawling and inching/looping gait constitutes a fundamental class of limbless locomotion and is often observed in many species such as caterpillars, earthworms, leeches, larvae, and C. elegans.In this work, we developed a computationally efficient 3D Finite Element (FE) unified framework for the locomotion of limbless organisms on frictional substrates. Muscle activity is simulated with a multiplicative decomposition of the deformation gradient, which allows mimicking a broad range of locomotion patterns in 3D contractile elastic solids.We propose a two-field FE formulation based on positions and velocities. Governing partial differential equations are transformed into equivalent time-continuous differential–algebraic equations (DAEs). Next, the optimal locomotion strategies are studied in the framework of optimal control theory. We resort to adjoint-based methods and deduce the first-order optimality conditions, that yield a system of DAEs with two-point end conditions. Hidden symplectic structure is discussed, and Symplectic Euler time integration of optimality conditions are employed. The resulting discrete first-order optimality conditions form a non-linear programming problem that is solved efficiently with the Forward Backward Sweep Method. Finally, some numerical examples are provided to demonstrate the comprehensiveness of the proposed computational framework and investigate the energy-efficient optimal strategy out of distinct locomotion patterns adopted by limbless organisms.

PSO‐based optimal placement of electric vehicle charging stations in a distribution network in smart grid environment incorporating backward forward sweep method

AbstractThe transition from conventional fossil‐fuel vehicles to electric vehicles (EVs) is critical for mitigating environmental pollution. The placement of electric vehicle charging stations (EVCS) significantly impacts the utility operator and electrical network. Inappropriately placed EVCS lead to challenges such as increased load, unbalanced generation, power losses, and reduced voltage stability. Incorporating distributed generation (DG) helps mitigate these issues by maximizing EV usage. This study focuses on optimizing EVCS and DG placement in radial distribution networks. The methodology employs a backward and forward sweep method for load flow analysis and utilizes the particle swarm optimization (PSO) algorithm to determine optimal EVCS and DG locations and sizes. This approach, validated on the IEEE‐33 bus system, outperforms existing methods. Results indicate a 2.5 times greater power loss reduction compared to simulated annealing (SA), 1.6 times better than artificial bee colony, and parity with genetic algorithm (GA). Overall, the PSO algorithm demonstrates superior optimization effectiveness and computational efficiency, showcasing 1–2.5 times better performance than other methodologies. Employing this approach yields significantly improved results, making it a promising technique for optimizing EVCS and DG placement in distribution networks.

NUMERICAL SOLUTION TO OPTIMAL CONTROL PROBLEMS USING COLLOCATION METHOD VIA PONTRYAGIN’S PRINCIPLE

In this study, Lucas polynomial approximate solution is considered to develop a collocation technique for solving optimal control problems with implementation in block using forward backward sweep method. The collocation block method developed is stable and convergent. The method is implemented using MATLAB code, and the examples show that forward-backward sweep methods with the collocation method is an efficient technique for solving optimal control problems as compared with some existing methods.

Assessment of topological boundaries for microgrids in an active power distribution network during emergencies

Microgrid (MG) operation has become an intriguing possibility to enhance the sustainability, reliability, and resilience of electricity distribution systems in emergencies. However, identifying suitable physical boundaries of MGs from an active power delivery infrastructure is a highly challenging task. This study describes a novel approach for determining the topological boundary of multiple MGs to restore power supply in a power distribution system during the unavailability of grid power supply. This method tries to enhance the self-adequacy of the MGs by increasing power flow within the MG boundaries. In this context, possible demand at the nodes of the power delivery infrastructure during an emergency is anticipated by an autoregressive integrated moving average (ARIMA) and long short-term memory (LSTM) network-based time series forecast models. A modified backward-forward sweep (MBFS) power flow analysis, tailored for islanded mode, is employed to assess the power flow status in the MGs during emergencies. The MGs are supplied with locally available dispatchable distributed generators (DDGs). A particle swarm optimization (PSO) algorithm intertwined with the MBFS power flow method has been employed to determine the boundary of MGs by identifying minimum power flow line in the shortest path between the consecutive DDGs. Further, this study demonstrates the evaluation of the shortest path between paths between the consecutive DDGs with the help of a breadth-first search (BFS) algorithm. The proposed strategy has been tested on a modified 33-bus, 69-bus and 118-bus power distribution test systems. The experimented results are verified with the results obtained from similar existing approaches to explore the opportunities in the proposed methodology.

Optimal control and cost-effectiveness analysis for leptospirosis epidemic

This paper aims to apply an optimal control theory for the autonomous model of the leptospirosis epidemic to examine the effect of four time-dependent control measures on the model dynamics with cost-effectiveness. Pontryagin's Maximum Principle was used to derive the optimality system associated with the optimal control problem. Numerical simulations of the optimality system were performed for different control strategies and the results were presented graphically with and without controls. The optimality system was simulated using the Forward–Backward Sweep method in the Matlab programme. The numerical results revealed that the combination of all optimal control measures is the most effective strategy for minimizing the spread and impact of disease in the community. Furthermore, a cost-effectiveness analysis was performed to determine the most cost-effective strategy using the incremental cost-effectiveness ratio approach and we observed that the rodenticide control-only strategy is most effective to combat the spread of disease when available resources are limited.

Cost-effective optimal control analysis of a COVID-19 transmission model incorporating community awareness and waning immunity

Abstract This article presents a cost-effective optimal control analysis of interventions applied to a S2EI2RS type deterministic compartmental model of COVID-19, considering community awareness and immunity loss. We introduce two time-dependent controls, namely, home quarantine and treatment, to the model for defining an optimal control problem (OCP). In addition to some basic qualitative properties, we obtain the reproductive threshold R 0 {R}_{0} by using the next-generation method and see the impact of controls on it. We also investigate the effect of community awareness and waning immunity, when no controls are applied. The existence and characterization of optimal controls is proved to establish the optimality system, and the OCP is solved using the forward–backward sweep method. The results are simulated using MATLAB. Our comparative cost-effective analysis indicates that implementing both control strategies simultaneously, along with community awareness, is the most optimal and sustainable way to flatten COVID-19 curves in a short period of time than that of implementing single controls. This article offers valuable insights that can assist policymakers and public health experts in designing targeted and effective control measures for COVID-19 and future epidemics in the post-COVID era. Therefore, this piece of work could be a valuable contribution to the existing literature.

Mathematical Modeling and Optimal Control of Intervention Strategies for A Banditry Model

This paper presents an optimal control of intervention strategies for the menace of Banditry taking into account media campaign against Banditry rehabilitation of Bandits detainees and use of military force against Banditry as control strategies. The Banditry free equilibrium, Banditry present equilibrium and the basic reproduction number of Banditry were obtained. The stability analysis results suggest that the Banditry free equilibrium is locally asymptotically stable when and otherwise when . The Boko Haram presence equilibrium is globally asymptotically stable when and unstable if . We used the three control strategies and updated the Banditry menace model. The optimal control issue was resolved using Pontryagin's Maximum Principle (PMP).It was discovered that there is a significant decrease in the population of Bandits and increase in the number of rehabilitated Bandits and detained Bandits when the control measures are implemented compared to the case without control. We solved the optimality control using a forward-backward sweep strategy implemented in MATLAB for numerical simulation. Additionally, we saw that the number of people detained fluctuates as the number of people receiving rehabilitation rises. We argue that in order to lessen or completely erase the menace caused by Bandits in society, the government should fund media campaigns and rehabilitation initiatives.

A two-phase power flow algorithm of traction power supply system based on traction substation-network decoupling

Power flow analysis of traction power supply system (TPSS) is an effective approach to assess supply capacity and power quality, serving the whole process of system design, operation and optimization. The coupling effect between adjacent power supply arms poses challenges for the accurate and efficient solution, especially with the penetration of power converters and energy equipment. This paper proposes a two-phase power flow decoupling algorithm. TPSS is divided into traction substation and two decoupled power supply arms by introducing current ratio coefficients and unit matrices. Specifically, the equivalent voltage source model of traction substation and the modified chain network model of arms are solved by using forward–backward sweep method and LU decomposition method, respectively. Then the TPSS power flow can be obtained by alternative iteration of two solving phases. Simulations verify the proposed algorithm exhibits great compatibility at various operation modes. Additionally, the power supply capacity is mapped to the algorithm convergence. Compared to conventional methods, the algorithm achieves superior performance on accuracy and efficiency.

Stability and optimal control analysis for studying the transmission dynamics of a fractional-order MSV epidemic model

In this research paper, we study the transmission dynamics of the maize streak virus disease in agriculture using fractional calculus. Our fractional-order model (FOM) consists of fractional differential equations within Caputo fractional derivative (CFD). Further, we investigate the mathematical analysis of this FOM such as the positivity and boundedness of the projected solutions, compute the control reproduction number (Rc) by the next-generation matrix method, examine the local stability by using Routh–Hurwitz conditions and global stability by using fractional LaSalle’s invariance principle for all possible equilibrium points. A sensitivity analysis is conducted on the parameters integrated into Rc to evaluate how accurately the parameter estimation fits. Additionally, we present further numerical results on the FOM to demonstrate the obtained analytical results. Then, we formulate the fractional optimal control problem (FOCP) depending on the suggested FOM with three control efforts u1, u2 and u3 called respectively, prevention, quarantine and insecticide chemical. Also, we study this FOCP analytically to derive the fractional necessary optimality conditions (NOCs) based on a kind of Pontryagin’s maximum principle. After that, we solve these fractional NOCs numerically where the state and co-state variables are subject to the left CFD. We present various strategies with different combinations of suggested controls to examine the best strategy for decreasing the transmission of MSV in maize plants, where each one of these strategies is able to reduce the maize streak disease (MSD) at the period of control time. We perform simulations of outcomes using MATLAB by developing the forward–backward sweep method utilizing the fractional Euler method. Moreover, some figures are presented to show the impact of both control interventions, change in weight factors and fractional order within the suggested strategies. We can observe that the fractional order plays a significant role in limiting the spread of MSD where the obtained results illustrated that the MSD can be reduced through the suggested FOM, which has a notable influence on plant epidemiology.

Optimal vaccination control for COVID-19 in a metapopulation model: a case of the Philippines

We investigate a contextual problem of how to distribute a limited supply of vaccines over a period of time in a country where different regions have its own vaccination capacities. Considering that daily vaccination will affect future disease progression, we aim to find a distribution strategy over time that can minimize the total infection and implementation costs. Lagrangian and Eulerian migrations connect our multi-patch COVID-19 model, and vaccination is added as a control measure. An optimal control problem with an isoperimetric constraint is formulated and solved using the Adapted Forward–Backward Sweep Method. In distributing 5 million vaccines in 50 days, simulations showed that the optimal control strategy could lead to a difference of reducing two hundred thousand infections in just one region.

Determination of maximum additional load for EV charging station considering practical security limits

Nowadays, the allocation of electric vehicle charging stations (EVCS) for the charging of electric vehicles (EVs) is essential, as random allocation may cause significant energy loss for the radial distribution system (RDS). Uncoordinated charging of EVs dominates the load profile of the RDS. Although a single EV has a negligible impact on the system, the combined effect of charging an EV cluster may violate the voltage security constraints of the RDS. Therefore, to avoid such circumstances, the loadability limit of each node of the RDS must be determined. Previously, conventional analytical methods were used to calculate the maximum loadability of the RDS node, where voltage magnitudes become less than the critical voltage limit. However, these approaches are not acceptable for the power industry, as it may push the system towards a blackout. Therefore, the appropriate capacity of the EVCS can only be determined if the voltage security limit of each node of the RDS follows its critical limit. Hence, in this paper, a modified forward-backward sweep (MFBS) algorithm is formulated to find the maximum additional load (MAL) of each node of the RDS considering non-unity power factor during the EV charging process. This algorithm may help the EVCS to determine its capacity or optimal number of charging ports directly during installation at an optimal location of RDS. For validation, the 33-bus and 69-bus RDSs have been used, and it can be seen that the EVCSs have been successfully installed in the optimal location of the test systems mentioned above without violating the voltage security limit of each node of the RDS.