Fuel Cost Function Research Articles

A multi-objective nonlinear integer programming model for mixed runway operations within the TMAs

AbstractGlobal air traffic demand has shown rapid growth for the last three decades. This growth led to more delays and congestion within terminal manoeuvring areas (TMAs) around major airports. The efficient use of airport capacities through the careful planning of air traffic flows is imperative to overcome these problems. In this study, a mixed-integer nonlinear programming (MINLP) model with a multi-objective approach was developed to solve the aircraft sequencing and scheduling problem for mixed runway operations within the TMAs. The model contains fuel cost functions based on airspeed, altitude, bank angle, and the aerodynamic characteristics of the aircraft. The optimisation problem was solved by using the $\varepsilon$ -constraint method where total delay and total fuel functions were simultaneously optimised. We tested the model with different scenarios generated based on the real traffic data of Istanbul Sabiha Gökçen Airport. The results revealed that the average total delay and average total fuel were reduced by 26.4% and 6.7%, respectively.

Multi-objective Optimal Scheduling Analysis of Power System Based on Improved Particle Swarm Algorithm

Economic Environmental Dispatching (EED) in power systems is a multi-variable, strongly constrained, non-convex, multi-objective optimization problem that is difficult to properly handle using traditional methods. However, the application of particle swarm optimization algorithms may result in insufficient population diversity and easy to fall into local optimization problems. Therefore, this paper proposes an adaptive backbone multi-objective particle swarm optimization (ABBMOPSO) method to solve the economic and environmental scheduling problems of power systems. This paper first analyzes the topology and computational flow of particle swarm optimization algorithms, and then constructs a multi-objective optimization research framework that integrates Pareto optimization principles for the scheduling of power generation units. The execution algorithm is the improved multi-objective particle swarm optimization algorithm (MOPSO). This paper establishes a mathematical model for the economic and environmental scheduling of power systems, which optimizes conflicting fuel cost functions and pollutant emission functions simultaneously, taking into account nonlinear constraints such as load balance constraints and unit operation constraints. The improved ABBMOPSO algorithm is used to optimize the solution to improve the global search ability of the EED model. The simulation data of seven units show that the ABBMOPSO algorithm has a minimum power generation cost of 588.1 $/h and a minimum pollutant emission of 0.192 t/h, which is significantly superior to other algorithms and reduces the number of iterations, with good feasibility.

Implementations of Golden Jackal Algorithm for Solving CCFELD Problems

This study offers the Golden Jackal Optimization (GJO) algorithm, an effective and trustworthy swarm optimization for tackling economic load dispatch (ELD) issues using cubic fuel cost functions. The presence of equal and unequal constraints of the non-smooth cost functions of a practical ELD has caused difficulties in finding an overall optimal result. The suggested GJO is tested first with quadratic cost functions as well as the cubic fuel cost functions to demonstrate its usefulness and efficiency. Three generator systems, five generator systems, six generating systems, 26 generators with quadratic and cubic fuel cost functions have all been used to assess the proposed GJO algorithm. Numerous case studies and evaluation with the other existing algorithms have substantiated that the suggested GJO technique yields outstanding outcomes.

Analysis of transmission line modeling routines by using offsets measured least squares regression ant lion optimizer in ORPD and ELD problems

This paper proposed an offset measured least regression based ALO to solve ORPD and ELD problems of IEEE 57 bus system designed with different transmission line models. These two problems are highly non-linear and non-convex defiance optimization of problem. The solution of ALO depends on exploration and exploitation if the difference between local and global variables is large, therefore chance to miss the best optimal solution. The weighted elitism phase of the algorithm gives diversified results because exploration is more biased toward elite particles. Which is due to decreasing of random walk to achieve the convergence characteristics. The proposed LSR-EALO can balance both exploration and exploitation, which improves the solution of optimization problem. Simulation is performed with proposed method on different IEEE 57 bus power system models, such as the positive sequence, 3-Phase PI, and distributed CP transmission lines based power systems, and lumped PI lines based low voltage hardware model (LVHM). In this paper, the ORPD problem was used to describe control variables like generator voltage, tap changers of transformers, and switching of capacitor banks subjected to power loss minimization function. Also, described voltage deviation and voltage stability index. Similarly, the ELD was described the active power allocation among generators to meet the sum of load demand and losses in the systems at minimum fuel cost function. And in depth analysis of the optimization results shows accuracy of control variables in ORPD and ELD problems. Also, the effectiveness of proposed method was also verified by comparing results with other meta heuristic algorithms.

A Surrogate-Assisted Adaptive Bat Algorithm for Large-Scale Economic Dispatch

Large-scale grids have gradually become the dominant trend in power systems, which has increased the importance of solving the challenges associated with large-scale economic dispatch (LED). An increase in the number of decision variables enlarges the search-space scale in LED. In addition to increasing the difficulty of solving algorithms, huge amounts of computing resources are consumed. To overcome this problem, we proposed a surrogate-assisted adaptive bat algorithm (GARCBA). On the one hand, to reduce the execution time of LED problems, we proposed a generalized regression neural network surrogate model based on a self-adaptive “minimizing the predictor” sampling strategy, which replaces the original fuel cost functions with a shorter computing time. On the other hand, we also proposed an improved hybrid bat algorithm (RCBA) named GARCBA to execute LED optimization problems. Specifically, we developed an evolutionary state evaluation (ESE) method to increase the performance of the original RCBA. Moreover, we introduced the ESE to analyze the population distribution, fitness, and effective radius of the random black hole in the original RCBA. We achieved a substantial improvement in computational time, accuracy, and convergence when using the GARCBA to solve LED problems, and we demonstrated this method’s effectiveness with three sets of simulations.

Predicting the environmental economic dispatch problem for reducing waste nonrenewable materials via an innovative constraint multi-objective Chimp Optimization Algorithm

The usage of conventional fossil fuels has aided fast economic growth while also having negative consequences, such as increased global warming and the destruction of the ecosystem. This paper proposes a novel swarm-based metaheuristic method called Chimp Optimization Algorithm (ChOA) to tackle the environmental, economic dispatch issue and reducing the waste nonrenewable materials. In this regard, two objective functions named fuel cost function and emission cost function are proposed. Unique constrained handling also solves the challenge of multi-objective optimization. Standard IEEE 30 bus with six generators and a 10-unit system are used to demonstrate the usefulness of ChOA. The result of ChOA is compared with Individual Best Memory Penalty Factor Grey Wolf Optimizer (IBMPF-GWO), Improved Whale Trainer (IWT), Chaotic Biogeography-Based Optimizer (CBBO), Non-Linear Migration BBO (NLBBO), Hybrid Gravitational Search Algorithm Particle Swarm Optimization (GSAPSO), Covariance Matrix Adaptation Evolution Strategy (CMA-ES), Differential Evolution-Crossover Quantum Particle Swarm Optimization (DE-CQPSO), Salp Swarm Algorithm (SSA), Dragonfly Algorithm (DA), and Fuzzy Grasshopper Optimization Algorithm (FGOA) to confirm its efficiency. For both single- and multi-objective optimization, ChOA's assessment index and convergence rate are superior to other benchmark algorithms, regardless of whether the goal is to reduce emissions or to reduce fuel costs. The efficacy and robustness of the ChOA in handling environmental economic dispatch problems have been shown by discovering a good compromise value.

Impact of parameter control on the performance of APSO and PSO algorithms for the CSTHTS problem: An improvement in algorithmic structure and results.

Cascaded Short Term Hydro-Thermal Scheduling problem (CSTHTS) is a single objective, non-linear multi-modal or convex (depending upon the cost function of thermal generation) type of Short Term Hydro-Thermal Scheduling (STHTS), having complex hydel constraints. It has been solved by many metaheuristic optimization algorithms, as found in the literature. Recently, the authors have published the best-achieved results of the CSTHTS problem having quadratic fuel cost function of thermal generation using an improved variant of the Accelerated PSO (APSO) algorithm, as compared to the other previously implemented algorithms. This article discusses and presents further improvement in the results obtained by both improved variants of APSO and PSO algorithms, implemented on the CSTHTS problem.

Enhanced Colliding Bodies Optimization Towards the Solution of Economic Load Dispatch Problem

This paper proposes application of enhanced colliding bodies optimization algorithm (ECBO) for solving the economic load dispatch problem, which aims to get minimum generation cost through economic scheduling of generating unit. The algorithm is a novel efficient optimization algorithm, and its idea is attained from collisions, which are one-dimensional between two or more bodies. Each agent involved in this collision is shaped as a body having defined mass and defined velocity. To analyze the performance of the proposed method, it is tested on four different test systems consisting of 3, 5, 13, and 18 generating units. Both convex and non-convex fuel cost function have been considered. Numerical results have been compared with various well-known algorithms. A significant improvement in the results has been observed. It has been farther noted that an average 5.1% better results were provided by ECBO in terms of generation cost compared to other algorithms. Moreover, the simulation time is also improved. Besides this, Kruskal-Wallis non-parametric test has been performed.

Investigation the Success of Semidefinite Programming for the Estimating of Fuel Cost Curves in Thermal Power Plants

Accurate estimation of fuel cost curve parameters in thermal power plants is of great importance because these parameters directly influence the economic dispatch calculations. In this paper, a semidefinite programming (SDP) approach was proposed for the estimation of fuel cost functions' parameters in thermal power plants. The parameter estimation problem was designed as a minimization problem, where the objective function was accepted as the total absolute error (TAE) in the study. Also, linear, quadratic, and cubic fuel cost functions were used to estimate the fuel cost parameters. Different fuel types such as coal, oil and gas were preferred for simulation studies. The results achieved from the semidefinite programming method were compared with that of particle swarm optimization (PSO), artificial bee colony (ABC), crow search algorithm (CSA) and least error square (LES) methods, respectively. The performance of the methods were compared according to the TAE parameter. Simulation results showed that SDP method is more successful than other methods considered in this paper. Clearly, the present paper showed that SDP has a higher potential to solve parameter estimation problems.

A combination of FA and SRPSO algorithm for Combined Heat and Power Economic Dispatch

This paper represents a hybrid Firefly and Self-Regulating Particle Swarm Optimization (FSRPSO) algorithm to solve optimal Combined Heat and Power Economic Dispatch (CHPED) problem. Valve point effect on fuel cost function of pure generation units, electrical power losses in transmission systems and feasible operating zones are taken into account in the CHPED problem. The CHPED refers to minimize total costs of fuel for electricity and heat generation supply to load demand. The proposed FSRPSO attempts to determine the start of the local search process properly by checking the previous global best. Thus, the FSRPSO is able to exploit strong points of both Firefly Algorithm (FA) and SRPSO mechanisms in order to balance between exploration and exploitation phases. Besides, for the sake of validation the proposed hybrid method, the FSRPSO is examined on 21 well-known benchmarks, and also a real engineering case i.e., two power systems for evaluating its performance compared with the SRPSO, FA, PSO, and other state-of-the-art algorithms. The obtained optimization results show that the proposed FSRPSO provides fast, mature and reliable optimum solutions and outperform other compared algorithms in diverse categories of benchmarks along with the studied CHPED problem.

A Modified Teaching—Learning-Based Optimization for Dynamic Economic Load Dispatch Considering Both Wind Power and Load Demand Uncertainties With Operational Constraints

Dynamic economic load dispatch (DELD), which determines the best generation scheduling for different power plants during the next 24 hours in order to meet the electricity demand as well as minimize the total energy cost, is a highly complex non-linear and non-convex problem. This study proposes an efficient modified teaching-learning-based optimization algorithm, called MTLBO, to effectively solve the DELD optimization problem in a power system containing thermal generations and wind power. The planning problem comprises the total fuel cost function with valve-point loading effect and the transmission power losses. Also, the uncertainties of wind power and load demand along with the various equality and inequality operational constraints such as power generation limits, ramp rate limits, prohibited operating zones and power balance are considered in the problem. Additionally, in the proposed MTLBO algorithm, the learning phase is properly integrated into the teaching phase to improve the convergence characteristic of the original TLBO. Moreover, in order to enhance the feature of local optima avoidance, interaction of up to five students are incorporated into the learning phase to improve the knowledge of each student. To exhibit the effectiveness of the proposed approach, the algorithm is applied into the 14 real test functions. In addition, several cases with 10 and 30 unit test systems are investigated over the planning period. Compared to the main TLBO algorithm which is mostly used optimization algorithms proposed in prior studies, the simulation results demonstrate the efficiency and superiority of the proposed optimization approach in terms of consistency, robustness, convergence rate and finding better plausible optimal solutions.

Combined Heat and Power Dynamic Economic Emissions Dispatch with Valve Point Effects and Incentive Based Demand Response Programs

In this paper, the Combined Heat and Power Dynamic Economic Emissions Dispatch (CHPDEED) problem formulation is considered. This problem is a complicated nonlinear mathematical formulation with multiple, conflicting objective functions. The aim of this mathematical problem is to obtain the optimal quantities of heat and power output for the committed generating units which includes power and heat only units. Heat and load demand are expected to be satisfied throughout the total dispatch interval. In this paper, Valve Point effects are considered in the fuel cost function of the units which lead to a non-convex cost function. Furthermore, an Incentive Based Demand Response Program formulation is also simultaneously considered with the CHPDEED problem further complicating the mathematical problem. The decision variables are thus the optimal power and heat output of the generating units and the optimal power curbed and monetary incentive for the participating demand response consumers. The resulting mathematical formulations are tested on four practical scenarios depicting different system operating conditions and obtained results show the efficacy of the developed mathematical optimization model. Obtained results indicate that, when the Incentive-Based Demand Response (IBDR) program’s operational hours is unrestricted with a residential load profile, the energy curtailed is highest (2680 MWh), the energy produced by the generators is lowest (38,008.53 MWh), power losses are lowest (840.5291 MW) and both fuel costs and emissions are lowest.

Fuzzy Logic Controlled Based Ant-Lion Optimization Hybridization for Economic Power Dispatch

The demand on the power system rising more rapidly is causing to increase the power system size and capacity. There is a need of interconnection of various generating stations to meet the increased load demand. Economical unit commitment is necessary for plant operation with the advancement in power system integration. The Economical Power Dispatch (EPD) is to find the most favourable combination of generating systems output powers which reduce the fuel cost by satisfying all system constraints. This research involves the fuzzy logic controller (FLC) has been hybridized with Ant-Lion Optimization (ALO) algorithm for EPD. By using this new hybrid technique, minimization of total operating cost by economically dispatch the power to meet the required load and also minimization of system total losses by optimum allocation of DG units were done. Fuel cost function and demand on system are modeled by fuzzy membership functions. The ALO is used to obtain the schedule the committed generating unit’s outputs so as to meet the required load demand. This proposed FLC based ALO technique executed with MATLAB software and applied on IEEE-30 system. Effectiveness of this projected algorithm is determined and evaluated with standalone techniques like conventional ALO, ALO-PSO algorithms.

A Novel Distributed Dynamic Economic Dispatch Based on Dual ADMM and IPM

This paper presents a novel distributed method for dynamic economic dispatch (DED) problems with cubic fuel cost functions based on the dual alternating direction method of multipliers (D‐ADMM) and interior point method (IPM). This scheme enables us to combine the excellent parallelism of ADMM with the superior convergence properties of the IPM. The idea adopted by the proposed algorithm is that the outer‐loop uses ADMM decoupling, and the inner‐loop uses IPM to solve the cubic polynomial optimization subproblems. When the unit set is divided into multiple partitions, D‐ADMM also has the nice central processing unit (CPU) runtime as the well as the number of iterations. In addition, we use a Decoupling‐Decomposition‐Backtracking and parallel improved multiple centrality corrections decoupling interior point method (DDB‐PIMCCD) to solve the aforementioned larger subproblems more efficiently. Finally, the numerical results, in both serial and parallel modes, on a set of 22 DED cases with the range of units from 8 to 1000 units show that the proposed method is very promising for large scale distributed DED problems. Because it can keep the unit information about each subset in secret to suit the market environment and can obtain high‐quality solutions with reasonable time. © 2020 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Optimal short-term hydro-thermal scheduling using multi-function global particle swarm optimization

<p>An optimal short-term hydro-thermal scheduling (ST-HTS) problem is solved in this paper using the multi-function global particle swarm optimization (MF-GPSO). A multi-reservoir cascaded hydro-electric system with a non-linear relationship between water discharge rate, power generation and net head is considered in this paper. The ST-HTS problem determines the optimal power generation of hydro and thermal generators which is aimed to minimize total fuel cost of thermal power plants during a determined time period. Effects of valve point loading and prohibited operating zones in the fuel cost function of the thermal power plants is examined. Power balance, reservoir volume, water balance and operation constraints of hydro and thermal plants are considered. The effectiveness and feasibility of MF-GPSO algorithm is examined on a standard test system, and the simulation results are compared with other algorithms presented in the literature. The results show that the MF-GPSO algorithm appears to be the best in terms of convergence speed and optimal cost compared with other techniques reported in the literature.</p>

Short Term Hydro-Thermal Scheduling Using Backtracking Search Algorithm

In this article, a new optimization technique, the backtracking search algorithm (BSA), is proposed to solve the hydrothermal scheduling problem. The BSA has mainly unique five steps: (i) Initialization; (ii) Selection – I; (iii) Mutation; (iv) Crossover; and (v) Selection – II; which have been applied to minimize fuel cost of the hydro-thermal scheduling problem. The BSA is very fast, robust, reliable optimization technique and gives an accurate, optimized result. Mutation and crossover are very effective steps of the BSA, which help to determine the better optimum value of the objective function. Here, four hydro and three thermal power generating units are considered. Performance of each committed generating units (hydro and thermal) are also analyzed using a new proposed algorithm, the BSA. A multi-reservoir cascaded hydroelectric with a nonlinear relationship between water discharge rate and power generation is considered. The valve point loading effect is also considered with a fuel cost function. The proposed optimum fuel cost obtained from the BSA shows the better result as compared to other techniques like particle swarm optimization (PSO), teaching learning-based optimization (TLBO), quasi-oppositional teaching learning-based optimization (QOTLBO), real-coded genetic algorithm (RCGA), mixed-integer linear programming (MILP) and krill herd algorithm (KHA), etc.

GWO-based estimation of input-output parameters of thermal power plants

The fuel cost curve of thermal generators was very important in the calculation of economic dispatch and optimal power flow. Temperature and aging could make changes to fuel cost curve so curve estimation need to be done periodically. The accuracy of the curve parameters estimation strongly affected the calculation of the dispatch. This paper aims to estimate the fuel cost curve parameters by using the grey wolf optimizer method. The problem of curve parameter estimation was made as an optimization problem. The objective function to be minimized was the total number of absolute error or the difference between the actual value and the estimated value of the fuel cost function. The estimated values of parameter that produce the smallest total absolute error were the values of final solution. The simulation results showed that parameter estimation using gray wolf optimizer method further minimized the value of objective function. By using three models of fuel cost curve and given test data, parameter estimation using grey wolf optimizer method produced the better estimation results than those estimation results obtained using least square error, particle swarm optimization, genetic algorithm, artificial bee colony and cuckoo search methods.

Large-scale economic load dispatch using squirrel search algorithm

PurposeEconomic load dispatch (ELD) is one of the crucial optimization problems in power system planning and operation. The ELD problem with valve point loading (VPL) and multi-fuel options (MFO) is defined as a non-smooth and non-convex optimization problem with equality and inequality constraints, which obliges an efficient heuristic strategy to be addressed. The purpose of this study is to present a new and powerful heuristic optimization technique (HOT) named as squirrel search algorithm (SSA) to solve non-convex ELD problems of large-scale power plants.Design/methodology/approachThe suggested SSA approach is aimed to minimize the total fuel cost consumption of power plant considering their generation values as decision variables while satisfying the problem constraints. It confers a solution to the ELD issue by anchoring with foraging behavior of squirrels based on the dynamic jumping and gliding strategies. Furthermore, a heuristic approach and selection rules are used in SSA to handle the constraints appropriately.FindingsEmpirical results authenticate the superior performance of SSA technique by validating on four different large-scale systems. Comparing SSA with other HOTs, numerical results depict its proficiencies with high-qualitative solution and by its excellent computational efficiency to solve the ELD problems with non-smooth fuel cost function addressing the VPL and MFO. Moreover, the non-parametric tests prove the robustness and efficacy of the suggested SSA and demonstrate that it can be used as a competent optimizer for solving the real-world large-scale non-convex ELD problems.Practical implicationsThis study has compared various HOTs to determine optimal generation scheduling for large-scale ELD problems. Consequently, its comparative analysis will be beneficial to power engineers for accurate generation planning.Originality/valueTo the best of the authors’ knowledge, this manuscript is the first research work of using SSA approach for solving ELD problems. Consequently, the solution to this problem configures the key contribution of this paper.

Multiobjective Electrical Power Dispatch of Thermal Units with Convex and Non Convex Fuel Cost Functions for 24 Hours Load Demands

There are a host of difficult issues with scheduling, operation, and control of integrated power systems. The electricity sector is changing rapidly, and one of the most important concerns is deciding operational strategies to meet electricity demand. It is a greater challenge to satisfy customer demand for power at a minimum cost. The operating characteristics of all generators may be different. In general, operating cost is not proportionate to the performance of these generators. Therefore challenge for power utilities to balance the total load between generators. For a specific load condition on energy systems, Economic Dispatch(ED) seeks to reduce the fuel costs of power generation units. Moreover, energy utilities have also an important task to reduce gaseous emission. So the ED problem can be recognized as a complicated multi-objective optimization problem (MOOP) with two competing targets, the minimal cost of fuel and the minimum emissions effects. This paper presented an efficient method, hybrid of particle swarm optimization (PSO) and a learning-based optimization (TLBO) for combined environmental issues because of gaseous emission and economic dispatch (CEED) problems. The results were shown and verified by PSO and TLBO for standard 3 and 6-generator frameworks with combined issues of emission and economic dispatch taking into account line losses and prohibited zones (POZs) on hourly demand for 24 hours.

A Fast Scheduling Method to Solve Economic Load Dispatch Problem

Optimal scheduling of the generating units in one hour ahead considerably affects the electricity cost because the fuel cost component will bring up the economic load dispatch problem. Fuel cost is an essential parameter to calculate the optimal cost function of the power systems subject to the operating constraints and transmission loss. Generally, the economic load dispatch problem is resolved through the iteration step and using many variables so that it uses long computation time. The accuracy can also be low because the point of the solution can fall near the minimum local point. This paper proposes a method to provide better efficiency and accuracy of the economic load dispatch problem. The methodology forms a fuel cost function in the quadratic equation mathematically derived in order to obtain a faster solution without iteration processes. The B-loss matrix determines the transmission loss after receiving the optimal solution without considering transmission losses. The method validation simulates the economic load dispatch for the 26-Bus power system and the 6-generating units. After comparing with the Genetic Algorithm, the proposed method can save fuel costs significantly of about $ 29876.46 in 24 hours, while computing time in executing the application program is short enough, namely 0.15 seconds.