Fuel Cost Function Research Articles

Hybrid genetic algorithm and particle swarm for optimal power flow with non-smooth fuel cost functions

This paper presents a hybrid genetic algorithm and particle swarm optimization (HGAPSO) for solving optimal power flow problem with non-smooth cost function and subjected to limits on generator real, reactive power outputs, bus voltages, transformer taps and power flow of transmission lines. In (HGAPSO), individuals in a new generation are created, not only by crossover and mutation operation as in (GA), but also by (PSO). The effectiveness of this algorithm is examined and tested for standard IEEE 30 bus system with six generating units. The results of the proposed technique are compared with that of PSO and other methods reported in the literature.

Using the Direct Search Method for Optimal Dispatch of Distributed Generation in a Medium-Voltage Microgrid

This paper proposes a simple and efficient approach for the optimal dispatch in a medium-voltage microgrid (MG) with various types of distributed generation (DG). The fuel costs generated by these DGs are determined using quadratic and linear functions dependent on the types of DGs. Instead of using the traditional Lagrange multiplier method for power system economic dispatch, the proposed direct search method (DSM) approach is able to handle several inequality constraints without introducing any multipliers and furthermore it can solve the non-derivative problems or the fuel cost functions being much more complicated. Accordingly, the DSM is proposed for determining the optimal dispatch of MGs with various types of DG to minimize generation costs under grid-tied and autonomous operations. Results demonstrate that the proposed DSM is a highly suitable and simple approach to determining the optimal dispatch in medium-voltage MGs with various types of DG.

Optimal power flow using artificial bee colony algorithm with global and local neighborhoods

Optimal power flow (OPF) is one of the most requisite tools for power system operation analysis. This problem has a complex mathematical formulation which is relatively hard to solve. This paper presents a swarm intelligence-based approach to solve the OPF problem. The proposed approach describes the use of a modified artificial bee colony (ABC) algorithm called ABC with global and local neighborhoods (ABCGLN) to determine the optimal settings of OPF control variables. ABCGLN is a recent modified version of basic ABC algorithm that can handle non-differentiable, non-linear, and multi modal objective functions. The ABCGLN approach is tested here on the standard IEEE 30-bus test system with three different objective functions for minimizing quadratic fuel cost function, piecewise quadratic cost function and quadratic cost function with valve point effects. The simulation results demonstrate the potential of ABCGLN algorithm of finding effective and robust quality solutions to solve OPF problem with various objective functions for the considered system as compared to those available in the literature.

Congestion management by determining optimal location of series FACTS devices using hybrid bacterial foraging and Nelder–Mead algorithm

In this paper, the Thyristor-Controlled Series-Compensated (TCSC) devices are located for congestion management in the power system by considering the non-smooth fuel cost function and penalty cost of emission. For this purpose, it is considered that the objective function of the proposed optimal power flow (OPF) problem is minimizing fuel and emission penalty cost of generators. A hybrid method that is the combination of the bacterial foraging (BF) algorithm with Nelder–Mead (NM) method (BF-NM) is employed to solve the OPF problems. The optimal location of the TCSC devices are then determined for congestion management. The size of the TCSC is obtained by using of the BF-NM algorithm to minimize the cost of generation, cost of emission, and cost of TCSC. The simulation results on IEEE 30-bus, modified IEEE 30-bus and IEEE 118-bus test system confirm the efficiency of the proposed method for finding the optimal location of the TCSC with non-smooth non-convex cost function and emission for congestion management in the power system. In addition, the results clearly show that a better solution can be achieved by using the proposed OPF problem in comparison with other intelligence methods.

Artificial bee colony optimization for economic dispatch with valve point effect

In recent years, various heuristic optimization methods have been proposed to solve economic dispatch (ED) problem in power systems. This paper presents the well-known power system ED problem solution considering valve-point effect by a new optimization algorithm called artificial bee colony (ABC). The proposed approach has been applied to various test systems with incremental fuel cost function, taking into account the valve-point effects. The results show that the proposed approach is efficient and robust when compared with other optimization algorithms reported in literature.

Application of chaos-based chaotic invasive weed optimization techniques for environmental OPF problems in the power system

This paper presents efficient chaotic invasive weed optimization (CIWO) techniques based on chaos for solving optimal power flow (OPF) problems with non-smooth generator fuel cost functions (non-smooth OPF) with the minimum pollution level (environmental OPF) in electric power systems. OPF problem is used for developing corrective strategies and to perform least cost dispatches. However, cost based OPF problem solutions usually result in unattractive system gaze emission issue (environmental OPF). In the present paper, the OPF problem is formulated by considering the emission issue. The total emission can be expressed as a non-linear function of power generation, as a multi-objective optimization problem, where optimal control settings for simultaneous minimization of fuel cost and gaze emission issue are obtained. The IEEE 30-bus test power system is presented to illustrate the application of the environmental OPF problem using CIWO techniques. Our experimental results suggest that CIWO techniques hold immense promise to appear as efficient and powerful algorithm for optimization in the power systems.

Hybrid Chemical Reaction Optimization Approach for Combined Economic Emission Short-term Hydrothermal Scheduling

—This article presents the hybridization of a newly developed, novel, and efficient chemical reaction optimization technique and differential evolution for solving a short-term hydrothermal scheduling problem. The main objective of the short-term scheduling is to schedule the hydro and thermal plants generation in such a way that minimizes the generation cost. However, due to strict government regulations on environmental protection, operation at minimum cost is no longer the only criterion for dispatching electrical power. The idea behind the environmentally constrained hydrothermal scheduling formulation is to estimate the optimal generation schedule of hydro and thermal generating units in such a manner that fuel cost and harmful emission levels are both simultaneously minimized for a given load demand. In this context, this article proposes a hybrid chemical reaction optimization and differential evolution approach for solving the multi-objective short-term combined economic emission scheduling problem. The effectiveness of the proposed hybrid chemical reaction optimization and differential evolution method is validated by carrying out extensive tests on two hydrothermal scheduling problems with incremental fuel-cost functions taking into account the valve-point loading effects. The result shows that the proposed algorithm improves the solution accuracy and reliability compared to other techniques.

Novel Adaptive Evolutionary Computation Approaches to the Dynamic Economic Load Dispatch Problems with Non-Smooth Fuel Cost Function

paper presents novel approaches to solving the dynamic economic load dispatch (DELD) problem with valve-point loading effects. In dynamic environments, optimization problems change over time. They are also called time dependent or dynamic time-linkage problems, where decisions made at a given time may affect output obtained in a later time. It is therefore expected of algorithms solving dynamic optimization problems to both locate optimal solutions of the given problem and keep track of such solutions as they change with time. An investigation was made of three optimization methods in conjunction with three smart mutation variants, on benchmark problem cases involving 5 and 10 generating units, the major test cases in the literature with comparative results for other algorithms. The results suggest that the third approach which exploits the dynamic nature of the problem was capable of superior to the other two approaches. Comparisons with all approaches so far in the literature that have addressed these problems show that these evolutionary computation approaches are superior to other algorithms.

Hybrid optimization algorithm for modeling and management of micro grid connected system

In this paper, a hybrid optimization algorithm is proposed for modeling and managing the micro grid (MG) system. The management of distributed energy sources with MG is a multi-objective problem which consists of wind turbine (WT), photovoltaic (PV) array, fuel cell (FC), micro turbine (MT) and diesel generator (DG). Because, perfect economic model of energy source of the MG units are needed to describe the operating cost of the output power generated, the objective of the hybrid model is to minimize the fuel cost of the MG sources such as FC, MT and DG. The problem formulation takes into consideration the optimal configuration of the MG at a minimum fuel cost, operation and maintenance costs as well as emissions reduction. Here, the hybrid algorithm is obtained as artificial bee colony (ABC) algorithm, which is used in two stages. The first stage of the ABC gets the optimal MG configuration at a minimum fuel cost for the required load demand. From the minimized fuel cost functions, the operation and maintenance cost as well as the emission is reduced using the second stage of the ABC. The proposed method is implemented in the Matlab/Simulink platform and its effectiveness is analyzed by comparing with existing techniques. The comparison demonstrates the superiority of the proposed approach and confirms its potential to solve the problem.

Cuckoo search algorithm for short-term hydrothermal scheduling

This paper proposes a cuckoo search algorithm (CSA) for solving short-term fixed-head hydrothermal scheduling (HTS) problem considering power losses in transmission systems and valve point loading effects in fuel cost function of thermal units. The CSA method is a new meta-heuristic algorithm inspired from the obligate brood parasitism of some cuckoo species by laying their eggs in the nests of other host birds of other species for solving optimization problems. The advantages of the CSA method are few control parameters and effective for optimization problems with complicated constraints. The effectiveness of the proposed CSA has been tested on different hydrothermal systems and the obtained test results have been compared to those from other methods in the literature. The result comparison has shown that the CSA can obtain higher quality solutions than many other methods. Therefore, the proposed CSA can be an efficient method for solving short-term fixed head hydrothermal scheduling problems.

A Lexicographic Optimization and Augmented ϵ-constraint Technique for Short-term Environmental/Economic Combined Heat and Power Scheduling

—In recent years, combined heat and power units have become significant elements in conventional power stations due their numerous merits, including operational cost savings and reduced emissions. In this regard, this article proposes a short-term multi-objective framework for the combined heat and power economic/emission dispatch problem. In addition, to more precisely model the problem, the non-linear forms of fuel cost functions and valve-point loading along with power transmission loss are considered. The objectives of the problem are total cost minimization as well as minimization of pollutant emissions; lexicographic optimization and the augmented epsilon-constraint technique are employed to solve the multi-objective problem. Also, a fuzzy decision making technique has been used to select the most preferred solution among the Pareto solutions. Afterward, a comprehensive comparison is performed between the results obtained from the proposed method and those derived from the non-dominated sorting genetic algorithm II, strength Pareto evolutionary algorithm 2, and multi-objective line-up competition algorithm, verifying the superiority of the presented approach for lower execution time, total cost, and emission. Furthermore, the proposed model is implemented on a large-scale test system while the execution time is rational.

Dynamic economic dispatch using Lbest-PSO with dynamically varying sub-swarms

Dynamic economic dispatch (DED) is one of the major planning problem in a power system. It is a non-linear optimization problem with various operational constraints, which includes the constraints of the generators operating characteristics and the system constraints. Its principal aim is to minimize the cost of power production of all the participating generators over a time horizon of 24 h, while satisfying the system constraints. This problem deals with non-convex characteristics if generation unit valve-point effects are taken into account. The paper intends to solve the DED problem with valve-point effects, using our modified form of Local-best variant of Particle Swarm Optimization (Lbest PSO) algorithm. We have tested our algorithm on 5-unit, 10-unit and 110-unit test system with non-smooth fuel cost functions to prove the effectiveness of the suggested method over different state of the art methods.

Environmental Economic Load Dispatch with Quadratic Fuel Cost Function Using Cuckoo Search Algorithm

In this paper, a Cuckoo Search Algorithm (CSA) is proposed for solving environmental economic load dispatch (EELD) problem with quadratic fuel function. Cuckoo Search is a new meta-heuristic algorithm inspired from the obligate brood parasitism of some cuckoo species by laying their eggs in the nests of other host birds of other species for solving optimization problems with promising results. However, Cuckoo Search has not been applied to EELD problem so far. Therefore, the paper presents application of CSA to the problem. The effectiveness of the proposed method is tested on several cases of dispatch and loads. The obtained result including fuel cost, emission and computation time from CSA are compared to those from other method reported in the paper. The comparison result has indicated that the proposed CSA is a very efficient method for solving EELD problem.

Cuckoo Search Algorithm for Emission Reliable Economic Multi-objective Dispatch Problem

ABSTRACTThis paper presents a novel emission/reliable/economic dispatch (ERED) problem using a newly developed multi-objective cuckoo search algorithm (CSA). Traditionally, electric power systems are operated in such a way that the total fuel cost is minimized regardless of the emission and reliability level of the system. Recently, the restructured power system stresses the need for non-polluting, reliable, and economic operation. Hence, three conflicting objective functions such as emission, reliability, and fuel cost functions are considered in the practical economic dispatch (ED) problem. The ERED problem is formulated as a non-smooth and non-convex multi-objective ED problem incorporating valve-point effects of thermal units. The CSA utilizes the breeding behaviour of cuckoos, where each individual searches the most suitable nest to lay an egg (compromise solution) in order to maximize the egg's survival rate and achieve the best habitat society. The fuzzy set theory is used to find a best compromise solution from the Pareto-optimal set. The effectiveness of the proposed methodology is tested on a benchmark of 6-unit test system, IEEE RTS 24 bus system, and IEEE 118 bus system. The results are validated and compared with the solution available in the existing literature.

NSGA-II Technique for Multi-objective Generation Dispatch of Thermal Generators with Nonsmooth Fuel Cost Functions

Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is applied for solving Combined Economic Emission Dispatch (CEED) problem with valve-point loading of thermal generators. This CEED problem with valve-point loading is a nonlinear, constrained multi-objective optimization problem, with power balance and generator capacity constraints. The valve-point loading introduce ripples in the input-output characteristics of generating units and make the CEED problem as a nonsmooth optimization problem. To validate its effectiveness of NSGA-II, two benchmark test systems, IEEE 30-bus and IEEE 118-bus systems are considered. To compare the Pareto-front obtained using NSGA-II, reference Pareto-front is generated using multiple runs of Real Coded Genetic Algorithm (RCGA) with weighted sum of objectives. Comparison with other optimization techniques showed the superiority of the NSGA-II approach and confirmed its potential for solving the CEED problem. Numerical results show that NSGA-II algorithm can provide Pareto-front in a single run with good diversity and convergence. An approach based on Technique for Ordering Preferences by Similarity to Ideal Solution (TOPSIS) is applied on non-dominated solutions obtained to determine Best Compromise Solution (BCS).

에너지 저장장치를 이용한 마이크로 그리드의 최적운영 및 신뢰도 지수 개선

The micro grid considered in this paper consists of a diesel generator, a photovoltaic array, a wind turbine, a fuel cell, and a energy storage system. This paper explains and simulates the micro grid components in terms of accuracy and efficiency of having a system model based on the costs of fuel as well as operation and maintenance. For operational efficiency, the objective function in a diesel generator consists of the fuel cost function similar to the cost functions used for the conventional fossil-fuel generating plants. The wind turbine generator is modeled by the characteristics of variable output. The optimization is aimed at minimizing the cost function of the system while constraining it to meet the customer demand and safety of micro grid. The operating cost in fuel-cell system includes the fuel costs and the efficiency for fuel to generate electric power. To develop the overall system model gives a possibility to minimize of the total cost of micro grid. The application of optimal operation can save the interruption costs as well as the operating costs, and improve reliability index in micro grid.

Solving practical power system problems using hierarchical interactive PSO strategy considering SVC controllers

This paper presents a hierarchical interactive particle swarm optimization (HIPSO) for solving the static multi objective optimal power flow (OPF) considering multi SVC controllers and dynamic economic dispatch (DED). This study introduces a variant of PSO using new mechanism search based dynamic adjustment of PSO parameters coordinated with a hierarchical strategy for reactive power planning stage to improve the performances of the original PSO in terms of solution quality and convergence characteristics. The HIPSO algorithm optimizes a combined control variables such as: active power generations, voltage control of generators, tap transformer and the reactive power of multi SVC Controllers installed at a specified buses to minimize fuel cost, total power loss and voltage deviation while satisfying the generators constraints and power system security. The proposed approach examined and applied to many practical test systems: IEEE 57-Bus, IEEE 118-Bus, 40 generating units and 10 generating units to solving; the static multi objective OPF with quadratic fuel cost function, the economic dispatch considering valve point effects and the dynamic economic dispatch considering both valve point effects and ramp rate limits. Simulation results compared to Matpower, to the standard PSO and others recent metaheuristic methods confirm the effectiveness of the proposed combined approach.

A Direct Search Method to solve Economic Dispatch Problem with Valve-Point Effect

Scarcity of energy resources, increasing power generation cost and ever-growing demand for electric energy necessitates optimal economic dispatch in today’s power systems. The main objective of economic dispatch is to reduce the total power generation cost, while satisfying various equality and inequality constraints. Traditionally in economic dispatch problems, the cost function for generating units has been approximated as a quadratic function which doesn’t provide accurate results. Moreover, to obtain accurate fuel cost, valve-point effect in thermal power plant has to be taken into account. The inclusion of valve-point effect makes the modeling of the fuel cost functions of generating units more practical. In this paper a new evolutionary algorithm called Pattern Search Technique, has been employed to solve economic dispatch problem with the valve-point effect. Using this technique the non-linear cost function is solved for three unit system and the results are compared with the traditional PSO and GA method. These results prove that Pattern Search method is capable of getting higher quality solution including mathematical simplicity, fast convergence, and robustness to solve hard optimization problems.

Improved Immune Algorithm for Power Economic Dispatch Considering Units with Prohibited Operating Zones and Spinning Reserve

This study proposes an improved immune algorithm (IIA) with multiplier updating (MU) for power economic dispatch (PED) considering units with both of prohibited operating zones (POZ) and spinning reserve. The IIA equipped with an accelerated operation and a migration operation can efficiently search and actively explore solutions. The MU is introduced to handle the equality and inequality constraints of the power system. To show the advantages of the proposed algorithm, three realistic examples are investigated, and computational results of the proposed method are compared with that of previous methods. The proposed approach (IIA-MU) integrates the IIA and the MU, revealing that the proposed approach has the following merits - ease of implementation; applicability to non-convex fuel cost functions; better effectiveness than previous methods; better efficiency than immune algorithm with the MU (IA-MU), and the requirement for only a small population in applying the optimal PED problem of generators with POZ and spinning reserve.

Solving Optimal Power Flow Using Modified Bacterial Foraging Algorithm Considering FACTS Devices

In this paper, a new Modified Bacterial Foraging Algorithm (MBFA) method is developed to incorporate FACTS devices in optimal power flow (OPF) problem. This method can provide an enhanced economic solution with the use of controllable FACTS devices. Two types of FACTS devices, thyristor controlled series compensators (TCSC) and Static VAR Compensator (SVC) are considered in this method. The basic bacterial foraging algorithm (BFA) is an evolutionary optimization technique inspired by the foraging behavior of the E. coli bacteria. The strategy of the OPF problem is decomposed in two sub-problems, the first sub-problem related to active power planning to minimize the fuel cost function, and the second sub-problem designed to make corrections to the voltage deviation and reactive power violation based in an efficient reactive power planning of multi Static VAR Compensator (SVC). The specified power flow control constraints due to the use of FACTS devices are included in the OPF problem. The proposed method decomposes the solution of such modified OPF problem into two sub problems’ iteration. The first sub problem is a power flow control problem and the second sub problem is a modified Bacterial foraging algorithm (MBFA) OPF problem. The two sub problems are solved iteratively until convergence. Case studies are presented to show the effectiveness of the proposed method.