Ramp Rate Limits Research Articles

A Multiobjective Bacterial Foraging Algorithm to Solve the Environmental Economic Dispatch Problem

In this article, multi-objective bacterial foraging with non-dominated sorting procedure is applied to solve the non-linear constrained environmental/economic dispatch problem. In the proposed work, we have considered the standard IEEE 30-bus 6-generator test system with fuel cost and emission as two conflicting objectives to be optimized simultaneously. The limits on generator real power and reactive power outputs, bus voltages and power flow of transmission lines, ramp rate limits and prohibited operating zones are considered as the constraints. The proposed work also includes the effect of having non-smooth cost characteristics to mimic the valve point loading effect. The simulation result reveals that the proposed approach is a competitive one to the existing methods for finding the best optimal Pareto front of two conflicting objectives and has the better robustness.

Two-stage network constrained robust unit commitment problem

For a current deregulated power system, a large amount of operating reserve is often required to maintain the reliability of the power system using traditional approaches. In this paper, we propose a two-stage robust optimization model to address the network constrained unit commitment problem under uncertainty. In our approach, uncertain problem parameters are assumed to be within a given uncertainty set. We study cases with and without transmission capacity and ramp-rate limits (The latter case was described in Zhang and Guan (2009), for which the analysis part is included in Section 3 in this paper). We also analyze solution schemes to solve each problem that include an exact solution approach and an efficient heuristic approach that provides tight lower and upper bounds for the general network constrained robust unit commitment problem. The final computational experiments on an IEEE 118-bus system verify the effectiveness of our approaches, as compared to the nominal model without considering the uncertainty.

Hybrid Artificial Immune System Approach for Profit Based Unit Commitment Problem

This paper presents a new approach with artificial immune system algorithm to solve the profit based unit commitment problem. The objective of this work is to find the optimal generation scheduling and to maximize the profit of generation companies (Gencos) when subjected to various constraints such as power balance, spinning reserve, minimum up/down time and ramp rate limits. The proposed hybrid method is developed through adaptive search which is inspired from artificial immune system and genetic algorithm to carry out profit maximization of generation companies. The effectiveness of the proposed approach has been tested for different Gencos consists of 3, 10 and 36 generating units and the results are compared with the existing methods.

Emission-Concerned Wind-EV Coordination on the Transmission Grid Side With Network Constraints: Concept and Case Study

This paper presents a study of emission-concerned wind-electric vehicle (EV) coordination on the transmission grid side. An aggregator model representing a cluster of controllable EVs is proposed, and is coordinated with large-scale wind power on the transmission side. Using these EV aggregators, a conceptual framework is developed for wind-EV coordination, based on a three-level hierarchy. At the top level, the control center determines the optimal plant outputs and EV charging strategies from the proposed wind-EV dispatch model, where emission costs, thermal plant generation, controllable EVs, and CO2 capture power plants are taken into account and set as multi-objectives. The time-varying number of EV connections, plant ramp rate limits, and network constraints, including interface and branch transmission capacities, are also considered in the model. The model is used to verify the benefits of wind-EV coordination in an IEEE 14-bus system. Compared with uncoordinated charging, wind curtailment, emissions, total optimized cost, and EV charging fees are all greatly reduced by coordination. Moreover, interface transmission capacity and discharging price are found to be important factors in coordination, and the impacts are investigated.

Gencos wind–thermal scheduling problem using Artificial Immune System algorithm

This paper presents an Artificial Immune System approach for solving generation scheduling problem of a Genco comprised of thermal and wind energy systems. Wind–thermal scheduling problem determine the time of instant to start up and shut down the generating units over a scheduled time period, while satisfying the ‘system’ and ‘generator’ constraints including minimum up/down time; ramp rate limits of thermal units and wind power constraints. In this work, the impact of wind energy on short term generation scheduling problem is analyzed through the adaptive search which is inspired from the Artificial Immune System. The effectiveness of the proposed approach is demonstrated through a Genco consists of 10 thermal units with 2 wind farms and the results for the near optimal schedule are discussed.

Gravitational Search Algorithm Optimization for Dynamic Economic Load Dispatch with Valve-Point Effects

The dynamic economic load dispatch problem (DELDP), with the consideration of valve-point effects, is a complicated non-linear constrained optimization problem with non-smooth and non-convex characteristics. The main goal of DELDP is to find out the optimal generation schedule of the generators corresponding to the most economical operating point of the system over the considered timing horizon. In this paper, a new swarm based optimization algorithm, so called gravitational search algorithm (GSA) has been proposed to solve the DELDP with considering valve-point effects and transmission power loss constraints. The performance of the proposed method is rigorously tested for optimality, convergence, robustness and computational efficiency on a 10-unit test system with a 24-h load demand at each 1-h time intervals which is so well-known and common in literature. The proposed algorithm also takes care of different constraints like power balance, ramp rate limits and generation limits. The simulation results reveal that, compared with other methods reported in literatures recently, the proposed GSA method are capable of obtaining better quality solutions with higher efficiency. In addition, sensitivity analysis has been performed on the controlling parameters of GSA to reach the best arrangement for them.

Robust, fast and optimal solution of practical economic dispatch by a new enhanced gradient‐based simplified swarm optimisation algorithm

Nowadays, the rising concern about the costs of fuel and operation of generating units in the energy control centre deserve progress of solution methodologies for the practical economic dispatch (ED) problems. ED aims to schedule the committed units’ output power while satisfying practical constraints and load demand. The generator ramp rate limits, non-convex and discontinuous nature of prohibited operating zones, non-smooth characteristic of valve-point effects, multi-fuel type of generation units, transmission line losses and the large number of units in practical power plants make this problem very hard to solve. In this study, a new solution method of integrating the classical gradient-based optimisation technique and a new enhanced simplified swarm optimisation algorithm is comprehensively presented and successfully applied to determine the feasible, robust, fast and globally or near-globally optimal solution within a rapid timeframe for the ED problems. The simulations are carried out on four-test systems, including 10-, 15-, 40- and 80-units using the proposed optimisation technique in the Fortran Power Station 4.0 software. The current proposal outperforms other methods showcased in the recent state-of-the art literature in the area.

Gbest guided artificial bee colony algorithm for environmental/economic dispatch considering wind power

The current energy consumption in most of the countries is weighing heavily on fossil fuels, which account for about 70–90% of total energy used. The ecological concerns about air pollution and global warming are encouraging wider use of clean renewable technologies such as wind and solar energy. In this paper, Gbest guided artificial bee colony algorithm (GABC) is applied to optimize the emission and overall cost of operation of wind–thermal power system. The random nature of wind power is modeled using weibull probability distribution function (PDF). Moreover, the uncertainty in wind power is considered in the cost model by including the power imbalance terms such as overestimation and underestimation costs of available wind power. To validate the effectiveness of proposed method, it is first applied to three standard test systems considering different technical constraints such as valve loading effect, prohibited zones, ramp rate limits, etc. In second part, the effect of wind power generation on dispatch cost and emission is analyzed for IEEE-30 bus test system. A comparative analysis with other similar optimization techniques reveals that the proposed technique has better solution accuracy and convergence results.

A new modified teaching-learning algorithm for reserve constrained dynamic economic dispatch

This paper presents a new optimization algorithm, named modified teaching-learning algorithm, to solve a more practical formulation of the reserve constrained dynamic economic dispatch of thermal units considering the network losses and operating limitations of the generating units (i.e., the valve loading effect and ramp rate limits). Unlike the previous approaches, three types of the system spinning reserve requirements are explicitly modeled in the problem and a new constraint-handling is proposed to satisfy them. The proposed teaching-learning optimization algorithm is a new population-based optimization method features between the teacher and learners (students). Therefore, this algorithm searches for the global optimal solution through two main phases: 1) the “teacher phase” and 2) the “learner phase”. Nevertheless, these two phases are not adequate for learning interaction between the teacher and the learners in the entire search space. Thus, in this paper a new phase named “modified phase” based on a self-adaptive learning mechanism is added to the algorithm to improve the process of knowledge learning among the learners and accordingly generate promising candidate solutions. The proposed framework is applied to 5-, 10-, 30-, 40-, and 140-unit test systems in order to evaluate its efficiency and feasibility.

Dynamic Constrained Economic/Emission Dispatch Scheduling Using Neural Network

In this paper, a Dynamic Economic/Emission Dispatch (DEED) problem is obtained by considering both the economy and emission objectives with required constraints dynamically. This paper presents an optimization algorithm for solving constrained combined economic emission dispatch (EED) problem and DEED, through the application of neural network, which is a flexible Hopfield neural network (FHNN). The constrained DEED must not only satisfy the system load demand and the spinning reserve capacity, but some practical operation constraints of generators, such as ramp rate limits and prohibited operating zone, are also considered in practical generator operation. The feasibility of the proposed FHNN using to solve DEED is demonstrated using three power systems, and it is compared with the other methods in terms of solution quality and computation efficiency. The simulation results showed that the proposed FHNN method was indeed capable of obtaining higher quality solutions efficiently in constrained DEED and EED problems with a much shorter computation time compared to other methods.

Chaotic self-adaptive differential harmony search algorithm based dynamic economic dispatch

Dynamic economic dispatch (DED) is one of the main optimization problems in electrical power system operation and control. DED problem is a non-smooth and non-convex problem when valve point effect, ramp-rate limits and prohibited operating zones of generation units are taken into account. This paper proposes an efficient chaotic self-adaptive differential harmony search (CSADHS) algorithm to solve the complicated DED problem in the presence of valve point effect, ramp-rate limits and prohibited operating zones constraints. In the proposed algorithm, chaotic self-adaptive differential mutation operator is used instead of pitch adjustment operator in the harmony search (HS) algorithm, to enhance the searching performance to find the quality solution. The effectiveness of the proposed algorithm is demonstrated on 10, 15 and 30 unit systems for a period of 24h. The simulation results obtained by the proposed algorithm are compared with the results obtained, using differential harmony search (DHS) algorithm, chaotic differential harmony search (CDHS) algorithm, and also with the results of other methods available in the literature. In terms of solution quality, the proposed algorithm is found to be better than other algorithms and in terms of speed of convergence, standard deviation of generation cost, and computational time, the proposed algorithm is better than DHS and CDHS algorithm.

Dynamic environmental economic dispatch using multiobjective differential evolution algorithm with expanded double selection and adaptive random restart

The dynamic environmental economic dispatch (DEED) model is presented in this paper, in which the fuel cost and emission effect over a certain period of time are optimized as conflicting objectives. It is a high dimensional, nonlinear constrained multiobjective optimization problem when generators’ valve point effect, ramp rate limits and power load variation are considered. This paper proposes a modified adaptive multiobjective differential evolution (MAMODE) algorithm to solve the problem. In MAMODE, expanded double selection and adaptive random restart operators are proposed to modify the evolutionary processes for avoiding premature and a dynamic heuristic constraint handling (DHCH) approach is introduced to deal with the complicated constraints. The DHCH can lessen infeasible solutions gradually. To illustrate the effectiveness of the method, four cases based on three test power systems are studied. The simulation result indicates that the DEED can be solved quickly. Comparison of numerical results demonstrates the proposed method has higher performance.

A new algorithm for combined heat and power dynamic economic dispatch considering valve-point effects

In this study, combined heat and power units are incorporated in the practical reserve constrained dynamic economic dispatch, which minimizes total production costs considering realistic constraints such as ramp rate limits and valve-point effects over a short time span. The integration of combined heat and power units and considering power ramp constraints for these units necessitate an efficient tool to cope with joint characteristics of electricity power-heat. Unlike pervious approaches, the system spinning reserve requirements are clearly formulated in the problem and a novel charged system search algorithm is proposed to solve it. In the proposed algorithm a novel self-adaptive learning framework, adaptive selection operation and repelling force modeling are used in order to increase the population diversity and amend the convergence criteria. The proposed framework is applied for three small, medium and large test systems in order to evaluate its efficiency and feasibility.

Economic load dispatch using θ-PSO

This paper presents a θ-particle swarm optimization (θ-PSO) based algorithm to solve constrained economic load dispatch (ELD) problems of thermal plants. The proposed methodology easily takes care of practical constraints such as transmission losses, ramp rate limits, and prohibited operating zones, and also deals with non-smoothness of cost function arising due to the use of valve point effects. The main evaluation mechanism of classical particle swarm optimization (CPSO) is modified in the novel θ-PSO by replacing the velocity vector with a phase angle vector. So, the positions are decided by the mapping of phase angles in θ-PSO. The performance of proposed algorithm has been tested on systems possessing 6, 13, 15, and 40 generating units involving varying degree of complexity. Detailed comparisons under equitable conditions are provided with prevalent approaches to measure the efficiency of the proposed algorithm. The findings affirm that the method outperforms the existing techniques in terms of solution quality and computational efficiency and can be a promising alternative approach for solving the ELD problems in practical power system.

Dynamic Economic Emission Dispatch Using Multi-Objective Hybrid Evolutionary Algorithm

Dynamic economic emission dispatch (DEED) is an important optimization task for power plants. The problem is a highly constrained multi-objective optimization problem involving conflicting objectives with both equality and inequality constraints. This paper introduces two objective functions of DEED model: the lowest generation cost and the smallest carbon emissions with power balance constraints, unit output constraints and unit ramp rate limits. Then the paper presents a multi-objective hybrid evolutionary algorithm (MHEA) to solve the DEED model. The MHEA is a hybrid optimization algorithm based on orthogonal initialization, improved differential operation with migration strategy, parameter adaptive control, multi-objective selection strategy and analytic hierarchy process based fuzzy technique (AFT). Numerical results of one test system demonstrate the capabilities of the proposed approach. Compared with other classical methods, the proposed approach gets better result.

An improved harmony search algorithm to solve economic load dispatch problems with generator constraints

This paper presents a new improved harmony search (IHS) algorithm to solve non-convex economic load dispatch problems in the power system. In the proposed IHS algorithm, multiple harmony memory consideration rates and dynamic pitch adjusting rate are used to generate a new harmony/solution vector with enhanced solution quality. The effectiveness of the proposed IHS algorithm has been successfully tested in the test systems which consists of six units with ramp rate limits, prohibited operating zones and transmission loss, thirteen units with valve point effect, and ten units with multiple fuel options and valve point effect. The results obtained using the proposed IHS algorithm are compared with the results of other techniques reported in the literature. The comparative results reveal that the proposed IHS algorithm has good searching capacity to find the global optimal solution, than the other methods reported in the literature and also has good convergence characteristic.

A hybrid differential evolution algorithm based on particle swarm optimization for nonconvex economic dispatch problems

This paper presents the design and application of an efficient hybrid heuristic search method to solve the practical economic dispatch problem considering many nonlinear characteristics of power generators, and their operational constraints, such as transmission losses, valve-point effects, multi-fuel options, prohibited operating zones, ramp rate limits and spinning reserve. These practical operation constraints which can usually be found at the same time in realistic power system operations make the economic load dispatch problem a nonsmooth optimization problem having complex and nonconvex features with heavy equality and inequality constraints.The proposed approach combines in the most effective way the properties of two of the most popular evolutionary optimization techniques now in use for power system optimization, the Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms. To improve the global optimization property of DE, the PSO procedure is integrated as additional mutation operator.The effectiveness of the proposed algorithm (termed DEPSO) is demonstrated by solving four kinds of ELD problems with nonsmooth and nonconvex solution spaces. The comparative results with some of the most recently published methods confirm the effectiveness of the proposed strategy to find accurate and feasible optimal solutions for practical ELD problems.

Optimal Operation of Wind-thermal generation using differential evolution

Numerous optimization paradigms have been developed for power system optimization tasks till date but none has found the level of acceptance which is being received by evolutionary soft computing methods. Traditional methods are found to be inefficient for complex practical problems with equality and inequality constraints therefore the complexity of the task reveals the necessity for development of efficient algorithms to accurately locate the optimum solution. The present paper proposes to solve complex constrained optimization problems using differential evolution (DE) with multiple mutation strategies. The role of control parameters and mutation strategies of DE algorithm in achieving the global best result is critically explored.The depleting reserves of fossil fuel and growing concern about environmental protection dictates the integration of renewable power resources into the power grid. Including wind power with the conventional power has become very popular in recent years due to the rapid development of technology in this field. Modeling of wind-thermal system is required to find the optimal wind generator capacity that can be integrated into the existing system such that all operating constraints are satisfied. The developed algorithm is tested on a standard test system taking into consideration the wind uncertainty and ramp-rate limits of thermal power units. The results clearly demonstrate the effectiveness of the proposed method in finding feasible and efficient globally optimal solutions

Application of Imperialist Competitive Algorithm to Solve Constrained Economic Dispatch

In the constrained dynamic ED problem, considering some practical operation constraints of generators, such as ramp rate limits and prohibited operating zones, electric power generation of units are scheduled. So, this paper, considering these constraints, presents a new optimization technique based on Imperialist Competitive Algorithm (ICA) to solve the Economic Dispatch (ED) problem in power systems. To show the efficiency of the proposed method, this algorithm is applied to solve constrained dynamic ED problem of two power systems with 6 and 15 units. The results are compared to those achieved from conventional methods such as Simulated Annealing (SA), Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). The experimental results show that the proposed method is capable to determine the solutions of ED problem more fast and accurate than other conventional approaches.

Reserve Constrained Dynamic Economic Dispatch: A New Fast Self-Adaptive Modified Firefly Algorithm

This paper provides a more practical formulation of the reserve constrained dynamic economic dispatch that considers highly realistic constraints, such as transmission losses, ramp rate limits, and valve-point effects over a short-term time span. Unlike the previous approaches, three types of system spinning reserve requirements are explicitly modeled in the problem and a new self-adaptive modified firefly algorithm is suggested to solve it. Firefly algorithm has some similar features with particle swarm optimization that hunts for the global or near-global optimal solutions through moving individuals, i.e., fireflies in the problem search space. Although this algorithm is completely suitable for tuning off its parameters, it suffers from the difficulties of trapping in local optima as some of the algorithms. To overcome this problem, a self-adaptive parameter tuning and mutation strategy has been utilized. The proposed technique is suitable from a regard of economical aspects, and is also appropriate for high-speed real-time application due to fast and less execution time. In order to evaluate the efficiency and feasibility of the proposed framework in practical power systems, four small, medium, and large test systems are presented as case studies.