Review on application and comparison of metaheuristic techniques to multi-area economic dispatch problem

This paper presents both application and comparison of the metaheuristic techniques to multi-area economic dispatch(MAED)problem with tie line constraints considering transmission losses,multiple fuels,valve-point loading and prohibited operating zones.The metaheuristic techniques such as differential evolution,evolutionary programming,genetic algorithm and simulated annealing are applied to solve MAED problem.These metaheuristic techniques for MAED problem are evaluated on three different test systems,both small and large,involving varying degree of complexity and the results are compared against each other.

A PI+R Control Scheme Based on Multi-Agent Systems for Economic Dispatch in Isolated BESSs

Battery energy storage systems(BESSs)are widely used in smart grids.However,power consumed by inner impedance and the capacity degradation of each battery unit become particularly severe,which has resulted in an increase in operating costs.The general economic dispatch(ED)algorithm based on marginal cost(MC)consensus is usually a proportional(P)controller,which encounters the defects of slow convergence speed and low control accuracy.In order to solve the distributed ED problem of the isolated BESS network with excellent dynamic and steady-state performance,we attempt to design a proportional integral(PI)controller with a reset mechanism(PI+R)to asymptotically promote MC consensus and total power mismatch towards 0 in this paper.To be frank,the integral term in the PI controller is reset to 0 at an appropriate time when the proportional term undergoes a zero crossing,which accelerates convergence,improves control accuracy,and avoids overshoot.The eigenvalues of the system under a PI+R controller is well analyzed,ensuring the regularity of the system and enabling the reset mechanism.To ensure supply and demand balance within the isolated BESSs,a centralized reset mechanism is introduced,so that the controller is distributed in a flow set and centralized in a jump set.To cope with Zeno behavior and input delay,a dwell time that the system resides in a flow set is given.Based on this,the system with input delays can be reduced to a time-delay free system.Considering the capacity limitation of the battery,a modified MC scheme with PI+R controller is designed.The correctness of the designed scheme is verified through relevant simulations.

Energy Economic Dispatch for Photovoltaic-Storage via Distributed Event-Triggered Surplus Algorithm

This paper presents a novel approach to economic dispatch in smart grids equipped with diverse energy devices.This method integrates features including photovoltaic(PV)systems,energy storage coupling,varied energy roles,and energy supply and demand dynamics.The systemmodel is developed by considering energy devices as versatile units capable of fulfilling various functionalities and playing multiple roles simultaneously.To strike a balance between optimality and feasibility,renewable energy resources are modeled with considerations for forecasting errors,Gaussian distribution,and penalty factors.Furthermore,this study introduces a distributed event-triggered surplus algorithm designed to address the economic dispatch problem by minimizing production costs.Rooted in surplus theory and finite time projection,the algorithm effectively rectifies network imbalances caused by directed graphs and addresses local inequality constraints.The algorithm greatly reduces the communication burden through event triggering mechanism.Finally,both theoretical proofs and numerical simulations verify the convergence and event-triggered nature of the algorithm.

Economic Power Dispatching from Distributed Generations: Review of Optimization Techniques

In the increasingly decentralized energy environment,economical power dispatching from distributed generations(DGs)is crucial to minimizing operating costs,optimizing resource utilization,and guaranteeing a consistent and sustainable supply of electricity.A comprehensive review of optimization techniques for economic power dispatching from distributed generations is imperative to identify the most effective strategies for minimizing operational costs while maintaining grid stability and sustainability.The choice of optimization technique for economic power dispatching from DGs depends on a number of factors,such as the size and complexity of the power system,the availability of computational resources,and the specific requirements of the application.Optimization techniques for economic power dispatching from distributed generations(DGs)can be classified into two main categories:(i)Classical optimization techniques,(ii)Heuristic optimization techniques.In classical optimization techniques,the linear programming(LP)model is one of the most popular optimization methods.Utilizing the LP model,power demand and network constraints are met while minimizing the overall cost of generating electricity from DGs.This approach is efficient in determining the best DGs dispatch and is capable of handling challenging optimization issues in the large-scale system including renewables.The quadratic programming(QP)model,a classical optimization technique,is a further popular optimization method,to consider non-linearity.The QP model can take into account the quadratic cost of energy production,with consideration constraints like network capacity,voltage,and frequency.The metaheuristic optimization techniques are also used for economic power dispatching from DGs,which include genetic algorithms(GA),particle swarm optimization(PSO),and ant colony optimization(ACO).Also,Some researchers are developing hybrid optimization techniques that combine elements of classical and heuristic optimization techniques with the incorporation of droop control,predictive control,and fuzzy-based methods.These methods can deal with large-scale systems with many objectives and non-linear,non-convex optimization issues.The most popular approaches are the LP and QP models,while more difficult problems are handled using metaheuristic optimization techniques.In summary,in order to increase efficiency,reduce costs,and ensure a consistent supply of electricity,optimization techniques are essential tools used in economic power dispatching from DGs.

Solving Multi-Area Environmental/Economic Dispatch by Pareto-Based Chemical-Reaction Optimization Algorithm

In this study, we present a Pareto-based chemicalreaction optimization(PCRO) algorithm for solving the multiarea environmental/economic dispatch optimization problems.Two objectives are minimized simultaneously, i.e., total fuel cost and emission. In the proposed algorithm, each solution is represented by a chemical molecule. A novel encoding mechanism for solving the multi-area environmental/economic dispatch optimization problems is designed to dynamically enhance the performance of the proposed algorithm. Then, an ensemble of effective neighborhood approaches is developed, and a selfadaptive neighborhood structure selection mechanism is also embedded in PCRO to increase the search ability while maintaining population diversity. In addition, a grid-based crowding distance strategy is introduced, which can obviously enable the algorithm to easily converge near the Pareto front. Furthermore,a kinetic-energy-based search procedure is developed to enhance the global search ability. Finally, the proposed algorithm is tested on sets of the instances that are generated based on realistic production. Through the analysis of experimental results, the highly effective performance of the proposed PCRO algorithm is favorably compared with several algorithms, with regards to both solution quality and diversity.

Black Widow Optimization for Multi Area Economic Emission Dispatch

The optimizationfield has grown tremendously,and new optimization techniques are developed based on statistics and evolutionary procedures.There-fore,it is necessary to identify a suitable optimization technique for a particular application.In this work,Black Widow Optimization(BWO)algorithm is intro-duced to minimize the cost functions in order to optimize the Multi-Area Economic Dispatch(MAED).The BWO is implemented for two different-scale test systems,comprising 16 and 40 units with three and four areas.The performance of BWO is compared with the available optimization techniques in the literature to demonstrate the strategy’s efficacy.Results show that the optimized cost for four areas with 16 units is found to be 7336.76$/h,whereas it is 121,589$/h for four areas with 40 units using BWO.It is also noted that optimization algo-rithms other than BWO require higher cost value.The best-optimized solution for emission is achieved at 9.2784e+06 tones/h,and it is observed that there is a considerable difference between the worst and the best values.Also,the suggested technique is implemented for large-scale test systems successfully with high precision,and rapid convergence occurs in MAED.

Modified Cuckoo Search Algorithm to Solve Economic Power Dispatch Optimization Problems

A modified cuckoo search(CS) algorithm is proposed to solve economic dispatch(ED) problems that have nonconvex, non-continuous or non-linear solution spaces considering valve-point effects, prohibited operating zones, transmission losses and ramp rate limits. Comparing with the traditional cuckoo search algorithm, we propose a self-adaptive step size and some neighbor-study strategies to enhance search performance.Moreover, an improved lambda iteration strategy is used to generate new solutions. To show the superiority of the proposed algorithm over several classic algorithms, four systems with different benchmarks are tested. The results show its efficiency to solve economic dispatch problems, especially for large-scale systems.

Optimal dispatching method for integrated energy system based on robust economic model predictive control considering source-load power interval prediction

Effective source-load prediction and reasonable dispatching are crucial to realize the economic and reliable operations of integrated energy systems(IESs).They can overcome the challenges introduced by the uncertainties of new energies and various types of loads in the IES.Accordingly,a robust optimal dispatching method for the IES based on a robust economic model predictive control(REMPC)strategy considering source-load power interval prediction is proposed.First,an operation model of the IES is established,and an interval prediction model based on the bidirectional long short-term memory network optimized by beetle antenna search and bootstrap is formulated and applied to predict the photovoltaic power and the cooling,heating,and electrical loads.Then,an optimal dispatching scheme based on REMPC is devised for the IES.The source-load interval prediction results are used to improve the robustness of the REPMC and reduce the influence of source-load uncertainties on dispatching.An actual IES case is selected to conduct simulations;the results show that compared with other prediction techniques,the proposed method has higher prediction interval coverage probability and prediction interval normalized averaged width.Moreover,the operational cost of the IES is decreased by the REMPC strategy.With the devised dispatching scheme,the ability of the IES to handle the dispatching risk caused by prediction errors is enhanced.Improved dispatching robustness and operational economy are also achieved.

ADMM-based Distributed Algorithm for Economic Dispatch in Power Systems With Both Packet Drops and Communication Delays

By virtue of alternating direction method of multipliers(ADMM), Newton-Raphson method, ratio consensus approach and running sum method, two distributed iterative strategies are presented in this paper to address the economic dispatch problem(EDP) in power systems. Different from most of the existing distributed ED approaches which neglect the effects of packet drops or/and time delays, this paper takes into account both packet drops and time delays which frequently occur in communication networks. Moreover, directed and possibly unbalanced graphs are considered in our algorithms, over which many distributed approaches fail to converge. Furthermore, the proposed schemes can address the EDP with local constraints of generators and nonquadratic convex cost functions, not just quadratic ones required in some existing ED approaches. Both theoretical analyses and simulation studies are provided to demonstrate the effectiveness of the proposed schemes.

Modified Shuffled Frog Leaping Algorithm for Solving Economic Load Dispatch Problem

In the recent restructured power system scenario and complex market strategy, operation at absolute minimum cost is no longer the only criterion for dispatching electric power. The economic load dispatch (ELD) problem which accounts for minimization of both generation cost and power loss is itself a multiple conflicting objective function problem. In this paper, a modified shuffled frog-leaping algorithm (MSFLA), which is an improved version of memetic algorithm, is proposed for solving the ELD problem. It is a relatively new evolutionary method where local search is applied during the evolutionary cycle. The idea of memetic algorithm comes from memes, which unlike genes can adapt themselves. The performance of MSFLA has been shown more efficient than traditional evolutionary algorithms for such type of ELD problem. The application and validity of the proposed algorithm are demonstrated for IEEE 30 bus test system as well as a practical power network of 203 bus 264 lines 23 machines system.

GA and PSO culled hybrid technique for economic dispatch problem with prohibited operating zones

This paper presents an efficient and reliable genetic algorithm (GA) based particle swarm optimization (PSO) tech- nique (hybrid GAPSO) for solving the economic dispatch (ED) problem in power systems. The non-linear characteristics of the generators, such as prohibited operating zones, ramp rate limits and non-smooth cost functions of the practical generator operation are considered. The proposed hybrid algorithm is demonstrated for three different systems and the performance is compared with the GA and PSO in terms of solution quality and computation efficiency. Comparison of results proved that the proposed algo- rithm can obtain higher quality solutions efficiently in ED problems. A comprehensive software package is developed using MATLAB.

Multiple objective particle swarm optimization technique for economic load dispatch

A multi-objective particle swarm optimization (MOPSO) approach for multi-objective economic load dispatch problem in power system is presented in this paper. The economic load dispatch problem is a non-linear constrained multi-objective optimization problem. The proposed MOPSO approach handles the problem as a multi-objective problem with competing and non-commensurable fuel cost, emission and system loss objectives and has a diversity-preserving mechanism using an external memory (call “repository”) and a geographically-based approach to find widely different Pareto-optimal solutions. In addition, fuzzy set theory is employed to extract the best compromise solution. Several optimization runs of the proposed MOPSO approach were carried out on the standard IEEE 30-bus test system. The results revealed the capabilities of the proposed MOPSO approach to generate well-distributed Pareto-optimal non-dominated solutions of multi-objective economic load dispatch. Com- parison with Multi-objective Evolutionary Algorithm (MOEA) showed the superiority of the proposed MOPSO approach and confirmed its potential for solving multi-objective economic load dispatch.

A low-carbon economic dispatch model for electricity market with wind power based on improved ant-lion optimisation algorithm

Introducing carbon trading into electricity market can convert carbon dioxide into schedulable resources with economic value.However,the randomness of wind power generation puts forward higher requirements for electricity market transactions.Therefore,the carbon trading market is introduced into the wind power market,and a new form of low-carbon economic dispatch model is developed.First,the economic dispatch goal of wind power is be considered.It is projected to save money and reduce the cost of power generation for the system.The model includes risk operating costs to account for the impact of wind power output variability on the system,as well as wind farm negative efficiency operating costs to account for the loss caused by wind abandonment.The model also employs carbon trading market metrics to achieve the goal of lowering system carbon emissions,and analyze the impact of different carbon trading prices on the system.A low-carbon economic dispatch model for the wind power market is implemented based on the following two goals.Finally,the solution is optimised using the Ant-lion optimisation method,which combines Levi's flight mechanism and golden sine.The proposed model and algorithm's rationality is proven through the use of cases.

A Hybrid Optimization Technique Coupling an Evolutionary and a Local Search Algorithm for Economic Emission Load Dispatch Problem

This paper presents an optimization technique coupling two optimization techniques for solving Economic Emission Load Dispatch Optimization Problem EELD. The proposed approach integrates the merits of both genetic algorithm (GA) and local search (LS), where it maintains a finite-sized archive of non-dominated solutions which gets iteratively updated in the presence of new solutions based on the concept of ε-dominance. To improve the solution quality, local search technique was applied as neighborhood search engine, where it intends to explore the less-crowded area in the current archive to possibly obtain more non-dominated solutions. TOPSIS technique can incorporate relative weights of criterion importance, which has been implemented to identify best compromise solution, which will satisfy the different goals to some extent. Several optimization runs of the proposed approach are carried out on the standard IEEE 30-bus 6-genrator test system. The comparison demonstrates the superiority of the proposed approach and confirms its potential to solve the multiobjective EELD problem.

Solution of Combined Heat and Power Economic Dispatch Problem Using Direct Optimization Algorithm

This paper presents the solution to the combined heat and power economic dispatch problem using a direct solution algorithm for constrained optimization problems. With the potential of Combined Heat and Power (CHP) production to increase the efficiency of power and heat generation simultaneously having been researched and established, the increasing penetration of CHP systems, and determination of economic dispatch of power and heat assumes higher relevance. The Combined Heat and Power Economic Dispatch (CHPED) problem is a demanding optimization problem as both constraints and objective functions can be non-linear and non-convex. This paper presents an explicit formula developed for computing the system-wide incremental costs corresponding with optimal dispatch. The circumvention of the use of iterative search schemes for this crucial step is the innovation inherent in the proposed dispatch procedure. The feasible operating region of the CHP unit three is taken into account in the proposed CHPED problem model, whereas the optimal dispatch of power/heat outputs of CHP unit is determined using the direct Lagrange multiplier solution algorithm. The proposed algorithm is applied to a test system with four units and results are provided.

Two-stage stochastic approach for spinning reserve allocation in dynamic economic dispatch

A novel approach was proposed to allocate spinning reserve for dynamic economic dispatch.The proposed approach set up a two-stage stochastic programming model to allocate reserve.The model was solved using a decomposed algorithm based on Benders' decomposition.The model and the algorithm were applied to a simple 3-node system and an actual 445-node system for verification,respectively.Test results show that the model can save 84.5 US $ cost for the testing three-node system,and the algorithm can solve the model for 445-node system within 5 min.The test results also illustrate that the proposed approach is efficient and suitable for large system calculation.

Dynamic economic dispatch combining network flow and interior point method

Under the environment of electric power market, economic dispatch (ED) problem should consider network constraints, unit ramp rates, besides the basic constraints. For this problem, it is important to establish the effective model and algorithm. This paper examines the decoupled conditions that affect the solution optimality to this problem. It proposes an effective model and solution method. Based on the look-ahead technique, it finds the number of time intervals to guarantee the solution optimality. Next, an efficient technique for finding the optimal solution via the interior point methods is described. Test cases, which include dispatching six units over 5 time intervals on the IEEE 30 test system with line flows and ramp constraints are presented. Results indicate that the computational effort as measured by iteration counts or execution time varies only modestly with the problem size.

Dynamic Economic Dispatch for Wind Power System Considering System Security and Spinning Reserve

In this paper, dynamic economic dispatch model is proposed for power systems with bulk wind power integration. The wind turbine generators are assumed to partially undertake the spinning reserve for the thermal generator. A double-layer optimization model is proposed. The outer layer use the differential evolution to search for the power output of thermal generators, and the inner layer use the primal-dual interior point method to solve the OPF of the established output state. Finally, the impact of spinning reserve with wind power on power system operating is validated.

Scenario-oriented hybrid particle swarm optimization algorithm for robust economic dispatch of power system with wind power

An economic dispatch problem for power system with wind power is discussed.Using discrete scenario to describe uncertain wind powers,a threshold is given to identify bad scenario set.The bad-scenario-set robust economic dispatch model is established to minimize the total penalties on bad scenarios.A specialized hybrid particle swarm optimization(PSO)algorithm is developed through hybridizing simulated annealing(SA)operators.The SA operators are performed according to a scenario-oriented adaptive search rule in a neighborhood which is constructed based on the unit commitment constraints.Finally,an experiment is conducted.The computational results show that the developed algorithm outperforms the existing algorithms.

Dynamic Economic Dispatch for Microgrids Including Battery Energy Storage

Microgrids integrate distributed renewable energy resources, controllable loads and energy storage in a more economic and reliable fashion. Battery energy storage units are essential for microgrid operation, which make microgird become a strong coupling system in the time domain. Hence, the traditional methods of static dispatch are no longer suitable for microgrids. This paper proposes a dynamic economic dispatch method for microgrids. Considering microgrid as a discrete time system, the dynamic economic dispatch is to find the optimal control strategy for the system in finite time period. Based on this idea, the dynamic economic dispatch model for microgrids is established, and then the corresponding dynamic programming algorithm is designed. Finally, an example of microgrid is given, and the dynamic economic dispatch results are compared with that of the static dispatch. The comparison confirms the effectiveness of the proposed dynamic dispatch method.