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.

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.

A Chance Constrained Optimal Reserve Scheduling Approach for Economic Dispatch Considering Wind Penetration

The volatile wind power generation brings a full spectrum of problems to power system operation and management, ranging from transient system frequency fluctuation to steady state supply and demand balancing issue. In this paper, a novel wind integrated power system day-ahead economic dispatch model, with the consideration of generation and reserve cost is modelled and investigated. The proposed problem is first formulated as a chance constrained stochastic nonlinear programming U+0028 CCSNLP U+0029, and then transformed into a deterministic nonlinear programming U+0028 NLP U+0029. To tackle this NLP problem, a three-stage framework consists of particle swarm optimization U+0028 PSO U+0029, sequential quadratic programming U+0028 SQP U+0029 and Monte Carlo simulation U+0028 MCS U+0029 is proposed. The PSO is employed to heuristically search the line power flow limits, which are used by the SQP as constraints to solve the NLP problem. Then the solution from SQP is verified on benchmark system by using MCS. Finally, the verified results are feedback to the PSO as fitness value to update the particles. Simulation study on IEEE 30-bus system with wind power penetration is carried out, and the results demonstrate that the proposed dispatch model could be effectively solved by the proposed three-stage approach. © 2017 Chinese Association of Automation.

Finite-time economic model predictive control for optimal load dispatch and frequency regulation in interconnected power systems

This paper presents a finite-time economic model predictive control(MPC)algorithm that can be used for frequency regulation and optimal load dispatch in multi-area power systems.Economic MPC can be used in a power system to ensure frequency stability,real-time economic optimization,control of the system and optimal load dispatch from it.A generalized terminal penalty term was used,and the finite-time convergence of the system was guaranteed.The effectiveness of the proposed model predictive control algorithm was verified by simulating a power system,which had two areas connected by an AC tie line.The simulation results demonstrated the effectiveness of the algorithm.

Two-Stage Optimal Dispatching of Wind Power-Photovoltaic-Solar Thermal Combined System Considering Economic Optimality and Fairness

Aiming at the problems of large-scale wind and solar grid connection,how to ensure the economy of system operation and how to realize fair scheduling between new energy power stations,a two-stage optimal dispatching model of wind power-photovoltaic-solar thermal combined system considering economic optimality and fairness is proposed.Firstly,the first stage dispatching model takes the overall economy optimization of the system as the goal and the principle of maximizing the consumption of wind and solar output,obtains the optimal output value under the economic conditions of each new energy station,and then obtains the maximum consumption space of the new energy station.Secondly,based on the optimization results of the first stage,the second stage dispatching model uses the dispatching method of fuzzy comprehensive ranking priority to prioritize the new energy stations,and then makes a fair allocation to the dispatching of the wind and solar stations.Finally,the analysis of a specific example shows that themodel can take into account the fairness of active power distribution of new energy stations on the basis of ensuring the economy of system operation,make full use of the consumption space,and realize the medium and long-term fairness distribution of dispatching plan.

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.

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 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.

Economic Load Dispatch with Daily Load Patterns Using Particle Swarm Optimization

ELD （economic load dispatch） problem is one of the essential issues in power system operation. The objective of solving ELD problem is to allocate the generation output of the committed generating units. The main contribution of this work is to solve the ELD problem concerned with daily load pattern. The proposed solution technique, developed based PSO （particle swarm optimization） algorithm, is applied to search for the optimal schedule of all generations units that can supply the required load demand at minimum fuel cost while satisfying all unit and system operational constraints. The performance of the developed methodology is demonstrated by case studies in test system of six-generation units. The results obtained from the PSO are compared to those achieved from other approaches, such as QP （quadratic programming）, and GA （genetic algorithm）.

Modeling of Combined Economic and Emission Dispatch Using Improved Sand Cat Optimization Algorithm

Combined Economic and Emission Dispatch(CEED)task forms multi-objective optimization problems to be resolved to minimize emission and fuel costs.The disadvantage of the conventional method is its incapability to avoid falling in local optimal,particularly when handling nonlinear and complex systems.Metaheuristics have recently received considerable attention due to their enhanced capacity to prevent local optimal solutions in addressing all the optimization problems as a black box.Therefore,this paper focuses on the design of an improved sand cat optimization algorithm based CEED(ISCOA-CEED)technique.The ISCOA-CEED technique majorly concen-trates on reducing fuel costs and the emission of generation units.Moreover,the presented ISCOA-CEED technique transforms the equality constraints of the CEED issue into inequality constraints.Besides,the improved sand cat optimization algorithm(ISCOA)is derived from the integration of tra-ditional SCOA with the Levy Flight(LF)concept.At last,the ISCOA-CEED technique is applied to solve a series of 6 and 11 generators in the CEED issue.The experimental validation of the ISCOA-CEED technique ensured the enhanced performance of the presented ISCOA-CEED technique over other recent approaches.

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.

A Multi-Agent Particle Swarm Optimization for Power System Economic Load Dispatch

A new versatile optimization, the particle swarm optimization based on multi-agent system (MAPSO) is presented. The economic load dispatch (ELD) problem of power system can be solved by the algorithm. By competing and cooperating with the randomly selected neighbors, and adjusting its global searching ability and local exploring ability, this algorithm achieves the goal of high convergence precision and speed. To verify the effectiveness of the proposed algorithm, this algorithm is tested by three different ELD cases, including 3, 13 and 40 units IEEE cases, and the experiment results are compared with those tested by other intelligent algorithms in the same cases. The compared results show that feasible solutions can be reached effectively, local optima can be avoided and faster solution can be applied with the proposed algorithm, the algorithm for ELD problem is versatile and efficient.

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.

Economic Load Dispatch Based on Efficient Population Utilization Strategy for Particle Swarm Optimization

In this paper, the efficient population utilization strategy for particle swarm optimization (EPUSPSO) is proposed to solve the economic load dispatch (ELD) problem of power system. This algorithm improves the accuracy and the speed of its convergence by changing the number of particles effectively, and improving the velocity equation and position equation. In order to verify the effectiveness of the algorithm, this algorithm is tested in three different ELD cases of power system include IEEE 3-unit case, 13-unit case, and 40-unit case, and the obtained results are compared with those obtained from other algorithms using the same system parameters. The compared results show that the algorithm can find the optimal solution effectively and accurately, and avoid falling into the local optimal problem;meanwhile, faster speed can be ensured in the case.

Addressing Economic Dispatch Problem with Multiple Fuels Using Oscillatory Particle Swarm Optimization

Economic dispatch has a significant effect on optimal economical operation in the power systems in industrial revolution 4.0 in terms of considerable savings in revenue.Various non-linearity are added to make the fossil fuel-based power systems more practical.In order to achieve an accurate economical schedule,valve point loading effect,ramp rate constraints,and prohibited operating zones are being considered for realistic scenarios.In this paper,an improved,and modified version of conventional particle swarm optimization(PSO),called Oscillatory PSO(OPSO),is devised to provide a cheaper schedule with optimum cost.The conventional PSO is improved by deriving a mechanism enabling the particle towards the trajectories of oscillatory motion to acquire the entire search space.A set of differential equations is implemented to expose the condition for trajectory motion in oscillation.Using adaptive inertia weights,this OPSO method provides an optimized cost of generation as compared to the conventional particle swarm optimization and other new meta-heuristic approaches.

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.

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.

CSO Algorithm for Economic Dispatch Decision of Hybrid Generation System

The aim of this research is to study the optimal economic dispatch （ED） through Cat Swarm Optimization （CSO） algorithm. Many areas in power systems require solving one or more nonlinear optimization problems. While analytical methods might suffer from slow convergence and the CSO can, therefore, be effectively applied to different optimization problems. In this paper, the CSO is also extended to coordinate wind and thermal dispatch and to minimize total generation cost. Results indicated that the CSO is superior to PSO in the fast convergence and better performance to find the global best solution.

Reference Point Based TR-PSO for Multi-Objective Environmental/Economic Dispatch

A reference point based multi-objective optimization using a combination between trust region (TR) algorithm and particle swarm optimization (PSO) to solve the multi-objective environmental/economic dispatch (EED) problem is presented in this paper. The EED problem is handled by Reference Point Interactive Approach. One of the main advantages of the proposed approach is integrating the merits of both TR and PSO, where TR has provided the initial set (close to the Pareto set as possible and the reference point of the decision maker) followed by PSO to improve the quality of the solutions and get all the points on the Pareto frontier. The performance of the proposed algorithm is tested on standard IEEE 30-bus 6-genrator test system and is compared with conventional methods. The results demonstrate the capabilities of the proposed approach to generate true and well-distributed Pareto-optimal non-dominated solutions in one single run. The comparison with the classical methods demonstrates the superiority of the proposed approach and confirms its potential to solve the multi-objective EED problem.