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...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.展开更多
Considering the special features of dynamic environment economic dispatch of power systems with high dimensionality,strong coupling,nonlinearity,and non-convexity,a GA-DE multi-objective optimization algorithm based o...Considering the special features of dynamic environment economic dispatch of power systems with high dimensionality,strong coupling,nonlinearity,and non-convexity,a GA-DE multi-objective optimization algorithm based on dual-population pseudo-parallel genetic algorithm-differential evolution is proposed in this paper.The algorithm is based on external elite archive and Pareto dominance,and it adopts the cooperative co-evolution mechanism of differential evolution and genetic algorithm.Average entropy and cubic chaoticmapping initialization strategies are proposed to increase population diversity.In the proposed method,we analyze the distribution of neighboring solutions and apply a new Pareto solution set pruning approach.Unlike traditional models,this work takes the transmission losses as an optimization target and overcomes complex model constraints through a dynamic relaxation constraint approach.To solve the uncertainty caused by integrating wind and photovoltaic energy in power system scheduling,a multi-objective dynamic environment economical dispatch model is set up that takes the system spinning reserve and network highest losses into account.In this paper,the DE algorithm is improved to form the DGAGE algorithm for the objective optimization of the overall power system,The DE algorithm part of DGAGE is combined with the JAYA algorithm to form the system scheduling HDJ algorithm for multiple energy sources connected to the grid.The effectiveness of the proposed method is demonstrated using CEC2022 and CEC2005 test functions,showing robust optimization performance.Validation on a classical 10-unit system confirms the feasibility of the proposed algorithm in addressing power system scheduling issues.This approach provides a novel solution for dynamic power dispatch systems.展开更多
The economic dispatch problem(EDP) of microgrids operating in both grid-connected and isolated modes within an energy internet framework is addressed in this paper. The multi-agent leader-following consensus algorithm...The economic dispatch problem(EDP) of microgrids operating in both grid-connected and isolated modes within an energy internet framework is addressed in this paper. The multi-agent leader-following consensus algorithm is employed to address the EDP of microgrids in grid-connected mode, while the push-pull algorithm with a fixed step size is introduced for the isolated mode. The proposed algorithm of isolated mode is proven to converge to the optimum when the interaction digraph of microgrids is strongly connected. A unified algorithmic framework is proposed to handle the two modes of operation of microgrids simultaneously, enabling our algorithm to achieve optimal power allocation and maintain the balance between power supply and demand in any mode and any mode switching. Due to the push-pull structure of the algorithm and the use of fixed step size,the proposed algorithm can better handle the case of unbalanced graphs, and the convergence speed is improved. It is documented that when the transmission topology is strongly connected and there is bi-directional communication between the energy router and its neighbors, the proposed algorithm in composite mode achieves economic dispatch even with arbitrary mode switching.Finally, we demonstrate the effectiveness and superiority of our algorithm through numerical simulations.展开更多
The exponential growth in the scale of power systems has led to a significant increase in the complexity of dispatch problem resolution,particularly within multi-area interconnected power grids.This complexity necessi...The exponential growth in the scale of power systems has led to a significant increase in the complexity of dispatch problem resolution,particularly within multi-area interconnected power grids.This complexity necessitates the employment of distributed solution methodologies,which are not only essential but also highly desirable.In the realm of computational modelling,the multi-area economic dispatch problem(MAED)can be formulated as a linearly constrained separable convex optimization problem.The proximal point algorithm(PPA)is particularly adept at addressing such mathematical constructs effectively.This study introduces parallel(PPPA)and serial(SPPA)variants of the PPA as distributed algorithms,specifically designed for the computational modelling of the MAED.The PPA introduces a quadratic term into the objective function,which,while potentially complicating the iterative updates of the algorithm,serves to dampen oscillations near the optimal solution,thereby enhancing the convergence characteristics.Furthermore,the convergence efficiency of the PPA is significantly influenced by the parameter c.To address this parameter sensitivity,this research draws on trend theory from stock market analysis to propose trend theory-driven distributed PPPA and SPPA,thereby enhancing the robustness of the computational models.The computational models proposed in this study are anticipated to exhibit superior performance in terms of convergence behaviour,stability,and robustness with respect to parameter selection,potentially outperforming existing methods such as the alternating direction method of multipliers(ADMM)and Auxiliary Problem Principle(APP)in the computational simulation of power system dispatch problems.The simulation results demonstrate that the trend theory-based PPPA,SPPA,ADMM and APP exhibit significant robustness to the initial value of parameter c,and show superior convergence characteristics compared to the residual balancing ADMM.展开更多
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,...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.展开更多
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 c...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.展开更多
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 electri...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.展开更多
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 econom...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.展开更多
Reducing pollutant emissions from electricity production in the power system positively impacts the control of greenhouse gas emissions.Boosting kernel search optimizer(BKSO)is introduced in this research to solve the...Reducing pollutant emissions from electricity production in the power system positively impacts the control of greenhouse gas emissions.Boosting kernel search optimizer(BKSO)is introduced in this research to solve the combined economic emission dispatch(CEED)problem.Inspired by the foraging behavior in the slime mould algorithm(SMA),the kernel matrix of the kernel search optimizer(KSO)is intensified.The proposed BKSO is superior to the standard KSO in terms of exploitation ability,robustness,and convergence rate.The CEC2013 test function is used to assess the improved KSO's performance and compared to 11 well-known optimization algorithms.BKSO performs better in statistical results and convergence curves.At the same time,BKSO achieves better fuel costs and fewer pollution emissions by testing with four real CEED cases,and the Pareto solution obtained is also better than other MAs.Based on the experimental results,BKSO has better performance than other comparable MAs and can provide more economical,robust,and cleaner solutions to CEED problems.展开更多
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 constrai...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.展开更多
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 rol...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.展开更多
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 decompose...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.展开更多
In this paper,an uncertain economic dispatch problem(EDP)is considered for a group of coopertive agents.First,let each agent extract a set of samples(scenarios)from the uncertain set,and then a scenario EDP is obtaine...In this paper,an uncertain economic dispatch problem(EDP)is considered for a group of coopertive agents.First,let each agent extract a set of samples(scenarios)from the uncertain set,and then a scenario EDP is obtained using these scenarios.Based on the scenario theory,a prior certifcation is provided to evaluate the probabilistic feasibility of the scenario solution for uncertain EDP.To facilitate the computational task,a distributed solution strategy is proposed by the alternating direction method of multipliers(ADMM)and a fnite-time consensus strategy.Moreover,the distributed strategy can solve the scenario problem over a weight-balanced directed graph.Finally,the proposed solution strategy is applied to an EDP for a power system involving wind power plants.展开更多
For the impact of intermittent resources＇ high penetration on the economic dispatch of islanded microgrid, a new economic dispatch method is presented to minimize the overall generating cost for islanded microgrid, c...For the impact of intermittent resources＇ high penetration on the economic dispatch of islanded microgrid, a new economic dispatch method is presented to minimize the overall generating cost for islanded microgrid, considering a cooperative strategy between diesel generator （hereinafter referred to as DE） and battery energy storage system （BESS）. The optimum economic operation range of DE and the optimal set-point between DE and BESS are presented in the cooperative dispatch strategy, in which BESS is used fully to enable DE in a lower cost and higher efficient way. The results are analyzed under various operation conditions and also prove the validity of the DrODosed method.展开更多
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 ef...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.展开更多
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...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.展开更多
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) pr...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.展开更多
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 mak...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.展开更多
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 co...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）.展开更多
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 incre...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.展开更多
文摘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.
基金funded by the Major Humanities and Social Sciences Research Projects in Zhejiang Higher Education Institutions,grant number 2023QN131National Innovation Training Program Project in China,grant number 202410451009.
文摘Considering the special features of dynamic environment economic dispatch of power systems with high dimensionality,strong coupling,nonlinearity,and non-convexity,a GA-DE multi-objective optimization algorithm based on dual-population pseudo-parallel genetic algorithm-differential evolution is proposed in this paper.The algorithm is based on external elite archive and Pareto dominance,and it adopts the cooperative co-evolution mechanism of differential evolution and genetic algorithm.Average entropy and cubic chaoticmapping initialization strategies are proposed to increase population diversity.In the proposed method,we analyze the distribution of neighboring solutions and apply a new Pareto solution set pruning approach.Unlike traditional models,this work takes the transmission losses as an optimization target and overcomes complex model constraints through a dynamic relaxation constraint approach.To solve the uncertainty caused by integrating wind and photovoltaic energy in power system scheduling,a multi-objective dynamic environment economical dispatch model is set up that takes the system spinning reserve and network highest losses into account.In this paper,the DE algorithm is improved to form the DGAGE algorithm for the objective optimization of the overall power system,The DE algorithm part of DGAGE is combined with the JAYA algorithm to form the system scheduling HDJ algorithm for multiple energy sources connected to the grid.The effectiveness of the proposed method is demonstrated using CEC2022 and CEC2005 test functions,showing robust optimization performance.Validation on a classical 10-unit system confirms the feasibility of the proposed algorithm in addressing power system scheduling issues.This approach provides a novel solution for dynamic power dispatch systems.
基金supported by the National Natural Science Foundation of China(62103203)
文摘The economic dispatch problem(EDP) of microgrids operating in both grid-connected and isolated modes within an energy internet framework is addressed in this paper. The multi-agent leader-following consensus algorithm is employed to address the EDP of microgrids in grid-connected mode, while the push-pull algorithm with a fixed step size is introduced for the isolated mode. The proposed algorithm of isolated mode is proven to converge to the optimum when the interaction digraph of microgrids is strongly connected. A unified algorithmic framework is proposed to handle the two modes of operation of microgrids simultaneously, enabling our algorithm to achieve optimal power allocation and maintain the balance between power supply and demand in any mode and any mode switching. Due to the push-pull structure of the algorithm and the use of fixed step size,the proposed algorithm can better handle the case of unbalanced graphs, and the convergence speed is improved. It is documented that when the transmission topology is strongly connected and there is bi-directional communication between the energy router and its neighbors, the proposed algorithm in composite mode achieves economic dispatch even with arbitrary mode switching.Finally, we demonstrate the effectiveness and superiority of our algorithm through numerical simulations.
基金funded by Guangxi Science and Technology Base and Talent Special Project,grant number GuiKeAD20159077Foundation of Guilin University of Technology,grant number GLUTQD2018001.
文摘The exponential growth in the scale of power systems has led to a significant increase in the complexity of dispatch problem resolution,particularly within multi-area interconnected power grids.This complexity necessitates the employment of distributed solution methodologies,which are not only essential but also highly desirable.In the realm of computational modelling,the multi-area economic dispatch problem(MAED)can be formulated as a linearly constrained separable convex optimization problem.The proximal point algorithm(PPA)is particularly adept at addressing such mathematical constructs effectively.This study introduces parallel(PPPA)and serial(SPPA)variants of the PPA as distributed algorithms,specifically designed for the computational modelling of the MAED.The PPA introduces a quadratic term into the objective function,which,while potentially complicating the iterative updates of the algorithm,serves to dampen oscillations near the optimal solution,thereby enhancing the convergence characteristics.Furthermore,the convergence efficiency of the PPA is significantly influenced by the parameter c.To address this parameter sensitivity,this research draws on trend theory from stock market analysis to propose trend theory-driven distributed PPPA and SPPA,thereby enhancing the robustness of the computational models.The computational models proposed in this study are anticipated to exhibit superior performance in terms of convergence behaviour,stability,and robustness with respect to parameter selection,potentially outperforming existing methods such as the alternating direction method of multipliers(ADMM)and Auxiliary Problem Principle(APP)in the computational simulation of power system dispatch problems.The simulation results demonstrate that the trend theory-based PPPA,SPPA,ADMM and APP exhibit significant robustness to the initial value of parameter c,and show superior convergence characteristics compared to the residual balancing ADMM.
基金supported in part by the National Key Research and Development Program of China(2017YFB0306400)in part by the National Natural Science Foundation of China(61573089,71472080,71301066)Liaoning Province Dr.Research Foundation of China(20175032)
文摘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.
文摘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.
基金National Natural Science Foundation of China,Grant/Award Number:51677059。
文摘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.
基金supported by the National Natural Science Foundation of China(62173219,62073210).
文摘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.
基金This research was supported by the Science&Technology Development Project of Jilin Province,China(YDZJ202201ZYTS555)the Science&Technology Research Project of the Education Department of Jilin Province,China(JJKH20220244KJ)。
文摘Reducing pollutant emissions from electricity production in the power system positively impacts the control of greenhouse gas emissions.Boosting kernel search optimizer(BKSO)is introduced in this research to solve the combined economic emission dispatch(CEED)problem.Inspired by the foraging behavior in the slime mould algorithm(SMA),the kernel matrix of the kernel search optimizer(KSO)is intensified.The proposed BKSO is superior to the standard KSO in terms of exploitation ability,robustness,and convergence rate.The CEC2013 test function is used to assess the improved KSO's performance and compared to 11 well-known optimization algorithms.BKSO performs better in statistical results and convergence curves.At the same time,BKSO achieves better fuel costs and fewer pollution emissions by testing with four real CEED cases,and the Pareto solution obtained is also better than other MAs.Based on the experimental results,BKSO has better performance than other comparable MAs and can provide more economical,robust,and cleaner solutions to CEED problems.
基金Project (Nos. 60074040 and 6022506) supported by the NationalNatural Science Foundation of China
文摘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.
基金The Science and Technology Project of the State Grid Corporation of China(Research and Demonstration of Loss Reduction Technology Based on Reactive Power Potential Exploration and Excitation of Distributed Photovoltaic-Energy Storage Converters:5400-202333241A-1-1-ZN).
文摘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.
基金Projects(51007047,51077087)supported by the National Natural Science Foundation of ChinaProject(2013CB228205)supported by the National Key Basic Research Program of China+1 种基金Project(20100131120039)supported by Higher Learning Doctor Discipline End Scientific Research Fund of the Ministry of Education Institution,ChinaProject(ZR2010EQ035)supported by the Natural Science Foundation of Shandong Province,China
文摘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.
文摘In this paper,an uncertain economic dispatch problem(EDP)is considered for a group of coopertive agents.First,let each agent extract a set of samples(scenarios)from the uncertain set,and then a scenario EDP is obtained using these scenarios.Based on the scenario theory,a prior certifcation is provided to evaluate the probabilistic feasibility of the scenario solution for uncertain EDP.To facilitate the computational task,a distributed solution strategy is proposed by the alternating direction method of multipliers(ADMM)and a fnite-time consensus strategy.Moreover,the distributed strategy can solve the scenario problem over a weight-balanced directed graph.Finally,the proposed solution strategy is applied to an EDP for a power system involving wind power plants.
基金the National Natural Science Foundation of China(No.61703068)the Scientific and Technological Research Program of Chongqing Municipal Education Commission(No.KJ1704097)+1 种基金the Chongqing Basic Science and Advanced Technology Research Project(No.cstc2016jcyjA1919)the Doctor Start-up Funding of Chongqing University of Posts and Telecommunications(No.A2016-05)
文摘For the impact of intermittent resources＇ high penetration on the economic dispatch of islanded microgrid, a new economic dispatch method is presented to minimize the overall generating cost for islanded microgrid, considering a cooperative strategy between diesel generator （hereinafter referred to as DE） and battery energy storage system （BESS）. The optimum economic operation range of DE and the optimal set-point between DE and BESS are presented in the cooperative dispatch strategy, in which BESS is used fully to enable DE in a lower cost and higher efficient way. The results are analyzed under various operation conditions and also prove the validity of the DrODosed method.
文摘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.
文摘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.
文摘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.
文摘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.
文摘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）.
基金supported by the National Natural Science Foundation of China(62103203)the General Terminal IC Interdisciplinary Science Center of Nankai University.
文摘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.
