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
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
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
Driven by the goal of“carbon neutrality”and“emission peak”,effectively controlling system carbon emissions has become significantly important to governments around the world.To this end,a novel two-stage low-carbo...Driven by the goal of“carbon neutrality”and“emission peak”,effectively controlling system carbon emissions has become significantly important to governments around the world.To this end,a novel two-stage low-carbon economic scheduling framework that considers the coordinated optimization of ladder-type carbon trading and integrated demand response(IDR)is proposed in this paper for the integrated energy system(IES),where the first stage determines the energy consumption plan of users by leveraging the price-based electrical-heat IDR.In contrast,the second stage minimizes the system total cost to optimize the outputs of generations with consideration of the uncertainty of renewables.In addition,to fully exploit the system’s emission reduction potential,a carbon trading cost model with segmented CO_(2) emission intervals is built by introducing a reward-penalty ladder-type carbon trading mechanism,and the flexible thermal comfort elasticity of customers is taken into account by putting forward a predicted mean vote index on the load side.The CPLEX optimizer resolves the two-stage model,and the study results on a modified IES situated in North China show the proposed model can effectively reduce carbon emissions and guarantee economical efficiency operation of the system.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
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
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
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
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. Whil...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.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
Integrated energy system optimization scheduling can improve energy efficiency and low carbon economy.This paper studies an electric-gas-heat integrated energy system,including the carbon capture system,energy couplin...Integrated energy system optimization scheduling can improve energy efficiency and low carbon economy.This paper studies an electric-gas-heat integrated energy system,including the carbon capture system,energy coupling equipment,and renewable energy.An energy scheduling strategy based on deep reinforcement learning is proposed to minimize operation cost,carbon emission and enhance the power supply reliability.Firstly,the lowcarbon mathematical model of combined thermal and power unit,carbon capture system and power to gas unit(CCP)is established.Subsequently,we establish a low carbon multi-objective optimization model considering system operation cost,carbon emissions cost,integrated demand response,wind and photovoltaic curtailment,and load shedding costs.Furthermore,considering the intermittency of wind power generation and the flexibility of load demand,the low carbon economic dispatch problem is modeled as a Markov decision process.The twin delayed deep deterministic policy gradient(TD3)algorithm is used to solve the complex scheduling problem.The effectiveness of the proposed method is verified in the simulation case studies.Compared with TD3,SAC,A3C,DDPG and DQN algorithms,the operating cost is reduced by 8.6%,4.3%,6.1%and 8.0%.展开更多
The objective of this paper is to assess an economic dispatch considering a power system portfolio, which includes predominant amount of hydro power and increasing quantities of intermittent renewables in relation to ...The objective of this paper is to assess an economic dispatch considering a power system portfolio, which includes predominant amount of hydro power and increasing quantities of intermittent renewables in relation to the total electric capacity. With growing importance of intermittent wind and solar generation taking part into power systems worldwide, there is need for greater chronological resolution to estimate the flexibility of the power system to offer firm capacity. In this way, a linear optimization model operating hourly is developed to calculate the minimum power system cost, while stablishing the capacity allocation to meet the projected load throughout one-year simulation, as an estimation of how the hourly economic dispatch impacts the scheduling of generators belonging to a power system with this portfolio composition. A central focus is how to operate the available hydro capacity to back up intermittent renewables, evaluating the physical hydro operating constraints, monthly energy balance and maximum power availability. A case study was simulated based on the Brazil’s power system configuration, showing that existing hydro capacity provide hourly flexibility to back-up intermittent renewables, potentially saving 1.2 Billion R$, about 3.6% of total system cost referred to 2019. It is worthwhile to realize that the developed methodology can be employed to other power systems with similar capacity portfolio structure for the purpose of calculating its optimum allocation for a specified region and target year.展开更多
Electricity network is a very complex entity that comprises several components like generators, transmission lines, loads among others. As technologies continue to evolve, the complexity of the electricity network has...Electricity network is a very complex entity that comprises several components like generators, transmission lines, loads among others. As technologies continue to evolve, the complexity of the electricity network has also increased as more devices are being connected to the network. To understand the physical laws governing the operation of the network, techniques such as optimal power flow (OPF), Economic dispatch (ED) and Security constrained optimal power flow (SCOPF) were developed. These techniques have been used extensively in network operation, planning and so on. However, an in-depth presentation showcasing the merits and demerits of these techniques is still lacking in the literature. Hence, this paper intends to fill this gap. In this paper, Economic dispatch, optimal power flow and security-constrained optimal power flow are applied to a 3-bus test system using a linear programming approach. The results of the ED, OPF and SC-OPF are compared and presented.展开更多
Economic Load Dispatch (ELD) is a process of scheduling the required load demand among available generation units such that the fuel cost of operation is minimized. The ELD problem is formulated as a nonlinear constra...Economic Load Dispatch (ELD) is a process of scheduling the required load demand among available generation units such that the fuel cost of operation is minimized. The ELD problem is formulated as a nonlinear constrained optimization problem with both equality and inequality constraints. In this paper, two test systems of the ELD problems are solved by adopting the Cuckoo Search (CS) Algorithm. A comparison of obtained simulation results by using the CS is carried out against six other swarm intelligence algorithms: Particle Swarm Optimization, Shuffled Frog Leaping Algorithm, Bacterial Foraging Optimization, Artificial Bee Colony, Harmony Search and Firefly Algorithm. The effectiveness of each swarm intelligence algorithm is demonstrated on a test system comprising three-generators and other containing six-generators. Results denote superiority of the Cuckoo Search Algorithm and confirm its potential to solve the ELD problem.展开更多
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 foss...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.展开更多
This article presents an application of generalized pattern search （PS） algorithm to solve economic load dispatch （ELD） problems with convex and non-convex fuel cost objective functions. Main objective of ELI） is...This article presents an application of generalized pattern search （PS） algorithm to solve economic load dispatch （ELD） problems with convex and non-convex fuel cost objective functions. Main objective of ELI） is to determine the most economic generating dispatch required to satisfy the predicted load demands including line losses. Relaxing various equality and inequality constraints are considered. The unit operation minhnum/maximum constraints, effects of valve-point and line losses are considered for the practical applications. Several case studies were tested and verified, which indicate an improvement in total fuel cost savings. The robustness of the proposed PS method have been assessed and investigated through intensive comparisons with reported results in recent researches. The results are very encouraging and suggesting that PS may be very useful tool in solving power system ELD problems.展开更多
This paper presents a robust interval economic dispatch(RIED)model for power systems with large-scale wind power integration.Differing from existing interval optimization(IO)approaches that merely rely on the upper an...This paper presents a robust interval economic dispatch(RIED)model for power systems with large-scale wind power integration.Differing from existing interval optimization(IO)approaches that merely rely on the upper and lower boundaries of random variables,the distribution information retained in the historical data is introduced to the IO method in this paper.Based on the available probability distribution function(PDF),wind power curtailment and load shedding are quantified as the operational risk and incorporated into the decision-making process.In this model,we need not rely on the forecasted value of wind power,which is randomly fluctuating and quite unpredictable.Furthermore,when the PDFs of wind power are taken into account,the resulting dispatch solution makes a good tradeoff between the generation cost and the operational risk.Finally,the RIED model yields an optimal dispatch solution for thermal units and the allowable intervals of wind power for the wind farms,which efficiently mitigates the uncertainty in wind power generation and provides more practical suggestions for system operators.Simulation studies are conducted on a modified IEEE-118 bus system and the results verify the effectiveness of the proposed RIED model.展开更多
High penetration level of renewable energy has brought great challenges to operation of power systems,and use of flexible resources(FRs)is becoming increasingly important.Flexibility of power systems can be improved b...High penetration level of renewable energy has brought great challenges to operation of power systems,and use of flexible resources(FRs)is becoming increasingly important.Flexibility of power systems can be improved by changing generation arrangements,but the interests of some market participants may be harmed in the process.This study proposes a stochastic economic dispatch model with trading of flexible ramping products(FRPs).To calculate changes in revenue and reasonably compensate units that provide FRs,multisegmented marginal bidding for energy is simulated by linearizing generation cost,and an optimal market clearing strategy for FRPs is developed according to changes in clearing energy and marginal clearing price.Then,the correlation between prediction errors of wind speeds among different wind farms is determined based on a joint distribution function modeled by the copula function,and quasi-Monte Carlo simulation(QMC)is used to generate wind power scenarios.Finally,numerical simulations of modified IEEE-30 and IEEE-118 bus systems is performed with minimum comprehensive cost as the objective function.This verifies the proposed model could effectively deal with wind variability and uncertainty,stabilize the marginal clearing price of the electricity market,and ensure fairness in the market.展开更多
The intermittency of renewable energy generation,variability of load demand,and stochasticity of market price bring about direct challenges to optimal energy management of microgrids.To cope with these different forms...The intermittency of renewable energy generation,variability of load demand,and stochasticity of market price bring about direct challenges to optimal energy management of microgrids.To cope with these different forms of operation uncertainties,an imitation learning based real-time decision-mak-ing solution for microgrid economic dispatch is proposed.In this solution,the optimal dispatch trajectories obtained by solving the optimal problem using historical deterministic operation patterns are demonstrated as the expert samples for imitation learning.To improve the generalization performance of imitation learning and the expressive ability of uncertain variables,a hybrid model combining the unsupervised and supervised learning is utilized.The denoising autoencoder based unsupervised learning model is adopted to enhance the feature extraction of operation patterns.Furthermore,the long short-term memory network based supervised learning model is used to efficiently characterize the mapping between the input space composed of the extracted operation patterns and system state variables and the output space composed of the optimal dispatch trajectories.The numerical simulation results demonstrate that under various operation uncertainties,the operation cost achieved by the proposed solution is close to the minimum theoretical value.Compared with the traditional model predictive control method and basic clone imitation learning method,the operation cost of the proposed solution is reduced by 6.3% and 2.8%,respectively,overa test period of three months.展开更多
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.
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 State Grid Shandong Electric Power Company Economic and Technical Research Institute Project(SGSDJY00GPJS2100135).
文摘Driven by the goal of“carbon neutrality”and“emission peak”,effectively controlling system carbon emissions has become significantly important to governments around the world.To this end,a novel two-stage low-carbon economic scheduling framework that considers the coordinated optimization of ladder-type carbon trading and integrated demand response(IDR)is proposed in this paper for the integrated energy system(IES),where the first stage determines the energy consumption plan of users by leveraging the price-based electrical-heat IDR.In contrast,the second stage minimizes the system total cost to optimize the outputs of generations with consideration of the uncertainty of renewables.In addition,to fully exploit the system’s emission reduction potential,a carbon trading cost model with segmented CO_(2) emission intervals is built by introducing a reward-penalty ladder-type carbon trading mechanism,and the flexible thermal comfort elasticity of customers is taken into account by putting forward a predicted mean vote index on the load side.The CPLEX optimizer resolves the two-stage model,and the study results on a modified IES situated in North China show the proposed model can effectively reduce carbon emissions and guarantee economical efficiency operation of the system.
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.
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supported in part by the Scientific Research Fund of Liaoning Provincial Education Department under Grant LQGD2019005in part by the Doctoral Start-up Foundation of Liaoning Province under Grant 2020-BS-141.
文摘Integrated energy system optimization scheduling can improve energy efficiency and low carbon economy.This paper studies an electric-gas-heat integrated energy system,including the carbon capture system,energy coupling equipment,and renewable energy.An energy scheduling strategy based on deep reinforcement learning is proposed to minimize operation cost,carbon emission and enhance the power supply reliability.Firstly,the lowcarbon mathematical model of combined thermal and power unit,carbon capture system and power to gas unit(CCP)is established.Subsequently,we establish a low carbon multi-objective optimization model considering system operation cost,carbon emissions cost,integrated demand response,wind and photovoltaic curtailment,and load shedding costs.Furthermore,considering the intermittency of wind power generation and the flexibility of load demand,the low carbon economic dispatch problem is modeled as a Markov decision process.The twin delayed deep deterministic policy gradient(TD3)algorithm is used to solve the complex scheduling problem.The effectiveness of the proposed method is verified in the simulation case studies.Compared with TD3,SAC,A3C,DDPG and DQN algorithms,the operating cost is reduced by 8.6%,4.3%,6.1%and 8.0%.
文摘The objective of this paper is to assess an economic dispatch considering a power system portfolio, which includes predominant amount of hydro power and increasing quantities of intermittent renewables in relation to the total electric capacity. With growing importance of intermittent wind and solar generation taking part into power systems worldwide, there is need for greater chronological resolution to estimate the flexibility of the power system to offer firm capacity. In this way, a linear optimization model operating hourly is developed to calculate the minimum power system cost, while stablishing the capacity allocation to meet the projected load throughout one-year simulation, as an estimation of how the hourly economic dispatch impacts the scheduling of generators belonging to a power system with this portfolio composition. A central focus is how to operate the available hydro capacity to back up intermittent renewables, evaluating the physical hydro operating constraints, monthly energy balance and maximum power availability. A case study was simulated based on the Brazil’s power system configuration, showing that existing hydro capacity provide hourly flexibility to back-up intermittent renewables, potentially saving 1.2 Billion R$, about 3.6% of total system cost referred to 2019. It is worthwhile to realize that the developed methodology can be employed to other power systems with similar capacity portfolio structure for the purpose of calculating its optimum allocation for a specified region and target year.
文摘Electricity network is a very complex entity that comprises several components like generators, transmission lines, loads among others. As technologies continue to evolve, the complexity of the electricity network has also increased as more devices are being connected to the network. To understand the physical laws governing the operation of the network, techniques such as optimal power flow (OPF), Economic dispatch (ED) and Security constrained optimal power flow (SCOPF) were developed. These techniques have been used extensively in network operation, planning and so on. However, an in-depth presentation showcasing the merits and demerits of these techniques is still lacking in the literature. Hence, this paper intends to fill this gap. In this paper, Economic dispatch, optimal power flow and security-constrained optimal power flow are applied to a 3-bus test system using a linear programming approach. The results of the ED, OPF and SC-OPF are compared and presented.
基金Fundacao de Amparo a Pesquisa do Estado de Sao Paulo for the financial support(Process FAPESP No 2011/08108-0).
文摘Economic Load Dispatch (ELD) is a process of scheduling the required load demand among available generation units such that the fuel cost of operation is minimized. The ELD problem is formulated as a nonlinear constrained optimization problem with both equality and inequality constraints. In this paper, two test systems of the ELD problems are solved by adopting the Cuckoo Search (CS) Algorithm. A comparison of obtained simulation results by using the CS is carried out against six other swarm intelligence algorithms: Particle Swarm Optimization, Shuffled Frog Leaping Algorithm, Bacterial Foraging Optimization, Artificial Bee Colony, Harmony Search and Firefly Algorithm. The effectiveness of each swarm intelligence algorithm is demonstrated on a test system comprising three-generators and other containing six-generators. Results denote superiority of the Cuckoo Search Algorithm and confirm its potential to solve the ELD problem.
基金The authors are grateful to the Raytheon Chair for Systems Engineering for funding.
文摘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.
文摘This article presents an application of generalized pattern search （PS） algorithm to solve economic load dispatch （ELD） problems with convex and non-convex fuel cost objective functions. Main objective of ELI） is to determine the most economic generating dispatch required to satisfy the predicted load demands including line losses. Relaxing various equality and inequality constraints are considered. The unit operation minhnum/maximum constraints, effects of valve-point and line losses are considered for the practical applications. Several case studies were tested and verified, which indicate an improvement in total fuel cost savings. The robustness of the proposed PS method have been assessed and investigated through intensive comparisons with reported results in recent researches. The results are very encouraging and suggesting that PS may be very useful tool in solving power system ELD problems.
基金supported by the National Natural Science Foundation of China(51937005)the Natural Science Foundation of Guangdong Province(2019A1515010689)the Oversea Study Program of Guangzhou Elite Project(GEP).
文摘This paper presents a robust interval economic dispatch(RIED)model for power systems with large-scale wind power integration.Differing from existing interval optimization(IO)approaches that merely rely on the upper and lower boundaries of random variables,the distribution information retained in the historical data is introduced to the IO method in this paper.Based on the available probability distribution function(PDF),wind power curtailment and load shedding are quantified as the operational risk and incorporated into the decision-making process.In this model,we need not rely on the forecasted value of wind power,which is randomly fluctuating and quite unpredictable.Furthermore,when the PDFs of wind power are taken into account,the resulting dispatch solution makes a good tradeoff between the generation cost and the operational risk.Finally,the RIED model yields an optimal dispatch solution for thermal units and the allowable intervals of wind power for the wind farms,which efficiently mitigates the uncertainty in wind power generation and provides more practical suggestions for system operators.Simulation studies are conducted on a modified IEEE-118 bus system and the results verify the effectiveness of the proposed RIED model.
基金supported by the National Natural Science Foundation of China 51937005the Natural Science Foundation of Guangdong Province 2019A1515010689.
文摘High penetration level of renewable energy has brought great challenges to operation of power systems,and use of flexible resources(FRs)is becoming increasingly important.Flexibility of power systems can be improved by changing generation arrangements,but the interests of some market participants may be harmed in the process.This study proposes a stochastic economic dispatch model with trading of flexible ramping products(FRPs).To calculate changes in revenue and reasonably compensate units that provide FRs,multisegmented marginal bidding for energy is simulated by linearizing generation cost,and an optimal market clearing strategy for FRPs is developed according to changes in clearing energy and marginal clearing price.Then,the correlation between prediction errors of wind speeds among different wind farms is determined based on a joint distribution function modeled by the copula function,and quasi-Monte Carlo simulation(QMC)is used to generate wind power scenarios.Finally,numerical simulations of modified IEEE-30 and IEEE-118 bus systems is performed with minimum comprehensive cost as the objective function.This verifies the proposed model could effectively deal with wind variability and uncertainty,stabilize the marginal clearing price of the electricity market,and ensure fairness in the market.
基金supported in part by the National Natural Science Foundation of China(No.52177119).
文摘The intermittency of renewable energy generation,variability of load demand,and stochasticity of market price bring about direct challenges to optimal energy management of microgrids.To cope with these different forms of operation uncertainties,an imitation learning based real-time decision-mak-ing solution for microgrid economic dispatch is proposed.In this solution,the optimal dispatch trajectories obtained by solving the optimal problem using historical deterministic operation patterns are demonstrated as the expert samples for imitation learning.To improve the generalization performance of imitation learning and the expressive ability of uncertain variables,a hybrid model combining the unsupervised and supervised learning is utilized.The denoising autoencoder based unsupervised learning model is adopted to enhance the feature extraction of operation patterns.Furthermore,the long short-term memory network based supervised learning model is used to efficiently characterize the mapping between the input space composed of the extracted operation patterns and system state variables and the output space composed of the optimal dispatch trajectories.The numerical simulation results demonstrate that under various operation uncertainties,the operation cost achieved by the proposed solution is close to the minimum theoretical value.Compared with the traditional model predictive control method and basic clone imitation learning method,the operation cost of the proposed solution is reduced by 6.3% and 2.8%,respectively,overa test period of three months.
