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
The paper proposes a novel H∞ load frequency control(LFC) design method for multi-area power systems based on an integral-based non-fragile distributed fixed-order dynamic output feedback(DOF) tracking-regulator cont...The paper proposes a novel H∞ load frequency control(LFC) design method for multi-area power systems based on an integral-based non-fragile distributed fixed-order dynamic output feedback(DOF) tracking-regulator control scheme. To this end, we consider a nonlinear interconnected model for multiarea power systems which also include uncertainties and timevarying communication delays. The design procedure is formulated using semi-definite programming and linear matrix inequality(LMI) method. The solution of the proposed LMIs returns necessary parameters for the tracking controllers such that the impact of model uncertainty and load disturbances are minimized. The proposed controllers are capable of receiving all or part of subsystems information, whereas the outputs of each controller are local. These controllers are designed such that the resilient stability of the overall closed-loop system is guaranteed. Simulation results are provided to verify the effectiveness of the proposed scheme. Simulation results quantify that the distributed(and decentralized) controlled system behaves well in presence of large parameter perturbations and random disturbances on the power system.展开更多
This paper is devoted to investigate the robust H∞sliding mode load frequency control(SMLFC) of multi-area power system with time delay. By taking into account stochastic disturbances induced by the integration of re...This paper is devoted to investigate the robust H∞sliding mode load frequency control(SMLFC) of multi-area power system with time delay. By taking into account stochastic disturbances induced by the integration of renewable energies,a new sliding surface function is constructed to guarantee the fast response and robust performance, then the sliding mode control law is designed to guarantee the reach ability of the sliding surface in a finite-time interval. The sufficient robust frequency stabilization result for multi-area power system with time delay is presented in terms of linear matrix inequalities(LMIs). Finally,a two-area power system is provided to illustrate the usefulness and effectiveness of the obtained results.展开更多
In this study, we present a Pareto-based chemicalreaction optimization(PCRO) algorithm for solving the multiarea environmental/economic dispatch optimization problems.Two objectives are minimized simultaneously, i.e.,...In this study, we present a Pareto-based chemicalreaction optimization(PCRO) algorithm for solving the multiarea environmental/economic dispatch optimization problems.Two objectives are minimized simultaneously, i.e., total fuel cost and emission. In the proposed algorithm, each solution is represented by a chemical molecule. A novel encoding mechanism for solving the multi-area environmental/economic dispatch optimization problems is designed to dynamically enhance the performance of the proposed algorithm. Then, an ensemble of effective neighborhood approaches is developed, and a selfadaptive neighborhood structure selection mechanism is also embedded in PCRO to increase the search ability while maintaining population diversity. In addition, a grid-based crowding distance strategy is introduced, which can obviously enable the algorithm to easily converge near the Pareto front. Furthermore,a kinetic-energy-based search procedure is developed to enhance the global search ability. Finally, the proposed algorithm is tested on sets of the instances that are generated based on realistic production. Through the analysis of experimental results, the highly effective performance of the proposed PCRO algorithm is favorably compared with several algorithms, with regards to both solution quality and diversity.展开更多
This paper presents a novel approach to solve the Multi-Area unit commitment problem using particle swarm optimization technique. The objective of the multi-area unit commitment problem is to determine the optimal or ...This paper presents a novel approach to solve the Multi-Area unit commitment problem using particle swarm optimization technique. The objective of the multi-area unit commitment problem is to determine the optimal or a near optimal commitment strategy for generating the units. And it is located in multiple areas that are interconnected via tie lines and joint operation of generation resources can result in significant operational cost savings. The dynamic programming method is applied to solve Multi-Area Unit Commitment problem and particle swarm optimization technique is embedded for computing the generation assigned to each area and the power allocated to all committed unit. Particle Swarm Optimization technique is developed to derive its Pareto-optimal solutions. The tie-line transfer limits are considered as a set of constraints during the optimization process to ensure the system security and reliability. Case study of four areas each containing 26 units connected via tie lines has been taken for analysis. Numerical results are shown comparing the cost solutions and computation time obtained by using the Particle Swarm Optimization method is efficient than the conventional Dynamic Programming and Evolutionary Programming Method.展开更多
This work proposes a novel nature-inspired algorithm called Ant Lion Optimizer (ALO). The ALO algorithm mimics the search mechanism of antlions in nature. A time domain based objective function is established to tune ...This work proposes a novel nature-inspired algorithm called Ant Lion Optimizer (ALO). The ALO algorithm mimics the search mechanism of antlions in nature. A time domain based objective function is established to tune the parameters of the PI controller based LFC, which is solved by the proposed ALO algorithm to reach the most convenient solutions. A three-area interconnected power system is investigated as a test system under various loading conditions to confirm the effectiveness of the suggested algorithm. Simulation results are given to show the enhanced performance of the developed ALO algorithm based controllers in comparison with Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Bat Algorithm (BAT) and conventional PI controller. These results represent that the proposed BAT algorithm tuned PI controller offers better performance over other soft computing algorithms in conditions of settling times and several performance indices.展开更多
Joint chance constraints(JCCs)can ensure the consistency and correlation of stochastic variables when participating in decision-making.Sample average approximation(SAA)is the most popular method for solving JCCs in un...Joint chance constraints(JCCs)can ensure the consistency and correlation of stochastic variables when participating in decision-making.Sample average approximation(SAA)is the most popular method for solving JCCs in unit commitment(UC)problems.However,the typical SAA requires large Monte Carlo(MC)samples to ensure the solution accuracy,which results in large-scale mixed-integer programming(MIP)problems.To address this problem,this paper presents the partial sample average approximation(PSAA)to deal with JCCs in UC problems in multi-area power systems with wind power.PSAA partitions the stochastic variables and historical dataset,and the historical dataset is then partitioned into non-sampled and sampled sets.When approximating the expectation of stochastic variables,PSAA replaces the big-M formulation with the cumulative distribution function of the non-sampled set,thus preventing binary variables from being introduced.Finally,PSAA can transform the chance constraints to deterministic constraints with only continuous variables,avoiding the large-scale MIP problem caused by SAA.Simulation results demonstrate that PSAA has significant advantages in solution accuracy and efficiency compared with other existing methods including traditional SAA,SAA with improved big-M,SAA with Latin hypercube sampling(LHS),and the multi-stage robust optimization methods.展开更多
Current urban transport and energy systems are gradually being integrated and developed towards a state of multi-area interconnection.This paper proposes a decentralized optimization approach of multi-area power-trans...Current urban transport and energy systems are gradually being integrated and developed towards a state of multi-area interconnection.This paper proposes a decentralized optimization approach of multi-area power-transport coupled systems(PTCSs)based on this change.To begin with,models concerning optimal power flow and mixed equilibrium flow are defined to describe flow patterns,respectively.Considering the traffic assignment model is non-linear and challenging to solve,this paper converts it into an equivalent variational inequality(Ⅵ).With this foundation,a decentralized optimization model is proposed,and decoupling strategies are investigated.To solve the problem effectively,an improved algorithm applicable to the decentralized optimization of PTCSs,supported by the Ⅳ tool,is proposed.In addition,a rigorous convergence analysis of the proposed algorithm was conducted.Simulations indicate the proposed algorithm solves the problem with good results and can guarantee convergence within a reasonable time frame.展开更多
In terms of the multi-area optimal power flow (OPF) problem, the optimized objectives are always a fuel cost function expressed by a second-order polynomial. However, the valve-point loading effect, whose cost curve i...In terms of the multi-area optimal power flow (OPF) problem, the optimized objectives are always a fuel cost function expressed by a second-order polynomial. However, the valve-point loading effect, whose cost curve is a transcendental function formed by the superposition of the sine and polynomial function, will make the objective function non-convex and non-differentiable. Conventional distributed optimization technologies can hardly make a solution directly. Therefore, it is necessary to realize a distributed solution for multi-area OPF from another point of view. In this paper, we constitute a new double-layer optimization mechanism. The proposed distributed meta-heuristic optimization (DMHO) algorithm is put on the top layer to optimize the dispatching of each area, and in each iteration a distributed power flow calculation method is embedded as the bottom layer to minimize the mismatch of power balance. Numerical experiments demonstrate that the proposed approach not only implements a multi-area OPF distributed solution but also accelerates the convergence rate, improves the solution accuracy and enhances the robustness. In addition, a fully decentralized computation experiment is performed in an actual distributed environment to test its practicability and computation efficiency.展开更多
This paper proposes a decentralized robust two-stage dispatch framework for multi-area integrated electric-gas systems (M-IEGSs), with the consideration of Weymouth and linepack equations of tie-pipelines. The overall...This paper proposes a decentralized robust two-stage dispatch framework for multi-area integrated electric-gas systems (M-IEGSs), with the consideration of Weymouth and linepack equations of tie-pipelines. The overall methodology includes the equivalent conversion for the robust two-stage program and the decentralized optimization for the equivalent form. To obtain a tractable and equivalent counterpart for the robust two-stage program, a quadruple-loop procedure based on the column-and-constraint generation (C&CG) and the penalty convex-concave procedure (P-CCP) algorithms is derived, resulting in a series of mixed integer second-order cone programs (MISOCPs). Then, an improved I-ADMM is proposed to realize the decentralized optimization for MISOCPs. Moreover, three acceleration methods are devised to reduce the computation burden. Simulation results validate the effectiveness of the proposed methodology and corresponding acceleration measures.展开更多
Over the last few years, lots of attentions have been given to the demand response(DR) for the frequency control. DR can be incorporated with traditional frequency control method and enhance the stability of the syste...Over the last few years, lots of attentions have been given to the demand response(DR) for the frequency control. DR can be incorporated with traditional frequency control method and enhance the stability of the system. In this paper, the frequency control strategy of DR for a multiarea power system is specially designed. In order to quickly stabilize the frequency of different areas, the tie-line power is adopted as the additional input signal of DR. To get the optimal parameters of the control system, the frequency control problem is formulated as a multi-objective optimization problem, and the parameters such as the integral gains of secondary frequency control, the frequency bias parameters, and coefficients of DR are optimized. Numerical results verify the effectiveness of the proposed method.展开更多
Continued expansion of the power grid and the increasing proportion of wind power centralized integration leads to requirements in sharing both energy and reserves among multiple areas under a hierarchical control str...Continued expansion of the power grid and the increasing proportion of wind power centralized integration leads to requirements in sharing both energy and reserves among multiple areas under a hierarchical control structure,which successively requires a correction between schedule plans within multi-time scale.In order to address this problem,this paper develops an information integration method integrating complicated relationships among fuel cost,total thermal power output,reserve capacity,owned reserves and expectations of load shedding and wind curtailment,into three types of time-related relationship curves・Furthermore,a multi-time scale tieline energy and reserves allocation model is proposed,which contains two levels in the control structure,two time scales in dispatch sequence and multiple areas integrated within wind farms as scheduling objects・The efficiency of the proposed method is tested in a 9-bus test system and IEEE 118-bus system.The results show that a cross-regional control center is able to approach the optimal scheduling results of the whole system with the integrated uploaded relationship curves.The proposed model not only relieves energy and reserve shortages in partial areas but also allocates them to more urgent need areas in a high effectivity manner in both day-ahead and intraday time scales.展开更多
To improve accuracy and efficiency in power systems dynamic modeling,the distributed online modeling approach is a good option.In this approach,the power system is divided into sub-grids,and the dynamic models of the ...To improve accuracy and efficiency in power systems dynamic modeling,the distributed online modeling approach is a good option.In this approach,the power system is divided into sub-grids,and the dynamic models of the sub-grids are built independently within the distributed modeling system.The subgrid models are subsequently merged,after which the dynamic model of the whole power system is finally constructed online.The merging of the networks plays an important role in the distributed online dynamic modeling of power systems.An efficient multi-area networks-merging model that can rapidly match the boundary power flow is proposed in this paper.The iterations of the boundary matching during network merging are eliminated due to the introduction of the merging model,and the dynamic models of the sub-grid can be directly“plugged in”with each other.The results of the calculations performed in a real power system demonstrate the accuracy of the integrated model under both steady and transient states.展开更多
The increasing penetration of renewable energy sources(RESs)brings great challenges to the frequency security of power systems.The traditional frequency-constrained unit commitment(FCUC)analyzes frequency by simplifyi...The increasing penetration of renewable energy sources(RESs)brings great challenges to the frequency security of power systems.The traditional frequency-constrained unit commitment(FCUC)analyzes frequency by simplifying the average system frequency and ignoring numerous induction machines(IMs)in load,which may underestimate the risk and increase the operational cost.In this paper,we consider a multiarea frequency response(MAFR)model to capture the frequency dynamics in the unit scheduling problem,in which regional frequency security and the inertia of IM load are modeled with high-dimension differential algebraic equations.A multi-area FCUC(MFCUC)is formulated as mixed-integer nonlinear programming(MINLP)on the basis of the MAFR model.Then,we develop a multi-direction decomposition algorithm to solve the MFCUC efficiently.The original MINLP is decomposed into a master problem and subproblems.The subproblems check the nonlinear frequency dynamics and generate linear optimization cuts for the master problem to improve the frequency security in its optimal solution.Case studies on the modified IEEE 39-bus system and IEEE 118-bus system show a great reduction in operational costs.Moreover,simulation results verify the ability of the proposed MAFR model to reflect regional frequency security and the available inertia of IMs in unit scheduling.展开更多
This paper presents both application and comparison of the metaheuristic techniques to multi-area economic dispatch(MAED)problem with tie line constraints considering transmission losses,multiple fuels,valve-point loa...This paper presents both application and comparison of the metaheuristic techniques to multi-area economic dispatch(MAED)problem with tie line constraints considering transmission losses,multiple fuels,valve-point loading and prohibited operating zones.The metaheuristic techniques such as differential evolution,evolutionary programming,genetic algorithm and simulated annealing are applied to solve MAED problem.These metaheuristic techniques for MAED problem are evaluated on three different test systems,both small and large,involving varying degree of complexity and the results are compared against each other.展开更多
Multi-Area Multi-Fuel Economic Dispatch (MAMFED) aims to allocate the best generation schedule in each area and to offer the best power transfers between different areas by minimizing the objective functions among the...Multi-Area Multi-Fuel Economic Dispatch (MAMFED) aims to allocate the best generation schedule in each area and to offer the best power transfers between different areas by minimizing the objective functions among the available fuel alternatives for each unit while satisfying various constraints in power systems. In this paper, a Fuzzified Squirrel Search Algorithm (FSSA) algorithm is proposed to solve the single-area multi-fuel economic dispatch (SAMFED) and MAMFED problems. Squirrel Search Algorithm (SSA) mimics the foraging behavior of squirrels based on the dynamic jumping and gliding strategies. In the SSA approach, predator presence behavior and a seasonal monitoring condition are employed to increase the search ability of the algorithm, and to balance the exploitation and exploration. The suggested approach considers the line losses, valve point loading impacts, multi-fuel alternatives, and tie-line limits of the power system. Because of the contradicting nature of fuel cost and pollutant emission objectives, weighted sum approach and price penalty factor are used to transfer the bi-objective function into a single objective function. Furthermore, a fuzzy decision strategy is introduced to find one of the Pareto optimal fronts as the best compromised solution. The feasibility of the FSSA is tested on a three-area test system for both the SAMFED and MAMFED problems. The results of FSSA approach are compared with other heuristic approaches in the literature. Multi-objective performance indicators such as generational distance, spacing metric and ratio of non-dominated individuals are evaluated to validate the effectiveness of FSSA. The results divulge that the FSSA is a promising approach to solve the SAMFED and MAMFED problems while providing a better compromise solution in comparison with other heuristic approaches.展开更多
Multi-area combined economic/emission dispatch(MACEED)problems are generally studied using analytical functions.However,as the scale of power systems increases,ex isting solutions become time-consuming and may not mee...Multi-area combined economic/emission dispatch(MACEED)problems are generally studied using analytical functions.However,as the scale of power systems increases,ex isting solutions become time-consuming and may not meet oper ational constraints.To overcome excessive computational ex pense in high-dimensional MACEED problems,a novel data-driven surrogate-assisted method is proposed.First,a cosine-similarity-based deep belief network combined with a back-propagation(DBN+BP)neural network is utilized to replace cost and emission functions.Second,transfer learning is applied with a pretraining and fine-tuning method to improve DBN+BP regression surrogate models,thus realizing fast con struction of surrogate models between different regional power systems.Third,a multi-objective antlion optimizer with a novel general single-dimension retention bi-objective optimization poli cy is proposed to execute MACEED optimization to obtain scheduling decisions.The proposed method not only ensures the convergence,uniformity,and extensibility of the Pareto front,but also greatly reduces the computational time.Finally,a 4-ar ea 40-unit test system with different constraints is employed to demonstrate the effectiveness of the proposed method.展开更多
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.
文摘The paper proposes a novel H∞ load frequency control(LFC) design method for multi-area power systems based on an integral-based non-fragile distributed fixed-order dynamic output feedback(DOF) tracking-regulator control scheme. To this end, we consider a nonlinear interconnected model for multiarea power systems which also include uncertainties and timevarying communication delays. The design procedure is formulated using semi-definite programming and linear matrix inequality(LMI) method. The solution of the proposed LMIs returns necessary parameters for the tracking controllers such that the impact of model uncertainty and load disturbances are minimized. The proposed controllers are capable of receiving all or part of subsystems information, whereas the outputs of each controller are local. These controllers are designed such that the resilient stability of the overall closed-loop system is guaranteed. Simulation results are provided to verify the effectiveness of the proposed scheme. Simulation results quantify that the distributed(and decentralized) controlled system behaves well in presence of large parameter perturbations and random disturbances on the power system.
基金supported in part by the National Natural Science Foundation of China(61673161)the Natural Science Foundation of Jiangsu Province of China(BK20161510)+2 种基金the Fundamental Research Funds for the Central Universities of China(2017B13914)the 111 Project(B14022)the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)
文摘This paper is devoted to investigate the robust H∞sliding mode load frequency control(SMLFC) of multi-area power system with time delay. By taking into account stochastic disturbances induced by the integration of renewable energies,a new sliding surface function is constructed to guarantee the fast response and robust performance, then the sliding mode control law is designed to guarantee the reach ability of the sliding surface in a finite-time interval. The sufficient robust frequency stabilization result for multi-area power system with time delay is presented in terms of linear matrix inequalities(LMIs). Finally,a two-area power system is provided to illustrate the usefulness and effectiveness of the obtained results.
基金partially supported by the National Natural Science Foundation of China(61773192,61773246,61603169,61803192)Shandong Province Higher Educational Science and Technology Program(J17KZ005)+1 种基金Special Fund Plan for Local Science and Technology Development Lead by Central AuthorityMajor Basic Research Projects in Shandong(ZR2018ZB0419)
文摘In this study, we present a Pareto-based chemicalreaction optimization(PCRO) algorithm for solving the multiarea environmental/economic dispatch optimization problems.Two objectives are minimized simultaneously, i.e., total fuel cost and emission. In the proposed algorithm, each solution is represented by a chemical molecule. A novel encoding mechanism for solving the multi-area environmental/economic dispatch optimization problems is designed to dynamically enhance the performance of the proposed algorithm. Then, an ensemble of effective neighborhood approaches is developed, and a selfadaptive neighborhood structure selection mechanism is also embedded in PCRO to increase the search ability while maintaining population diversity. In addition, a grid-based crowding distance strategy is introduced, which can obviously enable the algorithm to easily converge near the Pareto front. Furthermore,a kinetic-energy-based search procedure is developed to enhance the global search ability. Finally, the proposed algorithm is tested on sets of the instances that are generated based on realistic production. Through the analysis of experimental results, the highly effective performance of the proposed PCRO algorithm is favorably compared with several algorithms, with regards to both solution quality and diversity.
文摘This paper presents a novel approach to solve the Multi-Area unit commitment problem using particle swarm optimization technique. The objective of the multi-area unit commitment problem is to determine the optimal or a near optimal commitment strategy for generating the units. And it is located in multiple areas that are interconnected via tie lines and joint operation of generation resources can result in significant operational cost savings. The dynamic programming method is applied to solve Multi-Area Unit Commitment problem and particle swarm optimization technique is embedded for computing the generation assigned to each area and the power allocated to all committed unit. Particle Swarm Optimization technique is developed to derive its Pareto-optimal solutions. The tie-line transfer limits are considered as a set of constraints during the optimization process to ensure the system security and reliability. Case study of four areas each containing 26 units connected via tie lines has been taken for analysis. Numerical results are shown comparing the cost solutions and computation time obtained by using the Particle Swarm Optimization method is efficient than the conventional Dynamic Programming and Evolutionary Programming Method.
文摘This work proposes a novel nature-inspired algorithm called Ant Lion Optimizer (ALO). The ALO algorithm mimics the search mechanism of antlions in nature. A time domain based objective function is established to tune the parameters of the PI controller based LFC, which is solved by the proposed ALO algorithm to reach the most convenient solutions. A three-area interconnected power system is investigated as a test system under various loading conditions to confirm the effectiveness of the suggested algorithm. Simulation results are given to show the enhanced performance of the developed ALO algorithm based controllers in comparison with Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Bat Algorithm (BAT) and conventional PI controller. These results represent that the proposed BAT algorithm tuned PI controller offers better performance over other soft computing algorithms in conditions of settling times and several performance indices.
基金supported by the National Natural Science Foundation of China(No.51977042)。
文摘Joint chance constraints(JCCs)can ensure the consistency and correlation of stochastic variables when participating in decision-making.Sample average approximation(SAA)is the most popular method for solving JCCs in unit commitment(UC)problems.However,the typical SAA requires large Monte Carlo(MC)samples to ensure the solution accuracy,which results in large-scale mixed-integer programming(MIP)problems.To address this problem,this paper presents the partial sample average approximation(PSAA)to deal with JCCs in UC problems in multi-area power systems with wind power.PSAA partitions the stochastic variables and historical dataset,and the historical dataset is then partitioned into non-sampled and sampled sets.When approximating the expectation of stochastic variables,PSAA replaces the big-M formulation with the cumulative distribution function of the non-sampled set,thus preventing binary variables from being introduced.Finally,PSAA can transform the chance constraints to deterministic constraints with only continuous variables,avoiding the large-scale MIP problem caused by SAA.Simulation results demonstrate that PSAA has significant advantages in solution accuracy and efficiency compared with other existing methods including traditional SAA,SAA with improved big-M,SAA with Latin hypercube sampling(LHS),and the multi-stage robust optimization methods.
基金supported by National Natural Science Foundation of China under grant 52307087.
文摘Current urban transport and energy systems are gradually being integrated and developed towards a state of multi-area interconnection.This paper proposes a decentralized optimization approach of multi-area power-transport coupled systems(PTCSs)based on this change.To begin with,models concerning optimal power flow and mixed equilibrium flow are defined to describe flow patterns,respectively.Considering the traffic assignment model is non-linear and challenging to solve,this paper converts it into an equivalent variational inequality(Ⅵ).With this foundation,a decentralized optimization model is proposed,and decoupling strategies are investigated.To solve the problem effectively,an improved algorithm applicable to the decentralized optimization of PTCSs,supported by the Ⅳ tool,is proposed.In addition,a rigorous convergence analysis of the proposed algorithm was conducted.Simulations indicate the proposed algorithm solves the problem with good results and can guarantee convergence within a reasonable time frame.
基金supported by the National Natural Science Foundation of China(52177087)High-end Foreign Experts Project(G2022163018L)Guangdong Basic and Applied Basic Research Foundation(2024A1515030192).
文摘In terms of the multi-area optimal power flow (OPF) problem, the optimized objectives are always a fuel cost function expressed by a second-order polynomial. However, the valve-point loading effect, whose cost curve is a transcendental function formed by the superposition of the sine and polynomial function, will make the objective function non-convex and non-differentiable. Conventional distributed optimization technologies can hardly make a solution directly. Therefore, it is necessary to realize a distributed solution for multi-area OPF from another point of view. In this paper, we constitute a new double-layer optimization mechanism. The proposed distributed meta-heuristic optimization (DMHO) algorithm is put on the top layer to optimize the dispatching of each area, and in each iteration a distributed power flow calculation method is embedded as the bottom layer to minimize the mismatch of power balance. Numerical experiments demonstrate that the proposed approach not only implements a multi-area OPF distributed solution but also accelerates the convergence rate, improves the solution accuracy and enhances the robustness. In addition, a fully decentralized computation experiment is performed in an actual distributed environment to test its practicability and computation efficiency.
文摘This paper proposes a decentralized robust two-stage dispatch framework for multi-area integrated electric-gas systems (M-IEGSs), with the consideration of Weymouth and linepack equations of tie-pipelines. The overall methodology includes the equivalent conversion for the robust two-stage program and the decentralized optimization for the equivalent form. To obtain a tractable and equivalent counterpart for the robust two-stage program, a quadruple-loop procedure based on the column-and-constraint generation (C&CG) and the penalty convex-concave procedure (P-CCP) algorithms is derived, resulting in a series of mixed integer second-order cone programs (MISOCPs). Then, an improved I-ADMM is proposed to realize the decentralized optimization for MISOCPs. Moreover, three acceleration methods are devised to reduce the computation burden. Simulation results validate the effectiveness of the proposed methodology and corresponding acceleration measures.
基金supported in part by the University Science Research Project of Jiangsu Province (No. 16KJB470009)
文摘Over the last few years, lots of attentions have been given to the demand response(DR) for the frequency control. DR can be incorporated with traditional frequency control method and enhance the stability of the system. In this paper, the frequency control strategy of DR for a multiarea power system is specially designed. In order to quickly stabilize the frequency of different areas, the tie-line power is adopted as the additional input signal of DR. To get the optimal parameters of the control system, the frequency control problem is formulated as a multi-objective optimization problem, and the parameters such as the integral gains of secondary frequency control, the frequency bias parameters, and coefficients of DR are optimized. Numerical results verify the effectiveness of the proposed method.
基金supported in part by the Science and Technology Project of Central Branch of SGCC(SGHZ0000DKJS 1900228)in part by the National Natural Science Foundation of China(51707136).
文摘Continued expansion of the power grid and the increasing proportion of wind power centralized integration leads to requirements in sharing both energy and reserves among multiple areas under a hierarchical control structure,which successively requires a correction between schedule plans within multi-time scale.In order to address this problem,this paper develops an information integration method integrating complicated relationships among fuel cost,total thermal power output,reserve capacity,owned reserves and expectations of load shedding and wind curtailment,into three types of time-related relationship curves・Furthermore,a multi-time scale tieline energy and reserves allocation model is proposed,which contains two levels in the control structure,two time scales in dispatch sequence and multiple areas integrated within wind farms as scheduling objects・The efficiency of the proposed method is tested in a 9-bus test system and IEEE 118-bus system.The results show that a cross-regional control center is able to approach the optimal scheduling results of the whole system with the integrated uploaded relationship curves.The proposed model not only relieves energy and reserve shortages in partial areas but also allocates them to more urgent need areas in a high effectivity manner in both day-ahead and intraday time scales.
基金supported by the National Key Basic Research Program of China(973 Program)(2013CB228204)the National Natural Science Foundation of China(51137002,51190102,51407060).
文摘To improve accuracy and efficiency in power systems dynamic modeling,the distributed online modeling approach is a good option.In this approach,the power system is divided into sub-grids,and the dynamic models of the sub-grids are built independently within the distributed modeling system.The subgrid models are subsequently merged,after which the dynamic model of the whole power system is finally constructed online.The merging of the networks plays an important role in the distributed online dynamic modeling of power systems.An efficient multi-area networks-merging model that can rapidly match the boundary power flow is proposed in this paper.The iterations of the boundary matching during network merging are eliminated due to the introduction of the merging model,and the dynamic models of the sub-grid can be directly“plugged in”with each other.The results of the calculations performed in a real power system demonstrate the accuracy of the integrated model under both steady and transient states.
基金supported by the Science and Technology Project of State Grid Hebei Electric Power Company Limited(No.kj2021-073)。
文摘The increasing penetration of renewable energy sources(RESs)brings great challenges to the frequency security of power systems.The traditional frequency-constrained unit commitment(FCUC)analyzes frequency by simplifying the average system frequency and ignoring numerous induction machines(IMs)in load,which may underestimate the risk and increase the operational cost.In this paper,we consider a multiarea frequency response(MAFR)model to capture the frequency dynamics in the unit scheduling problem,in which regional frequency security and the inertia of IM load are modeled with high-dimension differential algebraic equations.A multi-area FCUC(MFCUC)is formulated as mixed-integer nonlinear programming(MINLP)on the basis of the MAFR model.Then,we develop a multi-direction decomposition algorithm to solve the MFCUC efficiently.The original MINLP is decomposed into a master problem and subproblems.The subproblems check the nonlinear frequency dynamics and generate linear optimization cuts for the master problem to improve the frequency security in its optimal solution.Case studies on the modified IEEE 39-bus system and IEEE 118-bus system show a great reduction in operational costs.Moreover,simulation results verify the ability of the proposed MAFR model to reflect regional frequency security and the available inertia of IMs in unit scheduling.
文摘This paper presents both application and comparison of the metaheuristic techniques to multi-area economic dispatch(MAED)problem with tie line constraints considering transmission losses,multiple fuels,valve-point loading and prohibited operating zones.The metaheuristic techniques such as differential evolution,evolutionary programming,genetic algorithm and simulated annealing are applied to solve MAED problem.These metaheuristic techniques for MAED problem are evaluated on three different test systems,both small and large,involving varying degree of complexity and the results are compared against each other.
文摘Multi-Area Multi-Fuel Economic Dispatch (MAMFED) aims to allocate the best generation schedule in each area and to offer the best power transfers between different areas by minimizing the objective functions among the available fuel alternatives for each unit while satisfying various constraints in power systems. In this paper, a Fuzzified Squirrel Search Algorithm (FSSA) algorithm is proposed to solve the single-area multi-fuel economic dispatch (SAMFED) and MAMFED problems. Squirrel Search Algorithm (SSA) mimics the foraging behavior of squirrels based on the dynamic jumping and gliding strategies. In the SSA approach, predator presence behavior and a seasonal monitoring condition are employed to increase the search ability of the algorithm, and to balance the exploitation and exploration. The suggested approach considers the line losses, valve point loading impacts, multi-fuel alternatives, and tie-line limits of the power system. Because of the contradicting nature of fuel cost and pollutant emission objectives, weighted sum approach and price penalty factor are used to transfer the bi-objective function into a single objective function. Furthermore, a fuzzy decision strategy is introduced to find one of the Pareto optimal fronts as the best compromised solution. The feasibility of the FSSA is tested on a three-area test system for both the SAMFED and MAMFED problems. The results of FSSA approach are compared with other heuristic approaches in the literature. Multi-objective performance indicators such as generational distance, spacing metric and ratio of non-dominated individuals are evaluated to validate the effectiveness of FSSA. The results divulge that the FSSA is a promising approach to solve the SAMFED and MAMFED problems while providing a better compromise solution in comparison with other heuristic approaches.
文摘Multi-area combined economic/emission dispatch(MACEED)problems are generally studied using analytical functions.However,as the scale of power systems increases,ex isting solutions become time-consuming and may not meet oper ational constraints.To overcome excessive computational ex pense in high-dimensional MACEED problems,a novel data-driven surrogate-assisted method is proposed.First,a cosine-similarity-based deep belief network combined with a back-propagation(DBN+BP)neural network is utilized to replace cost and emission functions.Second,transfer learning is applied with a pretraining and fine-tuning method to improve DBN+BP regression surrogate models,thus realizing fast con struction of surrogate models between different regional power systems.Third,a multi-objective antlion optimizer with a novel general single-dimension retention bi-objective optimization poli cy is proposed to execute MACEED optimization to obtain scheduling decisions.The proposed method not only ensures the convergence,uniformity,and extensibility of the Pareto front,but also greatly reduces the computational time.Finally,a 4-ar ea 40-unit test system with different constraints is employed to demonstrate the effectiveness of the proposed method.
