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
In this paper,a strength-constrained unit commitment(UC)model incorporating system strength constraints based on the weighted short-circuit ratio(WSCR)is proposed.This model facilitates the comprehensive assessment of...In this paper,a strength-constrained unit commitment(UC)model incorporating system strength constraints based on the weighted short-circuit ratio(WSCR)is proposed.This model facilitates the comprehensive assessment of area-wide system strength in power systems with high inverter-based resource(IBR)penetration,thereby contributing to the mitigation of weak grid issues.Unlike traditional models,this approach considers the interactions among multiple IBRs.The UC problem is initially formulated as a mixed-integer nonlinear programming(MINLP)model,reflecting WSCR and bus impedance matrix modification constraints.To enhance computational tractability,the model is transformed into a mixed-integer linear programming(MILP)form.The effectiveness of the proposed approach is validated through simulations on the IEEE 5-bus,IEEE 39-bus,and a modified Korean power system,demonstrating the ability of the proposed UC model enhancing system strength compared to the conventional methodologies.展开更多
Stochastic unit commitment is one of the most powerful methods to address uncertainty. However, the existingscenario clustering technique for stochastic unit commitment cannot accurately select representative scenario...Stochastic unit commitment is one of the most powerful methods to address uncertainty. However, the existingscenario clustering technique for stochastic unit commitment cannot accurately select representative scenarios,which threatens the robustness of stochastic unit commitment and hinders its application. This paper providesa stochastic unit commitment with dynamic scenario clustering based on multi-parametric programming andBenders decomposition. The stochastic unit commitment is solved via the Benders decomposition, which decouplesthe primal problem into the master problem and two types of subproblems. In the master problem, the committedgenerator is determined, while the feasibility and optimality of generator output are checked in these twosubproblems. Scenarios are dynamically clustered during the subproblem solution process through the multiparametric programming with respect to the solution of the master problem. In other words, multiple scenariosare clustered into several representative scenarios after the subproblem is solved, and the Benders cut obtainedby the representative scenario is generated for the master problem. Different from the conventional stochasticunit commitment, the proposed approach integrates scenario clustering into the Benders decomposition solutionprocess. Such a clustering approach could accurately cluster representative scenarios that have impacts on theunit commitment. The proposed method is tested on a 6-bus system and the modified IEEE 118-bus system.Numerical results illustrate the effectiveness of the proposed method in clustering scenarios. Compared withthe conventional clustering method, the proposed method can accurately select representative scenarios whilemitigating computational burden, thus guaranteeing the robustness of unit commitment.展开更多
The Unit Commitment Problem(UCP)corresponds to the planning of power generation schedules.The objective of the fuel-based unit commitment problem is to determine the optimal schedule of power generators needed to meet...The Unit Commitment Problem(UCP)corresponds to the planning of power generation schedules.The objective of the fuel-based unit commitment problem is to determine the optimal schedule of power generators needed to meet the power demand,which also minimizes the total operating cost while adhering to different constraints such as power generation limits,unit startup,and shutdown times.In this paper,four different binary variants of the Bald Eagle Search(BES)algorithm,were introduced,which used two variants using S-shape,U-shape,and V-shape transfer functions.In addition,the best-performing variant(using an S-shape transfer function)was selected and improved further by incorporating two binary operators:swap-window and window-mutation.This variation is labeled Improved Binary Bald Eagle Search(IBBESS2).All five variants of the proposed algorithm were successfully adopted to solve the fuel-based unit commitment problem using seven test cases of 4-,10-,20-,40-,60-,80-,and 100-unit.For comparative evaluation,34 comparative methods from existing literature were compared,in which IBBESS2 achieved competitive scores against other optimization techniques.In other words,the proposed IBBESS2 performs better than all other competitors by achieving the best average scores in 20-,40-,60-,80-,and 100-unit problems.Furthermore,IBBESS2 demonstrated quicker convergence to an optimal solution than other algorithms,especially in large-scale unit commitment problems.The Friedman statistical test further validates the results,where the proposed IBBESS2 is ranked the best.In conclusion,the proposed IBBESS2 can be considered a powerful method for solving large-scale UCP and other related problems.展开更多
Electric power system is one of the most important and complex engineering in modern society, supplying main and general power for social production and social life. Meanwhile, since it is a productive system with bo...Electric power system is one of the most important and complex engineering in modern society, supplying main and general power for social production and social life. Meanwhile, since it is a productive system with both high input and output, it has an obvious economic significance to improve its operating efficiency. For an example, an unit is 10 GW scale, if its standard coal consumption can be decreased with 1 g/kW·h, it can save about 5 000 tons standard coal per year. It will be discussed mainly that how to establish optimization model and its numerical algorithm for operating management of the electric power system. The idea on establishing optimization model is how to dispatch work state of units or power plants, so that total cost of fuel consumption for generation is reduced to the minimum. Here the dispatch is to decide which unit or plant to operate, which unit or plant to stop running, how much power should be generated for those operating units or plants at each given time interval.展开更多
Generally, the procedure for Solving Security constrained unit commitment (SCUC) problems within Lagrangian Relaxation framework is partitioned into two stages: one is to obtain feasible SCUC states;the other is to so...Generally, the procedure for Solving Security constrained unit commitment (SCUC) problems within Lagrangian Relaxation framework is partitioned into two stages: one is to obtain feasible SCUC states;the other is to solve the economic dispatch of generation power among all the generating units. The core of the two stages is how to determine the feasibility of SCUC states. The existence of ramp rate constraints and security constraints increases the difficulty of obtaining an analytical necessary and sufficient condition for determining the quasi-feasibility of SCUC states at each scheduling time. However, a numerical necessary and sufficient numerical condition is proposed and proven rigorously based on Benders Decomposition Theorem. Testing numerical example shows the effectiveness and efficiency of the condition.展开更多
Unit commitment (UC) is to determine the optimal unit status and generation level during each time interval of the scheduled period. The purpose of UC is to minimize the total generation cost while satisfying system d...Unit commitment (UC) is to determine the optimal unit status and generation level during each time interval of the scheduled period. The purpose of UC is to minimize the total generation cost while satisfying system demand, reserve requirements, and unit constraints. Among the UC constraints, an adequate provision of reserve is important to ensure the security of power system and the fast-response reserve is essential to bring system frequency back to acceptable level following the loss of an online unit within a few seconds. In this paper, the authors present and solve a UC problem including the frequency-based reserve constraints to determine the optimal FRR requirements and unit MW schedules. The UC problem is solved by using Lagrangian Relaxation-based approach and compared with the actual system schedules. It is observed that favorable reserve and unit MW schedules are obtained by the proposed method while the system security is maintained.展开更多
Bilateral electric power contract is settled based on contract output curve. This paper considered the bilateral transactions execution, new energy accommodation, power grid security and generation economy, considerin...Bilateral electric power contract is settled based on contract output curve. This paper considered the bilateral transactions execution, new energy accommodation, power grid security and generation economy, considering the executive priority of different power components to establish a multi-objective coordination unit commitment model. Through an example to verify the effectiveness of the model in promoting wind power consumption, guaranteeing trade execution, and improving power generation efficiency, and analyzed the interactions to each other among the factors of wind power, trading and blocking. According to the results, when wind power causes reverse power flow in the congestion line, it will promote the implementation of contracts, the influence of wind power accommodation to trade execution should be analyzed combined with the grid block, the results can provide reference for wind power planning.展开更多
The solar and wind renewable energy is developing very rapidly to fulfill the energy gap. This specific increasing share of renewable energy is a reaction to the ecological trepidations to conciliate economics with se...The solar and wind renewable energy is developing very rapidly to fulfill the energy gap. This specific increasing share of renewable energy is a reaction to the ecological trepidations to conciliate economics with security due to the new challenges in power system supply. In solar and wind renewable energy, the only partially predictable is the output with very low controllability which creates unit commitment problems in thermal units. In this research paper, a different linear formulation via mixed integer is presented that only requires “binary variables” and restraints concerning earlier stated models. The framework of this model allows precisely the costs of time-dependent startup & intertemporal limitations, for example, minimum up & down times and a ramping limit. To solve the unit commitment problem efficiently, a commercially available linear programming of mixed-integer is applied for sizeable practical scale. The results of the simulation are shown in conclusions.展开更多
This paper presents a new hybrid approach that combines Modified Priority List (MPL) with Charged System Search (CSS), termed MPL-CSS, to solve one of the most crucial power system’s operational optimization problems...This paper presents a new hybrid approach that combines Modified Priority List (MPL) with Charged System Search (CSS), termed MPL-CSS, to solve one of the most crucial power system’s operational optimization problems, known as unit commitment (UC) scheduling. The UC scheduling problem is a mixed-integer nonlinear problem, highly-dimensional and extremely constrained. Existing meta-heuristic UC solution methods have the problems of stopping at a local optimum and slow convergence when applied to large-scale, heavily-constrained UC applications. In the first step of the proposed method, initial hourly optimum solutions of UC are obtained by Modified Priority List (MPL);however, the obtained UC solution may still be possible to be further improved. Therefore, in the second step, the CSS is utilized to achieve higher quality solutions. The UC is formulated as mixed integer linear programming to ensure the tractability of the results. The proposed method is successfully applied to a popular test system up to 100 units generators for both 24-hr and 168-hr system. Computational results show that both solution cost and execution time are superior to those of published methods.展开更多
This paper presents a new method based on an immune-tabu hybrid algorithm to solve the thermal unit commitment （TUC） problem in power plant optimization. The mathematical model of the TUC problem is established by a...This paper presents a new method based on an immune-tabu hybrid algorithm to solve the thermal unit commitment （TUC） problem in power plant optimization. The mathematical model of the TUC problem is established by analyzing the generating units in modem power plants. A novel immune-tabu hybrid algorithm is proposed to solve this complex problem. In the algorithm, the objective function of the TUC problem is considered as an antigen and the solutions are considered as antibodies, which are determined by the affinity computation. The code length of an antibody is shortened by encoding the continuous operating time, and the optimum searching speed is improved. Each feasible individual in the immune algorithm （IA） is used as the initial solution of the tabu search （TS） algorithm after certain generations of IA iteration. As examples, the proposed method has been applied to several thermal unit systems for a period of 24 h. The computation results demonstrate the good global optimum searching performance of the proposed immune-tabu hybrid algorithm. The presented algorithm can also be used to solve other optimization problems in fields such as the chemical industry and the power industry.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
How to solve unit commitment and load dispatch of power system by genetic algorithms is discussed in this paper. A combination encoding scheme of binary encoding and floating number encoding and corresponding genetic ...How to solve unit commitment and load dispatch of power system by genetic algorithms is discussed in this paper. A combination encoding scheme of binary encoding and floating number encoding and corresponding genetic operators are developed. Meanwhile a contract mapping genetic algorithm is used to enhance traditional GA’s convergence. The result of a practical example shows that this algorithm is effective.展开更多
GAs are general purpose optimization techniques based on principles inspired from the biological evolution using metaphors of mechanisms, such as natural selection, genetic recombination and survival of the fittest. B...GAs are general purpose optimization techniques based on principles inspired from the biological evolution using metaphors of mechanisms, such as natural selection, genetic recombination and survival of the fittest. By use of coding betterment, the dynamic changes of the mutation rate and the crossover probability, the dynamic choice of subsistence, the reservation of the optimal fitness value, a modified genetic algorithm for optimizing combination of units in thermal power plants is proposed. And through taking examples, test result are analyzed and compared with results of some different algorithms. Numerical results show available value for the unit commitment problem with examples.展开更多
Grid integration of wind power is essential to reduce fossil fuel usage but challenging in view of the intermittent nature of wind.Recently,we developed a hybrid Markovian and interval approach for the unit commitment...Grid integration of wind power is essential to reduce fossil fuel usage but challenging in view of the intermittent nature of wind.Recently,we developed a hybrid Markovian and interval approach for the unit commitment and economic dispatch problem where power generation of conventional units is linked to local wind states to dampen the effects of wind uncertainties.Also,to reduce complexity,extreme and expected states are considered as interval modeling.Although this approach is effective,the fact that major wind farms are often located in remote locations and not accompanied by conventional units leads to conservative results.Furthermore,weights of extreme and expected states in the objective function are difficult to tune,resulting in significant differences between optimization and simulation costs.In this paper,each remote wind farm is paired with a conventional unit to dampen the effects of wind uncertainties without using expensive utility-scaled battery storage,and extra constraints are innovatively established to model pairing.Additionally,proper weights are derived through a novel quadratic fit of cost functions.The problem is solved by using a creative integration of our recent surrogate Lagrangian relaxation and branch-and-cut.Results demonstrate modeling accuracy,computational efficiency,and significant reduction of conservativeness of the previous approach.展开更多
Unit commitment(UC), as a typical optimization problem in electric power system, faces new challenges as energy saving and emission reduction get more and more important in the way to a more environmentally friendly s...Unit commitment(UC), as a typical optimization problem in electric power system, faces new challenges as energy saving and emission reduction get more and more important in the way to a more environmentally friendly society. To meet these challenges, we propose a UC model considering energy saving and emission reduction. By using real-number coding method, swap-window and hill-climbing operators, we present an improved real-coded genetic algorithm(IRGA) for UC. Compared with other algorithms approach to the proposed UC problem, the IRGA solution shows an improvement in effectiveness and computational time.展开更多
This paper presents a new algorithm for solving unit commitment (UC) problems using a binary-real coded genetic algorithm based on k-means clustering technique. UC is a NP-hard nonlinear mixed-integer optimization pro...This paper presents a new algorithm for solving unit commitment (UC) problems using a binary-real coded genetic algorithm based on k-means clustering technique. UC is a NP-hard nonlinear mixed-integer optimization problem, encountered as one of the toughest problems in power systems, in which some power generating units are to be scheduled in such a way that the forecasted demand is met at minimum production cost over a time horizon. In the proposed algorithm, the algorithm integrates the main features of a binary-real coded genetic algorithm (GA) and k-means clustering technique. The binary coded GA is used to obtain a feasible commitment schedule for each generating unit;while the power amounts generated by committed units are determined by using real coded GA for the feasible commitment obtained in each interval. k-means clustering algorithm divides population into a specific number of subpopulations with dynamic size. In this way, using k-means clustering algorithm allows the use of different GA operators with the whole population and avoids the local problem minima. The effectiveness of the proposed technique is validated on a test power system available in the literature. The proposed algorithm performance is found quite satisfactory in comparison with the previously reported results.展开更多
Considering the economics and securities for the operation of a power system, this paper presents a new adaptive dynamic programming approach for security-constrained unit commitment (SCUC) problems. In response to t...Considering the economics and securities for the operation of a power system, this paper presents a new adaptive dynamic programming approach for security-constrained unit commitment (SCUC) problems. In response to the “curse of dimension” problem of dynamic programming, the approach solves the Bellman’s equation of SCUC approximately by solving a sequence of simplified single stage optimization problems. An extended sequential truncation technique is proposed to explore the state space of the approach, which is superior to traditional sequential truncation in daily cost for unit commitment. Different test cases from 30 to 300 buses over a 24 h horizon are analyzed. Extensive numerical comparisons show that the proposed approach is capable of obtaining the optimal unit commitment schedules without any network and bus voltage violations, and minimizing the operation cost as well.展开更多
The study of unit commitment (UC) aims to find reasonable schedules for generators to optimize power systems’ operation. Many papers have been published that solve UC through different methods. Articles that systemat...The study of unit commitment (UC) aims to find reasonable schedules for generators to optimize power systems’ operation. Many papers have been published that solve UC through different methods. Articles that systematically summarize UC problems’ progress in order to update researchers interested in this field are needed. Because of its promising performance, stochastic programming (SP) has become increasingly researched. Most papers, however, present SP’s UC solving approaches differently, which masks their relationships and makes it hard for new researchers to quickly obtain a general idea. Therefore, this paper tries to give a structured bibliographic survey of SP’s applications in UC problems.展开更多
This paper deals with a Unit Commitment (UC) problem of a power plant aimed to find the optimal scheduling of the generating units involving cubic cost functions. The problem has non convex generator characteristics, ...This paper deals with a Unit Commitment (UC) problem of a power plant aimed to find the optimal scheduling of the generating units involving cubic cost functions. The problem has non convex generator characteristics, which makes it very hard to handle the corresponding mathematical models. However, Teaching Learning Based Optimization (TLBO) has reached a high efficiency, in terms of solution accuracy and computing time for such non convex problems. Hence, TLBO is applied for scheduling of generators with higher order cost characteristics, and turns out to be computationally solvable. In particular, we represent a model that takes into account the accurate higher order generator cost functions along with ramp limits, and turns to be more general and efficient than those available in the literature. The behavior of the model is analyzed through proposed technique on modified IEEE-24 bus system.展开更多
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.
基金partially supported by Korea Electrotechnology Research Institute(KERI)Primary research program through the National Research Council of Science&Technology(NST)funded by the Ministry of Science and ICT(MSIT)(No.25A01038)partially supported by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(No.RS-2024-00218377).
文摘In this paper,a strength-constrained unit commitment(UC)model incorporating system strength constraints based on the weighted short-circuit ratio(WSCR)is proposed.This model facilitates the comprehensive assessment of area-wide system strength in power systems with high inverter-based resource(IBR)penetration,thereby contributing to the mitigation of weak grid issues.Unlike traditional models,this approach considers the interactions among multiple IBRs.The UC problem is initially formulated as a mixed-integer nonlinear programming(MINLP)model,reflecting WSCR and bus impedance matrix modification constraints.To enhance computational tractability,the model is transformed into a mixed-integer linear programming(MILP)form.The effectiveness of the proposed approach is validated through simulations on the IEEE 5-bus,IEEE 39-bus,and a modified Korean power system,demonstrating the ability of the proposed UC model enhancing system strength compared to the conventional methodologies.
基金the Science and Technology Project of State Grid Corporation of China,Grant Number 5108-202304065A-1-1-ZN.
文摘Stochastic unit commitment is one of the most powerful methods to address uncertainty. However, the existingscenario clustering technique for stochastic unit commitment cannot accurately select representative scenarios,which threatens the robustness of stochastic unit commitment and hinders its application. This paper providesa stochastic unit commitment with dynamic scenario clustering based on multi-parametric programming andBenders decomposition. The stochastic unit commitment is solved via the Benders decomposition, which decouplesthe primal problem into the master problem and two types of subproblems. In the master problem, the committedgenerator is determined, while the feasibility and optimality of generator output are checked in these twosubproblems. Scenarios are dynamically clustered during the subproblem solution process through the multiparametric programming with respect to the solution of the master problem. In other words, multiple scenariosare clustered into several representative scenarios after the subproblem is solved, and the Benders cut obtainedby the representative scenario is generated for the master problem. Different from the conventional stochasticunit commitment, the proposed approach integrates scenario clustering into the Benders decomposition solutionprocess. Such a clustering approach could accurately cluster representative scenarios that have impacts on theunit commitment. The proposed method is tested on a 6-bus system and the modified IEEE 118-bus system.Numerical results illustrate the effectiveness of the proposed method in clustering scenarios. Compared withthe conventional clustering method, the proposed method can accurately select representative scenarios whilemitigating computational burden, thus guaranteeing the robustness of unit commitment.
文摘The Unit Commitment Problem(UCP)corresponds to the planning of power generation schedules.The objective of the fuel-based unit commitment problem is to determine the optimal schedule of power generators needed to meet the power demand,which also minimizes the total operating cost while adhering to different constraints such as power generation limits,unit startup,and shutdown times.In this paper,four different binary variants of the Bald Eagle Search(BES)algorithm,were introduced,which used two variants using S-shape,U-shape,and V-shape transfer functions.In addition,the best-performing variant(using an S-shape transfer function)was selected and improved further by incorporating two binary operators:swap-window and window-mutation.This variation is labeled Improved Binary Bald Eagle Search(IBBESS2).All five variants of the proposed algorithm were successfully adopted to solve the fuel-based unit commitment problem using seven test cases of 4-,10-,20-,40-,60-,80-,and 100-unit.For comparative evaluation,34 comparative methods from existing literature were compared,in which IBBESS2 achieved competitive scores against other optimization techniques.In other words,the proposed IBBESS2 performs better than all other competitors by achieving the best average scores in 20-,40-,60-,80-,and 100-unit problems.Furthermore,IBBESS2 demonstrated quicker convergence to an optimal solution than other algorithms,especially in large-scale unit commitment problems.The Friedman statistical test further validates the results,where the proposed IBBESS2 is ranked the best.In conclusion,the proposed IBBESS2 can be considered a powerful method for solving large-scale UCP and other related problems.
文摘Electric power system is one of the most important and complex engineering in modern society, supplying main and general power for social production and social life. Meanwhile, since it is a productive system with both high input and output, it has an obvious economic significance to improve its operating efficiency. For an example, an unit is 10 GW scale, if its standard coal consumption can be decreased with 1 g/kW·h, it can save about 5 000 tons standard coal per year. It will be discussed mainly that how to establish optimization model and its numerical algorithm for operating management of the electric power system. The idea on establishing optimization model is how to dispatch work state of units or power plants, so that total cost of fuel consumption for generation is reduced to the minimum. Here the dispatch is to decide which unit or plant to operate, which unit or plant to stop running, how much power should be generated for those operating units or plants at each given time interval.
文摘Generally, the procedure for Solving Security constrained unit commitment (SCUC) problems within Lagrangian Relaxation framework is partitioned into two stages: one is to obtain feasible SCUC states;the other is to solve the economic dispatch of generation power among all the generating units. The core of the two stages is how to determine the feasibility of SCUC states. The existence of ramp rate constraints and security constraints increases the difficulty of obtaining an analytical necessary and sufficient condition for determining the quasi-feasibility of SCUC states at each scheduling time. However, a numerical necessary and sufficient numerical condition is proposed and proven rigorously based on Benders Decomposition Theorem. Testing numerical example shows the effectiveness and efficiency of the condition.
文摘Unit commitment (UC) is to determine the optimal unit status and generation level during each time interval of the scheduled period. The purpose of UC is to minimize the total generation cost while satisfying system demand, reserve requirements, and unit constraints. Among the UC constraints, an adequate provision of reserve is important to ensure the security of power system and the fast-response reserve is essential to bring system frequency back to acceptable level following the loss of an online unit within a few seconds. In this paper, the authors present and solve a UC problem including the frequency-based reserve constraints to determine the optimal FRR requirements and unit MW schedules. The UC problem is solved by using Lagrangian Relaxation-based approach and compared with the actual system schedules. It is observed that favorable reserve and unit MW schedules are obtained by the proposed method while the system security is maintained.
文摘Bilateral electric power contract is settled based on contract output curve. This paper considered the bilateral transactions execution, new energy accommodation, power grid security and generation economy, considering the executive priority of different power components to establish a multi-objective coordination unit commitment model. Through an example to verify the effectiveness of the model in promoting wind power consumption, guaranteeing trade execution, and improving power generation efficiency, and analyzed the interactions to each other among the factors of wind power, trading and blocking. According to the results, when wind power causes reverse power flow in the congestion line, it will promote the implementation of contracts, the influence of wind power accommodation to trade execution should be analyzed combined with the grid block, the results can provide reference for wind power planning.
文摘The solar and wind renewable energy is developing very rapidly to fulfill the energy gap. This specific increasing share of renewable energy is a reaction to the ecological trepidations to conciliate economics with security due to the new challenges in power system supply. In solar and wind renewable energy, the only partially predictable is the output with very low controllability which creates unit commitment problems in thermal units. In this research paper, a different linear formulation via mixed integer is presented that only requires “binary variables” and restraints concerning earlier stated models. The framework of this model allows precisely the costs of time-dependent startup & intertemporal limitations, for example, minimum up & down times and a ramping limit. To solve the unit commitment problem efficiently, a commercially available linear programming of mixed-integer is applied for sizeable practical scale. The results of the simulation are shown in conclusions.
文摘This paper presents a new hybrid approach that combines Modified Priority List (MPL) with Charged System Search (CSS), termed MPL-CSS, to solve one of the most crucial power system’s operational optimization problems, known as unit commitment (UC) scheduling. The UC scheduling problem is a mixed-integer nonlinear problem, highly-dimensional and extremely constrained. Existing meta-heuristic UC solution methods have the problems of stopping at a local optimum and slow convergence when applied to large-scale, heavily-constrained UC applications. In the first step of the proposed method, initial hourly optimum solutions of UC are obtained by Modified Priority List (MPL);however, the obtained UC solution may still be possible to be further improved. Therefore, in the second step, the CSS is utilized to achieve higher quality solutions. The UC is formulated as mixed integer linear programming to ensure the tractability of the results. The proposed method is successfully applied to a popular test system up to 100 units generators for both 24-hr and 168-hr system. Computational results show that both solution cost and execution time are superior to those of published methods.
基金Project partially supported by the Lamar Research Enhancement Grant and the National Science Foundation Grant (No. DUE-0737173) to Dr. W. Zhu at Lamar University
文摘This paper presents a new method based on an immune-tabu hybrid algorithm to solve the thermal unit commitment （TUC） problem in power plant optimization. The mathematical model of the TUC problem is established by analyzing the generating units in modem power plants. A novel immune-tabu hybrid algorithm is proposed to solve this complex problem. In the algorithm, the objective function of the TUC problem is considered as an antigen and the solutions are considered as antibodies, which are determined by the affinity computation. The code length of an antibody is shortened by encoding the continuous operating time, and the optimum searching speed is improved. Each feasible individual in the immune algorithm （IA） is used as the initial solution of the tabu search （TS） algorithm after certain generations of IA iteration. As examples, the proposed method has been applied to several thermal unit systems for a period of 24 h. The computation results demonstrate the good global optimum searching performance of the proposed immune-tabu hybrid algorithm. The presented algorithm can also be used to solve other optimization problems in fields such as the chemical industry and the power industry.
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.
文摘How to solve unit commitment and load dispatch of power system by genetic algorithms is discussed in this paper. A combination encoding scheme of binary encoding and floating number encoding and corresponding genetic operators are developed. Meanwhile a contract mapping genetic algorithm is used to enhance traditional GA’s convergence. The result of a practical example shows that this algorithm is effective.
基金Supported by the Natural Science Foundation of Hubei Province (2006ABA222)
文摘GAs are general purpose optimization techniques based on principles inspired from the biological evolution using metaphors of mechanisms, such as natural selection, genetic recombination and survival of the fittest. By use of coding betterment, the dynamic changes of the mutation rate and the crossover probability, the dynamic choice of subsistence, the reservation of the optimal fitness value, a modified genetic algorithm for optimizing combination of units in thermal power plants is proposed. And through taking examples, test result are analyzed and compared with results of some different algorithms. Numerical results show available value for the unit commitment problem with examples.
基金supported in part by the Project Funded by ABB and U.S.National Science Foundation(ECCS-1509666)
文摘Grid integration of wind power is essential to reduce fossil fuel usage but challenging in view of the intermittent nature of wind.Recently,we developed a hybrid Markovian and interval approach for the unit commitment and economic dispatch problem where power generation of conventional units is linked to local wind states to dampen the effects of wind uncertainties.Also,to reduce complexity,extreme and expected states are considered as interval modeling.Although this approach is effective,the fact that major wind farms are often located in remote locations and not accompanied by conventional units leads to conservative results.Furthermore,weights of extreme and expected states in the objective function are difficult to tune,resulting in significant differences between optimization and simulation costs.In this paper,each remote wind farm is paired with a conventional unit to dampen the effects of wind uncertainties without using expensive utility-scaled battery storage,and extra constraints are innovatively established to model pairing.Additionally,proper weights are derived through a novel quadratic fit of cost functions.The problem is solved by using a creative integration of our recent surrogate Lagrangian relaxation and branch-and-cut.Results demonstrate modeling accuracy,computational efficiency,and significant reduction of conservativeness of the previous approach.
基金the National Natural Science Foundation of China(Nos.61004088 and 61374160)
文摘Unit commitment(UC), as a typical optimization problem in electric power system, faces new challenges as energy saving and emission reduction get more and more important in the way to a more environmentally friendly society. To meet these challenges, we propose a UC model considering energy saving and emission reduction. By using real-number coding method, swap-window and hill-climbing operators, we present an improved real-coded genetic algorithm(IRGA) for UC. Compared with other algorithms approach to the proposed UC problem, the IRGA solution shows an improvement in effectiveness and computational time.
文摘This paper presents a new algorithm for solving unit commitment (UC) problems using a binary-real coded genetic algorithm based on k-means clustering technique. UC is a NP-hard nonlinear mixed-integer optimization problem, encountered as one of the toughest problems in power systems, in which some power generating units are to be scheduled in such a way that the forecasted demand is met at minimum production cost over a time horizon. In the proposed algorithm, the algorithm integrates the main features of a binary-real coded genetic algorithm (GA) and k-means clustering technique. The binary coded GA is used to obtain a feasible commitment schedule for each generating unit;while the power amounts generated by committed units are determined by using real coded GA for the feasible commitment obtained in each interval. k-means clustering algorithm divides population into a specific number of subpopulations with dynamic size. In this way, using k-means clustering algorithm allows the use of different GA operators with the whole population and avoids the local problem minima. The effectiveness of the proposed technique is validated on a test power system available in the literature. The proposed algorithm performance is found quite satisfactory in comparison with the previously reported results.
文摘Considering the economics and securities for the operation of a power system, this paper presents a new adaptive dynamic programming approach for security-constrained unit commitment (SCUC) problems. In response to the “curse of dimension” problem of dynamic programming, the approach solves the Bellman’s equation of SCUC approximately by solving a sequence of simplified single stage optimization problems. An extended sequential truncation technique is proposed to explore the state space of the approach, which is superior to traditional sequential truncation in daily cost for unit commitment. Different test cases from 30 to 300 buses over a 24 h horizon are analyzed. Extensive numerical comparisons show that the proposed approach is capable of obtaining the optimal unit commitment schedules without any network and bus voltage violations, and minimizing the operation cost as well.
文摘The study of unit commitment (UC) aims to find reasonable schedules for generators to optimize power systems’ operation. Many papers have been published that solve UC through different methods. Articles that systematically summarize UC problems’ progress in order to update researchers interested in this field are needed. Because of its promising performance, stochastic programming (SP) has become increasingly researched. Most papers, however, present SP’s UC solving approaches differently, which masks their relationships and makes it hard for new researchers to quickly obtain a general idea. Therefore, this paper tries to give a structured bibliographic survey of SP’s applications in UC problems.
文摘This paper deals with a Unit Commitment (UC) problem of a power plant aimed to find the optimal scheduling of the generating units involving cubic cost functions. The problem has non convex generator characteristics, which makes it very hard to handle the corresponding mathematical models. However, Teaching Learning Based Optimization (TLBO) has reached a high efficiency, in terms of solution accuracy and computing time for such non convex problems. Hence, TLBO is applied for scheduling of generators with higher order cost characteristics, and turns out to be computationally solvable. In particular, we represent a model that takes into account the accurate higher order generator cost functions along with ramp limits, and turns to be more general and efficient than those available in the literature. The behavior of the model is analyzed through proposed technique on modified IEEE-24 bus system.
