To maintain the frequency stability of power systems integrated with large-scale renewable energy sources(RESs),a frequency-constrained unit commitment(FCUC)model is proposed,which incorporates a coordinated frequency...To maintain the frequency stability of power systems integrated with large-scale renewable energy sources(RESs),a frequency-constrained unit commitment(FCUC)model is proposed,which incorporates a coordinated frequency control strategy of wind turbines and energy storage system(WT-ESS),a vital component for enhancing frequency regulation capacity of wind farms.Analytical formulations for the maximum rate of change of frequency(RoCoF)and steady-state frequency deviation are derived for both serial control and parallel control,accounting for the output-limited state of energy storage under serial control.To address the problem of solution slowness caused by the strong nonlinear frequency nadir constraints,a model-based multi-directional bilayer solution method is proposed.This method employs the simulation model to detect whether the frequency nadir constraint is active and generates parallel optimized cuts in three directions.Simulation results on the IEEE 39-bus test system demonstrate that the proposed FCUC model and solution method could accurately reflect the primary frequency regulation(PFR)characteristics of WT-ESS.Furthermore,the coordinated frequency control strategy effectively reduces overall operating costs while ensuring frequency security.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
In coastal regions of China,offshore wind farm ex-pansion has spurred extensive research to reduce operational costs in power systems with high penetration of wind power.However,frequent extreme weather conditions suc...In coastal regions of China,offshore wind farm ex-pansion has spurred extensive research to reduce operational costs in power systems with high penetration of wind power.However,frequent extreme weather conditions such as typhoons pose substantial challenges to system stability and security.Pre-vious research has intensively examined the steady-state opera-tions arising from typhoon-induced faults,with a limited em-phasis on the transient frequency dynamics inherent to such faults.To address this challenge,this paper proposes a frequen-cy-constrained unit commitment model that can promote ener-gy utilization and improve resilience.The proposed model ana-lyzes uncertainties stemming from transmission line failures and offshore wind generation through typhoon simulations.Two types of power disturbances resulting from typhoon-in-duced wind farm cutoff and grid islanding events are revealed.In addition,new frequency constraints are defined considering the changes in the topology of the power system.Further,the complex frequency nadir constraints are incorporated into a two-stage stochastic unit commitment model using the piece-wise linearization.Finally,the proposed model is verified by nu-merical experiments,and the results demonstrate that the pro-posed model can effectively enhance system resilience under ty-phoons and improve frequency dynamic characteristics following fault disturbances.展开更多
Heavy renewable penetrations and high-voltage cross-regional transmission systems reduce the inertia and critical frequency stability of power systems after disturbances.Therefore,the power system operators should ens...Heavy renewable penetrations and high-voltage cross-regional transmission systems reduce the inertia and critical frequency stability of power systems after disturbances.Therefore,the power system operators should ensure the frequency nadirs after possible disturbances are within the set restriction,e.g.,0.20 Hz.Traditional methods utilize linearized and simplified control models to quantify the frequency nadirs and achieve frequency-constrained unit commitments(FCUCs).However,the simplified models are hard to depict the frequency responses of practical units after disturbances.Also,they usually neglect the regulations from battery storage.This paper achieves FCUCs with linear rules extracted from massive simulation results.We simulate the frequency responses on typical thermal-hydro-storage systems under diverse unit online conditions.Then,we extract the rules of frequency nadirs after disturbances merely with linear support vector machine to evaluate the frequency stability of power systems.The algorithm holds a high accuracy in a wide range of frequency restrictions.Finally,we apply the rules to three typical cases to show the influences of frequency constraints on unit commitments.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
The quantum hybrid algorithm has recently become a very promising and speedy method for solving larger-scale optimization problems in the noisy intermediate-scale quantum(NISQ)era.The unit commitment(UC)problem is a f...The quantum hybrid algorithm has recently become a very promising and speedy method for solving larger-scale optimization problems in the noisy intermediate-scale quantum(NISQ)era.The unit commitment(UC)problem is a fundamental problem in the field of power systems that aims to satisfy the power balance constraint with minimal cost.In this paper,we focus on the implementation of the UC solution using exact quantum algorithms based on the quantum neural network(QNN).This method is tested with a ten-unit system under the power balance constraint.In order to improve computing precision and reduce network complexity,we propose a knowledge-based partially connected quantum neural network(PCQNN).The results show that exact solutions can be obtained by the improved algorithm and that the depth of the quantum circuit can be reduced simultaneously.展开更多
As power systems expand,solving the unit commitment problem(UCP)becomes increasingly challenging due to the curse of dimensionality,and traditional methods often struggle to balance computational efficiency and soluti...As power systems expand,solving the unit commitment problem(UCP)becomes increasingly challenging due to the curse of dimensionality,and traditional methods often struggle to balance computational efficiency and solution optimality.To tackle this issue,we propose a problem-structure-informed quantum approximate optimization algorithm(QAOA)framework that fully exploits the quantum advantage under extremely limited quantum resources.Specifically,we leverage the inherent topological structure of power systems to decompose large-scale UCP instances into smaller subproblems,which are solvable in parallel by limited number of qubits.This decomposition not only circumvents the current hardware limitations of quantum computing but also achieves higher performance as the graph structure of the power system becomes more sparse.Consequently,our approach can be extended to future power systems that are larger and more complex.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
Renewable energy sources(RES)such as wind turbines(WT)and solar cells have attracted the attention of power system operators and users alike,thanks to their lack of environmental pollution,independence of fossil fuels...Renewable energy sources(RES)such as wind turbines(WT)and solar cells have attracted the attention of power system operators and users alike,thanks to their lack of environmental pollution,independence of fossil fuels,and meager marginal costs.With the introduction of RES,challenges have faced the unit commitment(UC)problem as a traditional power system optimization problem aiming to minimize total costs by optimally determining units’inputs and outputs,and specifying the optimal generation of each unit.The output power of RES such as WT and solar cells depends on natural factors such as wind speed and solar irradiation that are riddled with uncertainty.As a result,the UC problem in the presence of RES faces uncertainties.The grid consumed load is not always equal to and is randomly different from the predicted values,which also contributes to uncertainty in solving the aforementioned problem.The current study proposes a novel two-stage optimization model with load and wind farm power generation uncertainties for the security-constrained UC to overcome this problem.The new model is adopted to solve the wind-generated power uncertainty,and energy storage systems(ESSs)are included in the problem for further management.The problem is written as an uncertain optimization model which are the stochastic nature with security-constrains which included undispatchable power resources and storage units.To solve the UC programming model,a hybrid honey bee mating and bacterial foraging algorithm is employed to reduce problem complexity and achieve optimal results.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
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
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
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 focused on generation scheduling problem with consideration of wind, solar and PHES (pumped hydro energy storage) system. Wind, solar and PHES are being considered in the NEPS (northeast power system) o...This paper focused on generation scheduling problem with consideration of wind, solar and PHES (pumped hydro energy storage) system. Wind, solar and PHES are being considered in the NEPS (northeast power system) of Afghanistan to schedule all units power output so as to minimize the total operation cost of thermal units plus aggregate imported power tariffs during the scheduling horizon, subject to the system and unit operation constraints. Apart from determining the optimal output power of each unit, this research also involves in deciding the on/off status of thermal units. In order to find the optimal values of the variables, GA (genetic algorithm) is proposed. The algorithm performs efficiently in various sized thermal power system with equivalent wind, solar and PHES and can produce a high-quality solution. Simulation results reveal that with wind, solar and PHES the system is the most-cost effective than the other combinations.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
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 bot...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
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
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
基金supported in part by the National Natural Science Foundation of China(No.52107082)by Major Talents Program of Guangxi of China.
摘要To maintain the frequency stability of power systems integrated with large-scale renewable energy sources(RESs),a frequency-constrained unit commitment(FCUC)model is proposed,which incorporates a coordinated frequency control strategy of wind turbines and energy storage system(WT-ESS),a vital component for enhancing frequency regulation capacity of wind farms.Analytical formulations for the maximum rate of change of frequency(RoCoF)and steady-state frequency deviation are derived for both serial control and parallel control,accounting for the output-limited state of energy storage under serial control.To address the problem of solution slowness caused by the strong nonlinear frequency nadir constraints,a model-based multi-directional bilayer solution method is proposed.This method employs the simulation model to detect whether the frequency nadir constraint is active and generates parallel optimized cuts in three directions.Simulation results on the IEEE 39-bus test system demonstrate that the proposed FCUC model and solution method could accurately reflect the primary frequency regulation(PFR)characteristics of WT-ESS.Furthermore,the coordinated frequency control strategy effectively reduces overall operating costs while ensuring frequency security.
基金supported by the Science and Technology Project of State Grid Hebei Electric Power Company Limited(No.kj2021-073)。
摘要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.
基金This paper was supported by the Science and Technology Development Fund,MacauSAR(No.001/2024/SKL).
摘要In coastal regions of China,offshore wind farm ex-pansion has spurred extensive research to reduce operational costs in power systems with high penetration of wind power.However,frequent extreme weather conditions such as typhoons pose substantial challenges to system stability and security.Pre-vious research has intensively examined the steady-state opera-tions arising from typhoon-induced faults,with a limited em-phasis on the transient frequency dynamics inherent to such faults.To address this challenge,this paper proposes a frequen-cy-constrained unit commitment model that can promote ener-gy utilization and improve resilience.The proposed model ana-lyzes uncertainties stemming from transmission line failures and offshore wind generation through typhoon simulations.Two types of power disturbances resulting from typhoon-in-duced wind farm cutoff and grid islanding events are revealed.In addition,new frequency constraints are defined considering the changes in the topology of the power system.Further,the complex frequency nadir constraints are incorporated into a two-stage stochastic unit commitment model using the piece-wise linearization.Finally,the proposed model is verified by nu-merical experiments,and the results demonstrate that the pro-posed model can effectively enhance system resilience under ty-phoons and improve frequency dynamic characteristics following fault disturbances.
基金supported by the research project from China Three Gorges Corporation(No.202103386).
摘要Heavy renewable penetrations and high-voltage cross-regional transmission systems reduce the inertia and critical frequency stability of power systems after disturbances.Therefore,the power system operators should ensure the frequency nadirs after possible disturbances are within the set restriction,e.g.,0.20 Hz.Traditional methods utilize linearized and simplified control models to quantify the frequency nadirs and achieve frequency-constrained unit commitments(FCUCs).However,the simplified models are hard to depict the frequency responses of practical units after disturbances.Also,they usually neglect the regulations from battery storage.This paper achieves FCUCs with linear rules extracted from massive simulation results.We simulate the frequency responses on typical thermal-hydro-storage systems under diverse unit online conditions.Then,we extract the rules of frequency nadirs after disturbances merely with linear support vector machine to evaluate the frequency stability of power systems.The algorithm holds a high accuracy in a wide range of frequency restrictions.Finally,we apply the rules to three typical cases to show the influences of frequency constraints on unit commitments.
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).
摘要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supported in part by the China Postdoctoral Science Foundation(Grant No.2023M740874)。
摘要The quantum hybrid algorithm has recently become a very promising and speedy method for solving larger-scale optimization problems in the noisy intermediate-scale quantum(NISQ)era.The unit commitment(UC)problem is a fundamental problem in the field of power systems that aims to satisfy the power balance constraint with minimal cost.In this paper,we focus on the implementation of the UC solution using exact quantum algorithms based on the quantum neural network(QNN).This method is tested with a ten-unit system under the power balance constraint.In order to improve computing precision and reduce network complexity,we propose a knowledge-based partially connected quantum neural network(PCQNN).The results show that exact solutions can be obtained by the improved algorithm and that the depth of the quantum circuit can be reduced simultaneously.
摘要As power systems expand,solving the unit commitment problem(UCP)becomes increasingly challenging due to the curse of dimensionality,and traditional methods often struggle to balance computational efficiency and solution optimality.To tackle this issue,we propose a problem-structure-informed quantum approximate optimization algorithm(QAOA)framework that fully exploits the quantum advantage under extremely limited quantum resources.Specifically,we leverage the inherent topological structure of power systems to decompose large-scale UCP instances into smaller subproblems,which are solvable in parallel by limited number of qubits.This decomposition not only circumvents the current hardware limitations of quantum computing but also achieves higher performance as the graph structure of the power system becomes more sparse.Consequently,our approach can be extended to future power systems that are larger and more complex.
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
摘要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.
摘要Renewable energy sources(RES)such as wind turbines(WT)and solar cells have attracted the attention of power system operators and users alike,thanks to their lack of environmental pollution,independence of fossil fuels,and meager marginal costs.With the introduction of RES,challenges have faced the unit commitment(UC)problem as a traditional power system optimization problem aiming to minimize total costs by optimally determining units’inputs and outputs,and specifying the optimal generation of each unit.The output power of RES such as WT and solar cells depends on natural factors such as wind speed and solar irradiation that are riddled with uncertainty.As a result,the UC problem in the presence of RES faces uncertainties.The grid consumed load is not always equal to and is randomly different from the predicted values,which also contributes to uncertainty in solving the aforementioned problem.The current study proposes a novel two-stage optimization model with load and wind farm power generation uncertainties for the security-constrained UC to overcome this problem.The new model is adopted to solve the wind-generated power uncertainty,and energy storage systems(ESSs)are included in the problem for further management.The problem is written as an uncertain optimization model which are the stochastic nature with security-constrains which included undispatchable power resources and storage units.To solve the UC programming model,a hybrid honey bee mating and bacterial foraging algorithm is employed to reduce problem complexity and achieve optimal results.
基金the Science and Technology Project of State Grid Corporation of China,Grant Number 5108-202304065A-1-1-ZN.
摘要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.
摘要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.
基金supported in part by the Project Funded by ABB and U.S.National Science Foundation(ECCS-1509666)
摘要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)
摘要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.
基金Supported by the Natural Science Foundation of Hubei Province (2006ABA222)
摘要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.
摘要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.
摘要This paper focused on generation scheduling problem with consideration of wind, solar and PHES (pumped hydro energy storage) system. Wind, solar and PHES are being considered in the NEPS (northeast power system) of Afghanistan to schedule all units power output so as to minimize the total operation cost of thermal units plus aggregate imported power tariffs during the scheduling horizon, subject to the system and unit operation constraints. Apart from determining the optimal output power of each unit, this research also involves in deciding the on/off status of thermal units. In order to find the optimal values of the variables, GA (genetic algorithm) is proposed. The algorithm performs efficiently in various sized thermal power system with equivalent wind, solar and PHES and can produce a high-quality solution. Simulation results reveal that with wind, solar and PHES the system is the most-cost effective than the other combinations.
摘要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.
摘要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.
摘要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.
摘要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.