The increasing penetration of renewable energy resources degrades the frequency stability of power systems.The present work addresses this issue by proposing a look-ahead dispatch model of power systems based on a lin...The increasing penetration of renewable energy resources degrades the frequency stability of power systems.The present work addresses this issue by proposing a look-ahead dispatch model of power systems based on a linear alternating current optimal power flow framework with nonlinear frequency constraints.Meanwhile,the poor efficiency for solving this formulation is addressed by introducing a physics-informed neural network(PINN)to predict key frequency-control parameter values accurately.The PINN ensures that the learned results are applicable to the original physical frequency dynamics model,and applying the predicted parameter values enables the resulting dispatch model to be solved quickly and efficiently using readily available commercial solvers.The feasibility and advantages of the proposed model are demonstrated by the results of numerical computations applied to a modified IEEE 118-bus test system.展开更多
This paper introduces a method for modeling the entire aggregated electric vehicle(EV)charging process and analyzing its dispatchable capabilities.The methodology involves developing a model for aggregated EV charging...This paper introduces a method for modeling the entire aggregated electric vehicle(EV)charging process and analyzing its dispatchable capabilities.The methodology involves developing a model for aggregated EV charging at the charging station level,estimating its physical dispatchable capability,determining its economic dispatchable capability under economic incentives,modeling its participation in the grid,and investigating the effects of different scenarios and EV penetration on the aggregated load dispatch and dispatchable capability.The results indicate that using economic dispatchable capability reduces charging prices by 9.7%compared to physical dispatchable capability and 9.3%compared to disorderly charging.Additionally,the peak-to-valley difference is reduced by 64.6%when applying economic dispatchable capability with 20%EV penetration and residential base load,compared to disorderly charging.展开更多
With the development of fast communication technology between ego vehicle and other traffic participants,and automated driving technology,there is a big potential in the improvement of energy efficiency of hybrid elec...With the development of fast communication technology between ego vehicle and other traffic participants,and automated driving technology,there is a big potential in the improvement of energy efficiency of hybrid electric vehicles(HEVs).Moreover,the terrain along the driving route is a non-ignorable factor for energy efficiency of HEV running on the hilly streets.This paper proposes a look-ahead horizon-based optimal energy management strategy to jointly improve the efficiencies of powertrain and vehicle for connected and automated HEVs on the road with slope.Firstly,a rule-based framework is developed to guarantee the success of automated driving in the traffic scenario.Then a constrained optimal control problem is formulated to minimize the fuel consumption and the electricity consumption under the satisfaction of inter-vehicular distance constraint between ego vehicle and preceding vehicle.Both speed planning and torque split of hybrid powertrain are provided by the proposed approach.Moreover,the preceding vehicle speed in the look-ahead horizon is predicted by extreme learning machine with real-time data obtained from communication of vehicle-to-everything.The optimal solution is derived through the Pontryagin’s maximum principle.Finally,to verify the effectiveness of the proposed algorithm,a traffic-in-the-loop powertrain platform with data from real world traffic environment is built.It is found that the fuel economy for the proposed energy management strategy improves in average 17.0%in scenarios of different traffic densities,compared to the energy management strategy without prediction of preceding vehicle speed.展开更多
The purpose of this study was to describe and analyze how and why contradictions recurrently arise regarding how incoming emergency calls at dispatch centers should be assessed,sorted,and handled.The study is based on...The purpose of this study was to describe and analyze how and why contradictions recurrently arise regarding how incoming emergency calls at dispatch centers should be assessed,sorted,and handled.The study is based on data from documents,study visits,and interviews with representatives from dispatch operators in a Swedish context.The results identify competing alarm and healthcare logics that are incompatible,which leads to contradictions between the national and regional approaches and,consequently,makes collaboration more difficult and affects the precision of emergency call assessment.The study also shows that the assessments of emergency calls are governed more by which logic is applied than by the assessor's formal competence.The study highlights the importance of feedback and subsequent analysis from the health service to the initial call assessment stage,which can improve the alarm logic's weaknesses with over-triage,without extending the response time.We also focused on the mechanisms required to develop and maintain a long-term sustainable alarm function.展开更多
Electromagnetic technology used in logging while drilling(LWD) provides the resistivity distribution around a borehole within a range of several tens of meters.However,a blind zone appears in front of the drill bit wh...Electromagnetic technology used in logging while drilling(LWD) provides the resistivity distribution around a borehole within a range of several tens of meters.However,a blind zone appears in front of the drill bit when operating in high-angle wells,limiting the ability to detect formations ahead of the drill bit.Look-ahead technology addresses this issue and substantially enhances the proactive capability of geological directional drilling.In this study,we examine the detection capabilities of various component combinations of magnetic dipole antenna.Based on the sensitivity of each component to the axial information,a coaxial component is selected as a boundary indicator.We investigate the impact of various factors,such as frequency and transmitter and receiver(TR) distance,under different geological models.This study proposes 5 and 20 kHz as appropriate frequencies,and 10-14 and 12-17 m as suitable TR distance combinations.The accuracy of the numerical calculation results is verified via air-sea testing,confirming the instrument's detection capability.A test model that eliminated the influence of environmental factors and seawater depth is developed.The results have demonstrated that the tool can recognize the interface between layers up to 21.6 m ahead.It provides a validation idea for the design of new instruments as well as the validation of detection capabilities.展开更多
The integration of deep learning into smart grid operations addresses critical challenges in dynamic load forecasting and optimal dispatch amid increasing renewable energy penetration.This study proposes a hybrid LSTM...The integration of deep learning into smart grid operations addresses critical challenges in dynamic load forecasting and optimal dispatch amid increasing renewable energy penetration.This study proposes a hybrid LSTM-Transformer architecture for multi-scale temporal-spatial load prediction,achieving 28%RMSE reduction on real-world datasets(CAISO,PJM),coupled with a deep reinforcement learning framework for multi-objective dispatch optimization that lowers operational costs by 12.4%while ensuring stability constraints.The synergy between adaptive forecasting models and scenario-based stochastic optimization demonstrates superior performance in handling renewable intermittency and demand volatility,validated through grid-scale case studies.Methodological innovations in federated feature extraction and carbon-aware scheduling further enhance scalability for distributed energy systems.These advancements provide actionable insights for grid operators transitioning to low-carbon paradigms,emphasizing computational efficiency and interoperability with legacy infrastructure.展开更多
The exponential growth in the scale of power systems has led to a significant increase in the complexity of dispatch problem resolution,particularly within multi-area interconnected power grids.This complexity necessi...The exponential growth in the scale of power systems has led to a significant increase in the complexity of dispatch problem resolution,particularly within multi-area interconnected power grids.This complexity necessitates the employment of distributed solution methodologies,which are not only essential but also highly desirable.In the realm of computational modelling,the multi-area economic dispatch problem(MAED)can be formulated as a linearly constrained separable convex optimization problem.The proximal point algorithm(PPA)is particularly adept at addressing such mathematical constructs effectively.This study introduces parallel(PPPA)and serial(SPPA)variants of the PPA as distributed algorithms,specifically designed for the computational modelling of the MAED.The PPA introduces a quadratic term into the objective function,which,while potentially complicating the iterative updates of the algorithm,serves to dampen oscillations near the optimal solution,thereby enhancing the convergence characteristics.Furthermore,the convergence efficiency of the PPA is significantly influenced by the parameter c.To address this parameter sensitivity,this research draws on trend theory from stock market analysis to propose trend theory-driven distributed PPPA and SPPA,thereby enhancing the robustness of the computational models.The computational models proposed in this study are anticipated to exhibit superior performance in terms of convergence behaviour,stability,and robustness with respect to parameter selection,potentially outperforming existing methods such as the alternating direction method of multipliers(ADMM)and Auxiliary Problem Principle(APP)in the computational simulation of power system dispatch problems.The simulation results demonstrate that the trend theory-based PPPA,SPPA,ADMM and APP exhibit significant robustness to the initial value of parameter c,and show superior convergence characteristics compared to the residual balancing ADMM.展开更多
With the intensification of the energy crisis and the worsening greenhouse effect,the development of sustainable integrated energy systems(IES)has become a crucial direction for energy transition.In this context,this ...With the intensification of the energy crisis and the worsening greenhouse effect,the development of sustainable integrated energy systems(IES)has become a crucial direction for energy transition.In this context,this paper proposes a low-carbon economic dispatch strategy under the green hydrogen certificate trading(GHCT)and the ladder-type carbon emission trading(CET)mechanism,enabling the coordinated utilization of green and blue hydrogen.Specifically,a proton exchange membrane electrolyzer(PEME)model that accounts for dynamic efficiency characteristics,and a steam methane reforming(SMR)model incorporating waste heat recovery,are developed.Based on these models,a hydrogen production–storage–utilization framework is established to enable the coordinated deployment of green and blue hydrogen.Furthermore,the gas turbine(GT)unit are retrofitted using oxygenenriched combustion carbon capture(OCC)technology,wherein the oxygen produced by PEME is employed to create an oxygen-enriched combustion environment.This approach reduces energy waste and facilitates low-carbon power generation.In addition,the GHCT mechanism is integrated into the system alongside the ladder-type CET mechanism,and their complementary effects are investigated.A comprehensive optimization model is then formulated to simultaneously achieve carbon reduction and economic efficiency across the system.Case study results show that the proposed strategy reduces wind curtailment by 7.77%,carbon emissions by 65.98%,and total cost by 12.57%.This study offers theoretical reference for the low-carbon,economic,and efficient operation of future energy systems.展开更多
The economic dispatch problem(EDP) of microgrids operating in both grid-connected and isolated modes within an energy internet framework is addressed in this paper. The multi-agent leader-following consensus algorithm...The economic dispatch problem(EDP) of microgrids operating in both grid-connected and isolated modes within an energy internet framework is addressed in this paper. The multi-agent leader-following consensus algorithm is employed to address the EDP of microgrids in grid-connected mode, while the push-pull algorithm with a fixed step size is introduced for the isolated mode. The proposed algorithm of isolated mode is proven to converge to the optimum when the interaction digraph of microgrids is strongly connected. A unified algorithmic framework is proposed to handle the two modes of operation of microgrids simultaneously, enabling our algorithm to achieve optimal power allocation and maintain the balance between power supply and demand in any mode and any mode switching. Due to the push-pull structure of the algorithm and the use of fixed step size,the proposed algorithm can better handle the case of unbalanced graphs, and the convergence speed is improved. It is documented that when the transmission topology is strongly connected and there is bi-directional communication between the energy router and its neighbors, the proposed algorithm in composite mode achieves economic dispatch even with arbitrary mode switching.Finally, we demonstrate the effectiveness and superiority of our algorithm through numerical simulations.展开更多
To address the issues of unclear carbon responsibility attribution,insufficient renewable energy absorption,and simplistic carbon trading mechanisms in integrated energy systems,this paper proposes an electricheat-hyd...To address the issues of unclear carbon responsibility attribution,insufficient renewable energy absorption,and simplistic carbon trading mechanisms in integrated energy systems,this paper proposes an electricheat-hydrogen integrated energy system(EHH-IES)optimal scheduling model considering carbon emission stream(CES)and wind-solar accommodation.First,the CES theory is introduced to quantify the carbon emission intensity of each energy conversion device and transmission branch by defining carbon emission rate,branch carbon intensity,and node carbon potential,realizing accurate tracking of carbon flow in the process of multi-energy coupling.Second,a stepped carbon pricing mechanism is established to dynamically adjust carbon trading costs based on the deviation between actual carbon emissions and initial quotas,strengthening the emission reduction incentive.Finally,a lowcarbon economic dispatch model is constructed with the objectives of minimizing operation cost,carbon trading cost,wind-solar curtailment penalty cost,and energy loss.Simulation results show that compared with the traditional economic dispatch scheme 3,the proposed schemel reduces carbon emissions by 53.97%and wind-solar curtailment by 68.89%with a 16.10%increase in total cost.This verifies that the model can effectively improve clean energy utilization and reduce carbon emissions,achieving low-carbon economic operation of EHH-IES,with CES theory ensuring precise carbon flow tracking across multi-energy links.展开更多
Considering the special features of dynamic environment economic dispatch of power systems with high dimensionality,strong coupling,nonlinearity,and non-convexity,a GA-DE multi-objective optimization algorithm based o...Considering the special features of dynamic environment economic dispatch of power systems with high dimensionality,strong coupling,nonlinearity,and non-convexity,a GA-DE multi-objective optimization algorithm based on dual-population pseudo-parallel genetic algorithm-differential evolution is proposed in this paper.The algorithm is based on external elite archive and Pareto dominance,and it adopts the cooperative co-evolution mechanism of differential evolution and genetic algorithm.Average entropy and cubic chaoticmapping initialization strategies are proposed to increase population diversity.In the proposed method,we analyze the distribution of neighboring solutions and apply a new Pareto solution set pruning approach.Unlike traditional models,this work takes the transmission losses as an optimization target and overcomes complex model constraints through a dynamic relaxation constraint approach.To solve the uncertainty caused by integrating wind and photovoltaic energy in power system scheduling,a multi-objective dynamic environment economical dispatch model is set up that takes the system spinning reserve and network highest losses into account.In this paper,the DE algorithm is improved to form the DGAGE algorithm for the objective optimization of the overall power system,The DE algorithm part of DGAGE is combined with the JAYA algorithm to form the system scheduling HDJ algorithm for multiple energy sources connected to the grid.The effectiveness of the proposed method is demonstrated using CEC2022 and CEC2005 test functions,showing robust optimization performance.Validation on a classical 10-unit system confirms the feasibility of the proposed algorithm in addressing power system scheduling issues.This approach provides a novel solution for dynamic power dispatch systems.展开更多
In order to address the synergistic optimization of energy efficiency improvement in the waste incineration power plant(WIPP)and renewable energy accommodation,an electricity-hydrogen-waste multi-energy system integra...In order to address the synergistic optimization of energy efficiency improvement in the waste incineration power plant(WIPP)and renewable energy accommodation,an electricity-hydrogen-waste multi-energy system integrated with phase change material(PCM)thermal storage is proposed.First,a thermal energy management framework is constructed,combining PCM thermal storage with the alkaline electrolyzer(AE)waste heat recovery and the heat pump(HP),while establishing a PCM-driven waste drying system to enhance the efficiency of waste incineration power generation.Next,a flue gas treatment method based on purification-separation-storage coordination is adopted,achieving spatiotemporal decoupling between waste incineration and flue gas treatment.Subsequently,a two-stage optimal dispatching strategy for the multi-energy system is developed:the first stage establishes a dayahead economic dispatch model with the objective of minimizing net system costs,while the second stage introduces model predictive control(MPC)to realize intraday rolling optimization.Finally,The optimal dispatching strategies under different scenarios are obtained using the Gurobi solver,followed by a comparative analysis of the optimized operational outcomes.Simulation results demonstrate that the proposed system optimizes the output and operational states of each unit,simultaneously reducing carbon trading costs while increasing electricity sales revenue.The proposed scheduling strategy demonstrates effective grid peak-shaving functionality,thereby simultaneously improving the system’s economic performance and operational flexibility while providing an innovative technical pathway for municipal solid waste(MSW)resource utilization and low-carbon transformation of energy systems.展开更多
A chance-constrained energy dispatch model based on the distributed stochastic model predictive control(DSMPC)approach for an islanded multi-microgrid system is proposed.An ambiguity set considering the inherent uncer...A chance-constrained energy dispatch model based on the distributed stochastic model predictive control(DSMPC)approach for an islanded multi-microgrid system is proposed.An ambiguity set considering the inherent uncertainties of renewable energy sources(RESs)is constructed without requiring the full distribution knowledge of the uncertainties.The power balance chance constraint is reformulated within the framework of the distributionally robust optimization(DRO)approach.With the exchange of information and energy flow,each microgrid can achieve its local supply-demand balance.Furthermore,the closed-loop stability and recursive feasibility of the proposed algorithm are proved.The comparative results with other DSMPC methods show that a trade-off between robustness and economy can be achieved.展开更多
This paper presents a novel approach to economic dispatch in smart grids equipped with diverse energy devices.This method integrates features including photovoltaic(PV)systems,energy storage coupling,varied energy rol...This paper presents a novel approach to economic dispatch in smart grids equipped with diverse energy devices.This method integrates features including photovoltaic(PV)systems,energy storage coupling,varied energy roles,and energy supply and demand dynamics.The systemmodel is developed by considering energy devices as versatile units capable of fulfilling various functionalities and playing multiple roles simultaneously.To strike a balance between optimality and feasibility,renewable energy resources are modeled with considerations for forecasting errors,Gaussian distribution,and penalty factors.Furthermore,this study introduces a distributed event-triggered surplus algorithm designed to address the economic dispatch problem by minimizing production costs.Rooted in surplus theory and finite time projection,the algorithm effectively rectifies network imbalances caused by directed graphs and addresses local inequality constraints.The algorithm greatly reduces the communication burden through event triggering mechanism.Finally,both theoretical proofs and numerical simulations verify the convergence and event-triggered nature of the algorithm.展开更多
The launch of the carbon-allowance trading market has changed the cost structure of the power industry.There is an asynchronous coupling mechanism between the carbon-allowance-trading market and the day-ahead power-sy...The launch of the carbon-allowance trading market has changed the cost structure of the power industry.There is an asynchronous coupling mechanism between the carbon-allowance-trading market and the day-ahead power-system dispatch.In this study,a data-driven model of the uncertainty in the annual carbon price was created.Subsequently,a collaborative,robust dispatch model was constructed considering the annual uncertainty of the carbon price and the daily uncertainty of renewable-energy generation.The model is solved using the column-and-constraint generation algorithm.An operation and cost model of a carbon-capture power plant(CCPP)that couples the carbon market and the economic operation of the power system is also established.The critical,profitable conditions for the economic operation of the CCPP were derived.Case studies demonstrated that the proposed low-carbon,robust dispatch model reduced carbon emissions by 2.67%compared with the traditional,economic,dispatch method.The total fuel cost of generation decreases with decreasing,conservative,carbon-price-uncertainty levels,while total carbon emissions continue to increase.When the carbon-quota coefficient decreases,the system dispatch tends to increase low-carbon unit output.This study can provide important guidance for carbon-market design and the low-carbon-dispatch selection strategies.展开更多
The convergence of Internet of Things(IoT),5G,and cloud collaboration offers tailored solutions to the rigorous demands of multi-flow integrated energy aggregation dispatch data processing.While generative adversarial...The convergence of Internet of Things(IoT),5G,and cloud collaboration offers tailored solutions to the rigorous demands of multi-flow integrated energy aggregation dispatch data processing.While generative adversarial networks(GANs)are instrumental in resource scheduling,their application in this domain is impeded by challenges such as convergence speed,inferior optimality searching capability,and the inability to learn from failed decision making feedbacks.Therefore,a cloud-edge collaborative federated GAN-based communication and computing resource scheduling algorithm with long-term constraint violation sensitiveness is proposed to address these challenges.The proposed algorithm facilitates real-time,energy-efficient data processing by optimizing transmission power control,data migration,and computing resource allocation.It employs federated learning for global parameter aggregation to enhance GAN parameter updating and dynamically adjusts GAN learning rates and global aggregation weights based on energy consumption constraint violations.Simulation results indicate that the proposed algorithm effectively reduces data processing latency,energy consumption,and convergence time.展开更多
Battery energy storage systems(BESSs)are widely used in smart grids.However,power consumed by inner impedance and the capacity degradation of each battery unit become particularly severe,which has resulted in an incre...Battery energy storage systems(BESSs)are widely used in smart grids.However,power consumed by inner impedance and the capacity degradation of each battery unit become particularly severe,which has resulted in an increase in operating costs.The general economic dispatch(ED)algorithm based on marginal cost(MC)consensus is usually a proportional(P)controller,which encounters the defects of slow convergence speed and low control accuracy.In order to solve the distributed ED problem of the isolated BESS network with excellent dynamic and steady-state performance,we attempt to design a proportional integral(PI)controller with a reset mechanism(PI+R)to asymptotically promote MC consensus and total power mismatch towards 0 in this paper.To be frank,the integral term in the PI controller is reset to 0 at an appropriate time when the proportional term undergoes a zero crossing,which accelerates convergence,improves control accuracy,and avoids overshoot.The eigenvalues of the system under a PI+R controller is well analyzed,ensuring the regularity of the system and enabling the reset mechanism.To ensure supply and demand balance within the isolated BESSs,a centralized reset mechanism is introduced,so that the controller is distributed in a flow set and centralized in a jump set.To cope with Zeno behavior and input delay,a dwell time that the system resides in a flow set is given.Based on this,the system with input delays can be reduced to a time-delay free system.Considering the capacity limitation of the battery,a modified MC scheme with PI+R controller is designed.The correctness of the designed scheme is verified through relevant simulations.展开更多
Dynamic Economic Emission Dispatch(DEED)aims to optimize control over fuel cost and pollution emission,two conflicting objectives,by scheduling the output power of various units at specific times.Although many methods...Dynamic Economic Emission Dispatch(DEED)aims to optimize control over fuel cost and pollution emission,two conflicting objectives,by scheduling the output power of various units at specific times.Although many methods well-performed on the DEED problem,most of them fail to achieve expected results in practice due to a lack of effective trade-off mechanisms between the convergence and diversity of non-dominated optimal dispatching solutions.To address this issue,a new multi-objective solver called Multi-Objective Golden Jackal Optimization(MOGJO)algorithm is proposed to cope with the DEED problem.The proposed algorithm first stores non-dominated optimal solutions found so far into an archive.Then,it chooses the best dispatching solution from the archive as the leader through a selection mechanism designed based on elite selection strategy and Euclidean distance index method.This mechanism can guide the algorithm to search for better dispatching solutions in the direction of reducing fuel costs and pollutant emissions.Moreover,the basic golden jackal optimization algorithm has the drawback of insufficient search,which hinders its ability to effectively discover more Pareto solutions.To this end,a non-linear control parameter based on the cosine function is introduced to enhance global exploration of the dispatching space,thus improving the efficiency of finding the optimal dispatching solutions.The proposed MOGJO is evaluated on the latest CEC benchmark test functions,and its superiority over the state-of-the-art multi-objective optimizers is highlighted by performance indicators.Also,empirical results on 5-unit,10-unit,IEEE 30-bus,and 30-unit systems show that the MOGJO can provide competitive compromise scheduling solutions compared to published DEED methods.Finally,in the analysis of the Pareto dominance relationship and the Euclidean distance index,the optimal dispatching solutions provided by MOGJO are the closest to the ideal solutions for minimizing fuel costs and pollution emissions simultaneously,compared to the latest published DEED solutions.展开更多
In renewable energy systems,energy storage systems can reduce the power fluctuation of renewable energy sources and compensate for the prediction deviation.However,if the renewable energy prediction deviation is small...In renewable energy systems,energy storage systems can reduce the power fluctuation of renewable energy sources and compensate for the prediction deviation.However,if the renewable energy prediction deviation is small,the energy storage system may work in an underutilized state.To efficiently utilize a renewable-energy-sided energy storage system(RES),this study proposed an optimization dispatching strategy for an energy storage system considering its unused capacity sharing.First,this study proposed an unused capacity-sharing strategy for the RES to fully utilize the storage’s unused capacity and elevate the storage’s service efficiency.Second,RES was divided into“deviation-compensating energy storage(DES)”and“sharing energy storage(SES)”to clarify the function of RES in the operation process.Third,this study established an optimized dispatching model to achieve the lowest system operating cost wherein the unused capacity-sharing strategy could be integrated.Finally,a case study was investigated,and the results indicated that the proposed model and algorithm effectively improved the utilization of renewable-energy-side energy storage systems,thereby reducing the total operation cost and pressure on peak shaving.展开更多
In the increasingly decentralized energy environment,economical power dispatching from distributed generations(DGs)is crucial to minimizing operating costs,optimizing resource utilization,and guaranteeing a consistent...In the increasingly decentralized energy environment,economical power dispatching from distributed generations(DGs)is crucial to minimizing operating costs,optimizing resource utilization,and guaranteeing a consistent and sustainable supply of electricity.A comprehensive review of optimization techniques for economic power dispatching from distributed generations is imperative to identify the most effective strategies for minimizing operational costs while maintaining grid stability and sustainability.The choice of optimization technique for economic power dispatching from DGs depends on a number of factors,such as the size and complexity of the power system,the availability of computational resources,and the specific requirements of the application.Optimization techniques for economic power dispatching from distributed generations(DGs)can be classified into two main categories:(i)Classical optimization techniques,(ii)Heuristic optimization techniques.In classical optimization techniques,the linear programming(LP)model is one of the most popular optimization methods.Utilizing the LP model,power demand and network constraints are met while minimizing the overall cost of generating electricity from DGs.This approach is efficient in determining the best DGs dispatch and is capable of handling challenging optimization issues in the large-scale system including renewables.The quadratic programming(QP)model,a classical optimization technique,is a further popular optimization method,to consider non-linearity.The QP model can take into account the quadratic cost of energy production,with consideration constraints like network capacity,voltage,and frequency.The metaheuristic optimization techniques are also used for economic power dispatching from DGs,which include genetic algorithms(GA),particle swarm optimization(PSO),and ant colony optimization(ACO).Also,Some researchers are developing hybrid optimization techniques that combine elements of classical and heuristic optimization techniques with the incorporation of droop control,predictive control,and fuzzy-based methods.These methods can deal with large-scale systems with many objectives and non-linear,non-convex optimization issues.The most popular approaches are the LP and QP models,while more difficult problems are handled using metaheuristic optimization techniques.In summary,in order to increase efficiency,reduce costs,and ensure a consistent supply of electricity,optimization techniques are essential tools used in economic power dispatching from DGs.展开更多
基金supported by the National Natural Science Foundation of China(No.52077060).
文摘The increasing penetration of renewable energy resources degrades the frequency stability of power systems.The present work addresses this issue by proposing a look-ahead dispatch model of power systems based on a linear alternating current optimal power flow framework with nonlinear frequency constraints.Meanwhile,the poor efficiency for solving this formulation is addressed by introducing a physics-informed neural network(PINN)to predict key frequency-control parameter values accurately.The PINN ensures that the learned results are applicable to the original physical frequency dynamics model,and applying the predicted parameter values enables the resulting dispatch model to be solved quickly and efficiently using readily available commercial solvers.The feasibility and advantages of the proposed model are demonstrated by the results of numerical computations applied to a modified IEEE 118-bus test system.
基金State Grid Henan Power Company Science and Technology Project‘Key Technology and Demonstration Application of Multi-Domain Electric Vehicle Aggregated Charging Load Dispatch’(5217L0240003).
文摘This paper introduces a method for modeling the entire aggregated electric vehicle(EV)charging process and analyzing its dispatchable capabilities.The methodology involves developing a model for aggregated EV charging at the charging station level,estimating its physical dispatchable capability,determining its economic dispatchable capability under economic incentives,modeling its participation in the grid,and investigating the effects of different scenarios and EV penetration on the aggregated load dispatch and dispatchable capability.The results indicate that using economic dispatchable capability reduces charging prices by 9.7%compared to physical dispatchable capability and 9.3%compared to disorderly charging.Additionally,the peak-to-valley difference is reduced by 64.6%when applying economic dispatchable capability with 20%EV penetration and residential base load,compared to disorderly charging.
文摘With the development of fast communication technology between ego vehicle and other traffic participants,and automated driving technology,there is a big potential in the improvement of energy efficiency of hybrid electric vehicles(HEVs).Moreover,the terrain along the driving route is a non-ignorable factor for energy efficiency of HEV running on the hilly streets.This paper proposes a look-ahead horizon-based optimal energy management strategy to jointly improve the efficiencies of powertrain and vehicle for connected and automated HEVs on the road with slope.Firstly,a rule-based framework is developed to guarantee the success of automated driving in the traffic scenario.Then a constrained optimal control problem is formulated to minimize the fuel consumption and the electricity consumption under the satisfaction of inter-vehicular distance constraint between ego vehicle and preceding vehicle.Both speed planning and torque split of hybrid powertrain are provided by the proposed approach.Moreover,the preceding vehicle speed in the look-ahead horizon is predicted by extreme learning machine with real-time data obtained from communication of vehicle-to-everything.The optimal solution is derived through the Pontryagin’s maximum principle.Finally,to verify the effectiveness of the proposed algorithm,a traffic-in-the-loop powertrain platform with data from real world traffic environment is built.It is found that the fuel economy for the proposed energy management strategy improves in average 17.0%in scenarios of different traffic densities,compared to the energy management strategy without prediction of preceding vehicle speed.
文摘The purpose of this study was to describe and analyze how and why contradictions recurrently arise regarding how incoming emergency calls at dispatch centers should be assessed,sorted,and handled.The study is based on data from documents,study visits,and interviews with representatives from dispatch operators in a Swedish context.The results identify competing alarm and healthcare logics that are incompatible,which leads to contradictions between the national and regional approaches and,consequently,makes collaboration more difficult and affects the precision of emergency call assessment.The study also shows that the assessments of emergency calls are governed more by which logic is applied than by the assessor's formal competence.The study highlights the importance of feedback and subsequent analysis from the health service to the initial call assessment stage,which can improve the alarm logic's weaknesses with over-triage,without extending the response time.We also focused on the mechanisms required to develop and maintain a long-term sustainable alarm function.
基金co-funded by the National Key Research and Development Program of China under Grant (2019YFA0708301)the CAS Project for Young Scientists in Basic Research (Grant No.YSBR-082)Research Instrument and Equipment Development Project of Chinese Academy of Sciences (GJJSTD20210008)。
文摘Electromagnetic technology used in logging while drilling(LWD) provides the resistivity distribution around a borehole within a range of several tens of meters.However,a blind zone appears in front of the drill bit when operating in high-angle wells,limiting the ability to detect formations ahead of the drill bit.Look-ahead technology addresses this issue and substantially enhances the proactive capability of geological directional drilling.In this study,we examine the detection capabilities of various component combinations of magnetic dipole antenna.Based on the sensitivity of each component to the axial information,a coaxial component is selected as a boundary indicator.We investigate the impact of various factors,such as frequency and transmitter and receiver(TR) distance,under different geological models.This study proposes 5 and 20 kHz as appropriate frequencies,and 10-14 and 12-17 m as suitable TR distance combinations.The accuracy of the numerical calculation results is verified via air-sea testing,confirming the instrument's detection capability.A test model that eliminated the influence of environmental factors and seawater depth is developed.The results have demonstrated that the tool can recognize the interface between layers up to 21.6 m ahead.It provides a validation idea for the design of new instruments as well as the validation of detection capabilities.
文摘The integration of deep learning into smart grid operations addresses critical challenges in dynamic load forecasting and optimal dispatch amid increasing renewable energy penetration.This study proposes a hybrid LSTM-Transformer architecture for multi-scale temporal-spatial load prediction,achieving 28%RMSE reduction on real-world datasets(CAISO,PJM),coupled with a deep reinforcement learning framework for multi-objective dispatch optimization that lowers operational costs by 12.4%while ensuring stability constraints.The synergy between adaptive forecasting models and scenario-based stochastic optimization demonstrates superior performance in handling renewable intermittency and demand volatility,validated through grid-scale case studies.Methodological innovations in federated feature extraction and carbon-aware scheduling further enhance scalability for distributed energy systems.These advancements provide actionable insights for grid operators transitioning to low-carbon paradigms,emphasizing computational efficiency and interoperability with legacy infrastructure.
基金funded by Guangxi Science and Technology Base and Talent Special Project,grant number GuiKeAD20159077Foundation of Guilin University of Technology,grant number GLUTQD2018001.
文摘The exponential growth in the scale of power systems has led to a significant increase in the complexity of dispatch problem resolution,particularly within multi-area interconnected power grids.This complexity necessitates the employment of distributed solution methodologies,which are not only essential but also highly desirable.In the realm of computational modelling,the multi-area economic dispatch problem(MAED)can be formulated as a linearly constrained separable convex optimization problem.The proximal point algorithm(PPA)is particularly adept at addressing such mathematical constructs effectively.This study introduces parallel(PPPA)and serial(SPPA)variants of the PPA as distributed algorithms,specifically designed for the computational modelling of the MAED.The PPA introduces a quadratic term into the objective function,which,while potentially complicating the iterative updates of the algorithm,serves to dampen oscillations near the optimal solution,thereby enhancing the convergence characteristics.Furthermore,the convergence efficiency of the PPA is significantly influenced by the parameter c.To address this parameter sensitivity,this research draws on trend theory from stock market analysis to propose trend theory-driven distributed PPPA and SPPA,thereby enhancing the robustness of the computational models.The computational models proposed in this study are anticipated to exhibit superior performance in terms of convergence behaviour,stability,and robustness with respect to parameter selection,potentially outperforming existing methods such as the alternating direction method of multipliers(ADMM)and Auxiliary Problem Principle(APP)in the computational simulation of power system dispatch problems.The simulation results demonstrate that the trend theory-based PPPA,SPPA,ADMM and APP exhibit significant robustness to the initial value of parameter c,and show superior convergence characteristics compared to the residual balancing ADMM.
基金supported by National Natural Science Foundation of China(52477101)Natural Science Foundation of Jiangsu Province(BK20210932).
文摘With the intensification of the energy crisis and the worsening greenhouse effect,the development of sustainable integrated energy systems(IES)has become a crucial direction for energy transition.In this context,this paper proposes a low-carbon economic dispatch strategy under the green hydrogen certificate trading(GHCT)and the ladder-type carbon emission trading(CET)mechanism,enabling the coordinated utilization of green and blue hydrogen.Specifically,a proton exchange membrane electrolyzer(PEME)model that accounts for dynamic efficiency characteristics,and a steam methane reforming(SMR)model incorporating waste heat recovery,are developed.Based on these models,a hydrogen production–storage–utilization framework is established to enable the coordinated deployment of green and blue hydrogen.Furthermore,the gas turbine(GT)unit are retrofitted using oxygenenriched combustion carbon capture(OCC)technology,wherein the oxygen produced by PEME is employed to create an oxygen-enriched combustion environment.This approach reduces energy waste and facilitates low-carbon power generation.In addition,the GHCT mechanism is integrated into the system alongside the ladder-type CET mechanism,and their complementary effects are investigated.A comprehensive optimization model is then formulated to simultaneously achieve carbon reduction and economic efficiency across the system.Case study results show that the proposed strategy reduces wind curtailment by 7.77%,carbon emissions by 65.98%,and total cost by 12.57%.This study offers theoretical reference for the low-carbon,economic,and efficient operation of future energy systems.
基金supported by the National Natural Science Foundation of China(62103203)
文摘The economic dispatch problem(EDP) of microgrids operating in both grid-connected and isolated modes within an energy internet framework is addressed in this paper. The multi-agent leader-following consensus algorithm is employed to address the EDP of microgrids in grid-connected mode, while the push-pull algorithm with a fixed step size is introduced for the isolated mode. The proposed algorithm of isolated mode is proven to converge to the optimum when the interaction digraph of microgrids is strongly connected. A unified algorithmic framework is proposed to handle the two modes of operation of microgrids simultaneously, enabling our algorithm to achieve optimal power allocation and maintain the balance between power supply and demand in any mode and any mode switching. Due to the push-pull structure of the algorithm and the use of fixed step size,the proposed algorithm can better handle the case of unbalanced graphs, and the convergence speed is improved. It is documented that when the transmission topology is strongly connected and there is bi-directional communication between the energy router and its neighbors, the proposed algorithm in composite mode achieves economic dispatch even with arbitrary mode switching.Finally, we demonstrate the effectiveness and superiority of our algorithm through numerical simulations.
文摘To address the issues of unclear carbon responsibility attribution,insufficient renewable energy absorption,and simplistic carbon trading mechanisms in integrated energy systems,this paper proposes an electricheat-hydrogen integrated energy system(EHH-IES)optimal scheduling model considering carbon emission stream(CES)and wind-solar accommodation.First,the CES theory is introduced to quantify the carbon emission intensity of each energy conversion device and transmission branch by defining carbon emission rate,branch carbon intensity,and node carbon potential,realizing accurate tracking of carbon flow in the process of multi-energy coupling.Second,a stepped carbon pricing mechanism is established to dynamically adjust carbon trading costs based on the deviation between actual carbon emissions and initial quotas,strengthening the emission reduction incentive.Finally,a lowcarbon economic dispatch model is constructed with the objectives of minimizing operation cost,carbon trading cost,wind-solar curtailment penalty cost,and energy loss.Simulation results show that compared with the traditional economic dispatch scheme 3,the proposed schemel reduces carbon emissions by 53.97%and wind-solar curtailment by 68.89%with a 16.10%increase in total cost.This verifies that the model can effectively improve clean energy utilization and reduce carbon emissions,achieving low-carbon economic operation of EHH-IES,with CES theory ensuring precise carbon flow tracking across multi-energy links.
基金funded by the Major Humanities and Social Sciences Research Projects in Zhejiang Higher Education Institutions,grant number 2023QN131National Innovation Training Program Project in China,grant number 202410451009.
文摘Considering the special features of dynamic environment economic dispatch of power systems with high dimensionality,strong coupling,nonlinearity,and non-convexity,a GA-DE multi-objective optimization algorithm based on dual-population pseudo-parallel genetic algorithm-differential evolution is proposed in this paper.The algorithm is based on external elite archive and Pareto dominance,and it adopts the cooperative co-evolution mechanism of differential evolution and genetic algorithm.Average entropy and cubic chaoticmapping initialization strategies are proposed to increase population diversity.In the proposed method,we analyze the distribution of neighboring solutions and apply a new Pareto solution set pruning approach.Unlike traditional models,this work takes the transmission losses as an optimization target and overcomes complex model constraints through a dynamic relaxation constraint approach.To solve the uncertainty caused by integrating wind and photovoltaic energy in power system scheduling,a multi-objective dynamic environment economical dispatch model is set up that takes the system spinning reserve and network highest losses into account.In this paper,the DE algorithm is improved to form the DGAGE algorithm for the objective optimization of the overall power system,The DE algorithm part of DGAGE is combined with the JAYA algorithm to form the system scheduling HDJ algorithm for multiple energy sources connected to the grid.The effectiveness of the proposed method is demonstrated using CEC2022 and CEC2005 test functions,showing robust optimization performance.Validation on a classical 10-unit system confirms the feasibility of the proposed algorithm in addressing power system scheduling issues.This approach provides a novel solution for dynamic power dispatch systems.
文摘In order to address the synergistic optimization of energy efficiency improvement in the waste incineration power plant(WIPP)and renewable energy accommodation,an electricity-hydrogen-waste multi-energy system integrated with phase change material(PCM)thermal storage is proposed.First,a thermal energy management framework is constructed,combining PCM thermal storage with the alkaline electrolyzer(AE)waste heat recovery and the heat pump(HP),while establishing a PCM-driven waste drying system to enhance the efficiency of waste incineration power generation.Next,a flue gas treatment method based on purification-separation-storage coordination is adopted,achieving spatiotemporal decoupling between waste incineration and flue gas treatment.Subsequently,a two-stage optimal dispatching strategy for the multi-energy system is developed:the first stage establishes a dayahead economic dispatch model with the objective of minimizing net system costs,while the second stage introduces model predictive control(MPC)to realize intraday rolling optimization.Finally,The optimal dispatching strategies under different scenarios are obtained using the Gurobi solver,followed by a comparative analysis of the optimized operational outcomes.Simulation results demonstrate that the proposed system optimizes the output and operational states of each unit,simultaneously reducing carbon trading costs while increasing electricity sales revenue.The proposed scheduling strategy demonstrates effective grid peak-shaving functionality,thereby simultaneously improving the system’s economic performance and operational flexibility while providing an innovative technical pathway for municipal solid waste(MSW)resource utilization and low-carbon transformation of energy systems.
基金Supported by the National Natural Science Foundation of China(No.U24B20156)the National Defense Basic Scientific Research Program of China(No.JCKY2021204B051)the National Laboratory of Space Intelligent Control of China(Nos.HTKJ2023KL502005 and HTKJ2024KL502007)。
文摘A chance-constrained energy dispatch model based on the distributed stochastic model predictive control(DSMPC)approach for an islanded multi-microgrid system is proposed.An ambiguity set considering the inherent uncertainties of renewable energy sources(RESs)is constructed without requiring the full distribution knowledge of the uncertainties.The power balance chance constraint is reformulated within the framework of the distributionally robust optimization(DRO)approach.With the exchange of information and energy flow,each microgrid can achieve its local supply-demand balance.Furthermore,the closed-loop stability and recursive feasibility of the proposed algorithm are proved.The comparative results with other DSMPC methods show that a trade-off between robustness and economy can be achieved.
基金The Science and Technology Project of the State Grid Corporation of China(Research and Demonstration of Loss Reduction Technology Based on Reactive Power Potential Exploration and Excitation of Distributed Photovoltaic-Energy Storage Converters:5400-202333241A-1-1-ZN).
文摘This paper presents a novel approach to economic dispatch in smart grids equipped with diverse energy devices.This method integrates features including photovoltaic(PV)systems,energy storage coupling,varied energy roles,and energy supply and demand dynamics.The systemmodel is developed by considering energy devices as versatile units capable of fulfilling various functionalities and playing multiple roles simultaneously.To strike a balance between optimality and feasibility,renewable energy resources are modeled with considerations for forecasting errors,Gaussian distribution,and penalty factors.Furthermore,this study introduces a distributed event-triggered surplus algorithm designed to address the economic dispatch problem by minimizing production costs.Rooted in surplus theory and finite time projection,the algorithm effectively rectifies network imbalances caused by directed graphs and addresses local inequality constraints.The algorithm greatly reduces the communication burden through event triggering mechanism.Finally,both theoretical proofs and numerical simulations verify the convergence and event-triggered nature of the algorithm.
基金supported by the Science and Technology Project of State Grid Liaoning Electric Power Co.,Ltd.(No.2023YF-82).
文摘The launch of the carbon-allowance trading market has changed the cost structure of the power industry.There is an asynchronous coupling mechanism between the carbon-allowance-trading market and the day-ahead power-system dispatch.In this study,a data-driven model of the uncertainty in the annual carbon price was created.Subsequently,a collaborative,robust dispatch model was constructed considering the annual uncertainty of the carbon price and the daily uncertainty of renewable-energy generation.The model is solved using the column-and-constraint generation algorithm.An operation and cost model of a carbon-capture power plant(CCPP)that couples the carbon market and the economic operation of the power system is also established.The critical,profitable conditions for the economic operation of the CCPP were derived.Case studies demonstrated that the proposed low-carbon,robust dispatch model reduced carbon emissions by 2.67%compared with the traditional,economic,dispatch method.The total fuel cost of generation decreases with decreasing,conservative,carbon-price-uncertainty levels,while total carbon emissions continue to increase.When the carbon-quota coefficient decreases,the system dispatch tends to increase low-carbon unit output.This study can provide important guidance for carbon-market design and the low-carbon-dispatch selection strategies.
基金supported by China Southern Power Grid Technology Project under Grant 03600KK52220019(GDKJXM20220253).
文摘The convergence of Internet of Things(IoT),5G,and cloud collaboration offers tailored solutions to the rigorous demands of multi-flow integrated energy aggregation dispatch data processing.While generative adversarial networks(GANs)are instrumental in resource scheduling,their application in this domain is impeded by challenges such as convergence speed,inferior optimality searching capability,and the inability to learn from failed decision making feedbacks.Therefore,a cloud-edge collaborative federated GAN-based communication and computing resource scheduling algorithm with long-term constraint violation sensitiveness is proposed to address these challenges.The proposed algorithm facilitates real-time,energy-efficient data processing by optimizing transmission power control,data migration,and computing resource allocation.It employs federated learning for global parameter aggregation to enhance GAN parameter updating and dynamically adjusts GAN learning rates and global aggregation weights based on energy consumption constraint violations.Simulation results indicate that the proposed algorithm effectively reduces data processing latency,energy consumption,and convergence time.
基金supported by the National Natural Science Foundation of China(62103203)the General Terminal IC Interdisciplinary Science Center of Nankai University.
文摘Battery energy storage systems(BESSs)are widely used in smart grids.However,power consumed by inner impedance and the capacity degradation of each battery unit become particularly severe,which has resulted in an increase in operating costs.The general economic dispatch(ED)algorithm based on marginal cost(MC)consensus is usually a proportional(P)controller,which encounters the defects of slow convergence speed and low control accuracy.In order to solve the distributed ED problem of the isolated BESS network with excellent dynamic and steady-state performance,we attempt to design a proportional integral(PI)controller with a reset mechanism(PI+R)to asymptotically promote MC consensus and total power mismatch towards 0 in this paper.To be frank,the integral term in the PI controller is reset to 0 at an appropriate time when the proportional term undergoes a zero crossing,which accelerates convergence,improves control accuracy,and avoids overshoot.The eigenvalues of the system under a PI+R controller is well analyzed,ensuring the regularity of the system and enabling the reset mechanism.To ensure supply and demand balance within the isolated BESSs,a centralized reset mechanism is introduced,so that the controller is distributed in a flow set and centralized in a jump set.To cope with Zeno behavior and input delay,a dwell time that the system resides in a flow set is given.Based on this,the system with input delays can be reduced to a time-delay free system.Considering the capacity limitation of the battery,a modified MC scheme with PI+R controller is designed.The correctness of the designed scheme is verified through relevant simulations.
基金supported by the National Natural Science Foundation of China under Grant No.61802328,61972333,and 61771415.
文摘Dynamic Economic Emission Dispatch(DEED)aims to optimize control over fuel cost and pollution emission,two conflicting objectives,by scheduling the output power of various units at specific times.Although many methods well-performed on the DEED problem,most of them fail to achieve expected results in practice due to a lack of effective trade-off mechanisms between the convergence and diversity of non-dominated optimal dispatching solutions.To address this issue,a new multi-objective solver called Multi-Objective Golden Jackal Optimization(MOGJO)algorithm is proposed to cope with the DEED problem.The proposed algorithm first stores non-dominated optimal solutions found so far into an archive.Then,it chooses the best dispatching solution from the archive as the leader through a selection mechanism designed based on elite selection strategy and Euclidean distance index method.This mechanism can guide the algorithm to search for better dispatching solutions in the direction of reducing fuel costs and pollutant emissions.Moreover,the basic golden jackal optimization algorithm has the drawback of insufficient search,which hinders its ability to effectively discover more Pareto solutions.To this end,a non-linear control parameter based on the cosine function is introduced to enhance global exploration of the dispatching space,thus improving the efficiency of finding the optimal dispatching solutions.The proposed MOGJO is evaluated on the latest CEC benchmark test functions,and its superiority over the state-of-the-art multi-objective optimizers is highlighted by performance indicators.Also,empirical results on 5-unit,10-unit,IEEE 30-bus,and 30-unit systems show that the MOGJO can provide competitive compromise scheduling solutions compared to published DEED methods.Finally,in the analysis of the Pareto dominance relationship and the Euclidean distance index,the optimal dispatching solutions provided by MOGJO are the closest to the ideal solutions for minimizing fuel costs and pollution emissions simultaneously,compared to the latest published DEED solutions.
文摘In renewable energy systems,energy storage systems can reduce the power fluctuation of renewable energy sources and compensate for the prediction deviation.However,if the renewable energy prediction deviation is small,the energy storage system may work in an underutilized state.To efficiently utilize a renewable-energy-sided energy storage system(RES),this study proposed an optimization dispatching strategy for an energy storage system considering its unused capacity sharing.First,this study proposed an unused capacity-sharing strategy for the RES to fully utilize the storage’s unused capacity and elevate the storage’s service efficiency.Second,RES was divided into“deviation-compensating energy storage(DES)”and“sharing energy storage(SES)”to clarify the function of RES in the operation process.Third,this study established an optimized dispatching model to achieve the lowest system operating cost wherein the unused capacity-sharing strategy could be integrated.Finally,a case study was investigated,and the results indicated that the proposed model and algorithm effectively improved the utilization of renewable-energy-side energy storage systems,thereby reducing the total operation cost and pressure on peak shaving.
文摘In the increasingly decentralized energy environment,economical power dispatching from distributed generations(DGs)is crucial to minimizing operating costs,optimizing resource utilization,and guaranteeing a consistent and sustainable supply of electricity.A comprehensive review of optimization techniques for economic power dispatching from distributed generations is imperative to identify the most effective strategies for minimizing operational costs while maintaining grid stability and sustainability.The choice of optimization technique for economic power dispatching from DGs depends on a number of factors,such as the size and complexity of the power system,the availability of computational resources,and the specific requirements of the application.Optimization techniques for economic power dispatching from distributed generations(DGs)can be classified into two main categories:(i)Classical optimization techniques,(ii)Heuristic optimization techniques.In classical optimization techniques,the linear programming(LP)model is one of the most popular optimization methods.Utilizing the LP model,power demand and network constraints are met while minimizing the overall cost of generating electricity from DGs.This approach is efficient in determining the best DGs dispatch and is capable of handling challenging optimization issues in the large-scale system including renewables.The quadratic programming(QP)model,a classical optimization technique,is a further popular optimization method,to consider non-linearity.The QP model can take into account the quadratic cost of energy production,with consideration constraints like network capacity,voltage,and frequency.The metaheuristic optimization techniques are also used for economic power dispatching from DGs,which include genetic algorithms(GA),particle swarm optimization(PSO),and ant colony optimization(ACO).Also,Some researchers are developing hybrid optimization techniques that combine elements of classical and heuristic optimization techniques with the incorporation of droop control,predictive control,and fuzzy-based methods.These methods can deal with large-scale systems with many objectives and non-linear,non-convex optimization issues.The most popular approaches are the LP and QP models,while more difficult problems are handled using metaheuristic optimization techniques.In summary,in order to increase efficiency,reduce costs,and ensure a consistent supply of electricity,optimization techniques are essential tools used in economic power dispatching from DGs.
