A PI+R Control Scheme Based on Multi-Agent Systems for Economic Dispatch in Isolated BESSs

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.

Imitation Learning Based Real-time Decision-making of Microgrid Economic Dispatch Under Multiple Uncertainties

The intermittency of renewable energy generation,variability of load demand,and stochasticity of market price bring about direct challenges to optimal energy management of microgrids.To cope with these different forms of operation un-certainties,an imitation learning based real-time decision-mak-ing solution for microgrid economic dispatch is proposed.In this solution,the optimal dispatch trajectories obtained by solv-ing the optimal problem using historical deterministic operation patterns are demonstrated as the expert samples for imitation learning.To improve the generalization performance of imita-tion learning and the expressive ability of uncertain variables,a hybrid model combining the unsupervised and supervised learn-ing is utilized.The denoising autoencoder based unsupervised learning model is adopted to enhance the feature extraction of operation patterns.Furthermore,the long short-term memory network based supervised learning model is used to efficiently characterize the mapping between the input space composed of the extracted operation patterns and system state variables and the output space composed of the optimal dispatch trajectories.The numerical simulation results demonstrate that under vari-ous operation uncertainties,the operation cost achieved by the proposed solution is close to the minimum theoretical value.Compared with the traditional model predictive control method and basic clone imitation learning method,the operation cost of the proposed solution is reduced by 6.3%and 2.8%,respective-ly,overa test period of three months.

Energy Economic Dispatch for Photovoltaic-Storage via Distributed Event-Triggered Surplus Algorithm

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.

Economic Power Dispatching from Distributed Generations: Review of Optimization Techniques

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.

A low-carbon economic dispatch model for electricity market with wind power based on improved ant-lion optimisation algorithm

Introducing carbon trading into electricity market can convert carbon dioxide into schedulable resources with economic value.However,the randomness of wind power generation puts forward higher requirements for electricity market transactions.Therefore,the carbon trading market is introduced into the wind power market,and a new form of low-carbon economic dispatch model is developed.First,the economic dispatch goal of wind power is be considered.It is projected to save money and reduce the cost of power generation for the system.The model includes risk operating costs to account for the impact of wind power output variability on the system,as well as wind farm negative efficiency operating costs to account for the loss caused by wind abandonment.The model also employs carbon trading market metrics to achieve the goal of lowering system carbon emissions,and analyze the impact of different carbon trading prices on the system.A low-carbon economic dispatch model for the wind power market is implemented based on the following two goals.Finally,the solution is optimised using the Ant-lion optimisation method,which combines Levi's flight mechanism and golden sine.The proposed model and algorithm's rationality is proven through the use of cases.

Modeling of Combined Economic and Emission Dispatch Using Improved Sand Cat Optimization Algorithm

Combined Economic and Emission Dispatch(CEED)task forms multi-objective optimization problems to be resolved to minimize emission and fuel costs.The disadvantage of the conventional method is its incapability to avoid falling in local optimal,particularly when handling nonlinear and complex systems.Metaheuristics have recently received considerable attention due to their enhanced capacity to prevent local optimal solutions in addressing all the optimization problems as a black box.Therefore,this paper focuses on the design of an improved sand cat optimization algorithm based CEED(ISCOA-CEED)technique.The ISCOA-CEED technique majorly concen-trates on reducing fuel costs and the emission of generation units.Moreover,the presented ISCOA-CEED technique transforms the equality constraints of the CEED issue into inequality constraints.Besides,the improved sand cat optimization algorithm(ISCOA)is derived from the integration of tra-ditional SCOA with the Levy Flight(LF)concept.At last,the ISCOA-CEED technique is applied to solve a series of 6 and 11 generators in the CEED issue.The experimental validation of the ISCOA-CEED technique ensured the enhanced performance of the presented ISCOA-CEED technique over other recent approaches.

Black Widow Optimization for Multi Area Economic Emission Dispatch

The optimizationfield has grown tremendously,and new optimization techniques are developed based on statistics and evolutionary procedures.There-fore,it is necessary to identify a suitable optimization technique for a particular application.In this work,Black Widow Optimization(BWO)algorithm is intro-duced to minimize the cost functions in order to optimize the Multi-Area Economic Dispatch(MAED).The BWO is implemented for two different-scale test systems,comprising 16 and 40 units with three and four areas.The performance of BWO is compared with the available optimization techniques in the literature to demonstrate the strategy’s efficacy.Results show that the optimized cost for four areas with 16 units is found to be 7336.76$/h,whereas it is 121,589$/h for four areas with 40 units using BWO.It is also noted that optimization algo-rithms other than BWO require higher cost value.The best-optimized solution for emission is achieved at 9.2784e+06 tones/h,and it is observed that there is a considerable difference between the worst and the best values.Also,the suggested technique is implemented for large-scale test systems successfully with high precision,and rapid convergence occurs in MAED.

Two-Stage Low-Carbon Economic Dispatch of Integrated Demand Response-Enabled Integrated Energy System with Ladder-Type Carbon Trading

Driven by the goal of“carbon neutrality”and“emission peak”,effectively controlling system carbon emissions has become significantly important to governments around the world.To this end,a novel two-stage low-carbon economic scheduling framework that considers the coordinated optimization of ladder-type carbon trading and integrated demand response(IDR)is proposed in this paper for the integrated energy system(IES),where the first stage determines the energy consumption plan of users by leveraging the price-based electrical-heat IDR.In contrast,the second stage minimizes the system total cost to optimize the outputs of generations with consideration of the uncertainty of renewables.In addition,to fully exploit the system’s emission reduction potential,a carbon trading cost model with segmented CO_(2) emission intervals is built by introducing a reward-penalty ladder-type carbon trading mechanism,and the flexible thermal comfort elasticity of customers is taken into account by putting forward a predicted mean vote index on the load side.The CPLEX optimizer resolves the two-stage model,and the study results on a modified IES situated in North China show the proposed model can effectively reduce carbon emissions and guarantee economical efficiency operation of the system.

Modified Cuckoo Search Algorithm to Solve Economic Power Dispatch Optimization Problems

A modified cuckoo search(CS) algorithm is proposed to solve economic dispatch(ED) problems that have nonconvex, non-continuous or non-linear solution spaces considering valve-point effects, prohibited operating zones, transmission losses and ramp rate limits. Comparing with the traditional cuckoo search algorithm, we propose a self-adaptive step size and some neighbor-study strategies to enhance search performance.Moreover, an improved lambda iteration strategy is used to generate new solutions. To show the superiority of the proposed algorithm over several classic algorithms, four systems with different benchmarks are tested. The results show its efficiency to solve economic dispatch problems, especially for large-scale systems.

GA and PSO culled hybrid technique for economic dispatch problem with prohibited operating zones

This paper presents an efficient and reliable genetic algorithm (GA) based particle swarm optimization (PSO) tech- nique (hybrid GAPSO) for solving the economic dispatch (ED) problem in power systems. The non-linear characteristics of the generators, such as prohibited operating zones, ramp rate limits and non-smooth cost functions of the practical generator operation are considered. The proposed hybrid algorithm is demonstrated for three different systems and the performance is compared with the GA and PSO in terms of solution quality and computation efficiency. Comparison of results proved that the proposed algo- rithm can obtain higher quality solutions efficiently in ED problems. A comprehensive software package is developed using MATLAB.

Multiple objective particle swarm optimization technique for economic load dispatch

A multi-objective particle swarm optimization (MOPSO) approach for multi-objective economic load dispatch problem in power system is presented in this paper. The economic load dispatch problem is a non-linear constrained multi-objective optimization problem. The proposed MOPSO approach handles the problem as a multi-objective problem with competing and non-commensurable fuel cost, emission and system loss objectives and has a diversity-preserving mechanism using an external memory (call “repository”) and a geographically-based approach to find widely different Pareto-optimal solutions. In addition, fuzzy set theory is employed to extract the best compromise solution. Several optimization runs of the proposed MOPSO approach were carried out on the standard IEEE 30-bus test system. The results revealed the capabilities of the proposed MOPSO approach to generate well-distributed Pareto-optimal non-dominated solutions of multi-objective economic load dispatch. Com- parison with Multi-objective Evolutionary Algorithm (MOEA) showed the superiority of the proposed MOPSO approach and confirmed its potential for solving multi-objective economic load dispatch.

Two-stage stochastic approach for spinning reserve allocation in dynamic economic dispatch

A novel approach was proposed to allocate spinning reserve for dynamic economic dispatch.The proposed approach set up a two-stage stochastic programming model to allocate reserve.The model was solved using a decomposed algorithm based on Benders' decomposition.The model and the algorithm were applied to a simple 3-node system and an actual 445-node system for verification,respectively.Test results show that the model can save 84.5 US $ cost for the testing three-node system,and the algorithm can solve the model for 445-node system within 5 min.The test results also illustrate that the proposed approach is efficient and suitable for large system calculation.

Dynamic economic dispatch combining network flow and interior point method

Under the environment of electric power market, economic dispatch (ED) problem should consider network constraints, unit ramp rates, besides the basic constraints. For this problem, it is important to establish the effective model and algorithm. This paper examines the decoupled conditions that affect the solution optimality to this problem. It proposes an effective model and solution method. Based on the look-ahead technique, it finds the number of time intervals to guarantee the solution optimality. Next, an efficient technique for finding the optimal solution via the interior point methods is described. Test cases, which include dispatching six units over 5 time intervals on the IEEE 30 test system with line flows and ramp constraints are presented. Results indicate that the computational effort as measured by iteration counts or execution time varies only modestly with the problem size.

Solution of Combined Heat and Power Economic Dispatch Problem Using Direct Optimization Algorithm

This paper presents the solution to the combined heat and power economic dispatch problem using a direct solution algorithm for constrained optimization problems. With the potential of Combined Heat and Power (CHP) production to increase the efficiency of power and heat generation simultaneously having been researched and established, the increasing penetration of CHP systems, and determination of economic dispatch of power and heat assumes higher relevance. The Combined Heat and Power Economic Dispatch (CHPED) problem is a demanding optimization problem as both constraints and objective functions can be non-linear and non-convex. This paper presents an explicit formula developed for computing the system-wide incremental costs corresponding with optimal dispatch. The circumvention of the use of iterative search schemes for this crucial step is the innovation inherent in the proposed dispatch procedure. The feasible operating region of the CHP unit three is taken into account in the proposed CHPED problem model, whereas the optimal dispatch of power/heat outputs of CHP unit is determined using the direct Lagrange multiplier solution algorithm. The proposed algorithm is applied to a test system with four units and results are provided.

Dynamic Economic Dispatch for Microgrids Including Battery Energy Storage

Microgrids integrate distributed renewable energy resources, controllable loads and energy storage in a more economic and reliable fashion. Battery energy storage units are essential for microgrid operation, which make microgird become a strong coupling system in the time domain. Hence, the traditional methods of static dispatch are no longer suitable for microgrids. This paper proposes a dynamic economic dispatch method for microgrids. Considering microgrid as a discrete time system, the dynamic economic dispatch is to find the optimal control strategy for the system in finite time period. Based on this idea, the dynamic economic dispatch model for microgrids is established, and then the corresponding dynamic programming algorithm is designed. Finally, an example of microgrid is given, and the dynamic economic dispatch results are compared with that of the static dispatch. The comparison confirms the effectiveness of the proposed dynamic dispatch method.

CSO Algorithm for Economic Dispatch Decision of Hybrid Generation System

The aim of this research is to study the optimal economic dispatch （ED） through Cat Swarm Optimization （CSO） algorithm. Many areas in power systems require solving one or more nonlinear optimization problems. While analytical methods might suffer from slow convergence and the CSO can, therefore, be effectively applied to different optimization problems. In this paper, the CSO is also extended to coordinate wind and thermal dispatch and to minimize total generation cost. Results indicated that the CSO is superior to PSO in the fast convergence and better performance to find the global best solution.

Economic Load Dispatch with Daily Load Patterns Using Particle Swarm Optimization

ELD （economic load dispatch） problem is one of the essential issues in power system operation. The objective of solving ELD problem is to allocate the generation output of the committed generating units. The main contribution of this work is to solve the ELD problem concerned with daily load pattern. The proposed solution technique, developed based PSO （particle swarm optimization） algorithm, is applied to search for the optimal schedule of all generations units that can supply the required load demand at minimum fuel cost while satisfying all unit and system operational constraints. The performance of the developed methodology is demonstrated by case studies in test system of six-generation units. The results obtained from the PSO are compared to those achieved from other approaches, such as QP （quadratic programming）, and GA （genetic algorithm）.

Scenario-oriented hybrid particle swarm optimization algorithm for robust economic dispatch of power system with wind power

An economic dispatch problem for power system with wind power is discussed.Using discrete scenario to describe uncertain wind powers,a threshold is given to identify bad scenario set.The bad-scenario-set robust economic dispatch model is established to minimize the total penalties on bad scenarios.A specialized hybrid particle swarm optimization(PSO)algorithm is developed through hybridizing simulated annealing(SA)operators.The SA operators are performed according to a scenario-oriented adaptive search rule in a neighborhood which is constructed based on the unit commitment constraints.Finally,an experiment is conducted.The computational results show that the developed algorithm outperforms the existing algorithms.

Low Carbon Economic Dispatch of Integrated Energy System Considering Power Supply Reliability and Integrated Demand Response

Integrated energy system optimization scheduling can improve energy efficiency and low carbon economy.This paper studies an electric-gas-heat integrated energy system,including the carbon capture system,energy coupling equipment,and renewable energy.An energy scheduling strategy based on deep reinforcement learning is proposed to minimize operation cost,carbon emission and enhance the power supply reliability.Firstly,the lowcarbon mathematical model of combined thermal and power unit,carbon capture system and power to gas unit(CCP)is established.Subsequently,we establish a low carbon multi-objective optimization model considering system operation cost,carbon emissions cost,integrated demand response,wind and photovoltaic curtailment,and load shedding costs.Furthermore,considering the intermittency of wind power generation and the flexibility of load demand,the low carbon economic dispatch problem is modeled as a Markov decision process.The twin delayed deep deterministic policy gradient(TD3)algorithm is used to solve the complex scheduling problem.The effectiveness of the proposed method is verified in the simulation case studies.Compared with TD3,SAC,A3C,DDPG and DQN algorithms,the operating cost is reduced by 8.6%,4.3%,6.1%and 8.0%.

Comparison between dynamic programming and genetic algorithm for hydro unit economic load dispatch

The hydro unit economic load dispatch （ELD） is of great importance in energy conservation and emission reduction. Dynamic programming （DP） and genetic algorithm （GA） are two representative algorithms for solving ELD problems. The goal of this study was to examine the performance of DP and GA while they were applied to ELD. We established numerical experiments to conduct performance comparisons between DP and GA with two given schemes. The schemes included comparing the CPU time of the algorithms when they had the same solution quality, and comparing the solution quality when they had the same CPU time. The numerical experiments were applied to the Three Gorges Reservoir in China, which is equipped with 26 hydro generation units. We found the relation between the performance of algorithms and the number of units through experiments. Results show that GA is adept at searching for optimal solutions in low-dimensional cases. In some cases, such as with a number of units of less than 10, GA＇s performance is superior to that of a coarse-grid DP. However, GA loses its superiority in high-dimensional cases. DP is powerful in obtaining stable and high-quality solutions. Its performance can be maintained even while searching over a large solution space. Nevertheless, due to its exhaustive enumerating nature, it costs excess time in low-dimensional cases.