Finite-time economic model predictive control for optimal load dispatch and frequency regulation in interconnected power systems

This paper presents a finite-time economic model predictive control(MPC)algorithm that can be used for frequency regulation and optimal load dispatch in multi-area power systems.Economic MPC can be used in a power system to ensure frequency stability,real-time economic optimization,control of the system and optimal load dispatch from it.A generalized terminal penalty term was used,and the finite-time convergence of the system was guaranteed.The effectiveness of the proposed model predictive control algorithm was verified by simulating a power system,which had two areas connected by an AC tie line.The simulation results demonstrated the effectiveness of the algorithm.

Modified Shuffled Frog Leaping Algorithm for Solving Economic Load Dispatch Problem

In the recent restructured power system scenario and complex market strategy, operation at absolute minimum cost is no longer the only criterion for dispatching electric power. The economic load dispatch (ELD) problem which accounts for minimization of both generation cost and power loss is itself a multiple conflicting objective function problem. In this paper, a modified shuffled frog-leaping algorithm (MSFLA), which is an improved version of memetic algorithm, is proposed for solving the ELD problem. It is a relatively new evolutionary method where local search is applied during the evolutionary cycle. The idea of memetic algorithm comes from memes, which unlike genes can adapt themselves. The performance of MSFLA has been shown more efficient than traditional evolutionary algorithms for such type of ELD problem. The application and validity of the proposed algorithm are demonstrated for IEEE 30 bus test system as well as a practical power network of 203 bus 264 lines 23 machines system.

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.

A Hybrid Optimization Technique Coupling an Evolutionary and a Local Search Algorithm for Economic Emission Load Dispatch Problem

This paper presents an optimization technique coupling two optimization techniques for solving Economic Emission Load Dispatch Optimization Problem EELD. The proposed approach integrates the merits of both genetic algorithm (GA) and local search (LS), where it maintains a finite-sized archive of non-dominated solutions which gets iteratively updated in the presence of new solutions based on the concept of ε-dominance. To improve the solution quality, local search technique was applied as neighborhood search engine, where it intends to explore the less-crowded area in the current archive to possibly obtain more non-dominated solutions. TOPSIS technique can incorporate relative weights of criterion importance, which has been implemented to identify best compromise solution, which will satisfy the different goals to some extent. Several optimization runs of the proposed approach are carried out on the standard IEEE 30-bus 6-genrator test system. The comparison demonstrates the superiority of the proposed approach and confirms its potential to solve the multiobjective EELD problem.

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.

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）.

A Multi-Agent Particle Swarm Optimization for Power System Economic Load Dispatch

A new versatile optimization, the particle swarm optimization based on multi-agent system (MAPSO) is presented. The economic load dispatch (ELD) problem of power system can be solved by the algorithm. By competing and cooperating with the randomly selected neighbors, and adjusting its global searching ability and local exploring ability, this algorithm achieves the goal of high convergence precision and speed. To verify the effectiveness of the proposed algorithm, this algorithm is tested by three different ELD cases, including 3, 13 and 40 units IEEE cases, and the experiment results are compared with those tested by other intelligent algorithms in the same cases. The compared results show that feasible solutions can be reached effectively, local optima can be avoided and faster solution can be applied with the proposed algorithm, the algorithm for ELD problem is versatile and efficient.

Economic Load Dispatch Based on Efficient Population Utilization Strategy for Particle Swarm Optimization

In this paper, the efficient population utilization strategy for particle swarm optimization (EPUSPSO) is proposed to solve the economic load dispatch (ELD) problem of power system. This algorithm improves the accuracy and the speed of its convergence by changing the number of particles effectively, and improving the velocity equation and position equation. In order to verify the effectiveness of the algorithm, this algorithm is tested in three different ELD cases of power system include IEEE 3-unit case, 13-unit case, and 40-unit case, and the obtained results are compared with those obtained from other algorithms using the same system parameters. The compared results show that the algorithm can find the optimal solution effectively and accurately, and avoid falling into the local optimal problem;meanwhile, faster speed can be ensured in the case.

Cuckoo Search for Solving Economic Dispatch Load Problem

Economic Load Dispatch (ELD) is a process of scheduling the required load demand among available generation units such that the fuel cost of operation is minimized. The ELD problem is formulated as a nonlinear constrained optimization problem with both equality and inequality constraints. In this paper, two test systems of the ELD problems are solved by adopting the Cuckoo Search (CS) Algorithm. A comparison of obtained simulation results by using the CS is carried out against six other swarm intelligence algorithms: Particle Swarm Optimization, Shuffled Frog Leaping Algorithm, Bacterial Foraging Optimization, Artificial Bee Colony, Harmony Search and Firefly Algorithm. The effectiveness of each swarm intelligence algorithm is demonstrated on a test system comprising three-generators and other containing six-generators. Results denote superiority of the Cuckoo Search Algorithm and confirm its potential to solve the ELD problem.

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 Dispatch with Multiple Fuel Options Using CCF

This paper presents an efficient analytical approach using Composite Cost Function (CCF) for solving the Economic Dispatch problem with Multiple Fuel Options (EDMFO). The solution methodology comprises two stages. Firstly, the CCF of the plant is developed and the most economical fuel of each set can be easily identified for any load demand. In the next stage, for the selected fuels, CCF is evaluated and the optimal scheduling is obtained. The Proposed Method (PM) has been tested on the standard ten-generation set system;each set consists of two or three fuel options. The total fuel cost obtained by the PM is compared with earlier reports in order to validate its effectiveness. The comparison clears that this approach is a promising alterna-tive for solving EDMFO problems in practical power system.

Addressing Economic Dispatch Problem with Multiple Fuels Using Oscillatory Particle Swarm Optimization

Economic dispatch has a significant effect on optimal economical operation in the power systems in industrial revolution 4.0 in terms of considerable savings in revenue.Various non-linearity are added to make the fossil fuel-based power systems more practical.In order to achieve an accurate economical schedule,valve point loading effect,ramp rate constraints,and prohibited operating zones are being considered for realistic scenarios.In this paper,an improved,and modified version of conventional particle swarm optimization(PSO),called Oscillatory PSO(OPSO),is devised to provide a cheaper schedule with optimum cost.The conventional PSO is improved by deriving a mechanism enabling the particle towards the trajectories of oscillatory motion to acquire the entire search space.A set of differential equations is implemented to expose the condition for trajectory motion in oscillation.Using adaptive inertia weights,this OPSO method provides an optimized cost of generation as compared to the conventional particle swarm optimization and other new meta-heuristic approaches.

Economic Dispatch with Convex and Non-Convex Fuel Cost Functions Including Line Losses Using Pattern Search

This article presents an application of generalized pattern search （PS） algorithm to solve economic load dispatch （ELD） problems with convex and non-convex fuel cost objective functions. Main objective of ELI） is to determine the most economic generating dispatch required to satisfy the predicted load demands including line losses. Relaxing various equality and inequality constraints are considered. The unit operation minhnum/maximum constraints, effects of valve-point and line losses are considered for the practical applications. Several case studies were tested and verified, which indicate an improvement in total fuel cost savings. The robustness of the proposed PS method have been assessed and investigated through intensive comparisons with reported results in recent researches. The results are very encouraging and suggesting that PS may be very useful tool in solving power system ELD problems.

算力-热力灵活性协同的数据中心能量管理方法

随着数字经济产业快速发展,数据中心成为电能消耗的重要部分。多样化的数据处理需求、大量的计算用电及制冷用电,在带来高能耗问题的同时也为数据中心的运行调度提供了灵活性。因此,协同考虑计算灵活性和热灵活性,制定数据中心优化运行策略,可有效提高能源利用效率,提升数据中心运行经济性。该文提出一种考虑算力-热力灵活性协同的数据中心能量管理方法。首先,考虑数据负载灵活调度、冷却系统温度变化以及冷热通道热惯性等精细化要素,实现了信息技术设备和冷却设备的协同建模。其次,进行模型的线性化转换,降低了求解难度。在此基础上,实现了基于灵活性协同的数据中心能量管理,从而降低数据中心运行能耗及成本。最后通过算例验证了所提方法的有效性。

基于等微增率并计及机组功率约束的火电机组最优负荷分配精确解

火电机组最优负荷分配是电力系统经济运行的重要模型,也是电力系统本科生专业基础课《电力系统分析》的重要教学内容之一。经典教科书采用等微增率方法求解该问题,并给出了相应的物理含义。由于等微增率法是基于不考虑火电机组上下界物理约束而推导出来的,部分教科书补充了计及火电机组上下界物理约束时的情况,即如果某台机组的无约束最优解违背了上(下)界约束,则将该机组对应的最优解限制到相应的出力上(下)界,然后对其余火电机组再进行重新的等微增率分配。然而,简单算例表明,补充求解方法的适用范围是有限的。为此,该文对火电机组最优负荷分配问题进行重新探索,推导教材方法适用的一个充分条件与一个必要条件。面向本科生与研究生,分别提出考虑机组上下界约束后的最优负荷分配方法,并进行严格的理论推导。理论推导与大量的仿真算例表明,在机组数量较少时,教材中的求解方法有可能适用,而机组数较多时,可能出现不适用的情况。该文所提方法可以将适用范围扩展到机组数量较多的场景,并且进行严格理论推导。希望该文可以为《电力系统分析》教学过程与教材修订提供帮助。

水电站机组负荷降维优化分配中的时间尺度效应

时间尺度是影响水电站负荷优化分配结果的重要因素。为探究时间尺度对水电站负荷分配的影响,研究论述了水电站调度中的时空尺度效应内涵及出现的原因,提出了包含发电耗水量、跨越振动区次数、机组启停次数、求解耗时等的尺度效应量化指标,并以ZM水电站为研究对象,基于水电站机组负荷优化分配模型,逐次递进分析了典型日考虑负荷过程随机性与负荷水平的水电站机组负荷优化分配尺度效应。结果表明:1)时间尺度越小更易捕捉负荷变化与水库运行过程,电站负荷优化分配的耗水量、机组启停与跨越振动区次数越大。时间尺度越大更易忽视或弱化机组启停以及跨越振动区等行为,产生潜在的安全运行风险。2)考虑负荷过程的随机性时,水电站负荷优化分配同样呈现尺度效应现象,但其影响程度与时间尺度大小影响相当。3)负荷水平越小或越大,不同时间尺度下电站机组运行方式变化较小,时间尺度效应越不显著;负荷水平居中时,时间尺度效应相对显著。研究结果可为水电站负荷优化分配的时间尺度选择以及模型降维求解算法提供科学依据。

基于荷-储碳流模型的电力系统双层优化调度

为减少高耗能机组出力,同时增加风电消纳能力,考虑负荷和储能两类灵活调用资源,提出基于荷-储碳放流模型的电力系统双层经济低碳优化调度方法。基于电力系统碳排放流理论,分别建立负荷和储能设备的碳排放流模型;设计考虑荷-储协同优化的低碳调度策略,在负荷侧建立基于负荷节点碳势的电-碳耦合价格需求响应模型,同时鉴于荷侧降碳调节的局限性,在储能侧建立基于碳流模型的低碳调度策略,实现荷-储协同低碳调度策略;考虑经济性和低碳性,建立包含上层经济调度、下层低碳调度的双层优化调度模型。通过改进IEEE-14节点系统对优化调度方法进行仿真验证,结果表明:提出的优化调度方法在保证经济性的同时,减少了弃风,并降低了高耗能机组出力,从而有效降低了全系统的碳排放。

经济负荷分配的Hopfield神经网络计算

介绍了Hopfield神经网络(HNN)原理及其在机组经济负荷分配(EconomicLoadDispatch,ELD)中的应用。首先将ELD问题映射到Hopfield神经网络模型,然后利用HNN的动力特性搜索最优分配。仿真结果与分段结构优化方法和模拟退火(SimulatedAnnealing,SA)方法进行比较,表明HNN方法能找到近乎全局最优解,可有效地解决经济负荷分配问题。且易于在计算机上实现,有实际应用价值。

免疫遗传算法及其在电力系统EELD中的应用

电力系统EELD问题是一个满足一定约束条件的多目标优化问题,利用基于进化策略的免疫遗传算法对这一问题求解.将发电燃料成本和污染控制成本视为抗原,各电力生产单元发电量的最优解视为抗体,以一个含有5个电力生产单元的燃煤电力系统模型为对象,给出利用免疫遗传算法解决这一问题的主要方法和步骤.并与基于遗传算法和Hopfield神经网络方法进行比较分析.结果证明此算法可以优化分配电力系统中各电力单元发电量,达到环境经济合理配置.

多智能体量子多目标进化算法及其在EELD问题中的应用

环境经济负荷分配问题是电力系统中重要的多目标优化问题。求解多目标优化问题的关键在于找到尽可能多的Pareto最优解。在基于量子进化理论,智能体的竞争、学习能力和生物的进化策略的基础上,提出了一种用于求解多目标优化问题的量子编码的多智能体进化算法。该方法将智能体分布在多智能体网络环境中,智能体之间通过量子进化来生成问题的可行解。将该算法应用于经济环境负荷分配的两目标(燃料成本和NOx排放)与三目标(燃料成本,NOx排放和SO2排放)优化问题,通过与经典多目标优化算法进行比较,表明了该算法的有效性。