Optimal dynamic economic dispatch of generation: A review

This paper presents a review of the research of the optimal power dynamic dispatch problem. The dynamic dispatch problem differs from the static economic dispatch problem by incorporating generator ramp rate constraints. There are two different formulations of this problem in the literature. The first formulation is the optimal control dynamic dispatch (OCDD) where the power system generation has been modeled as a control system and optimization is done in the optimal control setting with respect to the ramp rates as input variables. The second one is a later formulation known as the dynamic economic dispatch (DED) where optimization is done with respect to the dispatchable powers of the committed generation units. In this paper we first outline the two formulations, then present an overview on the mathematical optimization methods, Artificial Intelligence (AI) techniques and hybrid methods used to solve the problem incorporating extended and complex objective functions or constraints. The DED problem in deregulated electricity markets is also reported.     

Effects of ramp-rate limits on unit commitment and economicdispatch

The authors propose an algorithm to consider the ramp characteristics in starting up and shutting down the generating units as well as increasing and decreasing power generation. They consider the inclusion of ramping constraints in both unit commitment and economic dispatch. Since implementing ramp-rate constraints is a dynamic process, dynamic programming (DP) is a proper tool to treat this problem. To overcome the computational expense which is the main drawback of DP, this study initially employs artificial intelligence techniques to produce a unit commitment schedule which satisfies all system and unit operation constraints except unit ramp-rate limits. Then, a dynamic procedure is used to consider the ramp properties as units are started up and shut down. According to this adjustment, maximum generating capabilities of units will change the unit operation status instead of following a step function. Finally, a dynamic dispatch procedure is adopted to obtain a suitable power allocation which incorporates the unit generating capability information given by unit commitment and unit ramping constraints, as well as the economical considerations. Two examples are presented to demonstrate the efficiency of the method     

Application of linear programming redispatch technique to dynamicgeneration allocation

Consideration is given to dispatch problems that involve the allocation of system generation optimally among generating units while tracking a load curve and observing the power rate limits of the units, system spinning reserve requirements, and other security constraints. Two methods are used in the solution of the problem. The first method is a quadratic programming technique combined with a linear programming redispatch technique. The latter utilizes a linear programming formulation of the dynamic dispatch problem about the base case static economic dispatch solution. The second method is based on the Dantzig-Wolfe decomposition technique. Tests and computer results of four systems of different combinations of units and intervals are given to show the advantages of the techniques proposed     

电力系统动态经济调度优化问题的膜计算方法

将膜计算方法用于求解电力系统动态经济调度优化问题。首先利用二次罚函数将多约束经济调度问题转化为无约束优化问题,对于膜计算的3个基本要素——膜内对象、膜结构和进化规则,该方法以各发电机组24时段的出力值作为膜内对象;采用具有嵌套结构的类细胞膜型膜结构,包含并行基本膜和拟高尔基体膜;在基本膜内执行交叉规则、变异规则、修正规则和保留规则,拟高尔基体被激活后执行移位规则、提取规则和目标导向规则。通过膜内对象不断进化择优,从而实现对动态经济调度问题的求解。基于IEEE 39和IEEE 118节点测试系统的算例,表明该文所提方法能够有效求解电力系统动态经济调度优化问题,与遗传算法和粒子群算法相比,该方法的计算结果和稳定性均更优,具有很好的应用前景。     

考虑多种约束条件的机组组合新算法

提出了考虑系统降出力备用约束、机组出力变化速率、线路潮流约束和断面传输功率约束的机组组合新算法。算法没有引入任何乘子,计算单调收敛,速度快,并且不需要初始可行解。用ＩＥＥＥ ２４母线系统对算法进行了验证,结果表明,算法对各种约束条件的处理正确,解的质量好。     

Clonal selection algorithm for power generators maintenance scheduling

This paper introduces a technique based on the one of the artificial immune system (AIS) technique known as the clonal selection algorithm (CSA) to obtain the optimal maintenance schedule outage of generating units. Based on a weekly load profile, the proposed technique provides the optimal maintenance window and calculates the optimal output power from each generator over a one year horizon. The maintenance scheduling problem is decoupled into two interrelated sub-problems namely, the maintenance scheduling and the power system sub-problems. The CSA is used to solve the maintenance scheduling subproblem to obtain the optimal maintenance outage of each unit. Based on the schedule generated by the CSA, the economic dispatch iterative lambda technique is used to find the optimal output power from each unit. Due to the search nature of the CSA, infeasible solutions may be introduced during the solution process. Therefore, a local search technique is used to watch the feasibility of the new solutions. The paper reports test results of the proposed algorithm to find the optimal maintenance schedule of the IEEE 30 bus system with 6 generating units and the IEEE 118 bus system with 33 generating units. Results are compared against the results obtained by complementary decision variables structure (CDV) and the evolutionary programming based techniques. Results are encouraging and indicate the viability of the proposed CSA technique.     

电力市场环境下含风电机组的环境经济调度模型及其仿真

电力市场环境下的传统经济调度不考虑环境补偿因素。文章在传统经济调度的基础上,考虑各机组和各种能源的环境成本,提出了火电机组名义环境补偿成本,用电方不需实际支付费用,发电方排污特性越好,火电机组的名义环境补偿成本越低;同时考虑了风电备用容量补偿成本,反映风电接入系统后火电热备用容量的变化;建立了电力市场环境下含风电机组的环境经济调度模型。基于Matlab优化工具箱,对一个包含2个火电机组和1个风电机组的系统进行优化仿真,结果表明：基于所提出的模型,环境友好的发电机组或能源将获得更大的调度权重。     

A Framework for Economic Load Frequency Control Design Using Modified Multi-objective Genetic Algorithm

This article deals with the coordination of security-constrained economic dispatch and load frequency control in an interconnected power system. The realistic and performance optimization inherent of the load frequency control (LFC) and security-constrained economic dispatch are fully considered without simplifying assumptions. For this purpose, modeling security-constrained economic dispatch as a discontinuous control action in the continuous frequency response model of a power system is well addressed. Considering conflict behavior of LFC and security-constrained economic dispatch beside the powerfulness of the multi-objective genetic algorithm (GA) to solve high-dimensional problems with conflicted objective functions makes it attractive for the automatic generation control coordination problem. The employed security-constrained economic dispatch utilizes the advantages of dynamic economic dispatch to achieve more realistic results. The GA is used to compute the decentralized control parameters and centralized generation levels of the on-line units to achieve an acceptable operating point. A significant modification in convergence speed has been performed by using LFC model properties in corporation with the genetic algorithm, so the proposed method gives considerable promise for implementation in multi-area power systems. The efficiency of the proposed algorithm and modification is demonstrated on a three control area power system.     

A clonal algorithm to solve economic load dispatch

This paper presents a novel optimization approach to constrained economic load dispatch (ELD) problem using artificial immune system (AIS). The approach utilizes the clonal selection principle and evolutionary approach wherein cloning of antibodies is performed followed by hypermutation. The proposed methodology easily takes care of transmission losses, dynamic operation constraints (ramp rate limits) and prohibited zones and also accounts for non-smoothness of cost function arising due to the use of multiple fuels. Simulations were performed over various systems with different number of generating units and comparisons are performed with other prevalent approaches. The findings affirmed the robustness, fast convergence and proficiency of proposed methodology over other existing techniques.     

基于一致性理论的独立微电网分布式动态经济调度

独立微电网是提高可再生能源利用率的有效途径,动态经济调度是微电网系统运行的重要环节。文中给出了独立微电网动态经济调度模型,提出了一套基于一致性理论的分布式实现方法,各参与者依靠本地计算以及邻居间的少量信息交互实现系统优化。计算分为两个阶段:在第一阶段,各单元通过平均一致性算法获得全网信息,并以最大化利用可再生能源为目标预设可控负荷的用电计划;在第二阶段,各单元通过更新发电机或储能系统时段间的出力上下限,将原问题解耦为一系列单时段经济调度问题,再采用一致性牵引算法根据等微增率准则逐个计算每个时段的最优出力。通过仿真算例验证了所提模型与算法的有效性。     

节能发电调度发电计划编制算法

在发电计划的编制过程中,如何实现机组发电序位表是体现节能发电要求的关键所在,为此,提出了发电计划编制核心算法。该算法基本原理为:根据全网负荷、分区负荷预测以及节能发电序位表,确定机组开机方式,然后采用等微增率法分配机组发电量;通过引入设备利用率系数分配机组发电曲线以满足系统安全运行和调峰要求,并修正机组发电曲线以满足运行约束条件,最终得到机组发电曲线。结合江苏电网以火电机组为主的特点,利用该算法进行节能调度发电试验日发电计划编制,验证了算法的合理性。     

一种改进型粒子群优化算法在电力系统经济负荷分配中的应用

针对机组数不同的电力系统设计优化方案,提出将基于有效群体利用策略的粒子群算法应用到经济负荷分配问题的解决中。该改进算法通过有效改变粒子数目,并改进了速度位移方程,加快了算法的收敛速度,同时提高其收敛精度。为验证该算法的有效性,针对机组数不同的电力系统经济负荷分配进行了测试,并与其他优化算法进行了比对测试。结果证明了该算法可高效准确地找到最优解,有效避免了陷入局部最优的问题,并保证了较快的运行速度。     

The solution of scheduling of thermal units by mathematical programming techniques

In this paper, the thermal units scheduling problem is considered from both its aspects: the selection of units to be placed in operation, and the load distribution among them. The solution of these problems can be found by considering two separate, but mutually dependent optimization problems, with a general objective of minimizing the system operating costs, subject to demand and operating constraints. Both optimization problems are formulated as mathematical programming problems. The first, usually called the unit commitment problem, is solved by a dynamic programming method. The second, which represents the economic dispatch problem, is solved by both dynamic and linear programming techniques. The solution methods are applied to a real power system, consisting of twelve generating units. The mathematical algorithms for the solution of specified problems are presented and the results of some computer studies on the selected sample system are given.     

Stochastic Hopfield artificial neural network for unit commitment and economic power dispatch

This paper presents a Hopfield artificial neural network for unit commitment and economic power dispatch. The dual problem of unit commitment and economic power dispatch is an example of a constrained mixed-integer combinatorial optimization. Because of uncertainties in both the system load demand and unit availability, the unit commitment and economic power dispatch problem is stochastic. In this paper we model forced unit outages as independent Markov processes, and load demand as a normal Gaussian random variable. The (0,1) unit commitment-status variables and the hourly unit loading are modelled as sample functions of appropriate random processes. The problem variables over which the optimization is done are modelled as sample functions of random processes which are described by Ito stochastic differential equations. The method is illustrated by a simple example of a power system having three machines which are committed and dispatched over a four-hour period. In the method, unit commitment and economic dispatch are done simultaneously.     

Optimal generation scheduling with ramping costs

In this paper, a decomposition method is proposed which relates the unit ramping process to the cost of fatigue effect in the generation scheduling of thermal systems. The objective of this optimization problem is to minimize the system operation cost, which includes the fuel cost for generating the required electrical energy and starting up decommitted units, as well as the rotor depreciation during ramping processes, such as starting up, shutting down, loading, and unloading. According to the unit fatigue index curves provided by generator manufacturers, fixed unit ramping-rate limits, which have been used by previous studies, do not reflect the physical changes of generator rotors during the ramping processes due to the fatigue effect. By introducing ramping costs, the unit on/offstates can be determined more economically by the proposed method. The Lagrangian relaxation method is proposed for unit commitment and economic dispatch, in which the original problem is decomposed into several subproblems corresponding to the optimization process of individual units. The network model is employed to represent the dynamic process of searching for the optimal commitment and generation schedules of a unit over the entire study time span. The experimental results for a practical system demonstrate the effectiveness of the proposed approach in optimizing the power system generation schedule     

风电并网电力系统动态经济调度问题的研究

通过优化火电机组出力,研究风电并网后,电力系统的短期动态经济调度问题。优化模型中引入了上、下旋转备用,以此应对风电功率预测误差给系统调度带来的波动。在基本粒子群优化算法基础上,提出了3种改进策略:先采用"循环处理策略"和"优先启停策略"生成问题的可行解,然后采用"机会停机策略"进一步优化可行解。经典算例结果表明,本文提出的策略稳定性好、寻优速度快、优化结果好,具有高效的搜索能力和适应性。     

Generation scheduling with thermal stress constraints

This paper describes a scheduling method for representing the thermal stress of turbine shafts as ramp rate constraints in the thermal commitment and dispatch of generating units. The paper uses Lagrangian relaxation for optimal generation scheduling. In applying the unit commitment, thermal stress over the elastic limit is used for calculating the ramping cost. The thermal stress contribution to generation cost requires the calculation of a set that includes thermal stress at the end of each time step; this requirement presents a complicated problem which cannot be solved by an ordinary optimization method such as dynamic programming. The paper uses an improved simulated annealing method to determine the optimal trajectory of each generating unit. Furthermore, the paper uses linear programming for economic dispatch in which thermal stress limits are incorporated in place of fixed ramp rate limits. The paper illustrates the economics of frequently ramping up/down of low cost generating units versus the cost of replacement of their turbine rotors with a shorter life span. The experimental results for a practical system demonstrate the effectiveness of the proposed method in optimizing the power system generation scheduling.     

基于等风险约束的机组日运行调度

本文从一个新的角度探讨了电力系统机组日运行调度问题。以系统等运行风险度和机组投运前导时间为约束,旋转备用为目标函数,建立了求解机组日运行计划的动态规划数学模型并提出了相应的算法。该方法可与常规的机组最优投入方法结合,进一步研究大型发电系统的可靠、安全、经济运行。     

A security constrained environmental/economic power dispatch technique using F-MSG algorithm for a power system area including limited energy supply thermal units

A security constrained non-convex environmental/economic power dispatch problem for a lossy electric power system area including limited energy supply thermal units is formulated. An iterative solution method based on modified subgradient algorithm operating on feasible values (F-MSG) and a common pseudo scaling factor for limited energy supply thermal units are used to solve it. In the proposed solution method, the F-MSG algorithm is used to solve the dispatch problem of each subinterval, while the common pseudo scaling factor is employed to adjust the amount of fuel spent by the limited energy supply thermal units during the considered operation period. We assume that limited energy supply thermal units are fueled under take-or-pay (T-O-P) agreement.The proposed dispatch technique is demonstrated on IEEE 30-bus power system with six thermal generating units having non-convex cost rate functions. Two of the generating units are selected as gas-fired limited energy supply thermal units. Pareto optimal solutions for the power system, where the constraint on the amount of fuel consumed by the limited energy supply thermal units is not considered, are calculated first. Later on, the same Pareto optimal solutions for the power system, where the fuel constraint is considered, are recalculated, and the obtained savings in the sum of optimal total fuel cost and total emission cost are presented. The dispatch problem of the first subinterval of the test system was solved previously by means of differential evolution (DE), and a hybrid method based on combination of DE and biogeography based optimization (BBO) for the best cost and the best emission cases in the literature. The results produced by these methods are compared with those of produced by the proposed method in terms of their total cost rate, emission rate and solution time values. It is demonstrated that the proposed method outperforms against the evolutionary methods mentioned in the above in terms of solution time values especially when the exact model of the test system is considered.     

考虑机组爬坡速度和网络安全约束的经济调度解耦算法

在电力系统经济调度中，由于机组爬坡速度、电网静态安全等约束的引入，在整个考虑周期内，机组的调度决策不仅具有空间上的关联，还具有时间上的关联，从而其调度模型不易求解。然而，在实际进行机组调度决策时，空间上和时间上的前后关联度并不是很强。也就是说，未来对机组现时刻的运行状态产生影响的时间段是有限的。基于这一思想，在整个运行周期内，研究未来多长时间对机组现时刻的最优状态不构成影响，即基于前瞻技术，在确保整体最优的前提下，提出按一定的序列单时段解耦求解模型，借助内点法进行求解。以IEEE可靠性分析的试验系统为例对本文算法在各种情况下进行分析比较，表明本文算法在计算代价上有一定优势，并且可以灵活应用到多种场合。