计及可行解恢复的高载能负荷-新能源有功-无功协调调度

高载能负荷具有较强的用电调节能力,可通过与新能源协调促进新能源消纳。考虑节点电压约束和内部电网潮流方程的高载能负荷自调度问题是一个混合整数非线性非凸问题,现有的求解器难以求解。而采用线性潮流等简化方法求得的自调度结果不够精确,无法保证实际运行时的节点电压约束。针对以上问题,首先采用二阶锥松弛方法对原问题进行凸化以降低问题求解难度,进而采用基于交流潮流的可行解恢复过程以保证二阶锥松弛后的自调度结果精确合理。通过对比线性潮流自调度结果、基于二阶锥松弛的自调度结果、采用可行解恢复的自调度结果和原始自调度模型的结果,证明采用可行解恢复过程的自调度结果避免了基于线性潮流或基于二阶锥松弛的自调度解不精确问题。同时,相比利用现有商业求解器直接求解原问题,采用该方法可以在较短的时间内快速求得一组优化结果,有效地降低了原问题求解的难度。     

复杂时段耦合型约束水电站群短期变尺度优化调度方法

复杂时段耦合型约束是制约大规模水电短期优化调度高效求解的主要因素之一。提出了一种水电站群变尺度优化调度方法,旨在通过增大时段步长,以弱化甚至消除时段耦合型约束,进而提高算法搜索效率,改善优化调度质量。在求解过程中,首先将原问题转换为多个具有相同调度周期、相同目标和控制需求但不同步长的水电站群优化调度问题,并按照步长从大到小的顺序依次求解各问题,面临问题的初始解由前一阶段大步长问题的优化出力结果确定,直至完成最小步长问题即原问题的优化求解。所提方法通过云南电网水电站群仿真调度实例得到验证,与单一尺度优化方法相比,结果质量和计算效率均得到不同程度地改善。     

基于连续线性规划的梯级水电站优化调度

梯级水电站优化调度是一个多时段、多变量和多约束条件的大规模优化问题,其求解过程非常复杂。文章尝试采用连续线性规划的优化方法来解决梯级水电站长期优化调度问题。通过采用泰勒级数一阶描述形式,对优化调度目标函数和约束条件中的非线性约束进行线性化处理,建立了基于连续线性规划算法的优化调度数学模型,提出了用连续线性规划技术求解梯级水电站优化调度问题的算法,并采用迭代步长的动态比例缩减因子保证算法能快速准确地收敛到优化问题的最优解。利用Matlab7.0编制连续线性规划梯级水电站优化调度程序,一个两级梯级水电站群的仿真分析结果表明,该算法可用于求解梯级水电站优化调度问题,并可快速得到非线性问题的最优解。     

基于启发式线性规划的大规模安全约束调度快速求解方法

提升大规模安全约束经济调度优化模型的求解性能是开展大电网跨省区电力电量全局优化平衡的前提与基础。首先分析问题的物理特性,通过并行计算求解不考虑机组爬坡约束的分时段约束松弛模型。基于对松弛解的分析获得可用于指导安全约束经济调度模型改进的有用信息,以约束剔除和约束增加的方式提出了基于启发式线性规划的大规模安全约束经济调度快速求解方法。将所提算法运用于新英格兰10机扩展系统和中国实际电网,验证了所提算法的正确性和有效性。     

采用基于分解的多目标进化算法的电力环境经济调度

为了准确、快速地求解电力系统环境经济调度(environmental economic dispatching,EED)问题,将基于分解的多目标进化算法(multi-objective evolutionary algorithm based on decomposition,MOEA/D)应用于电力调度领域,提出了基于MOEA/D的多目标环境经济调度算法。该算法首先采用Tchebycheff法将整个EED Pareto最优前沿的逼近问题分解为一定数量的单目标优化子问题,然后利用差分进化同时求解这些子问题,并在算法中加入约束处理及归一化操作,以获得最优的带约束EED问题的调度方案。最后,应用模糊集理论为决策者提供最优折中解。对IEEE 30节点测试系统进行仿真计算,并与其它智能优化算法的调度方案对比。结果表明,该算法有效可行,且具有很好的收敛速度和求解精度。     

含高比例风电系统随机备用调度研究

高比例风电并网对电力系统备用容量调节能力提出极大的挑战。为弥补风电场计划出力与实际出力之间的偏差，电力调度须额外预留上、下旋转备用容量。利用随机机会约束优化理论，计及违反安全约束风险，提出了一种考虑风电出力不确定性与自动发电控制(automatic generation control,AGC)机组出力特性的日前随机备用调度模型。首先，基于马尔可夫链蒙特卡洛(Markov chains Monte Carlo,MCMC)法生成风电出力场景，并利用违反机会约束的概率及置信参数自动确定所需生成场景数量。其次，全面考虑了AGC机组备用出力特性及运行约束，并将备用成本纳入目标函数，可同时得到常规机组最优出力计划与AGC机组备用容量的最优分配系数。最后，将所构造的随机备用调度模型等效为半定规划(semidefiniteprogramming,SDP)问题进行直接求解。通过IEEE 30节点系统进行算例分析，验证了所构造的随机备用调度模型的有效性。     

采用多目标纵横交叉算法的电力系统动态环境经济调度

针对带非线性约束的电力系统动态环境经济调度问题,提出一种多目标纵横交叉算法。对动态调度中燃料费用和污染排放两个相互约束、冲突的目标同时进行优化。求解过程中,结合非约束支配策略,提出一种双交叉机制,增强粒子穿越非可行区域的能力,使得生成的帕累托最优解落在可行区域内。通过边缘探索,增强算法的全局搜索能力。同时,采用外部存档集合储存非劣解,并通过拥挤度对比,保持非劣解的多样性。最后,采用模糊决策理论获得最优折中解。对10机电力系统的仿真结果验证了所提方法的有效性与优越性。     

多目标环境经济发电调度的标准化法向约束方法

将标准化法向约束(normalized normal constraint,NNC)方法用于求解电力系统环境经济发电调度问题,同时考虑发电调度的发电成本和污染气体排放量最小两个优化目标。通过NNC方法将发电调度的多目标优化问题转化为一系列的单目标优化问题,求解这些单目标问题得到完整、均匀分布的Pareto解集,然后采用伪权向量法从中选择出满意的折中解。结合NNC方法粗粒度空间上可并行的计算优势,将其采用多核并行计算技术加以实现,以提高其计算效率。对IEEE-30和IEEE-118系统测试,验证该方法的有效性和可行性,采用多核并行计算实现后,可以快速、完整地得到环境经济发电调度多目标优化问题均匀分布的Pareto解集,具有广阔的应用前景。     

计及碳排放量约束的多区域互联电力系统分布式低碳经济调度

针对多区域互联系统考虑全局不等式约束的低碳经济调度分布式求解问题，提出一种分布式低碳经济调度优化方法。首先，为实现多区域互联系统低碳化运行，利用互联系统碳排放量约束调控各区域中发电单元出力，构建低碳经济调度模型；随后，基于对偶理论和变量分解方法对多区域互联系统低碳经济调度模型进行分解，将低碳经济调度问题分解为与各区域相关的子问题，再利用交替方向乘子法（ADMM）搭建各区域协同优化求解框架；迭代求解过程中，通过迭代互联区域之间相邻单元或节点拉格朗日乘子信息的交换实现分布式低碳经济调度模型求解，该经济调度优化模型，在有效降低各区域间信息传递量、充分保障各区域单元信息隐私性要求的同时，满足优化区域“即插即用”的需求；最后，通过IEEE 6节点测试系统和72节点测试系统进行算例分析，验证了所提方法的有效性。     

变负荷条件下追踪电力系统安全最优运行轨迹的参数化方法

提出一种追踪线性约束下凸可分规划问题最优解轨迹的参数化方法。该参数优化算法可在对偶松弛凸可分规划算法的主循环之外,通过少量参数化扩展得到。参数分析表明最优解轨迹的性态是一条分段线性曲线,解轨迹上的破点和不可行现象存在密切关系。将这种方法应用到电力系统有功最优潮流问题中,得到一种统一经济调度和安全约束调度的参数化安全约束调度(security constrained economic dispatch,SCED)新算法,它可快速追踪变负荷条件下系统安全最优运行轨迹。算法在IEEE14-300节点测试系统及2个省级实际系统上通过测试,数值试验和几何分析表明了该方法的计算特性和物理内涵,同时清楚地显示了目前调度模式中存在的问题和改进方向。     

相同机组调度与竞标问题研究

本文在对利用拉格朗日松驰法解决大型电力市场综合资源的调度与竞标时所碰到的相同机组问题进行了讨论,认为改进电力市场竞标模式并不是解决相同机组调度与竞标问题的根本方法。     

Coevolutionary Algorithm Based on Lagrangian Method for Hydrothermal Generation Scheduling

The coevolutionary algorithm (CEA) based on the Lagrangian method is proposed for hydrothermal generation scheduling. The main purpose of hydrothermal generation scheduling is to minimize the overall operation cost and the constraints satisfied by scheduling the power outputs of all hydro and thermal units under study periods, given electrical load and limited water resource. In the proposed method, a genetic algorithm is successfully incorporated into the Lagrangian method. The genetic algorithm searches out the optimum using multiple-path techniques and possesses the ability to deal with continuous and discrete variables. Regardless of the objective function characteristic the genetic algorithm does not have to modify the design rules and possesses the ability to go over local solutions toward the global optimal solution. The genetic algorithm can improve the disadvantages of the traditional Lagrangian method, which updates Lagrange multipliers according to the degree of system constraint violation by the gradient algorithm, and further searches out the global optimal solution. The developed algorithm is illustrated and tested on a practical Taiwan power system. Numerical results show that the proposed CEA based on the Lagrangian method is a very effective method for searching out the global optimal solution.     

Lagrangian relaxation hybrid with evolutionary algorithm for short-term generation scheduling

Short-term generation scheduling is an important function in daily operational planning of power systems. It is defined as optimal scheduling of power generators over a scheduling period while respecting various generator constraints and system constraints. Objective of the problem includes costs associated with energy production, start-up cost and shut-down cost along with profits. The resulting problem is a large scale nonlinear mixed-integer optimization problem for which there is no exact solution technique available. The solution to the problem can be obtained only by complete enumeration, often at the cost of a prohibitively computation time requirement for realistic power systems. This paper presents a hybrid algorithm which combines Lagrangian Relaxation (LR) together with Evolutionary Algorithm (EA) to solve the problem in cooperative and competitive energy environments. Simulation studies were carried out on different systems containing various numbers of units. The outcomes from different algorithms are compared with that from the proposed hybrid algorithm and the advantages of the proposed algorithm are briefly discussed.     

Scheduling of hydrothermal power systems

The authors present a method for scheduling hydrothermal power systems based on the Lagrangian relaxation technique. By using Lagrange multipliers to relax system-wide demand and reserve requirements, the problem is decomposed and converted into a two-level optimization problem. Given the sets of Lagrange multipliers, a hydro unit subproblem is solved by a merit order allocation method, and a thermal unit subproblem is solved by using dynamic programming without discretizing generation levels. A subgradient algorithm is used to update the Lagrange multipliers. Numerical results based on Northeast Utilities data show that this algorithm is efficient, and near-optimal solutions are obtained. Compared with previous work where thermal units were scheduled by using the Lagrangian relaxation technique and hydro units by heuristics, the new coordinated hydro and thermal scheduling generates lower total costs and requires less computation time     

Optimization-based scheduling of hydrothermal power systems withpumped-storage units

This paper presents an optimization-based method for scheduling hydrothermal systems based on the Lagrangian relaxation technique. After system-wide constraints are relaxed by Lagrange multipliers, the problem is converted into the scheduling of individual units. This paper concentrates on the solution methodology for pumped-storage units. There are, many constraints limiting the operation of a pumped-storage unit, such as pond level dynamics and constraints, and discontinuous generation and pumping regions. The most challenging issue in solving pumped-storage subproblems within the Lagrangian relaxation framework is the integrated consideration of these constraints. The basic idea of the method is to relax the pond level dynamics and constraints by using another set of multipliers. The subproblem is then converted into the optimization of generation or pumping; levels for each operating state at individual hours, and the optimization of operating states across hours. The optimal generation or pumping level for a particular operating state at each hour can be obtained by optimizing a single variable function without discretizing pond levels. Dynamic programming is then used to optimize operating states across hours with only a few number of states and transitions. A subgradient algorithm is used to update the pond level Lagrangian multipliers. This method provides an efficient way to solve a class of subproblems involving continuous dynamics and constraints, discontinuous operating regions, and discrete operating states     

遗传算法在电力系统日有功优化调度中的应用

随着电力市场的不断深入，系统的有功优化调度在电力系统运行中占有越来越重要的地位。针对这一特点，本文提出了在多约束条件下，寻求全网经济效益最优的算法，先用遗传算法求解机组组合，再用等微增率法求解负荷的最优分配，在求解的过程中，采用不同听方法来处理各种约束条件。通过模拟系统的实例验算表明了所提出的算法十分有效。     

Optimal Scheduling of Spinning Reserve with Transmission Constraints

An effective method is proposed to schedule spinning reserve optimally. The method considers the transmission constraint in the whole scheduling process. To get the feasible solution faster, transmission line limits are first relaxed using the Lagrangian Relaxation technique. In the economic dispatch, after unit generation and spinning reserve are allocated among the committed units to satisfy the system andunit constraints, the schedule is then modified by a linear programming algorithm to avoid line overloads. The schedule is then updated by a probabilistic reserve assessment to meet a given risk index. The optimal value of the risk index is selected via a cost/benefit analysis based on the tradeoff between the total Unit Commitment (UC) schedule cost and the expected cost of energy not served. Finally, a unit decommitment technique is incorporated to solve the problem of reserve over-commitment in the Lagrangian Relaxation–based UC. The results of reserve scheduling with the transmission constraint are shown by the simulation runs performed on the IEEE reliability test system.     

发电经济调度可行解判据及其求解方法

发电经济调度问题是一个经典混合整数规划问题,然而用拉格朗日松弛法得到的对偶解对原问题通常是不可行的,要获得可行解必须先得到一种可行的机组组合.本文分析了现有可行化条件中存在的问题,提出了一个易于检验的可行化条件,并证明它是充分必要的.随后,介绍了获得可行解的方法.     

A solution for unit commitment using Lagrangian relaxation combined with evolutionary programming

This paper proposes an approach which combines Lagrangian relaxation principle and evolutionary programming for short-term thermal unit commitment. Unit commitment is a complex combinatorial optimization problem which is difficult to be solved for large-scale power systems. Up to now, the Lagrangian relaxation is considered the best to deal with large-scale unit commitment although it cannot guarantee the optimal solution. In this paper, an evolutionary programming algorithm is used to improve a solution obtained by the Lagrangian relaxation method: Lagrangian relaxation gives the starting point for a evolutionary programming procedure. The proposed algorithm takes the advantages of both methods and therefore it can search a better solution within short computation time. Numerical simulations have been carried out on two test systems of 30 and 90 thermal units power systems over a 24-hour periods.     

电力市场环境下解决机组组合问题的新方法

机组组合问题是电力市场环境下编制短期发电计划所面临的主要问题,在满足各种约束条件的情况下,如何合理地开、停机组、以及负荷如何在运行的发电机组之间经济地分配是一个比较困难的问题,特别是由于发电机组出力上升、下降速度的限制,使这个问题一直没有很好的解决方法。提出一种组合优化方法解决这一问题,即用启发式方法确定机组组合,用分段线性规划算法分配功率,并满足各种约束条件,特别是可以处理发电机组出力上升、下降速度约束、经实际系统检验是一种非常有效的算法。