Augmented Lagrange Hopfield network based Lagrangian relaxation for unit commitment

This paper proposes an augmented Lagrange Hopfield network based Lagrangian relaxation (ALHN-LR) for solving unit commitment (UC) problem with ramp rate constraints. ALHN-LR is a combination of improved Lagrangian relaxation (ILR) and augmented Lagrange Hopfield network (ALHN) enhanced by heuristic search. The proposed ALHN-LR method solves the UC problem in three stages. In the first stage, ILR is used to solve unit scheduling satisfying load demand and spinning reserve constraints neglecting minimum up and down time constraints. In the second stage, heuristic search is applied to refine the obtained unit schedule including primary unit de-commitment, unit substitution, minimum up and down time repairing, and de-commitment of excessive units. In the last stage, ALHN which is a continuous Hopfield network with its energy function based on augmented Lagrangian relaxation is applied to solve constrained economic dispatch (ED) problem and a repairing strategy for ramp rate constraint violations is used if a feasible solution is not found. The proposed ALHN-LR is tested on various systems ranging from 17 to 110 units and obtained results are compared to those from many other methods. Test results indicate that the total production costs obtained by the ALHN-LR method are much less than those from other methods in the literature with a faster manner. Therefore, the proposed ALHN-LR is favorable for large-scale UC implementation.     

Reserve constrained multi-area economic dispatch employing differential evolution with time-varying mutation

For a power pool that involves several generation areas interconnected by tie-lines, the objective of economic dispatch (ED) is to determine the most economical generation dispatch strategy that could supply the area load demands without violating the tie-line capacity constraints. The objective of multi-area economic dispatch (MAED) is to determine the generation levels and the interchange power between areas which would minimize total fuel cost while satisfying power balance constraint, upper/lower generation limits, ramp rate limits, transmission constraints and other practical constraints. In reserve constrained MAED (RCMAED) problem inter-area reserve sharing can help in reducing the operational cost while ensuring that spinning reserve requirements in each area are satisfied. The tie-line limits too play a pivotal role in optimizing the cost of operation. The cost curves of modern generating units are discontinuous and non-convex which necessitates the use of powerful heuristic search based methods that are capable of locating global solutions effectively, with ease. This paper explores and compares the performance of various differential evolution (DE) strategies enhanced with time-varying mutation to solve the reserve constrained MAED (RCMAED) problem.The performance is tested on (i) two-area, four generating unit system, (ii) four area, 16-unit system and (iii) two-area, 40-unit system. The results are found to be superior compared to some recently published results.     

采用混合智能算法的含风电电力系统多目标优化调度

为了增强含风电电力系统的安全性和稳定性,提出一种计及运行风险及备用成本的含风电电力系统环境经济调度新模型。在目标函数中加入了系统运行风险指标和正、负旋转备用成本;增加了系统可靠性约束条件,确保了较低的系统运行风险,并同时获取正、负旋转备用量。采用一种新型高效的场景生成技术来描述风电功率的随机性。基于花授粉算法及差分进化算法提出一种具有时变模糊选择机制的多目标优化算法。将所提模型及求解方法在具有一个并网风电场的4机组系统中进行仿真。分析了各参数变化对系统运行的影响,并与其他两种启发式智能算法进行比较,验证了所提模型及算法的可行性和有效性。     

旋转备用的经济分配及其内点法实现

在最优潮流中,发电机组出力通常是独立变量,然而系统的旋转备用约束增加了发电机组出力间的耦合关系。基于非线性内点法针对实时旋转备用最优分配问题提出了一种解耦算法,使得发电机约束矩阵和网络约束矩阵在最优潮流中能够单独进行得到。进一步推导得到一个降阶的KKT(Karush-Kuhn-Tucker)系统,其规模由网络自身大小决定,仅通过修改扩展海森矩阵元素即可计及旋转备用约束的影响,并使用先进的超级稀疏技术全面分析、研究了该降阶KKT系统的稀疏结构。该算法涉及的旋转备用也包括了切负荷。     

Unit commitment using Lagrangian relaxation and particle swarm optimization

Unit commitment (UC) is a NP-hard nonlinear mixed-integer optimization problem. This paper proposes ELRPSO, an algorithm to solve the UC problem using Lagrangian relaxation (LR) and particle swarm optimization (PSO). ELRPSO employs a state-of-the-art powerful PSO variant called comprehensive learning PSO to find a feasible near-optimal UC schedule. Each particle represents Lagrangian multipliers. The PSO uses a low level LR procedure, a reserve repairing heuristic, a unit decommitment heuristic, and an economic dispatch heuristic to obtain a feasible UC schedule for each particle. The reserve repairing heuristic addresses the spinning reserve and minimum up/down time constraints simultaneously. Moreover, the reserve repairing and unit decommitment heuristics consider committing/decommitting a unit for a consecutive period of hours at a time in order to reduce the total startup cost. Each particle is initialized using the Lagrangian multipliers obtained from a LR that iteratively updates the multipliers through an adaptive subgradient heuristic, because the multipliers obtained from the LR tend to be close to the optimal multipliers and have a high potential to lead to a feasible near-optimal UC schedule. Numerical results on test thermal power systems of 10, 20, 40, 60, 80, and 100 units demonstrate that ELRPSO is able to find a low-cost UC schedule in a short time and is robust in performance.     

Solving dynamic economic dispatch problem with security constraints using bacterial foraging PSO-DE algorithm

This paper presents a heuristic optimization methodology, namely, Bacterial foraging PSO-DE (BPSO-DE) algorithm by integrating Bacterial Foraging Optimization Algorithm (BFOA), Particle Swarm Optimization (PSO) and Differential Evolution (DE) for solving non-smooth non-convex Dynamic Economic Dispatch (DED) problem. The DED problem exhibits non-smooth, non-convex nature due to valve-point loading effects, ramp rate limits, spinning reserve capacity, prohibited operating zones and security constraints. The proposed hybrid method eliminates the problem of stagnation of solution with the incorporated PSO and DE operators in original bacterial foraging algorithm. It achieves global cost by selecting the bacterium with good foraging strategies. The bacteria with good foraging strategies are obtained in the updating process of every chemo-tactic step by the PSO operator. The DE operator fine tunes the solution obtained through bacterial foraging and PSO operator. A 3- and 7-unit systems for static economic dispatch, a 26-bus, 6-generator test system and an IEEE 39-bus, 10-unit New England test systems are considered to show the effectiveness of the proposed method over other methods reported in the literature.     

旋转备用对电网可靠性的影响及优化配置研究

旋转备用(Spinning Reserve,SR)的不同分配方案会导致不同的电网可靠性水平。从改善大电网运行可靠性的角度出发,综合考虑机组类型和爬坡速率、元件可靠性参数、网络拓扑结构以及传输容量限制等因素,将SR的优化分配纳入到最优负荷削减模型中。利用该模型不等式约束中控制参数的拉格朗日乘子的物理意义,推导出系统电力不足期望对各机组备用容量的灵敏度表达式,提出了根据该灵敏度结果进行备用优化配置的启发式思路。同时以SR成本与用户停电损失之和最小为目标,通过同步联合优化确定SR的总量与配置方案。RBTS测试系统的仿真结果表明了所提方法的有效性和正确性。     

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.     

一种考虑网络损耗及线路过负荷的火力发电机起停计划方法

以面向实际应用为目的，提出了一种考虑输电网络损耗及线路过负荷约束的火力发电机起停计划方法。首先用动态规划法建立一个不含约束条件的初始解，然后运用启发式方法对初始解进行修正使之逐个满足各约束条件得到运行可能解，并通过修改各发电机的起动优先顺序使此过程反复进行直至得到（准）最佳解。在此过程中引入最优潮流计算考虑输电网络损耗及线路过负荷等网络因素对发电机起停计划的影响成为可能，并提出一种调节发电机出力和改变发电机起停计划相结合的消除线路过负荷的方法。在一个8机44母线的测试系统上对提案方法进行了各种条件下的试算，验证了所提出的方法对解决考虑网络因素影响的发电机起停计划问题有效性。计算结果还表明：不仅线路过负荷起停计划问题的有效性。计算结果还表明：不公线路过负荷约束，网络损耗也对发电机起停 计划有较大影响。     

Control area performance improvement by extended securityconstrained economic dispatch

An algorithm for solving the extended security constrained economic dispatch (ESCED) problem with real-time economic dispatch grade speed and reliability is presented. The ESCED problem is formulated by adding a regulating margin and ramp rate constraints to the network security constrained economic dispatch problem previously solved by the CEDC algorithm. Starting with Newton's method to optimize the Lagrangian, the ESCED is developed by superimposing on Newton's method eight major components called tracking start initialization, hessian pre-elimination, implicit dual variable calculations, regulating margin sensitivity coefficient calculations, traumatic event evaluation, constraint relaxation, implicit ramp rate constraint implementation, and relaxed incremental cost calculations. Test results are also presented     

适应大规模风电接入的电力系统旋转备用优化模型与求解

以经济性为评价指标,综合考虑系统有功平衡、机组爬坡和有功约束、节点电压约束、线路热稳极限和旋转备用总量需求等条件,建立了含风电的随机最优模型。通过场景生成和消减,建立了风功率的随机模型,并最终得到了在预测误差范围之内的10种风功率出力场景。在求解算法方面,引入了基于模糊聚类的改进小生境遗传算法,并在IEEE10机39节点系统进行了仿真验算,得到系统在多个场景下的出力曲线和旋转备用容量要求。结果表明,改进小生境遗传算法与其它算法相比,在保证系统安全运行的前提下,可以有效降低系统的运行费用。     

发电厂热备用容量的优化分配和成本分析

在竞争的发电市场环境下，备用作为一种重要的辅助服务，其成本分析是一个急待解决的问题，对发电厂热备用容量进行优化分配和成本分析，采用电能收益和备用容量收益总和最大化的目标函数。解算方法首先是根据发电厂总的发电负荷约束获得机组的经济组合，其次是将负荷在各机组间进行经济分配实现热备用容量的优化分配，热备用容量的成本采用其机会成本等值，方法简单，计算结果符合工程实际，研究结果表明，发电厂在计及备用收益和满足发电机组最低出力约束的条件下开机台数越多总收益也越大；在给定的时段和相应的电能电价下，备用容量成本随发电厂出力的增加而增加，在给定的时段和相应的发电出力下，备用容量成本随电价的增加而有较大的增加。     

含抽水蓄能电网安全约束机组组合问题的混合整数线性规划算法

抽水蓄能机组的投运对电网发电调度计划的制定具有很大影响,建立了含抽水蓄能机组电网的安全约束机组组合模型。以考虑了抽水蓄能机组启停费用的所有机组总运行费用为目标函数,根据抽水蓄能机组的不同运行工况给出旋转备用容量的解析表达式,同时在系统功率平衡约束中考虑了网络损耗的影响,并考虑了抽水蓄能机组的运行调度约束及网络安全约束。为了保证模型求解的可靠性和提高模型求解的计算效率,将目标函数进行分段线性化,并根据抽水蓄能机组的运行特点将其旋转备用容量约束等价转化为线性表达式。同时采用一种动态分段线性化方法近似逼近网络损耗,从而将机组组合模型转化为混合整数线性规划模型,并采用成熟的数学优化求解器CPLEX进行求解。对某实际23机306节点电网算例的计算结果表明,所提出的混合整数线性规划调度模型的网损逼近效果合理正确,算法求解速度快,具有较好的工程实用价值。     

基于随机规划的正负旋转备用容量求解方法

为研究正负旋转备用容量对电力系统运行费用的影响,提出了一种随机规划二阶段补偿模型,其目标函数包括计划运行费用和补偿费用。在不同正负备用容量情况下,采用拉格朗日松弛法和Monte Carlo模拟对模型进行求解,结果表明：系统的总运行费用随着负备用的增加始终单调递增; 当系统中负荷和风电功率的随机性较强时,最大和最小正旋转备用之间存在最优值使得总运行费用最小。最后采用粒子群(PSO)智能算法对10机系统的最优正旋转备用容量进行了求解。     

Energy and ancillary service dispatch through dynamic optimal power flow

This paper presents an approach based on dynamic optimal power flow (DOPF) to clear both energy and spinning reserve day-ahead markets. A competitive environment is assumed, where agents can offer active power for both demand supply and ancillary services. The DOPF jointly determines the optimal solutions for both energy dispatch and reserve allocation. A non-linear representation for the electrical network is employed, which is able to take transmission losses and power flow limits into account. An attractive feature of the proposed approach is that the final optimal solution will automatically meet physical constraints such as generating limits and ramp rate restrictions. In addition, the proposed framework allows the definition of multiple zones in the network for each time interval, in order to ensure a more adequate distribution of reserves throughout the power system.     

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。     

考虑输电网络影响的火电机组优化组合的一种实用算法

提出一种考虑输电网络损耗及线路过负荷的火电机组优化组合的实用算法。用动态规划法建立一个初始解,运用启发式手法对初始解进行修正,使之逐个满足各约束条件,得到运行可能解,并通过更新发电机起动优先顺序使此过程反复进行直至得到(准)最佳解。在求解过程中引入最优潮流计算,使考虑输电网络损耗及线路过负荷等网络因素对发电机组优化组合的影响成为可能,并提出一种调节发电机出力和改变发电机组合相结合的消除线路过负荷的方法。在IEEE-118母线(36机)系统上对所提出的算法进行了各种条件下的仿真计算,考察了网络损耗及线路过负荷对发电机组优化组合的影响,验证了所提算法对解决考虑输电网络因素影响的发电机组优化组合问题的有效性。     

基于局部随机搜索粒子群优化算法的电站短期发电优化调度

为提高粒子群优化(PSO)算法搜索精度、加快后期收敛速度,提出一种新的PSO算法,即局部随机搜索PSO算法。该算法用于求解电力系统的短期发电优化调度问题时,不仅要求满足电站实际运行中的系统负荷平衡约束,而且要考虑机组爬坡约束、出力限制区约束等非线性约束。给出了局部随机搜索PSO算法的步骤及短期发电优化调度问题求解方法。通过应用所提出的算法和其他文献提出的PSO算法、改进快速进化规划(IFEP)算法对15机系统的优化调度计算相比,证明所提出的算法最优解的发电费用最低,分别减少了3.8%和1%。     

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。     

基于Queen-bee进化的遗传算法在电力系统经济调度中应用

为提高遗传算法的寻优能力,引入模拟自然界蜂王繁殖的改进型遗传算法(QEBGA)。概述了QEBGA的实现过程,指出基本遗传算法(SGA)采用轮盘赌选择机制选择种群个体,以普通变异算子对种群作变异操作;而QEBGA采用启发式选择机制选择种群个体,按比例分别以普通变异算子和强变异算子对种群作变异操作。详述了电力系统经济调度问题表述为极小化下的总费用函数及约束优化问题。最后,用6台发电机系统和13台发电机系统的模拟实验比较了QEBGA和SGA两种算法在优化性能上的差异,实验结果说明了相同种群规模下,QEBGA的寻优时间小于SGA;系统规模越大,QEBGA在计算精度上的优势就越突出。