Extraction of affine invariant features for shape recognition based on ant colony optimization

A new approach to extraction of affine invariant features of contour image and matching strategy is proposed for shape recognition.Firstly,the centroid distance and azimuth angle of each boundary point are computed.Then,with a prior-defined angle interval,all the points in the neighbor region of the sample point are considered to calculate the average distance for eliminating noise.After that,the centroid distance ratios（CDRs） of any two opposite contour points to the barycenter are achieved as the representation of the shape,which will be invariant to affine transformation.Since the angles of contour points will change non-linearly among affine related images,the CDRs should be resampled and combined sequentially to build one-by-one matching pairs of the corresponding points.The core issue is how to determine the angle positions for sampling,which can be regarded as an optimization problem of path planning.An ant colony optimization（ACO）-based path planning model with some constraints is presented to address this problem.Finally,the Euclidean distance is adopted to evaluate the similarity of shape features in different images.The experimental results demonstrate the efficiency of the proposed method in shape recognition with translation,scaling,rotation and distortion.

Optimal control of quadratic functionals for affine nonlinear systems

In this paper we analyze the optimal control problem for a class of afflne nonlinear systems under the assumption that the associated Lie algebra is nilpotent. The Lie brackets generated by the vector fields which define the nonlinear system represent a remarkable mathematical instrument for the control of affine systems. We determine the optimal control which corresponds to the nilpotent operator of the first order. In particular, we obtain the control that minimizes the energy of the given nonlinear system. Applications of this control to bilinear systems with first order nilpotent operator are considered.

OPTIMIZATIONOFTHECONTINUOUSAFFINITY－RECYCLEEXTRACTIONPROCESS

Single step and multi step CARE processes are optimized by computer simulations based on the mathematical model proposed previously. The product of purification factor and recovery yield is used as the objective function for optimizing a single step process. The objective function for the optimization of a multi step process is considered to obtain an anticipated product purity at a maximum recovery yield and a minimum number of CARE inividuals. Pairs of the operating conditions (eluant and affinity recycle flow rates) exist to give the maximums of above objective functions when membrane rejections to ligates and contaminants are equal in value. The optimum affinity recycle flow rate decreases with the increase of membrane rejections and equilibrium binding fractions of ligates. For a multi step process, when contaminants are rejected less than ligate, only one pair of the optimum eluant and affinity recycle flow rates exists.

Performance of Suboptimal Controllers for Affine-Quadratic Problems

In this article, affine-quadratic control problems are studied. Error bounds are derived for the difference between the performance indices corresponding to the optimal and a class of suboptimal controls. In particular, it is shown that the performance of these suboptimal controls is close to that of the optimal control whenever the error in estimating the costate initial condition is small.

EXACT LINEARIZATION BASED MULTIPLE-SUBSPACE ITERATIVE RESOLUTION TO AFFINE NONLINEAR CONTROL SYSTEM

To the optimal control problem of affine nonlinear system, based on differential geometry theory, feedback precise linearization was used. Then starting from the simulative relationship between computational structural mechanics and optimal control, multiple-substructure method was inducted to solve the optimal control problem which was linearized. And finally the solution to the original nonlinear system was found. Compared with the classical linearizational method of Taylor expansion, this one diminishes the abuse of error expansion with the enlargement of used region.

An Improved Affine-Scaling Interior Point Algorithm for Linear Programming

In this paper, an Improved Affine-Scaling Interior Point Algorithm for Linear Programming has been proposed. Computational results of selected practical problems affirming the proposed algorithm have been provided. The proposed algorithm is accurate, faster and therefore reduces the number of iterations required to obtain an optimal solution of a given Linear Programming problem as compared to the already existing Affine-Scaling Interior Point Algorithm. The algorithm can be very useful for development of faster software packages for solving linear programming problems using the interior-point methods.

Inertial Proximal ADMM for Separable Multi-Block Convex Optimizations and Compressive Affine Phase Retrieval

Separable multi-block convex optimization problem appears in many mathematical and engineering fields.In the first part of this paper,we propose an inertial proximal ADMM to solve a linearly constrained separable multi-block convex optimization problem,and we show that the proposed inertial proximal ADMM has global convergence under mild assumptions on the regularization matrices.Affine phase retrieval arises in holography,data separation and phaseless sampling,and it is also considered as a nonhomogeneous version of phase retrieval,which has received considerable attention in recent years.Inspired by convex relaxation of vector sparsity and matrix rank in compressive sensing and by phase lifting in phase retrieval,in the second part of this paper,we introduce a compressive affine phase retrieval via lifting approach to connect affine phase retrieval with multi-block convex optimization,and then based on the proposed inertial proximal ADMM for 3-block convex optimization,we propose an algorithm to recover sparse real signals from their(noisy)affine quadratic measurements.Our numerical simulations show that the proposed algorithm has satisfactory performance for affine phase retrieval of sparse real signals.

基于改进仿射算法的主动配电网区间调度

针对高渗透率分布式可再生能源的不确定性和仿射算法结果的保守性影响调度计划的问题,提出基于改进仿射算法的主动配电网区间优化调度模型及其求解方法。以区间变量表征分布式可再生能源中风机和光伏出力的不确定性,利用带有误差修正机制的灰色马尔可夫模型得到风机和光伏出力的区间预测值。建立综合考虑主动配电网运行约束和灵活性指标,以综合运行费用最低和净负荷波动最小为目标的主动配电网多目标区间优化调度数学模型。在仿射算法的非线性运算中引入区间泰勒公式,提出一种改进仿射算法并将其应用于主动配电网潮流计算,并通过CPLEX和INTLAB对调度模型进行联合求解。修改的IEEE 33节点系统的仿真结果表明,区间优化调度可为调度人员提供更直观的主动配电网状态量上、下界信息,而且所提方法的计算效率更高,所得区间结果的保守性、可靠性和有效性更优。

基于区间理论的油田综合能源系统优化规划

针对油田的能源结构和用能负荷的特征,构建了油田综合能源系统架构;考虑可再生能源出力的不确定性和油田多元负荷用能的随机性,建立了光伏、光热出力的区间模型,热负荷区间模型和基于价格型响应的电负荷区间模型;通过分析设备投资成本的时间价值和区域碳中和途径,建立一种计及源荷不确定性的综合能源系统规划模型,并结合仿射算法和区间序关系,将不确定性优化问题转化为确定性的多目标优化问题进行求解。算例分析表明,油田综合能源系统架构符合油田能源禀赋和负荷实际耦合情况,设备配置方案投资回收年限短,不确定性权重系数越高,投资越大,年净收益区间越大,结果验证了规划方法的有效性。与传统鲁棒凸规划优化方法相比,所提方法为决策者提供了满足区间约束的解集,避免了规划方案的保守性。

考虑净负荷不确定性的配电网负荷恢复仿射可调鲁棒优化方法

为应对负荷恢复过程中源荷双重不确定性问题,提出了基于仿射可调鲁棒优化的配电网负荷恢复调整策略。第1阶段基于净负荷预测场景,建立一个以最大化加权负荷恢复量为目标函数的优化模型,决策最优的负荷恢复量;第2阶段采用仿射策略,利用预算不确定集来描述净负荷的不确定性,构建考虑净负荷误差的负荷恢复调整方案。在求解过程中,对双线性变量进行对偶变换得到可快速求解的线性规划模型。最后,在改进33节点和123节点配电系统进行仿真验证,结果表明:相比于传统的鲁棒优化方法,该方法降低了优化结果的保守性,有助于加快负荷恢复,减小停电损失。

基于点估计仿射可调鲁棒优化的含储能电力系统实时调度

为应对大规模风电的接入,建立一种机组与储能联合参与自动发电控制的电力系统实时调度模型,并提出一种点估计仿射可调鲁棒优化来处理风电不确定性。不同于传统仿射可调鲁棒调度优化基准运行成本,点估计仿射可调鲁棒调度优化期望运行成本以提高系统经济性。提出利用确定性的点估计法来实现对期望运行成本的快速、精确评估。所提模型为一混合整数双线性约束问题,采用一种“预估-矫正”的凸化方法来求解该难题,预估阶段对储能的状态变量进行松弛,而矫正阶段直接对其状态变量进行矫正。最后,引入一种凸函数差优化进一步凸化2个阶段的双线性约束问题,以提高含储能实时调度的求解质量。在IEEE39、118以及300节点3个系统的仿真验证了所提模型及方法的有效性。

基于非线性仿射的风电场电压实时计算和优化方法

该文提出一种基于非线性仿射的风电场电压实时计算和优化方法。首先,以网损和并网电压波动综合最小为目标,建立风电场多时段动态无功优化模型,利用半不变量法分析风电功率不确定性对机端电压的影响,采用改进内点法实现模型的高效求解;其次,提出一种非线性仿射方法,快速准确地获得计及风电功率波动后的系统电压状态,并通过计算风机无功调节量来实现系统电压实时优化;再次,设计考虑风电功率对机端电压和并网电压综合影响的事件触发算法,降低风电功率波动平缓时风机的无功控制频率;最后,在我国某实际风电场的仿真试验表明,非线性仿射法能够快速获得系统实时电压状态,电压实时优化方法能够有效地防止机端电压越限并减小并网电压波动。

基于仿射可调鲁棒的非预期全场景可行机组组合

非预期性是指当前决策无法依赖于未来尚未实现的不确定参数,是电力调度时序决策的因果逻辑和基本原则。全场景可行性是指不确定参数所有可能的实现值都存在一种可行决策结果与之对应,是电力调度的最终目标。随着新能源的大规模并网,电力系统的运行需要应对显著的不确定性,因此在电力调度的过程中考虑决策过程的非预期性并使决策结果满足全场景可行性变得愈发重要。为此,该文探讨非预期性和全场景可行性的内在机理,并构造非预期性约束和满足全场景可行且场景数目有限的场景集;然后,建立一种基于场景的非预期全场景可行机组组合模型,以提供满足全场景可行性的机组组合结果。鉴于上述机组组合模型的规模巨大且求解困难,利用仿射可调鲁棒模型处理全场景可行机组组合问题,提出基于仿射可调鲁棒的非预期全场景可行机组组合模型。该模型仅以少量保守性和最优性损失,换取了模型规模的指数级显著减小和问题求解效率的显著提升,可以被认为是非预期全场景可行机组组合问题的有效解决方案。最后,基于IEEE-118测试系统,详细分析考虑决策过程非预期性和决策满足全场景可行性在电力调度中的求解效率和保守性,论证所提基于仿射可调鲁棒的非预期全场景可行机组组合模型的优势。

追踪源荷实时变化的仿射最优电-气能流在线计算方法

随着新能源渗透率的逐步提高,电-气互联系统的运行态势更为复杂多变。为响应源荷的实时变化,该文提出一种仿射最优电-气能流在线计算方法。首先,利用泰勒展开与隐式有限差分法构建天然气动态模型,并采用流速基值自适应校正方法提高模型准确性。其后,利用仿射算术描述系统的源荷不确定性,将最优能流由确定域拓展至仿射域,构建仿射最优电-气能流模型。在此基础上,通过离线优化获取最优调度方案关于噪声元的仿射解析表达式,利用噪声元追踪源荷的实时变化,进而在线获取决策方案。所提方法依据即时信息快速决策,可满足实时调度需求。最后,通过算例分析验证了所提动态模型的准确性,表明所提在线方法的调度性能接近具有完备预测信息的最优调度。

计及新能源出力相关性的多能源微网仿射实时优化调度

为计及新能源出力相关性对多能源微网运行的影响,并响应源荷实时变化,提出一种计及新能源出力相关性的多能源微网仿射实时优化调度方法。首先,在多能源微网中引入Kalina循环,实现热电联产机组的灵活经济输出。其次,考虑源荷不确定性以及风光出力相关性对多能源微网运行的影响,构建并求解计及风光出力相关性的多能源微网仿射优化模型。再次,在获得优化方案变化范围的基础上,实时计算各仿射噪声元的取值,从而获取多能源微网实时调度轨迹。最后,仿真结果验证了所提方法能够充分计及不确定性和相关性的双重影响,有效应对源荷实时变化,并提升系统运行经济性。

基于多面体不确定集合的电力系统灵活性量化评估方法

随着风电、光伏等新能源接入比例的不断提高,源荷不确定性增强扩大了电力系统的运行灵活性需求。为准确量化电力系统的灵活性需求,制定兼顾灵活性与经济性的优化方案,提出了一种基于多面体不确定集合的电力系统灵活性量化评估方法。首先,采用多面体不确定集合量化多个光伏电站出力的波动性、不确定性及相关性特征,进而分析净负荷波动区间,构建电力系统灵活性需求量化模型。其次,基于仿射策略建立考虑灵活性需求的仿射可调鲁棒优化模型,并将所建立的鲁棒优化模型转化为混合整数线性规划模型进行求解。最后,基于6节点系统与IEEE 57系统,在不同不确定性场景下对比所提模型的优化结果,验证了该方法在系统的灵活性需求量化评估的有效性。

基于AP-WOA-GRU的分布式光伏集群电压越限动态预测

针对整县光伏背景下规模化分布式光伏接入配电网导致的电压波动问题,提出了一种基于近邻传播聚类(affinity propagation,AP)与鲸鱼算法(whale optimization algorithm,WOA)优化门控循环单元(gated recurrent unit,GRU)的分布式光伏集群电压越限预测方法。首先,在考虑分布式光伏地理坐标气象特征的基础上,添加基于配电网节点负荷密度因素的位置特征,采用近邻传播聚类方法,在不指定聚类数目的情况下划分具有近似气象特征和地理位置特征的分布式光伏集群,提高模型训练效果及适应性;然后,采用鲸鱼优化算法全局搜索GRU模型的最优训练参数,进一步提高模型的训练速度和预测精度;最后,利用WOA-GRU组合模型实现配电网节点电压与环境温度、光照强度的关联匹配,进而实现区域配电网电压波动及电压越限情况的整体预测。实验证明:所提出的方法能够有效提高预测精度及训练速度,强化预测模型的适应能力,具有较好的经济性和实用性。

基于DG不确定仿射模型的综合能源系统低碳优化规划方法

针对风电、光伏等新能源分布式发电系统(distributedgenerator,DG)受环境因素变化导致出力不确定、现有碳交易模型交易价格固定导致减碳成本增多的问题,提出基于DG不确定仿射模型的综合能源系统低碳优化规划方法。首先,根据环境条件建立基于矩阵形式仿射算法的DG出力模型,降低DG出力不确定性对综合能源系统优化规划的影响。其次,将碳排放量作为惩罚措施引入综合能源系统优化规划中,改进传统碳交易模型,降低综合能源系统碳排放量。然后,基于差分进化粒子群优化算法,对建立的综合能源系统低碳规划模型求解,避免算法在寻优过程陷入局部最优。最后,在IEEE33节点系统上的仿真结果表明,所提规划方法比传统随机优化和区间优化规划方法分别降低了8.68%和2.93%的总投资成本,比传统固定碳交易价格模型降低了6.28%的碳排放量。

Global and Local Convergence of a New Affine Scaling Trust Region Algorithm for Linearly Constrained Optimization

Chen and Zhang [Sci. China, Set. A, 45, 1390-1397 （2002）] introduced an affine scaling trust region algorithm for linearly constrained optimization and analyzed its global convergence. In this paper, we derive a new affine scaling trust region algorithm with dwindling filter for linearly constrained optimization. Different from Chen and Zhang＇s work, the trial points generated by the new algorithm axe accepted if they improve the objective function or improve the first order necessary optimality conditions. Under mild conditions, we discuss both the global and local convergence of the new algorithm. Preliminary numerical results are reported.

Distributionally Robust Optimal Dispatch of Virtual Power Plant Based on Moment of Renewable Energy Resource

Virtual power plants can effectively integrate different types of distributed energy resources,which have become a new operation mode with substantial advantages such as high flexibility,adaptability,and economy.This paper proposes a distributionally robust optimal dispatch approach for virtual power plants to determine an optimal day-ahead dispatch under uncertainties of renewable energy sources.The proposed distributionally robust approach characterizes probability distributions of renewable power output by moments.In this regard,the faults of stochastic optimization and traditional robust optimization can be overcome.Firstly,a second-order cone-based ambiguity set that incorporates the first and second moments of renewable power output is constructed,and a day-ahead two-stage distributionally robust optimization model is proposed for virtual power plants participating in day-ahead electricity markets.Then,an effective solution method based on the affine policy and second-order cone duality theory is employed to reformulate the proposed model into a deterministic mixed-integer second-order cone programming problem,which improves the computational efficiency of the model.Finally,the numerical results demonstrate that the proposed method achieves a better balance between robustness and economy.They also validate that the dispatch strategy of virtual power plants can be adjusted to reduce costs according to the moment information of renewable power output.