Fuzzy正项几何规划的对偶形式的研究

应用Ｆｕｚｚｙ值集的理论和α－截集的概念，在［１］的基础上，研究了Ｆｕｚｚｙ正项几何规划的对偶形式，证明了对偶定理和最优解的存在定理，导出了Ｆｕｚｚｙ正项几何规划的对偶算法．     

结合半正定规划和非线性规划模型的OPF混合优化算法研究

以内点法求解最优潮流(optimal power flow,OPF)的经典非线性规划模型已得到广泛应用,但无法保证解的全局最优性。而求解OPF的半正定规划模型,在一定条件下能获得全局最优解,但存在计算时间长和可能无法获得可行解的缺点。因此,文中提出一种结合非线性规划和半正定规划模型两者优势求解OPF问题的混合优化方法,以实现在更短的时间内获得全局最优解。首先,提出验证由内点法求解OPF非线性规划模型(nonlinear programming,NLP)所得解是否为全局最优的充分条件。若非全局最优,则基于OPF的半正定规划模型给出由该局部最优解出发的下降方向,并通过步长控制得到新的初值,交由内点法重新求解OPF的非线性规划模型。算例测试结果表明,该算法在避免求解完整半正定模型需耗费大量时间的同时,能够有效跳出非线性规划模型的局部最优解,收敛到全局最优解或更优的解。     

城网无功补偿规划的优化方法

通过对网络最优无功潮流计算方法和无功补偿容量最优配置规划方法的阐述和分析，建立正确的数学模型，运用线性规划方法任意选定电网的初始运行点，在初始运行点处对目标函数及运行约束方程进行线性化，而后运用线性规划求出控制电量的解。再经过潮流计算求出对应于“解”的电网所有运行点参数，在此运行点处对目标函数及运行约束方程进行线性化，重新用线性规划求解。这样经重复进行计算，逐步逼近非线性规划的解，最终得到城网无功补偿规划的优化方法。     

《简单的线性规划问题》教学设计

教材分析 本节课是北师大版普通高中《数学》必修5第三章《不等式》中《简单的线性规划问题》的第二课时,本节课既是上节课求最优解的巩固和发展,又是解决生活最优化问题的基础。在学生学习了平面区域的前提下,与学生共同探究最优解问题及其几何意义。     

基于数学优化的电力网规划模型的理论研究

本文指出了电力网规划模型固有的非线性特性,以及对其实施线性化的数学方法和过程。并且,应用数学优化中的库恩－塔克理论,论证了线性化后的规划模型与原始的非线性规划模型具有完全相同的最优解。从而为建立及求解电力网的线性规划模型提供了数学依据。     

基于灰色动态规划的梯级电站防洪发电效益研究

梯级电站防洪主要包括电站大坝防洪、库区上游及下游防洪问题,又需要保留汛期蓄水以供发电,由此就带来防洪与发电效率之间的优化问题。文中利用灰色动态规划进行了3级梯级电站的防洪与发电之间的优化计算,获得了最优解,并将其与一般线性规划求解进行了比较分析。因一般线性规划是静态的,不能适应研究对象系统的发展变化,解的漂移大。而灰色动态规划克服了这一缺点,获得了较为满意的优化效果。     

自适应进化规划及其在多目标最优潮流中的应用(Ⅱ)--基于自适应进化规划的多目标最优潮流

电力系统多目标最优潮流是一个极其复杂的非线性规划问题,其解算方法目前仍处于研究阶段,而开发高效、快速、可靠的最优潮流算法是一项相当艰巨的工作。鉴于此,文中探讨了自适应进化规划在电力系统多目标最优潮流应用中的问题。在优化模型、遗传操作等方面进行了研究,进一步拓展了电力系统最优潮流计算方法的应用前景。通过30节点IEEE试验系统的算例表明自适应进化规划算法十分有效,具有广泛的应用价值。     

自适应进化规划及其在多目标最优潮流中的应用（Ⅱ）：基于自适？…

电力系统多目标最优潮流是一个极其复杂的非线性规划问题,其解算方法目前仍处于研究阶段,而开发高效、快速、可靠的最优潮流算法是一项相当艰巨的工作。鉴于此,文中探讨了自适应进行规划在电力系统多目标最优潮流应用中的问题。通过３０节点ＩＥＥＥ试验系统的算例表明自适应进行规划算法十分有效,具有广泛的应用价值。     

自适应进化规划及其在多目标最优潮流中的应用(Ⅱ)--基于自适应进化规划的多目标最优潮流

电力系统多目标最优潮流是一个极其复杂的非线性规划问题,其解算方法目前仍处于研究阶段,而开发高效、快速、可靠的最优潮流算法是一项相当艰巨的工作.鉴于此,文中探讨了自适应进化规划在电力系统多目标最优潮流应用中的问题.在优化模型、遗传操作等方面进行了研究,进一步拓展了电力系统最优潮流计算方法的应用前景.通过30节点IEEE试验系统的算例表明自适应进化规划算法十分有效,具有广泛的应用价值.     

平抑高比例新能源发电功率波动的风-光-储容量最优配比

发展新能源是应对环境污染和能源危机的根本性措施,有助于推动“双碳”目标的实现。可再生能源发电固有的间歇性、波动性给电网规划和运行带来严峻挑战。针对高比例新能源电力系统,分析了以最小功率波动为目标的新能源和储能容量最佳配比。立足风光资源的互补性,构建了最小化系统功率波动的风光最优配比模型,并提出了基于线性规划的求解算法。最后建立了面向平滑新能源出力的储能容量配置参数线性规划模型,得到波动性指标关于储能容量的解析表达式,并根据成本确定了最优储能容量。所提方法为政策制定提供了可视化工具以及比单一最优解更加丰富的信息。     

Fuzzy Logic Based Successive LP Method for Reactive Power Optimization

This paper presents a new Successive Fuzzy Linear Programming (SFLP) method for Reactive Power Optimization (RPO) to minimize the transmission loss and improve the voltage profile. The SFLP method uses Fuzzy LP (FLP) model in the Successive Linear Programming (SLP) framework to solve the RPO problem. In the FLP model, the objective and each of the constraints are assigned a satisfaction parameter. The satisfaction parameter corresponding to the objective quantifies the degree of closeness of the objective in the current state to the optimum. The satisfaction parameter corresponding to a constraint describes the degree of enforcement of that constraint. By maximizing the minimum of these satisfaction parameters, the objective as well as the constraint enforcements are maximized. The SFLP method of RPO is efficient and reliable in scheduling systems having severe under-voltages and insufficient reactive power, as the method is capable of maximizing the enforcement of the violated load bus voltage constraints, minimizing the transmission loss while simultaneously enforcing all the other constraints strictly. This method uses compactly stored, factorized constant matrices in all the LP steps, both for the construction of the FLP model as well as for the power flow solution. The control variables used in this method are generator bus voltage magnitudes, reactive powers of switchable VAR sources, and on-load tap changer (OLTC) settings of transformers. The method was tested on IEEE test systems and on a practical electric utility system. The merits of the proposed method compared to the SLP method using non-fuzzy approach are brought out.     

An optimal design of single tuned filter in distribution systems

This paper proposes an optimal design of single tuned shunt passive filter for the Underground Ramsis Metro Substation (URMS) using linear programming technique as a conventional technique and fuzzy linear programming (FLP) technique as a modern technique. The optimal filter parameters are obtained to overcome the harmonics generated in the voltage and current waveforms, due to the non-linear characteristics of the rectifiers, which distort the voltage and current waveforms at the point of common coupling (PCC). The harmonic levels are analyzed at different loading conditions using the fast Fourier transform (FFT) on MATLAB optimization program. The proposed optimal design of harmonic filter is based on minimizing the cost of the filter parameters and its losses. Both techniques are applied on the system under study. From the results, the THD levels of the line current and the bus voltage are reduced to be within the standard limits. A comparison between the optimal design filters is carried out using the LP and FLP techniques. However, the lowest cost of filter is obtained using the FLP technique.     

一类矩阵反问题的最小二乘逼近解

通过求得一个特殊的投影算子，给出了在实反对称矩阵类中矩阵反问题的最小二乘解的一般形式，提供了求矩阵反问题的最小二乘解逼近解的数值方法．     

模糊Petri网络知识表示方法及其在变压器故障诊断中的应用

Petri网络理论以图形化的方法直观地描述了离散事件系统的各种关系和行为，且以网络理论、代数理论等作为数学基础，适合于描述异步并发现象的计算机系统模型和对并行及并发系统进行行为分析的有效工具，在人工智能领域中正得到越来越广泛的应用。该文从模糊产生式系统出发，提出一种模糊Petri网络知识表示方法及其严密的推理算法，论述了利用模糊Petri网络(FPN)进行知识表示及推理的矩阵运算算法，为模糊知识的表示提供了一种有效的工具，并首次将其应用于电力变压器故障诊断中，“描述了故障征兆与故障的关系，使用了比传统专家系统更深的知识。与传统的专家系统相比，利用此理论及方法仅仅使用简单的矩阵计算，大大减少诊断时间，提高了准确度。最后通过实例对此算法进行了测试，表明该模型方法快速、准确。     

Fault Location Observability Using Phasor Measurement Units in a Power Network Through Deterministic and Stochastic Algorithms

This article studies deterministic and stochastic algorithms for placing minimum number of phasor measurement units (PMUs) in a power system in order to locate any fault in the power system. The optimization problem is initially formulated in a mixed integer linear programing framework with binary-valued variables as well as in a binary integer linear programing model. Then, the optimization problem is formulated as an equivalent non-linear programing model, minimizing a quadratic objective function subject to equality non-linear constraints defined over a bounded and closed set. The problem is solved by using a Sequential Quadratic Programming algorithm. The non-linear program is illustrated with a 7-bus test system. Also, stochastic algorithms such as binary-coded genetic algorithm and particle swarm optimization have been implemented in solving the optimal PMU placement under fault condition. The accuracy of suggested algorithms is independent from the fault type and its resistance. The optimization models are applied to the IEEE systems. The numerical results indicate that the proposed algorithms locate minimizers at the optimal objective function value in complete agreement with those obtained by branch-and-bound algorithms.     

具有不连续非线性项的抛物型方程组解的存在性

本文研究具有不连续非线性项的抛物型方程组解的存在性.我们利用上下解方法和单调算子的不动点定理,证明了解的存在性.     

一类非线性退缩抛物型方程组解的唯一性

本文讨论一类非线性退缩抛物型方程组解的唯一性.在一定条件之下,得到一维的Field—Noyes 方程组第一边值问题广义解的唯一性结论.     

水电站群补偿径流调节的线性规划模型及其应用

本文阐述了水电站群径流补偿调节线性规划模型的思路、数学模型、算法和结构,并讨论了模型的目标函数问题。应用该模型在微机上成功地进行了水电站群的优化开发和电力系统的电源优选。该模型在理论上有一定发展,并具有计算简便和运行速度快的优点。     

APPLICATION OF EXTENDED EVOLUTIONARY PROGRAMMING TO SVC PLACEMENT

An extended evolutionary programming (EXEP) technique is proposed for optimal solution of the SVC placement in voltage stability enhancement. Multiple genetic transformation operators are used to ensure that the global optimal solution can be obtained. The problem is posed as the minimization of the function whose objectives are to increase the reactive power margin, the reactive power spinning reserve and the system voltage profile. At the same time it is required that the transmission losses are reduced and the additional cost of new SVC devices is minimal. All the operational inequality constraints are transformed to the objective function by using quadratic and cosine penalty functions. Numerical results show that EXEP technique is superior to simulated annealing(SA) technique.     

Implementing Fuzzy Reasoning Petri-Nets for Fault Section Estimation

Fuzzy reasoning Petri-nets (PNs) is a promising technique to tackle the complexities of power system fault section estimation. This paper addresses several key issues in implementing fuzzy reasoning PNs for fault section estimation, which include optimal design of structure of diagnosis models to avoid large matrix size, utilization of fuzzy logic parameters to effectively handle uncertainties, realization of matrix execution algorithm to achieve parallel reasoning and adaptability, and integration of more reliable input data to enhance estimation accuracy. Case studies are presented to demonstrate the estimation capability under complex scenarios. An implementation solution residing in a control center is proposed.