A tutorial description of an interior point method and itsapplications to security-constrained economic dispatch

The authors deal with the use of successive linear programming (SLP) for the solution of the security-constrained economic dispatch (SCED) problem. They tutorially describe an interior point method (IPM) for the solution of linear programming (LP) problems, discussing important implementation issues that really make this method far superior to the simplex method. A study of the convergence of the SLP technique and a practical criterion to avoid oscillatory behavior in the iteration process are also proposed. A comparison of the proposed method with an efficient simplex code (MINOS) is carried out by solving SCED problems on two standard IEEE systems. The results show that the interior point technique is reliable, accurate, and more than two times as fast as the simplex algorithm     

深度学习辅助约束辨识的电力市场快速出清方法

日前电力市场出清需要求解大规模安全约束经济调度问题,尽管实际采用线化处理方法,但需要考虑N－1场景下的大量安全约束,导致其规模庞大,难以快速求解。提出了一种深度学习辅助的日前市场快速出清方法,以满足快速出清计算场合的应用需求。首先,设计基于深度神经网络的安全约束经济调度模型计算框架,将深度学习技术应用于日前电力市场出清计算过程,兼顾安全约束经济调度模型的求解速度和求解精度;其次,提出面向起作用约束辨识的深度学习策略,从特征向量、深度神经网络结果处理2个方面,实现安全约束经济调度起作用约束集的辨识,并将其纳入日前市场出清模型,以简化模型的复杂度;最后,在接入新能源的IEEE 30标准测试系统中验证了所述方法的有效性。利用深度神经网络预辨识安全约束经济调度模型的起作用约束,有利于降低模型复杂度,提高日前市场出清的计算效率。     

深度学习辅助约束辨识的电力市场快速出清方法

日前电力市场出清需要求解大规模安全约束经济调度问题,尽管实际采用线化处理方法,但需要考虑N－1场景下的大量安全约束,导致其规模庞大,难以快速求解。提出了一种深度学习辅助的日前市场快速出清方法,以满足快速出清计算场合的应用需求。首先,设计基于深度神经网络的安全约束经济调度模型计算框架,将深度学习技术应用于日前电力市场出清计算过程,兼顾安全约束经济调度模型的求解速度和求解精度;其次,提出面向起作用约束辨识的深度学习策略,从特征向量、深度神经网络结果处理2个方面,实现安全约束经济调度起作用约束集的辨识,并将其纳入日前市场出清模型,以简化模型的复杂度;最后,在接入新能源的IEEE 30标准测试系统中验证了所述方法的有效性。利用深度神经网络预辨识安全约束经济调度模型的起作用约束,有利于降低模型复杂度,提高日前市场出清的计算效率。     

考虑经济性可靠性的输电网二层规划模型及混合算法

建立考虑经济性可靠性的输电网确定性二层线性规划模型,将可靠性问题以约束加入到经济性规划问题中,改变了传统输电网规划建模方式,实现规划方案在高可靠性条件下的经济性最优。模型上层规划目标采用线路建设成本最小,约束为待架线路数目约束;下层规划目标为切负荷最小,约束为常规运行约束,且严格满足N-1安全约束,实现最优规划方案的N-1安全运行要求。提出采用改进小生境遗传算法(improved niche genetic algorithm,INGA)和原始-对偶内点法(prime-dual interior point method,PDIPM)相结合的混合算法,并对上述模型进行求解,利用小生境遗传算法处理上层规划的整数变量,进行全局寻优;对下层规划采用原始-对偶内点算法进行快速求解,提高算法速度和收敛性。18节点系统和46节点系统的结果表明该模型和算法是有效的。     

Optimal reactive dispatch through interior point methods

An implementation of an interior point method to the optimal reactive dispatch problem is described. The interior point method used is based on the primal-dual algorithm and the numerical results in large scale networks (1832 and 3467 bus systems) have shown that this technique can be very effective to some optimal power flow applications     

Analysis of FACTS devices on Security Constrained Unit Commitment problem

This paper focuses on solving Security Constrained Unit Commitment (SCUC) problem using ABC algorithm incorporating FACTS devices. The objective of the SCUC problem is to obtain the minimum operating cost simultaneously maintaining the security of the system. The SCUC problem is decomposed into Unit Commitment (UC), the master problem and Security-Constrained Economic Dispatch (SCED) as the sub-problem. The existing generation constraints, such as hourly power demand, system reserves, and minimum up/down time limits, ramp up/down limits are included in the SCUC problem formulation. The ability of FACTS devices to control the power flow through designated routes in transmission lines and thereby reducing the overloading of lines are studied. The solution of SCUC problem is also analyzed during a single line outage contingency. The SCUC is carried out incorporating FACTS devices such as SVC, TCSC, STATCOM, SSSC, UPFC and IPFC. The modeling of the FACTS devices within the power system network and finding a suitable location are discussed. The SCUC has been solved and validated on an IEEE 118-bus test system and a practical South Indian 86 bus utility.     

A study of the homogeneous algorithm for dynamic economic dispatchwith network constraints and transmission losses

This paper presents a study of the homogeneous interior point (HIP) method for the economic dispatch problem that combines both independent blocks of constraints (generation demand balance, network flows) and coupling constraints (ramping) into a single optimization problem. By approximating the network constraints through the DC load flow, and the transmission losses through the B-matrix loss formula, the problem is reduced to a convex optimization problem that possesses nonlinear inequality constraints and free variables. The HIP algorithm is specialized in solving this problem, it yields either an approximate global optimum solution or detects possible infeasibility or unboundedness of the problem. The algorithm is tested on the IEEE 14, 30, 57, and 118 bus test systems dispatched over 10 half-hour intervals. The results show that the algorithm is practically efficient     

Application of pattern search method to power system security constrained economic dispatch with non-smooth cost function

Direct search methods are evolutionary algorithms used to solve optimization problems. (DS) methods do not require any information about the gradient of the objective function at hand while searching for an optimum solution. One of such methods is Pattern Search (PS) algorithm. This paper presents a new approach based on a constrained pattern search algorithm to solve a security constrained power system economic dispatch problem (SCED) with non-smooth cost function. Operation of power systems demands a high degree of security to keep the system satisfactorily operating when subjected to disturbances, while and at the same time it is required to pay attention to the economic aspects. Pattern recognition technique is used first to assess dynamic security. Linear classifiers that determine the stability of electric power system are presented and added to other system stability and operational constraints. The problem is formulated as a constrained optimization problem in a way that insures a secure-economic system operation. Pattern search method is then applied to solve the constrained optimization formulation. In particular, the method is tested using three different test systems. Simulation results of the proposed approach are compared with those reported in literature. The outcome is very encouraging and proves that pattern search (PS) is very applicable for solving security constrained power system economic dispatch problem (SCED). In addition, valve-point effect loading and total system losses are considered to further investigate the potential of the PS technique. Based on the results, it can be concluded that the PS has demonstrated ability in handling highly nonlinear discontinuous non-smooth cost function of the SCED.     

求解无功优化的非线性同伦内点法

在无功优化计算中，由于严格的节点电压限制，网络拓扑的变化或无功电源的不足等多种原因可能会导致原问题不存在最优解。采用常规的优化方法或内点方法还不能有交地检测出这种不可行问题。该文基于非线性同伦内点法提出了检测无功优化不可行问题的新算法，该算法不仅能在原问题有解的情况下求出近似的最优解，而且能通过同伦变量的值快速并准确地判别出原问题是否出现了不可行情况，并以IEEE30节点系统为试验系统，对采用非线性同伦内点法的优化计算结果的正确性与检测优化计算中出现的不可行问题的有效性进行了验证。     

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。     

SCUC／SCED问题分析

安全约束机组组合（SCUC）与安全约束经济调度（SCED）同时考虑电力系统运行的安全性和经济性,在国外受到广泛关注．基于现代混合整数规划（MIP）算法的SCUC近几年得到实际应用和快速发展,文中对SCUC／SCED研究的最新进展进行了综述。概述了SCUC问题的优化模型和算法的研究状况,分类介绍了基于MIP算法的SCUC研究进展．并分析和评述了主要方法、原理及其优缺点,进一步提出我国开展SCUC／SCED研究急待解决的问题。     

计及N-1安全准则的智能配电网多目标重构策略

智能配电网背景下,N-1安全准则是配电网安全运行中的重要准则,而现有文献中的配电网重构模型均未计及N-1安全准则,所得重构结果未必满足安全性要求。为解决这一基础性问题,文中提出了一种计及N-1安全准则的配电网多目标重构新策略。首先,基于配电系统安全域(DSSR)中安全距离这一概念,定义了安全距离均值、安全距离均衡度、安全距离均衡比3个量化描述N-1安全的指标。其次,给出了以降低网损和减小安全距离均衡比为综合优化目标的配电网多目标重构模型。然后,应用改进遗传和动态小生境差分进化的混合算法对该配电网多目标重构模型进行求解。最后,考虑静态重构和动态重构两种情境,通过算例对比所提模型与现有文献模型,结果均表明,文中模型所得重构结果满足N-1安全准则,综合考虑系统经济性、安全性下更优,验证了所提模型和求解算法的正确有效性。     

A Heuristic Constructive Algorithm for Capacitor Placement on Distribution Systems

This paper presents a heuristic constructive algorithm (HCA) for optimal capacitor placement on distribution systems. This is a nonlinear mixed integer optimization problem. In the proposed approach, the integer variables are represented using sigmoid function, thus interior point optimal power flow formulation can be applied to obtain sensitivity indexes based on Lagrange multipliers, reactive power, and bus voltage. The methodology is applied to two power distribution systems, and the results are compared with those obtained using a genetic algorithm approach.      

Contingency constrained optimal reactive power flow procedures forvoltage control in planning and operation

The paper presents a preventive secure contingency constrained approach to power system voltage profile optimization suitable both for VAr planning and for short term reactive scheduling. The solution of the problems is based upon the implementation of two optimal reactive power flow (ORPF) programs: the first relevant to determining a workable state (security aspect); and the second relevant to attaining the optimal and secure point (global target). The first ORPF is solved by recursively employing a linear programming algorithm, whilst the second is based on the Han-Powell algorithm. In the paper, emphasis is given to the introduction of the contingency constraints in the ORPF models. The N-1 security constraints are explicitly introduced in the programs in order to obtain an operating point preventive-secure with respect to a selected contingency set. The performances of the procedures are shown by presenting the numerical results obtained from their applications to a small test network and to the large ENEL transmission system     

Impact of the Transformer Tap-Ratio Control on the Electricity Market Equilibrium

In this paper, the primal-dual nonlinear interior point method has been used as a basis for the derivation of a novel supply function equilibrium (SFE) algorithm for modeling the strategic interactions in the electricity market, using the ac network model, which incorporates modeling of the transformer tap-ratio control. The algorithm is used to investigate the impact of transformer tap-ratio control on the electricity market equilibrium and the effect of the interactions between network constraints and transformer tap-ratio control. The interior point social welfare optimization problem is combined with the optimization problem for maximizing the profit of each strategic generating firm in the market. The final combined single-level SFE problem is solved iteratively based on solution techniques of the interior point method. Numerical examples illustrate the effect of network constraints and especially the impact of transformer tap-ratio control on market equilibrium.     

基于混沌优化与线性内点法的最优潮流算法

求解最优潮流是一项基本而重要的工作，文中将混沌优化与线性内点法相结合，提出了一种新的混合优化算法，并应用该方法进行电力系统最优潮流的计算。混沌优化方法利用混沌运动特定的内在遍历性、随机性和规律性等特点跳出局部最优点，接近最优点；同时，利用预测-校正原-对偶内点法在最优点的邻域内局部寻优，提高了收敛速度和求解精度。通过对IEEE 14、30和57节点试验电力系统的数值计算，验证了算法的有效性。     

华东网调日计划安全校核系统及其扩展

阐述了华东网调日计划安全校核工作的基本内容和特点;围绕安全校核系统的具体实现,介绍了该系统的模块组成、数学模型;在此基础上讨论了其核心计算方法——带约束的经济调度(SCED)算法,并比较了节能调度模式下该计算过程与安全校核系统的异同,对SCED的输入和输出数据稍加改造,增加优化模块,使其适用于节能调度;用实际算例说明了安全校核系统的作用。     

考虑电压约束裕度的无功优化及其内点解法

常规无功优化算法的目标函数一般为满足电压限制下的有功损耗最小,这将使优化后个别母线的电压非常接近其合格范围的上限,使电压合格率下降,成为系统安全运行的隐患。根据实际运行中对这一安全裕度的方法仍存在一些问题。根据实际运行中对这一安全裕度的模糊要求,该文提出了在常规算法中引入模糊约束以解决这一问题。采用原-对偶内点算法详细地推导了带有模糊安全约束裕度的逐次二次规划数学模型。算例的结果表明：带有模糊约束的逐次二次规划内点法可以实现在满足电压安全约束下的网损最小,其网损的损失很小,而优化后的电压合格裕度却有较大的增加。     

A PC based state estimator interfaced with a remote terminal unitplacement algorithm

In this paper a new remote terminal unit (RTU) placement algorithm is presented. The objective of this algorithm is to place a minimum set of RTUs which satisfies three important constraints of the problem-observability, absence of critical measurements, and reliability requirements defined in terms of RTU loss. The problem is solved in a single stage. The results of this algorithm are interfaced with a linear programming (LP) state estimator. This estimator only uses the voltage measurements, and the active and reactive power flows in the lines for the development of the coupled state-estimation Jacobian H-matrix. The injection measurements are not currently included, though in practice they can be easily added to the estimator model. The inclusion of the injection measurements will enlarge the use of the presented algorithm. The RTU placement algorithm and its link with the LP estimator are tested on IEEE standard bus systems. Using the proposed RTU set, the test results presented show that the LP estimator has very good filtering capabilities when operated with or without bad data, and that the loss of any RTU does not have any significant impact on the solution