An efficient brute-force solution to the network reconfigurationproblem

The authors suggest a method for determining a minimal-loss radial configuration for a power distribution network, using an exhaustive search algorithm. While exhaustive, the method is highly efficient, deriving its efficiency from the use of graph-theoretic techniques involving semi-sparse transformations of a current sensitivity matrix. The algorithm can he applied to networks of moderate size and has advantages over existing algorithms for network reconfiguration in that it guarantees a globally optimal solution (under appropriate modeling assumptions), and is easily extended to take account of phase imbalance and network operation constraints. A 33-bus example is used to demonstrate the operation of the algorithm     

基于网络流和内点法的电力系统动态经济调度

该文用线性约束网络流来描述电力系统动态经济调度问题,它在计及机组出力上下界约束和输电元件传输功率上下界约束的同时,也考虑了电力网络中功率的流动应遵循的自然规律—K irchhoff定律,确保了网络流模型解与直流模型解的一致性,并用内点法进行求解。内点法克服了传统方法难以精确处理不等式约束的弊端,使计算结果更精确。同时采用变量重组、矩阵既约和约束松弛技术,减少计算量,加快了计算速度。计算结果表明:该文方法是可行和有效的。     

Order Reduction of Power Systems by Modal Truncated Balanced Realization

In this paper, a general approach for constructing reduced-order models of power system models based on a truncated balanced realization (TBR) linear reduction procedure is described. The method enables efficient computation of Gramian covariance matrices in terms of the system frequency response, and it can be used for control design and sensitivity analysis. The method guarantees convergence of the controllability and observability Gramians and avoids the need for frequency sweep of the transfer function matrix. A key innovation for the TBR-based reduced-order models introduced in this paper is the use of modal information to approximate the controllability and observability Gramians. With this approach, the connection between the linear system modes and the Gramians is clarified, and the contribution of critical system motion modes to the collective dynamics is readily determined. Conditions for convergence of the model and approximation methods are then investigated, and the issues of accuracy, applicability, and computational effort are discussed. The technique is tested on two real-world test power systems.     

含暂态能量裕度约束多故障最优潮流计算

借助暂态能量裕度对发电机有功和无功出力的解析灵敏度，将暂态能量裕度约束直接加入最优潮流模型中，建立含暂态能量裕度约束多故障最优潮流逐次线性规划模型，采用单纯形法求解，取得了较好的效果。此外，还提出了根据大步长单故障最优潮流近似计算获得的暂态能量裕度进行故障扫描方法，并寻找到同一失稳模式下影响系统稳定的关键故障，验证了满足关键故障稳定性要求的最优潮流解可以同时满足同失稳模式下的其它故障的稳定约束。新英格兰10机39节点系统的最优潮流及暂态稳定计算验证了所提方法的有效性。所有优化结果均用一个在电力系统中广泛使用的暂态稳定仿真程序进行了验证。     

Design of linear phase FIR filters via linear complementarity problem approach

In this paper, the design of constrained linear phase finite impulse response (FIR) filters is considered. The problem is formulated as a linear complementarity problem (LCP), which is solved using Lemke's algorithm. The LCP is a refined mathematical formalism with useful theoretical results. The digital filters presented meet efficiently the specifications of the magnitude response error. The used algorithm is a direct one and therefore, there is no need for matrix inversion. However, in the iterative methods that are frequently used, the bulk of the design computation is concerned with the evaluation of matrix inversion in order to solve a system of equations. Examples to illustrate the proposed method are presented. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

电力市场下发电机组计划检修模型

发电机组的计划检修作为防止机组老化失效的主要方法,在确保电力系统可靠运行方面起着重要作用。文中对市场环境下机组检修策略模型及算法进行了综述,并提出了进一步研究的问题。在市场环境下,制定机组检修计划时应当考虑系统运行的可靠性和发电公司的经济利益2个方面。通常,首先由发电公司确定本公司机组的计划检修时段,然后由独立系统运营商（ISO）考虑系统可靠性充裕度后按一定的原则调整机组检修计划;前者确保了发电公司的经济利益,体现了其独立的经济实体地位,后者保证了系统的安全可靠运行。对于该优化问题,一般采用遗传算法、模拟退火算法等启发式方法或者整数规划法、Benders解耦法等数学规划方法加以求解。     

Delay‐dependent model reduction for continuous‐time switched state‐delayed systems

This paper studies the problem of exponential H_∞ model reduction for continuous‐time switched delay system under average dwell time (ADT) switching signals. Time delay under consideration is interval time varying. Our attention is focused on the construction of the desired reduced order models, which guarantee that the resulting error systems under ADT switching signals are exponentially stable with an H_∞ norm bound. By introducing a block matrix and making use of the ADT approach, delay‐dependent sufficient conditions for the existence of reduced order models are derived and formulated in terms of strict linear matrix inequalities (LMIs). Owing to the absence of non‐convex constraints, it is tractable to construct an admissible reduced order model. The effectiveness of the proposed methods is illustrated via two numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

An integrated technico-economical methodology for solving reactivepower compensation problem

This paper provides a trade-off methodology for the solving reactive power compensation (RPC) problem. It is based on the full integration of two technical and economical aspects of the problem, that were previously considered either separately or combined as an objective function and its constraints. Minimization of the cost-economic function is based on the use of Y-matrix method. Voltage profile improvement is accomplished through a simplex algorithm based on the use of a sensitivity matrix (S). This paper proposes a modified computation of S in order to fit within the overall integration. The affinity of both technical and economical approaches, promotes this integration: both are based on linear programming techniques, coupled to the same load flow, and use similar Y and Z matrix components. The symmetry and sparsity characteristics of the Y matrix allow the reduction of the required mathematical calculations. This trade-off technique is tested on the IEEE 39-bus system. The modified simplex approach resulted in lower reactive power allocation while maintaining competitive voltage profile. Tests also showed that neither the technical nor the economical solution is complete by itself. A large scope of possible RPC allocations, is therefore provided to the decision maker to define his priorities and seek an `optimal decision'     

Weighted least absolute value power system state estimation using rectangular coordinates and equivalent measurement functions

This paper presents a new efficient computation technique for robust power system state estimation based on weighted least absolute value (WLAV) criterion. The proposed method employs rectangular form of state variables and equivalent measurements technique in order to obtain the linear measurement functions with linear constraints of state variables. The state estimation problem is then formulated as an optimization problem with a set of equality and inequality constraints. A solution method based on interior point algorithm is also proposed. Tests with several IEEE standard systems have been performed to investigate the performance of the proposed algorithm. Results indicate that the proposed state estimator gives promising performance compared with weighted least square (WLS) based estimation algorithms using state variables in polar forms. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Optimal Spinning Reserve Allocation with Full AC Network Constraints Via a Nonlinear Interior Point Method

An effective optimal spinning reserve allocation (OSRA) method is proposed in this paper using Optimal Power Flow (OPF). It enables optimal allocation of spinning reserve and load curtailment incorporating full AC network constraints and dynamic restriction on generation such as ramp-rate constraints. A Primal-Dual Interior Point (PDIP) method, which can efficiently handle both equality constraints and inequality constraints, is employed to solve the formulated dynamic OPF problem. In this model, spinning reserve and load curtailment constraints impose an interdependency between the generation output of units which usually are separable in conventional Newton OPF. A decomposition algorithm is therefore derived to handle the interdependency so that the constraint matrix of generation and that of network can be handled separately by slightly changing the entries of Hessian matrix. Therefore, the proposed method is not only still able to utilize the elegant super sparsity technique of Newton method, but also eliminates its ineffective binding active set determination procedure. Furthermore, the influences of spinning reserve on spot price (SP) are also discussed. A shift effect is observed.     

实际报价结算下的灵敏度矩阵消除阻塞的算法

为了保证系统运行的安全性提出了一种基于灵敏度矩阵的阻塞消除算法,在按机组实际报价结算时,针对出现阻塞的支路,形成相应的灵敏度系数矩阵,以调整费用最小为目标函数,整体解决过载支路的阻塞。它以过载支路的过载量和相应的发电机组的灵敏度系数和调整量的乘积形成等式约束,并和目标函数构成拉格朗日函数,采用拉格朗日求极值的方法,通过推导得出各发电机的调整量。整个计算过程只需求解一个线性方程组,计算较为简单快捷。通过对IEEE9和IEEE30节点系统两个算例的计算,验证了所提算法的正确性和有效性。     

求解动态无功优化问题的混合免疫遗传算法

无功优化是电力系统运行中提高经济性和电压安全性的重要措施,为防止静态无功优化可能导致无功控制设备的频繁操作,考虑并联电容器投切组数和有载调压变压器变比档位的调节次数约束,建立了电力系统动态无功优化模型。提出免疫遗传算法与非线性内点法相结合的混合算法进行求解,其中免疫遗传算法处理离散变量,非线性内点法处理连续变量,并在免疫遗传算法中设计独特的编码方式,使抗体能够自动满足动态约束。采用IEEE14系统的24时段无功优化问题进行仿真计算,动态无功优化后离散控制设备的调节次数很少,有功损耗比静态优化结果仅有轻微增加,算例结果验证了混合免疫算法的有效性。     

电力系统潮流算法的几点改进

对电力系统传统潮流算法进行了如下几点改进：①提出了基于诺顿等值的多平衡节点处理方法。该方法既能解算具有多个平衡平点的同一电网潮流问题。也能够同时解算相互解列的、各自内部具有多个平衡节点的不同子网潮流问题。②针对小阻抗和零阻抗网络参数易导致节点导纳矩阵病态并影响潮流收敛速度和精度的同时,提出了基于节点等效附加注入的小阻抗和零阻抗处理方法。该方法可使节点导纳矩阵良性化,从而保证算法快速、准确地收敛。③针对PQ分解法的收剑性敏感于R/X比的问题,提出了基于节点等效附加注入的改进PQ分解法,使适用于高压输电系统的PQ分解法能够成功地应用于具有大R/X比的低压配电网潮流解算中。     

考虑暂态稳定约束的联络线最大传输功率计算

由于确定电力系统联络线最大功率时要考虑其故障时对系统暂态稳定的影响,故提出了一种基于能量函数灵敏度的考虑暂态稳定约束的联络线最大传输功率计算方法。该法首先确定网络在临界或失稳情况下的能量裕度及能量裕度对各发电机有功出力的灵敏度,再用等步长法和二分法按各发电机能量裕度灵敏度的大小调整有功出力,结合时域仿真法的判稳校验求出考虑暂态稳定约束的联络线极限传输功率。该法计算简单、快速,较好的解决了考虑暂态稳定约束后计算负担过重和直接法偏于保守的问题。2个算例仿真测试证实了该法的有效性。     

A solution to security constrained non-convex economic dispatch problem by modified subgradient algorithm based on feasible values

A security constrained power dispatch problem with non-convex total cost rate function for a lossy electric power system is formulated. Then, an iterative solution method proposed by us and based on modified subgradient algorithm operating on feasible values (F-MSG) is used to solve it.Since all equality and inequality constraints in our nonlinear optimization model are functions of bus voltage magnitudes and phase angles, off-nominal tap settings and susceptance values of svar systems, they are taken as independent variables. Load flow equations are added to the model as equality constraints. The unit generation constraints, transmission line capacity constraints, bus voltage magnitude constraints, off-nominal tap setting constraints and svar system susceptance value constraints are added into the optimization problem as inequality constraints. Since F-MSG algorithm requires that all inequality constraints should be expressed in equality constraint form, all inequality constraints are converted into equality constraints by the method, which does not add any extra independent variable into the model and reducing the solution time because of it, before application of it to the optimization model.The proposed technique is tested on IEEE 30-bus and IEEE 57 bus test systems. The minimum total cost rates and the solution times obtained from F-MSG algorithm and from the other techniques are compared, and the outperformance of the F-MSG algorithm with respect to the other methods in each test system is demonstrated.     

State controllability computation technique for linear time‐varying systems by using Taylor series approximation

This article presents a technique to determine the controllability Grammian matrix (CGM) for linear time‐varying systems by using truncated Taylor polynomial vector and the operational matrix of integration. An important property of this algorithm is that it starts by integrating the Lyapunov differential matrix equation in terms of the CGM. However, the algorithm does not use the mathematical integration processes actually, but uses the truncated Taylor polynomial vector and the operational matrix of integration. Thus, the problem is reduced to solving a linear set of algebraic equations with constant coefficients consisting of the Taylor polynomial constant coefficients of each of the CGM elements. Numerical results and error curves are given to illustrate the improvements achieved by the proposed algorithm. Copyright © 2008 John Wiley & Sons, Ltd.     

A mathematical programming approach to service restoration for distribution systems

This paper aims to develop a suitable power system restoration method by using mathematical programming (MP). Generally, the problem of determining the target configuration can be formulated as a mixed integer programming (MIP) problem. Whether or not each branch is included in a target system is expressed as a 0–1 variable, while the other constraints such as the demand and supply balance conditions are formulated in terms of continuous variables. Although an MP‐based method can obtain an optimal solution under specified operational constraints, in the case of large‐scale problems the solution time often exceeds the computation time that is practically available due to combinatorial explosion. The object of this paper is to develop an efficient solution algorithm for service restoration in distribution systems. First, an MIP problem is solved to determine the sound network configuration that maximizes the available power to the out‐of‐service area, then an MIP problem is solved to determine the target configuration for the out‐of‐service network. The proposed method has been applied to distribution system restoration problems, and simulation results demonstrate its effectiveness. © 2001 Scripta Technica, Electr Eng Jpn, 135(4): 35–42, 2001     

Voltage optimization using augmented Lagrangian functions andquasi-Newton techniques

The authors shows how the application of augmented Lagrangian functions and quasi-Newton techniques can be utilized for power system voltage optimization. The developed algorithm is attractive for three reasons: it can accommodate power system constraints in a straightforward manner, it is capable of reaching a solution even from infeasible starting-points, and it converges in a few iterations. The proposed algorithm offers substantial improvements in computational efficiency due to: reduction in the dimensionality of the formulation by exploiting variable reduction and active-reactive decoupling in the AC-network, sparse matrix techniques to generate selectively the required sensitivities, and an active set strategy that relaxes all inactive constraints. Computer runs have been performed, and the results prove the efficiency of the algorithm     

改进牛顿–拉夫逊电阻层析成像图像重建算法

为了满足电阻层析成像图像重建算法应用于两相流领域的精度与实时性要求,提出一种改进牛顿–拉夫逊算法。针对牛顿–拉夫逊算法局部收敛的特点,将线性反投影算法成像结果作为新算法初始电阻率分布估计值,并利用基于改进粒子群算法的平衡法对海森矩阵进行预处理,降低条件数。同时在新算法迭代过程中,当振荡次数超过设定值时,采取自动更新灵敏度矩阵的策略。仿真与实验结果表明,与线性反投影算法、兰德韦伯算法及简化牛顿–拉夫逊算法相比,新算法降低了图像重建误差,有效提高了图像重建质量;而与标准牛顿–拉夫逊算法相比,新算法在满足成像精度前提下,避免了每次迭代均需更新灵敏度矩阵的缺点,提高了算法收敛速度。