An efficient algebraic approach to observability analysis in state estimation

An efficient and compact algebraic approach to state estimation observability is proposed. It is based on transferring rows to columns and vice versa in the Jacobian measurement matrix. The proposed methodology provides a unified approach to observability checking, critical measurement identification, determination of observable islands, and selection of pseudo-measurements to restore observability. Additionally, the observability information obtained from a given set of measurements can provide directly the observability obtained from any subset of measurements of the given set. Several examples are used to illustrate the capabilities of the proposed methodology, and results from a large case study are presented to demonstrate the appropriate computational behavior of the proposed algorithms. Finally, some conclusions are drawn.     

A simple factorization-based observability analysis and meter placement method

A simple factorization-based observability analysis and meter placement method is presented in this paper. Measurement Jacobian matrix is extended to include non-existing branch flow measurements so that observable islands are identified simultaneously when extra candidate measurements are placed to make the network observable if initially the system is unobservable. The method is described in detail along with numerical examples, which illustrates its effectiveness.     

Optimal placement of PMUs to maintain network observability using a modified BPSO algorithm

This paper presents a novel approach to optimal placement of Phasor Measurement Units (PMUs) for state estimation. At first, an optimal measurement set is determined to achieve full network observability during normal conditions, i.e. no PMU failure or transmission line outage. Then, in order to consider contingency conditions, the derived scheme in normal conditions is modified to maintain network observability after any PMU loss or a single transmission line outage. Observability analysis is carried out using topological observability rules. A new rule is added that can decrease the number of required PMUs for complete system observability. A modified Binary Particle Swarm Optimization (BPSO) algorithm is used as an optimization tool to obtain the minimal number of PMUs and their corresponding locations while satisfying associated constraint. Numerical results on different IEEE test systems are presented to demonstrate the effectiveness of the proposed approach.     

A new method for redundancy analysis of measurements applied to three-phase state estimation

In this paper, a new method based on the properties of the Gram matrix is proposed to verify the redundancy of measurements in three-phase state estimation. The Gram matrix is constructed using rows of the measurement Jacobian matrix as vectors. The method can be used for measurement systems planning or updating of three-phase networks so that the overall system remain observable even under possible branch contingencies and loss of measurements. It is a fast and robust numerical method based on the Gram matrix factorization that is easy to implement. A small numerical example that shows the application of the method is presented.     

一种新的分布式电力系统状态估计算法

随着电力系统的发展,区域电网互联,形成了规模更大的系统。为了适应这一趋势,电力系统状态估计应采用分布式算法。在配置少量PMU的基础上,将分区后的边界等式约束条件通过拉格朗日乘子计入整体目标函数,将分布式状态估计的问题转化为一个带等式约束的最优化问题,实现了电力系统状态估计的分布式计算。该算法不仅提高了状态估计的速度,而且可在不必改动原有状态估计模块的基础上,很容易地加入等式约束的修正模块。最后通过IEEE14节点和IEEE30节点系统的模拟仿真,验证了该算法的有效性和优越性。     

Optimal PMU placement method for complete topological and numerical observability of power system

This paper presents a new method of optimal PMU placement (OPP) for complete power system observability. A two-stage PMU placement method is proposed, where stage-1 finds out the minimum number of PMUs required to make the power system topologically observable and stage-2 is proposed to check if the resulted PMU placement (from stage-1) leads to a full ranked measurement Jacobian. In case the PMUs placed, ensuring topological observability in stage-1, do not lead to the Jacobian of full rank, a sequential elimination algorithm (SEA) is proposed in stage-2 to find the optimal locations of additional PMUs, required to be placed to make the system numerically observable as well. The proposed method is tested on three systems and the results are compared with three other topological observability based PMU placement methods. The simulation results ensure the complete system observability and also demonstrate the need of using stage-2 analysis along with the topological observability based PMU placement methods.     

A sensitivity analysis method to compute the residual covariance matrix

In state estimation, the covariance matrix of residuals is used to compute the normalized residuals and to detect erroneous measurements. This paper describes a method based on sensitivity analysis that allows computing the residual covariance matrix. The proposed method is estimator-independent, i.e., it is suitable for most solution approaches based on mathematical programming procedures. Several case studies illustrate the technique proposed. Relevant conclusions are finally drawn.     

Detection of false data injection attacks on power systems using graph edge-conditioned convolutional networks

State estimation plays a vital role in the stable operation of modern power systems, but it is vulnerable to cyber attacks. False data injection attacks (FDIA), one of the most common cyber attacks, can tamper with measurement data and bypass the bad data detection (BDD) mechanism, leading to incorrect results of power system state estimation (PSSE). This paper presents a detection framework of FDIA for PSSE based on graph edge-conditioned convolutional networks (GECCN), which use topology information, node features and edge features. Through deep graph architecture, the correlation of sample data is effectively mined to establish the mapping relationship between the estimated values of measurements and the actual states of power systems. In addition, the edge-conditioned convolution operation allows processing data sets with different graph structures. Case studies are undertaken on the IEEE 14-bus system under different attack intensities and degrees to evaluate the performance of GECCN. Simulation results show that GECCN has better detection performance than convolutional neural networks, deep neural networks and support vector machine. Moreover, the satisfactory detection performance obtained with the data sets of the IEEE 14-bus, 30-bus and 118-bus systems verifies the effective scalability of GECCN.     

电力系统不良数据检测与辨识方法的现状与发展

电力系统不良数据的存在会降低电力系统状态估计的收敛性能, 甚至造成电力系统状态估计的失败。回顾了国内外对电力系统不良数据检测与辨识方法的历史现状与发展,从对检测和辨识不良数据的各种方法研究的时间顺序以及类别上出发,将其分成基于传统方法和基于新理论方法这两大类并对其分别进行了详细阐述,分析了各个算法的自身特点以及存在的问题,并对该领域值得进一步研究的问题和方向进行了展望。     

A method for determining pseudo‐measurement state values for topology observability of state estimation in power systems

This paper proposes a new technique for determining state values in power systems. Recently, it has been useful for carrying out state estimation with PMU (Phasor Measurement Unit) data. The authors have developed a method for determining state values with an artificial neural network (ANN) considering topology observability in power systems. The ANN has the advantage of approximating nonlinear functions with high precision. The method evaluates pseudo‐measurement state values of data which are lost in power systems. The method has been successfully applied to the IEEE 14‐bus system. © 2012 Wiley Periodicals, Inc. Electr Eng Jpn, 179(2): 27–34, 2012; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21235     

华东电网两级分布式状态估计试点建设及运行分析

指出华东调度中心—变电站两级分布式状态估计充分利用变电站内大量冗余的量测信息,对形成覆盖变电站状态估计结果的高精度局部估计,进而进行全局协调,可获得更可靠的全网实时状态估计结果。介绍了华东电网两级分布式状态估计系统建设应用情况,对试点厂站内、调度主站端状态估计结果进行了分析比较,结果表明其对全网状态估计计算结果有较明显的改善作用。     

A review of cyber security risks of powersystems: from static to dynamic false dataattacks

With the rapid development of the smart grid and increasingly integrated communication networks, power gridsare facing serious cyber-security problems. This paper reviews existing studies on the impact of false data injectionattacks on power systems from three aspects. First, false data injection can adversely affect economic dispatch byincreasing the operational cost of the power system or causing sequential overloads and even outages. Second,attackers can inject false data to the power system state estimator, and this will prevent the operators fromobtaining the true operating conditions of the system. Third, false data injection attacks can degrade thedistributed control of distributed generators or microgrids inducing a power imbalance between supply anddemand. This paper fully covers the potential vulnerabilities of power systems to cyber-attacks to help systemoperators understand the system vulnerability and take effective countermeasures.     

Optimal location and parameter setting of UPFC for enhancing power system security based on Differential Evolution algorithm

This paper presents a new approach based on Differential Evolution (DE) technique to find out the optimal placement and parameter setting of Unified Power Flow Controller (UPFC) for enhancing power system security under single line contingencies. Firstly, we perform a contingency analysis and ranking process to determine the most severe line outage contingencies considering line overloads and bus voltage limit violations as a Performance Index. Secondly, we apply DE technique to find out the optimal location and parameter setting of UPFC under the determined contingency scenarios. To verify our proposed approach, we perform simulations on an IEEE 14-bus and an IEEE 30-bus power systems. The results we have obtained indicate that installing UPFC in the location optimized by DE can significantly enhance the security of power system by eliminating or minimizing the overloaded lines and the bus voltage limit violations.     

A new coordination strategy of SSSC and PSS controllers in power system using SOA algorithm based on Pareto method

Along with the development of power grids and increasing the use of Flexible AC Transmission System (FACTS) devices, complex and unexpected interactions will be increased in power system. With considering to the non-linearity of power system, operating point changes and reaction between power system and FACTS devices, using of linear methods are not suitable for controller design. Therefore, the nonlinear model to design of Power System Stabilizer (PSS) and Static Synchronous Series Compensator (SSSC) coordinated controllers is considered here. In this paper, a new multi-objective function as an optimization problem is proposed for this coordination process. Also a beneficial strategy to solve this optimization problem using Seeker Optimization Algorithm (SOA) based on Pareto optimum method with high convergence speed is presented. In order to evaluate the performance of the proposed method, coordination strategy is applied on a four-machine system under different contingencies. The results of the proposed multi-objective function are obtained and compared with others in this system and finally, superior ability of the proposed method is observed.     

A new control strategy for the optimization of Distributed MPPT in PV applications

In this paper, a new control strategy allowing to optimize the performances of PV systems adopting Distributed Maximum Power Point Tracking (DMPPT) is presented and discussed. Such a strategy is based on the evaluation of an estimate of the optimal operating range of the inverter input voltage and on the evaluation of an estimate of the optimal operating voltages of the PV modules. The main advantage of the proposed technique is represented by the possibility to evaluate in closed-form the above estimates, provided that the PV modules short circuit currents are known. The closed-form evaluation of the above estimates allows in turn the fast identification of a set of optimal operating points for the inverter and for the PV modules; such a fast identification allows to obtain a marked increase of the speed of tracking of the maximum power point of the whole PV system. Moreover, a further advantage of the proposed technique is represented by the capability to avoid that the operating value of the inverter input voltage remains trapped in the neighborhood of a suboptimal operating point thus lowering the energetic efficiency of the PV system, as it may happen when standard MPPT techniques (such as the Perturb and Observe technique) are adopted.     

A new approach to eliminating of chaotic ferroresonant oscillations in power transformer

Ferroresonance is a complex phenomenon, which can result in thermal and electrical stresses on power system equipments. It can also cause chaotic oscillations in power system. In this paper, a new method is proposed to restrict and damp ferroresonant oscillations, which is based on a new of fault current limiter (FCL). In this method in order to restrict chaotic ferroresonance oscillations, a kind of fault current limiters (FCL) is used which has been used to restrict unwanted high current flow in power system before.To study the ferroresonance nonlinear dynamics, in this paper, the chaos theory is used. By using this theory, the changes in system parameters which can cause chaotic ferroresonant oscillations, can be reviewed and analyzed in details. The behavior of the system during ferroresonance occurrence, with and without using proposed FCL, is discussed in bifurcation and phase plane diagrams. By using these diagrams, the behavioral changes of the system can be easily seen in two cases. The simulation results strongly show the effectiveness of using the proposed FCL for restricting the ferroresonant oscillations.     

Convergence analysis of the quasi‐OBE algorithm and related performance issues

‘Quasi‐OBE’ (QOBE) is an adaptive set identification and filtering algorithm which is based on the principles of optimal bounding ellipsoid processing, but which has other geometric and classic least‐squares interpretations which greatly enhance its application potential. In particular, because of its unusual optimization criterion, the ellipsoidal membership set associated with QOBE is more likely to retain (i.e. to move in the parameter space with) the system model's ‘true parameters, ’ say θ _*, when those parameters are time varying. Moreover, in the unlikely event that θ _* moves outside the set, the integrity of the point‐set estimation remains intact, and the estimator provably converges under known conditions. The consistency of the set estimation can be restored at any time using typical ‘rescue procedures’ if desired. Understanding convergence performance is very critical to successful QOBE application. Convergence analysis of both the central point estimate and measures of the hyperellipsoidal membership set is presented. The main results give conditions for point estimate convergence, and show that set convergence to a point is not possible. Implications of these convergence results for practical application are discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

提高前向神经网络泛化性能和实时性能的新算法

提出一种基于正则化最小二乘的前向神经网络快速学习的混合算法。该算法将正则化方法和基于单个权值的局部化快速算法的优势结合起来，并加入隐节点删除算法，极大地提高了前向网络的泛化性能和实时性能，学习收敛速度快，精度较高。仿真结果表明了该混合算法的有效性。     

基于灵敏度分析的多区域互联电力系统状态估计

研究了多区域互联电力系统的状态估计问题,提出了基于灵敏度分析的互联电力系统的状态估计方法.该方法将互联系统联络线两端子系统状态估计独立计算所得线路功率不匹配量作为各子系统的虚拟变化量测量,基于各子系统量测量、状态量和功率估计值之间的灵敏度关系,计算修正各子系统状态量和功率估计值,迭代求解互联系统状态估计解.仿真试验结果充分说明该状态估计方法计算结果准确、速度快,且在互联系统计算中心无法获得部分子系统数据情况下,能够最大限度地准确给出互联的可观测系统状态估计解.     

基于SCADA及PMU多时段量测信息的独立线路参数估计方法

基于单一线路两端的监控与数据采集系统(supervisory control and data acquisition system,SCADA)和相量采集装置(phasor measurement unit,PMU)多时段量测信息,建立了5种独立线路的约束最小二乘参数估计模型,其中,量测方程分别由线路两端有功、无功和电压幅值的SCADA量测、电流与电压相量的PMU量测以及线路两端电压相角差的PMU虚拟量测组合形成,约束方程为参数变量的上下限约束。采用Matlab的lsqnonlin优化函数求解参数估计问题,并基于多条典型线路的模拟量测信息仿真分析了所有模型的适用条件。结果表明,在负荷较重、线路较长条件下,利用所建含PMU量测的4种模型,都可以有效估计出线路的阻抗参数。