State estimation and bad data processing for systems including PMU and SCADA measurements

Conventional state estimators (SE) are based on real-time measurements, consisting of bus voltages and active and reactive power flows and injections, and estimate the voltage phasors of the network buses. Until recently, these measurements were obtained only through SCADA. With the advent of GPS synchronized measurements obtained by phasor measurement units (PMU), effective techniques are required to incorporate the extremely accurate PMU measurements into state estimation, in order to improve its performance and observability. This paper develops a non-linear weighted least squares estimator by modeling the current phasor measurements either in rectangular or in polar coordinates and compares the two approaches. Any numerical problems arised at flat start or for lightly loaded lines, are resolved. The error amplification, due to the current phasor measurement transformation from polar into rectangular coordinates, is also investigated. The normalized residual test is used to effectively identify any bad data in the conventional and phasor measurements. The proposed techniques are tested with the IEEE 14-bus system.     

Fast identification of bad data in power system tracking state estimation

‘Physical’ removal of suspect bad data and re-estimation during identification requires recalculation of gain matrices and re-ordering of lists that graph them, and is thus time-consuming. A ‘mathematical’ removal technique is presented which avoids re-ordering and retriangularisation of gain matrices but nevertheless delivers precisely the same state estimates. Numerical tests reveal no degradation in convergence when mathematical removal is used. Pseudomeasurement replacement of bad data is advocated when the measurement set, after removal, becomes unobservable. Test results indicate that replacement by either the previous measurement or an estimate based on previous scan states works well provided the pseudomeasurements are de-emphasised by increasing their variances whenever the changes in power system states between measurement scans are much greater than 0.001 p.u.     

A reduced model for bad data processing in state estimation

A reduced model theory for bad data processing is proposed which utilizes the concept of error residual spread areas. Based on the reduced model theory, statistical indices can be defined for each error residual spread area, and therefore existing detection and identification techniques can be applied separately for each error residual spread area. In this way, errors can be isolated in smaller regions of the system, making it possible to avoid the search for bad data in the global system. Results from several test cases on power systems show the effectiveness and robustness of the method     

Sequential bad data analysis in state estimation using orthogonaltransformations

The sequential identification of multiple bad data in power system state estimation using orthogonal transformations is described. The method involves iteratively building a list of suspect bad data based on their normalized residuals. The measurements are then analyzed for their estimated errors, and the suspect list is pruned to reveal the bad data. Valid measurements are then returned to the system for completing the solution. As part of this development, a new method of computing and updating the residual covariance matrix is also presented. Test results on the IEEE 30-bus system are presented     

A distributed state estimator for electric power systems

The author develops a theoretically robust and computationally efficient distributed state estimator to solve the weighted least square state estimation problem by using distributed computation. This distributed state estimator is used in decentralized control and executes in a data communication network that is assumed to be topologically the same as and physically in parallel with the power network. Several attractive satellite functions can be obtained which include: (1) reduction of the time-skew problem; (2) freedom from the power network topological error; (3) easy identification of the unobservable states; and (4) bad data detection and identification. The computational complexity of this distributed state estimator was analyzed. This state estimator was simulated on several cases of the IEEE 30-bus system. The numerical accuracy of the simulation results is satisfactory, and the estimated computation time including the communication delay demonstrates the excellent computational performance of the distributed state estimator     

Integral state estimation for well-conditioned and ill-conditioned power systems

This paper describes a generalized integral solution method to solve the power system state estimation problems for well-conditioned and ill-conditioned power systems. By simple graph analysis, the condition number, which is derived from the simple graph analysis, can be used for justification and determination of various power system operating situations. The modified fast decoupled state estimation method for well-conditioned power systems and the Crout decomposition method for ill-conditioned power systems are formulated and discussed in this paper. Simulations and results are discussed to support the feasibility and effectiveness of the proposed methods for well- and ill-conditioned power system state estimation.     

A mathematical model of an electric power system for dynamic state estimation

In this paper the derivation of a mathematical model of power system state-time behaviour is treated. A power system under normal operating conditions is considered. The mathematical model of the system state behaviour is expressed in terms of the state transition matrix. This model enables future system states to be predicted. The Kalman filter is utilized for the power system dynamic state estimation. A brief summary of representative test results is given.     

A unified approach for the solution of power flows in electric power systems including wind farms

This paper proposes a solution approach of the power flow problem to assess the steady-state condition of power systems with wind farms in a single frame of reference, in which the state variables of the wind generators are combined with the nodal voltage magnitudes and angles of the entire network for a unified iterative solution through the Newton-Raphson method. Different wind energy conversion systems (WECS) are mathematically derived from the steady-state representation of the induction generator. Suitable strategies for initializing the state variables of the wind generators are also proposed in this paper. Lastly, three numerical examples are presented to numerically illustrate the applicability of the proposed approach.     

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。     

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.     

配电系统不良数据修正方法的研究

对GM(1,1)基本模型中第一个数据不起作用的结论作了全新的简洁的推导,提出了计及第一个数的零加数GM(1,1)模型,提高了原始数据的利用率.在此基础上,结合电力负荷呈连续性和日周期性变化的特性,提出了用于负荷数据修正的零加数GM(1,1)组合预测方法.该方法通过从两个角度选取原始序列进行零加数建模,采用关联度的分析方法,将预测值进行线性组合.实验证明,零加数模型的预测精度优于原始模型的预测精度,且组合预测比单一序列预测在计算精度上有明显的提高.     

配电系统不良数据修正方法的研究

对GM(1,1)基本模型中第一个数据不起作用的结论作了全新的简洁的推导,提出了计及第一个数的零加数GM(1,1)模型,提高了原始数据的利用率。在此基础上,结合电力负荷呈连续性和日周期性变化的特性,提出了用于负荷数据修正的零加数GM(1,1)组合预测方法。该方法通过从两个角度选取原始序列进行零加数建模,采用关联度的分析方法,将预测值进行线性组合。实验证明,零加数模型的预测精度优于原始模型的预测精度,且组合预测比单一序列预测在计算精度上有明显的提高。     

On-line estimation of low frequency modes in electric power systems

An efficient adaptive estimation algorithm is presented to recursively identify the low frequency modes disturbing the steady-state operation of electric power systems. The hazardous situation of two (or more) modes approaching each other can thus be detected and avoided by redistributing the active power loading over the power network. The proposed algorithm has low computational burden which makes it suitable for real-time applications. A numerical example is included to demonstrate the convergence properties of the estimation algorithm.