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     

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     

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 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.     

High-precision voltage-measuring method using fast sampled data for electric power systems

Control and protection equipment in power systems requires higher sensitivity and operational reliability to meet today's changing power system requirements. The voltage-measuring deviation requirement for advanced voltage and var control equipment is less than 0.1 percent under conditions of harmonic distortion in the voltage waveform and power-system frequency variation. Studies on digital signal processing suitable for electric power systems showed that these requirements are satisfied using fast sampling and very fast 32-bit floating point operations by a Digital Signal Processor (DSP). This paper describes the design philosophy of a high-precision power system voltage-measuring method using fast sampled data. In addition, total voltage-measuring deviation characteristics under a combination of the techniques are described along with digital filter characteristics, frequency-measuring deviation characteristics, frequency variation versus gain-compensation characteristics of a digital filter, and peak value operating principles.     

Steady state analysis of power systems including the effects of control devices

A new power flow model based on a power-perturbation technique has been developed for the steady state analysis of large complex power systems. The model includes the complex load representation and control characteristics of various generators; it also incorporates the effect of automatic load-frequency control, load shedding, generation shedding and on-line tap-changing transformers. When a power system is dynamically stable following a major disturbance, the system will be in an alert on an emergency state, having an energy imbalance. In the proposed technique this imbalance is compensated for according to the steady state characteristics of the control devices and load or generation shedding. The load shedding is activated on the basis of frequency deviation, voltage limits, and line ratings. Thus, the new method allows the study of the power flow under abnormal conditions as well as normal conditions. The major advantage of the procedure is its inherent simplicity and rapid convergence behaviour, resulting in a quick post-transient load flow solution in a quasidynamic manner. The feasibility of the technique is demonstrated by numerical examples and results of cases run on the American Electric Power Systems are included.     

Fault section estimation in electric power systems using an optimization immune algorithm

This paper proposes a methodology based on the unconstrained binary programming (UBP) model and an optimization immune algorithm (IA) to estimate fault sections in electric power systems. The UBP model is formulated using the parsimonious set covering theory for associating the alarms of the protective relay functions informed by the SCADA (supervisory control and data acquisition) system and the expected states of the protective relay functions. The IA is developed to minimize the UBP model and to estimate the fault sections as quickly and reliably as possible. The proposed methodology is tested using part of the South-Brazilian electric power system. The control parameters of the IA are set to reach the maximum computational efficiency and reduction of the processing time. The results show the methodology's potential to estimate fault sections in electric power system control centers in real-time.     

Detection of topology errors by state estimation [power systems]

Errors in the telemetered data of breaker and switch status, through the network topology processor in the EMS (energy management system) computer, may result in errors in the determination of the current network topology of the system. The use of normalized residuals that result from state estimation is proposed for the detection of topology errors. Three types of topology errors are considered: line or transformer outage, bus split, and shunt capacitor/reactor switching. Conditions for detectability of topology errors are presented. The conditions are tested on the IEEE 30 bus system, and the results confirm the theoretical predictions. The problem of topology error identification is also discussed     

A recursive measurement error estimation identification method forbad data analysis in power system state estimation

A recursive measurement error estimation identification algorithm is proposed for identifying multiple interacting bad data in power system static state estimation. A set of linearized formulae are developed and used to recursively calculate normalized residuals and normalized measurement error estimates upon which the bad data identification method is based. Sparse vector and partial factor modification techniques are used in the recursive identification calculations. Neither the submatrix of the residual sensitivity matrix, W_ss, nor state reestimation is needed in the whole identification process. Digital tests on various power systems, including a 171 bus real system, are done to show the validity and efficiency of the proposed bad data identification method     

A computational comparison of steady state load shedding approachesin electric power systems

This paper presents a formulation of the optimal steady state load shedding problem that uses the sum of the squares of the difference between the connected active and the reactive load and the supplied active and reactive power. The latter are treated as dependent variables modelled as functions of bus voltages only. An investigation of the performance of the proposed algorithm over a range of generation deficits as well as overload conditions is presented. Testing is done using IEEE 14, 30, 57, and 118 bus power systems, representing small and medium power systems. The optimal results are compared with results obtained using two earlier approaches. The results obtained using the proposed approach appear to give a better optimal state of the power system