Power System Nonlinear State Estimation Using Distributed Semidefinite Programming

Guest Editorial: Situational awareness of integrated energy systems

This paper applies a custom model order reduction technique to the distribution grid state estimation problem. Specifically, the method targets the situation where, due to pseudo-measurement uncertainty, it is advantageous to run the state estimation solver potentially thousands of times over sampled input perturbations in order to compute probabilistic bounds on the underlying system state. This routine, termed the Accelerated Probabilistic State Estimator (APSE), efficiently searches for the solutions of sequential state estimation problems in a low dimensional subspace with a reduced order model (ROM). When a sufficiently accurate solution is not found, the APSE reverts to a conventional QR factorization-based Gauss-Newton solver. The resulting solution is then used to preform a basis expansion of the low-dimensional subspace, thus improving the reduced model solver. Simulated test results, collected from the unbalanced three-phase 8500-node distribution grid, show the resulting algorithm to be almost an order of magnitude faster than a comparable full-order Gauss-Newton solver and thus potentially fast enough for real-time use.

Objective: State estimation is used as a necessary tool for online monitoring, analysis and control of power systems. The main objective of this paper is to deal with static state estimation using the snap shot data and dynamic state estimation which accounts for the time varying behaviour of power system states in to consideration. Methods/Analysis: Effects of inclusion of PMU measurements along with the available metered data have been explored using the weighted least square state estimation technique in this paper. A comparative analysis of static state estimation with and without bad data has been carried out and the bad data has been identified and eliminated by using largest normalized residue test. Findings: To investigate the time varying nature of the system states linear state estimator with second order approximation and kalman filter techniques has been proposed in this paper. Case studies are conducted on IEEE 14 bus test system and the test results obtained from non linear, linear first order, second order and kalman filter techniques have been compared. Application/Improvements: Correction of state variables are obtained using linear state estimation with first order and second order approximation and kalman filter techniques has been compared to get the better state estimation algorithm.

We propose a state estimation approach, enhanced with prior information, for dynamic magnetic resonance imaging (MRI). In state estimation the time series of system states are estimated, utilizing the observation and state evolution models and the dynamic time-varying measurements. In this work the state estimation algorithm is the Kalman filter (KF), where the state estimation formulation is complemented with an anatomical structural prior. In our previous work we used two different methods to include prior information to KF. In the first method the observation matrix was augmented with anatomical prior information and in the second method a heuristic total variation (TV) denoising was applied to each Kalman recursion. While the TV method was faster and better than the augmented one, the TV method lacked a sound mathematical background. In this work, we include the prior information in the state evolution model allowing for significantly faster computation compared to the previous augmented method, yet retaining the solid mathematical background and the same quality of the estimate.The proposed approach is evaluated using simulated functional MRI (fMRI) data and experimental, golden angle sampled, small animal dynamic contrast-enhanced MRI data from a rat brain. When using a state estimation method, we can improve the temporal resolution compared to conventional methods by using only one spoke of radial data for each estimate. We compare the results to the augmented Kalman filter and a sliding window method. The results show that the proposed method produces equally good results when compared to the augmented Kalman filter, but allows for over five times shorter computational times.

Inferential measurement of SAG mill parameters II: state estimation

Observability analysis for state estimation using Hachtel’s augmented matrix method

This paper is concerned about the state estimation of power systems, which contain flexible ac transmission system devices. Specifically, the formulation of state estimation in order to incorporate the detailed steady state models of the unified power-flow controller (UPFC) is investigated. This formulation involves the use of equality and inequality constraints that account for the limits associated with the device operation and ratings. Furthermore, in addition to its use as an estimator, the developed estimator can also be used to determine the required settings for the control parameters of UPFCs for a given operating condition. Computational issues concerning initialization, step length, and matrix conditioning are also discussed and practical solutions are offered. Simulations on IEEE test systems of sizes ranging from 14 to 118 buses are presented to demonstrate the use of the developed program both as a state estimator and as a tool for setting the parameters of unified power-flow controllers.

In this paper a new approach for a three-phase Distribution System State Estimator (DSSE) is presented. It utilizes the most types of analog real time measurements (including voltage and current magnitude, active and reactive power measurements). The correct utilization is supported by topology analysis and creation of measurement areas. Loads are modeled based on historical or AMR information. The estimation problem is solved by weighted least squares error method. Applying traditional state estimation on distribution networks, by using load data as pseudo measurement, causes state estimation formulations that have very large size. Approach presented in this paper is based on network reduction which reduces size of the problem. The approach is very fast and provides feasible results.

For nonlinear discrete systems with dual unknown inputs, there are many limitations regarding previous nonlinear filters. This paper proposes two new, improved square-root cubature Kalman filtering (ISRCKF) algorithms to estimate system states and dual unknown inputs. Improved square-root cubature Kalman filtering 1 (ISRCKF1) introduces an innovation that first obtains the unknown input estimates from the measurement equation, then updates the innovation to derive the unknown input estimates from the state equation, then uses the already obtained estimates of the dual unknown inputs to correct the one-step estimate of the state, and finally the minimum variance unbiased estimate of the state is obtained. Improved square-root cubature Kalman filtering 2 (ISRCKF2) builds a unified innovation feedback model, then applies the minimum variance unbiased estimation (MVUE) criterion to obtain the estimates of system states and dual unknown inputs, refining a more concise recursive filter but requiring stronger assumptions. Finally, simulation results demonstrate that the above two algorithms can achieve the optimal estimates of system states and dual unknown inputs simultaneously, and ISRCKF2 further enhances the accuracy of both state and dual unknown inputs estimation, which verifies the validity of the proposed algorithms.

We consider semidefinite programming (SDP) formulations of certain truss topology optimization problems, where a lower bound is imposed on the fundamental frequency of vibration of the truss structure. These SDP formulations were introduced in Ohsaki et al. (Comp. Meth. Appl. Mech. Eng. 180:203–217, 1999). We show how one may automatically obtain symmetric designs, by eliminating the ‘redundant’ symmetry in the SDP problem formulation. This has the advantage that the original SDP problem is substantially reduced in size for trusses with large symmetry groups.

In this paper, the set-membership state and parameter estimation problems are considered for linear time-varying systems. The noises in the system are unknown but bounded and the variation of parameters is considered as a bounded expansion. The entire estimator is an interactive estimation of parameters and states. In parameter estimation, the exact set of parameter estimates may be non-convex because of the uncertain states. A polytopic linear parameter varying (LPV) enclosure of the system regression expression is constructed as a convex relaxation. The result of parameter estimation is a set to include the true parameter of the model. Meanwhile, in the state estimation, a similar LPV enclosure of the state-space model is also used to bound the state matrix uncertainties. This LPV enclosure in the state estimation is narrowed by the parameter estimation, and then the set of state estimates is computed to include the true state. The constrained zonotope (CZ) is used to describe sets of interest and the necessary set operations are expanded to LPV mapping. Because of the highly adjustable accuracy of CZ, the proposed algorithm can make a better trade-off between computational accuracy and efficiency. Finally, a numerical example is given to illustrate the effectiveness of the proposed algorithm.

State estimator is an important tool for online monitoring, analysis and control of power systems. With the increased use of phasor measurement units in a power grid, utilization of synchro phasor measurements in State Estimation (SE) becomes essential. Conventional State Estimation (CSE) has been done from measurements obtained by Supervisory Control And Data Acquisition (SCADA) systems. Linear State Estimation (LSE) is done using phasor measurements alone. The paper presents a hybrid method called Two Stage State Estimation (TSSE), wherein the states of the system are estimated by incorporating both the SCADA measurements and phasor measurements. Simulations are done on IEEE 14 bus, IEEE 30 bus and IEEE 118 bus systems and results are compared.

This paper deals with fault-tolerant-based load frequency control in multi-area power systems. First, by using sliding mode observer technique, the system states and faults are figured out combined with the designed derivative and proportional gains. Upon the state estimates, sliding mode controller is synthesized to keep the asymptotical stability performance of the fault system.

We present a distributed observer for nonlinear systems, which can be used to estimate the state of a central plant with unknown parameters using a network of sensors that measure noisy linear combinations of the state. Our state estimator is based on the unscented Kalman filter and the dual Kalman filter method, which runs two Kalman filters in parallel for both state and parameter estimation. This allows us to improve estimates of the central plants parameters in order to improve state estimates, and vice versa. Furthermore, using results from stochastic stability analysis, we prove that under certain conditions the expected value of the proposed algorithm's estimation error is bounded. This result also shows us that as t goes to infinity, the error bound scales as a function of the largest eigenvalue of the sensor noise covariance matrix. Lastly, we demonstrate the ability of our state estimator to accurately track the state of nonlinear systems through simulations.

In this chapter, a wide-area integrated method including a set of algorithms for transmission lines fault analysis is introduced. The proposed method is based on extension and modification of state estimation formulation. Thus, the method is applicable to both symmetrical and asymmetrical networks as well as all fault types including symmetrical and asymmetrical ones. The method exploits the capacities of state estimation formulation and the solution algorithm of weighted least squares (WLS) to reduce the effect of inherent errors on the fault location accuracy and detection and elimination of bad data in the measurement vectors. For this purpose, an error model of the measurement chain including instrument transformers and PMUs is proposed. This model is used to design measuring errors covariance matrix in the state estimation formulation. The performance of the proposed method has been investigated through numerous fault events simulated on different locations of all transmission lines of the IEEE 118-bus test system.KeywordsAsymmetrical faultsBad data detectionFault locationMeasurement chain errorState estimationUntransposed transmission lines