State Estimation in Smart Distribution System With Low-Precision Measurements

The presence of an accurate and efficient system state estimator is a precondition for supervision and closed-loop-control of low voltage grids. Such an estimator has to perform in consecutive periods of minutes. Between two periods in most cases, only the measurement values will change, but sometimes also the measurement model. This paper gives suggestions on how to improve the computationally efficiency of state estimation algorithms that have to perform in such an environment. The efficiency improvements are achieved by the application of advanced matrix inversion methods. Further the use of a linear measurement model and the application of the standard augmented matrix approach for solving the state estimation formula is suggested. However, these improvements can also be applied to other measurement models and estimation methods. The efficiency of the improvements is benchmarked against standard methods for different real grid operation cases. In particular, cases when new measurements are added or measurement values get lost are considered. The final result of the paper is an adjustable, robust and efficient algorithm for low voltage state estimation, presented in a way to support manufacturers and operators to implement and maintain it. The paper is a contribution in the field of static state estimation and short-term operation in distribution systems, in particular, low voltage grids.

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.

Accurate and reliable state estimation is the core stone for flexible operation and control of active smart grids. Through the current expansion of integrating DG units in low voltage networks, the network operation is becoming more complex than before. However, real-time monitoring and control through state estimation is a routine task for the transmission system operators (TSO's) due to the availability of measurement data. The distribution system operators (DSO's) are trying to extend their monitoring and control for medium and low voltage network in order to enable smart grid applications. With the current rollout of smart meters, which are considered as a key component of future smart grids, there would be enough metering data in the distribution networks (voltage, current, active and reactive power consumption and generation) available at every customer connection point. This paper aims to develop a method to solve the problem of meter placement for low voltage system state estimation through deciding which measurement data from the installed smart meters should be considered in the state estimation algorithms in order to improve on the uncertainty of the estimated voltage and its phase angle at every node in the network. (4 pages)

In this letter, filtering over wireless communication channels subject to packet losses is considered. The packet losses are assumed to follow a Bernoulli distribution. The latter is interpreted as a special case of a Markov process for which hybrid filtering theory is shown to provide an exact solution. Unlike existing works where only the linear optimal state estimate is derived as a linear function of measurements, this paper shows that the optimal state estimate is in fact a nonlinear function of measurements. In addition, the optimal estimator is derived explicitly. Illustrative examples compare the performance of the linear optimal estimator and the optimal estimator, and show that the latter offer superior performance, in particular for unstable systems.

—Fast and accurate state estimation has a crucial role in practical implementation of state feedback-based controllers. But most of the states are not accessible or economically feasible to measure and must be estimated. Although such controllers are normally designed offline, their dynamic performance is evaluated online. Hence, having high speed with acceptable accuracy is an essential feature for estimators. In this article, a state estimator based on an artificial neural network incorporated into a linear optimal regulator is introduced. First, an extended Kalman filter is designed, then an estimator based on a proposed feed-forward neural network structure is elaborated after much effort on promising neural network structures. Different neural networks are trained using the data collected from the extended Kalman filter, and a qualified and shapeable alternative for the extended Kalman filter in reducing its drawbacks is obtained. The optimum structure is identified when minimum state estimation error is achieved. Significant speed and sufficient accuracy are the main advantages of the proposed structure to be used online for state estimation. Dynamic performance of the system equipped with the linear optimal regulator plus different estimators is examined and compared to a single-machine/infinite-bus power system in MATLAB (The MathWorks, Natick, Massachusetts, USA).

In this thesis we study problems arising in the design of sense and respond systems and present analytical solutions to them as well as results from experiments dealing with real systems. Sense and respond systems employ sensors and other sources of data to sense what is happening in their environments, process the obtained information, and respond appropriately. A goal of the processing stage is to reconstruct the best possible estimate of the state of the environment using messages received from sensors. Due to the large number of messages that need to be processed, it is desirable to have algorithms that can incrementally process the received measurements and recover the state. The state estimation process becomes more problematic if measurements obtained from the sensors are noisy or they are sent at unpredictable times. First, we study models of state estimation and present algorithms that can incrementally compute accurate linear state estimates of the surrounding environment. Second, we define a framework called predicate signaling that allows us to make tradeoffs between message generation rates and the quality of the state estimate through specification of suitable predicates. We show how predicate signaling generalizes commonly used signaling schemes and present a detailed analysis based on stochastic processes to evaluate schemes based on predicate signaling.

While various industries heavily rely on electrochemical sensors for air and liquid quality monitoring and control, many electrochemical sensors are cross-sensitive to one or more interfering gases in addition to the target component, which may cause incorrect readings and lead to improper control measures. In this study, we proposed a direct algebraic approach-based state estimation and output decomposition algorithm which is suitable for state estimation for a class of nonlinear dynamic systems with output measurements that are highly cross-sensitive to multiple interfering gases. Using the cross-sensitive sensor measurement and its successive time derivatives, the proposed methodology can provide a closed-form solution for the actual system state estimation in a systematic way. The established state estimation algorithm was successfully validated in a numeric example. The proposed state estimation and output decomposition algorithm is applicable to a broad class of nonlinear dynamic systems which use sensors that are cross-sensitive to multiple interfering gases in order to improve the performance of the systems.

Simultaneous seismic input and state estimation with optimal sensor placement for building structures using incomplete acceleration measurements

The AC-DC hybrid microgrid is a credible evolution path for the microgrid. State estimation in complex distribution network is a significant foundation for the safe operation. In AC-DC hybrid microgrid, centralised state estimation algorithms have quite a few deficiencies such as large communication capacity and privacy protection. In response to these obstacles, this paper proposed a novel distributed state estimation algorithm. First, a three-stage state estimation model was established for AC-DC hybrid microgrid, in which the second stage is a nonlinear transform for the linearisation of the nonlinear state estimation progress so that the first and third stage can solve the linear state estimation problem. Furthermore, the Lagrangian relaxation method was ultilised for the distributed problem solution. In the proposed algorithm, AC subsystems and DC subsystems respectively execute state estimation through local information, and the overall consistency of the system state estimation can be eventually achieved according to the transfer iteration of the boundary information. The computational efficiency and convergence of the proposed method was ensured owing to the combination of bilinear theory and Lagrangian relaxation. Simulation results indicate that the proposed method can achieve its goal and be superior to existing method in efficiency.

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.

Knowing the probability of failure in real-time i.e. the probability that a system violates some constraints is decisive for aerospace applications in the presence of state uncertainty. However, it often involves stochastic prediction of the constraints on the upcoming system’s trajectory, which is computationally demanding. In addition, the trajectory prediction depends on the accuracy of the current state estimate, e.g. the navigation system, whose errors are usually not accounted for. This paper studies the impact of the state estimate error on the failure probability calculation, obtained by Monte Carlo trajectory sampling. The failure probability error is first shown to be made of two terms depending on the current state estimation error and the number of Monte Carlo samples. Then, an iterative Least Square estimator is introduced to refine the failure probability estimation without significantly increasing the computational load. It is theoretically shown to converge and lowers the failure probability estimation error of 33% in simulation. The approach is illustrated on a constrained stochastic control application: the atmospheric reentry of a vehicle inspired from SpaceX’s Starship (SXS). The proposed method allows the failure probability estimate to be more accurate despite the unavoidable disturbances yielded by the state estimation algorithm and the Monte Carlo discrete sampling, in particular when the available computational load is limited onboard.

An adaptive approach is presented for optimal estimation of a sampled stochastic process with finite-state unknown parameters. It is shown that for processes with an implicit generalized Markov property that the optimal (conditional mean) state estimates can be formed from (i) a set of optimal estimates based on known parameters, and (ii) a set of "learning" statistics which are recursively updated. The formulation thus provides a separation technique which simplifies the optimal solution of this class of nonlinear estimation problems. Examples of the separation technique are given for prediction of a non-Gaussian Markov process with unknown parameters and for filtering the state of a Gauss-Markov process with unknown parameters. General results are given on the convergence of optimal estimation systems operating in the presence of unknown parameters. Conditions are given under which a Bayes optimal (conditional mean) adaptive estimation system will converge in performance to an optimal system which is "told" the value of unknown parameters.

The task of simultaneous localization and mapping (SLAM) is to build environmental map and locate the position of mobile robot at the same time. FastSLAM 2.0 is one of powerful techniques to solve the SLAM problem. However, there are two obvious limitations in FastSLAM 2.0, one is the linear approximations of nonlinear functions which would cause the filter inconsistent and the other is the “particle depletion” phenomenon. A kind of PSO & H∞-based FastSLAM 2.0 algorithm is proposed. For maintaining the estimation accuracy, H∞ filter is used instead of EKF for overcoming the inaccuracy caused by the linear approximations of nonlinear functions. The unreasonable proposal distribution of particle greatly influences the pose state estimation of robot. A new sampling strategy based on PSO (particle swarm optimization) is presented to solve the “particle depletion” phenomenon and improve the accuracy of pose state estimation. The proposed approach overcomes the obvious drawbacks of standard FastSLAM 2.0 algorithm and enhances the robustness and efficiency in the parts of consistency of filter and accuracy of state estimation in SLAM. Simulation results demonstrate the superiority of the proposed approach.

For analysis, operation and planning of a power system, state estimation and power flow analysis are important tools. Accurate state estimation enables active monitoring of power systems. The state estimation with minimum data is important for reducing the complexity in the state estimation process. In this paper, a state estimation based on the Weighted Least Squares (WLS) method with minimum data (12 measurement) is considered. The state estimation is done with different measurement data that is 62 measurement data, 18 measurement data and 12 measurement data for 6 bus test system. A comparison between these different measurements data is also analyzed in terms of the state estimated.

Data-driven model-based analysis of electrophysiological data is an emerging technique for understanding the mechanisms of seizures. Model-based analysis enables tracking of hidden brain states that are represented by the dynamics of neural mass models. Neural mass models describe the mean firing rates and mean membrane potentials of populations of neurons. Various neural mass models exist with different levels of complexity and realism. An ideal data-driven model-based analysis framework will incorporate the most realistic model possible, enabling accurate imaging of the physiological variables. However, models must be sufficiently parsimonious to enable tracking of important variables using data. This paper provides tools to inform the realism versus parsimony trade-off, the Bayesian Cramer-Rao (lower) Bound (BCRB). We demonstrate how the BCRB can be used to assess the feasibility of using various popular neural mass models to track epilepsy-related dynamics via stochastic filtering methods. A series of simulations show how optimal state estimates relate to measurement noise, model error and initial state uncertainty. We also demonstrate that state estimation accuracy will vary between seizure-like and normal rhythms. The performance of the extended Kalman filter (EKF) is assessed against the BCRB. This work lays a foundation for assessing feasibility of model-based analysis. We discuss how the framework can be used to design experiments to better understand epilepsy.