State Estimation Model Research Articles

On the Real-Time Quantification of Flexibility Provided by District Heating Networks Considering Dynamic Temperature Distribution

District heating networks (DHNs) can provide electrical power systems (EPSs) flexibility by utilizing heat storage abilities. There are three challenges to the real-time quantification of the flexibility offered by the DHN. First, the balance between the heat supply and consumption in the long term must be considered. Second, the robustness and economy of the quantified result must be guaranteed. Third, the reliable dynamic temperature distribution in the DHN must be obtained. Thus, this paper designs a flexibility-providing mechanism for the DHN to interact with the EPS, consisting of the service period and the recovery period. The real-time quantification of the flexibility of the DHN is formulated as an optimization problem, where both flexibility revenue and the operation cost increase in the CHP units are considered. A novel thermal dynamic state estimation (TDSE) model with a bad data filtering process is proposed, which is used to provide the dynamic temperature distribution to support the real-time quantification of the flexibility. Numerical results verified that the proposed real-time quantification model has advantages in ensuring the benefits of the DHN. The performance of the TDSE in providing data support for flexibility quantification is also verified. Finally, key factors impacting the quantified flexibility are exploited by simulations.

New power system operational state estimation with cluster of electric vehicles

The access of distributed generation (DG) and a large number of electric vehicles (EVs) have changed the operation mode of power system. Its reliability and stability are facing more and more challenges. Therefore, it is very important to accurately estimate the state of the power system. This paper discusses a new power system state estimation method that is based on the shuffled frog leaping pigeon-inspired optimization algorithm (SFL-PIOA). Firstly, establish EV charging load model and distributed generation probability model (including photovoltaic power generation and wind power generation). Then, considering EVs and DG, the state estimation model of the new power system is built. The objective function and constraint conditions are established, and then the improved SFL-PIOA is used to solve the model. Finally, a simulation example is given to compare the improved algorithms (SFL-PIOA) to initial algorithm (PIOA). The results verify the feasibility and effectiveness of the improved method.

Robust three-phase state estimation for PV-Integrated unbalanced distribution systems

As the increasing penetration of renewable energy brings uncertainty and fluctuation into the operating conditions of distribution systems, distribution system state estimation (DSSE) needs to track not only the state of the network, but also the state of the renewable energy sources robustly and under unbalanced conditions. Aiming at delivering comprehensive situational awareness of distribution systems hosting solar photovoltaic (PV) power plants, this paper proposed a joint state estimation model for unbalanced distribution systems integrated with single-phase and three-phase PV power plants, as well as an extended weighted least absolute value (EWLAV) estimation algorithm for handling simultaneous measurement errors and control input errors. The proposed state estimation model considers various loss components of single-phase and three-phase power electronic converters, and is applicable to general unbalanced conditions including unbalanced phasing and parameters of distribution lines, PV power plants, and loads. The proposed EWLAV algorithm leverages sparse l1 optimization principles and can identify and suppress the gross errors in both measurements and converter control inputs. Simulation results show that the developed model can reliably reflect the characteristics of three-phase unbalanced distribution networks and PV plants, and the EWLAV algorithm produces unbiased results under simultaneous measurement errors and control input errors, which conventional estimators such as the weighted least squares (WLS) and weighted least absolute values (WLAV) cannot achieve.

Analytical Four-Dimensional Ensemble Variational Data Assimilation for Joint State and Parameter Estimation

The joint state and parameter estimation problem is an important issue in data assimilation. An adjoint free data assimilation method, namely analytical four-dimensional ensemble variational (A-4DEnVar) data assimilation method, was developed to provide a solution for the joint estimation problem. In the algorithm, to estimate the adjoint model reasonably, the ensemble initial conditions and parameters are generated by Gaussian noise whose covariance is constructed by multiplying a very small factor by their background error covariance. The ensemble perturbations are calculated with respect to background states rather than the ensemble mean. Next, the usage of temporal cross covariances makes it possible to avoid the adjoint model and estimate the gradient in 4DVar. Furthermore, we update the solution iteratively with a linear search process to improve the stability and ensure the convergence of the algorithm. The method is tested using the three-variable Lorenz model (Lorenz-1963) to illustrate its efficiency. It is shown that A-4DEnVar results in similar performance with 4DVar. Sensitivity experiments show that A-4DEnVar is able to assimilate observations successfully with different settings. The proposed method is able to work as well as 4DVar and avoid adjoint models for the joint state and parameter estimation.

A Multiarea State Estimation for Distribution Networks Under Mixed Measurement Environment

A grand challenge for the state estimation (SE) method in large-scale distribution networks lies in how to deal with the increasing computational tasks. This article addresses the issue and proposes a novel multiarea architecture for the unbalanced distribution network SE method. The first step of the method is to introduce an innovative multiarea state estimation (MASE) model using microphasor measurement units ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> PMU) mixed with conventional supervisory control and data acquisition (SCADA) systems, with both the coordinate tensions and synchronization issues considered. The proposed model contains a SCADA measurement delay estimator and a MASE algorithm. Then, the hybrid state estimation (HSE) model is solved in a distributed way. In each subarea, the HSE problem is solved locally with minimal data exchanges among neighbor subareas. Case studies show the accuracy and efficiency enhancements obtainable of the proposed MASE method with respect to existing ones.

A Novel Smart Method for State Estimation in a Smart Grid Using Smart Meter Data

Smart grids have brought new possibilities in power grid operations for control and monitoring. For this purpose, state estimation is considered as one of the effective techniques in the monitoring and analysis of smart grids. State estimation uses a processing algorithm based on data from smart meters. The major challenge for state estimation is to take into account this large volume of measurement data. In this article, a novel smart distribution network state estimation algorithm has been proposed. The proposed method is a combined high-gain state estimation algorithm named adaptive extended Kalman filter (AEKF) using extended Kalman filter (EKF) and unscented Kalman filter (UKF) in order to achieve better intelligent utility grid state estimation accuracy. The performance index and the error are indicators used to evaluate the accuracy of the estimation models in this article. An IEEE 37-node test network is used to implement the state estimation models. The state variables considered in this article are the voltage module at the measurement nodes. The results obtained show that the proposed hybrid algorithm has better performance compared to single state estimation methods such as the extended Kalman filter, the unscented Kalman filter, and the weighted least squares (WLS) method.

A statistical method for pre-estimating impacts from a disaster: A case study of floods in Kaduwela, Sri Lanka

Quantification of impacts from a disaster is an important aspect in effectively managing the systemic risks arising from hazards. At present, damage assessments use complex modelling techniques which require time, capital, and a vast amount of data. This paper provides a scientific solution in finding an effective and rapid method to identify the extent of impact from a disaster event, by developing a statistical estimation model for disaster impacts using Multi-Criteria Analysis (MCA) and Pearson Correlation test. In the model developed, impacts of disasters are evaluated by considering the interconnected nature of systems and cascading nature of disasters, based on a Sri Lankan case study. Data from the case study, which denotes characteristics of floods, are used to correlate data categories containing details relevant to human activities in a disaster. Findings from the Pearson Correlation show strong correlations of 0.6–0.85 between modified variables. Also, the results of the MCA show that there are multiple correlations between the selected variables. These correlations can be used in deriving mathematical models to estimate human impacts. The models were tested for accuracy through a similarity test, by calculating the deviations of the model created, using the original figures. The model developed for calculating the affected population provided accurate outputs and a deviation of 0.98 when compared with the original data. The modelling process presented in this study could be further enhanced using additional data. Furthermore, it could be applied in analysing the rapid and approximate estimation of impacts on humans, due to events of disasters.

Efficient Implementation of Continuous-Discrete Extended Kalman Filters for State and Parameter Estimation of Nonlinear Dynamic Systems

The extended Kalman filter (EKF), one of the most popular state estimators for nonlinear uncertain dynamic systems, is considered here in its continuous-discrete (CD) form. The CD version enhances the EKF's accuracy but requires robust and computationally efficient numerical integration methods. The purpose of this article is to present several new efficient integration methods suited to the implementation of the CD-EKF and to compare them to classical implementations such as the Dormand–Prince 4/5 and Euler methods. They are first applied on two proposed nonlinear parameter estimation testbenches and to the stiff Curtiss and Hirschfelder model for state and parameter estimation. Then, they are applied to the estimation of the iron losses of a high-speed permanent-magnet synchronous motor. The results show that for highly nonlinear dynamic systems or for a low to medium sampling frequency, the implicit implementation of the EKF provides a better accuracy and convergence safety. For less nonlinear functions and a higher sampling frequency, classical explicit methods obviously give similar results in a lower computation time.

Robust Dynamic State Estimator of Integrated Energy Systems Based on Natural Gas Partial Differential Equations

The reliability and precision of dynamic database are vital for the optimal operating and global control of integrated energy systems. One of the effective ways to obtain the accurate states is state estimations. A novel robust dynamic state estimation methodology for integrated natural gas and electric power systems is proposed based on Kalman filter. To take full advantage of measurement redundancies and predictions for enhancing the estimating accuracy, the dynamic state estimation model coupling gas and power systems by gas turbine units is established. The exponential smoothing technique and gas physical model are integrated in Kalman filter. Additionally, the time-varying scalar matrix is proposed to conquer bad data in Kalman filter algorithm. The proposed method is applied to an integrated gas and power systems formed by GasLib-40 and IEEE 39-bus system with five gas turbine units. The simulating results show that the method can obtain the accurate dynamic states under three different measurement error conditions, and the filtering performance are better than separate estimation methods. Additionally, the proposed method is robust when the measurements experience bad data.

PMU-Based State Estimation for Networks Containing LCC-HVDC Links

This letter proposes an equality-constrained weighted least squares (WLS) state estimation model for networks containing LCC-HVDC links. Voltage and current phasor measurements for the AC network are provided by phasor measurement units (PMUs) and DC voltage and current measurements for the DC transmission lines are acquired by appropriate DC sensors. AC&#x002F;DC coupling equations and zero injections are treated as equality constraints. Simulation results for a 6-bus hybrid AC&#x002F;DC network are shown to validate the proposed model and algorithm.

A Framework for Constrained Static State Estimation in Unbalanced Distribution Networks

State estimation plays a key role in the transition from the passive to the active operation of distribution systems, as it allows to monitor the networks and provides the necessary information to perform control actions. However, designing state estimators for distribution systems is challenging, due to the characteristics of the networks, such as limited measurement availability. Furthermore, the features of the distribution system present significant local variations, e.g., voltage level and number and type of customers, which makes it hard to design a “one-size-fits-all” state estimator. This paper introduces a unifying framework that allows to easily implement and compare diverse unbalanced static state estimation models. This is achieved by formulating state estimation as a general constrained optimization problem. The advantages of this approach are described and supported by numerical illustration on a large set of real distribution feeders. The framework is also implemented in software and made available open-source.

Data-driven state estimation of integrated electric-gas energy system

As the energy consumption in the world continues to increase, the integrated energy systems combined with multiple types of energy are gradually developing to enhance the utilization efficiency of each type of energy. However, some issues bring challenges to the state estimation of the coupled electric-gas integrated energy system. The issues include that measurement data of the integrated energy system has low redundancy, there exists a large measurement error of the integrated energy system, and the measurement devices of the electric and gas network are not standardized in terms of sampling time units. Considering that the data-driven model has high portability and the ability to distill and summarize information, the data-driven state estimation model of the electric-gas coupled integrated energy system is established in this paper. Bayesian learning is used to obtain the probabilistic statistical features of the measurement data. Super Latin sampling is applied to generate the complete measurement data. The rationality of the generated data is checked by the energy flow analysis of the integrated energy system to obtain the training sample set for the deep learning network. A hybrid deep learning network coupled with the convolutional neural network and long and short-term memory is proposed, and the root mean square error is utilized to train the hybrid deep learning network, which effectively improves the error accuracy of the state estimation of the electric-gas coupled integrated energy system. Compared with the classical model-driven method of state estimation, the arithmetic simulation verifies the effectiveness of the proposed method.

Closing the Control Loop with Time-Variant Embedded Soft Sensors and Recurrent Neural Networks.

Embedded soft sensors can significantly impact the design and control of soft-bodied robots. Although there have been considerable advances in technology behind these novel sensing materials, their application in real-world tasks, especially in closed-loop control tasks, has been severely limited. This is mainly because of the challenge involved with modeling a nonlinear time-variant sensor embedded in a complex soft-bodied system. This article presents a learning-based approach for closed-loop force control with embedded soft sensors and recurrent neural networks (RNNs). We present learning protocols for training a class of RNNs called long short-term memory (LSTM) that allows us to develop accurate and robust state estimation models of these complex dynamical systems within a short period of time. Using this model, we develop a simple feedback force controller for a soft anthropomorphic finger even with significant drift and hysteresis in our feedback signal. Simulation and experimental studies are conducted to analyze the capabilities and generalizability of the control architecture. Experimentally, we are able to develop a closed-loop controller with a control frequency of 25 Hz and an average accuracy of 0.17 N. Our results indicate that current soft sensing technologies can already be used in real-world applications with the aid of machine learning techniques and an appropriate training methodology.

Electrochemical impedance correlation analysis for the estimation of Li-ion battery state of charge, state of health and internal temperature

Electrochemical impedance spectroscopy (EIS) is an effective characterization tool for a multitude of battery states including state of charge (SoC), state of health (SoH) and internal temperature (IT). The intrinsic relationship between equivalent circuit elements and components of an impedance spectra (frequency, real, imaginary and phase) could be exploited to estimate the battery state at a given point of time without the need of continuous historical tracking information. Identification and analysis of battery state sensitive impedance variables is paramount for the development of any impedance-based battery management system (BMS). In this paper, correlation analysis between equivalent circuit elements and impedance spectra of multiple commercial Li-ion polymer batteries at varying SoC, SoH and IT levels was performed to identify and quantify the degree of dependence. Curve fitting techniques were used to fit the measured Impedance spectra on to an equivalent circuit model (ECM) to extract the circuit elements. Pearson's r correlation matrix was employed for quantifying the degree of correlation between each impedance variable and state parameter. Optimal impedance variables that demonstrated high dependence with SoC, SoH and IT are then proposed in this paper. Knowledge of this information is of high value to develop a direct impedance-based state estimation models for real time battery management systems.

Deep Learning Enables Exoboot Control to Augment Variable-Speed Walking

Ankle exoskeletons have the potential to improve mobility, but common controllers are often inflexible to variations in tasks, such as changes in walking speed. To enable effective variable-speed exoboot control, we developed and validated a two-headed convolutional neural network trained to (1) classify stance versus swing and (2) predict the phase during stance, which was then mapped to a desired exoboot torque. This Machine Learning Estimator (MLE) was trained from nine participants walking at three speeds and four exoboot assistance levels. A Time-Based Estimator (TBE) that predicted gait phase from the two previous stride durations was used to apply realistic torques during MLE training and served as a within&#x2013;participant control condition. The MLE was validated online with three new participants walking at a range of speeds and torques, both interpolating within and extrapolating outside the training set. Online validation accuracy (RMSE) across tested speeds and torque levels was 3.9&#x0025;. On a simple walking task in which treadmill speed was varied sinusoidally between 1.1 and 1.6 m&#x002F;s with a 30 s period, the three participants exhibited a mean 5.2&#x0025; decrease in metabolic expenditure with the MLE compared to no-exo (boots only), but exhibited a 5.4&#x0025; increase when walking with the TBE. The MLE more accurately predicted heel strike and toe off events (heel strike Mean Absolute Error: 9.6 ms; toe off MAE: 13.2 ms) than the TBE (heel strike MAE: 19.1 ms; toe off MAE: 34 ms). These positive results validated the potential of using a deep learning model for gait state estimation to effectively control an ankle exoskeleton across variable walking speeds.

Data-Driven Modeling for Transferable Sea State Estimation Between Marine Systems

Sea state estimation is beneficial for marine systems to enhance on-board decision-making and improve work efficiency. In the era of ship intelligence, artificial intelligence has greatly promoted the technology of sensing environment, such as by using the deep learning. However, it is difficult to collect enough motion data from a marine system to train a deep learning model. In addition, the model for sea state estimation is trained using the data from a specific marine system; applying the model directly to another marine system may result in performance degradation. In this paper, a supervised transfer learning based framework for sea state estimation (STLSSE) is proposed. The STLSSE focuses on knowledge transfer when the collected data for the source marine system is sufficient but the collected data of the target marine system is scarce. In STLSSE, a data pairing algorithm is proposed to determine the relationship of the source and the target marine system. Based on these paired data, a Siamese convolutional neural network, including a new proposed residual fully convolutional network and two novel attention modules, is designed for the semantic alignment. Moreover, the conventional contrastive loss is improved to characterize the distributions when there are only few samples in the target marine system. The extensive comparisons between STLSSE and state-of-the-art transfer learning approaches show its superior performance. The comparisons with state-of-the-art attention modules has verified the competitiveness of the proposed attention modules. The key parameters and each component of STLSSE are emphasized in the ablation and sensitivity studies.

A Comprehensive Framework for Robust AC/DC Grid State Estimation Against Measurement and Control Input Errors

Thispaper proposes a systematic framework of the AC&#x002F;DC grid state estimation with high accuracy, computational tractability, and robustness against measurement and control input errors. First, tractable lossy models of bidirectional isolated DC&#x002F;DC voltage source converters (VSCs), bidirectional DC&#x002F;AC VSCs, and DC lines for state estimation are developed. Then, the state variables of the DC grid are selected, and measurement equations are derived. Finally, combined with the state estimation model of AC grids, a general framework for the robust AC&#x002F;DC transmission grid state estimation against both measurement errors and control input errors is presented. Simulation results show that the proposed framework can effectively capture the operating state of the AC&#x002F;DC grid, and suppress the impact of simultaneous measurement errors and control input errors.

Aircraft 4D Trajectory Prediction in Civil Aviation: A Review

Aircraft four dimensional (4D, including longitude, latitude, altitude and time) trajectory prediction is a key technology for existing automation systems and the basis for future trajectory-based operations. This paper firstly summarizes the background and significance of the trajectory prediction problems and then introduces the definition and basic process of trajectory prediction, including four modules: preparation, prediction, update, and output. In addition, the trajectory prediction methods are summarized into three types: the state estimation model, the Kinetic model, and the machine learning model, and in-depth analysis of various models is carried out. Further, the relevant databases required for the study are introduced, including the aircraft performance database, aircraft monitoring database, and meteorological database. Finally, challenges and future development directions of the current trajectory prediction problem are summarized.

Nonlinear Reduced Models for State and Parameter Estimation

State estimation aims at approximately reconstructing the solution $u$ to a parametrized partial differential equation from $m$ linear measurements when the parameter vector $y$ is unknown. Fast numerical recovery methods have been proposed in Maday et al. [Internat. J. Numer. Methods Engrg., 102 (2015), pp. 933--965] based on reduced models which are linear spaces of moderate dimension $n$ that are tailored to approximate the solution manifold ${\cal M}$ where the solution sits. These methods can be viewed as deterministic counterparts to Bayesian estimation approaches and are proved to be optimal when the prior is expressed by approximability of the solution with respect to the reduced model [P. Binev et al., SIAM/ASA J. Uncertain. Quantif., 5 (2017), pp. 1--29]. However, they are inherently limited by their linear nature, which bounds from below their best possible performance by the Kolmogorov width $d_m({\cal M})$ of the solution manifold. In this paper, we propose to break this barrier by using simple nonlinear reduced models that consist of a finite union of linear spaces $V_k$, each having dimension at most $m$ and leading to different estimators $u_k^*$. A model selection mechanism based on minimizing the PDE residual over the parameter space is used to select from this collection the final estimator $u^*$. Our analysis shows that $u^*$ meets optimal recovery benchmarks that are inherent to the solution manifold and not tied to its Kolmogorov width. The residual minimization procedure is computationally simple in the relevant case of affine parameter dependence in the PDE. In addition, it results in an estimator $y^*$ for the unknown parameter vector. In this setting, we also discuss an alternating minimization (coordinate descent) algorithm for joint state and parameter estimation that potentially improves the quality of both estimators.

Coarse reduced model selection for nonlinear state estimation

State estimation is the task of approximately reconstructing a solu- tion u of a parametric partial differential equation when the parameter vector y is unknown and the only information is m linear measurements of u. Cohen et al. [arXiv:2009.02687, Nov. 2020] proposed a method to use a family of linear reduced spaces as a generalised nonlinear reduced model for state estimation. A computable surrogate distance is used to evaluate which linear estimate lies closest to a true solution of the pde problem. In this article we propose a strategy of coarse computation of the surrogate distance while maintaining a fine mesh reduced model, as the computational cost of the surrogate distance is large relative to the reduced modelling task. We demonstrate numerically that the error induced by the coarse distance is dominated by other approximation errors.