Power System State Estimation Solution With Zero Injection Constraints Using Modified Newton Method and Fast Decoupled Method in Polar Coordinate

如何保证零注入节点的注入功率在状态估计结果中严格为0是电力系统状态估计研究中的重要问题。在直角坐标下,由于零注入约束为线性约束,可使用修正牛顿法来有效地解决这一问题。因此,借鉴直角坐标下修正牛顿法的思路,提出了极坐标下的修正牛顿法和修正快速解耦估计。这些方法的计算流程与传统的极坐标下的牛顿法和快速解耦估计非常相似,计算速度与大权重法相当,同时能够保证零注入约束严格满足。仿真结果验证了所得结论。

A SCR method for uncertainty estimation in geodesy non-linear error propagation: Comparisons and applications

We review three derivative-free methods developed for uncertainty estimation of non-linear error propagation, namely, MC(Monte Carlo), SUT(scaled unscented transformation), and SI(sterling interpolation). In order to avoid preset parameters like as these three methods need, we introduce a new method to uncertainty estimation for the first time, namely, SCR(spherical cubature rule), which is no need for setting parameters. By theoretical derivation, we prove that the precision of uncertainty obtained by SCR can reach second-order. We conduct four synthetic experiments, for the first two experiments, the results obtained by SCR are consistent with the other three methods with optimal setting parameters, but SCR is easier to operate than other three methods, which verifies the superiority of SCR in calculating the uncertainty. For the third experiment, real-time calculation is required, so the MC is hardly feasible. For the forth experiment, the SCR is applied to the inversion of seismic fault parameter which is a common problem in geophysics, and we study the sensitivity of surface displacements to fault parameters with errors. Our results show that the uncertainty of the surface displacements is the magnitude of ±10 mm when the fault length contains a variance of 0.01 km^(2).

Goal-oriented error estimation applied to direct solution of steady-state analysis with frequency-domain finite element method

Based on the concept of the constitutive relation error along with the residuals of both the origin and the dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed. It leads to the high quality locM error bounds in the problem of the direct-solution steady-state dynamic analysis with a frequency-domain finite element, which involves the enrichments with plural variable basis functions. The solution of the steady-state dynamic procedure calculates the harmonic response directly in terms of the physical degrees of freedom in the model, which uses the mass, damping, and stiffness matrices of the system. A three-dimensional finite element example is carried out to illustrate the computational procedures.

Deep learning-based battery state of charge estimation:Enhancing estimation performance with unlabelled training samples

The estimation of state of charge(SOC)using deep neural networks(DNN)generally requires a considerable number of labelled samples for training,which refer to the current and voltage pieces with knowing their corresponding SOCs.However,the collection of labelled samples is costly and time-consuming.In contrast,the unlabelled training samples,which consist of the current and voltage data with unknown SOCs,are easy to obtain.In view of this,this paper proposes an improved DNN for SOC estimation by effectively using both a pool of unlabelled samples and a limited number of labelled samples.Besides the traditional supervised network,the proposed method uses an input reconstruction network to reformulate the time dependency features of the voltage and current.In this way,the developed network can extract useful information from the unlabelled samples.The proposed method is validated under different drive cycles and temperature conditions.The results reveal that the SOC estimation accuracy of the DNN trained with both labelled and unlabelled samples outperforms that of only using a limited number of labelled samples.In addition,when the dataset with reduced number of labelled samples to some extent is used to test the developed network,it is found that the proposed method performs well and is robust in producing the model outputs with the required accuracy when the unlabelled samples are involved in the model training.Furthermore,the proposed method is evaluated with different recurrent neural networks(RNNs)applied to the input reconstruction module.The results indicate that the proposed method is feasible for various RNN algorithms,and it could be flexibly applied to other conditions as required.

State Estimation of Distribution Network Considering Data Compatibility

Considering that the measurement devices of the distribution network are becoming more and more abundant, on the basis of the traditional Supervisory Control And Data Acquisition (SCADA) measurement system, Phasor measurement unit (PMU) devices are also gradually applied to the distribution network. So when estimating the state of the distribution network, the above two devices need to be used. However, because the data of different measurement systems are different, it is necessary to balance this difference so that the data of different systems can be compatible to achieve the purpose of effective utilization of the estimated power distribution state. To this end, this paper starts with three aspects of data accuracy of the two measurement systems, data time section and data refresh frequency to eliminate the differences between system data, and then considers the actual situation of the three-phase asymmetry of the distribution network. The three-phase state estimation equations are constructed by the branch current method, and finally the state estimation results are solved by the weighted least square method.

SAMPLED-DATA STATE ESTIMATION FOR NEURAL NETWORKS WITH ADDITIVE TIME–VARYING DELAYS

In this paper, we consider the problem of delay-dependent stability for state estimation of neural networks with two additive time–varying delay components via sampleddata control. By constructing a suitable Lyapunov–Krasovskii functional with triple and four integral terms and by using Jensen's inequality, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities(LMIs) to ensure the asymptotic stability of the equilibrium point of the considered neural networks. Instead of the continuous measurement,the sampled measurement is used to estimate the neuron states, and a sampled-data estimator is constructed. Due to the delay-dependent method, a significant source of conservativeness that could be further reduced lies in the calculation of the time-derivative of the Lyapunov functional. The relationship between the time-varying delay and its upper bound is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some less conservative stability criteria are established for systems with two successive delay components. Finally, numerical example is given to show the superiority of proposed method.

Recursive weighted least squares estimation algorithm based on minimum model error principle

Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.

Using Event-Based Method to Estimate Cybersecurity Equilibrium

Estimating the global state of a networked system is an important problem in many application domains.The classical approach to tackling this problem is the periodic(observation)method,which is inefficient because it often observes states at a very high frequency.This inefficiency has motivated the idea of event-based method,which leverages the evolution dynamics in question and makes observations only when some rules are triggered(i.e.,only when certain conditions hold).This paper initiates the investigation of using the event-based method to estimate the equilibrium in the new application domain of cybersecurity,where equilibrium is an important metric that has no closed-form solutions.More specifically,the paper presents an event-based method for estimating cybersecurity equilibrium in the preventive and reactive cyber defense dynamics,which has been proven globally convergent.The presented study proves that the estimated equilibrium from our trigger rule i)indeed converges to the equilibrium of the dynamics and ii)is Zeno-free,which assures the usefulness of the event-based method.Numerical examples show that the event-based method can reduce 98%of the observation cost incurred by the periodic method.In order to use the event-based method in practice,this paper investigates how to bridge the gap between i)the continuous state in the dynamics model,which is dubbed probability-state because it measures the probability that a node is in the secure or compromised state,and ii)the discrete state that is often encountered in practice,dubbed sample-state because it is sampled from some nodes.This bridge may be of independent value because probability-state models have been widely used to approximate exponentially-many discrete state systems.

Online Detection of State Estimator Performance Degradation via Efficient Numerical Observability Analysis

An efficient observability analysis method is proposed to enable online detection of performance degradation of an optimization-based sliding window visual-inertial state estimation framework.The proposed methodology leverages numerical techniques in nonlinear observability analysis to enable online evaluation of the system observability and indication of the state estimation performance.Specifically,an empirical observability Gramian based approach is introduced to efficiently measure the observability condition of the windowed nonlinear system,and a scalar index is proposed to quantify the average system observability.The proposed approach is specialized to a challenging optimizationbased sliding window monocular visual-inertial state estimation formulation and evaluated through simulation and experiments to assess the efficacy of the methodology.The analysis result shows that the proposed approach can correctly indicate degradation of the state estimation accuracy with real-time performance.

The SOC Estimation of Power Li-Ion Battery Based on ANFIS Model

On basis of traditional battery performance model, paper analyzed the advantage and disadvantage of SOC estimation methods, introduced Adaptive Neuro-Fuzzy Inference Systems which integrated artificial neural network and fuzzy logic have predicted SOC of battery. It’s a battery residual capacity model with more generalization ability, adaptability and high precision. By analyzing the battery charge and discharge process, the key parameters of SOC are determined and the experimental model is modified in MATLAB platform.Experimental results show that the difference of SOC prediction and actual SOC is below 3%.The model can reflect the characteristics curve of the battery. SOC estimation algorithm can meet the requirements for precision. The results have a high practical value.

An Embedded Consensus ADMM Distribution Algorithm Based on Outer Approximation for Improved Robust State Estimation of Networked Microgrids

Networked microgrids(NMGs)are critical in theaccommodation of distributed renewable energy.However,theexisting centralized state estimation(SE)cannot meet the demandsof NMGs in distributed energy management.The currentestimator is also not robust against bad data.This study introducesthe concepts of relative error to construct an improvedrobust SE(IRSE)optimization model with mixed-integer nonlinearprogramming(MINLP)that overcomes the disadvantage ofinaccurate results derived from different measurements whenthe same tolerance range is considered in the robust SE(RSE).To improve the computation efficiency of the IRSE optimizationmodel,the number of binary variables is reduced based on theprojection statistics and normalized residual methods,which effectivelyavoid the problem of slow convergence or divergenceof the algorithm caused by too many integer variables.Finally,an embedded consensus alternating direction of multiplier method(ADMM)distribution algorithm based on outer approximation(OA)is proposed to solve the IRSE optimization model.This algorithm can accurately detect bad data and obtain SE resultsthat communicate only the boundary coupling informationwith neighbors.Numerical tests show that the proposed algorithmeffectively detects bad data,obtains more accurate SE results,and ensures the protection of private information in all microgrids.

State of health estimation for lithium-ion battery based on particle swarm optimization algorithm and extreme learning machine

Lithium-ion battery State of Health(SOH)estimation is an essential issue in battery management systems.In order to better estimate battery SOH,Extreme Learning Machine(ELM)is used to establish a model to estimate lithium-ion battery SOH.The Swarm Optimization algorithm(PSO)is used to automatically adjust and optimize the parameters of ELM to improve estimation accuracy.Firstly,collect cyclic aging data of the battery and extract five characteristic quantities related to battery capacity from the battery charging curve and increment capacity curve.Use Grey Relation Analysis(GRA)method to analyze the correlation between battery capacity and five characteristic quantities.Then,an ELM is used to build the capacity estimation model of the lithium-ion battery based on five characteristics,and a PSO is introduced to optimize the parameters of the capacity estimation model.The proposed method is validated by the degradation experiment of the lithium-ion battery under different conditions.The results show that the battery capacity estimation model based on ELM and PSO has better accuracy and stability in capacity estimation,and the average absolute percentage error is less than 1%.

Physics and data-driven approach for online joint state and parameter estimation of electricity and steam networks

The electricity and steam integrated energy systems,which can capture waste heat and improve the overall energy efficiency,have been widely utilised in industrial parks.However,intensive and frequent changes in demands would lead to model parameters with strong time-varying characteristics.This paper proposes a hybrid physics and data-driven framework for online joint state and parameter estimation of steam and electricity integrated energy system.Based on the physical non-linear state space models for the electricity network(EN)and steam heating network(SHN),relevance vector machine is developed to learn parameters'dynamic characteristics with respect to model states,which is embedded with physical models.Then,the online joint state and parameter estimation based on unscented Kalman filter is proposed,which would be learnt recursively to capture the spatiotemporal transient characteristics between electricity and SHNs.The IEEE 39-bus EN and the 29-nodes SHN are employed to verify the effectiveness of the proposed method.The experimental results validate that the pro-posed method can provide a higher estimation accuracy than the state-of-the-art approaches.

Sequential Monte Carlo Method Toward Online RUL Assessment with Applications

Online assessment of remaining useful life(RUL) of a system or device has been widely studied for performance reliability, production safety, system conditional maintenance, and decision in remanufacturing engineering. However,there is no consistency framework to solve the RUL recursive estimation for the complex degenerate systems/device.In this paper, state space model(SSM) with Bayesian online estimation expounded from Markov chain Monte Carlo(MCMC) to Sequential Monte Carlo(SMC) algorithm is presented in order to derive the optimal Bayesian estimation.In the context of nonlinear & non-Gaussian dynamic systems, SMC(also named particle filter, PF) is quite capable of performing filtering and RUL assessment recursively. The underlying deterioration of a system/device is seen as a stochastic process with continuous, nonreversible degrading. The state of the deterioration tendency is filtered and predicted with updating observations through the SMC procedure. The corresponding remaining useful life of the system/device is estimated based on the state degradation and a predefined threshold of the failure with two-sided criterion. The paper presents an application on a milling machine for cutter tool RUL assessment by applying the above proposed methodology. The example shows the promising results and the effectiveness of SSM and SMC online assessment of RUL.

事件触发机制下配电网三相动态状态估计

随着高级量测体系的发展和智能电表的广泛应用,为配电网三相状态估计提供了丰富的终端量测信息。与此同时,大量的智能电表数据给配电网通信系统提出了更高的通信带宽和实时存储要求。为了缓解量测拥堵和时延现象,文中引入事件触发机制代替传统量测数据的周期性采样,在保证有效量测信息及时上传的同时减少通信成本和投资。在此基础上,针对配电网实时状态感知问题,提出了基于鲁棒集合卡尔曼滤波的配电网三相动态状态估计方法,在正常运行场景下,能够保持与无偏估计加权最小二乘法相近的估计精度;当含有坏数据时,该方法也拥有较强的鲁棒性。

一种高斯-重尾切换分布鲁棒卡尔曼滤波器

为降低实际应用中由强未知干扰和仪器故障对观测造成的影响,减轻随机和未建模干扰对系统的侵蚀,从而提升系统在非高斯噪声环境下的状态估计精度,提高滤波器的鲁棒性能,提出了一种基于高斯-重尾切换分布的鲁棒卡尔曼滤波器(Gaussian-heavy-tailed switching distribution based robust Kalman filter,GHTSRKF)。首先,通过自适应学习高斯分布和一种重尾分布之间的切换概率将噪声建模为GHTS(Gaussian-heavy-tailed switching)分布,所设计的GHTS分布可以通过在线调整高斯分布和新的重尾分布之间的切换概率来对非平稳重尾噪声进行建模,具有虚拟协方差的高斯分布用于处理协方差矩阵不准确的高斯噪声。其次,引入两个分别服从Categorical分布与伯努利分布的辅助参数将GHTS分布表示为一个分层高斯形式,进一步利用变分贝叶斯方法推导了GHTSRKF。最后,利用一个仿真场景对几种不同的RKFs(robust Kalman filters)进行了对比验证。结果表明,所提出的GHTSRKF算法的估计精度对初始状态的选取不敏感,精度优于其他RKFs,它的RMSEs最接近噪声信息准确的KFTNC(KF with true noise covariances)的RMSEs(root mean square errors),且当系统与量测噪声是未知时变高斯噪声时,相比于现有的滤波器,GHTSRKF具有更好的估计性能,从而验证了GHTSRKF的有效性。

1990-2020年中国的婚姻状况变迁

本文使用1990-2020年全国人口普查数据,应用多增-减婚姻生命表和间接估计法估算了我国人口的婚姻生命表,考察了我国人口的婚姻状况变迁模式。研究发现:(1)我国存在较为明显的婚姻推迟现象;(2)有配偶预期寿命占预期寿命的比重下降;(3)离婚水平有所增加,离婚预期寿命及其占预期寿命的比重不断提升,但整体离婚水平处于较低水平;(4)死亡水平的下降促使我国人口的丧偶预期寿命及其占预期寿命的比重有所降低。总体来看,我国当前仍是婚姻结构比较稳定的普婚型国家,但受婚姻推迟和离婚水平升高等影响,婚姻稳定性在未来可能进一步减弱。此外,女性婚姻状况的变迁趋势比男性更加明显,婚姻推迟和离婚现象更为突出。

含未知输入非线性系统的扩展平方根容积卡尔曼滤波算法

针对工程实际应用中存在的未知输入会导致经典的非线性滤波器状态估计精度下降甚至滤波发散的问题,提出了一种基于最小方差无偏估计(minimum variance unbiased estimation,MVUE)准则的扩展平方根容积卡尔曼滤波(extended square-root cubature Kalman filter,ESRCKF)算法。首先,结合上一时刻未知输入估计值对状态一步预测值进行修正,得到含未知输入条件下的状态预测值。其次,设计新息并采用加权最小二乘(weighted least squares,WLS)法获取当前时刻未知输入的无偏估计。最后,通过最小化协方差矩阵的迹,同时采用拉格朗日乘子法和舒尔补引理得到系统状态的最小方差无偏估计。仿真结果表明,相比于现有的非线性滤波算法,ESRCKF算法提高了在处理含未知输入非线性系统时的状态估计精度,并能同时实现系统状态和未知输入的最优估计,验证了该算法的有效性。

水下机器人移动式对接的全局路径规划方法

针对无人自主式水下机器人与母艇动态对接时面临的自主式水下机器人欠驱动操纵特性对全局路径的多几何约束要求,以及母艇运动带来的交会点动态变化导致路径的终端约束动态变化等难题,本文提出了一种自主式水下机器人的自主对接路径规划方法。该方法主要分为约束求解、运动规划和状态估计3部分。利用自主式水下机器人的动力学模型分析了在对接过程中的运动约束与终端约束;在运动约束和终端约束条件的前提下,基于势场法的思想分别设计了位置约束和姿态约束下的全局路径规划算法,同时提出母艇的位置、速度和姿态估计方法,并依此开展基于全局预测的路径规划方法的仿真。仿真结果表明:本文方法运算速度快、对母艇的状态具有很好的鲁棒性,并且满足运动约束和终端约束,可以在试验模拟真实自主式水下机器人归航时得到一条满足约束条件的光滑路径的路径规划算法。

基于频次与极值外推综合的载荷外推总体方法

载荷外推作为载荷谱编制的重要技术手段,当前研究缺乏对于载荷外推总体方法的全面梳理、马尔可夫稳态分布的求解方法适应性不够、缺乏不同非参频次外推方法的比较与选用原则,导致不便生成高精度载荷谱以支撑装备性能设计。围绕坦克在高机动和极限工况下的载荷谱编制问题,基于某坦克行进间身管位移数据样本,分别使用基于雨流矩阵及核密度估计的非参数外推法、基于马尔可夫链蒙特卡洛(Markov Chain Monte Carlo,MCMC)的信号重构法以及Metropolis-Hastings(简称MH)直接采样法进行了载荷频次外推,并针对MCMC的信号重构法提出了一种改良马尔可夫稳态分布的求解方法。应用所提出的频次-极值相结合的载荷外推总体方法对坦克身管位移进行了频次扩充与极值预测,并结合实车试验结果验证了方法的准确性。研究结果表明:改良的马尔可夫稳态分布求解方法是有效的;在样本长度足够、外推精度要求不甚高的情况下,MH直接采样法可作为一种新的频次外推方法;运用频次-极值相结合的载荷外推总体方法所得结果精度较高;形成的频次外推法选用原则对于载荷谱编制过程中的方法选择具有一定的指导意义。研究工作为装备载荷谱的高质量编制提供了成熟的技术路线和参考。