Evaluating the impact of uncertain parameters in power system dynamic simulations

There are typically uncertain parameters in power system models. This paper presents a computational method for evaluating the effect of parameter uncertainty on the dynamic behaviors of power systems. The effect of parameter uncertainty is represented by system trajectory or performance bounds around nominal values. Based on the notion of optimal power flow with transient stability constraints, a set of nonlinear optimization problems is formulated to determine the upper and lower bounds of system trajectories. A successive linear programming approach is suggested to solve these nonlinear optimization problems. The proposed method is evaluated by several test systems. The results show that the proposed method is valid and potentially useful in quantifying the effect of parameter uncertainty in power system dynamic simulations.     

Use of prior bounds on time constants and steady‐state gain in recursive parameter bounding

Computation of parameter bounds of a linear dynamical system, given input–output observations and bounds on model‐output error, has been developed as an alternative to classical parameter estimation using least squares, maximum likelihood or the prediction error method. When bounds on time‐domain plant behaviour are known in advance, they can be used to develop prior parameter bounds for discrete‐time rational transfer‐function parameters. These bounds can be used to initialize standard parameter‐bounding algorithms which process input–output observations to update the exact polytope feasible set or one of its outer bounding approximations such as an ellipsoid, orthotope or parallelotope. This paper presents a method to compute such prior bounds from bounds on time constants and steady‐state (dc) gain, often available from the physics of the system or from previous experience. The method finds subsets making up the prior feasible parameter set, recursively in model order, for any configuration of the pole ranges. An analysis leading to measures of the value of prior bounds, in terms of their chances of remaining active when new bounds derived from observations are imposed, is presented. A simulation study compares polytope updating with and without such initial bounds. The simulations investigate the influence of the tightness of time‐constant and steady‐state‐gain bounds in reducing the volume of the feasible sets obtained as observations are processed. The effects of initial bound tightness and signal‐to‐noise ratio on survival time of the prior bounds are also examined. Copyright © 2002 John Wiley & Sons, Ltd.     

基于重构系统的永磁交流伺服系统在线转动惯量辨识

为了使伺服系统在负载变动下得到优良的动态响应,提出了一种基于实际电机控制系统输入输出构建的非线性可调重构模型,对实际系统进行重构,并根据收敛之后的重构模型参数,完成电机关键机械参数的准确辨识。其中,全维观测器用来获得电机负载转矩状态观测量,与输入电磁转矩一同作为所构建的自适应机构的输入参数;当可调重构系统的输出与实际系统的输出为无差收敛时,实现对实际系统的重构。仿真和试验验证了该方法的可行性和有效性,能够对模型中预设的不同转动惯量进行准确的辨识。     

DG出力不确定性对交直流混合系统潮流影响的量化分析方法

交直流混合系统可以有效接纳多种分布式电源（distributed generation,DG）,为研究DG出力不确定性对交直流混合潮流的影响,提出了基于齐诺多面体和线性化潮流的量化分析方法。首先采用齐诺多面体建立DG功率注入的不确定集合,随后通过线性化交直流统一潮流模型,得到了状态量的不确定集合,其包含电压、相角等状态量所有可能的取值,从而分析系统在不确定条件下的运行安全性。文章将所提方法运用在含不同控制方式的交直流混合电网算例中,验证了所提方法的有效性和实用性。     

Persistent tracking and identification of regime‐switching systems with structural uncertainties: unmodeled dynamics,observation bias,and nonlinear model mismatch

This work focuses on tracking and system identification of systems with regime‐switching parameters, which are modeled by a Markov process. It introduces a framework for persistent identification problems that encompass many typical system uncertainties, including parameter switching, stochastic observation disturbances, deterministic unmodeled dynamics, sensor observation bias, and nonlinear model mismatch. In accordance with the ‘frequency’ of the parameter switching process, we divide the problems into two classes. For fast‐switching systems, the switching parameters are stochastic processes modeled by irreducible and aperiodic Markov chains. Because accurately tracking real‐time parameters in such systems is not possible because of the uncertainty principles, the effect of parameter switching is evaluated on their average by the stationary distribution of the Markovian chain and estimated by the least squares algorithms. We derive upper and lower bounds on identification errors, which characterize how identification accuracy depends on the earlier uncertainty terms. When the system parameters switch their values infrequently in a probabilistic sense, their values can be tracked based on input/output observations. Stochastic approximation algorithms with adaptive step sizes are used for such systems. Simulation studies are carried out to demonstrate that slowly varying parameters could be tracked with reasonable accuracy.Copyright © 2012 John Wiley & Sons, Ltd.     

模拟轧钢系统的研究与应用

模拟轧钢系统在调试过程中可以缩短调试时间,优化生产工艺参数,来代替试轧避免轧制损失;还可通过模拟轧钢随时检查现场的设备准备状态,减少设备的安全隐患,模轧时检测器状态采用编码报文方式来传输,保证信号传输和处理的稳定可靠,具有一定的参考价值。     

后向离散状态事件驱动电力电子仿真方法

为解决电力电子系统中的刚性状态方程数值解算困难问题,在后向量化状态系统(BQSS)算法的基础上提出一种后向离散状态事件驱动(BDSED)仿真方法。BDSED方法是隐式的,其关键在于如何选择一组合适的量化函数值组合,使得据此计算出的导数向量能够让各状态变量向其对应的量化函数值趋近。由于在每一步计算中,每一个状态变量下一时刻的量化函数都有两种取值,所以对于复杂高维系统,枚举的方式并不可行;同时各状态变量的量化函数值的确定存在互相耦合、相互制约的关系,导致问题更加困难。为解决该问题,提出一种基于有限状态机的实现方案,并在带非理想器件模型的变换器电路上进行了算例验证。仿真结果表明,基于有限状态机实现的BDSED能高效地选取量化函数值组合,在解算变换器等刚性系统时仿真效率明显优于DSED方法和传统的时间离散刚性解法。     

Observer‐based adaptive control for stochastic nonstrict‐feedback systems with unknown backlash‐like hysteresis

This paper studies an observer‐based adaptive fuzzy control problem for stochastic nonlinear systems in nonstrict‐feedback form. The unknown backlash‐like hysteresis is considered in the systems. In the design process, the unknown nonlinearities and unavailable state variables are tackled by introducing the fuzzy logic systems and constructing a fuzzy observer, respectively. By using adaptive backstepping technique with dynamic surface control technique, an adaptive fuzzy control algorithm is developed. For the closed‐loop system, the proposed controller can guarantee all the signals are 4‐moment semiglobally uniformly ultimately bounded. Finally, simulation results further show the effectiveness of the presented control scheme.     

Identification of network parameter errors

This paper describes a simple yet effective method for identifying incorrect parameters associated with the power network model. The proposed method has the desired property of distinguishing between bad analog measurements and incorrect network parameters, even when they appear simultaneously. This is accomplished without expanding the state or the measurement vectors. There is also no need to a priori specify a suspect parameter set. All these features are verified via simulations that are carried out using different-size test systems for various possible cases. Implementation of the method involves minor changes in the weighted least-squares state estimation code; hence, it can be easily integrated into existing state estimators as an added feature.     

Adaptive neural dynamic surface control of MIMO nonlinear time delay systems with time‐varying actuator failures

In this paper, an adaptive dynamic surface control approach is developed for a class of multi‐input multi‐output nonlinear systems with unknown nonlinearities, bounded time‐varying state delays, and in the presence of time‐varying actuator failures. The type of the considered actuator failure is that some unknown inputs may be stuck at some time‐varying values where the values, times, and patterns of the failures are unknown. The considered actuator failure can cover most failures that may occur in actuators of the systems. With the help of neural networks to approximate the unknown nonlinear functions and combining the dynamic surface control approach with the backstepping design method, a novel control approach is constructed. The proposed design method does not require a priori knowledge of the bounds of the unknown time delays and actuator failures. The boundedness of all the closed‐loop signals is guaranteed, and the tracking errors are proved to converge to a small neighborhood of the origin. The proposed approach is employed for a double inverted pendulums benchmark as well as a chemical reactor system. The simulation results show the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive observer design for nonlinear interconnected systems by the application of LaSalle's theorem

In this article, a class of nonlinear interconnected systems with uncertain time varying parameters (TVPs) is considered. Both the interconnections and the isolated subsystems are nonlinear. The differences between the unknown TVPs and their corresponding nominal values are assumed to be bounded where the nominal value is not required to be known. A dynamical system is proposed and then, the error systems between the original interconnected system and the designed dynamical system are analysed. A set of conditions is developed such that the augmented systems formed by the error dynamical systems and the designed adaptive laws are uniformly ultimately bounded. Specifically, the state observation errors are asymptotically convergent to zero based on the LaSalle's Theorem while the parameter estimation errors are uniformly ultimately bounded, and the classical condition of persistent excitation is not required. A case study on a coupled inverted pendulum system is presented to demonstrate the developed methodology, and simulation shows that the proposed approach is effective and practicable.     

Guaranteed recursive non‐linear state bounding using interval analysis

The problem considered here is state estimation in the presence of unknown but bounded state perturbations and measurement noise. In this context, most available results are for linear models, and the purpose of the present paper is to deal with the non‐linear case. Based on interval analysis and the notion of set inversion, a new state estimator is presented, which evaluates a set estimate guaranteed to contain all values of the state that are consistent with the available observations, given the perturbation and noise bounds and a set containing the initial value of the state. To the best of our knowledge, it is the first estimator for which this claim can be made. The precision of the set estimate can be improved, at the cost of more computation. Theoretical properties of the estimator are studied, and computer implementation receives special attention. A simple illustrative example is treated. Copyright © 2002 John Wiley & Sons, Ltd.     

适用于发展性故障的故障分量提取算法

提出了适用于发展性故障的故障分量提取算法。该算法首先计算发展性故障发生前保护安装处的故障分量,再根据发展性故障发生前保护安装处的电流和获取的故障分量求得非故障状态网络中的支路电流;发生发展性故障后,利用保护安装处的全电流减去求得的支路电流得到发展性故障后的故障分量电流。该算法不受电网参数波动和负荷变化的影响。在IEEE 9节点系统模型基础上,BPA仿真验证了算法的正确性。     

Robust time‐varying Kalman estimators for systems with packet dropouts and uncertain‐variance multiplicative and linearly correlated additive white noises

This paper is concerned with robust estimation problem for a class of time‐varying networked systems with uncertain‐variance multiplicative and linearly correlated additive white noises, and packet dropouts. By augmented state method and fictitious noise technique, the original system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst‐case system with conservative upper bounds of uncertain noise variance, the robust time‐varying Kalman estimators (filter, predictor, and smoother) are presented. A unified approach of designing the robust Kalman estimators is presented based on the robust Kalman predictor. Their robustness is proved by the Lyapunov equation approach in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Their accuracy relations are proved. The corresponding robust steady‐state Kalman estimators are also presented, and the convergence in a realization between the time‐varying and steady‐state robust Kalman estimators is proved. Finally, a simulation example applied to uninterruptible power system shows the correctness and effectiveness of the proposed results.     

Model‐free fault‐tolerant control approach for uncertain state‐constrained linear systems with actuator faults

This paper investigates the robust adaptive fault‐tolerant control problem for state‐constrained continuous‐time linear systems with parameter uncertainties, external disturbances, and actuator faults including stuck, outage, and loss of effectiveness. It is assumed that the knowledge of the system matrices, as well as the upper bounds of the disturbances and faults, is unknown. By incorporating a barrier‐function like term into the Lyapunov function design, a novel model‐free fault‐tolerant control scheme is proposed in a parameter‐dependent form, and the state constraint requirements are guaranteed. The time‐varying parameters are adjusted online based on an adaptive method to prevent the states from violating the constraints and compensate automatically the uncertainties, disturbances, and actuator faults. The time‐invariant parameters solved by using data‐based policy iteration algorithm are introduced for helping to stabilize the system. Furthermore, it is shown that the states converge asymptotically to zero without transgression of the constraints and all signals in the resulting closed‐loop system are uniformly bounded. Finally, two simulation examples are provided to show the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive output-feedback stabilization in prescribed time for nonlinear systems with unknown parameters coupled with unmeasured states

The prescribed-time output-feedback stabilization (ie, regulation of the state and control input to zero within a “prescribed” time picked by the control designer irrespective of the initial state) of a general class of uncertain nonlinear strict-feedback-like systems is considered. Unlike prior results, the class of systems considered in this article allows crossproducts of unknown parameters (without any required magnitude bounds on unknown parameters) and unmeasured state variables in uncertain state-dependent nonlinear functions throughout the system dynamics. We show that prescribed-time output-feedback stabilization (ie, both prescribed-time state estimation and prescribed-time regulation) is achieved through a novel output-feedback control design involving specially designed dynamics of an adaptation state variable and a high-gain scaling parameter in combination with a temporal transformation and a dual high-gain scaling based observer and controller design. While standard dynamic adaptation techniques cannot be applied due to crossproducts of unknown parameters and unmeasured states, we show that instead, the dynamics of the high-gain scaling parameter and adaptation parameter can be designed with temporal forcing terms to ensure that unknown parameters in system dynamics are dominated by a particular fractional power of the high-gain scaling parameter and the adaptation parameter after a subinterval (of unknown length) of the prescribed time interval. We show that the control law can be designed such that the system state and input are regulated to zero in the remaining subinterval of the prescribed time interval.     

Stability analysis and adaptive control for nonlinear discrete‐time systems with time delays and dead zone via state‐feedback technique

This research addresses the stability analysis and adaptive state‐feedback control for a class of nonlinear discrete‐time systems with multiple interval time‐varying delays and symmetry dead zone. The multiple interval time‐varying delays and symmetry dead zone are considered in the nonlinear discrete‐time system. The multiple interval time‐varying delays are bounded by the nonlinear function with unknown coefficients, and the symmetry dead zone is considered without the knowledge of the dead zone parameters. The adaptive state‐feedback controller is designed for the nonlinear discrete‐time systems with multiple interval time‐varying delays and dead zone. The discrete Lyapunov‐Krasovskii functional is introduced, such that the solutions of the closed‐loop error system converge to an adjustable bounded region and the state errors can be rendered arbitrarily small by adjusting the adaptive parameters. The designed adaptive state‐feedback controller does not require the knowledge of maximum and minimum values for the characteristic slopes of the dead zone. Finally, three simulation examples are given to show the effectiveness of the proposed methods.     

Adaptive control of stochastic nonlinear systems with Markovian switching

This paper is concerned with the problem of adaptive control for a class of stochastic nonlinear systems with Markovian switching, where the upper bounds of nonlinearities of stochastic Markovian jump systems are assumed to be unknown. Firstly, an adaptation law is developed to estimate these unknown parameters. Then, a class of adaptive state feedback controller is proposed such that not only the estimated errors are bounded almost surely but also, the states of the resulting closed‐loop system are asymptotically stable almost surely. Finally, a numerical example is given to show the validity of the results.Copyright © 2012 John Wiley & Sons, Ltd.     

Constructing numerically stable Kalman filter‐based algorithms for gradient‐based adaptive filtering

This paper addresses the numerical aspects of adaptive filtering (AF) techniques for simultaneous state and parameters estimation arising in the design of dynamic positioning systems in many areas of research. The AF schemes consist of a recursive optimization procedure to identify the uncertain system parameters by minimizing an appropriate defined performance index and the application of the Kalman filter (KF) for dynamic positioning purpose. The use of gradient‐based optimization methods in the AF computational schemes yields to a set of the filter sensitivity equations and a set of matrix Riccati‐type sensitivity equations. The filter sensitivities evaluation is usually carried out by the conventional KF, which is known to be numerically unstable, and its derivatives with respect to unknown system parameters. Recently, a novel square‐root approach for the gradient‐based AF by the method of the maximum likelihood has been proposed. In this paper, we show that various square‐root AF schemes can be derived from only two main theoretical results. This elegant and simple computational technique replaces the standard methodology based on direct differentiation of the conventional KF equations (with their inherent numerical instability) by advanced square‐root filters (and its derivatives as well). As a result, it improves the robustness of the computations against round off errors and leads to accurate variants of the gradient‐based AFs. Additionally, such methods are ideal for simultaneous state estimation and parameter identification because all values are computed in parallel. The numerical experiments are given. Copyright © 2015 John Wiley & Sons, Ltd.