随机激励下电力系统特性的计算分析

随着可再生能源发电和电动汽车的不断接入,随机激励对电力系统特性的影响日渐突出。为了研究电力系统在随机激励下的响应特性,首先,以可再生能源发电和电动汽车接入电网后所引起的功率波动作为随机激励,假设该激励的形式为高斯型白噪声,并基于单机无穷大系统,构造了带有随机功率激励项的非线性随机微分方程模型。其次,采用Heun数值方法,分析了仿真计算步长、随机激励强度以及随机激励步长对系统功角响应的影响。最后,根据系统功角响应功率谱特性,从频域的角度分析了功率随机激励下的功角响应特性,获得了相应的结论。     

随机振幅周期信号驱动的一阶线性系统的随机共振

在非对称双值噪声条件下,研究了随机幅度周期信号作用的含有乘性噪声的一阶线性系统的随机共振现象.利用随机平均法、Shapiro-Loginov公式和非对称双值噪声的属性,得到了平均输出幅度增益的精确表达式.分析表明,平均输出幅度增益对信号频率、系统参数、乘性噪声的强度、相关时间和非对称性存在非单调依赖关系,这种非单调依赖关系有最大值出现;平均输出幅度增益对乘性噪声与幅度噪声之间的关联噪声强度也存在非单调依赖关系,但这种非单调依赖关系出现的是最小值.适当的信号、噪声和系统参数可以使平均输出幅度增益取得最大值或最小值.     

论证振荡器相位噪声幂律谱的形成机理及低噪声振荡器的设计考虑

本文分析了振荡器输出信号中相位噪声功率谱密度与等效噪声电压相对功率谱密度的关系。简捷地推导出了LC反馈振荡器相位噪声幂律谱的一般表示式,得到了各种相位噪声分量与振荡器电路参数之间的关系并推广运用到晶体振荡器,所得到的全部结果给低噪声振荡器的设计、制作、频率稳定度的分析与相位噪声的测量提供了理论依据。     

基于相关运算的相位噪声检测方法

相位噪声是振荡器最重要的性能指标.准确测量相位噪声具有重要意义.本文提出采用相关运算来测量振荡器的相位噪声,不仅可以省去一个高精度的参考振荡器,而且理论上可以很准确地测量出被测源的相位噪声,通过仿真和现有测量方法的对比,验证了该方法的正确性,因此具有较强的实用价值.     

负荷随机扰动对电力系统电压稳定性的影响

运用非线性分岔理论与特征分析法对一个经典3节点电力系统的电压稳定性进行了详细分析.通过逐步增大系统参数Q1,求取系统方程平衡点的雅可比矩阵的特征根,结合特征分析法判定系统的稳定性态,得到了系统运行的2个稳定区间.在此基础上考虑负荷的随机性建立了该系统的随机模型--一个4维随机微分方程组,并运用随机欧拉法对该随机微分方程组进行了数值仿真计算.数值结果表明,当系统运行在稳定边界的一个小邻域内时,负荷的随机扰动造成随机的小幅正向或负向累积,使得系统突然失去电压稳定,失稳模式既可能为霍普夫型,也可能为鞍结型.     

随机激励条件下转子系统的主动振动控制

针对随机激励下线性转子系统的振动主动控制,给出了随机激励下受控柔性转子系统的状态空间模型,基于线性二次型高斯控制理论,提出了转子系统在白噪声和有色噪声激励下振动的最优控制策略。以一个柔性转子轴承系统为例,用数值方法研究了El.Centro地震激励作用下随机最优策略对转子-轴承系统的振动主动控制,并讨论了性能指标中不同权函数对控制效果的影响。结果表明:文中所提出的随机最优控制策略能有效地抑制转子系统的振动,控制效果随着与转子系统位移和速度相关的权矩阵的增大而变好,随着与控制相关的权矩阵的增大而变差。这对于旋转机械系统随机最优控制中权矩阵的选择具有一定的参考价值。     

基于System Generator的宽带电力线脉冲噪声实现方法

随机脉冲噪声是影响用电信息采集系统中宽带电力线载波(BPLC)通信的关键因素。目前的评估测试技术中缺乏标准化的宽带电力线噪声建模和实现方法。研究了经典的Middleton Class-A脉冲噪声模型,分析了二项分布逼近泊松分布的条件,从伯努利实验模型出发,依据Middleton Class-A模型的脉冲指数设定满周期线性同余法生成伪随机序列的阈值,通过判定阈值以获取特定强度的泊松序列。该序列在加权因子部分进行数值运算,得到特定状态的噪声方差,利用乘法器与高斯白噪声序列相乘。所提Class-A脉冲噪声的System Generator模块化设计方法能够实现快速的算法验证,通过对比现场可编程门阵列(FPGA)输出与理论随机脉冲噪声的统计特性,证明了该实现方法的有效性与准确性。     

Duffing系统临界态性能研究

Duffing系统临界态相变对弱信号检测研究非常重要,本文研究Duffing临界状态的性能.介绍了随机微分方程理论关于噪声对系统周期态影响的分析:然后为克服存在的过渡过程,建立改进的系统仿真模型.通过仿真试验分析Duffing系统临界态的性能,混沌态与大尺度周期态表现的性能差别深化了对混沌现象的认识;重点研究受噪声干扰的系统运动状态变化情况,得出系统运动越接近临界态越对嗓声敏感,噪声越强周期态运动容易再次跃迁回混沌态,说明随机微分方程理论分析临界状态结果不正确;实验结果还表明噪声是在某些特定条件下导致处于临界大尺度周期态运动的系统发生突变分叉跃迁回混沌状态,值得进一步深入研究.     

本振相位噪声对解调损失影响的评估方法研究

针对频率源的相位噪声随着频偏变化难以准确取值以致无法实现其对解调损失的影响进行评估的问题,提出了采用相位噪声等效面积法替代单点取值的方法。通过对相位噪声曲线分段计算面积再积分的方式计算相位噪声总功率,并以面积等效计算平均相位噪声功率。以计算的平均相位噪声功率为输入,在MATLAB中仿真PCM/BPSK调制解调过程受相位噪声的影响,并与相同条件下实际设备上的测试结果进行对比,两者在相同误码率水平下的E_(b)/N_(0)相差在0.7 dB范围内,扣除高斯白噪声下的解调损失后最大相差0.3 dB。对比试验表明,该方法可用于实际测试。     

随机共振及其微弱信号的自适应检测

本文简要介绍了随机共振(SR)原理、研究现状和测量方法,提出了非线性双稳态系统的参数自适应调节方法.根据系统输出与系统参数、输入信号之间的变化规律,得到了系统在不同频率范围的变化趋势,通过多个测量参数检测并做出判断,利用软件控制的方法明显提高了信噪比(SNR),免去了求解复杂的统计微分方程.数值仿真的结果验证了此方法的正确性.     

Phase noise characterization of oscillators through Ito calculus

Recent phase noise analysis techniques of oscillators mainly rely on solving a stochastic differential equation governing the phase noise process. This equation has been solved in the literature using a number of mathematical tools from probability theory like deriving the Fokker–Planck equation governing the phase noise probability density function. Here, a completely different approach for solving this equation in presence of white noise sources is introduced that is based on the Ito calculus for stochastic differential equations. Time‐domain analytical expressions for the correlation of the noisy variables of the oscillator are derived that in asymptotically large times give the steady‐state stochastic correlations as well as the power spectral densities of the variables. The validity of the new approach is verified by comparing its results against extensive Monte‐Carlo simulations. This approach is applied to an oscillator with a dielectric resonator at 4.127 GHz, and a very good agreement between its results with those of the Monte‐Carlo simulations and the previous approaches is observed. Copyright © 2014 John Wiley & Sons, Ltd.     

On stochastic modelling of linear circuits

In this paper, the deterministic modelling of linear circuits is replaced by stochastic modelling by including variance in the parameters (resistance, inductance and capacitance). Our method is based on results from the theory of stochastic differential equations. This method is general in the following sense. Any electrical circuit that consists of resistances, inductances and capacitances can be modelled by ordinary differential equations, in which the parameters of the differential operators are the functions of circuit elements. The deterministic ordinary differential equation can be converted into a stochastic differential equation by adding noise to the input potential source and to the circuit elements. The noise added in the potential source is assumed to be a white noise and that added in the parameters is assumed to be a correlated process because these parameters change very slowly with time and hence must be modelled as a correlated process. In this paper, we model a series RLC circuit by using the proposed method. The stochastic differential equation that describes the concentration of charge in the capacitor of a series RLC circuit is solved. Numerical simulations in MATLAB are obtained using the Euler–Maruyama method. Copyright © 2008 John Wiley & Sons, Ltd.     

Synchronous and asynchronous operation in dual‐band VCOs

We present a comprehensive analysis of the asynchronous and synchronous operations of fourth‐order oscillators underlying dual‐band voltage‐controlled oscillators. We analyze the occurrence of the self‐synchronization phenomenon (internal resonance) if the ratio of normal frequencies is nearly a ratio of integers, which is 1:3 in the cubic approximation of the nonlinear oscillator characteristic. In this case, we have the simultaneous presence of 2 oscillations with a frequency ratio 1:3, which was demonstrated to be very effective in generating high‐frequency signals in mm‐wave range. The analysis is carried out by developing an analytical approach relying on the averaging principle, as it follows the van der Pol method. The averaging equations, derived simply by a quadrature, allow us to analyze easily the stationary and transient oscillations, and their stability, both in asynchronous and synchronous operations. Expressions for the amplitudes and phases were derived for a cubic nonlinearity and verified by Spice simulations.     

基于拟哈密顿理论的随机电力系统暂态稳定性分析

蒙特卡洛法分析随机稳定性所需的计算量大,且难以同时考虑随机过程中发生的大量不确定性。基于拟哈密顿系统随机平均方法,提出随机电力系统暂态稳定性分析法。首先,根据扩展等面积法,将受扰多机系统动态映射为两群系统,建立其随机微分方程模型。忽略相关的非哈密顿因素,按哈密顿能量函数确定其安全区域。然后,考虑随机扰动、阻尼等的影响,对等效拟哈密顿系统进行随机平均,求出支配暂态能量转移的平均扩散方程,并基于扩散理论,根据系统条件可靠性分析切除时间、阻尼系数及激励强度等对随机电力系统暂态稳定性的影响。通过4机2区随机系统验证了该方法的有效性。     

Nonlinear magneto-electric response of giant magnetostrictive-piezoelectric composite sensors in harmonic and stochastic excitation

Nonlinear magneto-electric response characteristics of giant magnetostrictive-piezoelectric composite sensors in harmonic and stochastic magnetic fields are studied in this paper. Van der Pol nonlinear differential items are introduced to explain the hysteresis phenomena of both giant magnetostrictive material and piezoelectric ceramics. The nonlinear dynamic model of giant magnetostrictive-piezoelectric composite sensors in harmonic and stochastic magnetic fields is developed. The expression of dynamic response of the system is obtained, and the bifurcation characteristics of the system are analyzed. The results of this paper are helpful for optimal design and improvement of giant magnetostrictive-piezoelectric composite sensors.     

Phase noise characterization of subharmonic injection locked oscillators

In this work we present a detailed study of the phase noise of subharmonic injection locked oscillators (s‐ILOs). A new simple and efficient model has been presented for accurately predicting the phase noise of a microwave s‐ILO. The validity of the analytical technique is verified with measurement results obtained from a 5‐GHz fully differential Colpitts‐based s‐ILO. The results showed that a phase noise improvement of 12 dB at 1 kHz offset frequency compared to the free‐running case can be achieved, whereas the power consumption is 21 mW. Copyright © 2010 John Wiley & Sons, Ltd.     

Fully nonlinear oscillator noise analysis: an oscillator with no asymptotic phase

Oscillators exist in many systems. Detailed and correct characterization and comprehension of noise in autonomous systems such as oscillators is of utmost importance. Previous approaches to oscillator noise analysis are based on some kind of perturbation analysis, some linear and some nonlinear. However, the derivations of the equations for perturbation analysis are all based on information that is produced by a linearization of the oscillator equations around the periodic steady‐state solution, where it is assumed that the oscillator is orbitally stable and it has the so‐called asymptotic phase property. In this paper, we first discuss these notions from a qualitative perspective, and demonstrate that the asymptotic phase property is crucial in validating all of the previous approaches. We then present the case of a simple oscillator that is orbitally stable but without asymptotic phase, for which previous approaches fail. We then present a fully nonlinear noise analysis of this oscillator. We derive and compute nonlinear, non‐stationary and non‐Gaussian stochastic characterizations for both amplitude and phase noise. We arrive at results that are distinctly different when compared with the ones obtained previously for oscillators with asymptotic phase. We compare and verify our analytical results against extensive Monte Carlo simulations. Copyright © 2006 John Wiley & Sons, Ltd.     

Modelling and analysis of differential VCOs

We present a systematic non‐linear analysis of differential voltage controlled oscillators (VCOs), both bipolar and MOS. Using the standard device models, we derive the second‐order non‐linear equation describing the behaviour of these oscillators, which is formulated in a perturbation form. The solution of this equation is obtained as a particular case of the solution of the most general equation of second‐order oscillators, which is solved through a suitable perturbation method. Unlike a pure numerical analysis, simple analytical relationships are derived for predicting the steady‐state oscillation, its transient behaviour and for ascertaining the existence of a stable oscillation in differential VCOs. These relationships, leading to results which well agree with the SPICE simulations, are useful in both analysis and design. Copyright © 2004 John Wiley & Sons, Ltd.     

用于动态电能质量分析的交流电弧炉的建模与仿真

使用EMTDC软件包能实现一种新的电弧炉模型。与以往基于电弧阻抗的电弧炉模型不同 ,该模型从电弧炉的电弧能量方程出发 ,以电弧半径作为状态变量通过解非线性方程求出电弧半径与电流的关系。考虑到电弧炉冶炼过程中电弧的不稳定性以及频率为 8 8Hz的电压波动对视觉影响最为明显的事实 ,设计一频率范围为 4～ 14Hz的带通高斯白噪声叠加于电弧半径之上 ,并得到电弧电压 -电流的非线性时变特性。随后 ,给出电弧炉负荷的等效电路 ,即用一受加于其上的电流控制的受控电压源等效代替。最后 ,将此电弧炉模型并入一 10kV电网进行仿真。结果表明 ,用该模型仿真得到的电弧炉电弧电压的特性与实测的波形特性完全一致 ;此外 ,通过与传统的电弧炉模型进行比较 ,表明该模型在动态电能质量分析与检测研究中的应用优于传统方法。