Dynamic Tracking of The Steady State Power System Magnitude and Frequency Using Linear Kalman Filter a Variable Frequency Model

ABSTRACT

This paper presents the application of Kalman Filtering algorithm for tracking the power system voltage magnitude, the rate of change of the frequency, the frequency deviation as well as the voltage phase angle, when the the frequency of the voltage signal varies linearly with the time during the data window size. The proposed algorithm uses the digitized samples of the voltage signal at the relay location. Effects of sampling rate, data window size and the harmonics contaminating the voltage signal on the performance of the algorithm are studied. Furthermore, effects of the noise level are also investigated. A sample of the results obtained is reported in this paper.     

考虑多安全性约束的风电场穿透功率极限研究

穿透功率极限是含风电场电网规划中的重要问题。本文从梳理风电场穿透功率的多种约束条件入手,建立了包含系统潮流平衡、支路潮流、常规机组出力等约束条件的风电穿透功率极限计算模型,在此基础上引入了风电波动导致的系统频率偏差及电压偏差等安全性约束条件。提出了基于系统惯性中心频率的频率偏差指标和基于系统线性化方法的电压偏差指标,从安全性角度考虑了风电接入容量的影响因素。采用遗传算法对模型进行求解,相关算例证明了该方法的准确性和合理性。     

Generalized State Estimation of Flexible AC Power Systems Considering Wind Generators and Primary Frequency Control

This paper proposes a practical approach to incorporate the mathematical models of both fixed-speed and variable-speed wind turbine generators, automatic load frequency controls as well as voltage magnitude and frequency dependent loads into a weighted least squares-based state estimation algorithm suitable for the analysis of flexible alternating current (AC) transmission systems. As opposed to conventional static state estimators, where the inclusion of these electric components has been neglected so far, the proposed approach permits the determination of the steady state operation of a power system in the event of a supply-demand unbalance by estimating the magnitude of the frequency deviation from its nominal value. The state estimation is based on measurements related to those that should be obtained by a supervisory control and data acquisition (SCADA) system and phasor measurement units. For the purpose of this paper, the set of values associated with SCADA measurements (nodal power injections, power flows, and voltage magnitudes) and phasor measurement unit (PMU) measurements (voltage and current phasors) are generated from a power flow analysis of the network under study. Lastly, numerical simulations are reported to demonstrate the effectiveness of the proposed approach.     

EFFECTS OF INDUCTION MOTOR LOAD ON DYNAMIC STABILITY OF POWER SYSTEMS

Abstract

A study of the effects of induction motor load on the dynamic stability of power systems is presented in this paper. The power system is modelled as a multivariable system with load dynamics considered in the feedback path. The induction motor is represented by a transfer function matrix relating bus voltage magnitude and frequency to the active power and reactive power of the motor

Multivariable Nyquist criterion and eigenvalue analysis are used to investigate the effects of induction motor dynamics on system stability     

Estimating Of Steady State Voltage And Frequency Of Power Systems From Digitized Bus Voltage Samples

ABSTRACT

This paper presents a new efficient technique for estimating the voltage and frequency of power systems from digitized bus voltage samples. The new algorithm is based on the least absolute value error (LAV) approximation technique. The proposed algorithm is superior to the well-known least error squares technique (LS) used in Ref. 1, when the voltage samples contain bad data or noise in instrumentation and telemetry. The algorithm was tested on off-line simulated data. Results of the comparison between the least error squares technique and the new proposed algorithm are reported in this paper.     

基于深度Q学习的含用户侧储能微电网频率-电压数字化智能控制策略

频率与电压是衡量电能指标的重要标准。针对微电网受到负荷波动而引起的频率/电压调控问题,提出基于深度Q学习(deep Q-learning, DQN)的含用户侧储能微电网智能监控-控制策略。首先,通过考虑用户行为的随机性,增加了用户侧储能输出的随机约束,并引入四象限充放电的模型,构建用户侧储能的集群充放电模型,从而搭建出微电网频率-电压的协同控制模型。其次,设计基于DQN的频率/电压控制器结构与数字化智能控制平台,以系统实时的频率偏差、电压偏差与用户侧储能输出功率的上、下限约束为状态空间,以系统各机组出力为动作空间,并基于频率及电压2个控制目标,完成包含2个本地奖励的全局奖励函数的设计。算例结果表明：与传统PID控制器相比,所提DQN控制器能同时满足频率与电压的控制需求,更有效地应对负荷波动所引起的电能质量问题。     

An advanced method for eliminating impacts from frequency deviations in power system signal processing

Frequency deviation is a common problem for power system signal processing. Many power system measurements are carried out in a fixed sampling rate assuming the system operates in its nominal frequency (50 or 60 Hz). However, the actual frequency may deviate from the normal value from time to time due to various reasons such as disturbances and subsequent system transients. Measurement of signals based on a fixed sampling rate may introduce errors under such situations. In order to achieve high precision signal measurement appropriate algorithms need to be employed to reduce the impact from frequency deviation in the power system data acquisition process. This paper proposes an advanced algorithm to enhance Fourier transform for power system signal processing. The algorithm is able to effectively correct frequency deviation under fixed sampling rate. Accurate measurement of power system signals is essential for the secure and reliable operation of power systems. The algorithm is readily applicable to such occasions where signal processing is affected by frequency deviation. Both mathematical proof and numerical simulation are given in this paper to illustrate robustness and effectiveness of the proposed algorithm.     

Measurement of Voltage Flicker Magnitude and Frequency in a Power System For Power Quality Analysis

One must be able to accurately measure voltage flicker levels and its frequency. This paper introduces a new application of the least error squares (LES) state estimation algorithm to measure voltage flicker and its frequency. We use a linear model of the flicker voltage magnitude, its phase angle and frequency deviation, and the system voltage magnitude and its phase angle. The proposed algorithm uses digitized samples of the voltage signal. Effects of data size, sampling frequency, and number of samples on the estimated parameters are studied.     

计及风电高频保护的送端电网多直流协同频率控制

为解决中国能源与负荷逆向分布问题,大量高压直流输电工程正在建设或已经投运。针对送端电网中可能发生的直流闭锁导致的高频事件,计及风电机组的高频保护约束,研究了进行多回直流协同控制从而抑制电网频率偏移的方法,提出了以各健全直流总功率调制量最小为目标的多直流协同频率控制模型,通过一阶差分近似求解系统最大频率偏移相对于各受控直流功率的灵敏度,优化求解多直流协同频率控制策略。并进一步以某含高比例风电的送端电网为例,验证该方法在送端电网频率控制策略整定中的有效性。     

High Speed Digital Directional Comparison Relaying

ABSTRACT

A high speed directional comparison relay based on the evaluation of the locally measured deviations of the voltage and current from their prefault values is described in this paper. Signal processing techniques are used to damp out the exponentially decaying dc component and high frequency transient components so that the operation of the relay depends on the power frequency components of the voltage and current deviation signals. The direction to a fault is determined by detecting the first transgression of the fault trajectories across threshold boundaries in the deviation plane. Studies on a three phase power system model show that the direction to a fault is determined within a first few milliseconds following the inception of a fault.     

多端柔性直流输电系统动态附加频率控制策略

附加频率控制利用基于电压源型换流器的多端柔性直流输电(VSC-MTDC)系统直流电压变化传递故障交流系统频率变动,促使非故障交流系统所连电压源型换流器(VSC)消纳不平衡功率参与频率调节。然而固定下垂系数灵活性不足,在不平衡功率分配时忽略VSC实时运行状态与交流网络稳定性,无法保证系统参与频率调整的同时安全稳定运行。通过研究频率变动造成的功率不平衡量分配和直流电压下垂系数的定量关系,提出一种计及系统运行状态的VSC-MTDC动态附加频率控制策略,将VSC功率裕度和交流网络频率变化量引入下垂系数,动态调整不平衡功率的分配比例。仿真结果证明,应用动态附加频率控制进行频率调节后,频率偏差较小的交流网络在所连VSC功率裕度较大时能承担更多不平衡功率,而频率偏差较大的交流网络所连换流站不平衡功率配比下降,VSC-MTDC系统安全稳定运行水平得到显著改善。     

互联系统长期动态仿真的结构保留建模

为了研究互联电力系统在级联事件下的频率和电压长期动态特性及其控制,提出了一种网络结构保留的多区域互联系统长期动态仿真模型和算法.与动态潮流计算相似,模型假定系统已渡过初始的暂态稳定阶段且有足够阻尼,从而忽略同一控制区域的机组间相对摇摆,即假定每个控制区域具有统一的频率动态,即区域内惯量中心动态,以便仿真几分钟及更长时间的长期动态.IEEE 30节点3区域系统的仿真结果表明了文中建议的仿真模型的可行性和计算方法的有效性;与详细机电暂态仿真软件仿真结果的比较表明,"区域统一频率动态"假定引起的系统长期动态仿真误差在工程上可以接受.从而为进一步开展级联事件下的频率和电压长期动态的稳定控制和协调提供了仿真工具.     

改善独立微网频率动态特性的虚拟同步发电机模型预测控制

随着分布式能源在独立微网内的渗透率不断升高,系统惯量水平逐渐降低。虚拟同步发电机(VSG)由于能够模拟惯量,对系统频率的动态变化具有一定的阻尼作用,已逐步应用于微网中。针对新能源出力波动或负荷投切等导致微网内瞬时功率失衡,进而引起系统频率振荡甚至超过安全约束的问题,提出了基于模型预测控制(MPC)的VSG控制方法。建立了以频率变化率为约束,以频率偏差和VSG出力加权值为优化目标的预测模型。设计了根据系统频率及VSG输出电压—电流等物理量,利用预测模型计算所需功率增量,并据此改变VSG输入功率设定值的整体控制策略。同时,给出了预测模型的求解算法,并对算法收敛性进行分析,为关键参数的选取提供了依据。通过独立微网内负荷投切和分布式电源出力波动等典型工况下的仿真,验证了所提控制策略的正确性和有效性。     

CORRESPONDENCE: DISCUSSION OF “GENERALIZED ANALYSIS AND PERFORMANCE OF RELUCTANCE MOTORS”

Abstract

Based on the boundary theorems developed in [1], a method of voltage stability analysis referred to as the Eigen-Structure Analysis method, is developed that does not require the complicated nonlinear programming calculations for evaluation of the closest boundary condition corresponding to a given power network operating point with voltage controlled and PQ buses. An algorithm for determining the stability margin and its sensitivity to bus voltages and bus injections is proposed which is capable of handling large scale power systems by utilizing the sparse matrix techniques for saving computation time and memory space. The Eigen-Structure Analysis method is applied to a number of test system models. The simulation results confirm the theory and show that the proposed stability margin decreases monotonically to zero when the system approaches voltage collapse. Simulation results for 30-bus New England Test System are included in this paper.     

大量风电引入电网时的频率控制特性

大量风力发电引入电网时,会对电网的频率控制带来影响。在深入分析异步电动机频率特性的基础上,采用所开发的电力扰动装置对不同转矩特性的异步电动机的频率特性进行了测试。基于加权综合的思路建立了包含异步电动机的综合负荷的频率特性模型。同时分析了风力发电的出力特性。通过对一个包含风力发电的电网进行分析,论证了考虑负荷频率特性以后,在同样电网调频能力的情况下,频率波动的偏差会变小。     

An improved fast decoupled power flow model considering static power–frequency characteristic of power systems with large‐scale wind power

Large‐scale wind power (LSWP) integration may cause significant impact on power system frequency, so it is necessary to take frequency regulation issues into account in power system steady‐state operation analysis. An improved fast decoupled power flow model considering static power–frequency characteristic of power systems with LSWP is proposed in this paper. In this scheme, the active power of generators and loads are presented with their static power–frequency characteristics. The slack bus degenerates to the nodal voltage phase angle reference bus of the system, and all the generators with frequency regulation capability participate in unbalanced power regulation. The power flow calculation results can reveal the impact to the system frequency of operation mode change and load variation, and present the output adjustment of the generators. The proposed model can be solved conveniently by the block solving technology based on the fast decoupled power flow algorithm. The scheme presented in this paper has been tested on the IEEE standard 30‐bus test system by simulating basic operation and primary and secondary frequency regulation of the generators, which demonstrated the validity by the method. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

A Digital Measurement of Earth Fault Loop-Impedance Using a Parameter Estimation Algorithm

ABSTRACT

In electrical low voltage power system, a neutral earthing is used for protection against electrical shock hazards. Testing of the effectiveness of the earthing system could be achieved by measuring the system fault loop impedance Z. This paper presents a new application of least error squares (LES) parameter estimation algorithm for measurement of earth fault impedance, the proposed method uses the digitized samples of the instantaneous voltage across the fault loop impedance, effects of data window size, sampling rate and the voltage frequency drift on the accuracy of the impedance measurements are studied. Simulated test results are reported in this paper, which from the basis of our conclusion.     

电力系统软件测频的改进方法

频率是电力系统中一个非常重要的特征量,同时频率也是继电保护、测控等继电保护装置进行相应动作的重要判据,因此频率测量是电力系统测量装置中十分重要的环节。电力系统最常用的软件测频方法为离散傅氏算法,采用分段三次Herm ite插值对离散傅氏测频算法进行改进。所提出的新改进方法具有精度高,计算量相对不大,实时性好的优点。通过数值仿真,分析了本改进方法的时间响应数据窗、绝对误差和谐波对本方法的影响。理论和仿真结果都证明本方法的实用性好。     

基于Sigma点卡尔曼滤波器的电力频率跟踪新算法

通过变换,首先将三相电压信号转换成一复电压信号,再利用一种复数型Sigma点卡尔曼滤波(CSPKF)算法以改进对发生谐波畸变和随机噪声干扰的电力系统电压信号的频率进行动态估计和跟踪的过程。理论证明,CSPKF算法与现有的复数型扩展卡尔曼滤波(ECKF)算法相比具有更佳的跟踪精度和稳定性。此外,CSPKF算法还成功解决了所有卡尔曼滤波算法都必须面对的当算法收敛后,系统参数发生突变的情况下需要重置误差协方差矩阵来重新跟踪这些变化的问题,进一步提高了其跟踪速度。对几种暂态电力信号模型的算法仿真表明,CSPKF算法具有优异的动态跟踪性能,迅速跟踪频率和幅值变化的同时又保持了较低的跟踪误差。