基于SGEAC法的电力系统暂态稳定分析与控制
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摘要
随着国民经济的发展，电力的需求日益增加，电能已经成为现代社会不可或缺的一部分。现代电力系统一旦发生事故，就有可能威胁到社会稳定，造成重大的经济损失。因此，电力系统安全稳定运行是居民正常生活的保障，是电网正常运行的基本条件。为防止电网受大扰动后，系统暂态失去稳定，造成大面积停电事故，本文对电力系统的暂态稳定、紧急控制和预防控制算法进行了深入研究，评估电力系统的暂态稳定裕度，制定出合理的控制措施，确保电力系统能够安全稳定运行。
单机无穷大母线(One Machine Infinite Bus, OMIB)等值法定义了动态OMIB等值的稳定裕度，揭示了OMIB等值机械功率的调节对暂态稳定的影响。本文从OMIB等值和单机等面积定则原理(Single Generator Equal Area Criterion, SGEAC)的基础理论出发，研究和比较了OMIB等值和基于SGEAC法的2个单等值机组的暂态稳定、紧急控制和预防控制算法。研究表明单等值机组的稳定裕度、紧急控制和预防控制需调节的机械功率和OMIB等值机完全相等。更好地理解了基于不同等值机组暂态稳定的一致性以及各等值机组机械功率的调节对暂态稳定的影响。
选取短时间内OMIB等值或2个单等值机组的时域仿真数据，利用最小二乘法拟合出电磁力矩关于转子角的多项式函数。根据多项式函数和稳定裕度的定义式，得出了首摆失稳情况下各等值机紧急控制和预防控制需调节的最小机械功率的数学表达式。针对多摆失稳情况，比较和分析了各等值机首摆、二摆的稳定裕度与控制量之间的关系，提出了一种简单的临界控制量计算方法。通过实验仿真，验证了计算方法的准确性和有效性。
根据SGEAC法的特点，给出了系统的稳定判据、临界机群识别和紧急控制方案的选择等详细步骤，设计了电力系统暂态稳定紧急控制自动计算程序。在IEEE17机测试系统和实际大规模电力系统中对各种失稳模式进行了测试，测试结果表明该自动计算程序计算精度高、计算速度快，具有一定的实际工程应用价值。
随着现代电力系统以及新能源的大规模发展，电力系统中出现了大量含有时间常数极小的模型或元件，如双馈感应发电机等。本文根据Matlab/Simulink中的双馈感应发电机组模型编写了可适用于电力系统暂态仿真程序的风力发电机组动态模型，并利用牛顿迭代法精确求解双馈感应发电机组的初始值。通过在单机无穷大系统上的仿真计算，验证了双馈感应发电机组模型和初始值计算的准确性和适用性。
含有时间常数极小的模型或元件的出现使电力系统由原来的“非刚性”系统变成了“刚性”系统。传统的改进欧拉法或隐式梯形法均不适合求解“刚性”系统。本文根据电力系统自身特点，结合改进欧拉法和隐式梯形法的优点，提出一种可精确求解“刚性”系统的多步长快速数值积分方法，并从理论上分析了数值积分方法的数值稳定性与稳定域。利用该计算方法对简单“刚性”系统进行数值计算，计算结果与理论分析一致。
针对“刚性”电力系统，结合多步长快速数值积分方法，提出了一种电力系统快速暂态仿真方法。该方法在系统积分步长不变的情况下，通过可变参数改变含极小时间常数模型的积分步长。含极小时间常数模型在改变后的步长下进行数值计算，此过程无需求解电力系统网络方程。当含极小时间常数模型的积分时间和系统积分时间同步时，含极小时间常数模型与系统中其他模型统一进行精确的数值计算。含双馈感应发电机电网的暂态仿真结果表明，该仿真方法计算速度快、精度高，是一种有效、适用的计算方法。
分析了短路棒保护对双馈感应发电机组暂态特性的影响，仿真结果表明含有短路棒保护的双馈感应发电机组具有一定的故障穿越能力。利用SGEAC法对含风电场的电力系统进行了暂态稳定分析与控制，仿真结果表明SGEAC法同样适用于含风电场的电力系统，拓展了SGEAC法的应用范围。
With the development of the national economy, the ever-increasing demand ofelectric energy has made it an essential part in modern society. Any fault in themodern power system may be a threat to the social stability and economic growth.Therefore, the steady and safe operation of the power system is gurantee of people’sdaily life as well as the element of the grid operation. The main reason causing blackout is that the transient state of the power system works on unstable condition duringthe large disturbance. In view of the steady and safe of the power system, it proposesthe control method by estimating the transient stability margin based on the transientstability, preventive and emergency control algorithm in this paper.
The one machine infinite bus (OMIB) method, which have defined transientstability margin of dynamic OMIB, is shown that mechanical power adjustment basedon OMIB equivalent affects the transient stability. In this paper, in accordance of thebasic theory of OMIB equivalent and Single Generator Equal Area Criterion (SGEAC),the analysis of stability margin, the preventive and the emergent control of OMIBequivalent are studied and compared by using the equal area criterion based on OMIBand single equivalent. It is discovered that single equivalent based on the stabilitymargin, emergent and preventive mechanical power adjustment is exactly identicalwith the stability margin, emergent and preventive mechanical power adjustmentbased on OMIB equivalent. The understandings on the consistency based on differentequivalents and the influence between the mechanical power adjustment of eachequivalent and the transient stability are easier.
We choose the data of the OMIB equivalent or the single equivalent generators inshort time as the Time-domain simulate data. And fit the rotor angle’s polynomialfunction of electromagnetic torque. Then get the arithmetic expression of stabilitymargin, preventive and emergent mechanical power adjustment in each equivalentgenerator during the fist swing on unstable condition. On the basis of those arithmeticexpressions, a calculation method for the amount of critical control during eachequivalent generator on unstable condition after first swing is proposed in this paper.System transient stability analysis results by simulations verify the theoretical results.
In views of features of SGEAC method, it proposes an automatic calculationprogram to get the emergent mechanical power adjustment for the transient stability. This program in detail can verdicts the transient stability, distinguishes criticalgenerators, chooses the emergent control plan, and so on. The IEEE17test system andlarge-scale practical power system are checked out for evaluating the performance.Not only the high computational accuracy but also the fast counting rates are verifiedby the results of the tests. It is useful to the engineering application.
As modern power system and new energy developed dramatically along, powersystem including several sections with tiny time constant, such as double feedinduction generator (DFIG), is popular recently. According to the DFIG model inMatlab/Simulink, it builds a wind power generation model for transient simulateprogram in power system, and calculated the initial value of the DFIG by Newtoniterative method. The results by simulating on one machine infinite system verify theprecision of the theoretical model and computing method.
Because of the power system contained several sections with tiny time constant,the primary “nonrigid” power system is changed into “rigid” system. And it can not beanalyzed by the Euler method and the implicit trapezoid method. For this reason weproposed a new improved numerical method involved into the Euler method and theimplicit trapezoid method. This numerical method suits for the features of powersystem, can solve “rigid” system with high accuracy rate and is the multi-stepnumerical integration method with the analysis of the numerical stability and stabilitydomain. The consistency between the results calculated by that numerical method andtheoretical values are shown in the “rigid” system.
A fast transient simulation method linked with the multi-step fast numericalintegration method for rigid power system also is proposed in this paper. Underconstant system integration step size, the integration step size of sections with tinytime constant can be changed by the variable parameter. Thus the numericalcalculation method of the model with tiny time constant can be obtained by thechanged step size regardless of the solution of network equations in power system. Itis note that the model with tiny time constant should be taken exact numericalcalculation with other elements in power system when the integration time of themodel with tiny time constant synchronizes with the system’s integration time. Theresults from the simulation about the DFIG show that the proposed method with fastcalculation speed and high precision is effective and practical.
For transient features of DFIG affected by the protection of the crowbar, faultride-though capability of DFIG with crowbar are verified by the simulation results.The power system including the wind farm as object is analyzed and controlled by the SGEAC methods. According to the results obtained by the simulations, the SGEACmethod is feasible and its application range is obviously expanded.
单机无穷大母线(One Machine Infinite Bus, OMIB)等值法定义了动态OMIB等值的稳定裕度，揭示了OMIB等值机械功率的调节对暂态稳定的影响。本文从OMIB等值和单机等面积定则原理(Single Generator Equal Area Criterion, SGEAC)的基础理论出发，研究和比较了OMIB等值和基于SGEAC法的2个单等值机组的暂态稳定、紧急控制和预防控制算法。研究表明单等值机组的稳定裕度、紧急控制和预防控制需调节的机械功率和OMIB等值机完全相等。更好地理解了基于不同等值机组暂态稳定的一致性以及各等值机组机械功率的调节对暂态稳定的影响。
选取短时间内OMIB等值或2个单等值机组的时域仿真数据，利用最小二乘法拟合出电磁力矩关于转子角的多项式函数。根据多项式函数和稳定裕度的定义式，得出了首摆失稳情况下各等值机紧急控制和预防控制需调节的最小机械功率的数学表达式。针对多摆失稳情况，比较和分析了各等值机首摆、二摆的稳定裕度与控制量之间的关系，提出了一种简单的临界控制量计算方法。通过实验仿真，验证了计算方法的准确性和有效性。
根据SGEAC法的特点，给出了系统的稳定判据、临界机群识别和紧急控制方案的选择等详细步骤，设计了电力系统暂态稳定紧急控制自动计算程序。在IEEE17机测试系统和实际大规模电力系统中对各种失稳模式进行了测试，测试结果表明该自动计算程序计算精度高、计算速度快，具有一定的实际工程应用价值。
随着现代电力系统以及新能源的大规模发展，电力系统中出现了大量含有时间常数极小的模型或元件，如双馈感应发电机等。本文根据Matlab/Simulink中的双馈感应发电机组模型编写了可适用于电力系统暂态仿真程序的风力发电机组动态模型，并利用牛顿迭代法精确求解双馈感应发电机组的初始值。通过在单机无穷大系统上的仿真计算，验证了双馈感应发电机组模型和初始值计算的准确性和适用性。
含有时间常数极小的模型或元件的出现使电力系统由原来的“非刚性”系统变成了“刚性”系统。传统的改进欧拉法或隐式梯形法均不适合求解“刚性”系统。本文根据电力系统自身特点，结合改进欧拉法和隐式梯形法的优点，提出一种可精确求解“刚性”系统的多步长快速数值积分方法，并从理论上分析了数值积分方法的数值稳定性与稳定域。利用该计算方法对简单“刚性”系统进行数值计算，计算结果与理论分析一致。
针对“刚性”电力系统，结合多步长快速数值积分方法，提出了一种电力系统快速暂态仿真方法。该方法在系统积分步长不变的情况下，通过可变参数改变含极小时间常数模型的积分步长。含极小时间常数模型在改变后的步长下进行数值计算，此过程无需求解电力系统网络方程。当含极小时间常数模型的积分时间和系统积分时间同步时，含极小时间常数模型与系统中其他模型统一进行精确的数值计算。含双馈感应发电机电网的暂态仿真结果表明，该仿真方法计算速度快、精度高，是一种有效、适用的计算方法。
分析了短路棒保护对双馈感应发电机组暂态特性的影响，仿真结果表明含有短路棒保护的双馈感应发电机组具有一定的故障穿越能力。利用SGEAC法对含风电场的电力系统进行了暂态稳定分析与控制，仿真结果表明SGEAC法同样适用于含风电场的电力系统，拓展了SGEAC法的应用范围。
With the development of the national economy, the ever-increasing demand ofelectric energy has made it an essential part in modern society. Any fault in themodern power system may be a threat to the social stability and economic growth.Therefore, the steady and safe operation of the power system is gurantee of people’sdaily life as well as the element of the grid operation. The main reason causing blackout is that the transient state of the power system works on unstable condition duringthe large disturbance. In view of the steady and safe of the power system, it proposesthe control method by estimating the transient stability margin based on the transientstability, preventive and emergency control algorithm in this paper.
The one machine infinite bus (OMIB) method, which have defined transientstability margin of dynamic OMIB, is shown that mechanical power adjustment basedon OMIB equivalent affects the transient stability. In this paper, in accordance of thebasic theory of OMIB equivalent and Single Generator Equal Area Criterion (SGEAC),the analysis of stability margin, the preventive and the emergent control of OMIBequivalent are studied and compared by using the equal area criterion based on OMIBand single equivalent. It is discovered that single equivalent based on the stabilitymargin, emergent and preventive mechanical power adjustment is exactly identicalwith the stability margin, emergent and preventive mechanical power adjustmentbased on OMIB equivalent. The understandings on the consistency based on differentequivalents and the influence between the mechanical power adjustment of eachequivalent and the transient stability are easier.
We choose the data of the OMIB equivalent or the single equivalent generators inshort time as the Time-domain simulate data. And fit the rotor angle’s polynomialfunction of electromagnetic torque. Then get the arithmetic expression of stabilitymargin, preventive and emergent mechanical power adjustment in each equivalentgenerator during the fist swing on unstable condition. On the basis of those arithmeticexpressions, a calculation method for the amount of critical control during eachequivalent generator on unstable condition after first swing is proposed in this paper.System transient stability analysis results by simulations verify the theoretical results.
In views of features of SGEAC method, it proposes an automatic calculationprogram to get the emergent mechanical power adjustment for the transient stability. This program in detail can verdicts the transient stability, distinguishes criticalgenerators, chooses the emergent control plan, and so on. The IEEE17test system andlarge-scale practical power system are checked out for evaluating the performance.Not only the high computational accuracy but also the fast counting rates are verifiedby the results of the tests. It is useful to the engineering application.
As modern power system and new energy developed dramatically along, powersystem including several sections with tiny time constant, such as double feedinduction generator (DFIG), is popular recently. According to the DFIG model inMatlab/Simulink, it builds a wind power generation model for transient simulateprogram in power system, and calculated the initial value of the DFIG by Newtoniterative method. The results by simulating on one machine infinite system verify theprecision of the theoretical model and computing method.
Because of the power system contained several sections with tiny time constant,the primary “nonrigid” power system is changed into “rigid” system. And it can not beanalyzed by the Euler method and the implicit trapezoid method. For this reason weproposed a new improved numerical method involved into the Euler method and theimplicit trapezoid method. This numerical method suits for the features of powersystem, can solve “rigid” system with high accuracy rate and is the multi-stepnumerical integration method with the analysis of the numerical stability and stabilitydomain. The consistency between the results calculated by that numerical method andtheoretical values are shown in the “rigid” system.
A fast transient simulation method linked with the multi-step fast numericalintegration method for rigid power system also is proposed in this paper. Underconstant system integration step size, the integration step size of sections with tinytime constant can be changed by the variable parameter. Thus the numericalcalculation method of the model with tiny time constant can be obtained by thechanged step size regardless of the solution of network equations in power system. Itis note that the model with tiny time constant should be taken exact numericalcalculation with other elements in power system when the integration time of themodel with tiny time constant synchronizes with the system’s integration time. Theresults from the simulation about the DFIG show that the proposed method with fastcalculation speed and high precision is effective and practical.
For transient features of DFIG affected by the protection of the crowbar, faultride-though capability of DFIG with crowbar are verified by the simulation results.The power system including the wind farm as object is analyzed and controlled by the SGEAC methods. According to the results obtained by the simulations, the SGEACmethod is feasible and its application range is obviously expanded.
引文
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