电磁暂态算法比较及非线性模型研究

1、电磁暂态算法比较及非线性模型研究        【中文摘要】当今国内外在电力系统电磁仿真方面具有代表性的软件包括EMTP电磁暂态仿真计算程序、EMTPE电磁暂态仿真软件包、NETOMAC仿真计算程序、PSCAD/EMTDC仿真软件等,其中EMTP和EMTDC较为常用。EMTP结合了贝瑞隆方法和梯形法,可以对电力系统中从数微秒到数秒之间的电磁暂态过程进行仿真模拟。本课题在分析传统电力系统电磁暂态计算方法的基础上,主要针对非线性元件进行研究,分析电力系统非线性元件特性。本文提出了求解任意拓扑连接的非线性元件的新算法,并

2、对新算法进行了理论推导、证实和仿真分析。仿真结果表明,新算法理论正确,并能够在不连续点处消除数值振荡。本文具体的研究内容包括:1、分析了常用电磁暂态时域离散化方法的精度和稳定性。离散方法包括梯形法、向后欧拉法、向前欧拉法、Simpson法和Gear Second Order法。梯形法在低频时精度高,但是稳定性不好;向后欧拉法稳定性好,但是精度不够高;向前欧拉法是显式积分,稳定性较差;Simpson法精度较高,稳定性也较差;Gear 2法的精度和稳定性一般。2、分析比较非线性元件算法,即分段线性化和补偿法的优缺点。讨论EMTP和Microtran分段线性化方法的不同。Microtran分段线性化

3、方法的优点是,有效克服了段到段过渡时的“过冲”题目。补偿法用戴维南等效电路替换线性网络部分,用电流源等效非线性元件,根据叠加原理求解电路。补偿法的优点是可以减少运算时间,缺点是只适用于求解含少量非线性元件的电路。3、引进电磁暂态计算新模型算法,具体推导非线性元件的离散伴随电路模型。非线性微分方程一般没有解析解,为了验证新方法的正确性,巧妙地构建电路中非线性元件的伏安特性,使得电路有解析解。然后利用MATLAB对新算法离散伴随电路编程,得到电路的数值解,数值解与解析解完全吻合,从而验证了新算法的正确性。4、三角形连接的三个单相真非线性元件在ATP和EMTDC中不能运行,由于戴维南等效阻抗矩阵是奇

4、异矩阵,没有逆矩阵。本文利用新算法建立了非线性元件三角形连接的等效网络,并将其离散化得到伴随电路,利用MATLAB求解,得到了电路的计算结果,这表明新算法可以求解任意拓扑结构的非线性网络,体现了新算法的优越性。5、在非线性元件伏安特性或磁通-电流特性中,梯形法在不连续点处难以避免的会出现数值振荡题目,现有的ATP和EMTDC仿真软件都是通过CDA技术解决的,但是在仿真计算中,突变点处会出现错误的“毛刺”。本算法有效地消除了数值振荡,并且不会在突变点产生“毛刺”,这是新算法的又一突出优点。');【Abstract】 The power system electromagnetic tra

5、nsient simulation softwares include electromagnetic transient program, Electromagnetic Transient & Power electronics, Network Torsion Machine Control, Electro-Magnetic Transient in DC System and so on. EMTP and PSCAD/EMTDC are more commenly. EMTP is a numerical solution, combined Bergeron's

6、method and the trapezoidal rule, which can simulate the electromagnetic transient process from microseconds to seconds. A breakthrough to this subject is of great importance both in theory and reality, for analyzing and studying power system nonlinear characteristics as well as enhancing power syste

7、m stability and reliability. A new algorithm is put forward. Newton-Raphson discrete equivalent circuits for nonlinear resistors and linear companion circuits for nonlinear inductors are derived in detail, proved theoretically, and verified computationally. The simulation results show that the new a

8、lgorithm is corrent, and can elimate the numerical oscillation in the discontinuous points. The research includes the following contents:1. The * introduces the commonly discrete time-domain methods in electromagnetic transient and their accuracy and stability. It includes Trapezoidal, Backward Eule

9、r, Forward Euler, Simpson and Gear Second Order methods. Trapezoidal has high accuracy, but it is prone to generate numerical oscillations at discontinuities. Backward Euler is stable, but it has strong phase error. The Forward Euler is unstable. Simpson has very good response but is unstable. Gear

10、2 is a compromise between trapezoidal and Backward Euler.2. This thesis discusses the piecewise-linear and compensation, and summarizes advantages and disadvantages. Microtran piecewise-linear method proposed in this * is the basis of the new algorithm, the benefits are effective to overcome the seg

11、ment to segment transition overshoot, but CDA technology is needed to overcome numerical oscillation between segment and segment. Compensation is based on the Thevenin equivalent circuit. It substitutes the linear network, and the nonlinear element is placed by an equivalent current source. The supe

12、rposition principle is important. The compensation reduces the computing time, but it can only solve the network with few nonlinear elements.3. This thesis gives a new electromagnetic transient algorithm, derivates the discrete companion circuits. The nonlinear differential equation generally does n

13、ot have an analytic solution. However, in this particular case the characteristics of the nonlinear elements are purposely chosen such that an analytic solution exists. Newton-Raphson discrete equivalent circuits for nonlinear resistors and linear companion circuits for nonlinear inductors are deriv

14、ed in detail, proved theoretically, and verified by MATLAB programming.4. Triangle linking of three single-phase true-nonlinear elements in the EMTP can not run, because Thevenin equivalent impedance matrix is singular matrix, not inverse matrix. A few examples are solved by the new algorithm, highl

15、ighting the advantages of the algorithm. The algrithom canbe applied to arbitrary topological nonlinear network.5. In the V-A characteristics and flux-current characteristics, the trapezoidal mothod will lead to numerical oscillation near discontinuous points. ATP and EMTDC both adopt CDA technology to solve the problem, but "shoot" occurs in the si