In this paper, the idea of solving algebraic equations (AEs) through the fixed-point iterative method (FPIM) is generalized for the differential algebraic equations (DAEs) of power systems in order to analyze transient stability problems, which are particularly relevant when the number of DAEs in high-order models increase. In the loop form, reducing the number of variables by explicitly solving AEs is no longer required. It also allows for adding or removing the equations in order to easily analyze the effect of equations in the system's response. Furthermore, through the loop solving (LS) mechanism, the simplification assumption about power consumption in the PQ buses to fixed impedances is not necessary and the loads can be assumed with each arbitrary model. The LS mechanism is the first innovation provided hereby which facilitates the programming of high-order models and increases the accuracy of the system's response. On the other hand, because consistent and redundant variables are in place, solving DAEs in the loop form requires an iterative method with strong a convergence property that provides a convergent solution to the load flow (LF) AEs, and then a convergence solution for the DEs of the machines. This can be developed by extending the FPIM to the traditional Gauss-Siedel (GS) method, called modified GS (MGS), which is the second innovation herein. It can converge the solution of LF equations to the equilibrium point despite the numerical anomalies. Moreover, in order for the same performance as that of the MGS to be achieved, the Newton-Raphson (NR) method is first developed by a new formulation to full complex form, called complex based NR (CNR), which is the third innovation addressed hereby, and then applied with the same technique as that of the MGS to modified NR (MNR). The CNR increases the speed and simplicity of the LF computations and does not require decomposition of AE for both real and imaginary components; therefore, it simplifies the simulation training problems and reduces the computational time for large system dimensions. The proposed method is implemented in Simulink/MATLAB, tested and validated for the Western System Coordinated Council (WSCC) IEEE 9-bus system and compared with the results obtained by power system simulators, such as PowerWorld (PW) and SymPowerSystems (SPSs), and previous works published in the literature. Then, the experience gained from the first test is also applied to the IEEE 57-bus test system as a large scale system. The simulation results show the ability of the proposed method to represent the system's response for severe transient conditions, with better results than those achieved by previous methods. The new results are obtained from the effect of the network's transient on mechanical response of some synchronous machines. Also, the importance of removing damping coils in the system's transient response and the transition of response divergence during the severe fault with the method proposed hereby can be observed.

本文针对电力系统的微分代数方程（DAE）推广了采用定点迭代法（FPIM）求解代数方程（AEs）的思想，以分析暂态稳定问题。高阶模型中的DAE数量增加。在循环形式中，不再需要通过显式求解AE来减少变量的数量。它还允许添加或删除方程式，以便轻松分析方程式对系统响应的影响。此外，通过环路求解（LS）机制，不需要将PQ总线中的功耗降至固定阻抗的简化假设，并且可以使用每个任意模型来假设负载。LS机制是由此提供的第一个创新，它有助于对高阶模型进行编程并提高系统响应的准确性。另一方面，由于存在一致且冗余的变量，因此以循环形式求解DAE时需要一种具有强收敛性的迭代方法，该迭代方法可为潮流（LF）AE提供收敛解，然后为潮流（AE）提供收敛解。机器的DE。这可以通过将FPIM扩展到传统的Gauss-Siedel（GS）方法（称为改进的GS（MGS））来开发，这是本文的第二项创新。尽管存在数值异常，它仍可以将LF方程的解收敛到平衡点。此外，为了获得与MGS相同的性能，牛顿-拉夫森（Newton-Raphson（NR））方法首先通过新的配方发展为完全复杂的形式，称为基于复杂物的NR（CNR），这是本文提出的第三项创新，然后应用与MGS相同的技术进行修改NR（MNR）。CNR可以提高LF计算的速度和简便性，并且不需要分解实部和虚部的AE。因此，它简化了模拟训练问题并减少了大系统尺寸的计算时间。所提出的方法在Simulink / MATLAB中实现，针对西方系统协调委员会（WSCC）的IEEE 9总线系统进行了测试和验证，并与诸如PowerWorld（PW）和SymPowerSystems（SPS）等电力系统仿真器获得的结果进行了比较，以及以前发表在文献中的作品。然后，从第一次测试中获得的经验也作为大规模系统应用于IEEE 57总线测试系统。仿真结果表明，所提出的方法能够代表严重瞬态条件下的系统响应，其结果要比以前的方法更好。从网络瞬变对某些同步电机的机械响应的影响中获得了新的结​​果。而且，可以观察到在此提出的方法在严重故障期间去除阻尼线圈对于系统的瞬态响应和响应发散过渡的重要性。对严重瞬态条件的响应，其结果比以前的方法要好。从网络瞬变对某些同步电机的机械响应的影响中获得了新的结​​果。同样，可以观察到在此提出的方法在严重故障期间去除阻尼线圈对于系统的瞬态响应和响应发散过渡的重要性。对严重瞬态条件的响应，其结果比以前的方法要好。从网络瞬变对某些同步电机的机械响应的影响中获得了新的结​​果。同样，可以观察到在此提出的方法在严重故障期间去除阻尼线圈对于系统的瞬态响应和响应发散过渡的重要性。