Transient stability study of power systems with high-order models based on hybridizing loop solving and vector computation

Abstract

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.