计及光伏并网的电力系统频率特性和网络方程电压可解性分析

随着新能源大容量并网，电力系统面临转动惯量不足、电压支撑能力弱等问题，电力系统频率和电压稳定问题突出。考虑光伏并网情况，提出了量化电力系统频率特性和网络方程可解性的分析方法。一方面，基于电力系统近似全状态模型，通过状态变量时域响应的解析解，分析了系统参数对频率特征量的影响，证明了在全状态模型下光伏附加频率控制不改变系统惯量但能够增加系统阻尼。进一步，指出系统频率响应主要由主导模式决定，给出了主导特征值的解析计算式。另一方面，聚焦网络方程，分析雅可比矩阵奇异性等值条件，基于实对称矩阵的最小特征值提出一种量化电压可解性的负定性指标。并应用该负定性指标，借助图论分析方法论证了随着电网中光伏渗透率增加，电压可解性下降，电压稳定性恶化。最后，在4机11节点经典算例和实际电网中验证了上述分析方法的有效性。

Analysis of frequency characteristic and voltage solvability of network equation considering photovoltaic grid-connected power system

With the large-scale interconnection of new energy, the power system is facing problems such as insufficient of rotational inertia and weak voltage support capability, the frequency and voltage stability pro-blems become prominent. Considering the photovoltaic grid-connected situation, the analysis methods to quantify the frequency characteristics of power systems and the solvability of network equations are proposed. On the one hand, based on an approximate full-state model of power system, the influence of the system parameters on the frequency characteristic is analyzed through the analytical solution of the time-domain response for the state variables. It is proved that the photovoltaic supplementary frequency control under full-state model does not change the system inertia but can increase the system damping. Furthermore, it is pointed out that the frequency response of system is mainly determined by the dominant mode, and the analytical calculation formula of the dominant eigenvalues is given. On the other hand, focusing on network equations and analyzing the equivalence conditions of Jacobian matrix singularity, a negative qualitative index for quantifying the voltage solvability is proposed based on the minimum eigenvalue of real symmetric matrix. Using this negative qualitative index, and with the help of graph theory analysis, it is demonstrated that with the increase of photovoltaic penetration in the grid, the voltage solvability decreases and the voltage stability deteriorates. Finally, the effectiveness of the above analysis methods is verified using the typical 4-machine and 11-bus test system and an actual power system.