Abstract: After a disturbance in the power grid, frequencies at different buses are different, which is called spatial distribution of frequency. The frequency divider (FD) formula has been proposed to estimate the frequency distribution of a power grid, but the derivation of the formula involves some assumptions and simplifications which may lead to large errors. This work derives a formula to accurately estimate the frequency distribution based on the concept of complex frequency (CF), which considers both the changes in magnitude and angle of a phasor. By using this formula, we can understand the frequency spatial distribution mechanism of the power grid and reveal the inherent laws of frequency distribution, and demonstrate that the level of frequency distribution is related to the impedance distribution and voltage level of the network. Compared to FD, network resistance, load, magnitude and angle of voltages are all taken into consideration. The effectiveness of the formula is validated with simulation results in the IEEE 39-bus and IEEE 145-bus system.

Key words: complex frequency, frequency distribution, frequency divider, frequency dynamics