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Mathematical electrical model
Steady-state analysis load model: when simple, it is expressed by given active power and reactive power. In active power and frequency regulation, reactive power and voltage regulation, the load active power frequency characteristic model and reactive power voltage characteristic model are used.

Transient analysis load model: constant impedance model is used to analyze the generator power characteristics of multi-machine system, and it is approximately believed that the power absorbed by the load from the system is always proportional to the square of the load node voltage.

All of the above comes from? Power system stability analysis in Chen Heng and transient analysis in Li Guangqi. Read it carefully.