In the context of single load infinite bus system with load containing a group of induction motors

analysis method for macro law of induction motor cascading stall is proposed under certain assumptions. The method calculates PDF of cascading stall directly using formula from CASCADE model and hence Monte Carlo simulations are no longer needed. Cases studies verify that the method can achieve good accuracy when cascading stall happens moderately. The studies of impact factors of cascading stall reveal that 1) good linear relationship exists between load level and parameters for system initial shock and cascading propagation

and hence at critical condition

the probability of zero stall drops exponentially as load increases; 2) the space between contours of same expected stall number reflects the extent of cascading stall propagation

the smaller the space is

the easier cascading propagates

and hence

the bigger the probability of large scale of cascading stall is; 3) distribution of motor’s initial power and differences among motors’ initial power have very little impact on PDF of cascading stall scale