In the general probability flow calculations, for facilitating
the calculation, the amounts of power injected into the system
nodes are assumed to be independent, or is completely
relevant. But for an actual system, the load is affected by the
nature of load, climate, season, geographical position and
density of local residents, making the relation complex among
injections of nodes. Some nodes can be considered
independent of each other, and some nodes are between
independence and fully correlation, called imperfect
correlation. The analytical method using semi-invariants for
the calculation can not take imperfect correlated nodes into
account. In this paper, in order to use the method, the
covariance matrix between the nodes is decoupled with
associated method, and nodes can be equivalent to independent
nodes and to meet the requirements of semi-invariants method.