Dynamic Load are represented with lead-lag time constants to represent oscillations (ie motors part of the load) when you have step voltage. In the case of the static load only the steady-state relation between U and PQ are modelling.
The question is relevant if an appropriate static equivalent method can be devised for some dynamic phenomenon (sometimes available).
To my understanding, when we apply load statically, part of the work done is stored in the form of strain energy and the part is lost (complementary strain energy). They may be equal to each other or unequal depending on the force-deformation characteristics of the system (linear or nonlinear). We may interpret a portion of the complementary strain energy part as an equivalent representation of the static equivalency of damping. The rest of complementary strain energy may represent the hysteretic energy dissipation.