By retrospecting large-scale quasi-geostrophy theory and many kinds of balance equations and models,including some methods of the diagnosis of unbalanced flow,the authors make the concrete mathematics definitions for balance equations and imbalance equations as well as point out their physical meanings.Furthermore,the authors analyze many mesoscale strong-convective systems and conclude that there also exist balanced motions in the mesoscale convective system.But in the mesoscale strong-convective system the divergent wind is strong and the vertical motion cannot be neglected,so all those balance equations based on divergent equation are not adapt to be used in the analysis of mesoscale balanced or unbalanced motion.Thus it is presented to construct a kind of new balance equation which includes the divergence,vorticity and vertical motion simultaneously.After the scale-analysis of helicity equation,the authors find a balance equation which meets well that condition.On the basis of this,the authors infer horizontal divergence equation,vertical vorticity equation,continuity equation and thermal dynamic equation under the same approximations.All these equations form a set of new balance model.As to the new balance equation,the imbalance equation is to retain all other relative small terms in the primitive equation,thus it is equal to the helicity equation.If the unbalanced process is divided into two periods,the imbalance equation can be decomposed into two equations.Furthermore,it is found that the two periods of the unbalanced flow can separately be connected to the horizontal helicity and vertical helicity,that is,the horizontal helicity and vertical helicity can be taken as the tools of diagnosing unbalanced flow.