Abstract: Analyzing the active power carrying capacity and the source-network-load coordination remains a challenging issue in power grid security assessment. The dominant line load balance index derived from singular value decomposition of the time-sequential matrix of load rates can not only be converted into a dominant dynamic balance index for evaluating source-network-load coordination but also demonstrates consistency with mapped elastic potential energy trends. This characteristic can be used to characterize the active power carrying capacity and the power-angle security of the power grid. Case study simulations validate these properties. This quantitative index can be applied to optimize load distribution, improve grid structure, and guide targeted planning of power grids.