  The stability issue emerges as a growing number of diverse power apparatus
connecting to the power system. The stability analysis for such power systems
is required to adapt to heterogeneity and scalability. This paper derives a
local passivity index condition that guarantees the system-wide stability for
lossless power systems with interconnected, nonlinear, heterogeneous bus
dynamics. Our condition requires each bus dynamics to be output feedback
passive with a large enough index w.r.t. a special supply rate. This condition
fits for numerous existing models since it only constrains the input-output
property rather than the detailed dynamics. Furthermore, for three typical
examples of bus dynamics in power systems, we show that this condition can be
reached via proper control designs. Simulations on a 3-bus heterogeneous power
system verify our results in both lossless and lossy cases. The
conservativeness of our condition is also demonstrated, as well as the impact
on transient stability. It shows that our condition is quite tight and a larger
index benefits transient stability.
