  Zonal pricing is a well-suited mechanism to incentivize grid-supporting
behavior of profit-maximizing producers and consumers operating on a
large-scale power system. In zonal electricity markets, local system operators
create individual price zones, which provide appropriate price signals
depending on local grid conditions such as an excess or shortage of electrical
energy in certain regions. In this paper, a continuous-time zonal pricing
controller for AC power networks is presented that ensures frequency and
voltage stability as well as Pareto efficiency of the resulting closed-loop
equilibria. Based on a dynamic network model taking into account line losses
and power exchange with adjacent price zones, distributed control laws are
derived which require only neighbor-to-neighbor communication. Case studies on
the IEEE-57 bus system with different pricing concepts illustrate how zonal
prices enable consideration of regional supply and demand conditions as well as
increased robustness compared to an isolated grid operation.
