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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 real-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 that takes line losses and power exchange with adjacent price zones into account, distributed continuous-time control laws are derived which require only neighbor-to-neighbor communication. Application to a real-time congestion management strategy illustrates how spatially and temporally differentiated prices enable grid-supportive operation of the participants without interventions by a superordinate control authority. Effectiveness of different zonal pricing concepts compared to an isolated grid operation is demonstrated through simulations on the IEEE-57 bus system. [ABSTRACT FROM AUTHOR]