Urban power distribution networks (UDNs) play an important role but they have not been designed to sustain the ever- increasing growth of distributed generation such as solar. Because of the intermittency of such generation, UDNs are suffering from voltage and frequency fluctuations. Moreover, to maintain power quality and reliability, grid devices such as transformer taps are forced to be adjusted frequently, and rapidly reach their end of lives. In this paper, an urban network with one solar farm and several distributed generators is considered. It is assumed that the network is well-balanced, and economic dispatch (ED) is performed. With significant levels of solar penetration, such ED is challenging since (1) the intermittent nature of solar generation makes the problem stochastic and complicated; (2) AC power flow and tap changer equations make the problem highly nonlinear; and (3) discrete decisions (tap positions) makes the problem combinatorial. These difficulties will be resolved by (1) handling uncertainties through the use of Markov chains; (2) novel dynamic linearization through the use of absolute-value functions; (3) a decomposition and coordination approach with accelerated convergence. Testing results on a simple 3-bus and a modified 34- bus system demonstrate that the method converges fast, and has the potential to solve practical distribution ED problems.