The advent of smart power grid which plays a vital role in the upcoming smart city era is accompanied with the implementation of a monitoring tool, called state estimation. For the case of the unbalanced residential distribution grid, the state estimating operation which is conducted at a regional scale is considered as an application of the edge computing-based Internet of Things (IoT). While the outcome of the state estimation is important to the subsequent control activities, its accuracy heavily depends on the data integrity of the information collected from the scattered measurement devices. This fact exposes the vulnerability of the state estimation module under the effect of data-driven attacks. Among these, false data injection attack (FDI) is attracting much attention due to its capability to interfere with the normal operation of the network without being detected. This paper presents an attack design scheme based on a nonlinear physical-constraint model that is able to produce an FDI attack with theoretically stealthy characteristic. To demonstrate the effectiveness of the proposed design scheme, simulations with the IEEE 13-node test feeder and the WSCC 9-bus system are conducted. The experimental results indicate that not only the false positive rate of the bad data detection mechanism is 100 per cent but the physical consequence of the attack is severe. These results pose a serious challenge for operators in maintaining the integrity of measurement data.