Abstarct: Distribution System is an important part of a power system. Optimal operation of a distribution system needs to supervise and control accurately and completely. Thus, the measuring issue and state estimation have a great importance in new smart distribution grids. The measurement can be performed by the real-time measuring devices (PMUs) through a good communication infrastructure such as a Wireless Sensor Network (WSN). The first step in any analysis of state estimation is checking the observability of the system. It is very important to reduce measurement cost due to the high cost of PMUs used for observing the power network. Also the cost of communication equipment used for communication network observability should be decreased. So, the number of PMUs, their appropriate locations, type of the communication media and complete transfer of measurement data to the control center is noticeable. The main objective of this thesis is to find a trade-off between the observability of distribution system and the cost of measurement and sending data through infrastructure of wireless sensor network. For this purpose, a theorem tixtled “Network Connectivity” was proposed and proved. Then for the first time, an optimization problem was introduced so that considered the necessary constraints of observability adequacy of the power system and the communication network. The cost of measurement infrastructure and sending data was considered as the objective function. Besides, the impact of geographical restrictions on the number of optimized wireless sensor nodes (for communication network observability) also was studied. Finally, the problem was implemented on the IEEE 33-bus distribution system and the results were presented.