Abstarct: In recent years, with the development of electricity markets at the retail level and the increasing use of distributed and renewable energy resources, the concept of smartening the distribution network has been emerged. For a distribution smart grid, real-time monitoring of the network is of special importance. State estimation is considered an important tool for monitoring and operating the power network. To use state estimation, sufficient measurement devices are needed to make the network observable. A major challenge in distribution networks is the lack of an adequate number of measurement devices to make the network observable. To overcome this problem, virtual measurement devices can be used. Virtual measurement means assuming the presence of measurement devices at certain points in the network for some variables such as the load of a consumer or the generation of a power source. Then, the measured value by the device is used in the state estimation program, considering a mean value and a large error variance in the form of a normal (Gaussian) distribution function, using consumption or generation records. Professional state estimation programs are baxsed on Gaussian error distribution functions and work with the Weighted Least Squares (WLS) method. The use of normal distribution for points with renewable power injection increases the computation error due to the fact that the generation functions of these resources are not normal and follow other distributions such as Beta, Weibull, etc. Moreover, these distributions cannot precisely model their generation behavior. Additionally, algorithms like WLS cannot be used straightforwardly and efficiently with these distributions. In this thesis, by utilizing the Gaussian Mixture Model, non-normal distributions are divided into several normal distributions. The advantage of using this approach is the use of conventional and high-speed programs for state estimation in the distribution network. To compare the results, the Maximum Likelihood Estimation method is used for non-Gaussian functions using the Particle Swarm Optimization (PSO) algorithm. The obtained results demonstrate that this method can be used with sufficient accuracy. The data used is obtained from measurements of solar power generation at the ESPO Laboratory of Shahrood University of Technology and also from Elia, the Belgian power operator.