Frequency stability and stability of the grid voltages in the islands after an unusual event that leads to volatility and frequency fluctuations in the grid is very important and crucial for the proper functioning of the grid. Therefore, the stability analysis of micro grids is of particular importance. The stability analysis of conventional power systems is often done well, but in grid networks, it is necessary to check how the circuit functions, control and how to dampen fluctuations to ensure the stability of the grid. An appropriate mathematical model is essential for sustainability analysis. This dissertation presents modeling and stability analysis in the operating state of the islands of interconnecting, interconnecting, interconnecting, and interconnecting micro grids. For the modeling of all micro-grids, internal loop voltages and inverters and transducers are modeled in detail to observe all the modes of the grid for sustainability analysis. For ease of modeling, the overall system of the combined grid is divided into several subsections, the subsystems of the system are modeled with state-space equations, and finally all sub-sections are combined through the bases, and the overall model of the combined grid system is modeled in the form of state space equations. In the general modeling of the system, the bus voltages are used as a parameter for the connection of different micro grid components. In modeling the bus voltages, a virtual strength is used to connect the meshes to any arbitrary structure. Also, in a grid of direct current from the Boost converter to increase the voltage level of the distributed generation source used in previous work to facilitate system stability from the Buck converter. Due to the existence of some modes of relatively high frequency inverters and converters, the full dynamic network model is used instead of the algebraic impedance model. The complete model of the system is rooted around a work point, and the final-state matrix of the combined grid is used to extract special values. Using the extracted values, the stability of the combined grid system can be checked. In addition to conducting system stability, this study also identifies the relationship between system stability and system parameters, such as controller gain, in order to optimize the efficiency of controllers. Specific values or system modes indicate the frequency and rate of oscillation of component oscillations in the transient response of the system. The stability analysis of the grid also helps define the root of each mode and defines possible feedback signals for designing controllers to improve system stability. In the next simulation and modeling simulation, a mixed mesh grid is presented that demonstrates the correct and stable performance of the combined grid. Using the proposed model, the stability analysis of the specific values of the grid is done. Hybrid Microgrid, ac Microgrid, dc Microgrid, Modeling, Stability Analysis