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The electric spring (ES) is a contemporary device that has emerged as a viable alternative for solving problems associated with voltage and power stability in distributed generation-based smart grids (SG). In order to study the integration of ESs into the electrical network, the steady-state simulation models have been developed as an essential tool. Typically, these models require an equivalent electrical circuit of the in-test networks, which implies adding restrictions for its implementation in simulation software. These restrictions generate simplified models, limiting their application to specific scenarios, which, in some cases, do not fully apply to the needs of modern power systems. Therefore, a robust steady-state model for the ES is proposed in this work to adequately represent the power exchange of multiples ESs in radial micro-grids (µGs) and renewable energy sources regardless of their physical location and without the need of additional restrictions. For solving and controlling the model simulation, a modified backward–forward sweep method (MBFSM) is implemented. In contrast, the voltage control determines the operating conditions of the ESs from the steady-state solution and the reference voltages established for each ES. The model and algorithms of the solution and the control are validated with dynamic simulations. For the quasi-stationary case with distributed renewable generation, the results show an improvement higher than 95% when the ESs are installed. On the other hand, the MBFSM reduces the number of iterations by 34% on average compared to the BFSM.

A Robust Electric Spring Model and Modified Backward Forward Solution Method for Microgrids with Distributed Generation