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.

中文翻译：

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分布式发电微电网的鲁棒电弹簧模型和改进的后向求解方法

电动弹簧（ES）是一种现代设备，已成为解决基于分布式发电的智能电网（SG）中与电压和电源稳定性相关的问题的可行替代方案。为了研究ES集成到电网中，已将稳态仿真模型开发为必不可少的工具。通常，这些模型需要测试网络中等效的电路，这意味着要增加其在仿真软件中的实施限制。这些限制产生了简化的模型，将它们的应用限制在特定的情况下，在某些情况下，这些情况不能完全满足现代电力系统的需求。因此，在这项工作中，提出了一个稳定的ES稳态模型，以充分表示径向微电网（µGs）和可再生能源中多个ES的功率交换，而不管其物理位置如何，而无需其他限制。为了解决和控制模型仿真，实现了一种改进的后向-前向扫描方法（MBFSM）。相反，电压控制根据稳态解和为每个ES建立的参考电压来确定ES的工作条件。通过动态仿真验证了解决方案和控制的模型和算法。对于具有分布式可再生能源的准平稳情况，结果表明，安装ES时，改进率高于95％。另一方面，