Abstract This paper introduces an effective dynamic state estimator for Islanded Microgrids. Basing on a set of nonlinear Differential Algebraic equations representing the electrical grid and the energy sources, the Singular Perturbation Theory is used to obtain a modified mathematical representation of the Microgrid model to develop an effective dynamic state estimator based on the Unscented Kalman Filter. It is shown that Singular Perturbation Theory is a viable tool that permits the design of a dynamic estimator able to effectively recover the steady-state and dynamic states of the electrical grid, that is, the nodal voltages and the dynamic variables of generator units. Furthermore, the Microgrid state is suitably recovered using fewer measurements than those needed by conventional static estimators. The performance of the proposed scheme is evaluated using a practical Microgrid containing wind power and hydroelectric generators, under load and wind variations as well as three-phase faults. Also, this timely approach is compared with the Extended Kalman Filter for Differential Algebraic systems, demonstrating the superior effectiveness of the developed state estimator: the errors obtained by the new dynamic state estimator are 80% smaller than those obtained by the conventional Extended Kalman Filter, for the same applied noises. Moreover, a comparative study case with the Unscented Kalman Filter is included.

中文翻译：

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基于奇异摄动理论的孤岛微电网结构有效动态估计算法

摘要 本文介绍了一种有效的孤岛微电网动态状态估计器。基于一组表示电网和能源的非线性微分代数方程，奇异扰动理论用于获得微电网模型的修正数学表示，以开发基于无迹卡尔曼滤波器的有效动态估计器。结果表明，奇异扰动理论是一种可行的工具，它允许设计一个动态估计器，能够有效地恢复电网的稳态和动态状态，即节点电压和发电机组的动态变量。此外，使用比传统静态估计器所需的测量更少的测量来适当地恢复微电网状态。使用包含风力发电和水力发电机的实用微电网，在负载和风力变化以及三相故障的情况下评估所提出方案的性能。此外，这种及时的方法与用于微分代数系统的扩展卡尔曼滤波器进行了比较，证明了所开发状态估计器的卓越有效性：新动态状态估计器获得的误差比传统扩展卡尔曼滤波器获得的误差小 80%，对于相同的应用噪声。此外，还包括一个与无迹卡尔曼滤波器的比较研究案例。这种及时的方法与用于微分代数系统的扩展卡尔曼滤波器进行了比较，证明了所开发状态估计器的优越有效性：新动态状态估计器获得的误差比传统扩展卡尔曼滤波器获得的误差小 80%，对于相同的应用噪音。此外，还包括一个与无迹卡尔曼滤波器的比较研究案例。这种及时的方法与用于微分代数系统的扩展卡尔曼滤波器进行了比较，证明了所开发状态估计器的优越有效性：新动态状态估计器获得的误差比传统扩展卡尔曼滤波器获得的误差小 80%，对于相同的应用噪音。此外，还包括一个与无迹卡尔曼滤波器的比较研究案例。