The fault of a solar or wind power system changes under different factors, and there isn’t any clear relationship between a factor and its corresponding failure mode. Dr. Yau proposed a chaotic synchronization detection method to transform the initially extracted system signals into a chaos error distribution diagram. The centroid of this diagram was then taken as the characteristic value for diagnosis of the faults by type to reduce the number of the extracted characteristics and shorten the computing time. Then, the grey theory was used to predict the characteristic value in the next cycle. This value was the basis for fault prediction to detect potential signs before the occurrence of any faults. It was useful for the systems to cease the operations earlier and minimize the damage and maintenance cost. This result was published in the SCI journal IET Renewable Power Generation, 2015. On the other hand, Dr. Yau proposed a detection method that integrates the fractional-order Sprott chaotic synchronization system with the extension theory for monitoring the power quality disturbance. Compared with the integral-order Sprott chaotic system, the fractional-order Sprott chaotic system can generate dynamic errors that are easily compatible with the back-end matter-element model established of the extension theory, enabling accurate identification of power disturbance signals. The data on numerical simulations showed that the method proposed in this study performs better than those adopted in other literatures regarding the accuracy of power quality detection, and that the method is able to achieve 100% accuracy when applied to real-time monitoring. This result was published in the SCI journals IET Generation, Transmission & Distribution, 2015 and IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 2013.