Deteriorated quality of power leads to problems, such as equipment failure, automatic device resets, data errors, failure of circuit boards, loss of memory, power supply issues, uninterrupted power supply (UPS) systems generate alarm, corruption of software, and heating of wires in distribution network. These problems become more severe when complex (multiple) power quality (PQ) disturbances appear. Hence, this manuscript introduces an algorithm for identification of the complex nature PQ events in which it is supported by Stockwell's transform (ST) and decision tree (DT) using rules. PQ events with complex nature are generated in view of IEEE-1159 standard. Eighteen different types of complex PQ issues are considered and studied which include second, third, and fourth order disturbances. These are obtained by combining the single stage PQ events such as sag & swell in voltage, momentary interruption (MI), spike, flicker, harmonics, notch, impulsive transient (IT), and oscillatory transient (OT). The ST supported frequency contour and proposed plots such as amplitude, summing absolute values, phase and frequency-amplitude obtained by multi-resolution analysis (MRA) of signals are used to identify the complex PQ events. The statistical features such as sum factor, Skewness, amplitude factor, and Kurtosis extracted from these plots are utilized to classify the complex PQ events using rule-based DT. This is established that proposed approach effectively identifies a number of complex nature PQ events with accuracy above 98%. Performance of the proposed method is tested successfully even with noise level of 20 dB signal to noise ratio (SNR). Effectiveness of the proposed algorithm is established by comparing it with the methods reported in literature such as fuzzy c-means clustering (FCM) & adaptive particle swarm optimization (APSO), Wavelet transform (WT) & neural network (NN), spline WT & ST, ST & NN, and ST & fuzzy expert system (FES). Results of simulations are validated by comparing them with real time results computed by Real Time Digital Simulator (RTDS). Different stages for design of complex PQ monitoring device using the proposed approach are also described. It is verified that the proposed approach can effectively be employed for design of the online complex PQ monitoring devices. © 2020 Institute of Electrical and Electronics Engineers Inc.. All rights reserved.