promote and foster the development of systematic power disturbance detection methods that can be used for equipment condition monitoring. Current Signature Based Methods Disturbances associated with equipment failures usually involve the abnormalities of current signals. As a result, most of the published detection methods use current waveforms or RMS trends. In this subsection, several different current-based methods are reviewed. Abnormal Component Methods Superimposed abnormal component is the current signal from which normal load component has been removed. According to reference [2] and [3], superimposed abnormal component can be derived with equation 1: 1 iA, iB, iC for instantaneous values of the phases A, B and C currents; iFA, iFB, iFC stand for superimposed abnormal components of the phases A, B and C currents; k stands for a sample index and represents a present sample. In equation 1, NM should be an integer multiple of N1 which stands for the number of samples per power cycle. In both [2] and [3], NM is equal to two times N1, namely NM = 2N1. Abnormal components are very small under steady state, normal operating conditions [2]. During faults and other switching events, the above signals will be relatively more significant. If the abnormal components exceed pre-established limits, then a disturbance can be considered to occur. There are two different methods to determine if the abnormal components have exceeded pre-established limits, as follows. (1) Magnitude of Fundamental Frequency Abnormal Component After superimposed abnormal components have been calculated, the magnitudes of fundamental frequency component can be derived with DFT/FFT. If any of the magnitudes of fundamental frequency component exceeds a certain threshold, a disturbance is detected. In other words, if any of equation 2a), 2b) and 2c) is satisfied, a disturbance is detected. The thresholds can be pre-established or be estimated by analyzing previous cycles of current signals. 2a 2b
denoted by f(x). This deviation between and f(x) is denoted , and the distribution is estimated with the kernel density estimation approach [29]. For each cycle of current waveform signals, one KLD value is calculated and evaluated to determine if abnormality exists. The detection rule in Fig. 92 can be represented as follows. If the following equation is satisfied, an abnormality exists. 23 Dth is the abnormality detection threshold. Further details regarding the estimation of residual pdf by using the kernel density estimation and the calculation of KLD are provided in Appendix C and Appendix D, respectively. Selection of the Abnormality Detection Threshold The performance of the current method is highly dependent on a proper selection of the abnormality detection threshold. According to the signal detection theory [27], a proper threshold selection must account for an acceptable probability of false alarm. A false alarm occurs when normal data is classified as abnormal. For an arbitrary threshold value Dth, the false alarm probability in a certain period of time can be calculated as: 24 p(s) is the probability density function obtained by using KLD values calculated from waveform measurements with no abnormality, that were collected during a given period of time. The false alarm probability PFA is a monotonic non-increasing function of Dth. If the acceptable false alarm probability is α, the selected threshold Dth must be the smallest value that satisfies PFA(Dth) ≤ α. Mathematically, it can be expressed as follows: 25 A systematic threshold selection shall follow these steps: Step 1: Collect NKLD sets of the residual data of previous waveform cycles, where each set contains N samples; Step 2: For each set, estimate the probability density function of the N samples by employing the kernel density estimation. Then, calculate the divergence level (i.e., calculate the value of the KLD) between the kernel estimation and the theoretical Gaussian noise pdf. Each KLD value is a sample of p(s) function;