To detect and improve power quality, we first need to monitor and analyze the power quality disturbances. There have been many methods presented, such as Fourier transform [1] , wavelet transform [2] -[4] , S transform and so on. The Fourier transform is suitable to analyze stationary signals, and has a good effect on stationary disturbance like harmonics; the wavelet transform has advantage of analyzing singularity and nonstationary signals [5] [6] ; S transform is the inheritance and development of short-time Fourier transform and wavelet transform. So it has the advantages of the both [7] -[11] . And it analyzes signal features more comprehensively and it has been a hot research tool of power quality disturbance classification. They are all the time frequency transform methods. This paper presents a method based on the time domain analysis of the power quality disturbance signals and it has some advantages compared to the time frequency transform methods. It will be discussed in details in Section 4.

The general single-phase voltage signal can be expressed as the superposition of the fundamental wave voltage and the disturbance signals:

where is the RMS (root mean square) voltage with the system fundamental frequency; is the system fundamental angular frequency; is the initial phase angle; is the h_th harmonic RMS voltage; is the h_th harmonic initial phase angle; is the angular frequency between harmonic waveforms and not an integer multiple of the system fundamental frequency, for example, the frequencies of interharmonics and oscillatory transients; is the RMS voltage with angular frequency; is the initial phase angle of the angular frequency voltage; is the oscillatory transient attenuation constant. When, is the interharmonic RMS voltage and when, is the oscillatory transients RMS voltage; is the starting time; l(t) is the unit step function. Table 1 shows that characteristics of the disturbances which IEEE classified [12] . All the simulation parameters in this paper are chosen from Table 1 randomly.

In Equation (1), when is stationary, equal to the rating value and

Equation (1) represents the ideal voltage. So the voltage disturbance can be divided into two categories. One is the disturbances with the change of the amplitude, including voltage sag, swell, interruption, under voltage, over voltage, fluctuation, flicker and so on. The other is the additive disturbances, including harmonics, oscillatory transients, impulse voltage, interharmonics and so on. From the aspect of disturbance duration, we can also divide the disturbances into two categories. One is stationary disturbance, including voltage fluctuation and flicker, under voltage, over voltage, continuous interruption, harmonics, interharmonics and so on. The other is transient disturbances, including voltage sag, swell, instantaneous interruption, oscillatory transients, impulse voltage and so on. So the power quality disturbances can be divided into four categories by time domain features, shown in Table 2.

For voltage sag, swell and interruption has the similar characteristics, the author only takes voltage sag as the analyzing object. The other two can also be identified by the method presented in this paper.

If in Equation (1) is multiplied by, we can get:

where, , and

, and

, and

Equation (2) consists of three parts. First is DC component. Second is an AC component with an integer multiple system frequency. Third is an AC component with a non-integer multiple system frequency. After a full cycle (0 - T) integral of the (2) we can see that, and some AC components still exist in. Figure 1 is the curve of the full cycle integral of (2). In Figure 1(a) and Figure 1(b) only contain. Figure 1(c) contains and . Figure 1(d) and Figure 1(e) contain and. For is the sine wave AC value of non-integer multiple system frequency, after a full cycle integral. It shows the existence of the sine wave AC disturbance of non-integer multiple system frequency. The simulation parameters of the following pictures are chosen in the range of Table 1.

The square of Equation (1) is:

The expanded formula of (3) is long, but also is consists of three parts: DC component, an AC component with an integer multiple system frequency, an AC component with a non-integer multiple system frequency. In it:

The curve of a full cycle integral of (3) is shown in Figure 2.

By comparing Figure 1 and Figure 2, we can find that Figure 1(a) and Figure 1(b) are the same with Figure 2(a) and Figure 2(b) because there is no additive disturbance in the voltage sag and fluctuation and flicker. The harmonics is additive disturbance, so the U_d/U_N in Figure 2(c) is larger than U₁/U_N in Figure 1(c). And the dif-

ference between them is the amplitude of the additive disturbance. The oscillatory transients and in-

terharmonics are the additive disturbances. So the U_d/U_N in Figure 2(d) and Figure 2(e) is larger than the U₁/U_N in Figure 1(d) and Figure 1(e). And the difference is also the amplitude of additive disturbance

Though above analysis, some individual features of the power quality disturbance singles can be shown in time- domain:

1) Equation (2) has the effect of selecting system fundamental frequency. The DC component, which can be gotten by low pass filter from Equation (2), is the RMS voltage with system fundamental frequency, which is not affected by additive disturbance. And its change is equivalent to the amplitude disturbance of the RMS voltage (like voltage sag, swell, transient interrupt, under voltage, over voltage, continuous interrupt, fluctuation, flicker and so on).

2) The DC component of Equation (3) is the geometric sum of the RMS voltage with system fundamental frequency and all other additive disturbance RMS voltages. So the geometric difference of the Equation (3) and Equation (2)’s DC component is exactly equivalent to the amplitude of the additive disturbance (like harmonics, oscillatory transients, impulse voltage and interharmonics).

3) Figure 1(d) and Figure 1(e)’s curves contain and.The component exists usually because of the existence of the interharmonics and the oscillatory transients which are non-integer system fundamental frequency sine wave signal. indicates the existence of the interharmonics or oscillatory transients.

So, the next 4 features (F₁ - F₄) can be used to classify power quality single disturbances and the mixed disturbances can be considered as the “superposition” of the single disturbances. The calculating flow chart of the 4 features is shown in Figure 3.

1) is taken as a feature after Equation (2) is filtered by a low pass. Because of the (2)’s effect of frequency selection, F₁ is the system fundamental wave voltage amplitude variation value which is not affected by additive disturbance. It reflects the extent of the fundamental wave amplitude change. So the information of system fundamental RMS voltage change can be known from the extent of the F₁ change. Then it can be used to identify whether there are the voltage sag, swell, instantaneous interruption, under voltage, over voltage, continuous interruption, fluctuation and flicker in electrical singles (shown in Table 3).

2). N is the total sample points during the analysis period of time

(for F₂ is used to detect stationary additive disturbances, the analysis period of time can be enlarged. This paper takes, 100 cycles). is the RMS value of the additive disturbance during the analysis period of time. If, the additive disturbance must exist. If is stationary, the disturbance must be harmonics and is equivalent to THD. can be the threshold value of the harmonics and interharmonics.

3) If, means the average increment of the. It can be used to

classify the additive disturbances harmonics and interharmonics. If interharmonics exist in Equation (2), the curve of will contain AC component of non-integer system fundamental frequency (shown in Figure 1(c)

and Figure 1(e)). Then value of is much larger than that when only harmonics exist. The MATLAB simulation shows that when, interharmonics exist; when, only interharmonics exist; when, both harmonics and interharmonics exist.

4). is the maximum differential value of. The characteristic

that the amplitude of instantaneous disturbance changes fast determines a large number. But to stationary disturbance, is small or even zero. The value of F₄ can determine the instantaneous disturbances exist or not. The MATLAB simulation shows that the threshold can be 15. If, the instantaneous disturbance exists; if, no instantaneous disturbance exists. For instance, when shows amplitude disturbance exists, if, the disturbance should be instantaneous amplitude disturbance such as the voltage sag, swell, instantaneous interruption, and if, the disturbance should be stationary amplitude disturbance such as under voltage, over voltage, fluctuation and flicker and when shows no amplitude disturbance exists, if, the disturbance must be the additive instantaneous disturbance such as oscillatory transient.

Comparing with the other power quality disturbance classification methods using some kinds of transforms, the method presented by this paper has advantages as follows:

1) The single disturbance can be identified by one feature or the combination of some features. That means if one feature or some features satisfied some conditions, a disturbance or mixed disturbances can be sure. Then the disturbance classification will not be probable, but be definitive and the correct rate of the disturbance classification would be very high. And it makes the classification simpler. For example, as shown in Figure 4, if

and, only harmonics exist; if, and, only interharmonics exist; if, and, both harmonics and interharmonics exist.

2) The features extracted from one disturbance won’t change a lot for the existence of the other disturbance. This is shown clearly in Table 4. For example, when the voltage sag and harmonics both exist, which is used to identify voltage sag won’t change for the existence of harmonics. And (only harmonics exist,), which is used to identify harmonics changes a little by the existence of voltage sag (harmonics + voltage sag,). When the oscillatory transients exist in harmonics, increases a little (from 5.0 to 5.23). The harmonics and interharmonics are both additive disturbances, so is the approximate geometric

summation of their amplitude (, the simulation result in Table 4 is 5.37). For another ex-

ample, which is used to identify transient voltage sag and oscillatory transients will not change a lot for the existence of harmonics (voltage sag + harmonics,; oscillotary + harmonics,). This characteristic of the features is the key of the classifying the mixed disturbances. For the idea of this paper considers the mixed disturbances as the “superposition” of the single disturbances. For the characteristics above, all single or mixed disturbances can be classified correctly by simple classifying program, and the classifying results won’t conflict and are definitive.

3) The classifying features have clear physical meanings. So it profits the evaluation of the power quality disturbance. The physical meaning of is the per unit value of the system fundamental RMS voltage, so the amplitude of all the voltage amplitude disturbances can be gained from. And the starting time and the ending time of the transient amplitude disturbance can also be gained from (shown in Figure 1). The physical meaning of is the content of the additive disturbances. So gives the content of the harmonics and interharmonics accurately. The oscillatory amplitude and the attenuation constant of the oscillatory transients can be gained by fitted method from Figure 2(d).

4) The calculating time is much less, and profits to be used in real-time power quality disturbance classification.

5) The features extracted are low-pass filtered or the full cycle integral values, so it has good ability of noise proof.

Using the proposed power quality disturbance classification method, a PQ monitor is developed based on the TMS320F2812 DSP micro-processor. Semi-physical simulation, lab experiment and field measurement results have verified the proposed method.

Comparing with analyzing power quality disturbance signals in frequency domain, the method presented by this paper has some advantages. First, if one feature or some features satisfied some conditions, a disturbance or mixed disturbances can be sure. That is to say, the disturbance classification would not be probable, but be definitive. Second, the features extracted won’t change a lot for the existence of the other disturbances. This characteristic is the key of classifying the mixed disturbances. Third, the features have clear physical meanings. So it profits the evaluation of the disturbance parameters.