A Novel Fast Voltage Sequence Component Detector of Unbalanced Three-Phase System

The fast and accurate voltage sequence component detection of unbalanced three-phase system is of major importance for the industrial continuous processing. The traditional method is to calculate the voltage in dq synchronous reference frame. This results in low order harmonics and long detection time. A novel fast voltage sequence components detector is proposed in this paper. It is to calculate the sequence component projection on dq rotating reference frame with h times the fundamental angular velocity. Simulation results demonstrate the validity of the algorithm.


INTRODUCTION
Voltage sags are one of most severe power quality problems that the industrial process has to face [1]. It is defined as a decrease in RMS voltage to between 0.1 pu and 0.9 pu for durations from 0.5 cycles to 1 min, which is usually associated with system faults but can also be caused by switching heavy loads or starting large motors [2]. Most voltage sags are unbalanced event deteriorating the power quality [3]. It can cause voltage sensitive industrial loads to malfunction [4][5][6][7][8], leading to severe economic losses, malfunction of voltage sensitive industrial loads.
Thus, the fast and accurate voltage sequence component detection of unbalanced three-phase system is of major importance for the normal operation of industrial continuous processing. The voltage amplitude can be obtained by Park transformation [9], [10]. The positive-and negative-sequence components become the DC component and second harmonics in the dq synchronous reference frame. Unfortunately, the second harmonics results in long detection time. A novel fast voltage sequence component detector is proposed in this paper. It is to calculate the voltage amplitude projection in dq reference frame rotating with h times the fundamental angular velocity. Simulation results verify the effectiveness of the algorithm.

PARK TRANSFORMATION
The unbalanced three-phase system can be expressed as where ω 1 is the fundamental angular velocity, U i and φ i (i=a,b,c) are the voltage amplitude and phase angle of phase voltage u i (i=a,b,c), respectively.
The unbalanced voltage can be decomposed into positive-and negative-sequence component. And it can be obtained by symmetrical components in αβ stationary reference frame as where U i and φ i (i=1,2) are the voltage amplitude and initial phase angle of the positive-and negative-sequence components, respectively.
By Park transformation, the positive-and negativesequence component become the DC component and second harmonic in the dq synchronous rotating reference frame, respectively. And the DC component can be obtained by eliminating the second harmonic which results in large time delay. A novel algorithm is proposed in this paper. It is to project the unbalanced three-phase voltage to the nonsynchronous dq rotating reference frame with angular velocity hω 1 . Then, the corresponding αβ to dq matrix can be expressed as Thus, the dq components can be obtained shown at the bottom of the page. It can be observed that the positive-and negative-sequence component become the h-1 and h+1 harmonic components in the dq reference frame of hω 1 angular velocity, respectively.

MOVING AVERAGE FILTER
where T ω is the filter window width. Its transfer function can be described as where h is the harmonic order, T is fundamental period, ω 1 =2π/T.
For instance, MAF(T/2) can filter out all the h=2k harmonic components. Then the h+1 harmonics in u dq (t) can be eliminated by MAF(T/(h+1)) and the corresponding h-1 harmonics can be derived shown at the bottom of the page. (9)and (10) illustrate that the MAF(T/(h+1)) results in amplitude reduction and phase shift of the h-1 harmonic component in dq reference frame.
Thus, the voltage amplitude of positive-sequence component can be derived as The negative-sequence component can also be obtained by utilizing the MAF(T/(h-1)) to eliminate the h-1 harmonic components. Fig.1 shows the detection diagram of the proposed algorithm, where PLL is synchronization unit providing phase information for Park transformation. The estimated fundamental frequency f 1` is feedback to MAF to improve filtering effect. The detection time is T/(h+1). In addition, the negative-sequence component can also be obtained by eliminating the h-1 harmonics with detection time T/(h-1).

Fig1. Detection diagram of positive-sequence components
It needs to be observed that the positive-and negative sequence components become h+1 and h-1 harmonics by negative Park transformation. Then the detection time of negative-sequence component is T/(h+1).

SIMULATION VERIFICATION
In order to verify the accuracy of the algorithm, the time domain simulations in MATLAB/Simulink environment were carried out by using 10 kHz discrete fixed-step solver. The per unit (pu) is used in this paper. Fig.2 shows the voltage waveform. At t=0.03s, the positivesequence component is dropped to be 0.6 pu.   3 shows the detection results. The h=11 is utilized in this paper. Fig.3(a) is the u d (t) obtained by Park transformation. It is composed by h=10 and h=12 harmonics. Fig.3(b) is the u _ d (t) filtered by MAF(T/12). It can be observed that there is only h=10 harmonic. Fig.3(c) is the estimated voltage amplitude of positive-sequence component. The system detection time is the filter time of MAF which is T/12. It illustrates that the voltage amplitude can be calculated fast and accurately.

CONCLUSIONS
A novel fast voltage sequence component detector of unbalanced three-phase system is proposed in this paper. It is to calculate the corresponding voltage components in dq rotating reference frame of hω 1 angular velocity. The positive-and negative-sequence components become the h-1 and h+1 harmonics, respectively. As the sequence components become harmonics of high order, the system filter time is reduced substantially. And the voltage can be estimated with fast response. Simulation results verify the effectiveness of the algorithm.