A Novel Universal Grid Voltage Sag Detection Algorithm

Zaiming Fan Student Member IEEE The School of Computing, Engineering and

Physical Sciences University of Central Lancashire

Preston, PR1 2HE, UK zmfan@uclan.ac.uk

Xiongwei Liu Member IEEE The School of Computing, Engineering and

Physical Sciences University of Central Lancashire

Preston, PR1 2HE, UK Xliu9@uclan.ac.uk

Abstract--Low voltage rid through (LVRT) requires a wind turbine controller to be able to provide rapid response to any power grid voltage sag, which in turn demands a rapid and accurate detection technique of power grid voltage sag. Different voltage sag detection methods have been proposed, such as peak voltage detection, root mean square (RMS) detection, Fourier Transform, conventional DQ transform and its modified versions, such as matrix method and αβ transform. Peak voltage detection and RMS method demand at least half a cycle for the voltage sag depth information to become available, and for a three-phase power grid, they need three separate modules for the three-phase grid voltage sag detection, which is undesirable. Fourier transform can return accurate steady-state voltage information of the supply phases, however it can take up to one cycle for the voltage sag depth information to be measured accurately. Conventional DQ transform is only suitable for three-phase symmetrical voltage sag, and its modified versions are generally too complex and slow. This paper proposes a novel DQ transform solution for fast and accurate detection of any single phase, two-phase or three-phase symmetrical and asymmetrical voltage sag. This novel DQ transform algorithm is simpler and more universal than other techniques proposed by other researchers and/or used in the industry.

Keywords -- voltage sag, voltage sag detection

I. INTRODUCTION With the rapid growth of wind power generation, its

impact on power grid has been increasing. For this reason, new Grid Codes for wind power plants have been introduced in recent years, in which the low voltage ride through (LVRT) requirement for wind turbine grid connection has been in force in many countries.

The LVRT requirement is that the wind turbine must work properly should a low voltage fault occurs. The LVRT requires actions to be taken by the wind turbine controller responding to the voltage sag ratio and the fault duration. Different countries or utilities present slightly different requirements in terms of the voltage characteristics of LVRT.

Figure 1 depicts the voltage profiles of various LVRT requirements in European countries [2].

Fig. 1. Voltage profiles of various LVRT requirements in European countries

In order to ensure safe operation of the power grid network and implement the LVRT function for a wind power system fast and accurate detection of any power grid voltage sag fault is of paramount importance.

II. REVIEW OF GRID VOLTAGE SAG DETECTION TECHNIQUES

There are different power grid voltage sag detection methods in the literature. Traditional techniques include peak voltage detection [4], root mean square (RMS) detection [7] and Fourier Transform [1,3,8].

A. Peak Voltage Detection Monitoring the peak voltage of the power grid is the

simplest method of voltage sag detection. It is achieved by equaling the differential function of the supply phase voltage to zero, as described in Eq.(1), and then comparing the supply voltage value at that instant with a reference.

0)( =dt

tdv (1)

where )(tv is the voltage of single phase supply.

Peak voltage detection measures the voltage sag depth, start and end times. This method is simple, however it can take

978-1-4577-1600-3/12/$26.00 © 2012 IEEE

up to half a cycle for the voltage sag depth information to become available and may pick up noise which affects the differential function [3]. For a three-phase power grid, it demands three separate modules for the three-phase grid voltage sag detection, which is undesirable.

B. RMS Detection The root mean square (RMS) voltage monitoring is based

on averaging previous sampled data for half a cycle or one cycle, as illustrated in Eq.(2).

∑=

=

=2/

1

22 Ni

iiv

Nv (2)

where N is the sample number during one cycle, iv is the sample voltage of a single phase supply.

RMS voltage monitoring detects the voltage sag depth, start and end times. This method is simple, however it takes at least half a cycle for the voltage sag depth information to be detected [5]. Again, for a three-phase power grid, it demands three separate modules for the three-phase grid voltage sag detection, which is undesirable.

C. Applying the Fourier Transform to Each Phase Applying the Fourier transform to each phase voltage can

return both magnitude and phase of the phase voltage within the supply three-phase power grid. This is particularly useful if harmonics are present in the power grid.

Fourier transform can return accurate steady-state voltage information of the supply phases, however it is an averaging function and mathematically complex and computational expensive, which can take up to one cycle for the voltage sag depth information to be measured accurately.

Modern techniques of power grid voltage sag detection are all based on space vector transformation, in which conventional DQ transform is the foundation for three-phase symmetrical voltage sag detection.

D. DQ Transform The DQ transform is an obvious method because it uses

the space vector control method. The static three-phase voltage can be converted into a rotational orthogonal d-q frame, as described by the following equation.

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

+−−−

+−=⎥

⎦

⎤⎢⎣

⎡

c

b

a

q

d

vvv

ttt

ttt

vv

)3

2cos()3

2cos(cos

)3

2sin()3

2sin(sin

32

πωπωω

πωπωω (3)

where tωsin and tωcos are the same sine and cosine components of phase A voltage before the transformation.

A symmetrical three-phase voltage can be expressed as

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

+

−=⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

)3

2sin(

)3

2sin(sin

πω

πωω

t

tt

Vvvv

c

b

a (4)

Combining Eq.(4) and Eq.(3) results in the voltage vector in the d-q frame

⎩⎨⎧

==

0q

d

vVv (5)

Eq.(5) reveals that dv will return the state of the grid voltage at any instant, i.e. detect whether or not a voltage sag exists.

The DQ transform can detect three-phase symmetrical voltage sag in real time and is the simplest detection technique of symmetrical voltage sag. However for asymmetrical voltage sag dv will include a sine wave and this technique is no long valid [3]. The authors proved that dv fluctuates as the three-phase voltage asymmetrically falls down (please refer to Section 5).

In order to detect asymmetrical voltage sag, a few modified versions of DQ transform have been proposed, including modified DQ transform [3] and αβ transform [3]. It is worth pointing out that Fitzer [3] proposed a matrix method to calculate the phase shift and voltage reduction of the power grid. The matrix strategy includes two mathematical transforms, i.e. Park transform and Clark transform. The algorithm obtains the voltage amplitude by means of the DQ vectors, which is a well-known modified DQ detection technique today. Even though it is claimed that the modified DQ detection technique is much quicker than the Fourier transform [6] from the operation speed point of view, the algorithm is complicated and computational expensive.

Both modified DQ and αβ transforms can well detect both symmetrical and asymmetrical voltage sags, however they use at least two mathematical transformations, which is very complicated and computational expensive.

Due to the issues discussed above, it is of both practical and economic value to find a strategy for the controller with a simple and rapid mathematical algorithm to detect the three-phase AC voltage sag.

The algorithm proposed below is a novel DQ transform solution for fast and accurate detection of any single phase, two-phase or three-phase symmetrical and asymmetrical voltage sags. This novel DQ transform algorithm is simpler and more universal than other techniques proposed by other researchers and/or used in the industry.

III. MATHEMATICAL MODEL OF A NOVEL DQ TRANSFORM

The symmetrical voltage of a three-phase power grid can be expressed as

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

+

−=⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

)3

2cos(

)3

2cos(cos

max

πω

πωω

t

tt

vvvv

c

b

a (6)

Let’s set

⎩⎨⎧

==

tvvtvv

q

d

ωω

sincos

max

max (7)

Substituting Eq.(7) to Eq.(6), we have

⎥⎦

⎤⎢⎣

⎡

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

−−

−=⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

q

d

c

b

a

vv

vvv

33

21

23

21

01 (8)

Inversing the matrix, we have

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−

−−=⎥

⎦

⎤⎢⎣

⎡

c

b

a

q

d

vvv

vv

23

230

21

211

32 (9)

and the voltage amplitude can be expressed as 22

max qd vvvV +== (10)

Eq.(9) shows that any change of the three-phase voltage will influence dv .

In order to ensure that dv and qv are synchronized in Eq.(7), qv can be obtained through derivation of dv ,

maxmax

( cos ) sindq

dv d v t v t vdt dt

ω ω ω ω= = − = − (11)

Hence

dtdvv d

q ω−= (12)

In practical application, the derivation of discrete values in unit time is the present sampling value minus the previous sample. Therefore, the complicated derivative operation can be simplified and become the operation of subtraction.

Fig.2. Flowchart of the filtering strategy

Because the right hand side of Eq.(12) contains the derivative of dv , the value of qv probably is significantly

large when the grid voltage fluctuates. Consequently, the output of the derivative needs filtering. Because the continuous signals are without discontinuities, if the sampling rate is fast enough, the delay introduced does not affect the control, it can be shifted several sampling periods. The sample is not immediately outputted, when the sample value is continuously the same as previous samples for a predetermined sample numbers, the sampling signal is then outputted. However, there can be several instruction cycles of delay using the strategy above. With contemporary high speed processing, several instruction cycles only take a few nanoseconds, which can be neglected when processing signals are sampled at millisecond intervals. The flowchart of the filtering strategy is given in Figure 2.

IV. MATLAB/SIMULINK MODEL

Figure 3 shows the MATLAB/Simulink model of the proposed grid voltage sag detector. The block labelled fluctuation in the model is a custom model. It is employed to allow the user to simulate a voltage source with the desired fluctuation. The figure shows that the model only uses the dv signal and the qv signal is not used. The filter in the model is an s-builder block, which is used to implement the flowchart in Figure 2.

Fig. 3. Model of the voltage sag detection

V. SIMULATION Figure 4 shows a comparison of the detection results

obtained with the conventional DQ transform and the proposed novel DQ transform.

(a) Phase C drops down 20%

(b) Conventional DQ transform & novel DQ transform

Fig. 4. Only Phase C with 20% drop

In Figure 4(a), phase C of the power source drops by 20%. The blue line in Figure 4(b) is the detection result obtained by

Vd

Vq

f(u)

sqrt(d^2+q^2)

f(u)

sqrt(d '^2+q'^2)

dq Ampl i tude

Out1

WaveformGenerator

T erm inator

Original 3 Phase

-K-

Gain SoftFi l teru y

Fi l ter

du/dt

Derivative

Ampletude

K*u

3S/2S

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-400

-200

0

200

400Power voltage sag

Time in second (s)

Am

plitu

de(V

)

Ua

UbUc

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2340

350

360

370

380

390

400

Time in second (s)

Am

plitu

de(V

)

DQ transform & novel DQ transform

Novel DQ transformDQ transform

the conventional DQ transform and shows significant oscillation. The red line is the outcome the proposed novel DQ transform, showing a consistent and accurate detection.

Fig. 5. Both phase A and phase C with voltage sag

Figure 5 shows the results of another simulation in which both phase A and phase C drop by 20%. As the figure illustrates, these results are consistent with the previous simulation.

Figure 6 shows the simulation results when the grid is operated under normal condition. The outcomes from the conventional DQ transform and the proposed novel DQ transform overlap each other. It demonstrates that the proposed novel DQ transform works in the normal condition as well.

Fig. 6. Under normal condition

VI. CONCLUSION A new power grid voltage sag detection algorithm based

on a novel EQ transform with a simple filter is proposed in this paper. The novel DQ transform uses only a single module of DQ transform and returns the voltage sag depth, start and end times of any single phase, two-phase or three-phase symmetrical or asymmetrical voltage sag, which means it is a universal power grid voltage sag detection algorithm. The simulations demonstrate superior performance than any other techniques proposed by other researchers and/or used in the industry. It provides an economic and reliable solution of power grid voltage sag detection for low voltage rid through

for wind power plants. Further physical implementation and field testing will be carried out in the near future.

VII. REFERENCES

[1] B.Bae, J.Jeong, J.Lee, B.Han, Novel Sag Detection Method for Line-Interactive Dynamic Voltage Restorer. IEEE Transactions on Power Delivery 25 (2010) 1210-1211.

[2] Chia-Tse Lee, Che-Wei Hsu, Po-Tai Cheng, A Low-Voltage Ride-Through Techinique for Grid-Connected Converters of Distributed Energy Resources. IEEE Transactions on industry applications 47 (2011) 1821-1832.

[3] Chris Fitzer, Mike Barnes, Peter Green, Voltage Sag Detection Technique for a Dynamic Voltage Restorer. International Journal of Renewable Energy Research 40 (2004) 203-202.

[4] Hui-Yung Chu, Hurng-Liahng Jou, Chinag-Lien Huang, Transient Response of a peak Voltage Detector for Sinusoidal Signals. IEEE Transactions on Electronics 39 (1992) 74-79.

[5] Kai Ding, K.W.E.Cheng, X.D.Xue, B.P.Divakar, C.D.Xu, Y.B.Che, D.H.Wang, P.Dong, A Novel Detection Mothod for Voltage Sags. IEEE Conference Publications2006) 250-255.

[6] Raj Naidoo, Pragasen Pillay, A New Method of Voltage Sag and Swell Detection. IEEE Transactions on Power Delivery 22 (2007) 1056-1063.

[7] S.M.Deckmann, About Voltage Sags and Swells Analysis. IEEE Conference Publications 1 (2002) 144-148.

[8] Wen-Ren Yang, Wen-Xun, Yang, Discrete Wavelet Transform and Short-Time Fourier Transform Applications: Wafer Microcrack and Voltage Sag Detection. IEEE Conference Publications2010) 31-35.

VIII. BIOGRAPHIES Zaiming Fan was born in Yongzhou, China, in 1973. He received his

BEng (Hons) degree from the University of Central Lancashire, UK, in 2010. At present, he is registered as a postgraduate research student at the University of Central Lancashire. His research area is wind turbine control system.

Xiongwei Liu was born in Xiangtan, China, in 1965. He received his BEng (Hons) degree from National University of Defense Technology, Changsha, in 1985, and his MSc (Distinction) and PhD degrees from Harbin Institute of Technology in 1988 and 1991 respectively.

His employment experience included Northwestern Polytechnical University, Huaqiao University, Leeds Met University, University of Hertfordshire and University of Central Lancashire. His research interests include wind energy engineering, renewable energy technologies, smart grid and microgrid, and intelligent energy management system.

He received a research fellowship from Alexander-von-Humboldt Foundation of Germany, which allowed him to visit Ruhr University Bochum, as a research fellow for 18 months from 1993. In 1999 he was awarded a Bronze Medal by Huo Yingdong Education Funding Council and a Model Worker Medal by the Mayor of Quanzhou, China, due to his excellent contributions in higher education when he served as a professor at Huaqiao University. He received a research fellowship from Chinese Scholarship Council, which allowed him to visit Technical University Berlin as a senior research fellow for 6 months in 2000.

Xiongwei Liu is currently working as Chair Professor of Energy and Power Management and Head of Wind Energy Engineering Research Group at the University of Central Lancashire.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-400

-200

0

200

400Power voltage sag

Time in second (s)

Am

plitu

de(V

)

Ua

UbUc

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2310

320

330

340

350

360

370

380

390

400

Time in second (s)

Am

plitu

de(V

)

DQ transform & novel DQ transform

Novel DQ transformDQ transform

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-400

-300

-200

-100

0

100

200

300

4003 Phase Power Voltage without sag

Times (sec)

Am

plitu

de(V

)

Va

VbVc

0 0.05 0.1 0.15 0.20

255075

100125150175200225250275300325350375400

DQ instantaneous detection & New way

Times (Second)

Am

plitu

de(V

)

DQ Detection

New Way