2013 Sixth International Conference on Advanced Computational Intelligence October 19-21,2013, Hangzhou, China

Power Quality Assessment of Offshore Wind Farm Based on PSCAD/EMTDC Models

Ruixiang Sun, Wenjun Yan, Qiang Yang, Zhejing Bao, and Jie Zhang

Abstract-This work aims to carry out an assessment of

power quality at the Point of Common Coupling (PCC) in the

scenario of offshore wind farm integrated into the power

network whilst reduce the impact of index discrepancy and

uncertainty. We acquire the judgmental matrix by using

analytic hierarchy process (AHP) and obtain the index weights

for power quality assessment by combining the compatibility

matrix methodology and entropy weight method with

connection degree modeling in Set Pair Analysis (SPA) theory.

The compatibility matrix method can effectively address the

challenge that it is difficult to inspect the consistency by

judgmental matrix. The power quality index weights

determination can vary for different experts. The existing

analytical solutions have not thoroughly considered the issue of

index discrepancy and uncertainty. We adopt SPA theory to

cope with and minimize the certainty and uncertainty which are

introduced from the differences of subjective knowledge of

experts. The proposed assessment approach is studied through

numerical analysis based on the power quality measurements

obtained from PSCAD/EMTDC models. The statistical and

fuzzy judgmental method is applied to process the

measurements. As a result, the power quality assessment can be

estimated.

I. INTRODUCTION

DUE to the urgent demand on utilizing renewable power generation resources and low-carbon power supply across the overall world, much research effort has been

made to investigate the potentials of renewable energy, e.g. offshore wind power generation, and tickle the outstanding technical challenges. In general, as the offshore wind can provide more consistent and strong wind, the offshore wind turbines operate at higher capacity factors. Although it has these benefits, wind speed characterizes the variation, intermittence, and randomness. And confused flowing and tower-shadow effect are also the influencing factors of wind power unit. All of these can bring fluctuation of wind turbine output which will lead to power fluctuations [1]. As the wind power penetration into the grid is increasing quickly, the

'The authors would like to appreciate the financial support from the National High-Tech R&D Program of China (863 Program) (Nos. 2012AA051704 and 201 IAA05Al13) and the National Science Foundation of China under grant No. 51107113.

Ruixiang Sun is with the College of Electrical Engineering, Zhejiang University, Hangzhou, 310027, China (email: sunruixiangnihao@126.com).

Wenjun Yan is with the College of Electrical Engineering, Zhejiang University, Hangzhou, 310027, China (email: wj.yan@126.com).

Qiang Yang is with the College of Electrical Engineering, Zhejiang University, Hangzhou, 310027, China (email: qyang@zju.edu.cn).

Zhejing Bao is with the College of Electrical Engineering, Zhejiang University, Hangzhou, 310027, China (email: zjbao@zju.edu.cn).

Jie Zhang is with the College of Electrical Engineering, Zhejiang University, Hangzhou, 310027, China (email: zj5823@126.com).

influence of wind turbines on the power quality is becoming an important issue [2]-[4]. Various sources give different definitions of power quality. The Institute of Electrical and Electronics Engineers (IEEE) dictionary states that "power quality is the concept of powering and grounding sensitive equipment in a matter that is suitable to the operation of that equipment." The International Electrotechnical Commission (1EC) definition of power quality, as in IEC61000-4-30, is as follows: "Characteristics of the electricity at a given point on an electrical system, evaluated against a set of reference technical parameters [5]." In [6], the author showed that power quality can be defined as: "the measure, analysis, and improvement of the bus voltage to maintain a sinusoidal waveform at rated voltage and frequency." Poor electric power quality has many harmful effects on power system devices and end users. These effects are often not known until the failure occurs. Even if failures do not occur, poor power quality decreases the lifetime of power system components and end-use devices and increase losses [6]. So the requirement for high security, quality, reliability, and availability of an electric power supply will increase urgently [7].

The quantifiable outcomes of power quality comprehensive evaluation are one of the evidences for judging advantages and disadvantages of power quality. It is conducive to form market mechanism that electric charge is fixed according to the quality. Power quality assessment system is a multi-quality index system and its evaluation process is complex [8]. In [9], it structures the judgmental matrix through AHP and calculates the index weights by second order linear programming not by eigenvector method. Then the evaluation result is obtained by probability statistics. In [10], the comprehensive weights of power quality indexes are determined by using AHP and entropy weight. The thinking of spatial distance measurement is applied to comprehensive evaluation of power quality. These methods ignore discrepancy and uncertainty case. In order to solve this problem, we combine SPA and compatibility matrix methodology and entropy weight method to determine the index weights of power quality. And then by applying probability statistics and fuzzy judgmental method, the objective comprehensive evaluation result can be concluded.

The rest of the paper is organized as follows: section II is construction of determining index weights model; section III is the comprehensive assessment based on probability statistics and fuzzy judgmental method; section IV presents a case study applying the proposed analytical solution; and finally the conclusive remarks are given and the future work is pointed out in section V.

978-1-4673-6343-3/13/$3l.00 ©2013 IEEE 339

II. DETERMINING INDEX WEIGHTS MODEL

In this paper, we make comprehensive evaluation on the six power quality indexes from technical guide for power quality assessment ruled by State Grid Corporation of China. The details of indexes and corresponding qualified range are listed in Table 1 [11].

TABLE I INDEXES OF POWER QUALITY AND LIMITING VALUE

Power Quality Index

supply voltage deviation

voltage fluctuation

voltage flicker severity

total hannonic distortion(THD)

unbalance factor

frequency deviation

A. Set Pair Analysis

Parameter

UI/% U,/%

U3 U4/% U5/%

flHz

Qualified Range

:::; 10 :::;3 :::; 0.8 :::;2 :::;2 50 ± 0.2

Set Pair Analysis was proposed to address the certainty and uncertainty issue as a system by connection degree [12]. The basic idea of SPA can be summarized as follows: SPA can be used to analyze the characteristics of a set of pairs under the background of certain problem. And then it sets up two sets' identity-discrepancy-contrary connection degree expression which is under the designated background.

fl = a+bi+cj (I) In expression (I), "a", "b", and " c" are respectively

identity degree, discrepancy degree, and contrary degree of the two sets under certain circumstances. " i " is the coefficient of discrepancy degree which is limited as i E [-1,1] . " j" is the coefficient of contrary degree specified

as -1. "a" and " c" are relatively certain. "b" is relatively uncertain. The comparative uncertainty is produced by complexity, variability, and subjectivity of understanding and depiction for objective entity.

Experts have different opinions on the same relation when they determine the index weights. The differences are called uncertainty. It is more accurate that many experts perform the evaluation instead of one expert. Suppose there are r experts,

and index set is X = {Xk} ( k = 1,2,···,n) . Each expert

structures comparison matrix by means of comparing one

index to another. And then we get comparison matrix M zkl ( z = 1,2,· ", r; k = I, 2,· .. , n; I = 1,2,· .. , n) which stands

for the z expert's opinion about the relationship between any

two indexes [13]. For example, XZ23 denotes the second

index's degree of importance by comparing second index with third index. In this paper, we use a nine-point scale of

AHP methodology. When XZ23 is "3", it denotes that second

index's importance is slightly more superior than the third one.

Xzll xzI2 xzln

Obviously, there is xzkl = _1_ . We build connection

xzlk degree modeling fLqkl that describes relative importance

between any two indexes by using matrix form of connection degree. Thus the connection degree modeling expression is as follows:

all al2 aln bll bl2 bin

flqkl = Akl + Bk1i = a21 a22 a2n b21 + . b22 b2n i.

ani an2 ann bnl bn2 bnn

X,kl ;:::: 1 _rn { X� J

Where, akl -max {x,J , (4)

X,kl � 1 , (z = 1,2,' ··,r;k = 1,2,···,n;1 = 1,2," ·,n)

(z = 1 2 ... r k = 1 2 ... n' I = 1 2 ... n) " " " " ' "

(5)

(3)

Akl is identity matrix which describes the experts' same

opinion about relative importance between indexes. And Bkl is discrepancy matrix which describes the experts' different opinions about relative importance between indexes.

Although experts have different opinions about the relationship between indexes, the viewpoints on these are not contrary in general. The experts' opinions are similar but have discrepancy. It is consistent with the actual situation. That is to say, it couldn't happen that the index XI is

extremely important than the index X2 (its scale value XI' is 9),

and at the same time index X2 is extremely important than the

index XI (its scale value X21 is 9).

akl shows the experts' common opinions that could be

certain absolutely. The experts' comprehensive opinion can

be obtained considering two conditions: xzkl ;:::: 1 and xz1k :::; 1 .

When xzkl ;:::: 1 , the scale value at least satisfies min { x'k/} .

And namely the scale value y > min { x'k/} and

When

1 a 'k = max {xz1k} = . on account of xzkl =--

mm {xzk/} xz1k 1

Therefore, akl = - . In this way, identity matrix Akl makes a'k

the two scale values standing for the relationship between

index X k and index XI be one-to-one correspondence.

Mzkl =

xz21 xz22 xz2 n (2) B. Index Weights Determination

xzn1 xzn2 xznn

340

Compatibility matrix method gives an effective solution for determining the index weights. In AHP, the factors of

evaluation are uncertain and complicated [14]. It is difficult to distinguish the degree of importance between indexes when comparison matrix is high order and the quantity of criterion is large. All of these cause that it is difficult to inspect the consistency by comparison matrix. So comparison matrix should be adjusted for many times until the requirement of consistency is satisfied [15]. However, compatibility matrix method can directly realize the requirement of consistency without testing consistency. It simplifies computational process.

We deal with identity matrix Akl using compatibility

matrix methodology. In [14], the derivation of compatibility matrix methodology has been described. Here we use the formula and conclusion. And then we can get basis matrix

Dkl which can primarily determine the vector quantity of

index weights. n

Where, Dkl = (dk/) , dkl = n II Qkp • Qpl satisfying the p=1

1 condition dkk = 1 and dkl = - , where dkl is the element of

d1k basis matrix Dkl; QIq) and Qpl are the elements of identity

matrix Akl . So the index weights OJk are as follows:

s=1

/I

Where, Cs = /I IT dkl• 1=1

( k = 1, 2, . . " n) . (6)

(7)

The entropy concept was proposed by Shannon and Weaver. It is a measure of uncertainty in information formulated in terms of probability theory. The entropy method is well suited for determining weight by using index entropy [16]. So we use entropy weight method to dispose

discrepancy matrix Bkl ' obtaining the weight of Bkl which

reflects the discrepancy degree of the experts' opinions. 1) According to the traditional entropy conception, the

entropy of each index can be defined as follows [17]-[ 18]: "

Hk = -(L J;, 1nJ;) / In n. (8) 1=1

(k = 1, 2, . . . , n; I = 1,2, . . . , n) n

Where hi = bkl / L bkl ' and bkl is the element of the 1=1

discrepancy matrix Bkl .

Obviously, when J;, = 0 , In hi is insignificance. So J;, is amended and defined as follows:

n

hi = (1 + bkl) / L (1 + bkl)· (9) 1=1

2) Calculate the entropy weight of each index:

341

k=1 n

Expression (10) satisfies the condition: "I '7k = 1 . In this k=1

paper, n = 6 . According to expression (6) and (10), we can obtain the index weights.

Since the discrepancy coefficient i E [0,1] , the index

weights are range value not constant. With people making much deeper research on power quality and understanding it more plentiful, the range value of the discrepancy coefficient will be dwindled down. And then the range value of index weights will also be dwindled down. It is shown that the degree of experts' cognition discrepancy and subjective randomness will decrease. The certainty degree of index weights will increase. So that the power quality index weights are more objective and realistic.

III. COMPREHENSIVE ASSESSMENT BASED ON PROBABILITY

ST ATISTICS AND Fuzzy JUDGMENTAL METHOD

The step of power quality comprehensive level assessment is as follows [19]-[20]:

1) Suppose the total time of assessment is T . Each evaluated index is divided into m grades within qualified range according to national standard. The span of each grade

is b.q = ¢ / m, where m � 10 and m is integer. ¢ is a

index's limit of national standard. The scope of stage k is

[tk,tk+t]. m m m

2) Sum up the time of each index's absolute value in stage

k: r( k) = L t j , where t j is the time of period j for each

index's absolute value in stage k. 3) Get the probability distribution of each index's absolute

value in stage k : � = r(k) / T . And then we can get the

probability distribution vector of each index according to

each rank-order: S�lXIII) = [�, Pz,'" }�J . Thus we can obtain

the matrix S(6Xm) which consists of probability distribution

vectors of six evaluated indexes.

4) The vector of power quality index weights Wr(IX6) has

been determined above. And then probability distribution matrix multiples by corresponding index weight vector:

T �IXm) = Wr(IX6) X S(6Xm)' where �'(IX6) = W . At last we get

the result of comprehensive assessment for power quality by

�IXm) multiplying by power quality level vector L(mXI) : R = �IXm) X L(mXI) •

In this paper, we need to pre-process the data of each index at first. When there are some data of one index over qualified range as national standard stated, the quality of corresponding index is unqualified. And then we thought that the power quality of the PCC is unqualified. The electric power department should adopt corresponding measures to improve

the unqualified index in order to make power system recover from abnormal condition. In this paper, each power quality index will be divided into 10 grades within qualified range

according to national standard, as shown in table II [20]. In this way, we get the power quality level vector

r L(IOXI) =[1,2,3,4,5,6,7,8,9,10] .

Here, we apply fuzzy judgmental method. So when the assessment result is out of any range, the degree is formulated in adjacent domains.

Quality Level

[1,2] [3,4] [5,6] [7,8]

[9,10]

(10, -1«0)

TABLE II POWER QUALITY LEVELS

Degree of Excellence

super excellent

good fair

qualified

unqualified

IV. A CASE STUDY

Because of its abundant wind energy resource, an offshore wind farm with a 50 MW capacity locating about 20 km out of the east coast of Laizhou Bay in Shan dong province in China is under construction. Since this offshore wind farm has not been built, our research is to simulate the real project and acquire emulated data for analyzing and evaluating power quality. The equivalent modeling of the offshore wind farm under construction has been implemented on PSCAD/EMTDC, as shown in Fig.2. The simulation time is 1219 seconds. And the wind speed of offshore wind farm is shown in Fig.l.

� '0 Ql Ql 0. If) '0 C .�

200 400 600 time/s

800 1000

Fig. I. Wind speed of offshore wind fann.

A. Calculating Index Weights

1200

Nine experts compare the six power quality indexes in pairs of offshore wind farm. They fulfill the pairwise comparison by using a nine-point scale of AHP methodology. And then the reciprocal matrices of pairwise comparisons are constructed, constituting a group of evaluation matrix. It is

Mkl = (Mlk/' M2kl,"', M9kl) . The sequence of indexes

placed in the judgmental matrix is as follows: supply voltage deviation, voltage fluctuation, voltage flicker severity, total harmonic distortion (THD), unbalance factor, and frequency deviation. Here we give two experts' judgmental matrixes for example [21]:

342

I 112 112 I I 113 2 2

MIkI = I 112

2 2 112 2 2 112

112 I I 113

I 112 113 112 I 113 2 2 112 3 2 112

2 112 I 112 112 I I 113 I 112 112 112 I 113 3 2 2 3 3 1 3 2 2 2 3 1

According to expression (4) and (5), we can respectively get the following matrix

1 112 112 1 I 113 0 0 -116 -1/2 0 0 2 I 2 112 0 0 0 0 0 2 2 112 I 0 0 I 0 0

Akl = I 112' Bk/= I -112 -1/2 0 I -116 I 1/2 112 I I 113 0 0 0 -1/2 0 0 3 2 2 2 3 0 0 0 I 0 0

By using compatibility matrix methodology, matrix Akl turns

into

Dkl =

1.6984

1.6984

0.5888 0.5888 0.7418 0.3240

1.2599 1.6984 0.5503

1.2599 1.6984 0.5503

1.3480 0.7937 0.7937 1.3480 0.4368

0.5888 0.5888 0.7418 0.3240

3.0862 1.8171 1.8171 2.2894 3.0862

According to expression (7), we can get

CS(6XI) = [0.6608, l.l224, l.l224, 0.8908, 0.6608, 2.0395f .

And then from expression (6), the weight of identity matrix

Akl can be obtained as follows:

= (0.1017,0.1728,0.1728,0.1371,0.1017, 0.3139l .

According to expression (8)-(10), the entropy weight of

Bkl is calculated as follows:

= [0.0701,0.1265,0.1697,0.4379,0.0692, 0.1265f .

Considering the discrepancies among experts are little, the coefficient i = 0.08 . And then we can get the index weights which are as follows:

W = [0.0994,0.1694,0.1726,0.1594,0.0993, 0.3000f .

B. Sensitivity Analysis of Index Weights

Because of the discrepancy coefficient i E [0,1] , the values

of index weights are likely to be different. It will lead to the result's change of comprehensive evaluation [22]. So it is necessary to study the sensitivity of index weights when the discrepancy coefficient i is changed. The order of index weights' value is as follows:

wind farm O.0396ohm 7.32mH O.69kY/35kV

�-----------------------

r--transformer line impedance

35kV/220kV O.52ohm O.028H O.Olohm O. IH U=220kV

grid equivalent impedance

submarine cables

Fig. 2. System configuration of grid-connected offshore wind farm.

{J)6 > W, > W2 > W4 > WI � W5

(J)6 > W, > W4 � W2 > � > W5

W4 � W6 > W, > W2 > � > Ws The sorted result is as follows:

/ >- V3 >- V2 >- V4 >- VI >- Vs

/ >- V3 >- V4 >- V2 >- VI >- Vs

/ >- V4 >- V3 >- V2 >- VI >- Vs V4 >- / >- V3 >- V2 >- VI >- Vs

C. Evaluation 0/ Power Quality Level

iE [0,0.1146)

iE [0.1146,0.1331)

i E [0.1331,0.5678)

i E [0.5678,1]

iE [0,0.1146)

i E [0.1146,0.1331)

i E [0.1331,0.5678)

i E [0.5678,1]

Monitoring the voltage and frequency value of phase A at PCC where the voltage value is 220 kV, we can get simulation data. The data are recorded from stationary condition. We analyze and calculate the data on MATLAB. And the values of six power quality indexes are acquired. It is shown in Fig.3. Since we have not used equipments for power quality improvement, two indexes are over qualified range as national standard stated. In order to make comprehensive assessment of power quality, we get rid of the unqualified data. And at these points we use limiting value instead. By applying statistical approach, we can get that the probabilities of frequency deviation and THD whose values are over qualified range are respectively 0.0003 and 0.0117.

Fig. 3(a) is composed of 406 points. They stand for the Root Mean Square (RMS) of instantaneous voltage calculated each 3 seconds. So the value of X-axis should be mUltiplied by 3 seconds. The supply voltage deviation is caused by reactive power. The sag among 150 and 300 seconds is produced by huge fluctuations.

According to Table I, the values of voltage fluctuation and unbalance factor are in qualified range in Fig. 3(b) and (e).

Fig. 3( c) is the instantaneous flicker sensation. According to national standard, voltage flicker severity is calculated each 10 minutes based on instantaneous flicker sensation. But we can't use this criterion. Because we don't have enough data to calculate probability distribution vector of voltage flicker severity and simulation time is limited. So we apply the instantaneous flicker sensation instead. In this way, we can get probability distribution vector of voltage flicker severity from simulation data.

343

;?, 2.06 g,:: c ,g 2.04 '" '> {g 2.02 Q) en 2 .l!l 0 > 1.980

;?, g,:: 0.4 c 0 � 0.2 ::::J t5 ::::J Q) 0 en .l!l 0 > -0.20

Q; 0.5 "" 0.4 .2 ""c �.g 0.3 Q)� � a5 0.2 COO .£!l oo E

0.1

3

?f!. 2 o I f-

� 0.1 c '" � 0.05 c �

50 100 150 200 250 300 350 time/3s

(a) Supply voltage deviation

200 400 600 800 1000 time/s

(b) Voltage fluctuation

200 400 600 800 1000 time/s

(c) Instantaneous flicker sensation

200

200

400 600 time/s

800 1000

(d) Total harmonic distortion (THD)

400 600 800 1000 time/s

(e) Unbalance factor

400

1200

1200

1200

1200

N � 0 � . ;; '" "0 >­u c

0.4 0.2

0 � -0.2 0-� -0.4 L-__ -'--__ -'-__ -'-__ -"-__ ---' ___ L--l

o 200 400 600 time/s

800

(f) Frequency deviation Fig. 3. Power quality indexes.

1000 1200

From simulation data, the result of comprehensive evaluation on power quality can be obtained. According to

expression v(lxm) = Wr(lX6) X S(6Xm) , we can get the matrix

V,l,ml = [04572 0 1404 0 1629 00585 0.0584 0.0511 0.0358 00203 00097 0.0059] Where, the probability distribution matrix of six evaluated

indexes is as follows: 0.0049 0.9951

0 9854 0.0146 0 5735 0.4004 0.0248 0.0009 0 0003 0.0001

0.0018 0.0338 0.1273 0.2193 0.2355 0.182 0.1105 0.0547 0.0351 ·

0.3067 0.2267 0.1809 0 1269 0 078 0 045 0 0225 0 0091 0.0032 0 0011

Then the result of comprehensive assessment for power

quality can be calculated by R = v(IXm) X L(mxI) . The final result

is 2.6184. According to the table II on power quality levels, the result of comprehensive assessment for power quality is between 2 and 3. It means that power quality is much more excellent. Thus it can be seen that the assessment result is objective based on the proposed method in this paper. It can reflect the real condition.

v. CONCLUSION AND FUTURE WORK

We determine the comprehensive index weights by combining compatibility matrix methodology and entropy weight method with SPA theory. It can decrease even eliminate the system uncertainty that is produced by the experts' different opinions. And the final assessment result is calculated by probability statistics and fuzzy judgmental method which assure the result objective and precise. The proposed scheme can monitor the power quality of offshore wind power integration and perfect market mechanism that electric charge is fixed according to the quality. The shortcoming of this paper is that the method of determining discrepancy coefficient i is not perfect.

Our future work will concentrate on perfecting the discrepancy coefficient i and researching more available scheme on power quality assessment. The aim of comprehensive evaluation on power quality is to grasp the global performance of offshore wind power integration. It is meaningful to improve power quality when power quality can't satisfy the need of power system devices and end users. So the improvement on power quality is also the key emphasis in work.

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