Multi-input Multi-output Method for Power Quality Monitoring

J.Y. ZHAO Faculty of Computer Engineering, Huaiyin

Institute of Technology Huaian, China

jszhaojy@163.com Den Tao

Huaiyin Institute of Technology

Huaian, China

W.H. DING

Faculty of Electronic and Electrical Engineering,

Huaiyin Institute of Technology

Huaian, China

Dwh0875@163.com Bian Shan

Huaiyin Institute of Technology Huaian, China

Abstract— For power quality mornitoring, most

methods test simple input signal, but for each tested

object there are many input and output signals. These

signals usually exit relevances between valtage and

current. This paper proposes a test model of Multi-

Input Multi-Output (MIMO) model including theory

and algorithm design. The theory of the derivation

process is given based on mean of least squares (LS).

The algorithm is designed in the form of MIMO

matrix iterative. To confirm the order of polynomial it

introduces a method of gradient descent. As an example

of application a simulation is given. The comparation

shows that it can get all inter harmonics parameters in

whole frequency range in once test. It is already used as

power quality monitoring in power system. The system

may be served as a reference that requires dynamic

monitoring system in parallel with inter-harmonic.

Key words: Power quality; Multiple Input Multiple

Output; Harmonics test

I INTRDUCTION With a large number of using non-linear elements,

electric power system faces serious problem about power

quality. At present, most researches is aimed at integer

harmonics instead of Inter harmonics[1,2,3 ]. It’s defficult to

accurate test Inter harmonics correctly in a traditional way

as the inter harmonics with some characters like time varying.

Many literatures propose analysis methods for inter

harmonic.They support that the Vector Machine (SVM) [6]inter

harmonic Analytical method take with some validity. But it is

not the estimator method based on signal model. The method

employ the Wavelet Transform, The adaptive optimal nuclear

time frequency distribution (AOKTFR) [4,5,6] and traditional

time/measure Conjoint Analysis. But Aliasing frequency

domain and poor resolution ratio at high frequence is can’t

avoid . Analysis methods like Prony 、 Pisarenco[7] and

independent element analysis [8 ]belong to Subspace

estimation method make huge mean error when the signal is

because it has not take effection of noise into consideration[9，

10]. And the method support the point that phase is random

distributed and information of phase is can’t be given[7]. It’s

estimated that The improved TLS-ESPR-IT method[10] has

higher accuracy while the noise variance coming from inter

harmonics analysis result affect accuracy of arithmetic. In

project fact, inter harmonics distributing widely ,no matter

based on FFT、WaveLet or subspace method ,always cut out

parts of signal to analysis and can’t avoid phenomenon like

picket fence effect and frequency leakage. These methods take

huge Nonsynchronous sampling error and can’t get accurate

harmonics parameters in power grid harmonics test.

This paper given a broadband identification method

based on Multiple Inputs Multiple Outputs (MIMO) model,

using total least squares estimate, get the inter harmonics

parameters of whole band by copy number fitting MIMO

frequency response. Resolution dynamic testing system

978-1-4577-0547-2/12/$31.00 ©2012 IEEE

developed independently.

The paper Orginzed in fellows. In section II we present

multiple Input multiple Output(MIMO)model. Section III is

algorithm design and VI is simulation. Last section is

conclution.

II MULTI-INPUT MULTI-OUTPUT THEORE

A. Test Model of Multi-input Multi-outpu fort power quality

To build power quality testing model, the tested system

can be regarded as MIMO system like Fig 1. The productions

current signal )(sIi with inter harmonics dues to standard

power voltage signal )(sU j excitation with non-liner or

inter harmonics voltage elements.

Fig. 1 MIMO system of power quality test

Writen in matrix, we can get

)()(

)(

)(

)()()(

)()()(

)(

)()(

1

121

11211

1

sUsG

sU

sU

sgsgsg

sgsgsg

sI

sIsI

pqpq

p

q

=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⋅⋅⋅⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⋅⋅⋅=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⋅⋅⋅=

or )()()( 1 sUsIsG −⋅= .

Assurme the length of data are N, the frequency response funtion is:

1)-N,0,1, k (,)()()( …==

kUkIkG . （1）

The distribute software control and detailed test process is

shown in Fig 2. The test parameters of configure system in

engine software manage system and syntronization test

domian inter harmonic signal for synergy all terminals are

translated by FFT algorithm to calculate frequency response )(ˆ kG .

B. Theory of MIMO algorithm

Get frequency response from the MIMO test .Then get the feduency pole of current and voltage by fitting copy number of brodband. As aresult, get the inter harmonic

parameters of whole frequency domain.

For )(sG , if qxpCsN ∈)( exits and pxqCsD ∈)(

is nonsingular matrix, frequency reponse )(sG can be

presented:

Fig. 2 Diagram of frequency response measurement

11

21

11

21

1 )()()(ααα

βββ

+++

+++=⋅= −

−−

sss

sssDsNsG p

pp

qq

Lets ω=s , employ orthogonal function system

sfkj

k eW ωω −=)( ,

as the multnomial bases for fitting follows:

jk

n

kkj BWN ∑

==

1)()( ωω qj ,,1= ，

pqCB ×∈

k

n

kk AWD ∑

−

==

1

0)()( ωω (

ppk CA ×∈ ).

…

)(sG

)(1 sU )(2 sU

)(sU

)(1 sI )(2 sI

)(sIq

N

Ｙ

N

Ｙ

Setup sampling frequency Nfs ,

cooperation success？

)}]([{)()}]([{)(

niFFTkInuFFTkU

==

uu

iu

SS

kG ˆˆ

)(ˆ =

Suppose inspireresponse channel

Allow cooperating maximum number?

Test )(),( nuni

cooperation count

Report result of test

N

The next problem is to caculate facters jkB ， kA .

Order ][ 1TT

qT αββθ = , whrer

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

=

jn

j

j

j

B

B

B

2

1

β ,

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

=

nA

AA

2

1

α .

Create error function

)(),(),(),( 1fjffjf GDNjE ωαωβωθω −= − ,

where )( fjG ω is the j line frequency response matrix,

],,1[ Ff ∈ .

The mean error function can be shown by matrix:

⎥⎦

⎤⎢⎣

⎡=

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

=αβ

θω

θω

θω

θ jjj

F

YX

jE

jEjE

jE ][

),(

),(

),(

)(2

1

，

Employ Frobenious norm matrix to show least squares(LS)，

and let )(θl equation set being non-liner,

)]([

))()((

)),(),(()(

1

1

11

∑

∑

∑∑

=

=

==

⎥⎦

⎤⎢⎣

⎡

⎥⎥⎦

⎤

⎢⎢⎣

⎡=

=

=

q

j

j

jTj

jjTTj

q

jj

Hj

F

ffjf

Hj

q

j

QS

SRtr

EEtr

EEtrl

αβ

αβ

θθ

θωθωθ

For easy to solve，change non-liner LS to liner LS，and let

),(),(),()( αωθωθω ffjfls

j DEE =

))()()((1

kfjfkjk

n

kk AGWBW ωωω −= ∑

=. (2)

The gloable mean error function can be shown as

)]([

))()((

)),(),(()(

1

1

11

∑

∑

∑∑

=

=

==

⎥⎦

⎤⎢⎣

⎡

⎥⎥⎦

⎤

⎢⎢⎣

⎡=

=

=

q

j

j

jTj

jjTTj

q

jj

Hj

F

ffjf

Hj

q

j

QS

SRtr

EEtr

EEtrl

αβ

αβ

θθ

θωθωθ

Where

][ jHjj XXrealR = ,

][ jHjj YXrealS = , ][ j

Hjj YYrealQ =

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

=)()(

)()( 11

FnFj

nj

j

WW

WW

Xωω

ωω (3)

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⊗−

⊗−

=)()]()([

)()]()([ 111

FjFnFj

jnj

j

GWW

GWW

Yωωω

ωωω. (4)

Let

⎪⎪⎩

⎪⎪⎨

⎧

=∂

∂

=∂∂

0)(

0)(

αθ

βθ

l

l

j get Equ.（5）

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

−=

=

−= ∑=

αβ

α

jTjj

n

q

jnj

Tnj

Tnjnjn

SR

M

SRSQM

0

)(1

,,,,

(5)

From Equ.(4), we use interative method to get njY ,

njQ , njS , in order n of polynomial.

)]()([ 1,, ωω jnnjnj GWYY ⊗= − ，

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⊗⊗⊗

⊗=

−

−−

)]()()][()([)()(

)()(

1,

1,1,,

ωωωωωω

ωω

jnH

jHnnj

Hj

Hn

jnHnjnj

njGWGWYGW

GWYQQ

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⊗

⊗=

−

−−

))()()()(

)()(

1,

1,1,,

ωωωω

ωω

jnH

nnjH

n

jnH

njnjnj

GWWYW

GWXSS (6)

When found out α and jβ ，the next work is to fit

frequency sponse curve.

III ALGORITHM DESIGN In order to get the dynamic range and channel phase shift

of the test terminal, the method of test uses the international

general dynamic testing standards. Test and computing

spectrum usually use 1 kHz sine signal as input in Standard.

We optimize and realize the algorithm MIMO recognition on

parallel broadband.

The order n-th is used in the above method as given

valume. In fact, we have two methods to get it. One is that it

needs eyes to observe the steady-state figure and judge

whether Frequency distribution has tended vertical line before

calculation, but it can not realize automatic identification of

computer. This paper presents a method used recursive in n. As Fig. 3, given nk ,σ as innitial value, threshold fit the

accuracy 0.03. They act conditions as termination. The

program is calculated until close to the conditions. Now the k

is the order number which is required. Then the nonzero

component of α and jβ can be calculated.

Fig. 3 Improve algorithm of parallel broadband

IV VERIFICATION OF MIMO IN BROADBAND RECOGNITION

Figure 5 is the results of MIMO model with broadband

identification algorithm. The peak and valley of the curve are

legible from static figure. Figure 6 is linear fitting with sliding

window. In Table 1 and Table 2, Freq-Parallel in first line is

automatic identification result by MIMO. Freq-Person in

second line is result by person methods. The frequency errors

are less than 1%. In the relatively higher harmonic wave

amplitude recognition error is less than 1%. And in the

relatively lower harmonic wave amplitude (< 0.5%).

Recognition error is relatively big, but it does not affect using

in practical application. Comparison shows that this method is

feasible.

V CONCLUSIONS The harmonics can be measured in at the same time by

the method of multiple inputs multiple output in all the

frequency range. The method solves problems on low testing

precision and unable to realize automatic measurement caused

by the leakage of frequency and fence effect. The harmonic

dynamic test system which is tested and analysed by

master-slave structure is established based on DSP ADC DAC

FPGA Ethernet chips, which break through the traditional

dynamic test and the analysis of system structure. The feature

research is on parallel tests network on power quality by the

way of a wired or wireless.

Fig. 5 MIMO identification results

Fig. 6 linear fitting with sliding window

Table 1 compares of frequency from MIMO and person methods(Hz)

Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Freq_Parallel 48.33 57.41 105.55 108.19 111.54 164.11 182.68 182.65 196.44 274.75 275.04 286.30 292.68 320.82 375.66

Freq_Person 48.23 57.43 105.55 108.21 111.56 164.09 182.65 182.62 196.42 274.79 275.00 286.36 292.62 320.80 375.45

Table 2 compares of amplitudes from MIMO and person methods (V)

Mode 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Freq_Parallel 100.49 6.73 5.38 1.40 0.83 0.59 4.80 0.79 0.24 0.18 0.86 0.59 0.49 0.68 0.45

Freq_Person 100.50 6.70 5.40 1.40 0.80 0.60 4.80 0.80 0.20 0.20 0.90 0.60 0.50 0.70 0.44

N

Y

initialization nk ,σ

?kσσ >

calculate YX ,

calculate M

SVD of M

calculate α jβ

records n=k

k

n

kk AWD ∑

==

0)()( ωω

jk

n

kkj BWN ∑

==

0)()( ωω

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