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J. Electromagnetic Analysis & Applications, 2009 Published Online September 2009 in SciRes (www.SciRP.org/journal/jemaa)

Copyright © 2009 SciRes JEMAA

CONTENTS

Volume 1 Number 3 September 2009 Current Distortion Evaluation in Traction 4Q Constant Switching Frequency Converters

M. Brenna, F. Foiadelli, M. Roscia, D. Zaninelli………………………………………………………129

Rotating Capacitor and a Transient Electric Network

H. Sarafian, N. Sarafian…………………………………………………………………………………138

Delta Modulation With PI Controller—A Comparative Study

A. I. Maswood, S. Anjum………………………………………………………………………………145

Energy Comparison of Seven MPPT Techniques for PV Systems

A. Dolara, R. Faranda, S. Leva…………………………………………………………………………152

Optimal Power System Restoration and Reconfiguration in Distribution Circuit Using BFAM and BPSO

K S. Kumar, T. Jayabarathi……………………………………………………………………………163

Islanding Detection Method for Multi-Inverter Distributed Generation

A. Cardenas, K. Agbossou, M. L. Doumbia……………………………………………………………170

Effect of Warm Ionized Plasma Medium on Radiation Properties of Mismatched Microstrip Termination

A. Al-Sawalha…………………………………………………………………………………………181

Fault Diagnosis Based on ANN for Turn-to-Turn Short Circuit of Synchronous Generator Rotor Windings

H. Z. Ma, L. Pu…………………………………………………………………………………………187

An Approach to Harmonic State Estimation of Power System

N. C. Zhou, L. Lin, J. Z. Zhu……………………………………………………………………………192

Journal of Electromagnetic Analysis and Applications (JEMAA)

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J. Electromagnetic Analysis & Applications, 2009, 3: 129-137 doi:10.4236/jemaa.2009.13021 Published Online September 2009 (www.SciRP.org/journal/jemaa)


129

Current Distortion Evaluation in Traction 4Q Constant Switching Frequency Converters

M. BRENNA1, F. FOIADELLI1, M. ROSCIA2, D. ZANINELLI1

1The Politecnico di Milano–Department of Energy, Milano, Italy; 2Department of Tecnologie e Progettazione, Università di Bergamo, Bergamo, Italy. Email: morris.brenna, federica.foiadelli, [email protected], [email protected] Received April 14th, 2009; revised July 13th, accepted August 2nd, 2009.

ABSTRACT

The paper deals with the power quality analysis of interlaced four quadrant (4Q) converters with constant switching frequency. These are in fact the input stages of the locomotives and high speed trains supplied by 25 kV, 50 Hz and 15 kV, 16.7 Hz lines. Due to the high power needed for the trains circulation, the 4Q converter can absorb distorted cur-rents, whose harmonic content can affect the signaling systems and communication devices. The presence of more con-verters gives the opportunity, using dedicated commutation strategy, to interlace them in order to reduce the harmonic content in the absorbed current. In the paper a suitable model of more 4Q converters is developed. The control logic implemented in the model allows the evaluation of the harmonic contribution of both single converter and the interlaced configuration. The analysis is carried out through electromagnetic transient simulations.

Keywords: Four Quadrant (4Q) Converter, Interlacing, Traction Systems, Power Quality Analysis, Commutation Strategy

1. Introduction

The four quadrant converter (4Q) is the actual best choice to supply the DC voltage link from AC power contact line. A typology of distributed power high speed electric trains having as input stages more 4Q converters [1] has been considered.

The presence of more converters is necessary to guar-antee a good redundancy in case of failure and gives the opportunity, using dedicated control logics, to interlace them in order to reduce the harmonic content of the ab-sorbed current. The high power requested by the train for its acceleration in starting phase and for the auxiliary services needs high power converters that do not allow high switching frequencies. Consequently the absorbed current presents a high ripple value characterized by high harmonic current components that cannot be tolerated by the system. Indeed the track circuit used for signaling and communication for the traffic management and safety employs signal currents overlapped with the power ones. These currents can have low frequencies (50 Hz and 178 Hz) in the traditional signaling system, or they are in the audio frequencies range for the new European ERTMS/ETCS one. Therefore, the harmonics produced by the 4Q converter can disturb the communications of the track circuit, degrading the safety of the trains circu-

lation. On the other hand the 4Q converter has the main benefit to give a nearly sinusoidal line current in both directions of energy flow and the mitigation of reactive power drawn from the line. In fact the 4Q converter is based on the use of forced commutation switches (GTO, IGBT) and presents a sinusoidal current absorption in phase with the contact line voltage. Moreover, this con-verter is intrinsically bidirectional and then it can be used both for traction and regenerative braking phases.

The aim of this paper is an analysis of the current ab-sorbed by the high speed trains through a suitable model of more 4Q converters. Thanks to a control logic applied in this work, it is possible to interlace two or more con-verters in order to evaluate the harmonic contribution of both single converter and the interlaced configuration. The simulation results obtained with an electromagnetic analysis will be presented.

2. Mathematical Model of the 4Q Converter

The principle scheme reported in Figure 1 shows how the four-quadrant converter is structurally equal to a single phase voltage source inverter and employs the same switches used for the motor drives. This is an advantage

Current Distortion Evaluation in Traction 4Q Constant Switching Frequency Converters 130

because the various branches can have a modular con-struction [2]. The system includes: he transformer secondary side; four switches (GTO or IGBT), T1 ÷ T4; four freewheeling diodes D1 ÷ D4; a DC link with capacitive middle circuit C be-

tween the terminals AK and working at the im-posed voltage Vd=cost;

a second harmonic filter L2–C2 placed downstream the main bridge, tuned to a frequency f2=2·f1 dou-ble to the line one.

The system has two main purposes. The first one is the absorption from the contact line, at a voltage e1 and fre-quency f1, of a current having the fundamental harmonic i1 in phase with e1 and with low harmonic content, in order to respect the following conditions:

1

~1 distortion factorcos 1 power factor

(1)

The second purpose is the absorption from the line of a power with a mean value P1, pulsing at the frequency 2·f1 and the supply of the three-phase motor drive inverters connected to the dc link with a continuous power Pd.

In order to study the behaviour of this converter, the modelling process starts by a mathematical representation of the discrete operation modes of the converter. The discrete model describes each working mode through separate equations. Figure 2 shows a simplified repre-senttation of the two-level converter from which the discrete model is derived.

i1

e1 e2

T1

T2 T4

T3

D1

D2

D3

D4

M

K

N

A i

is

L2

C2

C Vd

+

-

Id

Figure 1. Principle scheme of a four-quadrant converter. e1=line voltage at a frequency f1; i1=line current

Figure 2. Equivalent circuit of a four-quadrant converter

In the equivalent circuit of Figure 2, the transformer secondary side is represented by: an ideal voltage generator (e2=e1/h, where h is the

transformer ratio); an inductance L, equivalent to the leakage trans-

former one; a resistances Rs mainly due to the switches; load resistances R0; DC link capacitance C.

Considering the state variables is and vc, the converter state equations are the following:

22 2 sin( )s c

diL R i v E t

20

C C

dtdv v

C idt R

(2)

where ω is the angular frequency. Rewriting these equa-tions in matricial format, it comes out:

2 2 2

0

10 s

1 1/0 0s

C C

i R iL Ed

v R vC dt

in( )t

(3)

or ExAxZ where x is the state vector and is its time derivative.

x

Taking into account that the converter is a two level type, there is another possible operation mode, described by the following matrix A:

0

1

1 1/sR

AR

(4)

Looking at the matrix A, it is possible to note that in these two operation modes the first element of the first row and the second one of the second row are the same. Therefore, the state equation can be rewritten to:

2

0

0 s

1/0 0sRL E

x xRC

in( )t

1

(5)

where depends from the operation mode and can as-sumes the value 1 or -1.

In this analysis, the switches resistance Rs has been ne-glected.

The transformer leakage reactance depends by the contact line frequency:

1 2X L f L (6)

and it causes a lagging phase shift of an angle ψ between the converter voltage 2V and the supply one 2E . Therefore the first harmonic component of voltages and current become:

2 2 1 2 2 1 2 2 12 sin , 2 sin , 2 sini I t e E t v V t (

where the rms value of the AC voltage v2 is related to th

7)

e DC one Vd through a proportional coefficient:



(8)

The a

whe

DC link voltage of the single-phase converter has significant ripple component at twice the supply fre-

quency. In fact, as it is possible to note in Figure 1 and reported in [3], the current i given by the 4Q converter to the middle circuit is composed by two components:

sd iIi

re:

22 cos sind

k EI k I

X

(9)

is the direct component of the i(t) r

esponsible of the power absorption, and

2 1cos 2si k I t (10)

is an harmonic at the frequency f2=2·f1, with the follow-ing rms value:

2s

k II 2 tan

2 2

k E

X

(11)

The is(t) is absorbed by the dat

orption the input current

edicated filter L2–C2 tuned frequency f2 so that into the dc section that feeds the

motor inverter flows the only continuous component Id. Referring to the control, a smart modulation [4] has

been applied, where the input current follows a suitable sinusoidal reference in order to have a sinusoidal absorp-tion, as explained in the following paragraph.

3. Current Modulation

In order to have a sinusoidal absfollows a suitable sinusoidal reference.

The AC reference current is obtained by multiplying the AC line voltage with a suitable equivalent conduc-tance, in accordance with

1( ) ( )i t G v t (12)

where i is the phasor of the AC phase current and 1v is

the fun amental component of the AC contact line volt-age.

The AC voltage contains the fundamental componentan

d

d the component v" corresponding to the perturbations

present in the AC line (i.e. harmonics), the Park vector of the AC voltage being

''1( ) ( ) ( )v t v t v t (13)

Thus, the instantanve

eous real power, expressed as Park ctor, is given by

* *( ) Ra ap t v i 1

"2 *1 1

e Re

Re

v i G v v

G v G v v

(14)

where is the complex conjugated value of *1v 1v .

id th e sin-gle phase converter, the AC - DC power balance is given

by

Cons ering null power losses associated wi th

*1( ) Re DC DCp t v v v i (15)

and the DC current, neglectipressed with

ng the ripple, can be ex-

*1

1

ReDC

v vv i G

DCv

(16)

Considering the currena non-linear relation between the DC voltage v , the con-tro

ts flowing through the DC bus, dc

l variable G and the load current iload is obtained

*1Re

2DC

load

v vdvCi G

dt

" *211

Re

DC

loadDC DC

v

v vvi G G

v v

(17)

Since V1 can be considered constant, the (17) can be linearized as follows:

2 21 1

2DCd v V VC

dt V

2

" *1Re

DCDC DC

loadDC

G G v dV

v vwhere d i G

V

(18)

d represents a perturbation, due to the AC line distur-bances and the DC ripple.

Its transfer function is

For the DC voltage control, a proportional–integral (PI)controller has been chosen.

IP DC

kG k F s v

s

(19)

where F(s) is the transfer functiorequired for reducing the DC bus ripple.

puting the val-ue

n of the low pass filter

The Equations (18) and (19) constitute the closed loop of the DC voltage control that allows com

s of the PI parameters. In a first approximation the transfer function F(s) can be neglected, obtaining

2 2DC

sv s d

V VC G2 1 1

2 P IDC DC DC

s s k kV V V

(20)

The denominator, considering a damping ratio of 0.707, constrains the PI controller parameters to respect the fol-lowing relations:

21 1

aP

VG Gk

V

nd I P

DC DC DC

k kV V C

(21)

4. Model of the System

retical analysis above de-he system has been imple-

In order to validate the theoscribed, a suitable model of tmented in the EMTP-ATP dynamic simulation tool. The data employed for the modelization refer to a real High Speed Train operating in Italy in 25kV–50Hz lines. This

22 cos dV k V

E




132

Figure 3. Traction circuit schematic diagram of the Italianhigh speed train

Figure 4. Block diagram of the implemented model of the system

ach. Every motor drive is supplied by double 4Q

um peak power equal to 1500kW. Th

l one. The power circuit has been modeled with th

the two input stage 4Q co

s can be identified. The first one is the DC lin

Interlacing of the Converters

requency [5] lets an opportunely shifting of the switching time for

l absorbed cu

s re

f the angle φ. Therefore the Fourier se-rie

vehicle is constituted by two locomotives with two motor drives econverters input stage through the main transformer as depicted in Figure 3.

Each 4Q converter is sized for a rated power equal to 900kW and a maxim

ese are relevant power values for a switching converter that has to be small and light enough to be installed on-board.

The 4Q converters are constituted by a power part and a contro

e circuital elements already available in EMTP-ATP. The MODELS language has been used for implementing the proposed converter control.

The final schematic model is reported in Figure 4, where it is shown only one of

nverters. In the block diagram represented in Figure 4 three

control loopk voltage control loop constituted by the voltage

measurement, the low-pass filter explained in the previ-

ous paragraph, the comparison with the reference value V0ref and the PI controller. Its output is the value of the equivalent conductance G that keeps the DC link voltage constant varying the power requested or injected by the traction motors and auxiliary services. The second loop is the reference current generator. It considers the input voltage measurement followed by a filter dedicated to the high frequency disturbances. The obtained value multi-plied with the equivalent conductance G gives the refer-ence current that the converter, through the switching modulation, has to generate in order to balance the input and output powers. The third loop is related to the DC component compensation in the AC input current. In fact its output value is a constant current that, algebraically added to the reference one, allows to cancel the DC component avoiding the saturation of the input trans-former.

5. The

The use of modulation techniques at constant f

the different 4Q converters onboard the train. The final goal is to interlace more converters in order

to diminish the harmonic content in the totarrent. The interlacing operation gives a shifting through

the current waves coming out from the converters that have to be the one that minimize the harmonic content.

In order to preliminary study the benefit of the inter-lacing practice, two boost converters are considered. A

ported in Figure 5, their current waves are shifted of a generic angle φ.

The two waves have the same duty cycle δ and they are only shifted o

s f and f' of the two converters are the following:

01

( ) cos( ) ( )n nf t A A n t B sen n t

01

)n n t n'( ) cos( ) (f t A A n t n B sen n

b

Applying the known trigonometric formula, the f' cae rewritten as:

n

Figure 5. Waves shifting of the two interlaced boost con-verters currents


Figure 6. Behavior of the THD, varying the duty cycle δ and the shifting φ between the currents absorbed by the two boost

Applying the known trigonometric formula, the f' can

)

)

converters

be

here:

rewritten as:

w

'n cos( ) (

' cos( ) (n n

n n n

A A n B sen n

B B n A sen n

Considering that the current absorbed by the train is th

)

e sum of the currents absorbed by the two converters, the resulting function to consider for the THD calculus is given by the sum of the two functions, that means:

( ) ( ) '( )tf t f t f t

01

' '' cos( ) '' (n nA A n t B sen n t

with n'' 'n nA A A and n'' 'n nB B B .

his case the ab HD is define following: In t solute T d as

2

1nTHD Z (22)

with 2

it is possible to no e THD calculation the

first harmonic has been also considere referred to the sw

cycle δ, her

ha

THD is null for δ=0.5

he

2 2( '') ( '')n n nZ A B .

As te, in th

d , itching frequency, because all the ripple is an undesir-

able component. The THD so calculated is function of the shifting angle φ between the two waves and of the duty

e supposed the same for the two converters. In order to underline the THD dependence from the

parameters δ and φ, a simulation in Matlab environment

01

' cos( ) ' ( )n n

s been carried out. The (22) has been considered, varying the duty cycle between 0.1 and 0.9 and the shift-ing between 0 and 2π and supposing the current ripple amplitude equal to the 1% of the continuous component. The result is reported in Figure 6.

From Figure 6 it is possible to make some considera-tions. First of all, as expected, theand φ=π, because it is the only case in which the two tri-angle waves are symmetric and in opposite phase, there-fore all harmonics are cancelled.

From the optimal point, the THD initially grow fast, both varying δ and φ, underlining the fact that also small dissymmetry in the two converters switching diminish the advantages given by the interlacing. The optimal shifting φ is always equal to π and in this case the THD is always minor than the case of not interlaced converters (φ=0).

Finally, the THD is directly proportional to the ripple amplitude respect to the DC component, and for this t

'( )f t A A n t B sen n t



Figure 7. Shifting of the four switching frequencies

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02-400

-300

-200

-100

0

100

200

300

400

500

t [s]

V [

V]

line voltage

Figure 8. Line voltage waveform measured on the secondary side of an auxiliary transformer

effective value

account the different typologies of inter-

mally running on

s coming out from the practical cases are operable locomotives and electro trains norhigher than the ones reported in Figure 6, considering the relevant current undulation due to the low switching fre-quencies.

Taking into

the railway lines, it is possible to note that after each input transformer there are 2 or 4 4Q converters. Each converter is supplied by a dedicated winding of the main transformer.



ch converter switching frequency has to be re

ain fr

g frequencies.

mutation instants are calculated st

Model for Harmonic Analysis and Simulation Results

the 4Q conve configu-

low short circuit level of the rail-w

due to the resonance phenomena alje

during a measurements survey

tude [%]

It comes out that, in order to have a good interlacing, the shift of ea

spectively equal to ½ or ¼ of the switching period. In this way the ripple of the current absorbed by the

transformer due to all the 4Q converters has the mequency equal to two or four times the switching one

with the advantages of a minor amplitude and easier fil-tration.

In Figure 7 is possible to note the shifting of the four switchin

Analyzing the smart modulation here applied, it is pos-sible to note as the com

arting from points on the reference current that have the same time distance. The interlacing can be easily ob-tained intercalating these time instants referred to the different converters.

6. 4Q Converters

In order to evaluate the harmonic contribution ofrters in single operation and in interlaced

ration, some numerical simulations are carried out, using ATP/EMTP program.

These converters are often supplied by a distorted in-put voltage, due to the

ay lines and a greater harmonic content allowed by the dedicated standards. A typical waveform measured on the secondary side of the transformer for auxiliary services ins reported in Figure 8.

The most significant components are reported in Table 1. This distortion is mainly

ong the line, also enhanced by the harmonic current in-cted by the trains. In order to have a correct operation of

the 4Q converters it is necessary to have a cleaner input voltage obtained installing LC filters in the input stage. Moreover, the greater components (>50th) are carefully

Table 1. Harmonic content of the line voltage recorded

Harmonics Order Frequency [Hz]

Harmonic Ampli-

1 50 100

3 150 7.14

15 750

1

25 1250 5.1

6.12

19 950 5.1

21 1050 2.76

23 1150 3.06

filtered to oid interferen signaling syIn this a alysis, each onverter has be

consideri the following characteristics: Hz;

equency: 500 Hz. e converter have been

, while the DC load with presents the current

ab

mines the input cur-re is

f the switches. This DC compo-ne

its

ach half period.

av ce with stem. n

ng 4Q c en studied

rated voltage of the contact line: 25 kV, 50 transformation ratio of the onboard transformer:

25/0.7 kV; DC link voltage: 1800 V; rated power: 900 kW; switching frThe power components of th

modeled with ideal switchescurrent generator. A negative value re

sorbed during the traction phase, while a positive one represents the regenerative braking.

In the controller are implemented two control loops. The first one gives the value of conductance G that

multiplied by the input voltage deternt reference. The value of the equivalent conductance G obtained through PI controller comparing the measure

of the DC link voltage with its reference in order to keep the DC voltage constant at its nominal value of 1800 V. The function of this controller is to guarantee the equiva-lence between the input power and the one absorbed by the load. In order to assure a uniform power absorption among the various converters, there is only one regulator for all the converters.

The second loop is necessary to cancel the DC com-ponent in the AC current that can be generated by the low switching frequency o

nts can be dangerous for the onboard transformer be-cause can saturate the magnetic core. Indeed this trans-former is not oversized due to the need to reduce its weight and volume. Therefore it is really sensible to the direct current component. Because the four 4Q converters are supplied by four independent transformer windings, it is necessary to adopt one of these regulators for each converter. In Figure 9 the current absorbed by one 4Q converter and its Fourier analysis are reported. It is pos-sible to note a high ten order components corresponding to the switching frequency, but also an appreciable third harmonic. This last one is due to the difficulty to follow up the sinusoidal reference having a so low switching frequency.

The interlacing of the four converters has really re-duced the harmonic content, as it is well represented in Figure 10, where the current absorbed at pantograph and

Fourier analysis are reported. In particular there are no more harmonics at the switching frequency, but there is still the third harmonic, due, as told before, to the low switching frequencies.

What told above is confirmed by Figure 11, where it is possible to note that there is a difficulty of the converter to switch at the end of e



0 5 10 15 20 25 300,0

0,2

0,4

0,6

0,8

1,0

harmonic order

Figure 9. Current absorbed by one 4Q converter and its Fourier analysis

cing in improving the current waveform, e out of service of one converter has been considered.

Th

es out again. In fact it is

e end of each ha

als with a power quality analysis regarding the modern interoperable high speed

ore four quadrant (4Q) converters.

In fact, in the

In order to better evaluate the contribution of the four converters interlath

is condition can occur during the train operation. The current absorbed at pantograph in this second case

with only three 4Q converters working and its Fourier analysis are reported in Figure 12.

It is possible to note the worst harmonic content re-spect to the previous case and, most of all, the contribu-tion of the switching frequency com

evident the presence of the ten order component. Re-garding the third harmonic, the situation is not changed, always due to the low switching frequency.

In Figure 13 is reported the shifting of the three switching frequencies and also in this case it is evident the difficulty of the converter to switch at th

lf period.

7. Conclusions

The paper dethe input stage of trains constituted by mIn fact, the use of the 4Q converter allows to overcome the limits imposed by traditional rectifier.

However, the high power needed for the train accelera-tion, in the order of 6000 kW per locomotive, does not allow to have high switching frequencies.

0 5 10 15 20 25 300,0

0,2

0,4

0,6

0,8

1,0

harmonic order Figure 10. Current at pantograph in case of four 4Q con-verters working and its Fourier analysis

Figure 11. Currents absorbed by all the four 4Q converter interlaced

quently the absorbed current presents a high rip le value not always tolerable by the system.

rrent at th

of the interlacing in improving the cur-re

recent realization they reach the maximum value of 500 Hz. Conse

pThe presence of more converters gives the opportunity,

using dedicated control logics, to interlace them in order to reduce the harmonic content of the absorbed cu

e pantograph. Computer simulations have been carried out using a

suitable model of more 4Q converters, for determining the contribution

nt waveform. First, the case of four interlaced 4Q converters has




137

0 5 10 15 20 25 300,0

0,2

0,4

0,6

0,8

1,0

harmonic order

Figure 12. Current at pantograph in case of three 4Qverters working and its Fourier analysis

con-

Figure 13. Currents absorbed by three 4Q converterlaced

ed operation allows the reducing of the absorbed urrent ripple, since the equivalent switching frequen

erformances of the

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four times the single converter one. However the low harmonic components, such as the third one, cannot be canceled by this solution, therefore they have to be fil-tered by traditional LC passive filters.

The second case analyzed regards a condition that can occur during the train operation such as the out of service of one converter. In this situation the p

fact

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[5] M. S. Carmeli, F. Castelli Dezza, and G. Superti F“Constant frequency current modulation algorithm based on linkage flux,” PESC’03, Power Electronics Specialists Conference, Acapulco, Mexico, 15–19 June 2003.

[6] F. Foiadelli, G. C. Lazaroiu, and D. Zaninelli, “Probabil-istic method for harmonic analysis in railway system,” 2005 IEEE PES General Meeting, San Francisco (USA), 12–17 June 2004.

[7] P. Pinato and D. electric traction system overhead lines,” IEEE X Interna-tional Conference on Harmonics and Quality of Power, Rio De Janeiro (Brasil), 6–9 October 2002.

[8] W. Runge, “Control of line harmonfour-quadrant-converter in AC tractive stock by means of filter and transformer,” in Proc. EPE’97, pp. 3.459–3.464, 1997.

[9] A. Cap

or and harmonic comparison of AC railway power electronic traction converter circuits,” Fifth European Conference on Power Electronics and Applications, pp. 235–240, 13–16 Sep. 1993.



Rotating Capacitor and a Transient Electric Network

Haiduke SARAFIAN1, Nenette SARAFIAN2

1The Pennsylvania State University, York, PA 17403; 2Nenette Sarafian, Hershey Medical Center. Emall: [email protected], [email protected] Received May 16th, 2009; revised July 10th, 2009; accepted July 16th, 2009.

ABSTRACT

This paper presents a rotating parallel-plate capacitor; one of the plates is assumed to turn about the common vertical axis through the centers of the square plates. Viewing the problem from a purely geometrical point of view, we evaluate the overlapping area of the plates as a function of the rotated angle. We then envision the rotation as being a mechani-cal continuous process. We consider two different rotation mechanisms: a uniform rotation with a constant angular velocity and, a rotation with a constant angular acceleration—we then evaluate the overlapping area as a continuous function of time. From the electrostatic point of view, the time-dependent overlapping area of the plates implies a time-dependent capacitor. Such a variable, a time-dependent capacitor has never been reported in literature. We insert this capacitor into a series with a resistor, forming a RC circuit. We analyze the characteristics of charging and dis-charging scenarios on two different parallel tracks. On the first track we drive the circuit with a DC power supply. We study the implications of the rotation modes. We compare the response of each case to the corresponding traditional constant capacitor of an equivalent RC circuit; the quantified results are intuitively just. On the second track, we drive the circuit with an AC source. Similar to the analysis of the first track, we generate the relevant electrical characteris-tics. In the latter case, we also analyze the sensitivity of the response of the circuit with respect to the frequency of the source. The analyses of the circuits encounter nontrivial differential equations. We utilize Mathematica [1] to solve these equations.

Keywords: RC-Series Transient Electric Network, Rotating Parallel-Plate Capacitor, Mathematica

1. Introduction and Motivation

It is a far-fetched concept to think about a conventional transient electrical circuit and incorporate its signal char-acteristics into a discrete and abstract geometry problem. The authors have even taken the initiative one step fur-ther relating these two basic concepts to kinematics. This article shows how these three discrete concepts are brought together and molded into one coherent and unique research project. A thorough literature search of the standard undergraduate and graduate physics texts and reference books reveals the lack of any similar analysis [2]. In the course of quantifying the signal analysis we encounter challenging nontrivial differential equations. In our experience in analyzing comparable technical problems it is proven that Mathematica is the most convenient and efficient tool of choice. Utilizing its coherent and simultaneously applicable symbolic, nu-meric and graphic features assists the authors to focus on the physics issues of interest. Mathematica’s tools also suppress the challenges of developing basic computer

programs from the ground-up. The flow chart of this article including the Introduction

contains three additional sections. In Section I, as a pure geometry problem we apply Mathematica to evaluate the overlapping area of the two rotated squares about their common vertical axis. We then incorporate the rotational kinematics and view the rotation as a mechanical process and consider two different scenarios: 1) a symmetric, uniform rotation; and 2) an asymmetric, accelerated rota-tion. In Section 3, we view the overlapping squares as being two parallel metallic plates that are separated by a gap forming a parallel-plate capacitor. Following the tra-ditional textbook approach [2], we assume the gap is much smaller than the dimensions of the square. This suppresses the fringe effects. Since the area of the over-lapping plates evaluates the capacitance of the capacitor, the rotating plates make the capacitor variable. Technical literatures, particularly Mathematica-based reference books such as [3] contain a wealth of references within

Rotating Capacitor and a Transient Electric Network 139

themselves, yet lack our novel view. It is the ultimate objective of this project to analyze the electric signal characteristic response of the electrical network to the kinematics of the rotating plates. Specifically, in this arti-cle, we address the modifications of the characteristic signal responses of the electrical circuits composed of a resistor connected in a series with our designed, time-dependent capacitor. In particular, we analyze the characteristics of the RC circuits driven with DC as well as AC sources. The third and conclusion section, in con-junction with our recent analysis, descriptively outlines the results of more generalized cases.

, , , tan ,2 2 2

1 - tan L2 ( ), ,2 21 tan

2L L

- tan , 2 2 2

L La b c

L

2. Analysis

2.1 Geometry

Figure 1 shows two identical overlapping squares. The bottom square designated with non-prime vertices is fas-tened to the xy coordinate system. The top square, desig-nated with prime vertices is rotated counter clockwise about the common vertical axis through the common ori-gin O by an angle θ. The squares have the side length of L and the rotation angle θ is the angle between the semi

diagonals 1op and '

1op

To evaluate the overlapping area of these two squares we evaluate the area of trapezoid oabco; the overlapping area then equals four times the latter. The intersecting points of the rotated sides of the top square with the sides of the bottom one are labeled a, b, and c. Utilizing the coordinates of these points, the area of the trapezoid is the sum of the areas of two triangles abc, and oac.

Figure 1. Display of two rotated squares. The bottom square is fastened to the xy coordinate system, the top square is rotated counter clockwise by θ radian

To evaluate the coordinates of a, b, and c we write the

equations for the slanted lines, ' '4 1p p and ' '

1 2p p and

intersect them with the sides of the bottom square. Inter-

section of the former with the 4 1p p and 1 2p p gives the coordinates of a and b, respectively. Similarly, the

intersection of the latter with 1 2p p yields the coordi-

nates of c. Theses are:

0,0,1;o

(1) To evaluate the areas of the needed triangles, we con-

vert the above coordinates into Mathematica code. The inserted 1's in the third position of the coordinates of the origin and the intersecting points are for further calcula-tions.

[ , ] , [ ],1;2 2 2

L La L Tan

1 [ ]2

TanL L

[ , ] ( ), ,1;

2 21 [ ]2

b LTan

[ , ] [ ], ,1;2 2 2

L Lc L Tan

We define two auxiliary lists,

[ , ] [ , ], [ , ],abc L a L b L c[ , ];L

[ , ] , [ , ], [ , ];oac L o a L c L

Figure 2. The normalized values of the overlapping area of the squares as a function of the rotation angle



Figure 3. The graphs are the normalized values of the overlapping areas for: a) a uniform rotation with =/2rad/s, (the left graph) and b) a uniform angular acceleration with = rad/s2 (the right graph)

The needed areas are, 1

[ , ] [ [ , ]];2

areaABC L Det abc L

1[ , ] [ [ , ]];

2areaOAC L Det oac L therefore,

[ , ] [ , ] [ , ];areaOABCO L areaOAC L areaABC L

We divide the value of the overlapping area by the area of the square, L2, and plot its normalized values as a function of the rotation angle . Figure 2 shows the nor-malized area begins and ends at the same values. The value of the area after a /4 radian turn drops to about 83% of the maximum value. The plot as one anticipates is symmetric about /4. The Mathematica codes follow,

Plot[4 areaOABCO[L,]/L2,,0,/2,TicksRange [0,/2,/16],Automatic,PlotRange0,1,AxesLabel ",rad","normalizedarea",GridLinesRange[0,/2,/32],Automatic];

2.2 Modes of Mechanical Rotations

In this section we extend the analysis of Subsection 2.1. Here, instead of viewing the rotation as being a discrete and purely geometrical concept, we view it as a kinematic process. We set the rotation angle ( )t t ; that is, we

introduce the continuous time parameter t. For 2

ω =T

Figure 4. The schematics of a DC driven RC circuit. Throwing

the DPDT switch onto as charges the capacitor, while throw-

ing the switch onto bs discharges the charged capacitor

with the period 4T s , we explore the uniform rotation. For an asymmetrical case, we consider a rotation with a constant angular acceleration. According, for the latter, to rotate the square by 90° in one second we set

21

2t ,with

2

rad

s . The corresponding normal-

ized overlapping areas are displayed in Figure 3.

The Mathematica codes follows,

UniformRotation = Plot [4 areaOABCO [L,]/L2/./2t,t,0,1,TicksRange[0,1,1/8],Automatic, PlotRange0,1,AxesLbel"t,s","area",GridLines Range[0,1,1/16], Automatic];

AcceleratedRotation=Plot [4areaOABCO[L,]/L2/./2t2,t,0,1,TicksRange[0,1,1/8],Automatic, PlotRange0,1,AxesLabel"t,s","area", GridLines Range[0,1,1/16], Automatic];

Show [GraphicsArray[UniformRotation, Accelerated- Rotation]];

3. Electrical Networks

Now we consider a RC series circuit. One such circuit driven by a DC power supply is shown in Figure 4. The circuit is composed of two loops. Throwing the DPDT (Double-Pole Double-Throw) switch to as position

charges the capacitor, while setting the switch to a bs discharges the charged capacitor.

As we pointed out in the Introduction, in this section we view the overlapping squares as being two parallel metallic plates that are separated by a gap forming a par-allel-plate capacitor. Since the capacitance of a paral-lel-plate capacitor is in proportion to the overlapping area of the plates, the continuous rotation of the plates makes the capacitor time-dependent. It is the objective of this section to analyze the characteristics of the electric re-sponse of one such time-dependent capacitor in the charging and discharging processes.



3.1 Characteristics of Charging and Discharging a DC Driven RC Circuit with Time-Dpendent Uniformly Rotating Plates

1t

e

table C0Discharge=Table [t,N[ /.1./6], t,0,1, 1/16]; listC0Discharge=ListPlot [tableC0D ischarge, Pl- otStylePointSize[0.02], GrayLevel [0], GridLines-> Range [0,1,1/8], Automatic, Ticks R ange [0,1,1/8], Automatic];

For the charging process we apply Kirchhoff circuit law [2], this gives

tableCtUniformDis-

charge=Table[k,

0( ) 1 1( ) 0

( )

AdQ tQ t

dt A t (2) 21

[ /. ,4 [ , ] 2

LNIntegrate k

areaOABCO Le

,0, ]

/.1./6,k,0,1,1/16]; For the sake of convenience, we assume V C0=1,

where C0 is the capacitance of the parallel-plate with the plates completely overlapped, Q(t) and A(t) are the ca-pacitor's charge and the overlapping area at time t, re-spectively; A0 is the area of one of the squares; and

0RC is the time-constant of the circuit. For a con-

stant, time independent capacitor, 0( )A t A , and Equa-

tion (2) yields the standard solution ( )Q t

listCtUniformDis-charge=ListPlot[tableCtUniformDischarge,PlotStylePointSize[0.02],GrayLevel[0.5]];

s12=Show[listC0Discharge,listCtUniformDischarge, A-xesLbel"t,sec","Q",PlotRangeAutomatic,0., 1.02,Plot Label->"Dis charging"];

1t

e

Show[GraphicsArray[s34,s12,UniformRotation],ImageSize600];

. In

this equation the maximum charge is normalized to unity. For the rotating plates, however, Equation (2) does not

have an analytic solution. We apply Mathematica NDSolve along with an appropriate initial condition and solve the equation numerically—this yields Q(t). Graphically, we compare its characteristics vs. the char-acteristics of an equivalent RC circuit, this is shown Fig-ure 5. The Mathematica code follows,

It is interesting to note that the charging and discharg-ing signals respond differently to the time-varying ca pacitors; the impact of the time-dependent capacitor is more pronounced for the former. Moreover, for the value of the chosen time-constant of the circuit, =1/6 s, al-though the time-independent capacitor reaches its plateau within one second, the variable capacitor requires a longer time span.

solQUniformRotation=With[=1./6, NDSolve[Eva- luate[(Q'[t]+1/ L2/(4 areaOABCO[L,]/./2 t) Q[t] -1/)]0,Q[0]0,Q[t],t,0,1]];

3.2 Characteristics of Charging and Discharging DC Driven RC Circuit with Time-Dependent Accelerated Rotating Plates

1t

e

s34=Plot [1- /.1./6,Q [t]/. solQUniformRota-tion,t,0,1,PlotStyleGrayLevel[0],GrayLevel [0.5], AxesLabel"t,sec","Q", PlotLabel->"Charging",Plot- RangeAutomatic,0,1.02,GridLinesRange [0,1, 1/8],Automatic];

Similarly, we analyze the characteristics of the dis-charging process. Equation (2) for the corresponding dis-

charging process is, 0( ) 1( ) 0

( )

AdQ tQ t

dt A t

One may comfortably also apply the analysis of Subsec-tion 3.1 to generate the characteristic curves associated with the uniformly accelerated rotating plates. The Mathematica codes may easily be modified to yield the needed information. The codes along with the associated graphic outputs are:

solQAcceleratedRotation=With [=1./6,NDSolve [- Evaluate [(Q'[t]+1/L2/(4areaOABCO [L,]/./2 t2) Q [t]-1/)]0,Q[0]0,Q[t],t,0,1]];

. This equa-

tion for a constant, time independent capacitor,

0 ( )A A t , yields ( ) 1

( ) 0dQ t

Q tdt

, and gives

( )t

Q t e

. For the rotating capacitor, however, its solu-

tion is

0

0

1

( )( )Q t

1t

e

s56=Plot[1- /.1./6,Q[t]/.solQAcceleratedRotation,t,0,1,PlotStyleHue[0.7],Dashing[0.02], Gr- ayLevel[0.5],AxesLabel"t,sec","Q",PlotLabel-> "Charging",PlotRangeAutomatic,0,1.02,GridLines

tA

dA

eRange[0,1,1/8],Autmatic,TicksRange[0,1,1/8],A

. To solve the latter we apply

Mathematica NIntegrate. This yields the needed values. The results are displayed in Figure 5. The Mathematica code follows,

utomatic];

tableCtAcceleratedDischarge=Table[k, 2

,0, ]21[ /. ,4 [ , ] 2

LNIntegrate k

areaOABCO Le

/.1./6,k,0,1,1/16];



Figure 5. Display of charging (the left graph) and discharging (the right graph) signals of uniformly rotating plates. In each graph the black and the gray curves/dots are the signals of the time-independent and time dependent capacitors, respectively. For a comprehensive understanding these graphs are to be incorporated with the left graph of Figure 3

Figure 6. Display of charging (the left graph) and discharging (the right graph) signals of uniformly accelerated plates. The color codes are the same as Figure 5. For a comprehensive understanding these graphs are to be incorporated with the right graph of Figure 3

listCtAcceleratedDischarge=ListPlot[tableCtAccelerat- edDischarge,PlotStylePointSize[0.02],GrayLevel [0.5],GridLinesRange[0,1,1/8],Automatic,Ticks Range [0,1,1/8],Automatic];

s78=Show[listC0Discharge,listCtAcceleratedDischarge,AxesLabel"t,sec","Q",PlotRangeAutomatic,0.,1.02,PlotLabel->"Discharging"];

Show[GraphicsArray[s56,s78,AcceleratedRota-tion]];

To form an opinion about the characteristics of the charging signal for the variable capacitor, one needs to view it together with the far right graph of Figure 3. The rotating plates in this case are accelerated, meaning that for identical time intervals, the overlapping area at the beginning is greater than the overlapping area at the end of the interval. The effects of the asymmetrical rotation are most clearly visible at the tail of the signal. Similar to the uniform rotation (see the lift graph of Figure 5) the impact of the non-uniform rotation for the discharge sig-nal is negligible.

3.3 Characteristics of Charging and Discharging an AC Driven RC Circuit with Time Dependent Capacitor

In this section we analyze the charging and the discharg-

ing characteristics of an RC series circuit driven with an AC source. Schematically speaking, this implies in Fig-ure 4 we replace the DC power supply with an AC source. For this circuit, Kirchhoff's law yields

0( ) 1 1( ) sin(2 ) 0,

( )

AdQ tQ t ft

dt A t

(3)

In this equation f is the frequency of the signal and the voltage amplitude is set to one volt.

Equation (3) is a non-trivial differential equation. To solve this equation, we apply NDSolve along with the corresponding initial condition. The response of the cir-cuit is compared to the equivalent circuit with a constant capacitor. The Mathematica code follows,

solQac=NDSolve[Evaluate[(Qac'[t]+1/ L2/L2 Qac[t] -1/ Sin[2 f t])/.1./6,f0.6]0,Qac[0]0,Qac[t], t,0,1];

plotQac=Plot[Qac[t]/.solQac,t,0,1,PlotStyleGrayLevel[0],AxesLabel"t,sec","Q",PlotLabelAC Driver, DisplayFunctionIdentity];

solQactUniform Rotation=NDSolve [Evaluate [(Qact' [t]+1/L2/(4area OABCO [L,]/./2t) Qact[t]-1/ Sin- [2ft])/.1./6,f0.6]0,Qact[0]0,Qact[t], t,0,1];



Figure 7. Display of the charge on the capacitor vs. time. The solid black curve is the signal of the time-independent capacitor. The solid and dashed gray curves are the signals of the time-dependent capacitors for uniform and acceler-ated rotations, respectively

Figure 8. Display of two rotated rectangles. The bottom rectangle is fastened to the xy coordinate system; the top rectangle is rotated counter clockwise by radian

Figure 9. Display of charging (the left graph) and discharging (the right graph) signals of uniformly accelerated plates. In both graphs the light gray curves are the overlapping area; the black curves are the time-independent capacitor’s signals, while the medium gray curves are the corresponding time-dependent signals

plotQactUniformRotation=Plot[Qact[t]/.solQact Unifo- rmRotion,t,0,1,PlotStyleGrayLevel[0.5],AxesLabel "t,sec","Q", PlotLabelAC Driver];solQact Accel-erated Rotation=NDSolve [Evaluate [(Qact'[t]+1/ L2/(4 areaOABCO[L,]/./2 t2) Qact[t]-1/ Sin[2 f t])/. 1./6,f0.6]0,Qact[0]0,Qact[t],t,0,1];

plotQactAcceleraedRotion=Plot[Qact[t]/.olQactAcce- leratedRotation,t,0,1,PloStyleDashing[0.02],Gr- ayLevel[0.5],AxesLabel"t,sec","Q",PlotLabelAC Driver];Show[plotQac,plotQactUniformRotation,plotQa- ctAcceleratedRotation,ImageSize300];

Utilizing the Mathematica code, one may analyze the frequency sensitivity response of the circuit. As the result of one such analysis, we observe that the differences be-tween the time-independent vs. the time-dependent sig-nals are more pronounced with a frequency domain of less than 1 Hz.

4. Conclusions

Since the inception of the first version of this project, “the square plates” the authors have extended the scope

of their investigation. The idea of rotating the plates of a parallel-plate squared capacitor is sound; however, as we addressed in the aforementioned text the area of the overlapping plates at its best is reduced to only 83% of the maximum area. The square geometry puts a limit to the overlapping area of the rotated plates, limiting the impact of the corresponding time-dependent capacitor on the characteristic signals. To enhance the impact, a po-tential remedy is to replace the square plates with less symmetric flat objects, e.g. a rectilinear or a curvilinear shape such as a rectangle or an ellipse, respectively. For the rectangular plates, for instance, by adjusting the length and the width of the rectangle one is able to reduce the value of the overlapping area at will. This, in turn, more effectively impacts the capacitance of the time-dependent capacitor. The unevenness of the sym-metry of the rectangle about its perpendicular axis through the center of the rectangle results a host of mathematical challenges. The evaluation of the overlap-ping area of the rotated rectangles, contrary to the square plate case, is composed of three different configurations; one such configuration is shown in Figure 8. The



Figure 10. Display of two rotated ellipses. The bottom ellipse is fastened to the xy coordinate system; the top ellipse is rotated counter clockwise by radian

other two configurations are shown in [4]. The character-istics of the associated charging and discharging signals for uniformly accelerated plates with dimensions L/W = 8/2 are shown in Figure 9. The changes in the character-istic signals in comparison to the counterparts, Figure 6, are drastic. Mathematical analysis and the detailed solu-tion of the differential equations describing the intricacies of the rectangular plates are discussed in length in [4].

The authors also have extended their investigations to consider curvilinear plates, such as a pair of elliptical plates. Figure 10 is borrowed from [5]. Mathematical and detailed calculations resulting in the value of the overlap-ping area of the plates are discussed in [5]. Reference [5] also includes the characteristic charging and discharging signals as well. Given the comparable dimensions of the rectangles in [4] vs. the dimensions of the ellipses in [5]

we reasoned the similarity of their output signals. To avoid the repetition of showing their similar transient electric signals we omit displaying the latter. An inter-ested reader is encouraged to review reference [5].

As indicated in the Introduction, the authors have pro-posed a unique research project that has brought together three different subject areas: Geometry, Mechanics, and Electrical Network. Mathematica, with its flexible and easy to use intricacies, is chosen as the ideal tool to ana-lyze the project and address the “what-if” scenarios. As pointed out in the text, some of the derived results are intuitively just. And for the hard to predict cases, we ap-plied Mathematica to analyze the problem. As an open-ended question and research oriented project, one may attempt to modify the presented analysis along with the accompanied codes to investigate the response of parallel RC circuits. It would also be complimentary to our theoretical analysis to manufacture a rotating capaci-tor to supplement the experimental data.

REFERENCES

[1] S. Wolfram, “The mathematica book,” 5th Ed., Cam-bridge University Publication, 2003.

[2] D. Halliday, R. Resnick, and J. Walker, “Fundamentals of physics extended,” 8th Ed, John Wiley and Sons, 2007; J. D. Jackson, “Classical Electrodynamics”, 3rd Ed, John Wiley and Sons, 1998.

[3] M. Trott, “The mathematica guidebook for graphics,” Springer, 2004.

[4] H. Sarafian, “Rotating rectangular parallel-plate capacitor and a transient electric circuit”, International Mathematica Symposium, IMS, 2008.

[5] H. Sarafian, “Rotating elliptical parallel-plate capacitor and a transient electric circuit”, International Conference on Computational Science and its Application, ICCSA’08, pp. 291–296, Springer 2008.


J. Electromagnetic Analysis & Applications, 2009, 3: 145-151 doi: 10.4236/jemaa.2009.13023 Published Online September 2009 (www.SciRP.org/journal/jemaa)


145

Delta Modulation with PI Controller—A Comparative Study

A. I. MASWOOD, S. ANJUM

School of Electrical & Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore. Email: [email protected]

Received March 7th, 2009; revised May 25th, 2009; accepted June 12th, 2009.

ABSTRACT

The paper discusses the application of PWM delta modulation with PI controller as an alternative to the standard PWM techniques for providing gating signals to the voltage source inverters. Its inherent characteristics of constant volts/Hertz control without feedback complexity and boosting of the fundamental voltage makes it an excellent choice for motor drive applications. This paper discusses the comparison between a basic delta modulation, the advanced Delta modulation with PI controller and an optimized DMPI. It is shown that in addition to the aforementioned advan-tages, VSI with optimized DMPI produces superior load current/voltage waveforms compared to simple DMPI, when IGBT is employed as a switching device for the inverter. Since the tacho feedback or other traditional speed sensing means is not permissible in sealed motor or the pump, a novel method is used to monitor the motor speed from the ter-minal quantities like voltage, current, and motor input power factor.

Keywords: Delta Modulation, PI Controller, Voltage Source Inverter, Constant v/f Control

1. Introduction

The fundamental aim of any PWM switching is to elimi-nate the lower order harmonics at relatively minimal commutation of inverter switches. Attraction of the delta modulation (DM) technique is that it guarantees that the on and off time of the inverter switches will never fall below a given minimum value. DM technique is an es-tablished alternative to the traditional sinusoidal PWM switching used in Commercial voltage source inverters driving AC motors. Previous work on DM [1–4] has dis-cussed the objectives, qualities and advantages of delta modulation (DM) technique already from a very specific point of view.

This work gives an overview of the DM from its basic version to the latest state of the art form, i.e. DM with built-in proportional Integral controller.

The adaptive or the rectangular DM has the inherent ability to track the reference signal within a well defined hysteresis threshold level and provides the desired V/f characteristic. The optimal switching frequency and the harmonic control can be easily achieved by:

• Adjusting the integrator R, C parameters. • Changing the reference signal VR amplitude. • Controlling the hysteresis threshold level. • Changing the time constant In the circuit of Figure 1, if the reference Sine wave

signal VR is maintained at the same level of modulation,

the ratio of the fundamental voltage of the modulated wave to frequency remains constant at all frequencies. This is true for PWM mode of operation. The phenome-non is only valid up to the base frequency, which is the fundamental frequency of the reference wave VR. To investigate these aforementioned important properties of the delta modulator, initially a basic DM circuit in PSIM simulation environment is developed.

Figure 1. Basic delta modulator

Delta Modulation with PI Controller—A Comparative Study 146

V/f Characteristics

In delta modulation, finding the base frequency i.e. fre-quency up to which the DM retains constant V/f charac-teristic, is quite important. Above the base frequency the inverter enters constant voltage region (CVR). The CVR may lead to the saturation of the motor’s magnetic core and is to be avoided [2]. Figure 2(a) shows the V/f rela-tionship of fundamental voltage versus the operating fre-quency of the input source Vr.

2. Performance Parameters of DM

Various performances of DM are discussed by: 1) Changing the time constants of DM 2) Changing the hysteresis gap of the DM 3) Changing voltage amplitude of the input source Vr. 4) Using PI controller with DM.

2.1 Changing the Time Constant ( )

In delta modulation circuit shown above the positive and negative slops of carrier wave V2 depends on the time constant τ =R3C of inverter circuit, using some variations in the time constant by changing R3, different ripple fre-quency of the carrier waveform can be achieved. Fourier analysis for the harmonic variation of V1 with the changes in time constant τ is carried out for the various values of operating frequencies of the source VR. The results are shown in Figures 2 and 3.

It has been observed, that by making time constant of inverter circuit to τ/3 by changing R3 to 27k, the linearity stage of V/f characteristic is extended to 300Hz. This is three times the standard base frequency which is 100Hz, and the fundamental voltage amplitude is reduced and also there is change in harmonic amplitude of V1.

Using a time constant of 3τ (R3=204k) harmonic am-plitude of switching output voltage of DM (V1) is re-duced, however the base frequency has been reduced to 50 Hz, this is two times smaller than base fre-quency(100Hz).

Therefore, it is found from DM operation that, the base frequency is inversely proportional to the inverter time constant τ. A range of R3 value from 27k to 68k is attrac-tive for optimal performance of the DM circuit.

2.2 Changing the Hysteresis Gap of Delta Modulator

The hysteresis gap can be changed by changing feed forward resistor R2 having VR and the τ as constants. Thus by using hysteresis 5 % ,10% and 20 % by changing resistor R2, Fourier analysis for the harmonic variation of V1 was carried out for various frequencies of VR. V/f characteristic with variation of hysteresis gap from 5% to 20% is shown in Figure 4. The actual harmonic

0

0.2

0.4

0.6

0.8

1

1.2

10 20 30 40 50 60 70 80 90 100 110 120 130FREQUENCY

NO

RM

AL

ISE

D V

OL

TA

GE

(a)

0

0.2

0.4

0.6

0.8

1

1.2

10 20 30 40 50 70 90 110

frequency

norm

alis

ed v

oltage

(b)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

10 20 30 40 50 60 70 80 90 100

110

120

130

140

150

FREQUENCY

NO

RM

AL

ISE

D V

OL

TA

GE

(c)

Figure 2. (a) Normalized voltage verses frequency distribu-tion with time constant τ, (b) V/f characteristic with time constant 3τ, (c) V/f Characteristic with time constant τ/3

spectrum is not shown as the aim of Delta modulation is to boost the fundamental output voltage (V), which is shown in its normalized form.

It is found from the DM performance that, a lower hys-teresis gap provides for a wider base frequency, but the changes in the base frequency are minimal for the various values of hysteresis gap. R2 range of 100k to 200k is optimal for optimum performance of the DM.



0

0.2

0.4

0.6

0.8

1

1.2

10 30 50 70 90 110

130

200

300

FREQUENCY

NO

RM

AL

ISE

D V

OL

TA

GE

Figure 3. Fundamental component of normalized voltage verses frequency for different time constant

HYSTERESIS COMPARISON

0

0.2

0.4

0.6

0.8

1

1.2

20 30 40 50 60 70 80 90 100 110 120 130FREQUENCY

NO

RM

AL

ISE

D V

OL

TA

GE

10%hysteresis 5% hysteresis 20% hysteresis

Figure 4. Effect of Constant V/f characteristic with varia-tion of Hysteresis gap, 5%, 10%, and 20%

0

0.2

0.4

0.6

0.8

1

1.2

10 20 30 40 50 60 70 80 90 100 110 120

FREQUENCY

NO

RM

ALIS

ED V

OLTAG

E

Figure 5. Normalized fundamental voltage vs. frequency characteristics for variation of VR from 2V to 8V

2.3 Changing the Reference Signal Amplitude (VR)

Under this mode the time constant and the hysteresis gap are kept constant. In normal DM operation, VR is held constant. However, if in some applications the base fre-quency needs to be varied without changing the time constant and the hysteresis gap, it can be achieved by changing VR only. It is found that VR is inversely related to the base-frequency fb. This is shown in Figure 4. A range of 3 to 5 volts for the input source VR is suitable for optimum performance of DM.

3. Properties of DM with PI Control

A PI controller is used to boost up the fundamental volt-age of the delta modulator [6,8].The PI controller is inte grated to the delta modulator (DMPI) as shown in Figure 6(a). Fourier analysis was done for three different values of the feedback resister Rf. The respective fundamental output voltages are shown in Figure 6(b).

As observed from the test that, PI controller helps to boost the fundamental voltage widening the gap between the fundamental and harmonic voltages, and it is also observed that the PI introduces a disturbance to the line-arity of the V/f characteristics. The low voltage percentage boost is calculated from the above figures for each value of Rf based on the gen-eral DM circuit in Figure 1 & Figure 6(a) means Rf value equals to infinity. It is clear from the above tabulated

Figure 6(a). Circuit schematic of Delta-modulator with PI controller

FUNDAMENTAL VOLTAGE AT VARIOUS "Rf" VALUES

0

0.2

0.4

0.6

0.8

1

1.2

20 30 40 50 60 70 80 90 100 110 120FREQUENCY

NO

RM

AL

ISE

D V

OL

TA

GE

FOR Rf=68K FOR Rf=100K FOR Rf=150K

Figure 6(b). A comparison of fundamental normalized volt-age for different values of the Rf



Table 1. Low voltage boosting through Rf

Rf (Ω) Fundamental Value at fm

50Hz

Low Voltage Boost

Infinity 6.5370 -

150K 7.009 7.220%

100K 7.4114 13.376%

68K 8.1785 25.1109%

45K (optimal) 9.5 35.12

results that with proper selection of Rf, the fundamental voltage amplitude can be boost up to 35.10% as long as the operating frequency is within the base frequency. A range of 45k to 100k is suitable for Rf value for the op-timum performance of DMPI.

3.1 Optimized Delta Modulator with PI Control

A final and optimum performance based Delta Modulator with PI controller is suggested for inverter (VSI) with the following optimal values: R2=125K, R3=45K, Rf=45k. The harmonic spectrum of switching output voltage of DM (V1) is obtained with suggested optimized DMPI with modulating frequency of 50Hz and 100Hz are shown in Figure 7.

(a)

(b)

Figure 7. Harmonic spectrum of switching output voltage of DM i.e. V1 at modulating frequency (a) 50Hz (b) 100Hz

As one can see in the above figures, the optimized DMPI with modified component values shifts the domi-nant harmonics towards higher frequencies preferably from the 11th harmonic position. This optimized DMPI model is now used as a driver circuit for the voltage source inverter.

4. Delta Modulator as the Driver

We have selected the above discussed delta modulation (basic DM, DM with PI) techniques for generating the switching gate signal for the IGBT’s of inverter. Analysis of the performance of proposed rectifier-inverter topol-ogy [4] carried out for resistive-inductive load.

4.1 Performance of Inverter with Basic DM

Rectified DC supply is applied given to an IGBT inverter with the basic delta modulator and it is tested for a RL load(R=18Ohms, L=95mH) at 50Hz and 100Hz operating Frequencies (see in Figures 8 and 9).

4.2 Performance of Inverter with DMPI

Study is conducted with the delta modulator inverted with PI controller, and it is observed for same resistive inductive load at 50 and 100Hz operating frequencies as shown in Figures 10 and 11.

It can be seen in the Figure 10(b), there is an 11% boost in the amplitude of fundamental component of output phase voltage of inverter for 50 Hz operation of DMPI with respect to basic DM characteristics shown in Figure 8(b).

4.3 Performance Comparison of Inverter with Basic DM and with DMPI

The output phase voltage of the inverters has been stud-ied for both the delta modulation (DM and DMPI) tech-niques for a range of frequencies with R-L load. The normalized fundamental voltage versus frequency char-acteristics is plotted and it is shown below. It is seen from the Figure 12, that introduction of PI controller helps to boost up the fundamental voltage compared to that of basic DM. The PI controller also introduces slight dis-turbance to the V/f characteristic but the linearity is still maintained up to the range of base frequency of 100 Hz.

5. Optimized DMPI with IGBT Inverter

Rectifier-inverter performance is studied with the opti-mized DMPI, which we have discussed earlier. Opti-mized DMPI is used to drive the driver circuit for the overall three phase inverters and the output harmonic spectrum generated by the inverter circuit is shown below. It is observed that improved version of DMPI is able to shift the more dominant harmonics to the higher frequen-cies.



(a) (b)

Figure 8. (a) Phase voltage waveform with basic DM at 50 Hz. (b) Phase voltage frequency spectrum at 50 Hz

(a) (b)

Figure 9. (a) Phase voltage waveform with basic DM at 100 Hz. (b) Phase voltage frequency spectrum at 100 Hz

(a) (b)

Figure 10. (a) Phase voltage waveforms with DM with PI, at 50 Hz. (b) Phase voltage frequency spectrum at 50 Hz

(a) (b)

Figure 11. (a) Phase voltage waveform with DM with PI, at 100 Hz. (b) Phase voltage frequency spectrum at 100 Hz



5.1 Experimental Results & Drive Application

Figure 14 shows the time domain sample of DM output waveform captured from oscilloscope (Fluke spectrum analyzer). The voltage is normalized with respect to the inverter input dc bus voltage. The spectrum shows the absence of the low frequency harmonics and a high (96.8%) fundamental DM output voltage. Traces of 3rd harmonic still is present due to imperfection in gating signal timing. The output characteristics of the experi-mental prototype Delta-Modulator is studied at different modulating signal Vr frequency and magnitude levels in order to achieve maximum inverter fundamental output voltage. The results are compared and confirmed with the ones from simulation.

In submersible motor pump application, the DMPI method uses either the voltage or the current variation to maintain the constant slip operation. This is known as the speed variation and is used because the pump production and the efficiency are dependent on the speed of the pump. The operational characteristic of the overall sys-tem is shown in Figure 15.

The experimental motor employed is a 1.5 HP squirrel cage submersible induction motor. The motor parameters are given in the Appendix. The variation of inverter voltage, frequency and the resulting motor slip are ob-tained for a sudden change in load, as shown in Figure 15. When the motor load is increased, the slip increases re-sulting in a slowdown. The inverter responds by increas-ing the terminal voltage and frequency. The motor slip eventually decreases and settles to the steady state value after few oscillations. These characteristics also reflect the constant v/f operation of the DM inverter.

6. Conclusions

From the above study of DM techniques, and various comparisons between them, it has been concluded that delta modulation with PI controller helps to provide con-stant V/F characteristics and boosting of the fundamental voltage especially at low operating frequency. The opti-

FUNDAMENTAL HARMONIC COMPARISON BETWEEN BASIC DM AND DMPI

0

50

100

150

200

250

10 20 30 40 50 60 70 80 90

100

110

120

130

140

150

FREQUENCY

FU

ND

AM

EN

TA

L V

OLTA

GE

DMPI BASIC DM

Figure 12. The normalized fundamental voltage versus fre-quency characteristics

Figure 13. Harmonic spectrum for VSI output voltage using optimized DM with PI

Figure 14. Inverter output waveform from oscilloscope

Figure 15. Change of slip, frequency and fundamental voltage for an increase in load at 50Hz operation

mized DM brings about a significant decrease in the harmonic contents towards the 13th harmonic. The DMPI inverter with higher voltage boosting capability and con-stant V/f characteristic without the feed-back complexity leads to lighter and more economical inverter and the optimized DM inverter with attenuation of low-order harmonics lead to reduced filter size.

It was observed that the motor torque and speed can be instantaneously computed solely from its terminal elec-


Delta Modulation with PI Controller—A Comparative Study


151

trical parameters. It was shown how the DMPI does eliminate the problems existing in SMM. The results of the experimental setup show that the proposed method handles load change overshoots and oscillations with ease, especially where frequency variation with load change is not warranted.

REFERENCES

[1] P. D. Ziogas, “The delta modulation techniques in static PWM inverters,” IEEE Transactions on Ind. Applications, pp.199–04, Mar/Apr. 1981.

[2] M. A. Rahman, J. E. Quacioe, and M. A. Chowdhury, “Performance analysis of delta modulated PWM,” IEEE Transactions in Power Electronics, Vol. PE–2, No. 3, pp. 227–233, July 1987.

[3] T. C. Green, J. C. Salmon and B. W. Willams, “Investiga-tion of delta modulation and of subharmonic elimination techniques,” IEEE PESC Record, Vol. 1, April 1988.

[4] M. A. Rahman, J. E. Quacioe, and M. A. Chowdhury, “Harmonic minimization in Delta modulated inverters using Tuned filters,” IEEE PESC Record, Vol. 1, April 1988.

[5] A. I. Maswood, P. D. Ziogas, and G. Joos, “Problems and solutions associated with the operation of phase controlled rectifiers under unbalanced input voltage conditions,”

IEEE Transactions on Industry Applications, U.S.A, Vol. 27, No. 4, pp. 765–772, July/August 1991.

[6] A. I. Maswood and M. A. Rahman, “A survey of delta modulation techniques, characteristics & sub harmonic elimination for VSI,” Electric Machines and Power Sys-tems Journal, U.S.A., Vol. 26, No. 6, pp. 435–448, July 1998.

[7] A. I. Maswood and S. Wei, “A novel current source PWM drive topology with specific harmonic elimination switching patterns,” IEEE Canadian Conference on Elec-trical & Computer engineering, CCECE, Halifax, Nova Scotia, May 8–10, 2000.

[8] A. I. Maswood and M. A. Rahman, ”A PWM voltage source inverter with PI controller, performance parame-ters under non-ideal conditions,” published in the Electric Power Systems Research [EPSR] Journal, U.S.A, Vol. 38, No. 1, pp 19–24, 1996.

[9] A. I. Maswood and M. H. Rashid, “A novel method of harmonic assessment generated by 3–Phase AC-DC con-verters under unbalanced supply conditions,” IEEE Trans-actions on Industry Applications, U.S.A, Vol. 24, No. 4, pp. 590–597, July/August 1988.

[10] M. H. Kheraluwala and D. M. Divan, “Delta modulation strategies for resonant link inverters,” IEEE Transactions on Power Electronics, Vol. 5, No. 2, pp. 220–227, April 2000.




A. DOLARA, R. FARANDA, S. LEVA

Department of Energy of Politecnico di Milano, Via la Masa 34, 20156, Milano, Italy. Email: [email protected], roberto.faranda, [email protected] Received May 14th, 2009; revised July 3rd, 2009; accepted July 12th, 2009.

ABSTRACT

In the future, solar energy will be a very important energy source. Several studies suppose that more than 45% of the energy in the world will be generated by photovoltaic array. Therefore it is necessary to concentrate our forces to re-duce the application costs and to increment their performance. In order to reach the last aspect, it is important to note that the output characteristic of a photovoltaic array is nonlinear and changes with solar irradiation and cell’s tem-perature. Therefore a Maximum Power Point Tracking (MPPT) technique is needed to maximize the produced energy. This paper presents a comparative study of seven widely-adopted MPPT algorithms; their performance is evaluated using, for all the techniques, a common device with minimum hardware variations. In particular, this study compares the behaviors of each technique in presence of solar irradiation variations.

Keywords: Maximum Power Point Tracking (MPPT), Photovoltaic (PV), PV Performance Comparison, Renewable Energy, DC-DC Converter.

1. Introduction

Solar energy is one of the most important renewable en-ergy sources. As opposed to the conventional not renew-able sources such as gasoline, coal, etc. solar energy is clean, inexhaustible and free. The main applications of photovoltaic (PV) systems are in either stand-alone (wa-ter pumping, domestic and street lighting, electric vehi-cles, military and space applications) [1] or grid-con-nected configurations (hybrid systems, power plants) [2].

Unfortunately, PV generation systems have two major problems: the conversion efficiency in electric power generation is low (in general less than 17%, especially under low irradiation conditions), and the amount of electric power generated by solar arrays changes con-tinuously with weather conditions.

Moreover, the solar cell V-I characteristic is nonlinear and changes with irradiation and temperature. In general, there is a point on the V-I or V-P curve only, called the Maximum Power Point (MPP), at which the entire PV system (array, inverter, etc.) operates with maximum efficiency and produces its maximum output power. The location of the MPP is not known, but can be located, either through calculation models or by search algorithms. Maximum Power Point Tracking (MPPT) techniques are used to maintain the PV array’s operating point at its MPP.

Many MPPT techniques have been proposed in the lit-

erature; examples are the Perturb and Observe (P&O) method [2–5], the Incremental Conductance (IC) method [2–6], the Artificial Neural Network method [7], the Fuzzy Logic method [8], etc.. The P&O and IC techniques, as well as variants thereof, are the most widely used.

Because of the large number of methods for MPPT, in the last years researchers and practitioners in PV systems have presented survey or comparative analysis of MPPT techniques. As a matter of fact, some papers present comparative study among only few methods [5,6] and one paper presents a survey and a discussion of several MPPT methods [10]. Another paper [11] presents a ranking of ten widely adopted MPPT algorithms (P&O, modified P&O, Three Point Weight Comparison [12], Constant Voltage, IC, IC and CV combined [13], Short Current Pulse [14], Open Circuit Voltage [15], the Tem-perature Method and methods derived from it [16]), based on simulations, under the energy production point of view. The MPPT techniques are evaluated considering different types of insolation and solar irradiance varia-tions and calculating the energy supplied by a complete PV array.

In this paper, the attention will be focused on experi-mental comparisons between some of these techniques, considering several irradiation conditions. Therefore, the

Energy Comparison of Seven MPPT Techniques for PV Systems 153

Figure 1. Block diagram of the whole experimental system aim of this work is to compare several widely adopted MPPT algorithms between them in order to understand which technique has the best performance. The evalua-tion of the algorithms’ performance is based on the power measurement valuating the total energy produced by the panel during the same test cycle. In this work, respect to the MPPT algorithm compared by simulations, the methods that need temperature or irradiance measure-ments are not considered for sake of simplicity. Indeed, as described in [11], these techniques do not have very high performance and they are too expensive. In the simulations, the considered MPPT techniques have been implemented strictly following the description indicated in the references: no MPPT algorithm is preferred and no MPPT techniques have been realized with more attention respect to the others.

In particular, without lack of generality, we will focus our attention on a stand-alone photovoltaic system con-structed by connecting the DC-DC converter between the solar panel and a dc load.

2. Experimental System

The experimental comparison among the different MPPT techniques has been performed realizing the whole sys-tem in the Power Quality Laboratory of Department of Energy at the Politecnico di Milano.

The experimental system is constituted by three main elements (Figure 1): the DC-DC converter, the PV-panels and the solar simulator.

2.1 The DC-DC Converter

It has been realized a single device constituted by a DC-DC converter [17] and other components able to im-plement all the different MPPT techniques here analyzed, including Open Circuit Voltage (OV) [14] and Short Current Pulse (SC) [13] which required to insert further static switches to open the circuit or to create the short-circuit condition, in order to compare the results. All the MPPT techniques here described are easily ob-

tained changing the software compiled in the microcon-troller. In this way the differences in the measured energy load depend mainly on the software used for the imple-mentation of the particular MPPT technique.

The choice of a stand-alone system, and hence the choice of using a DC-DC converter, reflects some indus-trial configurations composed by a first DC-DC conver-sion stage, in which usually the control of MPPT tech-niques is implemented, a second filter stage, and eventu-ally a DC-AC conversion stage.

The DC-DC converter developed includes the power and control boards as shown in Figure 2. The control board is constituted by all the components

that need for the implementation of the various MPPT algorithms already illustrated in [10–16]. The microcon-troller, in this case a Microchip dsPIC30f4012, is the core of the control board.

The command connection to the power board is pro-vided by means of driver circuits which allow the valves commutation.

The interface between control and power circuits is realized with optoinsulators and Hall effect transducers to

Figure 2. (a) Stand-alone PV system analyzed. DC-DC con-verter’s (b) power and (c) control boards



guarantee the necessary metallic insulation required be-tween these boards. Such connection allows not only to drive the valve in PWM mode and hence to implement the different MPPT techniques without modifying the power components, but also to acquire the PV voltage and current signals.

In particular, the voltage and current measurements are made by Hall effect transducers; they are perfectly suit-able for this application indeed they are able to detect continuous components, furthermore they can guarantee very low losses during the measurement and insulation between the control board and the power one, and finally they have a wide enough bandwidth.

There are a lot of DC-DC conversion circuits. In the present work the boost configuration is chosen. It is very spread thanks to its high reliability respect to other more complex configurations, to the reduced number of com-ponents and also to the high-minded experience in its operation. The complete power device scheme is shown in Figure 3.

The boost section is realized by two accumulation units, L and Cout, the static switch T1 and the diode D3.

Moreover, the diode D1 is put into the circuit to protect the PV-panel against negative current which could dam-age it.

The equivalent measures of the PV-panel voltage, VPV, and current, IPV, are obtained by inserting the voltage transducer V and the current one A in the circuit as re-ported in Figure 3.

Figure 3 shows the circuit elements Tv0, Tsc, K1, K2, Cin and D2; that have been inserted to:

measure the PV-panel open circuit voltage, that is necessary in OV technique, through the opening of Tv0 valve, in this case D2 is short-circuited through K2;

measure the PV-panel short-circuit current, that is necessary in the SC technique, through the closure of Tsc valve, in this case Tv0 is short-circuited through K1.

During the tests of other MPPT techniques, the valve Tsc is kept open, while Tv0 and D2 are short-circuited, re-spectively through K1 and K2 switches, to increase con-verter efficiency removing their power losses. It is impor-

Figure 3. Scheme of the power device

tant to underline that, in each MPPT algorithms, the DC-DC converter power losses do not influence the MPP because the system acquires the PV voltage and current.

It is important to note that in the SC MPPT technique it is necessary to insert the D2 diode to avoid, during the short-circuit test, the discharging of Cin placed at boost input. Such capacitor is always inserted in each tech-niques analysed to limit the high frequency harmonic components.

The prototype converter has been sized for the voltage of 3 in-series modules and the current of 3 in-parallel modules. In particular, in correspondence of the Standard Test Condition (STC), therefore at 1000 W/m2 and 298 K, we have:

a maximum open circuit voltage equal to 21.8 V and a maximum short-circuit current equal to 13.05 A with the modules in parallel configura-tion;

a maximum open circuit voltage equal to 65.4 V and a maximum short-circuit current equal to 4.35 A with the modules in series configuration.

The DC-DC converter is designed to work at the MPP with a duty cycle of 25%. The DC-DC converter sizing, with a security margin, leads to the following data: switching frequency of 20 kHz, nominal current of 15 A, and nominal voltage of 150 V.

The IGBT IRG4PC30KD electronic valves are chosen. These components integrates an ultrafast recycling diode and present small switching losses also in presence of high switching frequency.

2.2 PV Panel

The PV panels here considered are the poly-crystalline 70 W PV-module by Helios Technology. Its main speci-fications are shown in Table 1.

2.3 Solar Simulator

The sunlight simulator have to guarantee low spatial non-uniformity and low temporal instability of irradiance, moreover it have to generate a significant power output from PV-system and finally it have to allow different irradiance levels on the PV-panel. The solar simulator used in the present tests is realized by using both incandescent and halogen lamps. The maxi-mum power of the solar simulator is 2.8 kW and its size is 1200 mm long and 600 mm wide.

Combining the lamps, it is possible to have, with ade-quate uniformity, four different irradiation levels equal to 0 W/m2, 272 W/m2, 441 W/m2 and 587 W/m2.

3. MPPT Control Algorithm

There are many MPPT methods available in the literature; the most widely-used techniques are described in



Table 1. Electrical characteristics of PV panel in STC

Symbol Quantity Value

PMPP Maximum Power 70 W

VMPP Voltage at PMPP 17 V

IMPP Voltage at IMPP 4.11 A

ISC Short-Circuit Current 4.35 A

VOV Open-Circuit Voltage 21.8 V

NOCT Nominal Operating Cell Temperature 43±2 °C

the following sections, starting from the simplest method.

3.1 Constant Voltage Method

The Constant Voltage (CV) algorithm is the simplest MPPT control method. The operating point of the PV array is, each nth step, kept near the MPP by regulating the array voltage and matching it to a fixed reference voltage VREF equal to the VMPP of the characteristic PV module (see Table 1) or another pre-valuated best voltage value [16]. The CV method assumes that insulation and temperature variations on the array are insignificant on the VMPP, and that the constant reference voltage VREF is an adequate approximation of the real MPP. Therefore, the operating point is never exactly at the MPP and different data have to be adopted for different geographical regions.

The CV method needs the measurement of the PV ar-ray voltage VPV in order to set up the duty-cycle of the DC/DC boost converter as shown in Figure 4.

It is important to observe that when the PV panel is in low insulation conditions, the CV technique is, generally, more effective than either the P&O method or the IC method (analyzed below), as shown in [11]. Thanks to this characteristic, the CV method is often combined to-gether with other MPPT techniques.

Measurement of VPV

VPV = VREFYES

YESVPV > VREF

δ(n+1) = δ(n) + Δδ δ(n+1) = δ(n) - Δδ

NO

NO

Figure 4. Flow chart of the CV method

3.2 Short-Current Pulse Method

The Short-Current Pulse (SC) method achieves the MPP by giving a reference current IREF to the power converter controller. In fact, the optimum operating current for maximum output power is proportional to the short-circuit current ISC under various conditions of irradi-ance level S as follows [12]:

REF 1 SC I S k I S (1)

where k1 is a proportional constant. This control algorithm requires the measurement of

the current ISC. To obtain this measurement, it is neces-sary to introduce a static switch in parallel with the PV array, in order to create the short-circuit condition. It is important to note that when VPV=0 no power is supplied by the PV system and consequently no energy is generated.

The SC method needs the measurement of the PV ar-ray current IPV in order to set up the duty-cycle of the DC/DC boost converter (see Figure ).

3.3 Open Voltage Method

The Open Voltage (OV) method is based on the observa-tion that the voltage VMPP is always close to a fixed per-centage of the open-circuit voltage VOV. Production spread, temperature, and solar insulation levels change the position of the MPP within a 2% tolerance band. This technique uses 76% of VOV as reference value VREF (at which the maximum output power can be obtained); in general, this value is very close to the VMPP.

This control algorithm requires measurements of the voltage VOV when the circuit is opened. Here again it is necessary to introduce a static switch into the PV system; for the OV method the switch must be used to open the circuit. When IPV=0 no power is supplied by the PV sys-tem and consequently no energy is generated. Also in this method measurement of the PV array voltage VPV is re-quired by the regulator (see Figure 6).

3.4 Perturb and Observe Methods

The P&O algorithms operate by periodically perturbing (i.e. incrementing or decrementing) the array terminal voltage and comparing the PV output power with that of the previous perturbation cycle. If the PV array operating



Measurement of IPV

NO

NO

PV short-circuit condition

PV work condition IPV < IREF

δ(n+1) = δ(n) - Δδδ(n+1) = δ(n) + Δδ

IPV = IREF

Refresh reference?

Measurement of ISC

IREF = k1 ISC

NOYES

YES

YES

Figure 5. Flow chart of the SC method

Measurement of VPV

NO

NO

PV short-circuit condition

PV work condition VPV > VREF

δ(n+1) = δ(n) - Δδδ(n+1) = δ(n) + Δδ

VPV = VREF

Refresh reference?

Measurement of VOV

VREF = k2 VOV

NOYES

YES

YES

Figure 6. Flow chart of the OV method

voltage changes and power increases (dP/dVPV>0), the control system moves the PV array operating point in that direction; otherwise the operating point is moved in the opposite direction. In the next perturbation cycle the al-gorithm continues in the same way.

A common problem in P&O algorithms is that the ar-ray terminal voltage is perturbed every MPPT cycle; therefore when the MPP is reached, the output power

oscillates around the maximum, reducing the generable power by the PV system. This is mainly true in constant or slowly-varying atmospheric conditions but also under rapidly changing atmospheric conditions [17].

There are many different P&O methods available in the literature. In this paper we consider the classic, the optimized and the three-points P&O algorithms.

In the classic P&O technique (P&Oa), the perturba-



10

1PV PVP n P n

n n

Figure 7. Flow chart of the P&Oa method tions of the PV operating point have a fixed magnitude (see Figure 7). In our analysis, the magnitude of pertur-bation Δδ is 0.35% of PV array VOV. In the optimized P&O technique (P&Ob), an average of several samples of the array power is used to dynamically adjust the magni-tude of the perturbation of the PV operating point. This adjusting is realized by valuating MOV and calculating the parameter a(n) as reported in Figure 8. In the three-point weight comparison method (P&Oc), the perturbation direction is decided by comparing the PV output power on three points of the P-V curve, and valuating the pa-rameter M as shown in Figure 9. These three points are the current operation point A, a point B perturbed from point A, and a point C doubly perturbed in the opposite direction from point B.

All these three algorithms require the measurement of the PV array voltage VPV and of the PV array current IPV.

3.5 Incremental Conductance Method

The Incremental Conductance (IC) algorithm is based on the observation that the following equation holds at the MPP [2]:

(dIPV/dVPV)+(IPV/VPV)=0 (2)

where IPV and VPV are the PV array current and voltage, respectively. When the operating point in the P-V plane is to the right of the MPP, it is verified (dIPV/dVPV)+ (IPV/VPV)<0, whereas when it is to the left of the MPP this (dIPV/dVPV)+(IPV/VPV)>0.

The MPP can thus be tracked by comparing the in-stantaneous conductance IPV/VPV to the incremental con-ductance dIPV/dVPV. Therefore, if the quantity (dIPV/dVPV) +(IPV/VPV) is more than ε, its sign means a power produc-tion decrement and indicates the correct direction of per-

turbation leading to the MPP. Once MPP has been reached, the operation of PV array is maintained at this point and the perturbation stopped unless a change in dIPV is noted. In this case, the algorithm decrements or incre-ments the PV array voltage VPV to track a new MPP. The increment size determines how fast the MPP is tracked.

The IC method offers good performance under rapidly changing atmospheric conditions. The classic IC algo-rithm requires the measurement of the PV array voltage VPV and current IPV in order to determine the correct per-turbation direction.

4. Numerical Results

The measurements have been performed several times in order to cut off deviations caused by interferences and/or environmental factors in this system. The most important environmental factor, that hardly influence the PV-panel behaviour, is its temperature. In order to maintain the PV-panel temperature equal in all tests and to preserve this parameter into a little range during tests, all experi-ments are made starting from the same PV-panel’s tem-perature, and the duration of tests has been reduced as short as possible avoiding overheating.

Due to energy absorbed from the network, available space constraints and especially economic constraints associated to the dimensions of the solar simulator, the test campaign involved a single module described in Table 1.

In order to realize a precise analysis of the perform-ance of the different MPPT techniques, they are experi-mentally compared taking into account two different ir-radiation diagrams. The first one, Case 1 (Figure 11), is characterized by medium and medium-high irradiation levels of 441 W/m2 and 587 W/m2 with a time of 180 s and the second one, Case 2 (Figure 12), with low, lo- w-medium, medium-high irradiation levels of 0 W/m2, 272 W/m2, 441 W/m2 and 587 W/m2, with a time of 160 s (Case 2 include a 10 s interval without irradiation).

Every MPPT technique analysis starts when the initial steady state condition of each case is reached.

A couple of samples of voltage and current is available every 10 ms, and P&Oa, P&Ob, IC, CV, OV and SC al-gorithms can perform an iteration for each couple of val-ues; only P&Oc needs 3 measurement of power instead of 1.

Duty-cycle variation amplitude Δδ is 0.5% for all techniques except P&Ob, in witch Δδ is proportional to the ratio and it ranges between 0.5% and 2.7%. A reduced duty-cycle variation value decreases the speed of the algorithm dynamic behaviour but it increases the pre-cision in reaching MPP.

/dP dV

The P&Oa technique performs very well with low ra-diance values: in this condition the P-V curve is very smooth near the maximum. The P&Ob logic with vari-able step is able to reduce steady state oscillations and, at the same time, to provide higher response speeds at me-



Figure 8. Flow chart of the optimized P&Ob method

Measurement of Vb(n), Ib(n);Pb(n) = Vb(n) Ib(n)

Pb(n) ≥ Pa(n)

M = M + 1

Pa(n) > Pc(n)

M = 2

M = - 2

M = M - 1

YES NO

M = M + 1 M = M - 1

YES NO

V(n+1) = Va(n)δ(n+1) = δ(n)

V(n+1) = Vb(n)δ(n+1) = δ(n) + Δδ

V(n+1) = Vc(n)δ(n+1) = δ(n) - 2·Δδ

YES NO

YES NO

δ(n)b = δ(n)a + Δδ

Measurement of Va(n), Ia(n);Pa(n) = Va(n) Ia(n)

Measurement of Vc(n), Ic(n);Pc(n) = Vc(n) Ic(n)

δ(n)c = δ(n)b – 2 Δδ

δ(n)a = δ(n)

Refresh reference?

M = 0

Figure 9. Flow chart of the optimized P&Oc method




159

Figure 10. Flow chart of the IC method

Figure 11. Irradiation diagram of Case 1 Figure 12. Irradiation diagram of Case 2 dium-high irradiance level with respect to the P&Oa ap-proach with fixed Δδ. This technique is very slow in reaching MPP when irradiance level is low because

is small. /dP dV

Case 2 shows the main disadvantage of the IC tech-nique: for low radiance values the technique works on a P-V curve with a derivative close to zero in a large inter-val around the maximum value, therefore it is not able to properly identify the MPP. It results in oscillations around the MPP with a reduced output energy value.

The P&Oc technique compare the power of three dif-ferent working points as described in Fig. 9. The algo-rithm modifies the duty-cycle, in function of the obtained results, to reach the MPP value as described in [12]. The increment (or decrement) of the duty-cycle amplitude is constant and the algorithm performs an iteration every 10 ms.

The CV technique is optimized for a single radiance value; the performance of this technique is strongly re-lated with the voltage set point. It provides satisfying results, but they are not as good as the ones provided by P&O and IC techniques.


MPPT Technique Case 1 Case 2

P&Oa

P&Ob

P&Oc

IC

CV

OV

SC

Figure 13. Power generated by the PV array in the Case 1 and Case 2 by different optimized MPPT methods (solid line) and ideal (dot-dashed line) MPPT method



Further considerations may regard OV and SC tech-niques. They require additional valves for, respectively, the measurement of the PV open circuit voltage and of the PV short-circuit current.

Concerning the OV technique, it refreshes the voltage reference value every 3 s through the open voltage meas-urement (for this measurement is necessary 10 ms with-out power generation). The ratio of the open voltage and the MPP voltage is not strictly constant with temperature, and the technique can be optimized only for a single temperature value. For this reason the converter per-formance with OV technique is in general better than CV, but is not as good as the ones provided by P&O and IC techniques because of the voltage drop on Tv0 and the necessary measurement time. It is important to underline that the voltage drop on Tv0 is equal to about 1.5 V, which implies a significant reduction of the load voltage, and hence of the output power. This is a significant feature in the evaluation of the converter efficiency.

Analogous considerations regard the SC technique. In this case the voltage drop that reduces converter’s output power is due to the D2 valve and it is about 0.6 V. This technique refreshes the reference current value once again every 3 s through the short-circuit current meas-urement (for this measurement is necessary 10 ms with-out power generation). The voltage applied to the PV-panel during the measurement step is the voltage drop on Tsc. In this condition the measured current can be approximated to the real short-circuit current.

Figure 13 shows the power generated from the PV-panel with the same converter configuration and dif-ferent MPPT techniques in the two cases. The diagrams also show the ideal power, obtained by using an ideal MPPT technique that is equal to the maximum power that the PV-panel can produce. These values are measured directly on the PV-panel under test in STC. For this rea-son MPPT ideal curve must be considered only as a qualitative reference to compare tests’ results. It is im-portant to observe that the uncertain in the PV voltage and current measurements and the small difference in the environmental conditions between each tests suggest that the results cannot be a good reference to calculate the efficiency of the single MPPT algorithm. In these condi-tions, even an uncertain of 0.5% in the measurements could produce an uncertain in the relative power losses that could be more than 10%.

Table 2 summarizes the performances of the different techniques in the two radiation cases and the differences respect to the ideal MPPT algorithm.

5. Conclusions

This paper has presented a comparison among some of the more diffused Maximum Power Point Tracking tech-niques in relation to their energy performance. In par-ticular, different types of solar insolation characterized by

low and medium irradiation level are considered, and the energy supplied by a complete PV array is experimen-tally evaluated. The whole system—including the DC-DC converter and the lighting system—is arranged in the Power Quality Laboratory of Department of Energy of the Politecnico di Milano. The different MPPT tech-niques have been implemented following the directions indicates in the papers listed in the references; no one has been preferred or better improved respect to the others.

The results show that the best MPPT technique is the modified P&O (P&Ob). The logic turned out to be effec-tive in both the situations here considered, providing al-ways the highest efficiency. P&Ob technique shows its limit in the response to the irradiance variation at low irradiance level.

The IC technique has an efficiency lower than the P&O techniques, but its response time is quite independ-ent to the irradiation values and its efficiency increase with the irradiance level. This technique can be a good alternative to the P&O techniques in applications charac-terized by high, fast and continuous radiance variations, e.g. the PV applications in transportation.

The two techniques are also equivalent concerning the costs and the software complexity; in particular both the techniques require a microcontroller with medium/higher performances than the ones required by other techniques, due to the necessity of high computation capability.

Among the other hill climbing techniques, the P&Oa method presents acceptable results: this algorithm can be a good alternative to the two previous techniques. Instead the P&Oc method, even if characterized by output energy values analogous to the P&Oa, has a more complex algo-rithm and a lower reactivity, with no benefit in terms of performances. Furthermore, given the features required by the controller, the P&Ob technique is better than the P&Oc one.

The P&Oa technique requires a microcontroller which has lower computational capability constraints with re-spect to the best technique here considered. It is therefore necessary to evaluate if the cost gap between the two microcontrollers can justify the lower performances of the technique.

It is necessary to underline that the maximum irradi-ance level obtained from solar simulator is about half than the real irradiance from the sun. In these conditions the performance of IC are quite less than the P&O tech-niques ones because the MPP in the PV power character-istic has a derivative close to zero for a quite large volt-age variation. In the present analysis the CV, OV and SC techniques turned out to be the worst ones. Their performances are lower than the ones obtained with P&Ob techniques es-pecially in case of conditions very different from the ra-diance value in correspondence of which these techniques have been modeled. Moreover, OV and SC techniques



Table 2. Energy generated as a function of MPPT technique and irradiance input

MPPT Technique

Case 1 Case 2

Energy [J] Rank Difference respect to

the ideal case Energy [J] Rank

Difference respect to the ideal case

Ideal 4493 - - 3298 - - P&Oa 4282 2 -4,7% 3144 2 -4,7% P&Ob 4346 1 -3,3% 3212 1 -2,6% P&Oc 4278 3 -4,8% 3135 3 -4,9%

IC 4215 4 -6,2% 3117 4 -5,5% CV 4201 5 -6,5% 3100 6 -6,0% OV 4200 6 -6,5% 3104 5 -5,9% SC 4088 7 -9,0% 2942 7 -10,8%

requires additional valves in the converter that decrease its efficiency and the output power.

The CV technique is still a very simple logic which provides a very good efficiency for radiance values closed to 700 W/m2, with low costs. Hence, generally this technique can be selected only if there is the necessity to minimize the control system cost.

However the cost of a microcontroller currently low, so that the implementation of the P&O type techniques is anyway preferred.

REFERENCES

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[3] W. Wu, N. Pongratananukul, W. Qiu, K. Rustom, T. Kas-paris, and I. Batarseh, “DSP-based multiple peack power tracking for expandable power system,” in Proc. APEC, pp. 525–530, 2003.

[4] C. Hua and C. Shen, “Comparative study of peak power tracking techniques for solar storage system,” in Proc. APEC, pp. 679–685, 1998.

[5] D. P. Hohm and M. E. Ropp, “Comparative study of maximum power point tracking algorithms using an ex-perimental, programmable, maximum power point track-ing test bed,” in Proc. Photovoltaic Specialist Conference, pp. 1699–1702, 2000.

[6] K. H. Hussein, I. Muta, T. Hoshino, and M. Osakada, “Maximum power point tracking: an algorithm for rapidly chancing atmospheric conditions,” IEE Proc.-Gener. Transm. Distrib., Vol. 142, pp. 59–64, 1995.

[7] X. Sun, W. Wu, X. Li, and Q. Zhao, “A research on photovoltaic energy controlling system with maximum power point tracking,” in Power Conversion Conference, pp. 822–826, 2002.

[8] T. L. Kottas, Y. S. Boutalis, and A. D. Karlis, “New maximum power point tracker for PV arrays using fuzzy controller in close cooperation with fuzzy cognitive net-work,” IEEE Trans. Energy Conv., Vol. 21, pp. 793–803, 2006.

[9] I. S. Kim, M. B. Kim, and M. Y. Youn, “New maximum power point tracking using sliding-mode observe for es-timation of solar array current in the grid-connected photovoltaic system,” IEEE Trans. Ind. Electron., Vol. 53, pp. 1027–1035, 2006.

[10] Y. T. Hsiao and C. H. Chen, “Maximum power tracking for photovoltaic power system,” in Proc. Industry Appli-cation Conference, pp. 1035–1040, 2002.

[11] G. J. Yu, Y. S. Jung, J. Y. Choi, I. Choy, J. H. Song, and G. S. Kim, “A novel two-mode MPPT control algorithm based on comparative study of existing algorithms,” in Proc. Photovoltaic Specialists Conference, pp. 1531–1534, 2002.

[12] T. Noguchi, S. Togashi, and R. Nakamoto, “Short-current pulse-based maximum-power-point tracking method for multiple photovoltaic-and-converter module system,” IEEE Trans. Ind. Electron., Vol. 49, pp. 217–223, 2002.

[13] D. Y. Lee, H. J. Noh, D. S. Hyun, and I. Choy, “An im-proved MPPT converter using current compensation method for small scaled PV-applications,” in Proc. APEC, pp. 540–545, 2003.

[14] M. Park and I. K. Yu, “A study on optimal voltage for MPPT obtained by surface temperature of solar cell,” in Proc. IECON, pp. 2040–2045, 2004.

[15] T. Takashima, T. Tanaka, M. Amano, and Y. Ando, “Maximum output control of photovoltaic (PV) array,” in Proc. 35th Intersociety Energy Convers. Eng. Conf. Ex-hib., pp. 380–383, 2000.

[16] P. C. M. de Carvalho, R. S. T. Pontes, D. S. Oliveira, D. B. Riffel, R. G. V. de Oliveira, and S. B. Mesquita, “Control method of a photovoltaic powered reverse osmosis plant without batteries based on maximum power point track-ing,” in Proc. IEEE/PES Transmiss. Distrib. Conf. Expo.: Latin America, pp. 137–142, 2004.

[17] T. Esram and P. L. Chapman, “Comparison of photo-voltaic array maximum power point tracking techniques,” IEEE Trans. Energy Conv., Vol. 22, pp. 439–449, 2007.




163


K. Sathish KUMAR, T. JAYABARATHI

School of Electrical Sciences, VIT, Vellore, Tamil Nadu, India. Email: [email protected] Received June 19th, 2009; revised July 30th, 2009; accepted August 7th, 2009.

ABSTRACT

This paper approaches the problem of restoring a faulted area in an electric power distribution system after locating and isolating the faulted block and reconfiguring the system. Through this paper we are going to explain the power system restoration technique using brute-force attack method (BFAM) and binary particle swarm optimization (BPSO). This is a technique based on the possible combination in mathematical analysis which is explained in the introduction. After isolating the fault, main concentration will be towards the reconfiguration of the restored system using BPSO. Here due to fault in the system near-by agent will be affected and become useless and will go in the non-working mode. Now in order to restore these near-by loads we will give a new connection called NO (Normally Open. Using these switch system will be restored with power availability. After restoration using the BFAM, the BPSO will be used in or-der to provide the stable configuration. The output of the BFAM will be used as input for the BPSO and then we will reconfigure our system in order to provide the stable configuration. The effectiveness of the proposed BFAM and BPSO is demonstrated by simulating tests in a proposed distribution network and verified the results using the Matlab and C programming.

Keywords: Brute-Force Attack Method, Power System Restoration and Particle Swarm Optimization

1. Introduction

The key elements of power system are its continuity and reliability. If these two elements are deviated from their normal condition then it may leads to the system in ab-normal conditions which may be either alert state or emergency state. Both shouldn’t be entertained in the system. If condition reaches to the extreme state then we may have to shut down our system, this leads to a heavy loss in terms of money and customer satisfaction. This is the area on which many real time researches are going on and still future can’t be predicted. So up to 99%, continu-ity of the system can be maintained but due to fault, 1% can’t be predicted. Hence the assurance to the customers that their system is 100% efficient cannot be given. In order to overcome this problem and for system recon-figuration we just go through a process called restoration. It is nothing but process of maintaining power balance after fault. The main aim of system restoration is to re-store as many as loads possible which are being affected by faulted nodes by considering available power without violating constraints of the system. Through this paper

we have implemented a technique for power system res-toration which uses the BFAM and finally reconfigure itself using the BPSO. First section of our paper includes the introduction and basic idea of the BFAM. In this sec-tion we will have an idea how we achieve our restoration process using this technique after a fault. The second section will give a real time analysis of restoration proc-ess using the BPSO using transmission and distribution parameters. In this section we take the output solution of the restoration in BPSO as input and final output is used to reconfigure the system. In the third section we com-pared the proposed BPSO using the BFAM. In section four, an attempt has been made to find a new method for restoration using BPSO and BFAM considering their advantages with each other.

2. Brute Force Attack Method

Through this method we are going to explain the power system restoration technique for fault analysis and the restoration using BFAM. This is a new technique based

Optimal Power System Restoration and Reconfiguration in Distribution Circuit Using BFAM and BPSO 164

on the possible combination in mathematical analysis. For a three digit number we have possible thousand com-binations (000–999) and there is an only one solution by taking all the possible combination and arranging them we can get our required one solution. In the same way, in our power system if a node has fault then its near-by agents will make all the possible combination with the near-by node starting(1st) to end(nth) and then will go up to the last load and the best solution path out of these combination will be used for the restoration. Here we have compared the BFAM with the restoration using multi-agent technique [1–3]. Due to the fault in the load they are unable to receive the power. Hence our aim is to restore the faulted load considering the various factors like time, amount of power available to the feeder and system continuity. The constraints are The system’s radial structure must be maintained

during the analysis. Restore maximum possible load within the out-of

service area with the available feeder power. The plan must not overload any equipment or system

component with its rated value. The numbers of switching operation should be

minimum in order to save the power losses. After reconfiguration the system should maintain its

continuity and reliability.

3. Problem Formulation

In this section we will formulate a system so that we can perform an analysis on this system after a fault. We can represent any system with the nodes (N) formed by the network blocks and switches (S) which connects the two blocks that may be in opened or closed position. Feeder is one of the parameter of the system which supplies the power to the system and has the demand power and extra power. Hence for each load its required power must be known to us. Thus by calculating the demand of each node we will calculate the total demand of any feeder. Now after finding total demand of the feeder we can find the reserve capacity by subtracting the total demand of the load with from the total capacity of the system load is also a one of the important parameter of the system which consumes the power supplied by the generating part of the system. In addition, we are going to consider a three feeder system for simplicity. The real system is very large and we generalized this method for a large system also. Beside these parameters there is one more special connection between the loads of feeder one to the load of other feeder. This special connection is working in such a way that, connection is NO (normally open) condition when there is no fault in the system, but it will close as soon as there is a fault in the feeder. Now we analyse our system as a tree which have its sub-tree con-nected in a proper path. The advantage of tree configura-

tion is that it is efficient in order to maintain distribution feeder continuity and radiality. Now in figure 1 the status of a 3 feeder network having 5 loads in each feeder is shown. In general the feeder will work normally and each feeder will provide the necessary amount of power to each load depending upon their requirement and some amount of power will always be there as in reserve mode. Now initially the switch D will be in NO (normally open) condition as there is no fault in the system. As soon as there is a fault in the system the whole of the system status of system will change.

4. Fault Analysis

In the power system we cannot give the assurance that system will work 100% efficiently. Even 0.1% irregular-ity in the system can lead to a big fault in the system. But we could restore the system after the fault by alternate path. If fault occurs in the system the loads which are getting the power through the faulted load, will also affects because of the fault. Hence because of the fault the healthy loads will be affected. So we can’t restore the faulted load and we have to repair it manually, that is the only option we have for the faulted load. For the affected load we have a different option, to apply the same amount of power to this load through another way. With the help of another feeder, we can restore this load now just after a fault the faulted load will be disconnected from the near-by connected load. Now these near-by loads will make a sub-trees that have to be restored. Now in this system there are two sub-trees, they are load 3 and load 4–6 that is to be restored. Here each of sub-trees is basically a sub problem that we must solve separately because they have no direct relation after the fault. The sub-tree formed is depends on the faulted block. In the proposed system the feeder 1 and 2 are having extra 10–10 unit and feeder 3 is having 5 units and each blocks in the feeder requires 5 units. Now in the proposed sys-tem if a fault is present at load 2. The near-by loads of the faulted load will separate themselves from the faulted load in order to save the non-faulty loads from the faulty dead. After a fault the un-served load will make the list of sub-tree. Now this sub-tree will be equivalent to a sub-problem and that must be solved separately. In the above case if fault at load 2, then its near-by agents 1, 3 & 5 will separate themselves from the faulted load 2. Before fault the power is supplied through load 2 for the loads 3–5 & 6. Because of the fault in load 2, loads 3–5, 6 will become useless and they will be out off from the network. At this stage our aim is to restore these loads through another way. Now those blocks which are in off condition will find the possible path starting from the initial block (1) to the end block (18) and then these blocks will check the power availability to the feeder and then blocks will be restored according to the power avail-



ability of the feeder. If all the feeders don’t have addi-tional power for the blocks then in that condition our blocks can’t be restored. After the separation of near-by agent from the faulted load the special switch D will come in to the network. In the above system the switch D will close for the load 3–5 & 6. Hence they will get re-quired amount of power from the near-by feeder and can restore themselves. Hence load 3 connects itself from load 14 of feeder 3 and it will be restored. Now feeder 3 is having zero additional units, load 4 and 5 will con-nected itself from the load 11 and 12 of feeder 2 and it can be restored. Now feeder 2 is having 0 buffer unit, finally the load 6 will not be restored as no feeder is hav-ing additional amount of units.

Now our algorithm maintains a list of solution, which is initially vacant and to which the solutions are added as they are found as the maximum number of solution in the list and it can be changed by the operator. In the list the best solution will be taken as the final conclusion for our fault analysis.

4.1 The Steps in the Algorithm

1) Identify the block in which the fault is occurred. 2) Open all switches connected to that block in order to

isolate it. For each switch that is opened, a sub-tree is generated, which have to be restored, except for the switch that connects the faulted block to a block the feeder is still feeding normally (a block that is “before” the fault).

3) Based on step 2, make change in the bus connec-tivity matrix and from the load status array. Put zero in bus connection matrix for no connection between node and put zero for unfed node in load status array. If there is a connection between two unfed node(load[i,j]=1) change it by loop Switch(load[i,j]=2).

4) Create a list of the blocks still being fed and con-taining at this moment only the blocks the substation is still feeding, if any.

5) Check if there is a loop switch between a fed block and an unfed one. (Possible connections are represented as 2 in bus-connectivity matrix).

6) The unfed block which is only connected to faulted block (node or load) cannot be restored.

7) If there is a loop switch between fed and unfed block, check the feeder at which the fed block is getting power.

8) If that feeder has additional power for unfed block, connect the fed and unfed node and make necessary changes in the load connectivity matrix and load status array.

9) Now move to next unfed block and repeat from step 4.

10) After checking the each unfed block, repeat again from step 4 for ‘n’ times where n=no of fault node (block) from starting.

11) Check the load status and which node the value to load status is zero and that cannot be restored.

5. Fitness Function

To make the stability and reliability of the distribution it is very important to keep the load balancing via feeder reconfiguration so that network could be enhanced. The objective of this optimization problem can be expressed by the minimization of the load balancing index (LBI) as in [5]:

LBI= 2

1

| |( )

N ii Ri

i

IL

I

where

N: Total number of branches in the system after restora-tion, Li: Length of branch i, Ii: Complex current flow in branch i,

RiI : Current rating (ampacity) of bus i.

The LBI value should be minimum in-order to get the best solution by adjusting the switch position. According to the switch operation the complex current is flowing through sectionalized switches in the simplified model [6]. The reconfiguration problem cannot be solved by the traditional methods because of the non linearity of the system after the fault.

6. PSO

The PSO algorithm was first proposed by Eberhart and Kennedy [7]. In PSO method, each individual is treated as particle in the H-dimensional search space. Each indi-vidual in the search space has some velocity which is dynamically adjusted according to its own and its neighbour’s the moving experience.

6.1 BPSO

For a big system having more than one feeder, then feeder to feeder connection will be established through the tie and sectionalized switches which will work only in the fault condition in order to supply the additional power through the alternate path. Now using the fitness function of this system our process will find all the possible com-bination of solutions for the restoration and then recon-figure itself by using the BPSO method. This method is proved to be a very efficient way of reconfiguring the network. By removing the faulted node from the network and restoring the system by isolating the faulty load. Various components of the power system have the ability to withstand just above the rated capacity [4]. Some nodes are affected by the faulted node, will create an un-balance in the network which may lead to failure in the buses. So it needs to be reconfigured as fast as possible in order to save it from the severe fault. In a binary PSO,



Feeder 1

1

Figure 1. System working in normal condition when there is no fault in the system trajectories of Vih are changed in the probability that a coordinate will take on zero or one value or in between them [8]. The moving velocity is defined in terms of changes of probability that a bit will be in one state or the other depending on the trajectory of Vih. Thus a particle moves in a state space restricted to 0 and 1 on each di-mension, where Vih represents the probability of bit Xih taking the value 1. In other words, if Vih =0.45, then there is 45% chance that Xih will be 1, and 55% chance that Xih will be 0. With this definition, pih and xih can take inte-gers 0 or 1, and vih, since it is probability and it must lie within the interval [0, 1]. Hence for the proper explana-

tion we can determine the function of this probability as shown below- For h=1: H

1 1

( ) 2 2 ( );ih ih

ih ih gh ih

V w v c rand

p x c rand p x

If ( ( ))ihrand S v then xih=1

else xih=0 (3)

end end S(x) = 1

1 xe

where S(x) sigmoid limiting transformation.

4

3

5

2

6

14

7 8 9

11

10

12

13 15

18

17 16

Feeder 2

Feeder 3



1

4

3

5

2

6

7 8 9

11

10

12

13 15

14

18

17 16

Feeder 2

Feeder 1

Feeder 3

Figure 2. System after restoration with the help of near-by feeder when fault is there in block 2

Figure 3. Analysis through C



While applying the BPSO method there are some con-straints that we have to follow in order to maintain the continuity and radiality of the system. Each feeder should be in active state in the whole

system. To maintain the radial structure of the system at

least one branch from one feeder to another must be in open state otherwise the radiality of the system will be lost. The Potential limit for buses should be between minimum and maximum value. Beside this the operating conditions of the tie-switches will be also kept in mind [9]: In the system at least one tie switch will be in closed

position and all other in open position. The power flow should take place in load side end it should not flow in the feeder side.

6.1.1 Algorithm [10] 1) Set the population size (n), maximal iteration number and stop criterion.

2) Randomly select n feasible solutions of x, compute p for each x, pg is minimum in all pi, and the initial values of vi is zero.

3) Using (2), calculate vi for particle i. 4) Use (7), to update i. 5) Calculate the feeder load balancing index. 6) If the fitness value of particle i is better than the pre-

vious pi, then set it to pi. If the best p is better than pg, then set it to pg.

7) If stop criterion is satisfied, pg is optimal solution, otherwise, go to step 3.

Now from the BFAM we are restoring our system by taking the best possible solution. For this system the ini-tial status and parameter of this system will be known to us. Now we will form the bus connectivity matrix for our system and for any fault in the system we will get a dif-ferent load connectivity matrix after the fault analysis corresponding to the load status and finally our system will give required solution for the proper restoration. The output of the fault analysis which will be stored in a variable will be the input of BPSO. Now corresponding to this BPSO we will get a final best solution which will be used for reconfiguration of the system. In this solution we keep the nearby switch of faulted load have to always at off state by proper logical AND operation. After this we will get our final solution and implement the same procedure for the reconfiguration.

7. Result Analysis

In the Figure 1 given in the last suppose fault is there in the load 2 than results for the restoration in the c pro-gramming will be-Enter the no of fault load=2 Demand node 1 is separated from 2 Demand node 3 is separated from 2

Demand node 5 is separated from 2 Demand node status is: - 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 Demand node 3 is connected to demand node 14, De-mand node 3 is restored.

Extra power Feeder1=10, Feeder2=10, Feeder3=0, Demand node 4 is connected to demand node 11, De-mand node 4 is restored. Extra power Feeder1=10

Feeder2=5, Feeder3=0 Demand node 5 is connected to demand node 4, Demand node 5 is restored. Extra power Feeder1=10, Feeder2=0, Feeder3=0 Demand node 6 cannot be restored Demand node 2 cannot be restored (Figure 3)

8. Conclusions

Through this paper an attempt has been made to restore the faulted area in the power system and finally reconfig-ured the system in the stable state. The above process can be implemented in a real time network and can be used for the restoration through BFAM and reconfiguration through BPSO. Also we perform the fault analysis in a real time network and simulated the results in the MATLAB and C programming. We have implemented the BFAM to get the priority based solution. We find that the results found from the analysis are matching with the actual data. Hence the above method can be used to per-form the analysis of fault and to restore, reconfigure the system in a real network. The restored network is shown in the Figure 2 and the prospective analysis is given in the result analysis (7) and the proof in C is shown in the Figure 3. But the conventional methods are limited only for less number of loads.

REFERENCES

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[3] K. Manjunath and M. R. Mohan, “A new hybrid multi-o- bjective quick service restoration technique for electric power distribution systems,” Science Direct, Electrical Power and Energy Systems, Vol. 29, pp. 51–64, 2007.

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169

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Islanding Detection Method for Multi-Inverter Distributed Generation

Alben CARDENAS, Kodjo AGBOSSOU, Mamadou Lamine DOUMBIA

Institut de recherche sur l'hydrogène (IRH), Département de Génie Électrique et Génie Informatique, Université du Québec à Trois-Rivières, Trois-Rivières (Québec), Canada. Email: Alben.cardenasgonzalez, [email protected]. Received May 21st, 2009; revised July 23rd, 2009; accepted August 23rd, 2009.

ABSTRACT

Islanding detection is an essential function for safety and reliability in grid-connected distributed generation (DG) sys-tems. Several methods for islanding detection are proposed, but most of them may fail under multi-source configura-tions, or they may produce important power quality degradation which gets worse with increasing DG penetration. This paper presents an active islanding detection algorithm for Voltage Source Inverter (VSI) based multi-source DG sys-tems. The proposed method is based on the Voltage Positive Feedback (VPF) theory to generate a limited active power perturbation. Theoretical analyses were performed and simulations by MATLAB /Simulink /SimPowerSystems were used to evaluate the algorithm’s performance and its advantages concerning the time response and the effects on power quality, which turned out to be negligible. The algorithm performance was tested under critical conditions: load with unity power factor, load with high quality factor, and load matching DER’s powers.

Keywords: Distributed Generation (DG), Interconnected Power Systems, Islanding Detection, Power Generation, Voltage Positive Feedback.

1. Introduction

The Distributed Energy Resources (DER) including Dis-tributed Generation (DG) and Distributed Storage (DS) are, as renewable energy resources, very important to improve power distribution reliability and capability. Their penetration is increasing nowadays and their utili-zation shows potential for rural utility solutions [1]. The Hydrogen Research Institute (HRI) has designed and developed a renewable energy (RE) system which in-cludes Photovoltaic (PV) arrays, Fuel Cells (FC) and Wind Turbine Generators (WTG) with an energy storage capability using electrolytic hydrogen [2]. This RE sys-tem operates presently in stand-alone mode. It can be adapted for rural dispersed generation solutions and in-terconnected with the electric utility grid by using in-verter based interfaces (DC/AC static converter). Figure 1(a) is a simplified diagram of the basic RE unit as im-plemented at HRI. Figure 1(b) shows the possible multi- source DER system presently under construction.

An important technical issue with utility interfaced DER systems is unintentional islanding operation. The islanding condition occurs when the utility is discon-nected and the DG continues to supply power to the local load. This condition is not desirable because it can gener-ate voltage and frequency instability and power quality degradation; and it constitutes a great risk for mainte-

nance personnel. In view of the importance of human and equipment protection, unintentional islanding for DG operation is not tolerated [3]. For these reasons the detec-tion of unintentional islanding operation is required as rapidly as possible to allow the timely disconnection of the DG units. According to the IEEE 1547-2003 standard [4], the DG disconnection is required within two seconds after the utility disconnection. Consequently, for safety DER integration, Anti-Islanding (AI) protection is a re-quirement.

Remote and local techniques are used for islanding de-tection. Remote techniques such as Supervisory Control and Data Acquisition (SCADA), Trip (disconnect) Signal and Power Line Carrier Communication (PLCC) systems are centralized methods implemented on the utility side. They offer high performance and applicability on multi- source topologies. However, those centralized methods are expensive to implant [5]. On the other hand, local techniques include passive and active methods which are implemented on the DG side. Local passive methods have a large Non Detection Zone (NDZ), and hence are not useful for high DG penetration. A solution for the NDZ reduction is the utilisation of local active anti-islanding methods.

Islanding Detection Method for Multi-Inverter Distributed Generation 171

Figure 1. Simplified diagram of stand-alone RE system implemented at HRI and the possible multi-source DER system

Those active methods are currently based on the injec-

tion of voltage, frequency or output power perturbations, and the subsequent monitoring for the detection of changes in electric parameters to confirm islanding con-dition. Those methods can detect the islanding condition, but one of their problems is that they can fail when mul-tiple sources are connected at PCC, because the effect produced by one source may be interfered by another one if synchronization between the multiple converters is not possible. Another drawback of active methods is that they can cause power quality disturbances as Total Voltage Harmonic Distortion (TVHD) increase and voltage and frequency fluctuations or instability. These problems become bigger if the introduced perturbation is increased to make possible the islanding detection [6,7], especially in systems with high penetration.

Use of the Correlation Function combined with active methods is proposed in [8,9] and [10] for multi-source topologies. In [8], the correlation function is combined with an active method that introduces a constant alternat-ing perturbation of reactive power (±5% and ±10%), the anti-islanding algorithm is implanted in only one (master unit) of multiple DGs, and the others units use a passive anti-islanding scheme. The detection time depends on the output power of the master unit and on the reactive power perturbation level. In [9] and [10], the correlation func-tion is combined with an active algorithm that introduces a user defined or random (M-sequence) perturbation of the output voltage (fixed to ±2V for 120V/60Hz system). The correlation function may change with the number of connected DGs, and consequently a threshold adjustment is necessary if the number of units change.

In this article we propose an active islanding detection method based on Voltage Positive Feedback (VPF) and passive method Under/Over Voltage Protection and Un-der/Over Frequency Protection (U/OVP-U/OFP). The proposed method can be used on multi-source configura-tions, and allows both unity power factor and power fac-

tor improvement operation modes. This method intro-duces a limited active power perturbation proportional to measured variations of PCC voltage (VPCC). Simulations using MATLAB™/Simulink™ and SimPowerSystems ™ are carried out to validate the algorithm under several operating conditions.

2. Power Control Scheme

The system we consider is illustrated in Figure 1, where several DG units are interconnected with the utility at PCC. Each unit has an IGBT voltage source inverter (VSI) and its active and reactive power control using a current control scheme [11] as shown by Figure 2.

In this power control scheme, the output current fun-damental magnitude (IINV(1)) and phase angle (I) are calculated respectively using (1) and (2).

)cos()1(

*

IPCC

INVINV V

PI

(1)

*

*

1tanINV

INVI

P

Q (2)

where, PINV* and QINV

* are respectively the reactive and active power external set points for the DG unit.

The power angle I represents the phase angle between the inverter output fundamental current and the fundamental voltage measured at PCC. The resultant set-point current (3) is used to generate the switching signals for the IGBT bridge inverter, using Hysteresis Current Control (HCC) or Sinusoidal Pulse Width Modulation (SPWM) techniques.

)2()1(* IINVINV ftSinII (3)

where and f are the phase angle and frequency of the voltage measured at PCC, and t is time in seconds.

Considering that the proposed algorithm (see Section 3)



Figure 2. Power control scheme for single grid connected DG unit

Figure 3. Voltage positive feedback with d-q current control scheme

introduces an active power perturbation that is added to the external set point, we are not limited to the Figure 2 power control scheme, and it may be changed to another one such as the d-q transformation based power control scheme [3]. Notice that the d-q control scheme is con-venient when decoupled active and reactive power con-trol is required principally in three phase systems.

3. Islanding Detection Algorithm

This section describes the voltage positive feedback princi-ple and the proposed active islanding detection algorithm.

3.1 Voltage Positive Feedback Islanding Detection Methods

Positive feedback with d-q current control based family of islanding detection methods is presented in [12] and [13]. These methods consider the relation between the active (P) and reactive (Q) powers with the voltage magnitude (V) and frequency (f) as shown in (4) and (5), and the effects of current magnitude and angle deviation on the output active and reactive powers.

RVP

2 (4)



LCVQ 12 (5)

where, =2f, and R, C and L are the resistance, capaci-tance and inductance of the resonant load. This family of islanding detection methods includes fre-quency and magnitude of voltage positive feedback based schemes. The positive feedback is used to generate a low frequency perturbation signal (∆id or ∆iq) that is added to the id

* and/or iq* set points.

Figure 3 shows the principle of Voltage Positive Feedback (VPF) with d-q current control scheme. The d-axis component of VPCC (Vd) is monitored and filtered using a band pass filter (BPF) to obtain the voltage varia-tion ∆Vd, this voltage variation is amplified with a preset gain G (A/V) and used as d-axis current perturbation (∆id). The d-axis current perturbation signal affects di-rectly the inverter output power and consequently the VPCC magnitude and frequency in islanded mode. A satu-ration block is used to limit the output current perturba-tion. As a result, on islanding condition a rising deviation of frequency (df) or magnitude (dV) of VPCC is observed, and this deviation can trip U/OVP or U/OFP for DG safety disconnection.

An important characteristic of the VPF based methods is the low power quality degradation in contrast with other active methods that use distorted signals injection, as proposed in [14] and [15].

On the other hand, the time necessary to generate the trip signal using the VPF based method is determined by the load quality factor qF (6) and the feedback preset gain G. One simple way to improve the response speed is to increase G, but this solution increases the risk of voltage or frequency instability, especially in multi-source to-pologies.

L

CR

PC

QL

Q

Fq

Figure 4. Proposed voltage positive feedback scheme

voltage measured at PCC (VRMS) as the feedback variable to generate a limited active power perturbation. The ba-sics of the proposed scheme are presented in Figure 4. The VRMS (after the LPF filter) is compared with a refer-ence voltage VREF, and the difference ∆V is used to cal-culate the active power perturbation ∆P.

The reference voltage VREF[k+1] is set initially equal to the nominal RMS voltage (VNOM), and is subsequently updated only on System Stable Condition (SSC) using the historic RMS average voltage VAV (7). Otherwise, the new voltage reference (VREF[k+1]) is set equal to the old reference value (VREF[k]) according to (8). The SSC is defined as the condition where both the power and the voltage perturbations (∆P and ∆V) are stable.

(6)

The Sandia Voltage Shift (SVS) method [6] uses the utility voltage to calculate the output current amplitude; in this method the average voltage of the utility is com-pared with the actual voltage in each electric cycle (or- half cycle) to calculate the current perturbation that is amplified by a preset gain.

In both methods, SVS as well as VPF with d-q transforma-tion, the output voltage at the islanding condition is forced to the trip points of the U/OV protection by an important output current reduction or increase, and it is finally the U/OVP that shuts down the power converter. This important perturbation of the output current before the disconnection may affect the load, and is not appropriate if stand-alone operation of the system is desired after the safety disconnection.

3.2 Proposed Voltage Positive Feedback Scheme

We propose to use the VPF concept, taking the RMS

m

VV

m

iikRMS

kAV

1 (7)

where, m is the number of samples considered for the average calculation.

(8)

The active power perturbation ∆P is calculated using the maximal allowed power perturbation ∆PMAX, the minimal power perturbation ∆PMIN, a gain factor G, and the difference between VREF and VRMS, according to (9,10) and (11).

(9)

otherwiseV

SSCV

tV

V

kREF

kAV

NOM

kREF

,

,

0,

1

MAXCMAX

MAXCMINC

MINCMIN

k

PPP

PPPP

PPP

P

,)sgn(

,

,)sgn(

1



GPPC

* (10)

REF

REFRMS

VVV (11)

3.3 Parameter Selection

The parameters ∆PMIN, ∆PMAX and G are selected to pro-duce a low active power variation in the interconnected mode and a low voltage variation in the islanding detec-tio

V).

nnected mode, the active power deviation is reduced to minimal ∆PMIN on voltage stability condition. The expected evolution of voltages (VREF and VRMS) and the active power perturbation for the islande

n period. Considering an ideal utility source, the volt-age error in the interconnected operation mode may be close to zero, but in practice a minimal error is always resent, and this error affects the real output power. We set the ∆PMIN near the mean active power perturbation cal-culated using the typical utility voltage variations (εMIN). Based on the measured voltage of the utility, we take a εMIN=0.167% (0.2V at 120V) as the minimal voltage error. This εMIN allows us to set a minimal active power perturbation ∆PMIN=0.5% using a gain of G=3. At the islanding condition, if the system operates at unity power factor, this ∆PMIN introduces a voltage variation of 0.25% (0.3V at 120

To limit the effects on the output voltage in the detec-tion period, we set the ∆PMAX=2.5% to produce a maxi-mal voltage error ε= 1.24% (1.5V at 120V). This set-ting permits the islanding detection without output volt-age degradation if the load and DG powers are close or matched.

3.4 Expected Operation of the Proposed Algorithm

In grid co

d mode is

Figure 5. Expected effect of the proposed VPF scheme un-der islanding condition

Figure 6. Expected effect of the proposed VPF scheme un-der voltage reduction and normal voltage variation

shown by Figure 5. Before the utility disconnection (t<t0), the normal voltage variation can generate a minimal ac-tive power deviation without important effect on Vvo S<

produces a negative increasing of ∆P until its saturation at t=t1. The SSC condition is reached with VRMS stabConsequently, the VREF is updated and th

oltage variation.

3.5 Islanding Confirmation

If the average of the magnitude of the active power per-tu

AV

ed to two thresholds values ∆PAC (Active Counter) and ∆PRC (Reset Counter) to activate or a time counter (TC). If the TC count is larger than a plimit of time TMAX, the islanding condition can be confirmed.

RMS

tage. After the utility disconnection (t>t0), if VRM

l

VREF, the negative ∆PMIN and the VPF effect produce a progressive VRMS reduction and negative increase of ∆P, until the ∆P saturation at t=t1.

The SSC condition is reached at t=t2 with voltage sta-bilization, and VREF is updated to VAV. Consequently, a reduction and a subsequently positive increase of ∆P are expected to produce a voltage level increase (from t2 to t4). The power perturbation is saturated at t=t3, and a new SSC is reached at t=t4. A cyclic power perturbation and a voltage level oscillation can be observed and used to con-firm the islanding condition.

The expected trajectories for a voltage variation are presented in Figure 6. In this case, if an important voltage variation is occurred at t=t0, the VPF effect

ilization at t=t2. e active power

perturbation is reduced to ∆PMIN. Subsequently the minimal active power perturbation may be observed as an effect of the normal v

rbation (∆PAV) is calculated and observed during a de-tection period TDET, then under islanding condition the expected profile of this variable is shown in Figure 7, and we can use this new variable to establish the islanding condition. For islanding condition confirmation, the ∆P is compar

to reset reset




175

Figure 7. Expected magnitude average of the a

ctive power perturbation on islanding condition

osed anti-islanding protection scheme

3.6 Classic VPF Methods and Proposed Method Comparison

Figure 8. Simplified diagram of the prop

In the example of Figure 7, the utility is disconnected

at t=t0, the activation of TC is produced at t=t1, and the islanding condition is confirmed at t=t2.

We set the reset and the activation thresholds of time counter (TC) as ∆PRC=30% and ∆PAC =90% of the ∆PMAX, and TMAX=9 electric cycles (150ms).

If the DG and load powers don’t match, the classical solutions as U/OVP and U/OFP can be employed to con-firm rapidly the islanding condition. The combination of the proposed algorithm with the classic passive method (U/OVP and U/OFP) produces a fast islanding detection in all output power conditions. A simplified diagram othe proposed anti-islanding protection scheme is pre-

between the proposed The most important differencemethod and the known voltage positive feedback meth-ods, such as SVS and others VPF methods, is that the proposed method does not produce the U/OVP-U/OFP trip if it is not really necessary. That is essentially be-cause in the proposed method the detection is not based on the forced deviation of voltage or frequency beyond the trip points. That way, the ride-trough operation of the DER system is possible if the load and DG powers are close or matched at the instant of the utility disconnec-tion.

f

sented in Figure 8.


It is known that the classical VPF methods have low impact on power quality; however, as mentioned in [16], the voltage instability risk is high when the classic VPF methods are employed with a strong feedback gain and when most of the local load is supplied by the DG. In contrast the proposed method uses a limited active power perturbation that does not produce voltage or frequency instability risk.

On the other hand, considering that the proposed method uses an active power perturbation that is added to the external set point, the proposed method may be easily implemented in current controlled or in phase angle (power angle) controlled inverters.

4. Simulation Results

or preliminarorithm, we consider two scenarios: unity power factor

operation and power factor improvement operation. The power converters of the DG units are connected at PCC with a 120V/60Hz grid source. We consider two different disconnection modes, as shown by Figure 9, where the main circuit breaker (CB1) disconnects the utility, and the secondary circuit breaker (CB2a or CB2b) is the con-trolled switch operated by the anti-islanding (AI) control. In the first case, with the islanding confirmation, the DG units are shutting down and are disconnected by breaker CB2a. In the second case, we consider the possibility of automatic operational mode change from the grid-con-nected mode to the stand-alone mode when the DG sys-tem can supply the totality of the load power: in this case CB2b is opened and CB2a remains closed to allow the supply of power to the load with safety disconnection from the utility. Otherwise, the DG units are turned off and disconnected after the islanding detection as in the first case.

The simulations are carried out using Matlab/Simu- linkTM for the islanding detection algorithm and the power control schemPowerSystemsTM for

entation.

e most difficult si

4.

ntly a voltage and an active power

Fg

y validation of the islanding detection al-

e implementation, and using Sim-the power devices models imple-

mThe load RLC elements are calculated to obtain quality

factor values between 0.5 and 2.5. The load and DG sys-tem power match is considered as th

tuation. The anti-islanding parameters setup is presented in the

Appendix.

1 Results for Islanding Detection in DG Unity Power Factor Operation

Figure 10 presents the active power and voltage deviation; the grid, load and DG output currents; and Total Voltage Harmonic Distortion (TVHD) of VPCC, for a system with three grid-connected DG units, with load at unity power factor and quality factor qF=2.5. The grid is disconnected at t=0 and subseque

Figure 9. DG unit disconnection modes

perturbations are observed.

We can also observe that the disco signal is gen-erated before 14 electric cycles (233ms), and the algo-

le before and after the islanding condition.

Similar traces are obtained for systems with one and six DG units. The time needed for the islanding confir-mation (TIC) using the proposed algorithm in the systems working at unity power factor is presented in Table 2.

In this case we consider also that the DG and load power are matched. We can notice that this time is al-ways lower than 2 seconds as recommended by the IEEE 1547-2003 standard. The simulation results show that the islanding event is confirmed faster for the systems with a high number of DG units.

As expected, the performance of the proposed method is increased if an active power mismatch is considered between the DG and the load. Table 3 shows the simula-tion results for the time needed for the islanding confir-mation (TIC) in a system with 3 DG units operating at unity power factor. In this case, we consider different conditions of active power mismatch (12) between the DG and the load.

nnect

rithm effect on voltage TVHD is negligib

LOAD

DGLOAD

PPPP (12)

rtant variation in the voltage measured at PCC is observed with the islanding condition. In this case the O/UVP acts and disconnects

4.2 Results for Islanding Detection in DG Power

F In all simulated cases, as shown by Table 4, the

If P is greater than 0.2 an impo

the DG units within 2 electric cycles.

Factor Improvement Operation

For power factor improvement operation mode, the load RLC elements are calculated to produce an inductive power factor PF=0.95 and a quality factor qF=2.5. The DG system is configured to supply the active and reactive load powers. The performance of the islanding detection method was evaluated for systems with 3 and 9 DG units operating in power factor improvement mode with different load power factors, and considering a high load quality factor (q =2.5).



Table 1. Comparison of classic VPF methods and proposed method

Method Characteristic Classic VPF

methods Proposed

Forced trip of U/OVP–U/OFP. Yes Not Negative impact on power quality.

Risk of voltage instability in multi-inverter configurasystems with high penetration.

Low Low

tions and/or High Low

islanding condition was confirmed within 13 electric cycles (216ms).

The simulation traces for a system with six DG units operating in the power factor impro

Table 4. Time necessary for the islanding confirmation us-ing the pr DG units

rating in the pow

TIC (Cycles) vement mode are mulation result shows that

fast detection of the island-

TIC (Cycles)

presented in Figure 11. This sithe proposed method offers ing condition in the systems working in the power factor improvement mode; in this case the disconnection signal is generated within 11 electric cycles (183ms).

The performance of the proposed method was also evaluated in the power factor improvement mode, con-sidering different load quality factor. In this case, we consider a system with 3 DG units operating in power improvement mode, with load power factor between 0.85 and 0.98 (0.85PF0.98), and load quality factor of 1.0, 1.5 and 2.5 (qF=1.0, qF=1.5, qF=2.5). The simulation results show that the time needed for the islanding con-firmation is similar for different conditions of the load quality factor and the power factor. As shown in Table 4, the islanding confirmation in the simulated cases is reached within 12.5 electric cycles (208ms)

4.3 Results for Automatic Change of DG Operating Mode from Grid-Connected to Stand-Alone Mode after the Islanding Detection

We tested the performance of the proposed islanding detection method and observed the effect of the algo-rithm on the power quality when the stand-alone opera-tion of DG is allowed after the islanding detection. In

Table 2. Time necessary for the islanding confirmation us-ing the proposed method in the systems operating at unity power factor

qF 1 DG unit 3 DG units 6 DG units 2.5 15.20 13.7 10.8 1.0 13.80 12.8 11.6 0.5 13.30 11.8 11.5

Table 3. Time necessary for the islanding confirmation us-ing the proposed method in the systems with 3 DG units when the DG and load powers don’t match

TIC (Cycles)

P 0 0.02 0.05 0.10 0.15 0.20

PF=1.0 13.7 11.5 11.5 11.5 11.5 2.0

oposed method in systems with 3 and 9 er factor improvement mode ope

qF DG units

PF=0.98 PF=0.95 PF=0.90 PF=0.85

9 12.5 12.5 13.0 12.5 2.5

3 12.5 12.5 12.5 12.0 1.5 3 12.5 12.0 12.5 12.5

1.0 3 12.0 12.0 12.5 12.5

this case the AI protection opens the breaker CB2b to disconnect the DG system from the utility at the island-ing confirmation.

Figure 12 shows the VPCC voltage and DG1 output current (IINV) traces before and after the islanding condi-tion, the disconnection signal, the TCHD of the I and th

INV

de within a few cycles (10.75 cycles) after grid disconnection. The Total Current Harmonic Distortion (TCHD) and TVHD are always mless than 2%. According the 1547-IEEE standard [4], the m

tection algorithm

is is generated

racteristics are imposed by the DG system

e TVHD of the VPCC for a system composed by four DG units. In this case, the DG system and load powers were matched, and the load elements were calculated for unity power factor (PF=1.0) and high quality factor (qF=2.5).

The simulation results show that the system can change its operational mode from grid connected mode to Stand-alone mo

aintained at

aximal allowed TCHD of DG is 5% and the TVHD measured at PCC must be less than 2.5%. As in the pre-vious cases, the grid is disconnected at t=0. After the grid disconnection (t>0), the islanding deproduces the output power perturbation to detect the isla nding condition nding condition. In this case, the isla

confirmed and the disconnect signalwithin 10.75 electric cycles. Then, at t=10.75 cycles, CB2 is opened and the system changes its operation mode from the grid-connected mode (on islanding condi-tion) to the Stand-Alone mode. In the stand-alone mode, the voltage chaoutput power. In the simulated case, the VPCC voltage reaches its nominal level in the stand-alone mode be-cause the DG and load powers are matched. In a practical situation, and with a variable load power, the voltage and frequency control is possible by controlling the active



Figure 10. Simulation results for islanding detection on a thretor mode. Load PF=1.0 and qF=2.5

e grid connected DG units system operating in unity power fac-

with six grid- connected DG units, operating in power factor F . Sim tion lts et f ystem im ent mode

igure 11 ula resu for islanding d ection or a sprovem



Figure 12. Simulation results for islanding detection and operational mode change from grid connected to stand-alone mode for four grid connected DG units system operating in unity power factor mode and reactive output powers using the Voltage-Power Droop/Frequency-Reactive power Boost scheme (VPD/ FQB) as mentioned in [3] and as proposed in [17].

5. Conclusions

This paper presents an active islanding detection algo-rithm for multi-source DG systems. The proposed algo-rithm is based on the voltage positive feedback. Theo-retical analyses are provided and simulation results show that the proposed islanding detection algorithm offers fast anti-islanding protection with negligible impact on power quality. This method may be useful for systems with single or multiple grid connected DG units. The synchronization between the different DG units is theo-retically not required due to the fact that all units use a common variable to generate their local anti-islanding protection.

Considering its fast response and the negligible effect on power quality, this anti-islanding scheme could be used to allow the operation of the grid-connected distrib-uted generation systems with safety disconnection. In contrast with commonly used methods, that force the

possible the stand-alone operation of the DG system after the islanding is confirmed, and that without interruption of the load power. The proposed method is easy and inexpensive to im-

plant. The detection algorithm may be added to the pro gram of the power control unit to use the same digital processor.

Current and future works include the implementation of the algorithm using FPGA for the experimental vali-dation under real and critical scenarios using multi-in-verter configurations.

6. Acknowledgments

This work was supported by the LTE Hydro-Québec and the Natural Sciences and Engineering Research Council of Canada.

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[12] Z. Ye, L. Li, L. Garces, C. Wang, R. Zhang, M. Dame, R. Walling, and N. Miller, “A new family of active anti-islanding schemes based on DQ implementation for grid-connected inverters,” IEEE 35th Annual Power Elec-tronics Specialists Conference–2004–PESC–04, Vol. 1, pp. 235–241, 2004.

[13] Z. Ye, R. Walling, L. Garces, R. Zhou, L. Li, and T. Wang, “Study and development of anti-islanding control for grid-connected inverters,” General Electric Global Research Center Niskayuna, New York, NREL/SR-560- 36243, 2004.

[14] M. E. Ropp, M. Begovic, and A. Rohatgi, “Analysis and performance assessment of the active frequency drift method of islanding prevention,” IEEE Transactions on Energy Conversion, Vol. 14, No. 3, pp. 810–816, 1999.

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Appendix

A. Grid and DG Units Characteristics

Grid voltage: 120V-60Hz Grid line inductance: Ls= 0.05mH DG type: IGBT-VSI, 1kW, 120V-60Hz DG Output filter: L=5mH, C=0.1F

B. Setup of Islandin

∆PMAX= 2.5%, ∆PMIN = 0.5%∆P = 0.75% ∆P = 2.25%RC , AC , MAX




181


Ayman Al-SAWALHA

Physics Department, College of Science, King Faisal University, Saudi Arabia. Email: [email protected] Received April 14th, 2009; revised July 13th, 2009; accepted August 2nd, 2009.

ABSTRACT

Study of radiation properties of mismatched microstrip termination is carried out in warm ionized electron plasma me-dium. Linearised hydrodynamic theory coupled with vector wave technique is used to investigate radiation patterns and radiated power of a microstrip mismatched termination in one component electron plasma media for different plasma to source frequencies .These properties are used to compare the performance of an open circuit discontinuity with those of matched microstrip termination. Matched terminations are found more suitable for applications at higher frequen-cies than an open circuit discontinuity in the plasma medium though in free space they are less suitable.

Keywords: Mismatched Termination, Open Circuit Discontinuity, Matched Microstrip Termination, Ionized Plasma

1. Introduction

Microstrip antenna has proven to be an effective, light weight and quite inexpensive radiator for aerospace vehi-cles [1]. Many workers have reported radiation properties of different microstrip radiators in free space [2–4]. Me-tallic and dielectric losses, breakdown effect at higher power level and radiations from discontinuities, however, limits the application of a microstrip line structure over the ground plane [5]. Radiations from microstrip discon-tinuity become quite dominant at microwave frequencies and hence become major limiting factor. Hence, it is al-ways necessary to control them somehow. Radiations from an open circuit microstrip discontinuities are inves-tigated recently [6] in an ionized plasma medium of infi-nite thickness. Radiations from a mismatched termination in an ionized plasma medium are investigated in this communication. Using these relations, performance of two other types of discontinuities viz. a matched micro-strip termination and an open circuit microstrip termina-tion are investigated in free space as well as in ionized hot plasma medium.

In strip line structure, field does not lie uniformly in between the conducting patch and the ground plane but some fringe fields leak in the air near the edges of the strip. Dielectric polarization beneath the strip takes place which gives rise to the polarization current in addition to the already existing strip current [5]. Considering both these currents together, radiation patterns and radiated

power by a mismatched termination are obtained for dif-ferent plasma to source frequency ( P ) . With the

presence of an actual ionized plasma medium, effective permittivity of structure changes marginally in compari-son to the effective permittivity in free space and hence resonance frequency also changes marginally [7]. It is found that percent deviation in frequency is about 0.003% in the presence of an ionized plasma media of infinite thickness which dose not affects predicted results seriously.

2. Radiation Field Expressions

The geometry and coordinate system of a mismatched microstrip termination is shown in Figure 1.

A strip line above the ground plane is located along the z-axis of the coordinate system. The thickness of the di-electric substrate is considered to be , width of strip

,relative permeability and permittivity " "h

" "w 1r and

1r respectively.

It is considered here that the termination mismatches the strip. Far fields are obtained by considering a mag-netic current density alone with a perfect electric current condition.

For strip line configuration, the integration to find elec-tric field using vector potential is carried out over a cross

Effect of Warm Ionized Plasma Medium on Radiation Properties of Mismatched Microstrip Termination 182

section which gives a combination of currents formed by polarization current ( along x-axis) and a strip current (along z-axis).

Let the strip current be

( )jk z jk zs oI I e Re (1)

where

2eff

o

j

k

R R e

o is the wavelength in free space, eff is the effective

dielectric constant of substrate material, R is the re-

flection coefficient at the end of the line and its limiting value lies in between 0 and 1, and is the phase angle

between the incident wave and the reflected wave. Assuming current amplitude is to be constant a cross

the strip line, the surface current density in z-direction for end fed line will become

ˆj ts s zJ I e i (2)

The polarization current density in x-direction will be

1 ˆ2 j tsp x

IJ h e

z

i (3)

where xi and zi are unit vectors in the x and z direc-

tion respectively and is the actual dielectric constant of the substrate material.

Considering the presence of both these currents to-gether and following the method of [8], the expressions for the radiation patterns are obtained in electromagnetic mode as well as in electroacoustic mode.

These expressions are:

2.1 In Electromagnetic Mode

( )

2 2

2 2

2 2

2 2

60

( cos ) ( )cos

( cos )cos

( ) cos ( cos )

( cos )

ej t ro o

e

j hw IE e

r

A A

A

A AR

A

(4)

( )60

cos cossin

( cos ) ( cos )

ej t ro O

e

j hw IE e

r

A AR

A A

(5)

Figure 1. The geometry and coordinate system of a mis-matched microstrip termination where:

( sin sin2

sin( sin sin )2

( sin sin )2

ee

wj

ee

w

ew

)

2

2

2

1

eo

p

A

A

e is the propagation constant in electromagnetic mode.

o is the propagation constant in free space (radian/m)

p is the angular plasma frequency ( )

1sec

is the angular source frequency ( ) 1sec

2.2 In Electroacoustic Mode

2

2 2

( )

2 ( )

(cos sin cos )

( cos )

(sin cos cos )

( cos )

p

p p op

p

p

p j t r

p

p

p

wh IE

r

k

ke

kR

k

(6)

where

( sin sin )2

sin( sin sin )2

( sin sin )2

p

pw

j

pp

p oo

w

ew

cA



-14-12-10-8-6-4-20

0

30

60

90

120

150

180

210

240 300

330

-14-12-10-8-6-4-20

Pow

er in

dB

A=1.0 A=0.2

270

Figure 2. E radiation patterns for 1.0A and 0.2A , 0.7 ,R

-16

-14

-12

-10

-8

-6

-4

-2

0

0

30

60

90

120

150

180

210

240

270

300

330

-16

-14

-12

-10

-8

-6

-4

-2

0

Pow

er in

dB

A= A=

Figure 3. E radiation patterns for 1.0A and 0.2A , 0.7 ,R

A : is the propagation constant in plasma mode.

These value of E , E and pE are computed and

plotted in Figures (2–4) for two different values of plasma to source frequency. Computations are carried out

for , , op-

eration frequency = 1.2GHz ,

0.158h c m 0.471 , 2.31, 3.0w cm

E Patterns in free space are almost uni-

form. Radiation intensity in the end fire direction is slightly more than the radiation intensity in

( 1.0A )

)

)

( 0o

the broadside direction . On increasing plasma

to source frequency

( 90o ( 0.2)A , radiation pattern modifies

drastically and direction of maximum intensity shifts

0.7R and .



50 52 54 56 58 600

10

20

30

40

Ep in

dB

Theta in degree

Figure 4. pE radiation pattern in plasma for 0.2A , 0.7 ,R

Table 1. 3dB beamwidth in and planes for 1.0A and 0.2A

E E

Free Space ( 1.0A )

Plasma ( 0.2)A

Free Space ( 1.0)A

Plasma ( 0.2A )

3dB Front

direction

3dB Back

direction

3dB Front

direction

3dB Back

direction

3dB Front

direction

3dB Back

direction

3dB Front

direction

3dB Back

direction

108o 116o 0o 120o 104o 106o 82o 114o

from to direction and minimum

appears at ( . Almost similar behaviors appear for

( 0o

) )( 180o

)0o

pE patterns. These patterns in the free space ( 1.0A )

are almost symmetric in all the four quadrants, but for higher plasma to source frequency value ( , the

3dB beam width in direction is much smaller

than in direction.

0.2)A

( 0 )o

)( 1 80o

pE radiation patterns indicate that only one lobe ap

pears in the to range. One substituting 50o 60o 1.0R

and all the expressions obtained for mismatched microstrip termination reduce immediately to those of open circuit microstrip discontinuity [6]. Similarly on substituting 0R and , expressions for micro-

strip matched termination can be obtained [8].

3. Radiated Power

The power radiated by the microstrip mismatched termination through upper half space is obtained by using Poynting vector. For different values of plasma to source frequencies, expressions for radiated power are obtained by using the method of [8].These expressions are:

3.1 For Electromagnetic Mode

2

2 2 2

22 22 2 2

1 2

02

15

cos cos sin

o oe

e

h w AIP

S S d

d

(7)

where

2 2

2 2

1 2 2

2 2

( cos ) ( ) cos

( cos )

( ) cos ( cos )

( cos )

A A

AS

A AR

A

And

2

cos cos

( cos ) ( cos

A AS R

A A )

and the radiation resistance in electromagnetic mode

eR can be defined as

2

2 ee

o

PR

I (8)



3.2 For Electroacoustic Mode

2 4 2 /2

2 2 2 2/2 0

2

(cos sin cos ) /[

( cos )8 ( )

/ (sin cos cos )] sin

( cos )

p p o pp

po p

pp

p

mh I kP

ke n

kR X d d

k

(9)

and the radiation resistance in plasma mode pR can be

defined as

2

2..................................(10)p

po

PR

I

These values of and eR pR

0 0

are computed and plotte

for different values of plasma to source frequencies in Figure 5.In the electromagnetic mode, power radiated in free space ( ) is maximum but decreases on in-creasing plasma to source frequency. On the other hand, plasma mode field patterns give a quasi periodic pattern. Initially, radiated power in plasma mode is less than the radiated power in electromagnetic mode but it over takes in between the range

1.A 0

.25A to .

During the voyage in free space, aerospace vehicle in-teracts with plasma media and radiates electroacoustic waves in addition to the usual electromagnetic waves. Presence of the electroacoustic wave is mainly responsi-ble for such variation in this plasma media.

It is evident from the expressions of radiated power that they are a function of reflection coefficient. The variations of radiated power in free space or 1.0A ( p 0)

and in plasma media (0 1)p

are pre-

sented for both electromagnetic mode and longitudinal plasma mode in Figure 6.

In free space ,radiated power in electro-

magnetic mode is maximum for

1.0A

0R (matched ter-

mination).As mismatch increases, radiated power de-creases and becomes minimum at 0.8R .Thereafter it

becomes almost uniform up to 1.0R (open circuit mi-

crostrip termination).On increasing the plasma to source frequency , the radiated power by a matched

termination becomes quite small in comparison to its free space value . On increasing

A

A

0.2

1.0 R value, radi-

ated power in electromagnetic mode increases continu-ously but it always remains less than the free space value even for an open circuit termination( 1.0R ).

In longitudinal plasma mode, radiated power at for a matched termination ( 0.2A ) ( 0R ) is low

but increases continuously up to 1.0R (open circuit

termination). The total power radiated in free

space

( e pP P )

( 0)pP is low for an open circuit termination.

4. Conclusions

Effect of the presence of plasma medium on the different discontinuities is observed here by considering different

plasma to source frequency ( )p

values.

It can be concluded from the present study that for op-eration in free space an open circuit discontinuity better than a matched termination operating at very high fre-quencies. In the plasma media, matched termination is

1.010-1

100

101

102

0.8 0.6 0.4 0.2 0.010

100

101

102

-1

Re

A

Re

Rp

Rp

Figure 5. Radiation resistance in EM mode and in plasma mode for different A and 0.7 ,R

0.0 0.2 0.4 0.6 0.8 1.00.01

0.1

1

10

0.01

0.1

1

10

Re(

ohm

)

R

Re(A=0.2)

Re(A=1.0)

Rp(A=0.2)

Rp(A=0.95)

Rp(

ohm

)

Figure 6. eR and pR for different values of R and




186

better than an open circuit discontinuity because total radiated power is less for matched termination than an open ended termination. More radiations from any dis-continuity cause less utility of that structure. Hence, a matched termination is suitable with an antenna in plasma media though open circuit discontinuity suits more in free space. A theoretical effort is made here in this communication which requires experimental verifi-cation, though simulation of plasma media in laboratory is very difficult.

REFERENCES

[1] R. E. Post and D. T. Stephenson, IEEE Transactions, AP P–29,129 P–133, 1981.

[2] J. R. James and G. J. Wilson, Microwave option and acoustics, 1,165 P–174, 1974.

[3] K. R. Carver and J. W. Mink, IEEE Transactions, AP–29, 1024, 1981.

[4] A. G. Derneryd, IEEE Transactions, AP–24,846–851, 1976.

[5] M. D. Abouzahra and L. Lewin, IEEE Transactions, MTT P–27,722 P–723, 1979.

[6] D. Bhatnagar, Journal of Inst. Electronic and Telecom. Engrs. 38, 13 P–16, 1992.

[7] M. V. Schneider, Bell System Tech. J. 48, 1421 P–1444. 1969.

[8] A. M. Salem, D. Bhatnagar, J.of Plasma Physics, Vol.56, Pt.1, 25 P–34, 1996.



187

Fault Diagnosis Based on ANN for Turn-to-Turn Short Circuit of Synchronous Generator Rotor Windings

H. Z. MA, L. PU

Electrical Engineering Department, Hohai University, Nanjing, China. Email: [email protected], [email protected] Received March 15th, 2009; revised June 8th, 2009; accepted June 26th, 2009.

ABSTRACT

Rotor winding turn-to-turn short circuit is a common electrical fault in steam turbines. When turn-to-turn short circuit fault happens to rotor winding of the generator, the generator terminal parameters will change. According to these parameters, the conditions of the rotor winding can be reflected. However, it is hard to express the relations between fault information and generator terminal parameters in accurate mathematical formula. The satisfactory results in fault diagnosis can be obtained by the application of neural network. In general, the information about the severity level of the generator faults can be acquired directly when the faulty samples are found in the training samples of neural net-work. However, the faulty samples are difficult to acquire in practice. In this paper, the relations among active power, reactive power and excitation current are discovered by analyzing the generator mmf with terminal voltage constant. Depending on these relations, a novel diagnosis method of generator rotor winding turn-to-turn short circuit fault is proposed by using ANN method to obtain the fault samples directly, without destructive tests.

Keywords: Generator, Rotor Winding, Turn-to-turn Short Circuit, ANN, Diagnosis

1. Introduction

The statistical material form China Electric Power Re-search Institute indicated that the rotor winding turn-t- o-turn short circuit is a common electrical fault in a gen-erator [1,2]. However, minor turn-to-turn short circuit will not affect the normal operation of generator unit, so it is often ignored. But if this fault develops, something serious will appear, such as remarkable increasing of ro-tor current, higher temperature of winding, deceasing of reactive power, distortion of voltage, vibration of gen-erator unit and many other mechanical faults. Therefore, estimation of the early signs of failure severity and its develop trends can be made based on the identification of the fault’s early signals, and this task has gradually be-come important in condition-based maintenance of gen-erators [2,3].

At present, there have been many scholars studying in the monitoring of rotor winding turn-to-turn short circuit worldwide [2–5]. Albright proposed differential search-c- oil test method: Its diagnosing effect is good for a gen-erator under on-load and three phase short circuit, but

one-time location is difficult to make under load and it is not sensitive to minor turn-to-turn short circuit. Russian scholar B. T. Carsman proposed to detect turn-to-turn short circuit based on the circulating current in stator par-allel branch, but this method depends on the structure of stator winding. Travelling-wave method based on online diagnosing technique for rotor winding turn-to-turn short circuit is immature. The alternating impedance method and loss method are often-adopted in experiment, but the method can not give an accurate conclusion in monitor-ing miner rotor winding turn-to-turn short circuit all the time. Further more, it is difficult to realize with the affec-tion of the factors like slot wedge etc. [6–8].

This paper analyses the fault mechanism and mmf (magnetomotive force) for generator rotor winding turn-to-turn short circuit. It discovers that when the ma-chine terminal voltage is in the condition of constant, there exist certain relations among active power, reactive power and field current. Thus it finds a kind of experi-ment on the electrical engineering which does not need to carry on a destructiveness experiment, but can obtain fault sample. And then it makes use of artificial neural network to carry out fault diagnosis for generator rotor winding turn-to-turn short circuit.

* This work project was supported by National Natural Science Foundation of China (No. 50477010), China Education Ministry’s Foundation Program for Excellent Young Teachers in Universities and Importance Natural Sci-ence Foundation of Hohai University.

Fault Diagnosis Based on ANN for Turn-to-Turn Short Circuit of Synchronous Generator Rotor Windings188

2. Causes of Rotor Winding Turn-to-Turn Short Circuit

The causes of rotor winding turn-to-turn short circuit mainly include manufacture and operation. For example, the mounting of rotor end winding is not firm; spacer block becomes loose; the trimming of leading wire sol-dered joint is not good; there are remaining metal scales inside rotor protective ring; the dynamic forces such as centrifugal force cause displacement deformation of high-speed rotating rotor winding; the choking of rotor winding causes local overheating, which makes turn-to -turn insulation to burn down.

Otherwise, while the generator is operating or con-verting from the static state to the dynamic state, due to the abrasion of the turn-to-turn insulation or the relative dislocation caused by the relative motion between the turns in rotor, the turns may contact each other. When this fault has developed to a certain extent, the turn-to- turn shot circuit will happen. As a result of the emergence of this, the Effective magnetic field of generator will de-crease, and the generator reactive power will be affected. Those lead to imbalance in the magnetic circuit which causes vibration, and then “monopole potential” and “monopole current” will be produced to magnetize the generator shaft seriously. In addition, partial over heating in fault point may be extended to grounding fault in rotor windings.

3. Mmf Based Analysis of Electromagnetic Characteristics of Generator Rotor Winding Turn-to-Turn Short Circuit

3.1 Analysis of Mmf under Rotor Winding Turn-to-Turn Short Circuit

Spatial distribution of mmf in rotor windings is shown in Figure 1 Just like Figure 1(b), while the generator units are operating normally, the spatial distribution of Mmf is trapezoidal-like, ignoring the minor intermittent of mmf which is caused by the grooves. The mmf will loss par-tially, while short-circuit happens in rotor windings. This kind of loss will result in partial loss of shorted magnetic pole, so that the average and amplify of shorted magnetic pole will decrease as shown in Figure 1(c). Therefore, the spatial distribution of mmf in the turn-to-turn short circuit can be considered as that in demagnetization. So the equivalent effect of short-circuit can be considered as a mmf with the opposite direction adding on the main mmf of short circuit.

The mmf of rotor winding under normal condition is represented by 0F , the mmf caused by short-circuited

turns is represented by F , after short circuit, the rotor mmf is

0

'F F F

Figure 1. Spatial distribution of mmf in rotor windings

aF

1fF

fF

F

'F

'

aF

aF

E

arIxIj

IU

0E

Figure 2. Magnetic-electronic potential vector of generators considering saturation The mmf-emf vector diagram of non-salient poles gen-erator considering saturation is shown in Figure 2 .

The air-gap mmf fundamental component F

is esta-

blished by exciting mmf fundamental component 1fF

and armature reaction mmf fundamental component aF

,

i.e.

1f aF F F

(1)

Reduced to the exciting mmf wave, it can be got: '

f'

aF F F

(2)

where, f f fF w I , is the turn number of rotor winding;

is exciting current; the phase angle of fw

fI

, smaller than the former value. 11.35 w

a

w k IF

p


Fault Diagnosis Based on ANN for Turn-to-turn Short Circuit of Synchronous Generator Rotor Windings


189

in time-space vector diagram is the same as I , is the 1w

series number of stator winding phase, is the coeffi-

cient of stator winding. wk

Suppose terminal voltageU , active output and reac-tive output are invariants, then stator current

P

Q I and

power factor angle become invariable. And x has

little relation to the saturation level. (r )aIE U jx .

Then the angle between E

'

and is unchangeable. So

that the angle between

I

F

and '

aF

will not change. Be-

cause of this, fF

is unchangeable. If the working condi-

tion of a generator before and after rotor winding fault remains unchanged, in order to satisfy the air-gap com-posite flux condition, fI will increase, but does not

change, from this it can be see: the relation betweenU , , , not only manifest the state of the rotor

winding, but also reflects the effective turn number of the rotor winding.

fw I f

P Q fI

3.2 Impact of Exciting Current on Rotor Winding Turn-to-Turn Short Circuit Diagnosis

The relation betweenU , P , Q , fI can manifest the state

of the rotor winding. The exciting current of a gen-

erator under normal operation can be calculated by the mathematical Equation, and then compared with meas-ured exciting current , the existence of rotor winding

turn-to-turn short circuit can be determined, furthermore

the calculation of relative deviation

0fi

fci

0

0

% fc f

f

i i

i

can be used to estimate the severity of the fault. 100%

4. ANN Diagnosis Method for Generator Rotor Winding Turn-to-Turn Short Circuit

Recently it is mainly according to the measurement of the generator terminal parameters which namely generator active power , reactive power , the generator ter-

minal voltage U , current , field voltage and other generator parameters, uses a formula calculation to ac-quire the field current

P Q

I

0fI which operates under nor-

mally flows, and then compare the measurement of actual electric current '

fI with to diagnose rotor Winding

Turn-to-turn Short Circuit fault of generators. 0fI

This kind of method needs to consider the influence of magnetic field saturation, and it needs accurate mathe-matics model and the parameter of generator in the meantime. The parameter of generator will also have va-riety change along with the operating way and the variety

change of operating conditions. The accuracy of online recognition is not very high, therefore there exists a cer-tain error margin.

The artificial neural network (ANN) does not need ac-curate mathematics model and the detailed parameters of generator, and it has no interference to the operation of generator in the meantime. It only needs to measure the generator terminal parameters accurately, and depends on a great deal of training samples. Through sufficient net-work trains, diagnosis can be directly carried out of the faults operated under dissimilar ways. By having faulty sample, we can not only diagnose the faults, but also es-timate the seriousness of short-circuit.

The terminal voltage U of generator is generally a rated voltage, which could be supposed to be constant. According to the analysis of the basis generator magnetic field, certain , Q will correspond to certainP fF , namely

certain of . So the relation of , andf fw I P Q fI can

reflect the turn-to-turn short circuit fault, with the gen-erator parameter , Q ,P fI as the ANN importation, and

circles of turn-to-turn short circuit have the percent of total number of full circles % as the output.

The key of the fault diagnosis which carries on with ANN to is to obtain the train samples. The selection of normal samples can take in various samples in normally operation in the P-Q diagram of generator, but in the ac-tual power station for guaranteeing the “ergodicity” of samples, we could detect the generator parameters with long hours at normal operation conditions.

In order to estimate the severity of generator faults and the number of short-circuit turns, the faulty samples of generators are needed. Relatively speaking, to acquire the samples of the generators under normal operation condi-tion is still easy, but to obtain generator fault samples is usually very difficult. The general method is to do a de-structive experiment in dynamic simulation laboratory, short connecting several turns of the rotor windings of generator factitiously. This kind of method can barely be carried out on the engineering.

This paper uses the method of balancing the mmf to obtain fault sample of the generator under turn-to-turn short circuit of rotor winding. Suppose turn-to-turn short circuit fault occurs to generator at the rated condition, before and after the short-circuit, , ,U are constant.

By analysing the magnetic field we can know the mag-netic field will maintain constant, and suppose the

short-circuit turns of the total rotor winding number is

P Q

f fw I

%, after the fault, the field current is:

1

1 %f fNI I

(3)

where, —the rated value of the field current.fNI

Fault Diagnosis Based on ANN for Turn-to-Turn Short Circuit of Synchronous Generator Rotor Windings190

Changing the number of short-circuit turns, we will get a series of faulty samples. And also we can acquire faulty samples under different operation conditions.

5. Simulation

To verify the credibility of this method, we can adopt cultural heritage [9] generator parameters, see Table 1; and then take its normal operating samples. The rated operate conditions of the fault sample can be seen in Table 2. In Table 2, α % is the short-turns as percentage of the total rotor winding turns number. We can carry out network training, and then carry out fault diagnosis; the fault samples can be seen in Table 3. From Table 3, α%(actual) is the factitiousness number of short-turns as percentage of the total number of rotor winding turns in dynamic simulation laboratory. a%(emulation) is the number of short-turns simulated by computer as percent-age of the total number of rotor winding turns.

The back propagation artificial neural network(BP) is used here, and the active function adopts S type function. The BP network adopts 3 layers. As it is shown in Figure 3, the first layer has three importation nodes, hide layer has four nodes, and exportation layer has one node. The generator parameters contain active power, reactive power, exciting current, and all these parameters are nor-malized values. Table 3 shows the results simulated by MATLAB. According to this, the actual results con-firmed the BP network diagnoses.

In a word, this method has realized the direct acquisi-tion of fault’s seriousness and the solution of fault sam-ples’ acquisition which are difficult to get.

In particular process, the current and the terminal voltage of stator windings are measured by CT (Cur-rent Transformer) and PT(Potential Transformer), and the exciting current

IU

fI is measured by current converter.

Here, select the CT and PT used to measure system pa-rameters as the measure equipment. The generator capac-ity and voltage level decide the selection of them. And the hall current converter produced by Swiss company LEM is used to measure in rotor winding. The pa-

rameters andU are used to calculate both the active power and reactive power Q .

fI

IP

After training, this method is applied to all kinds of load. By measuring andU of normal generator in all running states, we can obtain the corresponding

and Q by calculating. The training of ANN needs ,

and to obtain the relationship among the parame-

ters( , and

I

P

Q

P

fI

P Q fI ) in all the running states.

5. Conclusions

While ANN is applied to the fault diagnosis of generator, the most difficult part is the acquirement of the

Figure 3. Schematic diagram of ANN

Table 1. Parameters of synchronous machine

Model number MJF-30-6 Rated Voltage/V 400 Rated Current/A 43.3

Power Factor 0.8 Rotor Current/A 2

fw /turn 100

Table 2. Diagnostic patterns in neural training

P(*) Active Power

Q(*) Reactive Power

fI (*)

Exciting Current

α % Short-turn Number as Percentage of Total

Winding turns Number in Rotor

1 1 1.053 5

1 1 1.111 10

1 1 1.25 20

1 1 1.429 30

Table 3. The comparison between the output of the neural network and the actual output

P(*) Active Power

Q(*) Reactive Power

fI (*)

Exciting Current

%(actual) Short-turn Number as Percentage of Total

Winding Turns Number in Rotor

%(emulation)Short-turn Num-ber as Percentage of Total Wind-ing Turns Num-

ber in Rotor

0.42555 0.51906 0.963 1.21 2.56

0.4295 0.5102 0.9771 3.91 4.86

0.4289 0.5054 0.99832 6.07 7.00

0.4325 0.5001 1.02026 10.06 9.48

0.4309 0.4899 1.06012 12.93 13.32

0.4168 0.4678 1.0765 14.83 15.50

fault samples among training samples. This paper analy-ses generator turn-to-turn short circuit of rotor winding fault and according to the certain operation of generator, namely active power , reactive power Q , terminal

voltageU keep constant, and the field current in

reases, but the mmf

P

fI

f f fF w I maintains constant.


Fault Diagnosis Based on ANN for Turn-to-Turn Short Circuit of Synchronous Generator Rotor Windings 191

Faulty samples are obtained through direct calculation, turn-to-turn short circuit fault of rotor winding is diag-nosed by making use of artificial neural network, and we could obtain seriousness level of fault information di-rectly. That method can avoid damage experimenting and it is convenient in engineering.

The shortcoming of this method is that it could not lo-cate the faulty position. After diagnosing and confirming the existence of the fault, if we assist it with other ways such as traveling wave method, location of fault can be carried out.

REFERENCES

[1] W. J. Wang and L. Gui, “Present situation and improve-ment of relay protection for large sized generator trans-former set of 600~1000MW,” Huadian Technology, Vol. 30, No. 1, pp. 5–8, 2008.

[2] W. Q. Li, “Prevention and fault diagnosis of turbogen-erator,” Beijing: Chinese electric power publisher, 2002.

[3] S. Wan, H. M. LI and Y. G. LI, “Analysis of generator vibration characteristic on rotor winding inter-turn short circuit fault,” Proceedings of the CSEE, Vol. 25, No. 10, pp. 122–126, 2005.

[4] H. W. Fang, C. L. Xia and J. Xiu, “Analysis of generator electro-magnetic torque on armature winding inter-turn

short circuit fault,” Proceedings of the CSEE, Vol. 27, No. 15, pp. 83–87, 2007.

[5] G. G. Mao, “Reasons of failures occurred in large capac-ity turbogenerators in China,” Power System Technology, Vol. 24, No. 11, pp. 1–7, 2000.

[6] R. J. Streifel, R. J. Marks II, and M. A. EI-Sharkawi, “De-tection of shorted-turns in the field winding of turbine -generator rotors using novelty detectors development and field test,” IEEE Trans on Energy Conversion, Vol. 11, No. 2, pp. 312–317, 1996.

[7] A. S. Kulkarni, M. A. El-Sharkawi, R. J. Marks II, G. Andexler, X. Jian, and I. Kerszenbaum, “Development of a technique for on-line detection of shorts in field wind-ings of turbine-generator rotors: Circuit design and test-ing,” IEEE Trans on Energy Conversion, Vol. 15, No. 1, pp. 8–13, 2000.

[8] S. E. Guttormsson, R. J. Marks II, and M. A. EI-Sharkawi, “Elliptical novelty grouping for on-line short-turn detec-tion of excited running rotors,” IEEE Transactions on En-ergy Conversion, Vol. 14, No. 1, pp. 16–22, 1999.

[9] D. W. Auckl, I. E. D. Pickup, and R. Shuttleworth, “Novel approach to alternator field winding inter-turn fault detection,” IEE Proc., Gener., Transm., Distrib., Vol. 142, No. 2, pp. 97–102, 1995.





Niancheng ZHOU1, Li LIN1, Jizhong ZHU1,2

1State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, Chongqing, China; 2AREVA T&D Inc., 10865 Willows Rd. NE, Redmond, USA Email: [email protected] Received March 17th, 2009; revised June 15th, 2009; accepted June 22nd, 2009.

ABSTRACT

This paper presents the harmonic state estimation (HSE) based on the Total Least Squares (TLS) through comprehen-sively considering the harmonic network parameter error and measurement system error. The proposed approach is tested on the IEEE 14–bus harmonic testing system. The satisfied results are obtained.

Keywords: State Estimation, Harmonic Analysis, Measurement Errors, Total Least Squares, Probability, Uncertainty

1. Introduction

The harmonic state estimation (HSE) in power system estimates the harmonic state in whole network according to the measured values of limited points [1–3]. The prob-lem of harmonic state estimation was first proposed by Heydt in 1989 [1], where HSE is handled as an inverse problem of harmonic power flow, and the adopted algo-rithm for estimating the harmonic state and identifying the harmonic source is least square estimation. Since it is difficult to obtain accurately all system parameters for a non-fundamental frequency harmonic network, the pa-rameter error always exists. However, the existing HSE methods only consider the harmonic measurement error, and ignore the effect of parameter error to harmonic state estimation, which is addressed in this paper.

2. HSE Based on TLS

Since the parameter error always exists in non-funda-mental frequency harmonic network, the mathematical model of HSE should consider not only the impact of measurement error, but also the impact of parameters error. Therefore, the HSE mathematical model can be expressed as:

true true Hx H x z + z (1)

where, H is the parameter matrix (m×n) containing the relationship between the measured values and the state variables. x is the undetermined state vector (n×1). Htrue is the parameter matrix containing the truth values. v is the parameter error matrix (m×n). ztrue is the measure-ment vector (m×1) related to the truth values, which are

unknown variables. ε is the measurement error vector (m×1). z is the measurement vector (m×1).

The harmonic state estimation Equation (1) is an over-determined linear system. In this paper, the TLS method is proposed to solve such HSE problem. The estimation method of TLS is trying to estimate the noise matrix v and the noise vector ε to meet the exact solution of linear system. Select v and ε to make a minimum of

2 2

F1 1 1

[ ]m m n

ii i j

v

2ij vε (2)

where, is the element of matrix v, and εi is the i-th

element of ε. ijv

Let H H= z , ，Equation (1) can be written as fol-

lows:

TLS

- 1( [ v])H

x

0

(3)

where, 0 is an m-dimension vector in which all the ele-ments are 0.

In general, because of the existence of noise, the aug-

mented matrix H is full rank. If m>n+1, the rank of ma-

trix H is (n+1). Using the singular value decomposi-tion (SVD) method, the matrix can be expanded as fol-lows:

1

1

[ , ]n

Ti i i

i

H z H u w

(4)



193

where, σi is the singular value of matrix H , arranging in the decreasing order of values, ui and wi are left singu-lar vector containing m elements and right singular vector containing (n+1) elements, respectively.

Let’s define rank approximate value as the minimum of the sum of various perturbations in matrix H . It is given as follows [4]:

1

ˆn

Ti i i

i

H u w

(5)

Moreover, error matrix [ v ] is given as follows：

1 1 1[ ] Tn n nu w (6)

From Equations (3) and (5), we can get

1

TLS 1,1

- 1n

nw

w

x (7)

According to [4], when the noise sequence meets the central limit theorem conditions of independent identical distribution, the standard TLS estimation is unbiased.

For the h-th harmonic, the harmonic power flow Equa-tion can be expressed as follows:

h h h Y V I (8)

In this paper, the node harmonic voltage vector

is used as measuring point, and the node harmonic injec-tion current is used as state variables. If different

measurements and state variables are selected, the similar state estimation expression can still be obtained through the matrix transformation. If parameters error and meas-urement error are considered simultaneously, that is, harmonic impedance matrix error and harmonic node voltage measurement error are considered together, the relationship between measurements and state variables can be obtained as follows:

( )v h

( )I h

true true( ) ( ) ( ( ) ( )) ( )V h h Z h v h I h (9)

According to Equations (3–7), the estimated value of the node harmonic injection current, ( )TLSI h , can be com-

puted. Thus, the harmonic state estimation is solved.

3. Simulation Results and Analysis

The proposed TLS based HSE approach is examined us-ing the IEEE–14 node harmonic test system, which in-cludes two harmonic sources, one is high voltage direct current (HVDC) transmission system's terminal located at node 3, and another is static var compensator (SVC) lo-cated at node 8. The node harmonic voltages located at buses 2–12 are selected as the measurement data.

The following several combination modes are used for simulation analysis, respectively:

1) Case 1: Both measurement error and parameters er-ror obey normal distribution with zero mean and different

variances; 2) Case 2: Measurement error obeys uniform distribu-

tion of zero mean, parameters error obeys normal distri-bution of zero mean;

3) Case 3: Measurement error obeys normal distribu-tion of zero mean; parameters error obeys uniform dis-tribution of zero mean.

Assume that the errors are independent. The sampling frequency is selected as 10000. In order to do comparison easily, the three-phase harmonic simulation is computed to obtain the true value, which is used to compare with the estimated value of harmonic state estimation.

During the simulation, superimpose a random error at each node harmonic voltage and each element of har-monic impedance matrix. The errors are produced by the normrnd function in Matlab. The variance is selected as 1% of the absolute value of each element in the matrix.

Due to the limitation of the space, this paper only gives the analysis of case 2. In this case, it is needed to deter-mine the upper and lower limit of the uniform distribu-tion of the measurement error U[a,b]. Considering that the measurement error is the random signal, which has the similar definition with the noise in signal processing [5], we determine the values of a and b through the use of the signal-to-noise ratio (SNR) in signal processing.

101 ( / )S USNR g P P (10)

where, PS is the maximum true value in various meas-urements. PU is the variance of measurement error, which is the uniform distribution.

In this paper, the signal-to-noise ratio SNR is selected as 20, together with the error is zero mean (that is, a = – b). Then, the upper and lower limits of the uniform dis-tribution can be obtained through the following Equation:

/10 2/10 ( ) /12SNRU SP P b a (11)

Thus, the random sequence of measurement error can be obtained according to the upper and lower limit of uniform distribution. Then, the measurement value in-cluding uniform distribution error can be obtained by superimposing it to the true value.

The results are shown in Figures 1–4. Figure 1 shows the error cumulative probability density curve of the cal-culation results. Node harmonic injection current and harmonic voltage estimation are shown in Figures 2 and 3. The probability density curves of harmonic injection cur-

Figure 1. Harmonic current injections estimation relative error at bus 3



194

Figure 2. Harmonic current injections

Figure 3. Harmonic bus voltages

rent estimation values are shown in Figure 4. The results show that the probability density curves of all harmonic injection current estimation values obey normal distribu-tion approximately. For the low-order harmonic, its con-fidence interval of probability density curve is relatively wide.

4. Conclusions

This paper has studied the harmonic state estimation

Figure 4. The probability density curve of the harmonic current injections estimated value at bus 3 (HSE) through considering comprehensively the meas urement error and parameters error. The proposed method is the Total Least Squares (TLS) and statistical approach. The details of HSE model based on TLS are presented, and error analysis for the HSE is conducted by using the probability density function and cumulative probability density function. The proposed method and algorithm are tested on IEEE 14-node harmonic network. The simulation results show the effectiveness and cor-rectness of the paper.

REFERENCES

[1] G. T. Heydt, “Identification of harmonic sources by a state estimation technique,” IEEE Trans., Power Delivery, Vol. 4, No. 1, pp. 569–576, 1989.

[2] A. P. S. Meliopoulos, F. Zhang, and S. Zelingher, “Power system harmonic state estimation,” IEEE Trans., Power Delivery, Vol. 9, No. 3, pp. 1701–1709, 1994.

[3] Z. P. Du, J. Arrillaga, N. Watson, and S. Chen, “Identifi-cation of harmonic sources of power systems using state estimation,” IEE Proceedings – Generation, Transmission and Distribution, Vol. 146, No. 1, pp. 7–12, 1999.

[4] C. Fu, “The probability distribution of measurement er-rors,” Journal of Chengdu Institute of Radio Engineering, Vol. 3, No. 3, pp. 56–65, 1981.

[5] G. S. Hu, Digital Signal Processing, Beijing: Qing Hua University Publishing House, 2004.

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