15th INTERNATIONAL MULTIDISCIPLINARY

15th INTERNATIONAL MULTIDISCIPLINARY SCIENTIFIC GEOCONFERENCE SGEM2015

INFORMATICS, GEOINFORMATICS AND REMOTE SENSING CONFERENCE PROCEEDINGS

VOLUME I - - - - - - - - - - - - - - - - - INFORMATICS, GEOINFORMATICS PHOTOGRAMMETRY AND REMOTE SENSING - - - - - - - - - - - - - - - - - -

18-24, June, 2015 Albena, BULGARIA

DISCLAIMER This book contains abstracts and complete papers approved by the Conference Review Committee. Authors are responsible for the content and accuracy.

Opinions expressed may not necessarily reflect the position of the International Scientific Council of SGEM.

Information in the SGEM 2015 Conference Proceedings is subject to change without notice. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of the International Scientific Council of SGEM.

Copyright © SGEM2015 All Rights Reserved by the International Multidisciplinary Scientific GeoConferences SGEM Published by STEF92 Technology Ltd., 51 “Alexander Malinov” Blvd., 1712 Sofia, Bulgaria Total print: 5000 ISBN 978-619-7105-34-6 ISSN 1314-2704 DOI: 10.5593/sgem2015B21

INTERNATIONAL MULTIDISCIPLINARY SCIENTIFIC GEOCONFERENCE SGEM Secretariat Bureau Phone: Fax:

+359 2 4051 841 +359 2 4051 865

E-mails: URL:

[email protected] | [email protected] www.sgem.org

Organizers, International Scientific Committee

ORGANIZERS                     

BULGARIAN ACADEMY OF SCIENCES ACADEMY OF SCIENCES OF THE CZECH REPUBLIC LATVIAN ACADEMY OF SCIENCES POLISH ACADEMY OF SCIENCES RUSSIAN ACADEMY OF SCIENCES SERBIAN ACADEMY OF SCIENCES AND ARTS SLOVAK ACADEMY OF SCIENCES NATIONAL ACADEMY OF SCIENCES OF UKRAINE INSTITUTE OF WATER PROBLEM AND HYDROPOWER OF NAS KR NATIONAL ACADEMY OF SCIENCES OF ARMENIA SCIENCE COUNCIL OF JAPAN THE WORLD ACADEMY OF SCIENCES (TWAS) EUROPEAN ACADEMY OF SCIENCES, ARTS AND LETTERS ACADEMY OF SCIENCES OF MOLDOVA MONTENEGRIN ACADEMY OF SCIENCES AND ARTS CROATIAN ACADEMY OF SCIENCES AND ARTS, CROATIA GEORGIAN NATIONAL ACADEMY OF SCIENCES ACADEMY OF FINE ARTS AND DESIGN IN BRATISLAVA TURKISH ACADEMY OF SCIENCES BULGARIAN INDUSTRIAL ASSOCIATION BULGARIAN MINISTRY OF ENVIRONMENT AND WATER

HONORED ORGANIZER BULGARIAN ACADEMY OF SCIENCES

EXCLUSIVE SUPPORTING PARTNER

INTERNATIONAL SCIENTIFIC COMMITTEE Informatics, Geoinformatics and Remote Sensing 

PROF. ING. ALEŠ ČEPEK, CSC., CZECH REPUBLIC



PROF. G. BARTHA, HUNGARY



PROF. DR. DAMIR MEDAK, CROATIA

15th International Multidisciplinary Scientific GeoConferences SGEM2015



PROF. PETER REINARTZ, GERMANY



PROF. DR. JÓZSEF ÁDAM, HUNGARY



PROF. RUI MIGUEL MARQUES MOURA, PORTUGAL



PROF. DR. ING. KAREL PAVELKA, CZECH REPUBLIC



PROF. DR. MARCEL MOJZES, SLOVAKIA



ASSOC. PROF. DR MILAN HOREMUZ, SWEDEN



DR. TIBERIU RUS, ROMANIA



DR. MARKO KREVS, SLOVENIA

Section Informatics

USE OF NUMERICAL SIMULATION TO STUDY CAPACITIVE LOADS WHICH IS CONNECTING TO AN AC POWER SOURCE

Assoc. Prof. PhD. Eng. Titu Niculescu Lecturer PhD. Eng. Dragoș Păsculescu University of Petrosani, Romania

ABSTRACT The paper presents a new and a modern method for studying the electrical RLC circuits which are connected to an AC power source, using the MATLAB-SIMULINK software package. The capacitive circuits which are switched on an AC power source at the initial moment are presented in the paper. We can determine the capacitor current variation forms, the capacitor voltage in transient regime by using this virtual medium, in two different regimes: the oscillating regime and the a-periodic regime. Each presented case contains an analytical presentation of the phenomenon, but it also contains the diagrams of current and voltage capacitors. The diagrams were obtained by three methods which use this software package. Keywords: capacitive circuit, diagrams, differential equation, Simulink, simulation model, SimPowerSystems INTRODUCTION There is considered a RLC series circuit with concentrated parameters which will be connected to an AC power source. This situation is met in practice in case if we want to connect a capacitor banks to a voltage network to compensate the power factor. In this case can occur over-voltages or over currents during transient regime, which can cause issues for system sizing. The inductivity of junction wire forms with the capacitors an oscillating circuit (Fig. 1). k

R

L

i(t) C

e(t )

~

u(t )

Fig. 1 Capacitor connecting to an AC voltage source The differential equation for transitory phenomena is presented below, where “u(t)” is the capacitor voltage. LC

d 2 u(t) du( t )  RC  u ( t )  U m sin(t  ) dt 2 dt

(1)

in which  is the initial phase of voltage when the circuit was connected.

391


THEORETICAL CONSIDERATIONS The oscillatory regime: If we consider the R resistance of the circuit very low, the Laplace’s method applied to this circuit conducts to the following solution: U m sin(t    1 )

u(t) 

1 C R  (  L) 2 C 2



DU m e  t sin( e t   ) 2LC  e2

(2)

where  is a dumping factor: 

R 2L

(3)

and 0 is the resonance angular frequency of the circuit: 0 

1

(4)

LC

There have been also used the following notations: e  02   2

(5)

D  A 2  B 2  2AB cos(  )

(6)

tg 

A sin   B sin  A cos   B cos 

  3   ;

  2  

(7) (8)

1  arctg

2   2

(9)

 2  arctg

 e  

(10)

 3  arctg

 e  

(11)

A

B

2 0

1  2  (1  )  ( )2 e e 1

  (1  ) 2  ( ) 2 e e

(12)

(13)

It is noticed that the capacitors voltage at its terminals contain a periodic component and a damped oscillatory component, which is canceled after a while from the connection moment. The solution for capacitor current results from expression (2):

392

Section Informatics

i  I m cos(t   1 ) 

DU m e t 2e L

    cos(e t   )  sin( e t   ) e  

(14)

where: Um

Im 

(15)

1 R (  L) 2 C 2

The current circuit contains also a periodic component and a damped oscillatory component, which disappears after a while from the connection moment[1], [5], [10]. 800

25

600

20

15 400 10

current[A]

voltage[V]

200

0

5

0

-200 -5 -400 -10

-600

-800

-15

0

0.005

0.01

0.015

0.02 time[sec]

0.025

0.03

0.035

0.04

Fig. 2 Capacitor voltage diagram in the oscillatory regime

-20

0

0.005

0.01

0.015

0.02 time[sec]

0.025

0.03

0.035

0.04

Fig. 3 Capacitor current diagram in the oscillatory regime

Diagrams in Fig. 2 and Fig .3 are based on analytical expressions (2) and (14), and are plotted for the following value of electric circuit parameters, in MATLAB environment by programing: Uef = 380 [V]; R= 2 [Ω]; L= 10 [mH]; C= 50 [µF]; F=50 [Hz]; ᴪ = 0.64[rad]. The a-periodic regime: We consider that the resistance R is very high (    0 ) and: e   2   02

(16)

the original solution for equation (1) in this situation is: u (t ) 

U m sin( t    1 ) 1 C R 2  (  L ) 2 C



U m  02  e ( e )t sin(  2   ) e ( e )t sin(  3   )      2  e  ( e   ) 2   2 ( e   ) 2   2  

(17)

In the expression which gives the instantaneous voltage in this regime, there have been made the following notations: 1  arctg

2 02   2

(18)

 2  arctg

   e

(19)

393


3  arctg



(20)

e  

Based on equation (17) is obtained the expression current in the a-periodic regime: U m (   e ) sin(  3  )  e  ( e ) t i  I m cos(t    1 )   [ 2 e L ( e   ) 2   2 

(   e ) sin(  2  )  e ( e )t ( e   ) 2   2

(21)

]

where Im is given by equation (15). Equations (17) and (21) give the following MATLAB diagrams in the a-periodic regime: 120

20

100 15 80 10 60 5

current[A]

voltage[V]

40

20

0

0 -5 -20 -10 -40 -15 -60

-80

0

0.01

0.02

0.03

0.04

0.05 time[sec]

0.06

0.07

0.08

0.09

0.1

Fig. 4 Capacitor voltage diagram in the aperiodic regime

-20

0

0.01

0.02

0.03

0.04

0.05 time[sec]

0.06

0.07

0.08

0.09

0.1

Fig. 5 Circuit current diagram in the aperiodic regime

The diagrams from Fig. 4 and Fig. 5 were obtained for following value of input parameters: Uef = 380 [V]; R= 30 [Ω]; L= 1 [mH]; C= 500 [µF]; F=50 [Hz]; Ψ =0. SIMULINK MODEL OF CAPACITIVE CIRCUIT The SIMULINK model for capacitor current in the a-periodic regime was made in agreement with the mathematics form (1). This model allows the generation of capacitor current and voltage diagram for all regimes (Fig. 6)[8], [11].

Fig. 6 Simulation model for capacitor current in the a-periodic regime 394

Section Informatics

This model integrates the differential equation (1) and allows tracing the forms of voltage and current variation regardless of operating regime[2], [3]. For the set of values corresponding to the oscillating regime are obtained the diagrams from Fig. 7 and Fig.8:

Fig. 7 Capacitor voltage diagram in the oscillatory regime

Fig. 8 Capacitor current diagram in the oscillatory regime

The flowcharts of Fig. 7 and Fig. 8 were plotted for the same values of electrical parameters as for the diagrams in Fig. 2 and Fig. 3. It can be noticed that the two sets of diagrams render identical dependences[4], [5]. If in the numerical simulation from Fig. 6 are given parameters which correspond to the a-periodic regime, it can be obtained the variation forms specific for this regime[6]:

Fig. 9 Capacitor voltage diagram in the aperiodic regime

Fig. 10 Capacitor current diagram in the aperiodic regime

SIMPOWERSYSTEMS MODEL OF CAPACITIVE CIRCUIT Study of capacitor connection can be made using SimPowerSystems, which is included in MATLAB software package. SimPowerSystems model of the circuit from Fig. 1 is presented below (Fig. 10). For parameters values corresponding to the oscillatory regime, the model from Fig. 11 generates the diagrams of capacitor current and the capacitor voltage from Fig. 12 and Fig. 13[7], [9]. 395


Fig. 11 SimPowerSystems model of the circuit

Fig. 12 Variation of capacitive voltage in oscillatory regime

Fig. 13 Variation of capacitive current in oscillatory regime

For the parameters values corresponding to the a-periodic regime, the simulation model from Fig. 11 generates the following diagrams for the capacitor current and capacitor voltage[12]:

Fig. 14 Capacitor voltage diagram in the a- Fig. 15. Variation of capacitor current in aperiodic regime periodic regime It is noticed that the transitory regime lasts approximately 0.04-0.1 sec. for given parameters values, then the permanent regime appears. 396

Section Informatics

Variation forms when these are plotted using SIMPOWERSYSTEMS model are the same types of variation obtained by the other two methods. CONCLUSIONS All three methods presented for studying the transitory phenomena which appear when connecting capacitor banks to an AC power source, lead to the same conclusions. The variation forms of electrical parameters are identical in all three cases. The first case presented, which is based on MATLAB programming space, is more complicated, because it involves solving the differential equation (1), finding solutions in every regime and creating programs for each situation: two programs for voltage and current in the oscillating mode and two programs for these parameters in the aperiodic regime. The second method presented simplifies this problem because it does not require knowledge of mathematics needed to solve equation (1). Based on this equation was developed a Simulink model that integrates a second order differential equation. This model is unique because it leads to getting forms for voltage and current variation in both regimes, depending on the values of circuit parameters. The third method presented is the fastest and does not require knowledge for numerical integration of the differential equation (1). It is based on SIMPOWERSYSTEMS software package and requires only "drawing" the circuit and its sizing for each regime. The most hazardous regime is the oscillating regime and this is the most common regime which we can meet in practice for compensating the power factor. In this case, oscillating over-voltages may occur which have to be taken into account when sizing the systems. The values of these voltages depend on the connection moment, which is given by the initial phase of the AC voltage. The connecting of capacitors banks to a power source, at low voltage, can be performed directly without dumping resistance (oscillatory regime). The frequency of current oscillations at the connection moment is approximately 1 kHz. This can take place at low voltage for capacitor banks to 25 kVAr. It is important that the electric charge on the capacitor which is connected to be initially zero. Otherwise high value over current may occur in the after connecting moment. There has to be mentioned the fact that these developed models can be used to generate explicit dependence for every real value of the circuit parameters. REFERENCES [1]

* * * Software Matlab 2012a

[2]

Saracin C.G. Electrical Installations, (in Romanian), MatrixRom Publishing House, Bucharest, Romania, 2008

[3]

Hortopan Gh. Electrical devices, (in Romanian), Didactical and Pedagogical Publishing House, Bucharest, Romania, 1980

397


[4]

Horgos M. et al. Aspects of voltage dips, causes of production and their effect on consumers, Proceedings of the International Conference on ENERGY and ENVIRONMENT TECHNOLOGIES and EQUIPMENT (EEETE '10) SPONSOR and ORGANIZER: Faculty of IMST, Politehnica University, Bucharest, Romania Published by WSEAS Press ISSN: 1790-5095 ISBN: 978960-474-181-6, pp. 41 – 45

[5]

Golovanov N. a.s.o. Electricity consumers. Materials, Measurements, Devices, Installations, (in Romanian), AGIR Publishing House, Bucharest, Romania, 2009

[6]

Ghinea I. & Firteanu V. MATLAB numerical calculation, graphics, (in Romanian), Teora Publishing House, Bucharest, Romania, 2000

[7]

Pasculescu D. & Niculescu T. & Pana L. Uses of Matlab software to size intrinsic safety barriers of the electric equipment intended for use in atmospheres with explosion hazard, International Conference on Energy and Environment Technologies and Equipment (EEETE '10), “Politehnica” University, Bucharest, Romania Published by WSEAS Press ISSN: 1790-5095 ISBN: 978-960-474-1816, pag.17 – 21, 2010

[8]

Halunga-Fratu S. & Fratu O. Simulation of analogic and digital transmission systems using Matlab/Simulink environment, (in Romanian), MatrixRom publishing House, Bucharest, Romania, 2004

[9]

Surianu F.D. Industrial electrical networks, (in Romanian), Orizonturi Universitare Publishing House, Timisoara, Romania, 1999

[10] Tudorache T. Calculation environments in electrical engineering MATLAB, (in Romanian), MatrixRom publishing House, Bucharest, Romania, 2006 [11] Petrilean D.C. Mathematical Model for the Determination of the Non -Stationary Coefficient of Heat Transfer in Mine Works, Proceedings of the 19th WSEAS American Conference on Applied Mathematics (AMERICAN-MATH '13), Cambridge, MA, USA, January 30 -February 1, ISBN: 978-1-61804-158-6, pp.124-130, 2013. [12] Petrilean D.C. & Irimie S.I. Solutions to increase the energetic efficiency of pneumatic mining distribution networks, Conference: "9th WSEAS International Conference on ENERGY, ENVIRONMENT, ECOSYSTEMS and SUSTAINABLE DEVELOPMENT" (EEESD '13), Lemesos, Cyprus, March 2123, ISBN: 978-1-61804-167-8, pp. 43-48, 2013.

398