Study of simple inductive-capacitive series circuits using MATLAB software package

Transcription

1 ecen Advance in ircui, Syem and Auomaic onrol Sudy of imple inducive-capaciive erie circui uing MAAB ofware package NIUESU IU, PĂSUESU DAGOŞ Faculy of Mechanical and Elecrical Engineering Univeriy of Peroani Sr. Univeriaii nr. 0, 33006, Peroani, jud. Hunedoara OMANIA Abrac: hi paper preen a modern mehod for approaching he elecrical circui uing he MAAB- SIMUINK package program. he imple erie circui which are wiched on a D volage a he iniial momen are preened below. We can deermine he curren variaion form and he reacive elemen volage, by uing hi virual medium. Each preened cae conain an analyical preenaion of he problem, bu i alo conain elecrical diagram of elecrical parameer. he diagram were obained by differen mehod which ue hi program package. Key-Word: Simulink, imulaion model, differenial equaion, diagram, SimPowerSyem. Inducive erie circui We will conider he erie circui wih concenraed parameer from. A he iniial momen, he k circui wicher i cloed and we inend o udy he behavior and variaion of circui elecrical parameer afer connecion. he differenial equaion which correpond o he raniory regime immediaely afer cloing i he following: di i E () he curren expreion hrough he circui afer cloing i he oluion of he differenial equaion of he circui (). where: E i( ) (- e ) () (3) and i repreen he ime conan of he circui. he volage expreion on he coil afer connecion i: u ) di E e (4) (. SIMUINK model of he circui he SIMUINK model of he circui afer cloing wa done on ground of equaion () where he derivaive of he curren wa eparaed. di ( E - i) (5) he SIMUINK model obained in hi way i hown in Fig. and wa creaed in order o allow he drawing of he curren diagram hrough he circui and he volage on he coil, for differen value of he reiance and he E D.. volage. Sep 50 Add Produc / Inegraor du/ Derivaive Scope I Scope U Fig. SIMUINK model of he inducive circui a cloing he k wicher i realized uing a volage ep ignal which i applied a he erminal of he circui, o imulae he cloing of he k wicher. [] We will obain he diagram from Fig. and Fig.3. ISBN:

2 ecen Advance in ircui, Syem and Auomaic onrol u( ) E(- e ) (8) where, repreen he ime conan of he circui. he circui curren afer cloing i given by: i du E e (9) Fig. Variaion of he coil volage afer cloing. SIMUINK model of he circui he SIMUINK model of he circui afer cloing wa done on ground of equaion (7) where he volage derivaive wa eparaed. du ( E - u) (0) Add Sep Produc Inegraor Scope U du/ 500 Derivaive Produc Scope I Fig.3 Variaion of he circui curren -- Produc Divide. SUDY OF HE APAIIVE SEIES IUIS We will conider he erie circui wih concenraed parameer. A he iniial momen, he k circui wicher i cloed and we wan o udy he curren variaion hrough he circui and he capacior volage variaion, afer connecion. he inegral equaion which correpond o he raniory regime immediaely afer cloing i given by: Fig.4 SIMUINK model of he circui a cloing he k wicher i realized uing he ame volage ep ignal which i applied a he erminal of he circui, o imulae he cloing of he k wicher. he Simulink model from Fig.4 creae he diagram from Fig.5 and Fig.6. i i E (6) Equaion (6) i equivalen wih differenial equaion du u E (7) he expreion of he capacior volage afer cloing i he oluion of differenial equaion (7): Fig.5 he capacior volage variaion ISBN:

3 ecen Advance in ircui, Syem and Auomaic onrol r r i( ) e - e -0 (6) E (7) where r and r are he roo of he characeriic equaion: r - (8) r - - Fig.6 he curren variaion afer cloing We will conider he iuaion when δ <ω 0. he following noaion wa made: or 3. SUDY OF HE INDUIVE- APAIIVE SEIES IUIS We will conider he erie circui wih concenraed parameer. A he iniial momen, he k circui wicher i cloed and we inend o udy he behavior and variaion of circui elecrical parameer afer connecion. [5] he inegral-differenial equaion which correpond o he raniory regime of he conidered circui i he following: or: di i i E () d u du u he following noaion are made: he circui amorizaion: he circui peronal pulaion. E () (3) 0 (4) - 0 (5) We will conider he iuaion when 0 or, which will be checked by he reior in he circui. onequenly, he olving of he differenial equaion give he following oluion: 0 - ' (9) onequenly, he olving of he differenial equaion give he following oluion: where: r r u( ) E [- ( re - )] re u( ) E[- e in( ' ' )] (0) ' E - i( ) e in ' () ' ' arcco () 3. SIMUINK model of he circui he SIMUINK model of he circui afer cloing wa done on ground of he econd order differenial equaion (), which i pu in he form (3) where he higher order derivaive i eparaed: d u du [ E - - u] 0 (3) he SIMUINK model from Fig.7 generae he volage capacior and he curren hrough he circui during he raniory regime. o hi purpoe, wo value of he reior are conidered, which correpond o wo imporan regime: Aperiodic regime; Ocillaory regime. For each regime he capacior volage and he circui curren variaion diagram are ploed. ISBN:

4 ecen Advance in ircui, Syem and Auomaic onrol Sep Add -K- / Inegraor Inegraor ScopeU 500 du/ -- -K- du/ Derivaive ScopeI Fig. 7 SIMUINK model of he circui he SIMUINK model from Fig.7 lid o obain he following MAAB diagram, Fig. 8, Fig.9 according o he equaion (6) and (7) for a- periodic mode, and Fig.0, Fig. according o he equaion (0) and () for ocillaing mode. [] Fig. 0 he capacior volage variaion in he ocillaing regime Fig. 8 he volage capacior variaion in he a- periodic mode Fig. he curren variaion in he ocillaing regime he k wicher i realized by uing a volage ep ignal which i applied a he erminal of he circui, o imulae he cloing of he k wicher. hanging he value of reiance, auomaically lead o he updaing of he volage and curren char Fig. 9 he curren variaion in he a-periodic mode 3. Analyi of inducive-capaciive circui uing he SimPowerSyem ofware package he SimPowerSyem ofware package allow he udy of he circui behavior, when i i conneced o a volage ep or a uniary impule, uing oninou powerguy block. he curren variaion in he circui, he volage variaion of he capaciive elemen, or he frequency behavior of ISBN:

5 ecen Advance in ircui, Syem and Auomaic onrol he circui for differen value of circui elemen can be udied. he MAAB ofware package conain SimPowerSyem of Simulink, which can imulae he elecrical circui and analyze differen operaing regime. [3] Becaue he ignal ep repone or pule generae a raniory regime, he circui behavior in hee condiion can be udied. he imulaion i hown in Fig.. he advanage of hi imulaion mehod i ha he circui can be eed a boh ignal, uni ep and uniary impule, and lead o everal ype of ypical circui diagram. wo e of value were choen in hi cae for circui parameer, which correpond o wo pecial regime. In he imulaion model from Fig. we ued a onrolled Volage Source conrolled by a ep volage ignal. In hi way, he wicher cloing can be imulaed. he SimPowerSyem ofware package allow he obaining of a lo of diagram for a circui. So, we will udy he capacior volage diagram and curren diagram for he wo occurring regime: A-periodic regime: Ocillaing regime. - = 0 4 [ H], he circui inducance; - = 0 [nf], he circui capaciy. Fig.3 he capacior volage variaion in he a- periodic mode + Sep - onrolled Volage Source oninuou pow ergui i + - urren Meauremen Volage Meauremen Fig. SimPowerSyem model of he circui v + - ScopeI ScopeU Fig.4 he capacior volage variaion in he ocillaing regime he POWEGUY block permi he analyi and ploing of he frequency characeriic of he capacior volage, where he frequency in logarihmic coordinae wa conidered on he horizonal axi (BODE diagram). [4]. Volage capacior he a-periodic loading of he capacior lead o he obaining of he capacior volage variaion diagram when he uni ep and he uniary impule are applied o he inpu. hee char are preened below. he following value of elecrical parameer were conidered: For a-periodic regime: - E = 4 [V], he ep volage applied; - =,5 [kω], he elecrical circui reiance; - = 0 4 [ H], he circui inducance; - = 0 [nf], he circui capaciy. For ocillaing regime: - E = 4 [V], he ep volage applied; - = 0 [Ω], he elecrical circui reiance; Fig.5 Frequency diagram of he volage wing on he capaciive elemen. Sudy of circui curren o udy he circui curren variaion he ame procedure i ued. A-periodic loading of he capacior lead o obaining he curren variaion ISBN:

6 ecen Advance in ircui, Syem and Auomaic onrol diagram when he uni ep and he uniary impule are applied o he inpu. he a-periodical and ocillaing regime according o hee value are obained in he following char (Fig.6 and Fig.7): In he diagram from Fig.8 we can oberve a maximum of curren which correpond o a reonance regime. We can deermine he reonance frequencie for an inducive-capaciive circui uing he imulaion circui model and he SimPowerSyem ofware package. Wih POWEGUY block, oher elecrical circui parameer can be deermined. Fig.6 he curren variaion for ignal ep and impule in a-periodic mode Fig.7 he curren variaion for ignal ep and impule in he ocillaing regime he POWEGUY block allow he analyi and ploing of frequency curren characeriic, where he frequency in logarihmic coordinae wa conidered on he horizonal axi (BODE diagram). Fig.8 Frequency diagram of he curren wing hrough he circui 4. oncluion An imporan concluion of hi paper i ha he udy can be exended o ome more complex circui and hee can be udied wih hi modern mehod which involve he ue of virual medium. In order o realize he imulaing model which inegrae he differenial equaion, he baic idea i o eparae in he lef member of equaion, he higher order derivaive. he analyical expreion obained in he righ member of he equaion underlie he achievemen of he imulaing model by mean of pecific block of he virual medium. In he cae of complex circui, he imulaing model i conceived on a differenial equaion yem. eference: [] Arad, S., Arad, V., Avram,., Polluan Diperion imulaion uing Malab Sofware for emen Facory aial. Proc. of SWEMP00, DIGIA Univeriy of agliari, Prined in Ialia by Grafiche Ghiani, ISBN , pp , agliari, Ialia, 00. [] M. ahimo, A. Kopa, U. Schlapbach, J.Vobecky,. Schnell, S. Klaka,he Bi-mode Inulaed Gae ranior (BiG) A poenial echnology for higher power applicaion Proc. ISPSD09, June 009. [3] Dobra. Simulaion of dela modulaion yem uing ome analog filer deign, Annal of he Univeriy of Peroşani, omania, vol. 7, 005. [4] iberiu udorache Medii de calcul in ingineria elecrica MAAB,, Ediura Marixom, Bucurei 006. [5] Niculecu iu Sudy of inducive-capaciive circui uing he Simulink ofware package, ISBN , Hard cover, Publiher: Inech, Publihed: May 3, 0 under BY 3.0 licene, in ubjec echnology ISBN: