A Specialized Software Package Useful In The Analysis Of The Harmonic Current Flow In Networks With Large Power Static Converters

Transcription

1 SEECE OPICS in MHEMIC MEHOS and COMPUION ECHNIQUES in EECRIC ENGINEERING Speciaized Software Package Usefu In he naysis Of he Haronic Current Fow In Networks With arge Power Static Converters VIORE VRVR, MRCE ISRE* epartents of Eectrica Engineering Fundaentas and * Power Engineering echnica University Gheorghe sachi of Iasi Str.. I. Mangeron 23 Iasi, ROMNI viore_varvara@ee.tuiasi.ro, istrate@ee.tuiasi.ro bstract: - ogether with the wide use of the non-inear eeents in the eectrica circuits, the appearance of the non-sinusoida steady state is inevitaby. Presenty, we cannot speak about the avoidance of this probe and we ust find ethods to diinishing its negative effects. In point of iportance, the ain distorted oads in the eectrica networks are the arge power converters, the eectrica traction beonging to this category. In a rea running state, the eectrica network contains various circuit eeents whose behavior during the haronic steady state is difficut to be odeed, soe coputing sipifications being thus copusory. ue to the cuuative effect, these sipifications can ead to an incorrect interpretation of facts, both fro a quantitative and quaitative point of view. his is why it is recoended to use a speciaized software package that aows the anaysis of a copex eectrica network in a non-sinusoida state and which offers the possibiity of siuating different energetic situations in which the network can run at a certain oent. Key-Words: - power static converters, distorted steady state, haronics Introduction Fro the haronic point of view, for the study of an eectrica network we ust, first of a, ake sure that the configuration of the network and the haronic ipedances of the syste are known. For the fundaenta frequency, the paraeters of the network ay be considered as having practicay constant vaues, but with different frequencies their vaues odify. he siutaneous study of the non-syetrica and non-sinusoida states using the three-phase ode is difficut to achieve. hat is why in the anaysis of the non-sinusoida state it is recoended to use the singe-phase anaysis, by considering the network to be syetrica and by reducing it to a singe phase. he knowedge in detai of the network s structure, in different running states, aows the design of an exact coputing schee, avoiding thus the possibe errors that ight occur when sipified schees are used. nother requireent in the haronic studies of the eectrica networks is the knowedge of the frequency characteristic of the equivaent ipedance [], [2]. arge power converters [of MW order] represent the ain source of haronics in the power syste [], [2]. he eectrica raiway traction represents, at present, fro the haronic studies point of view, a non-inear concentrated oad. he haronic currents produced by it fow to the power syste, to the capacitor banks and to the other inear or non-inear oads connected to the network. In rea operating conditions, referring to a point of the network, if the haronic source is far away, it acts as an idea haronic votage generator and if it is cose it acts as an idea haronic current generator. 2 Software Package Presentation he study of the frequency characteristic of the ipedance seen fro the haronic generator bars, the behaviour of each of the network s branch that is passed by the haronic current and their contribution to the eventuay apifications of the votages, represent decisive eeents in haronic current fow contro in an eectrica network [], [2]. he raiway traction represents an eectrica oad variabe in tie, the oad variation being accopanied by a variation of the required power fro the network. n iportant characteristic of the tie evoution of the haronic states is that it is the sae for a ong period of tie (i.e. a year). In rea operation states, for a given point of the network, if ISSN: ISN:

2 SEECE OPICS in MHEMIC MEHOS and COMPUION ECHNIQUES in EECRIC ENGINEERING the haronic source is far away it works as an idea haronic votage generator and if it is cose, as a current one [3]. In the anayzed case, the eectrica equipent of the ocootive, the ain non-inear eeent of the circuit, is repaced with an idea haronic current generator, the other circuit s eeents being repaced with their haronic ipedances. he equivaent schee of the network that suppies the eectric traction, reduced to a singe phase is presented in Fig.. ~ I h G a I 27, kv I kv I I I I Equivaent receiver and equivaent capacitor bank Fig.- he equivaent singe-phase schee of a network that suppies the eectric traction 0 kv he foowing notations were used: - the syste ipedance seen fro the 0 kv bars; - the 0 kv ine ipedance which suppies the substation; - the ipedance of the suppying transforer 0/27. kv; - the ipedance of the transforer of the eectric ocootive 27./ kv; - the ipedance of the capacitor bank instaed on the eectric ocootive; - the ipedance of the inear equivaent oad suppied fro the sae 0 kv bars as the substation; - the ipedance of the equivaent power factor capacitor bank; I,,,,, - the haronic current that fows in each of the branches of the network. he haronic current on each of the network s branches, I, ay be estiated, depending on the haronic current injected by the haronic generator, I h, with the hep of soe copex quantities,, defined as foows: I I, (,,,, ) () h + + N, (2) N +, (3) N, +, (4) + +,, () + +,, (6) +. (7) + Here, represents the haronic current in reative units (r.u.) that fows in the branch; - the haronic current (r.u.) absorbed by the capacitor bank instaed on the branch; - the haronic current (r.u.) that fows to the and branches; - the haronic current (r.u.) that fows to syste; - the haronic current (r.u.) that fows in the branch (to the inear oad); - the haronic current (r.u.) absorbed by the equivaent power factor capacitor bank. hese quantities satisfy the foowing reations:, +,. (8) + + For the haronic anaysis of this kind of network, the authors iagined a software package that heps the coputation of the copex haronic ipedance of the network seen fro the 0 kv bars and of the copex haronic currents (r.u.) that fow in each branch of the network. he variation of the apparent power of the inear equivaent oad, of the equivaent reactive power instaed on 0 kv bars and of the required power of the non-sinusoida oad can siuate different energetic situations in which the network ay run. ISSN: ISN:

3 SEECE OPICS in MHEMIC MEHOS and COMPUION ECHNIQUES in EECRIC ENGINEERING he software ay run for the ipicit vaues assigned to the variabes or for the input data provided by the user as regards the foowings: - the genera paraeters of the syste, - the distribution ine and the paraeters of the raiway substation, - the transforers, - the capacitor banks. herefore, for a particuar network, the foowing data ust be provided: - the vaue of the three-phase short-circuit apparent power [MV] of the syste on the 0 kv bars (S k ) - ipicity 000; resistance of the syste (n ) - ipicity 0; - the ength of the 0 kv ine [k], () - ipicity ; - the resistance vaue on the unit ength of the distribution ine [Ω/k], (r 0 ) - ipicity 0.7; - the vaue of the votage at which the haronic generator is connected [kv], (U ) - ipicity 27.; - the short-circuit votage of the transforer fro the branch [%], (U sc ) - ipicity 0.; - the rated three-phase apparent power [MV] of the transforer fro the branch (transforer 0/27. kv), (S n ) - ipicity 6; - the tota active power osses of the transforer fro the branch [kw], (P k ) - ipicity 08; - the short-circuit votage of the transforer fro the branch [%], (U sc ) - ipicity 7; - the rated three-phase apparent power [MV] of the transforer fro the branch (transforer 27./ kv), (S n ) - ipicity 0; - the tota active power osses of the transforer fro the branch [kw], (P k ) - ipicity 8; - the initia vaue (ipicity E-0), fina vaue (ipicity 20) and the variation rate (ipicity 0.) for the reactive power [MVr] instaed on the branch, (Q ); resistance of the capacitor bank for the branch, (n ) - ipicity 000; - the initia vaue (ipicity E-0), fina vaue (ipicity 20) and the variation rate (ipicity 0.) for the reactive power [MVr] instaed on the branch, (Q ); resistance of the capacitor bank for the branch, (n ) - ipicity 000; - the initia vaue (ipicity ), fina vaue (ipicity 29) and the variation rate (ipicity 3) for the reactive power [MVr] required by the branch, (Q ); - the initia vaue (ipicity 0), fina vaue (ipicity 00) and the rate of variation (ipicity 0) for the active power [MW] deanded by the branch, (P ); - the initia vaue (ipicity 0), fina (ipicity 0) and the variation rate (ipicity 0) for the frequency, (f); - the r..s. vaue of the haronic current injected by the haronic generator, (I h ) ipicity. he situation when the power factor capacitor banks or those on the raiway engine are not connected is focused upon by assigning the E-0 vaue to Q, respective Q. he f, Q, Q, Q, P quantities are oop variabe. he user can obtain the running resuts of the software concerning the frequency vaue, the r..s vaues and the arguents of the copex equivaent ipedance and of the haronic current fro each of the branches. he software aows, through the chosen variation rate of the frequency, the deterination of those frequencies for which the equivaent ipedance at the generator bars takes extree vaues, with the possibiity of finding out in which conditions the series or parae resonances ay appear. In order to identify the extree vaues of each quantity, the software has been provided with a specia option. y using the Extree Option, the extree vaues can be deterined ore quicky. We ust however specify which quantity is anaysed (e,,,,,,.) with the oop variation of the f, Q, Q, Q, P quantities. When an extree vaue was found, five vaues are dispayed, two before and two after the critica point, together with the vaues taken by the frequency and by Q, Q, Q, P. he resuts of every running session of the software are dispayed in Microsoft Exce, where the faciities offered can be used. 3 Haronic State naysis Considering an eectrica network of a given structure and corresponding to a certain energetic situation, we can anayse the haronic variation of the equivaent ipedance seen fro the bars of the haronic generator and the infuence of different quantities upon it. For exape, Fig. 2 shows how the haronic current fows in different branches (the variation of the coefficients) versus the haronics order, for the situation in which the copensation of the reactive power is axiu, Q 2.7, Q 3.6 [ MVr]. In the studied haronic doain there take pace three resonances. he first is a parae one, ISSN: ISN:

4 SEECE OPICS in MHEMIC MEHOS and COMPUION ECHNIQUES in EECRIC ENGINEERING corresponding to the frequency f P, a series one corresponding to f S and again a parae one corresponding to f 2P. On each haronic, the currents are in phase or in opposition with the injected haronic current (Q 2.7, Q 3.6) Haronics order Fig.2 - he haronic currents fow in different branches (the variation of the coefficients) vs the haronics order for the situation in which the copensation of the reactive power is axiu For frequencies ower than f P ost of the haronic current fows to the syste and ess to the inear receiver ( > > > ). he quantities,,,, show the avaiabiity in receiving the haronic current of that branch, a high vaue eaning a high avaiabiity. he vaues on fundaenta are ow but have a high positive sope, a parae resonance being prepared. he phases of the quantities and are approxiatey the sae and are shifted 80 degrees in coparison with the phases of the quantities and. Corresponding to the f p frequency, the current that osciates between the inductive reactance of the syste and the capacitive reactance of the capacitor bank fro the kv bar is high because the current that corresponds to the haronic which order is cose to this frequency has an iportant aount. his current deterines an iportant distortion of the votage wave. he current that fows in the capacitor bank is.7 ties higher than the fundaenta current and can ead to the burn of the fusibe and to the disconnection of a part of the battery. hrough the 0/27, kv transforer fows a current whose vaue equas the current that fows through the capacitors connected at the kv bar. he distortion factor ay exceed the iposed requireents. If the oad of the transforer is high it works in the zone of non-inearity and it becoes a new source of haronic current. o the syste can fow an iportant haronic current because, corresponding to the parae resonance frequency, the absorption coefficient is of an iportant vaue. so, the votage wave distortions on this side ay be iportant. he batteries connected for power factor iproveent are ess subject to iportant haronic current fow as, for the first haronic parae resonance, the absorption coefficient of the haronic current is ow. he inear consuer is passed, for the first parae resonant frequency, by a sa haronic current and is ess affected by the appearance of this state. For frequencies f P < f < fs, the haronic current fow through the capacitors connected at the kv bar becoes prevaent ( > > > ); the coefficient takes vaues reativey iportant and can apify the ow-order odd haronics that fa within this frequency doain so that, the effective or peak vaue becoes dangerous for capacitors. coefficients prepare the eergence of a series resonance. he capacitor banks fro the branch and the inear have a descending sope and consuer are ess affected on this frequency range. he phase shift between (its arguent is about 80 degrees) and, and is aost 80 degrees. For the frequency corresponding to the series resonance, the capacitive reactance of the capacitors fro the kv bar and the network s equivaent inductive reactance seen fro the sae bar created a fiter for the current of the sae frequency. he coefficients of absorption of a sides,,,, take sa vaues, the ost iportant current passes through the capacitors fro kv bar. For the frequency f S,, and are parae (their arguents taking vaues around zero) and in opposition with (its arguent taking vaues around 80 degrees). For frequencies higher than f S, the avaiabiity in receiving the haronic current of the power ISSN: ISN:

5 SEECE OPICS in MHEMIC MEHOS and COMPUION ECHNIQUES in EECRIC ENGINEERING factor iproveent capacitor branch, of the syste and of the inear receiver increase and of the branch which contains capacitors connected at the kv bar decreases. fter a certain frequency, and doinant, being sa. becoe he inear consuer absorbs the owest haronic current. he phase shift between,, and, is approxiatey zero (their arguents taking vaues cose to 0 degrees) and is 80 degrees regarding. Since the avaiabiity in receiving the haronic current of each side do not reach significant eves and the currents corresponding to these frequencies are sa, for this frequency doain phenoena are not expected to deviate fro nora functioning. For the second parae resonance, between the reactance of the capacitors connected to iprove the power factor and the inductive reactance of the syste (in particuar) is estabished an energy osciation. he coefficient does not pose an extree on this frequency, has a axiu (of a vaue ower than that corresponding to the first parae resonance), and have axius (with upper vaues than those corresponding to the first parae resonance). When resonance occurs, arg, arg, arg are in the first quadrant (vaues around zero) and in opposition with arg which has vaues around 80 degrees. Fro a sides, the syste is affected ost by the appearance of this resonance observing that the coefficient is big. ut, because the haronic current corresponding to this frequency is sa, no particuar probes are expected he operating state is characterized by: - the capacitors fro the kv bar: because of the big current, the fuse can burn and a part of the battery is disconnected; so, the parae resonant frequency decreases; - the transforer fro the traction substation: operating at a big oad, the votage distortion factor exceeds the axiu required by reguations; - syste: athough the haronic current that fows through the syste is the ost iportant as weight, because the short-circuit power at the bars is big, the operation does not deviate fro the nora range; - for the power factor capacitors: even if the second parae resonance is fet significant by this side, because it takes pace on a high frequency it doesn t cause a significant increase of the current; the operation is registering as nora; - the inear consuer: regardess the aount of the apparent power requested, the inear consuer is east affected by the existence of the distorting state. 4 Concusion he proposed software aows a copex anaysis of the distribution networks that suppy a concentrated non-inear oad running in a nonsinusoida steady state. It can be usefu in the survey of the behavior of the networks where deforing eeents of circuit are connected. With the hep of the oop variabe quantities, different energetic situations in which a copex network ay run at a given oent, can be siuated. he resuts ay be usefu in the design process for the estabishent of the ocation where the raiway substations ust be connected to the power syste or in the anageent process of the distribution networks, by identifying, in iposed situations, concrete soutions of running. References: [] rie.., Neguş C., Goovanov C., Goovanov N. Haronic Poution in Power Systes Operating in Syetrica Steady State, Ed. cad., ucureşti, 994. [2] rriaga J. Power Syste Haronics, Wiey & Sons, New York, 98 [3] rriaga. Coputer Modeing of Eectrica Power Systes, Wiey & Sons; New York,992 [4] Rosan H., Savin Gh., inear Eectric Circuits Inst. Poit., Iaşi, 974. [] Georgescu G., Istrate M., Varvara V., Eectric Power ransission and istribution, vo II, Ed. Venus, Iasi 200. [6] Varvara V., Cârţină Gh. Signas, Circuits and Networks in Nonsinusoida Steady State, Ed. Venus, Iaşi, 200. [7] Varvara V., Georgescu Gh., he Manifestation of the istorted State in Eectrica Power Suppy Systes, u. Inst. Poit Iasi, o V (IX) fasc.2, 2009, pp 9-0. [8] Varvara V. Georgescu Gh., he istorting State in Pubic istribution Systes and its epora Evoution, Energy echnoogies, /2009, pp.0-7. ISSN: ISN: