Guide for electrical design engineers Power Quality Grzegorz TKACZEWSKI & Artur KOS AGH-University of Science & Technology STATIC FC/TCR COMPENSATOR FOR ARC FURNACE COMPENSATION Power Quality

Power Quality www.leonardo-energy.org 1. INTRODUCTION Industrial facilities are source of major disturbances to power system due to mo re and more large power loads being installed that, apart of their good function al properties, are characterized by negative impact on the quality of power. Suc h loads are the cause of the supply voltage distortion, unbalance and fluctuatio ns. Depending on the load type, such disturbances may occur separately or concur rently. These disturbances are propagated through distribution systems to other users' networks, impair operating conditions of equipment and, in extreme cases, prevent operation of electrical equipment sensitive to such disturbances. Among industrial loads, having the most adverse impact on a power system due to the e mitted disturbances, are steelworks electric arc furnaces. They cause mainly: unbalance of currents and voltages, current and voltage distortion, fluctuations of active and reactive power, supply voltage fluctuations and flicker [6]. The adverse impact of non-linear loads on a power system can be mitigated by mea ns of compensation equipment like fixed capacitor (FC), thyristor controlled rea ctor (TCR) - FC/TCR. The purpose of FC/TCR compensator is compensation of the fu ndamental component reactive power and filtering selected current harmonics. Suc h compensator is an example of the indirect compensation method in which, depend ing on the needs of the voltage restorer or the reactive power compensator funct ion, the value of the sum of two current components is controlled: fundamental h armonic of the capacitor current iFC, operated mostly as high harmonics filter(s ) (the FC section) fundamental harmonic of the reactor current iTCR controlled b y means of a phase-controlled thyristor AC switch (the TCR section) [8]. 2

Static FC/TCR Compensator for Arc Furnace Compensation www.leonardo-energy.org 2. FC/TCR COMPENSATOR Fig. 1. Diagram of the static VAR compensator comprising a fixed capacitor bank and reactors whose reactive currents are controlled by means of thyristor AC swi tches Fig. 2. Diagram of the three-phase static compensator with a phase-controlled re actor section The FC/TCR compensator consists of a fixed capacitor bank divided into several t hree-phase sections incorporating reactors, utilized also as high-order current harmonics filters, and parallel reactors whose fundamental current harmonic is c ontrolled means of thyristor AC switches. The reactors' current can be controlle d in a continuous manner from zero, if the switch is turned off, to its maximum value, when the reactor is directly connected to the source. The compensator sch ematic diagram is shown in figure 1. The capacitor banks generate capacitive rea ctive current of non-controlled value, whereas the reactor section (TCR) current is controlled within the range from zero to the current of a reactor being conn ected directly to the source. The reactive current fundamental harmonic of such compensator is: ik = -iC + iL where: iC the fundamental harmonic of the capacito r bank current (noncontrolled value) iL the fundamental harmonic of the inductiv e unit current (controlled value) ik the fundamental harmonic of the compensator current. Under symmetrical control conditions and balanced circuit parameters ( the same phase reactances and equal thyristors' control angles) the 3-rd harmoni c and its multiples do not occur. 3 (1)

Power Quality www.leonardo-energy.org The compensator enables continuous control of reactive current over the range fr om -Ic to -Ic + IL. Maximum voltage across the AC switches' thyristors does not exceed the amplitude of the phase-to-phase voltage of a power system, i.e. it is more than two times smaller than the voltage across the thyristors switching th e capacitor bank sections. The phase current of FC-TCR reactor section is times larger than the thyristor switches (reactors') currents [2]. The three-phase com pensator circuit is shown in figure 2. The compensator comprises delta connected , fixed inductance reactors (L/2) whose current fundamental harmonic is controll ed by the phase control of thyristor AC switches (ST) in each delta branch. AC s witches are controlled by the control system in order to control either the supp ly voltage (voltage restores) or to compensate the load reactive current, depend ing on the compensation system purpose. Optimum utilization of the applied thyri stors is often provided by a step-down transformer (Tr) with the leakage reactan ce higher than in typical applications, hence the reactors' reactance can be red uced (in the extreme case to zero). The delta connection of reactors is justifie d in both technical and economic terms. The presented configuration allows reduc ing the thyristors' current ratings and considerably reduces the supply current harmonic content as compared to a star -connected circuit of the same power. Thu s, the compensator voltage-current characteristic encompasses the area of induct ive and capacitive loadings within boundaries determined by the capacitor bank a nd reactors' powers. It should be emphasized that the compensator is a source of odd harmonics and, if the control angles of antiparallel connected thyristors a re unequal, even harmonics also occur. Triplen harmonics in the compensator curr ent are cancelled by delta connection of reactor branches. Odd harmonics can be mitigated by means of two 6-pulse circuits supplied from a three-winding Yyd tra nsformer with 30 phase shift between the secondary side voltages, or by the use o f suitable filters [10]. 3 3. HIGH-ORDER HARMONICS FILTERS Passive filtering of high harmonic consists in connecting in parallel with the l oad generating a given harmonic, a series LC circuit whose series resonant frequ ency is tuned to the filtered harmonic frequency (Fig. 3). 4

Static FC/TCR Compensator for Arc Furnace Compensation www.leonardo-energy.org Fig. 3. Schematic diagram of the supply network, a non-linear load represented b y a current source, and the high-harmonic filter; CF, LF, RF the filter capacita nce, inductance and resistance, respectively The inductive and capacitive reacta nces of LC series filter are subtracting one from the other. For the series reso nance frequency their absolute values are equal and their difference is zero. Th us, at this specific frequency, the filter is practically a short circuit. The r emaining equivalent resistance, mainly that of the reactor winding, is very smal l. The reactance of the filter LC components connected in series is: 2 X h 2 F X 1 X F (h ) = X L (h ) X C (h ) = hX L C = X C h L = X C 2h X h h harmo ic order, F Xc XL

the filter atural relative freque cy , reacta ce of the filter capacitor for th e fu dame tal harmo ic, reacta ce of the filter reactor for the fu dame tal harm o ic. As follows from the relatio (2), the filter reacta ce is ear to zero for the h armo ic h, whose freque cy is close to the filter atural relative freque cy F. I co seque ce of co ecti g the filter betwee the source phases the curre t w ith the freque cy close to the filter atural freque cy, ge erated by a o li e ar load, flows through the filter thereby reduci g the harmo ic curre t flow thr ough the source. The filter reacta ce for h> F is i ductive, whereas for h< F it is capacitive. Si ce for the fu dame tal harmo ic the filter has a capacitive c haracter, it is used for reactive power compe satio [2,3]. 3.1. Pri ciples of passive filters desig The basic data ecessary for the filter desig are: data co cer i g the source o f high harmo ics, i.e. amplitude freque cy spectrum of the o li ear load, the fu dame tal harmo ic reactive power required for the compe satio purposes, etc. data co cer i g the power supply etwork, i.e. freque cy characteristic of the power system impeda ce at the poi t of commo co ectio (PCC) or, i the abse c e of such characteristic, the short circuit capacity together with the schematic diagram a d tech ical specificatio of eighbourhood of the co sidered poi t of the filter co ectio , the spectrum of i itial voltage distortio at the co sid ered poi t, permissible voltage harmo ic distortio factor THD as per co ditio s of supply, a d harmo ic co te t (p.u.) etc. 5

Power Quality www.leo ardo e ergy.org data co cer i g the filter, i.e. the locatio of its i stallatio , the selected structure, tech ical specificatio s of passive eleme ts to be used, etc. [7]. All further co sideratio s are carried out u der the followi g simplifyi g assum ptio s: the source of high harmo ics is a ideal curre t source, the filter resi sta ce RF, i ducta ce LF a d capacita ce CF, are lumped eleme ts a d their value s are co sta t over the co sidered freque cy i terval, the filter is exclusively loaded with the fu dame tal harmo ic a d the harmo ic to which it is tu ed. The filter etwork load equivale t circuit diagram is show i figure 3. The power supply etwork is represe ted by the ideal AC voltage source a d the equivale t resista ce a d i ducta ce: X S = 1 .1 U 2 S SC Ls = 1 .1 U 2 1 S SC 100 R S = 0 .1 X S (3) where: SSC is the su ly network short-circuit ca acity, U is hase-to- hase vol tage at the oint of connection. The load is re resented by the source high-harm onic currents and the load im edance Zo. The ur ose of the filter is: com ensat ion of the load fundamental harmonic reactive ower, mitigation of high-harmonic s emitted by the load to the ower system [4]. 3.2. Single branch filters The single branch filter is a sim le structure which can easily be analyzed. In this section a matrix method for designing a grou of single-frequency filters i s used. The diagram of the single-frequency filter and its frequency-im edance c haracteristic are shown in figure 4 [4]. Assuming RF = 0, the im edance at the f iltered frequency is 0 (this assum tion will hold true in further considerations ): Z F ( r ) = j r LF j 1 = 0 r = nr * 1 = r CF 1 LF C F 6

Static FC/TCR Compensator for Arc Furnace Compensation .leonardo energy.org LF = 1 1 = 2 2 C F n r 1 C F 2 r (4)

here: Nr r = nr * 1 1

L F C F 1 1 = j = j Z F ( r ) = jLF j C F C F 2 2 1 n 12 C F C F 2 r C F 1 = j 2 n r2 r2 n r2 r2 C F (5) 1 n r212 2 Z F ( r ) = j C F n r2 r2 (6) Fig. 4. The single frequency filter diagram and its frequency impedance characte ristics for RF 0, Xc the filter capacitive reactance, XL the filter inductive r eactance, ZF the filter impedance, IF the filter current, U the filter operating voltage 7

For the harmonic

ith angular frequency :

the resonant frequency order angular frequency of the filter series branch the fundamental harmonic angular frequency ().

Po er Quality .leonardo energy.org = k * 1 , k=1 filter tuned to the fundamental harmonic. Z F ( r ) = j 12 nr212 1 n2 = j 2 r nr212 C F 1 nr C F 1 , (7)

At the fundamental angular frequency the imaginary part of the filter impedance is directly proportional to the filter operating voltage and inversely proportio nal to reactive po er to be compensated: 2 UN Im(Z F ( n ) ) = j Q , (8) j j 2 N U 1 n 1 = j 2 * Q C F 1 nr 2 N 2 r 2 r , CF = n r2 1 Q * 2 nr 1U 2 N (9) U n 1 1 =j 2 * Q C F 1 nr , (10) Q the load's reactive po er to be compensated. The capacitance and inductance v alues in given branches are computed from relations: n r2 1 1 Q F C i = 1 U N 2 n r2 1 L = 1 = i 2 2 r C i n r 12 C i (11) 8

Static FC/TCR Compensator for Arc Furnace Compensation .leonardo energy.org 4. AN EXAMPLE OF FC/TCR COMPENSATOR DESIGN Fig. 5. Diagram of the net ork supplying a non linear load an arc furnace, to be compensated using the FC/TCR compensator

4.1. Determining the compensation po er value In order to determine the compensator po er shall be kno n the economically just ified (specified in a contract ith utility company) po er factor at the given p oint of a po er system as specified by the utility company. In the general case the capacitor bank po er is determined from the formula: Qk = P tg 1 tg 2 , here: Qk reactive po er to be installed, P the load(s) active po er,

(12) tg 1 tg 2 po er factor prior to compensation, po er factor after compensation. The capacitor bank design and sizing should take into account problems that may occur during the system operation due to the presence of high order harmonics an d resonance effects. Detuning from resonance is achieved using an antiresonance reactor connected in series ith capacitor bank. The antiresonance reactor is us ed hen the voltage distortion level is ithin 9

Po er Quality .leonardo energy.org

acceptable limits, the capacitor bank shall also be protected against overloadin g ith high harmonic currents. An inadequate selection of the capacitor bank par ameters, as ell as the cooperating reactors, may lead to capacitor damages due to overvoltages and overcurrents and, consequently, preclude operation of the co mpensation system [1,9]. Short circuit capacity of the 110kV net ork is SSC110kV = 500 [MVA] Short circuit capacity of the 6kV net ork is SSC6kV = 16.9 [MVA] Tr ansformer rated po er STr = 20 [MVA] Transformer short circuit voltage uz% = 13. 5 Maximum averaged consumed active po er: 10.13 [MW] Maximum averaged consumed r eactive po er: 13.54 [MVAr] Apparent po er: SP = 2 PP2 + Q P = 16 . 91[ MVA ] (13) The arc furnace load current: I obc = SP 16,91 * 106 = = 1626.9[ A] 3 *U N 3 * 6000 (14) Hence the po er factor: tg = Q P P P = 1.34 (15) Required po er factor: tg dyr = 0.3 (16) Required compensation po er: Qkomp = P (tg tg dyr ) = 10.5 [MVAr] (17) It is assumed that reactive po er that should be compensated ill increase up to 11 [MVAr]. The transformer reactance: 10

Static FC/TCR Compensator for Arc Furnace Compensation .leonardo energy.org X Tr 2 u z % * U N = 0.24[] = 100 * S Trt (18) The net ork short circuit reactance is: 0.35 []

4.2. Determining the voltage distortion factor prior to compensation a) At the 6 kV side Harmonic currents In measured at the 6 kV side during the arc furnace operation as the only load in the po er net ork, are listed in table 1. The voltage distor tion factor THD at the 6kV busbars ithout the compensation circuit is calculate d using the formula: THDU = (U ) 13 2 N% 2 (19)

U n % = 3 * I n * n * X z ( 6 kV ) * 100 UN (20)

X z ( 6 kV ) = X S + X Tr =0.59 [] (21) Table 1. Harmonic current values and corresponding harmonic voltage content Harmonic order 1 2 3 4 5 6 7 8 9 10 11 12 13 Harmonic current In [A] 1626.9 21.93 32.55 9.30 38.73 8.83 7.85 5.95 4.60 2.88 4.03 1.15 2.30 Voltage harmonic content [%] 1.49 3.32 1.27 6.59 1.80 1.87 1.62 1.41 0.98 1.51 0.47 1.02 THDU6kV= 8,61%, THDdop6kV = 5% [11] 11

here: In In harmonic current, n harmonic order, XZW(6kV) nce at the 6kV side, UN voltage at busbars (6kV)

here: UN%

the percentage voltage harmonic content of the given harmonic.

the net ork reacta

Po er Quality .leonardo energy.org THDU6kV > THDdop6kV The above inequality sho s the necessity of high harmonics compensation.

(22) b) At the 110kV side The voltage distortion factor is determined from relation (19), but the percenta ge voltage harmonic content for the given harmonic UN% is calculated form anothe r formula: U N % = 1.1 * bN % * n * S10 max S SC (23) here: bn% percentage content of the harmonic of order n in a nonlinear load c urrent; it depends on the load type, the factor values are listed in table 2., n harmonic order, SSC short circuit capacity (500 MVA), S10max maximum 10 mi nute apparent po er of a nonlinear load, equal to the arc furnace maximum po er calculated from the formula (13). Table 2. The percentage content b% of the nth harmonic in the arc furnace current versus the transformer nominal po er Furnace transformer rated po er i Harmonic order 2 % 36 26 26 16 7 3 % 25 20 13 18 10 4 % 8 5 4 6 4 5 % 10 7 5 8 5 6 % 4 2 1 3 1 7 % 3 MVA 2.5 5 10 16 50 3 2 3 2 9 % 2 2 1 2 2 11 % 1 1 1 1 1 13 25 % 0 0 0 0 0 Table 3. Harmonic current values and corresponding harmonic voltage content Harmonic order 2 3 4 5 6 7 9 10 13 bn [%] Voltage harmonic content [%] 1.19 2.01 0.89 1.49 0.67 0.78 0.67 0.41 0.00 16 18 6 8 3 3 2 1 0 12

Static FC/TCR Compensator for Arc Furnace Compensation .leonardo energy.org THDU110kV= 3.18%, THDdop110kV = 1.5% [11] THDU110kV > THDdop110kV (24) The above inequality also sho s the necessity for high harmonics compensation.

4.3. Guidelines for sizing high harmonics filters In the analysed example the static compensator and passive filters section shall operate under the follo ing conditions: the arc furnace is supplied from a 110/6 kV transformer voltage distortion facto r THDU at the point of common connection at 110kV busbars should not exceed 1.5% reactive po er to be compensated is 11 MVAr dominant harmonic currents at 6kV bu sbars are the 3 rd and 5 th harmonic currents (32.55A for the 3 rd harmonic and 38.73A for the 5 th harmonic, respect ively) the FC/TCR compensator ill be connected at 6kV. 4.4 Selecting high harmonics filters parameters Initial design data are: the po er net ork nominal voltage Us maximum reactive po er the filter can injec t into the po er system. The capacitor bank rated po er depends on: maximum magnitude of the filtered current harmonic capacitor overload current (a s specified by the manufacturer) capacitor voltage utilization factor, expressed by the formula (25) [5]: ku = US 3U Nbat (25) here: US is the supply net ork voltage, UNbat is the capacitor bank rated volta ge. In order to reduce THD factor to the required level, the harmonic of the lar gest magnitude shall be filtered out hile reactive po er consumed by the arc fu rnace shall be compensated. 4.4.1. Determining the required po er of the 5 th ha rmonic filter a) The required compensation po er has been allocated bet een the fitter braches proportionally to the values of eliminated harmonic currents: 13

Po er Quality .leonardo energy.org Qkomp = 11 [Mvar] the 5 th harmonic current is: I5 = 38.8 [A] b) Due to series c onnection of the resonance reactor and capacitor bank the voltage across capacit ors ill be knf times higher than the busbars voltage: k nf here: nF harmonic order. The voltage rise is (table 4): 2 nF = 2 nF 1 (26) For the 5 th harmonic knf = 52 = 1.042 52 1 (27) Table 4. The knf factor value of the nth harmonic order. nF knf 2 1.333 3 1.125 4 1.067 5 1.042 7 1.021 11 1.008

c) The nominal voltage of the filter capacitor bank shall satisfy the relation: UNbat.F5 1.042* 6 *1.1= 6.88 kV The value1.1 results from po er net ork voltage variations +/ 10% UN (11) d) Considering the above requirements the capacitor ba nk of "Y" company make, ith the follo ing parameters has been selected: Rated r eactive po er... Rated current. Rated voltage 12] 1.1 Un [12] (28) 14

Static FC/TCR Compensator for Arc Furnace Compensation .leonardo energy.org e) Since the reactive po er delivered by the 5 th harmonic filter is expressed b y formula (29) [2]: QUz 5 U = Q NbatF 5 S U CN = Q NbatF 5 (k u )2 2 (29)

where: QUz5 the reactive power i jected by capacitor to power system, QNbatF5th e capacitor rated power, US power etwork voltage, UCN capacitor ba k voltage, kU capacitor voltage utilizatio factor. Thus, the rated power of the 5 th har mo ic filter capacitor ba k is: QNbatF 5 U = QUz 5 CN U S 7600 = 11 * 106 = 17.65[ M var] 6000 2 2 (30) 4.4.2. The reactor sizi g [5] From the co ditio X DF 3 = X bat (31) where: SR the series reso a ce freque cy. a) The required reacta ce of reactor i s determi ed: 2 U NbatF 5 7600 = = 3.27[] QNbatF 5 17.65 * 106 X NbatF 5 = X DF 3 = LDF 3 = (32) X bat 3.04 = = 0.13[] (33) 1 = 0.12 = 0.41[ mH ] 314 (34) for series reso a ce:

2 SR

2 SR 25 X DF 3

b) For the filter detu ed from reso a ce below rsz the i ducta ce values will b e 15

Power Quality www.leo ardo e ergy.org larger. For the series reso a t freque cy order equal 4.5 the i ducta ce will be : LDF 4,5 = LDF 5 52 = 0.52[mH ] 4.52 (35) Whereas for the series reso a t freque cy order equal 4.7 the i ducta ce will be : LDF 4, 7 52 = LDF 5 = 0.47[mH ] 4.7 2 (36) For both filters have bee selected special desig reactors of "Z" compa y make, with i ducta ce values calculated as above a d 2% i ducta ce toleratio . The re actors are provided with taps that allow matchi g their i ducta ce to 4.5 or 4.7 detu i g. 4.4.3. Filter co figuratio for si gle curre t harmo ic Capacitor ba ks are co ected i a double star co figuratio with star poi ts co ected. I s uch co figuratio a malfu ctio (short circuit) of a si gle does ot cause sig i fica t i crease i phase curre ts. The desig ed topology allows for a simple a d cheap protectio agai st the battery i ter al failures, or capacity cha ges due to i ter al short circuits, by measuri g the curre t i the co ductor co ecti g star poi ts usi g a curre t tra sformer. Fig. 6. Diagram of the si gle curre t harmo ic filter comprisi g reactors, capac itor ba k divided i to two sectio s a d symmetry co trol by mea s of measuri g t he equalizi g curre t I betwee eutral poi ts of both sectio s 16

Static FC/TCR Compe sator for Arc Fur ace Compe satio www.leo ardo e ergy.org

4.4.4. Simulatio tests of the desig ed filter The freque cy impeda ce character istics for the desig ed filter were determi ed usi g the Matlab software package . a) For series reso a t freque cy order 4.7 charts 1, 2 a d 3 10 9 8 7 Z(w [Ohm] ) 6 5 4 3 2 1 0 0 100 200 300 400 f [Hz] 500 600 700 Chart 1. Freque cy impeda ce characteristics of the supply etwork (blue) a d th e 5 th harmo ic filteri g bra ch (red); each characteristic determi ed i dividua lly 5 4.5 4 3.5 Z(w) [Ohm] 3 2.5 2 1.5 1 0.5 0 0 100 200 300 400 f [Hz] 500 600 700 Chart 2. Freque cy impeda ce characteristics of the supply etwork (blue) a d th e 5 th harmo ic filteri g bra ch (gree ) a d the equivale t impeda ce (red) 17

Power Quality www.leo ardo e ergy.org 10 9 8 7 Z( )/Z(wo) 6 5 4 3 2 1 0 0 100 200 300 400 f [Hz] 500 600 700 Chart 3. Freque cy characteristic of the supply etwork a d the filter equivale t impeda ce related to the equivale t impeda ce at f=50Hz b) For series reso a t freque cy order 4.5 charts 4, 5 a d 6 10 9 8 7 Z(w) [Ohm] 6 5 4 3 2 1 0 0 100 200 300 400 f [Hz] 500 600 700 Chart 4. Freque cy impeda ce characteristics of the supply etwork (blue) a d th e 5 th harmo ic filteri g bra ch (red); each characteristic determi ed i dividua lly 18

Static FC/TCR Compe sator for Arc Fur ace Compe satio www.leo ardo e ergy.org

5 4.5 4 3.5 Z(w) [Ohm] 3 2.5 2 1.5 1 0.5 0 0 100 200 300 400 f [Hz] 500 600 700 Chart 5. Freque cy impeda ce characteristics of the supply etwork (blue) a d th e 5 th harmo ic filteri g bra ch (gree ) a d the equivale t impeda ce (red) 10 9 8 7 6 5 4 3 2 1 0 0 100 200 300 400 f [Hz] 500 600 700 Chart 6. Freque cy characteristic of the supply etwork a d the filter equivale t impeda ce related to the equivale t impeda ce at f=50Hz 19 Z( )/Z(wo)

Power Quality www.leo ardo e ergy.org 4.4.5. Parallel reso a ce calculatio s The equivale t impeda ce of the desig ed th harmo ic filter with equivale t circuit as i figure 7: Fig. 7. The equivale t circuit of the source a d the parallel filter for a si gl e harmo ic The equivale t impeda ce of the above circuit is expressed by the for mula: Z z ( ) = 2 X d X c 2 ( X tr + X d ) X c ; it is expressed by the relatio :

X tr

( ) (37) Parallel reso a ce occurs whe

Z

2 ( X Tr X d ) X c = 0

(38)

r =

Xc X tr + X d (39) The 5 th harmo ic filter parallel reso a ce relative freque cy is: for detu i g degree equal 4.5: for detu i g degree equal 4.7: 2.82 2.11 4.4.6. Verificatio of the 5 th harmo ic capacitor ba k for overload curre t The filter power (the capacitor ba k a d reactor co ected i series) is: Q ' NF 5 (U N )2 = (6000)2 = X Z (1) 2.92 = 11.46MVar (40) 20

Static FC/TCR Compe sator for Arc Fur ace Compe satio www.leo ardo e ergy.org a d:

X Z (1) = X DF 5(1) + X NbatF 5(1) = 3.14[] where: XdF5(1) the reactor reacta ce at the freque cy of 50 Hz, XbatF5(1) the capacitor reacta ce at the freque cy of 50 Hz The rated curre t of the 5 th harm o ic capacitor battery [5] is: (41) I Nbat , F 5 = ' QNF 5 12,34 * 106 = = 870.46[ A] 3 * U Nbat 3 * 7600 (42) I order to verify the 5 th harmo ic capacitor battery for the overload curre t co ditio , it has bee assumed that both the fu dame tal harmo ic a d the filter ed harmo ic curre ts flow i the filter. The curre t i the 5 th harmo ic filter i g bra ch is calculated from the formula: 2 I batF = I 12 + I (43) The followi g co ditio shall be verified to preve t the capacitors curre t over load: 2 I = ki I p 2 b 2 k u2 I Nbat . F where: (44) b capacitors' maximum voltage overload factor, p capacitors' maximum curre t o verload factor ( 1.1) [12] ku capacitors' voltage utilizatio factor, formula (25 ) I the filtered th harmo ic curre t. The capacitors' curre t utilizatio f actor ki is: ki = 1 p ku2 2 (45) The overload factor p determi es maximum curre t overload of a capacitor (for ca pacitors used i filters its value is 1.5 [12]). It is assumed that filter bra c h for the give harmo ic is loaded with this harmo ic curre t a d, additio ally, with small curre ts of other o filtered harmo ics. Their i flue ce is take i to accou t by reduci g the p2 value i a ma er i dicated i table 5:

21

Power Quality www.leo ardo e ergy.org Table 5. Overload factor High order harmo ics take i to accou t High order harmo ics ot take i to accou t p=1.3 1.6 1.69 (1.5) 2.16 2.25 I the case of co sidered 5 th harmo ic filter the curre t will be: I1 5 = ku I Nbat .F 5 = 0.789 * 870.46 = 687.20[ A] (46) ku = where: 6000 US = = 0.789 3U Nbat 7600 (47) (48) 2 I batF 5 = I12 5 + I ki = 1 p 2 ku2 = 0.784 (49) (45) ki I batF 3 = 0.784 * 688.29 = 539.65 [A] Thus, the relatio : 870.46 [ A] 2 I = 539.65[A] p 2 b 2 k u2 (51) I Nbat . F is satisfied. 2 I = k i I batF 5 p 2 b 2 k u2 (52) 4.4.7. Verificatio of THDU value Total harmo ic voltage distortio factor THDU is expressed by the formula: THDU = U Uf 2 ( ) (53) 22

= 687.202 + 38.82 = 688.29[A]

Static FC/TCR Compe sator for Arc Fur ace Compe satio www.leo ardo e ergy.org where: U Uf = 3 U ( ) = I ( ) Z ( ) UN= 6kV, Z( ) from the formula (37). (54) (55)

Table 6. Harmo ic co te t a d total harmo ic voltage distortio factor THDU Curre t harmo ic order 2 3 4 5 6 7 8 9 10 11 12 13 THDU U for detu i g 4.7 209.35 36.92 2.56 3.58 3.04 4.33 4.36 4.15 3.05 4.89 1.57 3. 48 6.15 U for detu i g 4.5 241.31 33.38 1.90 6.23 3.68 4.94 4.87 4.58 3.34 5.33 1.71 3. 77 7.04 As see from table 6, the voltage distortio factor was reduced but its value st ill exceeds the required level 6.15%. THDUF5= 6.15%, THDdop6kV = 5% [11], THDU6k V > THDdop6kV. It is thus ecessary to desig from the begi i g a compe sator t hat elimi ates more tha o e harmo ic, comprisi g a larger umber of bra ches. 4.5. Selectio of compo e ts for the 3 rd a d 5 th harmo ic filters 4.5.1 Determi i g the required filter power a) The required compe satio power has bee allocated betwee the fitter braches proportio ally to the values of elimi ated harmo ic curre ts: 23

Power Quality www.leo ardo e ergy.org Qkomp = QuzF3 + QuzF5 = 11 Mvar I3 = 32.5 A I5 = 38.8 A I3 + I5 =131.4 A (56) Quz 3 = I3 Qkomp = 4.8[ MVar ] I5 + I3 I5 Qkomp = 5.71[ MVar ] I5 + I3 (57) QuzF 3 = (58) b) The voltage rise is: for the 3 rd harmonic ku = ku = 32 = 1.125 32 1 52 = 1.042 52 1 (59) for the 5 th harmonic (60) c) The nominal voltages of filters capacitor banks ill satisfy the relation: for the 3 rd harmonic UNbat.F3 1.125*6*1.1 = 7.43 [kV] for the 5 th harmonic UNb at.F3 1.042* 6 *1.1= 6.88 [kV] (61) (62)

The value1.1 results from the assumed po er net ork voltage possible rise by 10% [11]. d) Considering the above requirements the capacitor bank of "Y" company m ake ith follo ing parameters has been selected: Rated reactive po er .......... ............................................................... 9 MVar Rated cur rent ........................................................................... ........... 1000 A Rated voltage...7800 V Capacitance .............. ..................................... 21.3 uF Capacitance tolerance ............ .................................................. 5/+10 % [12] Current overloa d ............................................................................. 1.5 In [12] Voltage overload (Voltage overload factor) ......................... ...........1.1 Un [12] e) The required po ers of the 3 rd and 5 th harmonic filters are expressed by fo rmulas [2]: QUz 3 U = Q NbatF 3 S U CN

= Q NbatF 3 (k u )2 24 2 (63)

Static FC/TCR Compe sator for Arc Fur ace Compe satio www.leo ardo e ergy.org QUz 5 U = Q NbatF 5 S U CN = Q NbatF 5 (k u )2 2 (64) He ce rated powers of capacitor ba ks are: QNbatF 3 U = QUz 3 CN U S U = QUz 5 CN U S

7600 = 4.80 * 106 = 7.70[ M var] 6000 2 2 (65) QNbatF 5 7600 = 5.71 * 106 = 9.16[ M var] 6000 2 2 (66) 4.5.2 Sizi g the reactors [5] From the co ditio X DF 3 = X bat (67) where: SR the series reso a ce freque cy, a) The required reacta ce of the reac tor has bee determi ed: for the 3 rd harmo ic filter 2 U NbatF 3 = = 7.51[] QNbatF 3 X NbatF 3 X DF 3 = LDF 3 = (55) (56) X bat = 0.83[] 1 = 2.66[mH ] for series reso a ce:

2 SR

2 SR X DF 3

(57) for the 5 th harmo ic filter X NbatF 4 = X DF 5 = 2 U NbatF 5 = 6.31[] QNbatF 5 (58) (59) 25 X bat = 0.25[]

2 SR

Power Quality www.leo ardo e ergy.org LDF 5 = X DF 5 1 = 0.80[mH ] (60)

LDF 3 4,5 = LDF 3 LDF 5 4, 7 = LDF 5 32 = 3.82[mH ] 2.52 5 = 0.99[mH ] 4.52 2 (61) (61) Whereas for degree of detu i g from reso a ce equal 2.7 a d 4.7 for the 3 rd a d 5 th harmo ic, respectively, the i ducta ces will be: LDF 3 4, 7 = LDF 3 LDF 5 4, 7 = LDF 5 32 = 3.28[mH ] 4.7 2 5 = 0.91[mH ] 4.7 2 2 (61) (61) For both filters have bee selected special desig reactors of "Z" compa y make, with i ducta ce values calculated as above, a d 2% i ducta ce toleratio . The r eactors are provided with taps that allow matchi g their i ducta ce to the degre e of detu i g: 2.5 a d 4.5, 2.7 a d 4.7, 2.8 a d 4.8. 4.5.3. Simulatio tests of the desig ed filters The desig ed filter freque cy impeda ce characteristics we re determi ed for selected parameters usi g the Matlab software package: a) For series reso a t freque cy order equal 2.7 a d 4.7 charts 7,8 a d 9 26

b) For the filter detu ed from reso a ce below rsz the i ducta ce values will b e larger. For the degree of detu i g from reso a ce equal 2.5 a d 4.5 for the 3 rd a d 5th harmo ic, respectively, the i ducta ces will be:

Static FC/TCR Compe sator for Arc Fur ace Compe satio www.leo ardo e ergy.org

10 9 8 7 Z(w) [Ohm] 6 5 4 3 2 1 0 0 100 200 300 400 f [Hz] 500 600 700 Chart 7. Freque cy impeda ce characteristics for the degree of detu i g 2.7 a d 4.7 of the supply etwork (blue), the 3 rd harmo ic filteri g bra ch (gree ) a d the 5 th harmo ic filteri g bra ch (red); each characteristic determi ed i divi dually 5 4.5 4 3.5 Z(w) [Ohm] 3 2.5 2 1.5 1 0.5 0 0 100 200 300 400 f [Hz] 500 600 700 Chart 8. Freque cy impeda ce characteristics of the supply etwork (blue), the 3 rd harmo ic filteri g bra ch (blue), the 5 th harmo ic filteri g bra ch (gree ) a d the equivale t impeda ce (red) 27

Power Quality www.leo ardo e ergy.org 10 9 8 7 6 5 4 3 2 1 0 0 100 200 300 400 f [Hz] 500 600 700 Chart 9. Freque cy characteristic of the supply etwork a d the filter equivale t impeda ce related to the equivale t impeda ce at f=50Hz For series reso a t fr eque cy order equal 2.5 a d 4.5 charts 10,11 a d 12 Z( )/Z(wo) 10 9 8 7 Z(w) [Ohm] 6 5 4 3 2 1 0 0 100 200 300 400 f [Hz] 500 600 700 Chart 10. Freque cy impeda ce characteristics of the supply etwork (blue), the 3 rd harmo ic filteri g bra ch (gree ) a d the 5 th harmo ic filteri g bra ch (r ed); each characteristic determi ed i dividually (red) 28

Static FC/TCR Compe sator for Arc Fur ace Compe satio www.leo ardo e ergy.org

5 4.5 4 3.5 Z(w) [Ohm] 3 2.5 2 1.5 1 0.5 0 0 100 200 300 400 f [Hz] 500 600 700

10 9 8 7 6 5 4 3 2 1 0 0 100 200 300 400 f [Hz] 500 600 700 Chart 12. Freque cy characteristic of the supply etwork a d the filter equivale t impeda ce for the degree of detu i g 2.5 a d 4.5 related to the equivale t im peda ce at f=50Hz Z( )/Z(wo) 29

Chart 11. Freque cy impeda ce characteristics of the supply etwork (blue), the 3 rd harmo ic filteri g bra ch (blue), the 5 th harmo ic filteri g bra ch (gree ) a d the equivale t impeda ce

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for the 3 rd harmo ic filter: for the 5 th harmo ic filter: 1.46 2.34 4.5.5. Verificatio of the capacitor ba k for overload curre t: a) For the 3 rd harmo ic filter: The filter power is: Q a d: ' NF 5 (U N )2 = (6000)2 = X Z (1) 6.67 = 5.40[ MVar ] (62) (63) X Z 3(1) = X DF 3(1) + X NbatF 3(1) = 6.67[] The rated curre t of the 3 rd harmo ic capacitor ba k is: I Nbat , F 3 = ' QNF 3 5,4 * 106 = = 409.91[ A] 3 * U Nbat 3 * 7600 (64) The co ditio for preve ti g capacitors curre t overload is:

I1 3 = ku I Nbat .F 3 = 0,78 * 391.25 = 323.61[ A] 2 I batF 3 = I12 + I = 323.612 + 32.52 = 325.24[A] (65) (66) Thus, the relatio : 409.91[ A] 2 I = 255.01[A] p 2 b 2 ku2 (67) 30

4.5.4. Parallel reso a subsectio 4.4.5. The gree 2.5 a d 4.5 is: lter: 3.58 a d for the

ce calculatio s: The schematic diagram a d formulas as i parallel reso a ce relative freque cy for the detu i g de for the 3 rd harmo ic filter: 2.64 for the 5 th harmo ic fi detu i g degree 2.7 a d 4.7 it is:

Static FC/TCR Compe sator for Arc Fur ace Compe satio www.leo ardo e ergy.org I NbatF is satisfied. 2 I

= k i I batF 3 p 2 b 2 k u2

(68) b) For the 3 rd harmo ic filter The filter power is: ' Q NbatF 5 = (U N )2 X Z (1) = 5.94[ MVar ] (69) a d: X Z 5(1) = X DF 5(1) + X NbatF 5(1) = 6.06[] The rated curre t of the 3 rd harmo ic capacitor ba k is: (70) I Nbat , F 5 = ' QNbatF 5 = 451.55[ A] 3 * U Nbat (71) The co ditio for preve ti g capacitors curre t overload is:

I1 5 = ku I NbatF = 356.48[A] 2 I batF 5 = I12 + I = 358.58[A] (72) (73) Thus, the relatio : 451.55[A] 2 I = 281.14[A] p 2 b 2 ku2 (74) I NbatF is satisfied. 2 I = k i I batF 5 p 2 k u2 (75) 4.5.6. Verificatio of THDU value Calculatio s of total harmo ic voltage distort io factor THDU have bee carried out as i subsectio 4.4.7. 31

Power Quality www.leo ardo e ergy.org Table 7. Voltage harmo ic perce tage co te t a d total harmo ic voltage distorti o factor THDU for the 3 rd a d 5 th harmo ic filter Curre t harmo ic U for detu i g degree U for detu i g degree order 2.7 a d 4.7 2.5 a d 4.5 8.73 9.32 2 29.63 31.62 3 18.93 8.79 4 6.90 10.81 5 4.43 5.00 6 5.5 5 6.00 7 5.23 5.56 8 4.76 5.02 9 3.40 3.57 10 5.34 5.60 11 1.69 1.76 12 3.70 3.8 6 13 1.12 1.1 THDU THDUF5= 1,1%, THDdop6kV = 5% [11], THDU6kV