New Concept for Harmonic Filtration in Distribution Networks of Industrial Firms M.Z. El-Sadek Electrical Engineering Dept. Assiut university Assiut-Egypt G. Shabib Electrical Engineering Dept High Institute Of Energy Aswan-Egypt M.R. Ghallab Upper Egypt Electrical Distribution Company Aswan- Egypt Abstract: This paper presents a new method for designing the parameters of harmonic filters used with distorting loads in industrial firms. It proposes using hybrid filters which composed of groups of single tuned harmonic filters and a shunt capacitor. The design takes into consideration as minimum as possible values of capacitors capacitance, and the avoidance of parallel resonance and considers the filter elements deviations from their adjusted values at the designed filters harmonic orders [1-9]. Economic and technical aspects are considered. Fig.(1):Rectification station and harmonic filter arrangement. The network and transformer short circuit reactance Xesc is defined by: Xesc=Xtsc+(N2/N1) ² Xsc (1) The active and reactive power consumed by the rectifier bridge (RB) load are: P=3E I cos φ ,Q=3E I sin φ (2) Where I is the fundamental current entering to the rectifier bridge and φ the phase angle between the induced voltage E and the fundamental current I1.The form of the current which enters (RB) is given in fig (2).[2] 1-Introduction: The large distorting loads of power system currents and voltages are converters, which are used as rectifiers or inverters that draw certain reactive power from the distribution networks. The flow of these excessive reactive power on the network, leads to heavy currents, excessive losses, large conductors cross sections and high voltage drops which may lead to voltage instability. The distorted currents may lead to blackouts of lamps, stand still of motors, annealing of lines, protection and control systems failure and errors in metering of KWHR. It must then have harmonic filtering devices and installation capable of doing double roles: elimination of the existing harmonics from the distribution network, and in the same time improvement in the50HZ power factor currents.[2] This paper presents an effective method, which allow to design the filter parameters, for converters feeding DC constant loads which works in permanent mode, such aluminum smelter plants, arc furnaces, sugar separation. This situation is also economical frequently in industrial applications of network feeding electrical traction systems (trains, trams,...etc) . In this study the connection of distribution transformers are assumed to be connected in such a manner that the line currents do not contain harmonic orders of third and triplen harmonics (connected to star/delta or isolated star/star). The proposed method is applied to a six pulse rectifier 3-phase bridge, with ideal characteristic currents 5, 7, 11 etc orders . Fig.(2):Line current in 6-pulse rectifier bridge Where α is the firing angle, γ is the commutation angle. The current waveform of fig.(2) is valid for any of transformer connection. The angle γ is a function of Xesc, and I the harmonic analysis of the current represented in fig.(2) allows for determination of the harmonic components RMS values. The fundamental component of this current is derived as follows: 3 2E 2max sin(2α + γ) sin γ 4πX esc (3) 3 2E 2max [γ − cos(2α + γ) sin γ] 4πX esc (4) I 1 cos ϕ1 = I1 sin ϕ1 = 2-Loads Reactive Power: Taking into consideration these relations given in (3),(4),the active and reactive power of equation (2) become: The equivalent schematic diagram of the studied system is given in fig.(1).This system consists of high voltage busbars of line voltage V,3-phase short-circuit power Ssc,, transformer turns ratio (N1/N2) and its short circuit reactance Xtsc, rectifier bridge (RB) and harmonic filter (HF). The transformer secondary voltage values are [4]: EA=E ejγc , EB= a²EA, EC= a EA . Where a= exp( j2л /3) P = 2 9 E max sin( 2 α + γ ) sin γ 4 π X esc (5) 2 (6) Q = 9 E max [ γ − cos( 2 α + γ ) sin γ ] 4πX esc In which, the reactive power consumed by the rectifier bridge (RB) is obtained. If we are interested in 1 compensating this reactive power at the 50 HZ components, then the phase angle between the busbar voltage and the fundamental current should be decreased from φ to φ΄ . Therefore the filters should fed the busbar by capacitive reactive power given by Q1 = P( tan φ1 – tan φ′1 ) (7) With cos φ΄1 is the new power factor, cos φ1 is the original power factor and P is the load power in KW or MW. V cm = For realizing harmonic filters (HF) ,different procedures are used .Frequently, we employ filters connected as single tuned filters for certain harmonic orders in addition to a high pass filter (damping filter) for higher harmonics [2]. This solution has the disadvantages of high losses in the high pass filters (damping filters) .Another more advantageous solution is adopted in this study based on the concept of simultaneous filters of the type single tuned filters and shunt capacitors connected to the busbar, in parallel with the single tuned filters. The shunt capacitors, which can operate with fewer losses, assure certain degree of harmonic filtering for the higher orders harmonics. In the same time, it feeds capacitive reactive power to the busbar, which are used for reactive power compensation at the fundamental frequency. Noting that the capacitors of the filters are subjected to voltages, which exceed those of the feeding busbar. Also it is necessary for limiting reactive power to minimum values, that the rest of the reactive power which must be compensated is fed from the shunt capacitor which is connected directly to the busbar.The international specification limit the over loading of capacitor in steady state conditions in the ranges V≤(1---1.1)Vn, I≤ (1.3----1.8)In, Q≤ (1---1.35)Qn (8) Where Vn, In, Qn are the nominal values of voltage, current and power of capacitors respectively [3]. we should have : Q ck = 2 + 1 X k 2 2 ck I 2 k m (19) k a 2k V 12 1 + X ck I 2k X ck k (22) Q cm = (21) a 2m V12 1 + X cm I 2m X cm m If we perform the derivatives with respect to Xck,Xcm , and quating these derivatives to zero {(∂Qck/∂Xck)=(∂Qcm/∂Xcm)=0}, we obtain the minimum values of capacitances as follows: (23) equal voltages at the filters capacitors terminals. If we consider that the filters are connected for two harmonic orders (k, m),the voltages at the capacitor terminals for these two filters are given by the following relations:1 Vk = Vm The reactive power fed by the capacitor of each filter is found by the sum of the reactive power at the fundamental frequency and that at the harmonic voltages and given by: 4.2 Dividing of Capacitor Capacitances for Obtaining Equal Voltages at The Filters Capacitors Terminals: This concept is based on assuming having V (11) I 2m 4.4 Dividing of Capacitor Capacitances Based on Minimum Capacitor Rating: The capacitors are divided equally among the arms of (9) filters C= Ctotal / n Where n is the number of filter arms. This the simplest concept. 2 k 2 cm In the case of the rectangular line currents form, this (20) relation necessitates: Ck / Cm = ( m / k )3/2 4.1 Dividing Of Equal Capacitors: a 1 X m 2 This concept is based on obtaining equal specific losses in capacitors. When this criteria is satisfied, the duration of capacitors life of all filters will be the same. The losses per capacitor unit (or what called specific losses) can be determined by means of the following relations: Pδk = ω tanδ (ak² V² + k Vk² ) (17) Pδm= ω tanδ ( am²V² + m Vm² ) (18) Where Vk,Vm represent harmonic voltage in the phase voltage, tan δ is the loss angle in capacitor insulations. When we assume that the loss angle (tan δ) has the same value for the charectracitic harmonics orders up to the order 13. Then, for Pδk = Pδm and ak ≈ am There are different criteria for dividing the total capacitors capacitance of filters among each shunt filter arms. Several criteria are proposed in this study. Each criteria will has some advantages and drawbacks. The optimal method is that which present technical and economical advantages. = V 12 + 4.3 Dividing of capacitors Capacitances for Obtaining Equal Specific losses: 4- Criteria For Dividing Capacitors Between Filter Arms [9]:- ck 2 m (12) With ak= k² /(k²-1), am= m² /(m²-1 ) Where Xck,Xcm represent the filter reactances at the fundamental frequencies (50 or 60 HZ) ,V is the fundamental phase voltage.(Ik,Im)are the harmonic current branches of the order(k and m) .Having given that for the harmonic frequencies ak=am ,then the voltages Vck,Vcm will be surely equal when: Ck/Cm= mIk/ kIm (13) In this ideal case where the line current is of rectangular form ,we found that : Ik= I1/ k , Im = I1/ m (14) Then, we obtain : Ck /Cm = m²/ k² (15) These relations agree with: k² Lk Ck ω² =m² Lm Cm ω² = 1 (16) The condition in eqs (15),(16) necessitates certainly the equality of the inductances of the filters (Lk = Lm). 3- Harmonic Filters: - V a , Cm = Im ma mωV1 Ck = Ik k a k ωV1 From which the condition of minimum capacitors is : Ck = m (24) (I k / I m ) . k Cm (10) 4.5 Optimum Capacitors Division : 2 Comparing relations (20), (24), we notice that criteria (4.3), (4.4) are equivalent. On the other hand, the condition (20) is practically satisfied in the case when we look for obtaining filter with minimum costs . Consequently from techno-economic point of view the most reasonable capacitor dividing technique is that used on equal specific losses criteria (criteria 4.4 ). With Q1k fundamental frequency system reactive power,Qck filter capacitor reactive power of order k, Qbk filter inductor reactive power. Q1k = ak V1² / Xck (28) We can determine the absorbed reactive power by the reactor by Calculating the difference Qbk = Qck – Q1k . take into consideration the relation (22) and (28)we obtain: 5. Proposed Harmonic Filter Design Procedure: 5.1 Harmonic Filter Capacities Rating Determination: (29) Q bk a 2k V 12 1 + X 2 k X ck k = ck I 2k If we consider the capacitance Ck of the capacitor as independent variable the expressions (21) and (29) Become: A B , Q ck = AC k + B (30) Q bk = 2 C k + k Ck C k The capacitor of the filters connected for harmonic order k is subjected to voltage according to the formula (10) while the capacitor connected directly to the busbar is subjected to the whole voltage. Having known that the capacitor in the schematic diagram of (HF) has the same size. The result is that the capacitors installed in the filters will have more voltage than that those connected directly to the busbar. For this reason the value of the capacitance of the filter capacitors must be as small as possible. A proposed method of calculation those minimum capacitors was previously displayed in section (4-4), in equation (23). The proposed filter design uses the minimum capacity rating value. Where A = ω ak² V1² , B = Ik² /kω 5.2 Filter Inductance Determination: Firstly we calculate the filters rating which is connected for harmonic order number 5.The filter size is determined by means of relation (20). The inductance of the coil of the fifth order filter taking into consideration the relation (14) will be: L k = 1 ω . k 2 k V . 1 − 1 Ik Fig.(3):Reactive powers (Qck,Q1k,Qbk) as a function in capacitor Ck. The curves Qck ,Qbk and Q1k are plotted in fig.(3), for various capacitances Ck. We notice that for values of the capacitance which exceed Ck min. , which corresponds to Qckmin in fig.(3) consequently the gain of the reactive power (Qck/Q1k) in this case is exceeded nearly in all bus bars. 5.6 Calculation of Circulated Current: The circulating current by the filter capacitor can be determined by means of the relation: (25) 5.3 Over Voltages And Over Currents: After this, it is necessary to verify the capacitor performance with respect to over voltages and over currents at steady state conditions. The voltage is determined by means of relation (9). By introducing the minimum value of Ck in the reactance Xck,and by making several calculations we obtain: (26) V ck = a k I ( k + 1) / k V 1 I ck = ωC − ωL k = k V X 2 ck 2 + I 1 2 k (32) k 5.7 Calculation of Reactive Power at Minimum Capacitance of Capacitors: The reactive power fed by the filter capacitor used for the harmonic order k can be evaluated by means of relation (21) which when the capacitor capacitance is minimum becomes: If not, it is advised to increase the capacitor capacitance by nearly 30% in order that the terminal voltage does not exceed 1.1 Vn .By this increase, an associated supplementary reactive power will be available at the fundamental frequency, it is given by Q1k=V1Ik1 or: V1 ( k + 1) / k I 2 k Which will lead for k=5 to Ick = 1.1 Ik. 5.4 Determination of Filter Current: 1 ck (31) If we introduce Ck min.we obtain: Which for k=5,it is Vck= 1.14V1 .Noting that the voltage at the filter capacitor terminals which is used for the 5th order harmonic exceeds 3.7% which is a limit value of specification . If the nominal capacitors voltage used in this filter is more than the network voltage, we can keep the capacitor capacitance at minimum value. (27) I k 1 = a = (33) Q a k V1 X ck ck = 2 a k k V1I k Noting that the reactive power fed by the capacitor will fulfill the specification limits at all conditions. 5.8 Parallel Connected Capacitor Rating: When Q1 represent the total reactive power which must be compensated and given by eq.(7) before, and when Q1k is the reactive power provided by the filter of order k.The 5.5 Filter Reactive Powers Calculation (Qck,Qbk,Q1k) : 3 reactive power of the capacitor which is connected directly to the busbar is given by : Qcb = Q1 - Q1k This capacitor is directly connected to the busbar of voltage V1.Therfore, this capacitor capacitance is given by Cb = Qcb / ω V1² (34) We can estimate the possibility of appearance of over voltages and over currents. In the capacitors, which are connected directly to busbar, we should know the value of distortion coefficient at that busbar, which represents the following step of the calculations. 5.11 Check Of Parallel Harmonic Resonance: In the circuit of fig.(4) ,besides the characteristic harmonics, other non characteristic harmonics can arise They are generated either by other distorting loads such as arc furnaces or by dissymmetry of network or unbalance of loads .In this case ,parallel resonance’s can happen. They are usually associated by over voltages, which can destroy the system devices. These conditions are attained when the total susceptance of the circuit becomes zero. This total susceptance, with frequency now is determined by the relation (37) and using the following relations: 5.9 Calculation of the Distortion Coefficient : For calculating this coefficient, the schematic diagram given in fig.(4),is used here we have neglected the ohmic resistances of the coil of the filters. Lesc represent the equivalent short circuit inductance at the busbar. Firstly we will consider only the filter connected for the harmonic order number 5 (k=5). (39) X cb = Substituting of eq. (36) into eq. (33) yields: 25 n 1 ωC 5 − + nω C b n 2 − 25 nω L esc After some manual calculations ,we obtain : ω2 Cb Lescn 4 −[25ω2 Lesc (C5 + Cb ) +1]n 2 + 25 (41) Bn = nωLesc (n 2 − 25) Therefore, there will be a current resonance when : (40) B n = − (42) ω² Cb Lesc n4 − [25 ω² Lesc ( C5 + Cb)+1]n²+25 =0 It is evident that, a voltage resonance occurs with n=5. There are two possible current resonance’s , the first at frequency less than 250 HZ ,the other at higher frequency .If the first resonance is very near to 200 HZ and the distorted loads include arc furnaces producing harmonics of order 4 , this indicate either the harmonic curve of the filter which connected to eliminate the 5th order harmonic current ,by connecting a damping resistance in parallel with the filter coil ,or by using additional (other) filter for eliminating the 4th order harmonic. The current resonance at frequencies more than 250 HZ will create resonance problems only if this frequency is sufficiently near one of the characteristic harmonics. If in addition to the filter of the 5th order harmonic, we use a 7th order harmonic filter, it will result from the harmonic frequencies analysis of the circuit in fig.(4),that a current resonance will be produced at frequency between 250 to 350 HZ .The 6th order harmonic is insignificant, over voltages cannot appear. We will reach to similar conclusions with filters connected to eliminate, the 11th and 13th order harmonics. In definite, between all possible parallel current resonances,that near 200 HZ is most dangerous. If at least one of the harmonic voltages (V7,V11,V13) exceeds the level 1% of the fundamental voltage, it is necessary to connect a filter tuned to an adequate order.Firstly,we introduce a filter tuned to the 7th order and we determine the harmonic level of the harmonic voltages V11,V13.If they are less than 1% of the fundamental voltage, there is no need for additional (supplementary) harmonic filters, if not (or in the inverse case),we introduce a filter tuned to the 11th order and may be a another one tuned to the 13th order harmonics. For the filters which are tuned to the harmonic orders 7th,11th,13th,we determine the minimum values of capacitors capacitances, using the relation(23). The voltages across the terminals of those capacitors,(a according to eq.(26) are: Fig(4): Schematic diagram of proposed harmonic filter and equivalent power system and harmonic source. In this case the spectrum of the voltage at that busbar contain the harmonic V7,V11,V13 which can be determined by means of the relations: V7 = I7/B7t , V11 = I11/B11t , V13 = I13/B13t (35) (36) B nt = −B − 5n 1 n + nX esc X cb With: where B5n is the susceptance of the filter connected for harmonic order number 5, Xesc =ωLesc is the equivalent system short circuit reactance and Xcb = (1/ωCb) is the reactance of the capacitor connected directly to the busbar, Bnt is the total susceptance of filter, system and shunt capacitor. Both of these reactance’s (Xesc,Xcb) are determined at the fundamental frequency. After making some calculations the capacitor susceptance at order k will become: B kn = ( k n 2 n − k 1 2 2 )( X ) (37) ck 5.10 Check Of Over Voltages And Over Currents: In the following we allow that the distortion coefficient of the busbar voltage is only acceptable, if each of the harmonic voltage V7,V11,V13 does not exceed 1% of the fundamental voltage, according to the recommendations of certain specifications limits. In this condition there is no danger of appearance of over voltage at the terminal of the capacitor Cb (in steady state condition). On the other hand, in all calculations, we attained that the RMS values of the current flowing into the capacitor does not exceed the value: Ib = I12 + I72 + I112 + I132 ≤ 1.02I1 1 25n B 5n = 2 ωC 5 , Xesc = ωLesc ωC b n − 25 (38) Which proves that the over current in the current which flow by the capacitors rest within the limits imposed by the specification. 4 Vc7 =1.09 V1 ,Vc11 =1.05 V1 ,Vc13 = 1.04 V1 They are less than the limiting levels allowed in the specification. Table(1) gives a comparative study of the different values of the filter capacitors and elements using the different criteria. From which, criteria (4.3), (4.4) are the most efficient. They give minimum capacitances. The table shows checking voltages and reactive powers. Table (4): Filters parameters for single tuned, damped and new technique for an aluminum smelter plant. (43) 5.12 Check of Resonance’s at Untuned Frequencies: The last aspect which should be taken into consideration for the correct appreciation of the function of the shunt harmonic filters (HF) is that the effects of untuning of the filters, which is usually an invoided situation in practice .the factor which contribute to the untuning of filters are the following: deviations in fabricating the coils and capacitors with respect to their nominal values of tuning; the variations of the network frequency, the variation of the capacitance as a function in temperature. For these reasons, each filter may has at its nominal frequency a non-zero reactance. If we transform ,the deviations in the inductance and in the capacitance in an equivalent deviation in frequency, we can show, by equation (42), that when the filter is only tuned to the 5th order harmonic and is connected to the bas bar, each positive deviation of frequency lead to lowering the parallel resonant frequencies ,while negative frequency deviation leads to augmenting (increasing) the parallel resonant frequency. A deviation of 2% of the network frequency leads approximately to 1.25 % variation in the parallel resonance frequencies. Similar analysis can be made for the cases where other filters of frequencies are connected to the network. The untuning of the filters has a harmful effect on the level of the harmonic voltage. Also, if the filter which used for the 5th order harmonic is the only filter which connected to the network, it will also exist harmonic voltage of order 5, in a manner that the distortion in the voltage may become unacceptable. In these situations, it is necessary to use the recent automatic adaptive filters or active filter. Filter rating C (µF) L (H) R (Ω) Cb (µF) Eq. voltage 2.842 0.029 0.558 136.6 8.39 3.118 5.272 Min. loss 2.186 0.038 1.014 138.26 8.109 4.087 4.02 Proposed k=11)) 2.186 0.038 1.318 Conclusions: A new technique for design of harmonic filter with more advantageous solution is adopted in this study. It is based on the concept of simultaneous filters of the single tuned filters type and shunt capacitors connected to the busbar, in parallel with the filters. Minimum capacitor capacitances are obtained and used in the filter design of orders 5th, 7th,11th, 13th and 23rd . The voltage across the terminals of those capacitors are found to be less than the limiting levels allowed in the specification. The resonance in the system is studied for the designed filter and avoided by special measures. References: [1] M.Z.El-Sadek," Power Systems Voltage Stability and Power Quality", Muchter Press, Assiut,Egypt,2002,ch 16. [2] D.E.Staeper and R.P.Stanford;" Reactive Compensation and Harmonic Suppression for Industrial Power Systems Using Thyristor Converters” .IEEE Trans,on.IA 12(1976) 3,P.232-254 [3] D.A.Gonzalez,J.C.Mccall,"Design of Filters to Reduce Harmonic Distortion in Industrial Power Systems".IEEE Trans.on Industry Applications, Vol.IA-23,No.3,May/June 1987,pp. 504-515 [4] Jos Arrillaga, Bruce C. Smith, Nevelle R. Watson,Alan R. Wood, “Power System Analysis" ,Book, John Wilery &Sons Ltd, England, 1997. [5] C.K. Duffy,R.P.Stratford,"Update of harmonic Standards IEEE-519.IEEE Recommended Practices And Requirements For Harmonic Control In Electrical Power System", IEEE Trans. On Industrial Applications, Vol.IA25, No.6 , Nov./Dec.1989,pp.1025-1034. [6]J. Arrillage, D. A. Bradly ,P. S. Bodger ,"Power System Hrmonics " John Wiley and Sons Inc.,New York, 1985. [7]H. M. Bedies, G. T. Heydt " Power Systems Harmonics Estimation and Monitors " Electric Machines and Power Systems,1992,pp. 94-102. [8]T.J .E. Miller, " Reactive Power Control in Power System " Book ,John Wiley ,London ,1982 The aluminum smelter plant of Nag-Hammady, Upper Egypt, is rated 400 MVA at average power factor of 0.9.The electrolysis rectification stations are 12-pulse uncontrolled rectifiers. The results of harmonic analyzer show that the 11th, 13th and 23rd order harmonic currents exceed the standard limits. By using the design of proposed technique filters for these three harmonic orders, and deciding that these filters should correct the 50 HZ power factor to 0.95. Having Q optimum =33, and Q coils =100. System voltage =132 KV. If the 11th , 13th and 23rd currents are found to be 10, 8 and 5 %. Table (1): Filters parameters using different criteria for dividing capacitors between filter arms ( k=11) Eq. Cap. 3.06 0.027 0.34 136.2 8.573 2.94 5.63 Damped k=23)) 3.4 0.006 12.1 - Table (4) gives a comparison between the parameters of a conventional single tuned filter, damped filter and the proposed filter. Damped filter require more resistance and has excessive losses. 6. Case Study: Filter rating Ck(µF) Lk (H) Cb(µF) Vck (KV) Qck(Mvar) Q1k ,, Qbk ,, Single (k=11) 3.4 0.025 2.5 - Min. Cap. 2.186 0.038 1.014 138.26 8.109 4.087 4.02 5 [9] J. D. Ainsworth , "Filers, Damping Circuits and Reactive VOLT/AMPS in HVDC Converters " Chapter 7 from "High Voltage Direct Current Converters in Systems " Book, 1988. 6