IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 4 Issue 1, January 2017 ISSN (Online) 2348 – 7968 | Impact Factor (2015) - 4.332 www.ijiset.com Design Analysis and Parametric Modeling of Harmonics Effects on a 1.5kva Single Phase Wooden Cross Cutting Machine Step Down

1 2 3 France O. AkpojedjeP ,P P YussufP O. AbuP P and Clement AgbeboayeP P 1,3 P DepartmentP of Electrical/Electronic Engineering Technology, National Institute of Construction Technology, Uromi, Nigeria. 2 P DepartmentP of Science Laboratory Technology, University of Benin, Benin City, Nigeria.

Abstract for the design, construction and operation of many This paper aims at x-raying the design analysis and electrical and electronics devices [4]. The principle parametric modeling of harmonics effects on a of operation is based on the basic principle of 1.5KVA single phase wooden cross cutting electromagnetic induction which was discovered by machine step down electric service transformer. Michael Faraday in 1813 [4]. The literature survey was considered and the are basically passive devices for research work was realised through analytical transforming and current [5]. One of the designs and parametric modeling of harmonics windings, generally termed as secondary winding, effects on a single phase, core type electric service transforms energy through the principle of mutual transformer which steps down the 240volts mains induction and delivers power to the load [5]. The voltage to the appropriate voltage level of 120volts. voltage levels at the primary and secondary The electric service transformer has efficiency of windings are usually different and any increase or 96.02% with maximum load efficiency of 42.69%, decrease of the secondary voltage is accompanied and 5.07% of total losses in the system. This by corresponding decrease or increase in current research work will be relevant to transformer [5]. Transformers are among the most efficient designers and students, as it exposes the full design machines; 95% efficiency being common in lower analysis and calculations of transformers; and its capacity ranges, while an efficiency of the order of basic parametric models. 99% is achievable in high capacity range [5]. Keywords: Design and analysis, losses, model, According to Evbogbai and Obiazi [6], magnetic flux density, parametric, transformer transformers can be manufactured from locally calculations materials as reported in their work titled "Design 1.0 INTRODUCTION and construction of small power transformers using Transformers are veritable tools in electrical power locally available materials". The study showed that system and their functions are significant especially electrical machines could be constructed locally in stepping up and stepping down (transformation) since Nigeria is blessed with iron, steel, and the of /currents for appropriate usage. The availability of copper and aluminum conductors for advent of transformer has given leverage to long the windings [4]. transmission of electricity from the point of In this research work we trying to get clear cut for production to the point of consumption. Electricity design analysis and parametric modeling of is a particularly attractive form of energy that can harmonics effect of a 1.5KVA single phase wooden be easily produced, transmitted and transformed cross cutting machine step down transformer in into other form of energy [1]. The transformation carpentry workshop of the School of Engineering of voltage and current in electricity supply is Technology, National Institute of Construction carried out by an apparatus called the transformer. Technology, Uromi, Nigeria. "Transformers are very useful in many electrical 1.2 TYPES OF TRANSFORMERS IN circuits. Consequently, the transformer is a device TERMS OF CONSTRUCTION which plays a vital and essential role in many Transformers are classified according to their facets of electrical engineering" [2]. Therefore, construction into two main types namely: Core and "Transformer is a static (stationary) piece of Shell types [7]: apparatus by means of which electric power in one a. Core Type Transformer circuit is transformed into electric power of the Every transformer consists of a magnetic same frequency in another circuit" [3]. It can raise circuit of laminated iron core with which or lower the voltage in a circuit but with the electric circuits, primary and corresponding decrease or increase in current secondary are linked. The coils in this [3].The importance of transformer in voltage type are cylindrical in form and placed transformation in our everyday life cannot be one inside the other with proper overemphasized [4]. Transformer forms the basis insulation between them. The portion of

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IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 4 Issue 1, January 2017 ISSN (Online) 2348 – 7968 | Impact Factor (2015) - 4.332 www.ijiset.com

the core over which comes the windings Window space factor KRwR = 10 = 0.33 is called limb or leg whereas the core 30 + kv which connects the two limbs are called the yoke. The cross - sectional area of the Type of construction : core type yoke is normally greater than that of the Cooling medium : Air Natural Air Natural limb but it may be equal also. (ANAN) b. Shell Type Transformer In the shell type of transformer, both the 1.4.2 DESIGN ANALYSIS AND windings, low voltage (L.V) and high CALCULATIONS voltage (H.V) are put around the central Core - Design limb. The winding is called the Sandwich The voltage per turn, E = K S winding where flat rectangular or circular t (1)

coils, alternately L.V and H.V., are ERtR = 0.98V arranged one above the other with the necessary insulation between them. The cross - sectional area of the central limb

is twice that of the side limbs as it carries Calculating the core area, ARi double the flux than the side limbs. Et Consequently, the width of the central Ai = limb is twice that of the side limbs 4.44FBm (2) keeping the same core depth throughout.

1.3 MATERIALS AND METHODS 2 A 1.5KVA, 240volts, single phase transformer ARi R= 35cmP transform the mains voltage to 120volts; 12.5amps to power a single phase wooden cross cutting Calculating the magnetic flux, φ machine in the Civil Engineering Department of m φ = A B the School of Engineering Technology in the m i m (3) National Institute of Construction Technology, φ Uromi, Edo State, Nigeria. The transformer was m = 4.38 mWb designed using indigenous knowledge in view of Calculating the diameter of circumscribing local materials available for its realization. The circle around core, d harmonics effect was analyzed to mitigate any Since the transformer is core type and square possible losses that may be caused by it. The section that is to be used. wooden cross cutting machine, its function is to 2 ARgrossR = 0.5dP P (4) provide cross cutting wooden materials for a specified purpose(s). The wooden cross cutting machine provides human-machine interface with its ARiR = kRsRARgi R (5)

function of optimizing cutting in wooden materials. Assuming kR sR = 0.9 A 1.4 DESIGN SPECIFICATIONS AND ⇒ d = i (6) ANALYSIS .0.9 x 0.5 1.4.1 DESIGN SPECIFICATIONS d = 8.82cm The machine design procedure for core and shell types of power and distribution transformers have Calculating the width of lamination been reported by [ 5 & 7]. The design differences Since, the core is to be square section, lies on the specifications of the machine to be Width of lamination is (a) = 0.71d (7) designed and plan. = 6.26cm The following are the specifications of the single Calculating the net window area (ARwR) phase wooden cross cutting machine step down The expression for the output power of a electric service transformer that the design strives to achieve. single phase transformer is: -3 KVAR1-ph R = S = 2.22f BRmRARiRARwR KRwR δx10P P (8) Power rating, S = 1.5KVA

Input voltage, VR1R = 240V 3 ARw R= S x10P ∕P 2.22f BRmRARiRKRwR δ Output voltage, VR R = 120V 2 Frequency, F = 50Hz 2 -2 ARwR = 32.18R RcmP Maximum flux density, B RmR = 1.25wbmP 2 6 2 RwR Rw R RwR Current density, δ = 2.5A/mmP P = 2.5x10P P Amp/mP However, A = H xW (9) Constant K = 0.8 Window Design

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Calculating the core dimensions TR1R = 245 turns

The centre - to - centre distance of the core is Calculating the secondary turn, TR2 twice the core width, i.e (stack) TR2R = VR2R/ ERtR (19)

This will be equal to 2x0.71d = 1.42d (10) TR2R = 122 turns = 12.52cm Calculating the conductor size for the Centre - to - centre distance between limbs primary and secondary windings

Limbs = WRwR x d The cross sectional of the conductor is: (11) A = I/δ (20)

R WRwR x d = 12.52 Calculating the primary conductor size, A1

From equation 20, AR1R = IR1R/δ RwR W = 12.52 - d 2 AR1R = 2.5mmP WRwR = 3.7cm Calculating the secondary conductor size, AR 2 From equation 20, AR2R = IR2R/δ

Therefore, HRwR = 8.70cm 2 AR2R = 5mmP Calculating overall core height, H Calculating the diameter of the conductor The overall core height, H 2 Area, A = πd 4 H = HRwR + 2(0.71d) (12) (21) H = 21.22cm 4a ∴ = Calculating the overall with of core, W d π (22) The overall width of core, W Where d = diameter of the conductor W = WRwR + d + 0.71d (13) W = 18.78cm Calculating the diameter of the primary

Yoke Design conductor, dR1 Calculating the stack height, SRh 4x2.5

R R Stack height, SR hR d1 = = 1.7mm π Ai Sh = Calculating the diameter of the secondary 0.9 x 0.71d

(14) conductor, dR2 35 = = 6.21cm 4x5 0.9 x 0.71 x 8.82 dR2R = = 2.52mm π

Calculating the number of lamination, RL n dR1R corresponds to standard wire gauge of 15

RLR n = stack height dR2R corresponds to standard wire gauge of 12

thickness of laminar (15) Calculating the window space factor, kRw

KR R = 10 = 0.33 w

nRLR = 207 (23) 30 + kv Calculating the current for both primary and

secondary circuits Calculating the mean length per turn (LRmtR) Given the output power, S = 1.5KVA for both primary and secondary coils

The primary voltage (Input voltage) VR1R = 240V

LRmtR = (LRmt1 R+ LRmt2R)/2 = πDRmR = π[d + WRwR/2] (24) Input current at the primary winding of the transformer is: LRmt R = 0.3352m

R IR1R = S/ VR1R (16) Calculating the length of primary turns, L1

R1R I = 6.25A Length of primary coils, LR1R = LRmtR x TR1R (25)

IR2R = S/ VR2R (17) LR1R = 82.12m ≈ 82m

IR2R = 12.5A Calculating the length of secondary turns, LR2 Given the voltage per turn, ERtR = 0.98V

Length of secondary coils, LR2R = LRmt R x TR2R (26) Calculating the primary turn, TR1

R R TR1R = VR1R/ ERtR (18) L2 = 40.89m ≈ 41m

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Calculating the resistance of the primary Calculating resistance drop per unit in the coils

winding, RR1 or winding for both primary and secondary

RR1R = ρLR1R/ AR1R (27) Calculating the resistance drop per unit winding

RR1R = 0.5584Ω for primary

Calculating the resistance of the secondary P.U. resistance drop, εRr1R = IR1R R1R/VR1R (41) winding, RR2 εRr1R = 0.0145pu RR2R = ρLR2R/ AR2R (28) Calculating resistance drop per unit winding for

R R R2 = 0.1390 Ω secondary

Calculating the yoke dimensions P.U. resistance drop, εRr2R = IR2R R2R/VR2R (42)

R Calculating the depth of the yoke, Dy εRr2R = 0.01458pu

DRyR = a = 2 x 0.71d (29) Calculating the of coils or turns for

DRyR = 12.52cm both primary and secondary windings

Calculating the area of the yoke, ARy Calculating the inductance of primary turns,

2 2 R ARy R= 1.2ARyR = 1.2 x 0.5dP P = 0.6 dP P (30) LL1 PR

2 LR R = T R RΦ/IR R (43) ARyR = 46.68cmP L1 1 1

LR L1R = 171.70 H Calculating the height of the yoke, hRy

hRyR = ARyR/DRyR (31) Calculating the inductance of secondary turns,

R hRy R= 3.73cm LL2

R R R R R R Calculating the weight of the iron core, WRic LL2 = T2Φ/I2 (44)

Weight of iron core = LR L2R = 42.75 H (iron volume) x (iron density) (32) Calculating the weight of iron in core and yoke Volume of iron core = total length of mean assembly

Weight of two limbs in a core = 2hR RAR R DR R (45) flux path (LR mR) x iron area (ARiR ) (33) w i L = 4.628kg LR mR = 2[WRwR + d] + 2[HRwR + a] (34)

R R R R

R R Weight of one yoke = WA D (46) Lm = 54.96cm y L = 6.663kg Volume of iron core = Lm x ARiR (35) 3 Calculating the core losses in limb and yoke = 1923.6cmP

R R R R Core loss in limb = 2 x weight of limb (47) Weight of iron core (Wic) = Lm x Ai x D (36) -3 = 9.256Watts = 1923.6 x 7.870 x10 P P = 15.138kg Calculating the weight of both primary and Core loss in yoke = 1.4 x weight of yoke (48) = 9.328Watts secondary coils or windings, WRcR

Total core loss (Iron loss) (PR R) = The weight of primary coils or winding, WRc1R i core loss in yoke + core loss in limb (49) WRc1R = DAR1R LmtT R1R

(37) PRiR = 18.584Watts

Total losses in the transformer (PR R) = copper losses WRc1R = 1.83kg T

R R R R

R R (P ) + iron losses (P ) The weight of secondary coils or winding, Wc2 c i

PR R = PR R+ PR R (50) WRc2R = DAR2R LmtT R2R (38) T c i - PR R= 62 x 10P 3P kW WRc2R = 1.82kg T

R Calculating the load for maximum efficiency Total weight of copper in transformer, WT For maximum efficiency to occur: WRTR = WRc1R + WRc2R (39) 2 = 3.65kg XP PRcR = PRi R(51)

Calculating the total , PR P c ⇒ = i (52) 2 2 X PRc R= IR1RP RP R1R + IR2RP RP R2R Pc (40) X = 0.4269

PRcR = 43.53 watts

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Meaning that the maximum efficiency occurs at are as follows: transformers, converters, generators, 0.4269 times of full load. Recall that the maximum motors, fluorescent lighting, electric ballast, arc efficiency of a distribution (service) transformer welding machine etc. occurs at or near 1/2 full load. The interest of harmonics effect is placed on the Calculating the efficiency of the service subject because of the harmfulness they have on transformer power system and its equipment. The harmonics

Efficiency at full load and unity P.F (ᶯRTR) = effect are enormous and they include: overheating, [Output power/Output power + losses] x 100 vibration, reduction of system efficiency, aging of system installation, poor system power factor, ᶯRTR = [Output power/Input power] X 100 (53) inaccurate operation of system protection

R R = 96.02% ᶯT equipment, humming of system machines, increase 1.5 PARAMETRIC MODELING AND 2 in system IP RP losses etc. ANALYSIS OF HARMONICS EFFECTS ON 1.5.2 PARAMETRIC MODELING OF ELECTRIC SERVICE TRANSFORMER HARMONICS EFFECTS ON ELECTRIC The impact of harmonics currents on transformers SERVICE TRANSFORMER is more serious on convectional conductors because "The effect of harmonics in electric service the resistive skin effect is enhanced within closely - transformer increase the eddy current and spaced transformer windings [8]. Harmonics are hysteresis losses in the system. But transformers one of the major power quality problems that are designed to deliver the required power to the exists. Harmonics are complex waveforms load with minimum losses at the fundamental produced due to the superposition of sinusoidal frequency"; though the multiple integer of the waves of different frequencies [3]. The flux fundamental frequency increases losses in the density in transformer is usually maintained at a system. Hence, the harmonics of the devices in the fairly high value in order to keep the required system are modeled through the copper losses since volume of iron to the minimum; but due to the non- the copper loss is the summation of eddy current linearity of magnetisation curve, some third loss (P ReR) and hysteresis (P RhR) losses in the system harmonic distortions are always produced [3]. respectively. If the output voltage is small, then the Most electric service transformers are highly output current increases which causes great heat vulnerable to overheating, leading to insulation and losses in the system. The total losses of a damage which causes the premature failure of the transformer are obtained by calculating the sum of transformer. As reported by [8], "The failure rate of these losses (P RcR). transformer caused by harmonics effect is very x 2 PRcR = PReR + PRhR = KRhRfBP PRpkR +KReR(fBRpkR)P P (54) high in India; around 25% per annum, which is Modeling copper losses under linear load condition favourably comparable to international norms of 1 - due to resistance is given as: 2%". Therefore, an attempt was made in this 2 2 PRcR = IP PRLR(RR1R + RR2R)/AP P (55) research work to analyse and carry out the Modeling nonlinear currents of different harmonic parametric modeling of harmonics effect on the frequency: 1.5KVA service transformer. ∞ = + θ + + θ (56) 1.5.1 CAUSES OF HARMONICS AND IL (t) I2Sin (wt 2 ) ∑ I2h Sin (hwt h ) h=1 EFFECTS ON ELECTRIC SERVICE When harmonic currents flow in the windings of TRANSFORMER the electric service transformer, then they The main sources or causes of harmonics in produces a voltage drop across the device electrical power system are non-linear loads that which lead to copper losses under harmonics produce harmonic voltage and current in the which is modeled as (PRchR): system. The nonlinear load that causes harmonics

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∞ ∞ 2 2 2 n   Pch = Rh1I h1 + Rh2 I h2 (57) I h ∑ ∑ IRTHDR =   (64) h=1 h=1 ∑   h=2  I (1)  Where PRchR is the copper losses under harmonic Consequently, the total harmonic distortion is environment, RRh1R and RR h2R are the primary and secondary winding resistance in the h - order the ratio between residue and effective value of fundamental wave function: harmonic respectively, while IRh1 R and IR h2 R are the n primary and secondary currents. 2 1.5.2.1 MODELING OF HARMONIC ∑Vh VOLTAGE AND CURRENT DISTORTIONS h=1 δ v = x 100% (65) The power quality of a system can be impressed by V1 improving or better still minimising the harmonic 1.5.2.4 MODELING OF HARMONIC LEVEL voltage and current distortions in power utility IN ELECTRIC SERVICE TRANSFORMER devices. The most prominent thing is voltage and The harmonic level of the electric service current which are non - sinusoidal quantities. transformer can be determined by the ratio between Harmonic voltage function is modeled as: the effective value of the considered harmonic and n effective value of the fundamental as shown in the Vh (t) = ∑Vh 2 Sin(hwt + Yh ) (58) parametric model below: = h 1 V Similarly, the harmonic current function is h YLevel = x 100% (66) modeled as: V1 n Where YRlevel Ris the harmonic level of the I (t) = I 2 Sin(hwt + Y − φ ) (59) h ∑ h h transformer, VR1R is the fundamental voltage h=1 and VR h Ris the harmonic voltage considered. Where VR R and IR R are the RMS of each h - harmonic h h 1.6 MITIGATION OF HARMONIC of voltage and current respectively while ω, ɸRhR and

R R EFFECT ON ELECTRIC SERVICE Yh are the angular frequency, Phase angle difference and phase angle respectively as well. TRANSFORMER 1.5.2.2 MODELING OF HARMONIC Harmonics affect transformers primarily in POWER DISTORTIONS two major ways: voltage harmonics and The harmonic active power is modeled as follows: current harmonics. "The voltage harmonics n produces additional losses in the transformer Ph = ∑Vh I h Cosφh (60) h=1 core as the higher frequency harmonic The harmonic reactive power is modeled as: voltages set up hysteresis loops, which n superimpose on the fundamental loop" [9]. Qh = ∑Vh I h S inφh (61) "The second and a more serious effect of = h 1 harmonics is due to harmonic frequency While the harmonic apparent power is currents in the transformer windings" [9]. The modeled as: harmonic currents increase the net RMS n n = 2 2 current flowing in the transformer windings S h Vh I h (62) 2 ∑ ∑ which results in additional IP RP losses [9]. h=1 h=1 Winding eddy currents are circulating 1.5.2.3 MODELING OF TOTAL HARMONIC currents induced in the conductors by the DISTORTION (THD) leakage magnetic flux [9]. And this winding The total harmonic distortion is expressed through eddy current increases the losses in the system the voltage and current distortion. by causing temperature rise in the windings. Hence, total voltage harmonic distortion VR R is THD In order to handle this losses and temperature modeled as: 2 effect the K - factor method is employed for n   Vh transformers that supply nonlinear load. VRTHDR =   (63) ∑   The K - factor transformer is designed to h=2 V(1)  accommodates the temperature rise caused by Similarly, the total current harmonic distortion current harmonic in the transformer windings. IRTHDR is modeled as: In addition to the fundamental frequency losses. K - factor is a constant that specifies the

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IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 4 Issue 1, January 2017 ISSN (Online) 2348 – 7968 | Impact Factor (2015) - 4.332 www.ijiset.com ability of the transformer to handle harmonic F = Frequency (Hertz) K = Constant heating, as a multiple of the normal eddy 2 δ = Current density (A/MP )P current losses which are developed by a KRwR = Window space factor sinusoidal current in the transformer BRmR = Magnetic flux density (Telsa)

windings. T R1R = Primary turns

A good engineering practice calls for the T R2R = Secondary turns 2 derating of transformer that serves nonlinear ARwR = Window area mP 2 ARyR = Area of yoke mP loads to an equivalent 80% of the nameplate 2 AR1R = Net core section mP KVA [8]. 2 AR1R = Primary conductor section mP The parametric modeling of the K - factor is 2 AR2R = Secondary conductor section mP

given as: dR1R = Primary conductor diameter, mm 2 2 dR2R = Secondary conductor diameter, mm k = ∑ I h h (h = 1, 2, 3,  n) (67) a = Thickness of lamination

R R Et = E.M.F. per turn

IRLR = Load current 1.7 CONCLUSION θ = Phase angle

Transformers are the major and most LRhR = Harmonic inductance important equipment in electrical power RRhR = Harmonic resistance system. Their role in changing voltage and ηRTR = Efficiency IR R = Harmonic current current levels cannot be overemphasized in h VRhR = Harmonic voltage electrical power system. Hence, the full design δRhR = Total harmonic distortion analysis and parametric modeling of YRLR = Harmonic level harmonics effect of a 1.5KVA single phase VRTHDR = Total harmonic distortion voltage wooden cross cutting machine step down IRTHDR = Total harmonic distortion current K = derating factor electric service transformer has been LR mtR = Mean length of turn successfully presented in this research work. ω = Angular frequency

The transformer designs have been obtained PRTR = Total power loss with step by step analysis and calculations in PRch R = Harmonic copper losses in power details. The methodology has been applied to LR L R = Inductance of windingR 1.5KVA single phase electric service Lm = Total length of mean flux path transformer with a rated frequency of 50Hz. εRrR = Resistance drop per unit of coils

The importance of this research work lies on WRcR = Weight of coils the fact that a step by step design analysis and WRicR = Weight of iron core calculations of a single phase electric service REFERENCES transformer was implemented with [1] F.O. Akpojedje, E.M. Okah and Y.O. parametric modeling of harmonics effect on Abu, "A Comparative Analysis of Three Phase the system. Also, the work gives general Induction Motor Performance Evaluation", guidelines to any person or designer who International Journal of Engineering and wants to carry out full design work of Techniques, Volume 2, Issue 3, May - June transformers and the construction of same. 2016. Pg. 64 - 75. List of Symbols and Abbreviations: [2] J.B. Gupta, "Theory & Performance of VR1R = Input voltage Electrical Machines", (Fourth Edition), VR2R = Output voltage AC = Alternating current Published by S.K. Kataria & Sons, 6, Guru

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IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 4 Issue 1, January 2017 ISSN (Online) 2348 – 7968 | Impact Factor (2015) - 4.332 www.ijiset.com Electrical and Power Engineering", 1(5), 2007. Pg. 537 - 542. [5] Bharat Heavy Electrical Limited, "Transformers" Tata Mcgraw - Hill Publishing Company Limited, Fifteenth, Reprint 2001, New Dehli, Pg. 1 [6] M.J.E. Evbogbai and A.M. Obiazi, "Design and Construction of Alternating Current Welding Machine Using Locally Available Materials", Global J. Mech. Eng., 2002. 3: 74 - 83. [7] R.K. Agarwal, "Principle of Electrical Machine Design", (Fourth Edition), S.K. Kataria & Sons, 4424/6, Guru Nanak Market, Nai Sarak, Delhi - 6. Pg. 192 - [8] Prof. Mack Grady, "Understanding Power System Harmonics", Department of Electrical & Computer Engineering, University of Texas at Austin. [email protected], www.ece.utexas.edu/~grady, (nd) [9] C. Sankaran, "Power Quality", CRC PRESS 2002, Uploaded by Maurits Paath, Retrieved on the 22nd December, 2016. Time: 09:45AM. www.academia.edu/...6/POWER_QUALITY_by_ C-SANKARAN.

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