Harmonics Modeling and Harmonic ActivityAnalysis of Equipments with Switch ModePower Supply using MATLAB and Simulink

B. Acarkan, Member, IEEE, K. ErkanDepartment of Electrical Engineering

Yildiz Technical University, 34349, Istanbul, Turkeyacarkangyildiz.edu.tr kerkangyildiz.edu.tr

Abstract-Power quality problems are increasing with the * Malfunction of electronic equipmentwidespread use of electronic equipments, which cause * Communication interferenceharmonic distortion of voltages and currents. Individually, a * Distorted supply voltagelow power single-phase nonlinear load may not pose many * increased power lossesserious harmonic problems but large concentrations of theseloads have the potential to raise harmonic voltages and * Errors inpowermeterigcurrents to unacceptable levels and harmonic current * Inadvertent thermal tripping of relays, circuit"pollution" is a one of the major power quality problem in breakers and protective devices [3]-[4].electrical power systems. In this study, nonlinear resistanceand harmonic models of the equipments with switch mode Terminal equations of electronic loads cannot be writtenpower supply (SMPS) are carried out using MATLABg. in form of v=R i or i=G v because of their switch modeAfterwards, Simulinko single-phase and three-phase power supplies. However, nonlinear characteristics ofsimulations are developed for both phase and neutral nonlinear loads can be described as follows:harmonic activity analysis. The symmetrical componentstheory is implemented under balanced nonsinusoidal F(i,v)=O (1)conditions.

Common nonlinear load characteristics of officeKeywords-Harmonics, power quality, nonlinear equipments are [5]:

modeling, the symmetrical components, MATLABg, * Instant current is not proportional to instant voltage,Simulink®.

* Current pulses arise on each maximum value of

I. INTRODUCTION voltage,* Even if terminal voltage waveform is sinusoidal, theHarmonic producing equipments are found in varied current waveform is nonsinusoidal,

locations from offices to manufacturing plants and they * The ratio between maximum value and rms value ofare becoming inevitable in daily life. Various harmonic the current differs,producing equipments are. * Terminal equation is represented by a nonlinear

* Personal computers function.* Electronic lighting ballasts* Variable and adjustable speed drives* Industrial process controlsH Electronic test equipment* Solid state controls* UPS systems* Medical equipments* Electronic household appliances.Harmonic currents generated by electronic equipments

increase power system heat losses and the power bills ofend users. Nonlinear loads injecting harmonic currents "n 22OsN 2- B3w MALcreate harmonic problems in the low voltage distribution | -------

system. The injected currents are propagated to alll -distribution circuits and lead to harmonic voltage |-distortion on the system [1]-[2]. Harmonic currents can A- J > - L |icause suchl problems as: . -- ---

* Overheating or derating of transformerl* Overloading neutral conductors ---e---------"* Excessive heating of wiring and connections ___tee_e______________________I* Damaging of capacitor banks* Resonance Fig. 1. Test rigs and sample waveform measurement screen (PC).

1 -4244-0743-5/07/$20.OO ©2007 IEEE 508

II. NONLINEAR MODELINGSolving a circuit, which contains more than one 'lg4

nonlinear element, with common analytic methods, is not Current T0nLpossible. If there is a single nonlinear element in a linearnetwork, construction of a load line permits a simple - a

graphical solution [5].

Circuits involving nonlinear elements can be solved inHl..i,N~b,, P

various ways depending on the nature of the problem and -+CURRENT UU Vthe form of the data. Newton-Raphson Iterative Method 2V3 213 2_

(NRIM)and Simulinki models are implemented to solve 2 AMPERI AMPER2 r AMPER r AMPER4 AMPER5 AMPER6 AMPER7 r AMPEnsingle-phase equivalent circuits. Test and measurement

RM20R5M1 S R5M1 S RMM1 7 R5M1 6; R5M15 R5M7RMi11

rigs are shown in "Fig. 1".

Fig. 3. SimulinkR9 model of nonlinear single-phase circuit consisting ofequipments with SMPS.

5 laSerjetVS l5je ~~5~~~~~~~r~--T--,___l_fitO01

F55Ed _ D. Harmonic Current Injection Model1. ------ -------------------Electronic equipments inspected in this study, because

%i 6iiiy-1= 1.45 ---n------------------ --,---- ------ --------- of their switch mode or rectifier power supply, haveI-P- 14 ------------I------ T------ I -------------I----spiked current waveforms that contain essentially odd

1.35 ------------ --------harmonics. Consequently, the equipments can be modeled1B4th d.g,.. poly-o

--------------- -- I - - as parallel harmonic current sources with definite125 /------+-------------- --------I-----t------q-------l--- magnitude and phase angle as other electronic loads [8].

_A6 1.Z FUI i 'I i I L_ 'i I nHarmonic current injection model of a single-phase5200 205 210 215 220 225 23 235 240 circuit is shown in "Fig. 4." Voltage levels of the

harmonic current spectrums varies with the AV= V.H_lg

Fig. 2 Nonlinear voltage-current characteristic of laser printer. i) i , i I; i| i, iA11N11111111 II

A. Nonlinear Voltage-Current CharacteristicsIn order to solve the nonlinear circuit via 1\ATLABI, C

nonlinear voltage-current characteristics of equipments arer I

220 1 2191 219 2 219 3 218 1 218 2 218 3

obtained using Curve Fitting toolbox from real measureddata. Polynomial type functions are implemented for the R -characteristics of all equipments "Fig. 2." 173

B. Newton-RaphsonIfterative Method ,Since.theNewton-RaphsonIterativeMethod forsolvingFig. 4. Single-phase SimulinkR harmonic current injection model.Since the Newton-Raphson method for solving F(x)=O

which can be a polynomial, or transcendental equation ofone variable is based on the Taylor's series involving the E. Symmetrical Component under nonsinusoidalderivatives of F(x), it can be extended to the solution of conditionstwo-equations FI(x,y)=O and F2(x,y)=O by application of The current in a balanced, three-phase nonsinusoidalTaylor's series involving partial derivatives of both F1 and system is given by [9],F2 with respect to x and y [6]. A MATLABR code hasbeen developed for analyzing nonlinear circuits usingNRIM with the V=F(J) characteristics. ia () = 2 I sin(ot) + 2 'h sin(hot + (h)

ib (t) = 2 I sin(ot - 120) + 2 Ih sin(h(ot - 120) + Ph) (2)C. Simulink Model ic (t) = 2 I sin(ot + 120°) + 2 Ih sin(h(ot + 1200) + Ph)

Nonlinear modeling with SimulinkR is easier, quickerand more flexible than developing a code. Because of aninsmerclopnntfr:using controlled current source in nonlinear model block,terminal equation must be in form of I=~F(V). Accordingthe circuit solution of Simulink model with nonlinear i tfnaetlfeunyresistance simulation, the voltage and current distribution 1Il F 1 rIZo0 iFolis obtained [7]. Nonlinear resistance model and L$o1 tL- a a2 11IL-10 1= (3)voltage-current distribution of a single-phase circuit are a1 1 ''shown in "Fig. 3." LI2 L 2 a iLI10 J L0J

509

ii. At the general harmonic h: equivalent circuits. According to voltage and currentFI 1 IFt F' -distributions corresponding harmonic current injection0 ± l 1 1 1 Ih fh models are implemented for three-phase Simulink®II =-1 a a IhZ(-h. 120 + fh) (4) models.3z22L 1 a2 a j LlhZ(h.12O° + 2h) Three-phase simulations are performed to compareI2i L1 a a --Ihl(h. 120' +Ph) phase and neutral current values and waveforms for

Three possible cases emerge from this general balanced (3 scenarios) and unbalanced (3 scenarios)condition, the cases of positive, negative and zero nonsinusoidal conditions. Balanced scenarios are carriedsequence harmonics. Harmonic phase sequences in a out for 4x18 W electronic ballasted fluorescent lightingbalanced three-phase power system are also given in fixtures, PCs and combination of lighting fixtures and PCsTable I [10]. for eight-equipment on the each phase line and the

TABLE I symmetrical components theory is also applied to verifyHARMONIC PHASE SEQUENCES neutral current analysis. Unbalanced scenarios include all

Harmonic Phase equipments mentioned above, and their combinations areOrder Sequence given in Table II. All measured equipments have

1 + antisymmetrical waveforms to the vertical axis at the3 origin. Because of their odd function properties only odd4 + harmonic components are taken into consideration in5 - models. A three-phase Simulink® model of second6 0 unbalanced scenario is shown in "Fig. 5." Symmetrical

components values of balanced Simulink® models areThe harmonics h=3n±1, for n integer, e.g. h=4,7,1, , given in Table III-IV-V.

have the same behaviour as the positive sequencefundamental quantity. TABLE II

EQUIPMENT CONFIGURATIONS OF UNBALANCED SCENARIOS-Io- 0 Case 1 Case 2 Case 3

IIIh2hL o'5'(5) Phase A B C A B C A B C

0 ~~~~~Notebook 1 I 2 - -2 computer

The triplen harmonics h=3n, for n integer, e.g. h=3, 6, Inkjet printer 1 - - 1 - - 1 - -

9,..., have the same behaviour as the zero sequence Data projector 1 - - 1 - - 2 - -

fundamental quantity. Fax machine 1 - - 1 - - 1 - -

UPS 1 1 1

[Io [Ih Ph]_

II 0 ~~~~(6) Hub 1 - - 1 - - 1 - -

I2 0 ~~~~~PC - 8 4 3

4x18Wfluo. - 8 - - 10 - - 4The harmonics h=3n-1, for n integer, e.g. h=2, 5, 8,...,

have the same behaviour as the negative sequencefundamental quantity [9].

-Io 0 t t t ;i ;Z

II 0 (7) 1l

III. NUMERICAL APPLICATION

As a simulation application a sample commercialbuilding is taken into consideration which comprisesequipments with SMPS such as electronic ballastedlighting fixtures, PCs, notebook computer, data projector,laser and inkjet printer, scanner, network hub, ups and faxmachine. The nominal supply voltage is 220 V and the t 3 3 3k 3 3t 3 3x 3 3 3xfundamental frequency is 50 Hz. Riser line cross-section is tI.6 mm2 and single-phase conductors' cross-section isA,III ]2,5 mm2 and conductor length is 5 m between equipments Lin installation structure. From laboratory measurements 110under sinusoidal voltage supply according to IEC Std. - -|||A +E 8SI61000-3-2, nonlinear equations of equipments areI C I 1obtained using MATLAB®/Curve Fitting Toolbox [1 1] . I tC |TDA TDB TNonlinear resistance models are applied to obtain voltage ,and current distributions in single-phase Simulink® Fig.5. Simulink model of unbalanced three-phase circuit (Case 2).

510

TABLE III expected [9]. According to Table II, current values ofTHE SYMMETRICAL COMPONENTS VALUES fundamental component and other harmonics are precisely(CIRCUIT WITH FLUORESCENT FIXTURES) appropriate. Thus, with the proposed models neutral

(A)2 Fundr3.n.i7 9.rde13 current values can be easily calculated using zero0Aud 2.23 5. 7 I. 1. sequence components even under nonsinusoidalIo'0.12 0 0 0.9156 0 0 cniin.Hroi ciiiso hs n etaI, 2.0052 0 0 1.3308 0 0 0.517 cniin.Hroi ciiiso hs n etaA2 0 0 1.7243 0 0 0.6431 0 conductors for balanced circuits are given in Table VI and

Harmonic order Table VII. Electronic ballasted fluorescent lines (Case 1)'0 12 and PC lines (Case 2) have extremely high harmonic-(A) 15. 17. 19. 21. 23. 25. 27.

lvl,wihaegetrta 7% ihhroi

Io 0.4856 0 0 0.3393 0 0 0.274 leeswhc argrartan10.Hih amocII 0 0 0.3897 0 0 0.2956 0 content of lighting fixtures can be observed also fromA2 0 0.4433 0 0 0.3061 0 0 Table III; third harmonic's current value is grater thanIO

~~Harmonic order fundamental component's value.

-(A) 29. 31. 33. 35. 37. 39 41. TABLE VIIo 0 0 0.2281 0 0 0.1929 0 HARMONIc ACTIVITIES OF BALANCED RiSER LINE'S PHASESII 0 0.2548 0 0 0.2048 0 0 Phase A B C'2 0.2747 0 0 0.2091 0 0 0.1817

Current THD_[ Current THD_[ Current THD1[TABLE IV ~~~~~~~cenario (A) N(O) (A) (Oo -(A) (O)

THE SYMMETRICAL COMPONENTS VALUES Case 1 4.0115 173.3 4.0115 173.3 4.0115 173.3

_____________(CIRCUIT WITH PCS) Case 2 7.2906 172.8 7.2906 172.8 7.2906 172.8

'0 12 Harmonic order Case 3 7.0586 76.01 7.0586 76.01 7.0586 76.01(A) Fund. 33. 55. 7. 9. II1. 13.

Io 0 3.5705 0 0 2.1705 0 0 Under balanced nonsinusoidal conditions, absence ofI, 3.65 11 0 0 2.7339 0 0 1.0587 fundamental component in neutral conductor of groundedI20 0 323610Harmonic611 star circuits make impossible calculation of THD values.

'0 12 In addition to THD values obtained from simulations-(A) 15. 17. 19. 21. 23. 25. 27. THDrms values are also calculated which give harmonic

Io 0.6199 0 0 0.2053 0 0 0. 1465 contents ratio to the rms value:II 0 0 0.1653 0 0 0.1983 0'2 0 0.3055 0 0 0.215 0 0

Harmonic order22'0 12 I

(A) 29. 31. 33. 35. 37. 39 41. THDJ ==

THD(ms == 8

Io 0 0 0.0572 0 0 0.0533 0(msII 0 0.0608 0 0 0.0623 0 0'2 0.0858 0 0 0.0728 0 0 0.0351 TABLE VII

NEUTRAL HARMONIc ACTIVITIES OF BALANCED CONFIGURATIONS

TABLE V Scenario Current (A) Harmonic DistortionTHE SYMMETRICAL COMPONENTS VALUES Simulink Calculated THD1 ( o THDJ[(ps)(0)

(CIRCUIT WITH FLUORESCENT FIXTURES AND PCS) Cs .69 720 0

'0 12 Harmonic orderCs 267 267 0(A) Fund. 3. 5. 7. 9. 11. 13. Cs 267 267 0

Io 0 1.9523 0 .51 0 0Case 3 7.7624 7.7624 -100

I, 5.6195 0 0 1.7369 0 0 1.2009'2 0 0 1.553 0 0 1.9778 0

Harmonicore Neutral current waveforms and harmonic current'0 12 spectrums for balanced scenarios are given in "Fig.6-7-8."(A) 15. 17. 19. 21. 23. 25. 27.Io 0.9991 0 0 0.2739 0 0 0.3476_________________________II 0 0 0.2883 0 0 0.4331 0 10------- ---- ---

'2 0 0.3843 0 0 0.3769 0 0h

'012 ______ Harmonic_order ____L~-

(A) 29. 3. 33. 35. 37. 39 41. -'o 0 0 ~~~~~~~0.2658 0 0 0.1901 0 -10 --I-

'1 0 0.1953 0 0 0.1619 0 0 I.1 00u ii uu01 015 &i

2010 ----I -

o-

~~~~1o I -- 1 L -~~~~~~~~~~~~~~~~~~~~~~~~~~~---- --

C CUlJ C0C2 CC0 IC0 CU.0 .( C 0.i 0U2123 .4 M5 IIIOTime (s Timn s

r harmonic 1R7116 (A) F nilarnzrtital ', a314 (.o 10] J

80 4,100~~~~~~~~~~~~~~~~~~~~~LC

2C 41 IJ EYL 03 2u JT W 0CC 200 4111] 0111] EIiJL 1 CCU0 C120 1W010 IEOOI 20CU

Frequniicy (Hz)~en~

Fig. 7. Neutral current waveform and harmonic spectrum of balanced Fig. 9. Neutral current waveform and harmonic spectrum of unbalancedthree-phase circuit (Case 2). three-phase circuit (Case 1).

20~~~~~~~I110-II I ~~~~~~~~~~~~~~~~~~~~~ -- -- --

10 --

LI-m'-F~~~~~~~~~~~~~~~~~~~~~~~~~~~!7------II __--

0 0lii1 0L12 UI us LI L4 0.05 0 06 - 0I 11 0.02 IJ0 0 04 DLI5 0.06

Z 3rI 1armonifc 5.58 (A) F)indarental. &WY83 (A

0 20 00 60 BF O1 10 1400 1iJO 1 i00 200 200: 4Ci 600U Wi0 1 OIrO 1 200E 14CIO 1 E-0 1 300 210]CFre Tenc (Hz Frequency (H:)

Fig. 8. Neutral current waveform and harmonic spectrum of balanced Fig. 10. Neutral current waveform and harmonic spectrum of unbalancedthree-phase circuit (Case 3). three-phase circuit (Case 2).

Harmonic activities related to unbalanced scenarios aregiven in Table VIII and Table IX. Unbalanced connectionof the loads affects significantly neutral waveforms and 6

harmonic current distributions (e.g. magnitudes of the 3rdharmonics have decreased and magnitudes of the 5th, 7th ------

and 1 Ith harmonics have dramatically increased inI L0 U01 0.02 OM0 U04 OO05 106

unbalanced scenarios). Neutral current waveforms andFrdmrtlL5

Time Cs)harmonic current spectrums for unbalanced scenarios are 1W0 FuJrlna11i?given in "Fig.9-1O-1 1." 8

TABLE VIIIHARMONIc ACTIVITIES OF UNBALANCED RiSER LINE'S PHASES 4

Phase ~~~A B C 20

Current THD_[ Current THD_[ Current THD1[00 M 406 BOO IO 12 140 160 IO 2000Scnro (A) (Oo - (A) (Oo .(A) (Oo Frequency (t)

Case 1 1.3547 41.48 7.2906 172.84 4.0115 173.27 - Fig. 11 Neutral current waveform and harmonic spectrum of unbalancedCase 2 1.3547 41.48 3.6189 173.28 4.9984 175.75 three-phase circuit (Case 3).

injection model is a most common model used for REFERENCESmodeling electronic equipments. This study combines [1] J.S. Lai and T.S. Key, "Effectiveness of harmonic mitigationsuccessfully various techniques for harmonic analysis of equipment for commercial office buildings," IEEE Transactions onthe equipments with SMPS on the basis of measurement. Industry Applications, vol.33, no.4, pp. 1065-1110, 1997.Current waveforms can be derived from any point of the [2] Y. Du, J. Burnett, Z. Fu and L. Wang, "Evaluation of harmoniccircuitregtwavording harmoniscaerl manalysis.pomtOIlimits in large office buildings," APSCOM-97, Fourth Internationalcircuit regarding harmonic analysis. Conference on Advances in Power System Control, vol.2,

The symmetrical components theory is applied pp. 747-752, Hong Kong, 11-14 Nov.1997.prosperously under nonsinusoidal conditions for neutral [3] W. Jewell and D.J. Ward, "Single phase harmonic limits," PSERCharmonic activity analysis and simulation results are EMI, Power Quality and Safety Workshop, Wichita State

University, Kansas, 18-19 Apr. 2002.verified. In the comparison of neutral current values in [4] S. Hansen, P. Nielsen and F. Blaabjerg, "Harmonic cancellation byTable VII and IX, calculated values from neutral current mixing nonlinear single-phase and three-phase loads," IEEEwaveforms and Simulink® values are equal except Case 2 Transactions on Industry Applications, vol. 36, no.1, pp. 152-159,and Case 3 of unbalanced scenarios with negligible and 2000.acceptable dioffer balancedsentiation ou s currnenti alues od [5] B. Acarkan, S. Zorlu and 0. Kilis, "Nonlinear resistance modelingacceptable differentiation. Although rms current values of using matlab and simulink in estimation of city street lightingthe phase lines are very close each other in Case 3, total harmonic activity," IEEE EUROCON 2005, The Internationalharmonic distortion is greater than 150%. The worst Conference on Computer as a Tool, vol. 2, pp. 1251-1254, Belgrade,circuit configuration is Case 1 with the 201.66% of total 21-24 Nov. 2005.

h m c i ro A n t c et ao s i[6] Y.C. Pao, EngineeringAnalysis, CRC Press LCC, 2001.harmonic distortion. All neutral current waveforms vary '7ALB-Dcmnain w.ahok.o[7] MATLAB - Documentation: www.mathworks.com

also significantly from each other. [8] IEEE Task Force on Harmonics Modeling and Simulation,The numerical application has shown that, harmonic "Modeling devices with nonlinear voltage-current characteristics

activity is affected from number and characteristics of for harmonic studies", IEEE Transactions on Power Delivery,equipmets,*cicuit tpologyand imbalance of the phase [ vol. 19, no. 4, pp. 1802-1811, 2004.equipments, circuit topology ancl Imoalanc OT tne pnase [9] E. Acha and M. Madrigal, Power System Harmonics: Computer

lines. Besides the harmonic mitigation techniques, circuit Modelling andAnalysis, J. Wiley and Sons, Chichester, 2001.configurations (e.g. connection of the additional loads to [10] IEEE Tutorial on Harmonics Modeling and Simulation, Modelingthe appropriate phase line), load imbalance must be and Simulation of Power System Harmonics, IEEE Educational

Product, CD ROM, ISBN: 0-7803-4597-5, 1999.considered to reduce excessive harmonic activity. [11] Electromagnetic Compatibility (EMC) Part 3 Section 2: Limits forAs future studies, a graphical user interface tool can be Harmonic Current Emissions (equipment input current up to and

developed to give a dynamic and flexible aspect to the including 16 A per phase), IEC/EN Standard 61000-3-2, 2003.proposed models; and for several equipments ameasurement database can be implemented to simplifyanalysis.

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