Aalborg Universitet. Published in: Proceedings of The International conference on future Power Systems. Publication date: 2005

Transcription

1 Aalborg Universitet Harmonic Domain Modelling of a Distribution System using te DigSilent PowerFactory Software Wasilewski, J.; Wiecowski, Wojciec Tomasz; Bak, Claus Let Publised in: Proceedings of Te International conference on future Power Systems Publication date: 005 Document Version Accepted autor manuscript, peer reviewed version Link to publication from Aalborg University Citation for publised version (APA): Wasilewski, J., Wiecowski, W. T., & Bak, C. L. (005). Harmonic Domain Modelling of a Distribution System using te DigSilent PowerFactory Software. In Proceedings of Te International conference on future Power Systems General rigts Copyrigt and moral rigts for te publications made accessible in te public portal are retained by te autors and/or oter copyrigt owners and it is a condition of accessing publications tat users recognise and abide by te legal requirements associated wit tese rigts.? Users may download and print one copy of any publication from te public portal for te purpose of private study or researc.? You may not furter distribute te material or use it for any profit-making activity or commercial gain? You may freely distribute te URL identifying te publication in te public portal? Take down policy If you believe tat tis document breaces copyrigt please contact us at vbn@aub.aau.dk providing details, and we will remove access to te work immediately and investigate your claim. Downloaded from vbn.aau.dk on: november, 018

2 1 Harmonic domain modeling of a distribution system using te PowerFactory software Jacek Wasilewski, Wojciec Wiecowski and Claus Let Bak Abstract--Te first part of tis paper presents te comparison between two models of distribution system created in computer simulation software PowerFactory (PF). Model A is an existing simplified equivalent model of te distribution system used by Transmission System Operator (TSO) Eltra for balanced load-flow calculation and stability studies. Model B is accurate model of te distribution system created on te basis of te detailed data of te investigated network and is used as a reference. Te armonic impedance of te two models is compared. In te second part of te paper, te sensitivity of te armonic impedance to basic system parameters (load active power, motor load fraction and reactive power of PFC capacitors) is analyzed. Index Terms--Harmonic analysis, frequency domain analysis, power system modeling, simulation software I. INTRODUCTION INCE some time Danis TSO Eltra as recognized tat Sarmonic currents and voltages propagate in 400 kv transmission network. Te appearance of armonics may cause te malfunction of protective and measuring equipment. One of te reasons of te increase of armonic level is te constantly growing number of non-linear loads connected at te lower voltage levels, as for instance computers, fluorescent lamps, arc furnaces, etc. Te wole Eltra s transmission system is modelled using a computer simulation program PowerFactory (PF). Tis software is a computer aided engineering tool for analysis of electrical power systems. PF is equipped wit ready-to-use models of different power system components. Tis computer model of Eltra s transmission system is presently used for load-flow and stability studies. Terefore all 400 kv and 150 kv transmission lines and cables, large generators and autotransformers are modelled in details. Te lower voltage levels, i.e. 60 kv and below are represented as simplified J. Wasilewski is wit te Institute of Electrical Power Engineering, Warsaw University of Tecnology, Warsaw, Poland ( java81@o.pl). W. Wiecowski and C. L. Bak are wit te Institute of Energy Tecnology, Aalborg University, 90 Aalborg, Denmark ( wtw@iet.aau.dk, clb@iet.aau.dk). equivalent models. It as been decided tat te existing computer model sall be extended so it could be also used for armonic analysis. Te distribution network is connected in many places wit te transmission system and tat is wy it is expected tat teir impedance will ave a significant effect on te propagation of armonics on te transmission level. Te armonic impedance of a distribution system seen from te iger voltage side varies in te frequency. Terefore distribution feeders make a armonic filter function for flow of armonic currents in transmission system. For tat purpose one, representative part of distribution network is closely investigated. II. DESCRIPTION OF THE MODELLED DISTRIBUTION NETWORK Te analyzed distribution system belongs to te company Himmerlands Elforsyning (HEF) and is supplied from 150 kv busbar installed in Vilsted (L) substation. Suc a distribution feeder is sown in Fig. 1. 0,4kV 150kV 60kV PC lines cables 0kV PC lines cables large industrial loads PFC capacitors loads lines cables wind turbines PFC capacitors 0,7kV wind turbines 10kV Fig. 1. Simplified diagram of investigated distribution feeder. PFC capacitors CHP GS Analyzed distribution system contains te following 60/0 kv substations: Aggersund (AGG), Farsø (FSØ), Løgstør (LGS) and Nibe (NIB). Eac 60/0 kv substation includes one or two distribution transformers (10, 16, 0 and 5 MVA), single or double 60 kv and 0 kv busbar system, and PFC

3 capacitors, all of tem installed on te 0 kv voltage level. To all of te 60/0 kv substations some wind turbines are connected. All of tem are connected to te 0,4 kv and 0,7 kv network. Next group of distributed power generation constitutes combined eat and power plants (CHP). It is about 30% of te dispersed power generation in HEF distribution system. Te 0 kv network supplies small distribution substations 0/0,4 kv and large industrial loads. Te majority of te electrical energy consumers are supplied from te 0,4 kv network. Basic description of investigated distribution feeder is presented in Table I. TABLE I BASIC INFORMATION ABOUT ANALYZED DISTRIBUTION SYSTEM Rated apparent power of installed transformers in substations Total lengt of te 60 kv overead lines Total lengt of te 60 kv underground cables Installed active power of wind turbines Installed active power of CHP 150/60 kv 80 MVA 60/0 kv 10, 16, 0 and 5 MVA 54,5 km not appear kw 19 8 kw III. EQUIVALENT MODEL OF A DISTRIBUTION SYSTEM MODEL A Existing PF model of te transmission system is presently used for load flow and stability studies. For tat purpose, it is necessary to model in detail te wole 400 kv and 150 kv grids, but it is sufficient to model all te 60 kv level and below in simplified way using te network equivalents. Tis representation of a distribution system is called Model A and it is sown in Fig.. L3/L3_S1 L/L_SFIK t_ L3 - L t_ L3 - L total power generation in CHP. It is connected to 10 kv busbar and supplies 60 kv busbar troug an equivalent transformer representing all unit transformers installed in CHP. Te equivalent induction generator represents total power generated by wind turbines. It is connected to 0,7 kv busbar and supplies 60 kv busbar troug an equivalent transformer representing all transformers connected wind turbines and medium voltage network. All oter domestic and industrial loads are aggregated and modelled as one resistive and inductive load and connected directly to te 60 kv busbar. Te equivalent model does not include underground cables, overead lines and PFC capacitors. Transformer windings connections and neutral system of 60 kv network are not modelled, because Model A is used for balanced positivesequence load-flow calculations and zero-sequence impedance are of no importance for tis kind of analysis. IV. EXACT HARMONIC DOMAIN MODEL OF THE DISTRIBUTION SYSTEM MODEL B In order to verify if te existing Model A sufficiently accurate represents te armonic impedance of te distribution network seen from te transmission level, a very precise and detailed model of te distribution system as been created Model B. Very detailed data as been obtained from Eltra and HEF companies, and all te components ave been modelled using commonly accepted teories recommended in te armonic analysis literature [1], [6]-[8]. All of te armonic domain models will be described in te following sections. A. Overead lines and underground cables Te overead lines and underground cables are modelled by pi-circuit equivalent representation using distributed parameters [1]. Nominal line parameters can be expressed Z' R' + jx ' (1) Y ' jb' / Corrected model of line (cable) for armonic analysis is sown in Fig. 3. Zexact t_ L - Lb l_l t_ L - Lc Yexact Yexact Lb/Lb_S_SYM Lc/Lc_S_ASM Fig. 3. Exact equivalent pi-circuit model for line and cable. G ~ s_l_q_eq Fig.. Diagram of distribution system represented by Model A. G ~ a_l_w_eq Te generators and te loads are modelled as aggregated components. Te equivalent syncronous generator represents Z Y exact exact Z 0 sin( γl) 1 ( γl) tan Z 0 were γ Z'Y ' is a propagation constant and Z 0 Z' / Y ' is a caracteristic impedance. Due to te skin effect, te series conductor resistance is ()

4 3 frequency dependent. PF allows to model te frequency dependence using Frequency Polynomial Caracteristic [5]. b f y f a a (3) f ( ) (1 ) + 1 were te parameters a 1 and b 0,5. Te line frequency dependent resistance is expressed R' ( f ) R' y( f Tis line model is valid for positive-, negative- and zerosequence. Te long-line effect is more significant for underground cables, due to iger values of sunt capacitances in comparison wit overead lines [8]. B. Transformers Te transformers are modelled by a T equivalent circuit. Te parameters of te equivalent circuit are determined from te vector group, transformer ratio and te quantities computed from sort-circuit and open-circuit measurements. Due to te fact tat te natural resonant frequencies of transformers appear usually above 5 khz [4] and te winding capacitances are relatively small compared to line capacitances, te winding capacitances are not included in calculations. For positive- and negative-sequence, te equivalent model of transformer is sown in Fig. 4. R T / X T / R T / X T / Gµ Bµ Fig. 4. Te equivalent model of transformer for positive- and negativesequence. Te equivalent transformer model for zero-sequence is dependent on te winding connections. Investigated distribution system consists of six transformers wit Yy0 connection and two transformers wit YNy0 connection. For Normal Operating Condition (NOC), one of te transformers operates wit 60 kv neutral point compensated troug Petersen Coil (PC). Except te transformer grounded troug PC, te zero-sequence impedance for all oter transformers approaces infinity (Yy0 winding connection blocks flow for zero-sequence currents [4]). C. Syncronous macines Because of te large number of small size CHP units, it would be difficult and very time-consuming to obtain all te necessary parameters for eac particular CHP unit. Terefore, equivalent models for all CHP units connected to eac 0 kv substation are created. Te equivalent models are connected to 0 kv busbars troug 0/10 kv transformer adapted to equivalent generator rated apparent power. Te unit parameters for syncronous generators are taken from Model ) (4) A and referred to teir rated power value. It is assumed, tat all te generators are salient pole type. In Model B, te syncronous macine is represented for positive- and negativesequence by te stator resistance R st and average subtransient reactance value X av [7]. X ' ' d + X ' ' q X ' ' av (5) Z y( f ) R + jx ' ' (6) Te frequency dependence of stator resistance is modelled using (3). Te syncronous macines block zero-sequence armonic currents, because teir stator windings are connected in delta or ungrounded. Terefore zero-sequence impedance is infinite. D. Induction macines In te investigated network, all te wind turbines are te fixed speed induction macines compensated wit PFC capacitor banks [3]. In Model B, tey are built as equivalent models installed to 0,7 kv busbar and connected troug 0/0,7 kv tranformers to 0 kv busbar in eac distribution substation. Te value of transformer rated apparent power and value of equivalent generator rated apparent power are equal. Te reactive power consumed by induction generators is compensated by te PFC capacitor banks, wic are connected to 0,7 kv busbar Te unit rotor and stator parameters, syncronous and nominal speed values are taken from asyncronous generator equivalent in Model A. It is assumed tat all te induction macines are built as squirell cage type. In Model B, te asyncronous macine is represented for positive and negative sequence by te stator resistance R st, rotor resistance R r dependent on te slip, rotor reactance X st and stator reactance X r [1]. Te representation of induction macine is sown in Fig. 5. R1 X1 Fig. 5. Te induction macine model. sg Xm X R/S Te armonic impedance is expressed as R Z ag R1 + + j( X 1 + X ) (7) S S is apparent slip at te increased frequency ± ωs ωr S (8) ± ωs Te plus sign is for positive-sequence and te minus sign is for negative-sequence. Due to skin effect, te resistance is dependent on frequency by y(f ) formula, expressed in (3). Te magnetizing branc is st av

5 4 neglected, because all te parameters are taken wit te rotor locked. Te induction macines do not provide a pat for zerosequence armonic currents, because tey are connected in delta or ungrounded wye [8]. E. Load models Te one single rule of determining load equivalents for armonic analysis does not exist [6]. Te derivation of armonic resistance and reactance from given active P and reactive Q power flow will need additional information on te actual composition of te load. Power distribution companies sould provide te information about participation for eac type load in te system depending on te time of day. Te domestic loads constitute not only te main element of te damping component, but may affect te resonance conditions at iger frequencies. In Model B, a load model is represented as parallel impedance wit passive (resistance R and reactance X ) and motive part (resistance R 1 and reactance X 1 ) [6]. Suc representation is sown in Fig 6. Tese parameters are determined on te basis of load active power P and motor load fraction K. Passive Motive te power electronic loads are neglected in te analysis. V. THE COMPARISON OF MODEL A AND MODEL B Te magnitude and pase angle of te armonic impedance for Model A and Model B is sown in Fig. 7. Te armonic calculation as been carried out for positive- and negativesequence using frequency sweep option [5] Hz Om Hz Om Hz Om Hz Om L\L_SFIK: Magnitude of Network Impedance. Positive and Negative Sequence in Om, Model A L\L_S1: Magnitude of Network Impedance. Positive and Negative Sequence in Om, Model B Hz Hz Hz Hz Hz Om Hz Om L\L_SFIK: Angle of Network Impedance. Positive and Negative Sequence, Model A L\L_S1: Angle of Network Impedance. Positive and Negative Sequence, Model B Hz Hz Fig. 7. Positive- and negative-sequence armonic impedance for Model A and Model B Constant Y jx R jx1 R1 Te values of impedance magnitude for te most frequently appearing armonic currents are presented in Table II. Te discrepancy between values of impedance for Model A and B are significant. For instance, te discrepancy of impedance magnitude for 5 t armonic is above 100%. TABLE II IMPEDANCE MAGNITUDE FOR SELECTED HARMONIC ORDER Fig. 6. Load model representation. PF allows to model te loads by series resistance and reactance. Terefore, te load as been modelled by two separate impedances (passive and motive part). V R (9) ( 1 K )P V X1 X M (10) K KP X R 1 K (11) (1) K m is install factor ( 1,), X M is p.u. value of te motor locked rotor reactance expressed on te motor rating ( 0,) and K 3 is effective quality factor of te motor circuit ( 8). Modeling te power electronic loads is a more difficult problem, because besides being armonic sources, tese loads do not present a constant RLC configuration and teir nonlinear caracteristics cannot fit witin te linear armonic equivalent model [1]. In te absence of detailed information 1 3 m X 0, 1R Harmonic order Impedance magnitude Model A Model B 5 39,1Ω 13,3Ω 7 53,3Ω 18,5Ω 11 8,Ω 8,4Ω 13 96,7Ω 6,4Ω 3 170,0Ω 14,3Ω 5 184,7Ω 397,7Ω Te curve of armonic impedance magnitude for Model A is linear. Te pase angle approaces 90. In tis case, resonance effects do not appear, because te model does not include any capacitances. All te system components are modelled by resistance and reactance, terefore te curve of armonic impedance magnitude is linear. Looking at te armonic impedance for Model B, it can be seen, tat in te frequency range from 80 Hz up to approx. 800 Hz significant variations of te armonic amplitude and pase angle can be observed. It as been found out tat tese variations are related to te interaction between inductive system components and capacitance of PFC elements. Maximum and minimum values of armonic impedance magnitude and zero values for pase angle of armonic impedance are not at te same frequency value. It means tat

6 5 for discussed frequency range, te main resonance for all system components does not appear. Fig. 8 sows te influence of installed PFC capacitor banks on armonic impedance curve in mentioned frequency range. Te reference curve is performed for all PFC capacitors connected to te system. In case of disconnection of PFC devices from wind turbines busbar or from 0 kv busbar, it can be observed te less number of resonances at lower frequency range compare to reference curve In te end of considered frequency range, close to khz, te trend to parallel resonance effect is observed. All te distribution system components (inductive and capacitive) resonate to eac oter. Te resonance frequency is determined by te capacitance of 60kV lines, PFC devices and inductance of syncronous and asyncronous macines, transformers and loads. Te zero-sequence armonic impedance for Model A and Model B is presented in te Fig. 10. Parallel resonance X Hz 1.00E E E E E+3 Series resonance Hz Om Om 0.00E L\L_SFIK: Magnitude of Network Impedance, Zero Sequence in Om, Model A L\L_S1: Magnitude of Network Impedance, Zero Sequence in Om, Model B Hz/ Hz/ Hz/ L\L_S1: Net. Imp., Pos. Seq. in Om, te PFC capacitors at windmills are out of service L\L_S1: Net. Imp., Pos. Seq. in Om L\L_S1: Net. Imp., Pos. Seq. in Om, te PFC capacitors on 0kV busbar are out of service L\L_S1: Net. Imp., Pos. Seq. in Om, all te PFC capacitors are out of service L\L_SFIK: Angle of Network Impedance, Zero Sequence, Model A L\L_S1: Angle of Network Impedance, Zero Sequence, Model B 000. Fig. 8. Te influence of installed PFC capacitors on armonic impedance for Model B in low frequency range. Te second area consists of te resonance effects at frequencies: 158,8 Hz (parallel resonance) and at 133, Hz (series resonance). It as been revealed tat it is determined by system components in one of te substations (AGG). In Fig. 9, te armonic impedance curves for different values of reactive power of PFC capacitor connected and to 0 kv busbar are sown. If reactive power decreases, te considered resonance sifts towards te main resonance at iger frequency. Te asyncronous macine equivalent includes low value of inductive reactance (in comparison wit all of macine equivalent models). Tis inductance resonates wit te PFC capacitor connected to te 0 kv busbar in te substation Hz Om Hz Om Fig. 10. Zero-sequence armonic impedance for Model A and Model B. Analyzing zero-sequence armonic impedance for Model A, te impedance magnitude and angle equals zero, because te models of transformers do not include zero-sequence parameters and te bot windings of transformers are wye connected wit directly grounded neutral point. Terefore, te way for zero-sequence flow as zero value of impedance. For Model B, two resonances are observed. Te parallel resonance appears at 7,105 Hz frequency. It is effect of a resonance between te inductance of PC and capacitance of 60 kv lines. Te inductance of PC is tuned to 50 Hz frequency. 1 L PC (13) 3 ω C0 Te distribution network sould not operate in overcompensated condition. Terefore te reactance value of PC is lower in comparison of total capacitive reactance of lines. Tis is te reason tat parallel resonance appears above 50 Hz frequency. Te amplitude of armonic impedance approaces infinity, because te resistance of PC used in Model B equals zero. Te series resonance at 1880,3 Hz frequency is observed. It is determined by zero sequence (inductive and capacitive) reactances of 60 kv lines L\L_S1: Net. Imp., Pos. Seq. in Om, AGG1_C1, Q 0,6 Mvar, reference curve L\L_S1: Net. Imp., Pos. Seq. in Om, AGG1_C1, Q 0,4 Mvar L\L_S1: Net. Imp., Pos. Seq. in Om, AGG1_C1, Q 0, Mvar L\L_S1: Net. Imp., Pos. Seq. in Om, AGG1_C1 disconnected Hz Om Hz Om Fig. 9. Te influence of PFC capacitor in AGG substation on armonic impedance MODIFICATION OF MODEL A Te curve of positive- and negative-sequence armonic impedance for Model A and Model B are not close. Te Model A does not include te resonance effects, because it does not consist capacitance components. Te discrepancy of impedance magnitude for Model A and Model B is significant. Besides, Model A does not take te impedance for zero-

7 6 sequence into consideration. To accomplis armonic impedance curve close to Model B, te modification of Model A for all sequences as been made. After te corrections are applied to tis model, Model A can be used for detailed armonic analysis, for instance on transmission system level as more accurate distribution feeder equivalent. Te substitute capacitance for distribution system is modelled by te 60 kv line representation connected to te main 60 kv busbar and operated in no-load state. Te line model includes only sunt capacitance parameters. Te values of series resistance and reactance sould be close to zero. Te line capacitance is modelled separately for positive-, negative- and for zerosequence. It is possible to use sunt capacitors instead, but ten it would be necessary to filter te zero sequence (for example, te sunt capacitor sould be also connected to te wye neutral point of transformer). For tis approac, te use of two components would be needed. First, for positive- and negative-sequence and second, for zero-sequence. Te susceptance for te 60 kv substitute line model can be expressed B k B SL( 1,) L (1,) L (1,) B B SL(0) k L(0) L(0) (14) (15) B L(1,) and B L(0) are positive-, negative- and zero-sequence total susceptance for all te 60 kv lines in investigated distribution system. Correction factors k L(1,) and k L(0) for positive-, negative- and zero-sequence are dependent on te type and te network structure. Minimum value of average discrepancy for k L(1,) 0,6 and k L(0) 0,7 was obtained. At tis moment, it is difficult to state if te calculated factor is correct for eac of distribution feeders. Tis problem sould be analyzed for selected distribution networks. Harmonic impedance curve for Model B and modified and unmodified Model A is presented in Fig Modified armonic impedance curve for Model A is close to armonic impedance curve for Model B only at iger frequencies ( khz). For lower values of frequency, te modification of Model A gives worse results compared to unmodified Model A. Te discrepancy between impedance magnitude for unmodified and modified Model A and impedance magnitude for Model B is sown in Fig. 1. Imedance magnitude discrepancy 50.00% 00.00% % % 50.00% 0.00% Harmonic order Unmodified Model A. Modified Model A. Fig. 1. Te comparison of discrepancy between positive- and negativesequence impedance magnitude for investigated cases. Analyzing te modification test of Model A for positive- and negative-sequence, it can be concluded, tat Model A sould not be corrected in tis way. Te value of armonic impedance discrepancy at significant frequency range for armonic analysis (up to 5 t armonic) is iger in comparison of unmodified Model A. In case of modification of Model A for zero-sequence, it is necessary to model te PC connected to te neutral point of wye winding in one of transformers. Te value of PC inductance is te same, like in Model B. Te resonance frequency is very close to te frequency for Model B (7,105 Hz). Except te lines capacitance and PC, te rest of system components sould not include te flow for zero sequence. Terefore, te load model and te 60 kv side of second transformer sould be ungrounded wye or delta connected. Te comparison of armonic impedance magnitude for Model B and modified on te basis of above-mentioned principles Model A is presented in Fig E E E E L\L_S1: Network Impedance. Positive and Negative Sequence in Om, Model B L\L_SFIK: Network Impedance. Positive and Negative Sequence in Om, unmodified Model A L\L_SFIK: Network Impedance. Positive and Negative Sequence in Om, modified Model A 000. Fig. 11. Te positive- and negative-sequence impedance magnitude for Model B, unmodified Model A and modified Model A. Looking at Fig. 11, te main resonance effect (above khz) for modified Model A is observed. It is determined by total capacitance and inductance of all components in Model A..00E E L\L_SFIK: Magnitude of Network Impedance, Zero Sequence in Om, modified Model A L\L_S1: Magnitude of Network Impedance, Zero Sequence in Om, Model B Fig. 13. Zero-sequence impedance magnitude for Model A and modified Model B. 000.

8 7 Looking at Fig. 14, te discrepancy values for zerosequence increase along wit te frequency % installed in 60/0 kv substations and below. Terefore, te paper suggests te modification of Model A for zerosequence only. Impedance magnitude discrepancy % 50.00% 00.00% % % II. ACKNOWLEDGMENT Te autors wis to gratefully acknowledge te contributions of J. Bak-Jensen from Himmerlands Elforsying and H. Abildgaard from Eltra for elp to get necessary data of investigated distribution power system % 0.00% Harmonic order Fig. 14. Te discrepancy of zero-sequence impedance magnitude between modified Model A and Model B. For significant armonic order (3, 9, 15, 1) te discrepancy between impedance magnitude for Model B and corrected Model A is relatively small. Te most important ting for zero sequence analyzing is correct neutral system representation. For 60 kv network, te only flow for zero sequence currents is troug te capacitance of 60 kv lines and PC. Tese system components cause te resonance effect a little bit above 50 Hz, due to te lower value of inductive reactance for PC tan te value of capacitive reactance for 60kV overead and cable lines. IX. REFERENCES [1] J. Arrillaga, B. C. Smit, N. R. Watson, A.R. Wood, Power System Harmonic Analysis, Cicester: Jon Wiley & Sons, 1997, p. 46, 104. [] S. Bolkowski, Teoria Obwodów Elektrycznyc, Warszawa: WNT, 1997, p [3] N. Jenkins, R. Allan, P. Crossley, D. Kirscen, G. Srbac, Embedded Generation, London: Te Institution of Electrical Engineers, 000, p.37. [4] S. Kujszczyk, Elektroenergetyczne Układy Przesyłowe, Warszawa: WNT, 1997, p [5] PowerFactory Users Manual, ver. 13.1, 005. [6] Task Force on Harmonic Modeling and Simulation, IEEE Power Eng. Soc. T&D Committee, "Impact of Aggregate Linear Load Modeling on Harmonic Analysis: A Comparison of Common Practice and Analytical Models," in IEEE Transactions on Power Delivery, Vol. 18, No., April 003, pp [7] A. C. Williamson: "Te Effects of System Harmonics upon Macines," in International Conference on Harmonics in Power Systems, UMIST, [8] W. Xu, "Component Modeling Issues for Power Quality Assessment," in IEEE Power Engineering Review, November 001, pp I. CONCLUSIONS Tis paper discussed and analyzed problems related to armonic calculations in PF software. In closing of te paper, te following conclusions can be drawn: Te detailed distribution system model (Model B) was created for armonic analysis. Eac of te system elements was created basis of te state of te art calculations of te armonic analysis literature. PF software makes possible to model system components in armonic domain in simple way. Model B was used as reference representation for armonic studies. Te most accurate verification of Model A is to make a measurement. Besides, more accurate system model (Model B) represents real armonic impedance to a larger extent tan Model A Using frequency sweep function in PF, te armonic impedance (magnitude and angle) was computed for Model A and B and compared. For all sequences, armonic impedance curves for Model A and Model B are not close (te discrepancy is significant). System components are not modelled for zero-sequence in Model A Terefore, applying Model A for armonic analysis, it is necessary to take into account big errors in calculation. Te modification of Model A makes a sense for only zerosequence. For significant armonic frequency range, te results are satisfied. Te modification test for positive- and negative-sequence as not been successful. Te results ave been worse compared to unmodified Model A. It is very difficult to model in simple way resonance effects determined by inductive and capacitive components X. BIOGRAPHIES Jacek Wasilewski was born in Elblag, Poland in He received te M.Sc. degree in electrical engineering from Warsaw University of Tecnology in 005. He carried out te semester project as a M.Sc. student at te Institute of Energy Tecnology, Aalborg University. He manages currently te electrical systems design office. Wojciec Wiecowski was born in Warsaw, Poland in He received te M.Sc. degree in electrical engineering from Warsaw University of Tecnology in 001. From 00 to 003 e worked for HVDC SwePol Link as a tecnical specialist. Since 003 e as been employed at te Institute of Energy Tecnology, Aalborg University, were e is currently a PD candidate. His interests include EMC, modeling of power system components and armonic measurements in ig voltage systems. Claus Let Bak was born in Ugelbølle near Årus, Denmark, on April 13, He received te B.Sc (electrical power eng.) degree in 199 from te engineering college in Årus and te M.Sc. (electrical power eng.) degree in 1994 from institute of energy tecnology, Aalborg University. From 1994 to 1999 e was working at Nordjyllandsværket power plant wit planning, design operation and maintenance of 150 and 60 kv substations and relay protection. He was employed as an assistant professor at te dept. Of power systems and ig voltage, institute of energy tecnology, Aalborg University in September 1999 and is currently olding a position as an Associate Professor. Main researc areas are: Hig voltage engineering wit focus on gaseous discarges and overead line corona, relay protection wit focus on power system simulation transient testing of relays.