Currents Physical Components (CPC) concept in wind farm harmonic current studies

Transcription

1 Currents Pyscal Components (CPC) concept n wnd farm armonc current studes L. Sanz and J. Cunll-Solà Department of Electrcal Engneerng E.T.S.E.I.B, Tecncal Unversty of Catalona (UPC) Av. Dagonal 647, 88 Barcelona (Span) Pone/Fax number: / , e-mal: sanz@ee.upc.edu Department of Electrcal Engneerng E.P.S.E.M, Tecncal Unversty of Catalona (UPC) Av. de les Bases 6-73, 84 Manresa (Span) Pone/Fax number: / , e-mal: cunll@ee.upc.edu Abstract. Very lttle nformaton about actual wnd farm armonc measurements s avalable n te lterature. Ts paper analyzes te armonc measurements of an 8 MW wnd farm wt te CPC concept to determne f tey are consumed or njected by te wnd farm and to study te dfferent reactve power defntons. Te CPC concept s an approac to power teory tat provdes a pyscal nterpretaton of power penomena n electrcal systems wt lnear, tme-nvarant (LTI) loads and armonc generatng loads (HGLs) suc as wnd farms. Key words Wnd power generaton, armoncs, power teory. HV Busbar MV Busbar (ac collector) kv.69 kv kv kv 5-Hz System v Total wnd farm power: x.8 MW kv.69 kv Power analyzer measurements. Introducton Te ncreasng number of wnd farms worldwde causes power qualty problems suc as armonc current emssons []-[6]. Tese emssons produce voltage dstorton n networks, and ter measurement and ncluson n WT power certfcates are terefore requred by current standards [7], [8]. Knowledge of tese emssons s fundamental to study te nfluence of wnd farms on network armonc dstorton. Altoug tey are a well-known topc, very few studes based on actual measurements ave been publsed []-[5]. Recently, te armonc current beavor of an 8 MW wnd farm was nvestgated from a large number of measurements n [9]. Te wnd farm armonc emssons were studed, and te nfluence of te wnd farm workng pont on tese emssons was extensvely analyzed. In addton, te probablty densty functons of te armonc magntudes and pase angles were dscussed and compared n detal wt analytcal and emprcal dstrbutons n te lterature. Wnd farm armoncs and, n partcular, power transmsson penomena can be analyzed by te CPC concept. Te CPC concept s currently te most advanced form of power teory of electrc systems wt perodc and sem-perodc voltages and currents. It explans power propertes of sngle- and tree-pase systems wt LTI loads and HGLs []-3]. WT SCIG P N = 6 kw Te paper analyzes te armonc current measurements n [9] and related power penomena by te CPC concept.. Wnd Farm Measurements A. Wnd Farm N = 3 WTs Fg.. One-lne dagram of te wnd farm. Te armonc currents of te wnd farm n te one-lne dagram of Fg. were extensvely studed n [9]. Te farm conssts of 3x6 kw WT squrrel-cage nducton generators (SCIGs) connected to te MV collector wt /.69 kv transformers. Te rated power of te wnd farm s P N = 8 MW and te rated current at te MV collector s I N = 5 A. A / kv transformer substaton connects te MV and HV busbars. B. Harmonc current measurements Measurements were carred out at te wnd farm MV collector (Fg. ) wt te power network analyzer AR5 L of CIRCUTOR (Fg. ) accordng to te requrements of IEC 64- [7] and IEC [8] standards. Te analyzer as a.5% voltage and current

2 THDI (%) 3 HDI (%)..8.4 HDI 5 (%) 3 HDI 7 (%) Fg.. Power network analyzer AR5-L of CIRCUTOR. accuracy class, a samplng frequency suffcent to evaluate up to te 63 rd armonc order and a Mb onboard memory to save all measured or calculated parameters for future retrevng. Te current clamps employed n te measurements ave a total full-scale accuracy of % wt a bandwdt of Hz to 5 khz. Te actve power, P, and voltage and current waveforms, v and, respectvely, were recorded over a 6-day perod wt a -mnute tme nterval between readngs, eac record beng te -mn average value. Te long storage perod made t possble to record data for te wole power range of te wnd farm, and te -mn average values provded suffcent accuracy of te voltage and current measurements. All te recorded voltage and current values were stored on a ard dsk and treated wt customzed MATLAB software for armonc analyss. Tus, assumng tat te magntude of te currents s statonary, te Fourer transform was appled to a -ms rectangular wndow provdng a 5-Hz frequency resoluton. THDI THDI (%) Te current and voltage armoncs (v and, respectvely) were evaluated up to te fftet order (.5 khz for 5-Hz systems): x() t x = x φ =,,5 ( x = v,). () x Fg. 4. Wnd farm armonc dstorton versus output power for te total measurement perod course. Te wnd farm armonc currents and te nfluence of te wnd farm workng pont on tem were analyzed. In addton, scatter plots of te armoncs (magntude and pase angle) versus te wnd farm output power were provded and te random beavor of te armoncs was examned from te expermental measurements. It could be observed tat te domnant armoncs belonged to te low-order set (n partcular, te gest were 5 t and 7 t ) and tat a g-order armonc pattern exsted n te current spectrum between. and. khz. A summary of te measurements n [9] s gven n Fg. 3 to Fg. 5 consderng te total and ndvdual armonc current dstortons as follows [7]: P/P N φ 5 (º) φ 7 (º) Date and Tme Fg. 3. Tme course of te total armonc dstorton and output power rato Fg. 5. Pase angles of te wnd farm 5 t and 7 t armonc currents versus output power for te total measurement perod course.

3 (t) 3. CPC n Sngle-Pase Crcuts wt HGLs Dstrbuton system v(t) Customer load Let us consder te sngle-pase network n Fg. 6, formed by two subnetworks, te dstrbuton system and te customer load, and te voltage and current, v(t) and (t), measured at te cross-secton between te dstrbuton system and te customer load. If v(t) and (t) belong to te lnear space L T,.e. Fg. 6. Cross-secton between dstrbuton system and customer load. 5 = THDI =, HDI = ( =,3 ), () I I N were I N s te wnd farm rated current and te fundamental and armonc magntudes of te current at te MV collector. Fg. 3 sows te tme course of te THDI and te wnd farm output power. Fg. 4 sows te scatter plot of te THDI and HDI ( =, 5 and 7) versus te wnd farm output power. Fg. 5 contans te pase angle scatter plots of te most sgnfcant armonc currents (.e., 5 t and 7 t armoncs) versus te output power. Te followng remarks on te measurements can be made: - Te fundamental current ncreases proportonally wt te wnd farm output power wle te armonc currents vary stocastcally. - In spte of te random beavor of wnd farm armonc currents, tese are usually modeled as fxed current njectons due to ter small varaton wt respect to te wnd farm operatng pont. In accordance wt IEC 6 standards, te magntudes adopted for armonc current njectons are generally te 95% non-exceedng probablty values of tese currents. - Determnstc models are usually based on te artmetc sum of te average or te 95% percentle values of measured wnd farm armonc currents. Tese models are te smplest ones and compensate for te lack of nformaton about armonc current pase angles. Neverteless, tey lead to overestmaton of system armonc dstorton because te random varaton of armoncs (n partcular ter pase angles) s dsregarded. In [9], a complete study of te wnd farm armonc current stocastc beavor was performed from te feld measurements. Te analyss of te wnd farm armonc measurements n [9] can be teoretcally supported wt te CPC concept. In partcular, te orgn of te armonc currents measured n te above study can be analyzed (.e. weter tese currents are consumed or njected by te wnd farm). Te CPC concept s an advanced form of power teory systems wt non-snusodal voltage and currents []-[3]. Tus, te next Secton summarzes some of te power teory concepts ntroduced by te CPC approac n te presence of HGL []. N x() t = x( t± kt), x () t dt < ( x = v,), T T (3) were k s any nteger number and T, called te perod of x(t), s a nonzero real number, tey can be expressed wt te Fourer seres: x() t = X + Re X e = x () t ( x = v,), j t ω (4) = were x (t) s te armonc of order of te quantty x(t), Η represents te set of armonc orders, ncludng =, of armoncs wt nonzero complex rms values X j X = X e α. (5) Te nstantaneous power at te cross-secton n Fg. 6 s te rate of electrc energy W(t) flow from te dstrbuton system to te customer load and can be expressed as a sum of armoncs as follows: dw () t pt () vtt ()() v () t (). t = = = (6) dt Te actve power s te average value of te nstantaneous power over a sngle perod of te voltage and current: were T * P = p() t = v()() t t Re V I T = = = VI cos ϕ = P ( ϕ = α α ), V I (7) P = V I cosϕ (8) s te actve power of te t armonc order. Te apparent power s defned as te product of te voltage and current rms values: (9) x() t = X ( x = v,),

4 P Z 5 e v Z C P (MW) 5 (a) P 5 Z.5 v j C P5 (kw).5 (b) Fg. 7. Equvalent crcuts: a) For armoncs Η A. b) For armoncs Η B. and t can be expressed as follows: S = v() t () t = Ps P r Q r s r s Vs V Η Η r V s, = P + V V + v = = P + D + Q () were D s and Q are te scattered and reactve power ntroduced by L. S. Czarneck [3] and Q = V I snϕ () s te reactve power of te t armonc order. Te power defntons ntroduced n () by te CPC concept provde better understandng of energy flow and power penomena n electrc systems and study procedures for te enancement of power transmsson effcency and qualty. Te errors n te defntons ntroduced n power teory by dfferent autors ave also been clarfed from te CPC concept, for example te defnton of reactve and dstorton power ntroduced n 97 by Budeanu and supported by te IEEE Standard Dctonary [4]: Q V I sn, D S P Q. () B = ϕ B = B Te pyscal penomena tat caracterze te armonc energy flows n non-snusodal condtons at te crosssecton n Fg. 6 can be analyzed from te pase angle ϕ between te voltage and te current armoncs, v and, at te cross-secton, or from te armonc actve power P (8). Tus, f ϕ π/, tere s an average component P7 (kw) Date and Tme Fg. 8. Tme course of te fundamental, fft and sevent armonc actve powers. of energy flow at te t armonc order from te dstrbuton system towards te customer load,.e. P. If ϕ > π/, tere s an average component of energy flow at te t armonc order from te customer load back te dstrbuton system,.e. P <. Consderng te prevous analyss, te set Η of all te armonc orders can be decomposed nto sub-sets Η A and Η B (Η A Η B = Η) as follows ΗA f ϕ π or P, Η B f ϕ π > or P <, and te voltage and currents can be expressed as x() t = x () t = x () t + x () t ( x = v,). A B (3) (4) Tat s, te consumer load can be consdered as a recever or a armonc source for te armoncs belongng to te sub-set Η A or Η B, respectvely. Ts

5 Q (Mvar) an LTI load and a armonc current source, respectvely, and te dstrbuton system s modeled as a armonc voltage source and a passve energy recever, respectvely. 4. CPC n Wnd Farm Study A. Actve power study QB (Mvar) Q (Mvar) Q5 (kvar) Q7 (kvar) Date and Tme decomposton allows te network n Fg. 6 to be descrbed as a superposton of te two networks n Fg. 7 snce sub-sets Η A and Η B do not contan common armonc orders (Η A Η B = ) and te voltage and currents belongng to tem are mutually ortogonal. In Fg. 7(a) and Fg. 7(b), te customer load s modeled as Fg. 9. Tme course of te reactve powers As mentoned n te prevous Secton, te sgn of te armonc actve powers P (8) allows determnng weter te wnd farm armonc currents occur because of te supply armonc voltages or tey are generated n te wnd farm. Tus, Fg. 8 sows te tme course of te fundamental and te most sgnfcant armonc actve powers measured at te MV collector of te wnd farm. From ts fgure, t can be noted tat - Te actve fundamental power P flows from te wnd farm back te dstrbuton system because ts sgn s negatve. Ts power nearly concdes wt te output power n Fg. 3 because te armonc power contrbuton s small. - Te actve fft and sevent armonc powers P 5 and P 7 flow from te wnd farm back te dstrbuton system because ter sgn s negatve, too. Ts means tat te measured armonc currents are generated by te wnd farm. B. Reactve power study Fg. 9 sows te tme course of te reactve powers calculated from te defntons presented n te prevous Secton [Czarneck, armonc and Budeanu reactve powers,.e. (), () and ()]. From ts fgure, t can be noted tat - Te Czarneck reactve power Q s always postve and ts cancellaton s aceved only wen all armonc reactve powers are cancelled. - Te Budeanu reactve power Q B s smply te sum of te armonc reactve powers of all armoncs and ts cancellaton does not necessarly mean te cancellaton of suc armonc powers. In fact, te pyscal meanng of te armonc reactve powers [.e., te ampltude of te alternatng component of te nstantaneous power (6)] s lost n te Budeanu defnton. - Ts fundamental reactve power Q nearly concdes wt te Budeanu reactve power because te armonc power contrbuton s small. Ts fundamental power corresponds to an nductve consumer and does not cange sgnfcantly over te tme course,.e. wt te dfferent wnd farm output powers. 5. Concluson Te paper presents te measurements of SCIGs wnd farm armonc beavor and analyzes te power armonc penomena from tese measurements and te CPC concept. Te armonc current njected from te wnd farm back te dstrbuton system s demonstrated wt te observaton of te actve armonc power sgn.

6 Te reactve power s calculated from ts dfferent defntons and te results are dscussed and compared. Acknowledgement Ts researc s carred out wt te fnancal support of grant DPI-5448, wc te autors gratefully acknowledge. References [] S. A. Papatanassou and M. P. Papadopoulos, Harmonc analyss n a power system wt wnd generaton, IEEE Trans. on Power Delvery, Vol., No. 4, October 6, pp [] S. T. Tentzeraks and S. A. Papatanassou, An nvestgaton of te armonc emssons of wnd turbnes, IEEE Trans. on Energy Converson, Vol., No., Marc 7, pp [3] D. Sculz and R. E. Hantsc, Investgaton of te current armonc parameters of wnd energy converters, n Proc. of te IEEE Power Tec. Conference 3, Vol. 3, June 3. [4] T. Trnger, T. Petru and C. Lljegren, Power qualty mpact of a sea located ybrd wnd park, IEEE Trans. on Energy Converson, Vol. 6, No., June, pp [5] J. I. Herrera, T. W. Reddoc and J. S. Lawler, Harmoncs generated by two varable speed wnd generatng systems, IEEE Trans. on Energy Converson, Vol. 3, No., June 988, pp [6] J. Balcells and D. Gonzalez, Harmoncs due to resonance n a wnd power plant, n Proc. of te IEEE ICHQP 995, pp [7] IEC 64-, Wnd Turbne Generator Systems, Part : Measurement and Assessment of Power Qualty Caracterstcs of Grd Connected Wnd Turbnes, st ed., December. [8] IEC 6-4-7, Electromagnetc Compatblty (EMC) Part 4 7: Testng and Measurement Tecnques-General Gude on Harmoncs and Interarmoncs Measurements and Instrumentaton, for Power Supply Systems and Equpment Connected Tereto, nd ed. August. [9] L. Sanz, J.J. Mesas, R. Teodorescu, P. Rodrguez, Determnstc and stocastc study of wnd farm armonc currents, IEEE Trans. on Energy Converson, accepted for publcaton (D.O.I.:.9/TEC ). [] L. S. Czarneck, Wat s wrong wt te Budeanu concept of reactve anddstorton power and wy t sould be abandoned, IEEE Trans. on Instrumentaton and Measurement, Vol. IM-36, No. 3, September 987, pp [] L. S. Czarneck, Currents Pyscal Components (CPC) n crcuts wt nonsnusodal voltages and currents. Part : Sngle-pase lnear crcuts, Electrcal Power Qualty and Utlzaton Journal, Vol. XI, No., 5, pp [] L. S. Czarneck, Powers n nonsnusodal networks: Ter nterpretaton, analyss, and measurement, IEEE Trans. on Instrumentaton and Measurement, Vol. 39, No., Aprl 99, pp [3] L. S. Czarneck, Scattered and reactve current, voltage and power n crcuts wt nonsnusodal waveforms and ter compensaton, IEEE Trans. on Instrumentaton and Measurement, Vol. 4, No. 3, June 99, pp [4] Te New IEEE Standard Dctonary of Electrcal and Electrotecncs Terms, IEEE, Inc., New York 997.