Wind Turbine Harmonics Caused by Unbalanced Grid Currents

Transcription

1 Electrical Power Quality and Utilisation, Journal Vol. XIII, No., 007 Wind Turbine Harmonics Caused by Unbalanced Grid Currents Klaus-Dieter Dettmann, Steffen Schostan, Detlef Schulz Helmut-Schmidt-University, GERMANY Summary: For wind turbines that feed into ublic grids limits for voltage and current harmonics must be assured. To verify that the actual levels are valid, measurements are necessary. Problems can occur to determine which art of these harmonics has its origin in the wind turbine. It is shown that also harmonics which originally have zero sequences can be transferred over a delta-star-transformer, if the currents of the wind turbine are asymmetric due to unbalanced loads. Measurements in an existing wind turbine configuration are discussed, which confirm the described effects. Key words: AC machines circuit analysis current measurement harmonic analysis harmonic distortion ower system harmonics ower system measurements sequences wind energy wind ower generation I. Introduction Wind turbines feeding into ublic grids must comly with several technical standards, e.g. EN 5060 and IEC 6000 [, ]. In these standards limits are secified for the voltage and current harmonics. To en sure that these limits are not exceeded dimen sioning cal culations are not sufficient. Furthermore measure ments must be erformed. For an analysis of the measurement results has to be considered that harmonics are not only generated by the wind turbine but exist in the grid, too. A tyical con figuration is shown in Figure. In this structure the wind turbine transformer is deltastar-wired with ungrounded star oint. Such a transformer blocks zero sequence currents. In the following sections it is described, how harmonics of balanced and unbalanced currents slit into sequences and what arameters are significant for these comonents. II. sequences of harmonic currents In Figure a a system of three-hase currents is shown, where the fundamental currents have the amli tudes î,, î,, î, and hase angles ϕ, ϕ, ϕ relative to the axis. The amlitudes of the υ-th harmonic are labeled with î,v, î,v and î,v ; the harmonic s hase angles γ,υ, γ,υ, γ,υ are measured relative to the zero crossing of the fundamental current of the same hase, see Figure b. In this context e.g. γ,6 means the hase angle of the sixth harmonic in hase. This angle relates to the eriod of that harmonic, i.e. γ,6 corresonds with one third of this har monic s full eriodic time. For more transarency we declare hase as a reference and introduce the amlitude differences î,υ, î,υ and the hase differences ϕ, ϕ, γ,υ, γ,υ, which describe the deviations from the balanced state in hases and. With these definitions the time behavior of the funda mental current: Fig.. Configuration of a grid-connected wind turbine Fig.. Definitions, a fundamental currents, b v-th harmonic and fundamental current in hase 7

2 i ( t = î sin( ω t ϕ,, i ( t = î sin( ω t ϕ,, j( ωt ϕ = e ( î î,,, j( ϕ 40 γ, γ, e Alying ( to these equations we get the desired sequences: i, ( t = î, sin( ω t ϕ can be written as: i ( t = î sin( ω t ϕ,, t = j( ω ϕ j γ e î, e ( î î,, {, j( ϕ ( 0 γ, γ, j( ϕ ( 40 γ, ( î î,, γ, } (4a i ( t = ( î î sin ( ω t ϕ 0 ϕ,,, i, ( t = ( î, î, sin( ω t ϕ 40 ϕ and harmonics of order υ can be reresented as: ( ( i, ( t = î, sin ( ω t ϕ γ, (a i ( t = ( î î sin( ( ω t ϕ 0 ϕ,,, γ γ,, (b t = j( ω ϕ j γ e î, e 0 ( î î,, {, j( ϕ ( 0 γ, γ, j( ϕ ( 40 γ, γ, î, î, } ( e j( ωt ϕ j γ, = e î, e ( î î,, ( î î,, { j( ϕ 0 γ, γ, j( ϕ 40 γ, γ, } (4b (4c i ( t = ( î î sin( ( ω t ϕ 40 ϕ,,, γ γ,, (c The ositive (, negative (- and zero (0 sequences of these currents can be calculated with the method of symmetrical comonents: î î î,, 0, î = [ T ] î î,,, a a with [ T ] = a a and a = 0 e j This method is a similarity transformation that does not contain the frequency in the transform matrix in contrast to Lalace transformation and Fourier transformation. Therefore it can be alied to the harmonic currents as well. At first the currents in ( and ( are reformulated with the comlex calculus:, j ( ωt ϕ j γ, = e î e, ( Before the effect of asymmetries is discussed let s have a look at the results for balanced currents. And balanced should mean ure symmetry, in contrast to VDE 088- or IEC , where a device is already called sym metric, if its rated currents in the three hases do not differ more than 0 % [, 4]. In this case we assume: î ϕ γ Making use of the condition: = î,, = ϕ = γ,, j( 0 ± n 60 j ( 40 ± n 60 e e with n =,,, the following sequences result: t î½ = j( ω ϕ γ e for = 47,,, 0 else j( ωt ϕ γ î e for = 58,,, = 0 else j( ωt ϕ = e ( î î,,, j( ϕ 0 γ, γ, e 0 j( ωt ϕ γ î e for = 69,,, = 0 else 8 Power Quality and Utilization, Journal Vol. XIII, No, 007

3 Table. Sequences of harmonics for balanced currents u ,-, These equations can be transformed with the hel of addi tion theorems for trigonometric functions. Introducing the abbreviations: Thus ositive, negative and zero sequences alternate with increasing harmonic order, as is shown in Table. Next we describe the effects of these sequences of balanced harmonics on rotating fields in electrical ma chines. and: ξf = ( ω t ϕ α ξb = ( ω t ϕ α III. Rotating Fields due to Harmonics in Three-Phase Machines The effect of harmonic sequences on the rotating field in the air-ga of three-hase machines is shown for a synchronous machine. At the terminals the balanced har monic voltages: u ( t = uû sin( ( ω t ϕ, u, ( t = uû sin( ( ω t ϕ 0 u, ( t = uû sin( ( ω t ϕ 40 are assumed, where ϕ is the hase shift of the first order voltage. For a machine with ole airs the distribution of the three hase fluxes Φ(α in the air ga is sinusoidal over the angle α, which is measured relative to the field axis of hase : Φ Φ ( α = Φ ( t cos ( α ( α = Φ ( t cos ( ( α 0 Φ ( α = Φ ( t cos( ( α 40 A A Φ A is the flux amlitude and α has a range of Alying the law of induction to equations (5 and (6, the following air ga flux results: with: Φres ( α, t = Φ ( α, t Φ ( α, t Φ ( α, t Φ t t A (5 (6 (7 uû ( α, = ω cos( ( ω ϕ cos ( α u ( = ( ( 0 û Φ α, t ω cos ω t ϕ cos ( ( α 0 u ( = ( ( 40 û Φ α, t ω cos ω t ϕ cos ( ( α 40 the resultant flux (7 can be rewritten as: Φ res, b [ cosξ ( cos( ( 0 uû = ω f cosξ ( cos( 0 ] where ξ f and ξ b describe one forward and one backward flux wave in the air ga. Evaluating this formula with resect to the harmonic order υ results in the following statements:. The air ga flux Φ res reresents a forward wave for harmonic orders, 4, 7,, i.e. for ositive sequen ces in Table,. Φ res reresents a backward wave for harmonic or ders, 5, 8,, i.e. for negative sequences in Table,. for harmonic orders divisible by the flux Φ res becomes ideally null, if leakage inductances are neglected. The small flux for zero sequences means that the inut imedance of a synchronous machine is very low for such harmonics; a connection of the machine s star oint should be avoided therefore. The angular frequency Ω f of the forward wave can be cal culated by setting ξ f to a secial value, e.g. zero: α = ( ω t ϕ α( t 0 = ω ϕ = ω ( t t Ωf In a machine the ositive sequence harmonic fields rotate with the v-fold velocity of the fundamental harmonic field. The same is true for negative sequence fields, but with oosite direction of rotation. Desite the higher velocity of these harmonic fields their ole itches, i.e. their wave lengths, remain the same, however. This behavior is different to harmonic waves caused by windings that are unevenly distributed around the stator. For those waves the equation: ξf = ( ω t ϕ α is valid. Therefore if an inut voltage is imressed with the fundamental frequency ω, these fields have a v-fold ole itch and rotate with a decreased angular frequency of /v times that one of the fundamental wave [5]. Due to the v-fold velocity of the harmonic fields of harmonic voltage inuts, torque harmonics and eddy currents arise in the machine. Relative to the rotor a forward comonent of the air ga field has the (υ--fold and the backward comonent a (υ-fold velocity that induce currents in the damer winding. (8 9

4 The damer currents with (υ- ω have a rotor field that can again be imagined as a sum of a forward and a back ward comonent with the same frequency and half am litude. These rotating fields induce harmonic voltages of υ ω and (υ- ω in the stator. So a ositive sequence υ-th harmonic imressed at the stator is resonded from the rotor with a υ-th and a (υ- th harmonic. That means a new harmonic is created by the machine. Similarly the resonse of negative sequence υ-th harmonics are a υ th and a (υ th harmonic. IV. Effects of unbalanced currents on Harmonics Until now the derived equations for harmonics have been discussed only for balanced currents and voltages. Next unbalanced imressed currents shall be considered. For this reason equations (4 are evaluated for different tyes of asymmetries. These calculations show that the sequence attern in Table I is only valid for balanced currents. Asymmetries cause a couling between ositive, negative and zero sequences. Thus each harmonic order can occur in every sequence. The strength of this effect is deendent on the degree of asymmetry and of its tye. At first unbalanced harmonic amlitudes i,υ, i,υ and i,υ are assumed. If the harmonic s amlitude varies in a range of 0% ( i,υ = -0 % and i,υ %, an originally ure zero sequence third harmonic converts with 6% of its amlitude to a ositive and with another 6% to a negative sequence. The same is true for the sixth harmonic. Next an asymmetry in the harmonic s hase angles is considered. Deviations of γ,υ = -0 and γ,υ lead to a ositive sequence of % and a negative sequence of 0% both in the third and sixth harmonic. For hase differences of ±0 these values increase to % and 8%. Very significant is the effect of an asymmetry in the hase angles of the fundamental current. Because of the factor ϕ in front of the fundamental hase deviations ϕ and ϕ in (4, these hase shifts are the more significant the higher the harmonic s order number is. For ±5 the transfer to the ositive and negative sequences is 6% and 4% resectively for the third harmonic or % and 4% for the sixth harmonic. These values show that the transfer effect is much greater for order six than for order. It increases for ±0, where the sixth harmonic has 67% ositive and % negative sequence. An extreme case occurs for ±0 ; in this situation the sixth harmonic is comletely converted to a ure ositive sequence. Let s have a look at the consequences of this transferring and mixing of sequences. In Figure the wind turbine is connected to the grid side over a delta-star transformer. This tye of transformer cannot transfer zero sequence currents from on side to the other, even if such a current is flowing in the star winding. But in the considered configuration the star oint is not connected to earth. So also on the star side, i.e. in the wind turbine, there occurs no zero sequence current. This means that in the case of balanced grid currents no harmonics with an order divisible by three can develo. Contrary to zero sequences the transformer can transfer ositive and negative sequences. As a result also harmonic orders, 6, 9 etc. can flow from the wind turbine to the grid, if such sequences occur with these orders due to unbalanced currents. This statement is essential for the evaluation of harmonic measurements, esecially if the origin of harmonics has to be found. Unbalanced currents in medium voltage grids can be caused e.g. by single hase loads that are connected to low voltage grids fed by the medium voltage. These loads are sread over the three hases to roduce a balanced load. But the result of this action is imerfect, because loads have a stochastic behavior. The ositive and negative sequences of the resulting current are transferred to the medium voltage grid over the 0kV/0.4kV-transformer, which is often deltastar-connected with a grounded neutral. If harmonic measurements are taken on the grid side of the wind turbine transformer, harmonics of the wind tur bine and from the grid are measured together. To make a decision, which art comes from the wind turbine, it would be helful to record the hase angles of the har monics, too, if the used equiment is caable of this fea ture. A further way to increase transarency is measuring har monics also at a time when the wind turbine does not feed ower into the grid. It is not sufficient to look at the voltage fall of the harmonics at the medium voltage cable. As is shown in [6], e.g. a sixth harmonic is fed by the wind turbine although the voltage fall of this harmonic lies in the direction from grid to turbine. This aarent incon sistency results from resonant effects with the harmonic filter and leads to higher harmonic levels as are really cre ated by the wind turbine. For this reason in a dimen sioning of filters even such harmonics should not be neglected that cannot be transferred over the transformer under balanced conditions. A further effect of the sequence couling due to unbalanced currents occurs in electrical machines. If divisible-by-three harmonic orders are artly transferred to ositive or negative sequences, in contrast to chater III these currents create rotating fields, too. In the following the described effects on the grid-connection shall be discussed with the hel of measu-rements, but firstly the examined system configuration is resented. V. Details of the analyzed configuration Before it is shown that measurements confirm the theoretical aroach, the wind turbine grid connection in Figure is described more thoroughly. The wind ower lant is develoed for the offshore area and tested in a tyical onshore grid connection. This wind turbine rototye with a rated ower of 5 MW consists of a. kv synchronous generator and a 4-quadrantconverter. The system is connected to a medium voltage transformer 0 kv /. kv, which is wired in a delta-star connection. The neutral oint is not connected to earth. An integrated harmonic filter dams the fifth, seventh und eleventh current harmonics. It con sists of series and arallel LC-circuits which are wired in a star-connection. Their 0 Power Quality and Utilization, Journal Vol. XIII, No, 007

5 neutral oint is grounded. This fact is imortant in order to roof the roagation of the divisible-by-three current harmonics and is taken u later. With a medium voltage cable a connection to the 0 kv / 0 kv transformer substation is established. VI. Measurements Now measurements shall substantiate the theoretical statements in the revious chaters. For that reason longterm measurements were erformed in order to generate a grid quality analysis. With two network analyzers data were recorded over a time eriod of some weeks at both ends of the cable, oints A and B, see Fiure.. Point A reresents the PCC. At this oint the wind turbine (WT feeds in; other loads in the 0 kv grid are connected to this bus bar over cables. Point B is rovided between the wind turbine transformer and its medium voltage cable. This oint lies in the rivate grid of the wind turbine oerator and thus outside the ublic grid. Here the limits of EN 5060 aly, which form the basis of the grid quality analysis. In this unified standards the limits of RMS-voltage, Total Harmonic Distortion (THD of voltage, long-term flicker, harmonics etc. are secified. The analyzers samle the voltage and current behavior and calculate offline the RMS-current, -voltage and all necessary arameters of the grid quality. These data are averaged and stored in a database on hard disc. The storage of mean average values makes ossible measure ments over several weeks or months. Such long eriods of time are necessary to cover the whole ower range of the wind turbine, because the fed ower deends on the wind velocity which is varying with time. In addition transient events can also be detected by adjustable trigger levels. More details of the measurement secifications are described in [6]. It has to be mentioned that no recording-features are included in the used equi ment to detect and store the hase angles of individual current harmonics relative to the fundamental frequency. An analysis with exact hase shifts of the harmonics can not be carried out therefore. Positive, negative and zero sequences of the total current were measured, however. Using these arameters, statements can be made about the current unbalance. The total three hase currents are calculated and slit into sequences. These calculation stes are included in the measurement software. The ratio of negative and ositive sequences as well as the ratio of zero and ositive sequences of the total current is seen in Figures and 4. It is shown that at both oints A (PCC and B (WT a negative sequence of the current occurs and therefore the rerequisite of unbalanced three-hase currents is given. The zero sequence is very low at oint B and can be neglected for further considerations. Differences of the negative sequences between oint A (PCC and B (WT result from the suerosition of current sequences from the medium voltage grid and the wind turbine. A zero sequence current at the 4-quadrant converter outut cannot transfer over transformer to the 0 kv level, see Figure. But as Fig.. Sequence ratios: negative sequences to ositive sequences and zero sequences to ositive sequences of total current at oint A (PCC Fig. 4. Sequence ratios: negative sequences to ositive sequences and zero sequences to ositive sequences of total current at oint B shown before, unbalanced three-hase currents can convert zero sequence current harmonics artly into osi tive and negative sequences. These can roagate over the wind turbine transformer and interfere with current sequences caused by the medium voltage grid. If zero sequences on the grid side exist, they can flow through the earth-caacitances of the medium voltage cable. Therefore the zero sequence at oint A (PCC is higher than at oint B. The residual current of zero sequences can flow to earth over the grounded star oint of the harmonic filter. In the next ste the sectra of the current harmonics at both oints A (PCC and B (WT are investigated. Fig. 5a and 5b show the ratios of current harmonics and the rated current, which equals to 44 A, over a time eriod of four weeks. During this time domain the wind turbine feeds into the grid. The sixth current harmonic is dominating. This fact is atyical for a grid sectrum; normally the third, fifth and seventh harmonics are the dominating ones. The high level of the sixth current harmonics is caused by an undesired effect of the double tuned filter, which dams the fifth, seventh and eleventh harmonics but increases the sixth one. The roof of this measured effect is exlained in detail in [6]. In our case this statement is secondary. The main focus is on the roagation of current harmonics with orders divisible by three over the medium voltage, deltastar-connected transformer with ungrounded star oint. In the next ste the ratio of current harmonics is investigated in

6 Fig. 5. Current harmonics with wind turbine feeding in a at oint A (PCC, b at oint B (wind turbine a time eriod in which no ower was ro duced by the wind turbine, see Figure 6. The level of the sixth current harmonic is essential lower as in eriods when ower roduction of the wind turbine occurs. It is visible that a high level of third current harmonic arises. In a balanced feeding, this current builds a zero sequence which needs a way to earth. In our case these current harmonics can flow to earth otential through the double tuned filter because its neutral oint is grounded. The comarison of the sectra in Fig 5 and Fig.6 makes clear that the high sixth current harmonic levels are roduced by the wind turbine configuration which con sists of the wind turbine rototye, a medium voltage transformer, the double tuned filter and a medium voltage cable. A zero sequence current cannot transfer over the delta-star-connected transformer, as described before, but ositive and negative sequences of the sixth harmonics, caused by unbalanced grid currents, roagate over this transformer. These harmonic currents interfere with the harmonic filter, the cable and the grid imedance so that a high level of sixth current harmonics arises during a ower roduction of the wind turbine. VII. Conclusion In wind turbine grid-connections also harmonics with or ders divisible by three can be transferred to the grid over a delta-star-wired transformer, if the loads have un balanced Fig. 6. Current harmonics with wind turbine switched off a at oint A (PCC, b at oint B (wind turbine currents. The asymmetries result in converting arts of zero sequence harmonics to ositive and negative se quences. For this effect hase shifts in the fundamental current that differ from balanced hase shifts are more significant than asymmetries in the harmonics. Fundamental hase deviations of ±5 lead to a transfer of 6 % of an origi nally ure zero sequence third harmonic to the ositive and 4 % to the negative sequence. For a sixth harmonic this transfer effect is greater, the same hase deviations result in values of % and 4 % resectively. With a fundamental hase deviation of ±0 the sixth harmonic converts comletely from zero to ositive sequence, be cause the corresondent hase shift in the harmonic is 6 0, i.e. the harmonic becomes symmetric. Thus the negative and zero sequences vanish for the sixth har monic in this secial case. With the originally zero sequence harmonics, which convert to ositive and/or negative sequences, roblems can arise, if harmonic filters cause resonant effects with those frequencies. Harmonic measurements have to take into ac count this effect, if the origin of such harmonics has to be found. References. EN 5060, Voltage Characteristics of electricity sulied by ublic distribution systems, March 000. IEC , 998, Electromagnetic comatibility Part -4: Limitation of emission of harmonic currents in low-voltage ower suly systems for equiment with rated current greater than 6 A Power Quality and Utilization, Journal Vol. XIII, No, 007

7 . VDE 088-, 006, Elektromagnetische Verträglichkeit (EMV Teil -: Grenzwerte Grenzwerte für Oberschwin gungsströme (Geräte- Eingangsstrom 6 A je Leiter 4. IEC , 005, Electromagnetic comatibility Part -: Limits Limits for harmonic current emissions (equiment inut current 6 A er hase 5. Müller G.: Betriebsverhalten rotierender elektrischer Maschinen. nd Edition, Berlin, Offenbach: VDE-Verlag, S c h o s t a n S. H, D e t t m a n n K. D. S c h u l z D. a n d P l o t k i n J. : Investigation of an Atyical Sixth Harmonic Current Level of a 5-MW Wind Turbine Configuration. In Proc. of IEEE Region 8 EUROCON 007, Warsaw, Poland Klaus-Dieter Dettmann was born at Pinneberg, Germany, on Aril 0, 954. In 97 he got his university entry qualification from Bismarckschule at Elmhorn. He studied electrical engineering with focus on electrical ower systems at the technical university in Hannover and took his diloma in 979. His doctorate in electrical engineering he got at the Helmut-Schmidt-University in Hamburg in 984, where he is working now as a research assistant and laboratory manager with Prof. Detlef Schulz in the area of electrical ower systems. His current research focus is on grid stability and inter-area oscillations. Address: Electrical Power Systems Helmut-Schmidt-University Holstenhofweg 85, 04 Hamburg Germany kd.det@hsu-hh.de Steffen Schostan was born at Prenzlau, Germany, on Setember 0, 978. In 998 he got his general qualification for university entrance from Städtisches Gymnasium at Prenzlau. After his basic military service he studied electrical engineering with focus on measurement and control technology at the technical university in Berlin. In 005 he took his diloma and changed to the Helmut-Schmidt- University in Hamburg. To date he is working there as a research assistant in the area of electrical ower systems. His current research focus is on the measurement and assessment of ower quality characteristics of grid connected wind turbines. Address: Electrical Power Systems Helmut-Schmidt-University Holstenhofweg 85, 04 Hamburg Germany steffen.schostan@hsu-hh.de D. Schulz was born in Guben, Germany, on July 8, 967. He graduated from the German Polytechnic School, Guben. Detlef Schulz received the Diloma Engineer in 997 from Technical University Cottbus. From 997 to 999 he was with ABB Industrial Automation in Cottbus. In 00 he received the Ph.D. from the Technical University Berlin. From 00 to 004 he was an EU-roject manager of the Technical University Berlin. The habilitation was finished at the Technical University Berlin in 006. From 004 to 005 he was a rofessor for Electrical Engineering and Wind Energy at the University of Alied Sciences in Bremerhaven/Cometence Center Wind Energy. Now he is a full rofessor for Electrical Power Systems of the Helmut-Schmidt-University Hamburg. His research areas are grid integration of distributed renewable energies and future ower system design. Address: Electrical Power Systems Helmut-Schmidt-University Holstenhofweg 85, 04 Hamburg Germany detlef.schulz@hsu-hh.de