Impact of Grid Impedance Variations on Harmonic Emission of Grid-Connected Inverters
IImpact of Grid Impedance Variations on HarmonicEmission of Grid-Connected Inverters
Bakhtyar Hoseinzadeh, Claus Leth Bak
Aalborg University, Denmark { bho,clb } @et.aau.dk Abstract —This paper addresses harmonic magnification due toresonance circuits resulting from interaction between uncertaingrid impedance and converter. The source of harmonic may beeither the grid or inverter. It is demonstrated that unknown andunpredictable grid impedance may result in variable resonancefrequency, which challenges robust design of LCL filter ofinverter.
Index Terms —Harmonic magnification, resonance circuit, gridimpedance, power electronics, voltage source inverter, grid-connected converter, strong grid, LCL filter.
I. I
NTRODUCTION
Nowadays, the widespread energy demand and global envi-ronmental concerns have accelerated development of renew-able energy sources, particularly wind and solar power [1–5].Rapid growth in penetration of renewable energy sources intopower system by further installation of them or replacementof existing conventional power plants, gradually weakensdominancy of synchronous machines compared to the powerelectronic based energy sources [6]. The built-in inverterof aforementioned non synchronous generations, significantlyaffects reliability and security margin of operation and controlof power system [7–10].Prevalence of high order harmonics, which is one of sideeffects of built-in power electronic converters in renewableenergy sources, inevitably imposes sharp changes on voltage,current and frequency profiles [11]. As a result, the harmoniclevel at point of common coupling may violate the permissiblelimits recommended by relevant standards and grid codes [12].The LCL filters employed in grid connected inverters areused to pass the fundamental frequency and attenuate the restof undesired high order harmonics, which are appeared in thecurrent and voltage profiles. Although, this goal is more orless achieved as an advantage of LCL filters, they interact withthe grid elements as a part of a resonance circuit at a pointclose to the source of harmonics, i.e. inverter [13]. Harmonicemission of inverter or the harmonics, which are comingform the grid side may trigger existing parallel and/or seriesresonance circuits. This phenomenon may magnify harmoniclevel exceeding the limits recommended by grid codes andstandards leading to distorted and hence undesired waveformsor in severe cases instability of inverter [14].In power electronic design, the LCL filter is designed insuch a way that the resonance frequency of LCL is locatedfar from the fundamental frequency [15]. In such a designprocedure, the grid impedance variation are not considered in design procedure due high uncertainty in prediction of gridimpedance, while the change in grid impedance results inremarkable shift in resonance frequency [16].Variable and unpredictable grid impedance affects the reso-nance frequency as an external factor, while there is an internalfactor, which is also not considered in the LCL filter design[2, 15]. The scale of wind park, i.e. number of parallel/radialconnection of wind park brunches changes the resonancefrequency. It means that increment in number of brunches,directly but not linearly decreases the resonance frequency.Estimation of grid dynamical behavior is rigorous due to itstime-variant topology, diversity of energy sources, unknownand unpredictable demand response. Stochastic nature andintermittent connectivity of high share of renewable energysources further deteriorate the situation [17]. It means that itwas assumed that the grid just consists of conventional powersystem elements, e.g. synchronous machines, transmissionlines and power electronic-free loads. Nowadays, not onlythere are plenty of inverter-based generation sources behindthe grid, but also the loads even contain harmonic emitterpower electronic devices. Therefore, modeling the grid bya simple voltage source with only fundamental frequencyin series with a set of constant inductor and resistor circuitmay not lead to a comprehensive evaluation of any recentlyproposed scientific solution dealing with current status of gridbehavior [18].II. F
REQUENCY S WEEP OF G RID I MPEDANCE
A. Field Measurement of Grid Impedance
A set of field measurements have been fulfilled to carryout frequency sweep of grid impedance at point of commoncoupling in a wind park. The offshore wind park consists of alarge number of wind turbines interconnected by collectionnetwork. The configuration of collection network includesseveral radial branches in parallel to harvest the power fromwind turbines. In each branch, a set of wind turbines areconnected together in parallel by short submarine cables.
B. Frequency Sweep Analysis
Fig. 1 indicates 24 distinct snapshots of grid impedancemeasured at point of common coupling using frequency sweepthrough the range from 0 to 1 KHz. The field measurementare carried out in different times under normal operationconditions. Various characteristics/behaviors in frequency re-sponse of the grid impedance are illustrated in this section. a r X i v : . [ c s . S Y ] A p r ig. 1: 24 frequency sweep snapshots of grid impedanceA practical/realistic range for grid impedance variations underdifferent conditions of grid is investigated, which should beconsidered to robust design of inverter controller and filteragainst grid impedance uncertainty.The data are originally provided in Cartesian coordinatesformat, i.e. R ( ω ) + jX ( ω ) , while its study in Polar coordi-nates ( | Z | ∠ Z ) is more common. Although, available snap-shot data may not reflect precise and general overview ofgrid impedance, their remarkable correlation, consistency andaccordance in most of cases is a good sign for analysis. Itmeans that the disparity of data is not widespread and theirclassification seems possible to reach a solid conclusion aboutfrequency response of wind farm collection network. However,the grid spectrum demonstrated in fig. 1 can be analyzed fromdifferent aspect of view:First, the frequency sweep clearly reveals that the gridreactance unexpectedly becomes negative per some partic-ular frequency ranges, which means that modeling of gridequivalent impedance using simple and popular assumptionof R + jLω may not be a precise hypothesis for a frequencyrange far from fundamental, i.e. for harmonic studies.Second, a glance observation confirms that considering aparticular and/or limited range for grid impedance may notbe realistic in practice. More important, the percentage ofvariations (uncertainty) is out of engineering imagination (e.g.almost 20 times around 600 Hz), which may challenge anyexisting inverter control scheme.Third, the dependency of grid reactance to frequency isexpected, since the reactance of grid elements, e.g. ca-bles/transformers, is inherently frequency dependent [13].Fig. 1 shows dependency of grid resistance to frequency,which should be investigated. The resistance of each individualelement, itself, is not frequency dependent or its correspondingsensitivity is negligible at least for frequency range of interestin harmonic study. The grid equivalent resistance may vary interm of frequency, if a part of it is bypassed by an internalLC resonant circuit at a particular frequency range as it is (a) Parallel resonance in series (b) Series resonance in parallel Fig. 2: Zeros in impedance transfer functionFig. 3: Overall layout of grid-connected wind turbineutilized to bypass the damping resistor at switching frequencyin C-type LCL filter design.Sharp plunges are observable in both resistance and reac-tance profiles, e.g. around 100, 450 and 600 Hz, which maybe due to existence of nearby/distant series and/or parallelresonance circuits. Fig. 2 indicates different possibility ofresonant circuits, which may come to exist due to interactionbetween grid impedance, inverter LCL filter and inverteroutput impedance. Fig. 2a shows the parallel resonance circuitin series with grid and inverter impedance. If the frequency ofa given current harmonic produced by either grid or inverteraccidentally matches the frequency of parallel resonance cir-cuit, the limited/negligible current harmonic is converted to aconsiderable voltage harmonic by passing through impedance z , which is theoretically infinite and practically a large value.Similar phenomenon may happen for dual circuit depicted inFig. 2b.High/low amplitude of z in Fig. 2a/2b may lead to mag-nification of voltage/current harmonics, which thereafter canbe also appeared in current/voltage profile by passing throughthe rest of existing elements, i.e. z and z . This phenomenonmay be frequently repeated in different frequencies, which isthe main concern of this paper.There is an particular curve in Fig. 1, which is inconsistentwith the others (yellow). This data has been measured atthe same bus, but in different period of time and operationcondition of both grid and wind power plant. However, itdoes not properly follow the overall trend of other patternsin term of behavior and therefore it enervates/challenges theaforementioned agreement about frequency response of gridimpedance. III. S IMULATION S ETUP
In order to investigate the impact of grid impedance vari-ations on performance and stability of grid connected windturbine, simulations are carried out in PSCAD 4.6 software.Fig. 3 indicates the structure of studied wind turbine withig. 4: DC Link & generator voltageFig. 5: Inverter voltagefocus on inner control loop of inverter. Each individual data ofmeasured grid impedance cases are converted to correspondingimpedance transfer function using a built-in block called Fre-quency Dependant Network Equivalent (FDNE) in PSCAD.IV. S
IMULATION R ESULTS
Figs. 4-7 indicate the simulation results in steady statethroughout 0.1 second of time. The waveforms depicted inFig. 4 are the voltage of DC link and three phase voltages ofgenerator ( V C ) as input of converter, respectively. The numberof minor peaks in DC link voltage profile per one period ofconverter waveform is equal to the number of power electronicswitches, i.e. 6, which is explicitly observable. Fig. 5 showsthe output voltage of inverter ( V L ). Comparing the voltagewaveforms of converter and inverter clearly indicates thatthe output of inverter is relatively distorted and polluted byharmonics. The amplitude of voltage curves in both figuresare almost equal to 850 V or equal to 600 V in rms quantity. Fig. 6: Active & reactive power of inverterFig. 7: Third harmonic amplitudeFig. 6 indicates active (solid blue line) and reactive (dashedred line) power of inverter equal to -0.58 MW and 20 MVar,respectively. Due to dominancy of fundamental harmoniccomparing to the other high order harmonics, the simulationresults associated with the fundamental harmonic of all cases1, 3, 13 and 24 are almost similar to each other. Therefore, forthe sake of similarity and space limitation in the paper, onlythe results of case 24 have been presented.The third harmonic magnitude of cases 1, 3, 13 and 24 areplotted in Fig. 7 with different colors. The permissible limit ofthird harmonic recommended by standard [19] is equal to 3 %,which has been specified with a solid and flat red color line.As can be seen, the aforementioned limit is violated by a highquantity of harmonic equal to almost 7%. It means that thethird harmonic is magnified by resonance circuits coming frominteraction of grid impedance and inverter internal impedance.. C ONCLUSION
Collection network of wind farms including lines, trans-formers and LCL filter of inverters in connection with gridimpedance may constitute a LC resonance circuit. Gridimpedance variation and uncertainty changes the resonancefrequency of resulting LC circuits in a widespread range.The resonance circuit/s may magnify harmonics produced byinverters or the harmonics coming from the grid side.R
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