1、New Positive-sequence Voltage Detector for Grid Synchronization of Power Converters under Faulty Grid Conditions P. Rodrguez, R. Teodorescu, I. Candela, A.V. Timbus, M. Liserre and F. Blaabjerg Technical University of Catalonia Department of Electrical Engineering Barcelona Spain prodriguezee.upc.ed
2、u Aalborg University Institute of Energy Technology Aalborg Denmark retiet.aau.dk Polytechnic of Bari Dept. of Electrotechnical and Electronic Eng.Bari Italy liserrepoliba.it Abstract This paper deals with a fundamental aspect in the control of grid-connected power converters, i.e., the detection of
3、 the positive-sequence component at fundamental frequency of the utility voltage under unbalanced and distorted conditions. Accurate and fast detection of this voltage component under grid faults is essential to keep the control over the power exchange with the grid avoiding to trip the converter pr
4、otections and allowing the ride-through of the transient fault. In this paper, the systematic use of well known techniques conducts to a new positive-sequence voltage detection system which exhibits a fast, precise, and frequency-adaptive response under faulty grid conditions. Three fundamental func
5、tional blocks make up the proposed detector, these are: i) the quadrature-signals generator (QSG), ii) the positive-sequence calculator (PSC), and iii) the phase-locked loop (PLL). A key innovation of the proposed system is the use of a dual second order generalized integrator (DSOGI) to implement t
6、he QSG. For this reason, the proposed positive-sequence detector is called DSOGI-PLL. A detailed study of the DSOGI-PLL and verification by simulation are performed in this paper. From the obtained results, it can be concluded that the DSOGI-PLL is a very suitable technique for characterizing the po
7、sitive-sequence voltage under grid faults. I. INTRODUCTION Grid synchronization is one the most important issues in the integration of power converter into power systems. In particular, this aspect becomes crucial in the connection of wind turbines (WT) to power systems. In recent years, rapid devel
8、opment of WT and increasing penetration of wind power generation have resulted in the reformulation of the grid connection requirements (GCR) for wind power 1. CGR of the most of the countries with a high rate of wind power penetration state that WT have to ride-through of transient faults to sustai
9、n generation. In such grid faults, the amplitude, phase and frequency of the utility voltages can show significant transient variations. Therefore the fast and accurate detection of the positive-sequence component of the utility voltage is necessary in order to keep generation up according to the GC
10、R. When it is assumed that the frequency of the utility is a constant and well-known magnitude, an algorithm based on the instantaneous symmetrical components (ISC) method can be easily implemented for effective detection of the positive-sequence component 2. In Europe the frequency is usually 500.1
11、 Hz and falls out of the 49-50.3 range very seldom 3. However, during a transient fault, the system frequency can show significant fluctuations. Regarding the GCR for wind power, the control system of the grid connected converter must ensure its fast adaptation to the faulty conditions, improving th
12、e fault tolerance of the wind generation system and avoiding the post-fault collapse of the power system because wind generators are lost. On the other hand, when the utility frequency is not constant, the positive-sequence detection system uses closed-loop adaptive methods in order to render it ins
13、ensitive to input frequency variations. The use of a phase-locked loop (PLL) is indeed the most representative example of such frequency adaptive methods. In three-phase systems, the PLLs are usually based on the synchronous reference frame (SRF-PLL) 4. Under ideal utility conditions, i.e., neither
14、imbalance nor harmonic distortion, the SRF-PLL yields good results. In case the utility voltage is distorted with high-order harmonics, the SRF-PLL can still operate satisfactorily if its bandwidth is reduced in order to reject and cancel out the effect of these harmonics on the output. But under vo
15、ltage unbalance however, the bandwidth reduction is not an acceptable solution since the overall dynamic performance of the PLL system would become unacceptably deficient 5. This drawback can be overcome by using a PLL based on the decoupled double synchronous reference frame (DSRF-PLL) 6. In the DS
16、RF-PLL, a decoupling network permits a proper isolation of the positive- and negative-sequence components. An alternative technique for frequency-adaptive positive-sequence detection is presented in 7. Such technique uses a single-phase enhanced phase-locked loop (EPLL) for each phase of the three-p
17、hase system allowing fundamental frequency adaptation. The phase voltages and its respective 90-degree shifted versions detected by the EPLL are used by the ISC method in order to detect the positive-sequence voltages of the three-phase system. Finally, a fourth single-phase EPLL is applied to the o
18、utput of the ISC method to estimate the phase-angle of the positive-sequence voltage. This work presents a new frequency-adaptive positive-sequence detection technique, namely the Dual Second Order Generalized Integrator PLL (DSOGI-PLL). This technique translates the three-phase voltage from the abc
19、 to the reference frames. A dual SOGI-based quadrature-signals generator (QSG) is used for filtering and obtaining the 90-degree shifted versions from the voltages. These signals act as inputs to the positive-sequence calculator (PSC) which lies on the ISC method on the domain. Finally, the positive
20、-sequence voltages are translated to the dq synchronous reference frame and a PLL (SRF-PLL) is employed to make the system frequency-adaptive. II. POSITIVE-SEQUENCE CALCULATION ON THE REFERENCE FRAME At early 30s, Lyon extended the use of the Fortescues symmetrical components method to the time-doma
21、in 8. Using that principle, the instantaneous positive-sequence component +abcv of a generic three-phase voltage vector =Tabc a b cvvvv is given by: 22232,111, .31Tabc a b c abcjvvv TaaTaaaeaa+=(1)Using the non-normalized Clarke transformation, the voltage vector can be translated from the abc to th
22、e reference frames as follow: ,1112 22.3 33022Tabcvv TT =(2)Therefore, the instantaneous positive-sequence voltage on the reference frame can be calculated by: 1211,12 + = = abc abcjTTTqTTT qeqvv vvv(3)where q is a phase-shift operator in the time-domain which obtains the quadrature-phase waveform (
23、90-degrees lag) of the original in-phase waveform. Transformation of (3) is implemented in the PSC of the proposed DSOGI-PLL and its right operation depends on the precision of the quadrature-phase signal provided to its input. It is worth to remark that the time-delay introduced by the q operator i
24、s dynamically set according the fundamental frequency of the input voltage. Therefore, the positive-sequence component calculated from the nth-order harmonic at the input voltage is given by: 1112nnqnq+=vv, (4)where the positive negative sign of n represents the positive negative-sequence of the inp
25、ut voltages. From (4), the harmonic rejection capability of the PSC on the reference frame can be summarized as in Table I, where cells for characteristic harmonics have been highlighted. The PSC does not act as a sequence changer. Consequently, if negative-sequence signals are applied to the PSC in
26、put they will arrive to its output with the same sequence but multiplied by the complex factor specified in Table I. In this sense, positive-sequence calculation of (3) is better than that shown in (1) since this second transformation is transparent for characteristic harmonics propagation. TABLE I
27、HARMONIC PROPAGATION IN THE PSC (+v WHEN 10n=v ) Input signals sequence Order n + - 1st10 0 2nd1245 1245 3rd0 10 4th1245 1245 5th10 0 A relevant aspect to be analyzed in the PSC is the error made in the positive-sequence estimation when the frequency setting the time-delay of the q operator, , diffe
28、rs from the actual center grid frequency, . In such unsynchronized conditions, the complex factor affecting to an nth-order harmonic at the input of the PSC is given by: 1211sin22cos2sgn( ) tan2nnnnnnnn +=+ = =CvCvCC(5)For the sake of clarifying, a numerical example is presented here. In this exampl
29、e, the frequency determining the time-delay of the q operator is 50Hz= whereas the actual grid frequency is 40Hz = . In such conditions, if the components of the grid voltage are 180 0+=v , 120 10=v and 510 30=v , the +v voltage at the PSC output is composed by 1179 9,+=Cv 113.13 91=Cv , and 557.07
30、15=Cv . The amplitude of +v is the same that of +v but its phase-angle is either 90-degrees lag or lead when the input voltage sequence is either positive or negative, respectively. This numerical example has been illustrated in Fig. 1, where the grid frequency changes from =50Hz to =40Hz at t=0.15s
31、 with =50Hz permanently. -150-100-50050100150vabc%-150-100-50050100150v+%0 0.1 0.2 0.3-150-100-50050100150t svabc+%Fig. 1. PSC output when grid frequency changes (=40Hz, =50Hz). (a)(b)(c)III. SECOND ORDER GENERALIZED INTEGRATOR FOR QUADRATURE-SIGNALS GENERATION A transport delay buffer was used to e
32、asily achieve the 90-degrees shifted version of vand vsignals in simulation of Fig. 1. Another simple quadrature-signals generator (QSG) can be implemented by means of a first-order all-pass filter. However, such techniques are not frequency-adaptive, which could give rise to errors in the positive-
33、sequence estimation, e.g. in Fig. 1. Moreover, these simple techniques do not block harmonics from the input signals. To overcome these drawbacks, the use of a single-phase EPLL is proposed in 7. The EPLL is actually an adaptive notch-filter based on minimizing the product of quadrature-signals 9 an
34、d whose frequency moves based on the fundamental frequency of the grid. Other advanced methods for frequency adaptive quadrature-signals generation have been reported in the literature, e.g., the Hilbert transformation-based PLL (HT-PLL) 10 or the inverse Park transformation-based PLL (IPT-PLL) 11,
35、however they become also complex. With the aim of simplifying, this work proposes the use of a second order generalized integrator (SOGI) 12-13 for quadrature-signals generation. The SOGI-QSG scheme is shown in Fig. 2(a) and its characteristic transfer functions are given by : 22() ()vksDs svsks =+(
36、6a)222() ()qv kQs sv sks =+(6b)where and k set resonance frequency and damping factor of the SOGI-QSG respectively. Bode plots from transfer functions of (6) are shown in Fig. 2(b) and 2(c) for several values of k. These plots show how the lower value of k the more selective filtering response, but
37、the longer stabilization time as well. A critically-damped response is achieved when 2k = . This value of gain results an interesting selection in terms of stabilization time and overshot limitation. If v is a sinusoidal signal with frequency , it can be expressed as a phasor v. Therefore the SOGI-Q
38、SG outputs can be calculated from (6) as follow: ()()2222221tankkk =+= = DvDvD(7a)2=QDqv QvQD(7b)It is worth to remark from (7), that qv is always 90-degrees lag respect to v , independently of the value of k, and . This is a very interesting feature for implementing kv vqv-60-40-20020Magnitude (dB)
39、10-1100101102103104-90-4504590Phase (deg)k=0.1k=1k=4-60-40-20020Magnitude (dB)10-1100101102103104-180-135-90-450Phase(deg)Frequency (Hz)k=0.1k=1k=4Fig. 2. SOGI-QSG. (a) SOGI-QSG scheme, (b) Bode plot of D(s), (c) Bode plot of Q(s). the 90-degrees phase-shifting of the q operator. However, (7) also e
40、vidences that the SOGI-QSG output signals will be wrong in both amplitude and phase when the SOGI-QSG resonant frequency, , does not match up to the input signal frequency, . The consequence of these errors will be analyzed in the next section. IV. POSITIVE-SEQUENCE DETECTOR USING A DUAL SOGI-QSG Th
41、e essential structure of the proposed positive-sequence detection system is shown in Fig. 3 where a dual SOGI-QSG (DSOGI-QSG) provides the input signals to the PSC on the reference frame. To evaluate the response of the system it will be supposed that the grid voltage suddenly experiments a complex
42、voltage sag (dip) type D as a (a)(b)(c)vvabcvvqvvqvv+v+vFig. 3. Positive sequence calculation based on DSOGI-QSG consequence of a fault condition which is cleared after 100ms 14. In this dip, the characteristic voltage is 0.6 20 and the positive-negative factor is 0.9 10 , both of them expressed in
43、p.u. respect to the perfectly balanced pre-fault voltage 10pf+=v . Consequently, the positive and negative sequence fault voltages are given by 0.747 14+=v and 0.163 8.63=v respectively. In this simulation, it is assumed that the DSOGI-QSG resonance frequency perfectly matches up with the grid frequ
44、ency, that is 250rad/s = . In addition, the gain of the DSOGI-QSG has been set at 2k = . Fig. 4 shows the response of the PSC under such operating conditions when the DSOGI-QSG is perfectly synchronized. The faulty phase-voltages are shown in Fig. 4(a) and the estimated positive-sequence phase-volta
45、ges in the natural abc reference frame are shown in Fig. 4(e). -150-100-50050100150vabc%-50050100150|v+|%0246+rad-1-0.500.51=+-+rad0 0.1 0.2 0.3-1000100t svabc+%Fig. 4. Response of the PSC in presence of unbalanced voltage sag. Fig. 4(b) shows the actual and estimated amplitude for the positive-sequ
46、ence component, +v , whereas its actual and estimated phase angle are shown in Fig. 4(c). These waveforms are calculated as follows: ()()221;tanvvvv+ +=+ =v . (8)Fig. 4(d) shows the error in phase-angle estimation. Plots of Fig. 4 confirm the good behavior of the proposed system, which is canceling
47、the steady-state error after one cycle of the grid voltage. As studied in Section III, when the grid frequency differs from the DSOGI-QSG resonance frequency, the input signals to the PSC show amplitude and phase errors. Nevertheless such signals are always orthogonal. This last characteristic makes
48、 easy to analyze how DSOGI-QSG errors are propagated through the PSC. Expressing the nthharmonic of vas the phasor nv , it can be concluded from (3) and (7) that the output of the PSC is given by: ()()()()()22222 2222122sgn( ) tan1sgn2nnn nnkkn nnnknnn +=+= +PvPvP , (9a); sgn( )2n + +=vv vv , (9b)where is the fundamental grid frequency, is the DSOG
