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Mitigation of subsynchronous oscillation in a VSC-HVDC connected offshore wind farm integrated to grid
Electrical Power and Energy Systems 109 (2019) 29–37
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Mitigation of subsynchronous oscillation in a VSC-HVDC connected offshore wind farm integrated to grid
T
Qibin Zhoua, Yang Dingb, Kun Maic, Xiaoyan Biand, , Bo Zhoua ⁎
a
Shanghai Key Laboratory of Power Station Automation Technology, School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China State Grid Shanghai Municipal Electric Power Company, Shanghai, China c Cangxian Power Supply Branch of State Grid Hebei Electric Power Supply Co. Ltd., Cangzhou, China d College of Electrical Engineering, Shanghai University of Electric Power, Shanghai, China b
ARTICLE INFO
ABSTRACT
Keywords: Offshore wind farm VSC-HVDC transmission Subsynchronous oscillation Participation factor
This paper focuses on analyzing and mitigating subsynchronous oscillations (SSO) in a doubly-fed induction generator (DFIG)-based offshore wind farm when connected to power grid through voltage source converter based HVDC (VSC-HVDC). Two dominant kinds of oscillation modes are found by modal analysis. One is subsynchronous shaft torsional oscillation (SSTO). However, only a little information exists in published literature regarding SSTO of an offshore wind farm. The other one, which in this paper is named as subsynchronous equipment interaction (SSEI), is due to the interaction between the converter controller of VSC-HVDC and that of wind farm. Research about SSEI is rare and lacks comprehensiveness. For further analysis and mitigation of SSO, participation factor (PF) analysis is conducted in this paper to find variables strongly correlated with SSTO and SSEI. Major contributions of this paper are (1) qualitative principle analysis of these two modes, (2) investigation of the influence of strongly-correlated variables on the oscillation characteristics of each mode and (3) application of damping controllers to comprehensively mitigate SSTO and SSEI.
1. Introduction The Square Butte high voltage direct current (HVDC) transmission system gave rise to the phenomena of subsynchronous oscillations (SSO) as early as in 1977 [1]. Similarly, SSO could occur in a wind farm feeding an HVDC system, for example, Xinjiang Province of China has witnessed SSO over a hundred times. This means that the study of SSO in wind farms is of great importance. On the one hand, the shaft of a generator set may be damaged or broken in the case of shaft torsional oscillation (STO). The destructiveness can be seen from the shaft failure of a turbine-generator occurred at the Mohave Generating Station in the 1970s, of which the subsynchronous shaft torsional oscillation (SSTO) was the culprit [2]. Therefore, the SSTO phenomenon must be considered when mitigating SSO. However, only a little information exists with respect to SSTO of a wind turbine generator (WTG) and most studies are about low-frequency shaft oscillation. A two-mass shaft model is established in [3] and then a damping controller is used to mitigate STO which is within the low frequency range. Reference [4] builds a three-mass shaft model of DFIG and STO can be observed in both low frequency and
⁎
subsynchronous frequency range using modal analysis. According to reference [5,6], if two-mass model is adopted, only the low-frequency oscillation exists. It is, however, further found by [5] that the larger the shaft stiffness, the larger the frequency of STO. It happens that the shaft stiffness of an offshore WTG is larger than that of an onshore one when adopting a two-mass shaft model. In reference [7,8], the shaft stiffness is several times more than that of a general onshore WTG. As a result, for an offshore wind farm, it is very likely that the shaft oscillation frequency falls within the subsynchronous range, namely the SSTO studied in this paper. On the other hand, there exists complex interaction between the converter controller of VSC-HVDC and that of wind farm [9]. Once disturbance occurs, a new form of SSO may be brought about. It is defined as subsynchronous equipment interaction (SSEI) in this paper for the convenience of expression. SSEI will lead to two consequences: (i) The current and power on line will oscillate at a subsynchronous frequency; (ii) Variation of electromagnetic torque of the generator will be excited on account of electro-mechanical coupling. So far, SSEI is short of in-depth research. Ref. [9] studies the distribution and propagation of SSO currents in modular multilevel converter based (MMC)-HVDC system through formula derivation. It
Corresponding author. E-mail address: [email protected] (X. Bian).
https://doi.org/10.1016/j.ijepes.2019.01.031 Received 27 August 2018; Received in revised form 22 December 2018; Accepted 20 January 2019 0142-0615/ © 2019 Published by Elsevier Ltd.
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verifies that SSO occurs due to the interaction between the controller of DFIG-based wind farm and that of MMC-HVDC system. However, oscillation characteristics are not observed and analyzed so that information deficiency and imperfection of mitigating measures can be easily caused. Countermeasures in SSO mitigation can be summarized as two categories: one is employing Flexible AC Transmission Systems (FACTS) [10,11] and the other is installing supplementary damping controller (SUDC). Apparently the latter one is more economic and has become a hot topic. A lot of literature, however, differs in the location of SUDC. Ref. [12] installs SUDC to the rotor-side converter (RSC) of a WTG but no explanation is provided. Ref. [13] chooses the optimum location through comparing all possible locations for SUDC within RSC and GSC. Nevertheless, it turns out to be time-consuming and other possible locations of the entire system are neglected. In [14], different locations for SUDC are compared using the residue-based analysis and root locus diagrams. Apparently, this is time-consuming as well and lacks a definite quantitative index. For improvement, strongly correlated variables of SSTO and SSEI are found through participation factor (PF) analysis in this paper. Thus the best location where SUDC is installed can be determined quickly and accurately. This paper focuses on comprehensively analyzing and mitigating SSTO and SSEI in DFIG-based offshore wind farm integrated to grid through VSC-HVDC. The dominant oscillation modes of SSTO and SSEI are found using modal analysis, followed by PF analysis aiming at finding strongly correlated variables. Then the effects of these variables on the oscillation characteristics of SSTO and SSEI are respectively observed by root-locus diagrams. To collectively mitigate SSTO and SSEI, a supplementary excitation damping controller (SEDC) and a subsynchronous damping controller (SSDC) are applied. Their effectiveness is verified under two different disturbance conditions based on the software DIgSILENT. The organization of this paper is as follows. Section 2 presents the system modeling. Section 3 performs modal analysis and PF analysis. Then the principle of SSTO and SSEI is analyzed qualitatively. Section 4 presents the oscillation characteristics of SSTO and SSEI. Section 5 presents the model of damping controllers. Their effectiveness is confirmed by time-domain simulation in Section 6. Section 7 concludes the paper.
Fig. 1. (a) Topology of a DFIG-Based offshore wind farm connected to grid through VSC-HVDC, (b) Two-mass shaft model.
2Ht *d t /dt = Tm 2Hg *d r / dt = Ks d s / dt = 2 fe (
Ks s Dg
s t
Dt r
t
Te
r )/ pn
(1)
where 2Ht and 2Hg are the inertial time constant of the wind turbine and the generator, respectively; t and r are the rotating speed of the wind turbine and the generator, respectively; s is the shaft torsion angle; Ks is the stiffness coefficient; Tm and Te are the mechanical torque and the electromagnetic torque, respectively; Dt and Dg are the damping coefficient of the wind turbine and the generator rotor, respectively. 2.2. Converter controllers of DFIG Fig. 2 [18] shows block diagrams of the rotor-side converter (RSC) and the grid-side converter (GSC) of DFIG, where the subscripts ‘s ’, ‘r ’, ‘d ’, ‘q’,‘ ref ’ denote stator, rotor, d-axis component, q-axis component and reference component respectively; The subscript ‘ g ’ represents the grid DFIG is connected to; Kp and Ki are the proportional coefficient and the integral coefficient respectively; Lr , Lm denote respectively rotor leakage inductance and mutual inductance of stator and rotor; Lr r =Lr + Lm ; Xt g is the transformer reactance connecting converters and the grid; x1,2, 7 are state variables. The inputs of RSC controller are the decoupled active power Ps and the generator terminal voltage Vs . Idr and Iqr are used to control the output active and reactive power of DFIG stator respectively. GSC is used for maintaining the voltage of the DC bus VDC and controlling its output reactive power. The former control task can be achieved by controlling Idg and the latter can be realized by controlling Iqg .
2. Study system and system model A typical topology of a DFIG-Based offshore wind farm connected to grid through VSC-HVDC is shown in Fig. 1(a) [15]. All DFIGs of the same operation states and parameters are connected to the same bus—the point of common coupling (PCC) via unit connection. The transformer of 35/110 kV is a step-up transformer and the one of 110/ 115 kV is a converter transformer. The VSC-HVDC link consists of the wind farm side VSC (WFVSC) and the grid side VSC (GSVSC). Detailed model of the shaft system and the converter controllers of both DFIG and VSC-HVDC is presented below.
2.3. Converter controllers of VSC-HVDC
2.1. Shaft system
The dq0 transformation is performed to describe the voltages and currents of the VSC-HVDC link with d(q)-axis components for electromechanical transient study. Then the differential equations-based model and control scheme of VSC can be obtained [19,20]. Thus the block diagrams of VSC controllers can be formed, as Fig. 3 [19,20] shows, where the subscripts ‘w ’ and ‘dc ’ represent the wind farm and the DC link respectively; ‘g’ represents the grid GSVSC is connected to; is the system angular frequency; L is the series inductance of AC side; x 8,9, 15 are state variables. For WFVSC, the control scheme is P-f control and V-Q control [20] to supervise and control the frequency and voltage of the wind farm. As
This paper adopts two-mass shaft model as shown in Fig. 1(b) [16,17]. One mass block is composed of wind turbine, hub and low speed shaft, while the other is formed by high speed shaft, gear box and generator. This simplified low-order shaft model not only meets the precision requirements of the analysis but also improves overall computational efficiency [17]. According to Fig. 1(b), the two-mass shaft model, based on per-unit system, can be described as:
30
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Fig. 4. The block diagram of PLL.
3. Modal analysis To observe the oscillation characteristics of the system, modal analysis including eigenvalue analysis and participation factor analysis is performed in this section. Besides, the principle of the two dominant modes is analyzed qualitatively. The system studied employs 20 DFIGs, each with a capacity of 5 MW. The rated capacities of WFVSC and GSVSC are both 150 MW. The DC voltage level is ± 150 kV and the length of DC transmission line is 100 km. The detailed setup of system data is given in Appendix A. 3.1. Eigenvalue analysis Prior to eigenvalue analysis, it’s necessary to determine the natural oscillation frequency of the shaft. For the two-mass shaft model of DFIG, the shaft natural oscillation frequency is given by:
1 2
fm = Fig. 2. The block diagram of DFIG converter controllers. (a) RSC controller, (b) GSC controller. (b) WFVSC controller, (b) GSVSC controller.
0 K s (Ht
+ Hg )/2Ht Hg
(2)
where 0 is the rated frequency of the system. Considering that the offshore wind farm adopts large-scale wind turbine, the stiffness coefficient is set at 1.37p.u. by calculation according to [21]. Ht and Hg are set as 1.9 and 0.2, respectively. Thus fm equals 5.50 Hz according to Eq. (2). In order to get the eigenvalues of the system, the equation of state is established after applying small disturbances as follows: (3)
d x / dt = A x
where A is the state matrix of the system; x is the state variable which contains that of DFIG ( xDFIG ) and that of VSC-HVDC ( xVSC HVDC ), as follows:
xDFIG = [
(a)
t,
r,
s,
ds ,
qs ,
idr , iqr , idg , iqg , uDC , us ,
x1, x2 , x3 , x 4 , x5 , x 6 , x 7 , where
ds
and
xVSC
HVDC
qs
1,
T 2]
are the d-q components of stator flux.
= [ id 1, iq 1, id 2, iq 2, ud 1, ud 2, idc , Q w , iqw , idw , Pw , Q g , iqg , idg , uac , x 8, x 9 , x10 , x11, x12 , x13, x14 , x15,
3,
T 4]
where the subscripts ‘ 1’ and ‘ 2 ’ refer to WFVSC and GSVSC, respectively. Table 1 shows the system eigenvalues obtained from the state matrix. In Table 1, the damping ratio of each mode is calculated by:
(b) Fig. 3. The block diagram of VSC controllers. (a) WFVSC controller, (b) GSVSC controller.
Table 1 Main oscillation modes.
for GSVSC, the voltage of DC link and the reactive power outputted to the AC grid are supposed to be controlled and stabilized. The PLL block is modeled as Fig. 4 shows, where Kp_PLL and Ki _PLL are the control parameters of PLL. In this paper, 1 and 2 are chosen as the state variables of PLL on the DFIG side while 3 and 4 are chosen as the state variables of PLL on the VSC side.
31
Mode
Eigenvalues
1 2 3 4 5 6 7
−2.36 ± j125.29 −0.92 ± j34.42 −5.37 ± j0.75 −16.44 ± j7.94 −51.27 ± j102.23 −89.15 ± j277.22 −330.28 ± j595.14
±j
Frequency f/Hz
Damping ratio ζ/%
19.94 5.48 0.12 1.26 16.27 44.12 94.72
0.02 0.03 0.99 0.90 0.45 0.31 0.49
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Fig. 6. Principle Analysis of SSEI and SSTO.
3.3. Principle analysis of SSTO and SSEI
(a)
How are SSTO and SSEI excited? The following qualitative principle analysis offers an explanation. For SSTO, as shown in Fig. 6, once a network disturbance occurs, a current variation i , whose frequency is fe , is brought about. When i flows into the DFIG stator, subsynchronous current components i ds\_ and i qs\_ , whose frequencies are both f0 fe , will appear and then generate a subsynchronous rotating magnetic field whose frequency is also f0 fe . Thus subsynchronous current components i'dr\_ and i'qr\_ will be induced in the rotor because of this magnetic field. Besides, i will induce voltage variation and current variation at the side of the grid, namely udg\_ , uqg\_ , i dg\_ and i qg\_ . Coincidentally, they are the input of GSC and will certainly influence RSC. As a result, new subsynchronous current components will be excited in the rotor winding under the regulation of RSC. The accumulation of i'dr\_ , i'qr\_ and these new components gives birth to two subsynchronous current components i dr\_ and i qr\_ whose frequencies are both f0 fe at the side of the rotor. If f0 fe approximately equals the shaft natural oscillation frequency fm , drastic shaft torsional vibration will occur, namely SSTO. For SSEI, owing to i , active and reactive power variation Pw\_ , Q w\_ will be excited and will be inputted into WFVSC. Under the regulation of WFVSC, a current variation whose components are i d 1_ and i q 1_ will appear. As a result, with the current variation flowing, the AC active power in the wind farm side will oscillate at a subsynchronous frequency and thus lead to the variation of generator electromagnetic torque Te . Te has a negative damping for the shaft torsional vibration which will be intensified if the mechanical damping of the shaft is insufficient, namely SSEI.
(b) Fig. 5. Results of participation factor analysis. (a) Participation factors of Mode 1, (b) Participation factors of Mode 2.
= - /
2
+
2
(4)
It is worth reminding that the real eigenvalues are not displayed since they have nothing to do with the oscillation modes. As a result, there are mainly seven oscillation modes, with two dominant modes indicated in bold, namely Mode 1 and 2. Mode 3 and 4 belong to low frequency and since their damping ratios are both larger than 0.1, the corresponding oscillations will attenuate fast; Mode 5 and 6 have big negative real parts so that they are relatively stable; Mode 7 belongs to supersynchronous oscillation.
4. Oscillation characteristics According to the analysis above, SSEI and SSTO are strongly related to x1, x2 , Qw and t . x1 corresponds to the outer active power loop whose proportional coefficient and integral coefficient are Kp1 and Ki1, respectively. x2 corresponds to the inner current loop whose proportional coefficient and integral coefficient are Kp2 and Ki2 , respectively. If one of Kp1, Ki1, Kp2 , Ki2 and t changes whilst the others remain unchanged, the root-locus diagrams of SSEI and SSTO can be obtained to analyze the oscillation characteristics of each mode in terms of the damping level and the oscillation frequency. It's well-known that the further the real part of an eigenvalue is away from the imaginary axis, the greater the positive damping. Moreover, the larger the imaginary part, the larger the oscillation frequency.
3.2. Participation factor analysis Based on the eigenvalue analysis implemented in section A, seven pairs of eigenvectors are obtained and thus participation factor analysis can be performed. The participation factor of each state variable related to mode 1 and 2 is shown in Fig. 5, omitting those values which are small or near to zero. It's obvious that mode 1 has a strong relationship with x1, x2 , Qw and mode 2 has a strong relationship with x2 , t, where x1 and x2 are corresponding to the active power control link of RSC; Qw refers to the input of WFVSC; and t refers to the speed of the shaft of wind turbine. It can be concluded that the converters of DFIG and VSV-HVDC will contribute to the occurrence of mode 1, so that it is classified as SSEI. Mode 2 has a frequency close to the shaft natural oscillation frequency and it is strongly related to the shaft speed, so that this mode is corresponding to the SSTO mode.
4.1. Oscillation characteristics of SSEI When parameters are changed in the range within the square bracket in Table 2, the root-locus diagrams of SSEI can be obtained and are shown in Fig. 7(a) and Fig. 8 respectively. From Figs. 7(a) and 8, observations can be made as follows: 32
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Table 2 Parameter setting of state variables. Para-meter
Case 1
Kp1
[1,15]
K i1 Kp2 K i2 t (rad/s)
20 2.3
50 0.2
Case 2
Case 3
Case 4
Case 5
5
5
5
5
20 2.3
20 2.3
[15,40] 2.3
20 [1.2,4.5]
[2.5,500] 0.2
50 [0.05,0.7]
50 0.2
50 0.2
Fig. 8. Influence of SSTO.
t
on the oscillation characteristics of mode (a) SSEI, (b)
(1) Similar to SSEI, Kp1 and Ki1 have little effect on the oscillation characteristics of SSTO. (2) When Kp2 gradually increases, the real part of the eigenvalue moves closer to the imaginary axis but still stays within the left half of the complex plane and the oscillation frequency slowly decreases. This means the system remains stable. When Ki2 increases, the real part also moves nearer to the imaginary axis and the oscillation frequency increases, which means the system stability gets weakened. (3) When t increases, the real part of the eigenvalue moves further away from the imaginary axis, which means the system stability improves.
(a)
5. Damping controllers The oscillation characteristics of SSEI and SSTO have paved the way for the site selection of damping controllers. To mitigate SSTO, DFIG_SEDC which is located at the excitation link of RSC with inputted can be employed. Through adjusting the excitation voltage of the generator, DFIG_SEDC can generate a supplementary electromagnetic torque TSEDC.To mitigate SSEI, VSC_SSDC which is located at the reactive link of WFVSC can be employed. By adjusting the reference value of the reactive power inputted to the outer loop control of WFVSC, VSC_SSDC also generates a supplementary electromagnetic torque TSSDC . Both TSEDC and TSSDC can provide a positive damping to compensate for the possible negative damping. In this way, the phase difference between Te and falls within 90°, where Te is the initial = t variation of electromagnetic torque and r.
(b) Fig. 7. Influence of Kp and Ki on the oscillation characteristics of mode (a) SSEI, (b) SSTO.
5.1. Location and model of DFIG_SEDC
(1) Kp1 and Ki1 have little effect on the oscillation characteristics of SSEI. (2) When Kp2 gradually increases, the real part of the eigenvalue moves closer to the imaginary axis and the oscillation frequency increases a little. Moreover, the real part becomes positive when Kp2 reaches a maximum value of 0.7, which means that the system has a negative damping for SSEI. When Ki2 increases, the real part shows little changes but the oscillation frequency reduces significantly, which means the system stability gets improved. (3) t has also small influence on the oscillation characteristics of SSEI.
Since SSTO is strongly related to the parameters of RSC and the speed of wind turbine t , the q-axis component of the rotor excitation voltage is chosen to be modified [22]. The modified block diagram of RSC controller is shown in Fig. 9(a) where Tw1 is the time constant of the DC-Elimination link which can eliminate the error introduced by signal offset; T1 and T2 are the time constants of phase-compensation link which can compensate the phase offset of each eigenvalue; KSEDC is the gain coefficient. In this paper, Tw1 is set as 5 s and the amplitude limitation is set as ± 0.1 p.u . T1 and T2 are determined by Eq. (8) [23].
4.2. Oscillation characteristics of SSTO
a = T2/ T1 = (1 sin )/(1 + sin ) T1 = 1/2 fc a
Similarly, changing the parameters according to Table 2, the rootlocus diagram of SSTO can be obtained and is shown in Fig. 7(b) and Fig. 8 respectively. Observations can be made as follows:
(8)
where fc is the frequency of each mode; is the phase angle to be compensated corresponding to some frequency point. In order to obtain of each mode, the complex torque coefficient approach realized by 33
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Fig. 10. The flow chart of the test signal method.
Fig. 9. The block diagram of modified controllers. (a) RSC controller with DFIG_SEDC added, (b) WFVSC controller with VSC_SSDC added.
time domain simulation – the Test Signal Method [24] is adopted in this paper.**
(a)
5.2. Location and model of VSC_SSDC Taking the broadband design of SSDC as a reference in [25], the AC bus voltage is inputted to generate a supplementary control signal of reactive power. The block diagram of WFVSC controller after adding VSC_SSDC is shown in Fig. 9(b). It is the reactive power inputted into WFVSC QW to which SSEI is strongly related that should be modified. In this way, QW =Q W\_ref + QSSDC QW . 6. Case studies Prior to case study, the complex torque coefficient-test signal method is applied to determine the parameters of DFIG_SEDC and VSC_SSDC. After that, both the modal analysis and the time-domain simulation are performed using DIgSILENT to detect whether they can effectively damping SSO.
(b) Fig. 11. (a) The electrical damping coefficient curve, (b) The angle Te lags by.
6.1. Parameters of DFIG_SEDC and VSC_SSDC To calculate the parameters of DFIG_SEDC and VSC_SSDC according to Eq. (8), complex torque coefficient-test signal method is adopted to determine . The flow chart is shown in Fig. 10 [126]. Mechanical torque of different frequencies ranging from 5 to 45Hz is exerted on the DFIG stator every time. Finally the electrical damping coefficient De ( f ) and the phase angle by which Te lags can be obtained. From the electrical damping coefficient curve shown in Fig. 11(a), De of mode 1 and mode 2 are both negative. This means SSEI and SSTO can easily occur when the system mechanical damping is insufficient. As shown in Fig. 11(b), the lag angle of mode 1 and 2 are 106° and 126° , respectively. Then we utilize two lead-lag blocks and the total compensation angle of the two blocks is set as Table 3 shows. Thus
Table 3 Parameter setting of
DFIG-SEDC
Modes
and
VSC-SSDC.
Compensation Angle 1 ( 2)
34
Time Constant
Gain
T1 (T3)
T2 (T4)
K
Mode 1-SSEI 19.94 Hz
DFIG_SEDC VSC_SSDC
94° 48°
0.019 0.012
0.003 0.005
12.4 5.7
Mode 2-SSTO 5.48 Hz
DFIG_SEDC VSC_SSDC
62° 41°
0.113 0.064
0.007 0.013
23.6 14.5
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Table 4 Eigenvalues of Mode 1 and 2 under different conditions. Conditions
Mode 1 19.94 Hz
Mode 2 5.48 Hz
Without DFIG_SEDC or VSC_SSDC With DFIG_SEDC With VSC_SSDC With DFIG_SEDC and VSC_SSDC
−2.36 ± j125.29 −3.20 ± j126.87 −3.76 ± j126.33 −5.15 ± j127.92
−0.92 ± j34.42 −1.79 ± j35.13 −2.14 ± j34.82 −3.38 ± j36.05
parameters of DFIG_SEDC and VSC_SSDC can be calculated by Eq. (8), as listed in Table 3. After the parameters of damping controllers are set according to Table 3, we perform the modal analysis again and the new simulation results are shown in Table 4. It becomes apparent that DFIG_SEDC or VSC_SSDC makes the real part of the eigenvalue move further away from the imaginary axis, which means the system stability is improved. Besides, when installed together, DFIG_SEDC and VSC_SSDC can make concerted effort to remarkably decrease the real part of the eigenvalue, which proves their effectiveness in damping SSO. In order to further prove that the location selected by PF analysis in this paper is the optimal one, DFIG_SEDC and VSC_SSDC are installed to alternative locations of the test system and the result of eigenvalues is presented in Table 5. The location selected by PF analysis and its simulation results are shown in bold. It is obvious that the real part of the eigenvalue move further away from the imaginary axis when DFIG_SEDC or VSC_SSDC is installed to locations selected by PF analysis. It can be concluded that the site selection method adopted by this paper is better.
(a)
(b)
6.2. Time-domain simulation For further study of the performance of DFIG_SEDC and VSC_SSDC, the dynamic variation of the electromagnetic torque is observed under different disturbance conditions: Case 1: the wind speed changes from 10 m/s to 13 m/s at 0.5 s and lasts for 0.075 s; Case 2: the wind speed changes from 8 m/s to 11 m/s at 1.25 s and lasts for 0.25 s; Case 3: a three-phase short circuit fault occurs near PCC at 0.5 s and lasts for 0.075 s; Case 4: a three-phase short circuit fault occurs near bus U2, which is connected to the AC grid, at 1.25 s and lasts for 0.25 s.
(c)
The simulation results of the four cases are illustrated in Fig. 12. In each case, the dynamic variation of the electromagnetic torque is compared when the system is equipped with different damping controllers. It can be concluded that the results of the four cases are consistent with each other from Fig. 12. Apparently, the variation of Te shows a drastic oscillation which attenuates slowly with no damping controllers installed to the system. When DFIG_SEDC is added, the oscillation of Te is to a great extent damped. Likewise, VSC_SSDC attenuates the Table 5 Eigenvalues of Mode 1 and 2 when locations.
DFIG_SEDC
or
VSC_SSDC
is installed to different
Damping controller
Locations
Mode 1 19.94 Hz
Mode 2 5.48 Hz
DFIG_SEDC
RSC: x2 RSC: x1 GSC: x5
−3.20 ± j126.87 −2.69 ± j125.65 −2.47 ± j125.48
−1.79 ± j35.13 −1.38 ± j34.63 −1.23 ± j34.56
VSC_SSDC
WFVSC: Q w WFVSC: x5 WFVSC: x10
−3.76 ± j126.33 −2.86 ± j125.60 −2.47 ± j125.31
−2.14 ± j34.82 −1.33 ± j34.63 −1.21 ± j34.58
(d) Fig. 12. Influence of different controller configurations on the curve of Te in (a) case 1, (b) case 2, (c) case 3, (d) case 4.
35
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oscillation when added individually. When DFIG_SEDC and VSC_SSDC are installed together, the wave attenuates even faster and reaches convergence earlier. The above results of time-domain simulation coincide with conclusions drawn from eigenvalue analysis and demonstrate that DFIG_SEDC can cooperate with VSC_SSDC on mitigating SSTO and SSEI Fig. 12(a) and (b) reflect results under disturbance occurred on the power supply side. Fig. 12(c) demonstrates the results simulated when faults happen on the power supply side while Fig. 12(d) the grid side. This means system stability can be significantly enhanced and improved under either static or transient disturbances with both DFIG_SEDC and VSC_SSDC installed.
new type of SSO may result from the interaction between different power electronic equipment, namely SSEI. In this paper, the SSO phenomenon has been investigated on the premise that a DFIG-based offshore wind farm is integrated to grid via VSC-HVDC. Firstly, the dominant oscillation modes are obtained using modal analysis. After that, state variables which are strongly correlated with the dominant modes are sieved out and their influence on the oscillation characteristics of each mode are analyzed then. It turns out that SSTO occurs along with SSEI which the interaction between DFIG converter controller and VSC controller is responsible for. Later, damping controllers are both installed in DFIG and VSC. The damping effect has been verified under static or transient disturbances using DIgSILENT.
7. Conclusions
Acknowledgment
Compared with onshore WTGs, offshore ones generally have larger shaft stiffness so that the SSTO phenomenon is very likely to happen. Moreover, when an offshore wind farm is connected to VSC-HVDC, a
This work was financially supported by Shanghai Science and Technology Project under grant (16020501000).
Appendix A The parameters of DFIG and VSC-HVDC are given in Table 6 and Table 7, respectively.
Table 6 Parameter setting of DFIG.
Table 7 Parameter setting of VSC-HVDC. Types
Para-meter
Value
HVDC
R
0.006 /km
X
VSC
Kp8
2
K i8
12
K i10 K i12 K i14
Kp10 Kp12 Kp14
2 1
Para-meter
Value
10 10
0.12 50
36
Para-meter
Value
0.4 /km
B
Kp9 Kp11 Kp13 Kp15
2
K i9
100
10
K i11 K i13 K i15
100
2
10
3.14 μS/kmµS/km 100 100
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References
[13] Mohammadpour HA, Santi E. SSR damping controller design and optimal placement in rotor-side and grid-side converters of series-compensated DFIG-based wind farm. IEEE Trans Sustain Energy 2015;6(2):388–99. [14] Fan L, Miao Z. Mitigating SSR using DFIG-based wind generation. IEEE Trans Sustain Energy 2012;3(3):349–58. [15] Wang L, Yang ZH, Prokhorov AV. Stability analysis of a hybrid multi-infeed HVDC system connected between two offshore wind farms and two power grids. 2016 IEEE industry applications society annual meeting, Portland, OR. 2016. p. 1–9. [16] Ali HR. The dynamic performance of grid-connected fixed-speed Wind Turbine Generator. 2014 6th international conference on information technology and electrical engineering (ICITEE), Yogyakarta. 2014. p. 1–5. [17] Xie Z, Xu Z, Zhang X, Yang S, Wang L. Improved power pulsation suppression of DFIG for wind shear and tower shadow effects. IEEE Trans Ind Electron 2017;64(5):3672–83. [18] Wu F, Zhang XP, Godfrey K, Ju P. Small signal stability analysis and optimal control of a wind turbine with doubly fed induction generator. IET Gener Transm Distrib 2007;1(5):751–60. [19] Imhof M, Andersson G. Dynamic modeling of a VSC-HVDC converter. Power engineering conference (UPEC), 2013 48th International Universities', Dublin. 2013. p. 1–6. [20] Tang GF. HVDC transmission technology based on voltage source converter. China Electric Power Press; 2010. p. 310–1. [in Chinese]. [21] Ackermann Thomas. Chapter 24. Introduction to the Modelling of Wind Turbines. Wind power in power systems. John Wiley & Sons, Ltd; 2005. p. 543–6. [22] Xie X, Guo X, Han Y. Mitigation of multimodal SSR using SEDC in the Shangdu series-compensated power system. IEEE Trans Power Syst 2011;26(1):384–91. [23] Xiang Zheng, Xu Z, Zhang J. A supplementary damping controller of TCSC for mitigating SSR. In: Power & energy society general meeting, 2009. PES '09. IEEE IEEE; 2009. p. 1–5. [24] Zheng Xu, Feng Z. A novel unified approach for analysis of small-signal stability of power systems. Power Eng Soc Winter Meet. 2002;2:963–7. [25] Rui-hua Song, Ji-ming Lin, Lian-geng Ban, Zu-tao Xiang. Study on the SSO damping characteristic and damping control of Mongolia-China HVDC transmission system. 2010 international conference on power system technology, Hangzhou. 2010. p. 1–5. [26] Jin Wang, Chunlin Guo, Xiangning Xiao, Rui Zheng. The study of complex torque coefficient approach's realization based on PSCAD/EMTDC. 2010 5th international conference on critical infrastructure (CRIS), Beijing. 2010. p. 1–4.
[1] Bahrman M, Larsen EV, Piwko RJ, Patel HS. Experience with HVDC – turbinegenerator torsional interaction at square butte. In: IEEE transactions on power apparatus and systems, vol. PAS-99, no. 3. p. 966–75; May 1980. [2] Walker DN, Bowler CEJ, Jackson RL, Hodges DA. Results of subsynchronous resonance test at Mohave. IEEE Trans Power Apparatus Syst. Sept. 1975;94(5):1878–89. [3] Kina A, Ludin GA, Senjyu T, Howlader AM, Danish MSS. Torsional oscillation damping control for wind turbine generator under strong wind conditions. 2016 IEEE region 10 conference (TENCON), Singapore. 2016. p. 942–5. [4] Liu Libo, et al. A Damping Method for Torsional Vibrations in a DFIG Wind Turbine System Based on Small-Signal Analysis. Electric Mach. Power Syst. 2017;45(5):560–73. [5] Yang Lin, Xiao Xiangning, Pang Chengzong, Li Chun. Effects of wind turbine generator's drive train model on subsynchronous oscillation. 2015 IEEE 2nd international future energy electronics conference (IFEEC), Taipei. 2015. p. 1–6. [6] Yang Lin, Xiao Xiang Ning, Pang Cheng Zong. Oscillation analysis of a DFIG-based wind farm interfaced with LCC-HVDC. Sci. China (Technol. Sci.) 2014;57(12):2453–65. [7] Li Yujun, Zheng Xu. Control strategy of grid integration using the flexible DC power transmission in offshore wind farm. East China Electric Power 2013;41(05):953–61. [in Chinese]. [8] Roy NK, Pota HR, Hossain MJ. Reactive power management of distribution networks with wind generation for improving voltage stability. Renew Energy 2013;58(10):85–94. [9] Lv J, Dong P, Shi G, Cai X, Rao H, Chen J. Subsynchronous oscillation of large DFIGbased wind farms integration through MMC-based HVDC. 2014 international conference on power system technology, Chengdu. 2014. p. 2401–8. [10] Varma RK, Auddy S, Semsedini Y. Mitigation of sub-synchronous resonance in a series-compensated wind farm using FACTS controllers. IEEE Trans Power Deliv 2008;23(3):1445–54. [11] Bak-Jensen B, El-Moursi MS, Abdel-Rahman MH. Novel STATCOM controller for mitigating SSR and damping power system oscillations in a series compensated wind parks. IEEE Trans Power Electr 2010;25(2):429–41. [12] Zhao B, Li H, Wang MY, et al. An active power control strategy for a DFIG-based wind farm to depress the subsynchronous resonance of a power system. Int J Electr Power Energy Syst 2015;69:327–34.
37
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Mitigation of subsynchronous oscillation in a VSC-HVDC connected offshore wind farm integrated to grid
T
Qibin Zhoua, Yang Dingb, Kun Maic, Xiaoyan Biand, , Bo Zhoua ⁎
a
Shanghai Key Laboratory of Power Station Automation Technology, School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China State Grid Shanghai Municipal Electric Power Company, Shanghai, China c Cangxian Power Supply Branch of State Grid Hebei Electric Power Supply Co. Ltd., Cangzhou, China d College of Electrical Engineering, Shanghai University of Electric Power, Shanghai, China b
ARTICLE INFO
ABSTRACT
Keywords: Offshore wind farm VSC-HVDC transmission Subsynchronous oscillation Participation factor
This paper focuses on analyzing and mitigating subsynchronous oscillations (SSO) in a doubly-fed induction generator (DFIG)-based offshore wind farm when connected to power grid through voltage source converter based HVDC (VSC-HVDC). Two dominant kinds of oscillation modes are found by modal analysis. One is subsynchronous shaft torsional oscillation (SSTO). However, only a little information exists in published literature regarding SSTO of an offshore wind farm. The other one, which in this paper is named as subsynchronous equipment interaction (SSEI), is due to the interaction between the converter controller of VSC-HVDC and that of wind farm. Research about SSEI is rare and lacks comprehensiveness. For further analysis and mitigation of SSO, participation factor (PF) analysis is conducted in this paper to find variables strongly correlated with SSTO and SSEI. Major contributions of this paper are (1) qualitative principle analysis of these two modes, (2) investigation of the influence of strongly-correlated variables on the oscillation characteristics of each mode and (3) application of damping controllers to comprehensively mitigate SSTO and SSEI.
1. Introduction The Square Butte high voltage direct current (HVDC) transmission system gave rise to the phenomena of subsynchronous oscillations (SSO) as early as in 1977 [1]. Similarly, SSO could occur in a wind farm feeding an HVDC system, for example, Xinjiang Province of China has witnessed SSO over a hundred times. This means that the study of SSO in wind farms is of great importance. On the one hand, the shaft of a generator set may be damaged or broken in the case of shaft torsional oscillation (STO). The destructiveness can be seen from the shaft failure of a turbine-generator occurred at the Mohave Generating Station in the 1970s, of which the subsynchronous shaft torsional oscillation (SSTO) was the culprit [2]. Therefore, the SSTO phenomenon must be considered when mitigating SSO. However, only a little information exists with respect to SSTO of a wind turbine generator (WTG) and most studies are about low-frequency shaft oscillation. A two-mass shaft model is established in [3] and then a damping controller is used to mitigate STO which is within the low frequency range. Reference [4] builds a three-mass shaft model of DFIG and STO can be observed in both low frequency and
⁎
subsynchronous frequency range using modal analysis. According to reference [5,6], if two-mass model is adopted, only the low-frequency oscillation exists. It is, however, further found by [5] that the larger the shaft stiffness, the larger the frequency of STO. It happens that the shaft stiffness of an offshore WTG is larger than that of an onshore one when adopting a two-mass shaft model. In reference [7,8], the shaft stiffness is several times more than that of a general onshore WTG. As a result, for an offshore wind farm, it is very likely that the shaft oscillation frequency falls within the subsynchronous range, namely the SSTO studied in this paper. On the other hand, there exists complex interaction between the converter controller of VSC-HVDC and that of wind farm [9]. Once disturbance occurs, a new form of SSO may be brought about. It is defined as subsynchronous equipment interaction (SSEI) in this paper for the convenience of expression. SSEI will lead to two consequences: (i) The current and power on line will oscillate at a subsynchronous frequency; (ii) Variation of electromagnetic torque of the generator will be excited on account of electro-mechanical coupling. So far, SSEI is short of in-depth research. Ref. [9] studies the distribution and propagation of SSO currents in modular multilevel converter based (MMC)-HVDC system through formula derivation. It
Corresponding author. E-mail address: [email protected] (X. Bian).
https://doi.org/10.1016/j.ijepes.2019.01.031 Received 27 August 2018; Received in revised form 22 December 2018; Accepted 20 January 2019 0142-0615/ © 2019 Published by Elsevier Ltd.
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verifies that SSO occurs due to the interaction between the controller of DFIG-based wind farm and that of MMC-HVDC system. However, oscillation characteristics are not observed and analyzed so that information deficiency and imperfection of mitigating measures can be easily caused. Countermeasures in SSO mitigation can be summarized as two categories: one is employing Flexible AC Transmission Systems (FACTS) [10,11] and the other is installing supplementary damping controller (SUDC). Apparently the latter one is more economic and has become a hot topic. A lot of literature, however, differs in the location of SUDC. Ref. [12] installs SUDC to the rotor-side converter (RSC) of a WTG but no explanation is provided. Ref. [13] chooses the optimum location through comparing all possible locations for SUDC within RSC and GSC. Nevertheless, it turns out to be time-consuming and other possible locations of the entire system are neglected. In [14], different locations for SUDC are compared using the residue-based analysis and root locus diagrams. Apparently, this is time-consuming as well and lacks a definite quantitative index. For improvement, strongly correlated variables of SSTO and SSEI are found through participation factor (PF) analysis in this paper. Thus the best location where SUDC is installed can be determined quickly and accurately. This paper focuses on comprehensively analyzing and mitigating SSTO and SSEI in DFIG-based offshore wind farm integrated to grid through VSC-HVDC. The dominant oscillation modes of SSTO and SSEI are found using modal analysis, followed by PF analysis aiming at finding strongly correlated variables. Then the effects of these variables on the oscillation characteristics of SSTO and SSEI are respectively observed by root-locus diagrams. To collectively mitigate SSTO and SSEI, a supplementary excitation damping controller (SEDC) and a subsynchronous damping controller (SSDC) are applied. Their effectiveness is verified under two different disturbance conditions based on the software DIgSILENT. The organization of this paper is as follows. Section 2 presents the system modeling. Section 3 performs modal analysis and PF analysis. Then the principle of SSTO and SSEI is analyzed qualitatively. Section 4 presents the oscillation characteristics of SSTO and SSEI. Section 5 presents the model of damping controllers. Their effectiveness is confirmed by time-domain simulation in Section 6. Section 7 concludes the paper.
Fig. 1. (a) Topology of a DFIG-Based offshore wind farm connected to grid through VSC-HVDC, (b) Two-mass shaft model.
2Ht *d t /dt = Tm 2Hg *d r / dt = Ks d s / dt = 2 fe (
Ks s Dg
s t
Dt r
t
Te
r )/ pn
(1)
where 2Ht and 2Hg are the inertial time constant of the wind turbine and the generator, respectively; t and r are the rotating speed of the wind turbine and the generator, respectively; s is the shaft torsion angle; Ks is the stiffness coefficient; Tm and Te are the mechanical torque and the electromagnetic torque, respectively; Dt and Dg are the damping coefficient of the wind turbine and the generator rotor, respectively. 2.2. Converter controllers of DFIG Fig. 2 [18] shows block diagrams of the rotor-side converter (RSC) and the grid-side converter (GSC) of DFIG, where the subscripts ‘s ’, ‘r ’, ‘d ’, ‘q’,‘ ref ’ denote stator, rotor, d-axis component, q-axis component and reference component respectively; The subscript ‘ g ’ represents the grid DFIG is connected to; Kp and Ki are the proportional coefficient and the integral coefficient respectively; Lr , Lm denote respectively rotor leakage inductance and mutual inductance of stator and rotor; Lr r =Lr + Lm ; Xt g is the transformer reactance connecting converters and the grid; x1,2, 7 are state variables. The inputs of RSC controller are the decoupled active power Ps and the generator terminal voltage Vs . Idr and Iqr are used to control the output active and reactive power of DFIG stator respectively. GSC is used for maintaining the voltage of the DC bus VDC and controlling its output reactive power. The former control task can be achieved by controlling Idg and the latter can be realized by controlling Iqg .
2. Study system and system model A typical topology of a DFIG-Based offshore wind farm connected to grid through VSC-HVDC is shown in Fig. 1(a) [15]. All DFIGs of the same operation states and parameters are connected to the same bus—the point of common coupling (PCC) via unit connection. The transformer of 35/110 kV is a step-up transformer and the one of 110/ 115 kV is a converter transformer. The VSC-HVDC link consists of the wind farm side VSC (WFVSC) and the grid side VSC (GSVSC). Detailed model of the shaft system and the converter controllers of both DFIG and VSC-HVDC is presented below.
2.3. Converter controllers of VSC-HVDC
2.1. Shaft system
The dq0 transformation is performed to describe the voltages and currents of the VSC-HVDC link with d(q)-axis components for electromechanical transient study. Then the differential equations-based model and control scheme of VSC can be obtained [19,20]. Thus the block diagrams of VSC controllers can be formed, as Fig. 3 [19,20] shows, where the subscripts ‘w ’ and ‘dc ’ represent the wind farm and the DC link respectively; ‘g’ represents the grid GSVSC is connected to; is the system angular frequency; L is the series inductance of AC side; x 8,9, 15 are state variables. For WFVSC, the control scheme is P-f control and V-Q control [20] to supervise and control the frequency and voltage of the wind farm. As
This paper adopts two-mass shaft model as shown in Fig. 1(b) [16,17]. One mass block is composed of wind turbine, hub and low speed shaft, while the other is formed by high speed shaft, gear box and generator. This simplified low-order shaft model not only meets the precision requirements of the analysis but also improves overall computational efficiency [17]. According to Fig. 1(b), the two-mass shaft model, based on per-unit system, can be described as:
30
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Fig. 4. The block diagram of PLL.
3. Modal analysis To observe the oscillation characteristics of the system, modal analysis including eigenvalue analysis and participation factor analysis is performed in this section. Besides, the principle of the two dominant modes is analyzed qualitatively. The system studied employs 20 DFIGs, each with a capacity of 5 MW. The rated capacities of WFVSC and GSVSC are both 150 MW. The DC voltage level is ± 150 kV and the length of DC transmission line is 100 km. The detailed setup of system data is given in Appendix A. 3.1. Eigenvalue analysis Prior to eigenvalue analysis, it’s necessary to determine the natural oscillation frequency of the shaft. For the two-mass shaft model of DFIG, the shaft natural oscillation frequency is given by:
1 2
fm = Fig. 2. The block diagram of DFIG converter controllers. (a) RSC controller, (b) GSC controller. (b) WFVSC controller, (b) GSVSC controller.
0 K s (Ht
+ Hg )/2Ht Hg
(2)
where 0 is the rated frequency of the system. Considering that the offshore wind farm adopts large-scale wind turbine, the stiffness coefficient is set at 1.37p.u. by calculation according to [21]. Ht and Hg are set as 1.9 and 0.2, respectively. Thus fm equals 5.50 Hz according to Eq. (2). In order to get the eigenvalues of the system, the equation of state is established after applying small disturbances as follows: (3)
d x / dt = A x
where A is the state matrix of the system; x is the state variable which contains that of DFIG ( xDFIG ) and that of VSC-HVDC ( xVSC HVDC ), as follows:
xDFIG = [
(a)
t,
r,
s,
ds ,
qs ,
idr , iqr , idg , iqg , uDC , us ,
x1, x2 , x3 , x 4 , x5 , x 6 , x 7 , where
ds
and
xVSC
HVDC
qs
1,
T 2]
are the d-q components of stator flux.
= [ id 1, iq 1, id 2, iq 2, ud 1, ud 2, idc , Q w , iqw , idw , Pw , Q g , iqg , idg , uac , x 8, x 9 , x10 , x11, x12 , x13, x14 , x15,
3,
T 4]
where the subscripts ‘ 1’ and ‘ 2 ’ refer to WFVSC and GSVSC, respectively. Table 1 shows the system eigenvalues obtained from the state matrix. In Table 1, the damping ratio of each mode is calculated by:
(b) Fig. 3. The block diagram of VSC controllers. (a) WFVSC controller, (b) GSVSC controller.
Table 1 Main oscillation modes.
for GSVSC, the voltage of DC link and the reactive power outputted to the AC grid are supposed to be controlled and stabilized. The PLL block is modeled as Fig. 4 shows, where Kp_PLL and Ki _PLL are the control parameters of PLL. In this paper, 1 and 2 are chosen as the state variables of PLL on the DFIG side while 3 and 4 are chosen as the state variables of PLL on the VSC side.
31
Mode
Eigenvalues
1 2 3 4 5 6 7
−2.36 ± j125.29 −0.92 ± j34.42 −5.37 ± j0.75 −16.44 ± j7.94 −51.27 ± j102.23 −89.15 ± j277.22 −330.28 ± j595.14
±j
Frequency f/Hz
Damping ratio ζ/%
19.94 5.48 0.12 1.26 16.27 44.12 94.72
0.02 0.03 0.99 0.90 0.45 0.31 0.49
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Fig. 6. Principle Analysis of SSEI and SSTO.
3.3. Principle analysis of SSTO and SSEI
(a)
How are SSTO and SSEI excited? The following qualitative principle analysis offers an explanation. For SSTO, as shown in Fig. 6, once a network disturbance occurs, a current variation i , whose frequency is fe , is brought about. When i flows into the DFIG stator, subsynchronous current components i ds\_ and i qs\_ , whose frequencies are both f0 fe , will appear and then generate a subsynchronous rotating magnetic field whose frequency is also f0 fe . Thus subsynchronous current components i'dr\_ and i'qr\_ will be induced in the rotor because of this magnetic field. Besides, i will induce voltage variation and current variation at the side of the grid, namely udg\_ , uqg\_ , i dg\_ and i qg\_ . Coincidentally, they are the input of GSC and will certainly influence RSC. As a result, new subsynchronous current components will be excited in the rotor winding under the regulation of RSC. The accumulation of i'dr\_ , i'qr\_ and these new components gives birth to two subsynchronous current components i dr\_ and i qr\_ whose frequencies are both f0 fe at the side of the rotor. If f0 fe approximately equals the shaft natural oscillation frequency fm , drastic shaft torsional vibration will occur, namely SSTO. For SSEI, owing to i , active and reactive power variation Pw\_ , Q w\_ will be excited and will be inputted into WFVSC. Under the regulation of WFVSC, a current variation whose components are i d 1_ and i q 1_ will appear. As a result, with the current variation flowing, the AC active power in the wind farm side will oscillate at a subsynchronous frequency and thus lead to the variation of generator electromagnetic torque Te . Te has a negative damping for the shaft torsional vibration which will be intensified if the mechanical damping of the shaft is insufficient, namely SSEI.
(b) Fig. 5. Results of participation factor analysis. (a) Participation factors of Mode 1, (b) Participation factors of Mode 2.
= - /
2
+
2
(4)
It is worth reminding that the real eigenvalues are not displayed since they have nothing to do with the oscillation modes. As a result, there are mainly seven oscillation modes, with two dominant modes indicated in bold, namely Mode 1 and 2. Mode 3 and 4 belong to low frequency and since their damping ratios are both larger than 0.1, the corresponding oscillations will attenuate fast; Mode 5 and 6 have big negative real parts so that they are relatively stable; Mode 7 belongs to supersynchronous oscillation.
4. Oscillation characteristics According to the analysis above, SSEI and SSTO are strongly related to x1, x2 , Qw and t . x1 corresponds to the outer active power loop whose proportional coefficient and integral coefficient are Kp1 and Ki1, respectively. x2 corresponds to the inner current loop whose proportional coefficient and integral coefficient are Kp2 and Ki2 , respectively. If one of Kp1, Ki1, Kp2 , Ki2 and t changes whilst the others remain unchanged, the root-locus diagrams of SSEI and SSTO can be obtained to analyze the oscillation characteristics of each mode in terms of the damping level and the oscillation frequency. It's well-known that the further the real part of an eigenvalue is away from the imaginary axis, the greater the positive damping. Moreover, the larger the imaginary part, the larger the oscillation frequency.
3.2. Participation factor analysis Based on the eigenvalue analysis implemented in section A, seven pairs of eigenvectors are obtained and thus participation factor analysis can be performed. The participation factor of each state variable related to mode 1 and 2 is shown in Fig. 5, omitting those values which are small or near to zero. It's obvious that mode 1 has a strong relationship with x1, x2 , Qw and mode 2 has a strong relationship with x2 , t, where x1 and x2 are corresponding to the active power control link of RSC; Qw refers to the input of WFVSC; and t refers to the speed of the shaft of wind turbine. It can be concluded that the converters of DFIG and VSV-HVDC will contribute to the occurrence of mode 1, so that it is classified as SSEI. Mode 2 has a frequency close to the shaft natural oscillation frequency and it is strongly related to the shaft speed, so that this mode is corresponding to the SSTO mode.
4.1. Oscillation characteristics of SSEI When parameters are changed in the range within the square bracket in Table 2, the root-locus diagrams of SSEI can be obtained and are shown in Fig. 7(a) and Fig. 8 respectively. From Figs. 7(a) and 8, observations can be made as follows: 32
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Table 2 Parameter setting of state variables. Para-meter
Case 1
Kp1
[1,15]
K i1 Kp2 K i2 t (rad/s)
20 2.3
50 0.2
Case 2
Case 3
Case 4
Case 5
5
5
5
5
20 2.3
20 2.3
[15,40] 2.3
20 [1.2,4.5]
[2.5,500] 0.2
50 [0.05,0.7]
50 0.2
50 0.2
Fig. 8. Influence of SSTO.
t
on the oscillation characteristics of mode (a) SSEI, (b)
(1) Similar to SSEI, Kp1 and Ki1 have little effect on the oscillation characteristics of SSTO. (2) When Kp2 gradually increases, the real part of the eigenvalue moves closer to the imaginary axis but still stays within the left half of the complex plane and the oscillation frequency slowly decreases. This means the system remains stable. When Ki2 increases, the real part also moves nearer to the imaginary axis and the oscillation frequency increases, which means the system stability gets weakened. (3) When t increases, the real part of the eigenvalue moves further away from the imaginary axis, which means the system stability improves.
(a)
5. Damping controllers The oscillation characteristics of SSEI and SSTO have paved the way for the site selection of damping controllers. To mitigate SSTO, DFIG_SEDC which is located at the excitation link of RSC with inputted can be employed. Through adjusting the excitation voltage of the generator, DFIG_SEDC can generate a supplementary electromagnetic torque TSEDC.To mitigate SSEI, VSC_SSDC which is located at the reactive link of WFVSC can be employed. By adjusting the reference value of the reactive power inputted to the outer loop control of WFVSC, VSC_SSDC also generates a supplementary electromagnetic torque TSSDC . Both TSEDC and TSSDC can provide a positive damping to compensate for the possible negative damping. In this way, the phase difference between Te and falls within 90°, where Te is the initial = t variation of electromagnetic torque and r.
(b) Fig. 7. Influence of Kp and Ki on the oscillation characteristics of mode (a) SSEI, (b) SSTO.
5.1. Location and model of DFIG_SEDC
(1) Kp1 and Ki1 have little effect on the oscillation characteristics of SSEI. (2) When Kp2 gradually increases, the real part of the eigenvalue moves closer to the imaginary axis and the oscillation frequency increases a little. Moreover, the real part becomes positive when Kp2 reaches a maximum value of 0.7, which means that the system has a negative damping for SSEI. When Ki2 increases, the real part shows little changes but the oscillation frequency reduces significantly, which means the system stability gets improved. (3) t has also small influence on the oscillation characteristics of SSEI.
Since SSTO is strongly related to the parameters of RSC and the speed of wind turbine t , the q-axis component of the rotor excitation voltage is chosen to be modified [22]. The modified block diagram of RSC controller is shown in Fig. 9(a) where Tw1 is the time constant of the DC-Elimination link which can eliminate the error introduced by signal offset; T1 and T2 are the time constants of phase-compensation link which can compensate the phase offset of each eigenvalue; KSEDC is the gain coefficient. In this paper, Tw1 is set as 5 s and the amplitude limitation is set as ± 0.1 p.u . T1 and T2 are determined by Eq. (8) [23].
4.2. Oscillation characteristics of SSTO
a = T2/ T1 = (1 sin )/(1 + sin ) T1 = 1/2 fc a
Similarly, changing the parameters according to Table 2, the rootlocus diagram of SSTO can be obtained and is shown in Fig. 7(b) and Fig. 8 respectively. Observations can be made as follows:
(8)
where fc is the frequency of each mode; is the phase angle to be compensated corresponding to some frequency point. In order to obtain of each mode, the complex torque coefficient approach realized by 33
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Fig. 10. The flow chart of the test signal method.
Fig. 9. The block diagram of modified controllers. (a) RSC controller with DFIG_SEDC added, (b) WFVSC controller with VSC_SSDC added.
time domain simulation – the Test Signal Method [24] is adopted in this paper.**
(a)
5.2. Location and model of VSC_SSDC Taking the broadband design of SSDC as a reference in [25], the AC bus voltage is inputted to generate a supplementary control signal of reactive power. The block diagram of WFVSC controller after adding VSC_SSDC is shown in Fig. 9(b). It is the reactive power inputted into WFVSC QW to which SSEI is strongly related that should be modified. In this way, QW =Q W\_ref + QSSDC QW . 6. Case studies Prior to case study, the complex torque coefficient-test signal method is applied to determine the parameters of DFIG_SEDC and VSC_SSDC. After that, both the modal analysis and the time-domain simulation are performed using DIgSILENT to detect whether they can effectively damping SSO.
(b) Fig. 11. (a) The electrical damping coefficient curve, (b) The angle Te lags by.
6.1. Parameters of DFIG_SEDC and VSC_SSDC To calculate the parameters of DFIG_SEDC and VSC_SSDC according to Eq. (8), complex torque coefficient-test signal method is adopted to determine . The flow chart is shown in Fig. 10 [126]. Mechanical torque of different frequencies ranging from 5 to 45Hz is exerted on the DFIG stator every time. Finally the electrical damping coefficient De ( f ) and the phase angle by which Te lags can be obtained. From the electrical damping coefficient curve shown in Fig. 11(a), De of mode 1 and mode 2 are both negative. This means SSEI and SSTO can easily occur when the system mechanical damping is insufficient. As shown in Fig. 11(b), the lag angle of mode 1 and 2 are 106° and 126° , respectively. Then we utilize two lead-lag blocks and the total compensation angle of the two blocks is set as Table 3 shows. Thus
Table 3 Parameter setting of
DFIG-SEDC
Modes
and
VSC-SSDC.
Compensation Angle 1 ( 2)
34
Time Constant
Gain
T1 (T3)
T2 (T4)
K
Mode 1-SSEI 19.94 Hz
DFIG_SEDC VSC_SSDC
94° 48°
0.019 0.012
0.003 0.005
12.4 5.7
Mode 2-SSTO 5.48 Hz
DFIG_SEDC VSC_SSDC
62° 41°
0.113 0.064
0.007 0.013
23.6 14.5
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Table 4 Eigenvalues of Mode 1 and 2 under different conditions. Conditions
Mode 1 19.94 Hz
Mode 2 5.48 Hz
Without DFIG_SEDC or VSC_SSDC With DFIG_SEDC With VSC_SSDC With DFIG_SEDC and VSC_SSDC
−2.36 ± j125.29 −3.20 ± j126.87 −3.76 ± j126.33 −5.15 ± j127.92
−0.92 ± j34.42 −1.79 ± j35.13 −2.14 ± j34.82 −3.38 ± j36.05
parameters of DFIG_SEDC and VSC_SSDC can be calculated by Eq. (8), as listed in Table 3. After the parameters of damping controllers are set according to Table 3, we perform the modal analysis again and the new simulation results are shown in Table 4. It becomes apparent that DFIG_SEDC or VSC_SSDC makes the real part of the eigenvalue move further away from the imaginary axis, which means the system stability is improved. Besides, when installed together, DFIG_SEDC and VSC_SSDC can make concerted effort to remarkably decrease the real part of the eigenvalue, which proves their effectiveness in damping SSO. In order to further prove that the location selected by PF analysis in this paper is the optimal one, DFIG_SEDC and VSC_SSDC are installed to alternative locations of the test system and the result of eigenvalues is presented in Table 5. The location selected by PF analysis and its simulation results are shown in bold. It is obvious that the real part of the eigenvalue move further away from the imaginary axis when DFIG_SEDC or VSC_SSDC is installed to locations selected by PF analysis. It can be concluded that the site selection method adopted by this paper is better.
(a)
(b)
6.2. Time-domain simulation For further study of the performance of DFIG_SEDC and VSC_SSDC, the dynamic variation of the electromagnetic torque is observed under different disturbance conditions: Case 1: the wind speed changes from 10 m/s to 13 m/s at 0.5 s and lasts for 0.075 s; Case 2: the wind speed changes from 8 m/s to 11 m/s at 1.25 s and lasts for 0.25 s; Case 3: a three-phase short circuit fault occurs near PCC at 0.5 s and lasts for 0.075 s; Case 4: a three-phase short circuit fault occurs near bus U2, which is connected to the AC grid, at 1.25 s and lasts for 0.25 s.
(c)
The simulation results of the four cases are illustrated in Fig. 12. In each case, the dynamic variation of the electromagnetic torque is compared when the system is equipped with different damping controllers. It can be concluded that the results of the four cases are consistent with each other from Fig. 12. Apparently, the variation of Te shows a drastic oscillation which attenuates slowly with no damping controllers installed to the system. When DFIG_SEDC is added, the oscillation of Te is to a great extent damped. Likewise, VSC_SSDC attenuates the Table 5 Eigenvalues of Mode 1 and 2 when locations.
DFIG_SEDC
or
VSC_SSDC
is installed to different
Damping controller
Locations
Mode 1 19.94 Hz
Mode 2 5.48 Hz
DFIG_SEDC
RSC: x2 RSC: x1 GSC: x5
−3.20 ± j126.87 −2.69 ± j125.65 −2.47 ± j125.48
−1.79 ± j35.13 −1.38 ± j34.63 −1.23 ± j34.56
VSC_SSDC
WFVSC: Q w WFVSC: x5 WFVSC: x10
−3.76 ± j126.33 −2.86 ± j125.60 −2.47 ± j125.31
−2.14 ± j34.82 −1.33 ± j34.63 −1.21 ± j34.58
(d) Fig. 12. Influence of different controller configurations on the curve of Te in (a) case 1, (b) case 2, (c) case 3, (d) case 4.
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Q. Zhou et al.
oscillation when added individually. When DFIG_SEDC and VSC_SSDC are installed together, the wave attenuates even faster and reaches convergence earlier. The above results of time-domain simulation coincide with conclusions drawn from eigenvalue analysis and demonstrate that DFIG_SEDC can cooperate with VSC_SSDC on mitigating SSTO and SSEI Fig. 12(a) and (b) reflect results under disturbance occurred on the power supply side. Fig. 12(c) demonstrates the results simulated when faults happen on the power supply side while Fig. 12(d) the grid side. This means system stability can be significantly enhanced and improved under either static or transient disturbances with both DFIG_SEDC and VSC_SSDC installed.
new type of SSO may result from the interaction between different power electronic equipment, namely SSEI. In this paper, the SSO phenomenon has been investigated on the premise that a DFIG-based offshore wind farm is integrated to grid via VSC-HVDC. Firstly, the dominant oscillation modes are obtained using modal analysis. After that, state variables which are strongly correlated with the dominant modes are sieved out and their influence on the oscillation characteristics of each mode are analyzed then. It turns out that SSTO occurs along with SSEI which the interaction between DFIG converter controller and VSC controller is responsible for. Later, damping controllers are both installed in DFIG and VSC. The damping effect has been verified under static or transient disturbances using DIgSILENT.
7. Conclusions
Acknowledgment
Compared with onshore WTGs, offshore ones generally have larger shaft stiffness so that the SSTO phenomenon is very likely to happen. Moreover, when an offshore wind farm is connected to VSC-HVDC, a
This work was financially supported by Shanghai Science and Technology Project under grant (16020501000).
Appendix A The parameters of DFIG and VSC-HVDC are given in Table 6 and Table 7, respectively.
Table 6 Parameter setting of DFIG.
Table 7 Parameter setting of VSC-HVDC. Types
Para-meter
Value
HVDC
R
0.006 /km
X
VSC
Kp8
2
K i8
12
K i10 K i12 K i14
Kp10 Kp12 Kp14
2 1
Para-meter
Value
10 10
0.12 50
36
Para-meter
Value
0.4 /km
B
Kp9 Kp11 Kp13 Kp15
2
K i9
100
10
K i11 K i13 K i15
100
2
10
3.14 μS/kmµS/km 100 100
Electrical Power and Energy Systems 109 (2019) 29–37
Q. Zhou et al.
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