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Travelling wave fault location principle for hybrid multi-terminal LCC-VSC-HVDC transmission line based on R-ECT
Electrical Power and Energy Systems 117 (2020) 105627
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Travelling wave fault location principle for hybrid multi-terminal LCC-VSCHVDC transmission line based on R-ECT
T
⁎
Dong Wang , Mengqian Hou School of Automation and Electronic Engineering, Qingdao University of Science & Technology, No. 99, Songling Road, Qingdao 266061, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: Travelling wave Fault location Hybrid multi-terminal LCC-VSC-HVDC Transmission line PSCAD/EMTDC
This paper investigates the fault location issue of hybrid multi-terminal high voltage direct current (HVDC) overhead transmission line based on the line commutated converter (LCC) and voltage source converter (VSC). There exists two issues that should be addressed: (i) the travelling wave (TW) fault location principle’s adaptability to multi-terminal network topology and converter structures; (ii) the transfer method of high frequency TW signal. Therefore, a novel TW fault location principle for the hybrid multi-terminal LCC-MMC-HVDC transmission line is proposed based on the Rogowski coli based electronic current transformer (R-ECT). Firstly, the high frequency TW transfer capability of the R-ECT is studied. Secondly, a novel TW fault location principle based on the secondary differential current travelling wave (D-CTW) is proposed. Eventually, in order to verify the high accuracy of the proposed principle, a typical ± 400 kV hybrid three-terminal LCC-VSC-HVDC transmission system is used for the case study based on PSCAD/EMTDC. Furthermore, its robustness against different fault locations, different fault resistances and different fault types is also investigated.
1. Introduction Hybrid multi-terminal LCC-VSC-HVDC transmission system has rapidly developed in recent years because of its advantages of large transmission capacity, high transmission efficiency and ability to construct asynchronous grid compared with conventional AC transmission systems. Compared with conventional LCC-HVDC transmission systems, because of the inherent characteristic of insulated gate bipolar transistor (IGBT) and high frequency pulse width modulation (PWM) strategy, it has no commutation failure issue and the ability to supply power to passive systems. Compared with conventional VSC-HVDC or modular multi-level converter (MMC) based HVDC transmission systems, it has much lager transmission capacity and lower construction cost. Besides, considering multi-terminal topology, it has less impact on the AC systems connected to inverter stations [1–6]. In recent years, the TW fault location principle has been widely utilized in modern power grids. It has high location accuracy and is almost immune to fault resistance, fault location and fault type. Various fault location principles for the HVDC transmission line (TL) have been proposed. For star-connected hybrid multi-terminal HVDC-TL, Wei et al. [7] proposed a novel fault location algorithm. It can identify the faulty branch correctly and locate the distance accurately only by using the arrival time of the initial TW. For multi-terminal HVDC topology of
⁎
offshore wind farms, Li et al. [8] proposed a novel fault location principle based on high-frequency components detected from the fault current signal. This method can accurately detect the fault on each line and classify the fault types. Taking cloud computing platform data and complicated networks into account, Deng et al. [9] proposed a multiterminal TW fault location method. It can quickly, accurately, and reliably locate the fault point under limited TW acquisition unit with optimal placement. Under unsynchronized two-end measurement and uncertain line parameters, Liang et al. [10] proposed a time-domain fault-location principle suitable for HVDC-TL. It can locate faults accurately on the HVDC lines even in the case of loss of signals from GPS. Using terminal measurements, Nanayakkara et al. [11] paid the attention to DC line faults in conventional HVDC transmission system with segments of cables and overhead lines. It has anti-interference ability. For definition of test requirements of HVDC circuit breakers, Belda et al. [12] analyzed faults in multi-terminal HVDC power grid. Fernandes et al. [13] proposed a two-terminal model TW based fault location method for HVDC systems according to aerial and ground mode TWs. In cases of uncertainties in line parameters, the method keeps the same fault location accuracy. Xun et al. [14] worked on the accurate TW fault location method of overhead line-cable hybrid line and analyzed the influencing factors. This method shows high accuracy on the twoterminal structure. In order to overcome the high grounding resistance
Corresponding author. E-mail address: [email protected] (D. Wang).
https://doi.org/10.1016/j.ijepes.2019.105627 Received 6 June 2019; Received in revised form 28 September 2019; Accepted 11 October 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.
Electrical Power and Energy Systems 117 (2020) 105627
D. Wang and M. Hou
Nomenclature LCC HVDC R-ECT VTW D-CTW PG PN SR CC
SCP VSC TW PWM CTW CT NG IGBT TL FI
line commutated converter high voltage direct current Rogowski coil based electronic current transformer voltage travelling wave differential current travelling wave positive pole to ground positive pole to negative pole smoothing reactor compensation capacitance
star connection point voltage source converter travelling wave pulse width modulation current travelling wave current transformer negative pole to ground insulated gate bipolar transistor transmission line filter inductor
2. TW transfer characteristic of R-ECT
for HVDC-TL, Zou et al. [15] proposed a novel TW based fault location principle using S-transform to analyze TW to demonstrate the characteristic and variation in time-frequency domain. Song et al. [16] proposed a fault location principle for VSC-HVDC-TL using the natural frequency current. It has validity, rapidity and accuracy characteristic. In fact, few research papers were focused on the TW fault location of the hybrid multi-terminal LCC-VSC-HVDC-TL, to which should be paid more attention since the hybrid systems are being widely developed. For this topic, there exists two issues that should be addressed: i) Taking the multi-terminal network topology and converter structures into account, the adaptability of proposed TW fault location principle requires to be investigated; ii) Due to the bandwidth of TW is between several kHz to several hundreds of kHz, how to accurately obtain the high frequency TW data also requires to be studied. As for the TW transfer equipment, R-ECT has several superiorities over conventional current transformer (CT). On one hand, the bandwidth of R-ECT is up to several hundreds of kHz which is much wider than that of conventional CTs, typically dozens of kHz. On the other hand, due to the special structure of the R-ECT, the secondary current is differential signal of primary current. Besides, the D-CTW has much more obvious mutations to be detected [17,18]. The main contribution of the paper is a novel TW fault location principle for multi-terminal LCC-VSC-HVDC overhead TL based on the differential output of R-ECT which aims to address the above mentioned issues. Comparing with conventional fault location principle, it has two main superiorities: (i) R-ECT has the capability to transfer whole bandwidth of CTW, and the secondary D-CTW has much more obvious mutations to be detected; (ii) The proposed fault location principle is suitable for hybrid multi-terminal LCC-VSC-HVDC topology; (iii) The proposed fault location principle has high fault location accuracy. The rest of the paper is organized as follows. In Section 2, the whole bandwidth TW transfer ability of R-ECT is studied. In Section 3, the novel fault location principle is proposed. In Section 4, a series of simulation results are provided to validate the proposed fault location principle’s robustness against different fault locations, different fault resistances and different fault types, followed by conclusions.
Fig. 1 provides the structure and equivalent circuit of R-ECT [17,18]. i1 is the primary current signal. u 0 is the induced voltage signal of secondary side. M is the mutual inductance of R-ECT. R 0 , C0 and L0 are equivalent resistance, equivalent capacitance and equivalent inductance of R-ECT, respectively. In order to acquire stable secondary sampling data, RS is installed as sampling resistance. Although R-ECT is a CT, the output of R-ECT is voltage signal. The detailed parameters of R-ECT in this paper is shown in Table 1. According to Fig. 1:
⎧u 0 (t ) = M di1 (t )/dt i2 (t ) = uS (t )/ RS + C0 duS (t )/dt ⎨ ⎩u 0 (t ) − uS (t ) = R 0 i2 (t ) + L0 di2 (t )/dt
(1)
Based on Laplace transformation, Eq. (1) can be described as:
⎧U0 (s ) = sMI1 (s ) I2 (s ) = US (s )/ RS + sC0 US (s ) ⎨ ⎩U0 (s ) − US (s ) = R 0 I2 (s ) + sL0 I2 (s )
(2)
where s is the complex frequency variable. Afterwards, the transfer function of R-ECT can be obtained:
H (s ) =
US (s ) RS Ms = I1 (s ) C0 L0 RS s 2 + (C0 R 0 RS + L0) s + R 0 + RS
(3)
Define f and j are the time frequency and imaginary number unit respectively, then s = 2πf j. Eq. (3) can be described as:
H (f ) =
4π 2RS Mf 2 (C0 R 0 RS + L0) + 2πRS Mf (R 0 + RS − 4π 2f 2 C0 L0 RS )j (R 0 + RS − 4π 2f 2 C0 L0 RS )2 + 4π 2f 2 (C0 R 0 RS + L0)2 (4)
Accordingly, the Bode plot of R-ECT is illustrated in Fig. 2. Hence, it can be concluded:
• Based •
on Fig. 2(a), the amplitude-frequency characteristic is a straight line with a slope of +20 dB/dec for the TW frequency bandwidth. The higher the frequency of primary signal is, the larger the amplitude of secondary signal is; Based on Fig. 2(b), the phase-frequency characteristic is
Fig. 1. Structure and equivalent circuit of R-ECT. 2
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thyristor based converter, power transformer, relay, AC filter, DC filter and large smoothing reactor (SR). The TW impedances of SR and TL are defined as ZSR and ZTL , respectively. After fault occurs, the incident VTW and CTW signals arrive at where relay locates. However, considering the large SR is a nature boundary, the VTW and CTW signals cannot pass through the SR and invade converter station. This indicates the VTW and CTW are totally reflected at LCC-HVDC converter station. Accordingly, based on Eq. (5), the VTW and CTW detected by the relay are:
Table 1 Detailed parameters of R-ECT Parameters
R0
L0
C0
M
RS
Values
0.4338 Ω
3.6924 μ H
2.3946 nF
0.1273 μ H
100 Ω
approximately a straight line with a constant value (+90 deg) for TW frequency bandwidth. Thus, the secondary output is the differential signal of primary input.
(
(
mulation model in Fig. 7. Apparently, there are a number of TW mutations after TL fault occurs; According to R-ECT transfer function in Eq. (4), the primary CTW is processed and the D-CTW signal is acquired as Fig. 3(b) shows. Exactly as the theoretical analysis above, the secondary output of RECT is the differential signal of the primary input. Besides, the DCTW has much obvious mutation to be identified.
(6)
3.3. VSC-HVDC inverter station VSC-HVDC converter station has several advantages over LCCHVDC converter station such as no commutation failure, ability to supply power to passive system and ability to construct multi-terminal topology. Especially, in order to avoid commutation issue, VSC-HVDC converter station is generally applied as inverter station in hybrid transmission system. Besides, in order to acquire high transmission capacity, a multi-terminal topology structure is adopted. Fig. 5(b) provides a typical structure of VSC-HVDC inverter station, consists of IGBT based converter, power transformer, relay, compensation capacitance (CC) and filter inductance (FI). The TW impedances of CC and TL are defined as ZCC and ZTL , respectively. Considering the large CC installed between TL and ground, for TW frequency bandwidth, ZCC ≈ 0 . In other words, for TW signal, the TL is approximately grounded directly [19]. After fault occurs, the incident VTW and CTW signals arrive at where relay locates. Accordingly, based on Eq. (5), the VTW and CTW detected by the relay are:
3. Typical transmission system 3.1. Reflection and refraction of TW Fig. 4 provides the typical TW reflection and refraction phenomenons [18]. As can be seen, the incident VTW (uin ) and CTW (iin ) propagate along line 1, and there are refraction and reflection at TW impedance discontinuity point (generally busbar or fault point). Besides, the TW impedances at line 1 and line 2 are Z1 and Z2 , respectively. The reflection VTW and CTW are url and irl , respectively. The refraction VTW and CTW are urr and irr , respectively. The forward direction of VTW is defined from TL to earth. The forward fault of CTW is its actual transmission direction. Therefore, the reflection and refraction coefficients of VTW and CTW are acquired by:
⎧ λ u = (Z2 − Z1)/(Z2 + Z1) ∈ (−1, 1) ⎪ λi = (Z2 − Z1)/(Z2 + Z1) ∈ (−1, 1) ⎨ βu = 2Z2/(Z2 + Z1) ∈ (0, +∞) ⎪ β = 2Z /(Z + Z ) ∈ (0, +∞) 1 2 1 ⎩ i
)
where u and i denote the VTW and CTW detected by the relay, respectively. uf and i f denote the incident VTW and CTW, respectively. λ u and λi denote the reflection and refraction coefficients, respectively.
• Fig. 3(a) describes the primary CTW signal acquired by PSCAD si•
)
ZSR − ZTL 2ZSR ⎧ ⎪u = (1 + λ u ) uf = 1 + ZSR + ZTL uf = ZSR + ZTL uf ⎨i = −(1 − λ ) i = − 1 − ZSR − ZTL i = − 2ZTL i i f ⎪ ZSR + ZTL f ZSR + ZTL f ⎩
To demonstrate the above theoretical analysis, a typical simulation is carried out of which the results are shown in Fig. 3. It can be seen that:
(
)
ZCC − ZTL ⎧ ⎪u = (1 + λ u ) uf = 1 + ZCC + ZTL uf ≈ 0 ⎨i = −(1 − λ ) i = − 1 − ZCC − ZTL i ≈ −2i f i f ⎪ ZCC + ZTL f ⎩
(
(5)
)
(7)
where u and i denote the VTW and CTW detected by the relay, respectively. uf and i f denote the incident VTW and CTW, respectively. λ u and λi denote the reflection and refraction coefficients, respectively.
where λ u , λi , βu and βi are VTW reflection coefficient, CTW reflection coefficient, VTW refraction coefficient and CTW refraction coefficient at TW discontinuity point, respectively.
4. TW fault location principle 3.2. LCC-HVDC rectifier station Based on the analysis in Section 3, due to the large CC installed between TL and ground, the VTW cannot be detected at VSC-HVDC inverter station. Therefore, a novel fault location principle is proposed based on the D-CTW output signal of R-ECT as following shows.
Generally, LCC-HVDC converter station is applied as rectifier station to acquire high transmission capacity, of which the typical topology is provided in Fig. 5(a). The LCC-HVDC converter station consists of
Fig. 2. Bode plot of R-ECT. 3
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Fig. 3. Comparison between primary CTW and secondary D-CTW.
Fig. 4. TW reflection and refraction.
4.1. CTW propagation characteristic Fig. 6 describes the CTW propagation process in multi-terminal LCCVSC-HVDC power grid. Assuming there are N ends and the multiterminal TLs are in star structure where ‘SCP’ denotes star connection point. Define the length of nth (1 ⩽ n ⩽ N ) TL is Dn . Assuming the fault happens at F in nth TL, and the length between F and nth converter station is ln . After the fault happens, the time that CTW arrives at nth relay is tn .
Fig. 6. CTW propagation characteristic.
the D-CTW of positive sequence can be obtained by:
in (k ) =
4.2. CTW arrival time detection
∑ k
in (k ) >
d 3
(9)
where in, + (k ) and in, − (k ) are the D-CTW sampling data of positive pole and negative pole at nth relay, respectively.
In this paper, the arrival time of CTW is detected using the D-CTW signal, which is acquired by the R-ECT. It can be described as: k+δ
in, + (k ) − in, − (k ) 2
4.3. Fault section identification algorithm (8)
After fault happens, it is necessary to identify fault section correctly before precise fault location. Based on Fig. 6, assuming the fault occurs between nth (1 ⩽ n ⩽ N ) converter station and SCP, therefore:
where k denotes the sampling point; in (k ) denotes the D-CTW sampling data of the positive sequence at nth relay; δ denotes the length of time window (δ = 3 in the paper); d denotes the peak value of D-CTW in data window. If Eq. (8) can be met, the time of kth sampling point represents CTW arrival time tn at nth relay. Based on the Karenbauer transformation algorithm [20], In Eq. (8),
Fig. 5. Typical structure of LCC-HVDC rectifier station and VSC-HVDC inverter station. 4
Electrical Power and Energy Systems 117 (2020) 105627
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⎧ v (t1 − t0) = D1 + Dn − ln ⎪· ·· ⎪ v (tn − 1 − t0) = Dn − 1 + Dn − ln ⎪ v (tn − t0) = ln ⎨ ⎪ v (tn + 1 − t0) = Dn + 1 + Dn − ln ⎪· ·· ⎪ v (tN − t0) = DN + Dn − ln ⎩
⎧ v (t1 − t0) − v (tn − t0) = (D1 + Dn − ln ) − ln ⎪· ·· ⎪ v (tn − 1 − t0) − v (tn − t0) = (Dn − 1 + Dn − ln ) − ln ⎨ v (tn + 1 − t0) − v (tn − t0) = (Dn + 1 + Dn − ln ) − ln ⎪· ·· ⎪ v (tN − t0) − v (tn − t0) = (DN + Dn − ln ) − ln ⎩ (10)
where t0 is fault start time; t1, t2, …, tN are the CTW arrival times at converter station 1, 2, …, N , respectively; D1, D2 , …, DN are the distances between SCP and converter station 1, 2, …, N , respectively; ln is the distance between F and nth converter station; v is CTW propagation speed along TL. Based on Eq. (14), one can define a (N − 1) × 1 order matrix:
where t0 is fault start time; t1, t2, …, tN are the CTW arrival times at converter station 1, 2, …, N , respectively; D1, D2 , …, DN are the distances between SCP and converter station 1, 2, …, N , respectively; ln is the distance between F and nth converter station; v is CTW propagation speed along TL. According to Eq. (10), define a fault section discrimination coefficient:
⎡ Δ1 ⎤ ⎡ vt1 − D1 ⎤ Δ = ⎢ Δ2 ⎥ = ⎢ vt2 − D2 ⎥ ⎢ · ·· ⎥ ⎢ · ·· ⎥ ⎢ ⎦ ⎣ vtN − DN ⎥ ⎣ ΔN ⎥ ⎦ ⎢
⎡ v (tn − t1) + D1 + Dn ⎤ · ····· ⎢ ⎥ ⎡ Ln,1 ⎤ ⎡ ln ⎤ Ln,2 ⎥ = ⎢ ln ⎥ = 1 ⎢ v (tn − tn − 1) + Dn − 1 + Dn ⎥ Ln = ⎢ ⎢ · ·· ⎥ ⎢· ··⎥ v (t − tn + 1) + Dn + 1 + Dn ⎥ 2⎢ ⎢ n ⎥ ⎢ L n, N − 1 ⎥ ⎢ l ⎥ · ····· n ⎦ ⎣ ⎦ ⎣ ⎢ ⎥ − + + v ( t t ) D D n N N n ⎣ ⎦
(11)
(15)
In order to acquire high fault location accuracy, after fault section is identified, the distance between F and nth converter station can be obtained by:
where Δn is fault section discrimination coefficient at nth (1 ⩽ n ⩽ N ) converter station. According to Eq. (10), Eq. (11) is derived as:
N −1
ln = ⎡ Dn − ln + vt0 ⎤ · ·· ⎢ ⎥ ⎡ Δ1 ⎤ ⎢ Dn − ln + vt0 ⎥ Δ = ⎢ Δ2 ⎥ = ⎢ ln − Dn + vt0 ⎥ ⎢ · ·· ⎥ ⎢ ⎥ Dn − ln + vt0 ⎥ ⎢ ΔN ⎥ ⎣ ⎦ ⎢ · ·· ⎢ ⎥ ⎢ ⎣ Dn − ln + vt0 ⎥ ⎦
(14)
∑ j = 1 L n, j N−1
(16)
5. Simulation 5.1. Simulation model (12)
According to Fig. 7, in order to verify the fault location accuracy of proposed principle, a typical ± 400 kV three-terminal LCC-VSC-HVDC model is established via the simulation software PSCAD/EMTDC. In the model, the detailed structures of LCC-HVDC rectifier station and VSCHVDC inverter station are exactly described in Fig. 5. The HVDC-TL adopts frequency depended model, and the DC resistances of TL and grounding wire are 0.02862 Ω/km and 2.8645 Ω/km , respectively. The SR, CC and FI are set to 0.2H, 1000 μ F and 0.0724H, respectively. Meanwhile, to acquire whole bandwidth of TW, the simulation rate is set to 1 MHz. F1-F9 denote different fault types (including PG, NG and PN) at different fault section. As for control strategy:
Based on Eq. (12), if F is between nth converter station and SCP, it can be concluded that:
Δn > Δ1 ≈ …≈Δn − 1 ≈ Δn + 1 ≈ …≈ΔN
(13)
Hence, Eq. (13) is the fault section identification criterion.
4.4. Fault location algorithm After fault section is identified via fault section identification algorithm in Section 4.3, which is assumed the fault is between nth converter station and SCP, then:
• According to Fig. 12 in Appendix A, the LCC-HVDC rectifier station adopts the constant DC current control strategy;
Fig. 7. Typical ± 400 kV three-terminal LCC-VSC-HVDC PSCAD simulation model. 5
Electrical Power and Energy Systems 117 (2020) 105627
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• According to Fig. 13(a) in Appendix B, the VSC-HVDC inverter •
l=
station I adopts the constant DC voltage control and constant AC voltage control strategies; According to Fig. 13(b) in Appendix B, the VSC-HVDC inverter station II adopts the constant reactive power control and constant AC voltage control strategies.
= 149.9278 km
In order to verify the accuracy of proposed TW fault location principle with different fault locations, a series of simulations are carried out, of which the simulation results are illustrated in Fig. 9 where Fig. 9 (a), (b) and (c) represent rectifier station to SCP, inverter station I to SCP and inverter station II to SCP, respectively. ΔL is fault location error and fault resistance is set to 0Ω. As can be seen, with different fault types, different fault sections and different fault locations, the fault location errors are basically less than 0.8 km, implying a good accuracy.
The paper sets a typical positive pole to ground fault which locates between rectifier station and SCP. The fault is 150 km away from rectifier station, and the grounding resistance is 0 Ω. Fig. 8 gives the typical fault simulation result. Thus:
• Fig. 8(a) describes the primary VTW signals of three terminals.
• •
Apparently, there exists VTW signals at LCC-HVDC rectifier station, and no VTW signals exist at VSC-HVDC inverter station. The simulation result exactly approves the theoretical analysis, and the fault location principle cannot be based on VTW signals; Fig. 8(b) describes the primary CTW signals of three terminals. Apparently, no matter LCC-HVDC rectifier station or VSC-HVDC inverter station, the CTW signal is obvious enough to be identified in fault location principle; Based on R-ECT, Fig. 8(c) describes the secondary CTW signals of three terminals. As can be seen, the mutation points of secondary CTW signals are much more obvious than primary CTW signals; Based on phase-mode transformation, Fig. 8(d) describes the positive sequence of CTW signals of three terminals. As can be seen, the CTW arrival time of three terminals are tlcc = 1.501 ms, tvsc1 = 2.839 ms and tvsc2 = 3.174 ms , respectively. Therefore, based on Eq. (11):
Δ = [178.799 km, 448.861 km, 449.026 km]T
(18)
5.3. Simulation with different fault locations
5.2. Typical fault simulation result
•
v (tlcc − tvsc1) + D1 + D2 + v (tlcc − tvsc2) + D1 + D3 4
5.4. Simulation with different fault resistances In order to verify the accuracy of proposed TW fault location principle with different fault resistances, a series of simulations are carried out, of which the simulation results are illustrated in Fig. 10 where Fig. 10 (a), (b) and (c) represent rectifier station to SCP, inverter station I to SCP and inverter station II to SCP, respectively. ΔL is fault location error and fault is located in the middle of TL of different sections. As can be seen, with different fault types, different fault sections and different fault resistances, the fault location errors are basically less than 0.6 km, implying a good accuracy. 5.5. Simulation with noise interference In order to verify the accuracy of proposed TW fault location principle with noise interference, a typical case study is provided as Fig. 11 shows. Hence:
(17)
According to Eq. (17), it is identified that the fault is between LCCHVDC rectifier station and SCP. Afterwards, the distance between fault location and rectifier station can be acquired by:
• Based on Fig. 8(c), typical Gaussian white noise (approximately 20%
Fig. 8. Typical fault simulation result. 6
Electrical Power and Energy Systems 117 (2020) 105627
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Fig. 9. Fault location errors with different fault locations.
Fig. 10. Fault location errors with different fault resistances.
Fig. 11. Typical fault simulation result with noise interference. Fig. 12. Control strategy of LCC-HVDC rectifier station.
•
Δ = [178.799 km, 448.861 km, 449.026 km]T
secondary CTW peak value) is added as Fig. 11(a) shows. As can be seen, though contain white noise, the mutation points of secondary CTW signals are still obvious to be identified; Based on phase-mode transformation, Fig. 11(b) describes the positive sequence of CTW signals of three terminals. As can be seen, the CTW arrival time of three terminals are tlcc = 1.501 ms, tvsc1 = 2.839 ms and tvsc2 = 3.174 ms , respectively. Therefore, based on Eq. (11):
(19)
According to Eq. (19), it is identified that the fault is between LCCHVDC rectifier station and SCP. Afterwards, the distance between fault location and rectifier station can be acquired by:
v (tlcc − tvsc1) + D1 + D2 + v (tlcc − tvsc2) + D1 + D3 4 = 149.9278 km
l=
7
(20)
Electrical Power and Energy Systems 117 (2020) 105627
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Fig. 13. Control strategy of VSC-HVDC inverter station (outer loop only).
Fig. 14. Detailed structure of HVDC-TL.
Therefore, though secondary CTW signals contain white noise, the fault location result is still accurate enough. However, it should be stated that the proposed fault location algorithm still has no anti-interference ability for impulse noise.
•
However, to pursuit the higher accuracy of fault location, the time synchronization system is required. It could be achieved using the global positioning system technology. Besides, the application scope of proposed fault location algorithm is only limited to hybrid multiterminal LCC-VSC-HVDC transmission system.
6. Summary Based on the differential output data of R-ECT, a novel TW fault location principle is proposed for the special structure of hybrid multiterminal LCC-VSC-HVDC transmission system, which includes CTW arrival time detection algorithm, fault section identification algorithm and fault location algorithm. The main superiorities of proposed fault location principle are twofold:
• High
principle has high accuracy under different fault types (PG fault, NG fault and PN fault), different fault locations (from relay to CP) and different fault resistances (0–300 Ω); Light data transmission burden. Only the CTW arrival times of all terminals require to be exchanged via the optical fiber.
Declaration of Competing Interest The authors declare that there is no conflict of interests regarding the republication of this paper..
fault location accuracy. The proposed TW fault location
8
Electrical Power and Energy Systems 117 (2020) 105627
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Appendix A. Control strategy of LCC-HVDC rectifier station Fig. 12 gives the control strategy of LCC-HVDC rectifier station. Appendix B. Control strategy of VSC-HVDC inverter station Fig. 13 gives the control strategy of VSC-HVDC inverter station. Appendix C. TW propagation velocity calculation Fig. 14 describes the structure of HVDC-TL. Based on Carson formula, Dommel proposed depth of complex penetration [19,21]:
P=
ρ 2πfμ
(21)
where ρ is the resistivity of earth ( ρ = 100 Ωm ); f is frequency; μ is the permeability of vacuum ( μ = 4π × 10−7 H/m ). Meanwhile, the equivalent radius of four bundled conductors is:
GMR =
4
4rd3
(22)
where r is radius of single bundled wire (r = 0.0134 m ). d is the distance between bundled wires (d = 0.450 m ). Ignoring mutual impedance, the inductance per length of HVDC-TL is:
LTL =
μ 2(h + P ) ln 2π GMR
(23)
Ignoring mutual conductance, the capacitance per length of HVDC-TL is:
CTL =
ε 2h ln 2π GMR
(24)
where ε is vacuum dielectric constant (ε = 8.854 × 10−12 H/m ). Eventually, the TW propagation velocity along HVDC-TL is [19]:
vTL =
1 = LTL CTL
2π με ln
2(h + P ) 2h ln GMR GMR
(25)
Appendix D. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.ijepes.2019.105627.
[11] Nanayakkara OMKK, Rajapakse AD, Wachal R. Location of DC line faults in conventional HVDC systems with segments of cables and overhead lines using terminal measurements. IEEE Trans Power Delivery 2012;27(1):279–88. https://doi.org/10. 1109/TPWRD.2011.2174067. [12] Belda NA, Plet CA, Smeets RPP. Analysis of faults in multiterminal HVDC grid for definition of test requirements of HVDC circuit breakers. IEEE Trans Power Delivery 2018;33(1):403–11. https://doi.org/10.1109/TPWRD.2017.2716369. [13] Fernandes PC, Naomira Gomes Venzi Gonçalves H, Melo e Silva K, Vigolvino Lopes F. Two-terminal modal traveling wave-based fault location method for HVDC systems. In: 2018 Workshop on Communication Networks and Power Systems (WCNPS); 2018. p. 1–4. doi:https://doi.org/10.1109/WCNPS.2018.8604378. [14] Xun L, Shungui L, Ronghui H, Jingwen A, Yunzhu A, Ping C, et al. Study on accuracy traveling wave fault location method of overhead line — cable hybrid line and its influencing factors. 2017 Chinese Automation Congress (CAC) 2017. p. 4593–7. https://doi.org/10.1109/CAC.2017.8243590. [15] Zou YT, Wang XL, Zhang HT, Liu CY, Zhou Q, Zhu WP. Traveling-wave based fault location with high grounding resistance for HVDC transmission lines. 2016 IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC) 2016. p. 1651–5. https://doi.org/10.1109/APPEEC.2016.7779773. [16] Song GB, Chu X, Cai XL, Gao SP, Ran MB. A fault-location method for VSC-HVDC transmission lines based on natural frequency of current. Int J Electrical Power Energy Syst 2014;63:347–52. https://doi.org/10.1016/j.ijepes.2014.05.069. [17] Wang D, Gao HL, Zou GB, Luo SB. Ultra-high-speed travelling wave directional protection based on electronic transformers. IET Gen Transmission Distrib 2017;11(8):2065–74. https://doi.org/10.1049/iet-gtd.2016.1694. [18] Wang D, Gao HL, Luo SB, Zou GB. Travelling wave pilot protection for LCC-HVDC transmission lines based on electronic transformers’ differential output characteristic. Int J Electrical Power Energy Syst 2017;93:283–90. https://doi.org/10.1016/ j.ijepes.2017.06.004. [19] Wang D, Hou MQ, Gao MY, Qiao F. Travelling wave directional pilot protection for hybrid HVDC transmission line. Int J Electrical Power Energy Syst 2019;107:615–27. https://doi.org/10.1016/j.ijepes.2018.12.028. [20] Wang D, Hou MQ, Gao MY, Qiao F. Travelling wave directional pilot protection for hybrid LCC-MMC-HVDC transmission line. Int J Electrical Power Energy Syst 2020;115:105431. https://doi.org/10.1016/j.ijepes.2019.105431. [21] DommelHW. EMTP theory book; 1986.
References [1] Yang XF, Xue Y, Chen BW, Lin ZQ, Mu YJ, Zheng TQ, et al. An enhanced reverse blocking MMC with DC fault handling capability for HVDC applications. Electric Power Syst Res 2018;163:706–14. https://doi.org/10.1016/j.epsr.2017.08.040. [2] Luo SB, Gao HL, Wang D, Zou GB. Non-unit transient based boundary protection for UHV transmission lines. Int J Electrical Power Energy Syst 2018;102:349–63. https://doi.org/10.1016/j.ijepes.2018.05.005. [3] Khazaei J, Idowu P, Asrari A, Shafaye A, Piyasinghe L. Review of HVDC control in weak AC grids. Electric Power Syst Res 2018;162:194–206. https://doi.org/10. 1016/j.epsr.2018.05.022. [4] Chen G, Hao M, Xu Z, Vaughan A, Cao J, Wang H. Review of high voltage direct current cables. CSEE J Power Energy Syst 2015;1(2):9–21. https://doi.org/10. 17775/CSEEJPES.2015.00015. [5] Zhang Y, Tai N, Xu B. Fault analysis and traveling-wave protection scheme for bipolar HVDC lines. IEEE Trans Power Delivery 2012;27(3):1583–91. https://doi.org/ 10.1109/TPWRD.2012.2190528. [6] Zou GB, Feng Q, Huang Q, Sun CJ, Gao HL. A fast protection scheme for VSC based multi-terminal DC grid. Int J Electrical Power Energy Syst 2018;98:307–14. https:// doi.org/10.1016/j.ijepes.2017.12.022. [7] Wei S, Yanfeng G, Yan L. Traveling-wave-based fault location algorithm for starconnected hybrid multi-terminal HVDC system. 2017 IEEE conference on energy internet and energy system integration (EI2) 2017. p. 1–5. https://doi.org/10.1109/ EI2.2017.8245645. [8] Li JW, Yang QQ, Mu H, Blond SL, He HW. A new fault detection and fault location method for multi-terminal high voltage direct current of offshore wind farm. Appl Energy 2018;220:13–20. https://doi.org/10.1016/j.apenergy.2018.03.044. [9] Deng F, Zeng XJ, Pan LL. Research on multi-terminal traveling wave fault location method in complicated networks based on cloud computing platform. Protect Control Mod Power Syst 2017;2(2):199–210. https://doi.org/10.1186/s41601-0170042-4. [10] Liang YS, Wang G, Li HF. Time-domain fault-location method on HVDC transmission lines under unsynchronized two-end measurement and uncertain line parameters. IEEE Trans Power Delivery 2015;30(3):1031–8. https://doi.org/10.1109/ TPWRD.2014.2335748.
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Travelling wave fault location principle for hybrid multi-terminal LCC-VSCHVDC transmission line based on R-ECT
T
⁎
Dong Wang , Mengqian Hou School of Automation and Electronic Engineering, Qingdao University of Science & Technology, No. 99, Songling Road, Qingdao 266061, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: Travelling wave Fault location Hybrid multi-terminal LCC-VSC-HVDC Transmission line PSCAD/EMTDC
This paper investigates the fault location issue of hybrid multi-terminal high voltage direct current (HVDC) overhead transmission line based on the line commutated converter (LCC) and voltage source converter (VSC). There exists two issues that should be addressed: (i) the travelling wave (TW) fault location principle’s adaptability to multi-terminal network topology and converter structures; (ii) the transfer method of high frequency TW signal. Therefore, a novel TW fault location principle for the hybrid multi-terminal LCC-MMC-HVDC transmission line is proposed based on the Rogowski coli based electronic current transformer (R-ECT). Firstly, the high frequency TW transfer capability of the R-ECT is studied. Secondly, a novel TW fault location principle based on the secondary differential current travelling wave (D-CTW) is proposed. Eventually, in order to verify the high accuracy of the proposed principle, a typical ± 400 kV hybrid three-terminal LCC-VSC-HVDC transmission system is used for the case study based on PSCAD/EMTDC. Furthermore, its robustness against different fault locations, different fault resistances and different fault types is also investigated.
1. Introduction Hybrid multi-terminal LCC-VSC-HVDC transmission system has rapidly developed in recent years because of its advantages of large transmission capacity, high transmission efficiency and ability to construct asynchronous grid compared with conventional AC transmission systems. Compared with conventional LCC-HVDC transmission systems, because of the inherent characteristic of insulated gate bipolar transistor (IGBT) and high frequency pulse width modulation (PWM) strategy, it has no commutation failure issue and the ability to supply power to passive systems. Compared with conventional VSC-HVDC or modular multi-level converter (MMC) based HVDC transmission systems, it has much lager transmission capacity and lower construction cost. Besides, considering multi-terminal topology, it has less impact on the AC systems connected to inverter stations [1–6]. In recent years, the TW fault location principle has been widely utilized in modern power grids. It has high location accuracy and is almost immune to fault resistance, fault location and fault type. Various fault location principles for the HVDC transmission line (TL) have been proposed. For star-connected hybrid multi-terminal HVDC-TL, Wei et al. [7] proposed a novel fault location algorithm. It can identify the faulty branch correctly and locate the distance accurately only by using the arrival time of the initial TW. For multi-terminal HVDC topology of
⁎
offshore wind farms, Li et al. [8] proposed a novel fault location principle based on high-frequency components detected from the fault current signal. This method can accurately detect the fault on each line and classify the fault types. Taking cloud computing platform data and complicated networks into account, Deng et al. [9] proposed a multiterminal TW fault location method. It can quickly, accurately, and reliably locate the fault point under limited TW acquisition unit with optimal placement. Under unsynchronized two-end measurement and uncertain line parameters, Liang et al. [10] proposed a time-domain fault-location principle suitable for HVDC-TL. It can locate faults accurately on the HVDC lines even in the case of loss of signals from GPS. Using terminal measurements, Nanayakkara et al. [11] paid the attention to DC line faults in conventional HVDC transmission system with segments of cables and overhead lines. It has anti-interference ability. For definition of test requirements of HVDC circuit breakers, Belda et al. [12] analyzed faults in multi-terminal HVDC power grid. Fernandes et al. [13] proposed a two-terminal model TW based fault location method for HVDC systems according to aerial and ground mode TWs. In cases of uncertainties in line parameters, the method keeps the same fault location accuracy. Xun et al. [14] worked on the accurate TW fault location method of overhead line-cable hybrid line and analyzed the influencing factors. This method shows high accuracy on the twoterminal structure. In order to overcome the high grounding resistance
Corresponding author. E-mail address: [email protected] (D. Wang).
https://doi.org/10.1016/j.ijepes.2019.105627 Received 6 June 2019; Received in revised form 28 September 2019; Accepted 11 October 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.
Electrical Power and Energy Systems 117 (2020) 105627
D. Wang and M. Hou
Nomenclature LCC HVDC R-ECT VTW D-CTW PG PN SR CC
SCP VSC TW PWM CTW CT NG IGBT TL FI
line commutated converter high voltage direct current Rogowski coil based electronic current transformer voltage travelling wave differential current travelling wave positive pole to ground positive pole to negative pole smoothing reactor compensation capacitance
star connection point voltage source converter travelling wave pulse width modulation current travelling wave current transformer negative pole to ground insulated gate bipolar transistor transmission line filter inductor
2. TW transfer characteristic of R-ECT
for HVDC-TL, Zou et al. [15] proposed a novel TW based fault location principle using S-transform to analyze TW to demonstrate the characteristic and variation in time-frequency domain. Song et al. [16] proposed a fault location principle for VSC-HVDC-TL using the natural frequency current. It has validity, rapidity and accuracy characteristic. In fact, few research papers were focused on the TW fault location of the hybrid multi-terminal LCC-VSC-HVDC-TL, to which should be paid more attention since the hybrid systems are being widely developed. For this topic, there exists two issues that should be addressed: i) Taking the multi-terminal network topology and converter structures into account, the adaptability of proposed TW fault location principle requires to be investigated; ii) Due to the bandwidth of TW is between several kHz to several hundreds of kHz, how to accurately obtain the high frequency TW data also requires to be studied. As for the TW transfer equipment, R-ECT has several superiorities over conventional current transformer (CT). On one hand, the bandwidth of R-ECT is up to several hundreds of kHz which is much wider than that of conventional CTs, typically dozens of kHz. On the other hand, due to the special structure of the R-ECT, the secondary current is differential signal of primary current. Besides, the D-CTW has much more obvious mutations to be detected [17,18]. The main contribution of the paper is a novel TW fault location principle for multi-terminal LCC-VSC-HVDC overhead TL based on the differential output of R-ECT which aims to address the above mentioned issues. Comparing with conventional fault location principle, it has two main superiorities: (i) R-ECT has the capability to transfer whole bandwidth of CTW, and the secondary D-CTW has much more obvious mutations to be detected; (ii) The proposed fault location principle is suitable for hybrid multi-terminal LCC-VSC-HVDC topology; (iii) The proposed fault location principle has high fault location accuracy. The rest of the paper is organized as follows. In Section 2, the whole bandwidth TW transfer ability of R-ECT is studied. In Section 3, the novel fault location principle is proposed. In Section 4, a series of simulation results are provided to validate the proposed fault location principle’s robustness against different fault locations, different fault resistances and different fault types, followed by conclusions.
Fig. 1 provides the structure and equivalent circuit of R-ECT [17,18]. i1 is the primary current signal. u 0 is the induced voltage signal of secondary side. M is the mutual inductance of R-ECT. R 0 , C0 and L0 are equivalent resistance, equivalent capacitance and equivalent inductance of R-ECT, respectively. In order to acquire stable secondary sampling data, RS is installed as sampling resistance. Although R-ECT is a CT, the output of R-ECT is voltage signal. The detailed parameters of R-ECT in this paper is shown in Table 1. According to Fig. 1:
⎧u 0 (t ) = M di1 (t )/dt i2 (t ) = uS (t )/ RS + C0 duS (t )/dt ⎨ ⎩u 0 (t ) − uS (t ) = R 0 i2 (t ) + L0 di2 (t )/dt
(1)
Based on Laplace transformation, Eq. (1) can be described as:
⎧U0 (s ) = sMI1 (s ) I2 (s ) = US (s )/ RS + sC0 US (s ) ⎨ ⎩U0 (s ) − US (s ) = R 0 I2 (s ) + sL0 I2 (s )
(2)
where s is the complex frequency variable. Afterwards, the transfer function of R-ECT can be obtained:
H (s ) =
US (s ) RS Ms = I1 (s ) C0 L0 RS s 2 + (C0 R 0 RS + L0) s + R 0 + RS
(3)
Define f and j are the time frequency and imaginary number unit respectively, then s = 2πf j. Eq. (3) can be described as:
H (f ) =
4π 2RS Mf 2 (C0 R 0 RS + L0) + 2πRS Mf (R 0 + RS − 4π 2f 2 C0 L0 RS )j (R 0 + RS − 4π 2f 2 C0 L0 RS )2 + 4π 2f 2 (C0 R 0 RS + L0)2 (4)
Accordingly, the Bode plot of R-ECT is illustrated in Fig. 2. Hence, it can be concluded:
• Based •
on Fig. 2(a), the amplitude-frequency characteristic is a straight line with a slope of +20 dB/dec for the TW frequency bandwidth. The higher the frequency of primary signal is, the larger the amplitude of secondary signal is; Based on Fig. 2(b), the phase-frequency characteristic is
Fig. 1. Structure and equivalent circuit of R-ECT. 2
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thyristor based converter, power transformer, relay, AC filter, DC filter and large smoothing reactor (SR). The TW impedances of SR and TL are defined as ZSR and ZTL , respectively. After fault occurs, the incident VTW and CTW signals arrive at where relay locates. However, considering the large SR is a nature boundary, the VTW and CTW signals cannot pass through the SR and invade converter station. This indicates the VTW and CTW are totally reflected at LCC-HVDC converter station. Accordingly, based on Eq. (5), the VTW and CTW detected by the relay are:
Table 1 Detailed parameters of R-ECT Parameters
R0
L0
C0
M
RS
Values
0.4338 Ω
3.6924 μ H
2.3946 nF
0.1273 μ H
100 Ω
approximately a straight line with a constant value (+90 deg) for TW frequency bandwidth. Thus, the secondary output is the differential signal of primary input.
(
(
mulation model in Fig. 7. Apparently, there are a number of TW mutations after TL fault occurs; According to R-ECT transfer function in Eq. (4), the primary CTW is processed and the D-CTW signal is acquired as Fig. 3(b) shows. Exactly as the theoretical analysis above, the secondary output of RECT is the differential signal of the primary input. Besides, the DCTW has much obvious mutation to be identified.
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3.3. VSC-HVDC inverter station VSC-HVDC converter station has several advantages over LCCHVDC converter station such as no commutation failure, ability to supply power to passive system and ability to construct multi-terminal topology. Especially, in order to avoid commutation issue, VSC-HVDC converter station is generally applied as inverter station in hybrid transmission system. Besides, in order to acquire high transmission capacity, a multi-terminal topology structure is adopted. Fig. 5(b) provides a typical structure of VSC-HVDC inverter station, consists of IGBT based converter, power transformer, relay, compensation capacitance (CC) and filter inductance (FI). The TW impedances of CC and TL are defined as ZCC and ZTL , respectively. Considering the large CC installed between TL and ground, for TW frequency bandwidth, ZCC ≈ 0 . In other words, for TW signal, the TL is approximately grounded directly [19]. After fault occurs, the incident VTW and CTW signals arrive at where relay locates. Accordingly, based on Eq. (5), the VTW and CTW detected by the relay are:
3. Typical transmission system 3.1. Reflection and refraction of TW Fig. 4 provides the typical TW reflection and refraction phenomenons [18]. As can be seen, the incident VTW (uin ) and CTW (iin ) propagate along line 1, and there are refraction and reflection at TW impedance discontinuity point (generally busbar or fault point). Besides, the TW impedances at line 1 and line 2 are Z1 and Z2 , respectively. The reflection VTW and CTW are url and irl , respectively. The refraction VTW and CTW are urr and irr , respectively. The forward direction of VTW is defined from TL to earth. The forward fault of CTW is its actual transmission direction. Therefore, the reflection and refraction coefficients of VTW and CTW are acquired by:
⎧ λ u = (Z2 − Z1)/(Z2 + Z1) ∈ (−1, 1) ⎪ λi = (Z2 − Z1)/(Z2 + Z1) ∈ (−1, 1) ⎨ βu = 2Z2/(Z2 + Z1) ∈ (0, +∞) ⎪ β = 2Z /(Z + Z ) ∈ (0, +∞) 1 2 1 ⎩ i
)
where u and i denote the VTW and CTW detected by the relay, respectively. uf and i f denote the incident VTW and CTW, respectively. λ u and λi denote the reflection and refraction coefficients, respectively.
• Fig. 3(a) describes the primary CTW signal acquired by PSCAD si•
)
ZSR − ZTL 2ZSR ⎧ ⎪u = (1 + λ u ) uf = 1 + ZSR + ZTL uf = ZSR + ZTL uf ⎨i = −(1 − λ ) i = − 1 − ZSR − ZTL i = − 2ZTL i i f ⎪ ZSR + ZTL f ZSR + ZTL f ⎩
To demonstrate the above theoretical analysis, a typical simulation is carried out of which the results are shown in Fig. 3. It can be seen that:
(
)
ZCC − ZTL ⎧ ⎪u = (1 + λ u ) uf = 1 + ZCC + ZTL uf ≈ 0 ⎨i = −(1 − λ ) i = − 1 − ZCC − ZTL i ≈ −2i f i f ⎪ ZCC + ZTL f ⎩
(
(5)
)
(7)
where u and i denote the VTW and CTW detected by the relay, respectively. uf and i f denote the incident VTW and CTW, respectively. λ u and λi denote the reflection and refraction coefficients, respectively.
where λ u , λi , βu and βi are VTW reflection coefficient, CTW reflection coefficient, VTW refraction coefficient and CTW refraction coefficient at TW discontinuity point, respectively.
4. TW fault location principle 3.2. LCC-HVDC rectifier station Based on the analysis in Section 3, due to the large CC installed between TL and ground, the VTW cannot be detected at VSC-HVDC inverter station. Therefore, a novel fault location principle is proposed based on the D-CTW output signal of R-ECT as following shows.
Generally, LCC-HVDC converter station is applied as rectifier station to acquire high transmission capacity, of which the typical topology is provided in Fig. 5(a). The LCC-HVDC converter station consists of
Fig. 2. Bode plot of R-ECT. 3
Electrical Power and Energy Systems 117 (2020) 105627
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Fig. 3. Comparison between primary CTW and secondary D-CTW.
Fig. 4. TW reflection and refraction.
4.1. CTW propagation characteristic Fig. 6 describes the CTW propagation process in multi-terminal LCCVSC-HVDC power grid. Assuming there are N ends and the multiterminal TLs are in star structure where ‘SCP’ denotes star connection point. Define the length of nth (1 ⩽ n ⩽ N ) TL is Dn . Assuming the fault happens at F in nth TL, and the length between F and nth converter station is ln . After the fault happens, the time that CTW arrives at nth relay is tn .
Fig. 6. CTW propagation characteristic.
the D-CTW of positive sequence can be obtained by:
in (k ) =
4.2. CTW arrival time detection
∑ k
in (k ) >
d 3
(9)
where in, + (k ) and in, − (k ) are the D-CTW sampling data of positive pole and negative pole at nth relay, respectively.
In this paper, the arrival time of CTW is detected using the D-CTW signal, which is acquired by the R-ECT. It can be described as: k+δ
in, + (k ) − in, − (k ) 2
4.3. Fault section identification algorithm (8)
After fault happens, it is necessary to identify fault section correctly before precise fault location. Based on Fig. 6, assuming the fault occurs between nth (1 ⩽ n ⩽ N ) converter station and SCP, therefore:
where k denotes the sampling point; in (k ) denotes the D-CTW sampling data of the positive sequence at nth relay; δ denotes the length of time window (δ = 3 in the paper); d denotes the peak value of D-CTW in data window. If Eq. (8) can be met, the time of kth sampling point represents CTW arrival time tn at nth relay. Based on the Karenbauer transformation algorithm [20], In Eq. (8),
Fig. 5. Typical structure of LCC-HVDC rectifier station and VSC-HVDC inverter station. 4
Electrical Power and Energy Systems 117 (2020) 105627
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⎧ v (t1 − t0) = D1 + Dn − ln ⎪· ·· ⎪ v (tn − 1 − t0) = Dn − 1 + Dn − ln ⎪ v (tn − t0) = ln ⎨ ⎪ v (tn + 1 − t0) = Dn + 1 + Dn − ln ⎪· ·· ⎪ v (tN − t0) = DN + Dn − ln ⎩
⎧ v (t1 − t0) − v (tn − t0) = (D1 + Dn − ln ) − ln ⎪· ·· ⎪ v (tn − 1 − t0) − v (tn − t0) = (Dn − 1 + Dn − ln ) − ln ⎨ v (tn + 1 − t0) − v (tn − t0) = (Dn + 1 + Dn − ln ) − ln ⎪· ·· ⎪ v (tN − t0) − v (tn − t0) = (DN + Dn − ln ) − ln ⎩ (10)
where t0 is fault start time; t1, t2, …, tN are the CTW arrival times at converter station 1, 2, …, N , respectively; D1, D2 , …, DN are the distances between SCP and converter station 1, 2, …, N , respectively; ln is the distance between F and nth converter station; v is CTW propagation speed along TL. Based on Eq. (14), one can define a (N − 1) × 1 order matrix:
where t0 is fault start time; t1, t2, …, tN are the CTW arrival times at converter station 1, 2, …, N , respectively; D1, D2 , …, DN are the distances between SCP and converter station 1, 2, …, N , respectively; ln is the distance between F and nth converter station; v is CTW propagation speed along TL. According to Eq. (10), define a fault section discrimination coefficient:
⎡ Δ1 ⎤ ⎡ vt1 − D1 ⎤ Δ = ⎢ Δ2 ⎥ = ⎢ vt2 − D2 ⎥ ⎢ · ·· ⎥ ⎢ · ·· ⎥ ⎢ ⎦ ⎣ vtN − DN ⎥ ⎣ ΔN ⎥ ⎦ ⎢
⎡ v (tn − t1) + D1 + Dn ⎤ · ····· ⎢ ⎥ ⎡ Ln,1 ⎤ ⎡ ln ⎤ Ln,2 ⎥ = ⎢ ln ⎥ = 1 ⎢ v (tn − tn − 1) + Dn − 1 + Dn ⎥ Ln = ⎢ ⎢ · ·· ⎥ ⎢· ··⎥ v (t − tn + 1) + Dn + 1 + Dn ⎥ 2⎢ ⎢ n ⎥ ⎢ L n, N − 1 ⎥ ⎢ l ⎥ · ····· n ⎦ ⎣ ⎦ ⎣ ⎢ ⎥ − + + v ( t t ) D D n N N n ⎣ ⎦
(11)
(15)
In order to acquire high fault location accuracy, after fault section is identified, the distance between F and nth converter station can be obtained by:
where Δn is fault section discrimination coefficient at nth (1 ⩽ n ⩽ N ) converter station. According to Eq. (10), Eq. (11) is derived as:
N −1
ln = ⎡ Dn − ln + vt0 ⎤ · ·· ⎢ ⎥ ⎡ Δ1 ⎤ ⎢ Dn − ln + vt0 ⎥ Δ = ⎢ Δ2 ⎥ = ⎢ ln − Dn + vt0 ⎥ ⎢ · ·· ⎥ ⎢ ⎥ Dn − ln + vt0 ⎥ ⎢ ΔN ⎥ ⎣ ⎦ ⎢ · ·· ⎢ ⎥ ⎢ ⎣ Dn − ln + vt0 ⎥ ⎦
(14)
∑ j = 1 L n, j N−1
(16)
5. Simulation 5.1. Simulation model (12)
According to Fig. 7, in order to verify the fault location accuracy of proposed principle, a typical ± 400 kV three-terminal LCC-VSC-HVDC model is established via the simulation software PSCAD/EMTDC. In the model, the detailed structures of LCC-HVDC rectifier station and VSCHVDC inverter station are exactly described in Fig. 5. The HVDC-TL adopts frequency depended model, and the DC resistances of TL and grounding wire are 0.02862 Ω/km and 2.8645 Ω/km , respectively. The SR, CC and FI are set to 0.2H, 1000 μ F and 0.0724H, respectively. Meanwhile, to acquire whole bandwidth of TW, the simulation rate is set to 1 MHz. F1-F9 denote different fault types (including PG, NG and PN) at different fault section. As for control strategy:
Based on Eq. (12), if F is between nth converter station and SCP, it can be concluded that:
Δn > Δ1 ≈ …≈Δn − 1 ≈ Δn + 1 ≈ …≈ΔN
(13)
Hence, Eq. (13) is the fault section identification criterion.
4.4. Fault location algorithm After fault section is identified via fault section identification algorithm in Section 4.3, which is assumed the fault is between nth converter station and SCP, then:
• According to Fig. 12 in Appendix A, the LCC-HVDC rectifier station adopts the constant DC current control strategy;
Fig. 7. Typical ± 400 kV three-terminal LCC-VSC-HVDC PSCAD simulation model. 5
Electrical Power and Energy Systems 117 (2020) 105627
D. Wang and M. Hou
• According to Fig. 13(a) in Appendix B, the VSC-HVDC inverter •
l=
station I adopts the constant DC voltage control and constant AC voltage control strategies; According to Fig. 13(b) in Appendix B, the VSC-HVDC inverter station II adopts the constant reactive power control and constant AC voltage control strategies.
= 149.9278 km
In order to verify the accuracy of proposed TW fault location principle with different fault locations, a series of simulations are carried out, of which the simulation results are illustrated in Fig. 9 where Fig. 9 (a), (b) and (c) represent rectifier station to SCP, inverter station I to SCP and inverter station II to SCP, respectively. ΔL is fault location error and fault resistance is set to 0Ω. As can be seen, with different fault types, different fault sections and different fault locations, the fault location errors are basically less than 0.8 km, implying a good accuracy.
The paper sets a typical positive pole to ground fault which locates between rectifier station and SCP. The fault is 150 km away from rectifier station, and the grounding resistance is 0 Ω. Fig. 8 gives the typical fault simulation result. Thus:
• Fig. 8(a) describes the primary VTW signals of three terminals.
• •
Apparently, there exists VTW signals at LCC-HVDC rectifier station, and no VTW signals exist at VSC-HVDC inverter station. The simulation result exactly approves the theoretical analysis, and the fault location principle cannot be based on VTW signals; Fig. 8(b) describes the primary CTW signals of three terminals. Apparently, no matter LCC-HVDC rectifier station or VSC-HVDC inverter station, the CTW signal is obvious enough to be identified in fault location principle; Based on R-ECT, Fig. 8(c) describes the secondary CTW signals of three terminals. As can be seen, the mutation points of secondary CTW signals are much more obvious than primary CTW signals; Based on phase-mode transformation, Fig. 8(d) describes the positive sequence of CTW signals of three terminals. As can be seen, the CTW arrival time of three terminals are tlcc = 1.501 ms, tvsc1 = 2.839 ms and tvsc2 = 3.174 ms , respectively. Therefore, based on Eq. (11):
Δ = [178.799 km, 448.861 km, 449.026 km]T
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5.3. Simulation with different fault locations
5.2. Typical fault simulation result
•
v (tlcc − tvsc1) + D1 + D2 + v (tlcc − tvsc2) + D1 + D3 4
5.4. Simulation with different fault resistances In order to verify the accuracy of proposed TW fault location principle with different fault resistances, a series of simulations are carried out, of which the simulation results are illustrated in Fig. 10 where Fig. 10 (a), (b) and (c) represent rectifier station to SCP, inverter station I to SCP and inverter station II to SCP, respectively. ΔL is fault location error and fault is located in the middle of TL of different sections. As can be seen, with different fault types, different fault sections and different fault resistances, the fault location errors are basically less than 0.6 km, implying a good accuracy. 5.5. Simulation with noise interference In order to verify the accuracy of proposed TW fault location principle with noise interference, a typical case study is provided as Fig. 11 shows. Hence:
(17)
According to Eq. (17), it is identified that the fault is between LCCHVDC rectifier station and SCP. Afterwards, the distance between fault location and rectifier station can be acquired by:
• Based on Fig. 8(c), typical Gaussian white noise (approximately 20%
Fig. 8. Typical fault simulation result. 6
Electrical Power and Energy Systems 117 (2020) 105627
D. Wang and M. Hou
Fig. 9. Fault location errors with different fault locations.
Fig. 10. Fault location errors with different fault resistances.
Fig. 11. Typical fault simulation result with noise interference. Fig. 12. Control strategy of LCC-HVDC rectifier station.
•
Δ = [178.799 km, 448.861 km, 449.026 km]T
secondary CTW peak value) is added as Fig. 11(a) shows. As can be seen, though contain white noise, the mutation points of secondary CTW signals are still obvious to be identified; Based on phase-mode transformation, Fig. 11(b) describes the positive sequence of CTW signals of three terminals. As can be seen, the CTW arrival time of three terminals are tlcc = 1.501 ms, tvsc1 = 2.839 ms and tvsc2 = 3.174 ms , respectively. Therefore, based on Eq. (11):
(19)
According to Eq. (19), it is identified that the fault is between LCCHVDC rectifier station and SCP. Afterwards, the distance between fault location and rectifier station can be acquired by:
v (tlcc − tvsc1) + D1 + D2 + v (tlcc − tvsc2) + D1 + D3 4 = 149.9278 km
l=
7
(20)
Electrical Power and Energy Systems 117 (2020) 105627
D. Wang and M. Hou
Fig. 13. Control strategy of VSC-HVDC inverter station (outer loop only).
Fig. 14. Detailed structure of HVDC-TL.
Therefore, though secondary CTW signals contain white noise, the fault location result is still accurate enough. However, it should be stated that the proposed fault location algorithm still has no anti-interference ability for impulse noise.
•
However, to pursuit the higher accuracy of fault location, the time synchronization system is required. It could be achieved using the global positioning system technology. Besides, the application scope of proposed fault location algorithm is only limited to hybrid multiterminal LCC-VSC-HVDC transmission system.
6. Summary Based on the differential output data of R-ECT, a novel TW fault location principle is proposed for the special structure of hybrid multiterminal LCC-VSC-HVDC transmission system, which includes CTW arrival time detection algorithm, fault section identification algorithm and fault location algorithm. The main superiorities of proposed fault location principle are twofold:
• High
principle has high accuracy under different fault types (PG fault, NG fault and PN fault), different fault locations (from relay to CP) and different fault resistances (0–300 Ω); Light data transmission burden. Only the CTW arrival times of all terminals require to be exchanged via the optical fiber.
Declaration of Competing Interest The authors declare that there is no conflict of interests regarding the republication of this paper..
fault location accuracy. The proposed TW fault location
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Appendix A. Control strategy of LCC-HVDC rectifier station Fig. 12 gives the control strategy of LCC-HVDC rectifier station. Appendix B. Control strategy of VSC-HVDC inverter station Fig. 13 gives the control strategy of VSC-HVDC inverter station. Appendix C. TW propagation velocity calculation Fig. 14 describes the structure of HVDC-TL. Based on Carson formula, Dommel proposed depth of complex penetration [19,21]:
P=
ρ 2πfμ
(21)
where ρ is the resistivity of earth ( ρ = 100 Ωm ); f is frequency; μ is the permeability of vacuum ( μ = 4π × 10−7 H/m ). Meanwhile, the equivalent radius of four bundled conductors is:
GMR =
4
4rd3
(22)
where r is radius of single bundled wire (r = 0.0134 m ). d is the distance between bundled wires (d = 0.450 m ). Ignoring mutual impedance, the inductance per length of HVDC-TL is:
LTL =
μ 2(h + P ) ln 2π GMR
(23)
Ignoring mutual conductance, the capacitance per length of HVDC-TL is:
CTL =
ε 2h ln 2π GMR
(24)
where ε is vacuum dielectric constant (ε = 8.854 × 10−12 H/m ). Eventually, the TW propagation velocity along HVDC-TL is [19]:
vTL =
1 = LTL CTL
2π με ln
2(h + P ) 2h ln GMR GMR
(25)
Appendix D. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.ijepes.2019.105627.
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