2011The International Conference on Advanced Power System Automation and Protection

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*Corresponding author (email: song.gb@mail.xjtu.edu.cn)

Natural Frequency Based Protection and Fault Location for VSC-HVDC Transmission Lines

SONG GuoBing*, Cai XinLei, Gao ShuPing, Suonan JiaLe, Li Guang

School of Electric Engineering, Xi’an Jiaotong University, Xi’an710049, China

Abstract With excellent priorities, Voltage Source Converter based HVDC (VSC-HVDC) will be the promising offset of HVDC transmission technology. This paper presents a protection and fault location method for VSC-HVDC transmission lines using one terminal current data. The proposed method is based on the natural frequency from the reflection process of traveling wave on a distributed parameters transmission line. As the presence of the large shunt capacitor on both terminals of the VSC-HVDC lines, the high frequency traveling wave is close to total reflection on the terminals. Therefore, the value of natural frequency of VSC-HVDC transmission lines is only related to fault distance and travelling wave speed, and the mag-nitude of natural frequency signal is related to the fault resistance. According to these characteristic, a single-end protection and fault location method is proposed. Compared with traveling wave method, the proposed natural frequency method is more simple and reliable. It does not need to detect accurate wave-front arriving instant with high sampling frequency. The proposed method is verified using the frequency-dependent line model in EMTDC. The simulations have shown that this me-thod is valid and is capable of locating the faults occurring on VSC-HVDC transmission lines quickly and accurately.

Keywords VSC-HVDC; HVDC transmission line; protection; fault location; spectrum analysis; natural frequency

1 Introduction

Since Voltage Source Converter based HVDC (VSC-HVDC) has originally excellent priorities, VSC-HVDC will be the promising offset of HVDC transmission technology, and it is important to study on the protection and accurate fault-location method for VSC-HVDC transmission lines to ensure the security of VSC-HVDC system. [1-4].

Most HVDC lines are used for transmission power over long distance, inevitably passing through complex terrain and operat-ing under harsh weather conditions. Therefore, it is extremely difficult to determine where a fault is occurring on the line. Be-sides, HVDC lines are mostly used as an interconnection between different power systems and carrying a large amount of power. Incapable of quickly locating and removing faults on an HVDC transmission line will destroy the stability of the power system and lead to serious social and economic consequences. Therefore, research on the accurate and fast fault-location techniques for HVDC transmission line is of great significance and of practical engineering value. However, it is extremely difficult to determine where a fault is occurring on HVDC transmission lines as a result of its long distance and frequency dependent parameter characte-ristic.

At present, the currently used fault-location techniques for HVDC transmission lines are mainly based on traveling wave method [5-14]. These traveling-wave-based methods have fast response and high accuracy. The results are not easily affected by the factors, such as bus con�guration, fault types, fault resistance,

and system parameters. However, they are also facing some in-surmountable technical problems (e.g. the detection of the wave-head is very difficult; it is depending on high sampling frequency; it is vulnerable to interference signals etc.). The time domain traveling wave method only use the initial transient signal to locate fault. Besides, for the time domain signal, the accurate estimation of the traveling wave speed is extremely difficult as the wave speed is frequency dependent.

Some non-traveling-wave fault-location algorithms for AC and DC lines are proposed in [15-16] based on distributed para-meter line model and the calculation of voltage distribution along the lines, which can yield the correct fault-location result from any section of data. In [16], a fault of HVDC line can be located using two terminal voltage and current data at a sampling rate of 100 kHz. The fault-location method is based on accurate calcula-tion of voltage distribution. It cannot yield accurate results if the frequency dependent parameters characteristic of the line is too obvious.

The concept of natural frequency is proposed in [17] based on distributed parameter model and it is used to locate fault for AC line in [18-20], which is different from the traditional time do-main traveling wave method. In [20], the relations of natural fre-quency, line length, wave speed and boundary conditions are derived in Laplace domain. The method can use any section of the post fault data to exact natural frequency and locate faults. So it is more reliable than the traditional time domain traveling wave method. Although it is designed for ac transmission lines, they can also be applied to locate faults on dc transmission lines be-cause there is no essential difference between ac and dc transmis-

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2011The International Conference on Advanced Power System Automation and Protection

sion lines except for the frequency at which electric energy is transmitted. Besides, the voltage of DC line keeps constant for the normal operation HVDC system. So the transient energy of DC line is very rich whether the fault occurs at any time. The natural frequency signal of VSC-HVDC DC lines is very obvious and easy to exact.

Combining to the VSC-HVDC structure, a protection and fault location method for VSC-HVDC transmission lines is pro-posed in this paper based on natural frequency of current, which is suitable for VSC-HVDC frequency-dependent parameters lines. The method is performed in frequency domain. Through the spectral analysis of current with Prony algorithm to obtain its natural frequency, a short data window is sufficient for detecting natural frequency to achieve satisfactory accuracy in practice. The proposed method is simple and reliable than the time domain traveling-wave fault-location.

2 VSC-HVDC System Structure

The schematic diagram of a bipolar VSC-HVDC system is shown in Figure 1. In the system, there is a VSC based converter station in each side, which consists of converter, transformer, AC filter, DC side capacitors and DC transmission lines. The trans-mission lines (positive and negative) are between K side and Mside, 1Ki and 2Ki are the current (positive and negative) meas-ured at K side.

2Ki

1Ki

Figure 1 VSC-HVDC transmission system

For AC lines, the transient energy is very small if voltage is

near zero when a fault occurs, thus, natural frequency signal is very weak and hard to extract from the spectrum. Different from AC lines, the voltage of DC line keeps constant for the normal operation VSC-HVDC system. So transient energy of DC line is very rich whether the fault occurs at any time. In addition, as there are shunt capacitors on the terminals of DC lines, the high frequency traveling wave is total reflection in the system side. So the natural frequency signal is very obvious and easy to extract in VSC-HVDC system. Therefore, as the current of current trans-former(CT) is generally used in modern traveling wave devices and the energy of current signal is very strong, the current of VSC-HVDC transmission lines can be used for the spectrum analysis and extraction of natural frequency.

3 VSC-HVDC Natural Frequency Analysis

In order to the analysis natural frequency of VSC-HVDC

transmission lines, the fault component net of distributed parame-ter transmission line of VSC-HVDC is given in Fig.2. In Figure 2,

, , ,R L G C are the resistance, inductance, conductance and capa-citance per-kilometer; l is the fault distance; v is the traveling wave speed; SZ FZ and cZ are system impedance, the impedance of fault point and characteristic impedance of the DC transmission line, respectively. FU is the additional DC voltage source at the fault point. 1� and 2� are the reflection coefficient at the system and fault point.

, , , , cR L G C Z

FZvSZ

1� 2�

FU

l

Figure 2 The fault component net of distributed parameter HVDC transmission line

When a fault occurs on the line, the wave of the fault point is

traveling from the fault point to the system and it will reflect be-tween the system and the fault point. The frequency spectra of the traveling waves propagating on transmission lines are of harmonic type of a fundamental characteristic frequency, called natural fre-quencies [18-20]. The characteristic equation of natural frequency in frequency domain is [20]

2 /1 21 e 0s l v�� � � � (1)

where s is the root of the characteristic equation; the real part of s is related to attenuation coefficients of natural frequency energy and the imaginary part of s corresponds to the value of natural frequency. 1� and 2� are reflection coefficient, depending on the impedance of system side and fault point.

1 S S( ) / ( + )C CZ Z Z Z� � � ,

2 F F( ) / ( + )C CZ Z Z Z� � � and ( (CZ R j L G j C� �� � � .If1

1 1 e j�� � � , 22 2 e j�� � � , it can be derived from (1) that:

1 2 2 /1 2e e ej j sl v� �� � � � (2)

According to Euler formula, the characteristic equation has in-finite roots, corresponding to infinite number of frequencies, thus:

1 2 1 2 1 2

1 2 1 2 1 2

ln ( 02

ln ( 22

v j kls

v j kl

� � � � � � �

� � � � � � �

� � � � � � ��� �� � � � � ��

(3)

where k is an integer, as the imaginary part of s corresponds to the value of natural frequency, natural frequency is

1 2 1 2

1 2 1 2

( ) 04

( ) 24

v klf

v kl

� � � � � � ��

� � � � � � ��

� � � � ��� �� � � ��

(4)

The dominant frequency of natural frequency is frequency with

2011The International Conference on Advanced Power System Automation and Protection

the lowest value and highest spectrum amplitude of all natural fre-quencies. For the 100km line, the dominant frequency of natural frequency is about 1500Hz, so the natural frequency is a high frequency components, and the shorter the line length, the higher the natural frequency.

Given the line parameters, using adequate frequency estimation methods to obtain any component of traveling wave natural fre-quencies (normally the dominant component), together with the boundary conditions (power system equivalent reactance), the dis-tance between two terminals which forms the natural frequencies can be accurately calculated. For fault induced traveling wave fre-quencies (local bus the one end, fault point the other), the length is naturally the fault distance.

According to Figure 1, there are large shunt capacitors on both terminals of the DC lines in VSC-HVDC. Therefore, in high fre-quency domain the system impedance SZ can be approximated and equivalent to

S 1 / sZ j C�� (5)

The sC is shunt capacitances of the positive and negative pole. So system impedance is equivalent to the capacitor impedance for natural frequency signal. Besides, in high frequency domain, the characteristic impedance of DC line can be simplified as

/cZ L C� (6)

When the transition resistance of the fault point is FR , it can be derived that the reflection coefficient of the system side and the fault point are:

1 (1/ / )/(1/ + / )s sj C L C j C L C� �� � � (7)

2 F F( / )/( / )R L C R L C� � � � (8)

If the characteristic impedance of DC transmission lines cZ is 400 �, the capacitor sC is 1000�F and FR =100�, at the fre-quency of 1000Hz, combining (5)~(8), it can be concluded that: 1. The value of capacitor impedance is 0.129�, which is a low

number compared to converter valve equivalent impedance. The system impedance can be equivalent to the capacitor impedance for natural frequency signal. 2. As characteristic impedance of the line is much larger than the

system impedance, so 1� is about -1 and 1� �� . It can be seen that the traveling wave signal is total reflection at system side of VSC-HVDC system. 3. According to (8), if F 0R � � , then 2� -1 and 2� �� , so when

metallic ground fault occurs, it is the total reflection at the fault point. If F 100R � � , then 2� =-0.6 and 2� �� ,so when it is not metallic ground fault, the fault point is not a total reflection, but the transition resistance only affects the magnitude of the signal, does not affect its phase (it is always � ). So the natural frequen-cy keeps constant when the transition resistance increases. Mani-fested in the frequency spectrum, when the transition resistance increases, the natural frequency keep unchanged, but there will be

some attenuation of spectrum amplitude. As the reflection of traveling wave signal between the system

side and fault point is the root causes of the natural frequency, therefore, there will be a stronger natural frequency signal in VSC-HVDC system. Combining to VSC-HVDC system struc-ture and equation (5)~(8), (4) can be simplified, the natural fre-quency of VSC-HVDC transmission line kf can be expressed as:

( )4 2

k kk

kv kvfl l� �

�� � � (9)

where k is an integer, kf is the k times for the natural fre-quency, kv is the traveling wave speed. By (9), when there is little changing of the traveling wave speed, the natural frequency spectrum approximately equal spaced spectrum with the same length, this feature can be used for selection of natural frequency.

4 Protection and fault location principle

The protection and fault location principle is based on the spectrum analysis of current to exact natural frequency. Then calculate the wave speed at the frequency, and obtain the fault distance. According to (9), the fault distance is

2k

k

kvlf

� (10)

where k is an integer, kf is the k times for the natural fre-quency, kv is the traveling wave speed at the corresponding frequency.

Theoretically, any natural frequency in the spectrum of the current can be used to locate faults accurately. As the amplitude of the first frequency (that is dominant frequency) is the maximum of all, so it can be used to locate. Thus, fault location formula is

1

12vl

f� (11)

It can be seen from (11) that accurate fault location depends on the accurately extraction of natural frequency and calculation traveling wave speed.

In order to accurately extract the natural frequency, the combi-nation of FFT and Prony algorithm is used to make spectrum estimation for short data window. The natural frequency main lobe band is selected through FFT, firstly. Using narrow band-pass filter, by a set of data within a small band after the filter, the accurate frequency values can be extracted through Prony algorithm.

When pole to pole fault or bipolar pole to ground fault occurs, there is no “modal mixing phenomenon ", the fault distance can be calculated accurately using the wave speed and natural frequency in mode domain. When single-phase to ground fault occurs over the AC line, it has been pointed out in [20] that the average wave speed of � mode and 0 mode can be chosen as the wave speed,

2011The International Conference on Advanced Power System Automation and Protection

which can yield accurate fault location result. The average wave speed of 0 mode and 1 mode signal wave speed can be used for the fault location of VSC-HVDC transmission lines when single pole to ground fault occurs.

In the high frequency domain, the wave speed changes a little, and it can be considered as a constant number. Therefore, when there is some error in the detection of natural frequency, it can be derived from (11) that the fault location error is:

2

12

1 1 1

1 22vd l l

d f f v� � � � (12)

It can be seen from (12) that when the fault distance increases, the influence of the detecting error of natural frequency on fault location error will increase. For the fault at the end of the 250km line, the corresponding fault location error is about 5km if there is 10Hz frequency error. When fault occurs at 50km, 10Hz fre-quency error is corresponding to only 0.2km of the distance measurement error. For the natural frequency based fault loca-tion method and a 250 km transmission line, in the range of, 10kHz sampling rate is sufficient to realize accurate fault loca-tion in the range(50 ~ 250 km); the current of the M side can be used to locate fault in the range(0 ~ 50 km). Thus, the proposed fault location principle can be implemented in recorder or protec-tion devices without adding new equipment.

As long as the natural frequency is detected accurately, the ac-curate fault location can be achieved. If the calculated fault dis-tance is less than the whole length, the protection can operate.

5 Simulations

In this paper, VSC-HVDC system built in PSCAD is used for the simulation and the direct current control strategy based on cascade PI controller is adopted in the control system [21-22]. In the system, the rated voltages are �60 kV and system capacity is 60MW. The frequency-dependent parameter transmission line model is used to simulate, whose length is 250km and its struc-ture can refer to [16]. The shunt capacitances ( sC )of the positive and negative pole are 1000�F. The PSCAD is used for power system fault simulation, and MATLAB is used for verifying al-gorithm. The modes are extracted by using mode transformation matrix [16]. The current of K side is used for the single-ended fault location. When a fault occurs at the end of the 250km line, the dominant natural frequency is about 600Hz, so the current is filtered through the high-pass filter first (the cut-off frequency is set to 400Hz) in this paper, then the spectrum analysis can be implemented.

When a fault occurs at the point of 200km from K-side by different transition resistance, the spectrum analysis results of 5ms data window with Prony algorithm by 1 mode current are shown in Figure 3, in which the data is sampled at a frequency of 10kHz. .

0 1000 2000 3000 4000 50000

20

40

60

f/Hz (a) FR =0�

0 1000 2000 3000 4000 50000

20

40

f/Hz (b) FR =50�

Figure 3 Spectrum estimation of natural frequency at K-side based on Prony al-gorithm when internal fault occurs

It can be seen from Figure 3 (a) that the natural frequency

spectrum VSC-HVDC DC transmission lines is approximately spaced spectrum with the same length, in which the dominant frequency of natural frequency is 739.69Hz. Therefore it can be calculated that the fault distance is 200.76km from (11). So the Prony algorithm is feasible for extracting natural frequency and accurately fault location. Figure 3 (b) indicates that when the transition resistance increases, the value of natural frequency keeps unchanged, but there will be some attenuation of amplitude in the spectrum. The FFT analysis results of mode current and pole current are given in Figure 4 when an internal positive pole to ground fault occurs at 100km from K-side.

0 1000 2000 3000 4000 50000

2000

4000

f/Hz (a) Spectrum of 1mode current

0 1000 2000 3000 4000 50000

2000

4000

f/Hz (b) Spectrum of 0 mode current

0 1000 2000 3000 4000 5000

0

5000

10000

f/Hz (c) Spectrum of positive pole current

0 1000 2000 3000 4000 5000

0

500

1000

f/Hz (d) Spectrum of negative pole current

Figure 4 Spectrum estimation of natural frequency based on Prony algorithm when fault occurs at positive pole and 100km from K-side

2011The International Conference on Advanced Power System Automation and Protection

Due to the coupling between the lines, there will be "modal mixing phenomenon" in the spectrum of mode current. The spectrum of mode current is more complex than the spectrum of fault pole current. So it is hard to exact the natural frequencies from mode current spectrum, however the current spectrum is relatively simple and easy to identify. Besides, as the decoupling matrix is a linear transformation, the natural frequency exacted from pole current is the same with the natural frequency exacted from mode current. Therefore, through the spectrum estimation of the current of fault pole, the corresponding main lobe of nat-ural frequency can be selected. After being filtered by narrow band pass filters (the narrow-band can be selected as 1300~1500Hz in Figure 4 (c)), the natural frequency can be exacted with Prony algorithm (the analysis result is 1420Hz). With the average speed 1 mode and 0 mode speed, it can be calculated that the fault distance is 100.55km. So for the pole to ground fault, as long as the natural frequency is extracted accu-rately, accurate fault location can be achieved as well.

In order to verify the validity of the proposed method, the re-sults of locating various-type faults occurring at different points with different transition resistances are given in this paragraph. Table I shows the fault location results from K side when pole to pole fault occurs with different transition resistances; Table 2 shows the fault location results of single pole to ground fault by 100� transition resistances. The simulation result is achieved at a sampling rate of 50 kHz. As the frequency dependent charac-teristic of 0 mode parameters is more significant than that of 1 mode parameters, so the average wave speed in Table 2 changes more obviously than the wave speed in Table 1.

Table 1 Results when fault occurs in bipolar pole

Fault Distance

( km)

Transition resistance

(�)

Dominant natural

frequency (Hz)

Traveling Wave speed

(km)

Results (km)

Error (%)

25 0 5980 298 514 24.96 -0.20

50 5960 298 501 25.04 0.20 100 5976 298 510 24.97 -0.12

75 0 1987 297 915 74.97 -0.04 50 1980 297 904 75.23 0.31 100 1975 297899 75.42 0.56

125 0 1180 297337 125.99 0.79 50 1180 297337 125.99 0.79 100 1183 297341 125.67 0.54

175

0 853 297163 174.19 -0.46 50 850 297158 174.80 -0.11 100 853 297163 174.19 -0.46

225 0 660 296 860 224.89 -0.05 50 660 296 860 224.89 -0.05 100 655 296 851 226.60 0.71

Table 2 Results when fault occurs in positive pole

Fault Distance

( km)

Dominant Natural fre-quency (Hz)

Average wave speed

(km/s) results (km) Error (%)

25 5810 290217 24.97 -0.12 75 1900 286754 74.46 -0.72 125 1130 283065 125.25 0.20 175 807 281276 174.27 -0.42 225 621 280114 225.53 -0.34

The results given in Tables 1 and Tables 2 have indicated that the proposed method can accurately locate faults regardless of where they are over the whole length of the line, with the largest error being less than 1%. The result is not affected by transition resistances and fault types. To achieve a more accurate fault location results rely on a more accurate signal processing and spectrum analysis tools.

6 Conclusion

In this paper, the natural frequency characteristic of VSC-HVDC DC transmission line is analyzed, and two conclu-sions are drown: 1.As the impact of the large shunt capacitor on both terminals of the DC lines in VSC-HVDC, the high frequency traveling wave is total reflection in the system side. Then it is found that the natural frequency of VSC-HVDC transmission lines is only associated to fault distance and the traveling-wave speed. The formula of natural frequencies for AC lines can be simplified; therefore, the natural frequency based fault location method in VSC-HVDC is simple and reliable.

2. For the normal operation VSC-HVDC system, the voltage of transmission lines keeps constant and will not be zero every cycle as the AC line. So whether the fault occurs at any time, the transient energy is very rich. Besides the natural frequency sig-nal is total reflection at the shunt capacitor, the natural frequency signals of DC lines is obvious and easy to exact by spectrum analysis tools.

Accordingly, a protection and fault-location method for VSC-HVDC transmission lines is presented. Different from the time domain traveling-wave methods in which only the wave-head is used, the proposed method can use any section of post fault data to exact natural frequency and locate faults, Be-sides, it is not affected by the fault position and transition resis-tance, and has high reliability and high accuracy.

This work was supported by the Key Program of National Natural Science of China (Grant No. 51037005) and National Natural Science Foundation of China un-der(Grant No. 50877061).

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