Voltage Distribution – Based Fault Location for Half-Wavelength Transmission Line with Large-Scale Wind Power Integration in China

Large-scale wind farms are generally far away from load centers, hence there is an urgent need for a large-capacity power transmission scheme for extremely long distances, such as half-wavelength transmission lines (HWTLs), which can usually span thousands of kilometers from large-scale wind farms to load centers. An accurate fault location method for HWTLs is needed to ensure safe and reliable operation. This paper presents the design of a modal voltage distribution–based asynchronous double-end fault location (MVD-ADFL) scheme, in which the phase voltages and currents are transformed to modal components through a Karenbauer transformation matrix. Then, the modal voltage distributions along transmission lines are calculated by voltage and current from double ends. Moreover, the minimums and intersection points of calculated modal voltages from double ends are defined as the fault location estimation. In order to identify incorrect fault location results and reduce calculation errors for the correct ones, air modal and earth modal voltage distributions are applied in the fault location estimations. Simulation results verify the effectiveness of the proposed approach under different fault resistances, distances, and types. Lastly, a real-time digital simulator (RTDS)–based hardware-in-the-loop (HIL) test is undertaken to validate the feasibility of implementing the proposed approach.


Introduction
Due to unprecedented worldwide population expansion and rapid economic growth in the past decade, an ever-increasing demand for electrical power is inevitable.Traditional fossil fuels, which supply more than one-quarter of global electricity power, are widely believed to be the main cause of severe global warming, and sustainable energy, such as wind, solar, biomass, tidal, and geothermal, has become a promising solution for continuous fossil fuel depletion [1][2][3][4].Nowadays, the cost of renewable energy power generation has decreased with the development of manufacturing and materials technology [5][6][7].In China, the installed capacity of wind power was more than 168 GW in 2016, which was an increase of 13.8% over the previous year [8].However, large-scale wind farms require strict climatic and geographic conditions, i.e., appropriate wind speed and annually stable and consistently abundant winds [9].In reality, such areas are often far away from the load centers [10].The high-voltage direct current (HVDC) transmission system is believed to be a plausible method for bulk power transmission over long distances [11], but the extremely high cost of ultra-high voltage power electronic devices is the main obstacle to wide application of HVDC.

Modelling of Parallel Multiconductor Transmission Lines
Three-phase transmission lines can be approximated by aggregating equivalent circuit segments distributed along the lines.A line segment with length dx can be represented by an equivalent resistor, inductor and capacitor (RLC) circuit, as illustrated in Figure 1, in which the parameters of three lines are assumed to be identical in this paper.The equations of lossy three-phase transmission lines with constant parameters can be written as where uμ and iμ are the voltage and current of phase μ (μ = A, B, and C), respectively; G0 and C0 are the conductance and capacitance per unit (p.u.) length between line and earth, respectively; G, C, and M are the conductance, capacitance, and mutual inductance between line and line in p.u., respectively; and R and L are the line resistance and inductance in p.u., respectively.If only one frequency component needs to be analyzed in voltage and current, the time-domain Equations ( 1) and ( 2) can be transformed to the following frequency-domain equation: The equations of lossy three-phase transmission lines with constant parameters can be written as where u µ and i µ are the voltage and current of phase µ (µ = A, B, and C), respectively; G 0 and C 0 are the conductance and capacitance per unit (p.u.) length between line and earth, respectively; G, C, and M are the conductance, capacitance, and mutual inductance between line and line in p.u., respectively; and R and L are the line resistance and inductance in p.u., respectively.If only one frequency component needs to be analyzed in voltage and current, the time-domain Equations ( 1) and ( 2) can be transformed to the following frequency-domain equation: where the angular frequency ω = 2πf ; U µ and I µ are the voltage and current of phase µ in the frequency domain, f is the fundamental frequency, and j is the imaginary unit.Equations ( 3) and ( 4) are the three-phase wave equations.
The wave equations can be obtained from Equations ( 3) and (4) as In order to reduce the complexity of the equation, phase A is taken as an example.The relationship between d 2 U A dx 2 and U A , d 2 I A dx 2 and I A can be written as Equations ( 7) and ( 8) are both ordinary differential equations, thus their solutions can be obtained as (A 7 e −γ 0 x + A 8 e γ 0 x ), (9) where The voltage and current of the sending end are denoted as The voltage and current after propagation along transmission lines with number of x can be written as where where γ 0 and γ 1 are the propagation constants and Z C0 and Z C1 are characteristic impedances, as follows: As shown in Equations ( 6)- (22), the voltage and current propagated along any transmission line will be affected by electromagnetic waves travelling along other parallel conductors due to the coupling of electromagnetic fields.If the characteristics of multiconductor transmission lines are symmetric, the electromagnetic wave propagating along those lines can be represented by the sum of three-phase voltage and current, with two different propagation constants and two different characteristic impedances.In order to simplify the analysis of travelling waves in multiconductor transmission lines, the impedance matrix and admittance matrix are transformed to diagonal matrices, of which each diagonal element denotes the impedance and admittance of an uncoupled circuit, Energies 2018, 11, 593 6 of 22 and the phase voltage and phase current are transformed to modal voltage and modal current that propagate along the special uncoupled circuit.In particular, most of the uncoupled circuits, e.g., air mode, represent the circuit between conductors, while one of them is the circuit named "earth mode" between line and earth.

Configuration of HWTL in China
The largest onshore wind farm in the world is located in Gangsu and Inner Mongolia in northern China, while the load centers are concentrated in southeast coastal areas thousands of kilometers away from.As a result, large amounts of electricity generated by the wind farm cannot be effectively transmitted to the load centers, which wastes a huge amount of wind power annually.On the other hand, the coastal load centers frequently encounter load-peak shifting in summer due to power shortages.In order to solve the dilemma of wasted wind power and power shortages in different areas, bulk power transmission technology over long distances becomes a crucial task.
The 1000 kV alternating current (AC) transmission line was implemented and has been operating as a demonstration project for ultra-high-voltage extra-long-distance transmission in China since 2009.The large-scale wind farms in northern China are nearly 3000 km away from load centers in Guangdong, as schematically shown in Figure 2, which makes half-wavelength transmission geographically possible.
of three-phase voltage and current, with two different propagation constants and two different characteristic impedances.In order to simplify the analysis of travelling waves in multiconductor transmission lines, the impedance matrix and admittance matrix are transformed to diagonal matrices, of which each diagonal element denotes the impedance and admittance of an uncoupled circuit, and the phase voltage and phase current are transformed to modal voltage and modal current that propagate along the special uncoupled circuit.In particular, most of the uncoupled circuits, e.g., air mode, represent the circuit between conductors, while one of them is the circuit named "earth mode" between line and earth.

Configuration of HWTL in China
The largest onshore wind farm in the world is located in Gangsu and Inner Mongolia in northern China, while the load centers are concentrated in southeast coastal areas thousands of kilometers away from.As a result, large amounts of electricity generated by the wind farm cannot be effectively transmitted to the load centers, which wastes a huge amount of wind power annually.On the other hand, the coastal load centers frequently encounter load-peak shifting in summer due to power shortages.In order to solve the dilemma of wasted wind power and power shortages in different areas, bulk power transmission technology over long distances becomes a crucial task.
The 1000 kV alternating current (AC) transmission line was implemented and has been operating as a demonstration project for ultra-high-voltage extra-long-distance transmission in China since 2009.The large-scale wind farms in northern China are nearly 3000 km away from load centers in Guangdong, as schematically shown in Figure 2, which makes half-wavelength transmission geographically possible.

Wavelength Calculation of Ultra-High-Voltage HWTL
Due to the long distance, the half-wavelength transmission line needs a high-voltage level to reduce energy loss.Thus most research on half-wavelength is based on ultra-high-voltage, such as 1000 kV or higher.In this paper, the 1000 kV tower implemented in Jingdongnan-Nanyang-Jingmen is studied as demonstrated in Figure 3.

Wavelength Calculation of Ultra-High-Voltage HWTL
Due to the long distance, the half-wavelength transmission line needs a high-voltage level to reduce energy loss.Thus most research on half-wavelength is based on ultra-high-voltage, such as 1000 kV or higher.In this paper, the 1000 kV tower implemented in Jingdongnan-Nanyang-Jingmen is studied as demonstrated in Figure 3.The air modal propagation constant γ1 and earth modal propagation constant γ0 become where R1, L1, and C1 are the air modal resistance, inductance, and capacitance, respectively, and R0, L0, and C0 are earth modal resistance, inductance, and capacitance, respectively.Wavelength is a variable that changes with the imaginary part of the propagation constant, therefore the air modal wavelength at fundamental frequency λ1 and the earth modal wavelength at fundamental frequency λ0 are written as It can be seen from Equations ( 25) and ( 26) that the air modal wavelength will be different from the earth modal wavelength.Although the phase voltage distribution satisfies the air modal halfwavelength distribution in normal operation due to the balanced three phases, the asymmetric parameters, unbalanced operation, or asymmetric fault may distort the voltage distribution along transmission lines.
If the multiconductor transmission lines are ideally transposed, the characteristic impedances of all air modes are identical.However, the characteristic impedance of earth mode usually varies greatly with frequency, due to its propagation channel between lines and ground, thus earth modal impedance is much different from air modal impedance.More specifically, if the transmission line is short, the voltage distribution along that line and the different modal characteristics have no The air modal propagation constant γ 1 and earth modal propagation constant γ 0 become where R 1 , L 1 , and C 1 are the air modal resistance, inductance, and capacitance, respectively, and R 0 , L 0 , and C 0 are earth modal resistance, inductance, and capacitance, respectively.Wavelength is a variable that changes with the imaginary part of the propagation constant, therefore the air modal wavelength at fundamental frequency λ 1 and the earth modal wavelength at fundamental frequency λ 0 are written as It can be seen from Equations ( 25) and ( 26) that the air modal wavelength will be different from the earth modal wavelength.Although the phase voltage distribution satisfies the air modal half-wavelength distribution in normal operation due to the balanced three phases, the asymmetric parameters, unbalanced operation, or asymmetric fault may distort the voltage distribution along transmission lines.
If the multiconductor transmission lines are ideally transposed, the characteristic impedances of all air modes are identical.However, the characteristic impedance of earth mode usually varies greatly with frequency, due to its propagation channel between lines and ground, thus earth modal impedance is much different from air modal impedance.More specifically, if the transmission line is short, the voltage distribution along that line and the different modal characteristics have no significant influence on line protection or overvoltage, but the half-wavelength line is too long to ignore the influence of different wavelength of modes.

Phase-Modal Transformation
Considering the different characteristics of air mode and earth mode, the phase current and voltage can be transformed into modal components by the Karenbauer transform matrix [31] as A two-port network is used to represent the ideally transposed line by where ϕ = 0, α, β and χ.U ϕs and I ϕs are the sending end voltage and current, respectively; U ϕx and I ϕx are voltage and current away from sending end with distance x, respectively; γ α , γ β , and γ χ are all equal to γ 1 ; and Z cα , Z cβ , and Z cχ are all equal to Z c1 .The modes α, β, and χ are all air modes with different circuits, while their characteristics are almost the same if the transmission lines are ideally transposed.On the other hand, the voltage distributed along transmission lines can also be obtained by the voltage and current of the receiving end, as follows: where U ϕlr and I ϕlr represent the voltage and current of receiving end, respectively, and l is the total length of faulty line.Here, each point in the ideally transposed line has the same voltage, calculated by Equations ( 28) and ( 29), but the fault point is a boundary of ideally transposed line, which makes the real voltage different from the calculated voltage.Since the transform matrix cannot decouple the fault point resulting from the three-phase unbalance at the fault point, the actual voltage and the calculated voltage are quite different in the region between the fault point and the remote end.

Fault Location of Phase-to-Ground Fault
The fault point separates the line into two sections, in which the actual voltage is similar to the calculated voltage at the near end but much different at the remote end.Hence, the calculated voltage from each end may obtain the same value at fault point but much different values at other points.The fault distance can be written as where x could be a complex number with a small imaginary part due to the numerical calculation error, thus the fault distance can be written as Energies 2018, 11, 593 where l is the line length.Equation (31) needs synchronized measurements from both ends.However, numerous factors, such as thunderstorms and electromagnetic interference, will degrade the synchronization accuracy.The fault location method with unsynchronized data from both ends shall be discussed.The angle of fundamental frequency voltage and current are time-varying, but their amplitude is stable when the fault transients are attenuated.Considering the voltage amplitude, Equation ( 30) can be rewritten as If the transmission lines are ideally transposed, the characteristic impedances of all air modes are almost the same.Thus, only the air modal circuit containing the faulty phase line is selected to calculate the voltage distribution.Thus, Equation (32) becomes Here, the calculated voltage distribution along transmission lines between the fault point and the remote end are quite different from the real voltage distribution.However, it may obtain intersection points with calculated voltage from another end casually.As a result, Equations (33a) and (33b) might contain multiple solutions, while additional conditions should be taken into account to accomplish an accurate fault location.Moreover, Equations (33a) and (33b) always have the similar fault location estimation near the fault point, and the characteristics of different modes lead to different periods of voltage distribution along transmission lines, so inaccurate fault location estimations can be eliminated by the significant difference between the air mode and earth estimations.Denoting the air mode fault location estimation as x 1 and the earth mode fault location estimation as x 0 , the following inequality needs to be satisfied: where η is the threshold between x 1 and x 0 , and η is set as 5% × 3000 km = 150 km in this paper.
The calculation error and non-ideal models may lead to some differences between fault location estimation of air mode and earth mode, while their mean value is used for an accurate fault location result x f1 as

Fault Location of Phase-to-Phase Fault
If the transmission line fault is a phase-to-phase fault, where the fault point is still insulated to ground, the earth modal voltage will equal zero.Hence, a fault location scheme without zero modal voltage has to be considered.
The modal voltage transformed by the phase-modal transformation matrix in Equation ( 27) can be regarded as the voltage in an independent two-conductor modal circuit formed by two phase lines.If two faulty phase lines are applied to form the air modal circuit, the voltage of the fault point will be the minimum.Therefore, the minimum of the calculated voltage along transmission lines can be calculated from double ends to locate the fault point of phase-to-phase fault.The fault location can be represented as Ideally, the minimum voltage distribution along transmission lines calculated by Equations (36a) and (36b) from double ends should be similar, and the next local minimum should be one-half air modal wavelength away, such that the fault point can be treated as the global minimum in almost all faults.In addition, the calculation error increases as the distance grows, hence most of the fault location is more reliable in dealing with near-end fault.The calculated distance of the fault point can be used as the weight ω r for receiving-end fault location estimation x r , and weight ω s for sending-end fault location estimation x s , which gives fault location result x f2 as where

Overall Fault Location Scheme
If the methods in Sections 4.2 and 4.3 are applied for a fault, the final fault location result x f can be written as To this end, the overall fault location scheme can be summarized in the following three procedures: (1) Determine the faulty phase and fault type by reference [13] with a low-frequency sampling rate.
(2) Apply transform matrix to obtain modal voltage and modal current, and choose an appropriate modal circuit containing double faulty phases for voltage distribution calculation and fault location.(3) If the fault type includes a ground fault, apply the intersection points of different modal voltage distributions to locate the fault distance.Otherwise, the fault distance will be located by both intersection points and minimum.
The overall flowchart of MVD-ADFL is demonstrated in Figure 4.

Simulation Model
A schematic diagram of the simulation model is depicted in Figure 5, while the tower shown in Figure 3 is used to calculate the transmission line parameters.Two hundred doubly fed induction generators [32] with 3 MW rated power and 25 m/s rated wind speed were considered for the wind farm, and were aggregated into an equivalent 600 MW generator in the model.The tower shown in Figure 3 was used to calculate the transmission line parameters.Bus M and bus N represent the sending and receiving end of transmission lines, respectively.

Simulation Model
A schematic diagram of the simulation model is depicted in Figure 5, while the tower shown in Figure 3 is used to calculate the transmission line parameters.Two hundred doubly fed induction generators [32] with 3 MW rated power and 25 m/s rated wind speed were considered for the wind farm, and were aggregated into an equivalent 600 MW generator in the model.The tower shown in Figure 3 was used to calculate the transmission line parameters.Bus M and bus N represent the sending and receiving end of transmission lines, respectively.

Simulation Model
A schematic diagram of the simulation model is depicted in Figure 5, while the tower shown in Figure 3 is used to calculate the transmission line parameters.Two hundred doubly fed induction generators [32] with 3 MW rated power and 25 m/s rated wind speed were considered for the wind farm, and were aggregated into an equivalent 600 MW generator in the model.The tower shown in Figure 3 was used to calculate the transmission line parameters.Bus M and bus N represent the sending and receiving end of transmission lines, respectively.International with a library of preprogrammed models and a design editor for building custom models to satisfy various levels of different modelling demands, was adopted to construct a simulation model of HWTL with large-scale wind power integration; version 4.5 was used in this study [33][34][35][36][37].The simulation tests were implemented based on the PSCAD/EMTDC model, a general-purpose time-domain simulation tool for studying transient behavior of electrical networks.A single line diagram of the simulation model is provided in Figure 6, and its parameters are given in Tables 1-3.Power Systems Computer Aided Design/Electromagnetic Transients including DC (PSCAD/EMTDC), an electromagnetic time-domain transient simulation environment created by Manitoba Hydro International with a library of preprogrammed models and a design editor for building custom models to satisfy various levels of different modelling demands, was adopted to construct a simulation model of HWTL with large-scale wind power integration; version 4.5 was used in this study [33][34][35][36][37].The simulation tests were implemented based on the PSCAD/EMTDC model, a general-purpose time-domain simulation tool for studying transient behavior of electrical networks.A single line diagram of the simulation model is provided in Figure 6, and its parameters are given in Tables 1-3.The frequency-dependent model was employed to represent transmission lines in the simulation.Table 4 shows the frequency-dependent parameters of transmission line when the fundamental frequency is 50 Hz, based on the tower shown in Figure 3 [38].The frequency-dependent model was employed to represent transmission lines in the simulation.Table 4 shows the frequency-dependent parameters of transmission line when the fundamental frequency is 50 Hz, based on the tower shown in Figure 3 [38].
It can be seen in Table 4 that the air mode wavelength is much larger than earth mode due to the differences between air modal circuit and earth modal circuit, hence the open-phase operation and unbalanced ground fault can induce quite different voltage distributions in air modal circuit and earth modal circuit.
Normally, wind farms are required to achieve maximum power point tracking to track the optimal active power curve, which is obtained by connecting each maximum power point at various wind speeds with the optimal active power curve determined by where K * = 0.5ρπR 5 C * P /(λ * ) 3 denotes the shape coefficient of optimal active power, R is the blade radius of the wind turbine, ρ is the air density, the optimal tip-speed ratio λ * = 7.4, and the maximum power coefficient C * P = 0.4019 [33].Hence, the power generated from the wind farm usually has a highly stochastic pattern, which will be injected into the main power grid [31].Figure 7a,b demonstrate the wind speed and produced active power of the wind farm, respectively.It can be seen in Table 4 that the air mode wavelength is much larger than earth mode due to the differences between air modal circuit and earth modal circuit, hence the open-phase operation and unbalanced ground fault can induce quite different voltage distributions in air modal circuit and earth modal circuit.
Normally, wind farms are required to achieve maximum power point tracking to track the optimal active power curve, which is obtained by connecting each maximum power point at various wind speeds with the optimal active power curve determined by Hence, the power generated from the wind farm usually has a highly stochastic pattern, which will be injected into the main power grid [31].Figure 7a,b demonstrate the wind speed and produced active power of the wind farm, respectively.The hardware-in-the-loop (HIL) test is a powerful and important technique that has been used worldwide in real-time experiments instead of practical experiments due to the complexity and large scale of real power systems.The Real-Time Digital Simulator (RTDS), which is capable of closed-loop testing of protection and control equipment, was adopted in this study to further validate the feasibility of hardware implementation.The configuration and experimental platform of HIL test are provided in Figures 8 and 9  The hardware-in-the-loop (HIL) test is a powerful and important technique that has been used worldwide in real-time experiments instead of practical experiments due to the complexity and large scale of real power systems.The Real-Time Digital Simulator (RTDS), which is capable of closed-loop testing of protection and control equipment, was adopted in this study to further validate the feasibility of hardware implementation.The configuration and experimental platform of HIL test are provided in Figures 8 and 9.A power system with a sampling rate of 20 kHz was implemented by #16 RTDS with four PB5 processor cards and one gigabit transceiver analog output card, which can output the voltage and current at bus M and bus N.Meanwhile, #17 RTDS with three PB5 processor cards and one gigabit transceiver analog input card was applied as an acquisition device with 10 kHz to acquire voltage and current output from #16 RTDS.The voltage and current acquired by #17 RTDS was transferred to digital data and stored in RTDS as Common format for Transient Data Exchange (COMTRADE) 1999 files, which were then transmitted to a PC with an IntelR Core™ i3 CPU at 2.52 GHz and 3 GB of RAM.Finally, the voltage and current waveforms were decoded from COMTRADE 1999 files in the PC to locate fault points by the proposed MVD-ADFL.
Denoting the fault distance as xfault, the relative fault location calculation error ε is defined as where l is the total length of fault line and xf is the fault location result.

Single Phase-to-Ground Fault
A phase-to-ground (AG) fault with 200 Ω fault resistance, 2400 km away from bus M, which occurred at 10 s with a total wind power of 180 MW, was investigated by simulation and HIL test.The calculated voltage distribution along transmission lines from bus M and bus N are shown in Figure 10.A power system with a sampling rate of 20 kHz was implemented by #16 RTDS with four PB5 processor cards and one gigabit transceiver analog output card, which can output the voltage and current at bus M and bus N.Meanwhile, #17 RTDS with three PB5 processor cards and one gigabit transceiver analog input card was applied as an acquisition device with 10 kHz to acquire voltage and current output from #16 RTDS.The voltage and current acquired by #17 RTDS was transferred to digital data and stored in RTDS as Common format for Transient Data Exchange (COMTRADE) 1999 files, which were then transmitted to a PC with an IntelR Core™ i3 CPU at 2.52 GHz and 3 GB of RAM.Finally, the voltage and current waveforms were decoded from COMTRADE 1999 files in the PC to locate fault points by the proposed MVD-ADFL.
Denoting the fault distance as xfault, the relative fault location calculation error ε is defined as where l is the total length of fault line and xf is the fault location result.

Single Phase-to-Ground Fault
A phase-to-ground (AG) fault with 200 Ω fault resistance, 2400 km away from bus M, which occurred at 10 s with a total wind power of 180 MW, was investigated by simulation and HIL test.The calculated voltage distribution along transmission lines from bus M and bus N are shown in Figure 10.A power system with a sampling rate of 20 kHz was implemented by #16 RTDS with four PB5 processor cards and one gigabit transceiver analog output card, which can output the voltage and current at bus M and bus N.Meanwhile, #17 RTDS with three PB5 processor cards and one gigabit transceiver analog input card was applied as an acquisition device with 10 kHz to acquire voltage and current output from #16 RTDS.The voltage and current acquired by #17 RTDS was transferred to digital data and stored in RTDS as Common format for Transient Data Exchange (COMTRADE) 1999 files, which were then transmitted to a PC with an IntelR Core™ i3 CPU at 2.52 GHz and 3 GB of RAM.Finally, the voltage and current waveforms were decoded from COMTRADE 1999 files in the PC to locate fault points by the proposed MVD-ADFL.
Denoting the fault distance as x fault , the relative fault location calculation error ε is defined as where l is the total length of fault line and x f is the fault location result.

Single Phase-to-Ground Fault
A phase-to-ground (AG) fault with 200 Ω fault resistance, 2400 km away from bus M, which occurred at 10 s with a total wind power of 180 MW, was investigated by simulation and HIL test.The calculated voltage distribution along transmission lines from bus M and bus N are shown in Figure 10.The fault location results of simulation and HIL tests are tabulated in Table 5.It can be clearly seen that the voltage distribution along transmission lines of HIL is almost the same as the that of the simulation, therefore the fault location results of the simulation and the HIL test are similar.The errors of fault location results based on the simulation and the HIL test are 2.46% and 0.33%, respectively.The fault location results of simulation and HIL tests are tabulated in Table 5.It can be clearly seen that the voltage distribution along transmission lines of HIL is almost the same as the that of the simulation, therefore the fault location results of the simulation and the HIL test are similar.The errors of fault location results based on the simulation and the HIL test are 2.46% and 0.33%, respectively.Here, both the intersection points and minimum method can be applied for fault location estimation of ABG fault.In the PSCAD simulation, the intersection point in air mode, 1495 km, and minimums, 1556 km and 1573 km, are all close to 1502 km, one of the intersection points in earth mode voltage distribution, therefore the fault location result is The fault location results of the simulation and the HIL tests are illustrated in Table 7.Here, both the intersection points and minimum method can be applied for fault location estimation.Lastly, the fault location results of the simulation and the HIL test are almost the same, and fault location errors are both 1.76%.The fault location results of the simulation and the HIL tests are illustrated in Table 7.Here, both the intersection points and minimum method can be applied for fault location estimation.Lastly, the fault location results of the simulation and the HIL test are almost the same, and fault location errors are both 1.76%.Future study will investigate the asymmetrical characteristics of non-ideally transposed line to improve the fault location performance of MVD-ADFL in a more practical scenario.

Figure 2 .
Figure 2. Geographical location of large-scale wind farm and load centers of China.

Figure 2 .
Figure 2. Geographical location of large-scale wind farm and load centers of China.

Figure 4 .
Figure 4. Overall flowchart of the modal voltage distribution based asynchronous double-end fault location (MVD-ADFL) method.

Figure 5 .
Figure 5. Schematic diagram of the simulation model.

Figure 4 .
Figure 4. Overall flowchart of the modal voltage distribution based asynchronous double-end fault location (MVD-ADFL) method.

Figure 5 .
Figure 5. Schematic diagram of the simulation model.

Figure 5 .
Figure 5. Schematic diagram of the simulation model.
Aided Design/Electromagnetic Transients including DC (PSCAD/EMTDC), an electromagnetic time-domain transient simulation environment created by Manitoba Hydro

Figure 6 .
Figure 6.Single line diagram of the simulation model in PSCAD.

Table 1 .
Parameters of the transformer at bus M.

Figure 6 .
Figure 6.Single line diagram of the simulation model in PSCAD.
coefficient of optimal active power, R is the blade radius of the wind turbine, ρ is the air density, the optimal tip-speed ratio

Figure 7 .
Figure 7. Wind speed and produced active power of the wind farm. .

Figure 7 .
Figure 7. Wind speed and produced active power of the wind farm.

Figure 8 .
Figure 8. Configuration of the hardware-in-the-loop (HIL) test.

Figure 9 .
Figure 9. Experimental platform of the HIL test.

Figure 9 .
Figure 9. Experimental platform of the HIL test.

Figure 9 .
Figure 9. Experimental platform of the HIL test.

Figure 10 .
Figure 10.A phase-to-ground (AG) fault with 200 Ω fault resistance, 2400 km away from bus M, with 1800 MW wind power.

Figure 10 .
Figure 10.A phase-to-ground (AG) fault with 200 Ω fault resistance, 2400 km away from bus M, with 1800 MW wind power.
(a) Air mode of simulation (b) Earth mode of simulation (c) Air mode of HIL test (d) Earth mode of HIL test

Figure 12 .
Figure 12.A double phase-to-ground (ABG) fault with 50 Ω fault resistance, 1500 km away from bus M, with 400 MW wind power.

Figure 12 .
Figure 12.A double phase-to-ground (ABG) fault with 50 Ω fault resistance, 1500 km away from bus M, with 400 MW wind power.

( 1 )
The proposed MVD-ADFL is based on transmission line parameters and voltage and current at fundamental frequency.Therefore, traditional low-frequency voltage and current measurement devices are applicable to MVD-ADFL, which offers wide implementation in practice.(2)The application of voltage amplitude avoids the accurate synchronization of double-end voltage and current.If synchronous voltage and current are available, they can be used to further reduce calculation errors in fault location.(3) Simulation results of different case studies have verified that MVD-ADFL is quite effective for different fault types, while it is insensitive to fault distance, fault resistance, and stochastic wind power variation.(4) The RTDS-based HIL test validates the feasibility of implementing MVD-ADFL in different cases.
1to A 4 and B 1 to B 4 are calculated from phase A, while A 5 to A 8 and B 5 to B 8 are from phases B and C. A

Table 2 .
Parameters of the transformer at bus N.

Table 3 .
Parameters of the wind turbine.

Table 1 .
Parameters of the transformer at bus M.

Table 3 .
Parameters of the wind turbine.

Table 4 .
Parameters of different modes.

Table 4 .
Parameters of different modes.

Table 5 .
Fault location estimation of AG fault.

Table 5 .
Fault location estimation of AG fault.
In the HIL test, the intersection point in air mode is 1553 km and the minimums are 1499 km and 1560 km.The fault location result is

Table 7 .
Location results of ABG fault.

Table 7 .
Location results of ABG fault.