Study on Transient Overvoltage of O ﬀ shore Wind Farm Considering Di ﬀ erent Electrical Characteristics of Vacuum Circuit Breaker

: For the study of transient overvoltage (TOV) in an o ﬀ shore wind farm (OWF) collector system caused by switching o ﬀ vacuum circuit breakers (VCBs), a simpliﬁed experimental platform of OWF medium-voltage (MV) cable collector system was established in this paper to conduct switching operation tests of VCB and obtain the characteristic parameters for VCB, especially dielectric strength parameters; also, the e ﬀ ectiveness of the VCB reignition model was veriﬁed. Then, PSCAD / EMTDC was used to construct the MV collector system of the OWF, and the e ﬀ ects of normal switching and fault switching on TOV amplitude, steepness, and the total number of reignition of the VCB were studied, respectively, with the experimental parameters and traditional parameters of dielectric strength of the VCB. The simulation results show that when the VCB is at the tower bottom, the overvoltage amplitude generated by the normal switching is the largest, which is 1.83 p.u., and the overvoltage steepness of the fault switching is the largest, up to 142 kV / µ s. The overvoltage amplitude and steepness caused by switching o ﬀ VCB at the tower bottom faultily with traditional parameters are about 2 and 1.5 times of the experimental parameters under the same operating condition.


Introduction
Large wind farms are moving from land to sea to provide a richer and more stable source of clean energy [1,2]. Being increasingly valued by countries around the world, the operation and maintenance of offshore wind farms (OWFs) have been paid more and more attention [3,4]. Large-scale OWFs use cables as the collector system. Thus, the loads of the cables cannot exceed the limit of the cable ampacity [5,6], and the cables should be insulated reliably [7,8]. Moreover, the safety of the tower terminal transformers needs to be carefully considered. In 2004, at Horns Rev, the largest OWF in Denmark at that time, almost all the tower terminal transformers suffered insulation fault accidents [9]. In [10], the authors reported an accident of transformer insulation damage occurred by switching off a vacuum circuit breaker (VCB) after connecting with the shunt reactor in Wailuo OWF. Studies have shown that the high-frequency (HF) overvoltage generated by the frequent switching on and off for VCBs was the main factor causing insulation fault of the transformers [11][12][13]. Lars Lijestrand et al. simulated and calculated the HF transient process of operating overvoltage generated by switching on a no-load transformer and switching off a no-load transformer under a et al. simulated and calculated the HF transient process of operating overvoltage generated by switching on a no-load transformer and switching off a no-load transformer under a single-phase grounding short-circuit fault in a medium-voltage (MV) collection grid of OWF [14]. Xuezhong Liu et al. established a test circuit for the MV cable simulation system of the wind farm and a simulation calculation platform of power-frequency overvoltage [15]. Combined with the simulation and field measurement data, the influence of VCB parameters and cable length on the transient overvoltage (TOV) generated by switching off the no-load transformer in the MV collector system of OWF was studied in [16]. PSCAD/EMTDC (Manitoba HVDC Research Centre, a division of MHI Ltd., Winnipeg, Canada) and DIgSILENT/PowerFactory (DIgSILENT GmbH, Gomaringen, Germany) were used to carry out simulation calculation of switching overvoltage when the operating feeder of the OWF was a long no-load cable, and it was compared with the measured data of the actual OWF in [17]. Although there have been a lot of studies on TOV of OWFs, they mainly focus on the qualitative analysis of amplitude and steepness of the switching on TOV in the power collector system. However, there is limited literature on the study of switching-off overvoltage in a power collector system and the quantitative analysis of the overvoltage steepness. Furthermore, with the improvement of manufacturing for VCBs, the traditional electrical parameters have not adapted to today's research.
This paper mainly introduces a reignition modelling method and model verification of VCB in the OWF collector system, and also studies the characteristics of switching TOV in an OWF collector system, respectively, with the experimental parameters and traditional parameters of the dielectric strength of VCB.
The structure of this article is as follows. In section 2, the models of double-fed induction generator (DFIG) and the VCB are established. In section 3, the switching reignition experiment of VCB is conducted on the established experimental platform. The characteristic parameters of VCB are obtained, and the validity of the model is verified. Section 4 introduces the switching mode of the internal electrical system in OWF. In section 5, a single-feeder MV cable collector system of OWF is constructed. The traditional parameters and experimental parameters are, respectively, used for the dielectric strength of the VCB model. The effects of normal switching and fault switching on TOV amplitude, steepness, and the total number of reignition at the high voltage side of the terminal transformer are compared. Finally, conclusions are drawn in section 6.

DFIG Model
DFIGs are widely used in OWFs. The simplified DFIG model is composed of a wound induction motor, wind turbine components, double-pulse width modulation (PWM) converter, control system components, and filters both on the stator side and rotor side of the motor [18,19], as shown in Figure  1. The stray capacitances generally include the capacitances between stator winding and shell, stator winding and rotor, and rotor and shell. However, as the capacitance of the HF filter in the wind turbine is much larger than the capacitances mentioned above, stray capacitance has little influence on overvoltage. The study is conducted on the high-voltage side of the terminal transformer, so the stray capacitance of the induction motor can be ignored [20]. In this paper, the rated capacity of the DFIG is 4 MW.

Rotor side converter
Stator side converter

VCB Model
For inductive circuits, after the current is cut off near the zero-crossing point, an overvoltage will be caused by current chopping, which may result in the first reignition. During reignition, HF current is generated due to the influence of circuit parameters. When the HF current is cut off, the equivalent capacitance and inductance on the load side will cause electromagnetic oscillation. This oscillation will result in higher voltage that may cause the contact gap to be broken down again. Also, the HF current may couple to the other phases, producing current zeros. Thus virtual chopping occurs, causing overvoltage in other phases [10,21]. In the process of multiple reignitions, the interval between the two reignitions is extremely short. Since the second reignition is based on the previous reignition, the reignition overvoltage has the characteristics of high steepness and high amplitude, The actual parameters of VCB are statistical and random. However, in order to study the switching overvoltage of the VCB, the parameters are set as constant values in this paper [22].

Chopping Current
When a VCB receives an opening instruction, the power frequency current is suddenly cut off before it reaches zero for the first time. The value of current at this time is called chopping current. When the load current varies in the range of 10 A-100 kA, the calculation for chopping current I ch of VCB is as the following empirical formula: where f is power frequency (s −1 ); I is current amplitude before cut-off in the first half cycle (A); and α and β are related to electrode size, material, gap distance, and circuit parameters, where α = 6.2 × 10 −16 s, β = 14.3. Normally, the chopping current of VCB is set as 3-8 A [22].

Dielectric Strength
When the VCB is switching to open, the dielectric strength between the contacts increases with the increase of the distance between the contacts. When the transient recovery voltage between the contacts exceeds the dielectric strength, the gap between the contacts will break down and reignite. There is an approximately linear relationship between the dielectric strength U b and the break time during reigniting, as described in the following [23]: where A is the rate of dielectric strength rise (kV/s); B is dielectric strength constant of VCB at the moment of contact separation (kV); t is simulation time (s); and t open is breaker opening time (s).

HF Arc Quenching Capability
When the HF current generated by the VCB reignition is close to zero, the VCB can extinguish it. Such an arc quenching capability can be described as the rate di/dt of the time change when the HF current is crossing zero. The HF current starts with a high rate of change that the VCB cannot turn off. However, with the attenuation of HF current, when the di/dt is less than a critical value when the current is crossing zero, the VCB will cut off HF current and turn it into a disconnected state, which is generally between 100-600 A/µs [24].

Arcing Voltage
In practice, the arc between contacts of the VCB will generate a voltage drop, and the arcing voltage is approximately 20 V [25]. A constant arcing voltage of 20 V is achieved by changing the value of controllable resistance in the customized model, as shown below [26]: where R arc is arcing resistance (Ω); u arc is arcing voltage (V); and i arc is arcing current (A). The VCB in the simulation is equivalent to the controlled resistance R with the parallel branch, as shown in Figure 2, where R s = 50 Ω, L s = 50 mH, C s = 200 pF [27]. The switching process of VCB is divided into four states in [21]. States 1-4 respectively represent the state before power frequency cut-off, transient voltage recovery, reignition, and complete switch-off. By measuring the VCB current i and the voltage u between two contacts, the C language is used to programming and solve the VCB chopping current I ch , dielectric strength U b , HF arc quenching ability, and arcing voltage u arc . The program flow chart is shown in Figure 3. At the time t ch when the chopping current occurring is more than 5 ms after the time t open when the VCB starts operating, it can be considered that the VCB has been completely opened and there will be no reignition. The controllable resistance is realized as a real-time control by calling the program in PSCAD. Initially, the closed VCB is in State 1 and R = 0. Arcing occurs when the VCB starts to separate, and the program adjusts the controllable resistor R according to Equation (5) to maintain the voltage across the contacts as arcing voltage. When i is less than I ch , the VCB enters State 2 after the first interruption, and R = 1 MΩ. When VCB is in State 2, if the transient voltage exceeds the dielectric strength, the VCB reignites and enters State 3, and the voltage across the contacts is the arcing voltage. When the VCB is in State 3, if the HF current quenching condition is satisfied, the current is cut off and the VCB returns to State 2, R = 1 MΩ. After multiple reignitions occur, when the transient recovery voltage cannot reach the dielectric strength, the VCB is successfully opened and remains in R = 1 MΩ.
The VCB in the simulation is equivalent to the controlled resistance R with the parallel branch, as shown in Figure 2, where Rs =50 Ω, Ls =50 mH, Cs=200 pF [27]. The switching process of VCB is divided into four states in [21]. States 1-4 respectively represent the state before power frequency cutoff, transient voltage recovery, reignition, and complete switch-off. By measuring the VCB current i and the voltage u between two contacts, the C language is used to programming and solve the VCB chopping current Ich, dielectric strength Ub, HF arc quenching ability, and arcing voltage uarc. The program flow chart is shown in Figure 3. At the time tch when the chopping current occurring is more than 5 ms after the time topen when the VCB starts operating, it can be considered that the VCB has been completely opened and there will be no reignition. The controllable resistance is realized as a real-time control by calling the program in PSCAD. Initially, the closed VCB is in State 1 and R=0. Arcing occurs when the VCB starts to separate, and the program adjusts the controllable resistor R according to Equation (5) to maintain the voltage across the contacts as arcing voltage. When i is less than Ich, the VCB enters State 2 after the first interruption, and R=1 MΩ. When VCB is in State 2, if the transient voltage exceeds the dielectric strength, the VCB reignites and enters State 3, and the voltage across the contacts is the arcing voltage. When the VCB is in State 3, if the HF current quenching condition is satisfied, the current is cut off and the VCB returns to State 2, R=1 MΩ. After multiple reignitions occur, when the transient recovery voltage cannot reach the dielectric strength, the VCB is successfully opened and remains in R=1 MΩ.

Transformer model
In this paper, the unified magnetic equivalent circuit (UMEC) model is adopted for transformers, which can represent the phase coupling of the transformer in PSCAD. At the same time, capacitors are connected in parallel between the high-voltage side, low-voltage side, and high and low voltage of the transformer to simulate the HF characteristics of the transformer [28].

Submarine cable model
The frequency dependent (phase) model in PSCAD is used to model submarine cables. The three-core cable structure is used in the simulation, and the specific setting parameters are shown in [28].

Description of Experimental Test System
The wiring diagram of the test system is shown in Figure 4. A transformer TX1 with a transformation ratio of 10 kV/35 kV and a capacity of 10 MVA is used to simulate the main transformer of the offshore booster station and provides a 35 kV power supply. One kilometer-long and 80 m-long submarine cables, named Cable1 and Cable2 with a cross-section of 35 mm 2 , are respectively connected to both sides of a 40.5 kV VCB to simulate the three-core MV cable between

Transformer Model
In this paper, the unified magnetic equivalent circuit (UMEC) model is adopted for transformers, which can represent the phase coupling of the transformer in PSCAD. At the same time, capacitors are connected in parallel between the high-voltage side, low-voltage side, and high and low voltage of the transformer to simulate the HF characteristics of the transformer [28].

Submarine Cable Model
The frequency dependent (phase) model in PSCAD is used to model submarine cables. The three-core cable structure is used in the simulation, and the specific setting parameters are shown in [28].

Description of Experimental Test System
The wiring diagram of the test system is shown in Figure 4. A transformer TX 1 with a transformation ratio of 10 kV/35 kV and a capacity of 10 MVA is used to simulate the main transformer of the offshore booster station and provides a 35 kV power supply. One kilometer-long and 80 m-long submarine cables, named Cable 1 and Cable 2 with a cross-section of 35 mm 2 , are respectively connected to both sides of a 40.5 kV VCB to simulate the three-core MV cable between the 35 kV busbar to the wind turbine at the beginning of the feeder and the transformer at the top of the tower to the VCB at the tower bottom. The technical characteristics of the VCB are shown in Table 1. A transformer TX 2 with a transformation ratio of 35 kV/ 0.69 kV and a capacity of 2 MVA simulates the terminal transformer of the wind turbine. A reactor with a capacity of 1.6 Mvar is set as the load, and its capacity is approximately 80% of TX 2 to ensure that the amplitude value of power frequency current flowing through the VCB is greater than the chopping current.  Table  1. A transformer TX2 with a transformation ratio of 35 kV/ 0.69 kV and a capacity of 2 MVA simulates the terminal transformer of the wind turbine. A reactor with a capacity of 1.6 Mvar is set as the load, and its capacity is approximately 80% of TX2 to ensure that the amplitude value of power frequency current flowing through the VCB is greater than the chopping current. In order to measure and record HF signals, a 150 kV high-voltage probe VD with a ratio of 10000:1, of which the model is NRV-150, is used in the experiment. It has an accuracy of 1% when the frequency of voltage ranges from 10 Hz to 1 MHz. The model of HF current transformer TA is Pearson D101, with a frequency bandwidth of 0.25 Hz-4 MHz and 50 kA peak current. During the experiment, the sampling rate of the digital oscilloscope is set as 40 Msa/s.

Model Verification
When chopping current occurs in the VCB, the magnetic energy stored in the inductive load (such as reactor, no-load transformer, or motor, etc.) is converted into the electric field energy of the load side capacitance (usually the capacitance of the submarine cable), and thus overvoltage is generated. Therefore, the chopping current value can be calculated by the amplitude Umax of the first overvoltage generated by the chopping current: where U0 is cut-off transient voltage (V); Un is power supply voltage (V); Lt is system equivalent inductance (H); and Ct is load side capacitance (F).
The reignition of the VCB is obvious when the inductive load is switched to separate. Therefore, the switching test is conducted under the condition of the inductive load to measure the three-phase voltage at the high-voltage side of TX2 and the B-phase current at the outlet side of the VCB. The waveform obtained from the experiment is shown in Figure 5a.  In order to measure and record HF signals, a 150 kV high-voltage probe VD with a ratio of 10000:1, of which the model is NRV-150, is used in the experiment. It has an accuracy of 1% when the frequency of voltage ranges from 10 Hz to 1 MHz. The model of HF current transformer TA is Pearson D101, with a frequency bandwidth of 0.25 Hz-4 MHz and 50 kA peak current. During the experiment, the sampling rate of the digital oscilloscope is set as 40 Msa/s.

Model Verification
When chopping current occurs in the VCB, the magnetic energy stored in the inductive load (such as reactor, no-load transformer, or motor, etc.) is converted into the electric field energy of the load side capacitance (usually the capacitance of the submarine cable), and thus overvoltage is generated. Therefore, the chopping current value can be calculated by the amplitude U max of the first overvoltage generated by the chopping current: where U 0 is cut-off transient voltage (V); U n is power supply voltage (V); L t is system equivalent inductance (H); and C t is load side capacitance (F). The reignition of the VCB is obvious when the inductive load is switched to separate. Therefore, the switching test is conducted under the condition of the inductive load to measure the three-phase voltage at the high-voltage side of TX 2 and the B-phase current at the outlet side of the VCB. The waveform obtained from the experiment is shown in Figure 5a. According to Equation (4) and Figure 5a, the chopping current of VCB calculated in this experiment is 3.6 A. In Figure 5a, the value of the breakdown voltage is considered to be the value of the dielectric strength at this time. After the contacts of VCB begin to separate, each time a reignition occurs, the value of the breakdown voltage and the corresponding time are recorded and linearly fitted according to Equation (2), as shown in Figure 6. The relationship between dielectric strength and time is obtained as follows: Since the HF arc quenching ability has little influence on the overvoltage, the critical value of di/dt is set as the average value of 350 A/μs in this paper [29], and the arcing voltage is set as 20 V. The PSCAD 4.6.2 is used to simulate and model the experimental system shown in Figure 4. The reignition model introduced in section 2.2 of this paper is adopted in the VCB model. By cooperating with the time logic device, the switching operation is realized at any time in the model, and the waveform is obtained by simulation, shown in Figure 5b. In the case of switching off inductive load, because of the chopping current, the rising rate of transient recovery voltage between two contacts of VCB is much faster than that of dielectric strength, which causes a lot of restrikes of VCB, as shown in Figure 5a, where B-phase is the first-opening phase. In Figure 5a, b, the amplitude and the total number of reignition of B-phase overvoltage are basically the same, and the amplitude of HF current is basically the same. However, due to the According to Equation (4) and Figure 5a, the chopping current of VCB calculated in this experiment is 3.6 A. In Figure 5a, the value of the breakdown voltage is considered to be the value of the dielectric strength at this time. After the contacts of VCB begin to separate, each time a reignition occurs, the value of the breakdown voltage and the corresponding time are recorded and linearly fitted according to Equation (2), as shown in Figure 6. The relationship between dielectric strength and time is obtained as follows: According to Equation (4) and Figure 5a, the chopping current of VCB calculated in this experiment is 3.6 A. In Figure 5a, the value of the breakdown voltage is considered to be the value of the dielectric strength at this time. After the contacts of VCB begin to separate, each time a reignition occurs, the value of the breakdown voltage and the corresponding time are recorded and linearly fitted according to Equation (2), as shown in Figure 6. The relationship between dielectric strength and time is obtained as follows: Since the HF arc quenching ability has little influence on the overvoltage, the critical value of di/dt is set as the average value of 350 A/μs in this paper [29], and the arcing voltage is set as 20 V. The PSCAD 4.6.2 is used to simulate and model the experimental system shown in Figure 4. The reignition model introduced in section 2.2 of this paper is adopted in the VCB model. By cooperating with the time logic device, the switching operation is realized at any time in the model, and the waveform is obtained by simulation, shown in Figure 5b. In the case of switching off inductive load, because of the chopping current, the rising rate of transient recovery voltage between two contacts of VCB is much faster than that of dielectric strength, which causes a lot of restrikes of VCB, as shown in Figure 5a, where B-phase is the first-opening phase. In Figure 5a, b, the amplitude and the total number of reignition of B-phase overvoltage are basically the same, and the amplitude of HF current is basically the same. However, due to the Since the HF arc quenching ability has little influence on the overvoltage, the critical value of di/dt is set as the average value of 350 A/µs in this paper [29], and the arcing voltage is set as 20 V. The PSCAD 4.6.2 is used to simulate and model the experimental system shown in Figure 4. The reignition model introduced in Section 2.2 of this paper is adopted in the VCB model. By cooperating with the time logic device, the switching operation is realized at any time in the model, and the waveform is obtained by simulation, shown in Figure 5b.
In the case of switching off inductive load, because of the chopping current, the rising rate of transient recovery voltage between two contacts of VCB is much faster than that of dielectric strength, which causes a lot of restrikes of VCB, as shown in Figure 5a, where B-phase is the first-opening phase. In Figure 5a,b, the amplitude and the total number of reignition of B-phase overvoltage are basically the same, and the amplitude of HF current is basically the same. However, due to the interference of external factors on the measuring equipment in the actual experiment, the measured HF current has many burrs, but its amplitude is relatively small compared with HF current generated by reignition. There is no burr in the simulation due to no external interference. As a result, the effectiveness of the VCB reignition model is well verified by the waveform of the switching TOV obtained in the experiment.

VCB Switching Modes of OWF Internal Electrical System
The switching modes of VCB inside the electrical system of OWF include normal switching and fault switching.
Normal switching: In this case, the no-load terminal transformer at the top of the tower is cut off; that is, after a certain wind turbine is out of operation, a corresponding VCB at tower bottom is switched off. Meanwhile, the rest wind turbines on the feeder remain in full load operation.
Fault switching: In this situation, the switching happens when wind turbines are in normal operation. Specifically, it includes two kinds of circumstances. One is that when the wind turbines are in full load operation on the whole feeder, the VCB at the beginning of the feeder is switched off. The second is that when the wind turbines are in full load operation on the whole feeder, a VCB at tower bottom is switched off.

Simulation System Setting
Wailuo OWF is located in Guangdong Province, China. Its installed capacity is 300 MW. In this section, Wailuo OWF is taken as an example to carry out simulation research. A calculation model of the internal electrical system of the OWF will be established based on the VCB and DFIG model mentioned above, as shown in Figure 7. The capacity of transformer T 0 is 180 MVA, with its ratio and leakage inductance of 220 kV/35 kV and 0.06, respectively. For transformer T n (n = 1, 2, . . . , 8), the capacity is 5 MVA, the ratio is 35 kV/0.69 kV, and the leakage inductance is 0.02 per unit. The external grid, which is connected to T 0 with a 20-km-long submarine cable, is represented by a 220 kV ideal voltage source. The length of L 1 is 80 m, and the wind turbine (WT) connects to the transformer directly. The length of L 2 between each wind turbine is 640 m, and L 0 is 5 km long. The cross-section area of submarine cables is 300 mm 2 . The three dielectric strength parameters of high-, medium-, and low-voltage have been proposed in [23] and have been used in many similar simulation studies. In this paper, the dielectric strength of "high voltage VCB", which is commonly used, is compared with the parameters obtained by experiments. In the simulation, the influence of two-parameter settings on overvoltage amplitude and steepness with normal switching and fault switching is compared. The parameters used are shown in Table 2. interference of external factors on the measuring equipment in the actual experiment, the measured HF current has many burrs, but its amplitude is relatively small compared with HF current generated by reignition. There is no burr in the simulation due to no external interference. As a result, the effectiveness of the VCB reignition model is well verified by the waveform of the switching TOV obtained in the experiment.

VCB Switching Modes of OWF Internal Electrical System
The switching modes of VCB inside the electrical system of OWF include normal switching and fault switching.
Normal switching: In this case, the no-load terminal transformer at the top of the tower is cut off; that is, after a certain wind turbine is out of operation, a corresponding VCB at tower bottom is switched off. Meanwhile, the rest wind turbines on the feeder remain in full load operation.
Fault switching: In this situation, the switching happens when wind turbines are in normal operation. Specifically, it includes two kinds of circumstances. One is that when the wind turbines are in full load operation on the whole feeder, the VCB at the beginning of the feeder is switched off. The second is that when the wind turbines are in full load operation on the whole feeder, a VCB at tower bottom is switched off.

Simulation System Setting
Wailuo OWF is located in Guangdong Province, China. Its installed capacity is 300 MW. In this section, Wailuo OWF is taken as an example to carry out simulation research. A calculation model of the internal electrical system of the OWF will be established based on the VCB and DFIG model mentioned above, as shown in Figure 7. The capacity of transformer T0 is 180 MVA, with its ratio and leakage inductance of 220 kV/35 kV and 0.06, respectively. For transformer Tn (n=1,2,…,8), the capacity is 5 MVA, the ratio is 35 kV/0.69 kV, and the leakage inductance is 0.02 per unit. The external grid, which is connected to T0 with a 20-km-long submarine cable, is represented by a 220 kV ideal voltage source. The length of L1 is 80 m, and the wind turbine (WT) connects to the transformer directly. The length of L2 between each wind turbine is 640 m, and L0 is 5 km long. The cross-section area of submarine cables is 300 mm 2 . The three dielectric strength parameters of high-, medium-, and low-voltage have been proposed in [23] and have been used in many similar simulation studies. In this paper, the dielectric strength of "high voltage VCB", which is commonly used, is compared with the parameters obtained by experiments. In the simulation, the influence of two-parameter settings on overvoltage amplitude and steepness with normal switching and fault switching is compared. The parameters used are shown in Table 2.

Parameters type A(kV/s) B(kV) traditional parameters
1.7×10 4 3.4 experimental parameters 7.355×10 4 0.69 Snapshots were taken after the stable operation of the system for 2 s, and each snapshot was started up and running for 0.08 s, with the simulation step length of 0.4 μs. In order to reduce the  Snapshots were taken after the stable operation of the system for 2 s, and each snapshot was started up and running for 0.08 s, with the simulation step length of 0.4 µs. In order to reduce the simulation time, a calculation model of the internal electrical system of OWF with eight DFIGs on a single feeder was built in this paper; the rated capacity of each DFIG is 4 MW. In the case of normal switching, the VCB is set to be switched off at the time of A-phase voltage zero-crossing. In the situation of fault switching, the VCB is set to be switched off at the time when A-phase current reaches the chopping current [30].

Relation Between Transformer Position and Overvoltage in Normal Switching
According to the circuit theory, when reignition occurs in the VCB, the TOV steepness on the high-voltage side of the terminal transformer is related to the current flowing through the capacitance of the high-voltage to the ground of the transformer, as shown in Equation (6): where u T is the voltage at the high-voltage side of the terminal transformer (V); i T is current in the capacitance of the high-voltage side to the ground of the terminal transformer (A); and C H is the capacitance of the high-voltage to the ground of the transformer (F). When any wind turbine on the feeder is out of operation, the terminal transformer and its 80 m connection cable are cut off. Then, the overvoltage on the high-voltage side of the terminal transformer on the feeder is measured, and the steepness is calculated. Since the rising rate of transient recovery voltage after switching is always lower than the rising rate of dielectric strength, they do not intersect, and there is no reignition. At this time, the amplitude and the steepness of the overvoltage at each position and the voltage waveform at the high-voltage side of transformer T 7 when switching off VCB 17 are respectively shown in Figures 8 and 9, in which overvoltage amplitude is per unit value as follows: simulation time, a calculation model of the internal electrical system of OWF with eight DFIGs on a single feeder was built in this paper; the rated capacity of each DFIG is 4 MW. In the case of normal switching, the VCB is set to be switched off at the time of A-phase voltage zero-crossing. In the situation of fault switching, the VCB is set to be switched off at the time when A-phase current reaches the chopping current [30].

Relation Between Transformer Position and Overvoltage in Normal Switching
According to the circuit theory, when reignition occurs in the VCB, the TOV steepness on the high-voltage side of the terminal transformer is related to the current flowing through the capacitance of the high-voltage to the ground of the transformer, as shown in Equation (6): where uT is the voltage at the high-voltage side of the terminal transformer (V); iT is current in the capacitance of the high-voltage side to the ground of the terminal transformer (A); and CH is the capacitance of the high-voltage to the ground of the transformer (F).
When any wind turbine on the feeder is out of operation, the terminal transformer and its 80 m connection cable are cut off. Then, the overvoltage on the high-voltage side of the terminal transformer on the feeder is measured, and the steepness is calculated. Since the rising rate of transient recovery voltage after switching is always lower than the rising rate of dielectric strength, they do not intersect, and there is no reignition. At this time, the amplitude and the steepness of the overvoltage at each position and the voltage waveform at the high-voltage side of transformer T7 when switching off VCB17 are respectively shown in Figures 8 and 9, in which overvoltage amplitude is per unit value as follows: 3 28.58 kV .
(7) Figure 8 shows that the overvoltage amplitude and the maximum steepness of the transformer in the normal switching occur at the point where the VCB cuts out the transformer; they are 1.83 p.u. and 0.2 kV/μs, respectively. The overvoltage amplitude on the high-voltage side of the transformer of the other wind turbines in normal operation is basically 1 p.u., and the overvoltage steepness decreases with the increase of the propagation distance of the incident wave.   When the dielectric strength of VCB is simulated with traditional parameters, since the dielectric strength rises slowly, reignition occurs easily. The total reignition times in normal switching with different parameters are shown in Table 3. At this time, the total number of reignition normal switching is 10-14 times. The voltage amplitude and steepness of the high-voltage side of the terminal transformer at each position are shown in Figure 10. Compared with the results with experimental parameters, the maximum overvoltage amplitude drops from 1.83 p.u. to 1.58 p.u. However, the maximum overvoltage steepness reaches 76.7 kV/μs, increasing by about 380 times. Table 3. Total reignition times in normal switching with different parameters.

Switching case
Traditional parameters Experimental parameters normal switching 10-14 0   Figure 8 shows that the overvoltage amplitude and the maximum steepness of the transformer in the normal switching occur at the point where the VCB cuts out the transformer; they are 1.83 p.u. and 0.2 kV/µs, respectively. The overvoltage amplitude on the high-voltage side of the transformer of the other wind turbines in normal operation is basically 1 p.u., and the overvoltage steepness decreases with the increase of the propagation distance of the incident wave.

Relation Between Transformer Position and Overvoltage in Fault Switching
When the dielectric strength of VCB is simulated with traditional parameters, since the dielectric strength rises slowly, reignition occurs easily. The total reignition times in normal switching with different parameters are shown in Table 3. At this time, the total number of reignition normal switching is 10-14 times. The voltage amplitude and steepness of the high-voltage side of the terminal transformer at each position are shown in Figure 10. Compared with the results with experimental parameters, the maximum overvoltage amplitude drops from 1.83 p.u. to 1.58 p.u. However, the maximum overvoltage steepness reaches 76.7 kV/µs, increasing by about 380 times.   When the dielectric strength of VCB is simulated with traditional parameters, since the dielectric strength rises slowly, reignition occurs easily. The total reignition times in normal switching with different parameters are shown in Table 3. At this time, the total number of reignition normal switching is 10-14 times. The voltage amplitude and steepness of the high-voltage side of the terminal transformer at each position are shown in Figure 10. Compared with the results with experimental parameters, the maximum overvoltage amplitude drops from 1.83 p.u. to 1.58 p.u. However, the maximum overvoltage steepness reaches 76.7 kV/μs, increasing by about 380 times.

Switching case
Traditional parameters Experimental parameters normal switching 10-14 0

VCB Switching at Feeder
When the wind turbines on the whole feeder line are in full-load operation, VCB 1 has no reignition in fault switching. The overvoltage waveform of the terminal transformer T 7 is shown in Figure 11. The overvoltage amplitude at the high-voltage side of the terminal transformer at all positions on the feeder is 1.27 p.u., and the maximum overvoltage steepness is about 0.1 kV/µs. When the traditional parameters are used in the simulation, VCB 1 will not have reignition. The simulation results of the two are consistent at this moment. When the wind turbines on the whole feeder line are in full-load operation, VCB1 has no reignition in fault switching. The overvoltage waveform of the terminal transformer T7 is shown in Figure 11. The overvoltage amplitude at the high-voltage side of the terminal transformer at all positions on the feeder is 1.27 p.u., and the maximum overvoltage steepness is about 0.1 kV/μs. When the traditional parameters are used in the simulation, VCB1 will not have reignition. The simulation results of the two are consistent at this moment.  During VCB17 switching, an overvoltage with an amplitude up to 1.42 p.u. is generated due to reignition. After reaching the high-voltage side of T8 through the 720 m cable, the overvoltage

VCB Switching at Tower Bottom
When the wind turbines on the whole feeder are in full load operation, the VCB at the tower bottom has fault switching, and the simulation results are shown in Figure 12; it indicated that switching VCB only causes overvoltage with amplitude of about 1.18-1.42 p.u. on the high-voltage side of the terminal transformer where it is located, and the steepness is 83.3-142 kV/µs. The voltage amplitude of the remaining terminal transformer is 1 p.u. The voltage waveforms of terminal transform T 7 when VCB 17 switching and its adjacent terminal transformer T 8 at the high-voltage side are respectively shown in Figure 13a,b. When the wind turbines on the whole feeder line are in full-load operation, VCB1 has no reignition in fault switching. The overvoltage waveform of the terminal transformer T7 is shown in Figure 11. The overvoltage amplitude at the high-voltage side of the terminal transformer at all positions on the feeder is 1.27 p.u., and the maximum overvoltage steepness is about 0.1 kV/μs. When the traditional parameters are used in the simulation, VCB1 will not have reignition. The simulation results of the two are consistent at this moment.

VCB switching at Tower Bottom
When the wind turbines on the whole feeder are in full load operation, the VCB at the tower bottom has fault switching, and the simulation results are shown in Figure 12; it indicated that switching VCB only causes overvoltage with amplitude of about 1.18-1.42 p.u. on the high-voltage side of the terminal transformer where it is located, and the steepness is 83.3-142 kV/μs. The voltage amplitude of the remaining terminal transformer is 1 p.u. The voltage waveforms of terminal transform T7 when VCB17 switching and its adjacent terminal transformer T8 at the high-voltage side are respectively shown in Figure 13a,b. During VCB17 switching, an overvoltage with an amplitude up to 1.42 p.u. is generated due to reignition. After reaching the high-voltage side of T8 through the 720 m cable, the overvoltage During VCB 17 switching, an overvoltage with an amplitude up to 1.42 p.u. is generated due to reignition. After reaching the high-voltage side of T 8 through the 720 m cable, the overvoltage amplitude rapidly attenuates, and the maximum steepness of voltage fluctuation also decreases from 123 kV/µs to 55.3 kV/µs. From Table 4, the total times of reignition in this condition is about 9-10. amplitude rapidly attenuates, and the maximum steepness of voltage fluctuation also decreases from 123 kV/μs to 55.3 kV/μs. From Table 4, the total times of reignition in this condition is about 9-10.
(a) (b)   Figure  14. Due to the slow growth rate of dielectric strength, the numbers of reignition increase significantly to 135-171 times, and the maximum overvoltage amplitude increases from 1.42 p.u to 2.96 p.u, which would cause the overvoltage amplitude of the terminal transformer at the high-voltage side of the adjacent wind turbine reaching 1.89 p.u.. Compared with the same condition when using experimental parameters, the amplitude of the switching terminal transformer increases about 2 times, and the overvoltage steepness increases about 1.5 times.   When traditional parameters are applied for simulation, the results are obtained shown in Figure 14. Due to the slow growth rate of dielectric strength, the numbers of reignition increase significantly to 135-171 times, and the maximum overvoltage amplitude increases from 1.42 p.u to 2.96 p.u, which would cause the overvoltage amplitude of the terminal transformer at the high-voltage side of the adjacent wind turbine reaching 1.89 p.u.. Compared with the same condition when using experimental parameters, the amplitude of the switching terminal transformer increases about 2 times, and the overvoltage steepness increases about 1.5 times. amplitude rapidly attenuates, and the maximum steepness of voltage fluctuation also decreases from 123 kV/μs to 55.3 kV/μs. From Table 4, the total times of reignition in this condition is about 9-10.

Conclusions
(a) (b)   Figure  14. Due to the slow growth rate of dielectric strength, the numbers of reignition increase significantly to 135-171 times, and the maximum overvoltage amplitude increases from 1.42 p.u to 2.96 p.u, which would cause the overvoltage amplitude of the terminal transformer at the high-voltage side of the adjacent wind turbine reaching 1.89 p.u.. Compared with the same condition when using experimental parameters, the amplitude of the switching terminal transformer increases about 2 times, and the overvoltage steepness increases about 1.5 times.

Conclusions
In this paper, a test platform for a simplified MV cable collection system in OWF that can demonstrate the reignition phenomenon of VCB was constructed, and the parameters of VCB were calculated through experiments to verify the validity of the customized VCB model. A cable collection system of OWF was built according to the above model. The dielectric strength parameters of the VCB measured by the experiment were used in the simulation to study the TOV generated, and the results were compared with those of the traditional dielectric strength parameters. The following conclusions are drawn: (1) The overvoltage amplitude of the high voltage side of the transformer at different positions was basically the same in switching off feeder VCB. When the tower bottom VCB had normal or fault switching, the overvoltage steepness decreased with the increase of the propagation distance of the incident wave. The voltage amplitudes at the high-voltage side of the transformers in other positions were slightly influenced. (2) With experimental parameters, the critical overvoltage occurred in switching off VCBs at the tower bottom, the overvoltage amplitude in normal switching was the largest, up to 1.83 p.u., while the steepness of the overvoltage generated in fault switching was the largest, up to 142 kV/µs, and the total numbers of reignition were 9-10 times. (3) Due to the difference of dielectric strength of the VCB, when using the experimental parameters measured in this study, the amplitude of overvoltage of the terminal transformer was reduced to 1/2, and the steepness was reduced to 1/1.5 compared with using the traditional parameters of VCB under the same operation condition, in case of switching off VCB at the tower bottom with wind turbines full loading. Therefore, it is recommended that the actual experimental parameters of VCBs should be adopted in the following researches.