Research on Lightning Overvoltage Characteristics of High-Voltage Diode Rectifier

Abstract

Failure of the high-voltage diode rectifier caused by lightning will cause huge losses. The traditional analysis of overvoltage induced by the high-voltage diode rectifier shell under lightning stroke cannot adapt to the overvoltage process caused by lightning stroke-induced conduction invading the inside of the high-voltage diode rectifier. Therefore, this paper proposes to establish a high-frequency equivalent model of the core components of the high-voltage diode rectifier, including diodes, reactors, transformers, and overhead lines. On this basis, a lightning overvoltage model of lightning-induced conduction into the high-voltage diode rectifier is built, and the transient process of diode lightning overvoltage under the constraint of reverse recovery charge is analyzed. Then, we describe the transient distribution of overvoltage in high-voltage diode rectifiers caused by lightning stroke. The transient distribution of overvoltage induced by lightning in series diodes under different diode equivalent models is analyzed by simulation. The simulation results show that the inconsistent parameters of series diodes can easily lead to diode damage due to uneven voltage distribution when lightning strikes. Therefore, this paper puts forward a scheme to reduce lightning damage, including selecting diodes with the same parameters and adding fast-melting fuses at the transformer’s secondary side and in front of the series diode bridge arm. The simulation shows that the scheme proposed in this paper can effectively prevent the high-voltage diode rectifier from being damaged by lightning strikes.

1. Introduction

Offshore wind power resources are abundant, and the installed capacity of offshore wind power is increasing rapidly. To save the cost of offshore wind power transmission, voltage source converter-based high-voltage direct current (VSC-HVDC) has become the first choice for offshore wind power transmission over 70 km offshore. However, the construction cost of VSC-HVDC is still high, and the DC transmission scheme based on the high-voltage diode rectifier can greatly reduce the construction cost, which has become an important development trend of offshore wind power transmission situated far out to sea. Limited by the material, design, and manufacturing process of high-voltage diode devices, the high-voltage diode rectifier is connected in series by a plurality of high-voltage diodes to realize voltage blocking. This kind of high-voltage diode rectifier, which is composed of a plurality of high-voltage diodes in series, is a typical lightning-sensitive device. The instantaneous high current in the process of lightning strikes easily leads to the breakdown of the series diodes of the high-voltage diode rectifier one by one, thus endangering its safe and stable operation. At present, China’s offshore wind power construction is concentrated on the southeast coast. Thunderstorms are frequent in these areas, which seriously threaten the safe operation of the whole DC transmission system. Moreover, China’s high-voltage transmission has a large geographical span, high voltage level, and high transmission power, which also increases the risk that lightning strikes invade the high-voltage diode rectifier through line conduction.

To improve the lightning protection performance of high-voltage diode rectifiers, domestic and foreign scholars have modeled and analyzed the lightning transient characteristics of HVDC transmission systems. The authors of [1] established the lightning-induced overvoltage model of the converter shell of the HVDC transmission system in the wind farm, and started with the influencing factors of limiting lightning overcurrent to suppress the overvoltage caused by lightning-induced. In [2], the definition and calculation method of lightning shielding failure rate (LSFR) of the wind turbine are presented. The authors of [3] established a wind turbine model and comprehensively described the lightning strike process and the destruction mechanism of the wind turbine. The lightning protection measures are put forward. An electrical model of the HVDC transmission system under lightning strike was constructed [4,5], and analyzed the induced overvoltage process of electrical equipment shell under lightning strike from the angle of electromagnetic field analysis. In [6,7], the overvoltage model of HVDC transmission system under the action of the lightning strike was established, and analyzed the lightning-induced overvoltage distribution characteristics of related equipment enclosures of ±800 kV UHVDC transmission system at high altitude. The authors of [8] show that blade rotation may have a considerable impact on the attack times of modern wind turbines, and due to the tall structure of wind turbines, the lightning current injected into the turbine by the return stroke will be affected by the reflection of the blade top, bottom and the junction with the static base of the turbine. The lightning overvoltage model of wind turbine blades was proposed [9,10], and analyzed the induced overvoltage distribution of wind turbine shell when wind turbine blades are struck by lightning. Furthermore, in [11] it is pointed out that safe and cost-effective design of wind turbine grounding (WTG) systems requires accurate modeling of local soil resistivity, especially when wind turbines are spatially distributed over a wide area with different soil types and characteristics. Relevant reference guidelines are provided by [12] for wind turbine lightning protection, and provides some guidelines. Reference [13] shows that depending on the conditions of the grounding system, surges propagating to nearby fans can sometimes become large and cause the arresters of unhit fans to burn out, especially during winter lightning strikes. The authors of [14] present a set of analytical formulas to evaluate circuit parameters for blades, pylons, three-phase cables, and single-pile foundations. Based on the circuit parameters, the circuit model is established, and the transient analysis of the offshore wind turbine when lightning strikes multiple blades is carried out. The above research mainly considers the induced overvoltage of the shell of the physical component after being struck by lightning but does not consider the overvoltage process where the lightning conduction invades the physical component.

The HVDC system of the deep-water wind farm is a complex multi-component system. If the lightning current invades the converter station or converter of the HVDC system along the conductor, the overvoltage caused may cause the HVDC system to shut down, resulting in serious consequences [15]. References [16,17] analyzed the overvoltage process of the converter station system caused by the series thyristor junction capacitance and the interlayer capacitance of converter components under the action of a lightning strike. In this study, the dynamic characteristics of semiconductor devices are equivalent to the parallel connection of junction capacitance and internal resistance, where reflecting the nonlinear voltage distribution caused by the semiconductor’s physical process is difficult. In [18], the effect of multi-pulse lightning stroke on the aging characteristics of ZnO varistor is analyzed. It is pointed out that pulse number and pulse interval play a decisive role in the aging speed of the ZnO varistor. Reference [19] designs a new IEC Class I arrester design based on the rheostat and spark gap. This model is only applicable to the working state of intermediate frequency rectification, but it is difficult to apply to the voltage distribution analysis of series diodes under lightning strikes, and it lacks the transient process analysis of lightning overvoltage of integral high-voltage diode rectifiers.

The above research mainly focuses on the analysis of the overvoltage process caused by lightning-induced physical component shell reconduction to the ground, without considering the overvoltage process caused by lightning-induced conduction or lightning-induced conduction to the HVDC transmission system and its components through lines. The overvoltage distribution caused by lightning-induced intrusion into the high-voltage diode rectifier and its series diodes is unclear, thus it is difficult to guide the lightning protection design and device selection of the high-voltage diode rectifier. Therefore, this paper proposes to establish an overvoltage analysis model of the high-voltage diode rectifier and its internal components struck by lightning and reveals the overvoltage distribution characteristics of the high-voltage diode rectifier and its internal series diodes under lightning. On this basis, an effective solution to avoid lightning damage is put forward, including selecting diodes with the same parameters and adding fast-melting fuses at the transformer’s secondary side and before of the diode bridge arm. Simulation results show that the scheme proposed in this paper is effective.

2. Modeling of the Lightning Strike Overvoltage of High-Voltage Diode Rectifier

Aiming at the diodes, which are the weakest component of the high-voltage diode rectifier, the transient process analysis model of overvoltage caused by its individual and its series structure’s lightning-induced conduction invasion into its interior is established. On this basis, the transient process analysis model of lightning overvoltage of the high-voltage diode rectifier is established.

2.1. Structure of High-Voltage Diode Rectifier

Although the process of a lightning stroke is short, the energy released instantly is huge. When lightning strikes invade the high-voltage diode rectifier and its components, it is necessary to establish an equivalent model that can characterize its high-frequency dynamic process, to analyze the transient voltage distribution inside the high-voltage diode rectifier. First of all, the internal structure of the high-voltage diode rectifier should be given, which mainly includes diodes and series diodes, step-up transformer, reactor, and overhead line. Its structure is shown in Figure 1.

2.2. Transient Modeling of Lightning Overvoltage for Core Components of High-Voltage Diode Rectifier

Due to the high-frequency saturation characteristics of the transformer and reactor and the distribution parameter characteristics of the overhead line, the lightning current and lightning voltage inside the high-voltage diode rectifier will be distorted after lightning-induced conduction into the rectifier, which will affect the rising slope, peak value, and falling rate of the lightning current and lightning voltage. Therefore, it is necessary to model the transient process of lightning strikes for all components of the high-voltage diode rectifier, including the transformer high-frequency saturation model, reactor high-frequency saturation model, and overhead line distribution parameter model.

2.2.1. Transient Modeling of Diode Lightning Overvoltage

As a semiconductor device, the diode is very sensitive to overvoltage. In particular, in the process of switching off the diode, once there is a lightning strike conduction invasion, a large voltage is loaded onto the series diodes instantaneously, and the voltage is not evenly distributed in multiple series diodes. It is very easy to cause one of the diodes in the process of switching-off serious heat and breakdown one by one, seriously affecting the safe and stable operation of the high-voltage diode rectifier. Therefore, it is very important to analyze the lightning overvoltage during reverse diode shutdown. Firstly, the model of the overvoltage transient process caused by the lightning strike conduction invasion of the individual and its series structure is established.

The voltage distribution borne by the diode in the turn-off process is related to the semiconductor material used and its design and manufacturing process, mainly manifested as the distribution of reverse voltage resistance of the PN junction, as shown in Figure 2.

The time scale of the diode switching process is at $\mu s$ level, which is similar to the ascent time of the steep wave of the lightning current. The following is a detailed analysis of the diode lightning overvoltage model under the restriction of reverse recovery charge and its transient distribution of overvoltage.

The diode-switching process can be divided into two stages: the minority carrier depletion stage (0–t₂) and the reverse recovery stage (t₃–t₄) of the PN junction. In the minority carrier depletion stage, the voltage at both ends of the diode remains in the on-voltage state in the t₁–t₂ period. In the t₂–t₃ stage, the voltage at both ends of the diode drops rapidly, and the diode gradually reaches the cut-off state after t₃ time. In the 0–t₂ period, combined with the charge state of the PN junction, the current model flowing through the diode is as follows:

(1)$i=\frac{q_E-q_M}{T_M}$

(2)$\frac{d{q}_M}{dt}+\frac{q_M}{\tau }=i$

(3)$q_E=\left(\tau +T_M\right)i$

where $i$ is the current flowing through the diode, $q_E$ is the charge amount of the PN junction, $q_M$ is the storage charge amount of the PN junction boundary, $T_M$ is the transfer time, and $\tau$ is the carrier life. $q_E$ is determined by PN junction material and can be expressed as:

(4)$q_E=I_S\tau (e^{\frac{v}{2V_{Tj}}}-1)$

where $\nu$ is the diode junction voltage, $I_S$ is the diode reverse saturation current, and $V_{Tj}$ is the voltage equivalent of temperature.

At this stage, since the diode is still in the conduction state and the current flowing through the diode is also affected by the current flowing through the high-voltage diode rectifier, the current flowing through the diode is:

(5)$i=i_F+at$

where $a$ is the rate of change of current, $a=\mathrm{d}i/\mathrm{dt}$.

In the minority carrier depletion stage, $q_M$ changes in the process of current attenuation and gradually depletes $q_E$. At this stage, $q_M$ can be resolved as:

(6)$q_M=i_F\tau -a{\tau }^2+a{\tau }^2{e}^{-\frac{t}{\tau }}+a\tau t$

In the $t_s$ time range, the current changes according to slope $a$, then

(7)$t_s=t_3-t_1=\frac{I_{RM}}{a}$

When $t>t_3$, according to Figure 2, the current can be expressed as:

(8)$i=I_{RM}{e}^{\frac{-\left(t-t_3\right)}{{\tau }_{rr}}}$

The reverse recovery time constant is ${\tau }_{rr}$, which is related to carrier lifetime $\tau$ and carrier transfer time $T_M$, and can be expressed as:

(9)$\frac{1}{{\tau }_{rr}}=\frac{1}{\tau }+\frac{1}{T_M}$

When $t>t_3$, the reverse recovery current is $I_{RM}/10$. Combined with Equation (8), $t_F$ can be expressed as:

(10)$t_F={\tau }_{rr}ln\left(10\right)$

Charge quantity in $t_s$ time:

(11)$Q_S=\frac{1}{2}\left(-I_{RM}\right)\frac{I_{RM}}{a}$

Charge quantity in $t_F$ time:

(12)$Q_F={\tau }_{rr}{I}_{RM}\left(1-e^{-\frac{t_4-t_3}{{\tau }_{rr}}}\right)=\frac{9}{10}{\tau }_{rr}{I}_{RM}$

(13)$Q_{rr}=Q_S+Q_F$

Then the reverse recovery time under the constraint of reverse recovery charge is:

(14)$t_{rr}=t_s+t_F=\frac{10}{9}\left(\frac{Q_{rr}}{I_{RM}}+\frac{I_{RM}}{2a}\right)\ln \left(10\right)+\frac{I_{RM}}{a}$

Therefore, when the maximum reverse current $I_{RM}$ is given, the reverse recovery time is jointly constrained by the reverse recovery charge amount and the current change rate. The larger the $Q_{rr}$, the longer the reverse recovery time. When the current change rate is larger, the reverse recovery time will approach $\frac{10}{9}\left(Q_{rr}/I_{RM}\right)ln\left(10\right)$. This also means that the amount of charge in the reverse recovery process is large at this time. When the reverse cut-off voltage and its change rate are large, it will bear a larger voltage and further oscillate with the saturated reactor. However, when the current change rate $a$ is a little small, the bearing pressure of multiple diodes in a series is negatively correlated with the reverse recovery time of each diode. That is, the longer the reverse recovery time is, the larger the $I_{RM}/a$ is, and the longer it takes for the diode to build the cut-off voltage, which makes the diode with a shorter reverse recovery time bear the higher voltage first. On the other hand, in the reverse recovery time, the change of current and charge quantity is not linear. Therefore, under the constraint of reverse recovery charge, the junction capacitance will also show time-varying characteristics in the reverse recovery time.

In the process of the forward conduction recovery, the dynamic recovery characteristics of the diode are mainly manifested in the process of the forward recovery voltage:

(15)$v_M=\frac{2V_T{T}_M{R}_{M0}at}{R_{M0}a\tau \left[t-\tau \left(1-e^{-t/\tau }\right)\right]+V_T{T}_M}$

where $R_{M0}$ is the initial equivalent resistance of the diode, which can be obtained from the diode parameter manual.

Therefore, the reverse cut-off model of the diode in the steady state and transient state is shown in Figure 3. Under the impact of a steep lightning current wave, the transient characteristics of the diode can be equivalent to nonlinear time-varying capacitance, and under steady-state operation, the diode can be equivalent to a parallel model of junction capacitance and internal resistance.

Based on the limitation of the diode’s forward conduction current and reverse withstand voltage, the high-voltage diode rectifier adopts multiple diodes in series to realize the transmission of large current and the blocking of high voltage. After several diodes are connected in series, the consistency of voltage distribution during turn-off is an important index of transient overvoltage performance under the lightning strike. Based on the transient overvoltage model of the lightning-induced intrusion of a single diode in the previous section, the transient overvoltage model of the lightning-induced intrusion of multiple diodes in series is constructed.

The equivalent circuit of the series diode of a single bridge arm of the high-voltage diode rectifier when it is turned off in reverse is shown in Figure 4. When the power frequency AC voltage is turned off, the time constant $\tau =RC$ of junction capacitance and reverse internal resistance is close to the power frequency time scale, thus the resistance cannot be ignored. Therefore, the RC parallel model is adopted as the diode equivalent model, and the diode equivalent model of the high-voltage diode rectifier in series is shown in Figure 4a. Among them, the diode junction capacitance and equivalent internal resistance can be obtained from the product manual.

2.2.2. Transient Modeling of the Transformer Lightning Overvoltage

The lightning current has a fast-rising rate and high amplitude, which can reach tens of kiloamperes in more than 10 us, showing a huge high-frequency component, whose frequency can be close to 1 MHz, forcing the transformer core to be saturated, and exciting the high-frequency capacitance characteristics between windings and between windings and ground. It is difficult to reflect the traditional T-type equivalent model operation characteristics of the transformer under the action of high frequency and high current, thus it is necessary to build a transformer high-frequency saturation model to characterize the transient process of the transformer the lightning overvoltage.

For the low-frequency part of the lightning overvoltage, the lightning wave transmits overvoltage through the winding, which is characterized by inductance. Part of this model can adopt a T-type equivalent model, including main magnetic energization inductance L_Tm, primary leakage inductance L_T1, leakage resistance R_T1, secondary leakage inductance L_T2, and leakage resistance R_T2. Because of the high amplitude of the lightning current, the main flux of the transformer is saturated, and L_Tm is in a state of saturation and low inductance. In the high-frequency part of the lightning current, the inductance of the winding is high impedance, the stray capacitance in the transformer is low impedance, and the lightning overvoltage characteristics of the transformer are capacitive coupling at high frequency, thus the model is shown in Figure 5. The relevant parameters of the transformer are shown in Table 1.

2.2.3. Transient Modeling of the Reactor Lightning Overvoltage

When faced with the lightning current impact, the reactor core quickly reaches saturation, thus the reactor modeling needs to consider its saturation characteristics and high-frequency characteristics. According to the flux linkage equation, this paper constructs a saturated reactor model:

(16)$i=i_L+v{G}_P$

(17)$v=N_w\frac{d\mathsf{\Phi }}{dt}$

(18)$\mathsf{\Phi }=\frac{L_{sat}}{N_w}{i}_L\pm {\mathsf{\Phi }}_{offset}$

where $\mathsf{\Phi }$ is the total flux of the transformer, $L_{sat}$ and L are saturated inductance and unsaturated inductance, $N_w$ is the number of winding turns, $i_L$ and $v$ are the inductance current and voltage, ${\mathsf{\Phi }}_{offset}$ is the saturated flux, and $G_P$ is the parasitic parallel conductivity.

When the reactor is saturated, its inductance gradually decreases. When the reactor is not saturated, the relationship between voltage and current changes linearly, that is, the inductance is constant. In this paper, when the inductance is constant, the inductance value is 300 μH, when it is saturated, the inductance value is not more than 20 μH, and the coil resistance is less than or equal to 2 mΩ. Reactor model with constant inductance:

(19)$\mathsf{\Phi }=\frac{L}{N_w}{i}_L$

2.2.4. Transient Modeling of the Overhead Line Lightning Overvoltage

After the three-phase AC unit is boosted by the transformer, it is transmitted to the high-voltage diode rectifier by overhead lines. When the high-voltage diode rectifier system is struck by lightning, the frequency of the lightning overvoltage is high, and the wave wavelength is close to the transmission distance. Therefore, the lumped parameter equivalent model cannot characterize the impact of the lightning overvoltage on overhead lines, thus the distributed parameter model is needed.

Capacities existing in overhead lines include unit length capacitance between lines and unit length capacitance between overhead lines and earth, which can be classified as unit length capacitance C_L in a single conductor model. The unit length inductance and unit length resistance in overhead lines are L₁ and R₁, respectively. The equivalent model of the unit overhead line is shown in Figure 6.

Among them, the unit length inductance and unit length capacitance are:

(20)$L_1=\frac{\mu }{2\pi }\mathit{ln}\frac{2h}{a}$

(21)$C_L=\frac{2\pi \epsilon }{\mathit{ln}\frac{2h}{a}}$

where $h$ is the height of overhead lines to the ground, $a$ is the radius of overhead lines, and $\epsilon$ is the permeability of overhead lines; $\epsilon$ is the dielectric constant of the dielectric around the overhead line.

2.3. Transient Modeling of Lightning Overvoltage in High-Voltage Diode Rectifier

According to the high-voltage diode rectifier system shown in Figure 1, each component model is electrically connected, and the electrical model of the high-voltage diode rectifier system under the lightning voltage impact is constructed by combining DC side capacitance and load, as shown in Figure 7.

3. Transient Analysis of the Lightning Overvoltage of the High-Voltage Diode Rectifier

Based on the electrical model of the high-voltage diode rectifier system under lightning strike, a class of high-voltage diode rectifiers is selected as the analysis object, and a simulation verification platform is built to analyze the overvoltage distribution characteristics of the high-voltage diode rectifier and its internal series diodes under lightning strike, to guide the lightning protection design and device selection of high-voltage diode rectifier in a high-voltage DC transmission system of the deep water wind farm.

3.1. Setting of Lightning Overvoltage Scene of the High-Voltage Diode Rectifier

Specific parameters of the selected high-voltage diode rectifier are shown in Table 1 and Table 2. The input lightning voltage waveform is shown in Figure 8. Verify:

• The impact of lightning will seriously affect the normal operation of the high-voltage diode rectifier system, increasing the risk of breakdown of some devices in the high-voltage diode rectifier;

• Inconsistent parameters and characteristics of series diodes when being invaded by lightning will lead to uneven voltage distribution on a single diode, resulting in series diodes being broken down one by one.

Table 2

Parameters of series diodes.

Parameter	Case 1	Case 2	Case 3
Qrr1\Qrr2\Qrr3	-	4500 ΜC\4000 μC\5000 μC	4500 μC\4000 μC\5000 μC
IRM1\IRM2\IRM3	-	90 A	90 A
Junction capacitance C1\C2\C3	6 μF\4 μF\5 μF	6 μF	6 μF\4 μF\5 μF
Reverse resistance R1\R2\R3	40 kΩ	40 kΩ	40 kΩ
RM01\RM02\RM03	0.163 mΩ	0.163 mΩ	0.163 mΩ
Threshold voltage	0.96 V	0.96 V	0.96 V
Peak forward voltage	1.45 V	1.45 V	1.45 V
Forward root mean square current	4740 A	4740 A	4740 A

Figure 8

Input lightning voltage waveform.

[Figure omitted. See PDF]

3.2. Transient Simulation Analysis of Lightning Overvoltage in Core Components of the High-Voltage Diode Rectifier

3.2.1. Transient Simulation Analysis of Transformer Lightning Overvoltage

Lightning strikes the overhead line and transmits lightning current to the secondary side of the transformer through the overhead line, injecting huge current and energy into the transformer. The voltage and current waveforms on the transformer at this time are shown in Figure 9.

When the transformer is struck by lightning, its power is about $3\times {10}^{11}$ VA, and its duration is about 0.5 s. The capacity of common transformers in high-voltage transmission lines is in the range of $3\sim 10\times {10}^6$ VA. Such a large amount of energy injection is likely to cause the burning of transformers, which seriously affects the safe operation of the high-voltage diode rectifier.

Installing a fast-fusing electronic fuse with a fusing voltage of 200 KV and a fusing power of $2\times {10}^6$ VA on the secondary side of the transformer can be considered, which will fuse within a few milliseconds of the lightning strike to ensure the safe operation of the transformer. At the same time, lightning protection devices can be installed on the primary side of the transformer, and various measures such as “three points and one place” and improving the specification of grounding materials can be adopted to reduce lightning damage.

3.2.2. Transient Simulation Analysis of Lightning Overvoltage in Reactors and Diodes

Lightning strikes on overhead lines transfer huge currents and energy to the reactor, which are buffered by the reactor and transferred to the diode group. The reactor adopts 300 μH linear inductance.

The voltage waveform on the inductor after being struck by lightning is shown in Figure 10. At this time, the inductor is subjected to a voltage shock with an amplitude as high as $6\times {10}^6$ V and a high frequency and high amplitude voltage shock lasting about 1 s. The large voltage, high frequency, and high amplitude voltage shock suffered at this time can easily cause the breakdown of the inductor.

For the series diode group, the influence of junction capacitance and reverse recovery charge on the voltage distribution on the series diode is analyzed below, as shown in Figure 11.

When the reverse recovery charges of series diode groups are the same, the RC parallel circuit model (junction capacitance with diode internal resistance) is adopted, and the voltage on each diode is distributed by the capacitance impedance. The junction capacitance impedance is negative, thus the larger the junction capacitance, the smaller the voltage the diode bears. After lightning strikes, due to the linear characteristics of the diode equivalent circuit, the voltage characteristics of each diode are consistent with those of steady-state operation as shown in Figure 11a–c.

The voltage distribution on the series diode group when the junction capacitance of the series diodes is the same and the reverse recovery charge amount is different is shown in Figure 11d–f. As can be seen from the figure, the diode with the smallest reverse recovery charge bears most of the voltage impact, which easily leads to the breakdown of a single diode, thus leading to the cascading breakdown of series diodes.

Under the action of a lightning strike, the lightning current rises rapidly, and its time scale is similar to that of diode reverse recovery. Therefore, after lightning strikes, the junction capacitance hardly affects the voltage distribution of series diodes, and the voltage distribution of series diodes is mainly affected by the reverse recovery charge amount, as shown in Figure 11g–i. In the rapid action of lightning current, the diode with less charge in the reverse recovery process will bear a larger voltage because the current rise rate is too fast. When the current change rate is small, the voltage distribution of the diode is mainly affected by the reverse recovery time. The shorter the reverse recovery time, the higher the voltage of the corresponding diode.

Due to the reverse recovery charge under the restriction of the nonlinear effect of capacity and lightning shock characteristics, high-voltage diode rectifier in series with the diode array, the voltage distribution in the unbalanced degree is higher, the lightning current shock stage and linear reverse recovery time within the constraints of two phases, smaller diode reverse recovery charge, and diode reverse recovery will suffer several times the rating voltage for a while. It is easy to cause diode breakdown, and then cause interlocking breakdown failure. The high-voltage diode rectifier operates safely and stably.

Therefore, diodes with the same specifications and characteristics must be used in the diode group, and the consistency of the diodes should be tested before installation, to avoid the breakdown of the diodes caused by the uneven distribution of lightning spot voltage on the series diodes.

The current flowing through the series diode circuit is shown in Figure 12. Within one second after being struck by lightning, the average current of the circuit is about $1\times {10}^4$ A.

According to the voltage waveform of the series diodes, it can be estimated that after the lightning strike, the energy absorbed by the single diode with the largest voltage is about 7 × 10 ^ 10 J. Such large energy injection will lead to the breakdown and burning of the diodes, even the breakdown and burning of the series diodes one by one, which seriously affects the safe and stable operation of the high-voltage diode rectifier.

Therefore, installing a suitable fast-fusing electronic fuse in front of each bridge arm of the high-voltage diode rectifier is considered, in order that the fuse will be formed within a few milliseconds of the lightning strike, and inert gas will be filled around the diode group to prevent the lightning voltage from breaking through the air to form a current loop. As a component of the high-voltage diode rectifier that is easily affected by lightning, it needs to be protected to improve its safe and stable operation.

3.3. Transient Simulation Analysis of Lightning Overvoltage in High-Voltage Diode Rectifier

Because of the lightning protection work of various components of the high-voltage diode rectifier, corresponding countermeasures are put forward in the last section, and the effectiveness of the solutions is verified below.

The voltage and current waveforms on the transformer after the fast fuse is added are shown in Figure 13. It can be seen that after being struck by lightning, the fuse is blown and the side of the secondary side is disconnected. The primary side of the transformer only bears a very short duration of voltage impact, and there will be a small concussion current, which ensures that the transformer is not damaged by lightning.

The voltage waveform on the reactor after the fast fuse is installed in front of the series diode bridge arm is shown in Figure 14d. After the lightning strike, there is only a very short duration of voltage shock on the reactor, and the current duration is very short, thus the reactor will not be burned. The voltage and current waveforms on the series diode are shown in Figure 14a–c,e. It can be seen that the series diode group works normally before the lightning strike, but after the lightning strike, the fuse is instantly blown, the voltage on the diode is close to zero, and no large energy flows, ensuring that the diode group will not be burned.

4. Conclusions

Based on the impulse characteristics of lightning current, the high-voltage diode rectifier system model is established in this paper, including the high-frequency saturation model of the transformer and reactor, the overhead line model, and the nonlinear capacitance model of the diode. The effect of the reverse recovery charge on the dynamic characteristics of the diode is emphatically analyzed, and the equivalent models of the diode at different time scales, including the time-varying capacitance model and the RC parallel model, are discussed based on the current change rate. It is pointed out that the RC parallel model is suitable for long time scale operation states, such as stable power frequency operation states. Time-varying capacitance models are suitable for short time scale operating states, such as fault states and lightning strike states. Finally, the simulation results show that:

• After lightning strikes, the core components of the high-voltage diode rectifier, including the transformer, reactor, series diode group, etc., are easily seriously affected and even lead to device damage, which seriously threatens the safe and stable operation of the high-voltage diode rectifier. A suitable fast-melting electronic fuse can be installed in front of each core component to block the lightning strike, and the device can be filled with inert gas, to prevent the lightning overvoltage from breaking the air and forming a current loop in the device, thus ensuring that the core device is not damaged;

• The voltage distribution of the series diode group is mainly influenced by junction capacitance and reverse recovery charge. Under the action of the lightning strike, the diode with a small reverse recovery charge and the diode with a short reverse recovery time will bear several times the rated voltage, which will easily cause diode breakdown, and then lead to a cascading breakdown, which will seriously affect the safe and stable operation of the high-voltage diode rectifier. Therefore, diodes with the same specifications and characteristics should be selected for the series diode group, and the consistency test should be conducted before installation.

This paper reveals the influence of the nonlinear process caused by reverse recovery charge under lightning overvoltage on voltage distribution of series diodes of the high-voltage diode rectifier and puts forward corresponding reference suggestions for lightning protection design and device selection of the high-voltage diode rectifier.

Author Contributions

G.P. built the model, simulated and verified it, and wrote the first draft; B.S. and H.W. helped to build the model; C.F. polished the manuscript; P.Y., J.Z. and Y.L. helped to modify the manuscript. All authors have read and agreed to the published version of the manuscript.

Conflicts of Interest

The authors declare no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures and Tables

Figure 1. Structure of high-voltage diode rectifier.

Figure 2. Turn-off process of the diode.

Figure 3. Dynamic equivalent circuit of diode turn-off process: (a) Low-frequency equivalent circuit; (b) high-frequency equivalent circuit.

Figure 4. Equivalent circuit of series diode turn-off process: (a) Low-frequency equivalent circuit; (b) high-frequency equivalent circuit.

Figure 5. High-frequency saturation equivalent circuit of the transformer.

Figure 6. Equivalent circuit of overhead line.

Figure 7. Transient physical model of lightning overvoltage for high-voltage diode rectifier.

Figure 9. Current and voltage waveform of transformer: (a) voltage waveform; (b) current waveform.

Figure 10. Voltage waveform on the reactor.

Figure 11. The diode voltage distribution under different constraints: (a) Junction capacitance C1 = 6 μF; (b) junction capacitance C2 = 4 μF; (c) junction capacitance C3 = 5 μF; (d) Qrr1 = 4500 μC; (e) Qrr2 = 4000 μC; (f) Qrr3 = 5000 μC; (g) junction capacitance C1 = 6 μF, Qrr1 = 4500 μC; (h) junction capacitance C2 = 4 μF, Qrr2 = 4000 μC; (i) junction capacitance C3 = 5 μF, Qrr3 = 5000 μC.

Figure 12. Series diode loop current waveform.

Figure 13. Current and voltage waveform on transformer after the fuse is added: (a) voltage waveform; (b) current waveform.

Figure 14. Voltage and current waveform on the series diode and reactor after the fuse is added: (a) voltage of diode 1; (b) voltage of diode 2; (c) voltage of diode 3; (d) voltage of reactor; (e) current of the series diode and reactor.

Table 1

Parameters of high-voltage rectifier.

Modules	Parameters	Value
Transformer	turn ratio	1:24
	LTm	0.7958 H
	LT1	127.3 μH
	RT1	0.001 Ω
	LT2	0.0733 H
	RT2	0.576 Ω
	CT1	300 pF
	CT2	190 pF
	CTg	300 pF
	CT	900 pF
Overhead lines	CL	0.3 μF/km
	L1	0.6 mH/km
	R1	0.02 Ω/km
	l1	20 km
	l2	10 km
	CL	0.3 μF/km
Reactor	Lsat	20 μH
	L	300 μH

References

1. Tian, J.; Chunyan, M.; Duan, Q.; Zhang, Z.; Wang, F.; Zhuo, F.; Yi, H. Influence of over-voltage Condition Brought by HEMP, Lightning over-voltage and Operating over-voltage during Commutation Period on Reliability of HVDC Converter Valve. Proceedings of the 2019 22nd International Conference on Electrical Machines and Systems (ICEMS); Harbin, China, 11–14 August 2019; pp. 1-4.

2. Yu, W.; Guo, Z.; Zhang, M.; Li, R.; Li, Q.; Liu, L.; Siew, W.H. A Quantitative Evaluation Method for Failure Risk of the Lightning Attachment System on Wind Turbine. Proceedings of the 2019 11th Asia-Pacific International Conference on Lightning (APL); Hong Kong, China, 12–14 June 2019; pp. 1-4. [DOI: https://dx.doi.org/10.1109/APL.2019.8816062]

3. Yang, T.; Yang, X. Lightning protection of wind turbines. Proceedings of the 2010 The 2nd International Conference on Industrial Mechatronics and Automation; Wuhan, China, 30–31 May 2010; pp. 60-63. [DOI: https://dx.doi.org/10.1109/ICINDMA.2010.5538095]

4. Davari, M.; Mousavi, O.A.; Salabeigi, I. Analysis and comparison of the lightning overvoltage in the AC connected and VSC based HVDC connected wind farms. Proceedings of the TENCON 2009–2009 IEEE Region 10 Conference; Singapore, 23–26 January 2009; pp. 1-6.

5. Sekioka, S.; Otoguro, H.; Funabashi, T. A Study on Overvoltages in Windfarm Caused by Direct Lightning Stroke. IEEE Trans. Power Deliv.; 2019; 34, pp. 671-679. [DOI: https://dx.doi.org/10.1109/TPWRD.2018.2883910]

6. Han, Y.; Tang, L.; Li, L.; He, Q.; Hao, Y.; Yao, S. Influence of lightning flashover criterion on the calculated lightning withstand level of ±800 kV UHVDC transmission lines at high altitude. IEEE Trans. Dielectr. Electr. Insul.; 2015; 22, pp. 185-191. [DOI: https://dx.doi.org/10.1109/TDEI.2014.004537]

7. Han, Y.; Chen, H.; Lu, Y.; Li, L. Research on DC Transient Overvoltage and Insulation Coordination of ±800 kV Converter Station. Proceedings of the 2011 Asia-Pacific Power and Energy Engineering Conference; Wuhan, China, 25–28 March 2011; pp. 1-4.

8. Rachidi, F.; Rubinstein, M.; Montanya, J.; Bermúdez, J.L.; Sola, R.R.; Solà, G.; Korovkin, N. A Review of Current Issues in Lightning Protection of New-Generation Wind-Turbine Blades. IEEE Trans. Ind. Electron.; 2008; 55, pp. 2489-2496. [DOI: https://dx.doi.org/10.1109/TIE.2007.896443]

9. Wang, Y.; Hu, W. Investigation of the Effects of Receptors on the Lightning Strike Protection of Wind Turbine Blades. IEEE Trans. Electromagn. Compat.; 2017; 59, pp. 1180-1187. [DOI: https://dx.doi.org/10.1109/TEMC.2016.2647260]

10. Garolera, A.C.; Cummins, K.L.; Madsen, S.F.; Holboell, J.; Myers, J.D. Multiple Lightning Discharges in Wind Turbines Associated with Nearby Cloud-to-Ground Lightning. IEEE Trans. Sustain. Energy; 2015; 6, pp. 526-533. [DOI: https://dx.doi.org/10.1109/TSTE.2015.2391013]

11. Goud, R.D.; Auditore, T.; Rayudu, R.; Moore, C.P. Frequency Domain Analysis of a Wind Turbine Generator Earthing System for Lightning Discharge Currents. IEEE Access; 2019; 7, pp. 60501-60512. [DOI: https://dx.doi.org/10.1109/ACCESS.2019.2915104]

12. Glushakow, B. Effective Lightning Protection for Wind Turbine Generators. IEEE Trans. Energy Convers.; 2007; 22, pp. 214-222. [DOI: https://dx.doi.org/10.1109/TEC.2006.889622]

13. Yasuda, Y.; Uno, N.; Kobayashi, H.; Funabashi, T. Surge Analysis on Wind Farm When Winter Lightning Strikes. IEEE Trans. Energy Convers.; 2008; 23, pp. 257-262. [DOI: https://dx.doi.org/10.1109/TEC.2007.905361]

14. Tao, S.; Zhang, X.; Wang, Y.; Yang, J. Transient Behavior Analysis of Offshore Wind Turbines during Lightning Strike to Multi-Blade. IEEE Access; 2018; 6, pp. 22070-22083. [DOI: https://dx.doi.org/10.1109/ACCESS.2018.2828043]

15. Han, Y.; Li, L.; Chen, H.; Lu, Y. Influence of Modeling Methods on the Calculated Lightning Surge Overvoltages at a UHVDC Converter Station Due to Backflashover. IEEE Trans. Power Deliv.; 2012; 27, pp. 1090-1095. [DOI: https://dx.doi.org/10.1109/TPWRD.2012.2190306]

16. Liu, C.L.; Shuai, Q.; Qi, L.; Cui, X.; Fang, C.; Wei, X. Quantitative analysis of voltage distribution within ±1100 kv HVDC converter valve tower under various triasient over-voltage conditions. Proceedings of the 2014 International Conference on Lightning Protection (ICLP); Shanghai, China, 11–18 October 2014; pp. 1558-1564.

17. Liu, C.; Gou, Y.; Yang, Z.; Yan, H.; Zhuo, F.; Wang, F. Research on Overvoltage Distribution of HVDC Converter Valve and Influence of Parasitic Capacitance in special environment. Proceedings of the 2019 IEEE 10th International Symposium on Power Electronics for Distributed Generation Systems (PEDG); Xi’an, China, 3–6 June 2019; pp. 178-182.

18. Zhang, C.; Li, C.; Lv, D.; Zhu, H.; Xing, H. An Experimental Study on the Effect of Multiple Lightning Waveform Parameters on the Aging Characteristics of ZnO Varistors. Electronics; 2020; 9, 930. [DOI: https://dx.doi.org/10.3390/electronics9060930]

19. Heckler, H.; Wosgien, J.; Wetter, M. New lightning current arrester design for onshore and offshore wind turbines. Proceedings of the 2011 International Symposium on Lightning Protection; Fortaleza, Brazil, 3–7 October 2011; pp. 241-246. [DOI: https://dx.doi.org/10.1109/SIPDA.2011.6088447]