The system structure of the hybrid HVDC system is shown in Figure 1. The offshore wind farms are connected to the offshore ac grid and a 12-pulse diode rectifier is used to transmit energy from the offshore ac grid to the HVDC transmission line. The power rating of the diode rectifier is equal to the capacity of the OWFs. For the conventional WTs, the ac grid voltages should be provided to realize the synchronization and the energy is needed for the black-start in the initial condition. However, the diode rectifier could not form the offshore grid voltages and transmit the active power in the opposite direction. Besides, harmonics and reactive power would be generated by the diode rectifier and should be compensated. Therefore, an auxiliary converter is applied to address these issues, which is connected in parallel with the diode rectifier at ac and dc sides.

In order to make up the drawbacks of the diode rectifier, the auxiliary converter must be fully controllable and able to transmit the active power bidirectionally. Because the auxiliary converter needs to provide the black-start energy for OWFs, the active power capacity of the auxiliary converter is about 2%–5% of the rated value of the system. In the steady-states, all the reactive power and harmonics should be compensated by the auxiliary converter. So the reactive power requirement is about 30%–40% of the rated value of the system. Chang and Cai, (2019) and Fang et al. (2022) proposed a high-ratio VSC to serve as the auxiliary converter in the hybrid HVDC system. The topology is shown in Figure 2A. This is also a new type of the modular multilevel converter, which can transmit the active power bidirectionally. The submodule branches (SMBs) withstand most of the HVDC voltage. Therefore, the dc voltage of the ac output unit (ACOU) is low and the submodules of the topology can be greatly reduced comparing with the traditional MMC. The operation principle and the parameter design methods of the hybrid converter have been fully introduced by Fang et al. (2022).

The SMBs and ACOU are all constructed by the half-bridge submodules, which are shown in Figure 2B. The self-power supply is used to supply the sub-control system and driver, which is directly acquired from the inner capacitor of the submodule. Therefore, only when the capacitor voltage is beyond a certain value, the half-bridge submodule is controllable. Before the auxiliary converter operates in the normal condition, the capacitor voltages of the submodules must be at the rated value, which makes the precharging process of the converter essential.

However, Figure 2A shows that this topology is asymmetrical, which is different from the traditional MMC. The conventional start-up and shut-down strategies cannot be used in this topology. SMBs would be firstly charged than ACOU and the energy imbalance would also exist. Therefore, the unique start-up and shut-down strategies and design methods should be proposed for this auxiliary converter.

For the hybrid HVDC system, the operation sequence is shown as follows.

1) Start-up process: Firstly, the onshore MMC should complete the precharging process and establish the HVDC voltage. Before the start-up process of the offshore hybrid converter begins, the HVDC link can be regarded as a dc source. Then turn on the switch K ₄ and complete the precharging process of the auxiliary converter. After the auxiliary converter fully starts, turn on the switch K ₂ and establish the offshore grid voltages. So the OWFs could realize the synchronization and achieve black-start. The voltage establishing and black-start processes have been explained fully in the past references, which are ignored in this paper.

In the hybrid HVDC converter, the auxiliary converter is the mainly energy storage and controllable element. Therefore, the key point of this system is on the startup and shutdown strategies of the auxiliary converter.

As for the auxiliary converter, the operation sequence is shown in Figure 3. The operation sequence is similar with the traditional MMC. It could also be divided into three parts.

1) Start-up process: After the HVDC voltage is established, turn on the switch K ₄ so the converter begins the uncontrollable precharging stage. The capacitor voltages of the submodules could not reach the rated value during this process. However, the capacitor voltages can meet the demands of the self-power supply so the auxiliary converter is controllable. Then during the controllable precharging stage, all the capacitor voltages of the submodules can be fully charged.

Although the operation process the auxiliary converter is similar with the traditional MMC, major differences exist in the specific implementation of each process between these two converters. Because of the asymmetry of auxiliary converter, the calculation method of the current-limiting resistor and the control strategies in the controllable precharging stage must be redesigned.

In the initial state, the switch K ₅ is turned off, which means the current-limiting resistor R _d1 is inserted to restrict the inrush current. Figure 4 shows the schematic diagram in the uncontrollable precharging stage. After the switch K ₄ is turned on, the capacitors of the tuned filter and the submodules are all charged from the HVDC link. According to Figure 4, the equivalent circuits of the auxiliary converter in the uncontrollable precharging stage are shown in Figure 5.

Because SMBs are series connected, they can be represented by a capacitor of which the capacitance is C _m1/N ₁. C _m1 is the capacitance of the submodule capacitor used in SMBs. N ₁ is the number of the submodules in SMBs. Also the arms of ACOU can be represented by the capacitors of which the capacitance is C _m2/N ₂. C _m2 is the capacitance of the submodule capacitor used in ACOU. N ₂ is the number of the submodules in the arm of ACOU. Therefore, the time domain equivalent circuit is shown in Figure 5A. L _m and R _m are the inductance and inner resistance of the arm inductor. C _bp is the tuned filter capacitor. L _bp and R _bp are the inductance and inner resistance of the tuned filter inductor.

The relationships between the capacitor voltages and dc voltages are shown as U dc = U 1 + U 2 U 1 = N 1 U m 1 U 2 = 2 N 2 U m 2 (1)

Where U _m1 and U _m2 are the capacitor voltages of the submodules used in SMBs and ACOU, U ₁ and U ₂ are the dc voltages of SMBs and ACOU. According to Figure 5A, U ₁ and U ₂ satisfy the following equation: U 1 / U 2 = 3 C m 2 2 N 2 N 1 C m 1 = 3 N 1 C m 2 2 N 2 C m 1 (2)

From Eqs 1, 2, the expressions of the voltages are U 1 = 3 N 1 C m 2 3 N 1 C m 2 + 2 N 2 C m 1 U dc U 2 = 2 N 2 C m 1 3 N 1 C m 2 + 2 N 2 C m 1 U dc U m 1 = 3 C m 2 U dc 3 N 1 C m 2 + 2 N 2 C m 1 U m 2 = C m 1 U dc 3 N 1 C m 2 + 2 N 2 C m 1 (3)

Therefore, the relationship between the voltages of submodule capacitors in SMBs and ACOU after the uncontrollable precharging stage is expressed as U m 1 / U m 2 = 3 C m 2 C m 1 = k 1 (4)

Usually for the modular characteristic, the submodules used in the converter are the same type, which makes U _m1 three times of U _m2. Therefore, huge energy imbalance would exist in the auxiliary converter between SMBs and ACOU after the uncontrollable precharging stage, which is different to the conventional MMC.

The value of the current-limiting resistor R _d1 would affect the peak value of the inrush current in uncontrollable precharging process. Therefore, the calculation method should be acquired to choose the proper value of this resistor. From Figure 5A, the frequency domain equivalent circuit can be acquired as shown in Figure 5B, where the equivalent value of the capacitor C _eq, the inductor L _eq and the resistor R _eq are expressed as C eq = 3 C m 1 C m 2 2 N 2 C m 1 + 3 N 1 C m 2 L eq = 2 3 L m R eq = 2 3 R m (5)

Hence, the precharging currents can be further derived as I 1 s = K 12 s 2 + K 11 s + K 10 T 4 s 4 + T 3 s 3 + T 2 s 2 + T 1 s 1 + T 0 I 2 s = K 22 s 2 + K 21 s + K 20 T 4 s 4 + T 3 s 3 + T 2 s 2 + T 1 s 1 + T 0 (6)

The expressions of the parameters in Eq. 6 are K 12 = U dc C eq L bp C bp , K 11 = U dc C eq R bp C bp , K 10 = U dc C eq K 22 = U dc C bp L eq C eq , K 21 = U dc C bp R eq C eq , K 20 = U dc C bp (7) T 4 = L eq C eq L bp C bp T 3 = C eq C bp R eq L bp + C eq C bp R bp L eq + C eq C bp R d 1 L bp + C eq C bp R d 1 L eq T 2 = L bp C bp + L eq C eq + C eq C bp R eq R bp + C eq C bp R d 1 R eq + C eq C bp R d 1 R bp T 1 = R eq C eq + R bp C bp + R d 1 C bp + R d 1 C eq T 0 = 1 (8)

It is hard to derive the time domain expression of the precharge current directly from Eq. 6. Therefore, the parameters of the system should be firstly acquired. Put theses parameters into Eqs 6–8, the frequency domain expression of the precharge current can be acquired. Also the time domain expression can be derived by the inverse Laplace-transformation. Hence, the relationship between the peak current and the current-limiting resistor can be gained.

Taking the parameters shown in Table 1 as the example, the relationship between the precharging current peak and the resistor R _d1 is shown in Figure 6. Assuming that I _set1 and I _set2 are the inrush current limit of the tuned filter and the submodules, when I _set1 is 600 A and I _set2 is 800A, the resistor R _d1 is selected as 108 Ω according to Figure 6.

After the current-limiting resistor is selected, the precharging current can be calculated and plotted according to Eqs 6–8. Besides, the corresponding simulation model is established in the Simulink. The calculation and simulation results of the precharging current are shown in Figure 7. From Figure 7 it can be seen that the calculation and simulation results are nearly the same, which verify the validity of the above analysis.

As mentioned before, the uncontrollable precharging process can only partly charge the submodule capacitors with huge energy imbalance between SMBs and ACOU. Therefore, the energy imbalance should be eliminated and the submodule capacitors should be charged to the rated value in the controllable precharging stage. Since the capacitor voltages have reached the demand value of the self-power supply after the uncontrollable precharge, the submodules become controllable.

For the auxiliary converter has the ability to generate the inner circulating voltages and current to balance the energy between SMBs and ACOU under normal condition, this operation principle can also be used during the controllable precharge stage, which is shown in Figure 8.

In Figure 8, the ACOU is equivalent by an inductor and an arm of submodules. Besides the dc voltages supported by the SMBs and ACOU, the circulating voltage u _cir is also generated in SMBs and ACOU. The circulating current control voltage Δu _cir is applied in SMBs to generate the circulating current i _cir. Figure 8 shows that the directions of the vectors of the circulating voltages in SMBs and ACOU are the opposite and the directions of i _cir and u _cir are on the same line. Hence, i _cir would generate the opposite active power in SMBs and ACOU. Ignoring the losses, the absolute value of the active power generated in SMBs and ACOU are the same and the energy is transformed between these two parts. By the circulating voltages and current, the energy balance could be achieved in the auxiliary converter. In order to charge submodule capacitors to the rated value, the dc current i _dc of the auxiliary converter is controlled by the voltage Δu _dc to increase the energy stored in the converter. Hence, the voltages in SMBs U _up and ACOU U _lo are expressed as U up = U 1 + u cir + Δ u cir − Δ u dc U lo = U 2 − u cir (9)

The control strategy of the auxiliary converter in the controllable precharging stage is shown in Figure 9. When the uncontrollable precharging stage is over, all the submodules are inserted. Firstly, the steady circulating voltages are generated in SMBs and ACOU. The amplitude of u _cir is gradually increased to the reference value. During this process, the submodules would be slightly charged and reach a new steady value. Taking this time as t _s1, the circulating current control module is applied to balance the capacitor voltages between the submodules in SMBs and ACOU. After the uncontrollable precharging process, the capacitor voltages in SMBs are 3 times of in ACOU and the dc voltages supported by SMBs and ACOU are U _dc1 and U _dc-U _dc1 respectively. This is determined by the characteristics of the topology. However, after the energy is balanced, the submodule capacitor voltages in the auxiliary converter are all the same. In this time, the dc voltages supported by the SMBs and ACOU should be according to the number of the submodules connected in series. Assuming that the dc voltages supported by SMBs and ACOU are U _dc2 and U _dc-U _dc2 respectively after the energy is balanced, the dc voltage components are expressed as U dc 1 = 3 N 1 3 N 1 + 2 N 2 U dc U dc 2 = N 1 N 1 + 2 N 2 U dc (10)

Taking this time as t _s2, the dc current control module is applied to charge the submodule voltages to the rated value furtherly. During this process, the circulating current control module is still used to maintain the energy balance. After all the submodules are fully charged, the start-up process of the auxiliary converter is finished and the control strategy can be switched to establish the offshore grid voltages.

In the energy feedback stage, the auxiliary converter tries to feed the storage energy in the submodules back to the HVDC link as much as possible. This stage can be regarded as the mirroring process of the controllable precharging stage. The control strategy shown in Figure 9 can also be used. The reference value u _cref is changed so the auxiliary converter discharge to the HVDC link. For the HVDC voltage is still supported by the converter, the capacitors cannot be fully discharged in this stage. The minimum value of the capacitor voltage is calculated as u cref _ m i n = U dc N 1 + 2 N 2 (11)

After the energy feedback process, turn off the switch K ₄ to disconnect the auxiliary converter from the HVDC link. Then turn off the switch K ₅ and turn on the switch K ₆ so that the tuned filter capacitor is discharged through the resistor R _d1 and R _d2, which is shown in Figure 10A. During this process, all the submodules are blocked. For the resistor R _d1 is designed for the uncontrollable precharging process, the discharging current of the tuned filter capacitor can be guaranteed below the limited value.

After this capacitor is fully discharged, turn on the switch K ₅ and insert the submodules group by group. For only several submodules are inserted to discharge every time, the voltage and power level of the energy dissipation resistor R _d2 can be a low value. As mentioned before, the submodule would be blocked automatically if the capacitor voltage is below a certain value. Therefore, the submodule capacitors cannot be fully discharged during this stage. The remaining voltage is discharged through the inner resistor R ₀ of the submodule as shown in Figure 10C, which is defined as the uncontrollable energy dissipation stage. Due to the large resistance of the inner resistor of the submodule, the discharging time in this stage is much more longer than other stages.

The simulation model is built in the Matlab/Simulink based on the parameters shown in Table 1. The system structure is shown in Figures 1, 2. In order to accelerate the simulating speed, the onshore MMC converter is replaced by a DC source. In the initial states, the capacitor voltages of the submodules are zero. Switches K ₁- K ₆ are turned off.

Figure 11 shows the simulation results of the start-up process. At 0s, the switch K ₄ is turned on hence the uncontrolled precharging stage S1 is started. It can be seen that the submodule capacitors are charged preliminary from Figure 11A. The capacitor voltage of SMBs is three times of the ACOU, which is consistent with the theoretical analysis. From Figure 11B, the tuned filter capacitor is fully charged in this stage. At 0.5 s, the circulating voltages generating stage begins, which is S2. In this stage, u _cir are formed in SMBs and ACOU gradually for the energy balancing process. The capacitors would be slightly charged. At 0.8 s, the circulating current control module is applied and energy balancing stage S3 begins. It can be seen that the submodule voltages of SMBs and ACOU are gradually approached. Eventually at 2 s, the capacitor voltages become the same. Then the dc current control module is applied at dc voltage charging stage S4. During this stage, the capacitor voltages of SMBs will reach the rated value firstly. Then through the energy balancing control, ACOU can be gradually charged. All the submodule capacitor voltages in the auxiliary converter will reach the rated value at 3 s and the precharging process is finished.

Figure 11C shows the circulating current during the start-up process. The simulation results in S1 are mainly shown in Figure 7. Figures 11C,D shows the simulation results of S2, S3, and S4. It can be seen that the circulating current is generated in S3 and S4 to balance the voltages of the submodules. The frequency of the circulating current is 300 Hz and the amplitude is limited to 500 A. Only when the capacitor voltages in SMBs and ACOU are different, the circulating current is generated. Figure 11D shows the dc current during the start-up process. In S3, the energy is flowing inside the auxiliary converter. So there is no dc current. In S4, the auxiliary converter charges from the dc side so that the dc current is instantly increased and the submodules are fully charged.

Figures 12, 13 shows the simulation results of the shut-down process. In the energy feedback stage S5, the capacitor voltages of the submodules in SMBs decrease firstly. Then, the capacitor voltages of the submodules in ACOU decrease by the circulating current control module. The operation principle of this stage is similar to S4. Eventually, all the capacitor voltages of the submodules decrease to 1400 V. At 1.5 s, turn off the switches K ₄, K ₅ and turn on the switch K ₆. The tuned filter capacitor discharges through R _d1 and R _d2 as shown in Figure 12C and 13B, which is S6. At 2.5 s, turn on the switch K ₅ and the energy dissipation stage S7 begins. Two submodules are inserted every time. The inserted submodules would discharge to 0.5 kV, which is the disenabling voltage U _blk of the self-power supply in the submodules. After about 2.3 s, all the submodules are discharged to 0.5 kV. From Figure 13A it can be seen that the discharging current of the submodules in SMBs is higher than in ACOU. This is because the inductor in the discharging circuit of the submodules in SMBs is 2/3L _m, which is 2L _m in ACOU. After the controllable energy dissipation stage, the submodule capacitors need to be fully discharged by the inner resistor. For the changing law of the voltages of the submodule capacitors is simple and the discharging time is very long, this process is not shown in the simulation results.

The hardware-in-the-loop experiments are conducted in the RT-LAB real time simulator and a general-purpose DSP controller, which is shown in Figure 14. The step time of RT-LAB is 10μs and the control frequency of DSP is 20 kHz. The parameters used in the experiments is also from Table 1. The host computer is used to establish the real-time simulation model in RT-LAB and program in the DSP controller. RT-LAB and DSP controllable communicate through a transfer board. The electrical quantities such as the voltages and currents would be measured and sampled firstly. Then those signals are transmitted to the DSP controller and the control signal are acquired and transmitted back to the RT-LAB to control the model of the hybrid DC converter. The host computer can control all the switches and decide the implementation of the control modules. The results are outputted by the RT-LAB and displayed in the scope.

Figure 15 shows the experimental results of the start-up and shut-down process. All the stages during the process are switched manually. Therefore, Stages S1-S7 are not continuous. The meanings of S1-S7 are the same as the simulation results discussed in Section 5. In the experimental results, u _c1 is the voltage of the submodule capacitors in SMBs. u _c2 is the voltage of the submodule capacitors in ACOU. u _bp is the voltage of the tuned filter capacitor. I _cir is the current flowing to the tuned filter. Since the submodules set in the experiments are not affected by the self-power supply, all the submodules can be fully discharged during the controllable energy dissipation stage. Figure 15A shows that the tuned filter capacitor is fully charged and the submodule capacitors are partly charged. u _c1 is still 3 times of u _c2 after the uncontrollable precharging stage S1. In S2, the circulating voltages are established in SMBs and ACOU. As a result, the capacitor voltages in SMBs and ACOU are balanced in S3 by the circulating current. In S4, all the submodules in the auxiliary converter are fully charged.

In S5, the shut-down process begins. Part of the storage energy in the submodules is fed back to the HVDC link. In S6, the tuned filter capacitor is fully discharged by the dissipation resistor. All the submodules can be fully discharged in S7. The experimental results are highly consistent with the simulation results and the analysis, which verify the validity of the proposed start-up and shut-down strategy of the hybrid dc converter.