HVDC Transmission Technology of Wind Power System with Multi-Phase PMSG

The high voltage DC (HVDC) transmission technology of wind power system, with multi-phase permanent magnetic synchronous generator (PMSG) is proposed in this paper. Each set of three-phase winding of the multi-phase PMSG was connected to a diode rectifier. The output of the diode rectifier was connected by several parallel isolated DC–DC converters. Each DC–DC converter was connected to a sub-module (SM). All SMs and two inductors were connected in a series. The proposed wind power system has several advantages including, transformerless operation, low cost, low voltage stress, and high fault tolerance. The maximum power point tracking (MPPT) and energy balance of the DC–DC converters were achieved by controlling the duty cycles of the DC–DC converters. The HVDC transmission was achieved by the nearest level control (NLC) with voltage sorting. The simulation model with 18-phase PMSG was established. Experimental results were also studied based on RT-Lab.


Introduction
Offshore wind farms (OWFs) have attracted considerable attention over recent years, as wind-based resource is particularly abundant far off shore [1].The design, characteristic analysis, and control of wind power systems, based on permanent magnetic synchronous generator PMSG, have been studied recently [2][3][4][5].The conventional transmission method for offshore wind farm is high voltage AC (HVAC) transmission [6].The voltage of PMSG is converted to a fixed frequency fixed magnitude voltage with the help of a back-to-back voltage source converter (VSC), and is then boosted to a relative high voltage by a transformer [7].Compared with HVAC transmission, high voltage DC (HVDC) transmission has received extensive attention for offshore wind farms as it shows significant advantages, such as no reactive power, less need for cable, and low power loss [8,9].
To achieve HVDC transmission, a hybrid AC-DC offshore wind power plant (OWPP) topology has been proposed in reference [10], as shown in Figure 1a.With this topology, the power is delivered to the DC grid by a centralized AC-DC rectifier, which is usually implemented by a multi-modular converter (MMC).The costs are heavy, as an offshore platform is needed to install the transformer and centralized rectifier.To reduce costs, the centralized AC-DC converter has been realized by use of a diode rectifier as highlighted in reference [11].However, in this case the DC voltage fluctuates significantly.An alternative was is to replace the distributed DC-AC converters with a centralized DC-AC converter, but the decrease in cost is limited [12].As a trade-off between HVDC and HVAC, the fractional frequency transmission system was proposed in reference [13].In this system, the AC-DC-AC converters are eliminated to reduce costs, but the system is only suitable for fixed speed wind power generators.
To remove the need for an offshore platform, the topology of DC power collection has been proposed in references [14,15], as is shown in Figure 1b.Each wind turbine is connected to the DC bus by an AC-DC-DC converter.As the terminal voltage of PMSG is usually low, high boost ratio is required [16].The H-bridge DC-DC topology is commonly used to improve the efficiency of DC-DC converters [17].The output voltage of a DC-DC converter is equal to the HVDC transmission voltage, which is commonly very high, so it is usually realized by MMC [18].A centralized DC-DC converter has been proposed in reference [19] to substitute the distributed DC-DC converters, which causes increased costs as it needs an offshore platform.
In reference [20], the DC sides of the converters were connected in series to boost the DC transmission voltage directly, as shown in Figure 1c.This system avoids the use of an offshore platform and high boost ratio DC-DC converters, but the voltage of every DC turbine is different under unequal wind speeds, which is a potential danger.One way is to reduce the captured energy of a wind power generator [21], which will deteriorate the efficiency of the wind farm.In reference [22], the onshore inverter station regulated the DC transmission current, while each wind turbine regulated its own injection power.In this way, the MPPT can be realized, but it is infeasible when there are several parallel clusters of series-connected wind turbines.In reference [23], an improved rotor speed control to store the energy in the wind turbine rotor was studied, but the PMSG faced the danger of overvoltage when the rotor stored such a high level of energy.In reference [24], flywheel energy storage system was applied for energy storage.In reference [25], an energy storage system (ESS) was connected to the DC bus of each wind power generation system to compensate the DC voltage fluctuation, which incurs a heavy cost burden.DC-AC converters are eliminated to reduce costs, but the system is only suitable for fixed speed wind power generators.
To remove the need for an offshore platform, the topology of DC power collection has been proposed in references [14,15], as is shown in Figure 1b.Each wind turbine is connected to the DC bus by an AC-DC-DC converter.As the terminal voltage of PMSG is usually low, high boost ratio is required [16].The H-bridge DC-DC topology is commonly used to improve the efficiency of DC-DC converters [17].The output voltage of a DC-DC converter is equal to the HVDC transmission voltage, which is commonly very high, so it is usually realized by MMC [18].A centralized DC-DC converter has been proposed in reference [19] to substitute the distributed DC-DC converters, which causes increased costs as it needs an offshore platform.
In reference [20], the DC sides of the converters were connected in series to boost the DC transmission voltage directly, as shown in Figure 1c.This system avoids the use of an offshore platform and high boost ratio DC-DC converters, but the voltage of every DC turbine is different under unequal wind speeds, which is a potential danger.One way is to reduce the captured energy of a wind power generator [21], which will deteriorate the efficiency of the wind farm.In reference [22], the onshore inverter station regulated the DC transmission current, while each wind turbine regulated its own injection power.In this way, the MPPT can be realized, but it is infeasible when there are several parallel clusters of series-connected wind turbines.In reference [23], an improved rotor speed control to store the energy in the wind turbine rotor was studied, but the PMSG faced the danger of overvoltage when the rotor stored such a high level of energy.In reference [24], flywheel energy storage system was applied for energy storage.In reference [25], an energy storage system (ESS) was connected to the DC bus of each wind power generation system to compensate the DC voltage fluctuation, which incurs a heavy cost burden.With the increasing capacity of wind power generators, the multi-phase PMSG has the advantages of low stator current and high fault tolerance [26].The mathematical model of a 12-phase flux-switching PMSG for wind power generation has been studied in [27].The series-connected multi-half-bridge modules converter for integrating m-phase PMSG with HVDC has been highlighted in [28], which can offer a transformerless operation with an AC-DC boosting gain of 2 m.However, the highest insulation level of generator phases is equal to the HVDC transmission voltage.Besides, the process has a problem of relatively low fault tolerant capability as a failure in any phase yields a complete system shutdown.To overcome the shortcomings mentioned above, this paper proposes a novel topology of wind power systems based on multi-phase PMSG with HVDC, which has the advantages of transformerless operation, low cost, low voltage stress of stator windings, and high fault tolerance.
This paper is organized as follows.The novel topology of wind power system based on multiphase PMSG with HVDC and its working principles are analyzed in Section II.The control methods of the novel topology are developed in Section III.The simulation and experiment are discussed in Section IV.Section V concludes this paper.With the increasing capacity of wind power generators, the multi-phase PMSG has the advantages of low stator current and high fault tolerance [26].The mathematical model of a 12-phase flux-switching PMSG for wind power generation has been studied in [27].The series-connected multi-half-bridge modules converter for integrating m-phase PMSG with HVDC has been highlighted in [28], which can offer a transformerless operation with an AC-DC boosting gain of 2 m.However, the highest insulation level of generator phases is equal to the HVDC transmission voltage.Besides, the process has a problem of relatively low fault tolerant capability as a failure in any phase yields a complete system shutdown.To overcome the shortcomings mentioned above, this paper proposes a novel topology of wind power systems based on multi-phase PMSG with HVDC, which has the advantages of transformerless operation, low cost, low voltage stress of stator windings, and high fault tolerance.
This paper is organized as follows.The novel topology of wind power system based on multi-phase PMSG with HVDC and its working principles are analyzed in Section 2. The control methods of the novel topology are developed in Section 3. The simulation and experiment are discussed in Section 4. Section 5 concludes this paper.

System Topology
The topology of the proposed wind power system with multi-phase PMSG is shown in Figure 2. The multi-phase PMSG has several sets of three-phase windings.Each set of three-phase winding is connected to a diode rectifier.The outputs of the diode rectifiers are connected by N parallel isolated DC-DC converters.Each DC-DC converter is connected to a SM.The diode rectifiers, N parallel isolated DC-DC converters, and N SMs, which are connected to the same set of three-phase winding, are regarded as a converter group.On the grid side, all SMs and two inductors are connected in a series, which has the same structure as one phase of MMC.Therefore, the control strategy for DC transmission voltage can refer to that of MMC.

System Topology
The topology of the proposed wind power system with multi-phase PMSG is shown in Figure 2. The multi-phase PMSG has several sets of three-phase windings.Each set of three-phase winding is connected to a diode rectifier.The outputs of the diode rectifiers are connected by N parallel isolated DC-DC converters.Each DC-DC converter is connected to a SM.The diode rectifiers, N parallel isolated DC-DC converters, and N SMs, which are connected to the same set of three-phase winding, are regarded as a converter group.On the grid side, all SMs and two inductors are connected in a series, which has the same structure as one phase of MMC.Therefore, the control strategy for DC transmission voltage can refer to that of MMC.

Converters ( group 1 to 6)
The first converter group  The use of a diode rectifier can greatly reduce the costs and enhance the reliability of the wind power generation system [29].However, when a diode rectifier is used in three-phase PMSG wind power generation system, the low order harmonics (mainly 5th and 7th) of stator currents will lead to high level of electromagnetic torque ripple.While in the multi-phase PMSG, the harmonic magneto motive forces, caused by harmonic currents, can be greatly weakened.Accordingly, the electromagnetic torque ripple decreases significantly.The stator coils are isolated from the high DC transmission voltage by isolated DC-DC converters.So, they only endure low voltage stress.The use of a diode rectifier can greatly reduce the costs and enhance the reliability of the wind power generation system [29].However, when a diode rectifier is used in three-phase PMSG wind power generation system, the low order harmonics (mainly 5th and 7th) of stator currents will lead to high level of electromagnetic torque ripple.While in the multi-phase PMSG, the harmonic magneto motive forces, caused by harmonic currents, can be greatly weakened.Accordingly, the electromagnetic torque ripple decreases significantly.The stator coils are isolated from the high DC transmission voltage by isolated DC-DC converters.So, they only endure low voltage stress.
Apparently, the larger the number of parallel isolated DC-DC converter is, the higher the grid voltage will be.N can be formulated by, where, U HVDC and U DR are the DC transmission voltage and DC side voltage of a diode rectifier, respectively.n phase is the phase number of multi-phase PMSG.K boost is the boost ratio of DC-DC converter.
Obviously, the analyses and conclusions exhibited in this paper are applicable for any multi-phase PMSG, only if the phase amount of PMSG is a multiple of three.

Working Principles
The stator currents are closely relative to the DC voltages of diode rectifiers.The higher the DC voltages are, the lower the stator currents will be.The rotor speed of PMSG is entirely determined by the stator currents.Therefore, to achieve speed control, and finally achieve MPPT, the DC voltages of diode rectifiers must be controlled which can be realized by controlling the duty cycles of isolated DC-DC converters.
The energy captured by PMSG will charge the SM capacitors, and then increase the voltages of the SM capacitors.When one SM is switched on (that means the upper IGBT being on and the lower IGBT being off), its capacitor will deliver energy to the HVDC grid and the capacitor voltage decreases.To sum up, we can know that if the voltages of the SM capacitors are controlled to be constant, the energy captured by PMSG will be entirely delivered to the HVDC grid.

Cost Analysis
The system costs are mainly relative to the power volume.Supposing that the power volume of PMSG is S, the total power volume of diode rectifiers is about 3.5S as each diode must endure line voltage and phase current.The total power volumes of IGBTs and diodes used in DC-DC converters are both 4S.The total power volume of IGBTs used in SMs is 2S.The total power volume of the high frequency transformers used in DC-DC converters is S.So the total power volumes of IGBTs, diodes and transformers used in the novel topology are 6S, 7.5S, and S, respectively.
For the topology shown in Figure 1a, the total power volume of IGBTs used in an AC-DC-AC converter is about 7S, as each IGBT must endure line voltage and phase current.The total power volume of IGBTs used in an MMC based centralized AC-DC converter is about 7S.For the topology shown in Figure 1b, the total power volume of IGBTs used in AC-DC converters is about 3.5S.The total power volume of IGBTs used in an MMC based DC-DC converter is 12S.For the topology shown in Figure 1c, the total power volume of IGBTs used in an AC-DC converter is about 3.5S.The total power volumes of IGBTs and diodes used in DC-DC converters are both 4S.
The costs and characteristics of the four topologies are compared, as given in Table 1.It can be seen that the power devices of the proposed topology are far less than those of topology one and topology two, while slightly more than those of topology three.But the novel topology doesn't need ESS, which is a heavy cost in engineering.Overall, the proposed topology has advantages in regards to cost.

Control Method
The control method is divided into two parts: The MPPT control and the DC transmission current control.The MPPT control aims to achieve optimal tip speed ratio.The DC transmission current control aims to deliver the power captured by PMSG to the DC transmission grid and balance the capacitor voltages of SMs.

MPPT Control
To achieve MPPT, the tip speed ratio is supposed to be at its optimal value [30].Thus the rotor speed reference ω re f is formulated by, where, λ opt is the optimal tip speed ratio, v is the wind speed, R is the blade radius.When the rotor speed is higher than ω re f , in order to achieve MPPT, the output currents of the diode rectifiers need to increase to lower down the rotor speed.Thus, the conventional PI controller, PID controller and PR controller can all be used to adjust the rotor speed.For convenience, the PI controller is chosen in this paper to get the diode rectifier output current reference i ref , where, ω is the rotor speed, k p1 and k i1 are the proportional and integral coefficients, respectively.The output voltage of the DC-DC converter is controlled to equal its rated value by DC transmission current controller, which will be discussed in the next section.If the duty cycle of DC-DC converter rises, the input voltage of DC-DC converter falls correspondingly.The decreasing input voltage of DC-DC converter causes the output current of diode rectifier rising.Therefore, if the output current of diode rectifier is higher than its reference, the input voltage of DC-DC converter needs to rise and the duty cycle needs to fall.As in Equation (3), the duty cycle of DC-DC converter D k is expressed by, where, i k is the output current of the kth diode rectifier; D k is the duty cycle of the DC-DC converter in the kth converter group; k p2 and k i2 are the proportional and integral coefficients, respectively.The input voltages of the parallel DC-DC converters, following the same diode rectifier, are the same, while the corresponding output voltages are not the same as the parameters can't be exactly the same.Accordingly, an energy balance controller is designed to ensure the energy balance of all DC-DC converters.
The average current of the parallel DC-DC converters is expressed by, where, i kj is the input current of the jth DC-DC converter in the kth converter group.
In order to balance the energy of DC-DC converters, a PI controller is used to get the extra duty cycle ∆D kj , as expressed by, where, k p3 and k i3 are the proportional and integral coefficients, respectively.The final duty cycle is achieved by (7), Energies 2018, 11, 3294 6 of 16 The scheme of MPPT controller is shown in Figure 3.

DC Transmission Current Control
The scheme of DC transmission current controller is shown in Figure 4.The DC transmission current id is proportional to the transmission power as the DC transmission voltage UHVDC is commonly constant.If the average value of all SM capacitor voltages is higher than its rated value, id is supposed to increase.Therefore the reference value of DC transmission current can be expressed by,

NLC
where, UCref is the rated capacitor voltage of SM, kp4 and ki4 are the proportional and integral coefficients, respectively.UC_ave is the average value of all SM capacitor voltages, and is formulated by, where, UCkj is the capacitor voltage of the jth SM in the kth converter group.
If the DC transmission current id is higher than its reference value id_ref, the DC transmission voltage UHVDC is supposed to fall to decrease the DC transmission current.Just like (3), UHVDC can be formulated by,

DC Transmission Current Control
The scheme of DC transmission current controller is shown in Figure 4.The scheme of MPPT controller is shown in Figure 3.

DC Transmission Current Control
The scheme of DC transmission current controller is shown in Figure 4.The DC transmission current id is proportional to the transmission power as the DC transmission voltage UHVDC is commonly constant.If the average value of all SM capacitor voltages is higher than its rated value, id is supposed to increase.Therefore the reference value of DC transmission current can be expressed by, where, UCref is the rated capacitor voltage of SM, kp4 and ki4 are the proportional and integral coefficients, respectively.UC_ave is the average value of all SM capacitor voltages, and is formulated by, where, UCkj is the capacitor voltage of the jth SM in the kth converter group.
If the DC transmission current id is higher than its reference value id_ref, the DC transmission voltage UHVDC is supposed to fall to decrease the DC transmission current.Just like (3), UHVDC can be formulated by, The DC transmission current i d is proportional to the transmission power as the DC transmission voltage U HVDC is commonly constant.If the average value of all SM capacitor voltages is higher than its rated value, i d is supposed to increase.Therefore the reference value of DC transmission current can be expressed by, where, U Cref is the rated capacitor voltage of SM, k p4 and k i4 are the proportional and integral coefficients, respectively.U C_ave is the average value of all SM capacitor voltages, and is formulated by, where, U Ckj is the capacitor voltage of the jth SM in the kth converter group.If the DC transmission current i d is higher than its reference value i d_ref , the DC transmission voltage U HVDC is supposed to fall to decrease the DC transmission current.Just like (3), U HVDC can be formulated by, where, k p5 and k i5 are the proportional and integral coefficients, respectively.Finally, the required DC transmission voltage U HVDC is realized by nearest level control (NLC) with voltage sorting [31].

Simulation Results
To verify the performances of the proposed topology and its control methods, a simulation model with MATLAB/SIMULINK was setup.The simulation parameters are listed in Table 2.In this simulation, the wind speed changed from 10.2 m/s to 8.9 m/s gradually during 1.0 s to 1.5 s.The simulation results are shown in Figure 5.
The DC transmission voltage and current were initially 12.015 kV and 157.5 A. From 1.0 s to 1.5 s, The DC transmission current changed from 157 A to 104.6 A gradually.Compared to that of before 1 s, the DC transmission voltage declined slightly after 1.5 s, as shown in Figure 5a clearly.The reason for this is that the reduction of DC transmission current weakened the anti-electromotive force of inductor.The wind power coefficient maintained a constant 0.48, which meant that the proposed controller could achieve MPPT [32], as shown in Figure 5b.
In Figure 5c, it can be seen that the terminal voltage of PMSG decreased from 690 V to 617 V, and its frequency decreased from 3.5 Hz to 3.068 Hz.The reason for this is that when the wind speed decreased, the rotor speed decreased to maintain the tip speed ratio at its optimal value.Accordingly, the amplitude and frequency of the terminal voltage of PMSG both decreased.
The electromagnetic torque was 1.1075 MN•m with a ripple of 0.17%.The ripple was very small because the special structure of eighteen-phase generator eliminated the bad effect induced by the low order harmonics of stator currents.Its main ripple frequency was 125 Hz, which was 36 times of fundamental frequency, approximately.After the wind speed changed to a new stable stage, the torque decreased to 847.98 kN•m with a ripple of less than 0.1%, which is shown in Figure 5d.During the process, the voltages of SM capacitors were all about 1000 V, while the currents of DC-DC converters decreases from 81.6 A to 59.3 A with a maximum unbalance degree of 1.3%, which are shown in Figure 5e,f with different color lines, respectively.These results indicate that the control scheme can achieve MPPT and HVDC transmission effectively.The DC transmission voltage and current were initially 12.015 kV and 157.5 A. From 1.0 s to 1.5 s, The DC transmission current changed from 157 A to 104.6 A gradually.Compared to that of before 1 s, the DC transmission voltage declined slightly after 1.5 s, as shown in Figure 5a clearly.The reason for this is that the reduction of DC transmission current weakened the anti-electromotive force of inductor.The wind power coefficient maintained a constant 0.48, which meant that the proposed controller could achieve MPPT [32], as shown in Figure 5b.
In Figure 5c, it can be seen that the terminal voltage of PMSG decreased from 690 V to 617 V, and its frequency decreased from 3.5 Hz to 3.068 Hz.The reason for this is that when the wind speed

One DC-DC Converter Breaks Down
In this simulation, the first DC-DC converter in the 1st converter group broke down and was cut off at 0.5 s.The simulation results are given in Figure 6.In this simulation, the first DC-DC converter in the 1st converter group broke down and was cut off at 0.5 s.The simulation results are given in Figure 6.As can be seen from Figure 6a, the DC transmission current suffered an obvious drop at 0.5 s, which was caused by the fact that the broken-down DC-DC converter couldn't deliver power anymore.The total power of PMSG was shared by the normal DC-DC converters immediately, with the control of energy balance controller.As a result, the DC transmission voltage and current were both equal to the results of simulation A, while the currents of the DC-DC converters rose from 81.6 A to 85.2 A, as shown in Figure 6f.As can be seen from Figure 6a, the DC transmission current suffered an obvious drop at 0.5 s, which was caused by the fact that the broken-down DC-DC converter couldn't deliver power anymore.The total power of PMSG was shared by the normal DC-DC converters immediately, with the control of energy balance controller.As a result, the DC transmission voltage and current were both equal to the results of simulation A, while the currents of the DC-DC converters rose from 81.6 A to 85.2 A, as shown in Figure 6f.
The electromagnetic torque ripple also slightly increased with a ripple frequency of 6 times of the fundamental frequency of the terminal voltage of PMSG, which is shown in Figure 6e.The reason is that the output power of the first converter group was less than those of the other five normal converter groups.
The wind coefficient also fluctuated around 0.48, as shown in Figure 6b.The capacitor voltage of the SM which was connected to the broken-down DC-DC converter decreased to 993 V, while the capacitor voltages of the normal SMs were all still 1000 V, which verifies the high fault tolerance of the proposed topology.

One Set of Three-Phase Winding Is Open Circuited
In this simulation, the first set of three-phase winding was open circuited at 0.5 s.The simulation results are given in Figure 7.
results are given in Figure 7.
As can be seen from Figure 7a, the DC transmission current dropped to 123 A when the first set of three-phase winding was open circuited suddenly, and the current ripple also increased.The current of each DC-DC converter was 96.7 A, as shown in Figure 7f with different color lines, respectively.The reason for this is that only five sets of three-phase windings were available to deliver the power, so the current became about 6/5 times that of its original value.
The fluctuation of wind coefficient also increased, as shown in Figure 7b.The torque ripple increased to 1.8%, which is because the MMF, excited by the five three-phase windings, was no longer symmetrical due to the lack of one set of three-phase winding.
The SM voltages are shown in Figure 7e with different color lines, respectively.It can be seen that although the voltage ripple increased to 1%, the capacitor voltages of SMs connected to the normal windings still fluctuated around 1000 V, which further proves the high fault tolerance of the topology.
Note that, the blue line and red line denote the DC transmission voltage and current in Figure 5a, 6a and 7a, respectively.

Experiment Results
The RT-Lab HILS experiment setup was applied to verify the performance of the proposed topology, as shown in Figure 8.The TMS320F28335 was selected as the DSP controller, and RT-lab OP5600 was used to simulate the wind power system with multi-phase PMSG.The experiment As can be seen from Figure 7a, the DC transmission current dropped to 123 A when the first set of three-phase winding was open circuited suddenly, and the current ripple also increased.The current of each DC-DC converter was 96.7 A, as shown in Figure 7f with different color lines, respectively.The reason for this is that only five sets of three-phase windings were available to deliver the power, so the current became about 6/5 times that of its original value.
The fluctuation of wind coefficient also increased, as shown in Figure 7b.The torque ripple increased to 1.8%, which is because the MMF, excited by the five three-phase windings, was no longer symmetrical due to the lack of one set of three-phase winding.
The SM voltages are shown in Figure 7e with different color lines, respectively.It can be seen that although the voltage ripple increased to 1%, the capacitor voltages of SMs connected to the normal windings still fluctuated around 1000 V, which further proves the high fault tolerance of the topology.
Note that, the blue line and red line denote the DC transmission voltage and current in Figures 5-7, respectively.

Experiment Results
The RT-Lab HILS experiment setup was applied to verify the performance of the proposed topology, as shown in Figure 8.The TMS320F28335 was selected as the DSP controller, and RT-lab OP5600 was used to simulate the wind power system with multi-phase PMSG.The experiment parameters were all the same of those in the simulations.

Experiment Results
The RT-Lab HILS experiment setup was applied to verify the performance of the proposed topology, as shown in Figure 8.The TMS320F28335 was selected as the DSP controller, and RT-lab OP5600 was used to simulate the wind power system with multi-phase PMSG.The experiment parameters were all the same of those in the simulations.

Wind Speed Changes
Figure 9 shows the experiment results when the wind speed changed from 10.2 m/s to 8.9 m/s gradually.
The DC transmission voltage was about 12 kV, while the DC transmission current decreased from 157 A to 104 A gradually.The electromagnetic torque also decreased from 1.1 MN•m to 0.85 MN•m as the wind speed decreased.The ripple of electromagnetic torque was very small, which highlights the advantage of multi-phase PMSG.The SM capacitor voltages fluctuated around 1 kV during the time of wind speed change.The currents of the DC-DC converters in the first converter group decreased from 82 A to 59 A. The experimental results indicated that the proposed control method could achieve MPPT and HVDC transmission effectively, and it also exhibited a good dynamic characteristic when wind speed changes.The DC transmission voltage maintained at 12 kV, while the DC transmission current decreased   The DC transmission voltage maintained at 12 kV, while the DC transmission current decreased at the time of DC-DC converter break down, which was caused by the sudden power loss of the broken-down DC-DC converter.After the broken-down DC-DC converter was cut off, the ripple of electromagnetic torque rose, which is in accordance with the simulation analysis.The first SM capacitor voltage decreased to 990 V after the broken-down DC-DC converter was cut off, which was due to that the first SM no longer absorbing energy and no longer participating in NLC.The current of the broken-down DC-DC converter declined to zero, while the currents of the normal DC-DC converters increased to 85 A with a ripple of 5 A. The experimental results indicated that the proposed topology exhibited high fault tolerance, and the control method can ensure the energy balance of DC-DC converters.The change of DC transmission voltage was tiny, while the DC transmission current dropped immediately when the first set of three-phase winding was open circuited, which was caused by the sudden power loss of the open circuited winding set.The ripple of electromagnetic torque was large, which was caused by the asymmetrical MMF.All normal SM capacitor voltages kept at 1000 V.The currents of DC-DC converters connected to the open-circuited winding set decreased to zero.In order to deliver the same power, the currents of the normal DC-DC converters increased to about 98 A. These experiment results confirm the validity of the control scheme.

Conclusions
The HVDC transmission technology of wind power system with multi-phase PMSG is proposed in this paper, which has the advantages of transformerless operation, low cost, low voltage stress, and high fault tolerance.The MPPT control, energy balance control, and transmission current control are discussed in detail.The simulation and experiment results showed that during the steady state, the ripple of electromagnetic torque was less than 0.17% and the unbalance degree of currents of DC-DC converters was only 1.3%.Furthermore, the power captured by PMSG can all be delivered to the grid by the normal converters when some converters suffer outage.Overall, our results show that the In order to deliver the same power, the currents of the normal DC-DC converters increased to about 98 A. These experiment results confirm the validity of the control scheme.

Conclusions
The HVDC transmission technology of wind power system with multi-phase PMSG is proposed in this paper, which has the advantages of transformerless operation, low cost, low voltage stress, and high fault tolerance.The MPPT control, energy balance control, and transmission current control are discussed in detail.The simulation and experiment results showed that during the steady state,

Figure 1 .
Figure 1.Topologies of traditional offshore wind farm: (a) Centralized rectifier; (b) DC power collection; (c) Series connected in DC side.

Figure 1 .
Figure 1.Topologies of traditional offshore wind farm: (a) Centralized rectifier; (b) DC power collection; (c) Series connected in DC side.

Figure 2 .
Figure 2. The topology of the proposed wind power generation system with multi-phase permanent magnetic synchronous generator (PMSG) based on high voltage DC (HVDC).

Figure 2 .
Figure 2. The topology of the proposed wind power generation system with multi-phase permanent magnetic synchronous generator (PMSG) based on high voltage DC (HVDC).

Figure 3 .
Figure 3.The scheme of the maximum power point tracking (MPPT) controller.

Figure 4 .
Figure 4.The scheme of DC transmission current controller.

Figure 3 .
Figure 3.The scheme of the maximum power point tracking (MPPT) controller.

Figure 3 .
Figure 3.The scheme of the maximum power point tracking (MPPT) controller.

Figure 4 .
Figure 4.The scheme of DC transmission current controller.

Figure 4 .
Figure 4.The scheme of DC transmission current controller.

Figure 5 .
Figure 5. Simulation results when system is on transient operation: (a) DC transmission voltage and current; (b) Wind power coefficient; (c) Terminal voltage of PMSG; (d) Electromagnetic torque; (e) sub-module (SM) capacitor voltages; (f) Currents of DC-DC converters.

Figure 5 .
Figure 5. Simulation results when system is on transient operation: (a) DC transmission voltage and current; (b) Wind power coefficient; (c) Terminal voltage of PMSG; (d) Electromagnetic torque; (e) sub-module (SM) capacitor voltages; (f) Currents of DC-DC converters.

Figure 6 .
Figure 6.Simulation results when one DC-DC converter breaks down: (a) DC transmission voltage and current; (b) Wind power coefficient; (c) Terminal voltage of PMSG; (d) Electromagnetic torque; (e) SM capacitor voltages; (f) Currents of DC-DC converters.

Figure 6 .
Figure 6.Simulation results when one DC-DC converter breaks down: (a) DC transmission voltage and current; (b) Wind power coefficient; (c) Terminal voltage of PMSG; (d) Electromagnetic torque; (e) SM capacitor voltages; (f) Currents of DC-DC converters.

Figure 7 .
Figure 7. Simulation results when one set of three-phase winding was open circuited: (a) DC transmission voltage and current; (b) Wind power coefficient; (c) Terminal voltage of PMSG; (d) Electromagnetic torque; (e) SM capacitor voltages; (f) Currents of DC-DC converters.

Figure 7 .
Figure 7. Simulation results when one set of three-phase winding was open circuited: (a) DC transmission voltage and current; (b) Wind power coefficient; (c) Terminal voltage of PMSG; (d) Electromagnetic torque; (e) SM capacitor voltages; (f) Currents of DC-DC converters.

Figure 7 .
Figure 7. Simulation results when one set of three-phase winding was open circuited: (a) DC transmission voltage and current; (b) Wind power coefficient; (c) Terminal voltage of PMSG; (d) Electromagnetic torque; (e) SM capacitor voltages; (f) Currents of DC-DC converters.

Figure 9 .
Figure 9. Experiment results when wind speed changes: (a) DC transmission voltage and current; (b) Terminal voltage of PMSG and electromagnetic torque; (c) SM capacitor voltages; (d) Currents of DC-DC converters.

Figure 10 .
Figure 10.Experiment results when one DC-DC converter broke down: (a) DC transmission voltage and current; (b) Terminal voltage of PMSG and electromagnetic torque; (c) SM capacitor voltages; (d) Currents of DC-DC converters.

Figure 9 . 16 Figure 9 .
Figure 9. Experiment results when wind speed changes: (a) DC transmission voltage and current; (b) Terminal voltage of PMSG and electromagnetic torque; (c) SM capacitor voltages; (d) Currents of DC-DC converters.4.2.2.One DC-DC Converter Breaks DownFigure10shows the experiment results when the first DC-DC converter in the first converter group broke down.

Figure 10 .
Figure 10.Experiment results when one DC-DC converter broke down: (a) DC transmission voltage and current; (b) Terminal voltage of PMSG and electromagnetic torque; (c) SM capacitor voltages; (d) Currents of DC-DC converters.

Figure 10 .
Figure 10.Experiment results when one DC-DC converter broke down: (a) DC transmission voltage and current; (b) Terminal voltage of PMSG and electromagnetic torque; (c) SM capacitor voltages; (d) Currents of DC-DC converters.

4. 2 . 3 .
Figure 11 shows the experiment results when the first set of three-phase winding was open circuited.

Figure 11 .
Figure 11.Experiment results when one set of three-phase winding was open circuited; (a) DC transmission voltage and current; (b) Terminal voltage of PMSG and electromagnetic torque; (c) SM capacitor voltages; (d) Currents of DC-DC converters.

Figure 11 .
Figure 11.Experiment results when one set of three-phase winding was open circuited; (a) DC transmission voltage and current; (b) Terminal voltage of PMSG and electromagnetic torque; (c) SM capacitor voltages; (d) Currents of DC-DC converters.The change of DC transmission voltage was tiny, while the DC transmission current dropped immediately when the first set of three-phase winding was open circuited, which was caused by the sudden power loss of the open circuited winding set.The ripple of electromagnetic torque was large, which was caused by the asymmetrical MMF.All normal SM capacitor voltages kept at 1000 V.The currents of DC-DC converters connected to the open-circuited winding set decreased to zero.In order to deliver the same power, the currents of the normal DC-DC converters increased to about 98 A. These experiment results confirm the validity of the control scheme.

Table 1 .
Costs and characteristics of four topologies.