Fault-Tolerant Control of ANPC Three-Level Inverter Based on Order-Reduction Optimal Control Strategy under Multi-Device Open-Circuit Fault

The multi-device open-circuit fault is a common fault of ANPC (Active Neutral-Point Clamped) three-level inverter and effect the operation stability of the whole system. To improve the operation stability, this paper summarized the main solutions currently firstly and analyzed all the possible states of multi-device open-circuit fault. Secondly, an order-reduction optimal control strategy was proposed under multi-device open-circuit fault to realize fault-tolerant control based on the topology and control requirement of ANPC three-level inverter and operation stability. This control strategy can solve the faults with different operation states, and can works in order-reduction state under specific open-circuit faults with specific combined devices, which sacrifices the control quality to obtain the stability priority control. Finally, the simulation and experiment proved the effectiveness of the proposed strategy.

fault tolerant control costs too much and has a much less application. The topologies of the cascaded multilevel converter (CMC) and modular multi-level converter (MMC) have the feature of modularity, which can use the module-level fault-tolerant control methods. The module-level fault-tolerant control methods can be divided into three types, mid-point displacement, DC bus voltage reset, and redundant module installation. The system-level fault-tolerant control is the one install a redundant inverter to replace the fault one during the malfunction occurring, ensuring the performance of the whole system unchanged. The common system redundancy includes series redundancy and parallel redundancy. A comparison of fault-tolerant control strategies were shown in ref. 22 . A SBPM-based SOH monitor was proposed in ref. 23 , which provides a practical method for the realization of fault-tolerant control. An in-situ voltage fault diagnosis method based on the modified Shannon entropy was  proposed in ref. 24 , which is capable of predicting the voltage fault in time through monitoring battery voltage during vehicular operations. Another practical method of design, control and analysis of fault tolerant soft-switching DC-DC converter was proposed in ref. 25 . Similarly, a variable slope trapezoidal reference signal based control for DC fault tolerant hybrid modular multilevel converter was studied in ref. 26 , which offers a very useful method for reference. In ref. 27 , the state-of-art equivalent circuit models for ultracapacitors are studied and the hybrid pulse power characterization test is conducted to collect the data for parameter identification, on which base the genetic algorithm is employed to extract the optimal model parameters to evaluate the model accuracy, complexity and robustness. In ref. 28 , a novel fractional-order model composed of a series resistor, a constant-phase-element (CPE), and a Walburg-like element, were proposed to emulate the UC dynamics. All these methods provided useful references for fault-tolerant control strategies.
The topology of active neutral-point clamped three-level inverter became a research hot spot on the moment it was proposed. It can balance the power losses of inverter power devices by choosing four zero switching states to reduce the failure possibility of those devices with high switching frequency. So, the ANPC inverter has a much higher operation stability compared with NPC inverters. However, it is not enough and it is necessary to realize the fault-tolerant control for ANPC inverters to meet the high stability requirement of inverters used in some import special occasions. The design of hardware fault tolerant control architecture for wind energy conversion system with DFIG based on reliability analysis was presented in ref. 29 . The power loss and the single device failure of ANPC three-level inverter were analyzed in ref. 30 . The stabilities of NPC three-level inverter and ANPC three-level inverter were analyzed and compared in ref. 31 , which pointed out that the ANPC inverter has a much higher stability than NPC inverter when some power devices break down. The possible open-circuit and short-circuit faults of single device in ANPC inverter were analyzed in theory in ref. 32 , and the corresponding fault-tolerant control method was proposed. The simulation and experiment results proved the effectiveness of the proposed method. Meanwhile, The open-circuit and short-circuit faults of multiple devices in ANPC inverter were analyzed in theory, too, but without simulation and experiment. In this paper, on the basis of the existing researches, the fault-tolerant control strategy of ANPC three-level inverter will be studied further to improve the stability.

Principle of Order-Reduction Optimal Control Strategy
The flow chart of the order-reduction optimal control strategy is shown in Fig. 2.  The topology of ANPC three-level inverter was shown in Fig. 3. It can be seen from the topology that the ANPC three-level inverter turn the two clamped diodes of each bridge arm from NPC three-level inverter into IGBT modules to add the flowing paths of the zero state.   Table 1, "healthy" means this phase works normally without fault device; "NRF" (No Reduction Fault) means this phase has faults, but this fault phase still can output three kinds of levels, "+", "0", and "−"; "NRF-2L" means has faults, but this fault phase only outputs two kinds of levels, "+" and "−"; "RF" (Reduction fault) means has faults, and this fault phase only outputs "0" level. For example, if Sa1/Da1, Sa2/Da2, Sa3/Da3 and      Sa4/Da4 are healthy, even though both Sa5 and Sa6 fail at the same, this fault phase will still work in "NRF" state, and output "+", "0", and "−"; if Sa2/Da2 and Sa5/Da5 works normally, even though all the power devices of this fault phase are in open-circuit state, this fault phase still works under "RF" state, and output "0" level.
It can be seen from Table 1 Fig. 4(d).
According to the output states of each phase in Table 1, the fault-tolerant control method under multi-device open-circuit fault of three-phase ANPC inverter can be summarized, and is shown in Table 2.
When one phase of three-phase ANPC three-level inverter breaks down, the operation under fault-tolerant control can be divided into three modes according to the output states of fault phase. In mode 1 and 2, the maximum modulation is the same as normal operation, while in mode 3, its maximum modulation decreases to 0.577. What's more, only under mode 1, the inverter outputs the same waveform quality as the normal one. The voltage vector diagram was introduced to illustrate the fault-tolerant control operation modes, and it is shown in Fig. 5. In Fig. 5, gray indicates the states that cannot output normally, and white indicates the states that can output normally.
When ANPC three-level inverter works under "healthy" or "NRF" state, each phase can still output "+", "0" and "−". The voltage vector diagram is shown in Fig. 5(a), and under this state, all the voltage vectors can still be used as normal to maintain the inverter work as normal. If one of the three phases works under NRF-2L state, the working condition of the inverter can be supposed to be much worse. All the three phases were supposed to be under NRF-2L state, and the voltage vector diagram is shown in Fig. 5(b), where the external hexagon still has six correct voltage vectors to be used. Therefore, the ANPC three-level inverter works under the same condition as the two-level inverter's. Although the waveform quality is reduced, its maximum modulation is the same as the one in normal state.
When one phase of the ANPC three-level inverter is under RF state and the other two phases are under healthy or NRF states, the voltage vector is shown in Fig. 5(c). It can be seen from Fig. 5(c) that the six voltage vectors of the inner hexagon is still valid as normal, which means the fault tolerant control is useful under this condition, but the maximum modulation is reduced to 0.577. Compared with the proposed fault states former,  there is a much worse operation state, one phase of the ANPC three-level inverter is under FR state and the other two phases both work under NRF-2L state. Under this state, the four valid voltage vectors are shown in Fig. 5(d). When the three-phase ANPC three-level inverter operates under this mode, its equivalent circuit is the same as four-switched three-phase inverter, and can realize the fault-tolerant control operation with the maximum modulation reduced to 0.577.
When phase A and B both work under RF state, even though phase C works under healthy state, only (00−), (000) and (00+) are can be valid. Under this condition, the ANPC three-level inverter can not work with fault-tolerant control according to what has been analyzed before. However, when the topology of the inverter is recomposed and only one capacitor of the DC-bus side is used to generate a two-level voltage waveform, the fault-tolerant control can be realized. For example, if Sa1/Da1, Sb1/Db1 and Sc1/Dc1 goes into open-circuit state at the same time, the fault phases can only output "0" and "−" level, and the voltage vector diagram is shown in Fig. 6.
Under this condition, the fault-tolerant control mode of ANPC three-level inverter can be equalled to a two-level inverter, whose maximum modulation decreased to 0.577. In the same way, if Sa4/Da4, Sb4/Db4, and Sc4/Dc4 come into open-circuit fault at the same time, the fault phase can only output "+" and "0" and the whole system will still work with fault-tolerant control.

Simulation and Experiment
Simulation. The Fig. 7. It can be seen from the Fig. 7(a) that the three-phase currents are no longer symmetrical, and the current of phase A has been changed. The phase voltage of phase A and the line voltage of A-B, as shown in Fig. 7(b) and (c) respectively, have also been distorted when Sa1and Sa4 come into open circuit. Meanwhile, the neutral-point voltage, as shown in Fig. 7(d), has been shifted, but it still can keep balance.
The three-phase currents, phase voltage of phase A, line voltage between phase A and B, and the neutral-point voltage were shown in Fig. 7 under Sa1 and Sa4 open-circuit fault in phase A with fault-tolerant control. It can be seen from Fig. 8(a) that even though the amplitudes of three-phase currents decreased, they were maintained symmetry. It can be seen from Fig. 8(b) that the phase voltage of phase A changed into 0 with fault-tolerant control after the fault occurrence of phase A. It can be seen from Fig. 8(c) that even though the amplitude of line voltage between phase A and B decreased, they were maintained symmetry. It can be seen from Fig. 8(d) that the neutral-point voltage shifted a little under fault-tolerant control compared with normal condition, but it can still keep balance.
The three-phase currents, phase voltage of phase A, line voltage between phase A and B, and the neutral-point voltage were shown in Fig. 9 under Sa1 and Sa5 open-circuit fault in phase A. It can be seen from Fig. 9(a) that the phase current of phase A changed most significantly. It can be seen from Fig. 9(b-d) respectively that the phase voltage of phase A, line voltage between phase A and B, and the neutral-point voltage had also changed or shifted. Meanwhile, the balance of neutral-point voltage was lost.
The three-phase currents, phase voltage of phase A, line voltage between phase A and B, and the neutral-point voltage were shown in Fig. 10 under Sa1 and Sa5 open-circuit fault in phase A with fault-tolerant control. It can be seen from Fig. 10(a) that even though the amplitudes of three-phase currents decreased, they were maintained symmetry. It can be seen from Fig. 10(b) that the phase voltage of phase A changed into 0 with fault-tolerant control after the fault occurrence of phase A. It can be seen from Fig. 10(c) that even though the amplitude of line voltage between phase A and B decreased, they were maintained symmetry. It can be seen from Fig. 10(d) that the neutral-point voltage shifted a little under fault-tolerant control compared with normal condition, but it can still keep balance.
The three-phase currents, phase voltage of phase A, line voltage between phase A and B, and the neutral-point voltage were shown in Fig. 11 under Sa5 and Sa6 open-circuit fault in phase A with fault-tolerant control. It can be seen from Fig. 11(a-d) respectively that the three-phase currents, phase voltage of phase A, line voltage between phase A and B decreased, neutral-point voltage were still kept as the same as the ones before fault occurrence. Therefore, when Sa5 goes into open-circuit fault, it can be maintained operation as normal without fault-tolerant control.
Since . The experiment platform is shown in Fig. 12. It can be found from Fig. 13(a) that, when Sa1and Sa4 come into open-circuit fault at the same time, the three-phase current was no longer symmetric, and the current of phase A changed most obviously. It can be found from Fig. 13(b) and (c) that phase voltage of phase A and line voltage between phase A and B distorted because of the open circuit of Sa2. As shown in Fig. 13(d), the neutral-point voltage shifted a little, but it still could keep balance.
It can be found from Fig. 14(a) that, when Sa1and Sa4 came into open-circuit fault at the same time and operated with fault-tolerant control, the amplitude of the three-phase current would decrease a little, but they are still symmetry. It can be found from Fig. 14(b) that phase voltage of phase A changed into 0 during the fault-tolerant control operation after the fault occurrence. As shown in Fig. 14(c), even though the line voltage between phase A and B decreased, it still can keep symmetry. Meanwhile, the neutral-point voltage which is shown in Fig. 14 It can be seen from Fig. 16(a) that even though the amplitudes of the three-phase currents have been decreased, they are still in symmetry. Under the fault-tolerant control, the phase voltage of phase A, shown in Fig. 16(b), changed into 0 after the fault occurrence. The amplitude of line voltage between phase A and B also decreased, which is shown in Fig. 16(c), and still can keep symmetry as three-phase currents did. Meanwhile, the neutral-point voltage which is shown in Fig. 16(d) can still keep balance.
The experiment results shown in Fig. 17 proved that the three-phase currents, phase voltage, line voltage and neutral-point voltage did not changed after the Sa5 and Sa6 open-circuit fault and can still output the same waveforms as the ones before fault occurrence. Therefore, it is unnecessary to apply the fault-tolerant control when Sa5 and Sa6 come into open-circuit fault, and the whole can maintain operating as normal.
These experiment results above are consistent with the simulation results. This order-reduction optimal control strategy can realize the fault-tolerant control to keep the system working in slowing down or output capacity reducing state to improve the reliability of the whole system.

Conclusions
To improve the operation stability, this paper summarized all the possible states of multi-device open-circuit fault and proposed an order-reduction optimal control strategy to realize fault-tolerant control based on the topology and control requirement of ANPC three-level inverter and operation stability. This control strategy can solve the faults with different operation states, and can works in order-reduction state under specific open-circuit faults with specific combined devices, which sacrifices the control quality to obtain the stability priority control. Finally, the simulation and experiment proved the effectiveness of the proposed strategy. This paper may offer a practical method potentially to solve the multi-device open-circuit problem in ANPC three-level inverters.
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