Proportion and failure analysis of full-bridge sub-modules in a hybrid MMC

: Isolating DC bipolar short-circuit fault is one of the difficulties faced by the flexible DC distribution system. This study aims to the hybrid modular multi-level converter (MMC). Firstly, the fault-blocking mechanism of a hybrid MMC is analysed. Through theoretical calculation, the influence of the proportion of full-bridge sub-modules η on the fault isolation capability is obtained in the process of bipolar short-circuiting of the hybrid MMC-isolated DC side. Finally, the hybrid MMC DC-side bipolar short-circuit fault is simulated and analysed by the simulation model built in PSCAD/EMTDC software. The fault blocking capability of hybrid MMC and the relationship between η and the full-bridge sub-module capacitance voltage after the fault isolation phase are verified, which provides a theoretical basis for the design of the withstand voltage of hybrid MMC full-bridge sub-module capacitors.


Introduction
In recent years, distributed generation has been integrated into power grids massively to form active distribution networks or isolated grids on the distribution side [1][2][3]. Distributed generation has the characteristics of randomness and intermittency, in order to make it safe and stable integration into the AC power grid, through the DC/AC or AC/DC/AC converter section. If the DC distribution network is introduced, the AC/DC link can be reduced, thus reducing the converter cost and reducing the loss. Once the DC distribution network was proposed, it caught the attention of many countries. Center for Power Electronics Systems of the United States' Virginia Polytechnic University and the University of North Carolina have proposed the concept of DC distribution network topology. Some universities in Japan, Europe, and China also carry out researches on the grid structure, control mode, economy, and reliability [4][5][6][7][8][9][10]. Fig. 1 shows the DC distribution network that is connected to the distributed power supply and supplies the local DC load.
As the DC distribution network in the DC fault rate is higher than the transmission line, effectively isolated DC fault as the problem must be faced. Conventional two-and three-level VSC and half-bridge multi-level converter (MMC) are not capable of effectively isolating the DC-side bipolar short-circuit fault by the inverter itself. Isolating the fault of the bipolar short circuit at the DC side is the challenge in practical engineering. In the general isolation DC-side bipolar short-circuit fault, there are three options, i.e. through the AC-side circuit breaker isolation fault isolation, through the DC-side circuit breaker fault isolation, and isolation by the inverter itself. The use of AC circuit breakers to cut off the connection between AC and DC systems has complex timing issues such as slow response time, and system recovery needs to go through pre-charging. The DC circuit breaker manufacturing process is not yet mature, and the protection strategy based on the DC circuit breaker fault is still difficult to apply. Therefore, it is usually used to isolate the DC-side short-circuit fault by the inverter itself [11].
In this paper, the half-bridge MMC, full-bridge MMC, and hybrid MMC as the object, and the magnitude of the fault current in the three kinds of MMCs is studied when the system has a bipolar short circuit at the DC side. Also, for the hybrid MMC, the influence of the number of full-bridge sub-modules (FBSM) η on fault isolation capability is analysed. At last, by building a simulation platform in PSCAD/EMTDC, verify their ability to limit the short-circuit current in the event of a bipolar short-circuit at the DC side.

Hybrid
MMC working principle and mathematical model Hybrid MMC is an improvement of the traditional half-bridge MMC, which the half-bridge MMC's half-bridge sub-module with full-bridge module instead. This section introduces the structure and basic working principle of the hybrid MMC and deduces the mathematical model of it.

Hybrid MMC working principle
The topology of the hybrid MMC is shown in Fig. 2. It consists of three phase units, each corresponding to an ABC three-phase, with two leg arms, up and down each phase. Suppose there are N submodules in each bridge arm, among which there are M half-bridge sub-modules and (N − M) FBSMs. According to the MMC working principle, the AC side of the MMC output voltage waveform is (N + 1) level sine wave.
Each sub-module of the hybrid MMC includes a capacitor. Supposing that the sub-module capacitor has been pre-charged to reach the normal operation voltage U C , each sub-module can output voltage +U C or 0. The sum of the output voltages of all submodules on the bridge arm constitutes the bridge arm voltage, where v p_j (j = a, b or c)represents the output voltage of the j-phase upper arm and v n_j (j = a, b or c) represents the output voltage of the j-phase lower arm. Using the reasonable switching control strategy to control the number of sub-modules input into each bridge arm, the output voltage of the bridge arm can be superimposed on the sine and DC components, of which the dc component is half of the DC-side voltage, i.e. U dc /2. The AC voltage components of the upper and lower arms are in phase difference of 180 degrees, so the sum of the output voltages of the upper and lower arms of each phase is the DC bus voltage U dc . As shown in Fig. 2, controlling the AC component of the upper and lower arm output voltages of each phase enables the hybrid MMC AC side to output the three-phase sinusoidal voltages u a , u b , and u c . The sum of the DC components of the upper arm and the lower arm can ensure that the output voltage of the DC side is constant U dc . In other words, the converter can control the AC-side voltage and DC-side voltage independently. In addition, each arm contains an arm inductance. For example, L pj (j = a, b or c) represents the jphase upper arm inductance, and L nj (j = a, b or c) represents the jphase lower arm inductance. The arm inductance is used to limit the overcurrent caused by a sudden change in voltage when the sub-module is switched on, in the extreme case, the arm reactor can be used to limit the fault current.
Like the VSC, the hybrid MMC is capable of both commutation and inverter operation, with four quadrant operations. The hybrid MMC with multi-level modulation forms the converter valve in series with the same power sub-module, providing higher waveform quality compared with three-level VSC, two-level VSC, and MMC at the same operating frequency. Fig. 3 shows a hybrid MMC three-phase equivalent circuit diagram, j = a, b or c, respectively, representing ABC three-phase. In the j phase, the upper and lower arm output voltages are equivalent to the controlled voltage sources v p_j and v n_j . With the arm series inductance L and the parasitic resistance R in series, the parasitic resistance R is used to characterise the converter power loss. U dc is the converter's DC-side voltage and I dc is the converter's DC-side current. u j is the j-phase output voltage of the hybrid MMC, and i j is the AC-side current of the converter. Corresponding to Fig. 3, v p_j is the sum of the output voltages of all the sub-modules of the j-phase upper arm of the hybrid MMC, i.e. the output voltage of the upper arm. v n_j is the sum of the output voltages of all the sub-modules of the j-phase lower arm of the hybrid MMC, i.e. the output voltage of the lower arm. According to Fig. 3, for the j-phase AC-side node O j of the converter, using Kirchhoff's current law, the upper arm current i p_j , the lower arm current i n_j , and the converter AC-side current i j satisfy the following relation:

Hybrid MMC mathematical model
Define the variable i dif_j , set the sum of the arm currents of the upper and lower arms to 2i dif_j , i.e.
According to (1) and (2), there is Equations (3) and (4) show that the AC-side current i j is equally divided by the upper arm and the lower arm. In addition to the AC current component, the upper and lower arm currents have a common component, which flows through both the upper and lower arms of the converter at the same time, and has no relation with the AC-side current. The component i dif_j is defined as the internal current of the j phase. According to Kirchhoff's voltage law, the voltage equations for the upper and lower arms of A phase are as follows: Add (5) and (6), and then replace (1) to obtain the output voltage differential equation of the hybrid MMC AC side: where e j is defined as the internal electromotive force of the j phase; e j is expressed as According to (2), (5), (6), the differential equation of internal dynamic characteristics of the hybrid MMC is as follows:

Hybrid MMC DC-side bipolar short-circuit fault analysis
In the DC distribution network, the introduction of the hybrid MMC, the biggest advantage is that it can isolate the DC-side bipolar short-circuit fault. In this section, we analyse the states of the half-bridge MMC and hybrid MMC, respectively, and focus on the process of the bipolar short-circuit fault isolation and currentblocking mechanism of the hybrid MMC.

Fault process analysis of the half-bridge MMC
When a bipolar short-circuit fault occurs on the DC side, a turn-off signal is applied to each sub-module's insulated-gate bipolar transistor (IGBT) to make each sub-module enter a blocking mode. However, the AC-side system can still form the path through the freewheeling diode D2 in each sub-module and provide the short- circuit current to the short-circuit point. The short-circuit current path shown in Fig. 4. And take phase A as an example, because the diode has a single-phase conduction characteristic, the short-circuit current positive half-wave can be circulated by the freewheeling diode D2 at the lower part of each half-bridge sub-module of the upper arm. Reach the positive DC bus P from the AC side of the inverter and do not pass through the sub-module capacitor C; the short-circuit current negative half-wave can be circulated by the freewheeling diode D2 at the lower part of each half-bridge submodule of the lower arm. From the negative DC bus to the inverter AC side, the same does not pass the sub-module capacitor C. At this point, the half-bridge MMC topology can be equivalent to a three-phase uncontrolled rectifier; as shown in Fig. 5, for the AC side, the system is similar to a three-phase short circuit.

Fault process analysis of the half-bridge MMC
FBSM has the ability to isolate the short circuit of the bipolar short-circuit at the DC side. As shown in Fig. 6, a blocking signal is applied to all IGBTs of the sub-module, i.e. the FBSM enters the latch mode, i.e. the FBSM enters the blocking mode. Whether the short-circuit current flows from the A terminal to the B terminal or from the B terminal to the A terminal, the sub-module capacitor is charged.
After a short-circuit fault occurs for a period of time, block the FBSM and half-bridge sub-modules to bring them into blocking mode. As can be seen from the previous section, the half-bridge sub-module can be equivalent to a freewheeling diode in series into the circuit, and the FBSM charges the capacitor unidirectionally. The FBSM is equivalent to the series connection of two freewheeling diodes and sub-module capacitors. Therefore, an equivalent circuit of a hybrid MMC with the DC bipolar shortcircuit can be obtained, as shown in Fig. 7.
According to Fig. 7, after a short-circuit fault occurs, each submodule enters the blocking mode. At this time, only the FBSM capacitor is connected to the faulty loop. The AC-side system charges the FBSM capacitors unidirectionally, and the FBSM capacitor's voltage increases. For all diodes of FBSMs, the FBSM capacitor's voltage direction is opposite to the diode conduction direction. The formation of the large enough back-voltage and ACside power supply is not enough to make each freewheeling diode conduction when all the capacitors in the circuit charge to a certain value. At this point, the short-circuit current is cut off, i.e. the hybrid MMC through the FBSM capacitor charging DC bipolar short-circuit fault isolation.

AC and DC system simulation model building:
This section sets up the AC and DC hybrid simulation system in the PSCAD/EMTDC simulation platform. As shown in Fig. 8, the left side is an AC power distribution system connected to the DC distribution converter station after being stepped down by the transformer. The rated voltage of the secondary side of the transformer is 2.2 kV and the DC system rated voltage is 4 kV. The converter station uses MMC as the converter. During the simulation, three topological MMCs (half-bridge MMC, full-bridge MMC, and hybrid MMC) are available. The DC system has a DCside bipolar short-circuit fault that verifies the ability of various inverter topologies to isolate the bipolar short-circuit at the DC side.
The topology of the converter station is shown in Fig. 9. Each bridge arm contains four sub-modules. The output voltage of the AC side is a five-level sine wave, and the sub-module capacitor voltage rating is 1 kV. SM1 to SM4 represent each arm's submodule number. The hybrid MMC used in this chapter contains two half-bridge sub-modules for each bridge, numbered SM1 and SM3, and two FBSMs numbered SM2 and SM4, respectively. For controlling, MMC adopts double closed-loop control, and the modulation mode uses the carrier phase-shift modulation mode of the hybrid MMC with the sub-module capacitor-voltage balancing control strategy [12]. Set the frequency of the hybrid-MMC carrier phase-shift modulation strategy to 1500 Hz.

Half-bridge MMC fault simulation:
The half-bridge MMC is used to simulate. At time t = 0.10 s, the DC-side bipolar shortcircuit fault occurs. After one cycle, t = 0.12 s, the sub-module's IGBTs are blocked and all the sub-modules enter the fault mode. Half-bridge MMC AC-side three-phase current, three-phase voltage, and A-phase upper and lower arm currents are shown in Fig. 10a-c, respectively, where i p is the bridge arm current and i n is the lower arm current.
According to Figs. 10a and b, the half-bridge MMC does not have the ability to isolate the DC-side bipolar short-circuit fault, after the fault occurs, although the sub-module enters the blocking mode, the short-circuit current can still flow through the freewheeling diode. At this time, the half-bridge MMC is equivalent to the uncontrollable rectifying circuit, and the voltage on the grid side of the converter drops obviously. As the freewheeling diode has single-phase conduction characteristics, the positive half-wave of each phase short-circuit current flows through the upper arm, and the negative half-wave of each phase short-circuit current flows through the lower arm, which is shown in Fig. 10c.

Half-bridge MMC fault simulation:
The hybrid MMC of each bridge arm contains two FBSMs and two half-bridge submodules. At time t = 0.10 s, the DC-side bipolar short-circuit fault occurs. After one cycle, t = 0.12 s, the sub-module's IGBTs are blocked and all the sub-modules enter the fault mode. The hybrid MMC AC-side three-phase current, three-phase voltage, and Aphase upper and lower arm currents are shown in Figs. 11a-c, respectively, where i p is the bridge arm current and i n is the lower arm current.
According to Fig. 11a and c, the hybrid MMC can block the DC-side bipolar short-circuit fault by blocking each sub-module, and there is no short-circuit current flowing through each leg of the inverter. As the short-circuit current fault is isolated, the converter's AC-side three-phase voltage did not drop, gradually approaching the system voltage.

Failure analysis
The hybrid MMC is equivalent to Fig. 12. ARM 1 -ARM 6 represent the six legs of a hybrid MMC. L p_j (j = a, b or c) and L n_j (j = a, b or c) represent the leg rest of the hybrid MMC. The fault circuit is shown by the red line in Fig. 12, and the loop consists of the FBSMs and the HBSMs of the upper arm ARM 1 of the phase A, the FBSMs and the HBSMs of the lower arm ARM 5 of the phase B, the bridge reactors L p_a and L n_b , and the line voltage between AB terminal of the inverter. Assuming that the effective value of the AC-side phase voltage is U s and the DC-side voltage is U dc , according to Fig. 12, the line voltage U AB between A and B in the loop is 6U s . The number of sub-modules for each bridge arm of a hybrid MMC is N, the number of half-bridge sub-modules is M, and the number of FBSMs is (N − M). So, the number of sub-modules in the loop is 2N, wherein the number of half-bridge sub-modules is 2M and the number of FBSMs is 2 (N − M). According to the operation principle of the hybrid MMC, the normal operation of each submodule capacitor runs at the voltage U dc /N.
When the DC-side bipolar short-circuit fault occurs, because the relay protection system detects the fault and sends a blocking signal, it takes a certain period of time. Therefore, before each submodule is locked, the hybrid MMC undergoes a short-circuit fault phase, and the short-circuit current and the sub-module capacitor's voltage drop. When each sub-module enters the blocking mode, the hybrid MMC enters the sub-module capacitor charging phase. The loop shown in Fig. 12 can be equivalent to the loop shown in Fig. 13 during the sub-module capacitor charging phase.
In Fig. 13, ignoring the parasitic resistance of the hybrid MMC, L eq equals the sum of the upper arm inductance L p_a of phase A and the lower arm inductance L n_b of phase B. All freewheeling diodes are equivalent to D eq due to the same direction, C a_upper represents the FBSM capacitance of the A-phase upper arm, C b_lower represents the FBSM capacitance of the B-phase lower arm, and the amplitude of the u AB is 6U s . There are totally 2(N − M) FBSM capacitors in the loop in the A-phase upper arm and the B-phase lower arm. It is assumed that the capacitance parameters of the sub-modules are exactly the same. When the inductance in the loop is not considered, the capacitance voltage of each submodule satisfies the following equation: where ∑ C n ∈ ARM 1 U C n corresponds to the sum of the capacitor voltages of the FBSMs of the arm ARM1 and ∑ C j ∈ ARM 5 U C j the sum of the capacitor voltages of the FBSMs of the arm ARM5 in Fig. 12.
In this case, the freewheeling diodes cannot meet the forward conducting condition, the AC system cannot continue to charge the sub-module capacitors, and the DC-side bipolar short-circuit fault is isolated. The hybrid MMC enters the fault isolation phase.
Since the capacitance parameters of each sub-module are identical, the FBSMs in Fig. 13 have the same capacitor voltage. As mentioned above, there are 2(N − M) FBSM capacitors connected in series in the loop; therefore, (11) can be written as where U C f is the capacitance voltage value after the FBSM capacitor completes charging after the hybrid MMC enters the fault isolation phase: Considering the influence of the L eq in the loop arm, i.e. L eq can maintain the loop current unchanged, when the short-circuit current decreases, L eq will sense the electromotive force in the opposite direction of the capacitor voltage, which will be superimposed on the power supply. As a result, the actual value of the FBSM voltage U C f _r after the completion of charging is higher than U C f , i.e.
The influence of L eq on the FBSM capacitor's voltage is related to the LC parameters of the entire loop shown in Fig. 13, such as the inductance of the arm reactor, the capacity of the sub-module capacitor, and the number of FBSMs. In addition, it is also related to the time of the hybrid MMC enters the latched state. When the FBSM proportion of the hybrid MMC is larger, the FBSM capacitance of the string-in loop is larger and the U C f _r is smaller. When the FBSM proportion η of a hybrid MMC is small, the FBSM capacitor's voltage U C f _r may be much higher than its voltage withstand value after entering the fault isolation phase. Although reducing η can reduce the cost of the hybrid MMC, in order to ensure that the hybrid MMC has the ability to cross-circuit short-circuit fault on the DC side, the value of η cannot be too low; otherwise, the sub-module capacitor will be broken down.
We can use U C f as a reference to the FBSM voltage-level designing. Define γ(γ ＞ 1) as the margin after considering the inductance L eq and other aspects. The FBSM capacitor's maximum voltage to withstand U C_max should meet the following criteria: Reducing η, the cost of FBSM can be saved, but the cost of the FBSM capacitor withstanding voltage levels is increased. So, the hybrid MMC design should be optimized to choose η.

Simulation
In the AC/DC hybrid system, as shown in Fig. 8, the converter is still a hybrid MMC with four sub-modules per arm, as shown in Fig. 9. Setting different η in the hybrid MMC, starting from t = 0.0 s. It can be observed that the converter enters the steady-state operation mode, when t = 0.05 s, and the DC-side bipolar shortcircuit fault occurs. Suppose that the fault is detected within twoand-a-half weeks after the fault, i.e. when t = 0.10 s, all the submodules will be blocked, and the converter will enter the submodule capacitor charging mode until the DC-side bipolar shortcircuit fault is completely isolated. Figs. 14-17 and Tables 1-4 show the capacitor voltage of each sub-module on the A-phase 4arm of the hybrid MMC under the condition of the DC-side bipolar short-circuit fault, respectively, when the number of FBSM is 1 to 4 (which is η = 0.25, 0.5, 0.75, and 1). Through the simulation results of the DC-side bipolar shortcircuit fault in Figs. 13-16, it can obviously be observed the submodule capacitor voltage discharge process during the short-circuit fault stage. After entering the short-circuit fault isolation phase, the FBSM capacitor's voltage value is related to the FBSM proportion η, and the sub-module capacitor voltage actual value is slightly higher than the calculated U C f . When the number of the FBSMs is 1 (η = 0.25), the FBSM capacitor's voltage is much higher than the rated voltage of the normal operation of 1 kV, so sub-module capacitors must be considered for a special withstand voltage. For the four-module hybrid MMC discussed in this paper, when the sub-module proportion η ≥ 0.25, the FBSM capacitor's voltage will not be higher than the rated voltage during normal operation after the fault phase, and there is no need to give special consideration to the FBSM capacitor's withstand voltage.

Conclusion
Effectively isolating the short-circuit fault of the bipolar shortcircuit on the DC side is a major challenge for the development of MMC-LVDC engineering. Isolating the fault through the converter itself is an ideal solution. The hybrid MMC is a practical converter topology which is able to isolate the short circuit at the DC side of the bipolar fault while taking economy into account. At present, the research on the hybrid MMC is not comprehensive. In this paper, the research on the process of the hybrid MMC-isolated DCbipolar short-circuit fault is studied. The influence of the proportion of FBSMs in the four submodule on the fault isolation capability is analysed. The main conclusions are as follows.
Reducing η can save the cost of FBSM but can increase the cost of the FBSM capacitor device's withstanding voltage levels. When the sub-module proportion η ≥ 0.25, the FBSM capacitor's voltage will not be higher than the rated voltage during normal operation after the fault phase, and there is no need to give special consideration to the FBSM capacitor's withstand voltage.