INTRODUCTION
In the case of increasingly depleting fossil energy, the flexible DC transmission technology (HVDC) based on Modular Multilevel Converter (MMC) topology provides a flexible and reliable technical solution for the development of new energy. The reasonable control strategy of MMC determines whether it can run normally and stably, so it is particularly important. Many scholars at home and abroad have done a lot of research and exploration on the control strategy of MMC and the balance control of capacitor voltage of submodule is one of the research focuses. The study of Rong et al.^{1} is suitable for the large number of submodules, for the high switching frequency of the converter and the huge amount of operation. The base method is introduced to reduce the sorting times, reduce the work burden of the converter and reduce the unnecessary switching signal. Aiming at the dynamic distribution of the voltage of the submodules through programmable gates array to complete the fast segmentation of the capacitor voltage^{2}. For the converter with pulse width modulation, the switching frequency of the submodule can be operated under the fundamental frequency condition by the cooperation of the switching signals of each submodule^{3}. Aiming at the problem of the switching frequency of submodules, a method of comparing the reference values is used^{4}. Dividing the submodules into two groups for switching can effectively reduce the switching frequency of the submodules. For the capacitor voltage in the MMC converter, the problems of fluctuation and high switching frequency of the submodules are divided into different groups for processing according to the voltage division^{5}. For engineering problems, realtime simulation and programming are used to complete the subblock voltage equalization control.
Since MMC usually contains hundreds of submodules in the project, the number of IGBT in so many submodules is more. Frequent switching of IGBT results in huge losses and shortened life. Therefore, research on how to reduce losses and reduce the switching frequency is particularly important. In current research, a change in the number of switching of the upper and lower arm submodules in the fronttoback period is proposed.
MATERIALS AND METHODS
Study area: The study was started in the month of August, 2018 at the Institute of Electric Power, Inner Mongolia University of Technology and the data were collected in the month of OctoberDecember, 2019.
Figure 1 shows the MMC and submodule structure. Each phase of the threephase modular multilevel converter includes two upper and lower bridge arms (i_{C}) and submodule voltage u_{C}, current i_{SM}. The relationship can be expressed as^{6}:
where, S is the switching function, S = 1 is on, S = 0 is off.
The voltage formula of the bridge arm:
where, u_{pi} with u_{ni} is the upper and lower arm voltage, S_{pij} u_{pij} is the switching state and capacitor voltage of the higharm submodule, S_{nij} u_{nij} is the switching state and capacitor voltage of the lower arm submodule, that is, each arm voltage is supported by the submodule capacitor voltages of all input states^{7}.

Fig. 1: 
Structure of MMC converter and submodule 

^{MMC: Modular multilevel converter } 

Fig. 2: 
The process of NLM 
Phase voltage is:
Modulation method: The most recent level of NLM modulation used in current research is a modulation method commonly used in MMC converters, which is a lowfrequency modulation, which is usually used in conjunction with a sorting algorithm. The NLM modulation is particularly suitable for multilevel converters and highfrequency converters compared with the modulation method, in a multilevel converter, it has a smaller calculation load, a relatively small workload, a lower harmonic content on the AC side and can output a better sinusoidal waveform^{8}.
Figure 2 is the process of NLM, the u_{spj} is the modulation wave voltage of the upper arm and the u_{snj} is the modulation wave voltage of the lower arm. It can get the number of submodules that should be put into on each arm by dividing submodule rated voltage^{9}. This process is the NLM, which can only determine the number of submodules switched, but cannot determine which submodules are switched, which need to be matched with the Algorithm for Capacitor Voltage Balance Control^{10}.
Maxmin function algorithm: Although the current submodule capacitor voltage balance control strategy can effectively control the capacitor voltage balance of the submodules, the high switching frequency has always been a difficult problem to solve^{11}, because it controls the submodule capacitor voltage in each cycle. After sorting, a large number of submodules will be switched on and off again, resulting in a high switching frequency and the switching loss will increase accordingly. Therefore, as the core of the switching principle of the submodule, the optimization of the capacitor voltage balance control strategy is particularly important^{12,13}.
Based on the sorting algorithm which was already known, current research uses a capacitor voltage balance control algorithm based on the maxmin value function (Program A), only the submodules with the largest or smallest capacitor voltages are changed to change their switching status.
The core content of the algorithm includes:
The core 1: In order to make as few submodules as possible to change the switching state in each control cycle, it is necessary to follow n_{p} (or n_{n}) the unit climbs or descends and the switching event traverses each level of MMC. In order to meet the above requirements, the sampling period of the controller must be lower than the shortest period between two adjacent switching events, which must follow formula of Eq. 4:
where, ω is the grid angular frequency, T_{S} is the sampling period. The N is bigger and Δt is smaller.
The core 2
Submodule selection method: Switching change according to the number of bridge arm submodules Δn different, the switching of the submodule can be divided into three working modes, as follows:
• 
Working mode 1: The change of switching number of each bridge arm submodule Δn>0 when selecting the Δn submodule, the bridge arm current is positive (or negative), the submodule is charged (discharged) and the capacitor with the smallest (or maximum) capacitor voltage is selected in the bypassed submodule Δn make investments 
• 
Working mode 2: Number of input submodules Δn<0 the bridge arm current is positive (or negative) and the submodule is charged (discharged). Select the largest (or the smallest) capacitor voltage among the submodules that have been put in Δn resection 
• 
Working mode 3: When the number of input submodules does not change, that is, Δn = 0, the bridge arm current is positive (or negative), the submodule is charged (discharged), when the capacitor voltage in the input state is the largest (or minimum) submodule and the capacitor module in the cutoff state is the smallest (or maximum). When the absolute value of the voltage difference between the two exceeds the set threshold, it is replaced, otherwise the original state is maintained 
Figure 3 shows the flow chart of the capacitor voltage balance control algorithm based on the MaxMin function. Δn>n_{on} (t)n_{on} (tΔt), n_{on} (t) is the number of submodules that need to be in the current cycle, n_{on} (tΔt) is the number of submodules that need to be in the previous cycle, i_{pn} is the bridge arm current and ΔU is the absolute value of the voltage difference between the submodule with the largest (or minimum) capacitor voltage in the input state and the submodule with the smallest (or maximum) capacitor voltage in the cutoff state, ΔU_{ref} is the decision threshold.

Fig. 3: 
Flowchart of capacitor voltage balance algorithm based on maxmin function 
Program A: 
MaxMin function algorithm (Fortran) 

RESULTS
A twoterminal 201level MMCHVDC transmission model is built in PSCAD/EMTDC as shown in Fig. 4. Its twoterminal AC system is active system it is used to simulate the operation of the MMCHVDC system.
Table 1 is the simulation parameters of MMCHVDC system. It is designed according to the relationship between voltage level, capacity and distance of HVDC transmission system. Table 2 is the parameters of controller. Fixed DC voltage control and fixed reactive power control are adopted on MMC1 side. Fixed active power control and fixed reactive power control are adopted on MMC2 side.
In order to verify the effectiveness of the capacitor voltage balance control under the maximum value function, the capacitor voltage balance control of the current sequencing algorithm and the proposed algorithm were simulated and verified, respectively.
Figure 5 is the capacitor voltage of submodule under sorting algorithm which was already known. Figure 6 is the capacitor voltage of submodule under the maxmin function algorithm. By comparing Fig. 5 and 6, it was found that the maxmin function algorithm cause the capacitance of the submodule with the largest capacitor voltage to have a deviation, but the deviation is low and it has little effect on the converter voltage. This is because the energy stored in the submodule is proportional to the square of its voltage.
Table 1: 
Simulation parameters of MMCHVDC system 

Table 2: 
Parameters of controller 


Fig. 4: 
MMCHVDC system structure 

Fig. 5: 
Capacitor voltage of submodule under sorting algorithm which was already known 

Fig. 6: 
Capacitor voltage of submodule under the maxmin function algorithm 

Fig. 7: 
Switching frequency of submodule under sorting algorithm which was already known 

Fig. 8: 
Switching frequency of submodule under the maxmin function algorithm 
Table 3: 
Trigger frequency of the submodules under the two algorithms 

Figure 7 is the switching frequency of submodule under sorting algorithm which was already known. Figure 8 is the switching frequency of submodule under the maxmin function algorithm. As is shown in Fig. 7 and 8, the switching frequency of submodule under the maxmin function algorithm decreased obviously in 4 cycles (1 cycle is 0.02 sec). Through a large number of experiments and collected relevant data. It can be seen in Table 3 that the average switching frequency of submodule under the maxmin value function capacitor voltage balance control is reduced from 1100262.5 Hz.
DISCUSSION
In May, 2006, State Grid Corporation of China established the Research Framework on the Key Technologies of HVDC System. Then the first MMCHVDC test project in China was completed in 2008^{14}. The key technology of MMCHVDC (the control strategy of MMC converter) is not perfect, especially the fluctuation limit of capacitance voltage, the switching frequency of submodule and the protection control of MMC.
Based on the multiple studies that were read while conducting this study, one of them was based in Guan and Xu^{15}. They studied the MMC control strategy, which can limit the switching frequency of submodules to some extent. Their study mainly aimed at limiting the voltage fluctuation of submodules, but the goal of this study is to reduce the switching frequency of submodules more often as is shown in Fig. 58 and Table 3. Wang et al.^{16} studied the modulation of MMC converters, which mainly focused on the application of two different modulation methods: NLM and CPSPWM in MMC. Their study did not link the modulation mode to the capacitor voltage equalization control, but this study combined NLM modulation with capacitor voltage equalization control. The research result of Luo et al.^{17 }showed that the calculation time of the MMC controller can be reduced effectively, which is similar to this study, both of them can reduce the operation time of the controller. This study achieved the goal of reducing the calculation time of the controller through the core algorithm 1, but their study achieved this goal by grouping the submodules. Chang et al.^{18} studied the capacitance equalization problem, which used FPGA (FieldProgrammable Gate Array) to sort the capacitance voltage of the submodule in real time. So that the operation time of the controller does not increase with the increase of the number of submodules, but also reduces the switching frequency of the submodule. There were various similarities in the results; both of them can reduce the operation time of the controller and reduce the switching frequency of the submodule at high level. The difference is that the operation time of the controller in this study is fixed. When the number of levels is low, the operation time of the controller in their study is higher than that in this study. So, it is only suitable for high level converters. A theory of closedloop charging strategy for MMC submodules is proposed by Zhang et al.^{19}. Their study has a good auxiliary role for this study. It helps to speed up the operation of MMC into the phase of submodule capacitance voltage control.
The current research focuses on the problem of high switching frequency of the MMCHVDC converter. On the one hand, it can effectively reduce the switching frequency and improve the life of the IGBT. On the other hand, it reduces the operation time of the MMC controller. As the direct current transmission system develops towards high voltage and high power, if there is no significant breakthrough in the future research on IGBT withstand voltage, then only by continuously optimizing the control strategy of the MMC converter can the stable control of the capacitance voltage be completed with the increasing number of submodules.
CONCLUSION
In current research, the submodule switching mode is divided into three types. Only change the switching status of Δn submodules with the largest or smallest capacitor voltage which have been selected. Advantages of the capacitor voltage balance control strategy under the maxmin function algorithm. The work mode has been optimized. The calculation of the maxmin value function takes less time than the sorting algorithm which was already known. Compared with the sorting algorithm which was already known, each control cycle basically only changes the switching state of a very small number of submodules. Ensuring extremely low IGBT tube switching frequency provides a new optimization strategy for capacitor voltage equalization control under the sequencing algorithm commonly used in MMCHVDC engineering, which can extend the service life of IGBT tubes in MMC systems and reduce investment.
SIGNIFICANCE STATEMENT
This study discover the maxmin function can effectively reduce the switching frequency of submodule in MMCHCDC project, that can be beneficial for raising the service life of IGBT in the submodule. So, that the cost of this link of MMCHVDC project can be reduced. At the same time, there is no negative effect on the fluctuation amplitude of the capacitance voltage of the submodule. In addition, the operation time of the algorithm is relatively broken and the workload is small. This study will help the researcher to uncover the critical areas of balance control for capacitor voltage of MMC that many researchers were not able to explore. Thus, a new theory on balance control for capacitor voltage of MMC may be arrived at.
ACKNOWLEDGMENT
Thanks to the teachers of Inner Mongolia University of Technology, for their permission and encouragement during their research work.