Research on SVPWM and Midpoint Potential Balancing Algorithm

of Improved NPC Three-Level Inverter

Deng Pan

*

, Jun Gao and Yicai Liu

Wuhan Business University, Wuhan 430056, Hubei, China

Keywords: 24 Sectors, Modulation Method, Estimation-Simulation-Correction, Adjustment Factor, Balancing

Algorithm, Midpoint Potential.

Abstract: The traditional NPC three-level inverter SVPWM control adopts a 36-sector seven-segment modulation

method, which involves a large number of trigonometric functions and coordinate transformations. This

paper proposes a improved control strategy using 24 sectors, and introduces the SVPWM modulation

method and implementation steps in detail. Compared with the 36-sector control method, the workload of

calculation and table checking is significantly reduced. At the same time, this paper proposes a simple

"estimation-simulation-correction" midpoint potential balance control algorithm, through a large number

of simulation verification, extract the best adjustment factor k to adjust the action time of the starting

negative small vector and the redundant small vector, and realize the balance control of the midpoint

potential. Finally, the correctness of the proposed control method is verified by Simulink simulation.

1 INTRODUCTION

Medium and low voltage AC motor speed

regulation system generally adopts two-level

inverter topology, with SVPWM modulation

technology for motor stator flux tracking, the

method is easy to implement by digital controller,

compared with traditional SPWM technology, The

output current waveform is better, and the voltage

output of the inverter link is relatively stable. Since

the maximum withstand voltage value of a single

MOSFET switch transistor is generally not high

(≤600V). In the field of medium and high voltage

and high power,three-level inverter topology is

adopted, With the help of SVPWM modulation

technology，the output level number increases and

the output waveform quality is higher. In addition,

the three-level inverter topology has less voltage

switching stress for a single switch tube (Zhang,

2020; Li, 2016; Yang, 2018).

The implementation steps of the three-level

inverter topologySVPWM algorithm are the

division of large and small sectors, the judgment of

the switching vector action sequence of each sector,

the calculation of the switching vector action time,

and the calculation of modulation fuze value.

Model establishment relies on a large number of

trigonometric operations and table queries (Li,

2016; Yang, 2018), and the frequent operation of

the switch tube will increase the disturbance of the

system, resulting in a decrease in control

performance and an increase in the harmonic

component of the output waveform (Zhang, 2020).

Literature (Zhang, 2020) proposes an improved

36-sector seven-segment modulation method,

which uses the coordinate translation method to

correct the reference voltage vector, but due to the

large number of sectors, the overall calculation

amount is large.Literature (Wang, 2022) proposes a

transformation method for split-inductive

three-level inverter.It reduces the performance

impact of short circuits on the circuit.Literature

(Zhao, 2008) introduces a three-level inverter

SVPWM method in 60° coordinate system, which

reduces sector judgment and trigonometric

operation from 36 sectors to 24 sectors, saving the

operation time, However, there are few textual

descriptions of the pulse-width modulation strategy

of the above methods. Literature (Wang, 2010)

introduces an LCL filter design method, The total

inductance value of the LCL filter can be

determined by the power supply power conditions

and ripple suppression requirements, and on this

basis, the inductance ratio and filter capacitance

value can be determined. The NPC three-level

topology has the problem of midpoint potential

imbalance, which is a difficult point to study the

structure. Literature (Song, 2004) provides a

Pan, D., Gao, J. and Liu, Y.

Research on SVPWM and Midpoint Potential Balancing Algorithm of Improved NPC Three-Level Inverter.

DOI: 10.5220/0012142200003562

In Proceedings of the 1st International Conference on Data Processing, Control and Simulation (ICDPCS 2023), pages 5-16

ISBN: 978-989-758-675-0

Copyright

c

2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

5

potential control method for injecting zero vector,

due to the different zero vector injection order in

different sectors, This method needs to first

determine the sector number, and then look up the

table to obtain the zero vector action time.

Literature (Fan, 2015) proposes to use optimization

of the last three virtual vectors to control the

midpoint potential balance. This method adopts

more approximation processing in the process of

virtual vector calculation, the cumulative error is

large. Literature (Ovalle, 2017) proposes to use two

adjacent small vectors to equivalently synthesize

medium vectors to adjust the action time of small

vectors and redundant small vectors. However, the

synthesized medium vector is composed of

asymmetric small vectors, and the influence of

small vectors on the midpoint potential cannot be

ignored. Literature (Song, 2012) provides a

closed-loop bidirectional buck-boost converter to

compensate for the impact of load disturbance on

the DC side voltage, which is theoretically mature.

However, BUCK/BOOST circuits need to be added,

and hardware and maintenance costs increase.

This paper proposes an SVPWM control

algorithm based on 24-sector improved NPC

three-level inverter, and introduces the SVPWM

modulation method and implementation steps in

detail.At the same time, a simple

"Estimation-simulation-correction" midpoint

potential balance algorithm is proposed, and the

optimal regulatory factor is extracted as the input

quantity for the time control of the initial negative

small vector and the redundant small vector

through a large number of simulation verification.

Finally, simulation is carried out to verify the

correctness of the above algorithm and control

strategy.

2 NPC THREE-LEVEL CIRCUIT

TOPOLOGY ANALYSIS

Figure 1 shows the topology diagram of the NPC

three-level circuit,Figure V

dc

is the DC-side supply

voltage,C

1

and C

2

are the DC side regulator

capacitor, D

5

、

D

6

、

D

11

、

D

12

、

D

17

、

D

18

are clamp diode

for A

、

B

、

C phase. Sa

1

~Sa

4

、

Sb

1

~Sb

4

、

Sc

1

~Sc

4

are

switch tubes,o is the neutral point on the DC

side.Since the regulator capacitors C1 and C2 are

equal, so there is 𝑈𝑐

= 𝑈𝑐

=

𝑉

.

Figure 1: NPC three-level circuit topology diagram.

Each phase bridge arm can output three

different levels,Define 𝑆

、

𝑆

、

𝑆

as three-leg

switch state variables,Take phase 𝐴 as an

example, 𝑆

、

𝑆

conduction, 𝑆

、

𝑆

disconnection,𝑈

=

𝑉

,

𝑆

=1 ; 𝑆

、

𝑆

conduction, 𝑆

、

𝑆

disconnection, 𝑈

=0 , 𝑆

=0 ; 𝑆

、

𝑆

disconnection,𝑆

、

𝑆

Conduction, 𝑈

= −

𝑉

, 𝑆

= −1 ,And 𝑆

and

𝑆

are in opposite states; 𝑆

and 𝑆

are in

opposite states.

The output state of bridge arms 𝐴

、

𝐵

、

𝐶 is

represented by switch function, Define three-phase

voltage as (Liu, 2012; Dang, 2016):

𝑈

=

𝑆

；

𝑈

=

𝑆

；

𝑈

=

𝑆

(1)

Equal amplitude transformation of three-phase

synthetic voltage vector, And expansion by Euler

formula:

𝑈=

2

3

𝑈

+ 𝑈

𝑒

+ 𝑈

𝑒

=

[(2𝑆

−𝑆

−𝑆

)+𝑗

√

3(𝑆

−𝑆

)] (2)

Combined (1, 2), 27 kinds of space voltage vectors

can be obtained, As shown in Figure 2. Four

voltage vectors can be obtained by ordering the

vector amplitude from large to small.

(1) The amplitude of large vector is

𝑉

,

For example:1 -1 -1;

(2) The amplitude of Medium vector is

√

𝑉

, For example:1 0 -1;

ICDPCS 2023 - The International Conference on Data Processing, Control and Simulation

6

Figure 2: Basic vector diagram of NPC three-level

inverter.

(3) The amplitude of Small vector is

𝑉

,

Small vectors are divided into positive small

vectors and negative small vectors. For example, 1

0 0 is a positive small vector, 0 -1 -1 is a negative

small vector;

(4) The zero vector amplitude is 0, such as 1

1 1 (Hu, 2017; Zhang, 2018; Wang, 2002).

3 ANALYSIS OF CONTROL

ALGORITHM BASED ON 24

SECTORS

3.1 Division of Large and Small Sectors

In order to guide the target flux to form a quasi

circular track, the voltage vector should be

switched to the appropriate sector at an appropriate

time, and the sector number must be agreed

first.Through Clarke transformation, three-phase

static 𝐴

、

𝐵

、

𝐶 coordinate systems can be

converted to two-phase static 𝛼

、

𝛽 coordinate

systems, As shown in Figure 3.The components

𝑈

、

𝑈

、

𝑈

of the rotation vector on the

𝐴

、

𝐵

、

𝐶 axes can be represented by the

components 𝑈

、

𝑈

of the reference vector in the

two-phase stationary coordinate system.

Define variables 𝑎

、

𝑏

、

𝑐,And make rules:

(1) If 𝑈

＞

0, 𝑎=1, otherwise 𝑎=0;

(2) If

√

3

𝑈

−𝑈

＞

0, 𝑏=1, otherwise 𝑏=0;

(3) If −

√

3

𝑈

−𝑈

＞

0, 𝑐=1, otherwise 𝑐=0;

Define 𝑁 as the large sector code, Take 𝑁=

𝐴+2𝐵+4𝐶, Table 1 shows the numbering rules of

large sectors (Zhang, 2018; Wang, 2002).

Table 1: Table of large sector numbering sequences.

Large sector

1

2

3

4

5

6

𝑎

1

0

1

0

1

0

𝑏

0

1

1

0

0

1

𝑐

0

0

0

1

1

1

Each large sector can be equally divided into

four small sectors, and 𝑛 is defined as the number

of small sectors, As shown in Figure 4,That is,

11~14 sectors, 21~24 sectors, 31~44 sectors, 41~44

sectors, 51~54 sectors, 61~64 sectors, A total of 24

small sectors.Next, It is necessary to determine the

position relationship between the target vector 𝑉

⃗

and the small sector.Taking the third sector as an

example, define the included angle between 𝑉

⃗

and 𝛼 axis as 𝜃,Then the component of 𝑉

⃗

on

coordinate axis 𝛼

、

𝛽 is:

𝑉

′

= 𝑉

× 𝑐𝑜𝑠𝜃

𝑉

′

= 𝑉

×sin𝜃

(3)

Figure 3: Large sector numbering chart. Figure 4: Small sector numbering diagram.

Research on SVPWM and Midpoint Potential Balancing Algorithm of Improved NPC Three-Level Inverter

7

Table 2: Table of voltage vector action order of small sectors.

Small Sector

𝑇

/4 𝑇

/2 𝑇

/2 𝑇

/2

𝑇

/2 𝑇

/2 𝑇

/4

31

0 -1 -1 0 0 -1 0 0 0 1 0 0

0 0 0

0 0 -1

0 -1 -1

32

0 -1 -1 1 -1 -1 1 0 -1 1 0 0

1 0 -1

1 -1 -1

0 -1 -1

33

0 -1 -1 0 0 -1 1 0 -1 1 0 0

1 0 -1

0 0 -1

0 -1 -1

34

0 0 -1

1 0 -1

1 1 -1

1 1 0

1 1 -1

1 0 -1

0 0 -1

It is easy to get the judgment

conditions:(1) 𝑉

+

√

𝑉

＜

, 𝑛=31; (2) 𝑉

−

√

𝑉

＞

, 𝑛=32; (3) 𝑉

＞

√

, 𝑛=34;

(4)Otherwise, 𝑛=33. For the other five large

sectors, when judging the corresponding small

sector, it is only necessary to convert angle a to

sector 3.

3.2 Determine the Switching Sequence

of Small Sectors

The operation rule of SVPWM is to determine the

three basic output space vectors according to the

space sector position of target voltage vector 𝑉

⃗

,

and calculate the action time of each basic vector.In

order to reduce the voltage stress of the switch as

much as possible, the adjacent negative small

vector of voltage vector 𝑉

⃗

is preferred as the

starting vector. According to the above rules, the

basic voltage vector of each small sector and the

vector action sequence are shown in Table 2 (only

the switching sequence of the third largest sector is

listed in the table, see Appendix 1 for details).If the

target voltage vector 𝑉

⃗

is in sector 31, the three

basic vectors selected for synthesis are 0 -1 -1、0 0

-1、0 0 0.The action time of each basic vector is

、

、

、

、

、

、

.

3.3 Determine the Action Time of

Three Basic Vectors

Figure 5: Third largest sector.

Take 31 sectors for example, The three basic

voltage vectors of the synthetic target voltage

vector 𝑉

⃗

are defined as 𝑉

⃗

、

𝑉

⃗

、

𝑉

⃗

, 𝑇

、

𝑇

、

𝑇

is the base vector response time, 𝑇

is the

sampling period,From the principle of volt-second

balance:

𝑉

⃗

𝑇

+ 𝑉

⃗

𝑇

+ 𝑉

⃗

𝑇

= 𝑉

⃗

𝑇

𝑇

+ 𝑇

+ 𝑇

= 𝑇

(4)

31 Sector Base Vector Voltage:

𝑉

=0,𝑉

=

𝑉

, 𝑉

=

𝑉

𝑒

(5)

The combination formula (4, 5) yields:

0+

𝑉

𝑇

+

𝑉

𝑒

𝑇

= 𝑉

𝑒

𝑇

(6)

Define intermediate variables

𝑚=

√

×

× 𝑇

,

It can be solved:

𝑇

= 𝑚𝑠𝑖𝑛(60−𝜃)

𝑇

= 𝑚𝑠𝑖𝑛𝜃

𝑇

= 𝑇

−𝑚𝑠𝑖𝑛( 𝜃+ 60)

(7)

Similarly, the basic vector action time for each

small sector can be solved as shown in Table 3

(only the basic vector action time for the third

largest sector is listed in the table, See Appendix 2

for details):

ICDPCS 2023 - The International Conference on Data Processing, Control and Simulation

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Table 3:

Timeline of basic vector action for each sector.

Small sector

𝑇

Time of action 𝑇

Time of action 𝑇

Time of action

31

𝑚𝑠𝑖𝑛(60−𝜃) 𝑚𝑠𝑖𝑛𝜃 𝑇

−𝑚𝑠𝑖𝑛(60+𝜃)

32

2𝑇

−𝑚𝑠𝑖𝑛(60+𝜃) 𝑇

−𝑚𝑠𝑖𝑛(60−𝜃) 𝑚𝑠𝑖𝑛𝜃

33

𝑇

−𝑚𝑠𝑖𝑛𝜃 𝑇

−𝑚𝑠𝑖𝑛(60−𝜃) −𝑇

+ 𝑚𝑠𝑖𝑛(60+𝜃)

34

𝑚𝑠𝑖𝑛(60−𝜃) −𝑇

+ 𝑚𝑠𝑖𝑛𝜃 2𝑇

−𝑚𝑠𝑖𝑛(60+𝜃)

3.4 Determine Switch Fuse Value

In order to minimize the harmonic component of

the output voltage of the inverter, a seven-segment

symmetric SVPWM modulation is usually used,

that is, the inverter outputs seven voltage vectors in

one switch cycle (Song, 2012). Figure 6 shows a

method to determine the switch start time. An

isosceles triangle is generated by the counter and

compared with a constant value to determine the

switch time. The constant value mentioned here is

the switch fuse value.

Figure 6: The corresponding diagram of the switching

time.

The seven time periods in the figure correspond to

six switch moments. The input moments of each

vector can be obtained by comparing the three

switch fuses

𝐴

、

𝐵

、

𝐶

in the figure with the

triangular wave.The amplitude of the triangle wave

in the graph is set to

, Period set to

𝑇

.When

the projection value of the triangular wave output

on the

𝑌

axis is in the range of 0-

𝐴

, the

corresponding vector trigger time is

.When the

projection value is within

𝐴

~

𝐵

range, the

corresponding vector trigger time is

（

+

）

,

When the projection value is within

𝐵

~

𝐶

range,

the corresponding vector trigger time is

（

+

+

）

,Therefore, the value of

𝐴

、

𝐵

、

𝐶

should

meet the following relationship:

⎩

⎪

⎨

⎪

⎧

𝐴=

𝐵= 𝐴+

=

+

𝐶= 𝐵+

=

+

+

(8)

Taking three sectors as an example, the comparison

relationship between the basic vector action time

and the switch state is shown in Figure 7. The

three-phase vector state corresponds to all the

switch states. The switching on and off times of the

switch devices are allocated to the corresponding

switch devices to complete the selection of the

main circuit switch devices.

Table 4 shows the trigger time table of

switching devices in each small sector (only the

third largest sector is taken as an example in the

table, see Appendix 3 for details).Define variable

𝑋=

, 𝑌=

+

, 𝑍=

+

+

, As the switch

status of the bridge arms of each phase is opposite

to each other, the table only lists the trigger time of

the two switches on the upper layer of each bridge

arm.In addition, if the state value in the table is 1, it

means that the switch cycle is high level, otherwise

it is low level.

Research on SVPWM and Midpoint Potential Balancing Algorithm of Improved NPC Three-Level Inverter

9

4

0

T

2

1

T

2

2

T

2

0

T

2

2

T

2

1

T

4

0

T

4

0

T

2

1

T

2

2

T

2

0

T

2

2

T

2

1

T

4

0

T

4

0

T

2

1

T

2

2

T

2

0

T

2

2

T

2

1

T

4

0

T

4

0

T

2

1

T

2

2

T

2

0

T

2

2

T

2

1

T

4

0

T

Figure 7: Seven-segment SVPWM modulation waveform (taking sector 3 as an example).

Table 4: Switching device trigger schedules for each sector.

𝑛

𝑆

𝑆

𝑆

𝑆

𝑆

𝑆

31

1 0

𝑋

0

𝑌

32

𝑋

1 0

𝑌

0

33

𝑌

1 0

𝑋

0

34

𝑋

1

𝑌

1 0

Figure 8: SVPWM control simulation model of a 24-sector NPC three-level inverter.

3.5 Simulation Verification

The simulation model built by Simulink is shown in

Figure 8, and the parameter settings are as follows:

the DC side voltage of the inverter 𝑉

is 500V,

the expected inverter output a rotation voltage

vector with a period of 0.02s and amplitude of

180V, and the defined cycle sampling frequency

𝐹

is 1e4Hz, and the sampling period 𝑇

is

1e-4s; The three-phase symmetrical load resistance

is 100𝛺, the inductance 𝐿

is 16e-6H, and the

capacitance 𝐶 is 16e-6F;The DC side voltage

stabilizing capacitor 𝐶

、

𝐶

is 500e-6F.Powergui

adopts Discrete mode, and the system sampling

frequency is set to 20 times of the periodic

sampling frequency.

Z

Z

Z

Z

ICDPCS 2023 - The International Conference on Data Processing, Control and Simulation

10

Figure 9: S-Function is used to determine large and small sectors.

Figure 10: Distribution of large sectors. Figure 11: Distribution of small sectors.

Figure 12: Sectors 31 and 32 judge the switching time

The S-Function function is used to judge the large

and small sectors, as shown in Figure 9. For the

judgment of small sectors, only the judgment

method of the third sector is listed in the figure, and

the judgment method of other sectors is the same.

Figure 10 and Figure 11 show the distribution of

large and small sectors after operation.

Figure 12 shows the judgment statement for the

trigger time of sector 31 and 32 switches. The

three-level SVPWM modulation trigger pulse can

be obtained by comparing the switch fuse value

with the Y-axis projection value of the modulated

triangle wave and strictly comparing the trigger

schedule of the switching devices in each sector

(Appendix 3). Set the simulation environment of

Simulink. The simulation start time is 0s and the

end time is 0.4s. Fixed step is adopted and Discrete

mode is adopted for the algorithm.

Research on SVPWM and Midpoint Potential Balancing Algorithm of Improved NPC Three-Level Inverter

11

Figure 13: Load phase voltage waveform Figure 14: Load line voltage waveform.

电容C1电压值

电容C2电压值

Figure 15: Capacitor C1 and C2 voltage values. Figure 16: Voltage difference between capacitors C1 and C2.

Figure 13 and Figure 14 are waveform diagrams of

three-phase load phase voltage and line voltage

respectively. The waveform period is 0.02s, in

which the amplitude of phase voltage is

𝑉

, and

there are

𝑉

and

√

𝑉

voltage vectors in the

waveform; The line voltage amplitude is 𝑉

, and

there are 𝑉

and

𝑉

voltage vectors in the

waveform. The simulation waveform further

verifies the conclusion in 2.1.

4 A SIMPLE MIDPOINT

POTENTIAL BALANCE

ALGORITHM BASED ON

"ESTIMATION-SIMULATION-

CORRECTION"

Further verify the influence of the above SVPWM

algorithm on the neutral point potential of the

inverter. Measure the two capacitor voltages and

the neutral point voltage of the DC bus respectively,

extend the simulation time to 2s, and obtain curves

as shown in Figures 15 and 16. After the simulation

starts, the voltage values of 𝐶

、

𝐶

capacitors are

roughly the same, the midpoint voltage is about 0V,

and there is almost no zero shift at the moment of

starting. The simulation lasts for 0.5s, the voltage

value of 𝐶

capacitor is about 260V, the voltage

value of 𝐶

capacitor is about 240V, The

differential pressure at both ends of capacitor 𝐶

and 𝐶

is about 20V. As time goes on, the offset of

the midpoint voltage increases, and the distortion of

the line voltage is obvious, which will interfere

with the steady state performance of the system

(Fan, 2015; Dang, 2016). When paired small

vectors act on the midpoint, they produce the same

line voltage, but their current values have the

opposite effect on the midpoint voltage,

counteracting part of the voltage imbalance (Zhang,

2018). To achieve a balanced control of the

midpoint potential, the action time of negative

small vectors and redundant small vectors can be

allocated (Jiang, 2014). An adjusting factor 𝑘 is

introduced to modify the on-off fuse of the starting

negative and redundant small vectors, thus

changing the on-off time of the switch tube.

Analyzing Figure 1, when the current flows

into the bus, when 𝑖

＜

0, 𝐶

is discharged, and 𝐶

is charged, the midpoint potential has an upward

trend; Conversely, 𝑖

＞

0, 𝐶

charge, 𝐶

discharge,

midpoint potential has a downward trend (Song,

2004). The S-Function function is used to

determine the value of the pair, and the input

amount is the voltage difference of capacitors 𝐶

、

𝐶

(𝑉

in the figure) and the current flowing

in/out of the DC bus.

ICDPCS 2023 - The International Conference on Data Processing, Control and Simulation

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Figure 17: The value of the capacitor voltage. Figure 18: Capacitor voltage difference.

The method of "Estimation-simulation -correction"

is adopted, and different parameters are estimated

respectively, verified by a large number of

simulations, and the obtained values are corrected.

The simulation results show that when 𝑖

＞

0

and 𝑉

＞

0 , 𝑘=0.7; when 𝑖

＞

0 and 𝑉

＜

0 ,

𝑘=0.3; when 𝑖

＜

0 and 𝑉

＞

0, 𝑘=0.3; when

𝑖

＜

0 and 𝑈

＜

0, 𝑘=0.7, In this way, the offset

suppression effect of the midpoint voltage of the

DC bus is better. After the 𝑘 value is introduced,

equation (8) is modified to obtain an optimized

switch fuze as shown in equation (9):

⎩

⎪

⎨

⎪

⎧

𝐴=

×

（

1+0.7

）

𝐵= 𝐴+

=

+

𝐶= 𝐵+

=

×(1−0.7) +

+

(9)

Modify the model parameters according to equation

(9), and the simulation time is extended to 6s, and

the voltage difference and midpoint voltage

waveform of the DC bus capacitor are shown in

Figures 17 and 18. In Figure 17, the stability value

of the DC side power supply 𝐶

is about 251V, the

stability value of 𝐶

is about 248V, and the voltage

difference between the readout capacitors 𝐶

、

𝐶

in Figure 18 is about 3V, and it tends to stabilize

over time, The simple algorithm better suppresses

the fluctuation of midpoint potential.

5 CONCLUSION

Based on the traditional 36 sector SVPWM control

algorithm, this paper proposes an improved 24

sector SVPWM control algorithm, and introduces

the modulation method and implementation steps of

this algorithm in detail. At the same time, a simple

"Estimation-simulation-correction" neutral point

potential balance control algorithm is proposed, and

the value method of regulating factor k is

introduced, as well as how to use the value of k to

allocate the action time of negative small vectors

and redundant small vectors. A simulation model is

built to verify the above algorithm. Combined with

the simulation results, the correctness of the

proposed control algorithm is proved.

ACKNOWLEDGEMENT

Fund: Wuhan Business College University-level

Scientific Research Project (2021KY017).

REFERENCES

Zhang Yunlei, Wang Qunjing, Hu Cungang, et al.

Research on a new low-voltage non isolated 17 level

converter and its control strategy. Chinese Journal

of Electrical Engineering, 2020, 40(4):1095-1105.

KAI Li, ZHAO Jiancheng,WU Wenjie. Performance

analysis of zero common‐mode voltagepulse‐width

modulation techniques for three ‐ level neutral point

clamped inverters. IET Power Electronics, 2016,

9(14):2654-2664.

Yang Yun,Tan Siew-Chong,Hui Shu Yuen Ron. Adaptive

reference model predictive control with improved

performance for voltage-source inverters. IEEE

Trans on Control Systems Technology, 2018, 26(2):

724-731.

Wang Xiaobiao, Xiao Huaping, Niu Chenhui, Yao

Zhongyuan, Xiao Huafeng. Research on the

construction method of highly reliable three-level

inverter. Chinese Journal of Electrical Engineering,

2022, 25 (4):839-849.

Song Qiang, Liu Wenhua, Yan Gangui, Wang Zhonghong.

Neutral point potential balance control method of

three-level NPC inverter based on zero sequence

voltage injection. Chinese Journal of Electrical

Engineering, 2004, 05(6):52-62.

Zhao Hui, Li Rui, Wang Hongjun, Yue Youjun. Research

on SVPWM method of three-level inverter in

60°coordinate system. Chinese Journal of Electrical

Research on SVPWM and Midpoint Potential Balancing Algorithm of Improved NPC Three-Level Inverter

13

Engineering, 2008, 30(5):405-413.

Wang Fusheng, Shao Zhang, Ping Liuping. Current

ripple analysis and LCL filter design of three-level

inverter. Power Electronics Technology, 2010,

44(11):76-84.

Ovalle A., Hernández M. E. Nonorthogonal-

Reference-Frame-Based SVPWM Framework for

Multilevel Inverters. IEEE Transactions on Power

Electronics, 2017, 32(6):4925-4938.

Fan Bo, Zhao Weigang, Liu Gang, Xie Dongdong Closed

loop control of neutral point potential balance of

three-level inverter based on optimized virtual

vector. Journal of Electrical Technology, 2015,

30(04):124-132.

Song Wensheng, Feng Xiaoyun. Internal relationship

between a single-phase three-level SVPWM

modulation and carrier SPWM. Journal of

Electrical Technology, 2012, 27(6):131-138.

Jiang Haipeng, Liu Yongqiang. Simplified SVPWM

double closed loop control of VIENNA rectifier

with neutral point potential balance control. Journal

of Motor and Control, 2014, 18(2):35-41. DOI:

10.15938/2014.02.007.

Liu Sensen, Li Bin, Hang Lijun, etc A new control

method of VIENNA rectifier when three-phase

power network is unbalanced. Chinese Journal of

Electrical Engineering, 2012, 32(21):54-62. DOI:

10.13334/j.0258-8013. pcsee. 2012.21.009.

Dang Chaoliang, the same as Qianfeng, etc. Proportional

repetitive control of Vienna rectifier based on

equivalent carrier SVM. Power Electronics

Technology, 2016, 50(12):59-62+70. DOI: CNKI:

SUN: DLDZ. 0.2016-12-021.

Hu Cungang, Ma Dajun, Wang Qunjing, et al. Loss

distribution balance control strategy for three-level

active neutral point clamped inverter. Journal of

Electrical Technology, 2017, 32(1):129-138.

Zhang Ming, Guo Yuanbo, Li Ze, et al. Output voltage

imbalance suppression method of three-level

inverter under fault tolerant control mode. Journal

of Electrical Technology, 2018, 33(22):5300-5310.

Wang Guangzhu. Study on the unbalance mechanism of

capacitor voltage on DC side of diode clamped

multilevel inverter. Chinese Journal of Electrical

Engineering, 2002, 22(12):111-117.

APPENDIX

Appendix 1: ACTION Sequence of Small Sector Voltage Vector

𝑛 𝑇

0

/4 𝑇

1

/2 𝑇

2

/2 𝑇

0

/2

𝑇

2

/2 𝑇

1

/2 𝑇

0

/4 𝑛 𝑇

0

/4 𝑇

1

/2 𝑇

2

/2 𝑇

0

/2 𝑇

2

/2 𝑇

1

/2 𝑇

0

/4

31

0-1 -1 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 -1 0 -1-1

11

0 0 -1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 0 0 -1

32

0-1 -1 1-1 -1 1 0 -1 1 0 0 1 0 -1 1-1 -1 0-1 -1

12

0 0 -1 01 -1 1 1 -1 1 1 0 1 1-1 0 1 -1 0 0 -1

33

0-1 -1 0 0 -1 1 0 -1 1 0 0 1 0 -1 0 0 -1 0-1 -1

13

0 0 -1 01 -1 0 1 0 1 1 0 0 1 0 0 1 -1 0 0 -1

34

0 0 -1

1 0 -1

1 1 -1

1 1 0

1 1 -1 1 0 -1 0 0 -1

14

-10 -1 -11-1 0 1 -1 0 1 0 0 1 -1 -11 -1 -10 -1

51

-10 -1 -10 0 0 0 0 0 1 0 0 0 0 -1 0 0 -10 -1

41

-1 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 -1 0 0

52

-10 -1 -11-1 -1 1 0 0 1 0 -1 1 0 -11 -1 -10 -1

42

-1 0 0 -10 1 -1 1 1 0 1 1 -1 1 1 -1 0 1 -1 0 0

53

-10 -1 -10 0 -1 1 0 0 1 0 -1 1 0 -1 0 0 -10 -1

43

-1 0 0 -10 1 0 0 1 0 1 1 0 0 1 -1 0 1 -1 0 0

54

-1 0 0 -11 0 -1 1 1 0 1 1 -1 1 1 -1 1 0 -1 0 0

44

-1-1 0 -1-11 -1 0 1 0 0 1 -1 0 1 -1-1 1 -1-1 0

61

-1-1 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 -1 0 -1-1 0

21

0 -1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 -1 0

62

-1-1 0 -1-1 1 0 -1 1 0 0 1 0 -1 1 -1-1 1 -1-1 0

22

0 -1 0 1-1 0 1 -1 1 1 0 1 1 -1 1 1 -1 0 0 -1 0

63

-1-1 0 0 -1 0 0 -1 1 0 0 1 0 -1 1 0 -1 0 -1-1 0

23

0 -1 0 1-1 0 1 0 0 1 0 1 1 0 0 1 -1 0 0 -1 0

64

0 -1 0 0 -1 1 1 -1 1 1 0 1 1 -1 1 0 -1 1 0 -1 0

24

0-1 -1 1-1-1 1 -1 0 1 0 0 1 -1 0 1-1 -1 0-1 -1

ICDPCS 2023 - The International Conference on Data Processing, Control and Simulation

14

Appendix 2: BASIC Vector Action Schedule of Each Sector

𝑛

Action time of 𝑇

0

Action time of 𝑇

1

Action time of 𝑇

2

31

𝑚𝑠𝑖𝑛( 60 −𝜃)

𝑚𝑠𝑖𝑛𝜃

𝑇

−𝑚𝑠𝑖𝑛( 60 + 𝜃)

32

2𝑇

−𝑚𝑠𝑖𝑛( 60 + 𝜃)

𝑇

−𝑚𝑠𝑖𝑛( 60 −𝜃)

𝑚𝑠𝑖𝑛𝜃

33

𝑇

−𝑚𝑠𝑖𝑛𝜃

𝑇

−𝑚𝑠𝑖𝑛( 60 −𝜃)

−𝑇

+ 𝑚𝑠𝑖𝑛( 60 + 𝜃)

34

𝑚𝑠𝑖𝑛( 60 −𝜃)

−𝑇

+ 𝑚𝑠𝑖𝑛𝜃

2𝑇

−𝑚𝑠𝑖𝑛( 60 + 𝜃)

11

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60−

（

𝜃

−60

）

)

𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60+

（

𝜃

−60

）

)

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛

（

𝜃−60

）

12

2𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60

+

（

𝜃−60

）

)

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛( 𝜃−60)

𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60

−

（

𝜃−60

）

)

13

𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛( 𝜃−60)

−𝑇

+

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛

（

60

+ 𝜃−60

）

𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60

−

（

𝜃−60

）

)

14

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60−

（

𝜃

−60

）

)1

2𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60

+

（

𝜃−60

）

)

−𝑇

+

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛( 𝜃

−60)

51

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60−

（

𝜃−120

）

)

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛

（

𝜃−120

）

𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60+

（

𝜃−120

）

)

52

2𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60

+

（

𝜃−120

）

)

𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60−

（

𝜃

−120

）

)

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛

（

𝜃−120

）

53

𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛

（

𝜃

−120

）

𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60−

（

𝜃

−120

）

)

−𝑇

+

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60

+

（

𝜃

−120

）

)

54

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60−

（

𝜃−120

）

)

−𝑇

+

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛

（

𝜃

−120

）

2𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60

+

（

𝜃

−120

）

)

41

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60−

（

𝜃−180

）

)

𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60+

（

𝜃

−180

）

)

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛

（

𝜃−180）

42

2𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60+

（

𝜃−180）)

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛( 𝜃−180)

𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60−

（

𝜃−180

）

)

43

𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛( 𝜃

−180)

−𝑇

+

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛

（

60

+ 𝜃−180）

𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60−

（

𝜃−180

）

)

44

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60−

（

𝜃−180）)

2𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60+

（

𝜃−180）)

−𝑇

+

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛( 𝜃

−180)

61

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60−

（

𝜃−240）)

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛

（

𝜃−240）

𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60+

（

𝜃−240）)

62

2𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60+ 𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛

（

𝜃−240）

Research on SVPWM and Midpoint Potential Balancing Algorithm of Improved NPC Three-Level Inverter

15

（

𝜃−240）)

（

𝜃−240）)

63

𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛

（

𝜃

−240）

𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60−

（

𝜃−240）)

−𝑇

+

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60

+

（

𝜃−240）

64

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60−

（

𝜃

−240）)

−𝑇

+

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛

（

𝜃

−240）

2𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60

+

（

𝜃−240）

21

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60−

（

𝜃

−300）)

𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60+

（

𝜃

−300

）

)

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛

（

𝜃-300）

22

2𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60

+

（

𝜃−300）)

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛( 𝜃−300)

𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60−

（

𝜃−300

）

)

23

𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛( 𝜃−300)

−𝑇

+

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛

（

60

+𝜃−300）

𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60−

（

𝜃−300

）

)

24

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60−

（

𝜃−300）)

2𝑇

−

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛(60+

（

𝜃−300）)

−𝑇

+

4

√

3

• 𝑚• 𝑇

• 𝑠𝑖𝑛( 𝜃

−300)

Appendix 3: TRIGGER Schedule of Switching Devices in Each Sector

𝑛

𝑆

1

𝑆

2

𝑆

1

𝑆

2

𝑆

1

𝑆

2

𝑛 𝑆

1

𝑆

2

𝑆

1

𝑆

2

𝑆

1

𝑆

2

31

1 0

𝑋

0

𝑌

11

1

𝑌

1 0

𝑋

32

𝑋

1 0

𝑌

0

12

𝑌

1

𝑋

1 0

33

𝑌

1 0

𝑋

0

13

1

𝑋

1 0

𝑌

34

𝑋

1

𝑌

1

0

14

0

𝑌 𝑋

1 0

51

0

𝑌

1 0

𝑋

41

0

𝑋

1

𝑌

1

52

0

𝑋

1 0

𝑌

42

0

𝑌

1

𝑋

1

53

0

𝑌

1 0

𝑋

43

0

𝑌

1

𝑋

1

54

0

𝑋

1

𝑌

1

44

0

0

𝑌 𝑋

1

61

0

𝑋

0

𝑌

1

21

𝑌

1 0

𝑋

1

62

0

𝑌

0

𝑋

1

22

𝑋

1 0

𝑌

1

63

0

𝑋

0

𝑌

1

23

𝑋

1 0

𝑌

1

64

𝑌

1 0

𝑋

1

24

𝑋

1 0

0

𝑌

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

ICDPCS 2023 - The International Conference on Data Processing, Control and Simulation

16