CN102013825B - Loss analysis method for diode clamping type three-level voltage source converter (VSC) - Google Patents

Abstract

The invention relates to a method for analyzing the loss of a diode-clamped three-level voltage source converter (Voltage Source Converter, VSC). It includes the following steps: 1) Analyze the conduction law of the diode-clamped three-level VSC, and establish a polynomial loss model for the insulated gate bipolar transistor (IGBT); 2) Calculate the conduction voltage drop of the IGBT and switching losses are expressed as a quadratic polynomial of the current; 3) The loss of the device is calculated by using a polynomial fitting method. The present invention adopts the polynomial fitting method to calculate the loss simply and quickly, and on this basis, analyze the change of the loss along with the power factor and the modulation degree, and the loss distribution of each device at different operating points, and give the selection of device parameters and Thermal design provides a basis and has great practical value.

Description

Loss analysis method of diode-clamped three-level voltage source converter

technical field

The invention is a diode-clamped three-level voltage source converter loss analysis method for analyzing the loss distribution of each device as the power factor and modulation change, which belongs to the diode-clamped three-level VSC loss Transformation techniques for analytical methods.

Background technique

Diode Clamped (Diode Clamped, also known as Neutral Point Clamped) three-level voltage source converter (Voltage Source Converter, referred to as VSC) main circuit structure, and flying capacitor clamped three-electric Compared with the level converter, the diode-clamped three-level converter has significant competitiveness. The cost of the clamping diode is lower than that of the flying capacitor, it is easy to package, and the control method is simple, so it has been widely used in many fields. Power loss affects the efficiency and economical operation of voltage source converters, and is a problem that must be paid attention to in practical engineering applications.

Loss estimation is an important basis for converter system design, device parameter selection and thermal design. The IGBT loss models established by scholars at home and abroad mainly focus on the loss model of the physical structure. It is not easy to apply the loss model based on physical structure to actual production, especially the determination of model parameters is a relatively complicated process, which is difficult for ordinary users.

Contents of the invention

The object of the present invention is to provide a simple, convenient, fast and practical method for analyzing the loss of a diode-clamped three-level voltage source converter in consideration of the above problems. The invention provides a basis for the selection of device parameters and thermal design.

The technical solution of the present invention is: the loss analysis method of the diode-clamped three-level voltage source converter of the present invention, which includes the following steps:

1) Analyze the conduction law of the diode-clamped three-level voltage source converter, and establish a polynomial loss model of the IGBT;

2) Express the turn-on voltage drop and switching loss of the IGBT as a quadratic polynomial of current;

3) Use the method of polynomial fitting to calculate the loss of the device.

The above step 3) is carried out according to the following specific steps:

a. According to the user manual provided by the IGBT manufacturer, use the polynomial fitting method to obtain the characteristic curve of the IGBT;

b. Analyze the conduction law of the diode-clamped three-level voltage source converter, and obtain the conduction duty ratio of each switch tube;

c. On-state loss calculation of switching devices:

Since the structure of the diode-clamped three-level converter is symmetrical, the IGBT modules and clamping diodes usually selected have the same characteristics, so only the four main switching tubes VT1, VT2, VD3, VD4 and the clamping The loss of diode VD5 is analyzed,

  

  

   

   

d. Switching loss calculation of switching devices

The formula for calculating the switching loss is

In the formula, T _o —power frequency period, T _s —switching period;

From this, the switching loss P _T1sw of VT1, the reverse recovery loss P _D5rec of VD5, the switching loss P _T2sw of VT2, and the reverse recovery loss P _D4rec of VD4

   

   

 

 

d. Loss calculation of diode-clamped three-level voltage source converter

The loss of the diode-clamped three-level converter is mainly the loss of the IGBT module, including the on-state loss and switching loss of the IGBT part, the on-state loss and reverse recovery loss of the antiparallel diode, and the on-state loss and reverse recovery loss of the clamping diode. State loss and reverse recovery loss, on this basis, analyze the change of loss with power factor and modulation degree.

The current on the AC side of the above-mentioned voltage source converter is a sinusoidal waveform, and the capacitor voltage on the DC side is balanced.

The present invention establishes the polynomial loss model of the IGBT by first analyzing the conduction law of the diode-clamped three-level voltage source converter; and then expresses the conduction voltage drop and switching loss of the IGBT as a quadratic polynomial of current; And the method of calculating the loss of the device by the method of polynomial fitting is simple, convenient, fast and practical. The invention provides a basis for the selection of device parameters and thermal design. The invention is a convenient and practical method for analyzing the loss of a diode-clamped three-level voltage source converter.

Description of drawings

Figure 1 is the topology of a single-phase diode-clamped three-level voltage source converter.

The left and right parts of Figure 2 are diagrams showing the variation of the on-state loss and switching loss of the external IGBT with the power factor and modulation degree.

The left and right parts of Figure 3 are the diagrams of the on-state loss and reverse recovery loss of the external diode as a function of power factor and modulation degree.

The left and right parts of Figure 4 are diagrams showing the variation of the on-state loss and switching loss of the IGBT with power factor and modulation degree.

The left and right parts of Figure 5 are diagrams of the on-state loss and reverse recovery loss of the diode inside as a function of power factor and modulation degree.

The left and right parts of Fig. 6 are the change diagrams of the on-state loss and reverse recovery loss of the clamp diode with the power factor and modulation degree.

The black in the columnar loss diagram shown in Figure 7-10 represents the on-state loss, and the white represents the switching loss. The five columnar losses shown from left to right represent the outer IGBT, outer diode, inner IGBT, and inner Loss plot of diode and clamping diode.

Fig. 7 is a loss distribution diagram when the power factor is 1 and the modulation degree is 1.

Fig. 8 is a loss distribution diagram when the power factor is -1 and the modulation degree is 1.

Fig. 9 is a loss distribution diagram when the power factor is 1 and the modulation degree is 0.05.

Fig. 10 is a loss distribution diagram when the power factor is -1 and the modulation degree is 0.05.

The symbols in the figure are: E, DC side voltage; M , modulation degree; pf , power factor; P _Toutcond , on-state loss of the external IGBT; P _Toutsw , switching loss of the external IGBT; P _Doutcond , on-state loss of the external diode ; P _Doutrec , the reverse recovery loss of the outer diode; P _Tincond , the on-state loss of the inner IGBT; P _Tinsw , the switching loss of the inner IGBT; P _Dincond , the on-state loss of the inner diode; P _inrec , the reverse of the inner diode Recovery loss loss; P _Dnpccond , the on-state loss of the clamping diode; P _Dnpcrec , the reverse recovery loss of the clamping diode; Tout, the outer IGBT; Dout, the outer diode; Tin, the inner IGBT; Din, the inner Diode; Dnpc, clamping diode.

The symbols in the text are: C ₁ =C ₂ are two DC capacitors, VT1, VT2, VT3, VT4 are 4 main switch tubes, VD1, VD2, VD3, VD4 are 4 freewheeling diodes, VD5, VD6 are two Clamping diodes, VT1 and VT4 are the outer IGBTs, VT2 and VT3 are the inner IGBTs, VD1 and VD4 are the outer diodes, VD2 and VD3 are the inner diodes, u _CE is the on-state voltage drop, i is the AC side current, E _Tsw is the switching energy.

Detailed ways

In the following, the current is 260A, the fundamental frequency is 50Hz, the switching frequency is 1500Hz, the junction temperature T _j =125°C, the DC voltage is 1800V, the selected IGBT module is FF450R17ME3, and the clamping diode BYM600A170DN2 is taken as an example to illustrate this method.

According to the characteristic curve provided by the user manual of IGBT and diode, the expressions of on-state voltage drop u _CE and E _Tsw are obtained by polynomial fitting method

  

  

The loss of the diode-clamped three-level converter is mainly the loss of the IGBT module, including the on-state loss and switching loss of the IGBT part, the on-state loss and reverse recovery loss of the antiparallel diode, and the on-state loss and reverse recovery loss of the clamping diode. state loss and reverse recovery loss. Since the structure of the diode-clamped three-level converter is symmetrical, the IGBT modules and clamping diodes usually selected have the same characteristics, so only the four main switching tubes VT1, VT2, VD3, VD4 and the clamping The loss of diode VD5 is analyzed,

Through the analysis of the conduction principle of the main circuit, the switching state of the device is obtained, as shown in Table 1.

Table 1 Switching state of the device

mark VT1 VT2 VT3 VT4 The output voltage P 1 1 0 0 E/2 0 0 1 1 0 0 N 0 0 1 1 -E/2

When the carrier in-phase stacked PWM modulation is used, the duty cycle of VT and VD can be obtained from the geometric relationship, that is, P?0, the duty cycle of VT is D _P = M sin( a + θ ), and the duty cycle of VD is D ₀₊ =1- D _P ; N?0, the duty cycle of VT is D _N =- M sin( a + θ ), the duty cycle of VD is D _0- =1- D _N , as shown in Table 2 .

Table 2 Duty cycle of VD

the VT1 VT2 VD3 VD4 VD5 0~π- θ D. _P 1 0 0 1- D _P π- θ -~π 0 1- D _N D. _N D. _N 1- D _N

From this, the calculation formula of on-state loss is obtained

  

  

The switching state is P?0, VT1 and VD5 commutate, and the switching loss is mainly the switching loss of VT1 and the reverse recovery loss of VD5. The switching state is N?0, VT2 and VD4 commutate, and the switching loss is mainly the switching loss of VT2 and the reverse recovery loss of VD4.

The formula for calculating the switching loss is

  

  

   

   

Figure 2-6 shows the variation of the loss of each device with the power factor and modulation degree. It can be seen that as the modulation degree M increases, the duty cycle of VT1 increases, and the on-state loss increases; the duty cycle of VT2 in [π-θ-~π] decreases, and the on-state loss decreases; The duty cycle of VD3 and VD4 increases, and the on-state loss increases; the duty cycle of VD5 decreases, and the on-state loss decreases. As the power factor pf decreases, the conduction time of VT1 decreases, and the conduction loss decreases; the conduction time of VT2 remains unchanged, but the conduction time with a large duty cycle decreases, and the conduction time with a small duty cycle increases , so the on-state loss decreases; the on-time of VD3 and VD4 increases, and the on-state loss increases; the on-time of VD5 remains unchanged, but the time of the two conduction stages and the corresponding duty cycle have changed, so On-state losses vary.

As the power factor pf decreases, the switching range of VT1 and VD5 narrows, so the switching loss decreases; the switching range of VT2 and VD4 becomes larger, and the switching loss increases.

Figure 7-10 is the loss distribution diagram of the diode-clamped three-level converter at the boundary, respectively, the modulation degree pf =1, M =1, pf =-1, M =1, pf =1, M = 0.05, and pf =-1, M =0.05.

It can be seen that the loss distribution diagram in these four cases is the most unbalanced. When the power factor pf = 1 and the modulation degree M = 1, the outer IGBT has the most loss; the power factor pf = -1 and the modulation degree M = 1 When the power factor pf = 1, when the modulation degree is very low, the clamping diode will cause the most loss; when the power factor pf = -1, and the modulation degree M is very low, the most loss will occur It is the IGBT inside.

The calculations of the above embodiments show that the diode-clamped three-level VSC loss analysis method provided by the present invention is simple, fast and practical, and provides a basis for device parameter selection and thermal design.

Claims (2)

1. a diode-clamped three-level voltage source converter loss analysis method is characterized in that comprising the following steps: 1) Establish a polynomial loss model for the loss of the three-level voltage source converter, in which the loss of the diode-clamped three-level converter includes the on-state loss of the IGBT part, the switching loss and the on-state loss of the antiparallel diode and Reverse recovery loss, and on-state loss and reverse recovery loss of the clamp diode; 2) According to the characteristic curve provided by the IGBT and diode user manual, the conduction voltage drop and switching energy loss value E _Tsw of the IGBT and diode are expressed as a quadratic polynomial of current by polynomial fitting method, Express the turn-on voltage drop of the IGBT as a quadratic polynomial of the current: u _CE = a _c + b _c i + c _c i ² ; Express the conduction voltage drop of a diode as a quadratic polynomial of current: u _CE =a _f +b _f i+c _f i ² ; Express the switching energy loss E _Tsw of the IGBT as a quadratic polynomial of the current: E _Tsw ＝(a _swon +b _swon i+c _swon i ² )+(a _swoff +b _swoff i+c _swoff i ² ) Express the switching energy loss E _Tsw of the diode as a quadratic polynomial of current: E _Tsw =a _D +b _D i+c _D i ² ; 3) Calculate the loss of the three-level voltage source converter, Among them, the above step 3) is carried out according to the following specific steps: a. Analyze the conduction duty cycle of each IGBT and diode device When the state of the single-phase bridge arm changes between positive voltage and zero, that is , the duty cycle of IGBT VT and diode VD is D _P and D ₀ +=1-D _P ; the state of the single-phase bridge arm changes between negative voltage and zero, namely

When , the duty cycle of VT and VD is D _N and D ₀ -=1-D _N ; b. On-state loss calculation of IGBT and diode devices Since the structure of the diode-clamped three-level converter is symmetrical, and the selected IGBT modules and clamping diodes have the same characteristics, only the on-state losses P _VT1cond , P _VT2cond , P _VD3cond , P _VD4cond , P _VD5cond for analysis and calculation; Among them, VT1 and VT2 are two IGBTs of the upper bridge arm of one phase of the voltage source converter, VD3 and VD4 are two freewheeling diodes of the lower bridge arm of the one phase of the voltage source converter, and VD5 is clamping diode; $\begin{array}{c}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; VT</span>}\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; cond</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\underset{\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; CE</span>}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; P</span>}}\mathrm{<span\; class="notranslate">\; d\&alpha;</span>}\\ <span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\underset{\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; I</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; sin</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; I</span>}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; P</span>}}\mathrm{<span\; class="notranslate">\; d\&alpha;</span>}\end{array}$ $\begin{array}{c}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; VT</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; cond</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\underset{\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; d\&alpha;</span>}<span\; class="notranslate">\; +</span>\\ \frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\underset{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&alpha;</span>}\end{array}$ $\begin{array}{c}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; VD</span>}\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; cond</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; VD</span>}\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; cond</span>}}\\ <span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\underset{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}\mathrm{<span\; class="notranslate">\; d\&alpha;</span>}\end{array}$ $\begin{array}{c}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; VD</span>}\mathrm{<span\; class="notranslate">\; 5</span>}\mathrm{<span\; class="notranslate">\; cond</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\underset{\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; 5</span>}}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; 5</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; P</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&alpha;</span>}\\ <span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\underset{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; 5</span>}}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; 5</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&alpha;</span>}\end{array}$ c. Switching loss calculation of IGBT and diode devices The formula for calculating the switching loss is ${\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; Tw</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{<span\; class="notranslate">\; \&Integral;</span>\mathrm{<span\; class="notranslate">\; E</span>}}_{\mathrm{<span\; class="notranslate">\; Tw</span>}}$ In the formula, T _o —power frequency period, f _s —switching frequency; E _Tsw is the switching energy loss value in the IGBT data sheet at a certain temperature; Thus, the switching loss P _T1sw of VT1, the reverse recovery loss P _D5rec of VD5, the switching loss P _T2sw of VT2, and the reverse recovery loss P _D4rec of VD4 can be obtained; $\begin{array}{c}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; sw</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; [</span>\underset{\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; swon</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; swon</span>}}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; swon</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&alpha;</span>}\\ <span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; swoff</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; swoff</span>}}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; swoff</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&alpha;</span>}<span\; class="notranslate">\; ]</span>\end{array}$ ${\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}\mathrm{<span\; class="notranslate">\; 5</span>}\mathrm{<span\; class="notranslate">\; rec</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\underset{\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}\mathrm{<span\; class="notranslate">\; 5</span>}}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}\mathrm{<span\; class="notranslate">\; 5</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&alpha;</span>}$ ${\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; sw</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; [</span>\underset{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; swon</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; swon</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; swon</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&alpha;</span>}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; swoff</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; swoff</span>}}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; swoff</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&alpha;</span>}<span\; class="notranslate">\; ]</span>$ ${\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; rec</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}\underset{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\overset{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{<span\; class="notranslate">\; \&Integral;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}\mathrm{<span\; class="notranslate">\; 4</span>}}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d\&alpha;</span>}<span\; class="notranslate">\; .</span>$ 2. The method for analyzing losses of a diode-clamped three-level voltage source converter according to claim 1, wherein the AC side current of the voltage source converter is a sinusoidal waveform, and the DC side capacitor voltage is balanced.

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