A Loss Calculation Method for NPC Three-Level Converters

Abstract

The present invention relates to the technical field of converter loss calculation, and particularly to a method for calculating the losses of an NPC three-level converter, which overcomes the technical defect of accurately calculating the losses of each power device of the rectifier and the inverter of the NPC three-level converter under traction and braking conditions with the NPC three-level bridge arm topology as the research object. The present invention gives the analytical expressions of the conduction losses and switching losses of each power device based on the SPWM modulation method in the inverter and rectifier topologies of the three-level NPC topology bridge arm. The conclusion is universal and can provide a loss calculation solution for any converter with unidirectional / bidirectional energy flow constituted by this bridge arm topology.

Description

Technical Field

[0001] The present invention relates to the technical field of converter loss calculation, and particularly relates to a method for calculating the loss of an NPC three-level converter. Background Art

[0002] Compared with the two-level topology, the NPC three-level topology has smaller harmonics in the output voltage and current, smaller voltage impact on each power device, and lower requirements for the withstand voltage level of the power device. Therefore, it is widely used in high-power energy conversion systems. Figure 1 The shown NPC three-level converter, which includes a single-phase rectifier and a three-phase inverter, is a commonly used topology circuit in high-power AC electric traction systems. Figure 2 It is the NPC three-level bridge arm topology, which is Figure 1 the basic unit of the NPC three-level converter in Figure 2 The shown topology structure has symmetry. T11 is an IGBT, and D11 is its reverse freewheeling diode FWD, which together form an IGBT power module with reverse freewheeling. T11 and D11, T12 and D12, T13 and D13, T14 and D14 are usually IGBT power modules with the same selection. D1 is a clamping diode, which has the same selection as D2. Therefore, from the structural point of view, there is also symmetry in the upper half bridge arm (T11 and D11, T12 and D12, D1) and the lower half bridge arm (T13 and D13, T14 and D14, D2) of the NPC three-level bridge arm. The losses of T11 and D11 are the same as those of T14 and D14, the losses of T12 and D12 are the same as those of T13 and D13, and the loss of D1 is the same as that of D2.

[0003] In the application of high-power electric traction systems, it is usually required that energy can flow bidirectionally to achieve energy recovery under braking conditions. For applications in the rail transit industry, each departure and arrival must experience a traction process and a braking process. How to accurately calculate the losses of each power device in the rectifier and inverter under traction and braking conditions is crucial for the life assessment of the entire converter.

[0004] Publication No. 202010496451.4 discloses an analytical calculation method for the switching losses of a single-phase NPC-type H-bridge cascaded inverter. This method solves the problem of calculating the conduction losses in the case of an indefinite number of switchings within the fundamental period in the pulse jump SVPWM modulation mode. This calculation is only applicable to the inverter operating condition, but does not consider the loss calculation in the case of current reversal.

[0005] Publication No. 201910387855.7 discloses a method for calculating the parallel loss of a diode-clamped three-level converter. Based on the generalized state-space averaging method, the DC component of the neutral-point potential drift of the diode-clamped three-level converter is obtained. According to the measured neutral-point potential drift, the equivalent admittance value of the parallel loss can be calculated, and the parallel loss within a unit time can be calculated. The loss calculation method solves the total loss of the entire converter under the SPWM modulation strategy, and is only applicable to the radiator design application. It cannot give the accurate loss of each device and provides guidance for applications such as junction temperature calculation.

[0006] Therefore, how to Figure 2 take the NPC three-level bridge arm topology as the research object and accurately calculate Figure 1 the losses of each power device of the rectifier and inverter of the NPC three-level converter shown in the traction and braking conditions is an urgent problem to be solved. Summary of the Invention

[0007] To overcome the technical defect of how to take the NPC three-level bridge arm topology as the research object and accurately calculate the losses of each power device of the rectifier and inverter of the NPC three-level converter in the traction and braking conditions, the present invention provides a method for calculating the losses of an NPC three-level converter.

[0008] The present invention provides a method for calculating the losses of an NPC three-level converter, which respectively includes the loss calculation methods of the inverter and the rectifier;

[0009] Among them, the loss calculation method of the inverter is:

[0010] Considering that the AC side of the NPC three-level converter is a motor, and the motor is an inductive load. By default, the current flowing from the DC side to the AC side is positive. The phase voltage and phase current models under the condition of positive current are established as:

[0011]

[0012] Among them, I is the amplitude of the phase current, V is the amplitude of the phase voltage, is the power factor angle; the definition of the power factor is different from the definition of the power factor in motor applications. The definition of the four-quadrant operation power system is adopted, that is, the power factor can be either positive or negative. When the power flow is to the motor side, it is positive, and at this time the power flow to the DC side is negative, and at this time

[0013] The NPC three-level bridge arm adopts the SPWM modulation method, and its working interval within a sine wave period is divided into X1, X2, X3, and X4. The range of X1 is The range of X2 is The range of X3 is The range of X4 is The operating characteristics and duty cycles of each device in each interval are shown in Table 1, where m is the modulation index;

[0014] Table 1 Operating characteristics and duty cycles of each device in the positive current NPC three-level bridge arm

[0015]

[0016] For each semiconductor device on the NPC three-level bridge arm, its on-state loss within a sine wave period T m is:

[0017]

[0018] where V sat (t) is the saturation voltage drop of the semiconductor device. In the calculation, according to the curve provided in the power device manual, it is converted into a function of current. Therefore, the conduction voltage drops of each semiconductor device in the NPC three-level bridge arm can be respectively:

[0019] The saturation voltage drop characteristics of each IGBT in the NPC three-level bridge arm adopt a first-order approximation: V ce (t) = r ce i(t) + V ce0 、

[0020] The saturation voltage drop characteristics of the FWD adopt a first-order approximation: V f (t) = r f i(t) + V f0 、

[0021] The saturation voltage drop of the clamping diode adopts a first-order approximation: V d (t) = r d i(t) + V d0 ;

[0022] According to the analysis of the conduction intervals and duty cycles of each device in Table 1, the on-state losses of each device can be obtained as:

[0023]

[0024]

[0025] Its definite integral analytical expression is:

[0026]

[0027] For the switching losses of each device, the average value of the sine wave current within the carrier period is used to approximately calculate each turn-on loss and turn-off loss, and the results are as follows:

[0028]

[0029] Among them, F sw is the triangular wave carrier frequency; E rec (I), E on (I), E off (I) are the switching loss energy corresponding to the current I on the switching loss vs. current curve in the device manual; U dcon_test is the DC side voltage used when testing E on vs. current I c curve; U dcoff_test is the DC side voltage used when testing E off vs. current I c curve; U dcrec_f_test is the DC side voltage used when testing E rec vs. current I f curve of the anti-parallel diode; U dcrec_d_test is the DC side voltage used when testing E rec vs. current I f curve of the clamping diode device; k ron is the gate correction coefficient calculated according to the E on vs. turn-on gate resistance R on curve; k roff is the gate correction coefficient calculated according to the E off vs. turn-off gate resistance R off curve, and the calculation methods of k ron and k roff are as follows:

[0030]

[0031] Among them, E on_r is the function expression of the turn-on gate resistance vs. current curve in the device manual, E off_r is the function expression of the turn-off gate resistance vs. current curve in the device manual, R on is the actual turn-on gate resistance used, R on_test is the gate resistance used when measuring the E on vs. current curve, R off is the actual turn-off gate resistance used, R off_test is the gate resistance used when measuring the E off vs. current curve;

[0032] Among them, the loss calculation method of the rectifier is:

[0033] Considering that the AC side of the NPC three-level converter is a transformer, which belongs to inductive characteristics, it is default that the current flowing to the AC side is positive. A phase voltage and phase current model is established under the condition of negative current:

[0034]

[0035] where I is the amplitude of the phase current and V is the amplitude of the phase voltage, is the power factor angle; the definition of the power factor is different from the definition of the power factor in motor applications. It adopts the definition of a four-quadrant operating power system, that is, the power factor can be either positive or negative. When the power flow to the DC side is positive, at this time the power flow to the power supply side is negative, at this time

[0036] The NPC three-level bridge arm adopts the SPWM modulation method. Its working interval within a sine wave period is divided into X1, X2, X3, and X4. The range of X1 is The range of X2 is The range of X3 is The range of X4 is The working characteristics and duty ratios of each device in each interval are shown in Table 2, where m is the modulation degree;

[0037] Table 2 Working characteristics and duty ratios of each device of the NPC three-level bridge arm with negative current

[0038]

[0039] For each semiconductor device on the NPC three-level bridge arm, its conduction loss within a sine wave period T m is:

[0040]

[0041] where V sat (t) is the saturation voltage drop of the semiconductor device. In the calculation, according to the curve provided in the power device manual, it is converted into a function of current. Therefore, the conduction voltage drops of each power device in the NPC three-level bridge arm can be respectively expressed as:

[0042] The saturation voltage drop characteristic of the IGBT adopts a first-order approximation: V ce (t) = r ce i(t) + V ce0 、

[0043] The saturation voltage drop characteristic of the FWD adopts a first-order approximation: V f (t) = r f i(t) + V f0 、

[0044] The saturation voltage drop of the clamping diode DIODE is approximated by a first-order approximation: V d (t) = r d i(t) + V d0 ;

[0045] According to the analysis of the conduction interval and duty cycle of each device in Table 2, the on-state losses of each device can be obtained as follows:

[0046]

[0047]

[0048] Calculating the above definite integral, the result is:

[0049]

[0050] For the switching losses of each power device, the average value of the sinusoidal current within the carrier period is used to approximately calculate each turn-on loss and turn-off loss, and the results are as follows:

[0051]

[0052] Among them, the definitions of each parameter are the same as above.

[0053] The technical solution provided by the present invention has the following advantages compared with the prior art: The present invention gives the analytical expressions of the on-state losses and switching losses of each power device based on the SPWM modulation method in the inverter and rectifier topologies of the three-level NPC topology bridge arm. The conclusion is universal and can provide a loss calculation solution for any energy unidirectional / bidirectional flowing converter composed of this bridge arm topology. Description of the Drawings

[0054] The drawings here are incorporated into the specification and constitute a part of this specification, showing embodiments consistent with the present invention, and are used together with the specification to explain the principles of the present invention.

[0055] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, for those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0056] Figure 1 It is the circuit topology of the NPC three-level converter described in the present invention;

[0057] Figure 2 For Figure 1 the basic unit in, that is, the NPC three-level bridge arm topology;

[0058] Figure 3 It is the voltage and current characteristic diagram of the three-level bridge arm of the positive current NPC topology;

[0059] Figure 4 It is the voltage and current characteristic diagram of the three-level bridge arm of the reverse current NPC topology. Specific implementation mode

[0060] In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the solution of the present invention will be further described below. It should be noted that, without conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

[0061] Many specific details are set forth in the following description in order to fully understand the present invention, but the present invention can also be implemented in other ways different from those described herein; obviously, the embodiments in the specification are only part of the embodiments of the present invention, rather than all of the embodiments.

[0062] An embodiment of the present invention provides a method for calculating the losses of an NPC three-level converter, which respectively includes the loss calculation methods of the inverter and the rectifier;

[0063] Among them, the loss calculation method of the inverter is:

[0064] Considering that the AC side of the NPC three-level converter is a motor, and the motor is an inductive load, it is defaulted that the current flowing from the DC side to the AC side is positive. The phase voltage and phase current models under the condition of positive current are established as:

[0065]

[0066] Among them, I is the amplitude of the phase current, V is the amplitude of the phase voltage, is the power factor angle; the power factor is defined differently from the definition of the power factor in motor applications. The definition of the four-quadrant operation power system is adopted, that is, the power factor can be either positive or negative. Taking the power flow to the motor side as positive, at this time the power flow to the DC side is negative, at this time

[0067] The NPC three-level bridge arm adopts the SPWM modulation method, and its working intervals within a sine wave period are divided into X1, X2, X3 and X4. The range of X1 is The range of X2 is The range of X3 is The range of X4 is Specifically as Figure 3 shown; the working characteristics and duty cycles of each device in each interval are shown in Table 1, where m is the modulation degree;

[0068] Table 1 Operating Characteristics and Duty Cycles of Each Device in the Positive Current NPC Three-Level Bridge Arm

[0069]

[0070] For each semiconductor device on the NPC three-level bridge arm, its conduction loss within a sine wave period T m is:

[0071]

[0072] where V sat (t) is the saturation voltage drop of the semiconductor device. In the calculation, according to the curve provided in the power device manual, it is converted into a function of current. Therefore, the conduction voltage drops of each semiconductor device in the NPC three-level bridge arm can be respectively:

[0073] The saturation voltage drop characteristics of each IGBT in the NPC three-level bridge arm adopt a first-order approximation: V ce (t) = r ce i(t) + V ce0 The saturation voltage drop characteristics of FWD adopt a first-order approximation: V f (t) = r f i(t) + V f0 、

[0074] The saturation voltage drop of the clamping diode adopts a first-order approximation: V d (t) = r d i(t) + V d0 ;

[0075] According to the analysis of the conduction intervals and duty cycles of each device in Table 1, the conduction losses of each device can be obtained as:

[0076]

[0077] Its definite integral analytical expression is:

[0078]

[0079] For the switching losses of each device, the average value of the sine wave current within the carrier period is used to approximately calculate each turn-on loss and turn-off loss, and the results are as follows:

[0080]

[0081]

[0082] where, F sw is the triangular wave carrier frequency; E rec (I), E on (I), E off(I) are the respective switching loss energies corresponding to the current I on the switching loss vs. current curve in the device manual; U dcon_test is the DC side voltage used when testing E on vs. current I c curve in the device manual; U dcoff_test is the DC side voltage used when testing E off vs. current I c curve in the device manual; U dcrec_f_test is the DC side voltage used when testing E rec of the anti-parallel diode vs. current I f curve in the device manual; U dcrec_d_test is the DC side voltage used when testing E rec of the clamping diode vs. current I f curve in the device manual; k ron is the gate correction coefficient calculated according to the curve of E on vs. the turn-on gate resistance R on curve in the device manual; k roff is the gate correction coefficient calculated according to the curve of E off vs. the turn-off gate resistance R off curve in the device manual, k ron and k roff are calculated as follows:

[0083]

[0084] where, E on_r is the function expression of the turn-on gate resistance vs. current curve in the device manual, E off_r is the function expression of the turn-off gate resistance vs. current curve in the device manual, R on is the actual turn-on gate resistance used, R on_test is the gate resistance used when measuring the curve of E on vs. current, R off is the actual turn-off gate resistance used, R off_test is the gate resistance used when measuring the curve of E off vs. current;

[0085] Among them, the loss calculation method of the rectifier is:

[0086] Considering that the AC side of the NPC three-level converter is a transformer, which has an inductive characteristic, it is defaulted that the current flowing to the AC side is positive, and a phase voltage and phase current model under the condition of negative current is established:

[0087]

[0088] Where, I is the amplitude of the phase current, and V is the amplitude of the phase voltage. is the power factor angle; the power factor is defined differently from that in motor applications. It adopts the definition of a four-quadrant operating power system, that is, the power factor can be either positive or negative. Taking the power flow to the DC side as positive, at this time the power flow to the power supply side is negative, at this time

[0089] The NPC three-level bridge arm adopts the SPWM modulation method, and its working interval within a sine wave period is divided into X1, X2, X3, and X4. The range of X1 is The range of X2 is The range of X3 is The range of X4 is Specifically, as shown in Figure 4 ; the working characteristics and duty cycles of each device in each interval are shown in Table 2, where m is the modulation degree.

[0090] Table 2 Working Characteristics and Duty Cycles of Each Device in the Current Negative NPC Three-Level Bridge Arm

[0091]

[0092] For each semiconductor device on the NPC three-level bridge arm, its on-state loss within a sine wave period T m is:

[0093]

[0094] Where, V sat (t) is the saturation voltage drop of the semiconductor device. In the calculation, according to the curve provided in the power device manual, it is converted into a function of current. Therefore, the conduction voltage drops of each power device in the NPC three-level bridge arm can be respectively expressed as:

[0095] The saturation voltage drop characteristic of the IGBT adopts a first-order approximation: V ce (t) = r ce i(t) + V ce0 ,

[0096] The saturation voltage drop characteristic of the FWD adopts a first-order approximation: V f (t) = r f i(t) + V f0 ,

[0097] The saturation voltage drop of the clamping diode DIODE adopts a first-order approximation: V d (t) = r d i(t) + V d0 ;

[0098] According to the analysis of the conduction interval and duty cycle of each device in Table 2, the on-state losses of each device can be obtained as follows:

[0099]

[0100]

[0101] Calculating the above definite integral, the result is:

[0102]

[0103] For the switching losses of each power device, the average value of the sinusoidal current within the carrier period is used to approximately calculate each turn-on loss and turn-off loss, and the results are as follows:

[0104]

[0105] Among them, the definitions of each parameter are the same as above.

[0106] Specifically, for Figure 1 the three-level topology shown, the same IGBT module and clamping diode are used. The following examples calculate the losses in its different operating states, and the characteristic parameters of the power devices are as follows:

[0107] IGBT power module model: ABB 5SNA 1500E330305,

[0108] IGBT saturation conduction voltage drop (first-order approximation): V ce =r ce I c +V ce0 =0.00129I c +1.239,

[0109] Diode saturation conduction voltage drop (first-order approximation): V f =r f I c +V f0 =0.0007I f +1.1,

[0110] Turn-on gate resistance correction coefficient: k ron =1.34;

[0111] Turn-off gate resistance correction coefficient: k roff =1.01;

[0112] Turn-on loss energy E on : E on (I c )=1.2616e-10I c 3-2.66e-7I c 2 +1.6021e-3I c +0.1514, turn-off loss energy E off :

[0113] E off (I c ) = 1.4315e-10*I c 3 -5.6495e-7I c 2 +2.41e-3I c +0.2166,

[0114] Reverse recovery loss energy E rec_f :

[0115] E rec_f (I f ) = 1.047e-10I f 3 -7.4605e-7I f 2 +2.1938e-3I f +0.277,

[0116] U dcon_test = 1800V,

[0117] U dcoff_test = 1800V,

[0118] U dcrec_f_test = 1800V,

[0119] Clamping diode model: Infineon DD800S330305,

[0120] Diode saturation conduction voltage drop (first-order approximation): V d = r d I d +V d0 = 0.00195I d +1.1295, diode reverse recovery loss energy E rec_d :

[0121] E rec_d (I f ) = 2.3005e-10I f 3 -9.6426e-7I f 2 +1.6075e-3I f +0.247,

[0122] Udcrec_d_test = 1800 V.

[0123] Example 1: An NPC three-level single-phase rectifier operates in the rectification state. According to Figure 1 the shown NPC three-level single-phase rectifier, the power flow is to the DC side, and the loss calculation method described in the present invention is used for calculation. Parameter input: modulation index m: 0.82; power factor 0.98; phase current amplitude I: 1200; switching frequency: 550 Hz.

[0124] Conduction loss:

[0125]

[0126] Switching loss:

[0127]

[0128] Example 2: An NPC three-level single-phase rectifier operates in the power feeding state to the power supply side. According to Figure 1 the shown NPC three-level single-phase rectifier, the power flow is to the AC side, and the loss calculation method described in the present invention is used for calculation.

[0129] Parameter input: modulation index m: 0.8, power factor -0.98, phase current amplitude I: 900, carrier frequency F sw : 550 Hz.

[0130] Conduction loss:

[0131]

[0132]

[0133] Switching loss:

[0134]

[0135] Example 3: An NPC three-level three-phase inverter operates in the inversion state, and the traction motor is working. According to Figure 1 the shown NPC three-level three-phase inverter, in the inversion state, the power flow is to the motor, and the loss calculation method described in the present invention is used for calculation.

[0136] Parameter input: modulation index m: 0.7, power factor 0.87, phase current amplitude I: 1200, carrier frequency F sw : 450 Hz.

[0137] Conduction loss:

[0138]

[0139] Switching loss:

[0140]

[0141] Embodiment 4: The NPC three-level three-phase inverter operates in the rectification state to perform electric braking on the motor. According to Figure 1 the shown NPC three-level three-phase inverter, the power flow direction is to the DC side, and it is calculated by the loss calculation method described in the present invention:

[0142] Parameter input: Modulation index m: 0.7, power factor -0.85, phase current amplitude I: 1000, carrier frequency F sw : 450 Hz.

[0143] Conduction loss:

[0144]

[0145] Switching loss:

[0146]

[0147]

[0148] The above are only specific embodiments of the present invention, enabling those skilled in the art to understand or implement the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments described herein, but rather to the broadest scope consistent with the principles and novel features invented herein.

Claims

1. A method for calculating the losses of an NPC three-level converter. The NPC three-level arm topology is the basic unit of the NPC three-level converter. In the NPC three-level arm topology, T11 is an IGBT, D11 is its reverse freewheeling diode FWD, and they together form an IGBT power module with reverse freewheeling. T11 and D11, T12 and D12, T13 and D13, T14 and D14 are IGBT power modules with the same selection. D1 is a clamping diode, which has the same selection as D2. It is characterized in that, The loss calculation methods respectively include the loss calculation methods of the inverter and the rectifier; Among them, the loss calculation method of the inverter is as follows: Considering that the AC side of the NPC three-level converter is a motor, and the motor is an inductive load. Assuming that the current flowing from the DC side to the AC side is positive, the phase voltage and phase current models under the condition of positive current are established as follows: i(t) = Isin(ωt), where I is the amplitude of the phase current and V is the amplitude of the phase voltage, is the power factor angle; among them, the power factor is defined differently from the definition of the power factor in motor applications, and the definition of the four-quadrant operation power system is adopted, that is, the power factor is positive when the power flow is to the motor side, and at this time the power factor is negative when the power flow is to the DC side, and at this time The NPC three-level arm uses the SPWM modulation method, and divides its working interval within a sine wave cycle into X1, X2, X3, and X4. The range of X1 is The range of X2 is The range of X3 is The range of X4 is The working characteristics and duty cycle of each device in each interval are shown in Table 1, where m is the modulation degree; Table 1 Working characteristics and duty cycles of each device in the NPC three-level bridge arm with positive current For each semiconductor device on the NPC three-level bridge arm, its conduction loss within a sine wave period T m is as follows: Where V sat (t) is the saturation voltage drop of the semiconductor device. In the calculation, according to the curve provided in the power device manual, it is converted into a function of current. Therefore, the conduction voltage drops of the semiconductor devices in each NPC three-level bridge arm can be respectively: The saturation voltage drop characteristics of each IGBT in the NPC three-level arm are approximated by a first order approximation: V ce (t) = r ce i(t) + V ce0 The saturation voltage drop characteristics of the FWD are approximated by a first order approximation: V f (t) = r f i(t) + V f0 and The saturation voltage drop of the clamping diode is approximated by a first order approximation: V d (t) = r d i(t) + V d0 ; According to the analysis of the conduction intervals and duty cycles of each device in Table 1, the conduction losses of each device can be obtained as follows: Its definite integral analytical expression is: For the switching losses of each device, the average value of the sinusoidal current within the carrier period is used to approximately calculate each turn-on loss and turn-off loss, and the results are as follows: Among them, F sw is the triangular wave carrier frequency; E rec (I), E on (I), E off (I) are the switching loss energy corresponding to the current I on the switching loss versus current curve in the device manual; U dcon_test is the DC side voltage used for testing E on versus current I c curve in the device manual; U dcoff_test is the DC side voltage used for testing E off versus current I c curve in the device manual; U dcrec_f_test is the DC side voltage used for testing E rec versus current I f curve of the anti-parallel diode in the device manual; U dcrec_d_test is the DC side voltage used for testing E rec versus current I f curve of the clamping diode device manual; k ron is the gate correction coefficient calculated according to the curve of testing E on versus the turn-on gate resistance R on curve in the device manual; k roff is the gate correction coefficient calculated according to the curve of testing E off versus the turn-off gate resistance R off curve in the device manual, k ron and k roff are calculated as follows: Among them, E on_r is the function expression of the curve of the turn-on gate resistance and current in the device manual, E off_r is the function expression of the curve of the turn-off gate resistance and current in the device manual, R on is the turn-on gate resistance actually used, R on_test is E on the gate resistance used when measuring the curve of E with respect to current, R off is the turn-off gate resistance actually used, R off_test is E off the gate resistance used when measuring the curve of E with respect to current; Among them, the loss calculation method of the rectifier is as follows: Considering that the AC side of the NPC three-level converter is a transformer, which has inductive characteristics. Assuming that the current flowing to the AC side is positive, the phase voltage and phase current models under the condition of negative current are established: i(t) = -I sin(ωt), where I is the amplitude of the phase current and V is the amplitude of the phase voltage, is the power factor angle; the power factor is defined differently from that in motor applications. It adopts the definition of a four-quadrant operating power system, that is, the power factor is positive when the power flow is to the DC side. At this time the power factor is negative when the power flow is to the power supply side. At this time The NPC three-level arm adopts the SPWM modulation method, and divides its working interval within a sine wave cycle into X1, X2, X3, and X4. The range of X1 is The range of X2 is The range of X3 is The range of X4 is The working characteristics and duty cycle of each device in each interval are shown in Table 2, where m is the modulation degree; Table 2 Working characteristics and duty cycles of each device in the NPC three-level bridge arm with negative current For each semiconductor device on the NPC three-level bridge arm, its conduction loss within a sine wave period T m is as follows: Among them, V sat (t) is the saturation voltage drop of the semiconductor device. In the calculation, according to the curve provided in the power device manual, it is converted into a function of current. Therefore, the conduction voltage drops of the power devices in each NPC three-level bridge arm can be respectively expressed as: The saturation voltage drop characteristic of the IGBT is approximated by a first order approximation: V ce (t) = r ce i(t) + V ce0 、 The saturation voltage drop characteristic of the FWD is approximated by a first order approximation: V f (t) = r f i(t) + V f0 、 The saturation voltage drop of the clamping diode DIODE is approximated by a first order approximation: V d (t) = r d i(t) + V d0 ; According to the analysis of the conduction intervals and duty cycles of each device in Table 2, the conduction losses of each device can be obtained as follows: Calculating the above definite integral, the result is: For the switching losses of each power device, the average value of the sinusoidal current within the carrier period is used to approximately calculate each turn-on loss and turn-off loss, and the results are as follows: Among them, the definitions of each parameter are the same as above.

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