CN113541522B - Control method for realizing four-quadrant operation full-range soft switching of three-phase inverter - Google Patents

Control method for realizing four-quadrant operation full-range soft switching of three-phase inverter Download PDF

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CN113541522B
CN113541522B CN202110827852.8A CN202110827852A CN113541522B CN 113541522 B CN113541522 B CN 113541522B CN 202110827852 A CN202110827852 A CN 202110827852A CN 113541522 B CN113541522 B CN 113541522B
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phase inverter
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CN113541522A (en
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陈建良
李宾
韩强
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Hebei University of Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/66—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output with possibility of reversal
    • H02M7/68—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output with possibility of reversal by static converters
    • H02M7/72—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output with possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/79—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output with possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M7/797—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output with possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/08—Circuits specially adapted for the generation of control voltages for semiconductor devices incorporated in static converters
    • H02M1/088—Circuits specially adapted for the generation of control voltages for semiconductor devices incorporated in static converters for the simultaneous control of series or parallel connected semiconductor devices
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/66—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output with possibility of reversal
    • H02M7/68—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output with possibility of reversal by static converters
    • H02M7/72—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output with possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B10/00—Integration of renewable energy sources in buildings
    • Y02B10/10—Photovoltaic [PV]

Abstract

The invention relates to a control method for realizing four-quadrant operation full-range soft switching of a three-phase inverter, which comprises the following steps of constructing a converter system, wherein the converter system comprises a three-phase inverter topology, a digital controller, a sampling circuit and a driving circuit; decomposing the phase current of the load to obtain components of a d axis and a q axis for current closed-loop control; DPWM is adopted for modulation to obtain a modulation wave; sampling the load phase current, the load phase voltage and the direct current bus voltage, and updating the carrier period in real time by the digital controller; the driving circuit drives the corresponding switching devices to realize soft switching in the whole range of all the switching devices. The critical switching frequency curve of the soft switch is realized by analyzing the switching devices under different power factors, and the minimum critical switching frequency curve is used as the switching frequency curve of all the switching devices for realizing the soft switch, so that the problem of high switching loss of the three-phase inverter when the three-phase inverter operates under different power factors is solved, and the switching frequency is higher.

Description

Control method for realizing four-quadrant operation full-range soft switching of three-phase inverter
Technical Field
The invention belongs to the technical field of power electronics, and particularly relates to a control method for realizing four-quadrant operation full-range soft switching of a three-phase inverter, wherein the direction of non-isolated high-frequency power conversion belongs to the field of control methods of three-phase inverters.
Background
Three-phase inverters are widely used in various industrial devices and domestic appliances, such as photovoltaic systems, static var generators or ac asynchronous motors, etc., in which reactive power is consumed, and therefore, the three-phase inverters are required to have a capability of generating or absorbing reactive power, that is, the three-phase inverters are required to operate under a non-unity power factor condition. In the traditional three-phase inverter, half of the switching devices are in a hard switching state when working, and the switching loss of the switching devices is large, so that the switching frequency of the switching devices is low. Due to the low switching frequency of the switching devices, the volume of the passive components is large, and therefore the power density of the inverter is also low. The soft switching technology can enable the switching device to work in a higher-frequency environment, so that the volume and the weight of the passive element are greatly reduced, and the efficiency and the power density of the inverter can be ensured to be at higher levels.
The soft switching of the switching devices of the conventional three-phase inverter is mostly realized by means of an auxiliary network, and can be divided into a Resonant Direct Current Loop (RDCL) and an Auxiliary Resonant Commutation Pole (ARCP) according to the position of the auxiliary network. Although zero voltage switching-on (ZVS) of the main switching device can be achieved by means of the auxiliary network, the control strategy of the inverter becomes complicated and the power density of the entire inverter cannot be maintained at a high level due to the increase of the number of passive components, switching devices in the auxiliary network. For realizing soft switching of an upper switching device and a lower switching device of the same bridge arm, the most direct method is to increase the ripple of the inverter side inductive current so that the inverter inductive current can flow bidirectionally in one switching period, thereby meeting the soft switching requirements of the upper switching device and the lower switching device of the same bridge arm, and the method for realizing soft switching is used in a single-phase inverter or a Power Factor Correction (PFC) circuit by learners. For a three-phase inverter, it is difficult to achieve soft switching of the switching devices of the three-phase inverter because there is coupling of the three-phase currents and the ripple of the inductor current of each phase is affected by the remaining two phases.
For the problem of coupling of three-phase currents of the three-phase inverter, some researchers propose to connect a neutral point of a filter capacitor with a neutral point of a direct-current bus so as to achieve decoupling of the three-phase currents, but the sum of the three-phase currents is always zero, so that a special modulation strategy is required to be adopted, and the three-phase inverter is easier to control.
Critical-reduction-Mode-Based Soft-Switching Modulation for Three-Phase PV Inverters With Reactive Power Transfer Capability discloses a Three-Phase photovoltaic inverter Reactive Power transmission Soft Switching technology Based on a current Critical Conduction Mode, wherein Discontinuous Pulse Width Modulation (DPWM) is adopted to realize decoupling of Three-Phase current, CRM (Critical Conduction Mode) control method is adopted to realize Soft Switching of a Switching device, but the change range of the Switching frequency is wider; in order to reduce the variation range of the switching frequency, this document employs a frequency synchronization (Fs sync) method. Because the zero-crossing time of the inductive current at the side of the three-phase inverter is not synchronous, the switching device corresponding to the first zero-crossing phase and the switching device corresponding to the second zero-crossing phase are controlled to be simultaneously turned off, and although frequency synchronization can be realized in the control mode, the current is interrupted. Under the working condition of non-unit power factor, the document only analyzes that the power factor is from 0.8 leading to 0.8 lagging, and soft switching of the switching device is to be realized under the full power factor range.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to solve the technical problem of providing a control method for realizing four-quadrant operation full-range soft switching of a three-phase inverter.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a control method for realizing four-quadrant operation full-range soft switching of a three-phase inverter is characterized by comprising the following steps of:
step one, a converter system is built, wherein the converter system comprises a three-phase inverter topology, a digital controller, a sampling circuit and a driving circuit; the three-phase inverter topology comprises a direct-current bus capacitor, a three-phase half-bridge circuit and an LCL filter, and each phase of bridge arm comprises two switching devices with complementary driving signals;
decomposing the load phase current to obtain d-axis and q-axis components for current closed-loop control; DPWM is adopted for modulation to obtain a modulation wave;
step three, the sampling circuit samples the load phase current, the load phase voltage and the direct current bus voltage, and the digital controller updates the carrier period in real time according to the formula (14); the driving circuit drives the corresponding switching devices to realize the soft switching of all the switching devices in the full range under any power factor;
Figure BDA0003174324440000021
wherein, VrmsRMS value of load phase voltage, M is modulation ratio, IrmsIs the RMS value of the load phase current, IbiasIs a bias current, L1Is the inverse ofA transformer side inductor.
Inverter side inductor L1The expression of (a) is:
Figure BDA0003174324440000022
in the formula (15), fsminIs the minimum switching frequency.
In DPWM, one power frequency period comprises six sectors, each sector occupies 60 degrees, the modulation wave of each sector consists of two parts, and the middle point of the sector is used as a demarcation point; the modulation wave expressions of 0-30 degrees and 30-60 degrees of the first sector are respectively expressed as formulas (5) and (6):
Figure BDA0003174324440000023
Figure BDA0003174324440000024
wherein m isa、mcRepresents a modulated wave of a, c phases, mb1、mb2Represents b-phase modulated waves, sita, at 0-30 DEG and 30-60 DEG1、sita2The values of (A) are respectively 0-30 degrees and 30-60 degrees;
the three-phase critical switching frequency expressions at 0-30 degrees and 30-60 degrees of the first sector are respectively expressed as expressions (8) and (9):
Figure BDA0003174324440000031
Figure BDA0003174324440000032
in formulae (8) and (9), fsa、fscRepresenting critical switching frequencies of phases a and c, fsb1、fsb2Represents b-phase critical switching frequency V of 0-30 DEG and 30-60 DEGdcIs a DC bus voltage va、vb、vcFor instantaneous value of load phase voltage ia2、ib2、ic2Is the instantaneous value of the load phase current;
the same minimum value exists at the two ends of the sector of the switching frequency curve under each power factor, and the minimum value of all the minimum values is taken as the switching frequency of the switching device so as to meet the soft switching requirements of all the switching devices under any power factor.
Compared with the prior art, the invention has the beneficial effects that:
1. according to the soft switching method based on the current ripple prediction, all switching devices can realize full-range soft switching on the premise of no auxiliary network. In addition, under the current ripple prediction soft switching method, the inverter side inductive current flows in two directions, so that the current ripple is large to ensure that a switching device can realize soft switching, and the method has the characteristic of high switching frequency, reduces the volume and weight of passive elements, and enables the power density of a three-phase inverter to be kept at a higher level.
2. In order to ensure that all switching devices can realize full-range soft switching, the invention adopts discontinuous five-segment space vector modulation, realizes the critical switching frequency curve of the soft switching by analyzing the switching devices under different power factors, finds the minimum critical switching frequency curve from the critical switching frequency curve, and takes the minimum critical switching frequency curve as the switching frequency curve of all the switching devices to realize the soft switching, thereby solving the problem of large switching loss of a three-phase inverter when the three-phase inverter operates under different power factors and keeping the efficiency of the three-phase inverter at a higher level.
3. For certain operating conditions (such as the dc bus voltage, the grid side voltage, and the output power are determined), the switching frequency does not change with the switching of the power factor. In particular, the switching frequency is constant whether the power factor jumps between inductive loads (e.g., the power factor switches from 0.8 to 0.5), capacitive loads (e.g., the power factor switches from-0.8 to-0.5), or both inductive and capacitive loads jump relative to each other (e.g., the power factor switches from-0.8 to 0.5 or 0.5 to-0.8). When switching at different power levels is performed after the dc bus voltage, the grid-side phase voltage, and the power factor are determined, the switching frequency decreases as the output power increases.
4. The invention does not need to sample the side inductive current of the inverter, does not need an auxiliary network to realize soft switching, and has smaller volume of passive elements, thereby having lower cost of the three-phase inverter.
Drawings
FIG. 1 is a topology block diagram of a three-phase inverter of the present invention;
FIG. 2 is a schematic diagram of an interrupted five-segment space vector modulation of the present invention;
FIG. 3 is a graph of switching frequency in a first sector at unity power factor;
FIG. 4 is a graph of switching frequency in a first sector at different power factors;
FIG. 5 is a graph of switching frequency in a first sector with a power factor of 0.8;
FIG. 6 is a graph of critical switching frequency in a first sector at different power factors;
fig. 7 is a waveform diagram of the three-phase inverter side inductor current and a waveform diagram of the three-phase grid current in one power frequency period with a power factor of 0.8.
Detailed Description
The technical solutions of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments, but the scope of the present invention is not limited thereto.
The invention relates to a control method (a method for short) for realizing four-quadrant operation full-range soft switching of a three-phase inverter, which comprises the following steps:
step one, building a control system, wherein the control system comprises a three-phase inverter topology, a digital controller, a sampling circuit and a driving circuit; the three-phase inverter topology comprises a direct-current power supply, a three-phase half-bridge circuit and a filter, wherein each phase of half-bridge circuit comprises two switching devices with complementary driving signals;
decomposing the phase current of the load; in order to realize three-phase current decoupling, discontinuous five-segment space vector (DPWM) modulation is adopted;
calculating d-axis and q-axis components of the load phase current by using the formula (1);
Figure BDA0003174324440000041
wherein gamma is the phase angle of the load phase voltage; i.e. iα、iβAlpha-axis and beta-axis components of the load phase current satisfy formula (2):
Figure BDA0003174324440000042
in the equation (2), the instantaneous value i of the load phase currenta2、ib2、ic2The expression of (a) is:
Figure BDA0003174324440000043
wherein, theta is a sector angle,
Figure BDA0003174324440000044
is the phase difference between the load phase voltage and the load phase current; i isrmsThe RMS (root mean square) value of the load phase current is expressed as:
Figure BDA0003174324440000045
in the formula (4), S is output power, VrmsRMS value of the load phase voltage;
as shown in fig. 2, one power frequency cycle includes six sectors, each sector occupies 60 °, and the modulation wave of each sector is composed of two parts, and the midpoint of the sector is used as a demarcation point; the amplitude of one-phase modulation wave is 0 or 1 at any moment, so that the other two-phase switching device is only required to be controlled; taking the first sector as an example, the modulation wave of the a phase is fixed to be zero at 0-30 degrees of the first sector, so that the switching states of the two switching tubes of the a phase are constant; the modulation wave of the c phase is fixed to be 1 at 30-60 degrees of the first sector, so that the switching states of the two switching tubes of the c phase are constant; the change of the phase sequence is eliminated, the characteristics of the modulation waves of other sectors are similar to those of the first sector, and the description is omitted;
the modulation wave expressions of 0-30 degrees and 30-60 degrees of the first sector are respectively expressed as formulas (5) and (6):
Figure BDA0003174324440000051
Figure BDA0003174324440000052
wherein m isa、mcRepresents a modulated wave of a, c phases, mb1、mb2Represents b-phase modulation wave, sita, at 0-30 DEG and 30-60 DEG1、sita2The values of (A) are respectively 0-30 degrees and 30-60 degrees; m is a modulation ratio and is expressed as:
Figure BDA0003174324440000053
wherein, VdcIs a dc bus voltage;
the three-phase critical switching frequency expressions at 0-30 DEG and 30-60 DEG of the first sector are respectively expressed as expressions (8) and (9):
Figure BDA0003174324440000054
Figure BDA0003174324440000055
in formulae (8) and (9), fsa、fscRepresenting critical switching frequencies of phases a and c, fsb1、fsb2B-phase critical switching frequency at 0-30 DEG and 30-60 DEGRate; i isbiasThe bias current is determined according to the output capacitance of the switch tube; v. ofa、vb、vcThe instantaneous value of the load phase voltage is expressed as:
Figure BDA0003174324440000056
similarly, the modulated waves of the other sectors can be obtained, which belongs to the conventional technical means in the field and is not described herein again.
Sampling the load phase current, the load phase voltage and the direct current bus voltage by using a sampling circuit, and updating a carrier period by using a digital controller;
equations (8) to (9) apply to both unity and non-unity power factors; fig. 3 is a three-phase switching frequency curve diagram of a first sector obtained under a unit power factor under a current ripple prediction soft switching method, in which a critical switching frequency curve with a lower frequency exists, and the frequency of the critical switching frequency curve is always the minimum in the whole sector, so that the critical switching frequency curve is used as a switching frequency curve to realize the soft switching of all switching devices in the full range;
as shown in fig. 4, by implementing soft switching for each phase of bridge arm under different power factors, it can be known from analysis of the switching frequency curve in the first sector that the switching frequency curve under the non-unit power factor is no longer symmetrical about the midpoint, but each switching frequency curve has the same minimum value at both end points of the sector, and the minimum values under different power factors are different; in order to meet the soft switching requirements of all the switching devices under any power factor, the minimum value of all the minimum values is used as the switching frequency of the switching devices. FIG. 5 is a graph of the switching frequency in the first sector with a power factor of 0.8, similar to the switching frequency in the first sector with unity power factor, where the switching frequency in the first sector with a non-unity power factor is also represented by fsb1And fsaFig. 6 is a graph of critical switching frequency in a first sector under different power factors;
as can be seen from fig. 6, when the power factor is 0.5, the minimum value of the minimum values of the switching frequency is θ and sita1The values of (A) are all zero,
Figure BDA0003174324440000067
is 60 °; will sita10 substituted formula (5) mb1The expression of (c) then has:
Figure BDA0003174324440000061
the value of theta is changed to 0, and the value of theta is changed to 0,
Figure BDA0003174324440000062
substituted formula (3) ib2The expression of (c) then has:
Figure BDA0003174324440000063
substitution of 0 for θ into formula (10) vbThe expression of (c) then has:
Figure BDA0003174324440000064
substituting formulae (11) to (13) for f of formula (8)sb1The expression is simplified to obtain a switching frequency general formula as shown in formula (14):
Figure BDA0003174324440000065
in the formula (14), L1The inverter side inductor is expressed as follows:
Figure BDA0003174324440000066
in the formula (15), fsminIs the minimum switching frequency;
the sampling circuit collects load phase voltage, load phase current and direct current bus voltage in real time and inputs the load phase voltage, the load phase current and the direct current bus voltage into the digital controller, the digital controller updates the carrier period in real time according to the formula (14), and the driving circuit drives corresponding switching devices to realize soft switching in the whole range of all the switching devices.
Example 1
As shown in fig. 1, the two-level three-phase voltage source inverter topology is adopted in the present embodiment, and the filter is an LCL filter; the switch device is a SiC MOSFET with the model of C3M0060065 k; the storage battery is used as a direct current power supply of the three-phase inverter, and the direct current bus voltage VdcIs 400V; the load is a power grid, and the RMS value V of the phase voltage of the loadrms110V, 3300VA rated power and fsminIs 100 kHz. When the three-phase inverter is in a non-unit power factor condition, the analysis under the inductive load and the capacitive load is similar, and the inductive load is taken as an example for explanation.
The filter capacitor of the LCL filter is C, and the alternating current side inductor is L2Bias current IbiasTaking 2A, calculating by the formula (15) to obtain the inverter side inductance L 110 muH; and for the filter capacitor C, controlling the reactive current flowing through the filter capacitor C to be less than 2% of the active current, wherein the value of the filter capacitor C is 4.7 muH. Comprehensively considering the inductance L on the AC side2And inverter side and ac side inductor current ripple, ac side inductor L2The value is 25 muH, and the model of the digital controller is TMS320F 28379S.
The operation structure of the three-phase inverter is simulated under all the above parameter conditions, and a three-phase inverter side inductor current waveform diagram and a three-phase grid current (alternating current side current) waveform diagram within one power frequency period with the power factor of 0.8 as shown in fig. 7 are obtained. As is clear from the figure, the three-phase waveforms are the same regardless of the phase difference between the three-phase inverter-side inductor current and the ac-side current, the inverter-side inductor current ripple is about 2 to 3 times the peak value of the ac-side current, the inverter-side inductor current ripple is large, and soft switching of the switching tubes can be realized. At any moment, the inverter side inductive current is larger than the bias current (2A), and in addition, the inverter side inductive current is larger than the set bias current before and after dynamic switching, so all switching tubes can realize full-range soft switching.
Nothing in this specification is said to apply to the prior art.

Claims (3)

1. A control method for realizing four-quadrant operation full-range soft switching of a three-phase inverter is characterized by comprising the following steps of:
step one, a converter system is built, wherein the converter system comprises a three-phase inverter topology, a digital controller, a sampling circuit and a driving circuit; the three-phase inverter topology comprises a direct-current bus capacitor, a three-phase half-bridge circuit and an LCL filter, and each phase of bridge arm comprises two switching devices with complementary driving signals;
decomposing the phase current of the load to obtain components of a d axis and a q axis for current closed-loop control; DPWM is adopted for modulation to obtain a modulation wave;
step three, the sampling circuit samples the load phase current, the load phase voltage and the direct current bus voltage, and the digital controller updates the carrier period in real time according to the formula (14); the driving circuit drives the corresponding switching devices to realize soft switching in the whole range of all the switching devices;
Figure FDA0003174324430000011
wherein, VrmsRMS value of load phase voltage, M is modulation ratio, IrmsIs the RMS value of the load phase current, IbiasIs a bias current, L1Is an inverter side inductor.
2. The control method for realizing four-quadrant operation full-range soft switching of the three-phase inverter according to claim 1, wherein the inverter side inductor L1The expression of (c) is:
Figure FDA0003174324430000012
in the formula (15), fsminIs the minimum switching frequency.
3. The control method for realizing four-quadrant operation full-range soft switching of the three-phase inverter according to claim 1, wherein in DPWM, one power frequency cycle comprises six sectors, each sector occupies 60 degrees, the modulation wave of each sector consists of two parts, and the middle point of each sector is taken as a dividing point; the modulation wave expressions of 0-30 degrees and 30-60 degrees of the first sector are respectively expressed as formulas (5) and (6):
Figure FDA0003174324430000013
Figure FDA0003174324430000014
wherein m isa、mcRepresents a modulated wave of a, c phases, mb1、mb2Represents b-phase modulation wave, sita, at 0-30 DEG and 30-60 DEG1、sita2The values of (A) are respectively 0-30 degrees and 30-60 degrees;
the three-phase critical switching frequency expressions at 0-30 degrees and 30-60 degrees of the first sector are respectively expressed as expressions (8) and (9):
Figure FDA0003174324430000021
Figure FDA0003174324430000022
in the formulae (8) and (9), fsa、fscRepresenting critical switching frequencies of phases a and c, fsb1、fsb2Represents b-phase critical switching frequency V of 0-30 DEG and 30-60 DEGdcIs a DC bus voltage va、vb、vcFor instantaneous value of load phase voltage ia2、ib2、ic2Is the instantaneous value of the load phase current;
the same minimum value exists at the two ends of the sector of the switching frequency curve under each power factor, and the minimum value of all the minimum values is taken as the switching frequency of the switching device so as to meet the soft switching requirements of all the switching devices under any power factor.
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