CN112838775B - Improved circulation calculation method for hybrid modular multilevel converter - Google Patents

Improved circulation calculation method for hybrid modular multilevel converter Download PDF

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CN112838775B
CN112838775B CN202110025448.9A CN202110025448A CN112838775B CN 112838775 B CN112838775 B CN 112838775B CN 202110025448 A CN202110025448 A CN 202110025448A CN 112838775 B CN112838775 B CN 112838775B
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张亮
管益涛
李丹栋
水恒华
霍乾涛
侯凯
过亮
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Nanjing Institute 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
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/483—Converters with outputs that each can have more than two voltages levels

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Abstract

The invention discloses an improved circulation calculation method of a mixed type modular multilevel converter, which comprises the following steps: establishing a mixed type modular multilevel converter circulation model; obtaining actual output voltage of each sub-module between each phase of upper bridge arm and each phase of lower bridge arm based on a modulation function method; deducing the voltage sum of all the submodules of the upper bridge arm and the lower bridge arm of each phase; assuming a circulation expression containing a direct current component, a frequency doubling harmonic component and a frequency quadrupling harmonic component, and substituting the circulation expression into a circulation model to obtain an equation to be solved; and deducing the amplitude and the phase angle of the double-frequency harmonic component and the amplitude and the phase angle of the quadruple-frequency harmonic component from the equation to be solved based on a time domain method. The invention adopts a time domain method when deducing the circulation expression, overcomes the defect that the traditional circulation calculation method can only solve the amplitude of the frequency doubling circulation component and neglects the error caused by the coupling quantity generated in the solution equation, and provides a theoretical basis for the inhibition research of the circulation frequency doubling component and the frequency quadrupling component in engineering.

Description

Improved circulation calculation method for hybrid modular multilevel converter
Technical Field
The invention belongs to the field of flexible direct current transmission, and particularly relates to an improved circulation calculation method of a hybrid modular multilevel converter.
Background
Compared with a traditional two-level and three-level Voltage Source Converter (VSC), the Modular Multilevel Converter (MMC) has the advantages of high efficiency, high output waveform quality, low switching frequency, modularization and the like. As an MMC basic element, a Half-Bridge Sub-module (HBSM) is simple in structure and low in control difficulty. However, a Half-Bridge MMC (HB-MMC) formed by Half-Bridge submodules cannot effectively limit short-circuit current through the converter itself when a bipolar short-circuit fault occurs on the dc side. A Full Bridge Sub-module (FBSM) can isolate a dc-side bipolar short circuit fault by latching of each IGBT, but has a larger number of switching devices than a half Bridge Sub-module. The novel Hybrid Modular Multilevel Converter (HMMC) not only utilizes the capability of the full-bridge submodule to isolate the double-pole short-circuit fault of the direct current side, but also considers the economy of the half-bridge submodule, and is suitable for flexible direct current power grid or alternating current-direct current hybrid power grid engineering.
The upper bridge arm current and the lower bridge arm current of each phase of the HMMC bear the power component output by the alternating current network side, and a part of harmonic bias components exist, are defined as circulating currents, and are derived from the problem of unbalance of capacitance and voltage among submodules of the HMMC. The circulating current is superposed in the upper and lower bridge arm currents of each phase of the HMMC, so that on one hand, the rated current capacity of the power switch device is improved, and the system cost is increased; on the other hand, the loss is increased, the power switch tube is heated seriously, and the service life of the device is influenced.
The HMMC circulating current mainly comprises a direct current component and even harmonics, does not contain odd harmonics, has the largest proportion of 2-order and 4-order low harmonics, and has larger influence on the running of an HMMC system along with the increase of the number of harmonics. In engineering practice, in order to optimize the performance of the MMC system, the mechanism analysis and suppression of the 2 nd and 4 th harmonic components in the circulating current are also an important point. At present, few documents are provided for analyzing and calculating the circulation mechanism of the novel HMMC topology, and the invention derives the circulation expression containing the direct current component, the second harmonic component and the fourth harmonic component in detail.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the problems in the prior art, the invention discloses an improved circulation calculation method of a hybrid modular multilevel converter, which is characterized in that a functional relation between circulation and bridge arm voltage is established according to the working principle and a basic equivalent circuit of HMMC, meanwhile, a mathematical expression of the bridge arm capacitance voltage of an HMMC system is deduced based on a switching function method, and then an HMMC circulation expression containing a direct current component, a frequency doubling component and a frequency quadrupling component is deduced.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the following technical scheme: an improved circulation calculation method for a hybrid modular multilevel converter is characterized by comprising the following steps:
s1, establishing a mathematical model of the hybrid modular multilevel converter to obtain an equivalent circuit model and a circulation model of the hybrid modular multilevel converter;
s2, analyzing the working characteristics of each submodule between each phase of upper bridge arm and each phase of lower bridge arm in the hybrid modular multilevel converter based on a modulation function method to obtain the actual output voltage of each submodule;
s3, deducing the voltage sum of all the submodules of the upper bridge arm and the lower bridge arm of each phase by combining the actual output voltage of each submodule in the step S2;
s4, assuming a circulation expression containing a direct current component, a second harmonic component and a fourth harmonic component, substituting the circulation expression and the voltage sum of each phase of upper bridge arm and lower bridge arm obtained in the step S3 into the circulation model obtained in the step S1 to obtain an equation to be solved, and extracting a second harmonic component equation and a fourth harmonic component equation in the equation to be solved;
and S5, deducing the amplitude and phase angle of the double-frequency harmonic component and the amplitude and phase angle of the quadruple-frequency harmonic component from a double-frequency component equation and a quadruple-frequency component equation of the equation to be solved based on a time domain method to obtain a circulation expression.
Preferably, in step S1, the circulation model of the hybrid modular multilevel converter is:
Figure BDA0002890163050000021
wherein L is0The inductance of the bridge arm; r0Is the equivalent loss resistance of the bridge arm; u shapedcIs a direct current side bus voltage; u. ofp_iAnd un_iI-phase upper bridge arm voltage and i-phase lower bridge arm voltage are respectively obtained; i.e. iizI-phase circulating current.
Preferably, in step S2, the actual output voltages of the single submodules of the i-phase upper bridge arm and the i-phase lower bridge arm of the hybrid modular multilevel converter are as follows:
Figure BDA0002890163050000022
wherein u iscp_io、ucn_ioThe actual output voltages of the single submodules of the i-phase upper bridge arm and the i-phase lower bridge arm are respectively obtained; sp_iAnd Sn_iRespectively the modulation functions of an i-phase upper bridge arm and a i-phase lower bridge arm, m (m is more than or equal to 0 and less than or equal to 1) represents the voltage modulation ratio, omega0Is the fundamental angular frequency; u. ofcp_i、ucn_iInstantaneous voltages of single sub-modules of the i-phase upper bridge arm and the i-phase lower bridge arm are respectively obtained; c0Capacitance for a single sub-module; i.e. icp_i、icn_iThe instantaneous currents respectively flow through the i-phase upper bridge arm submodule and the i-phase lower bridge arm submodule, and the expressions are as follows:
Figure BDA0002890163050000031
wherein ip_i、in_iI-phase upper bridge arm current and i-phase lower bridge arm current respectively; i.e. io_iOutputting current for the alternating current side;
in step S3, the sum of the voltages of all the submodules of the i-phase upper arm and the i-phase lower arm is:
Figure BDA0002890163050000032
and N is the number of the sub-modules on each bridge arm.
Preferably, in step S4, the circulation flow expression is:
iiz＝Iiz_dc+Iiz_2cos(2ω0t+θ2)+Iiz_4cos(4ω0t+θ4)
the equation for the second harmonic component is:
Figure BDA0002890163050000033
the quadruple frequency component equation is:
Figure BDA0002890163050000034
wherein, Iiz_dcIs a circulating DC component, and
Figure BDA0002890163050000035
Idcis a direct side bus current, and
Figure BDA0002890163050000036
p is active power; i isiz_2The amplitude of the double frequency harmonic component; theta2A phase angle that is a harmonic component of a double frequency; i isiz_4Is the amplitude of the quadruple frequency harmonic component; theta4The phase angle of the quadruple frequency harmonic component; i ismOutput current i for i-phase of AC sideo_iA peak value of (d);
Figure BDA0002890163050000037
leading the output current to the angle of the output voltage for the alternating current side;
then in step S5, the solution is Iiz_2And theta2、Iiz_4And theta4Comprises the following steps:
Figure BDA0002890163050000041
Figure BDA0002890163050000042
Figure BDA0002890163050000043
Figure BDA0002890163050000044
Figure BDA0002890163050000045
has the advantages that: the invention has the following remarkable beneficial effects:
the invention deduces an expression that the circulating current contains direct current component, frequency doubling component and frequency quadrupling component based on a time domain method, overcomes the defect that when the traditional MMC uses a phasor method to solve the circulating current, only frequency doubling circulating current amplitude can be solved, and a certain error caused by neglecting the coupling quantity in a solving equation is overcome, is simple and easy to operate, improves the accuracy, can provide reference for the selection of bridge arm inductance and power switching devices in sub-modules, and simultaneously provides a theoretical basis for the suppression of frequency doubling and frequency quadrupling components in the circulating current in engineering.
Drawings
Fig. 1 is a topology diagram of a hybrid modular multilevel converter according to the present invention;
fig. 2 is a flow chart of a circular current calculation of the hybrid modular multilevel converter according to the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings.
As shown in fig. 1, the novel three-phase Hybrid Modular Multilevel Converter (HMMC) topology is composed of 6 bridge arms, N sub-modules are arranged on each bridge arm, wherein each half-bridge sub-module contains H, and each full-bridge sub-module contains F.
The invention discloses an improved circulation calculation method of a hybrid modular multilevel converter, which aims at the topology of a novel hybrid modular multilevel converter, establishes the functional relation between circulation and bridge arm voltage according to the working principle and the basic equivalent circuit of the hybrid modular multilevel converter, and deduces the mathematical expression of bridge arm capacitance voltage of a hybrid modular multilevel converter system based on a modulation function method. As shown in fig. 2, the method comprises the following steps:
step one, establishing a mathematical model of the hybrid modular multilevel converter to obtain an equivalent circuit model and a circulation model of the hybrid modular multilevel converter.
According to the working principle of the hybrid modular multilevel converter, the circulation model of the hybrid modular multilevel converter is established as follows:
Figure BDA0002890163050000051
wherein L is0Is the inductance of the bridge arm, R0Is an equivalent loss resistance of the bridge arm, UdcIs a DC side bus voltage up_iAnd un_iI-phase upper and lower bridge arm voltages, iizI-phase circulating current.
And step two, analyzing the working characteristics of each sub-module between an upper bridge arm and a lower bridge arm in the hybrid modular multilevel converter based on a modulation function method to obtain the output characteristics of each sub-module.
Defining an AC side output voltage u for a steady state mathematical model of a hybrid modular multilevel convertero_iOutput current io_iComprises the following steps:
Figure BDA0002890163050000052
wherein, UmAnd ImOutput voltage u of i-phase on AC sideo_iAnd an output current io_iPeak value of, omega0Is the angular frequency of the fundamental wave,
Figure BDA0002890163050000053
the output current leads the angle of the output voltage.
According to an equivalent circuit model and a KCL law of the hybrid modular multilevel converter, the expressions of the currents of an upper bridge arm and a lower bridge arm are as follows:
Figure BDA0002890163050000054
wherein ip_iAnd in_iI-phase upper bridge arm current and i-phase lower bridge arm current.
Instantaneous current i flowing through upper bridge arm and lower bridge arm submodule capacitorscp_i、icn_iCan be expressed as:
Figure BDA0002890163050000061
wherein S isp_iAnd Sn_iAnd m (m is more than or equal to 0 and less than or equal to 1) represents a voltage modulation ratio.
Actual output voltage u of capacitor voltage of single submodule of upper bridge arm and lower bridge arm of hybrid modular multilevel convertercp_io、ucn_ioComprises the following steps:
Figure BDA0002890163050000062
wherein, C0Is a single sub-module capacitor; u. ofcp_i、ucn_iThe instantaneous voltages of the single sub-module capacitors of the upper bridge arm and the lower bridge arm are respectively.
And step three, combining the output characteristics of the sub-modules to deduce capacitance-voltage expressions of the upper bridge arm and the lower bridge arm.
Each bridge arm is provided with N sub-modules, and the total capacitance voltage u of the i-phase upper bridge arm and the i-phase lower bridge armp_i、un_iRespectively as follows:
Figure BDA0002890163050000063
the sum of the voltages of all capacitors of the i-phase bridge arm is:
Figure BDA0002890163050000064
and step four, assuming a circulation expression, and substituting the circulation expression and the capacitance and voltage expressions of the upper bridge arm and the lower bridge arm obtained in the step three into the circulation model obtained in the step one.
When the bus current I on the DC sidedcWhen the current flows into each phase of bridge arm, the bus current is equally divided and then enters into a single bridge arm, so the circulation current is expressed as:
Figure BDA0002890163050000071
wherein, Iiz_dcIs a circulating current direct current component; i.e. iiz_xRepresents the x harmonic component in the circulating current, and iiz_x＝Iiz_x cos(xω0t+θx) X is not less than 2 and is even number, Iiz_xRepresenting the amplitude, theta, of the x-th harmonic component in the circulating currentxRepresenting the x-order harmonic component phase angle.
Circulating DC component Iiz_dcCan have various expressions, e.g.
Figure BDA0002890163050000072
And
Figure BDA0002890163050000073
in the present invention, the
Figure BDA0002890163050000074
The calculation is performed as an example.
Therefore, from equation (3) and equation (8), we can obtain:
Figure BDA0002890163050000075
integrating the above equation to define
Figure BDA0002890163050000076
Wherein, Fp(t)、Fn(t) are respectively the integrated functions Sp_iip_i、Sn_iin_iA primitive function of (a); cp、CnIs a constant and represents the initial energy storage of the upper bridge arm and the lower bridge arm,and has Cp＝Cn。
Because the second harmonic and the fourth harmonic in the circulating current have the largest specific gravity, the circulating current also contains a small amount of even harmonic components with higher order, and the harmonic content is decreased with the increase of the harmonic number, in order to obtain a more accurate circulating current calculation result, the circulating current expression takes into account the second harmonic component and the fourth harmonic component in the circulating current:
iiz＝Iiz_dc+Iiz_2cos(2ω0t+θ2)+Iiz_4cos(4ω0t+θ4) (10)
the above formula (7) and formula (10) are substituted into the circulation model of the hybrid modular multilevel converter, i.e. formula (1), to obtain:
Figure BDA0002890163050000081
after mathematical transformation, the following formula can be obtained:
Figure BDA0002890163050000082
wherein, the direct current component is as follows:
Figure BDA0002890163050000083
the second harmonic component is as follows:
Figure BDA0002890163050000084
Figure BDA0002890163050000085
the quadruple frequency component is as follows:
Figure BDA0002890163050000091
Figure BDA0002890163050000092
the coupling components are as follows:
Figure BDA0002890163050000093
and step five, deriving a circulation expression containing a direct current component, a frequency doubling component and a frequency quadrupling component based on a time domain method.
The traditional method for solving the circulating current of the hybrid modular multilevel converter by adopting a phasor method can only solve the amplitude of double frequency circulating current, and has errors caused by neglecting coupling components. The invention not only considers the double frequency component and the direct current component in the circulation, but also realizes the calculation and the solution of the quadruple frequency component by the improvement of a specific circulation derivation calculation method, namely, a time domain analysis method is adopted, overcomes the error caused by neglecting the coupling component in the formula when the traditional algorithm calculates the circulation by using a phasor method, and improves the precision of the circulation calculation.
Separately extracting a second harmonic component and a related coupling component for analysis:
Figure BDA0002890163050000094
sin (2 ω) in equation (12)0t+θ2)、cos(2ω0t+θ2) And
Figure BDA0002890163050000095
decomposition into sin (2 omega)0t) and cos (2. omega.)0t), followed by sin (2 ω) on both sides of the equation0t) and cos (2. omega.)0the coefficients of t) are correspondingly equal.
And (3) independently extracting the quadruple frequency component and the related coupling component for analysis:
Figure BDA0002890163050000096
sin (4 omega) in formula (13)0t+θ4)、cos(4ω0t+θ4) And sin (4 ω)0t+θ2) Decomposition into sin (4 omega)0t) and cos (4. omega.)0t), followed by sin (4 ω) on both sides of the equation0t) and cos (4. omega.)0the coefficients of t) are correspondingly equal.
Therefore, the amplitude I of the second harmonic in the circulating current can be obtained by solvingiz_2And phase angle theta2Amplitude of the fourth harmonic Iiz_4And phase angle theta4：
Figure BDA0002890163050000101
Figure BDA0002890163050000102
Figure BDA0002890163050000103
Figure BDA0002890163050000104
In the hybrid modular multilevel converter, if the active power is P:
Figure BDA0002890163050000105
in summary, formula (14) is substituted into a circular current expression i containing a direct current component, a frequency doubling component and a frequency quadrupling componentizCan be expressed as:
iiz＝Iiz_dc+Iiz_2cos(2ω0t+θ2)+Iiz_4cos(4ω0t+θ4)
wherein the content of the first and second substances,
Figure BDA0002890163050000111
the above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (4)

1. An improved circulation calculation method for a hybrid modular multilevel converter is characterized by comprising the following steps:
s1, establishing a mathematical model of the hybrid modular multilevel converter to obtain an equivalent circuit model and a circulation model of the hybrid modular multilevel converter;
s2, analyzing the working characteristics of each submodule between each phase of upper bridge arm and each phase of lower bridge arm in the hybrid modular multilevel converter based on a modulation function method to obtain the actual output voltage of each submodule;
s3, deducing the voltage sum of all the submodules of the upper bridge arm and the lower bridge arm of each phase by combining the actual output voltage of each submodule in the step S2;
s4, assuming a circulation expression containing a direct current component, a second harmonic component and a fourth harmonic component, substituting the circulation expression and the voltage sum of each phase of upper bridge arm and lower bridge arm obtained in the step S3 into the circulation model obtained in the step S1 to obtain an equation to be solved, and extracting a second harmonic component equation and a fourth harmonic component equation in the equation to be solved;
and S5, deducing the amplitude and phase angle of the double-frequency harmonic component and the amplitude and phase angle of the quadruple-frequency harmonic component from a double-frequency component equation and a quadruple-frequency component equation of the equation to be solved based on a time domain method to obtain a circulation expression.
2. An improved circulation current calculation method for hybrid modular multilevel converter according to claim 1, wherein in step S1, the circulation current model of the hybrid modular multilevel converter is:
Figure FDA0003335661010000011
wherein L is0The inductance of the bridge arm; r0Is the equivalent loss resistance of the bridge arm; u shapedcIs a direct current side bus voltage; u. ofp_iAnd un_iI-phase upper bridge arm voltage and i-phase lower bridge arm voltage are respectively obtained; i.e. iizI-phase circulating current.
3. The improved circular current calculation method for the hybrid modular multilevel converter according to claim 2, wherein in step S2, the actual output voltages of the single submodules of the i-phase upper bridge arm and the i-phase lower bridge arm of the hybrid modular multilevel converter are as follows:
Figure FDA0003335661010000012
wherein u iscp_io、ucn_ioThe actual output voltages of the single submodules of the i-phase upper bridge arm and the i-phase lower bridge arm are respectively obtained; sp_iAnd Sn_iRespectively the modulation functions of an i-phase upper bridge arm and a i-phase lower bridge arm, m represents the voltage modulation ratio, m is more than or equal to 0 and less than or equal to 1, and omega0Is the fundamental angular frequency; u. ofcp_i、ucn_iInstantaneous voltages of single sub-modules of the i-phase upper bridge arm and the i-phase lower bridge arm are respectively obtained; c0Capacitance for a single sub-module; i.e. icp_i、icn_iThe instantaneous currents respectively flow through the i-phase upper bridge arm submodule and the i-phase lower bridge arm submodule, and the expressions are as follows:
Figure FDA0003335661010000021
wherein ip_i、in_iI-phase upper bridge arm current and i-phase lower bridge arm current respectively; i.e. io_iIs the output current of the i phase at the AC side;
in step S3, the sum of the voltages of all the submodules of the i-phase upper arm and the i-phase lower arm is:
Figure FDA0003335661010000022
and N is the number of the sub-modules on each bridge arm.
4. The improved hybrid modular multilevel converter circulation calculation method according to claim 3, wherein in step S4, the circulation expression is:
iiz＝Iiz_dc+Iiz_2cos(2ω0t+θ2)+Iiz_4cos(4ω0t+θ4)
the equation for the second harmonic component is:
Figure FDA0003335661010000023
the quadruple frequency component equation is:
Figure FDA0003335661010000024
wherein, Iiz_dcIs a circulating DC component, and
Figure FDA0003335661010000025
Idcis a direct side bus current, and
Figure FDA0003335661010000026
p is active power; i isiz_2The amplitude of the double frequency harmonic component; theta2A phase angle that is a harmonic component of a double frequency; i isiz_4Is the amplitude of the quadruple frequency harmonic component; theta4The phase angle of the quadruple frequency harmonic component; u shapemIs the output voltage u of the i-phase of the AC sideo_iPeak value of，ImOutput current i for i-phase of AC sideo_iA peak value of (d);
Figure FDA0003335661010000027
leading the output current to the angle of the output voltage for the alternating current side;
then in step S5, the solution is Iiz_2And theta2、Iiz_4And theta4Comprises the following steps:
Figure FDA0003335661010000031
Figure FDA0003335661010000032
Figure FDA0003335661010000033
Figure FDA0003335661010000034
Figure FDA0003335661010000035
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