CN110212799B - Passive backstepping control method for restraining circulating current of modular multilevel converter - Google Patents

Passive backstepping control method for restraining circulating current of modular multilevel converter Download PDF

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CN110212799B
CN110212799B CN201910549195.8A CN201910549195A CN110212799B CN 110212799 B CN110212799 B CN 110212799B CN 201910549195 A CN201910549195 A CN 201910549195A CN 110212799 B CN110212799 B CN 110212799B
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mmc
circulating current
passive
backstepping
restraining
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CN110212799A (en
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薛花
王育飞
潘哲晓
杨兴武
张宇华
田广平
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Shanghai University of Electric Power
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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
    • 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
    • H02M1/0003—Details of control, feedback or regulation circuits
    • H02M1/0038—Circuits or arrangements for suppressing, e.g. by masking incorrect turn-on or turn-off signals, e.g. due to current spikes in current mode control

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Abstract

The invention relates to a passive backstepping control method for restraining circular current of a modular multilevel converter, which comprises the following steps: s1, obtaining a PCHD model of MMC circulation according to the single-phase equivalent circuit of the MMC and based on an orthodefinite quadratic energy function; s2, constructing a PCHD model-based MMC circulating current suppression passive backstepping controller; s3, inputting the double frequency actual value and the reference value of the circulating current into an MMC circulating current restraining passive backstepping controller to output circulating current voltage compensation quantity; and S4, carrying out carrier phase shift modulation on the circulating current voltage compensation quantity, and controlling the on-off of a switch tube in the MMC submodule through the modulation wave to achieve the purpose of circulating current inhibition. Compared with the prior art, the PCHD model-based passive control and the back-stepping method are organically combined, the overall stability can be guaranteed, the rapid dynamic response can be realized, the control law is simple in operation, free of singular points, strong in robustness and obvious in circulation restraining effect.

Description

Passive backstepping control method for restraining circulating current of modular multilevel converter
Technical Field
The invention relates to the field of control of modular multilevel converters, in particular to a passive backstepping control method for restraining circulating current of a modular multilevel converter.
Background
At present, a Modular Multilevel Converter (MMC) is widely applied to a grid-connected system of a distributed power supply, a mathematical model of the MMC is simple, switching of output voltage can be achieved by controlling on and off of a switch tube in each submodule of the MMC, but because the MMC comprises a plurality of submodules and is switched in and out along with the switching-in and switching-out of each submodule, capacitor voltage in each submodule is difficult to reach complete balance, voltage imbalance between bridge arms is caused, and circulation is further formed.
In order to inhibit the circulation current generated in the MMC operation process, the traditional vector control method is not from the energy perspective, can not effectively control the nonlinear essence of the MMC, and once uncertain disturbance exists, the traditional vector control faces the challenges of disturbance resistance and robustness; the existing nonlinear control method solves the problem of nonlinear control to a certain extent, but has the defects of excessive energy loss of a system, poor transient performance, overlong adjusting time and slow dynamic response speed in the aspect of energy optimization.
Disclosure of Invention
The present invention is directed to overcoming the above-mentioned drawbacks of the prior art and providing a passive back-stepping control method for suppressing the circulating current of a modular multilevel converter.
The purpose of the invention can be realized by the following technical scheme: a passive back-stepping control method for inhibiting circulating current of a modular multilevel converter, comprising the steps of:
s1, obtaining a PCHD model of MMC circulation according to the single-phase equivalent circuit of the MMC and based on an orthodefinite quadratic energy function;
s2, constructing a PCHD model-based MMC circulating current suppression passive backstepping controller by adopting passive control and backstepping control theories;
s3, inputting the double frequency actual value and the reference value of the circulating current into an MMC circulating current restraining passive backstepping controller to output circulating current voltage compensation quantity;
and S4, carrying out carrier phase shift modulation on the circulating current voltage compensation quantity to generate a modulation wave, and controlling the on and off of a switch tube in the MMC submodule through the modulation wave to achieve the purpose of circulating current suppression.
Further, the step S1 specifically includes the following steps:
s11, obtaining a circulating current dynamic equation under a dq rotation coordinate system according to the single-phase equivalent circuit of the MMC;
s12, respectively selecting a state variable, an input variable and an output variable, and carrying out equivalent transformation on the circulation dynamic equation based on an orthometric quadratic energy function to obtain the PCHD model of the MMC circulation.
Further, the circulation dynamics equation in step S11 is specifically as follows:
Figure BDA0002104997090000021
wherein, ω is0At the fundamental angular frequency, LmIs bridge arm inductance, RmIs bridge arm resistance icirdAnd icirqD-axis components of two frequency doubling of three-phase circulating currentActual value and q-axis component actual value, ucirdAnd ucirqD-axis compensation quantity and q-axis compensation quantity of the three-phase circulating voltage are respectively, d is a differential operator, and t is time.
Further, the state variables, the input variables and the output variables in step S12 are specifically:
Figure BDA0002104997090000022
wherein x is a state variable, u is an input variable, y is an output variable, x1And x2D-and q-axis components, u, of the state variable, respectively1And u2D-and q-axis components, y, of the input variable, respectively1And y2D-axis component and q-axis component of the output variable, respectively;
the positive definite quadratic energy function is specifically as follows:
Figure BDA0002104997090000023
wherein, H (x) is the energy originally stored in the MMC loop nonlinear system;
the PCHD model of MMC circulation is specifically as follows:
Figure BDA0002104997090000024
Figure BDA0002104997090000031
Figure BDA0002104997090000032
Figure BDA0002104997090000033
wherein,
Figure BDA00021049970900000310
is the state variable x derivative with respect to time, j (x) is the interconnection matrix, r (x) is the damping matrix, g (x) is the port matrix.
Further, the step S2 specifically includes the following steps:
s21, defining a state variable error, and setting an expected energy function of the MMC loop closed-loop control system;
s22, combining the PCHD model of the MMC ring current and the expected energy function to obtain a state equation of the MMC ring current closed-loop system;
s23, determining the constraint conditions of the passive control law according to the state equation of the MMC closed-loop system, and obtaining the PCHD model-based MMC closed-loop restraining passive control law;
s24, based on a backstepping control theory, obtaining an MMC loop current suppression backstepping control law through an equivalent transformation loop current dynamic equation and defining a progressive tracking error;
and S25, constructing the MMC circulating current suppression passive backstepping controller by combining the MMC circulating current suppression passive control law and the MMC circulating current suppression backstepping control law.
Further, the desired energy function in step S21 is specifically:
Figure BDA0002104997090000034
Figure BDA0002104997090000035
Figure BDA0002104997090000036
x*＝[x1 * x2 *]
xe＝x-x*
wherein Hd(x) To the desired energy, Ha(x) To be introduced byState feedback controls the energy, x, of the injected systemeFor state variable error, D is the inductance matrix, x is the desired balance point,
Figure BDA0002104997090000037
and
Figure BDA0002104997090000038
the d-axis component and the q-axis component, respectively, of the desired balance point.
Further, the state equation of the MMC closed-loop system in step S22 is specifically as follows:
Figure BDA0002104997090000039
Figure BDA0002104997090000041
Figure BDA0002104997090000042
Jd(x)＝J(x)+Ja(x)
Rd(x)＝R(x)+Ra(x)
wherein, Jd(x) Interconnection matrix desired for the system, Rd(x) Damping matrix desired for the system, Ja(x) And Ra(x) Respectively an injected dissipation matrix and a damping matrix.
Further, the constraint conditions of the passive control law in step S23 are specifically:
Figure BDA0002104997090000043
Figure BDA0002104997090000044
Figure BDA0002104997090000045
Figure BDA0002104997090000046
selecting the injected dissipation matrix as 0:
Ja(x)＝0
namely, the method comprises the following steps:
u＝g-1(x)[(Jd(x)-Rd(x))D·x-(Jd(x)-Rd(x))D·x*-(J(x)-R(x))D·x]
＝g-1(x)[-Rd(x)D·x-(J(x)-Rd(x))D·x*+R(x)D·x]
＝g-1(x)[-Ra(x)D·x-(J(x)-Rd(x))D·x*]
the MMC circulation restraining passive control law based on the PCHD model specifically comprises the following steps:
Figure BDA0002104997090000047
wherein u is1 cirdAnd u1 cirqD-axis compensation quantity and q-axis compensation quantity i of passive control circulating current voltage respectively* cirdAnd i* cirqD-axis component reference value and q-axis component reference value, r, which are three-phase circulation frequency doublinga1And ra2All with injected positive damping parameters, i.e. injected damping matrix
Figure BDA0002104997090000048
Further, the loop flow dynamic equation in the step S24 is equivalently transformed into:
Figure BDA0002104997090000049
x1＝Lmicird
x2＝Lmicirq
Figure BDA0002104997090000051
a2＝2ω0
wherein, a1And a2All are equivalent transform coefficients;
the progressive tracking error is:
Figure BDA0002104997090000052
wherein e is1And e2Are respectively icirdAnd icirqThe progressive tracking error of (a) is,
the MMC circulation restraining backstepping control law specifically comprises the following steps:
Figure BDA0002104997090000053
wherein u is2 cirdAnd u2 cirqD-axis compensation amount and q-axis compensation amount, k, for controlling circulating voltage in reverse steps1And k2Are all backstepping control parameters.
Further, in step S3, the cyclic voltage compensation amount specifically includes:
Figure BDA0002104997090000054
compared with the prior art, the invention has the following advantages:
firstly, the MMC loop current is passively controlled based on a PCHD model, the minimum value of an energy function is obtained at an expected balance point through energy function shaping, the input and output energy of a control system is optimized, the energy loss is reduced, and the overall gradual stability of the system is ensured by utilizing the input and output mapping of the PCHD system.
The invention adopts a backstepping control theory, cancels the nonlinear term in the first-order derivative of the Lyapunov function by reserving the nonlinear term to satisfy the Lyapunov stability theorem, and simultaneously introduces the linear quantity, thereby effectively improving the transient performance of a control closed-loop system and realizing the rapid tracking of the circulation frequency-doubled component under internal and external disturbance.
The invention combines the passive backstepping control to carry out MMC circulation suppression, has simple control operation, short regulation time and strong robustness, and has stronger stability and faster response speed under the uncertain disturbance condition.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a single-phase equivalent circuit diagram of the MMC;
FIG. 3 is a block diagram of MMC loop current suppression passive backstepping control based on a PCHD model;
FIG. 4a is a DC side current waveform of the MMC in the embodiment;
FIG. 4b is a waveform of a phase upper and lower bridge arm currents of the MMC in the embodiment;
FIG. 4c is a waveform of a phase a upper and lower bridge arm submodule capacitor voltage of the MMC in the embodiment;
FIG. 4d is a three-phase interphase circulating current waveform of the MMC in the embodiment;
FIG. 4e is an interphase double frequency circular current waveform of the MMC in the embodiment;
FIG. 4f is an AC side three phase voltage waveform of the MMC in an embodiment;
FIG. 4g is the waveform of the three-phase current on the AC side of the MMC in the embodiment.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
As shown in fig. 1, a passive back-stepping control method for suppressing a circulating current of a modular multilevel converter includes the steps of:
s1, obtaining a PCHD model of MMC circulation according to the single-phase equivalent circuit of the MMC and based on an orthodefinite quadratic energy function;
s2, constructing a PCHD model-based MMC circulating current suppression passive backstepping controller by adopting passive control and backstepping control theories;
s3, inputting the double frequency actual value and the reference value of the circulating current into an MMC circulating current restraining passive backstepping controller to output circulating current voltage compensation quantity;
and S4, carrying out carrier phase shift modulation on the circulating current voltage compensation quantity to generate a modulation wave, and controlling the on and off of a switch tube in the MMC submodule through the modulation wave to achieve the purpose of circulating current suppression.
The method comprises the following steps:
from the single-phase equivalent circuit diagram of the modular multilevel converter shown in fig. 2, the loop current dynamic equation under dq rotation coordinate system can be obtained:
Figure BDA0002104997090000061
in the formula, ω0At the fundamental angular frequency, LmIs bridge arm inductance, RmIs bridge arm resistance icirdAnd icirqD-axis component actual value and q-axis component actual value, u, of three-phase circulation frequency doublingcirdAnd ucirqD-axis compensation quantity and q-axis compensation quantity of the three-phase circulating voltage are respectively, d is a differential operator, and t is time;
selecting a state variable x, an input variable u and an output variable y as follows:
Figure BDA0002104997090000071
wherein x is a state variable, u is an input variable, y is an output variable, and x1And x2D-and q-axis components, u, of the state variable, respectively1And u2D-and q-axis components, y, of the input variable, respectively1And y2D-axis component and q-axis component of the output variable, respectively;
designing an orthodefinite quadratic energy function:
Figure BDA0002104997090000072
performing equivalent transformation on the circulation dynamic equation (1) under the dq rotation coordinate system to obtain an MMC circulation PCHD model:
Figure BDA0002104997090000073
in the formula,
Figure BDA0002104997090000074
in order to be an interconnected matrix,
Figure BDA0002104997090000075
in order to be a damping matrix, the damping matrix,
Figure BDA0002104997090000076
is a port matrix;
the dissipation inequality can be derived from equations (3) and (4):
Figure BDA0002104997090000077
the left side of the formula (5) is increment of the whole MMC circulating system, the right side is externally supplied energy, the mapping u → x is strictly passive in output, and the system meets passivity conditions;
according to the system control performance target, setting the expected balance point of the MMC circulating system as follows:
Figure BDA0002104997090000078
defining a state variable error xe＝x-x*Setting an expected energy function of the MMC closed-loop control system:
Figure BDA0002104997090000079
in the formula,
Figure BDA00021049970900000710
h (x) is the energy originally stored in the MMC loop nonlinear system, Ha(x) To control the energy injected into the system by introducing state feedback;
H(x)、Ha(x)、Hd(x) The derivatives with respect to x are respectively
Figure BDA0002104997090000081
From the equations (4) and (7), the state equation of the MMC circulating closed-loop system can be obtained as follows:
Figure BDA0002104997090000082
in the formula, Jd(x)＝J(x)+Ja(x) Interconnection matrix desired for the system, Rd(x)＝R(x)+Ra(x) Damping matrix desired for the system, Ja(x)、Ra(x) Respectively an injected dissipation matrix and a damping matrix;
the obtained state feedback control law of the joint type (3) and the formula (9) meets the partial differential equation shown in the formula (10)
Figure BDA0002104997090000083
The desired interconnection matrix and damping matrix need to satisfy equations (11) and (12), respectively:
Figure BDA0002104997090000084
Figure BDA0002104997090000085
selection of Ja(x)＝0，
Figure BDA0002104997090000086
So that the control law is simple and feasible and the convergence rate of the system is controllable,
the combined vertical type (8) and the formula (10) can be obtained
Figure BDA0002104997090000087
The MMC circulation current suppression passive control law under the PCHD model obtained by the formula (13) is as follows:
Figure BDA0002104997090000088
in the formula u1 cirdAnd u1 cirqD-axis compensation quantity and q-axis compensation quantity i of passive control circulating current voltage respectively* cirdAnd i* cirqD-axis component reference value and q-axis component reference value, r, which are three-phase circulation frequency doublinga1And ra2Are all injected positive damping parameters;
on the basis of MMC loop passive control, reverse step control is added, a nonlinear item of the MMC loop system is reserved in a control strategy, and the dynamic response performance of the closed-loop system is improved.
The formula (1) can be equivalently transformed into
Figure BDA0002104997090000091
In the formula, a1And a2All are equivalent transform coefficients;
definition of icirdAnd icirqHas a progressive tracking error of
Figure BDA0002104997090000092
Derivative of progressive tracking error of
Figure BDA0002104997090000093
To achieve a system control objective e1→ 0 and e2→ 0, define the Lyapunov function as
Figure BDA0002104997090000094
The first derivative of the Lyapunov function can be obtained by combining the vertical type (16), the formula (17) and the formula (18) as
Figure BDA0002104997090000095
The expected balance point of the MMC circulating system is
Figure BDA0002104997090000096
Ignoring differential terms of state variable reference values
Figure BDA0002104997090000097
And
Figure BDA0002104997090000098
the MMC loop current inhibition backstepping control law is designed to
Figure BDA0002104997090000099
In the formula u2 cirdAnd u2 cirqD-axis compensation amount and q-axis compensation amount, k, for controlling circulating voltage in reverse steps1And k2Are all back-stepping control parameters;
the combined type (20) and the formula (14) derive the circulation voltage compensation quantity output by the MMC circulation restraining passive backstepping controller as
Figure BDA00021049970900000910
Namely, the method comprises the following steps:
Figure BDA0002104997090000101
the control block diagram of the MMC loop current suppression passive backstepping controller is shown in FIG. 3, and the loop current voltage compensation quantity (u) to be outputcird、ucirq) And inputting a carrier phase-shifting modulation module to generate a modulation wave and correspondingly send the modulation wave to the submodules of the bridge arms of each phase of the MMC, so as to control the working state of a switching tube in the submodules of the bridge arms of each phase of the MMC and realize the inhibition of the circulation current of each phase of the MMC.
A simulation model of a modular multilevel converter and loop current suppression is built in MATLAB/Simulink, the effectiveness of the loop current suppression is verified, and simulation parameters of the embodiment are shown in Table 1.
TABLE 1 simulation parameters
Simulation model parameters Numerical value
Number of submodules n/ 24
Submodule capacitor C/mF 2
Bridge arm inductance Lm/mH 5
Bridge arm resistance Rm/omega 5
Rated current on the AC sidePress uk/V 220
Frequency f/Hz of AC system 50
DC side voltage Udc/V 650
AC side inductance L/mH 1
Resistance R/m omega on AC side 100
Under the steady-state operation of the MMC system, a PCHD model-based circulation suppression passive backstepping control method is adopted for simulation test: the simulation time is set to 0.5s, and when t is 0.4s, the loop current suppression passive backstepping control is started, and the simulation results are shown in fig. 4a to 4 g.
Fig. 4a shows that the passive back-stepping circulation suppression method effectively reduces power pulsation on the direct current side and improves system stability;
as can be seen from the analysis of fig. 4b, when the loop current suppression is not adopted, the distortion of the bridge arm current on the a-phase is caused by the double-frequency negative-sequence loop current component; after t is 0.4s, implementing circulation current suppression passive backstepping control, wherein the MMC bridge arm current mainly comprises a direct current component and a fundamental frequency component, and is close to an ideal sine wave, so that the waveform quality is improved;
as can be seen from the analysis of fig. 4c, the suppression of the double frequency negative sequence component significantly reduces the dc capacitance and the sub-module capacitor voltage fluctuation;
from the analysis of FIG. 4d, the actual value of the double-frequency negative-sequence dq-axis component (i)cird，icirq) All can quickly track the reference value of the double frequency component of the given circulation
Figure BDA0002104997090000102
As can be seen from the analysis of fig. 4e, the three-phase circulating current waveform before t is 0.4s has an obvious frequency doubling characteristic, after the passive back-stepping control of circulating current suppression is started, the three-phase circulating current fluctuates at the direct-current component, which is consistent with the theoretical analysis result, the passive back-stepping circulating current suppression strategy is adopted, the frequency doubling circulating current component is effectively suppressed, and the circulating current suppression effect is obvious;
as can be seen from the analysis of FIG. 4f and FIG. 4g, the output external characteristics of the AC side are not affected after the MMC ring current is restrained, and the system runs stably.

Claims (8)

1. A passive back-stepping control method for circulating current suppression of a modular multilevel converter, comprising the steps of:
s1, obtaining a PCHD model of MMC circulation according to the single-phase equivalent circuit of the MMC and based on an orthodefinite quadratic energy function;
s2, constructing a PCHD model-based MMC circulating current suppression passive backstepping controller by adopting passive control and backstepping control theories;
s3, inputting the double frequency actual value and the reference value of the circulating current into an MMC circulating current restraining passive backstepping controller to output circulating current voltage compensation quantity;
s4, carrying out carrier phase shift modulation on the circulating current voltage compensation quantity to generate a modulation wave, and controlling the on and off of a switch tube in the MMC submodule through the modulation wave to achieve the purpose of circulating current suppression;
the step S2 specifically includes the following steps:
s21, defining a state variable error, and setting an expected energy function of the MMC loop closed-loop control system;
s22, combining the PCHD model of the MMC ring current and the expected energy function to obtain a state equation of the MMC ring current closed-loop system;
s23, determining the constraint conditions of the passive control law according to the state equation of the MMC closed-loop system, and obtaining the PCHD model-based MMC closed-loop restraining passive control law, wherein the constraint conditions of the passive control law are specifically as follows:
Figure FDA0002711560540000011
Figure FDA0002711560540000012
Figure FDA0002711560540000013
Figure FDA0002711560540000014
Jd(x)＝J(x)+Ja(x)
wherein H (x) is the energy originally stored in the MMC loop nonlinear system, J (x) is an interconnection matrix, R (x) is a damping matrix, g (x) is a port matrix, and H (x) isd(x) To the desired energy, Ha(x) To control the energy injected into the system by introducing state feedback, xeFor state variable error, D is the inductance matrix, x is the desired balance point, Jd(x) Interconnection matrix desired for the system, Rd(x) Damping matrix desired for the system, Ja(x) And Ra(x) Respectively for the injected dissipation matrix and the damping matrix, selecting the injected dissipation matrix as 0:
Ja(x)＝0
namely, the method comprises the following steps:
u＝g-1(x)[(Jd(x)-Rd(x))D·x-(Jd(x)-Rd(x))D·x*-(J(x)-R(x))D·x]
＝g-1(x)[-Rd(x)D·x-(J(x)-Rd(x))D·x*+R(x)D·x]
＝g-1(x)[-Ra(x)D·x-(J(x)-Rd(x))D·x*]
the MMC circulation restraining passive control law based on the PCHD model specifically comprises the following steps:
Figure FDA0002711560540000021
wherein u is1 cirdAnd u1 cirqD-axis compensation quantity and q-axis compensation quantity i of passive control circulating current voltage respectively* cirdAnd i* cirqD-axis component reference value and q-axis component reference value, omega, of three-phase circulating current frequency doubling0At the fundamental angular frequency, LmIs bridge arm inductance, RmIs bridge arm resistance icirdAnd icirqD-axis component actual value and q-axis component actual value r of three-phase circulation frequency doublinga1And ra2All with injected positive damping parameters, i.e. injected damping matrix
Figure FDA0002711560540000022
S24, based on a backstepping control theory, obtaining an MMC loop current suppression backstepping control law through an equivalent transformation loop current dynamic equation and defining a progressive tracking error;
and S25, constructing the MMC circulating current suppression passive backstepping controller by combining the MMC circulating current suppression passive control law and the MMC circulating current suppression backstepping control law.
2. The passive backstepping control method for restraining the circulating current of the modular multilevel converter according to claim 1, wherein the step S1 specifically comprises the following steps:
s11, obtaining a circulating current dynamic equation under a dq rotation coordinate system according to the single-phase equivalent circuit of the MMC;
s12, respectively selecting a state variable, an input variable and an output variable, and carrying out equivalent transformation on the circulation dynamic equation based on an orthometric quadratic energy function to obtain the PCHD model of the MMC circulation.
3. The passive backstepping control method for restraining the circulating current of the modular multilevel converter according to claim 2, wherein the circulating current dynamic equation in the step S11 is specifically as follows:
Figure FDA0002711560540000031
wherein, ω is0At the fundamental angular frequency, LmIs bridge arm inductance, RmIs bridge arm resistance icirdAnd icirqD-axis component actual value and q-axis component actual value, u, of three-phase circulation frequency doublingcirdAnd ucirqD-axis compensation quantity and q-axis compensation quantity of the three-phase circulating voltage are respectively, d is a differential operator, and t is time.
4. The passive backstepping control method for restraining the circulating current of the modular multilevel converter according to claim 3, wherein the state variables, the input variables and the output variables in the step S12 are specifically:
Figure FDA0002711560540000032
wherein x is a state variable, u is an input variable, y is an output variable, x1And x2D-and q-axis components, u, of the state variable, respectively1And u2D-and q-axis components, y, of the input variable, respectively1And y2D-axis component and q-axis component of the output variable, respectively;
the positive definite quadratic energy function is specifically as follows:
Figure FDA0002711560540000033
wherein, H (x) is the energy originally stored in the MMC loop nonlinear system;
the PCHD model of MMC circulation is specifically as follows:
Figure FDA0002711560540000034
Figure FDA0002711560540000035
Figure FDA0002711560540000036
Figure FDA0002711560540000037
wherein,
Figure FDA0002711560540000038
is the state variable differential over time, J (x) is the interconnection matrix, R (x) is the damping matrix, and g (x) is the port matrix.
5. The passive back-stepping control method for restraining the circulating current of the modular multilevel converter according to claim 4, wherein the desired energy function in the step S21 is specifically as follows:
Figure FDA0002711560540000041
Figure FDA0002711560540000042
Figure FDA0002711560540000043
x*＝[x1 * x2 *]
xe＝x-x*
wherein Hd(x) To the desired energy, Ha(x) To control the energy injected into the system by introducing state feedback, xeFor state variable error, D is the inductance matrix, x is the desired balance point,
Figure FDA0002711560540000044
and
Figure FDA0002711560540000045
the d-axis component and the q-axis component, respectively, of the desired balance point.
6. The passive backstepping control method for restraining modular multilevel converter circulating current according to claim 5, wherein the state equation of the MMC circulating closed-loop system in the step S22 is specifically as follows:
Figure FDA0002711560540000046
Figure FDA0002711560540000047
Figure FDA0002711560540000048
Jd(x)＝J(x)+Ja(x)
Rd(x)＝R(x)+Ra(x)
wherein, Jd(x) Interconnection matrix desired for the system, Rd(x) Damping matrix desired for the system, Ja(x) And Ra(x) Respectively an injected dissipation matrix and a damping matrix.
7. The passive backstepping control method for circulating current suppression of the modular multilevel converter according to claim 6, wherein the circulating current dynamic equation in the step S24 is equivalently transformed into:
Figure FDA0002711560540000049
x1＝Lmicird
x2＝Lmicirq
Figure FDA00027115605400000410
a2＝2ω0
wherein, a1And a2All are equivalent transform coefficients;
the progressive tracking error is:
Figure FDA0002711560540000051
wherein e is1And e2Are respectively icirdAnd icirqThe progressive tracking error of (a) is,
the MMC circulation restraining backstepping control law specifically comprises the following steps:
Figure FDA0002711560540000052
wherein u is2 cirdAnd u2 cirqD-axis compensation amount and q-axis compensation amount, k, for controlling circulating voltage in reverse steps1And k2Are all backstepping control parameters.
8. The passive backstepping control method for restraining the circulating current of the modular multilevel converter according to claim 7, wherein the circulating voltage compensation amount in the step S3 is specifically as follows:
Figure FDA0002711560540000053
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