CN113346777A - PI passive control method and system of modular multilevel converter - Google Patents

PI passive control method and system of modular multilevel converter Download PDF

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CN113346777A
CN113346777A CN202110464765.0A CN202110464765A CN113346777A CN 113346777 A CN113346777 A CN 113346777A CN 202110464765 A CN202110464765 A CN 202110464765A CN 113346777 A CN113346777 A CN 113346777A
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passive
mmc
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CN113346777B (en
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赵月
邹建龙
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Xian Jiaotong University
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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
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/36—Arrangements for transfer of electric power between ac networks via a high-tension dc link
    • 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
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/60—Arrangements for transfer of electric power between AC networks or generators via a high voltage DC link [HVCD]

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Abstract

The invention discloses a PI passive control method and a PI passive control system of a modular multilevel converter, wherein a bridge arm average model based on a controlled source is established, and a differential equation expressed by sigma-delta under a corresponding abc coordinate system is listed; deducing a state space model of the MMC bridge arm average model according to the established differential equation; establishing a port controlled dissipation Hamilton model of the MMC system by using a state space model of an MMC bridge arm average model; a port controlled dissipation Hamilton model of an MMC system is utilized, a PI passive feedback controller of a closed-loop system is designed by utilizing a passive control theory, and the control of the modular multilevel converter is realized through the PI passive feedback controller. The invention not only can realize the effective tracking of the expected track of the MMC system, but also can ensure the global progressive stability of the system according to the Lyapunov stability theory, thereby improving the robustness of the system.

Description

PI passive control method and system of modular multilevel converter
Technical Field
The invention belongs to the technical field of flexible direct current transmission, and particularly relates to a PI passive control method and system of a modular multilevel converter.
Background
Fossil energy represented by petroleum and coal is being increasingly exhausted, and its use efficiency is low and it causes great pollution to the environment, so that development, utilization of new energy and access to the power grid are becoming more and more urgent. The flexible direct current transmission technology can be used for transmitting electric energy with small capacity or large capacity, and is more suitable for asynchronous interconnection among power grids in different regions. The MMC not only can realize modular design, but also has the advantages of low loss, high waveform quality, strong fault processing capability and the like, so that the topological structure is the mainstream topology of the existing flexible direct current transmission project.
Since the MMC topology was proposed, various researchers have made a lot of research on the MMC's related control strategies. The MMC basic control strategy that is mainstream at present is a vector control strategy. The vector control strategy is to control the converter by using a PI controller under a dq coordinate system. The vector controller can be divided into an inner loop current controller and an outer loop power controller. And the outer ring power controller calculates the dq axis reference value of the output current of the inner ring current controller according to the reference values of the active power and the reactive power. The output current in the inner-ring current controller controls the dq-axis current to quickly track the reference value of the MMC by adjusting the differential mode voltage of an upper bridge arm and a lower bridge arm of the MMC; and the ring current suppression control adjusts the common mode voltage of the upper bridge arm and the lower bridge arm of the MMC so as to suppress the ring current to zero. And carrying out dq inverse transformation on the obtained differential mode voltage and common mode voltage, carrying out simple operation, and then obtaining trigger pulses of the upper and lower bridge arm sub-modules through a corresponding modulation algorithm, thereby realizing the control of the MMC. The control method is linear control, when the grid connection and a weak grid or an alternating current system are in fault, the system is likely to oscillate and even lose stability, and the MMC is a multivariable complex nonlinear system with strong coupling, so that the vector control has obvious limitations of slow dynamic response, poor decoupling effect of active power and reactive power, poor robustness and the like.
Disclosure of Invention
The technical problem to be solved by the present invention is to provide a PI passive control method and system for a modular multilevel converter, which considers power control and circulating current suppression control simultaneously, has better active power and reactive power decoupling effect, improves the steady state and dynamic response performance of an MMC system, and improves the robustness and global stability of the system.
The invention adopts the following technical scheme:
a PI passive control method of a modular multilevel converter comprises the following steps:
s1, establishing a controlled source-based bridge arm average model and listing a differential equation expressed by sigma-delta under a corresponding abc coordinate system;
s2, deducing a state space model of the MMC bridge arm average model according to the differential equation established in the step S1;
s3, establishing a port controlled dissipation Hamilton model of the MMC system by using the state space model of the MMC bridge arm average model obtained in the step S2;
and S4, designing a PI passive feedback controller of the closed-loop system by using the port controlled dissipation Hamilton model of the MMC system obtained in the step S3 and using a passive control theory, and realizing the control of the modular multilevel converter by the PI passive feedback controller.
Specifically, step S1 specifically includes:
s101, establishing an MMC bridge arm average model based on a controlled source;
s102, writing a differential equation expressed by sigma-delta under an MMC bridge arm average model abc coordinate system in a row mode;
and S103, analyzing frequency components of each sigma-delta variable, and determining that the electrical quantity represented by the delta variable comprises a fundamental frequency component, and the electrical quantity represented by the sigma variable comprises a direct current component and a negative sequence double frequency component.
Further, in step S102, a differential equation expressed by Σ - Δ in the MMC bridge arm average model abc coordinate system is specifically:
ac side voltage equation:
Figure BDA0003043305070000021
wherein the content of the first and second substances,
Figure BDA0003043305070000022
the difference between the upper and lower bridge arm currents of the j-th phase;
Figure BDA0003043305070000023
modulating voltage for a j-th phase bridge arm; u. ofsjThe voltage is the system voltage of the j-th alternating current side;
Figure BDA0003043305070000024
is the difference of the modulation coefficients of the upper and lower bridge arms of the jth phase;
Figure BDA0003043305070000025
is the sum of the modulation coefficients of the upper and lower bridge arms of the jth phase;
Figure BDA0003043305070000026
is the sum of the equivalent capacitance voltages of the upper and lower bridge arms of the jth phase;
Figure BDA0003043305070000027
is the difference between the equivalent capacitance voltages of the upper and lower bridge arms of the jth phase; rfIs the equivalent resistance of the transformer; l isfEquivalent leakage inductance of the transformer; l is0Upper and lower bridge arm inductors; l iseqIs an equivalent inductance on the AC side, ReqIs an equivalent resistance on the alternating current side;
the loop current equation:
Figure BDA0003043305070000028
wherein the content of the first and second substances,
Figure BDA0003043305070000029
is j phase circulation; u shapedcIs a direct current side voltage;
Figure BDA00030433050700000210
equivalent bridge arm capacitance-voltage equation:
Figure BDA0003043305070000031
wherein, CarmIs the equivalent bridge arm voltage.
Further, in step S103, the ac side outputs a current
Figure BDA0003043305070000032
Is composed of a fundamental frequency component and a fundamental frequency component,
Figure BDA0003043305070000033
consists of a fundamental frequency component; phase circulation current
Figure BDA0003043305070000034
Consists of direct current and negative sequence double frequency components,
Figure BDA0003043305070000035
consists of DC component and negative sequence double frequency component, and the value of the DC component is
Figure BDA0003043305070000036
Figure BDA0003043305070000037
Is composed of a fundamental frequency component and a fundamental frequency component,
Figure BDA0003043305070000038
the direct current double-frequency-sequence amplifier consists of a direct current component and a negative sequence double-frequency component;
Figure BDA0003043305070000039
is composed of only the fundamental frequency component(s),
Figure BDA00030433050700000310
the device consists of a direct current component and a negative sequence double frequency component in steady operation; when the three-phase MMC system is described by adopting a differential equation expressed by sigma-delta based on an abc coordinate system, the electrical quantity expressed by delta variable only contains fundamental frequency components, and the electrical quantity expressed by the sigma variable consists of direct current components and negative sequence double frequency components.
Specifically, in step S2, the state space model of the MMC bridge arm average model is specifically:
the equation of state for the dq0 axis component of the sum of the equivalent capacitance voltages is expressed as:
Figure BDA00030433050700000311
the equation of state for the dq0 axis component of the sum of the equivalent capacitance voltages is expressed as:
Figure BDA00030433050700000312
the equation of state for the dq0 axis component of the interphase current is expressed as:
Figure BDA00030433050700000313
the equation of state of the dq-axis component of the ac-side output current is expressed as:
Figure BDA0003043305070000041
wherein, the state space model contains 10 state variables, respectively
Figure BDA0003043305070000042
Figure BDA0003043305070000043
A dq axis component representing the difference between the equivalent capacitor voltages, a dq0 component representing the sum of the capacitor voltages, a dq0 component representing the sum of the currents flowing through the inductors, and a dq axis component representing the difference between the inductor currents in the system, wherein the 5 control variables are respectively
Figure BDA0003043305070000044
Figure BDA0003043305070000045
In addition, the model has 3 external input variables Udc、usd、usq。
Specifically, in step S3, the port-controlled dissipation hamiltonian model of MMC is represented as the derived state space model
Figure BDA0003043305070000046
Wherein x is a system state variable; j (x) is a system internal structure matrix; r (x) is a system dissipation matrix; g (x) is a system and external port interaction structure matrix; u is a system external input vector; y is the external output vector, and H (x) is the system energy storage function.
Specifically, step S4 specifically includes:
s401, setting an expected balance point of the MMC system;
s402, calculating a passive output vector of the bilinear MMC system according to the expected balance point of the MMC system in the step S401;
s403, according to the passive output vector of the bilinear MMC system obtained in the step S402, selecting a PI controller, combining the PI controller with passive control, and designing a closed-loop system PI passive feedback controller, wherein the PI passive control comprises an outer loop power controller and an inner loop PI passive controller, the outer loop power controller calculates a dq axis reference value of output current required by the inner loop PI passive controller according to reference values of active power and reactive power, the inner loop PI passive controller is divided into a passive output calculation part and a PI tracking control part, firstly, each state variable reference value and each state variable obtained through sigma-delta calculation and dq conversion are input into the inner loop PI passive controller, and the passive output vector of the closed-loop system is solved; then, a PI controller is used for tracking and controlling the passive output vector and outputting a control variable; inverse dq-inverting the output variable and [ Sigma-Delta [ ]]-1And calculating to obtain modulation coefficients of upper and lower bridge arms of the MMC, and obtaining trigger pulses of the upper and lower bridge arm sub-modules according to the modulation coefficients to realize control of the MMC system.
Further, in step S402, the passive output vector y of the bilinear MMC system is:
Figure BDA0003043305070000051
wherein y ═ y1 y2 y3 y4 y5]TIs the passive output vector of the closed-loop system,
Figure BDA0003043305070000052
Figure BDA0003043305070000053
dq-axis components representing the difference between the equivalent capacitor voltages in the systemA dq0 component of the sum of the quantities and the capacitor voltages, a dq 0-axis component of the sum of the currents flowing through the inductors, and a dq-axis component of the difference between the inductor currents,
Figure BDA0003043305070000054
Figure BDA0003043305070000055
respectively corresponding to the balance points of the state variables.
Further, in step S403, the closed-loop system PI passive feedback controller is:
Figure BDA0003043305070000056
wherein, KPh＞0、KIhGreater than 0 is proportional coefficient, integral coefficient, K in PI controlP＝diag(KPh)，KI＝diag(KIh)，γhFor the integral quantity of the introduced passive output vector, yhBeing the passive output vector of the closed-loop system, Δ mhIs the control variable increment introduced.
Another technical solution of the present invention is a PI passive control system of a modular multilevel converter, including:
the differential module is used for establishing a controlled source-based bridge arm average model and listing a differential equation expressed by sigma-delta under a corresponding abc coordinate system;
the derivation module is used for deriving a state space model of the MMC bridge arm average model according to a differential equation obtained by the differentiation module;
the modeling module is used for establishing a port controlled dissipation Hamilton model of the MMC system by utilizing a state space model of the MMC bridge arm average model obtained by the derivation module;
and the control module is used for designing a PI passive feedback controller of the closed-loop system by utilizing a passive control theory according to a port controlled dissipation Hamilton model of the MMC system of the modeling module, and realizing the control of the modular multilevel converter through the PI passive feedback controller.
Compared with the prior art, the invention has at least the following beneficial effects:
the invention relates to a PI passive control method of a modular multilevel converter, which comprises the steps of firstly establishing a bridge arm average model based on a controlled source according to an average switching function model of an MMC and listing a differential equation expressed by sigma-delta under a corresponding abc coordinate system, thus obtaining mathematical models of an alternating current side and a direct current side of the MMC, only considering the external characteristics of an alternating current system and a direct current system connected with the MMC, and facilitating the energy control of the system; secondly, harmonic components of each electrical quantity of the MMC can be analyzed according to the established differential equation, so that a state space model of the MMC can be deduced through multi-frequency coordinate transformation, state variables of the system can be set to be capacitor voltage and inductor current, the capacitor voltage and the inductor current are quantities related to energy stored by the system, and a foundation is laid for further realizing energy control. And then, a port controlled dissipation Hamilton model of the MMC is established according to the state space model, so that the process of energy exchange between the MMC system and the external environment is really described from the energy perspective. And finally, designing a PI (proportional integral) passive controller of the MMC according to a passive control theory, thereby realizing the energy control of the system.
Furthermore, compared with a detailed model, the bridge arm average model is established, the characteristic of capacitance and voltage between each submodule is ignored, and the electrical decoupling between the bridge arm and the submodules is realized.
Furthermore, a sigma-delta expression method under an abc coordinate system is adopted to establish a differential equation and perform harmonic analysis, so that each electrical quantity of the MMC can be effectively classified according to contained harmonic components, and the multi-frequency coordinate transformation is facilitated to establish a state space model.
Furthermore, an MMC state space model established through multi-frequency coordinate transformation can map steady-state values (periodic solution under an abc coordinate system) expected by the whole MMC system to steady-state balance points in a dq0 coordinate system, and a foundation is laid for establishing a port controlled dissipation Hamilton model of the MMC and realizing passive control of the MMC.
Furthermore, the MMC port controlled dissipation Hamilton model obtained by deduction according to the state space model can describe the process of energy exchange between the MMC system and the external environment from the energy perspective, the physical significance is more definite, and the MMC can be controlled based on energy conveniently.
Further, based on the passive control theory, firstly, a balance point expected by the system needs to be set to effectively track the expected track of the system.
Further, since the PI passive control is a global control method, and the active object is the passive output of the system, the passive output vector y of the MMC needs to be calculated according to the dissipation inequality in the passive theory, so that the active object of the system can be found, and the passive control of the system is realized.
Furthermore, because y is a passive output vector of the closed-loop system and the PI controller is strictly passive, a simple PI controller is selected to be combined with passive control to obtain the PI passive feedback controller of the MMC, and therefore the passive control of the system is achieved.
In conclusion, the differential equation, the state space model and the port controlled dissipation Hamilton model of the MMC are established, and the PI passive controller is designed according to the passive control theory, so that the expected track of the MMC system can be effectively tracked, the global progressive stability of the system is ensured according to the Lyapunov stability theory, and the robustness of the system is improved.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a three-phase MMC topology structure diagram;
FIG. 2 is a single bridge arm equivalent diagram;
FIG. 3 is a diagram of an average model of a three-phase MMC bridge arm;
FIG. 4 is a multi-frequency coordinate transformation diagram;
FIG. 5 is a PI passive control block diagram of an MMC;
fig. 6 is a diagram showing steady-state simulation results of active power, reactive power, dc voltage and external output three-phase current of a single-ended MMC system under a PI passive controller and a vector controller, respectively, where (a) is the active power, (b) is the reactive power, (c) is the dc voltage, and (d) is the external output three-phase current;
FIG. 7 is a bar graph of the relative amplitudes of the harmonics of the phase-a output current and a graph of the total harmonic distortion under two control strategies, wherein (a) is a first control strategy and (b) is a second control strategy;
fig. 8 is a diagram of a dynamic simulation result of active power and reactive power of a single-ended MMC system under a PI passive controller and a vector controller, respectively, where (a) is the active power and (b) is the reactive power.
Detailed Description
The invention discloses a PI passive control method of a modular multilevel converter, which comprises the following steps:
s1, establishing a controlled source-based bridge arm average model and listing a differential equation expressed by sigma-delta under an abc coordinate system;
s101, establishing an MMC bridge arm average model based on a controlled source;
referring to fig. 1, the MMC is composed of three phase units, each of which has an upper bridge arm and a lower bridge arm, and each of the bridge arms is composed of N sub-modules and a bridge arm reactor connected in series. And (3) assuming that the capacitance and voltage of all sub-modules on the same bridge arm of the MMC are equal and three phases run in a balanced manner, and establishing an equivalent MMC bridge arm average model based on a controlled source according to an average value model of the MMC based on a switching function model.
Referring to fig. 2 and fig. 3, the cascaded sub-modules of each bridge arm are equivalent to a controlled voltage source, and the direct current side is equivalent to a controlled current source connected in series with a capacitor, so as to obtain an equivalent bridge arm average model of the three-phase MMC.
S102, writing a differential equation expressed by sigma-delta under an MMC bridge arm average model abc coordinate system in a row mode;
introducing a modulation coefficient into each bridge arm in the bridge arm average model
Figure BDA0003043305070000081
The controlled voltage in the controlled voltage source is called the modulation voltage, for
Figure BDA0003043305070000082
It is shown that the controlled current in the controlled current source is called the modulation current, for
Figure BDA0003043305070000083
The relationship between the bridge arm current and the equivalent capacitance voltage is shown as follows:
Figure BDA0003043305070000084
wherein, the superscript U, L is an upper bridge arm and a lower bridge arm; subscript j represents the three phases a, b, c;
Figure BDA0003043305070000085
equivalent capacitance voltages of three-phase upper and lower bridge arms are obtained;
Figure BDA0003043305070000086
three-phase upper and lower bridge arm currents. And (3) establishing a differential equation model of the bridge arm average model by using a sigma-delta expression method in an abc coordinate system.
Defining:
Figure BDA0003043305070000087
Figure BDA0003043305070000088
Figure BDA0003043305070000089
Figure BDA00030433050700000810
calculated by the equations (3) to (5)
Figure BDA00030433050700000811
1) Ac side voltage equation
According to the three-column written AC side voltage equation of the upper and lower bridge arms, the two equations are added and connected in parallel to obtain the MMC AC side voltage equation of
Figure BDA0003043305070000091
Wherein u issjThe voltage is the system voltage of the j-th alternating current side; rfIs the equivalent resistance of the transformer; l isfEquivalent leakage inductance of the transformer; l is0Upper and lower bridge arm inductors;
Figure BDA0003043305070000092
2) equation of circulation
Subtracting the alternating-current side voltage equations of the upper and lower bridge arms, connecting the equations in parallel to obtain a vertical type (2) - (6) bridge arm average model circulation equation of
Figure BDA0003043305070000093
Wherein, UdcIs the dc side voltage.
3) Equivalent bridge arm capacitance voltage equation
Figure BDA0003043305070000094
Adding or subtracting the two formulas of formula (9), and combining with formula (2) and formula (4) to obtain the final product
Figure BDA0003043305070000095
S103, analyzing frequency components of each sigma-delta variable, and determining that when a three-phase MMC system is described by adopting a differential equation expressed by sigma-delta based on an abc coordinate system, the electrical quantity expressed by the delta variable only contains a fundamental frequency component, and the electrical quantity expressed by the sigma variable consists of a direct current component and a negative sequence double frequency component;
neglecting the third order and above components, the AC side outputs current
Figure BDA0003043305070000096
Consisting only of fundamental frequency components, as estimated by equation (7),
Figure BDA0003043305070000097
consisting of fundamental frequency components.
Neglecting third order and above components, phase circulation
Figure BDA0003043305070000098
Consists of direct current and negative sequence double frequency components, which are obtained by the formula (8),
Figure BDA0003043305070000099
consists of DC component and negative sequence double frequency component, and the value of the DC component is
Figure BDA00030433050700000910
Analysis of
Figure BDA00030433050700000911
And
Figure BDA00030433050700000912
the frequency component of (1).
The following analyses all neglected third order and above components.
Figure BDA00030433050700000913
And
Figure BDA00030433050700000914
the medium oscillation component is far smaller than the direct current component, and the value of the direct current component is approximately equal to UdcThen, according to the formula (3),
Figure BDA0003043305070000101
substituting the approximate result into formula (6), then
Figure BDA0003043305070000102
Thus, can obtain
Figure BDA0003043305070000103
Is composed of a fundamental frequency component and a fundamental frequency component,
Figure BDA0003043305070000104
consists of DC component and negative sequence double frequency component.
First formula in analytical formula (10), first term to the right of equal sign
Figure BDA0003043305070000105
Being the fundamental component, the second term
Figure BDA0003043305070000106
Is also a fundamental frequency component, and therefore
Figure BDA0003043305070000107
Consisting only of fundamental frequency components. The second expression in equation (10) is reanalyzed, the first term to the right of the equal sign
Figure BDA0003043305070000108
Composed of DC component and negative-sequence double-frequency component, the second term
Figure BDA0003043305070000109
Consists of two frequency multiplication components and, therefore,
Figure BDA00030433050700001010
in steady-state operation, the converter consists of a direct current component and a negative sequence double frequency component.
Therefore, when a three-phase MMC system is described by using a differential equation expressed by Σ - Δ based on the abc coordinate system, the electrical quantity expressed by the Δ variable contains only a fundamental frequency component, and the electrical quantity expressed by the Σ variable consists of a direct current component and a negative-sequence double-frequency component.
S2, deducing a state space model of the MMC bridge arm average model;
neglecting the third order and above harmonic components, the useful main harmonic component in the abc coordinate system in the system can be changed into the direct current quantity in the dq0 coordinate system by adopting the multi-frequency Park transformation, and the nonlinear structure of the system is not changed, and the Park transformation specifically adopted by each electric quantity is shown in fig. 4.
The Park transformation matrix adopted by the multi-frequency coordinate transformation is as follows:
Figure BDA00030433050700001011
Figure BDA00030433050700001012
1) difference of equivalent capacitance voltage
The first expression in the expression (10) gives a differential equation of the difference between the equivalent capacitor voltages in the abc coordinate system, that is
Figure BDA0003043305070000111
Each term in equation (13) is represented by a Park matrix and dq0 variables, i.e.
Figure BDA0003043305070000112
In the formula (14), the compound represented by the formula (I),
Figure BDA0003043305070000113
Figure BDA0003043305070000114
(symbol)
Figure BDA00030433050700001117
as Hadamard products of matrices, e.g.
Figure BDA0003043305070000115
Order to
Figure BDA0003043305070000116
Then equation (14) is written as
Figure BDA0003043305070000117
Two sides of the formula (15) are simultaneously multiplied by PωWherein
Figure BDA0003043305070000118
In the formula (16), the compound represented by the formula,
Figure BDA0003043305070000119
Figure BDA00030433050700001110
Figure BDA00030433050700001111
in a three-phase MMC system, the input grid current does not allow zero-sequence current to exist, so
Figure BDA00030433050700001112
The third row in the specification are all connected with
Figure BDA00030433050700001113
Multiplication, and therefore negligible, the third harmonic component present in the third row only affects the zero-axis component
Figure BDA00030433050700001114
Does not affect the dq axis component, neglects the frequency tripling component, and makes
Figure BDA00030433050700001115
So as to be simplified
Figure BDA00030433050700001116
Is shown as
Figure BDA0003043305070000121
Figure BDA0003043305070000122
Figure BDA0003043305070000123
Neglecting the frequency tripling component, let
Figure BDA0003043305070000124
Therefore, it is not only easy to use
Figure BDA0003043305070000125
The equation of state of the dq-axis component of the difference in equivalent capacitance voltage is expressed by equations (13) to (22):
Figure BDA0003043305070000126
2) sum of equivalent capacitance voltages
The second expression in the expression (10) gives a differential equation of the sum of the equivalent capacitance voltages in the abc coordinate system, i.e.
Figure BDA0003043305070000127
Each term of equation (24) is represented by a Park matrix and dq0 variables, i.e.
Figure BDA0003043305070000128
In the formula (25), the reaction mixture,
Figure BDA0003043305070000129
order to
Figure BDA00030433050700001210
Then equation (25) is written as
Figure BDA0003043305070000131
Two sides of the formula (26) are simultaneously multiplied by P-2ωWherein
Figure BDA0003043305070000132
In the formula (27), J-2ω＝-2Jω。
Figure BDA0003043305070000133
Figure BDA0003043305070000134
Figure BDA0003043305070000135
Figure BDA0003043305070000136
The third row in the specification are all connected with
Figure BDA0003043305070000137
The multiplication, and therefore the possible neglect,
Figure BDA0003043305070000138
simplified to
Figure BDA0003043305070000139
Figure BDA00030433050700001310
Figure BDA00030433050700001311
The six-fold frequency components are ignored,
Figure BDA00030433050700001312
simplified to
Figure BDA0003043305070000141
The equation of state of the dq0 axis component of the sum of the equivalent capacitance voltages is expressed by equations (24) to (33)
Figure BDA0003043305070000142
3) Circulating current between phases
Equation (8) gives the differential equation of the interphase circulating current in the abc coordinate system, i.e.
Figure BDA0003043305070000143
Each term in equation (35) is represented by a Park matrix and dq0 variables, i.e.
Figure BDA0003043305070000144
In the formula (36), the reaction mixture is,
Figure BDA0003043305070000145
two sides of the formula (36) are simultaneously multiplied by P-2ωLeft side of equal sign
Figure BDA0003043305070000146
Equal sign the right side is:
Figure BDA0003043305070000147
Figure BDA0003043305070000148
Figure BDA0003043305070000151
the six-fold frequency components are ignored,
Figure BDA0003043305070000152
simplified to
Figure BDA0003043305070000153
Figure BDA0003043305070000154
Because of the fact that
Figure BDA0003043305070000155
So as to be simplified
Figure BDA0003043305070000156
Is shown as
Figure BDA0003043305070000157
The equation of state of the dq0 axis component of the interphase circulating current is expressed by equations (35) to (43)
Figure BDA0003043305070000158
4) Output current at AC side
Equation (7) gives the differential equation of the output current on the AC side in the abc coordinate system, i.e.
Figure BDA0003043305070000159
Each term in equation (45) is represented by a Park matrix and dq0 variables, i.e.
Figure BDA0003043305070000161
Wherein the content of the first and second substances,
Figure BDA0003043305070000162
two sides of the formula (46) are simultaneously multiplied by PωLeft side of equal sign
Figure BDA0003043305070000163
Equal sign right side
Figure BDA0003043305070000164
Figure BDA0003043305070000165
Figure BDA0003043305070000166
Figure BDA0003043305070000167
Considering only the dq-axis component of the output current on the AC side, not considering the zero-axis component
Figure BDA0003043305070000168
And is
Figure BDA0003043305070000169
Then simplified
Figure BDA00030433050700001610
And
Figure BDA00030433050700001611
can be expressed as
Figure BDA00030433050700001612
Figure BDA00030433050700001613
The equation of state of the dq-axis component of the ac-side output current is expressed by equations (45) to (53)
Figure BDA0003043305070000171
According to the derivation, the establishment of the state space model of the three-phase MMC system is completed, including equation (23), equation (34), equation (44), and equation (54). The state space model contains 10 state variables, each of which is
Figure BDA0003043305070000172
Figure BDA0003043305070000173
Dq component representing the difference between equivalent capacitor voltages in the system, dq0 component representing the sum of capacitor voltages, and dq0 component representing the sum of currents flowing through inductorsThe dq-axis component of the difference between the magnitude and the inductor current, 5 control variables being
Figure BDA0003043305070000174
Figure BDA0003043305070000175
In addition, the model has 3 external input variables Udc、usd、usq。
S3, establishing a port controlled dissipation Hamilton model of the MMC system by using the state space model of the MMC bridge arm average model obtained in the step S2;
the energy stored in a three-phase MMC system is first analyzed. The storage elements in the system are inductors and capacitors, and thus the stored energy can be divided into energy stored on the inductor and energy stored on the capacitor. The energy stored by the inductors in the upper and lower bridge arms is expressed as
Figure BDA0003043305070000176
The energy stored in the inductor on the three-phase AC side is expressed as
Figure BDA0003043305070000177
Thus, all the energy stored by the inductors in a three-phase MMC system is
Figure BDA0003043305070000178
The energy stored in the equivalent capacitors of the upper and lower bridge arms of the MMC is
Figure BDA0003043305070000179
Using the Park transformation shown in FIG. 4, the total energy of the MMC system is represented by the dq variable
Figure BDA0003043305070000181
Setting system state variables
x＝Mz (60)
In the formula (60), the reaction mixture,
Figure BDA0003043305070000182
Figure BDA0003043305070000183
the system energy storage function can be expressed by equations (59) to (62)
Figure BDA0003043305070000184
Figure BDA0003043305070000185
Representing a Port-controlled dissipative Hamiltonian model of an MMC as a State space model derived from an energy storage function
Figure BDA0003043305070000186
In the formula (65), j (x) is a system internal structure matrix represented by formula (66); r (x) is a system dissipation matrix, represented by formula (67); g (x) is a system and external port interaction structure matrix, denoted (68); u is the system external input vector, represented by equation (69); y is the outer output vector, denoted (70).
Figure BDA0003043305070000191
Figure BDA0003043305070000192
Figure BDA0003043305070000193
Figure BDA0003043305070000194
Figure BDA0003043305070000195
Equations (65) - (70) are the port controlled dissipation Hamilton model of the MMC system.
And S4, designing a PI passive feedback controller of the closed-loop system.
Note that J (x) represented by the formula (66) contains a control variable, and the control variable
Figure BDA0003043305070000196
All occur linearly, and the system represented by equation (65) has an interactive product term of the state variable and the control variable, so that the system is known as a bilinear system.
J (x) is further represented as:
Figure BDA0003043305070000197
in formula (71), J0、J1、J2、J3、J4、J5Calculated by the formula (66), m is represented by
Figure BDA0003043305070000198
The port controlled dissipation Hamilton model for a single-ended MMC system, available from equations (65) and (71), is represented as
Figure BDA0003043305070000201
S401, setting an expected balance point of the MMC system
Considering that the system represented by equation (73) has a desired trajectory, that is, the MMC system has a desired steady state equilibrium point. Suppose a steady state balance point x for an MMC system*Is shown as
x*＝Mz* (74)
Figure BDA0003043305070000202
The steady state equilibrium point of the MMC system satisfies equation (76), i.e.
Figure BDA0003043305070000203
In the formula (76), the reaction mixture is,
Figure BDA0003043305070000204
-desired steady state equilibrium point of the control variable.
After the multi-frequency coordinate transformation shown in FIG. 4, the selected state variables are all DC quantities, so in the steady-state case the state variables are all constants, so equation (76) is written as
Figure BDA0003043305070000205
At this point, the stored energy in the system is at steady state equilibrium point x*Is a minimum value of
Figure BDA0003043305070000206
According to the control target of constant active power and constant reactive power, the method canIs calculated to obtain
Figure BDA0003043305070000207
Desired circulating current dq component
Figure BDA0003043305070000208
Zero component of circulating current
Figure BDA0003043305070000209
Then, the steady state balance point of other state variables and control variables of the MMC system is solved by equation (77).
S402, calculating a passive output vector of the bilinear MMC system
To design the passive output vector y of the closed-loop system, an incremental signal model Δ (·) ═ (·) - (·)*I.e. by
Δx＝x-x* (79)
Δm＝m-m* (80)
Regarding a control vector m in the system as an input vector of the system, storing a function
Figure BDA0003043305070000211
The requirement that the closed-loop system be passive, i.e. that the dissipative inequality be satisfied
Figure BDA0003043305070000212
(81) Is written as
Figure BDA0003043305070000213
The incremental model of the system also satisfies the dissipation inequality at this time, namely
Figure BDA0003043305070000214
By substituting formula (73) and formula (76) for formula (79), it is possible to obtain
Figure BDA0003043305070000215
Further calculated by equation (84)
Figure BDA0003043305070000216
Is composed of
Figure BDA0003043305070000217
Therefore, from equations (83) and (85), the output vector y of the closed-loop system is designed to be [ y ═ y1 y2 y3 y4 y5]TComprises the following steps:
yh＝(Jhz*)Tz,h＝1,2,3,4,5 (86)
in this case, when the control vector of the system input is m, the energy storage function is
Figure BDA0003043305070000218
The system satisfies the dissipation inequality, and is a strict passive system.
The passive output vector y of the closed-loop system is calculated by equation (86):
Figure BDA0003043305070000221
s403, PI passive global tracking controller design
The PI passive control is divided into an outer ring power controller and an inner ring PI passive controller, and the outer ring power controller calculates a dq axis reference value of output current required by the inner ring PI passive controller according to reference values of active power and reactive power; the reference values for the remaining required state variables are calculated according to equation (77); the inner loop PI passive controller is divided into a calculation passive output part and a PI tracking control part. Firstly, reference values of state variables and various shapes obtained by sigma-delta calculation and dq conversionAnd inputting the state variable into the inner ring PI passive controller, and solving a passive output vector of the closed-loop system by using a formula (87). And then, a PI controller is used for tracking and controlling the passive output vector and outputting a control variable. Carrying out dq inverse transformation on each output control variable and sigma-delta]-1And finally, the trigger pulse of the upper and lower bridge arm sub-modules can be obtained through a corresponding modulation algorithm, so that the control of the MMC is realized.
Because y is the passive output vector of the closed-loop system and the PI controller is strictly passive, a simple PI controller is selected to be combined with the passive control, and the PI passive feedback controller of the closed-loop system is designed as follows:
Figure BDA0003043305070000222
in the formula (88), KPh＞0、KIhGreater than 0 is proportional coefficient, integral coefficient, K in PI controlP＝diag(KPh)，KI＝diag(KIh) At this time, the energy function
Figure BDA0003043305070000231
The method can be directly used as the Lyapunov function of a passive system, and the stability of a closed-loop system can be ensured.
The following was demonstrated: derived from formula (89)
Figure BDA0003043305070000232
From the Lyapunov theorem of stability, the closed loop system is gradually stable, that is, when t → ∞ Δ x → 0, at which time x → x*。
Therefore, the PI passive control method not only can realize effective tracking of the expected track, but also can ensure the global asymptotic stability of the system.
In another embodiment of the present invention, a PI passive control system of a modular multilevel converter is provided, where the system can be used to implement the above PI passive control method of the modular multilevel converter, and specifically, the PI passive control system of the modular multilevel converter includes a differential module, a derivation module, a modeling module, and a control module.
The differential module is used for establishing a controlled source-based bridge arm average model and listing a differential equation expressed by sigma-delta under a corresponding abc coordinate system;
the derivation module is used for deriving a state space model of the MMC bridge arm average model according to a differential equation obtained by the differentiation module;
the modeling module is used for establishing a port controlled dissipation Hamilton model of the MMC system by utilizing a state space model of the MMC bridge arm average model obtained by the derivation module;
and the control module is used for designing a PI passive feedback controller of the closed-loop system by utilizing a passive control theory according to a port controlled dissipation Hamilton model of the MMC system of the modeling module, and realizing the control of the modular multilevel converter through the PI passive feedback controller.
In yet another embodiment of the present invention, a terminal device is provided that includes a processor and a memory for storing a computer program comprising program instructions, the processor being configured to execute the program instructions stored by the computer storage medium. The Processor may be a Central Processing Unit (CPU), or may be other general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), an off-the-shelf Programmable gate array (FPGA) or other Programmable logic device, a discrete gate or transistor logic device, a discrete hardware component, etc., which is a computing core and a control core of the terminal, and is adapted to implement one or more instructions, and is specifically adapted to load and execute one or more instructions to implement a corresponding method flow or a corresponding function; the processor provided by the embodiment of the invention can be used for the operation of the PI passive control method of the modular multilevel converter, and comprises the following steps:
establishing a controlled source-based bridge arm average model and listing a differential equation expressed by sigma-delta under a corresponding abc coordinate system; deducing a state space model of the MMC bridge arm average model according to the established differential equation; establishing a port controlled dissipation Hamilton model of the MMC system by using a state space model of an MMC bridge arm average model; a port controlled dissipation Hamilton model of an MMC system is utilized, a PI passive feedback controller of a closed-loop system is designed by utilizing a passive control theory, and the control of the modular multilevel converter is realized through the PI passive feedback controller.
In still another embodiment of the present invention, the present invention further provides a storage medium, specifically a computer-readable storage medium (Memory), which is a Memory device in a terminal device and is used for storing programs and data. It is understood that the computer readable storage medium herein may include a built-in storage medium in the terminal device, and may also include an extended storage medium supported by the terminal device. The computer-readable storage medium provides a storage space storing an operating system of the terminal. Also, one or more instructions, which may be one or more computer programs (including program code), are stored in the memory space and are adapted to be loaded and executed by the processor. It should be noted that the computer-readable storage medium may be a high-speed RAM memory, or may be a non-volatile memory (non-volatile memory), such as at least one disk memory.
One or more instructions stored in the computer-readable storage medium can be loaded and executed by the processor to implement the corresponding steps of the PI passive control method for the modular multilevel converter in the above embodiments; one or more instructions in the computer-readable storage medium are loaded by the processor and perform the steps of:
establishing a controlled source-based bridge arm average model and listing a differential equation expressed by sigma-delta under a corresponding abc coordinate system; deducing a state space model of the MMC bridge arm average model according to the established differential equation; establishing a port controlled dissipation Hamilton model of the MMC system by using a state space model of an MMC bridge arm average model; a port controlled dissipation Hamilton model of an MMC system is utilized, a PI passive feedback controller of a closed-loop system is designed by utilizing a passive control theory, and the control of the modular multilevel converter is realized through the PI passive feedback controller.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
According to the above design steps, a PI passive control block diagram of the MMC system is obtained as shown in fig. 5.
The PI passive control method not only can realize the effective tracking of the expected track of the MMC system, but also can ensure the global progressive stability of the system by the Lyapunov stability theory.
And (3) building a bridge arm average model of the single-ended rectification MMC system on the PSCAD/EMTDC platform, and comparing the simulation result with a model simulation result adopting a vector control strategy. The simulation system main circuit parameters and control parameters are shown in tables 1 and 2.
TABLE 1 Single-ended MMC System Main Circuit parameters
Figure BDA0003043305070000251
TABLE 2 PI Passive control parameter of single-ended MMC System
Figure BDA0003043305070000252
Steady state simulation: and performing simulation under the condition of steady-state working of the system by adopting a single-ended MMC model based on PI passive control (PI-PBC), and comparing the simulation result with the simulation result of the single-ended MMC model based on vector control (PI).
Fig. 6 is a steady-state simulation result of main electrical quantities of the single-ended MMC system, such as active power, reactive power, direct-current voltage, and externally-output three-phase current, respectively under the PI passive controller and the vector controller. According to simulation results, under the steady-state working condition, physical quantities of the single-ended MMC system, such as active power, reactive power, output voltage of a direct current side, output current of an alternating current side and the like, of the system under the action of the PI passive controller are controlled to be expected values. From the external active system, under the steady-state working condition, the PI passive control has a good control effect on the MMC passive system.
Under the steady-state working condition, observing fig. 6(a) - (c), it can be intuitively seen that the fluctuation range of the active power, the reactive power and the direct-current voltage is smaller and the fluctuation range of each state variable is smaller in the PI passive control compared with the vector control. The simulation results of active power, reactive power and direct-current voltage in the 1-4s steady state period under the two control strategies are specifically analyzed from data, and the comparison result is shown in table 3.
TABLE 3 comparison of Steady-State simulation results for two control strategies
Figure BDA0003043305070000261
As can be calculated from table 3, compared with the vector control, under the action of the PI passive controller, the fluctuation range of the active power is reduced by 0.0851%, the fluctuation range of the dc voltage is reduced by 0.5381%, and the fluctuation range of the reactive power is also reduced. Therefore, the conclusion is drawn that the fluctuation amplitude of physical quantities such as active power, reactive power and direct-current voltage of the system based on the PI passive control is smaller under the steady-state working condition, so that the system based on the PI passive control has more excellent steady-state performance.
Since the results of the three-phase output currents of the MMC system under the two control strategies cannot be intuitively compared in fig. 6(d), the a-phase output current is selected for fourier analysis, and the histogram of the relative amplitude of each subharmonic of the a-phase output current and the total harmonic distortion rate under the two control strategies are obtained as shown in fig. 7. As can be seen from fig. 7, compared with the action result of the vector control strategy, the third harmonic relative amplitude of the a-phase output current under the PI passive control is reduced by 0.8%, and the fifth and seventh harmonic contents are significantly reduced, wherein the fifth harmonic relative amplitude is reduced by 24.675%, the seventh harmonic relative amplitude is reduced by 22.96%, and the total harmonic distortion rate is reduced by 0.08%, so that the quality of the electric energy delivered to the power grid is higher.
Dynamic simulation: in order to test the dynamic performance of the PI passive controller, when the set time is 1.5s, the active power instruction value of the system is increased from 10MW to 15MW, and when the set time is 2.5s, the active power instruction value is decreased from 15MW to 10MW, and the simulation result is compared with the dynamic simulation result of the MMC model based on vector control. Fig. 8 is a dynamic simulation result of active power and reactive power of the single-ended MMC system under the PI passive controller and the vector controller, respectively.
Under the dynamic working condition, the analysis of fig. 8 can show that, compared with the vector control, the PI passive control has shorter time for the active power and the reactive power of the system to reach the steady state again under the action of the PI passive controller. Fig. 8(b) shows that, when active power jumps, the fluctuation degree of the reactive power under the passive PI control is much smaller than that under the vector control. The simulation results of the active power and the reactive power under the two control strategies within 1.5-2.5s are specifically analyzed from the data, and the comparison result is shown in table 4.
TABLE 4 comparison of dynamic simulation results of two control strategies
Figure BDA0003043305070000271
As can be calculated from table 4, when active power jumps, the rising time of active power is reduced by 1.5% and the adjustment time is reduced by 24.04% in the dynamic response process of 1s under the action of the PI passive controller, compared with the vector control. Therefore, when active power jumps, the dynamic response speed of the active power is faster in the passive PI control compared with the vector control. When active power jumps, reactive power fluctuates. The calculation of table 4 shows that, under the passive PI control, compared with the vector control, the time required for the reactive power to reach the steady state again is reduced by 15.36%, the maximum deviation of the reactive power is reduced by 0.2079Mvar, the fluctuation range of the reactive power is smaller, the decoupling effect of the active power and the reactive power is better than that under the vector control, and the system has stronger robustness.
In summary, the PI passive control method of the modular multilevel converter considers power control and circulating current suppression control, active power and reactive power are decoupled better, the stable state and dynamic response performance of the MMC system are stronger, and the robustness and global stability of the system are improved.

Claims (10)

1. A PI passive control method of a modular multilevel converter is characterized by comprising the following steps:
s1, establishing a controlled source-based bridge arm average model and listing a differential equation expressed by sigma-delta under a corresponding abc coordinate system;
s2, deducing a state space model of the MMC bridge arm average model according to the differential equation established in the step S1;
s3, establishing a port controlled dissipation Hamilton model of the MMC system by using the state space model of the MMC bridge arm average model obtained in the step S2;
and S4, designing a PI passive feedback controller of the closed-loop system by using the port controlled dissipation Hamilton model of the MMC system obtained in the step S3 and using a passive control theory, and realizing the control of the modular multilevel converter by the PI passive feedback controller.
2. The method according to claim 1, wherein step S1 is specifically:
s101, establishing an MMC bridge arm average model based on a controlled source;
s102, writing a differential equation expressed by sigma-delta under an MMC bridge arm average model abc coordinate system in a row mode;
and S103, analyzing frequency components of each sigma-delta variable, and determining that the electrical quantity represented by the delta variable comprises a fundamental frequency component, and the electrical quantity represented by the sigma variable comprises a direct current component and a negative sequence double frequency component.
3. The method according to claim 2, wherein in step S102, the differential equation expressed by Σ - Δ in the MMC bridge arm average model abc coordinate system is specifically:
ac side voltage equation:
Figure FDA0003043305060000011
wherein the content of the first and second substances,
Figure FDA0003043305060000012
the difference between the upper and lower bridge arm currents of the j-th phase;
Figure FDA0003043305060000013
Figure FDA0003043305060000014
modulating voltage for a j-th phase bridge arm; u. ofsjThe voltage is the system voltage of the j-th alternating current side;
Figure FDA0003043305060000015
is the difference of the modulation coefficients of the upper and lower bridge arms of the jth phase;
Figure FDA0003043305060000016
is the sum of the modulation coefficients of the upper and lower bridge arms of the jth phase;
Figure FDA0003043305060000017
is the sum of the equivalent capacitance voltages of the upper and lower bridge arms of the jth phase;
Figure FDA0003043305060000018
is the difference between the equivalent capacitance voltages of the upper and lower bridge arms of the jth phase; rfIs the equivalent resistance of the transformer; l isfEquivalent leakage inductance of the transformer; l is0Upper and lower bridge arm inductors; l iseqIs an equivalent inductance on the AC side, ReqIs an equivalent resistance on the alternating current side;
the loop current equation:
Figure FDA0003043305060000021
wherein the content of the first and second substances,
Figure FDA0003043305060000022
is j phase circulation; u shapedcIs a direct current side voltage;
Figure FDA0003043305060000023
equivalent bridge arm capacitance-voltage equation:
Figure FDA0003043305060000024
wherein, CarmIs the equivalent bridge arm voltage.
4. The method of claim 2, wherein in step S103, the AC side outputs current
Figure FDA0003043305060000025
Is composed of a fundamental frequency component and a fundamental frequency component,
Figure FDA0003043305060000026
consists of a fundamental frequency component; phase circulation current
Figure FDA0003043305060000027
Consists of direct current and negative sequence double frequency components,
Figure FDA0003043305060000028
consists of DC component and negative sequence double frequency component, and the value of the DC component is
Figure FDA0003043305060000029
Figure FDA00030433050600000210
Is composed of a fundamental frequency component and a fundamental frequency component,
Figure FDA00030433050600000211
the direct current double-frequency-sequence amplifier consists of a direct current component and a negative sequence double-frequency component;
Figure FDA00030433050600000212
is composed of only the fundamental frequency component(s),
Figure FDA00030433050600000213
the device consists of a direct current component and a negative sequence double frequency component in steady operation; when the three-phase MMC system is described by adopting a differential equation expressed by sigma-delta based on an abc coordinate system, the electrical quantity expressed by delta variable only contains fundamental frequency components, and the electrical quantity expressed by the sigma variable consists of direct current components and negative sequence double frequency components.
5. The method according to claim 1, wherein in step S2, the state space model of the MMC bridge arm average model is specifically:
the equation of state for the dq0 axis component of the sum of the equivalent capacitance voltages is expressed as:
Figure FDA00030433050600000214
the equation of state for the dq0 axis component of the sum of the equivalent capacitance voltages is expressed as:
Figure FDA0003043305060000031
the equation of state for the dq0 axis component of the interphase current is expressed as:
Figure FDA0003043305060000032
the equation of state of the dq-axis component of the ac-side output current is expressed as:
Figure FDA0003043305060000033
wherein, the state space model contains 10 state variables, respectively
Figure FDA0003043305060000034
Figure FDA0003043305060000035
A dq axis component representing the difference between the equivalent capacitor voltages, a dq0 component representing the sum of the capacitor voltages, a dq0 component representing the sum of the currents flowing through the inductors, and a dq axis component representing the difference between the inductor currents in the system, wherein the 5 control variables are respectively
Figure FDA0003043305060000036
Figure FDA0003043305060000037
The model also has 3 external input variables Udc、usd、usq。
6. The method of claim 1, wherein in step S3, the port-controlled dissipative hamiltonian model of MMC is represented by a derived state space model
Figure FDA0003043305060000038
Wherein x is a system state variable; j (x) is a system internal structure matrix; r (x) is a system dissipation matrix; g (x) is a system and external port interaction structure matrix; u is a system external input vector; y is the external output vector, and H (x) is the system energy storage function.
7. The method according to claim 1, wherein step S4 is specifically:
s401, setting an expected balance point of the MMC system;
s402, calculating a passive output vector of the bilinear MMC system according to the expected balance point of the MMC system in the step S401;
s403, according to the passive output vector of the bilinear MMC system obtained in the step S402, selecting a PI controller, combining the PI controller with passive control, and designing a closed-loop system PI passive feedback controller, wherein the PI passive control comprises an outer loop power controller and an inner loop PI passive controller, the outer loop power controller calculates a dq axis reference value of output current required by the inner loop PI passive controller according to reference values of active power and reactive power, the inner loop PI passive controller is divided into a passive output calculation part and a PI tracking control part, firstly, each state variable reference value and each state variable obtained through sigma-delta calculation and dq conversion are input into the inner loop PI passive controller, and the passive output vector of the closed-loop system is solved; then, a PI controller is used for tracking and controlling the passive output vector and outputting a control variable; inverse dq-inverting the output variable and [ Sigma-Delta [ ]]-1And calculating to obtain modulation coefficients of upper and lower bridge arms of the MMC, and obtaining trigger pulses of the upper and lower bridge arm sub-modules according to the modulation coefficients to realize control of the MMC system.
8. The method according to claim 7, wherein in step S402, the passive output vector y of the bilinear MMC system is:
Figure FDA0003043305060000051
wherein y ═ y1 y2 y3 y4 y5]TIs the passive output vector of the closed-loop system,
Figure FDA0003043305060000052
Figure FDA0003043305060000053
a dq axis component representing the difference between the equivalent capacitor voltages in the system, a dq0 component representing the sum of the capacitor voltages, a dq0 axis component representing the sum of the currents flowing through the inductors, and a dq axis component representing the difference between the inductor currents,
Figure FDA0003043305060000054
Figure FDA0003043305060000055
respectively corresponding to the balance points of the state variables.
9. The method according to claim 7, wherein in step S403, the PI passive control includes an outer loop power controller and an inner loop PI passive controller, the outer loop power controller calculates a dq-axis reference value of an output current required by the inner loop PI passive controller according to reference values of active power and reactive power, the inner loop PI passive controller is divided into two parts, namely a calculation passive output part and a PI tracking control part, and each state variable reference value and each state variable obtained through sigma-delta calculation and dq conversion are input into the inner loop PI passive controller to calculate a passive output vector of the closed-loop system; then, a PI controller is used for tracking and controlling the passive output vector and outputting a control variable; carrying out dq inverse transformation on each output control variable and sigma-delta]-1Calculating to obtain modulation coefficients of upper and lower bridge arms of the MMC, and finally obtaining trigger pulses of upper and lower bridge arm sub-modules through a corresponding modulation algorithm so as to realize control on the MMC; the closed loop system PI passive feedback controller is as follows:
Figure FDA0003043305060000061
wherein, KPh＞0、KIhGreater than 0 is proportional coefficient, integral coefficient, K in PI controlP＝diag(KPh)，KI＝diag(KIh)，γhFor the integral quantity of the introduced passive output vector, yhBeing the passive output vector of the closed-loop system, Δ mhIs the control variable increment introduced.
10. A PI passive control system of a modular multilevel converter is characterized by comprising:
the differential module is used for establishing a controlled source-based bridge arm average model and listing a differential equation expressed by sigma-delta under a corresponding abc coordinate system;
the derivation module is used for deriving a state space model of the MMC bridge arm average model according to a differential equation obtained by the differentiation module;
the modeling module is used for establishing a port controlled dissipation Hamilton model of the MMC system by utilizing a state space model of the MMC bridge arm average model obtained by the derivation module;
and the control module is used for designing a PI passive feedback controller of the closed-loop system by utilizing a passive control theory according to a port controlled dissipation Hamilton model of the MMC system of the modeling module, and realizing the control of the modular multilevel converter through the PI passive feedback controller.
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