CN112421976B - Three-level inverter power supply reduced-order modeling method based on hybrid system theory - Google Patents

Three-level inverter power supply reduced-order modeling method based on hybrid system theory Download PDF

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CN112421976B
CN112421976B CN202011000742.6A CN202011000742A CN112421976B CN 112421976 B CN112421976 B CN 112421976B CN 202011000742 A CN202011000742 A CN 202011000742A CN 112421976 B CN112421976 B CN 112421976B
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level inverter
current
power supply
voltage
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CN112421976A (en
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刘群英
衡一嘉
霍欣莉
章凡
李博文
蔡茂杰
张昌华
陈树恒
高斌
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University of Electronic Science and Technology of China
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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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/13—Differential equations

Abstract

The invention discloses a three-level inverter power supply order-reducing modeling method based on a hybrid system theory, which comprises the steps of firstly, building an electromagnetic transient model of a three-level inverter power supply in the form of ordinary differential equation, secondly, carrying out order-reducing treatment on the electromagnetic transient model based on a singular perturbation equivalent theory, and finally, utilizing the hybrid system Lyapunov stable theorem to carry out value-taking on parameters in the model after the order-reducing treatment, thereby determining a specific model after the order-reducing treatment; therefore, the transient stability is good under the condition that the order of the three-level inverter power supply reduced model is lower.

Description

Three-level inverter power supply reduced-order modeling method based on hybrid system theory
Technical Field
The invention belongs to the technical field of three-level inverters, and particularly relates to a three-level inverter power supply reduced-order modeling method based on a hybrid system theory.
Background
Systems comprising a system of discrete events and a system of continuous variables, which interact with each other, are called hybrid systems. Power systems are described by complex systems comprising continuous dynamics and discrete events, such as generators and loads, which can be viewed as continuous dynamic behavior, usually expressed by interrelated systems of differential and algebraic equations. The above-described feature of the power system is a mixture of continuous control and discrete control, and is thus a typical hybrid system. In recent years, great attention has been paid to the stability of hybrid systems, and many results have been obtained.
Since the end of the 19 th century, commercial ac power systems have been built, although voltage levels have increased, installed capacities have increased, and geographical areas have expanded, links such as power supplies, power grids, and loads have been mainly constituted by electromagnetic conversion equipment such as generators, transformers, and motors.
With the mature technology, electromagnetic conversion equipment is gradually replaced by power electronic conversion equipment, and the electromagnetic conversion equipment becomes an important trend for the development of power systems. Power primary systems are undergoing profound historical changes. The power electronic conversion equipment is applied to the scale of the power system and firstly appears on the side of a power load. The alternating current electric energy is converted into the electric energy in a corresponding form according to the load requirement, and the electric energy parameter is adjusted according to the change of the load level, so that the power utilization efficiency of the load can be greatly improved. The power supply widely adopts a three-level inverter, and the output of the three-level inverter has the advantages of higher electric energy quality, lower harmonic content, better electromagnetic compatibility, lower switching loss and the like, so the three-level inverter is widely applied to the field of medium-high voltage high-capacity alternating current speed regulation. The power electronization of the three-level inverter changes the dynamic characteristics of a power supply, and greatly influences the stability of the system. Especially under the situation that resources and loads are reversely distributed in China and large-scale renewable energy power generation is transmitted remotely through high-voltage direct current, the power electronization degree of a transmission-end power grid is high, and the situation of safety and stability is complex. Power electronic conversion equipment is penetrating the power system at an increasing level with its flexibility in power conversion, profoundly changing the dynamic behavior of the power system.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a three-level inverter power supply reduced order modeling method based on the hybrid system theory, and has good transient stability under the condition of ensuring that the three-level inverter power supply reduced order model has lower order.
In order to achieve the above object, the present invention provides a three-level inverter power supply reduced-order modeling method based on a hybrid system theory, which is characterized by comprising the following steps:
(1) constructing an electromagnetic transient model of the three-level inverter power supply in the form of ordinary differential equation;
Figure GDA0002796329280000021
where f (x, u), u is the input grid voltage, and x is the state variable x ═ x1,x2,x3,x4,ix,iy,ix_t,iy_t,ixL,iyL,ux,uy,ux_t,uy_t,θPLL]T，ux、uyFor the x-axis and y-axis components, i, of the capacitor voltage at the end of the three-level inverterxL,iyLX-and y-axis components of the current of the line L, ix,iyFor the x-and y-components of the output current, i, of a three-level inverterx_t,iy_tMeasuring the x-axis and y-axis components of the output current of a three-level inverter, ux_t,uy_tMeasuring the component of the capacitor voltage at the end of the three-level inverter on the x axis and the y axis; x is the number of1,x3Integrating variables, x, for the outer loop active and reactive power loops of a three-level inverter2、x4Integrating variables, theta, for the active and reactive current loops of the inner loop of a three-level inverterPLLEach component phase in the three-level inverter is locked by a phase-locked loop;
(2) reducing the order based on the singular perturbation equivalence theory;
(2.1) analyzing the electromagnetic transient model based on the multi-time scale characteristic of the singular perturbation equivalence theory, and reserving a fast dynamic attribute variable x1,x2,x3,x4And i will have mixed dynamic propertiesx,iyPart is reserved as mu ix,μiyμ takes the value (0, 1), thus reducing the state variable x to:
x＝[x1,x2,x3,x4,μix,μiy]T (2)
(2.2) rewriting the electromagnetic transient model of the three-level inverter into:
Figure GDA0002796329280000031
wherein the content of the first and second substances,
Figure GDA0002796329280000032
Pref、Qrefas reference values for active and reactive power, Kp1、Kp3Respectively corresponding to active power and reactive power proportional control link parameters, Ki1、Ki3Respectively corresponding to the integral control link parameters of active power and reactive power id、iqD-axis current and q-axis current, R, respectively, of the output current of the three-level inverterfIs the resistance value, X, of the coupling circuitfIs the reactance value of the coupling circuit, Ex、EyX-axis and y-axis components of an electromotive force in an output of the three-level inverter;
(3) carrying out value taking on mu by utilizing the hybrid system Lyapunov stable theorem;
(3.1) outputting the current mu i from the three-level inverterx,μiyInversely transforming the dq coordinate system into the abc coordinate system to obtain the three-phase current mu of the three-level inverteraia,μbib,μcic；
(3.2) controlling the working state of each bridge arm of the three-level inverter by using a space voltage vector modulation method;
Figure GDA0002796329280000033
(3.3) selecting the alternating current measurement inductive current and the direct current side capacitor voltage of the three-level inverter as state quantities xLyapunonv＝(μaia,μbib,μcic,udc)TSelecting three-level inverter AC side voltage and input DC source voltage as input quantity u ═ u (u ═ u)a,ub,uc,uin)T(ii) a Then, according to the hybrid system Lyapunov stability theorem, a Lyapunov function of the three-level inverter power supply and a corresponding state equation are established;
Vs＝(xLyapunonv-xref)T[(J-R)xLyapunonv+Bu] (5)
wherein x isrefJ, R, B is a variable to be determined as a reference state quantity;
the state equation of the three-level inverter power supply is as follows:
Figure GDA0002796329280000041
wherein R issIs equivalent resistance L of a three-level invertersIs equivalent inductance R of a three-level inverterinIs an internal resistance u of a three-level inverterinFor inputting a DC source voltage udcThe voltage is the direct-current side voltage of the three-level inverter;
then the sum of the output three-phase symmetrical voltage and current is zero, and the simplified state equation is as follows:
Figure GDA0002796329280000042
(3.3) according to the hybrid system Lyapunov function stability theorem, under the continuous conduction mode, establishing a basic circuit of the three-level inverter as follows:
Figure GDA0002796329280000043
(3.4) comparing the formula (7) with the formula (8):
Figure GDA0002796329280000044
Figure GDA0002796329280000045
Figure GDA0002796329280000051
Figure GDA0002796329280000052
wherein the content of the first and second substances,
Figure GDA0002796329280000053
(3.5) substituting the variable determined in step (3.4) into equation (5), and letting VsAnd (5) calculating the specific value of mu to complete the whole process of the three-level inverter power supply reduced-order modeling.
The invention aims to realize the following steps:
the invention relates to a three-level inverter power supply order-reducing modeling method based on a hybrid system theory, which comprises the steps of firstly, building an electromagnetic transient model of a three-level inverter power supply in the form of an ordinary differential equation, secondly, carrying out order-reducing treatment on the electromagnetic transient model based on a singular perturbation equivalent theory, and finally, utilizing the hybrid system Lyapunov stable theorem to carry out value taking on parameters in the model after the order-reducing treatment, thereby determining a specific model after the order-reducing treatment; therefore, the transient stability is good under the condition that the order of the three-level inverter power supply reduced model is lower.
Meanwhile, the three-level inverter power supply reduced-order modeling method based on the hybrid system theory has the following beneficial effects:
(1) compared with a classical DAE reduced-order model, the method has good simulation precision on the external characteristics of the power, and improves the simulation precision of slow dynamics and hybrid dynamics.
(2) Compared with a mixed simulation DAE reduced-order model, the method can obtain the accurate moment of instability under the condition of ensuring high-accuracy time domain simulation.
(3) The invention has good transient stability.
Drawings
FIG. 1 is a flow chart of a three-level inverter power supply reduced-order modeling method based on a hybrid system theory;
FIG. 2 is a diagram of a three-phase inverter topology;
FIG. 3 is a simplified circuit block diagram of a three-phase inverter power supply in modes I and VIII;
FIG. 4 is a simplified circuit block diagram of a three-phase inverter power supply in mode II;
FIG. 5 is a simplified circuit block diagram of a three-phase inverter power supply in mode III;
FIG. 6 is a simplified circuit block diagram of a three-phase inverter power supply in mode IV;
FIG. 7 is a simplified circuit block diagram of a three-phase inverter power supply in mode V;
FIG. 8 is a simplified circuit block diagram of the three-phase inverter power supply in mode VI;
FIG. 9 is a simplified circuit block diagram of the three-phase inverter power supply in mode VII;
FIG. 10 is a graph comparing the slow dynamic simulation effect of the reduced order model;
FIG. 11 is a comparison graph of current slow dynamic simulation effects of different reduced order models;
FIG. 12 is a graph comparing slow dynamic simulation effects of different reduced order models;
FIG. 13 is a comparison graph of output power curves before and after a power model reduction of a three-level inverter;
FIG. 14 is a schematic diagram of a transient stability condition of a three-level inverter power supply step-down model for the case;
fig. 15 is a schematic diagram of a transient stability condition of a three-level inverter power supply reduced-order model in case two.
Detailed Description
The following description of the embodiments of the present invention is provided in order to better understand the present invention for those skilled in the art with reference to the accompanying drawings. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.
Examples
FIG. 1 is a flow chart of a three-level inverter power supply reduced-order modeling method based on a hybrid system theory.
In this embodiment, as shown in fig. 2, a midpoint clamping type three-level inverter widely used in the medium-voltage high-power field is selected as a research object, and a detailed description is made on a three-level inverter power supply reduced-order modeling method based on the hybrid system theory, which specifically includes the following steps:
s1, building an electromagnetic transient model of the three-level inverter power supply in the form of ordinary differential equations;
Figure GDA0002796329280000061
where f (x, u), u is the input grid voltage, and x is the state variable x ═ x1,x2,x3,x4,ix,iy,ix_t,iy_t,ixL,iyL,ux,uy,ux_t,uy_t,θPLL]T，ux、uyFor the x-axis and y-axis components, i, of the capacitor voltage at the end of the three-level inverterxL,iyLX-and y-axis components of the current of the line L, ix,iyFor the x-and y-components of the output current, i, of a three-level inverterx_t,iy_tMeasuring the x-axis and y-axis components of the output current of a three-level inverter, ux_t,uy_tMeasuring the component of the capacitor voltage at the end of the three-level inverter on the x axis and the y axis; x is the number of1,x3Integrating variables, x, for the outer loop active and reactive power loops of a three-level inverter2、x4Integrating variables, theta, for the active and reactive current loops of the inner loop of a three-level inverterPLLEach component phase in the three-level inverter is locked by a phase-locked loop;
s2, performing order reduction processing based on the singular perturbation equivalence theory;
s2.1, analyzing the electromagnetic transient model based on the multi-time scale characteristic of the singular perturbation equivalent theory, wherein the adjustment of the internal electromotive force is mainly controlled by the integral variable x of the controller1～x4Dynamic response speed of (2) according to1～x4The real part of the strongly correlated characteristic root can judge the characteristic time scale, and the distribution of the characteristic root is based on x1～x4The strongly correlated characteristic root damping is much weaker than other characteristic roots, indicating that the power electronic power system exhibits multi-time scale characteristics. In addition, the current ix,iyIs also strongly associated with the slow feature root such that the number of slow dynamics is greater than the number of slow feature roots, ix,iyIt shows the characteristics of mixed dynamics, therefore, through analysis, we retain the fast dynamic property variable x1,x2,x3,x4And i will have mixed dynamic propertiesx,iyPart is reserved as mu ix,μiyμ takes the value (0, 1), thus reducing the state variable x to:
x＝[x1,x2,x3,x4,μix,μiy]T (2)
s2.2, rewriting the electromagnetic transient model of the three-level inverter into:
Figure GDA0002796329280000071
wherein the content of the first and second substances,
Figure GDA0002796329280000081
Pref、Qrefas reference values for active and reactive power, Kp1、Kp3Respectively corresponding to active power and reactive power proportional control link parameters, Ki1、Ki3Respectively corresponding to the integral control link parameters of active power and reactive power id、iqD-axis current and q-axis current, R, respectively, of the output current of the three-level inverterfIs the resistance value of the coupling circuit，XfIs the reactance value of the coupling circuit, Ex、EyX-axis and y-axis components of an electromotive force in an output of the three-level inverter;
s3, carrying out value taking on mu by utilizing the hybrid system Lyapunov stable theorem;
s3.1, outputting current mu i by the three-level inverterx,μiyInversely transforming the dq coordinate system into the abc coordinate system to obtain the three-phase current mu of the three-level inverteraia,μbib,μcic；
S3.2, controlling the working state of each bridge arm of the three-level inverter by using a space voltage vector modulation method;
Figure GDA0002796329280000082
s3.3, selecting the alternating current measured inductive current and the direct current side capacitor voltage of the three-level inverter as state quantities xLyapunonv＝(μaia,μbib,μcic,udc)TSelecting three-level inverter AC side voltage and input DC source voltage as input quantity u ═ u (u ═ u)a,ub,uc,uin)T(ii) a Then, according to the hybrid system Lyapunov stability theorem, a Lyapunov function of the three-level inverter power supply is established;
Vs＝(xLyapunonv-xref)T[(J-R)xLyapunonv+Bu] (5)
wherein x isrefJ, R, B is a variable to be determined as a reference state quantity;
with reference to fig. 2, according to the operating state of each bridge arm of the three-level inverter, the equation of state of the circuit structure in each mode can be written as follows:
in modes I and VIII, switch state SaSbSc000 and SaSbScThe simplified circuit is shown in fig. 3 as 111. From the state equations for the column write output current and capacitor voltage of the circuit of fig. 3, one can obtain,
Figure GDA0002796329280000083
in mode II, switch state SaSbScThe simplified circuit is as in fig. 4 at 001. From the state equations for the column write output current and capacitor voltage of the circuit of fig. 4, one can obtain,
Figure GDA0002796329280000091
in mode III, switch state SaSbSc010, the simplified circuit is as in fig. 5. From the state equations for the column write output current and capacitor voltage of the circuit of fig. 5, it can be derived,
Figure GDA0002796329280000092
in mode IV, switch state SaSbScThe simplified circuit is as in fig. 6 at 011. From the state equations for the column write output current and capacitor voltage of the circuit of fig. 6, one can obtain,
Figure GDA0002796329280000093
in mode V, on-off state SaSbScThe simplified circuit is as in fig. 7, 100. From the state equations for the column write output current and capacitor voltage of the circuit of fig. 7, it can be derived,
Figure GDA0002796329280000101
in mode VI, switch state SaSbScThe simplified circuit is shown in fig. 8 as 101. From the state equations for the column write output current and capacitor voltage of the circuit of fig. 8, one can obtain,
Figure GDA0002796329280000102
in mode VII, switch state SaSbScThe simplified circuit is shown in fig. 9 as 110. From the state equations for the column write output current and capacitor voltage of the circuit of fig. 9, it can be derived,
Figure GDA0002796329280000103
analyzing the state equation under each mode, the uniform expression form of the state equation of the three-level inverter power supply can be obtained as follows:
Figure GDA0002796329280000104
wherein R issIs equivalent resistance L of a three-level invertersIs equivalent inductance R of a three-level inverterinIs an internal resistance u of a three-level inverterinFor inputting a DC source voltage udcThe voltage is the direct-current side voltage of the three-level inverter;
then the sum of the output three-phase symmetrical voltage and current is zero, and the simplified state equation is as follows:
Figure GDA0002796329280000111
s3.3, according to the Lyapunov function stability theorem of the hybrid system, under the continuous conduction mode, establishing a basic circuit of the three-level inverter as follows:
Figure GDA0002796329280000112
s3.4, comparing the formula (7) with the formula (8) to obtain:
Figure GDA0002796329280000113
Figure GDA0002796329280000114
Figure GDA0002796329280000115
Figure GDA0002796329280000121
wherein the content of the first and second substances,
Figure GDA0002796329280000122
s3.5, substituting the variable determined in the step S3.4 into the formula (5), and enabling VsAnd (5) calculating the specific value of mu to complete the whole process of the three-level inverter power supply reduced-order modeling.
Simulation example:
a single-machine infinite system is taken as a research object, and external disturbance is set as power grid voltage drop for simulating transient stability response. The fault clearing time is 0.30s, the simulation time is 0-1.50 s, and the method comprises the following two scenes:
(1) case 1: the voltage of the power grid drops to 0.60pu, and the system is stable.
(2) Case 2: the voltage of the power grid drops to 0.40pu, and the system is unstable.
The simulation results of the reduced order model in Case1 on the dominant slow dynamic variable x are shown in fig. 10, where (a) the integral variable x of the active power loop is1(b) a reactive power loop integral variable x3(c) an active current loop integral variable x2(d) reactive current loop integral variable x4. Although the model is a slow dynamic variable, the classical DAE reduced-order model integrates the variable x to the outer loop1、x3Has better time domain simulation effect, but integrates variable x in inner loop2、x4The simulation error is very obvious; the three-level inverter power supply reduced-order model reserves more dynamic states, so that the simulation precision of the inner loop integral variable and the outer loop integral variable is higher.
Fig. 11 is a current slow dynamic output curve for a three-level inverter power supply step-down model, an electromagnetic transient model, and a classical DAE step-down model. As can be seen from FIG. 11, the output current i of the classical DAE reduced order model when a disturbance occursxAnd iyWill jump immediately. The same dynamics of the conventional electromagnetic transient model do not allow for a fast tracking of the process, but experience significant dc component attenuation. The three-level inverter power supply step-down model describes the process more accurately, and this phenomenon also leads to simulation errors of the inner loop regulator in fig. 10.
Fig. 12 (a) and (b) show output curve comparisons of s reactive power and terminal voltage in slow dynamic simulations of an electromagnetic transient model, a hybrid DAE reduced-order model, and a three-level inverter power supply reduced-order model. When the voltage drop is increased and the set voltage drops to 0.50pu, the order-reduced models all show the result of instability, but the respective phenomena are different. The active power, the reactive power and the terminal voltage are rapidly dispersed at about 0.14s after the fault occurs, and the system is in a instability state, wherein the instability state is caused by the active current idGrowth up to the network transmission limit causes singularities. Comparing the models can find that the integral of the three-level inverter power supply reduced model is automatically terminated at the divergence moment, so that the singularity occurrence moment can be accurately obtained; the mixed simulation DAE reduced-order model diverges after a period of instability, and the accurate moment of singularity occurrence cannot be obtained. The electromagnetic transient model continues to diverge after singularity occurs, presenting violent oscillations. Feasibility verification of a three-level inverter power supply reduced model;
time domain simulations may not fully characterize the adaptability of the modeling in some cases, and may be verified using stability indicators. Taking the Lyapunov energy function as a judgment basis, respectively setting three-phase short circuit disturbance in a single-machine infinite system, wherein the conditions are as follows:
case one, 0.2s, the fault starts and lasts for 0.1 s. And equating the system and calculating and analyzing the transient stability of the system.
Case two, failure starts at 0.2s and lasts for 0.3 s. And equating the system and calculating and analyzing the transient stability of the system.
Aiming at the above calculation examples, transient stability calculation is respectively carried out on the original system and the reduced order model system, the electromagnetic power change condition is observed, and analysis and comparison are carried out.
(a) Verifying the output power validity of the three-level inverter power supply reduced model;
fig. 13 is a comparison graph of output power curves before and after a reduction of a three-level inverter power model. The error between the reduced-order model and the actual system simulation curve is very small, the maximum error is 2.74%, and the reduced-order model can better reflect the dynamic response of the system after receiving disturbance.
(b) Analyzing the system stability of the three-level inverter power supply reduced model;
in this case, a system Stable Equilibrium Point (SEP) and an Unstable Equilibrium Point (UEP) are shown in fig. 14 (a). Stable equilibrium point SEP:
Figure GDA0002796329280000131
unstable equilibrium point UEP:
Figure GDA0002796329280000132
the three-level inverter power supply reduced system stability domain diagram is shown in (b) of fig. 14, and the three-level inverter power supply reduced system transient energy function is shown in (c) of fig. 14.
The critical energy V of the system under the fault is obtained through calculationcr11.7438 pu. As can be seen from (b) in fig. 14, the system operation point is at the center of the stable region; as can be seen from (c) in FIG. 14, the system transient process energy VcDoes not exceed the critical energy Vcr. The three-level inverter power supply step-down model is cut off when the three-phase short circuit fault occurs for 0.1 second, and the display system is not unstable and is consistent with the stable domain result of (b) in 14.
In case two, the critical energy is 11.7438pu, and (b) in fig. 15 plots the critical energy (straight line) and the transient energy together in order to reflect the instability time more clearly. As can be seen from (a) in fig. 15, the relative power angle starts to diverge at around 5s, and the system starts to destabilize. The same result can be obtained in the energy function of fig. 15, and the corresponding relationship is clear. From the critical stability region of (c) in fig. 15, it can be seen that each point is divergent and has a part crossing the critical curve, and the system is instable in transient state. Therefore, the simulation results prove that the transient stability of the power system can be correctly reflected by the established three-level inverter power supply reduced-order model.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.

Claims (1)

1. A three-level inverter power supply reduced-order modeling method based on a hybrid system theory is characterized by comprising the following steps:
(1) constructing an electromagnetic transient model of the three-level inverter power supply in the form of ordinary differential equation;
Figure FDA0003325726570000011
where f (x, u), u is the input grid voltage, and x is the state variable x ═ x1,x2,x3,x4,ix,iy,ix_t,iy_t,ixL,iyL,ux,uy,ux_t,uy_t,θPLL]T，ux、uyFor the x-axis and y-axis components, i, of the capacitor voltage at the end of the three-level inverterxL,iyLX-and y-axis components of the current of the line L, ix,iyFor the x-and y-components of the output current, i, of a three-level inverterx_t,iy_tMeasuring the x-axis and y-axis components of the output current of a three-level inverter, ux_t,uy_tMeasuring the component of the capacitor voltage at the end of the three-level inverter on the x axis and the y axis; x is the number of1,x3Integrating variables, x, for the outer loop active and reactive power loops of a three-level inverter2、x4Integrating variables, theta, for the active and reactive current loops of the inner loop of a three-level inverterPLLEach component phase in the three-level inverter is locked by a phase-locked loop;
(2) reducing the order based on the singular perturbation equivalence theory;
(2.1) analyzing the electromagnetic transient model based on the multi-time scale characteristic of the singular perturbation equivalence theory, and reserving a fast dynamic attribute variable x1,x2,x3,x4And i will have mixed dynamic propertiesx,iyPart is reserved as mu ix,μiyμ takes the value (0, 1), thus reducing the state variable x to:
x＝[x1,x2,x3,x4,μix,μiy]T (2)
(2.2) rewriting the electromagnetic transient model of the three-level inverter into:
Figure FDA0003325726570000012
wherein the content of the first and second substances,
Figure FDA0003325726570000021
Pref、Qrefas reference values for active and reactive power, Kp1、Kp3Respectively corresponding to active power and reactive power proportional control link parameters, Ki1、Ki3Respectively corresponding to the integral control link parameters of active power and reactive power id、iqD-axis current and q-axis current, R, respectively, of the output current of the three-level inverterfIs a coupling circuitResistance value, XfIs the reactance value of the coupling circuit, Ex、EyX-axis and y-axis components of an electromotive force in an output of the three-level inverter;
(3) carrying out value taking on mu by utilizing the hybrid system Lyapunov stable theorem;
(3.1) outputting the current mu i from the three-level inverterx,μiyInversely transforming the dq coordinate system into the abc coordinate system to obtain the three-phase current mu of the three-level inverteraia,μbib,μcic；
(3.2) controlling the working state of each bridge arm of the three-level inverter by using a space voltage vector modulation method;
Figure FDA0003325726570000022
(3.3) selecting the alternating current side inductive current and the direct current side capacitor voltage of the three-level inverter as state quantities xLyapunonv＝(μaia,μbib,μcic,udc)TSelecting three-level inverter AC side voltage and input DC source voltage as input quantity u ═ u (u ═ u)a,ub,uc,uin)T(ii) a Then, according to the hybrid system Lyapunov stability theorem, a Lyapunov function of the three-level inverter power supply and a corresponding state equation are established;
Vs＝(xLyapunonv-xref)T[(J-R)xLyapunonv+Bu] (5)
wherein x isrefJ, R, B is a variable to be determined as a reference state quantity;
the state equation of the three-level inverter power supply is as follows:
Figure FDA0003325726570000023
wherein R issIs equivalent resistance L of a three-level invertersIs equivalent inductance R of a three-level inverterinIs an internal resistance u of a three-level inverterinFor inputting a DC source voltage udcThe voltage is the direct-current side voltage of the three-level inverter;
then the sum of the output three-phase symmetrical voltage and current is zero, and the simplified state equation is as follows:
Figure FDA0003325726570000031
(3.4) according to the hybrid system Lyapunov function stability theorem, under the continuous conduction mode, establishing a basic circuit of the three-level inverter as follows:
Figure FDA0003325726570000032
(3.5) comparing the formula (7) with the formula (8):
Figure FDA0003325726570000033
Figure FDA0003325726570000034
Figure FDA0003325726570000035
Figure FDA0003325726570000036
wherein the content of the first and second substances,
Figure FDA0003325726570000041
(3.6) substituting the variable determined in step (3.5) into equation (5), and letting VsAnd (5) calculating the specific value of mu to complete the whole process of the three-level inverter power supply reduced-order modeling.
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