CN112003326A - Virtual synchronous generator system state feedback controller design method considering time lag - Google Patents

Virtual synchronous generator system state feedback controller design method considering time lag Download PDF

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CN112003326A
CN112003326A CN202010985258.7A CN202010985258A CN112003326A CN 112003326 A CN112003326 A CN 112003326A CN 202010985258 A CN202010985258 A CN 202010985258A CN 112003326 A CN112003326 A CN 112003326A
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time lag
feedback controller
state feedback
synchronous generator
state
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乐健
赵联港
周谦
朗红科
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Wuhan University WHU
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    • 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
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • 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
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • 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
    • H02M7/53—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 using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M7/537—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 using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters
    • 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
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • 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
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • 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
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/22—The renewable source being solar energy
    • 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
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/28—The renewable source being wind energy

Abstract

The invention relates to a power system virtual synchronous generator control technology, in particular to a design method of a virtual synchronous generator system state feedback controller considering time lag, which comprises the following steps: step 1, establishing a VSG control inverter grid-connected system state space model; step 2, considering time lag, rewriting a state space model; step 3, deducing a time lag stabilization condition through LMI according to the Lyapunov stability theorem; step 4, adding a state feedback controller; step 5, obtaining a new time lag stabilization condition of the system under the action of the state feedback controller; and 6, solving a state feedback controller equation according to the stable condition. According to the method, the influence of time lag on VSG control is effectively solved by designing the state feedback controller, so that the VSG system can meet ideal performance requirements, and the time lag stability of the virtual synchronous generator grid-connected system is improved.

Description

Virtual synchronous generator system state feedback controller design method considering time lag
Technical Field
The invention belongs to the technical field of control over virtual synchronous generators of power systems, and particularly relates to a design method of a state feedback controller of a virtual synchronous generator system considering time lag.
Background
Virtual Synchronous Generator (VSG) technology simulates the working principle of a Synchronous Generator by controlling an inverter, thereby obtaining the operation characteristics similar to the Synchronous Generator. Specifically, characteristics such as a body model, active frequency modulation and reactive voltage regulation of the synchronous generator are mainly simulated, so that the grid-connected inverter can be compared with the traditional synchronous generator in terms of an operation mechanism and external characteristics. In recent years, the equivalent inertia of a power system is reduced due to the fact that the number of grid-connected distributed power sources based on power electronic interfaces is continuously increased, so that the accidents of safety and stability of a power grid frequently occur and the quality of power supply voltage is deteriorated, and the requirements of reliability and safe operation of the system cannot be met by the traditional control means. The VSG technology introduces virtual inertia and damping in an inverter control system, so that the output external characteristics of the inverter have the similar rotating inertia, droop characteristics and damping characteristics of a synchronous generator, necessary frequency and voltage support can be provided for a power grid, the stability of the power system is improved, and the VSG technology is increasingly widely applied to modern power systems. However, the time lag generally exists in an actual VSG control system and is an important factor influencing the stability of the system, and the existing VSG control method does not consider the influence of the time lag, so that the stability performance of the system is reduced.
Therefore, in order to solve the above problems and ensure that the closed-loop system has desired performance, it is necessary to design the control law of the system by analyzing the mathematical model of the controlled object according to the performance requirement of the system. The existing time lag power system stability analysis and controller design generally utilizes an H-infinity design method, but the theory is limited because the selection of the weight function has no rule to be circulated; linear Matrix Inequality (LMI) technology has a unified solution step, and a feedback controller can be designed according to a derived time lag stabilization criterion. Firstly, the LMI method needs to express the stability criterion of the time-lag system as a group of linear matrix inequalities through the Lyapunov stability theory to obtain a system method for solving the time-lag stability. In the process of simplifying the LMI, a systematic method for solving the optimal weight matrix is obtained by introducing a free weight matrix method, so that the problem that no rule is adopted for selecting the weight function to be circulated can be avoided, the conservatism of the original method is greatly reduced, and the systematic method for solving the time lag stability is obtained. According to the theoretical method, a learner defines the nonlinear disturbance boundary of the system in a quadratic form according to the characteristics of system disturbance, provides the stable condition of the system by using an LMI method, provides the LMI method for analyzing the stability of the system on the basis, provides a design method of a feedback controller suitable for a multivariable system and obtains the feedback controller. However, although the LMI method has strong systematicness, the research on the analysis of the control stability and the robust control of the grid-connected VSG system which has strong nonlinearity and time lag is not deep at present, and the problem that the time lag VSG system can meet ideal performance requirements by designing a controller is a problem.
How to make stable control of the VSG system still remains the focus of research on VSG control. The existing VSG control method does not consider the influence of time lag, so that the stability performance of the system is reduced.
Disclosure of Invention
The invention aims to provide a VSG control-based grid-connected inverter, and the VSG system can meet an ideal performance requirement state feedback controller design method by establishing a time lag grid-connected inverter system integral state space model and adopting an LMI method to obtain a system time lag stability condition.
In order to solve the technical problems, the invention adopts the following technical scheme: the method for designing the state feedback controller of the virtual synchronous generator system with consideration of time lag comprises the following steps:
step 1, establishing a VSG control inverter grid-connected system state space model;
step 2, considering time lag, rewriting a state space model;
step 3, deducing a time lag stabilization condition through LMI according to the Lyapunov stability theorem;
step 4, adding a state feedback controller;
step 5, obtaining a new time lag stabilization condition of the system under the action of the state feedback controller;
and 6, solving a state feedback controller equation according to the stable condition.
In the above method for designing a state feedback controller of a virtual synchronous generator system considering time lag, the step 1 specifically includes:
controller measures three-phase voltage u of grid-connected pointabcThree-phase output current iabcAnd system frequency f, and voltage u under the electric dq coordinate system is obtained by adopting synchronous rotating coordinate transformationdqAnd current idqThe electrical angle theta required by coordinate transformation is calculated and given by a power frequency controller; calculating the output electromagnetic power P of the invertereReactive power QeVoltage amplitude U at grid connectionmCalculating an excitation regulation output voltage command U by using an excitation controller*The virtual impedance control link obtains an inverter output voltage instruction value E according to an excitation controller output instruction* dqThe current-voltage dual-loop controller derives an instruction u for generating a control pulse according to the instruction* dq-pwmThe inverter sends out a voltage with the characteristics of a synchronous generator according to the command;
according to the operation principle, the state equation of the system is obtained:
Figure BDA0002689010370000021
wherein: a. the0Is the system matrix of the system state equation.
In the above method for designing a state feedback controller of a virtual synchronous generator system considering time lag, the step 2 specifically includes:
for a VSG-containing grid-connected inverter system considering time lag, separating a state variable x (t) without time lag from a state variable x (t-tau) with time lag tau to respectively obtain a matrix A and a time lag matrix AdThe system equation becomes:
Figure BDA0002689010370000031
wherein:
Figure BDA0002689010370000032
is the initial trajectory of the system.
In the above method for designing a state feedback controller of a virtual synchronous generator system considering time lag, the step 3 specifically includes:
according to the Lyapunov stability theorem, a Lyapunov functional of a time-lag system is constructed by using a quadratic method and is as follows:
Figure BDA0002689010370000033
in the formula: p and Q are symmetric positive definite matrixes; w is a symmetric semi-positive definite matrix, such that the Lyapunov functional V (t) is positive definite;
the derivative of the Lyapunov functional with respect to time along the trajectory of the system can be obtained:
Figure BDA0002689010370000034
weight matrix N1,N2,X11,X12,X22To simplify, namely:
Figure BDA0002689010370000035
Figure BDA0002689010370000036
the derivative of the Lyapunov functional is simplified as:
Figure BDA0002689010370000037
in the formula:
Figure BDA0002689010370000038
f11＝PA+ATP+Q+N1+τX11+τATWA
Figure BDA0002689010370000041
Figure BDA0002689010370000042
according to the Lyapunov stability theorem, obtaining the condition for keeping time lag stable by an LMI method: for satisfying 0<τ<τmaxIf symmetric positive definite matrices P and Q exist, symmetric semi-positive definite matrices W, X11And X22An arbitrary matrix N1,N2And X12And satisfy phi<0 and Ψ ≧ 0, for any1(t) ≠ 0 is always
Figure BDA0002689010370000043
The system becomes progressively stable as can be seen by the Lyapunov theorem.
In the above method for designing a state feedback controller of a virtual synchronous generator system considering time lag, the step 4 specifically includes:
the system adds the control input u (t), and the linearized state equation is:
Figure BDA0002689010370000044
wherein: b is a control input matrix;
the LMI technology is utilized to design the following state feedback controllers, so that the closed loop system is ensured to be asymptotically stable:
u(t)＝Kx(t)
under the action of the state feedback controller, the closed loop control system becomes:
Figure BDA0002689010370000045
in the above method for designing a state feedback controller of a virtual synchronous generator system considering time lag, the step 5 specifically includes:
and substituting the changed system equation into a system time-lag stabilization condition to obtain a new system time-lag stabilization condition under the action of the state feedback controller, wherein the new system time-lag stabilization condition is as follows: for satisfaction of condition 0<τ<τmaxIf and only if there is a scalar quantity>0 and a symmetric positive definite matrix L, R, Z, an arbitrary matrix M1,M2The following inequality is satisfied, and the system is asymptotically stable;
Figure BDA0002689010370000046
wherein:
L＝P-1,Z＝P-1QP-1,R＝W-1,M1＝P-1N1P-1,M2＝P-1N2P-1
Figure BDA0002689010370000047
′13＝τL(AT+KTBT)
in the above method for designing a state feedback controller of a virtual synchronous generator system considering time lag, the step 6 specifically includes:
and solving a feedback matrix K of the VSG system state feedback controller considering the time lag by using an inequality so as to obtain the state feedback controller parameters which enable the VSG system to meet the control performance requirement when the time lag exists.
Compared with the prior art, the invention aims at the VSG controlled grid-connected inverter, and obtains the system time lag stable condition and the state feedback controller equation by establishing a time lag grid-connected inverter system integral state space model and adopting an LMI method. By designing the state feedback controller, the influence of time lag on VSG control is effectively solved, the VSG system can meet ideal performance requirements, and the time lag stability of the virtual synchronous generator grid-connected system is improved.
Drawings
FIG. 1 is a flow diagram of a virtual synchronous generator system feedback controller design that accounts for time lag as contemplated by an embodiment of the present invention;
fig. 2 is a diagram illustrating a structure of a system for controlling a grid-connected inverter based on a VSG according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the following embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. 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.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
The present invention is further illustrated by the following examples, which are not to be construed as limiting the invention.
The photovoltaic and fan grid-connected system based on the VSG control strategy is a research object, a unified time-lag state space model of an inverter, a line and a load is established, then a free weight matrix is converted into a core according to the Lyapunov stability theorem, a time-lag stable condition is obtained through an LMI method, state feedback control of the system is deduced according to the stable condition, a sufficient condition for stabilizing the state feedback system is obtained, the state feedback system is applied to the design of a system state feedback controller, and controller parameters can be solved through a linear matrix inequality, so that the time-lag stability of the virtual synchronous generator grid-connected system is improved.
The present embodiment is implemented by the following technical solutions, as shown in fig. 1, a flow chart of a feedback controller design of a VSG system considering time lag is provided in the present embodiment.
(1) Firstly, a VSG control inverter grid-connected system state space model needs to be established.
Based on VS as shown in FIG. 2G controls grid-connected inverter system structure chart, and the controller measures grid-connected point three-phase voltage u in the chartabcThree-phase output current iabcAnd system frequency f, and voltage u under the electric dq coordinate system is obtained by adopting synchronous rotating coordinate transformationdqAnd current idqThe electrical angle theta required by coordinate transformation is calculated and given by a power frequency controller; calculating the output electromagnetic power P of the invertereReactive power QeVoltage amplitude U at grid connectionmCalculating an excitation regulation output voltage command U by using an excitation controller*The virtual impedance control link obtains an inverter output voltage instruction value E according to an excitation controller output instruction* dqThe current-voltage dual-loop controller derives an instruction u for generating a control pulse according to the instruction* dq-pwmThe inverter issues a voltage having a synchronous generator characteristic according to the command.
According to the operation principle, the state equation of the system is obtained:
Figure BDA0002689010370000061
wherein: a. the0Is the system matrix of the system state equation.
(2) Rewriting the state space model in consideration of time lag; for a VSG-containing grid-connected inverter system considering time lag, separating a state variable x (t) without time lag from a state variable x (t-tau) with time lag tau to respectively obtain a matrix A and a time lag matrix AdThe system equation becomes:
Figure BDA0002689010370000062
wherein:
Figure BDA0002689010370000063
is the initial trajectory of the system.
(3) Deducing a time lag stability condition through LMI according to the Lyapunov stability theorem; according to the Lyapunov stability theorem, firstly, a Lyapunov functional of a time-lag system is constructed by a quadratic method, wherein the Lyapunov functional comprises the following steps:
Figure BDA0002689010370000064
in the formula: p and Q are symmetric positive definite matrixes; w is a symmetric semi-positive definite matrix, such that the Lyapunov functional V (t) is positive definite.
The derivative of the Lyapunov functional with respect to time along the trajectory of the system can be obtained:
Figure BDA0002689010370000065
weight matrix N1,N2,X11,X12,X22To simplify, namely:
Figure BDA0002689010370000071
Figure BDA0002689010370000072
then, the derivative of the Lyapunov functional is simplified to:
Figure BDA0002689010370000073
in the formula:
Figure BDA0002689010370000074
f11＝PA+ATP+Q+N1+τX11+τATWA
Figure BDA0002689010370000075
Figure BDA0002689010370000076
according to the Lyapunov stability theorem, obtaining the condition for keeping time lag stable by an LMI method: for satisfying 0<τ<τmaxIf symmetric positive definite matrices P and Q exist, symmetric semi-positive definite matrices W, X11And X22An arbitrary matrix N1,N2And X12And satisfy phi<0 and Ψ ≧ 0, for any1(t) ≠ 0 is always
Figure BDA0002689010370000077
Then the system becomes progressively stable as can be seen by Lyapunov theorem.
(4) Adding a state feedback controller; considering the system plus control input u (t), the linearized equation of state is:
Figure BDA0002689010370000078
wherein: and B is a control input matrix.
The LMI technology is utilized to design a state feedback controller, and the following state feedback controllers are designed to ensure that a closed loop system thereof is asymptotically stable:
u(t)＝Kx(t)
under the action of the state feedback controller, the closed loop control system becomes:
Figure BDA0002689010370000079
(5) obtaining a new time lag stabilization condition of the system under the action of the state feedback controller; the changed system equation is brought into the time-lag stabilization condition of the system, and the new time-lag stabilization condition of the system under the action of the state feedback controller is obtained as follows: for satisfaction of condition 0<τ<τmaxIf and only if there is a scalar quantity>0 and a symmetric positive definite matrix L, R, Z, an arbitrary matrix M1,M2Satisfying the following inequality, the system is asymptotically stableAnd (4) determining.
Figure BDA0002689010370000081
Wherein:
L＝P-1,Z＝P-1QP-1,R＝W-1,M1＝P-1N1P-1,M2＝P-1N2P-1
Figure BDA0002689010370000082
′13＝τL(AT+KTBT)
(6) solving a state feedback controller equation according to the stable condition; the feedback matrix K of the VSG system state feedback controller considering the time lag can be solved by using the inequality, so that the state feedback controller parameters which enable the VSG system to meet the performance requirement of control when the time lag exists are obtained.
While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention.

Claims (7)

1. The method for designing the state feedback controller of the virtual synchronous generator system considering time lag is characterized by comprising the following steps of: the method comprises the following steps:
step 1, establishing a VSG control inverter grid-connected system state space model;
step 2, considering time lag, rewriting a state space model;
step 3, deducing a time lag stabilization condition through LMI according to the Lyapunov stability theorem;
step 4, adding a state feedback controller;
step 5, obtaining a new time lag stabilization condition of the system under the action of the state feedback controller;
and 6, solving a state feedback controller equation according to the stable condition.
2. The design method of the virtual synchronous generator system state feedback controller considering the time lag as claimed in claim 1, wherein the step 1 is realized by:
controller measures three-phase voltage u of grid-connected pointabcThree-phase output current iabcAnd system frequency f, and voltage u under the electric dq coordinate system is obtained by adopting synchronous rotating coordinate transformationdqAnd current idqThe electrical angle theta required by coordinate transformation is calculated and given by a power frequency controller; calculating the output electromagnetic power P of the invertereReactive power QeVoltage amplitude U at grid connectionmCalculating an excitation regulation output voltage command U by using an excitation controller*The virtual impedance control link obtains an inverter output voltage instruction value E according to an excitation controller output instruction* dqThe current-voltage dual-loop controller derives an instruction u for generating a control pulse according to the instruction* dq-pwmThe inverter sends out a voltage with the characteristics of a synchronous generator according to the command;
according to the operation principle, the state equation of the system is obtained:
Figure FDA0002689010360000011
wherein: a. the0Is the system matrix of the system state equation.
3. The design method of the virtual synchronous generator system state feedback controller considering the time lag as claimed in claim 1, wherein the step 2 is realized by the following steps:
for a VSG-containing grid-connected inverter system considering time lag, state variables without time lag are obtained
Figure FDA0002689010360000012
Separating from the state variable x (t-tau) with the time lag tau to respectively obtain a matrix A and a time lag matrix AdThe system equation becomes:
Figure FDA0002689010360000013
wherein:
Figure FDA0002689010360000014
is the initial trajectory of the system.
4. The design method for the state feedback controller of the virtual synchronous generator system considering the time lag as claimed in claim 1, wherein the step 3 is realized by the following steps:
according to the Lyapunov stability theorem, a Lyapunov functional of a time-lag system is constructed by using a quadratic method and is as follows:
Figure FDA0002689010360000021
in the formula: p and Q are symmetric positive definite matrixes; w is a symmetric semi-positive definite matrix, such that the Lyapunov functional V (t) is positive definite;
the derivative of the Lyapunov functional with respect to time along the trajectory of the system can be obtained:
Figure FDA0002689010360000022
weight matrix N1,N2,X11,X12,X22To simplify, namely:
Figure FDA0002689010360000023
Figure FDA0002689010360000024
the derivative of the Lyapunov functional is simplified as:
Figure FDA0002689010360000025
in the formula:
Figure FDA0002689010360000026
f11＝PA+ATP+Q+N1+τX11+τATWA
Figure FDA0002689010360000029
Figure FDA00026890103600000210
according to the Lyapunov stability theorem, obtaining the condition for keeping time lag stable by an LMI method: for satisfying 0<τ<τmaxIf symmetric positive definite matrices P and Q exist, symmetric semi-positive definite matrices W, X11And X22An arbitrary matrix N1,N2And X12And satisfy phi<0 and Ψ ≧ 0, for any1(t) ≠ 0 is always
Figure FDA00026890103600000211
The system becomes progressively stable as can be seen by the Lyapunov theorem.
5. The design method for the virtual synchronous generator system state feedback controller considering the time lag as claimed in claim 1, wherein the step 4 is realized by the following steps:
the system adds the control input u (t), and the linearized state equation is:
Figure FDA0002689010360000031
wherein: b is a control input matrix;
the LMI technology is utilized to design the following state feedback controllers, so that the closed loop system is ensured to be asymptotically stable:
u(t)＝Kx(t)
under the action of the state feedback controller, the closed loop control system becomes:
Figure FDA0002689010360000032
6. the design method for the state feedback controller of the virtual synchronous generator system considering the time lag as claimed in claim 1, wherein the step 5 is realized by the following steps:
and substituting the changed system equation into a system time-lag stabilization condition to obtain a new system time-lag stabilization condition under the action of the state feedback controller, wherein the new system time-lag stabilization condition is as follows: for satisfaction of condition 0<τ<τmaxIf and only if there is a scalar quantity>0 and a symmetric positive definite matrix L, R, Z, an arbitrary matrix M1,M2The following inequality is satisfied, and the system is asymptotically stable;
Figure FDA0002689010360000033
wherein:
L＝P-1,Z＝P-1QP-1,R＝W-1,M1＝P-1N1P-1,M2＝P-1N2P-1
Figure FDA0002689010360000034
′13＝τL(AT+KTBT) 。
7. the design method for the state feedback controller of the virtual synchronous generator system considering the time lag as claimed in claim 1, wherein the step 6 is realized by the following steps:
and solving a feedback matrix K of the VSG system state feedback controller considering the time lag by using an inequality so as to obtain the state feedback controller parameters which enable the VSG system to meet the control performance requirement when the time lag exists.
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安海云: "基于自由权矩阵理论的电力系统时滞稳定性研究", 《中国优秀博硕士学位论文全文数据库(博士) 工程科技Ⅱ辑》 *

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