CN107947149B - Power system time lag dependence robust stability determination method based on Wirtinger inequality - Google Patents

Power system time lag dependence robust stability determination method based on Wirtinger inequality Download PDF

Info

Publication number
CN107947149B
CN107947149B CN201610890901.1A CN201610890901A CN107947149B CN 107947149 B CN107947149 B CN 107947149B CN 201610890901 A CN201610890901 A CN 201610890901A CN 107947149 B CN107947149 B CN 107947149B
Authority
CN
China
Prior art keywords
time
power system
lag
matrix
formula
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201610890901.1A
Other languages
Chinese (zh)
Other versions
CN107947149A (en
Inventor
李宁
孙永辉
卫志农
孙国强
郭敏
张世达
翟苏巍
王�义
武小鹏
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Hohai University HHU
Original Assignee
Hohai University HHU
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Hohai University HHU filed Critical Hohai University HHU
Priority to CN201610890901.1A priority Critical patent/CN107947149B/en
Publication of CN107947149A publication Critical patent/CN107947149A/en
Application granted granted Critical
Publication of CN107947149B publication Critical patent/CN107947149B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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
    • 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]

Landscapes

  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Supply And Distribution Of Alternating Current (AREA)
  • Other Investigation Or Analysis Of Materials By Electrical Means (AREA)

Abstract

The invention disclosesA power system time-lag dependence robust stability determination method based on a Wirtinger inequality considers uncertain parameters existing in a power system modeling process and is used for analyzing the maximum time-lag stability margin borne by a power system. The method comprises the following specific steps: s1: establishing a multi-time-lag power system model considering uncertain parameters; s2: determining a given time lag hiWhether or not the stability determination condition is satisfied: if so, the delay h is determinediThe time-lapse power system under the condition is asymptotically stable. The invention has wide application range and less conservation.

Description

Power system time lag dependence robust stability determination method based on Wirtinger inequality
Technical Field
The invention relates to the field of power systems, in particular to a power system time lag dependence robust stability determination method based on a Wirtinger inequality.
Background
With the continuous expansion of the power grid scale and the rapid development of Phasor Measurement Unit (PMU) technology, modern power systems gradually tend to have characteristics of large scale, multiple interconnection and the like. Therefore, the power grid stability control strategy gradually trends to global control from local control. In the global control strategy, especially due to the introduction of far-end signals, signal delay problems are inevitably generated, and researches show that the time lag can cause system control equipment to fail, and cause system performance deterioration and instability. Therefore, the knowledge of the time lag stability domain which can be borne by the power system is of great significance to safe and stable operation of the power grid.
Currently, the research on the time-lag system mainly focuses on two methods: frequency domain methods and time domain methods. The frequency domain method is mainly used for judging the stability of the system by solving the position of a system feature root, but has the problems of difficult solution and the like, and the method is difficult to consider the situation when uncertain parameters are contained in the system. Aiming at the defects of the frequency domain method, the commonly adopted method is a time domain method based on a Lyapunov direct method, a Lyapunov functional is constructed, a Lyapunov stability theory is utilized, the stability criterion of the system is deduced, finally, the time lag stability margin of the system is solved by means of a Linear Matrix Inequality (LMI), and more importantly, the method can carry out robust stability analysis on the time lag system containing uncertain parameters. However, the Lyapunov stability theory is a sufficient condition for judging the system stability, so the criterion obtained by the method has certain conservation, and how to reduce the criterion conservation becomes one of the important difficulties of the research of the method.
Disclosure of Invention
The purpose of the invention is as follows: the invention discloses a power system time lag dependence robust stability determination method based on a Wirtinger inequality, which can solve the defects in the prior art.
The technical scheme is as follows: the invention discloses a power system time lag dependence robust stability determination method based on a Wirtinger inequality, which comprises the following steps of:
s1: establishing a multi-time-lag power system model considering uncertain parameters according to the formula (1):
Figure BDA0001129130750000011
in the formula (1), hmax＝max(h1,h2,…,hm) M is the number of time-lag links contained in the system, hiFor a given time lag, i-1, …, m, x (t) ∈ RnIs a system state variable, n is the number of the system state variables, phi (t) is the initial state of the system,
Figure BDA0001129130750000021
is a coefficient matrix of the system, [ Delta A ]0… ΔAm]＝HF(t)[E0… Em]H and
Figure BDA0001129130750000022
are all known constant matrices, i 10, …, m, f (t) is a time-varying matrix and satisfies formula (2):
FTF≤I (2)
s2 if there is scalar > 0, positive definite matrix P ∈ R(m+1)n×(m+1)n(ii) a Positive definite matrix Ui∈Rn×nI is 1, …, m; positive definite matrix Wi∈Rn×nI is 1, …, m; matrix array
Figure BDA0001129130750000023
i 31, …, m-1, j-1, …, m,; matrix array
Figure BDA0001129130750000024
i2If the expression (3) is satisfied 1, …, and m +2, it is determined that the delay time h is longiThe time-lag power system under conditions is asymptotically stable;
Figure BDA0001129130750000025
in formula (3):
Figure BDA0001129130750000026
Figure BDA0001129130750000027
Figure BDA0001129130750000028
Figure BDA0001129130750000029
0mthe number of the m-numbered 0 s is,
Figure BDA00011291307500000210
Figure BDA0001129130750000031
Figure BDA0001129130750000032
Figure BDA0001129130750000033
and I is an identity matrix.
Has the advantages that: compared with the prior art, the invention has the following beneficial effects: the method for judging the stability of the system obtained by the Wirtinger inequality scaling skill greatly reduces the conservatism of the system, and also considers the influence of the mutual coupling problem caused by multiple time lags on the stability of the system, so that the method is suitable for a single time lag system and a multiple time lag system, and in addition, the method also considers the influence of uncertain parameters generated in the actual modeling process on the stability of the system. Therefore, the invention has wide application range and less conservation.
Drawings
FIG. 1 is a flow chart of a method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a WSCC three-machine nine-node power system according to an embodiment of the present invention;
fig. 3 is a stable region diagram of a WSCC three-machine nine-node power system according to an embodiment of the present invention.
Detailed Description
The technical scheme of the invention is further described in the following by combining the attached drawings and the detailed description.
The specific embodiment discloses a power system time lag dependence robust stability determination method based on a Wirtinger inequality, which comprises the following steps of:
s1: establishing a multi-time-lag power system model considering uncertain parameters:
in general, a single-lag power system with lag links can be described by using a set of differential algebraic equations, and then by linearization near the system operating point, the system can be finally expressed as:
Figure BDA0001129130750000034
in the formula (1), x (t) ∈ RnIs a system state variable; phi (t) is the initial state of the system; a. the0,A1∈Rn×nIs the coefficient matrix of the system, and h ∈ R is the system time lag constant.
If there are uncertain parameters in the system, the system (1) will transition to:
Figure BDA0001129130750000035
in formula (2): delta A0，ΔA1Represents a system parameter disturbance term and satisfies
[ΔA0ΔA1]＝HF(t)[E0E1](3)
H、E0And E1Is a known constant matrix, and F (t) is a time-varying matrix satisfying the condition
FTF≤I
Similar to the single-lag power system model, the multi-lag system can be generally described in the following form:
Figure BDA0001129130750000041
in the formula (4), hmax＝max(h1,h2,…,hm) M is the number of time-lag links contained in the system, hiFor a given time lag, i-1, …, m, x (t) ∈ RnIs a system state variable, n is the number of the system state variables, phi (t) is the initial state of the system,
Figure BDA0001129130750000042
is a coefficient matrix of the system, [ Delta A ]0… ΔAm]＝HF(t)[E0… Em]H and
Figure BDA0001129130750000043
are all known constant matrices, i 10, …, m, f (t) is a time-varying matrix and satisfies formula (5):
FTF≤I (5)
s2 if there is scalar > 0, positive definite matrix P ∈ R(m+1)n×(m+1)n(ii) a Positive definite matrix Ui∈Rn×nI is 1, …, m; positive definite matrix Wi∈Rn×nI is 1, …, m; matrix array
Figure BDA0001129130750000044
i 31, …, m-1, j-1, …, m; matrix array
Figure BDA0001129130750000045
i2When equation (6) is satisfied for 1, …, and m +2, it is determined that the delay time h is zeroiThe time-lag power system under conditions is asymptotically stable;
Figure BDA0001129130750000046
in formula (6):
Figure BDA0001129130750000047
Figure BDA0001129130750000048
Figure BDA0001129130750000049
Figure BDA0001129130750000051
Figure BDA0001129130750000052
Figure BDA0001129130750000053
Figure BDA0001129130750000054
Figure BDA0001129130750000055
and I is an identity matrix.
In the process of solving the time lag stability criterion, a common scaling technique is to use a Jensen inequality. This approach, while feasible, increases the conservation of results. The method provided by the invention adopts a brand-new inequality, namely a Wirtinger inequality, to scale, so that the conservation of the obtained result can be greatly reduced. First, three important arguments are given for the proposed method of the present invention.
Introduction 1: for a given positive definite matrix M > 0, the following inequalities hold for a continuously differentiable function x over the interval [ a, b ]:
Figure BDA0001129130750000056
wherein ξ1＝x(b)-x(a)，
Figure BDA0001129130750000057
Theorem 2 given a matrix of appropriate dimensions Q ═ QTH, E and the positive definite matrix R > 0, having:
Q+HFE+ETFTHT＜0 (8)
for all satisfy FTF ≦ R, if and only if λ > 0 is present, having:
Q+λHHT+λ-1ETRE＜0 (9)
lesion 3 for constant matrix W ∈ Rn×nScalar γ > 0 andscalar function
Figure BDA0001129130750000058
:[-γ,0]Satisfy integral
Figure BDA0001129130750000059
Then:
Figure BDA00011291307500000510
wherein
Figure BDA0001129130750000061
The following gives a proof of the stable decision conditions:
constructing a Lyapunov functional suitable for a multi-time-lag power system:
Figure BDA0001129130750000062
then, the formula (11) is derived to obtain (12):
Figure BDA0001129130750000063
wherein
Figure BDA0001129130750000064
Figure BDA0001129130750000065
Note that:
Figure BDA0001129130750000066
for derived Lyapunov function (6)
Figure BDA0001129130750000067
Using the treatment of theorem 1, the following results are obtained:
Figure BDA0001129130750000068
wherein:
Figure BDA0001129130750000071
for the last term in equation (12)
Figure BDA0001129130750000072
The treatment by the theory 3 can obtain:
Figure BDA0001129130750000073
therefore, it is not only easy to use
Figure BDA0001129130750000074
For any M, according to the Newton-Leibniz equationiI is 1, …, m +2 is true:
Figure BDA0001129130750000075
by substituting the formulae (13), (14) and (15) for the formula (12)
Figure BDA0001129130750000076
If the system robustness is to be asymptotically stabilized, equation (16) is only required to be less than zero, that is:
Figure BDA0001129130750000077
wherein:
Figure BDA0001129130750000078
using lemma 2 processing for the above equation can result:
Figure BDA0001129130750000079
finally, Schur theory is applied to the above formula, and the formula (10) can be obtained, thus obtaining the certificate.
One embodiment is described below:
the WSCC 3 machine 9 node system is shown in fig. 2, wherein time lag exists in the control loops of the generators 2 and 3, random disturbance exists in the amplification system of the excitation system, and for the sake of simplicity of analysis, the change rule of the random disturbance in the generators is the same, that is, the change rule is the same, that is, the WSCC 3 machine 9 node system is shown in fig. 2
Figure BDA00011291307500000710
Figure BDA0001129130750000081
Wherein the modeled system matrix A0，A1，A2，H，E0，E1，E2As follows:
Figure BDA0001129130750000082
Figure BDA0001129130750000083
Figure BDA0001129130750000084
Figure BDA0001129130750000091
Figure BDA0001129130750000092
table 1 shows the robust stability margin of a 3-machine 9-node system calculated by the method of the present invention when the disturbance r is 1.0, and fig. 3 depicts the system stability region determined by the method herein, where θ and Norm respectively represent:
Figure BDA0001129130750000093
TABLE 1
θ/° Norm/s
0 0.0816
20 0.0549
40 0.0451
60 0.0410

Claims (1)

1. The method for judging the time lag dependence robustness stability of the power system based on the Wirtinger inequality is characterized by comprising the following steps: the method comprises the following steps:
s1: establishing a multi-time-lag power system model considering uncertain parameters according to the formula (1):
Figure FDA0001129130740000011
in the formula (1), hmax＝max(h1,h2,…,hm) M is the number of time-lag links contained in the system, hiFor a given time lag, i-1, …, m, x (t) ∈ RnIs a system state variable, n is the number of the system state variables, phi (t) is the initial state of the system, Ai1∈Rn×nIs a coefficient matrix of the system, [ Delta A ]0… ΔAm]＝HF(t)[E0… Em]H and Ei1Are all known constant matrices, i10, …, m, f (t) is a time-varying matrix and satisfies formula (2):
FTF≤I (2)
s2 if there is scalar > 0, positive definite matrix P ∈ R(m+1)n×(m+1)n(ii) a Positive definite matrix Ui∈Rn×nI is 1, …, m; positive definite matrix Wi∈Rn×nI is 1, …, m; matrix Zi3j∈Rn×n，i31, …, m-1, j-1, …, m,; matrix Mi2∈Rn×n，i2If the expression (3) is satisfied 1, …, and m +2, it is determined that the delay time h is longiThe time-lag power system under conditions is asymptotically stable;
Figure FDA0001129130740000012
in formula (3):
Figure FDA0001129130740000013
Figure FDA0001129130740000014
Figure FDA0001129130740000015
Figure FDA0001129130740000016
Π＝diag{0,Υ,0m}，0mthe number of the m-numbered 0 s is,
Figure FDA0001129130740000021
Figure FDA0001129130740000022
θ＝diag{h1I,…,hmI}，
Figure FDA0001129130740000023
Figure FDA0001129130740000024
Figure FDA0001129130740000025
and I is an identity matrix.
CN201610890901.1A 2016-10-12 2016-10-12 Power system time lag dependence robust stability determination method based on Wirtinger inequality Active CN107947149B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201610890901.1A CN107947149B (en) 2016-10-12 2016-10-12 Power system time lag dependence robust stability determination method based on Wirtinger inequality

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201610890901.1A CN107947149B (en) 2016-10-12 2016-10-12 Power system time lag dependence robust stability determination method based on Wirtinger inequality

Publications (2)

Publication Number Publication Date
CN107947149A CN107947149A (en) 2018-04-20
CN107947149B true CN107947149B (en) 2020-10-16

Family

ID=61928745

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201610890901.1A Active CN107947149B (en) 2016-10-12 2016-10-12 Power system time lag dependence robust stability determination method based on Wirtinger inequality

Country Status (1)

Country Link
CN (1) CN107947149B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112965377B (en) * 2020-12-23 2022-03-15 合肥工业大学 Non-fragile robust control method of distributed power generation system

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB561775A (en) * 1942-11-25 1944-06-05 Alfred Mills Taylor Improvements in electric power transmission
CN101350523A (en) * 2008-09-02 2009-01-21 天津大学 Method for distinguishing stability of muilt-timelag electric power system
CN101645600A (en) * 2009-08-27 2010-02-10 天津大学 Discrimination method of double-delay dependent robust stability of power system
CN105958476A (en) * 2016-05-06 2016-09-21 河海大学 Method of determining stability of power system with time delay based on Wirtinger inequality

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB561775A (en) * 1942-11-25 1944-06-05 Alfred Mills Taylor Improvements in electric power transmission
CN101350523A (en) * 2008-09-02 2009-01-21 天津大学 Method for distinguishing stability of muilt-timelag electric power system
CN101645600A (en) * 2009-08-27 2010-02-10 天津大学 Discrimination method of double-delay dependent robust stability of power system
CN105958476A (en) * 2016-05-06 2016-09-21 河海大学 Method of determining stability of power system with time delay based on Wirtinger inequality

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
时变时滞电力系统鲁棒稳定性的改进型判据;孙国强等;《电力系统自动化》;20150210;第39卷(第03期);第59-61页 *

Also Published As

Publication number Publication date
CN107947149A (en) 2018-04-20

Similar Documents

Publication Publication Date Title
Jafari et al. He's variational iteration method for solving fractional Riccati differential equation
CN103941072B (en) A kind of electric power signal mutation parameter measuring method based on real number Strong tracking filter
CN112018758A (en) Modeling method of high-proportion new energy-containing alternating current-direct current hybrid system based on digital twinning
CN106383443B (en) Anti-interference control method and system
Narendra et al. Stability, robustness, and performance issues in second level adaptation
CN107450310B (en) Set value excitation closed-loop identification method of continuous process model
CN110110475B (en) Extended Kalman filtering method based on online learning fading factors
CN113486540A (en) Tidal numerical model water depth estimation method based on ensemble Kalman filtering
CN106786675B (en) Power system stabilizer and implementation method thereof
CN107947149B (en) Power system time lag dependence robust stability determination method based on Wirtinger inequality
CN104865944B (en) Gas separation unit control system performance estimating method based on PCA LSSVM
CN108170648B (en) non-Gaussian process monitoring method based on known data regression
Bin et al. A method to extract instantaneous features of low frequency oscillation based on trajectory section eigenvalues
CN105652795B (en) 3PTT-2R series-parallel numerical control machine tool servo system fault prediction device and method based on residual observer
Farhat et al. ℋ−/ℋ∞ fault detection observer for switched systems
Wang et al. Neural Networks Based Lyapunov Functions for Transient Stability Analysis and Assessment of Power Systems
CN104808090A (en) Electric signal mutation parameter measurement method based on improved strong tracking filter
Qing-wei et al. A practical approach of online control performance monitoring
CN112464811A (en) Method for accurately filtering high-frequency random noise in pumped storage unit runout signal
Zhang et al. Damage identification through finite element model updating using wavelet damage function
Alanqar et al. Practice-oriented system identification strategies for MPC of building thermal and HVAC dynamics
CN105373094A (en) Industrial process dynamic model identification apparatus based on data fast sampling
Feng et al. Integral partitioning approach to stability analysis and stabilization of distributed time delay systems
Ren et al. Minimum entropy incremental control for nonlinear stochastic systems with non-gaussian disturbances and uncertain parameters
CN113239608B (en) Floating wind power structure nonlinear effect evaluation method

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant