CN108092268A - A kind of wide area power system Convenient stable criterion under the influence of section time_varying delay - Google Patents

Abstract

The invention discloses the wide area power system Convenient stable criterions under the influence of a kind of section time_varying delay, it is seriously affected for time delay to what the stable operation of wide area power system generated, on the basis of the time_varying delay electric power system model of structure wide area section, it is proposed that a kind of new augmentation vector sum Lyapunov Krasovskii functional building methods；Then, when being parsed to Functional derivation, split using time lag, Wirtinger integral inequalities, Free matrix based integral inequalities and the methods of convex combination, reduce the error generated in resolving, the relatively low stability criteria of conservative has been obtained, has expanded the stable operation zone of system.Finally, by 11 node system simulation analysis of typical second-order system, one machine infinity bus system and four machines, illustrate compared with the existing methods, method of the invention expands the stable operation zone of system.

Description

Wide area power system stability discrimination method under influence of interval variable time lag

Technical Field

The invention relates to the technical field of power systems, in particular to a wide area power system stability judging method under the influence of interval variable time lag.

Background

With the development of our country society, the scale of the modern power system and the interconnection range of the power grid are continuously enlarged, the economic benefit of the operation of the power grid is improved, the dynamic process of the modern power system is more complicated, and the traditional local control mode cannot meet the control requirement of the safe and stable operation of the current large-scale power grid. In recent years, the rapid development of wide area measurement technology (WAMS) based on Phasor Measurement Unit (PMU) and the wide application of WAMS in power systems have promoted the development of modern global control of power systems ^[1-3] . In a wide area environment, when the overall monitoring control is carried out on the operation process of a power system, time delay phenomena exist in the transmission and processing processes of measurement and control signals, and the time delay phenomena are particularly obvious in the long-distance transmission process. Research has shown that even a small time lag may have a serious adverse effect on the stable operation of the power system ^[4] Therefore, the method has very important practical significance in researching the stability problem of the power system under the influence of time lag ^[5-6] 。

The existing method for analyzing the stability of the time-lapse power system mainly comprises two methods, namely a frequency domain method and a time domain method. The stability analysis of the time-lapse power system by adopting a frequency domain method is mainly characterized in that the stability of the system is judged by transforming a characteristic equation of the system and solving the distribution of characteristic values ^[7-8] The method can obtain the essential condition for system stability, but the calculation process is very complicated, and the method is difficult to apply when the operation state of the power system jumps or time-varying parameters are contained. Compared with a frequency domain method, the time domain method has obvious superiority when the operation state of the processing system jumps or contains time-varying parameters ^[9-10] The method is the most important method for analyzing the stability of the time-lapse power system at present. The L-K functional method based on the Lyapunov stability theory in the time domain method is most widely applied, the method provides sufficient conditions for system stability, and has certain conservative property, so that how to reduce the conservative property and expand the stable operation area of the system is a hot problem of research in recent years, and the method is provided by broad scholarsThe same research method ^[11-19] 。

In the aspect of functional construction, documents [11 and 12] respectively study the stability analysis and controller design problems of a constant-time-lag power system and a variable-time-lag power system by constructing a double-integral functional and a double-integral functional, and document [13] by constructing an augmented L-K functional and adopting a corresponding analysis method. In the aspect of functional derivative analysis, on the basis of constructing an L-K functional, a document [14] applies an N-L formula to introduce some loose terms into functional analysis, a document [15] applies a Jesen inequality method when processing the functional, a document [16] applies a free weight matrix method, a document [17] applies a generalized eigenvalue method, a document [18] applies a convex combination method, and a document [19] applies a Wirtinger integral inequality method, so that the stability analysis and control problem of a wide-area time-lag power system is researched. Although the conservatism of the time-lag power system stability criterion is reduced to a certain extent in the above documents, the disadvantages that model description is inaccurate, the structure of the L-K functional is simpler, and the method adopted by functional derivative analysis has certain limitation on reducing the conservatism exist, so that the obtained stability criterion has certain conservatism.

Disclosure of Invention

Aiming at the defects in the prior art, the invention aims to research the stability problem of a wide area power system under the influence of interval variable time lag and provides a method for judging the stability of the wide area power system under the influence of interval variable time lag, firstly, an interval variable time lag power system model is established, and on the basis, a new augmentation vector and a new L-K functional containing a triple integral term are constructed; then, the integral interval is processed in a segmented mode in the analysis process of the functional derivative, and the integral term in the functional derivative is estimated by adopting a double Wirtinger integral inequality, a Free-matrix-based integral inequality and a convex combination method, so that errors generated in the analysis process of the functional are reduced, and the conservation of the stability criterion is reduced.

To reach the main conclusion of the present invention, the following quotation is cited.

Introduction 1 ^[20] : for any given constant matrix M > 0, and differentiable functionsAnd a > b, the inequality shown below holds, namely:

wherein:

introduction 2 ^[21] : for any given constant matrix M > 0, and differentiable functionsAnd a > b, the following inequalities are satisfied:

wherein:

introduction 3 ^[22] : there is any positive integer m, n, variable a ∈ (0, 1), Z ^m×n > 0, matrixFor theIf matrix Y is present, and satisfiesThen the following holds:

introduction 4 ^[23] : let x(s) be E.R ^n×n Is a continuous function { x(s) | s ∈ [ a, b ]]Is the symmetric matrix B, L is the same as R ^3n×3n ，F∈R ^n×n The matrix G ∈ R ^3n×3n ，C、N∈R ^3n×n Satisfies the following conditions:

the following inequality holds:

wherein:

Ψ ₁ ＝[I -I 0]，

Ψ ₂ ＝[-I -I 2I]，

He(NΨ ₁ +CΨ ₂ )＝(NΨ ₁ +CΨ ₂ )+(NΨ ₁ +CΨ ₂ ) ^T 。

the purpose of the invention is realized by the following technical scheme:

a method for judging the stability of a wide area power system under the influence of interval time-lag comprises the following steps:

establishing a time-lag power system function model containing a wide area control loop

In the formula: x (t) is belonged to R ⁿ Is electric powerThe state variable of the system, x (t-h (t)) is the state variable after the time delay, A ₁ In order to be a matrix of the system,is [ -h,0 [ ]]The time lag h (t) of the upper continuous initial phasor function satisfies:

0≤h(t)≤h

wherein, the constant h is more than 0 and is the time lag upper bound of the system; constant value of mu ₁ ，μ ₂ Upper and lower bounds for the time lag derivative;

when there is a disturbance in the system, the system (1) then becomes of the form:

setting: [ Delta A, delta A ] ₁ ]＝HF ₀ [E _a ，E _b ]，ΔA，ΔA ₁ As disturbance terms of the system, H, E _a ，E _b Is a constant matrix of known dimensions, F ₀ For a varying matrix, the following condition is satisfied:i is an identity matrix;

step2. System function in Stepl, construct the System L-K functional

Wherein:

P＝P ^T ＞0，W＝W ^T ＞0，M＝M ^T ＞0，Q＝Q ^T ＞0，

R＝R ^T ＞0，Z＝Z ^T ＞0，F＝F ^T ＞0；

the derivation of V (t) along the solution trajectory of the system (1) can result in:

wherein:

∏＝[E _ij ](i，j＝1，2，...，7)

when in useThe system (1) is asymptotically stable;

step3. Based on the results in Step2, the system (1) stability discrimination theorem is obtained as follows:

given the constant h, mu ₁ ，μ ₂ If there is a positive definite symmetric matrix P ∈ R ^5n×5n ，W∈R ^2n×2n ，M∈R ^2n×2n ，Q∈R ^n×n ，R∈R ^n×n ，Z∈R ^n×n ，F∈R ^n×n The symmetric matrix B ∈ R ^3n×3n ，L∈R ^3n×3n And a matrix of appropriate dimensions G ∈ R ^3n×n ，N∈R ^{3n ×n} ，C∈R ^3n×n The system (1) is asymptotically stable such that the following matrix inequality holds:

∏＝[E _ij ]＜0，(i，j＝1，2，...，7) (5)

wherein:

E ₁₃ ＝-P ₁₃ -M ₁₂ +Y ₁₁ +Y ₂₁ -Y ₁₂ -Y ₂₂ ，

E ₁₅ ＝-P ₁₅ +(h-h(t))(P ₃₁ A+P ₃₂ +P ₃₄ +M ₂₁ A)+2Y ₁₂ +2Y ₂₂ ，

E ₂₃ ＝-Y ₁₁ +Y ₂₁ +Y ₁₂ -Y ₂₂ -2Z，

E ₃₃ ＝-R-4Z，

E ₃₄ ＝-h(t)P ₂₃ -2Y ₂₁ +2Y ₂₂ ，

E ₃₅ ＝(h(t)-h)P ₃₃ -M ₂₂ +6Z，

E ₃₆ ＝-h(t)P ₄₃ ，

E ₃₇ ＝(h(t)-h)P ₅₃ ，

E ₅₅ ＝(h(t)-h)P ₃₅ -12Z-3h ² F，

the L-K system functional constructed in Step2,in (2), a new augmentation vector is introduced:

step2. After constructing the L-K system functional, the derivation of V (t) along the solution trajectory of the system (1) is as follows:

the derivation of V (t) along the solution trajectory of the system (1) can result in:

will appear in equation (10)Integration interval of [ t-h, t ]]Divided into intervals [ t-h, t-h (t)]And [ t-h (t), t)]Respectively processing integral inequalities on two intervals by using a Wirtinger integral inequality, and then further processing by using a convex combination method;

will be that in equation (11)Integration interval [ t-h, t]Divided into intervals [ t-h, t-h (t)]And [ t-h (t), t)]Processing a double integral term and a double integral term generated after the division by using a double Wirtinger integral inequality and a Free-matrix-based integral inequality respectively;

obtaining:

integral term appearing in equation (10)Integral interval of [ t-h, t ]]Divided into intervals [ t-h, t-h (t)]And [ t-h (t), t)]On this basis, a Wirtinger integral inequality is applied to the integral inequalities in the two intervals for processing, and the following results are obtained:

wherein:

Γ ₁ ＝[1 -1 0 0 0 0 0]，Γ ₂ ＝[1 1 0 -2 0 0 0]，

Γ ₃ ＝[0 1 -1 0 0 0 0]，Γ ₄ ＝[0 1 1 0 -2 0 0]。

when the integral term in the formula (11) is first divided into integral intervals, i.e., the integral interval [ t-h, t ] is divided into the intervals [ t-h, t-h (t) ] and [ t-h (t, t ], the following can be obtained:

the double integral terms and the one-double integral terms generated after the division are respectively processed by a double Wirtinger integral inequality and a Free-matrix-based integral inequality to obtain:

wherein:

compared with the prior art, the invention has the following advantages and beneficial effects:

1. unlike the existing literature, a new augmentation vector is introduced here:

and the functional is constructed to include a triple integral term V ₅ (t), the time-lag information is fully utilized, and the conservatism of the conclusion is reduced;

2. integral term appearing in formula (10)Integration interval of [ t-h, t ]]Divided into intervals [ t-h, t-h (t)]And [ t-h (t), t)]Compared with the prior documents [12, 17, 19]]This interval is scaled to [ t-h (t), t [ ]]More fully utilizes the time lag section [ t-h, t-h (t)]Of the party is reducedConservation of the method. On the basis, a one-fold Wirtinger integral inequality is applied to the integral inequalities on two intervals respectively to process the integral inequalities and documents [18, 20 and 24 ]]Compared with a Jensen integral inequality, the method has smaller conservative property and is beneficial to expanding the stable operation area of the system;

3. the integral term in the formula (11) is firstly divided into integral intervals, namely the integral interval [ t-h, t ] is divided into an interval [ t-h, t-h (t) ] and [ t-h (t), t ], a double integral term and a double integral term which are generated after the division are respectively processed by a double Wirtinger integral inequality and a Free-matrix-based integral inequality, and compared with documents [20, 23 and 26], the method reduces errors generated in the analysis process and conservatism of a system stability conclusion.

Drawings

FIG. 1 is a comparison graph of the stability margin of the typical second-order skew system of the present invention and the documents [18, 24, 25 ].

FIG. 2 is a comparison graph of the present invention and the typical second-order system skew system stability margin of the documents [20, 24, 25 ].

Fig. 3 is a schematic diagram of a stand-alone infinity system.

FIG. 4 is a graph comparing the stable operating margin of the method of the present invention with that of the methods of documents [12, 14, 19].

Fig. 5 is a schematic diagram of a 4-machine 11-node system.

Detailed Description

The following examples are described in further detail, but the embodiments of the present invention are not limited thereto.

Examples

A method for judging the stability of a wide area power system under the influence of interval time-lag comprises the following steps:

establishing a time-lag power system function model comprising a wide area control loop:

in the formula: x (t) is belonged to R ⁿ Is the state variable of the power system, x (t-h (t)) is the state variable after time delay, A ₁ Is a matrix of the system and is,is [ -h,0 [ ]]An upper continuous initial phasor function; the time lag h (t) satisfies:

0≤h(t)≤h

wherein, the constant h is more than 0 and is the time lag upper bound of the system; constant value of mu ₁ ，μ ₂ The upper and lower bounds of the time-lag derivative.

When there is a disturbance in the system, the system (1) then becomes of the form:

setting: [ Delta A,. DELTA.A ₁ ]＝HF ₀ [E _a ，E _b ]，ΔA，ΔA ₁ As disturbance terms of the system, H, E _a ，E _b Being a constant matrix of known dimensions, F ₀ For a varying matrix, the following condition is satisfied:i is an identity matrix;

in the step, the construction process of the mathematical model (1) of the wide area interval variable time lag system is as follows:

in the power system model, a dynamic model of the generator is expressed by a third-order differential equation, and is specifically expressed as follows:

wherein:

wherein: x _d And X _q D-axis and q-axis synchronous reactance respectively; e _q Is the q-axis transient potential; x' _d Is the d-axis transient reactance; x _e Is a line reactance; i is _d Outputting current for a longitudinal axis of the generator; delta and omega are the power angle and the angular speed of the generator rotor respectively; omega ₀ Is an initial steady state value of angular velocity; t is a unit of _j Is the inertia time constant of the generator; p is a radical of formula _m Is mechanical power; p is a radical of _e Is the electromagnetic power; d is a damping coefficient; t' _d Transient time constant for d-axis; e _f Is the excitation potential; e _Q Is a hypothetical electromotive force; v is infinite bus voltage; v _g Is the excitation system terminal voltage. In order to ensure the reliability of the power system, an AVR excitation control mode is applied, and because a time lag phenomenon exists in the system, a dynamic equation of the excitation system can be expressed as follows:

wherein: t is _a Parameters of a generator excitation loop are obtained; k _a The amplification factor of the excitation loop is obtained;is the terminal voltage reference value;is an excitation potential reference value.

In summary, the power system state space model with time lag can be represented by equations (21) and (22):

linearizing equation (23) at its equilibrium point yields:

in the formula: x (t) is belonged to R ⁿ Is the state variable of the power system, x (t-h (t)) is the state variable after time delay, A ₁ Is a matrix of the system and is,is [ -h,0]An upper continuous initial phasor function; the time lag h (t) satisfies:

0≤h(t)≤h

wherein, the constant h is more than 0 and is the time lag upper bound of the system; constant value of mu ₁ ，μ ₂ The upper and lower bounds of the time lag derivative.

Constructing a new augmentation vector and an L-K functional based on Step1, analyzing a functional derivative by adopting a method with smaller conservative property, and giving a new stability conclusion of the wide area power system under the influence of time-varying time lag, wherein the L-K functional of the system is as follows:

wherein:

P＝P ^T ＞0，W＝W ^T ＞0，M＝M ^T ＞0，Q＝Q ^T ＞0，

R＝R ^T ＞0，Z＝Z ^T ＞0，F＝F ^T ＞0；

in the step, the specific process is as follows:

firstly, let:

constructing an L-K functional for a system (1):

derivation of V (t) along the system (1) solution trajectory can result in:

first, the method of the formula (10)Dividing the integral interval, and then sequentially applying the theorem 1 and the theorem 3 to obtain:

wherein:

Γ ₁ ＝[1 -1 0 0 0 0 0]，Γ ₂ ＝[1 1 0 -2 0 0 0]，

Γ ₃ ＝[0 1 -1 0 0 0 0]，Γ ₄ ＝[0 1 1 0 -2 0 0]；

will be that in equation (11)The integration interval is divided into:

after segmentation is processed by lemma 2Andobtaining:

after segmentation is processed by theorem 4Obtaining:

wherein:

in summary, the following formulas (7) to (16) give:

wherein:

∏＝[E _ij ](i，j＝1，2，...，7)

when in useThe system (1) is asymptotically stable;

step3. Based on the result in Step2, the system (1) stability discrimination theorem is obtained as follows:

given the constant h, μ ₁ ，μ ₂ If there is a positive definite symmetric matrix P ∈ R ^5n×5n ，W∈R ^2n×2n ，M∈R ^2n×2n ，Q∈R ^n×n ，R∈R ^n×n ，Z∈R ^n×n ，F∈R ^n×n The symmetric matrix B ∈ R ^3n×3n ，L∈R ^3n×3n And a matrix of suitable dimensions G ∈ R ^3n×n ，N∈R ^{3n ×n} ，C∈R ^3n×n The system (1) is asymptotically stable, such that the following matrix inequality holds:

∏＝[E _ij ]＜0，(i，j＝1，2，...，7) (5)

wherein:

E ₁₃ ＝-P ₁₃ -M ₁₂ +Y ₁₁ +Y ₂₁ -Y ₁₂ -Y ₂₂ ，

E ₁₅ ＝-P ₁₅ +(h-h(t))(P ₃₁ A+P ₃₂ +P ₃₄ +M ₂₁ A)+2Y ₁₂ +2Y ₂₂ ，

E ₂₃ ＝-Y ₁₁ +Y ₂₁ +Y ₁₂ -Y ₂₂ -2Z，

E ₃₃ ＝-R-4Z，

E ₃₄ ＝-h(t)P ₂₃ -2Y ₂₁ +2Y ₂₂ ，

E ₃₅ ＝(h(t)-h)P ₃₃ -M ₂₂ +6Z，

E ₃₆ ＝-h(t)P ₄₃ ，

E ₃₇ ＝(h(t)-h)P ₅₃ ，

E ₅₅ ＝(h(t)-h)P ₃₅ -12Z-3h ² F，

the method of the invention is applied to carry out simulation analysis:

example 1: a time-varying skew system (1) is considered, wherein:

when h is generated ₁ =0, μ =0.5, according to document [11 =]In conclusion, the obtained time lag upper bound is 2.42, and the time lag upper bound obtained by the method is 2.63. In addition, in table 1, μ (μ = - μ) is given ₁ ＝μ ₂ ) And when different values are taken, obtaining a maximum time lag upper bound for ensuring the stability of the system by adopting different methods. It can be seen that, by using the theorem of the present invention, the upper bound of the time lag is 6.0594 when μ =0, 4.7261 when μ =0.1, 2.6317 when μ =0.5, and 2.2539 when μ =0.8, which are all higher than those obtained by using the documents [18, 24, 25]]The maximum skew value obtained by the method of (1).

As shown in fig. 1, the stable operation region of the system obtained by the different methods is shown, and it can be seen that the method of the present invention determines a larger stable region than the documents [18, 24, 25 ].

TABLE 1 maximum time lag values at different values of μ

Example 2: consider a time-varying dead time system (1) in which:

as shown in Table 2, the maximum time lag upper bound is given by the different methods when μ is 0.1,0.2,0.5, and 0.8, respectively.

TABLE 2 maximum skew at different values of μ

μ	0.1	0.2	0.5	0.8
					[24]	5.901	3.839	2.003	1.404
[25]	5.823	3.824	2.008	1.357
					[20]	6.059	3.672	1.411	1.275
Theorem of law	6.3715	4.1502	2.1344	1.6251

As shown in fig. 2, the stability regions of the different systems are given. It is easy to see that, compared with the documents [20, 24, 25], the theorem of the invention reduces the conservative degree of the system stability criterion, and effectively enlarges the stable operation area of the system.

Example 3: a single-machine infinite system shown in figure 3 is selected to verify the effectiveness of the method provided by the invention, and the reference document of the value situation of the specific parameters of the system [19].

Wherein:

when the system is not disturbed, the maximum stability margin of the single-machine infinite system obtained by different methods is shown in table 3, the stability margin obtained by the method is 71.90ms, 65.4ms in the document [14], 61.3ms in the document [12], 65.4ms in the document [19] and 65.29ms in the document [11], and it is easy to see that the stability margin obtained by the method is the largest and the conclusion is less conservative.

TABLE 3 maximum value of time lag obtained by different methods

Method	[14]	[19]	[11]	[12]	Theorem of law
						h/ms	65.4	65.4	65.29	61.3	71.90

Further, assuming that random excitation amplification factor disturbance exists in the system, the excitation amplification factor after the disturbance is considered as follows:

K′ _A ＝K _A +r

wherein: k is _A Setting a value for the excitation amplification factor;

K′ _A to consider the excitation amplification factor after disturbance;

r is reaction pair K' _A A scalar of the perturbation.

Order matrix H, E _a ，E _b The values are respectively:

when r ∈ [0, 10], the maximum system skew values obtained by different methods when r =0.5,1,1.5,2, 10 (at an interval of 0.5) are obtained, respectively, are shown in table 4, and fig. 4 shows the skew stability margin of the single-machine infinite system obtained by different methods.

The time lag stability margin of the system gradually becomes smaller as the disturbance term r increases. Moreover, compared with documents [12, 14 and 19], it is easy to see that the method provided by the invention has smaller conservation of the stability criterion and larger system stable operation area.

TABLE 4 time lag maximums calculated from different r values

r	[14]	[12]	[19]	The invention
					0.5	0.0570	0.0587	0.0650	0.0713
1	0.0552	0.0576	0.0647	0.0702
					1.5	0.0534	0.0557	0.0643	0.0694
2	0.0516	0.0545	0.0639	0.0685
					3	0.0478	0.0515	0.0632	0.0669
4	0.0439	0.0479	0.0624	0.0654
					5	0.0397	0.0457	0.0617	0.0642
6	0.0353	0.0444	0.0609	0.0631
					7	0.0307	0.0417	0.0601	0.0619
8	0.0263	0.0392	0.0593	0.0608
					9	0.0220	0.0363	0.0586	0.0594
10	0.0180	0.0343	0.0578	0.0582

Example 4: and 4, selecting a 4-machine 11-node system, and further analyzing the effectiveness of the method in the conservative aspect of reducing the stability of the wide-area time-varying time-lag power system.

According to the document [11]]In the method, a modal analysis method is adopted to obtain a state matrix of the four-machine power system, and the matrix is subjected to order reduction treatment to obtain matrixes A and A ₁ Respectively as follows:

table 5 lists maximum time-lag upper bounds obtained by different methods, the time-lag upper bound obtained by the conclusion of the invention is 0.519s, and the theorem of the invention obtains a larger time-lag upper bound compared with 0.195s of the document [5], 0.288s of the document [17], 0.328s of the document [26] and 0.440s of the document [19], so that the conservative property of the wide-area time-varying time-lag system stability conclusion is verified to be reduced by the method provided by the invention, and the effectiveness of the method in a multi-computer system is also proved.

TABLE 5 maximum skew

Method	[5]	[17]	[26]	[19]	Theorem of law
						h/s	0.195	0.288	0.328	0.440	0.519

In summary, through the description of the embodiment, a person skilled in the art can better implement the present solution.

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Claims (5)

1. A method for judging the stability of a wide area power system under the influence of interval time-lag is characterized by comprising the following steps:

step1, establishing a time-lag power system function model containing a wide area control loop

In the formula: x (t) is belonged to R ⁿ Is the state variable of the power system, x (t-h (t)) is the state variable after time delay, A ₁ In order to be a matrix of the system,is [ -h,0 [ ]]The time lag h (t) of the upper continuous initial phasor function satisfies:

0≤h(t)≤h

wherein, the constant h&0 is the time lag upper bound of the system; constant value mu ₁ ,μ ₂ Upper and lower bounds for the time lag derivative;

when there is a disturbance in the system, the system (1) then becomes of the form:

setting: [ Delta A, delta A ] ₁ ]＝HF ₀ [E _a ,E _b ]，ΔA,ΔA ₁ As disturbance terms of the system, H, E _a ,E _b Being a constant matrix of known dimensions, F ₀ For a varying matrix, the following condition is satisfied:i is an identity matrix;

step2. System function in Step1, construct the System L-K functional

Wherein:

P＝P ^T >0，W＝W ^T >0，M＝M ^T >0，Q＝Q ^T >0，

R＝R ^T >0，Z＝Z ^T >0，F＝F ^T >0；

the derivation of V (t) along the solution trajectory of the system (1) can result in:

wherein:

∏＝[E _ij ](i,j＝1,2,…,7)

when the temperature is higher than the set temperatureThe system (1) is asymptotically stable;

step3. Based on the result in Step2, the system (1) stability discrimination theorem is obtained as follows:

given the constant h, mu ₁ ,μ ₂ If there is a positive definite symmetric matrix P ∈ R ^5n×5n ,W∈R ^2n×2n ,M∈R ^2n×2n ,Q∈R ^n×n ,R∈R ^n×n ,Z∈R ^n×n ,F∈R ^n×n The symmetric matrix B ∈ R ^3n×3n ,L∈R ^3n×3n To do so byAnd a matrix of appropriate dimensions G ∈ R ^3n×n ,N∈R ^3n×n ,C∈R ^3n×n The system (1) is asymptotically stable, such that the following matrix inequality holds:

∏＝[E _ij ]<0,(i,j＝1,2,…,7) (5)

wherein:

E ₁₃ ＝-P ₁₃ -M ₁₂ +Y ₁₁ +Y ₂₁ -Y ₁₂ -Y ₂₂ ，

E ₁₅ ＝-P ₁₅ +(h-h(t))(P ₃₁ A+P ₃₂ +P ₃₄ +M ₂₁ A)+2Y ₁₂ +2Y ₂₂ ，

E ₂₃ ＝-Y ₁₁ +Y ₂₁ +Y ₁₂ -Y ₂₂ -2Z，

E ₃₃ ＝-R-4Z，

E ₃₄ ＝-h(t)P ₂₃ -2Y ₂₁ +2Y ₂₂ ，

E ₃₅ ＝(h(t)-h)P ₃₃ -M ₂₂ +6Z，

E ₃₆ ＝-h(t)P ₄₃ ，

E ₃₇ ＝(h(t)-h)P ₅₃ ，

E ₅₅ ＝(h(t)-h)P ₃₅ -12Z-3h ² F，

2. the method according to claim 1, wherein the wide area power system stability under the influence of interval time-lag is determined by: the L-K system functional constructed in Step2,in (2), a new augmentation vector is introduced:

3. the method according to claim 2, wherein after constructing the L-K system functional, the derivation of V (t) along the solution trajectory of the system (1) is performed by using step 2:

the derivation of V (t) along the solution trajectory of the system (1) can result in:

will appear in equation (10)Integral interval of [ t-h, t ]]Divided into intervals [ t-h, t-h (t)]And [ t-h (t), t)]Respectively processing integral inequalities on two intervals by using a Wirtinger integral inequality, and then further processing by using a convex combination method;

will be that in equation (11)Integration interval [ t-h, t]Divided into intervals [ t-h, t-h (t)]And [ t-h (t), t)]Processing a double integral term and a double integral term which are generated after the division by using a double Wirtinger integral inequality and a Free-matrix-based integral inequality respectively;

obtaining:

4. the method according to claim 3, wherein the integral term appearing in the formula (10) is used as the integral termIntegration interval of [ t-h, t ]]Divided into intervals [ t-h, t-h (t)]And [ t-h (t), t)]On the basis, respectively applying a Wirtinger integral inequality to integral inequalities on two intervals for processing, and then applying a convex combination method for further processing to obtain:

wherein:

Γ ₁ ＝[1-1 0 0 0 0 0]，Γ ₂ ＝[1 1 0-2 0 0 0]，

Γ ₃ ＝[0 1-1 0 0 0 0]，Γ ₄ ＝[0 1 1 0-2 0 0]。

5. the method according to claim 3, wherein the integral term in the equation (11) is first divided into the integral intervals, i.e. the integral interval [ t-h, t ] is divided into the intervals [ t-h, t-h (t) ] and [ t-h (t), t ], so as to obtain:

the double integral terms and the one-double integral terms generated after the division are respectively processed by a double Wirtinger integral inequality and a Free-matrix-based integral inequality to obtain:

wherein: