CN112234612B - Power system probability stability analysis method considering random disturbance amplitude - Google Patents
Power system probability stability analysis method considering random disturbance amplitude Download PDFInfo
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Abstract
The application provides a power system probability stability analysis method considering random disturbance amplitude, which comprises the steps of obtaining a system probability stability index of the random disturbance amplitude based on local noise-state stability; the probability stability index based on the local noise-state stability represents the influence of the random disturbance amplitude on the probability stability of the system; and establishing algebraic conditions for system local noise-state stability based on the NSS-Lyapunov function to obtain algebraic relation between random disturbance amplitude and system probability stability, determining that the system meets the NSS-Lyapunov function conditions through a linear matrix inequality, and analyzing to obtain the system probability stability. The method can account for the randomness of the electromechanical transient process of the power system, and can save the calculation time required by the stable analysis of the probability small signal of the power system to a great extent.
Description
Technical Field
The application relates to the technical field of small signal stability analysis in a power system, in particular to a probability stability analysis method of the power system considering random disturbance amplitude.
Background
With large-scale wind power being connected to a power grid, a power system originally composed of controllable and schedulable synchronous power supplies is coupled with a large number of unsynchronized power supplies with random fluctuation, so that a modern power system is converted into a random-deterministic coupled power system. This stability problem for coupled power systems presents new challenges to the stability analysis theory and methodology of conventional power systems.
Small signal stabilization refers to the fact that when small disturbances occur (e.g., small changes in load or generator active output), the power system can still maintain synchronous operation, i.e., no divergent oscillations or continuous oscillations occur.
In the prior art, the schemes for analyzing the stability of the small signals of the power system under random disturbance mainly comprise two schemes, wherein the first scheme is an analysis method based on a deterministic model of the power system, but the analysis method ignores the randomness of the electromechanical transient process of the system caused by wind power output; the second solution is to study the influence of random disturbance amplitude on system stability by using monte carlo simulation, but this method needs to consume a lot of time, and for the probability stability study of a large-scale power system, it needs to spend a lot of time.
Disclosure of Invention
The application provides a power system probability stability analysis method considering random disturbance amplitude, which aims to solve the problems that the randomness of the electromechanical transient process of a power system cannot be considered and the calculation time required by the power system probability small signal stability analysis is long in the prior art.
The application provides a power system probability stability analysis method considering random disturbance amplitude, which specifically comprises the following steps:
s100, obtaining a system probability stability index of random disturbance amplitude based on local noise-state stability;
s200, representing the influence of the random disturbance amplitude on the probability stability of the system based on the probability stability index of the local noise-state stability;
s300, establishing algebraic conditions of system local noise-state stability based on an NSS-Lyapunov function, obtaining algebraic relation between random disturbance amplitude and system probability stability, determining that the system meets the NSS-Lyapunov function conditions through a linear matrix inequality, and analyzing to obtain the system probability stability.
In the preferred embodiment of the application, the specific calculation process of the system probability stability index for obtaining the random disturbance amplitude based on the local noise-state stability is as follows:
establishing a random differential equation model of the power system, dx=f (x) dt+g (x) Σdw,
wherein d represents differentiation, t represents time dimension, x represents n-dimensional real state vector, W represents r-dimensional random continuous disturbance vector, its element represents independent standard wiener process, Σ represents r x r-dimensional diagonal matrix, its diagonal element represents random disturbance amplitude, f (x) represents n x n-dimensional power system parameter matrix, g (x) represents n x r-dimensional random disturbance coupling strength matrix,
if epsilon>0, exist beta.epsilon.K ∞ And gamma E K ∞ So that
P{||x-x * ||≤β(||x 0 ||,t)+γ(||∑∑ T ||)}≥1-ε，
Balance point x of stochastic differential equation model of power system * For the local noise-state stabilization,
wherein P represents the probability that the probability is high, the term "x" refers to the euclidean norm 0 Representing the initial state, β (||x) 0 |, t) represents the influence of the system feature root on the system probability stability, γ (|Σ) T I) represents the influence of the random disturbance amplitude on the probability stability of the system, and epsilon represents the risk level of the system;
system probability stability index beta (||x) of random disturbance amplitude is obtained 0 |, t) and γ (|Σ) T ||)。
In the preferred embodiment of the present application, further, if the system is locally noise-state stable, and β (|x) 0 I, t) to 0, t to infinity, the stability probability of the system is P { |x-x * ||≤γ(||∑∑ T ||)}≥1-ε。
By adopting the technical scheme, when the characteristic root of the power system is positioned on the left half complex plane, beta (||x) 0 I, t) converges to 0 over time, at which time the probability of stability of the power system is determined by γ (ΣΣ) T |) decision; that is, when the time t→infinity is reached after the random small disturbance occurs, the power system state deviation is located in the interval [ -gamma (|Σ) T ||),γ(||∑∑ T ||)]The probability in is 1- ε, and is represented by the norm of the covariance matrix T The term "random disturbance" refers to the effect of random disturbance on the dynamic state deviation of the system.
In a preferred embodiment of the present application, the specific calculation process for characterizing the influence of the random disturbance amplitude on the system probability stability based on the probability stability index of the local noise-state stability is as follows:
establishing a random model of the power system as follows by a classical generator model and a constant load model
Wherein, sigma i dW i Random disturbance representing ith wind or photovoltaic power output, W i ∑ i Represents the random disturbance amplitude, W i Represents the ith standard wiener process, delta i Represents the rotor angle, ω, of the ith generator i Represents the angular velocity of the ith generator, H i Represents the inertia coefficient, P, of the ith generator mi Representing the mechanical power of the ith generator, E i Representing the internal voltage amplitude of the ith generator, E j Represents the internal voltage amplitude of the jth generator, D i Represents the damping coefficient, omega, of the ith generator N Represents synchronous rotation speed, B ij Imaginary part, y representing the (i, j) th element of the reduced admittance matrix i Representation systemOutput of system, c 1 And c 2 Is a weighting coefficient.
In the technical scheme, the random disturbance sigma i dW i Acting on the rotor equation of motion, a random variation in force or load can be represented.
By adopting the technical scheme, as the random change in the power system is mainly caused by random fluctuation of the output or the load of the generator, the random change of the generator and the load is used for establishing a power system random model by adopting a continuous random process, wherein when the generator adopts a model which is not a classical model but other generator models, the number of differential equations in the random model of the power system is increased, but the equation set is still contained; when the constant load model is not used and the other load models are used, only the first term on the right of the second equation in the above equation set will change.
In the preferred embodiment of the application, an algebraic condition of system local noise-state stability is established based on an NSS-Lyapunov function to obtain an algebraic relation between random disturbance amplitude and system probability stability, and the system is determined to meet the NSS-Lyapunov function condition through a linear matrix inequality, and the specific calculation steps of the system probability stability are obtained through analysis are as follows:
there is a real-valued non-negative function V (x) such that the family of K functions alpha 1 、α 2 、α 3 And alpha 4 Satisfy the following requirements
α 1 (||x||)≤V(x)≤α 2 (||x||)，
And hasV (x) is the NSS-Lyapunov function,
wherein Tr represents the sum of diagonal elements of the matrix, and if an NSS-Lyapunov function exists in the power system, the power system is stable in local noise-state;
linearizing a stochastic model of the power system, yielding dΔx=aΔ xdt +Σdw,
wherein x= [ delta ] 1 ,ω 1 ,...,δ i ,ω i ,...,δ n ,ω n ]N is the number of generators in the power system, w= [ W ] 1 ,...,W i ,...,W n ]Sigma represents an n x n dimension diagonal matrix with diagonal elements of Sigma i Deltax represents the distance of the state variable from the steady-state operating point, and A represents the power system parameter matrix;
since the power system has an NSS-Lyapunov function, the expression of the function gamma is
If the linear matrix is inequality A T Q+QA is less than or equal to-cQ, the stability probability of the system is
Wherein c>0, and is a scalar, c -1 For the reciprocal of c, Q is a positive definite symmetric matrix, and superscript T denotes the transpose operation.
In the above technical solution, the linear matrix inequality A T Q+QA is less than or equal to-cQ to judge beta (||x) 0 As can be seen from the function γ and the stability probability formula of the system, the upper limit γ (ΣΣ) of the dynamic state deviation Δx of the power system is known T I) is related to the risk level epsilon of the system, so that the probability that the dynamic state deviation of the power system is within the upper bound range of the dynamic state deviation of the power system can be obtained according to epsilon specified by power system dispatcher and the stability probability formula of the system.
In a preferred embodiment of the application, the feasibility of the linear matrix inequality is determined by solving a semi-positive programming problem.
In a preferred embodiment of the present application, further, the expression of the semi-positive programming problem is as follows:
block representing the planning problemThe strategy variable is an element of a positive definite symmetric matrix Q;
q >0 for guaranteeing the positive quality of the matrix Q;
A T Q+QA+cQ<0 for ensuring the existence of an NSS-Lyapunov function.
By adopting the technical scheme, the NSS-Lyapunov function can be constructed only when c >0 is adopted, and the obtained positive definite symmetric matrix Q is obtained.
Compared with the prior art, the power system probability stability analysis method considering the random disturbance amplitude has the following beneficial effects:
(1) The method for stably analyzing the small signal of the power system can account for the randomness of the electromechanical transient process of the power system, and can save the calculation time required by the stable analysis of the probability small signal of the power system to a great extent.
(2) The method and the device represent the influence of the random disturbance amplitude on the system stability probability by a time-independent value, and are more convenient for analyzing the probability stability of the power system by adopting a linear matrix inequality analysis method.
Drawings
In order to more clearly illustrate the technical solution of the present application, the drawings that are needed in the embodiments will be briefly described below, and it will be obvious to those skilled in the art that other drawings can be obtained from these drawings without inventive effort.
FIG. 1 is a flow chart of a method for power system probability stability analysis that accounts for random disturbance amplitude in accordance with the present application;
FIG. 2 (a) is a schematic diagram of the rotor angle response of the 1 st generator (G1) of the 50 generator test power system of the comparative example of the present application;
FIG. 2 (b) is a graphical representation of the rotor angle response of the 6 th generator (G6) of the 50 generators test power system in the comparative example of the present application;
fig. 2 (c) is a graph showing the rotor angle response of the 37 th generator (G37) of the 50-generator test power system in the comparative example of the present application.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present application more apparent, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments of the present application. The components of the embodiments of the present application generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the application, as presented in the figures, is not intended to limit the scope of the application, as claimed, but is merely representative of selected embodiments of the application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
It should be noted that: like reference numerals and letters denote like items in the following figures, and thus once an item is defined in one figure, no further definition or explanation thereof is necessary in the following figures.
Furthermore, the terms "comprises," "comprising," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a product or apparatus that comprises a list of elements is not necessarily limited to those elements expressly listed but may include other elements not expressly listed or inherent to such product or apparatus.
NSS: local noise-state stabilization, NSS-Lyapunov function: lyapunov function, wiener Process: wiener process, LMI: linear matrix inequality, semi-Definite Programming: and (5) semi-positive planning.
Referring to fig. 1, a flow chart of a method for analyzing probability stability of a power system, which takes into account random disturbance amplitudes.
As shown in fig. 1, the method for analyzing the probability stability of the power system, which is provided by the application and takes the random disturbance amplitude into account, specifically comprises the following steps:
s100, obtaining a system probability stability index of random disturbance amplitude based on local noise-state stability;
s200, representing the influence of the random disturbance amplitude on the probability stability of the system based on the probability stability index of the local noise-state stability;
s300, establishing algebraic conditions of system local noise-state stability based on an NSS-Lyapunov function, obtaining algebraic relation between random disturbance amplitude and system probability stability, determining that the system meets the NSS-Lyapunov function conditions through a linear matrix inequality, and analyzing to obtain the system probability stability.
Based on the above embodiment, the specific calculation procedure of step S100 is as follows:
s101, establishing a random differential equation model of the power system, dx=f (x) dt+g (x) ΣdW,
wherein d represents differentiation, t represents a time dimension, x represents an n-dimensional real state vector, W represents an r-dimensional random continuous disturbance vector, its elements represent an independent standard wiener process, Σ represents an r×r-dimensional diagonal matrix, its diagonal elements represent a random disturbance amplitude, f (x) represents an n×n-dimensional power system parameter matrix, and g (x) represents an n×r-dimensional random disturbance coupling strength matrix;
s102, if ε>0, exist beta.epsilon.K ∞ And gamma E K ∞ So that
P{||x-x * ||≤β(||x 0 ||,t)+γ(||∑∑ T ||)}≥1-ε，
Balance point x of stochastic differential equation model of power system * For the local noise-state stabilization,
wherein P represents the probability that the probability is high, the term "x" refers to the euclidean norm 0 Representing the initial state, β (||x) 0 |, t) represents the influence of the system feature root on the system probability stability, γ (|Σ) T I) represents the influence of the random disturbance amplitude on the probability stability of the system, and epsilon represents the risk level of the system;
s103 the processing unit is configured to, system probability stability index beta (||x) of random disturbance amplitude is obtained 0 |, t) and γ (|Σ) T ||)。
Further, if the system is locally noise-state stable, and β (|x) is based on the above embodiments 0 ||,t)→0，t→∞The stability probability of the system is P { |x-x * ||≤γ(||∑∑ T ||)}≥1-ε。
By adopting the technical scheme, when the characteristic root of the power system is positioned on the left half complex plane, beta (||x) 0 I, t) converges to 0 over time, at which time the probability of stability of the power system is determined by γ (ΣΣ) T |) decision; that is, when the time t→infinity is reached after the random small disturbance occurs, the power system state deviation is located in the interval [ -gamma (|Σ) T ||),γ(||∑∑ T ||)]The probability in is 1- ε, and is represented by the norm of the covariance matrix T The term "random disturbance" refers to the effect of random disturbance on the dynamic state deviation of the system.
Based on the above embodiment, the specific calculation procedure of step S200 is as follows:
s201, establishing a random model of the power system as a classical generator model and a constant load model
Wherein, sigma i dW i Random disturbance representing ith wind or photovoltaic power output, W i ∑ i Represents the random disturbance amplitude, W i Represents the ith standard wiener process, delta i Represents the rotor angle, ω, of the ith generator i Represents the angular velocity of the ith generator, H i Represents the inertia coefficient, P, of the ith generator mi Representing the mechanical power of the ith generator, E i Representing the internal voltage amplitude of the ith generator, E j Represents the internal voltage amplitude of the jth generator, D i Represents the damping coefficient, omega, of the ith generator N Represents synchronous rotation speed, B ij Imaginary part, y representing the (i, j) th element of the reduced admittance matrix i Representing system output, c 1 And c 2 Is a weighting coefficient.
In the technical scheme, the random disturbance sigma i dW i Acting on the rotor equation of motion, a random variation in force or load can be represented.
By adopting the technical scheme, as the random change in the power system is mainly caused by random fluctuation of the output or the load of the generator, the random change of the generator and the load is used for establishing a power system random model by adopting a continuous random process, wherein when the generator adopts a model which is not a classical model but other generator models, the number of differential equations in the random model of the power system is increased, but the equation set is still contained; when the constant load model is not used and the other load models are used, only the first term on the right of the second equation in the above equation set will change.
Based on the above embodiment, the specific calculation steps of step S300 are as follows:
s301, assuming a real-valued non-negative function V (x) exists, such that the K family of functions α 1 、α 2 、α 3 And alpha 4 Satisfy the following requirements
α 1 (||x||)≤V(x)≤α 2 (||x||)，
And hasV (x) is the NSS-Lyapunov function,
wherein Tr represents the sum of diagonal elements of the matrix, and if an NSS-Lyapunov function exists in the power system, the power system is stable in local noise-state;
s302, linearizing a stochastic model of the power system, obtaining dΔx=aΔ xdt +Σdw,
wherein x= [ delta ] 1 ,ω 1 ,...,δ i ,ω i ,...,δ n ,ω n ]N is the number of generators in the power system, w= [ W ] 1 ,...,W i ,...,W n ]Sigma represents an n x n dimension diagonal matrix with diagonal elements of Sigma i Deltax represents the distance of the state variable from the steady-state operating point, and A represents the power system parameter matrix;
s303, since the power system has an NSS-Lyapunov function, the expression of the function gamma is
S304, if the linear matrix inequality A T Q+QA is less than or equal to-cQ, the stability probability of the system is
Wherein c>0, and is a scalar, c -1 For the reciprocal of c, Q is a positive definite symmetric matrix, and superscript T denotes the transpose operation.
In the above technical solution, the linear matrix inequality A T Q+QA is less than or equal to-cQ to judge beta (||x) 0 As can be seen from the function γ and the stability probability formula of the system, the upper limit γ (ΣΣ) of the dynamic state deviation Δx of the power system is known T I) is related to the risk level epsilon of the system, so that the probability that the dynamic state deviation of the power system is within the upper bound range of the dynamic state deviation of the power system can be obtained according to epsilon specified by power system dispatcher and the stability probability formula of the system.
Further, based on the above embodiments, the feasibility of the linear matrix inequality is determined by solving a semi-positive programming problem.
Further, based on the above specific embodiment, the expression of the semi-positive programming problem is as follows:
the decision variable representing the planning problem is an element of a positive definite symmetry matrix Q;
q >0 for guaranteeing the positive quality of the matrix Q;
A T Q+QA+cQ<0 for ensuring the existence of an NSS-Lyapunov function.
By adopting the technical scheme, the NSS-Lyapunov function can be constructed only when c >0 is adopted, and the obtained positive definite symmetric matrix Q is obtained.
Examples
The practical application of the application is illustrated by a 50-generator test power system, which comprises 50 generators and 145 nodes, wherein the generators adopt a classical model, and the random change of power adopts white noise simulation.
According to the step S100 in the specific embodiment, the probability stability of the 50 power generator test power systems is examined; constructing a random model of a 50-generator test power system according to step S200, wherein random disturbance is applied to a first generator (G1), a sixth generator (G6) and a 37-th generator (G37), and the random disturbance amplitude of each generator is sigma according to the random model expression of the power system in step S201 1 ＝0.01，∑ 6 ＝0.03，∑ 37 =0.05; according to step S301, parameter c is set 1 、c 2 Sigma, ε, and c, function V (x) is selected based on the linear matrix inequality, and function α is determined based on step S304 1 、α 2 、α 3 And alpha 4 Linearizing the random model expression of the power system in step S201 at the power system steady operation point to obtain the expression in step S302, and then solving the three expressions of the semi-positive rule problem to verify whether the linear matrix inequality in step S304 in the above embodiment is satisfied, and if so, calculating the function γ (ΣΣ) according to the expression in step S303 T And (I) and finally, calculating the small signal stability probability of the 50 power generator test power system according to the expression of the stability probability of the system in the step S304.
In this embodiment, a random small disturbance is applied to the power system at time 0, and the power system satisfies the probability stability index and γ (ΣΣ) according to the calculation result of the above steps T I) = 3.5174, therefore, the system stability probability P { x +. 3.5174} is not less than 0.9, i.e., the power system dynamic state deviation is located in the interval [ -3.5174,3.5174)]The probability of (2) is not less than 0.9. And, the calculation processes of step S100, step S200 and step S300 in the above embodiment are repeated for different risk levels epsilon, respectively, so as to obtain corresponding system dynamic state deviation intervals and stability probabilities 1-epsilon, as shown in the following table 1。
TABLE 1 stability probability theory results for 50 Generator systems
Comparative example
The stability probability of 50 generator systems is analyzed by the existing monte carlo analysis method.
As shown in fig. 2 (a), 2 (b) and 2 (c), firstly, a Σ is selected, secondly, 1000 samples of system state traces are generated, secondly, a lower bound is obtained according to 5% quantile of each moment state trace, finally, an upper bound is obtained according to 90% quantile of each moment state trace, and the obtained results are shown in fig. 2 (a), 2 (b) and 2 (c), wherein fig. 2 (a) is a rotor angle response schematic diagram of G1 in a 50-generator test power system, fig. 2 (b) is a rotor angle response schematic diagram of G6 in a 50-generator test power system, fig. 2 (c) is a rotor angle response schematic diagram of G37 in a 50-generator test power system, wherein a solid line represents a sample trace of a generator rotor angle, and a dotted line represents a 90% confidence interval, and therefore, when the system is steady state, the samples of the rotor angle trace are located in the 90% confidence interval, and the stability probability is 0.9, which is consistent with the theoretical calculation results in the embodiment.
It should be noted that, the above method for analyzing with monte carlo only simply illustrates the step flow of the method, but the specific calculation and analysis process is not excessively illustrated, but the person skilled in the art can obtain the stable probability result according to the prior art, so the whole technical scheme of the application is not affected.
Further, in the present application, in order to more intuitively explain the difference in calculation efficiency between the comparative example and the embodiment of the present application, 10 generator test power systems and 50 generator test power systems are taken as examples, respectively, wherein the calculation process of the 10 generator test power systems is similar to that of the 50 generator test power systems, and thus, calculation times under the calculation methods of the embodiment and the comparative example are compared, and comparison results of the calculation times are shown in table 2 below, not specifically described.
Table 2 calculation time comparison of examples and comparative examples
| System size | Examples | Comparative example |
| 10-generator test power system | 0.019s | 99.92s |
| 50 generator test power system | 0.022s | 195.47s |
As can be seen from Table 2, the calculation efficiency of the analysis method of the embodiment is faster, and the calculation and analysis time is greatly saved, because the Monte Carlo analysis method belongs to a numerical calculation method, a large number of state track samples are required to be calculated, so that reliable probability information is obtained to judge the probability stability of the system, while the analysis method provided by the embodiment of the application only needs to calculate the expression of the stability probability of the system in the step S304, so that the probability stability of the system can be obtained once, and only involves basic matrix operation, the calculation and analysis process is simpler, and the calculation efficiency is higher.
The above-provided detailed description is merely a few examples under the general inventive concept and does not limit the scope of the present application. Any other embodiments which are extended according to the solution of the application without inventive effort fall within the scope of protection of the application for a person skilled in the art.
Claims (3)
1. The power system probability stability analysis method considering the random disturbance amplitude is characterized by comprising the following steps of:
s100, obtaining a probability stability index of the power system with random disturbance amplitude based on local noise-state stability, wherein the specific calculation process is as follows:
establishing a random differential equation model of the power system, dx=f (x) dt+g (x) Σdw,
wherein d represents differentiation, t represents time dimension, x represents n-dimensional real state vector, W represents r-dimensional random continuous disturbance vector, its element represents independent standard wiener process, Σ represents r x r-dimensional diagonal matrix, its diagonal element represents random disturbance amplitude, f (x) represents n x n-dimensional power system parameter matrix, g (x) represents n x r-dimensional random disturbance coupling strength matrix,
if epsilon>0, there isAnd->So that
P{||x-x * ||≤β(||x 0 ||,t)+γ(||∑∑ T ||)}≥1-ε，
Balance point x of stochastic differential equation model of power system * For the local noise-state stabilization,
wherein P represents the probability that the probability is high, the term "x" refers to the euclidean norm 0 Representing the initial state, β (||x) 0 |, t) represents the influence of the power system feature root on the probability stability of the power system, and gamma (|Σ) T I) represents the influence of the random disturbance amplitude on the probability stability of the power system, and epsilon represents the risk level of the power system;
power system probability stabilization to obtain random disturbance amplitudeIndex of sex beta (|) I x 0 |, t) and γ (|Σ) T ||)；
S200, representing the influence of the random disturbance amplitude on the probability stability of the power system based on the probability stability index of the local noise-state stability, wherein the specific calculation process is as follows:
establishing a random model of the power system as follows by a classical generator model and a constant load model
Wherein, sigma i dW i Representing the random disturbance of the ith wind or photovoltaic force, Σ i Represent the random disturbance amplitude dW i Represents the ith standard wiener process, delta i Represents the rotor angle, ω, of the ith generator i Represents the angular velocity of the ith generator, H i Represents the inertia coefficient, P, of the ith generator mi Representing the mechanical power of the ith generator, E i Representing the internal voltage amplitude of the ith generator, E j Represents the internal voltage amplitude of the jth generator, D i Represents the damping coefficient, omega, of the ith generator N Represents synchronous rotation speed, B ij Imaginary part, y representing the (i, j) th element of the reduced admittance matrix i Representing power system output, c 1 And c 2 Is a weighting coefficient;
s300, establishing algebraic conditions for local noise-state stability of the power system based on an NSS-Lyapunov function, obtaining algebraic relation between random disturbance amplitude and probability stability of the power system, determining that the power system meets the NSS-Lyapunov function conditions through a linear matrix inequality, and analyzing to obtain the probability stability of the power system, wherein the method comprises the following specific calculation steps:
there is a real-valued non-negative function V (x) such that the family of K functions alpha 1 、α 2 、α 3 And alpha 4 Satisfy the following requirements
α 1 (||x||)≤V(x)≤α 2 (||x||)，
And hasV (x) is the NSS-Lyapunov function,
wherein Tr represents the sum of diagonal elements of the matrix, and if an NSS-Lyapunov function exists in the power system, the power system is stable in local noise-state;
linearizing the stochastic model of the power system, yielding dΔx=aΔ xdt + Σdw,
wherein x= [ delta ] 1 ,ω 1 ,...,δ i ,ω i ,...,δ n ,ω n ]N is the number of generators in the power system, w= [ W ] 1 ,...,W i ,...,W n ]Sigma represents an n x n dimension diagonal matrix with diagonal elements of Sigma i Δx represents the distance of the state variable from the steady state operating point, a represents the power system parameter matrix;
since the power system has an NSS-Lyapunov function, the expression of the function gamma is
If the linear matrix is inequality A T Q+QA is less than or equal to-cQ, the stability probability of the power system is
Wherein c>0, and is a scalar, c -1 For the inverse of c, Q is a positive definite symmetric matrix, the superscript T denotes a transpose operation, and the feasibility of the linear matrix inequality is determined by solving a semi-positive definite programming problem.
2. The method of claim 1, wherein if the power system is locally noise-state stable and β (|x) 0 I, t) to 0, t to infinity, the stability probability of the power system is P { |x-x * ||≤γ(||∑∑ T ||)}≥1-ε。
3. The method for analyzing the probability stability of a power system according to claim 1, wherein the expression of the semi-positive programming problem is as follows:
the decision variable representing the planning problem is an element of a positive definite symmetry matrix Q;
q is more than 0, and is used for guaranteeing the positive quality of the matrix Q;
A T Q+QA+cQ < 0, for ensuring the presence of NSS-Lyapunov functions.
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