CN114117331B - Time-lapse power system small interference stable domain solving method and system based on value set - Google Patents
Time-lapse power system small interference stable domain solving method and system based on value set Download PDFInfo
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Abstract
The invention provides a method and a system for solving a small interference stable domain of a time-lapse power system based on a value set, which belong to the technical field of research of the stable domain of the power system and comprise the following steps: based on a plurality of uncertain time lags in the power system, establishing a Taylor model of a characteristic quasi-polynomial; estimating a value set of the characteristic quasi polynomial according to the established Taylor model of the characteristic quasi polynomial; zero removal judgment is carried out on the inner and outer estimates of the characteristic alignment polynomial value sets, so that a time-lag stable domain boundary is determined; and determining whether the corresponding area in the time lag space is a stable area according to the time lag stable area boundary. The invention provides a branch-and-bound method for solving a small interference time-delay stable domain of a power system based on zero elimination judgment of internal and external estimation of a value set of a characteristic alignment polynomial; the application of the value set method can simultaneously process the condition that a plurality of uncertainty time lags change in a large range; the application of the branch-and-bound method can achieve a sufficiently accurate time-lapse stable domain result with minimal conservation.
Description
Technical Field
The invention relates to the technical field of electric power system stability domain research, in particular to a value set-based time-lapse electric power system small-interference stability domain solving method and system considering the influence of communication time-lapse uncertainty.
Background
The wide area measurement system provides a new platform for stable analysis and control of the interconnected power grid. However, the communication time lag is an inherent attribute of the communication network, and the communication time lag of hundreds of milliseconds exists in the wide-area damping control loop, so that the time lag characteristic of the whole system is more remarkable, and the communication time lag becomes a typical time lag system, and seriously affects the performance of the wide-area damping controller and the stability of the closed-loop power system. Therefore, in order to maintain safe and stable operation of the power system, theoretical analysis and design research on the time lag system are necessary.
For a power system considering the influence of communication time lags, the dynamic evolution process of the system depends not only on the current state of the system, but also on the state at some time in the past. The characteristic equation of the time-lag power system is an overrun equation containing exponential time-lag terms and has infinite characteristic values. And the information flow is like traffic flow, and is influenced by a plurality of factors such as communication medium, bandwidth, data packet size and the like, and time lags caused by transmission and processing of wide area synchronous measurement in a communication channel have randomness and uncertainty. Compared with the fixed time lag situation, the mechanism of the stability research of the power system considering the uncertainty of the communication time lag is more complex and the analysis is more difficult. In the design process of the wide-area damping controller considering the influence of communication time lag, the value of the wide-area damping controller parameter to be optimally set within a certain range can be regarded as the parameter uncertainty of the system. And the uncertainty of the parameters of the wide-area damping controller is considered on the basis of the uncertainty of the communication time lag, so that the difficulty and complexity of stability analysis of the time lag power system are further increased.
At present, a common time-lag power system stability analysis method is to solve characteristic values under fixed time lags to perform characteristic analysis or to perform stability margin or stability domain analysis under the influence of a small amount of (2, 3 or even a single time lag). If there are multiple uncertain time lags in the system, the existing method is not applicable, and it is difficult to ensure the stability of the time lags under the condition of wide variation.
Disclosure of Invention
The invention aims to provide a method and a system for calculating and analyzing a small interference stable domain of a time-lapse power system based on a value set, which are used for analyzing and determining a time-lapse range for guaranteeing the small interference stability of the power system by considering the uncertainty influence of the time-lapse of wide area communication based on the concept of calculation and analysis of a characteristic quasi-polynomial value set of the power system, so as to solve at least one technical problem in the background technology.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
on one hand, the invention provides a value set-based time-lapse power system small interference stability domain solving method, which comprises the following steps:
Based on a plurality of uncertain time lags in the power system, establishing a Taylor model of a characteristic quasi-polynomial;
estimating a value set of the characteristic quasi polynomial according to the established Taylor model of the characteristic quasi polynomial;
Zero removal judgment is carried out on the inner and outer estimates of the characteristic alignment polynomial value sets, so that a time-lag stable domain boundary is determined;
and determining whether the corresponding area in the time lag space is a stable area according to the time lag stable area boundary.
Preferably, establishing the taylor model of the feature quasi-polynomial includes: calculating a Taylor model of each variable; and calculating based on the Taylor models of all the variables to obtain the Taylor model of the characteristic quasi-polynomial.
Preferably, estimating the set of values of the feature quasi polynomial from the taylor model of the established feature quasi polynomial includes: transforming Cheng Baen the polynomial part of the characteristic quasi polynomial Taylor model into a Stant polynomial in an equivalent way; estimating a set of values for the polynomial portion using the bernstein coefficients; and adding the remainder interval of the characteristic quasi polynomial Taylor model to each point of the inner and outer estimation of the polynomial value set to obtain the inner and outer estimation results of the complete quasi polynomial value set.
Preferably, determining the time-lapse stability domain boundary comprises: and solving a time-lag stable domain boundary by taking a zeroing principle as a stability criterion, and judging whether the current uncertain space is stable or not by zeroing judgment on the inner and outer estimation of the characteristic alignment polynomial value set.
Preferably, the zero-picking discrimination result includes:
if the external estimation of the characteristic quasi-polynomial value set does not contain a zero point, the accurate value set does not contain the zero point, and the system is stable;
if the internal estimate of the feature quasi-polynomial set of values contains a zero point, then the exact set of values contains a zero point and the system is unstable.
Preferably, if the zero point is located between the inner and outer estimates, it cannot be determined whether the accurate value set includes the zero point, and at this time, the uncertain space needs to be split to obtain a more accurate value set estimation result.
Preferably, the time lag stability domain boundary divides the time lag space into a plurality of disjoint areas, and a determined time lag point is taken out from each area and a characteristic value is calculated, so as to determine whether the corresponding area is a stability domain.
In a second aspect, the present invention provides a value set-based system for obtaining a small interference stable domain of a time-lapse power system, including:
The construction module is used for establishing a characteristic quasi-polynomial Taylor model based on a plurality of uncertain time lags in the power system;
The estimating module is used for estimating a value set of the characteristic quasi polynomial according to the established Taylor model of the characteristic quasi polynomial;
The judging module is used for judging zero removal through the inner and outer estimation of the characteristic alignment polynomial value set, and determining a time-lag stable domain boundary;
the determining module is used for determining whether the corresponding area in the time lag space is a stable area according to the time lag stable area boundary.
In a third aspect, the present invention provides a non-transitory computer readable storage medium for storing computer instructions which, when executed by a processor, implement a value set based time-lapse power system small-interference stability domain retrieval method as described above.
In a fourth aspect, the present invention provides an electronic device comprising: a processor, a memory, and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes the instructions for implementing the value set-based time lag power system small interference stability domain solving method.
The invention has the beneficial effects that: based on the zero removal judgment of the internal and external estimation of the value set of the characteristic alignment polynomial, a branch-and-bound method for solving the small interference time-lag stability domain of the power system is provided; the application of the value set method can process a plurality of uncertainty time lags at the same time, and can effectively consider the uncertainty of the controller parameters; the application of the branch-and-bound method can achieve a sufficiently accurate time-lapse stable domain result with minimal conservation.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic diagram of a value set estimation principle based on a bernstein transform according to an embodiment of the present invention.
Fig. 2 is a flowchart of a method for determining a boundary of a small interference time-lag stable domain according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of the internal and external estimation results of the polynomial partial value set of the characteristic quasi-polynomial taylor model of the second-order time-lag system according to the embodiment of the present invention.
Fig. 4 is a schematic diagram of the internal and external estimation results of the characteristic quasi-polynomial complete taylor model value set of the second-order time-lag system according to the embodiment of the present invention.
Fig. 5 is a schematic diagram of a characteristic quasi-polynomial value set estimation result of a second-order time-lag system under subspaces Y and Z according to an embodiment of the present invention.
Fig. 6 is a single-line schematic diagram of a four-machine two-area system according to an embodiment of the present invention.
Fig. 7 is a schematic diagram of a calculation result of a small interference time-lag stable domain boundary of a four-machine two-area system according to an embodiment of the present invention.
Fig. 8 is a schematic diagram of a calculation result of a small interference time-lag stable domain of a four-machine two-area system according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements throughout or elements having like or similar functionality. The embodiments described below by way of the drawings are exemplary only and should not be construed as limiting the invention.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless expressly stated otherwise, as understood by those skilled in the art. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, and/or groups thereof.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, the different embodiments or examples described in this specification and the features of the different embodiments or examples may be combined and combined by those skilled in the art without contradiction.
In order that the invention may be readily understood, a further description of the invention will be rendered by reference to specific embodiments that are illustrated in the appended drawings and are not to be construed as limiting embodiments of the invention.
It will be appreciated by those skilled in the art that the drawings are merely schematic representations of examples and that the elements of the drawings are not necessarily required to practice the invention.
Example 1
The embodiment 1 provides a system for solving a small interference stable domain of a time-lapse power system based on a value set, which is based on the idea of calculation and analysis of a characteristic quasi-polynomial value set of the power system, and is used for analyzing and determining a time-lapse range for guaranteeing the stability of the small interference of the power system by considering the uncertainty influence of wide area communication time-lapse, and solving the small interference time-lapse stable domain.
In this embodiment 1, the system for obtaining a small interference stable domain of a time-lapse power system based on a value set mainly includes the following functional modules:
The construction module is used for establishing a characteristic quasi-polynomial Taylor model based on a plurality of uncertain time lags in the power system;
The estimating module is used for estimating a value set of the characteristic quasi polynomial according to the established Taylor model of the characteristic quasi polynomial;
The judging module is used for judging zero removal through the inner and outer estimation of the characteristic alignment polynomial value set, and determining a time-lag stable domain boundary;
the determining module is used for determining whether the corresponding area in the time lag space is a stable area according to the time lag stable area boundary.
In this embodiment 1, the method for obtaining the small interference stable domain of the time-lapse power system based on the value set is implemented by using the small interference stable domain obtaining system of the time-lapse power system based on the value set, and includes:
establishing a characteristic quasi-polynomial Taylor model based on a plurality of uncertain time lags in the power system by utilizing a construction module;
estimating a value set of the characteristic quasi polynomial by using an estimation module according to the established Taylor model of the characteristic quasi polynomial;
Utilizing a judging module to carry out zero elimination judgment through the inner and outer estimation of the characteristic alignment polynomial value set, and determining a time-lag stable domain boundary;
and determining whether the corresponding area in the time lag space is a stable area or not by using a determining module according to the time lag stable area boundary.
The step of establishing the taylor model of the feature quasi-polynomial in this embodiment 1 includes: calculating a Taylor model of each variable; and calculating based on the Taylor models of all the variables to obtain the Taylor model of the characteristic quasi-polynomial.
Estimating the set of values of the feature quasi polynomial from the taylor model of the established feature quasi polynomial includes: transforming Cheng Baen the polynomial part of the characteristic quasi polynomial Taylor model into a Stant polynomial in an equivalent way; estimating a set of values for the polynomial portion using the bernstein coefficients; and adding the remainder interval of the characteristic quasi polynomial Taylor model to each point of the inner and outer estimation of the polynomial value set to obtain the inner and outer estimation results of the complete quasi polynomial value set.
In this embodiment 1, determining the time-lapse stability domain boundary includes: and solving a time-lag stable domain boundary by taking a zeroing principle as a stability criterion, and judging whether the current uncertain space is stable or not by zeroing judgment on the inner and outer estimation of the characteristic alignment polynomial value set.
Specifically, the zero removal discrimination result includes: if the external estimation of the characteristic quasi-polynomial value set does not contain a zero point, the accurate value set does not contain the zero point, and the system is stable; if the internal estimate of the feature quasi-polynomial set of values contains a zero point, then the exact set of values contains a zero point and the system is unstable. If the zero point is located between the inner and outer estimations, it cannot be determined whether the accurate value set contains the zero point, and at this time, the uncertain space needs to be split to obtain a more accurate value set estimation result.
The time lag stable domain boundary divides the time lag space into a plurality of disjoint areas, a determined time lag point is taken out from each area, and a characteristic value is calculated, so that whether the corresponding area is a stable domain is determined.
Example 2
In this embodiment 2, based on the concept of calculation and analysis of the characteristic quasi-polynomial value set of the power system, a method for analyzing and determining the time lag range for ensuring the stability of the small interference of the power system, that is, a method for solving the stability domain of the small interference time lag, is provided by considering the uncertainty influence of the time lag of the wide area communication.
The principle and the deduction process according to the method for solving the small interference time-lag stability domain described in the embodiment 2 are as follows:
Assuming that the system has l uncertain parameters and m uncertain time lags, the linearized time lag differential equation of the power system and the corresponding characteristic quasi-polynomials thereof can be expressed as:
where Deltax is the linearization state vector, I=0, 1,2, …, m for the state matrix. q is the vector of the parameter and,Τ is the time-lag vector and,
In order to ensure stable operation of the power system, all eigenvalues lambda are required to be always positioned on the left half complex plane, when the eigenvalues lambda are positioned on the imaginary axisThe system is critically stable during the process.
At this time, the feature quasi polynomial may be abbreviated as f (x), where,
The eigenvalue f (x) =0 is an transcendental equation, which is difficult to solve. The surmounts can be processed by utilizing the Taylor transformation, and the small interference stability domain can be analyzed and solved from the value set of the characteristic quasi-polynomials.
In this embodiment 2, in order to achieve the above object, the following technical scheme is adopted:
step 1: and establishing a Taylor model of the characteristic quasi polynomial.
A taylor model T (f (X))=p (u) +r (X) consisting of a general polynomial and remainder intervals is used to approximate the characteristic quasi polynomial f (X) to eliminate the exponential term, wherein,Normalized to x. The taylor model for each variable x i (i=1, 2, …, s) can be expressed as:
And (3) carrying out the following addition, multiplication and exponential operation on the Taylor model of each variable according to the expression of f (x), so as to obtain a complete Taylor model of f (x).
Where B (-) represents the operation of computing the polynomial value set boundary,Corresponding to all the entries of times m in p 1p2,Corresponds to all entries in p 1p2 which are greater than or equal to m+1.
Step 2: a set of values of a feature quasi polynomial is estimated.
The set of values of the feature quasi-polynomial can be effectively estimated based on the following bernstein transform.
In the method, in the process of the invention,Is a Bernstein basis function.Is the bernstein coefficient.
The specific process is divided into two steps and is shown in fig. 1:
(1) The set of values of the polynomial portion p (U) (U e U) is estimated. Its outer estimate P ex (U) can be represented by a convex hull of the bernstein coefficients. Let the outer estimate of the 4 edges E 1～E4 of a surface F on the space U be P ex(E1)～Pex(E4), the inner region enclosed by it can be regarded as the inner estimate of the value set on that surface.
(2) The set of values of the quasi polynomial f (X) (X e X) is estimated. The remainder bands R in and R ex are formed by adding the remainder interval R (X) to each point of the inner and outer estimates of the polynomial value set. Then the inner contour of R in is the inner estimate F in(X);Rex of the value set F (X) and the outer contour is the outer estimate F ex (X) of the value set F (X). The relation of the exact value set f (X) to the inner and outer estimates is:
Step 3: solving a time-lag stable domain boundary. And solving the time-lag stability domain boundary by taking the principle of zero removal as a stability criterion. And by carrying out zero removal judgment on the inner and outer estimates of the characteristic alignment polynomial value set, whether the currently uncertain space is stable or not can be judged. The zero-picking discrimination result comprises: 1) The external estimation of the characteristic quasi-polynomial value set does not contain zero, the accurate value set does not contain zero, and the system is stable; 2) If the internal estimation of the characteristic quasi-polynomial value set contains a zero point, the accurate value set certainly contains the zero point, and the system is unstable; 3) The zero point is located between the inner and outer estimates, and it cannot be determined that the accurate value set contains the zero point, and it cannot be determined whether the current uncertain space X is stable. At this time, the space X needs to be split to obtain a more accurate value set estimation result. Starting from this idea, a flow of solving the time-lag stability domain boundary in a branch-and-bound manner is summarized, as shown in fig. 2. The conservativeness introduced in the evaluation of the value set is reduced or eliminated in the branch-and-bound here.
Step 4: a small disturbance time lag stability domain is determined. And 3, dividing the time lag space into a plurality of disjoint areas by the time lag stability area boundary obtained in the step 3, taking out a determined time lag point from each area, calculating a characteristic value, and further determining whether the corresponding area is a stability area.
In this embodiment 2, the value set method can be applied to process a plurality of uncertainty time lags at the same time. The application of the branch-and-bound method can achieve a sufficiently accurate time-lapse stable domain result with minimal conservation.
Example 3
In this embodiment 3, a method for determining the stability of small interference of a power system under the influence of uncertain time lags is provided, and for convenience of presentation, a simple typical second-order time lag system is used as an example in this embodiment 3 to determine whether the power system with uncertain time lags is stable or not.
The state matrix and the time lag matrix of the system in this embodiment 3 are respectively:
a 0 = [ -2,0;0, -0.9] and a 1 = [ -1,0; -1, -1].
The feature quasi-polynomial is calculated as:
f＝λ2+(2e-τλ+2.9)λ+(e-2τλ+2.9e-τλ+1.8) (6)
The angular frequency range is [0,14] rad/s, the time lag tau epsilon [0,0.1] s, the uncertainty space is X=tau×omega= [0,0.1] × [0,14], the upper boundary of the complex plane is a virtual axis, and the step of judging the time lag stability is as follows:
Step 1: and (3) establishing a characteristic quasi polynomial (8 th order) Taylor model.
First, a taylor model of each variable is calculated: t (τ) =0.1u 1+[0,0],T(ω)＝14u2 + [0,0], where u 1,u2 ε [0,1] is the normalized variable. Then, the taylor model of the variable is operated on:
and further obtaining a Taylor model of the characteristic quasi polynomial f:
step 2: a set of values of a feature quasi polynomial is estimated. First, the polynomial part p (u) of the feature quasi polynomial taylor model is equivalently transformed into a bernstein polynomial in which, Is a Bernstein polynomial. The value set of p (u) is estimated using the bernstein coefficients, as shown in fig. 3. Then, the remainder interval R is added to each point of the inner and outer estimation of the polynomial value set, so as to obtain the inner and outer estimation results of the complete quasi polynomial f value set, as shown in fig. 4.
Step 3: and (5) zeroing, judging and splitting an uncertain space. By observing the inner and outer estimation result diagrams of the characteristic quasi-polynomial value set shown in fig. 4, it can be known that the zero-picking determination result is that the zero point is located between the inner and outer estimates, at this time, it cannot be determined whether the accurate value set contains the zero point, that is, whether the current uncertain space x=τxω= [0,0.1] × [0,14] is stable, and further, it is necessary to split the uncertain space. The choice of subdividing the uncertainty space X in dimension ω, resulting in the bernstein coefficients for both subspaces Y and Z are listed in tables 1 and 2, and the value set estimation in step 2 is re-performed for both subspaces, as shown in fig. 5.
TABLE 1 Bernstein coefficients of subspace Y
TABLE 2 Bernstein coefficients of subspace Z
By observing the inner and outer estimation result diagrams of the characteristic quasi-polynomial value set in the subspace Y shown in fig. 5, it can be known that the outer estimation F ex (Y) does not contain a zero point as a result of the zero removal discrimination, and the accurate value set F (Y) does not certainly contain a zero point, so that the system is stable in the subspace Y. The system is likewise stable in subspace Z. So far, it can be concluded that the system is stable with small disturbances under the influence of an indeterminate time lag τ e [0,0.1] s.
Example 4
In this embodiment 4, a four-machine two-area system is used as an example to describe how to determine the small interference stability domain of the system in the time lag space.
As shown in fig. 6, the single line diagram of the four-machine two-zone system described in this example 4 operates with a 400MW output from zone 1 to zone 2. Each generator is equipped with a thyristor exciter with high transient gain and a PSS using rotor speed as input. The wide area damping controller is mounted on G 1 of zone 1. The controller has the same lead-lag structure as the PSS and uses the relative rotor speed between G 2 (region 1) and G 3 (region 2) as the wide area feedback signal, the system has 56 state variables and 22 algebraic variables in total.
In this example 4, the time lags τ 1 and τ 2 of the two feedback channels of the wide-area damping system have uncertainty, τ 1∈[0,1]s,τ2 ε [0,1] s.
Setting the angular frequency range to ω ε [0,16] rad/s, the uncertainty space is X=τ 1×τ2 ω= [0,1] × [0,16].
First, a state space model and a characteristic quasi polynomial of the example system are established:
In the method, in the process of the invention, In the form of a system state matrix,Is a time lag matrix.
Then, the calculation of the time-lag stability domain boundary of the system of the present example is implemented according to steps 1 to 3, wherein step 1 (building the taylor model of the characteristic quasi-polynomial) and step 2 (estimating the value set of the characteristic quasi-polynomial) can refer to the specific explanation of the second-order time-lag system example in embodiment 3. Step 3 (solving the time-lag stable domain boundary) is to mark the unstable subspace obtained in the process of splitting the uncertain space X on the basis of step 3 (zero removal discrimination and splitting the uncertain space) of a typical second-order time-lag system example, and further, obtain the time-lag stable domain boundary on the time-lag plane τ 1×τ2, as shown in fig. 7.
And finally, determining the small interference time-lag stability domain of the system according to the step 4 in the technical scheme. The time lag plane tau 1×τ2 is divided into 6 disjoint areas at the time lag stable domain boundary shown in fig. 7, a determined time lag point is taken out from each area, and the characteristic value is calculated, if all the characteristic values are located on the left half complex plane, the corresponding area can be determined to be a stable domain, otherwise, the corresponding area is an unstable domain, and the result is shown in fig. 8.
Example 5
Embodiment 5 of the present invention provides a non-transitory computer readable storage medium for storing computer instructions, which when executed by a processor, implement a method for calculating a small-interference stable domain of a time-lapse power system based on a value set as described above, the method comprising:
Based on a plurality of uncertain time lags in the power system, establishing a Taylor model of a characteristic quasi-polynomial;
estimating a value set of the characteristic quasi polynomial according to the established Taylor model of the characteristic quasi polynomial;
Zero removal judgment is carried out on the inner and outer estimates of the characteristic alignment polynomial value sets, so that a time-lag stable domain boundary is determined;
and determining whether the corresponding area in the time lag space is a stable area according to the time lag stable area boundary.
Example 6
Embodiment 6 of the present invention provides a computer program (product) comprising a computer program for implementing a value set based time-lapse power system small interference stability domain derivation method as described above, when run on one or more processors, the method comprising:
Based on a plurality of uncertain time lags in the power system, establishing a Taylor model of a characteristic quasi-polynomial;
estimating a value set of the characteristic quasi polynomial according to the established Taylor model of the characteristic quasi polynomial;
Zero removal judgment is carried out on the inner and outer estimates of the characteristic alignment polynomial value sets, so that a time-lag stable domain boundary is determined;
and determining whether the corresponding area in the time lag space is a stable area according to the time lag stable area boundary.
Example 7
Embodiment 7 of the present invention provides an electronic device, including: a processor, a memory, and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes the instructions for implementing the value set-based time lag power system small interference stability domain solving method, which includes:
Based on a plurality of uncertain time lags in the power system, establishing a Taylor model of a characteristic quasi-polynomial;
estimating a value set of the characteristic quasi polynomial according to the established Taylor model of the characteristic quasi polynomial;
Zero removal judgment is carried out on the inner and outer estimates of the characteristic alignment polynomial value sets, so that a time-lag stable domain boundary is determined;
and determining whether the corresponding area in the time lag space is a stable area according to the time lag stable area boundary.
In summary, by analyzing the example results obtained by the method provided by the invention, the following conclusion can be drawn: the existence of a wide-area time lag can have an important influence on the stability of the power system, so that the stability of the system is poor. In the time-lag space, all stable operation points of the system form a stable domain of the time-lag power system, the time-lag space is divided into a plurality of connected stable regions and unstable regions by boundaries, and even the unstable regions contain stable regions. As in the present four-machine two-region system example, the system is stable with small interference at a fixed time lag (τ 1,τ2) = (0.6,0.4) s, at this time, it cannot be directly inferred that the system is stable with small interference over the entire time lag plane τ 1×τ2 = [0,0.6] × [0,0.4] s.
In the embodiment, not only can the system be judged whether to have small interference stable under the influence of uncertain time lags, but also the system can be used for determining the small interference stable domain of the system in a large-range time lag space, and all time lag operation points for ensuring the safety and stability of the system can be accurately obtained with minimum conservation.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While the foregoing description of the embodiments of the present invention has been presented in conjunction with the drawings, it should be understood that it is not intended to limit the scope of the invention, but rather, it should be understood that various changes and modifications could be made by one skilled in the art without the need for inventive faculty, which would fall within the scope of the invention.
Claims (7)
1. A method for solving a small interference stable domain of a time-lapse power system based on a value set is characterized by comprising the following steps:
Based on a plurality of uncertain time lags in the power system, establishing a Taylor model of a characteristic quasi-polynomial;
estimating a value set of the characteristic quasi polynomial according to the established Taylor model of the characteristic quasi polynomial;
Zero removal judgment is carried out on the inner and outer estimates of the characteristic alignment polynomial value sets, so that a time-lag stable domain boundary is determined;
Estimating the set of values of the feature quasi polynomial from the taylor model of the established feature quasi polynomial includes: transforming Cheng Baen the polynomial part of the characteristic quasi polynomial Taylor model into a Stant polynomial in an equivalent way; estimating a set of values for the polynomial portion using the bernstein coefficients; adding the remainder interval of the characteristic quasi polynomial Taylor model to each point of the inner and outer estimation of the polynomial value set to obtain the inner and outer estimation results of the complete quasi polynomial value set;
determining the time-lapse stability domain boundary includes: solving a time-lag stable domain boundary by taking a zeroing principle as a stability criterion, and judging whether the current uncertain space is stable or not by zeroing judgment on the inner and outer estimation of the characteristic alignment polynomial value set;
The zero-picking discrimination result comprises: if the external estimation of the characteristic quasi-polynomial value set does not contain a zero point, the accurate value set does not contain the zero point, and the system is stable; if the internal estimation of the characteristic quasi-polynomial value set contains a zero point, the accurate value set contains the zero point, and the system is unstable;
and determining whether the corresponding area in the time lag space is a stable area according to the time lag stable area boundary.
2. The value set-based time-lapse power system small interference stability domain solving method according to claim 1, wherein establishing a characteristic quasi-polynomial taylor model comprises: calculating a taylor model of each variable in the power system; and calculating based on the Taylor models of all the variables to obtain the Taylor model of the characteristic quasi-polynomial.
3. The method for solving the small interference stable domain of the dead time-lapse power system based on the value set according to claim 1, wherein if the zero point is located between the inner and outer estimations, it cannot be determined whether the accurate value set contains the zero point, and at this time, the uncertain space needs to be split to obtain a more accurate value set estimation result.
4. The method for obtaining the small interference stable domain of the dead time power system based on the value set according to claim 1, wherein the dead time stable domain boundary divides the dead time space into a plurality of disjoint areas, and a determined dead time point is taken out from each area and a characteristic value is calculated, so that whether the corresponding area is a stable domain is determined.
5. A value set-based small interference stable domain calculation system for a time-lapse power system, adopting the value set-based small interference stable domain calculation method for a time-lapse power system according to any one of claims 1 to 4, comprising:
The construction module is used for establishing a characteristic quasi-polynomial Taylor model based on a plurality of uncertain time lags in the power system;
The estimating module is used for estimating a value set of the characteristic quasi polynomial according to the established Taylor model of the characteristic quasi polynomial;
The judging module is used for judging zero removal through the inner and outer estimation of the characteristic alignment polynomial value set, and determining a time-lag stable domain boundary;
the determining module is used for determining whether the corresponding area in the time lag space is a stable area according to the time lag stable area boundary.
6. A non-transitory computer readable storage medium storing computer instructions which, when executed by a processor, implement the value set-based time-lapse power system small interference stability domain derivation method of any one of claims 1-4.
7. An electronic device, comprising: a processor, a memory, and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes the instructions for implementing the value set-based time-lapse power system small interference stability domain solving method according to any one of claims 1-4.
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