CN114117331A - Time-lag power system small-interference stable domain solving method and system based on value set - Google Patents
Time-lag 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 time-lag power system small disturbance stability domain solving method and system based on a value set, belonging to the technical field of power system stability domain research and comprising the following steps: establishing a Taylor model of a characteristic quasi polynomial based on a plurality of uncertain time lags in the power system; estimating a value set of the characteristic quasi-polynomial according to the built Taylor model of the characteristic quasi-polynomial; performing zero-removing discrimination on the internal and external estimation of the characteristic quasi polynomial value set to determine a time lag stable domain boundary; and determining whether the corresponding region in the time lag space is a stable region or not according to the time lag stable region boundary. The invention provides a branch and bound method for solving a small interference time-lag stable domain of a power system based on zero-removing discrimination of the value set internal and external estimation of a characteristic quasi polynomial; the application of the value set method can simultaneously process the condition that a plurality of uncertain time lags change in a large range; the application of the branch-and-bound method can realize that sufficiently accurate time lag stable domain results are obtained with minimum conservation.
Description
Technical Field
The invention relates to the technical field of power system stability domain research, in particular to a value set-based time-lag power system small-interference stability domain solving method and system considering communication time-lag uncertainty influence.
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 property 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 prominent, the system becomes a typical time lag system, and the performance of the wide-area damping controller and the stability of the closed-loop power system are seriously influenced. Therefore, in order to maintain safe and stable operation of the power system, theoretical analysis and design research must be performed on the time-lag system.
For a power system considering the influence of communication time lag, the dynamic evolution process of the system not only depends on the current state of the system, but also depends on the state at some past time. The characteristic equation of the time-lag power system is a transcendental equation containing exponential time-lag terms and has infinite characteristic values. And the information flow is like the traffic flow, and is influenced by a plurality of factors such as communication media, bandwidth, data packet size and the like, and the time lag caused by the transmission and processing of the wide area synchronous measurement in the communication channel has randomness and uncertainty. Compared with the fixed time lag situation, the mechanism of the power system stability research considering the communication time lag uncertainty is more complex and the analysis is more difficult. In the design process of the wide-area damping controller considering the communication time lag influence, the value of the wide-area damping controller parameter to be optimized and set in a certain range can be regarded as the parameter uncertainty of the system. The uncertainty of parameters of the wide-area damping controller is calculated on the basis of the communication time lag uncertainty, and the difficulty and complexity of time lag power system stability analysis are further increased.
At present, a common time lag power system stability analysis method is to solve characteristic values for characteristic analysis under a fixed time lag, or to perform stability margin or stability region analysis under the influence of a small amount of (2, 3 or even a single) time lag. If the system has a plurality of uncertain time lags, the existing method is not applicable, and the stability of the time lags under the condition of large-range change is difficult to ensure.
Disclosure of Invention
The invention aims to provide a method and a system for solving a small interference stability domain of a time-delay power system based on a value set, which are used for analyzing and determining a time-delay range for ensuring the small interference stability of the power system by considering the uncertainty influence of wide-area communication time-delay, so as to solve at least one technical problem in the background technology.
In order to achieve the purpose, the invention adopts the following technical scheme:
in one aspect, the invention provides a time-lag power system small interference stability domain solving method based on a value set, comprising the following steps:
establishing a Taylor model of a characteristic quasi polynomial based on a plurality of uncertain time lags in the power system;
estimating a value set of the characteristic quasi-polynomial according to the built Taylor model of the characteristic quasi-polynomial;
performing zero-removing discrimination on the internal and external estimation of the characteristic quasi polynomial value set to determine a time lag stable domain boundary;
and determining whether the corresponding region in the time lag space is a stable region or not according to the time lag stable region boundary.
Preferably, the creating of the taylor model of the characteristic quasi-polynomial includes: computing a taylor model for each variable; and (4) operating the Taylor models based on all the variables to obtain the Taylor model of the characteristic quasi-polynomial.
Preferably, estimating the value set of the characteristic quasi-polynomial according to the established taylor model of the characteristic quasi-polynomial comprises: equivalently transforming the polynomial part of the characteristic quasi-polynomial Taylor model into a Bernstein polynomial; estimating a set of values of the polynomial part using bernstein coefficients; and adding the remainder interval of the characteristic quasi-polynomial Taylor model to each point of the internal and external estimation of the polynomial value set to obtain the internal and external estimation results of the complete quasi-polynomial value set.
Preferably, determining the dead time stability domain boundary comprises: and solving the time lag stability domain boundary by taking the zero-removing principle as a stability criterion, and judging whether the current uncertain space is stable or not by performing zero-removing judgment on the internal and external estimation of the characteristic quasi polynomial value set.
Preferably, the result of the zero-rejecting discrimination 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 a zero point, and the system is stable;
if the internal estimate of the set of characteristic quasi-polynomial values contains a zero, then the accurate set of values contains a zero and the system is unstable.
Preferably, if the zero point is located between the inner estimation and the outer estimation, 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 stable domain boundary divides the time lag space into a plurality of disjoint regions, and a determined time lag point is taken out from each region and a characteristic value is calculated, thereby determining whether the corresponding region is a stable domain.
In a second aspect, the present invention provides a time-lag power system small disturbance stability domain solving system based on a value set, including:
the system comprises a construction module, a calculation module and a calculation module, wherein the construction module is used for establishing a Taylor model of a characteristic quasi polynomial based on a plurality of uncertain time lags in the power system;
the estimation module is used for estimating a value set of the characteristic quasi-polynomial according to the built Taylor model of the characteristic quasi-polynomial;
the discrimination module is used for carrying out zero elimination discrimination by internal and external estimation of the characteristic quasi polynomial value set to determine a time lag stable domain boundary;
and the determining module is used for determining whether the corresponding region in the time lag space is the stable region according to the time lag stable region 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 disturbance stability domain derivation 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 a processor is connected to the memory, 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 to make the electronic device execute the instructions to implement the time-lapse power system small-disturbance-stability-domain derivation method based on the value set.
The invention has the beneficial effects that: carrying out zero-removing discrimination based on the value set internal and external estimation of the characteristic quasi polynomial, and providing a branch-and-bound method for solving a small interference time-lag stable domain of the power system; the application of the value set method can simultaneously process a plurality of uncertain time lags and can also effectively consider the uncertainty of the parameters of the controller; the application of the branch-and-bound method can realize that sufficiently accurate time lag stable domain results are obtained with minimum 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.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a schematic diagram of a value set estimation principle based on bernstein transformation according to an embodiment of the present invention.
Fig. 2 is a schematic flow chart of a method for determining a small interference time lag stability domain boundary according to an embodiment of the present invention.
Fig. 3 is a diagram illustrating the inner and outer estimation results of the polynomial partial value sets 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 complete taylor model value set of the characteristic quasi-polynomial of the second-order time lag system according to the embodiment of the present invention.
Fig. 5 is a schematic diagram of a feature quasi-polynomial value set estimation result of the second-order time-lag system in the subspace Y and Z according to the embodiment of the present invention.
Fig. 6 is a single line schematic diagram of a four-machine two-zone system according to an embodiment of the 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-domain 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-computer 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 the same or similar elements or elements having the same or similar function throughout. The embodiments described below by way of the drawings are illustrative only and are not to 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 the context clearly indicates otherwise. 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, components, and/or groups thereof.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean 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 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, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
For the purpose of facilitating an understanding of the present invention, the present invention will be further explained by way of specific embodiments with reference to the accompanying drawings, which are not intended to limit the present invention.
It should be understood by those skilled in the art that the drawings are merely schematic representations of embodiments and that the elements shown in the drawings are not necessarily required to practice the invention.
Example 1
This embodiment 1 provides a time-lag power system small disturbance stability domain solving system based on a value set, where the system considers uncertainty influence of wide area communication time lag based on an idea of computation and analysis of a power system characteristic quasi-polynomial value set, analyzes and determines a time-lag range ensuring power system small disturbance stability, and solves a small disturbance time-lag stability domain.
In this embodiment 1, the system for obtaining a small disturbance stability domain of a time-lag power system based on a value set mainly includes the following functional modules:
the system comprises a construction module, a calculation module and a calculation module, wherein the construction module is used for establishing a Taylor model of a characteristic quasi polynomial based on a plurality of uncertain time lags in the power system;
the estimation module is used for estimating a value set of the characteristic quasi-polynomial according to the built Taylor model of the characteristic quasi-polynomial;
the discrimination module is used for carrying out zero elimination discrimination by internal and external estimation of the characteristic quasi polynomial value set to determine a time lag stable domain boundary;
and the determining module is used for determining whether the corresponding region in the time lag space is the stable region according to the time lag stable region boundary.
In this embodiment 1, the value set-based time lag power system small disturbance stability domain solving system is used to implement a value set-based time lag power system small disturbance stability domain solving method, which includes:
establishing a Taylor model of a characteristic quasi polynomial by using a construction module based on a plurality of uncertain time lags in the power system;
estimating a value set of the characteristic quasi-polynomial by using an estimation module according to the built Taylor model of the characteristic quasi-polynomial;
performing zero-removing discrimination by utilizing a discrimination module through internal and external estimation of a characteristic quasi polynomial value set to determine a time lag stable domain boundary;
and determining whether a corresponding region in the time-lag space is a stable region or not by using a determining module according to the time-lag stable region boundary.
The taylor model for establishing the characteristic quasi-polynomial in this embodiment 1 includes: computing a taylor model for each variable; and (4) operating the Taylor models based on all the variables to obtain the Taylor model of the characteristic quasi-polynomial.
Estimating the value set of the characteristic quasi-polynomial according to the established Taylor model of the characteristic quasi-polynomial comprises: equivalently transforming the polynomial part of the characteristic quasi-polynomial Taylor model into a Bernstein polynomial; estimating a set of values of the polynomial part using bernstein coefficients; and adding the remainder interval of the characteristic quasi-polynomial Taylor model to each point of the internal and external estimation of the polynomial value set to obtain the internal and external estimation results of the complete quasi-polynomial value set.
In this embodiment 1, determining the time lag stability domain boundary includes: and solving the time lag stability domain boundary by taking the zero-removing principle as a stability criterion, and judging whether the current uncertain space is stable or not by performing zero-removing judgment on the internal and external estimation of the characteristic quasi polynomial value set.
Specifically, the result of the zero-removing discrimination 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 a zero point, and the system is stable; if the internal estimate of the set of characteristic quasi-polynomial values contains a zero, then the accurate set of values contains a zero and the system is unstable. If the zero point is located between the inner estimation and the outer estimation, whether the accurate value set contains the zero point cannot be judged, and at the moment, the uncertain space needs to be split so as to obtain a more accurate value set estimation result.
The time lag space is divided into a plurality of disjoint areas by the time lag stable domain boundary, 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 or not is determined.
Example 2
In this embodiment 2, based on the idea of computing and analyzing a quasi-polynomial value set of characteristics of an electric power system, a method for analyzing and determining a time lag range for ensuring the stability of small interference of the electric power system, that is, a method for solving a small interference time lag stability domain, in consideration of uncertainty influence of wide area communication time lag is provided.
The principle and derivation process according to which the method for solving the small interference time-lag stability domain described in this embodiment 2 is as follows:
if 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-polynomial can be respectively expressed as:
wherein Δ x is a linearized state vector,
is the state matrix, i is 0,1,2, …, m. q is a vector of parameters and q is,
tau is a time-lag vector and,
in order to ensure the stable operation of the power system, all the characteristic values lambda are required to be always positioned on the left half complex plane, and when the characteristic values lambda are positioned on the imaginary axis
In the above, the system is critically stable.
At this time, the characteristic quasi-polynomial may be abbreviated as f (x), wherein,
the eigen equation f (x) 0 is a transcendental equation, and it is difficult to solve the eigen value. The small interference stability domain can be solved analytically starting from the value set of the characteristic quasi-polynomial by using Taylor transformation to process the transcendental terms.
In this embodiment 2, to achieve the above purpose, the following technical solutions are adopted:
step 1: and establishing a Taylor model of the characteristic quasi-polynomial.
Approximating the characteristic quasi-polynomial f (x) to eliminate exponential terms using a taylor model T (f (x)) consisting of a general polynomial and remainder interval, p (u)) + r (x),
the values are normalized for x. Each variable xiThe taylor model of (i ═ 1,2, …, s) can be expressed as:
and (3) performing addition, multiplication and exponential operation on the taylor models of the variables according to the expression of f (x) to obtain a complete taylor model of f (x).
Where B (-) represents the operation of computing the polynomial value set boundary,
corresponds to p1p2All the times in the item are less than or equal to m,
corresponds to p1p2All the times are more than or equal to m + 1.
Step 2: a set of values of a characteristic quasi-polynomial is estimated.
The value set of the feature quasi-polynomial can be efficiently estimated based on the bernstein transform as follows.
In the formula (I), the compound is shown in the specification,
is a bernstein basis function.
Is a bernstein coefficient.
The specific process is divided into two steps and is shown in fig. 1:
(1) the set of values for the polynomial part p (U) (U. epsilon. U) is estimated. Its outer estimate Pex(U) may be represented by a convex hull of bernstein coefficients. 4 edges E of a certain surface F on the space U1～E4Is estimated as Pex(E1)～Pex(E4) The inner region enclosed by it can be considered as an inner estimate of the value set on the surface.
(2) The set of values for quasi-polynomial f (X) (X ∈ X) is estimated. A remainder band R is formed by adding a remainder interval R (X) to each point of the inner and outer estimates of the polynomial value setinAnd Rex. ThenRinInner estimate F of inner contour value set F (X)in(X)；RexOuter estimate F of the outer contour as a set of values F (X)ex(X). The exact value set f (x) is then related to the inner and outer estimates by:
and step 3: and solving the time lag stability domain boundary. And solving the time lag stability domain boundary by taking the zero-rejecting principle as a stability criterion. And the internal and external estimation of the characteristic quasi polynomial value set is subjected to zero elimination judgment, so that whether the current uncertain space is stable can be judged. The result of zero-removing discrimination comprises: 1) the external estimation of the characteristic quasi-polynomial value set does not contain a zero point, so that the accurate value set does not contain a zero point, and the system is stable; 2) if the internal estimation of the characteristic quasi-polynomial value set comprises a zero point, the accurate value set definitely comprises the zero point, and the system is unstable; 3) if the zero point is located between the inner estimation and the outer estimation, 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. Based on the idea, the process of solving the time lag stability domain boundary in a branching and delimiting manner is summarized, as shown in fig. 2. Conservatism introduced in value set estimation is reduced or eliminated in branch-and-bound herein.
And 4, step 4: a small disturbance skew stabilization domain is determined. And 3, dividing the time-lag space into a plurality of disjoint areas by the time-lag stable domain boundary obtained in the step 3, taking a determined time-lag point out of each area, calculating a characteristic value, and further determining whether the corresponding area is a stable domain.
In this embodiment 2, the application of the value set method can simultaneously handle a plurality of uncertainty time lags. The application of the branch-and-bound method can realize that sufficiently accurate time lag stable domain results are obtained with minimum conservation.
Example 3
In this embodiment 3, a method for determining the stability of a small disturbance of an electric power system under an influence of an uncertain time lag is provided, and for convenience of display, a simple typical second-order time lag system is used as an example in this embodiment 3 to explain how to determine whether the electric power system with an uncertain time lag is stable.
The state matrix and the time lag matrix of the system in this embodiment 3 are respectively:
A0＝[-2,0；0,-0.9]and A1＝[-1,0；-1,-1]。
The characteristic 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 belongs to [0,0.1] s, the uncertain space is X is tau multiplied by omega is [0,0.1] X [0,14], and the boundary on the complex plane is an imaginary axis, at this time, the step of judging the time lag stability is as follows:
step 1: and (8 th order) Taylor model of the characteristic quasi-polynomial is established.
First, the taylor model for each variable is calculated: t (τ) ═ 0.1u1+[0,0],T(ω)＝14u2+[0,0]Wherein u is1,u2∈[0,1]Is a normalized variable. Then, the taylor model of the variables is operated:
and further obtaining a Taylor model of the characteristic quasi-polynomial f:
step 2: a set of values of a characteristic quasi-polynomial is estimated. First, a polynomial part p (u) of a characteristic quasi-polynomial taylor model is equivalently transformed into a bernstein polynomial as follows, wherein,
is a bernstein polynomial. The value set of p (u) is estimated using bernstein coefficients, as shown in fig. 3. Then, the remainder interval R is added to each point of the polynomial value intra-and-out estimation to obtain the complete quasi-polynomial f value intra-and-out estimation results, as shown in fig. 4Shown in the figure.
And step 3: zero-picking discrimination and splitting uncertain space. Observing the inner and outer estimation result graphs of the characteristic quasi-polynomial value set shown in fig. 4, it can be seen that the result of zero-removing discrimination is that the zero point is located between the inner and outer estimation, and at this time, it cannot be determined whether the precise value set includes the zero point, that is, it cannot be determined whether the current uncertain space X ═ τ × ω ═ 0,0.1] × [0,14] is stable, and further, it is necessary to split the uncertain space. The uncertainty space X is selected to be subdivided in the dimension ω to obtain bernstein coefficients under two subspaces Y and Z listed in tables 1 and 2, and the value set estimation in step 2 is performed again for the two subspaces, as shown in fig. 5.
TABLE 1 Bernstein coefficients of subspace Y
TABLE 2 Bernstein coefficients of subspace Z
Observing the characteristic quasi-polynomial value set inside and outside estimation result diagram in subspace Y shown in FIG. 5, it can be known that the result of zero-removing discrimination is outside estimation Fex(Y) contains no zero, then the exact value set F (Y) must contain no zero, and the system is stable in subspace Y. The same holds true for the system being stable in the subspace Z. By now, it can be concluded that the system is not certain of a time lag τ ∈ [0,0.1 ∈]The small interference is stable under the influence of s.
Example 4
In this embodiment 4, a four-machine two-area system is taken as an example to illustrate how to determine the small disturbance stability area of the system in the time lag space.
The single line diagram of the four-machine two-zone system described in this embodiment 4 is shown in fig. 6, at 1Zone was run with 400MW output to zone 2. Each generator is equipped with a thyristor exciter with high transient gain and a PSS using rotor speed as input. Wide area damping controller installed in zone 1G1The above. The controller has the same lead-lag structure as PSS, and uses G2(region 1) and G3(region 2) relative rotor speed as a wide-area feedback signal, the system has 56 state variables and 22 algebraic variables.
In this embodiment 4, the wide-area damping controller has two feedback channels with time lag τ1And τ2With uncertainty, τ1∈[0,1]s,τ2∈[0,1]s。
Setting angular frequency range as omega ∈ [0,16 ]]rad/s, then X is τ1×τ2×ω＝[0,1]×[0,1]×[0,16]。
Firstly, establishing a state space model and a characteristic quasi polynomial of the system of the embodiment:
in the formula (I), the compound is shown in the specification,
is a matrix of the states of the system,
is a time lag matrix.
Then, the calculation of the time lag stability domain boundary of the system of the present embodiment is realized according to steps 1 to 3, wherein step 1 (establishing a taylor model of the characteristic quasi-polynomial) and step 2 (estimating a value set of the characteristic quasi-polynomial) refer to the specific description of the second-order time lag system embodiment in embodiment 3. Step 3 (solving the time lag stability domain boundary) is the step 3 (zero-rejecting discrimination and splitting uncertain space) of the typical second-order time lag system exampleInterval) is obtained, an unstable subspace obtained in the process of splitting the uncertain space X is marked, and further, a time-lag plane τ is obtained1×τ2Upper dead time stability domain boundary as shown in fig. 7.
And finally, determining a small interference time-lag stable domain of the system according to the step 4 in the technical scheme. Skew plane tau is bounded at skew stabilization domain shown in FIG. 71×τ2Dividing into 6 disjoint areas, taking out a determined time lag point from each area and calculating a characteristic value, if all the characteristic values are located on the left half complex plane, determining that the corresponding area is a stable area, otherwise, determining that the corresponding area is an unstable area, and the result is shown in fig. 8.
Example 5
Embodiment 5 of the present invention provides a non-transitory computer-readable storage medium, where the non-transitory computer-readable storage medium is used to store computer instructions, and when the computer instructions are executed by a processor, the method for solving a small disturbance stability domain of a time-lapse power system based on a value set as described above is implemented, where the method includes:
establishing a Taylor model of a characteristic quasi polynomial based on a plurality of uncertain time lags in the power system;
estimating a value set of the characteristic quasi-polynomial according to the built Taylor model of the characteristic quasi-polynomial;
performing zero-removing discrimination on the internal and external estimation of the characteristic quasi polynomial value set to determine a time lag stable domain boundary;
and determining whether the corresponding region in the time lag space is a stable region or not according to the time lag stable region boundary.
Example 6
establishing a Taylor model of a characteristic quasi polynomial based on a plurality of uncertain time lags in the power system;
estimating a value set of the characteristic quasi-polynomial according to the built Taylor model of the characteristic quasi-polynomial;
performing zero-removing discrimination on the internal and external estimation of the characteristic quasi polynomial value set to determine a time lag stable domain boundary;
and determining whether the corresponding region in the time lag space is a stable region or not according to the time lag stable region boundary.
Example 7
establishing a Taylor model of a characteristic quasi polynomial based on a plurality of uncertain time lags in the power system;
estimating a value set of the characteristic quasi-polynomial according to the built Taylor model of the characteristic quasi-polynomial;
performing zero-removing discrimination on the internal and external estimation of the characteristic quasi polynomial value set to determine a time lag stable domain boundary;
and determining whether the corresponding region in the time lag space is a stable region or not according to the time lag stable region boundary.
In summary, the following conclusions can be drawn by analyzing the example results obtained by the method provided by the invention: the existence of the wide-area time lag has an important influence on the stability of the power system, so that the stability of the system is deteriorated. In the time lag space, all stable operation points of the system form a stable region 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 region comprises the stable region. At a fixed time lag (τ) as in the present four-machine two-zone system example1,τ2) Small interference is stable at (0.6,0.4) s, where it cannot be directly inferred that the entire time lag plane τ is present1×τ2＝[0,0.6]×[0,0.4]The system is small interference stable.
In the embodiment, whether the system is small-interference stable under the influence of uncertain time lag can be judged, the small-interference stable domain of the system in a large-range time lag space can be determined, and all time lag operating points for ensuring the safety and stability of the system can be accurately obtained with minimum conservation.
As will be appreciated by one skilled in the art, 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 flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams 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.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts based on the technical solutions disclosed in the present invention.
Claims (10)
1. A time-lag power system small disturbance stable domain solving method based on a value set is characterized by comprising the following steps:
establishing a Taylor model of a characteristic quasi polynomial based on a plurality of uncertain time lags in the power system;
estimating a value set of the characteristic quasi-polynomial according to the built Taylor model of the characteristic quasi-polynomial;
performing zero-removing discrimination on the internal and external estimation of the characteristic quasi polynomial value set to determine a time lag stable domain boundary;
and determining whether the corresponding region in the time lag space is a stable region or not according to the time lag stable region boundary.
2. The value set-based time-lapse power system small disturbance stability domain solving method of claim 1, wherein establishing a taylor model of a characteristic quasi-polynomial comprises: calculating a Taylor model of each variable in the power system; and (4) operating the Taylor models based on all the variables to obtain the Taylor model of the characteristic quasi-polynomial.
3. The value set-based time-lapse power system small-disturbance stability domain solving method of claim 1, wherein estimating the value set of the characteristic quasi-polynomial according to the established taylor model of the characteristic quasi-polynomial comprises: equivalently transforming the polynomial part of the characteristic quasi-polynomial Taylor model into a Bernstein polynomial; estimating a set of values of the polynomial part using bernstein coefficients; and adding the remainder interval of the characteristic quasi-polynomial Taylor model to each point of the internal and external estimation of the polynomial value set to obtain the internal and external estimation results of the complete quasi-polynomial value set.
4. The value set-based time-lapse power system small disturbance stability domain derivation method of claim 1, wherein determining a time-lapse stability domain boundary comprises: and solving the time lag stability domain boundary by taking the zero-removing principle as a stability criterion, and judging whether the current uncertain space is stable or not by performing zero-removing judgment on the internal and external estimation of the characteristic quasi polynomial value set.
5. The method according to claim 4, wherein the zero-rejecting decision 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 a zero point, and the system is stable;
if the internal estimate of the set of characteristic quasi-polynomial values contains a zero, then the accurate set of values contains a zero and the system is unstable.
6. The time-lag power system small-disturbance stability domain solving method based on the value set according to claim 5, wherein if the zero point is located between the inner estimation and the outer estimation, it cannot be determined whether the precise value set includes the zero point, and at this time, the uncertain space needs to be split to obtain a more precise value set estimation result.
7. The method according to claim 1, wherein the time lag stable domain boundary divides the time lag space into a plurality of disjoint regions, and a determined time lag point is taken from each region and a characteristic value is calculated to determine whether the corresponding region is a stable domain.
8. A time-lapse power system small disturbance stability domain solving system based on a value set is characterized by comprising the following steps:
the system comprises a construction module, a calculation module and a calculation module, wherein the construction module is used for establishing a Taylor model of a characteristic quasi polynomial based on a plurality of uncertain time lags in the power system;
the estimation module is used for estimating a value set of the characteristic quasi-polynomial according to the built Taylor model of the characteristic quasi-polynomial;
the discrimination module is used for carrying out zero elimination discrimination by internal and external estimation of the characteristic quasi polynomial value set to determine a time lag stable domain boundary;
and the determining module is used for determining whether the corresponding region in the time lag space is the stable region according to the time lag stable region boundary.
9. A non-transitory computer readable storage medium storing computer instructions which, when executed by a processor, implement the value set based skew power system small interference stability domain derivation method of any of claims 1-7.
10. An electronic device, comprising: a processor, a memory, and a computer program; wherein a processor is connected to the memory, a computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions to implement the value set based time-lapse power system small-disturbance-stability-domain derivation method according to any one of claims 1 to 7.
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