CN102280883A - Wide area pattern analysis method for dynamic simulation validation of power system - Google Patents

Abstract

The invention relates to a fuzzy segmentation method for dynamic simulation validation of a large power system. Aiming at the problem of inaccurate dynamic simulation of the large power system and in consideration of a huge number of measurement data and model parameters of the large power system, the invention discloses a wide area pattern which represents the influence of the model parameters on a temporal and spatial dynamic characteristic of the power system; aiming at a certain type of elements of the power system, a fuzzy mapping relation between the model parameter and the temporal and spatial dynamic characteristic of the power system is obtained according to clustering analysis of the wide area pattern of the model parameter of the element on different nodes; and the model parameter of the element of the system is subjected to segmentation correction according to the degree of the mapping relation based on the measurement data, and a priority sequence of the segmentation correction is provided. In the invention, an effective method for dynamic simulation validation of the large power system is provided; and by applying the method, the dynamic simulation precision of the large power system can be improved.

Description

A kind of wide area pattern analysis method that is used for the Electrical Power System Dynamic simulating, verifying

Technical field

Technical field under the present invention is Electrical Power System Dynamic simulating, verifying field.

Background technology

Electrical Power System Dynamic emulation is the basic tool that people are familiar with the large-scale power system dynamic behaviour, it relates to power system planning, design, operation and control many aspects, for example: the operational mode of power system dispatching center establishment need be carried out stable verification, the proposition of control measure and enforcement need its validity of checking, and these all be unable to do without Electrical Power System Dynamic emulation, and coarse dynamic simulation can cause the potential hazard in system's unnecessary increase investment or operation in building, the control.

WAMS Wide Area Measurement System, the metric data that WAMS can provide system to be disturbed back PMU installation node, as busbar voltage amplitude and phase angle, line power, generator's power and angle etc., this makes the dynamic simulation precision of estimating whole electric power system by measured data become possibility.Some practices or test show, the dynamic simulation output trajectory of some electric power system and system are subjected between the measurement record data after the disturbance very mistake is arranged, and under some limiting cases even have the difference of matter, illustrates that present dynamic emulation is inaccurate.This has brought difficulty for decision-making of electric power system engineering staff, serious threat the safety and economic operation of electric power system.Therefore need a kind of method that can effectively improve the Electrical Power System Dynamic simulation accuracy badly.

In the system modelling process, the check Verification of simulation model and the checking Validation working link that is absolutely necessary.Generally speaking, the check of model is that verification of model is in order to guarantee the behavior of the reflection real system that simulation model can be correct for the validity that guarantees simulation model simulation algorithm when using and the correctness of programming.At twentieth century six the seventies, along with development of computer, the electric power scientific worker has done a large amount of research work to the Dynamic Simulation Software of electric power system, and simulation algorithm etc. are mature on the whole.The research of Electrical Power System Dynamic validity of simulation is primarily aimed at the dynamic simulation verification of model.

The modelling verification work of Electrical Power System Dynamic emulation is carried out at two levels of element and system, introduces the development of these two levels below respectively.

Electric power system is made up of elements such as synchronous generator, prime mover and governing system, excitation system, electric power networks, electric loads, and the validity of each component models parameter has determined the validity of whole electric system simulation.At twentieth century six the seventies, the modeling work of elements such as electric power networks, synchronous generator, speed regulator, excitation system has all obtained very big development, electric load is because characteristics such as its certain randomness, diversity, dispersivenesses, its modeling work stays cool, the model that the electric power system industrial quarters generally adopts permanent power, constant-impedance, constant current or equivalent motor etc. to simplify.In order to advance the research work of load modeling, American Electric Power research institute had organized huge project in 1976, launch simultaneously in the U.S. and Canada, carry out respectively based on the statistics synthesis of element and the research of debating method, make load modeling work that new development arranged based on the total body examination that measures.In recent ten years, the accident of having a power failure on a large scale several times having taken place in the world, illustrated that by contrast simulation output trajectory and metric data analysis the load model of current employing is improper, and makes emulation and actual measurement be tending towards identical by model and the parameter of adjusting elements such as load.This makes people further recognize the importance of load modeling, start the load modeling research of a new round and put into practice upsurge, debate method for total body examination of load modeling especially, owing to have characteristics such as the certain randomness of load, diversity, dispersiveness, make it have time variation and space-variant in the dynamic characteristic that load identification node is shown.Descriptive power for the time change step response that improves certain node load model to this node load, survey the repeatedly disturbance record data of debating device installation node based on load, become on the basis of rule when the analysis and utilization dynamic load characteristic, applied statistical method can improve the descriptive power of load model that this node picks out and parameter thereof; Yet for large-scale power system, be difficult to survey all to be installed and debate device at each equivalent load bus place, because the load composition difference of each node, therefore the difference that has caused the dynamic load characteristic of each node can not be simply directly applies to other node with the dynamic load model of a node.In order to obtain the load model of each node of large-scale power system, proposed the statistics synthesis and debated the large-scale power system load modeling method that method combines with total body examination, at first use certain survey and debate the device installation load model parameters that node picked out and the load composition of this node, obtain being applicable to the load model parameters of the typical load composition of this area, again according to the statistics of the load composition of other load bus, use the load model parameters of typical load composition, obtain the load model parameters of these load buses based on the comprehensive ratio juris of statistics.

The progress of load modeling work effectively raises the precision of dynamic simulation, but be the solution load statistical method that time variation adopted in the load modeling work, in the large regional grid load modeling process to the survey of each node load composition, certain error is brought to dynamic simulation in the capital, and expend lot of manpower and material resources, present most electrical networks still the whole network adopt unified identical load model.In order further to improve the accuracy of Electrical Power System Dynamic emulation, the electric power system staff can be after system's generation disturbance, the measured data of each node during based on disturbance, current dynamic simulation result is made further contrast verification, be the dynamic simulation model parameter checking of system level, and the model by adjusting element and parameter reduce the error between emulation track and the actual measurement track.The model parameter method of adjustment of system level can be described as following optimization problem.

The model structure of each element of electric power system has all obtained ripe development, might as well suppose that the dynamic simulation error is inaccurate the causing of model parameter by element.If the measuring track that each PMU write down in the large-scale power system is Y _i(t), (i=1,2, L, n), with Y _i(t) corresponding dynamic simulation output trajectory is y _i(t), establish Y _i(t) and y _i(t) error between is ξ _i(t)=Y _i(t)-y _i(t), (i=1,2, Ln), the model parameter of dynamic element is X in the system _Kl, (k=1,2, L, p; P is the element number, l=1,2, L, q _kq _kBe the number of parameters of k element).With domestic certain large regional grid is example, this large regional grid has about 170 in synchronous generator, and the duty value that waits of 220kV grade has about 380, also has elements such as speed regulator, excitation system in addition, with each component models 10 parameters being arranged is example, and then the parameter of dynamic element is about 8900 in the system; If only take into account merit angle track, then the dynamic trajectory number in the system is about 170.

Under a certain disturbance, ξ _i(t) can be expressed as the function of dynamic element parameter in the system.

$\left[\begin{array}{cccc}{\mathrm{\ξ}}_1\left(t_0\right)& {\mathrm{\ξ}}_1\left(t_1\right)& L& {\mathrm{\ξ}}_1\left(t_m\right)\\ {\mathrm{\ξ}}_2\left(t_0\right)& L& L& {\mathrm{\ξ}}_2\left(t_m\right)\\ M& M& M& M\\ {\mathrm{\ξ}}_n\left(t_0\right)& L& L& {\mathrm{\ξ}}_n\left(t_m\right)\end{array}\right]=f\left[\begin{array}{cccc}{X}_{11}& X_{12}& L& X_{{1q}_1}\\ X_{21}& L& L& X_{{2q}_2}\\ M& M& M& M\\ X_{p1}& L& L& X_{{\mathrm{pq}}_p}\end{array}\right]---\left(1\right)$

The target function of this optimization problem is:

min?J[ξ _i(t _j)] (2)

Wherein i ∈ 1,2, L, n, j ∈ 0,1, L, m.Constraints is X _Klmin＜X _Kl＜X _Klmax, X _KlminAnd X _KlmaxGeneral electric power system staff's the experience that relies on is determined.

In the real work often the track of Select Error maximum as the target trajectory correction parameter, promptly

But this method has its weak point: when 1. a part of emulation trajectory error reduced, the phantom error of another part track might increase; 2. the target trajectory of Xuan Zeing is less to the sensitivity of most parameters, causes sensitivity not satisfy constraints than the correction result of small parameter, if carry out the trace sensitivity analysis before correction, because the parameter amount is huge, thereby it is too low to proofread and correct efficient.

In order to reduce the complexity that model parameter is provided with, often adopt the same class component with similar characteristic unified identical model and parameter to simplify processing in the reality, for example: the generator of similar model adopts identical model and parameter; Because the difficulty of load modeling, most so far large regional grids still the whole network adopt identical load model and parameter.Though the complexity that has reduced model parameter setting and adjustment is handled in this simplification, has further introduced error, has reduced simulation accuracy.

In model check, verification and validation field, the bigger dominant parameters of emulation track influence general application and approval have been obtained by the trace sensitivity searching.On traditional trace sensitivity application foundation, in order to overcome the deficiency of said system level model parameter correcting method, a kind of fuzzy piecemeal bearing calibration of model parameter has been proposed, i.e. wide area pattern analysis method Wide Area Pattern Analysis Method.Adopt this method, can find a certain class component model parameter of different nodes and the strong correlation relation of system's space-time dynamic characteristic, divide block correction according to this strong correlation relation to the model parameter of this element, and provided the priority orders of dividing block correction, overcome the deficiency of traditional system level corrected model parameter method.

Summary of the invention

The objective of the invention is in order to overcome the deficiency of traditional system level corrected model parameter method, at the accurate inadequately problem of large-scale power system dynamic simulation, and consider the characteristics of large-scale power system metric data and model parameter enormous amount, by defining in order to the wide area pattern of representation model parameter to electric power system space-time dynamic properties influence, at a certain class power system component, based on cluster analysis to this component models parameter wide area pattern of different nodes, obtain the FUZZY MAPPING relation between model parameter and the electric power system space-time dynamic characteristic, power according to mapping relations, divide block correction based on metric data to the model parameter of this element in the system, and provided the priority orders of dividing block correction; The present invention provides a kind of effective method, adopting said method can improve the dynamic simulation precision of large-scale power system for the checking of large-scale power system dynamic simulation.

The objective of the invention is to be realized by following technical scheme: a kind of wide area pattern analysis method that is used for the Electrical Power System Dynamic simulating, verifying is characterized in that it may further comprise the steps:

1. establishing known actual measurement track is the relative merit of each generator angle δ in the system _i(t), (i=1,2, L, n-1), wherein n is generating board number, the model parameter vector of element is:

X _k＝[X _k1，X _k2，...，X _kq] ^T (3)

K=1 wherein, 2, L, p, p are the number of this element in the system, and q is the number of parameters of this element, and described element is any one element in generator, speed regulator, excitation system or the load,

Different parameters is to the sensitivity level difference of system dynamic characteristic influence in this component models, make non-sensitive parameter get representative value in the actual engineering, only proofread and correct sensitive parameter the dynamic simulation precision of system is improved a lot, establishing in the formula (3) the bigger sensitive parameter of system dynamics behavioral implications is X _K1

2. define wide area pattern Wide Area Pattern, WAP

Defined parameters X _K1WAP to system's merit angular motion step response influence is that the relative merit of each machine angle is to X _K1The spatial sequence of trace sensitivity absolute value is designated as

${\mathrm{\&Gamma;}}_{{\mathrm{<figure-callout\; id="1"\; label="X\; k"\; filenames="HDA0000084482320000011.png,HDA0000084482320000012.png"\; state="\{\{state\}\}">X</figure-callout>}}_k}^{\mathrm{\&delta;}}={\mathrm{<figure-callout\; id="1"\; label="WAP\; X\; k"\; filenames="HDA0000084482320000011.png,HDA0000084482320000012.png"\; state="\{\{state\}\}">WAP</figure-callout>}}_{X_k}^{1_{}}={\left[\right|\frac{{\&PartialD;\mathrm{\&delta;}}_1\left(t\right)}{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="X\; k"\; filenames="HDA0000084482320000011.png,HDA0000084482320000012.png"\; state="\{\{state\}\}">X</figure-callout>}}_k}|,|\frac{{\&PartialD;\mathrm{\&delta;}}_2\left(t\right)}{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="X\; k"\; filenames="HDA0000084482320000011.png,HDA0000084482320000012.png"\; state="\{\{state\}\}">X</figure-callout>}}_k}|,L,|\frac{{\&PartialD;\mathrm{\&delta;}}_{n-1}\left(t\right)}{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="X\; k"\; filenames="HDA0000084482320000011.png,HDA0000084482320000012.png"\; state="\{\{state\}\}">X</figure-callout>}}_k}\left|\right]}^T---\left(4\right)$

By WAP as can be seen this component models parameter of certain node to the influence of system's space-time dynamic characteristic and this component models parameter Changing Pattern to system's different time, the influence of zones of different dynamic characteristic;

3. the fuzzy cluster analysis of wide area pattern

In the dynamic process after system is subjected to disturbance, WAP has embodied the mapping relations power of this component models parameter in different space-time dynamic tracks and the system, with all nodes that this element is connected in, the model parameter of some nodes has similar pattern to the WAP of system's space-time dynamic properties influence, by cluster analysis to WAP, can find stronger mapping relations between the component models parameter of some node and certain the space-time dynamic trajectory, and then divide block correction this component models parameter;

1. choosing of wide area pattern character vector: the category that the cluster analysis of this component models parameter wide area pattern of different nodes is belonged to pattern recognition.The problem that pattern recognition solves be with a mode assignments to be identified in mode class, wherein, mode class refers to the set of the pattern with same characteristic features, and the feature of a pattern is represented with the characteristic vector of this pattern, the difference of characteristic vector has been represented the essential difference between the different mode, for the wide area pattern of certain node component models parameter of expression to the system dynamic characteristic influence, its most important factor is, this component models parameter of this node is to which place of system, the dynamic trajectory of which has the greatest impact and the value of this peak response time, so choose the characteristic vector of each wide area pattern is:

${\mathrm{<figure-callout\; id="1"\; label="T\; X\; k"\; filenames="HDA0000084482320000011.png,HDA0000084482320000012.png"\; state="\{\{state\}\}">T</figure-callout>}}_{X_k}^{1_{}}=[x_{\mathrm{space}},y_{\mathrm{time}},z_{\mathrm{sens}}]---\left(5\right)$

Wherein, For

Characteristic vector; x _SpaceFor Obtain the space coordinates at maximum place, be the generator numbering herein; y _TimeFor

Obtain the time coordinate at maximum place; z _SensFor

Maximum;

2. Fuzzy Cluster Analysis method: this element WAP to the p of system node place carries out cluster analysis, and clustering method adopts fuzzy C-means clustering Fuzzy C-means Clustering, FCM, and the finite aggregate of establishing the WAP composition of p element is Γ={ Γ ₁, Γ ₂, L, Γ _p, predefined classification number is C, h _iBe that (1≤i≤C), i sample is expressed as μ about the degree of membership of j class for the center of each cluster _j(Γ _i), the clustering criteria function definition is

$J(U,V)=\underset{j=1}{\overset{C}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{\left[{\mathrm{\&mu;}}_j\left({\mathrm{\&Gamma;}}_i\right)\right]}^b{\left|\right|{\mathrm{\&Gamma;}}_i-h_j\left|\right|}^2---\left(6\right)$

|| Γ _i-h _j|| be Γ _iTo h _iBetween Euclidean distance; B is the FUZZY WEIGHTED index, and b is big more, and fog-level is just high more; U is the fuzzy partition matrix of Γ, and the element of the capable j row of its i is degree of membership μ _j(Γ _i); V is cluster centre h among the Γ _iSet; The FCM algorithm is exactly the U and the V that will obtain to make clustering criteria function minimum, and constraints is: each sample Γ _iDegree of membership sum to C class is 1, promptly

$\underset{j=1}{\overset{C}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_j\left({\mathrm{\&Gamma;}}_i\right)=1,$ i＝1，2，L，p (7)

Under the constraint of following formula, make J that (U is V) to μ _j(Γ _i) and h _iLocal derviation equal 0, ask J (U, minimum V),

$h_j=\frac{\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{\left[{\mathrm{\&mu;}}_j\left({\mathrm{\&Gamma;}}_i\right)\right]}^b{\mathrm{\&Gamma;}}_i}{\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{\left[{\mathrm{\&mu;}}_j\left({\mathrm{\&Gamma;}}_i\right)\right]}^b},$ j＝1，2，L，C (8)

${\mathrm{\&mu;}}_j\left({\mathrm{\&Gamma;}}_i\right)=\frac{{\left(\frac{1}{{\left|\right|{\mathrm{\&Gamma;}}_i-h_j\left|\right|}^2}\right)}^{\frac{1}{b-1}}}{\underset{k=1}{\overset{C}{\mathrm{\&Sigma;}}}{\left(\frac{1}{{\left|\right|{\mathrm{\&Gamma;}}_i-h_k\left|\right|}^2}\right)}^{\frac{1}{b-1}}},$ i＝1，2，L，p；j＝1，2，L，C (9)

The cluster step of FCM method is:

I:, select C cluster centre h arbitrarily for finite aggregate Γ _i

Ii: calculate the degree of membership of p sample according to formula (9), sample is divided into the C class to each class;

Iii: the cluster centre that recomputates each class according to formula (8);

Iv: return the ii step, no longer change up to cluster centre;

According to the FCM cluster result p element node is divided into the C class, and then it is right to obtain C group " actual measurement track---component models parameter " correction;

4. model parameter divides the priority of block correction to calculate

When this element was too much in the system, number of categories C was bigger, yet was not that each group " actual measurement track---component models parameter " is proofreaied and correct all of equal importance, and in order to distinguish not significance level on the same group, the correction priority index that defines each group is:

$P_{r\&CenterDot;i}=\frac{1}{n_{c\&CenterDot;i}}\underset{T\&Element;{\mathrm{\&Omega;}}_i}{\mathrm{\&Sigma;}}T\left(3\right)=\frac{1}{n_{c\&CenterDot;i}}\underset{T\&Element;{\mathrm{\&Omega;}}_i}{\mathrm{\&Sigma;}}{z}_{\mathrm{sens}},$ i＝1，2，LC (10)

Wherein, p _RiBe the correction priority index of i class, n _CiBe the number of element node in the i class, Ω _iBe the set of i class wide area pattern, T is the characteristic vector of wide area pattern, P _RiBig more, then mapping relations between actual measurement track and this component models parameter are strong more in such, should preferentially proofread and correct.

Use a kind of wide area pattern analysis method that is used for the Electrical Power System Dynamic simulating, verifying of the present invention, can find the component models parameter of different nodes and the strong correlation relation of system's space-time dynamic characteristic, divide block correction according to this strong correlation relation to the model parameter of this element, and provided the priority orders of dividing block correction, overcome the deficiency of traditional system level corrected model parameter method; Can be by definition in order to the wide area pattern of representation model parameter to electric power system space-time dynamic properties influence, at a certain class power system component, based on cluster analysis to this component models parameter wide area pattern of different nodes, obtain the FUZZY MAPPING relation between model parameter and the electric power system space-time dynamic characteristic, power according to mapping relations, divide block correction based on metric data to the model parameter of this element in the system, and provided the priority orders of dividing block correction; The present invention provides a kind of effective method, adopting said method can improve the dynamic simulation precision of large-scale power system for the checking of large-scale power system dynamic simulation.

Description of drawings

Fig. 1 is IEEE39 node system figure.

Fig. 2 is the wide area pattern of each load bus model parameter to system's space-time dynamic properties influence.

Fig. 3 is the feature space of each load bus wide area pattern.

Embodiment

The objective of the invention is to realize by following technical scheme: a kind of wide area pattern analysis method that is used for the Electrical Power System Dynamic simulating, verifying, it may further comprise the steps:

1. establishing known actual measurement track is the relative merit of each generator angle δ in the system _i(t), (i=1,2, L, n-1), wherein n is generating board number, the model parameter vector of element is:

X _k＝[X _k1，X _k2，...，X _kq] ^T (3)

K=1 wherein, 2, L, p, p are the number of this element in the system, and q is the number of parameters of this element, and described element is any one element in generator, speed regulator, excitation system or the load,

Different parameters is to the sensitivity level difference of system dynamic characteristic influence in this component models, make non-sensitive parameter get representative value in the actual engineering, only proofread and correct sensitive parameter the dynamic simulation precision of system is improved a lot, establishing in the formula (3) the bigger sensitive parameter of system dynamics behavioral implications is X _K1

2. define wide area pattern Wide Area Pattern, WAP

Defined parameters X _K1WAP to system's merit angular motion step response influence is that the relative merit of each machine angle is to X _K1The spatial sequence of trace sensitivity absolute value is designated as

${\mathrm{\&Gamma;}}_{{\mathrm{<figure-callout\; id="1"\; label="X\; k"\; filenames="HDA0000084482320000011.png,HDA0000084482320000012.png"\; state="\{\{state\}\}">X</figure-callout>}}_k}^{\mathrm{\&delta;}}={\mathrm{<figure-callout\; id="1"\; label="WAP\; X\; k"\; filenames="HDA0000084482320000011.png,HDA0000084482320000012.png"\; state="\{\{state\}\}">WAP</figure-callout>}}_{X_k}^{1_{}}={\left[\right|\frac{{\&PartialD;\mathrm{\&delta;}}_1\left(t\right)}{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="X\; k"\; filenames="HDA0000084482320000011.png,HDA0000084482320000012.png"\; state="\{\{state\}\}">X</figure-callout>}}_k}|,|\frac{{\&PartialD;\mathrm{\&delta;}}_2\left(t\right)}{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="X\; k"\; filenames="HDA0000084482320000011.png,HDA0000084482320000012.png"\; state="\{\{state\}\}">X</figure-callout>}}_k}|,L,|\frac{{\&PartialD;\mathrm{\&delta;}}_{n-1}\left(t\right)}{\&PartialD;{\mathrm{<figure-callout\; id="1"\; label="X\; k"\; filenames="HDA0000084482320000011.png,HDA0000084482320000012.png"\; state="\{\{state\}\}">X</figure-callout>}}_k}\left|\right]}^T---\left(4\right)$

By WAP as can be seen this component models parameter of certain node to the influence of system's space-time dynamic characteristic and this component models parameter Changing Pattern to system's different time, the influence of zones of different dynamic characteristic;

3. the fuzzy cluster analysis of wide area pattern

In the dynamic process after system is subjected to disturbance, WAP has embodied the mapping relations power of this component models parameter in different space-time dynamic tracks and the system, with all nodes that this element is connected in, the model parameter of some nodes has similar pattern to the WAP of system's space-time dynamic properties influence, by cluster analysis to WAP, can find stronger mapping relations between the component models parameter of some node and certain the space-time dynamic trajectory, and then divide block correction this component models parameter;

3. choosing of wide area pattern character vector: the category that the cluster analysis of this component models parameter wide area pattern of different nodes is belonged to pattern recognition.The problem that pattern recognition solves be with a mode assignments to be identified in mode class, wherein, mode class refers to the set of the pattern with same characteristic features, and the feature of a pattern is represented with the characteristic vector of this pattern, the difference of characteristic vector has been represented the essential difference between the different mode, for the wide area pattern of certain node component models parameter of expression to the system dynamic characteristic influence, its most important factor is, this component models parameter of this node is to which place of system, the dynamic trajectory of which has the greatest impact and the value of this peak response time, so choose the characteristic vector of each wide area pattern is:

${\mathrm{<figure-callout\; id="1"\; label="T\; X\; k"\; filenames="HDA0000084482320000011.png,HDA0000084482320000012.png"\; state="\{\{state\}\}">T</figure-callout>}}_{X_k}^{1_{}}=[x_{\mathrm{space}},y_{\mathrm{time}},z_{\mathrm{sens}}]---\left(5\right)$

Wherein,

For

Characteristic vector; x _SpaceFor Obtain the space coordinates at maximum place, be the generator numbering herein; y _TimeFor

Obtain the time coordinate at maximum place; z _SensFor Maximum;

4. Fuzzy Cluster Analysis method: this element WAP to the p of system node place carries out cluster analysis, and clustering method adopts fuzzy C-means clustering Fuzzy C-means Clustering, FCM, and the finite aggregate of establishing the WAP composition of p element is Γ={ Γ ₁, Γ ₂, L, Γ _p, predefined classification number is C, h _iBe that (1≤i≤C), i sample is expressed as μ about the degree of membership of j class for the center of each cluster _j(Γ _i), the clustering criteria function definition is

$J(U,V)=\underset{j=1}{\overset{C}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{\left[{\mathrm{\&mu;}}_j\left({\mathrm{\&Gamma;}}_i\right)\right]}^b{\left|\right|{\mathrm{\&Gamma;}}_i-h_j\left|\right|}^2---\left(6\right)$

|| Γ _i-h _j|| be Γ _iTo h _iBetween Euclidean distance; B is the FUZZY WEIGHTED index, and b is big more, and fog-level is just high more; U is the fuzzy partition matrix of Γ, and the element of the capable j row of its i is degree of membership μ _j(Γ _i); V is cluster centre h among the Γ _iSet; The FCM algorithm is exactly the U and the V that will obtain to make clustering criteria function minimum, and constraints is: each sample Γ _iDegree of membership sum to C class is 1, promptly

$\underset{j=1}{\overset{C}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_j\left({\mathrm{\&Gamma;}}_i\right)=1,$ i＝1，2，L，p (7)

Under the constraint of following formula, make J that (U is V) to μ _j(Γ _i) and h _iLocal derviation equal 0, ask J (U, minimum V),

$h_j=\frac{\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{\left[{\mathrm{\&mu;}}_j\left({\mathrm{\&Gamma;}}_i\right)\right]}^b{\mathrm{\&Gamma;}}_i}{\underset{i=1}{\overset{p}{\mathrm{\&Sigma;}}}{\left[{\mathrm{\&mu;}}_j\left({\mathrm{\&Gamma;}}_i\right)\right]}^b},$ j＝1，2，L，C (8)

${\mathrm{\&mu;}}_j\left({\mathrm{\&Gamma;}}_i\right)=\frac{{\left(\frac{1}{{\left|\right|{\mathrm{\&Gamma;}}_i-h_j\left|\right|}^2}\right)}^{\frac{1}{b-1}}}{\underset{k=1}{\overset{C}{\mathrm{\&Sigma;}}}{\left(\frac{1}{{\left|\right|{\mathrm{\&Gamma;}}_i-h_k\left|\right|}^2}\right)}^{\frac{1}{b-1}}},$ i＝1，2，L，p；j＝1，2，L，C (9)

The cluster step of FCM method is:

I:, select C cluster centre h arbitrarily for finite aggregate Γ _i

Ii: calculate the degree of membership of p sample according to formula (9), sample is divided into the C class to each class;

Iii: the cluster centre that recomputates each class according to formula (8);

Iv: return the ii step, no longer change up to cluster centre;

According to the FCM cluster result p element node is divided into the C class, and then it is right to obtain C group " actual measurement track---component models parameter " correction;

4. model parameter divides the priority of block correction to calculate

When this element was too much in the system, number of categories C was bigger, yet was not that each group " actual measurement track---component models parameter " is proofreaied and correct all of equal importance, and in order to distinguish not significance level on the same group, the correction priority index that defines each group is:

$P_{r\&CenterDot;i}=\frac{1}{n_{c\&CenterDot;i}}\underset{T\&Element;{\mathrm{\&Omega;}}_i}{\mathrm{\&Sigma;}}T\left(3\right)=\frac{1}{n_{c\&CenterDot;i}}\underset{T\&Element;{\mathrm{\&Omega;}}_i}{\mathrm{\&Sigma;}}{z}_{\mathrm{sens}},$ i＝1，2，LC (10)

Wherein, p _RiBe the correction priority index of i class, n _CiBe the number of element node in the i class, Ω _iBe the set of i class wide area pattern, T is the characteristic vector of wide area pattern, P _RiBig more, then mapping relations between actual measurement track and this component models parameter are strong more in such, should preferentially proofread and correct.

With reference to Fig. 1, be the concrete implementation step of example explanation wide area pattern analysis method with the IEEE39 node system, establishing element to be corrected is electric load.It is the generator node that the IEEE39 node system has 30～39 nodes, 3,19 nodes such as 4 grades are load bus, load model adopts integrated load model, parameter is as shown in table 1, wherein Mlf is the initial active load rate of motor, Rs is a stator resistance, Xs is a stator reactance, Rr is a rotor resistance, and Xr is the rotor reactance, and Tj is an inertia time constant, Xm is an excitation reactance, A is and the moment of resistance coefficient of rotating speed square direct ratio that B is and the moment of resistance coefficient of rotating speed direct ratio that pz is the meritorious constant-impedance coefficient of static load, qz is the idle constant-impedance coefficient of static load, pi is the meritorious constant current coefficient of static load, and qi is the idle constant current coefficient of static load, and kpm is motor shared initial meritorious ratio in synthetic load.Suppose that bus 4-bus 14 circuits and bus 4 distances 50% are in 1.0s～11s the three-phase ground short circuit takes place.Discover in 14 parameters of integrated load model, the bigger parameter of system dynamic characteristic influence is had initial active load rate Mlf, induction motor rotor resistance R _r, meritorious proportionality coefficient Kpm etc., be the content of example explanation wide area pattern analysis method so that the initial active load rate of integrated load model is proofreaied and correct below.Calculate the wide area pattern of the initial active load rate of each load bus according to formula (4), as shown in Figure 2 to the system relative merit of each generator angle.Generator 30～38 machines are with respect to the merit angle of 39 machines in abscissa 1～9 difference presentation graphs 1 of each wide area pattern among Fig. 2, and ordinate is a simulation time, and red point is the position at wide area pattern maximum place.

Table 1 integrated load model parameter value

Mlf	Rs	Xs	Rr	Xr	Tj	Xm	A	B	pz	qz	pi	qi	Kpm
														0.4	0.013	0.067	0.009	0.17	3	3.8	1.0	0	0.3	0.3	0.3	0.3	60％

Wide area pattern to each load bus is carried out fuzzy cluster analysis, characteristic vector distribute and cluster result as shown in Figure 3, same color be a class.For example: triangulation point is a class, and they are respectively the characteristic vectors of load bus 8 and load bus 20 wide area patterns.According to the position of characteristic vector as can be known: the mapping relations between the track of the relative merit with the 38-39 machine of the load model parameters of node 8 and node 20 angle are the strongest, promptly should be based on the load model parameters of the relative merit of 38-39 machine angle trajectory corrector node 8 and node 20.It proofreaies and correct the priority index

$P_{r\&CenterDot;1}=\frac{1}{n_{c\&CenterDot;1}}\underset{T\&Element;{\mathrm{\&Omega;}}_1}{\mathrm{\&Sigma;}}T\left(3\right)=\frac{1}{n_{c\&CenterDot;1}}\underset{T\&Element;{\mathrm{\&Omega;}}_1}{\mathrm{\&Sigma;}}{z}_{\mathrm{sens}}=\frac{1}{2}(10.375+13.573)=11.974---\left(11\right)$

In like manner, can obtain other " merit angle track---load model parameters " and proofread and correct proofreading and correct right correction priority index with each, as shown in table 2.

Table 2 is proofreaied and correct tabulation

Merit angle track	Load bus	Proofread and correct the priority index
			The 38-39 machine	8、20	11.974
The 38-39 machine	3、4、7、15、16、21、24、27、28、29	5.352
			The 38-39 machine	18、25、26	2.452
The 35-39 machine	12、23	2.325
			The 34-39 machine	31、39	0.378

As shown in Table 2: for the IEEE39 node system, when bus 4-bus 14 circuits and bus 4 distances 50% place generation three phase short circuit fault, during by actual measurement merit angle trajectory corrector load model parameters, should be at first based on the actual measurement merit angle trajectory corrector node 8 of 38-39 machine, the load model parameters at node 20 places; If simulation accuracy can't meet the demands, then survey the load model parameters that merit angle trajectory corrector node 3, node 4, node 7 etc. are located based on the 38-39 machine again; Carry out successively.

Claims (1)

1. wide area pattern analysis method that is used for the Electrical Power System Dynamic simulating, verifying is characterized in that it may further comprise the steps:

1. establishing known actual measurement track is the relative merit of each generator angle δ in the system _i(t), (i=1,2, L, n-1), wherein n is generating board number, the model parameter vector of element is:

X _k＝[X _k1，X _k2，...，X _kq] ^T (3)

K=1 wherein, 2, L, p, p are the number of this element in the system, and q is the number of parameters of this element, and described element is any one element in generator, speed regulator, excitation system or the load,

Different parameters is to the sensitivity level difference of system dynamic characteristic influence in this component models, make non-sensitive parameter get representative value in the actual engineering, only proofread and correct sensitive parameter the dynamic simulation precision of system is improved a lot, establishing in the formula (3) the bigger sensitive parameter of system dynamics behavioral implications is X _K1

2. define wide area pattern Wide Area Pattern, WAP

Defined parameters X _K1WAP to system's merit angular motion step response influence is that the relative merit of each machine angle is to X _K1The spatial sequence of trace sensitivity absolute value is designated as

By WAP as can be seen this component models parameter of certain node to the influence of system's space-time dynamic characteristic and this component models parameter Changing Pattern to system's different time, the influence of zones of different dynamic characteristic;

3. the fuzzy cluster analysis of wide area pattern

In the dynamic process after system is subjected to disturbance, WAP has embodied the mapping relations power of this component models parameter in different space-time dynamic tracks and the system, with all nodes that this element is connected in, the model parameter of some nodes has similar pattern to the WAP of system's space-time dynamic properties influence, by cluster analysis to WAP, can find stronger mapping relations between the component models parameter of some node and certain the space-time dynamic trajectory, and then divide block correction this component models parameter;

1. choosing of wide area pattern character vector: the category that the cluster analysis of this component models parameter wide area pattern of different nodes is belonged to pattern recognition.The problem that pattern recognition solves be with a mode assignments to be identified in mode class, wherein, mode class refers to the set of the pattern with same characteristic features, and the feature of a pattern is represented with the characteristic vector of this pattern, the difference of characteristic vector has been represented the essential difference between the different mode, for the wide area pattern of certain node component models parameter of expression to the system dynamic characteristic influence, its most important factor is, this component models parameter of this node is to which place of system, the dynamic trajectory of which has the greatest impact and the value of this peak response time, so choose the characteristic vector of each wide area pattern is:

Wherein,

For

Characteristic vector; x _SpaceFor

Obtain the space coordinates at maximum place, be the generator numbering herein; y _TimeFor

Obtain the time coordinate at maximum place; z _SensFor Maximum;

2. Fuzzy Cluster Analysis method: this element WAP to the p of system node place carries out cluster analysis, and clustering method adopts fuzzy C-means clustering Fuzzy C-means Clustering, FCM, and the finite aggregate of establishing the WAP composition of p element is Γ={ Γ ₁, Γ ₂, L, Γ _p, predefined classification number is C, h _iBe that (1≤i≤C), i sample is expressed as μ about the degree of membership of j class for the center of each cluster _j(Γ _i), the clustering criteria function definition is

|| Γ _i-h _j|| be Γ _iTo h _iBetween Euclidean distance; B is the FUZZY WEIGHTED index, and b is big more, and fog-level is just high more; U is the fuzzy partition matrix of Γ, and the element of the capable j row of its i is degree of membership μ _j(Γ _i); V is cluster centre h among the Γ _iSet; The FCM algorithm is exactly the U and the V that will obtain to make clustering criteria function minimum, and constraints is: each sample Γ _iDegree of membership sum to C class is 1, promptly

i＝1，2，L，p (7)

Under the constraint of following formula, make J that (U is V) to μ _j(Γ _i) and h _iLocal derviation equal 0, ask J (U, minimum V),

j＝1，2，L，C (8)

i＝1，2，L，p；j＝1，2，L，C (9)

The cluster step of FCM method is:

I:, select C cluster centre h arbitrarily for finite aggregate Γ _i

Ii: calculate the degree of membership of p sample according to formula (9), sample is divided into the C class to each class;

Iii: the cluster centre that recomputates each class according to formula (8);

Iv: return the ii step, no longer change up to cluster centre;

According to the FCM cluster result p element node is divided into the C class, and then it is right to obtain C group " actual measurement track---component models parameter " correction;

4. model parameter divides the priority of block correction to calculate

When this element was too much in the system, number of categories C was bigger, yet was not that each group " actual measurement track---component models parameter " is proofreaied and correct all of equal importance, and in order to distinguish not significance level on the same group, the correction priority index that defines each group is:

i＝1，2，LC (10)

Wherein, P _RiBe the correction priority index of i class, n _CiBe the number of element node in the i class, Ω _iBe the set of i class wide area pattern, T is the characteristic vector of wide area pattern, P _RiBig more, then mapping relations between actual measurement track and this component models parameter are strong more in such, should preferentially proofread and correct.

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