CN104834970B - A kind of water power cluster Dynamic Equivalence with generalization ability - Google Patents
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Abstract
The invention discloses a kind of water power cluster Dynamic Equivalence with generalization ability, this method comprises the following steps：Establish water power cluster dynamic equivalent model；Pick out the parameter of Equivalent Model under each disturbance；Form the initialization data for establishing extensive Equivalent Model；Establish the feature samples space of dynamic equivalent model parameter；Establish dynamic equivalent model and parameter with generalization ability.The present invention has good generalization ability, compensates for when carrying out dynamic equivalent to electric system with general evaluation method method at present, Equivalent Model and parameter are only capable of the deficiency of a certain specific disturbance of accurate description.
Description
Technical field
The invention belongs to electric system simulation fields, and in particular to a kind of water power cluster dynamic equivalent with generalization ability
Method.
Background technology
General only one of which region interested to the dynamic studies of large-scale power system, referred to as studies system；And
Only consider its influence to survey region without its internal structure is described in detail to the region away from this region farther out, in research
Region, referred to as perimeter.In research, external system is often subjected to dynamic equivalent to significantly reduce calculation amount and prominent master
Want feature.Currently, Dynamic Equivalence can be divided into 3 major class, respectively：Coherency method, mode method method and evaluation method method.
The basic thought of evaluation method method is to regard external system as " black box ", is required according to equivalence or Equivalent Model application purpose is selected
Equivalent Model replacement is selected, the parameter of Equivalent Model is then recognized by field measurement amount using the method for identification, realizes dynamic
Equivalence, equivalence require to be that section dominant oscillating mode is constant before and after ensureing equivalence.Dynamic equivalent core is to hold external system
To studying the influence of system, and this influence can be embodied by studying interconnection dynamic power flow, therefore the measurement in practical application
Then the information such as the oscillation of power or voltage change generally extracted from interconnection use identification algorithm to obtain Equivalent Model ginseng
Number.The advantages of this method is only not need the detailed data of external system according to boundary and the measurement of built-in system
It carries out, therefore better than other two methods.But the system response caused by different disturbances is different so that equivalent mould
Type and parameter are stringent only for the input and output under a certain specific disturbance, are unable to the other disturbances of accurate description.Therefore, it uses
Evaluation method method carries out equivalent time to identical perimeter, different due to being disturbed in research system, obtained Equivalent Model ginseng
Number is also not quite similar, and does not have generality.When the response curve to a certain unknown disturbance of acquisition in electric system simulation calculating
When, no matter select the parameter of Equivalent Model obtained by any known disturbance to be all a lack of foundation, error can not also be estimated.
Invention content
Technical problem to be solved by the present invention lies in the deficiencies for the above situation, provide one kind using metric data as base
Plinth, the electric system evaluation method method with generalization ability, in this method, Equivalent Model and parameter can not only describe specifically
It disturbs, also there is certain interpretability to other not given disturbances, make it have stronger generalization ability, and can become and divide
The general model for analysing research system security and stability, compensate at present with evaluation method method to electric system into Mobile state etc.
When value, Equivalent Model and parameter are only capable of the deficiency of a certain specific disturbance of accurate description.
In order to solve the above problem and reach above-mentioned purpose, a kind of water power collection group motion with generalization ability provided by the invention
State equivalence method is realized by the following technical programs：A kind of water power cluster Dynamic Equivalence with generalization ability, packet
Include following steps：
1) water power cluster dynamic equivalent model is established；
2) metric data being directed under different disturbances carries out equivalence to water power cluster dynamic equivalent parameter, and utilizes population
Optimization algorithm picks out the parameter of Equivalent Model under each disturbance according to response curve；
3) PCA methods pre-process dynamic equivalent model parameter in Statistics Application, reduce parameter dimensions, and formation is built
Found the initialization data of extensive Equivalent Model；
4) using support vector machines as tool, the feature samples space of dynamic equivalent model parameter is established；
5) multi-cure-fitting parameter identification is carried out to the supporting vector in feature samples space, established dynamic with generalization ability
State Equivalent Model and parameter.
Further, it is that equivalent generator model and equivalence are negative that water power cluster dynamic equivalent model is established in the step 1)
Lotus model.
Further, the metric data obtained in the step 2) is active power and reactive power song on interconnection
Line.
Further, it includes following steps that the step 3) establishes initialization data using PCA methods：
(3-1) is directed to all Equivalent Model parameters, calculates the average value per one-dimensional data；
(3-2) calculates the difference per one-dimensional data with its average value and builds covariance matrix；
(3-3) seeks the eigen vector of covariance matrix；
(3-4) calculate before q maximum eigenvalue contribution rate, the contribution rate be selected characteristic value and with own
The ratio of the sum of characteristic value, is larger than predetermined threshold, determines q values, wherein the predetermined threshold is 0.85 or 0.9, which is
Contribution rate is more than the number of predetermined threshold；
The matrix that the corresponding feature vector of preceding q maximum eigenvalue and Equivalent Model parameter are constituted is done product by (3-5), is obtained
Equivalent Model parameter after dimensionality reduction.
Further, the step 4) is to establish dynamic using support vector machines and according to the Equivalent Model parameter after dimensionality reduction
The feature samples space of Equivalent Model parameter, includes the following steps：
(4-1) sets kernel function K (xi, xj) it is Gaussian function, wherein i, j=1,2,3......p, p are of sample
Number, i.e., the number of Equivalent Model data after dimensionality reduction；xi, xjFor the sample in sample space, some equivalent mould as after dimensionality reduction
Shape parameter；
(4-2) solves the quadratic programming problem of following formula (1) using SMO algorithms, obtain the optimal solution of lagrange multipliers α to
Amount；
Wherein αi、αjRespectively represent sample point xi、xjLagrange multipliers.
(4-3) takes the α more than 0iCorresponding sample is supporting vector, and is introduced on the spherical surface of minimum sphere.
Further, the step 5) carries out multi-cure-fitting parameter identification to supporting vector, and establishing has generalization ability
Dynamic equivalent model and parameter, include the following steps：
(5-1) finds out the Equivalent Model parameter before corresponding dimensionality reduction according to supporting vector；
(5-2) finds out corresponding dominant eigenvalues response curve according to the Equivalent Model parameter before dimensionality reduction；
(5-3) carries out equivalent model parameter using multi-cure-fitting parameter identification as tool, using particle swarm optimization algorithm
Optimization, it is final to obtain Equivalent Model and parameter with generalization ability.
Compared with prior art, the beneficial effects of the present invention are：The base of a large amount of stability simulations is carried out in large scale electric network
On plinth, a kind of evaluation method method with generalization ability is provided, realizes that established Equivalent Model and parameter can not only describe
Specific disturbance also has stronger interpretability to other not given disturbances, can become analysis and research system safety
The general model of stability, it is equivalent when compensating at present with general evaluation method method to electric system progress dynamic equivalent
Model and parameter are only capable of the deficiency of a certain specific disturbance of accurate description.
Description of the drawings
Fig. 1 is a kind of specific one embodiment of water power cluster Dynamic Equivalence with generalization ability of the present invention
General flow chart.
Fig. 2 is a kind of specific one embodiment of water power cluster Dynamic Equivalence with generalization ability of the present invention
In, recognize different Equivalent Models and parameter flow chart under each disturbance.
Fig. 3 is a kind of specific one embodiment of water power cluster Dynamic Equivalence with generalization ability of the present invention
In, utilize PCA method dimensionality reduction flow charts.
Fig. 4 is a kind of specific one embodiment of water power cluster Dynamic Equivalence with generalization ability of the present invention
In, establish feature samples space flow chart using support vector machines.
Fig. 5 is a kind of specific one embodiment of water power cluster Dynamic Equivalence with generalization ability of the present invention
In, the optimal solution vector flow chart of lagrange multipliers α is solved using SMO algorithms.
Fig. 6 is a kind of specific one embodiment of water power cluster Dynamic Equivalence with generalization ability of the present invention
In, establish general Equivalent Model and parameter flow chart using multi-cure-fitting parameter identification.
Specific implementation mode
The invention will be further described below in conjunction with the accompanying drawings.
Embodiment 1：
As shown in FIG. 1, FIG. 1 is the method for the present invention general flow charts, include the following steps：
1) water power cluster dynamic equivalent model is established；
2) metric data being directed under different disturbances carries out equivalence to water power cluster dynamic equivalent model, and utilizes population
Optimization algorithm picks out the parameter of Equivalent Model under each disturbance according to response curve；
3) PCA methods pre-process dynamic equivalent model parameter in Statistics Application, reduce parameter dimensions, and formation is built
Found the initialization data of extensive Equivalent Model；
4) using support vector machines as tool, the feature samples space of dynamic equivalent model parameter is established；
5) multi-cure-fitting parameter identification is carried out to the supporting vector in feature samples space, established dynamic with generalization ability
State Equivalent Model and parameter.
Embodiment 2：
As a kind of specific implementation for realizing step 1), the dynamic equivalent model of foundation is to establish equivalent generator mould
Type and duty value model, including three rank generator models and static load model.Three rank generator model equations are as follows：
E’qFor q axis transient internal voltages；Ef0For excitation voltage initial value；KvFor voltage feedback factor；x’dWith xdRespectively d axis
Transient state reactance and synchronous reactance；xqFor q axis synchronous reactances；T’d0For d axis transient state open circuit time constants；TJFor inertia time constant；
D is damped coefficient；δ is q axis potentials EqWith the angle of terminal voltage；ω is rotor speed；TmFor machine torque；U is generator generator terminal
Voltage；idWith iq、udWith uqThe respectively electric current and component of voltage of d axis and q axis；EfFor stator excitation electromotive force.
Static load model equation is as follows：
Ps0、Qs0、V0、ω0Respectively steady-state operation when the active and reactive power of load absorption, load bus voltage magnitude
And angular frequency；Ps、Qs, V, ω be its actual value；NpAnd NqFor the active voltage characteristic index with reactive power of load；FpAnd FqFor
The active frequency characteristic index with reactive power of load.
Dynamic equivalent model shares 10 parameters, includes 6 parameters of three rank generator models, i.e.,：[xd、x’d、Kv、T
’d0、TJ, D] and static load model 4 parameters, i.e.,：[Np、Fp、Nq、Fq]。
As shown in Fig. 2, the dynamic equivalent model parameter picked out in step 2) under each disturbance includes the following steps：
(2-1) obtains system before equivalence active power, reactive power response curve on interconnection under a certain disturbance；
(2-2) treats identified parameters and is initialized according to above-mentioned Equivalent Model；
(2-3) calculates the active power and reactive power response curve obtained under this group of Equivalent Model parameter；
(2-4) judges object function J using the error of power response curve on interconnection as object functioniWhether it is less than pre-
Determine threshold value, as follows：
Wherein JiFor the corresponding object function of i-th of disturbance, N is the number of curve sampled point, Pk、QkTo survey wattful power
Rate, reactive capability curve sampled point, Pmk、QmkFor the sampled point in fitting active power, reactive capability curve.
If JiIt is then obtained for the Equivalent Model parameter under the specific disturbance less than predetermined threshold and jumps to step (2-6)；
Otherwise continue to calculate；
(2-5) is optimized using particle swarm optimization algorithm (by formula 5) Equivalent Model parameter, and it is equivalent to obtain new one group
Model parameter return to step (2-3)；
Wherein vkFor the velocity vector of k-th of particle, the speed of particle is limited in maximum speed v under normal conditionsmax
(vmax>0) in, even vk>vmax, then vk=vmax；If vk<-vmax, then vk=-vmax, the maximum speed v of particlemaxDesirable particle
The 10% of position value range.W is Inertia weight factor, and larger Inertia weight factor is conducive to jump out local minimum point, smaller
Inertia weight factor is conducive to carry out accurate local search, generally uses time-varying Inertia weight factor, i.e. w=w in practicemax-
(wmax-wmin)k/kmax, enable wmax=0.9, wmin=0.4, k are current iteration number, kmaxFor maximum iteration.c1And c2For
Studying factors, also known as aceleration pulse have respectively represented particle and have been promoted to itself individual extreme value pbest and group extreme value gbest
Acceleration weights, the two typically each takes 2.Rand is the random number between 0 to 1, xkFor the position where kth time iteration particle.
Population scale is too small to cause increasing considerably for iterations, decline that is excessive and can causing search efficiency generally to take 30-
50。
(2-6) judges whether current disturbance number is equal to maximum perturbation number, is to terminate to calculate, obtains under different disturbances
Different Dynamic Equivalent Model parameter；Otherwise, return to step (2-1) applies other different disturbances and recalculates.
As shown in figure 3, PCA methods include to the progress dimension-reduction treatment of dynamic equivalent model parameter in step 3) Statistics Application
Following steps：
(3-1) is directed to all Equivalent Model parameters, calculates the average value per one-dimensional data in 10 dimension datas；
(3-2) calculates the difference per one-dimensional data with its average value and builds covariance matrix；
(3-3) seeks the eigen vector of covariance matrix；
(3-4) calculate before q maximum eigenvalue contribution rate, the contribution rate be selected characteristic value and with own
The ratio of the sum of characteristic value, is larger than predetermined threshold, determines q values；
The matrix that the corresponding feature vector of preceding q maximum eigenvalue and Equivalent Model parameter are constituted is done product by (3-5), is obtained
Equivalent Model parameter after dimensionality reduction.
As shown in figure 4, step 4) is to establish dynamic etc. using support vector machines and according to the Equivalent Model parameter after dimensionality reduction
It is worth the feature samples space of model parameter, includes the following steps：
(4-1) sets kernel function K (xi, xj) it is Gaussian function, expression formula is as follows：
I, j=1,2,3......p, p are the number of sample, i.e., the number of Equivalent Model data after dimensionality reduction；xi, xjFor sample
Sample in space, some Equivalent Model parameter as after dimensionality reduction.
(4-2) solves the quadratic programming problem of following formula (7) using SMO algorithms, obtain the optimal solution of lagrange multipliers α to
Amount；
As shown in figure 5, solving above-mentioned quadratic programming problem using SMO algorithms, include the following steps：
(4-2-1) initializes lagrange multipliers, centre of sphere m, radius R as the following formula；
Sample x is calculated as follows in (4-2-2)iTo square d of the distance of the centre of spherei 2；
(4-2-3) according to above-mentioned result of calculation, the point for finding first violation KKT condition as the following formula is xy, and obtain it
Corresponding αy.If not finding, step (4-2-8) is arrived.Wherein C is regularization parameter, realizes the size to ball and is included
Compromise between sample number；
(4-2-4) is so that quadratic programming problem functional value is minimum in step (4-2), filters out sample point x as the following formulaz,
And obtain its corresponding αz；
(4-2-5) α to filtering out as the following formulayAnd αzUpdate is optimized, new α ' is obtainedyAnd α 'z；
Wherein,
(4-2-6) updates the centre of sphere as the following formula, updates d by step (4-2-2)2 yWith d2 z, and the radius of a ball is updated as the following formula；
(4-2-7) return to step (4-2-3) continues to calculate；
(4-2-8) completes optimal hypersphere and establishes, and algorithm terminates.
(4-3) takes the α more than 0iCorresponding sample is supporting vector, and is introduced on the spherical surface of minimum sphere.
As shown in fig. 6, step 5) carries out multi-cure-fitting parameter identification to the power response curve corresponding to supporting vector,
It obtains the Equivalent Model with generalization ability and parameter includes the following steps：
(5-1) finds out the Equivalent Model parameter before corresponding dimensionality reduction according to supporting vector；
(5-2) finds out corresponding dominant eigenvalues response curve according to the Equivalent Model parameter before dimensionality reduction；
(5-3) carries out equivalent model parameter using multi-cure-fitting parameter identification as tool, using particle swarm optimization algorithm
Optimization, it is final to obtain Equivalent Model and parameter with generalization ability.
Step (5-3) includes the following steps：
(5-3-1) reads the multigroup active power and reactive power response song of the interconnection under different disturbances to be fitted
Line；
(5-3-2) treats identified parameters and is initialized according to the Equivalent Model in step (1)；
(5-3-3) is directed to same group of Equivalent Model parameter, and emulation obtains multigroup power response curve when different disturbances；
(5-3-4) following formula carries out equivalent model parameter as object function, using particle swarm optimization algorithm (formula 5)
Optimization, obtains new Equivalent Model parameter；
Wherein,For the mean value of i-th measured curve；G is the number of disturbance.
(5-3-5) judges whether J is less than predetermined threshold, is to terminate multi-cure-fitting identification, obtaining has generalization ability
Equivalent Model parameter；Otherwise (5-3-3) is returned to continue to calculate.
To sum up, a kind of water power cluster Dynamic Equivalence with generalization ability of the present invention is grid-connected with extensive water power cluster
Based on interconnection metric data, by carrying out extensive analysis to the Equivalent Model parameter obtained under different disturbances, one is obtained
Equivalent Model and parameter of the group with generalization ability can not only explain the situation under current disturbance, same for unknown disturbance
With stronger interpretability.
The above content is combine specific preferred embodiment to the further description of the invention made, and it cannot be said that originally
The specific implementation mode of invention is confined to these explanations.For those of ordinary skill in the art to which the present invention belongs,
The other embodiment obtained in the case where not departing from technical scheme of the present invention, should be included within the scope of the present invention.
Claims (5)
1. a kind of water power cluster Dynamic Equivalence with generalization ability, which is characterized in that include the following steps：
1) water power cluster dynamic equivalent model is established；
2) metric data being directed under different disturbances carries out equivalence to water power cluster dynamic equivalent parameter, and utilizes particle group optimizing
Algorithm picks out the parameter of Equivalent Model under each disturbance according to response curve；
3) PCA methods pre-process dynamic equivalent model parameter in Statistics Application, reduce parameter dimensions, and formation is established general
Change the initialization data of Equivalent Model；
4) using support vector machines as tool, the feature samples space of dynamic equivalent model parameter is established；
5) multi-cure-fitting parameter identification is carried out to the supporting vector in feature samples space, establishes the dynamic etc. with generalization ability
It is worth model and parameter；
It includes following steps to establish initialization data using PCA methods in the step 3)：
(3-1) is directed to all Equivalent Model parameters, calculates the average value per one-dimensional data；
(3-2) calculates the difference per one-dimensional data with its average value and builds covariance matrix；
(3-3) seeks the eigen vector of covariance matrix；
(3-4) calculate before q maximum eigenvalue contribution rate, the contribution rate for selected characteristic value and with all features
The ratio of the sum of value, is larger than predetermined threshold, determines q values；
The matrix that the corresponding feature vector of preceding q maximum eigenvalue and Equivalent Model parameter are constituted is done product by (3-5), obtains dimensionality reduction
Equivalent Model parameter afterwards.
2. a kind of water power cluster Dynamic Equivalence with generalization ability according to claim 1, which is characterized in that institute
It is to establish equivalent generator model and duty value model to state and establish water power cluster dynamic equivalent model in step 1).
3. a kind of water power cluster Dynamic Equivalence with generalization ability according to claim 1, which is characterized in that institute
It is the active power and reactive capability curve on interconnection to state the metric data described in step 2).
4. a kind of water power cluster Dynamic Equivalence with generalization ability according to claim 1, which is characterized in that institute
Step 4) is stated to establish the feature of dynamic equivalent model parameter using support vector machines and according to the Equivalent Model parameter after dimensionality reduction
Sample space includes the following steps：
(4-1) sets kernel function K (xi, xj) it is Gaussian function, wherein i, j=1,2,3......p, p are the number of sample, i.e.,
The number of Equivalent Model data after dimensionality reduction；xi, xjFor the sample in sample space, some Equivalent Model ginseng as after dimensionality reduction
Number；
(4-2) solves the quadratic programming problem of following formula (1) using SMO algorithms, obtains the optimal solution vector of lagrange multipliers α；
Wherein αi、αjRespectively represent sample point xi、xjLagrange multipliers；
(4-3) takes the α more than 0iCorresponding sample is supporting vector, and is introduced on the spherical surface of minimum sphere.
5. a kind of water power cluster Dynamic Equivalence with generalization ability according to claim 1, which is characterized in that institute
It states step 5) and multi-cure-fitting parameter identification is carried out to supporting vector, establish dynamic equivalent model and ginseng with generalization ability
Number, includes the following steps：
(5-1) finds out the Equivalent Model parameter before corresponding dimensionality reduction according to supporting vector；
(5-2) finds out corresponding dominant eigenvalues response curve according to the Equivalent Model parameter before dimensionality reduction；
(5-3) optimizes equivalent model parameter using multi-cure-fitting parameter identification as tool, using particle swarm optimization algorithm,
It is final to obtain Equivalent Model and parameter with generalization ability.
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