CN111722057A - Clustering-based experimental microgrid load characteristic classification method - Google Patents
Clustering-based experimental microgrid load characteristic classification method Download PDFInfo
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Abstract
The invention belongs to the technical field of micro-grids, and particularly relates to a clustering-based experimental micro-grid load characteristic classification method. The invention comprises the following steps: analyzing the parameter sensitivity; and carrying out cluster analysis on the load model according to the analysis result. Aiming at the problem that load test data acquired by the current micro-grid is lack of integrity, the practical load modeling idea is adopted, load characteristics are considered in clustering, a foundation is laid for establishing a proper load model, the load model with similar characteristics is classified into one class, and the load model with larger characteristic difference is classified into different classes, so that a comprehensive model with common characteristics can be described. Aiming at the problems existing in the current test type micro-grid load characteristics and engineering application, firstly, the sensitivity of the comprehensive load characteristic parameters of the induction motor is analyzed, the load characteristics based on the density gradient clustering method are provided for classifying the load, the clustering process can be rapidly completed, and the method has the advantages of small calculated amount, simple and convenient process, capability of being used for large-scale data classification and the like in the micro-grid.
Description
Technical Field
The invention belongs to the technical field of micro-grids, and particularly relates to a clustering-based experimental micro-grid load characteristic classification method.
Background
In recent years, with the continuous development of micro-grid technology, the loads are diversified, and randomness and dispersity are gradually increased. The correct load characteristics and their classification play a crucial role in the development of micro-grids. According to the original load classification method, in practical application, only single or a plurality of groups of data are analyzed, so that the load characteristic data has unicity and is lack of uniformity. Particularly for a test type microgrid, the modeling improves the accuracy and the reliability of data, so that the calculation result can reflect the characteristics of the load more truly.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a clustering-based experimental microgrid load characteristic classification method. The load classification method aims to solve the problems of singleness and limitation of the existing load classification method.
The technical scheme adopted by the invention for realizing the purpose is as follows:
a clustering-based experimental microgrid load characteristic classification method comprises the following steps:
step 1, analyzing parameter sensitivity;
and 2, carrying out cluster analysis on the load model according to the analysis result.
The parameter sensitivity analysis comprises the following steps:
the load is described by connecting an induction motor of a 3-order electromechanical transient model in parallel with an equivalent load of a static load adopting a power exponent model, and a continuous dynamic model is described by the following state equation:
x(0)＝x0(2)
y(t)＝g(x(t),u(t),θ) (3)
h(x0,u0,θ)＝0 (4)
in the formula (I), the compound is shown in the specification,
is the phasor form of the state variable, x (t) is the state variable, u (t) is the input variable of the system voltage excitation, theta is the input variable with the identification parameter theta (α)TDetermine where α is an independent parameter column vector, α ═ R (R)s,x',T0',n,H)TWherein R issIs stator resistance, x' is equivalent impedance
xmIs mutual inductance between stator and rotor, xrIs rotor self-inductance; t is0' is time constant, n is torque coefficient, H is inertia time constant, β is non-independent parameter list vector, β is (T)L,e'd0,e'q0,s0,xs)T，TLIs torque coefficient, e'd0Is a transient initial potential, e 'on the direct shaft of the induction machine'q0Is a transient initial potential, s, on the quadrature axis of the induction motor0Is the initial slip of the induction motor, xsβ is determined by α and a steady state constraint equation (4), and particularly to the induction motor load, when stator electromagnetic transient is ignored, a per unit value state equation and an output equation of the synchronous coordinate system are respectively expressed by equations (5) and (6);
in the formulae (5) and (6),
representing the derivative, T ', of the transient potential on the direct axis of the induction motor over time T'0Is a time constant, e'dIs transient potential on the direct shaft of the induction machine, e'qThe transient potential on the quadrature axis of the induction motor is represented by e ', and e ═ e'd+je'q；xsIs the self-inductance of the stator, and x' is the equivalent impedance
xmIs mutual inductance between stator and rotor, xrIs rotor self-inductance; i.e. iqsFor the current in the quadrature axis of the stator of the induction motor, idsI is the current on the straight axis of the stator of the induction motor, i is the induction motor current, i is i ═ ids+jiqs(ii) a s is slip of induction motor, omegabIn order to synchronize the angular frequency of the signal,
representing the derivative of the transient potential on the quadrature axis of the induction motor over time t,
representing the derivative of slip of the induction motor with respect to time, H being the inertial time constant, TLIs a torque coefficient, n is a torque coefficient, RsFor the stator resistance, u denotes the system excitation voltage, u ═ uds+juqs，udsFor excitation on a straight axis, uqsExcitation on a quadrature axis;
let equation (5) be zero on the left, and add equation set (6), we can get the steady state equation:
h(x0,u0,yo,α,β)＝0 (7)
in equation (7), h is defined as a steady-state function, and the state variable x ═ e'd,e'q,s)TInput variable u ═ u (u)ds,uqs)TOutput variable y ═ ids,iqs)Tα is an independent parameter column vector, α ═ R (R)s,x',T0',n,H)Tβ is a dependent parameter list vector, β ═ TL,e'd0,e'q0,s0,xs)T；
Let the parameter theta be a typical induction motor parameter, yt(t) is the motor response under system voltage excitation u; if the parameter θ is changed, the motor response under the same excitation is yc(t)；
The response deviation caused by parameter variation is defined as:
in equation (8), J (θ) ═ J (α) is a response deviation function, and y ist(ti) Is the motor response under the action of the system voltage excitation u; if the parameter θ is changed, the motor response under the same excitation is yc(ti) (ii) a To [ y ]c(ti)-yt(ti)]TAnd [ yc(ti)-yt(ti)]Summing the products to obtain a response deviation;
the sensitivity L of the response deviation to the independent parameter alpha is the partial derivative of the response deviation J (theta) to alpha;
in the formula (9),
the individual parameter α is biased in response to the deviation J (theta),
indicating the response deviation J (theta) versus the stator resistance RsThe deviation is calculated and the deviation is calculated,
the response deviation J (theta) is expressed by calculating the partial derivative of the equivalent impedance x',
denotes response deviation J (θ) versus time constant T'0The deviation is calculated and the deviation is calculated,
the response deviation J (theta) is expressed by calculating the partial derivative of the torque coefficient n,
shows that the response deviation J (theta) is obtained by partial derivation of the inertia constant H,
representing motor response y under the same excitation varying the parameter thetac(ti) The independent parameters α are subjected to partial derivation and transposed on the basis thereof, yt(ti) Is the motor response under the action of the system voltage excitation u;
obtaining sensitivity L of the response deviation to the independent parameter of the motor according to the formulas (7) to (9); the sensitivity represents the response change caused by unit change of a parameter, namely the sensitivity of the response to the parameter change is reflected;
with independent parameter Δ αi(ΔRs,Δx',ΔT'0Δ n, Δ H) is the abscissa, sensitivity LiA function curve of the sensitivity is drawn in a mode that the excitation u is decreased in step and then recovered and each independent parameter is changed independently as a vertical coordinate;
sensitivity of the probe
And
large variation and sensitivity
And
is relatively small, i.e. response to the single-pairVertical parameter RsX 'and T'0Is more sensitive, and is slightly less sensitive to n and H;
the calculation shows that:
the sensitivity difference of each parameter is large, and the sensitivity of each parameter tends to increase along with the enhancement of excitation;
the sensitivity of the parameters is high, namely, the model response is sensitive to the values of the parameters; the parameters and the sensitivity are low, namely the sensitivity of the model response to the parameters is low, and in the parameter identification process, if the contribution caused by the change of a certain parameter cannot be seen in the model response due to the undersized parameter sensitivity, the identified result error is relatively large; on the contrary, if the model response can be sensitively affected by the contribution of the change of a certain parameter, the identified result is more accurate.
The cluster analysis of the load model comprises the following steps:
a. taking the actually measured response space as a characteristic quantity, and taking the Euclidean distance as a measurement in point density calculation;
b. calculating density distribution;
c. acquiring a clustering center;
d. and dividing boundary points, calculating threshold values among various classes and combining the threshold values.
The measured response space is used as a characteristic quantity, Euclidean distance is used as a measurement value in point density calculation, a sample close to standard disturbance intensity (15%) is selected from a sample set, a data point with the maximum amplitude and the minimum power is searched in the transient process of the sample, the data point with the maximum amplitude in the transient process of other samples is equal to the data point with the maximum amplitude in the transient process of other samples, the amplitudes of the two are calculated, namely the ratio of the difference between the initial power steady-state value and the transient minimum value is used as a proportional coefficient, and the amplitudes of other transient data points are expanded and contracted according to the proportional coefficient.
The calculating the density distribution includes:
let N be the data length of its transient process, then the two active sequences with the standard transient process time length are Pt(1)、Pt(2)、...、Pt(k)、...、Pi(N) and Pj(1)、Pj(2)、...、Pj(k)、...、PjThe distance between (N) is calculated by the formula:
in formula (10), Pi(k) And Pj(k) Respectively representing two active sequences in the transient process, and carrying out subtraction operation and square operation on the active sequences and then summing the active sequences to obtain dpi-jFor the distance between the two active response sequences, the distance dq between the reactive response sequencesi-jSimilar to formula (10);
the equation (10) reflects the distance between two active sequences, i.e. the similarity, and the distance between the reactive response sequences is recorded as dpi-jIs similar to formula (10);
dsi-jfor the comprehensive distance comprehensively reflecting the integral correlation of active power and reactive power, the calculation formula is as follows:
dsi-j＝(k1dpi-j+k2dqi-j)/(k1+k2) (11)
in the formulas (11) and (12), dsi-jIntegral distance, dp, representing the integral dependence of active and inactivei-jRepresenting the distance between two active response sequences, Pi(1) Is the initial value of i active sequence, Pj(1) Is the initial value of the active sequence of j, Qi(1) Is the initial value of i Wugong sequence, Qj(1) For the initial value of the reactive sequence of j, Abs () represents the function of the absolute value, k1,k2Representing a weight coefficient;
the point density of the sample i is the average distance, which is marked as D (i, n), and reflects the distance of the neighboring sample, and the calculation formula is:
D(i,n)＝∑dsi-j/n (13)
in the formula (13), D (i, n) represents the average distance, ds, of the samples i among the n samplesi-jIs shown asThe combined distance of the overall correlation of work and reactive power.
The obtained clustering center is obtained by comparing the densities of all sample points, for a certain unclassified sample point O, a sample point P with a higher density is selected from n adjacent points, the densities of the sample point P and the sample point P are compared, and if the density of the point P is less than that of the point O, the point O is used as a new-type clustering center; if the density of the P points is greater than that of the O points and the P is classified, classifying the O into the classification; if the P is not classified, the P point is used as a clustering center, and the process is carried out until all the points are classified.
The dividing of the boundary points, the calculation of the threshold values among all classes and the combination of the threshold values, comprises the following steps:
most points in the n adjacent points of the boundary point belong to which clustering center, namely, the point belongs to the category of the clustering center; if the quantity of the two sides is the same, classifying according to the distance;
when the number of clusters is large, merging the classes; setting two clusters as C1 and C2 respectively, wherein functions of the merging degrees of the two clusters are H (C1 and C2), confirming whether the two clusters are merged preferentially or not by utilizing the number of boundary points contained in each cluster and the threshold value of the number of common boundary points in the two clusters, wherein C1 and C2 represent the number of the boundary points contained in the clusters C1 and C2 respectively, and C is the number of the common boundary points of the two clusters; obtaining the minimum function value to be merged preferentially by the two classes, and when the number required by clustering is met or a common boundary value does not exist any more, the merging is terminated, namely the number of each class and the number of samples thereof can be determined, wherein the specific formula is as follows:
in the formula (14), H (C1, C2) represents the merging degree of clusters C1 and C2, C1 and C2 represent the number of boundary points contained in the clusters C1 and C2 respectively, C is the number of common boundary points of the two clusters, and log is logarithmic operation;
the load characteristics are clustered through the process, namely loads with approximate or similar load characteristics are classified into one class, and the same load model is used for describing the load characteristics of one class.
The cluster analysis of the load model specifically comprises the following steps:
preprocessing each sample data such as data smoothing, data expansion and contraction;
secondly, calculating the distance between every two samples to obtain the point density;
obtaining a clustering center and points belonging to the class in the field through comparison of point density in the field;
and adjusting boundary points and merging classes.
The clustering center can be used as an equivalent sample of the same-class load characteristic, and single-sample parameter identification is carried out on the clustering center, so that the model parameter of the same-class load characteristic can be obtained.
A computer storage medium having a computer program stored thereon, the computer program when executed by a processor implementing the steps of a cluster-based triage method for load characteristics of a microgrid.
The invention has the following beneficial effects and advantages:
aiming at the problem that load test data acquired by the current micro-grid is lack of integrity, the practical load modeling idea is adopted, load characteristics are considered in clustering, a foundation is laid for establishing a proper load model, the load model with similar characteristics is classified into one class, and the load model with larger characteristic difference is classified into different classes, so that a comprehensive model with common characteristics can be described.
Aiming at the problems of the current test type microgrid load characteristic and engineering application, the method firstly analyzes the sensitivity of the comprehensive load characteristic parameter of the induction motor, provides the load characteristic based on the density gradient clustering method to classify the load, can quickly finish the clustering process, and has the advantages of small calculated amount, simple and convenient process, capability of being used for large-scale data classification and the like in the microgrid.
Drawings
In order to facilitate the understanding and implementation of the present invention for those of ordinary skill in the art, the following detailed description is provided in conjunction with the accompanying drawings, but it should be understood that the scope of the present invention is not limited by the accompanying drawings.
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a voltage excitation diagram according to the present invention;
FIG. 3 is an active response diagram of a clustering center of the present invention;
FIG. 4 is a reactive response plot of a clustering center of the present invention;
FIG. 5 is a graph of an active fit of sample 19 of the present invention;
FIG. 6 is a reactive fit plot of sample 19 of the present invention;
FIG. 7 is a graph of sensitivity function (R) in the present inventionsVariation) of the graph;
FIG. 8 is a graph of the sensitivity function (x' change) of the present invention;
FIG. 9 is a sensitivity function curve (T 'in the present invention'0Variation) of the graph;
FIG. 10 is a graph of the sensitivity function (n change) of the present invention;
FIG. 11 is a graph of the sensitivity function (Hvariation) of the present invention;
FIG. 12 shows different excitation intensities in the present invention
Graph of the sensitivity function.
Detailed Description
The technical solution in the embodiment of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiment of the present invention. It is to be understood that the described embodiments are merely exemplary of the invention, and not restrictive of the full scope of the invention. Other embodiments, which can be derived by one of ordinary skill in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
The invention relates to a clustering-based experimental microgrid load characteristic classification method, which adopts a practical load modeling idea, analyzes the clustering process of load characteristics on the basis of analyzing the sensitivity of each parameter of an induction motor comprehensive model and establishes a proper load model so as to classify each type of load, and specifically comprises the following steps:
step 1, parameter sensitivity analysis.
The most important load in the motor type electric power system load is a dynamic load, so that the load is described by connecting an induction motor of a 3-order electromechanical transient model in parallel with an equivalent load of a static load adopting a power exponent model. In general, a continuous dynamic model can be described by the following equation of state:
x(0)＝x0(2)
y(t)＝g(x(t),u(t),θ) (3)
h(x0,u0,θ)＝0 (4)
wherein x (t) is the phasor form of the state variable, x (t) is the state variable, u (t) is the input variable for system voltage excitation, and theta is the band identification parameter represented by theta (α)TDetermine where α is an independent parameter column vector, α ═ R (R)s,x',T0',n,H)TWherein R issIs stator resistance, x' is equivalent impedance
xmIs mutual inductance between stator and rotor, xrIs rotor self-inductance; t is0' is time constant, n is torque coefficient, H is inertia time constant, β is non-independent parameter list vector, β is (T)L,e'd0,e'q0,s0,xs)T，TLIs torque coefficient, e'd0Is a transient initial potential, e 'on the direct shaft of the induction machine'q0Is a transient initial potential, s, on the quadrature axis of the induction motor0Is the initial slip of the induction motor, xsβ can be determined by α and a steady state constraint equation (4). in particular, in the case of an induction motor load, ignoring stator electromagnetic transients, the per-unit value state equation and the output equation of the synchronous coordinate system are represented by equations (5) and (6), respectively.
In the formulae (5) and (6),
representing the derivative, T ', of the transient potential on the direct axis of the induction motor over time T'0Is a time constant, e'dIs transient potential on the direct shaft of the induction machine, e'qThe transient potential on the quadrature axis of the induction motor is represented by e ', and e ═ e'd+je'q；xsIs the self-inductance of the stator, and x' is the equivalent impedance
xmIs mutual inductance between stator and rotor, xrIs rotor self-inductance; i.e. iqsFor the current in the quadrature axis of the stator of the induction motor, idsI is the current on the straight axis of the stator of the induction motor, i is the induction motor current, i is i ═ ids+jiqs(ii) a s is slip of induction motor, omegabIn order to synchronize the angular frequency of the signal,
representing the derivative of the transient potential on the quadrature axis of the induction motor over time t,
representing the derivative of slip of the induction motor with respect to time, H being the inertial time constant, TLIs the torque coefficient and n is the torque coefficient. RsFor the stator resistance, u denotes the system excitation voltage, u ═ uds+juqs，udsFor excitation on a straight axis, uqsIs the excitation on the quadrature axis.
Let equation (5) be zero on the left, and add equation set (6), we can get the steady state equation:
h(x0,u0,yo,α,β)＝0 (7)
in equation (7), h is defined as a steady-state function, and the state variable x ═ e'd,e'q,s)TInput variable u ═ u (u)ds,uqs)TOutput variable y ═ ids,iqs)Tα is an independent parameter column vector, α ═ R (R)s,x',T0',n,H)Tβ is a dependent parameter list vector, β ═ TL,e'd0,e'q0,s0,xs)T。
Let the parameter θ be a typical induction motor parameter, and define the response deviation caused by parameter variation as:
in equation (8), J (θ) ═ J (α) is a response deviation function, and y ist(ti) Is the motor response under the influence of the system voltage excitation u. If the parameter θ is changed, the motor response under the same excitation is yc(ti). To [ y ]c(ti)-yt(ti)]TAnd [ yc(ti)-yt(ti)]The products of which are summed to obtain the response deviation.
The sensitivity L of the response deviation to the independent parameter α is the partial derivative of the response deviation J (θ) to α:
in the formula (9), the reaction mixture is,
the individual parameter α is biased in response to the deviation J (theta),
indicating the response deviation J (theta) versus the stator resistance RsThe deviation is calculated and the deviation is calculated,
the response deviation J (theta) is expressed by calculating the partial derivative of the equivalent impedance x',
denotes response deviation J (θ) versus time constant T'0The deviation is calculated and the deviation is calculated,
the response deviation J (theta) is expressed by calculating the partial derivative of the torque coefficient n,
shows that the response deviation J (theta) is obtained by partial derivation of the inertia constant H,
representing motor response y under the same excitation varying the parameter thetac(ti) The independent parameters α are subjected to partial derivation and transposed on the basis thereof, yt(ti) Is the motor response under the influence of the system voltage excitation u.
From the above equations (7) to (9), the sensitivity L of the response deviation to the motor independent parameter can be obtained. Sensitivity represents the change in response caused by a unit change in a parameter, i.e., reflects the degree to which the response is sensitive to the change in the parameter.
In order to more fully understand the sensitive parameters, the independent parameter Δ α is plottedi(ΔRs,Δx',ΔT'0Δ n, Δ H) is the abscissa, sensitivity LiSensitivity function curve as ordinate fig. 7 to 11 are each an independent parameter Δ αi(ΔRs,Δx',ΔT'0Δ n, Δ H) alone, i.e., when other parameters are kept constant at typical values, as shown in fig. 7 to 11, in which fig. 7 is a sensitivity function curve (R) in the present inventionsVariation) of the graph; FIG. 8 is a graph of the sensitivity function (x' change) of the present invention; FIG. 9 is a sensitivity function curve (T 'in the present invention'0Variation) of the graph; FIG. 10 is a graph of the sensitivity function (n change) of the present invention; FIG. 11 is a sensitivity function of the present inventionGraph of curve (H variation).
As can be seen, sensitivity
And
large variation and sensitivity
And
is relatively small, in other words in response to the independent parameter RsX 'and T'0More sensitive and slightly less sensitive to n and H.
To determine the influence of the excitation magnitude on the sensitivity of the motor parameters, sensitivity function curves for a plurality of different excitation magnitudes are plotted on one coordinate axis as a step-down and then recovery of the excitation u, as an independent parameter T'0Sensitivity to change
The curves of (A) are examples, and 10%, 30%, 50%, and 70% respectively represent excitation intensities of 10% U0、30％U0、50％U0And 70% U0In a sensitivity function curve of (1), wherein U0The initial value of the steady-state voltage is shown in FIG. 12, and FIG. 12 shows the values of the excitation intensities of the present invention
Graph of the sensitivity function.
The calculation shows that:
the sensitivity difference of each parameter is large, and the sensitivity of each parameter tends to increase along with the enhancement of excitation;
the sensitivity of the parameters is high, namely, the model response is sensitive to the values of the parameters; the parameters and the sensitivity are low, namely the sensitivity of the model response to the parameters is low, and in the parameter identification process, if the contribution caused by the change of a certain parameter cannot be seen in the model response due to the undersized parameter sensitivity, the identified result error is relatively large; on the contrary, if the model response can be sensitively affected by the contribution of the change of a certain parameter, the identified result is more accurate.
And 2, carrying out cluster analysis on the load model according to the analysis result.
a. The measured response space is taken as a feature quantity, and the Euclidean distance is taken as a measurement in the point density calculation. Considering that the accuracy of the result is affected by the difference of the disturbance time length, the load data is preprocessed in the data preparation stage. Specifically, a sample close to the standard disturbance intensity (15%) is selected in the sample set, the data point with the maximum amplitude (the minimum power) is searched in the transient process of the sample set, the data point with the maximum amplitude in the transient process of other samples is equal to the data point with the minimum amplitude in the transient process of other samples, the ratio of the amplitudes of the two samples (namely the difference between the initial power steady-state value and the transient minimum value) is calculated to be respectively a proportionality coefficient, and the amplitudes of other transient data points are expanded and contracted according to the proportionality coefficient.
b. The density distribution is calculated.
Let N be the data length of its transient process, then the two active sequences with the standard transient process time length are Pi(1)、Pi(2)、...、Pi(k)、...、Pi(N) and Pj(1)、Pj(2)、...、Pj(k)、...、PjThe distance between (N) is calculated by the formula:
in the formula (10), Pi(k) And Pj(k) Respectively representing two active sequences in the transient process, and carrying out subtraction operation and square operation on the active sequences and then summing the active sequences to obtain dpi-jThe distance between the two active response sequences. Distance between reactive response sequences dqi-jSimilar to formula (10).
dsi-jThe calculation formula of (2) is as follows:
dsi-j＝(k1dpi-j+k2dqi-j)/(k1+k2) (11)
in the formulas (11) and (12), dsi-jIntegral distance, dp, representing the integral dependence of active and inactivei-jRepresenting the distance between two active response sequences, Pi(1) Is the initial value of i active sequence, Pj(1) Is the initial value of the active sequence of j, Qi(1) Is the initial value of i Wugong sequence, Qj(1) For the initial value of the reactive sequence of j, Abs () represents the function of the absolute value, k1,k2Representing the weight coefficients.
The point density of the sample i is the average distance, which is marked as D (i, n), and reflects the distance of the neighboring sample, and the calculation formula is:
D(i,n)＝∑dsi-j/n (13)
in the formula (13), D (i, n) represents the average distance of the sample i among the n samples, dsi-jThe composite distance representing the overall dependence of active and reactive.
c. And acquiring a clustering center.
Obtaining a clustering center by comparing the densities of all sample points, selecting a sample point P with a higher density from n adjacent points of a certain unclassified sample point O, comparing the densities of the sample point P and the sample point P, and taking the point O as a new-class clustering center if the density of the point P is less than that of the point O; and if the density of the P points is greater than that of the O points and the P points are classified, classifying the O points into the class, and if the P points are not classified, taking the P points as a clustering center. The above process is carried out until all points are classified.
d. And dividing boundary points, calculating threshold values among various classes and combining the threshold values.
Most points in the n adjacent points of the boundary point belong to which clustering center, namely, the point belongs to the category of the clustering center; if the quantity of the two sides is the same, the classification is carried out according to the distance.
However, when the number of clusters is large, class-to-class merging is required. Let two clusters be C1 and C2 respectively, the function of the merging degree is H (C1 and C2), and the threshold value of the number of boundary points contained in each cluster and the number of common boundary points in the two clusters is used to determine whether the two clusters are merged preferentially, C1 and C2 represent the number of boundary points contained in the clusters C1 and C2 respectively, and C is the number of common boundary points in the two clusters. Obtaining the minimum function value to be merged preferentially by the two classes, and when the number required by clustering is met or a common boundary value does not exist any more, the merging is terminated, namely the number of each class and the number of samples thereof can be determined, wherein the specific formula is as follows:
in the formula (14), H (C1, C2) represents the merging degree of the clusters C1, C2, C1, C2 represent the number of boundary points included in the clusters C1, C2, respectively, C is the number of boundary points common to both clusters, and log is a logarithm operation.
The clustering of the load characteristics is realized through the process, namely loads with close or similar load characteristics are classified into one class, and the same load model can be used for describing the load characteristics of one class.
Example 2
The cluster analysis of the load model specifically comprises the following steps:
preprocessing each sample data such as data smoothing, data expansion and contraction;
secondly, calculating the distance between every two samples to obtain the point density;
thirdly, obtaining a clustering center and points belonging to the class in the field through comparison of point density in the field;
and adjusting boundary points and merging classes.
The clustering of the load characteristics is realized through the process, namely loads with close or similar load characteristics can be classified into one class, and the same load model can be used for describing the load characteristics of one class.
Taking 20 load characteristic data of a certain Liaoning substation as an example, the load characteristic cluster is analyzed by adopting a density gradient-based clustering method, as shown in tables 1 and 2.
Since 20 load characteristic samples were classified into 4 types, n was taken as 3, and the classification results are shown in table 2. The method 1 is a clustering method based on density gradient, and the method 2 is a systematic clustering method using correlation coefficient as classification standard.
According to theoretical knowledge, the clustering center can be used as an equivalent sample of the same-class load characteristic, so that the model parameter of the same-class load characteristic can be obtained only by carrying out single-sample parameter identification on the clustering center.
Taking the second class of load characteristics, the class sample 14 is the cluster center, and the sample curve is shown in fig. 2-4.
Sensitivity analysis and parameter identification are carried out on equivalent loads of the induction motor parallel static load adopting the 3-order electromechanical transient model, and the equivalent model parameters of the 2 nd class load characteristics are obtained and are shown in table 3.
According to fitting error formula
The error between each model response and the corresponding actual measurement is calculated and compared with the fitting error obtained by the direct synthesis method of the actual measurement response space, as shown in table 4.
The calculation shows that the average error (0.992) of I is smaller than the average error (1.072) of II, so that the fitting effect of I is good. Fig. 5 and 6 represent the active and reactive fit curves of the equivalent model to samples 19 in class 2. It can be seen from the figure that the load characteristic equivalent model obtained after the sensitivity analysis and the parameter identification can be fitted to the measured sample without large deviation, and the method is proved to be a feasible load characteristic classification method.
Example 3
Based on the same inventive concept, an embodiment of the present invention further provides a computer storage medium, where a computer program is stored on the computer storage medium, and when the computer program is executed by a processor, the computer program implements the steps of the clustering-based classification method for load characteristics of a micro-grid test according to embodiment 1 or 2.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application 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 application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. 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.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.
TABLE 1 Transformer substation load disturbance situation
| Sample number | Time of acquisition | Disturbance magnitude Δ u/(%) |
| 1 | 2015-08-11T16:24:34 | 2.7 |
| 2 | 2015-08-21T16:43:45 | 6.7 |
| 3 | 2015-08-21T16:58:32 | 6.7 |
| 4 | 2015-08-21T17:34:21 | 6.7 |
| 5 | 2015-09-01T15:34:23 | 4.4 |
| 6 | 2015-09-12T20:12:47 | 11.2 |
| 7 | 2015-10-12T13:23:56 | 19.3 |
| 8 | 2015-12-03T18:56:34 | 3.78 |
| 9 | 2016-04-01T09:23:45 | 9.1 |
| 10 | 2016-12-25T10:15:34 | 14.2 |
| 11 | 2016-12-25T09:13:47 | 16.3 |
| 12 | 2016-12-28T19:53:25 | 10.6 |
| 13 | 2017-01-11T07:23:49 | 12.2 |
| 14 | 2017-03-01T17:43:55 | 12.6 |
| 15 | 2017-03-01T21:23:45 | 15.5 |
| 16 | 2017-03-02T03:00:45 | 14.5 |
| 17 | 2017-03-09T16:22:38 | 2.2 |
| 18 | 2017-03-11T15:47:18 | 11.7 |
| 19 | 2017-03-14T10:23:39 | 5.3 |
| 20 | 2017-03-14T11:29:59 | 7.2 |
TABLE 2 clustering result comparison
TABLE 3 identification results
| G | B | rs | X' | T0' | n | Tj | a |
| -0.522 | 1.397 | 0.150 | 0/409 | 0.076 | 0.137 | 0.734 | 9.412 |
TABLE 4 comparison of fitting errors
| Sample number | 7 | 8 | 11 | 13 | 16 | 19 |
| Ⅰ | 1.407 | 1.321 | 1.694 | 0.338 | 0.896 | 0.298 |
| Ⅱ | 1.639 | 1.536 | 1.204 | 0.923 | 0.220 | 0.912 |
Claims (10)
1. A clustering-based experimental microgrid load characteristic classification method is characterized by comprising the following steps: the method comprises the following steps:
step 1, analyzing parameter sensitivity;
and 2, carrying out cluster analysis on the load model according to the analysis result.
2. The method according to claim 1, wherein the method comprises the following steps: the parameter sensitivity analysis comprises the following steps:
the load is described by connecting an induction motor of a 3-order electromechanical transient model in parallel with an equivalent load of a static load adopting a power exponent model, and a continuous dynamic model is described by the following state equation:
x(0)＝x0(2)
y(t)＝g(x(t),u(t),θ)(3)
h(x0,u0,θ)＝0 (4)
in the formula (I), the compound is shown in the specification,
is the phasor form of the state variable, x (t) is the state variable, u (t) is the input variable of the system voltage excitation, theta is the input variable with the identification parameter theta (α)TDetermine where α is an independent parameter column vector, α ═ R (R)s,x',T0',n,H)TWherein R issIs stator resistance, x' is equivalent impedance
xmIs mutual inductance between stator and rotor, xrIs rotor self-inductance; t is0' is time constant, n is torque coefficient, H is inertia time constant, β is non-independent parameter list vector, β is (T)L,e'd0,e'q0,s0,xs)T，TLIs torque coefficient, e'd0Is a transient initial potential, e 'on the direct shaft of the induction machine'q0Is a transient initial potential, s, on the quadrature axis of the induction motor0Is the initial slip of the induction motor, xsβ is determined by α and a steady state constraint equation (4), and particularly to the induction motor load, when stator electromagnetic transient is ignored, a per unit value state equation and an output equation of the synchronous coordinate system are respectively expressed by equations (5) and (6);
in the formulae (5) and (6),
representing the derivative of the transient potential on the direct axis of the induction motor with respect to time T, T0'is a time constant, e'dIs transient potential on the direct shaft of the induction machine, e'qThe transient potential on the quadrature axis of the induction motor is represented by e ', and e ═ e'd+je'q；xsIs the self-inductance of the stator, and x' is the equivalent impedance
xmIs mutual inductance between stator and rotor, xrIs rotor self-inductance; i.e. iqsFor the current in the quadrature axis of the stator of the induction motor, idsI is the current on the straight axis of the stator of the induction motor, i is the induction motor current, i is i ═ ids+jiqs(ii) a s is slip of induction motor, omegabIn order to synchronize the angular frequency of the signal,
representing the derivative of the transient potential on the quadrature axis of the induction motor over time t,
representing the derivative of slip of the induction motor with respect to time, H being the inertial time constant, TLIs a torque coefficient, n is a torque coefficient, RsFor the stator resistance, u denotes the system excitation voltage, u ═ uds+juqs，udsFor excitation on a straight axis, uqsExcitation on a quadrature axis;
let equation (5) be zero on the left, and add equation set (6), we can get the steady state equation:
h(x0,u0,yo,α,β)＝0 (7)
in formula (7), is definedh is a steady state function, and the state variable x is (e'd,e'q,s)TInput variable u ═ u (u)ds,uqs)TOutput variable y ═ ids,iqs)Tα is an independent parameter column vector, α ═ R (R)s,x',T0',n,H)Tβ is a dependent parameter list vector, β ═ TL,e'd0,e'q0,s0,xs)T；
Let the parameter theta be a typical induction motor parameter, yt(t) is the motor response under system voltage excitation u; if the parameter θ is changed, the motor response under the same excitation is yc(t)；
The response deviation caused by parameter variation is defined as:
in equation (8), J (θ) ═ J (α) is a response deviation function, and y ist(ti) Is the motor response under the action of the system voltage excitation u; if the parameter θ is changed, the motor response under the same excitation is yc(ti) (ii) a To [ y ]c(ti)-yt(ti)]TAnd [ yc(ti)-yt(ti)]Summing the products to obtain a response deviation;
the sensitivity L of the response deviation to the independent parameter alpha is the partial derivative of the response deviation J (theta) to alpha;
in the formula (9),
the individual parameter α is biased in response to the deviation J (theta),
indicating the response deviation J (theta) versus the stator resistance RsThe deviation is calculated and the deviation is calculated,
the response deviation J (theta) is expressed by calculating the partial derivative of the equivalent impedance x',
denotes response deviation J (θ) versus time constant T'0The deviation is calculated and the deviation is calculated,
the response deviation J (theta) is expressed by calculating the partial derivative of the torque coefficient n,
shows that the response deviation J (theta) is obtained by partial derivation of the inertia constant H,
representing motor response y under the same excitation varying the parameter thetac(ti) The independent parameters α are subjected to partial derivation and transposed on the basis thereof, yt(ti) Is the motor response under the action of the system voltage excitation u;
obtaining sensitivity L of the response deviation to the independent parameter of the motor according to the formulas (7) to (9); the sensitivity represents the response change caused by unit change of a parameter, namely the sensitivity of the response to the parameter change is reflected;
with independent parameter Δ αi(ΔRs,Δx',ΔT'0Δ n, Δ H) is the abscissa, sensitivity LiA function curve of the sensitivity is drawn in a mode that the excitation u is decreased in step and then recovered and each independent parameter is changed independently as a vertical coordinate;
sensitivity of the probe
And
large variation and sensitivity
And
is relatively small, i.e. in response to the independent parameter RsX 'and T'0Is more sensitive, and is slightly less sensitive to n and H;
the calculation shows that:
the sensitivity difference of each parameter is large, and the sensitivity of each parameter tends to increase along with the enhancement of excitation;
the sensitivity of the parameters is high, namely, the model response is sensitive to the values of the parameters; the parameters and the sensitivity are low, namely the sensitivity of the model response to the parameters is low, and in the parameter identification process, if the contribution caused by the change of a certain parameter cannot be seen in the model response due to the undersized parameter sensitivity, the identified result error is relatively large; on the contrary, if the model response can be sensitively affected by the contribution of the change of a certain parameter, the identified result is more accurate.
3. The method according to claim 1, wherein the method comprises the following steps: the cluster analysis of the load model comprises the following steps:
a. taking the actually measured response space as a characteristic quantity, and taking the Euclidean distance as a measurement in point density calculation;
b. calculating density distribution;
c. acquiring a clustering center;
d. and dividing boundary points, calculating threshold values among various classes and combining the threshold values.
4. The method according to claim 3, wherein the method comprises the following steps: the measured response space is used as a characteristic quantity, Euclidean distance is used as a measurement value in point density calculation, a sample close to standard disturbance intensity (15%) is selected from a sample set, a data point with the maximum amplitude and the minimum power is searched in the transient process of the sample, the data point with the maximum amplitude in the transient process of other samples is equal to the data point with the maximum amplitude in the transient process of other samples, the amplitudes of the two are calculated, namely the ratio of the difference between the initial power steady-state value and the transient minimum value is used as a proportional coefficient, and the amplitudes of other transient data points are expanded and contracted according to the proportional coefficient.
5. The method according to claim 3, wherein the method comprises the following steps: the calculating the density distribution includes:
let N be the data length of its transient process, then the two active sequences with the standard transient process time length are Pt(1)、Pt(2)、...、Pt(k)、...、Pi(N) and Pj(1)、Pj(2)、...、Pj(k)、...、PjThe distance between (N) is calculated by the formula:
in formula (10), Pi(k) And Pj(k) Respectively representing two active sequences in the transient process, and carrying out subtraction operation and square operation on the active sequences and then summing the active sequences to obtain dpi-jFor the distance between the two active response sequences, the distance dq between the reactive response sequencesi-jSimilar to formula (10);
the equation (10) reflects the distance between two active sequences, i.e. the similarity, and the distance between the reactive response sequences is recorded as dpi-jIs similar to formula (10);
dsi-jfor the comprehensive distance comprehensively reflecting the integral correlation of active power and reactive power, the calculation formula is as follows:
dsi-j＝(k1dpi-j+k2dqi-j)/(k1+k2) (11)
in the formulas (11) and (12), dsi-jIntegral distance, dp, representing the integral dependence of active and inactivei-jRepresenting the distance between two active response sequences, Pi(1) Is the initial value of i active sequence, Pj(1) Is the initial value of the active sequence of j, Qi(1) Is the initial value of i Wugong sequence, Qj(1) For the initial value of the reactive sequence of j, Abs () represents the function of the absolute value, k1,k2Representing a weight coefficient;
the point density of the sample i is the average distance, which is marked as D (i, n), and reflects the distance of the neighboring sample, and the calculation formula is:
D(i,n)＝∑dsi-j/n (13)
in the formula (13), D (i, n) represents the average distance, ds, of the samples i among the n samplesi-jThe composite distance representing the overall dependence of active and reactive.
6. The method according to claim 3, wherein the method comprises the following steps: the obtained clustering center is obtained by comparing the densities of all sample points, for a certain unclassified sample point O, a sample point P with a higher density is selected from n adjacent points, the densities of the sample point P and the sample point P are compared, and if the density of the point P is less than that of the point O, the point O is used as a new-type clustering center; if the density of the P points is greater than that of the O points and the P is classified, classifying the O into the classification; if the P is not classified, the P point is used as a clustering center, and the process is carried out until all the points are classified.
7. The method according to claim 3, wherein the method comprises the following steps: the dividing of the boundary points, the calculation of the threshold values among all classes and the combination of the threshold values, comprises the following steps:
most points in the n adjacent points of the boundary point belong to which clustering center, namely, the point belongs to the category of the clustering center; if the quantity of the two sides is the same, classifying according to the distance;
when the number of clusters is large, merging the classes; setting two clusters as C1 and C2 respectively, wherein functions of the merging degrees of the two clusters are H (C1 and C2), confirming whether the two clusters are merged preferentially or not by utilizing the number of boundary points contained in each cluster and the threshold value of the number of common boundary points in the two clusters, wherein C1 and C2 represent the number of the boundary points contained in the clusters C1 and C2 respectively, and C is the number of the common boundary points of the two clusters; obtaining the minimum function value to be merged preferentially by the two classes, and when the number required by clustering is met or a common boundary value does not exist any more, the merging is terminated, namely the number of each class and the number of samples thereof can be determined, wherein the specific formula is as follows:
in the formula (14), H (C1, C2) represents the merging degree of clusters C1 and C2, C1 and C2 represent the number of boundary points contained in the clusters C1 and C2 respectively, C is the number of common boundary points of the two clusters, and log is logarithmic operation;
the load characteristics are clustered through the process, namely loads with approximate or similar load characteristics are classified into one class, and the same load model is used for describing the load characteristics of one class.
8. The method according to claim 1, wherein the method comprises the following steps: the cluster analysis of the load model specifically comprises the following steps:
preprocessing each sample data such as data smoothing, data expansion and contraction;
secondly, calculating the distance between every two samples to obtain the point density;
obtaining a clustering center and points belonging to the class in the field through comparison of point density in the field;
and adjusting boundary points and merging classes.
9. The method according to claim 1, wherein the method comprises the following steps: the clustering center can be used as an equivalent sample of the same-class load characteristic, and single-sample parameter identification is carried out on the clustering center, so that the model parameter of the same-class load characteristic can be obtained.
10. The computer storage medium of claim 1, wherein: the computer storage medium has stored thereon a computer program that, when executed by a processor, performs the steps of a clustering-based test microgrid load characteristic classification method of claims 1 to 9.
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