CN109408849B - Wind power plant dynamic equivalence method based on coherent unit grouping - Google Patents
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Abstract
The invention discloses a dynamic equivalence method for a wind power plant based on coherent unit grouping. The method comprises the following steps: modeling the environmental wind speed distribution; establishing a wake effect model according to mutual interference of input wind speeds when the units are irregularly arranged; aiming at the unit under irregular arrangement, analyzing the influence of dynamic characteristics caused by unequal lengths of connecting cables; solving a characteristic equation of an electromagnetic system of the doubly-fed wind generator, analyzing a dominant mode of the equation, and judging a coherence basis; taking the characteristic quantity obtained by the homomorphism judgment as a grouping basis of the wind turbine generators, and performing homomorphism grouping on the wind turbine generators in the farm by adopting a hierarchical clustering algorithm; and based on the grouping result, a capacity weighting method is adopted to complete the calculation of the system equivalent unit parameters. The method solves the problems of wake effect caused by irregular arrangement of units in the wind power plant under the influence of complex terrain and low equivalent model precision caused by current collection line impedance, reduces power errors of steady-state and dynamic simulation, and is suitable for establishing the equivalent model of the wind power plant.
Description
Technical Field
The invention belongs to the technical field of wind power plant modeling, and particularly relates to a dynamic equivalence method for a wind power plant based on coherent unit clustering.
Background
At present, wind power generation in the world has a large-scale development trend. With the large-scale development and the improvement of the localization rate, the MW-class wind power generation units are generally popularized and used in the industry, large wind power plants composed of dozens or even hundreds of units are increasing, the internal structures of the wind power plants are very complex, and how to reasonably and efficiently perform modeling analysis calculation on the wind power plants becomes an important subject.
For a large wind power plant, when people study the grid-connected characteristic, more attention is paid to the output characteristic of the large wind power plant as a whole rather than the specific situation of each unit, and if a detailed model for modeling each unit is adopted, the calculated amount is increased, and even dimension disaster is difficult to converge. In the process of analysis modeling, a proper wind power plant equivalent method is searched for carrying out reduced order aggregation on the large-scale wind power plant. When equivalent modeling is carried out on the wind power plant, the difference of the factors of the terrain space inside the wind power plant causes the difference of the wind speed among the wind power plants of the same type. Due to changes of wind speed and topological structures of current collection networks in the large-scale wind power plant caused by wake effects, landforms and the like, certain differences exist among the dynamic characteristics of all units in the large-scale wind power plant. The traditional wind power plant equivalence method does not consider the influence of terrain factors, and has the following problems: and the wake effect caused by the irregular arrangement of the units in the field under the influence of the complex terrain and the accuracy reduction of the equivalent model caused by the impedance of the current collecting line.
Disclosure of Invention
The invention aims to provide a dynamic equivalence method for a wind power plant based on coherent unit clustering, which is suitable for complex terrain.
The technical solution for realizing the purpose of the invention is as follows: a dynamic equivalence method for a wind power plant based on coherent unit grouping comprises the following steps:
step 4, solving a characteristic equation of the electromagnetic system of the doubly-fed wind generator, analyzing a dominant mode of the equation, and judging a homodyne basis;
and 6, based on the grouping result, calculating the system equivalent unit parameters by adopting a capacity weighting method.
Further, step 1, modeling the ambient wind speed distribution specifically includes:
the wind speed statistical law is close to Weibull distribution, and the statistical probability density function f (v) and the distribution function F (v) of the wind speed v are as follows:
wherein v is the wind speed, k is the shape parameter, and c is the scale parameter;
the wind speed change model is established according to the terrain as follows:
where v is the wind speed over height H, v 0 Is a reference height H 0 The length d is the barrier shielding coefficient, and if the ground surface barriers are scattered, the value of d is 0.
Further, step 2, establishing a wake effect model according to mutual interference of the input wind speeds when the units are irregularly arranged, specifically:
wherein, i, j are upstream and downstream units respectively, x ij Is upstream and downstreamHorizontal distance of the units, h i 、h j Altitude, R, of upstream and downstream units respectively i 、R j Radius of impeller of upstream and downstream wind turbine, R i (x ij ) For the wake effect radius of an upstream wind turbine at a downstream wind turbine position, A rotor ＝πR j 2 Is the swept area of the wind wheel blade, A shadow,ij Is the wake overlap area;
area A of the wake overlap shadow,ij The calculation formula of (c) is as follows:
wherein, d ij Is the distance between the horizontal central axes of the upstream wind turbine and the downstream wind turbine, and delta h is | h j -h i And | is the altitude difference between the two units, and when Δ h is 0, the model is the multi-wake effect model under the flat ground.
Further, the step 3 is to analyze the influence of the dynamic characteristics caused by unequal lengths of the connecting cables on the unit in the irregular arrangement, and specifically includes the following steps:
in order to analyze the influence of unequal lengths of unit connecting cables under irregular arrangement on dynamic operating characteristics, a doubly-fed fan model on a current collecting line is built in MATLAB, and simulation analysis is carried out on a dynamic process under large disturbance.
Further, the step 4 of solving the characteristic equation of the electromagnetic system of the doubly-fed wind generator, analyzing the dominant mode of the doubly-fed wind generator, and judging the basis of coherence, specifically as follows:
the characteristic equation of the electromagnetic system of the doubly-fed wind generator is as follows:
judging the dominant mode and observed quantity on which the coherence should be based by adopting a single-machine multi-order dynamic model to obtain the optimal dominant observed quantity as the coherent observed quantity; wherein,Δx＝[Δi qs ,Δi ds ,Δi qr ,Δi dr ,Δi qg ,Δi dg ,Δω r ,Δv dc ] T ，Δi qs and Δ i ds D and q axis components of the stator current, respectively; Δ i qr And Δ i dr D-axis and q-axis components of the rotor current, respectively; delta i qg And Δ i dg D and q axis components of the current of the network side controller are respectively; Δ ω r Is the generator rotor speed; Δ v dc Is a direct current capacitor voltage; a is a characteristic matrix of the system;
characteristic equation of electromagnetic system of doubly-fed wind generator
And calculating a characteristic root of the system, calculating a damping ratio according to a real part and an imaginary part of the characteristic root, and judging a dominant mode.
Further, the feature quantity obtained by the identity discrimination in the step 5 is taken as a basis for clustering wind turbine generators, and a hierarchical clustering algorithm is adopted to perform identity clustering on the wind turbine generators in the farm, specifically as follows:
step 5.1, acquiring complete dynamic tracks of leading feature vectors of all wind generation sets in a set time period by using offline data of a wind power plant;
step 5.2, calculating a correlation coefficient for each group of characteristic quantity tracks according to a coherence discrimination principle;
variable x i And x j Correlation coefficient C of ij Is defined as:
where n represents the number of samples in the variable, k represents the kth sample in the variable, p represents the number of groups of variables, x ki 、x kj Respectively representing the kth sample in the ith set of variables and the kth sample in the jth set of variablesA sample is obtained;
step 5.3, hierarchical clustering is carried out, wherein initially, current variable sample points of all units are respectively classified into a group, and the distance between variables and the distance between groups are specified;
distance d between variables ij Defined by the correlation coefficient as follows:
d ij ＝1-C ij ,i＝1,2,…,p；j＝1,2,…,p
step 5.4, merging the two groups with the closest distance into a new group, calculating the distance between the new group and other groups, repeating the merging of the two groups with the closest distance, reducing one group each time until the current variables of all the units are merged into one group, finally forming a clustering tree diagram, and determining the units to be divided into several groups and the unit information contained in each group according to the clustering tree diagram;
in hierarchical clustering, G is used to represent cluster, and there are m sets in G, i.e. m sets of current vectors, represented by column vector x i Where i is 1,2, …, m; d is a radical of ij Represents the element x i And x j A distance between, D KL Then represents the cluster G K And a cluster G L The distance between the current points is defined in a mode of a complete track of a current vector, and the mean value of the square distance between sampling points at each moment is defined by a mean-like law, so that G K And G L Square distance between them
Comprises the following steps:
if group G K And G L Form a new group, denoted as G M Then G is M With any of the original groups G J Square distance between them
The recurrence formula of (c) is:
wherein n represents the number of sets in the group; by defining clustering thresholds
n K 、n L 、n M Respectively represent a cluster G K 、G L 、G M The number of units contained; deducing the above formula to obtain a recurrence formula of the square distance between clusters as follows:
further, the step 6 of calculating the system equivalent unit parameters by adopting a capacity weighting method based on the clustering result is as follows:
the equivalent parameters are calculated as follows:
wherein A is the equivalent machine blade wind sweeping area; a. the i 、c pi 、v i Respectively the swept area, the wind energy utilization coefficient and the input wind speed of the ith unit in the cluster; m is the number of units in the machine group; s i 、Z Gi 、H ti 、H gi 、K i 、D i Rated capacity, generator impedance, wind turbine inertia time constant, generator rotor inertia time constant, shafting stiffness coefficient and damping coefficient of the ith unit are respectively set; s. the Ti 、Z Ti Rated capacity and impedance of the machine-end transformer of the ith unit; equivalent impedance Z of current collection network eq In the formula, Z li The line impedance of the branch of the ith unit; p Zi To flow through impedance Z li Total power of (c); p is Zs To flow through an equivalent impedance Z eq Total power of (d); s. the eq 、S T_eq 、H t_eq 、H g_eq 、K eq 、D eq 、Z G_eq 、Z T_eq Respectively representing the equivalent rated capacity of the equivalent unit, the equivalent rated capacity of a generator-end transformer, an equivalent wind turbine inertia time constant, an equivalent generator rotor inertia time constant, an equivalent shafting stiffness coefficient, a damping coefficient, the equivalent generator impedance and the equivalent generator-end transformer impedance; v. of eq 、c p_eq Respectively representing the input wind speed and the equivalent wind energy utilization coefficient of the equivalent machine; z eq Is the equivalent impedance of the collector network.
Compared with the prior art, the invention has the following remarkable advantages: (1) the influence of the actual terrain on the input wind speed and the effect of the current collection network impedance in the dynamic process are effectively designed, so that the accuracy of equivalent calculation is improved; (2) dominant characteristic quantities of the dynamic process of the doubly-fed wind generator are calculated and analyzed, so that the obtained rotor current is used as a basis for judging a coherent unit, and the grouping effectiveness is improved; (3) and a hierarchical clustering algorithm is adopted, so that the unit in the same group has higher similarity, and different groups show difference.
Drawings
FIG. 1 is a schematic flow diagram of a dynamic equivalence method for a wind power plant based on coherent unit clustering.
FIG. 2 is a schematic diagram illustrating the effect of wake effect in the present invention.
FIG. 3 is a schematic diagram of a topographic location of a wind farm in an embodiment of the present invention.
Fig. 4 is a schematic diagram of connection of the wind turbine generator set on the current collecting line according to the embodiment of the present invention.
FIG. 5 is a diagram illustrating a simulation of a dynamic process of a wind turbine generator with unequal cable lengths according to an embodiment of the present invention, where (a) is a d-axis current I of a rotor current of the wind turbine generator dr The dynamic disturbed curve diagram of (b) is the q-axis current I of the rotor of the unit qr Dynamic disturbed graph of components.
FIG. 6 is a hierarchical clustering result tree diagram according to an embodiment of the present invention.
FIG. 7 is a schematic diagram of the equivalent power comparison of the method of the present invention with the conventional method, wherein (a) is a comparison diagram of the equivalent wind farm output active power of the equivalent machine with the conventional single-machine equivalent method and the actual detailed model, and (b) is a comparison diagram of the equivalent wind farm output reactive power of the equivalent machine with the conventional single-machine equivalent method and the actual detailed model.
Detailed Description
The invention is described in further detail below with reference to the following figures and specific embodiments:
with reference to fig. 1, the dynamic equivalence method for the wind power plant based on the coherent unit grouping comprises the following steps:
Because large onshore wind power plants are usually located in mountainous areas, the unit arrangement in the wind power plants is not simple in parallel arrangement of rows and columns, and the arrangement position, the height and the like of the unit arrangement are irregular due to the influence of the environment, such as gradient, topographic relief, ground roughness, obstacles and the like. Complex terrain affects the wind speed distribution within the field. Defining the ambient wind speed profile may use wind resource simulation software, WAsP.
The wind speed statistical law is close to Weibull distribution, and the statistical probability density function f (v) and the distribution function F (v) of the wind speed v are as follows:
wherein v is the wind speed, k is the shape parameter, and c is the scale parameter;
the wind speed change model is established according to the terrain as follows:
where v is the wind speed over height H, v 0 Is a reference height H 0 The upper wind speed and the length d are barrier shielding coefficients, and if the ground surface barriers are scattered, the value of d is 0.
And 2, establishing a wake effect model according to mutual interference of input wind speeds when the units are arranged irregularly.
The wake effect generated when each unit in a field is distributed dispersedly influences the input wind speed, the influence of the wake effect is less considered in the traditional equivalence research, the wake effect is further aggravated by the influence of the terrain factor, one wind turbine can be influenced by the wake effect of more than one other unit in different degrees, the integral model is shown in fig. 2, and the input wind speed acting on a mixed wake point is as follows:
wherein, i, j are upstream and downstream units respectively, x ij Is the horizontal distance of upstream and downstream units, h i 、h j Altitude, R, of upstream and downstream units, respectively i 、R j Radius of impeller of upstream and downstream wind turbine, R i (x ij ) For the wake effect radius of an upstream wind turbine at a downstream wind turbine position, A rotor ＝πR j 2 For the swept area of the wind wheel blades, A shadow,ij Is the wake overlap area;
after the influence of the terrain on the wind speed is determined, the effect of wake effect generated when each unit in the field is distributed on the input wind speed of the unit is considered, and the area A of the overlapping part of the wake is shadow,ij The calculation formula of (a) is as follows:
wherein d is ij Is the distance between the horizontal central axes of the upstream wind turbine and the downstream wind turbine, and delta h is | h j -h i And l is the altitude difference between the two units, and particularly, the model of the multi-wake effect under the flat ground is obtained when Δ h is equal to 0.
when the lengths of connecting cables among multiple units on a row of collecting lines under a complex terrain are unequal, in order to observe the influence of the connecting cables on the dynamic operating characteristics, a double-fed fan model on one collecting line is built in an MATLAB (matrix laboratory), and simulation analysis is carried out on the dynamic process under large disturbance.
Step 4, solving a characteristic equation of the electromagnetic system of the doubly-fed wind generator, analyzing a dominant mode of the equation, and judging a homodyne basis;
the characteristic equation of the electromagnetic system of the doubly-fed wind generator is as follows:
the doubly-fed induction wind motor is decoupled from a power grid, and a power angle cannot be directly measured, so that a single-machine multi-order dynamic model is adopted to judge a dominant mode and observed quantities on which the coherence should be based, and an optimal dominant observed quantity is obtained and serves as a coherent observed quantity; wherein Δ x ═ Δ i qs ,Δi ds ,Δi qr ,Δi dr ,Δi qg ,Δi dg ,Δω r ,Δv dc ] T ，Δi qs And Δ i ds D-axis and q-axis components of the stator current, respectively; delta i qr And Δ i dr D-axis and q-axis components of the rotor current, respectively; Δ i qg And Δ i dg D and q axis components of the network side controller current respectively; Δ ω r Is the generator rotor speed; Δ v dc Is a direct current capacitor voltage; a is the feature matrix of the system.
Characteristic equation of electromagnetic system of doubly-fed wind generator
And calculating to obtain a characteristic root of the system, calculating a damping ratio according to a real part and an imaginary part of the characteristic root, and judging the dominant mode.
And 5, taking the characteristic quantity obtained by the homodyne discrimination as a grouping basis of the wind turbine generator, and performing homodyne grouping on the wind turbine generator in the farm by adopting a hierarchical clustering algorithm.
The hierarchical clustering method enables the units in the same group to have higher similarity and different groups to show difference, gives results and then selects groups, and comprises the following steps:
step 5.1, acquiring a complete dynamic track of leading feature vectors of all wind generation sets in a certain time period by using offline data of a wind power plant;
step 5.2, calculating the correlation coefficient of each group of characteristic quantity tracks according to the principle of coherence discrimination;
variable x i And x j Coefficient of correlation C ij Is defined as:
where n represents the number of samples in the variable, k represents the kth sample in the variable, p represents the number of groups of variables, x ki 、x kj Respectively representing the kth sample in the ith group of variables and the kth sample in the jth group of variables;
step 5.3, hierarchical clustering is carried out, wherein initially, current variable sample points of all units are respectively classified into a group, and the distance between variables and the distance between groups are specified;
the distance between variables can be defined by the correlation coefficient as follows:
d ij ＝1-C ij ,i＝1,2,…,p；j＝1,2,…,p
step 5.4, merging the two groups with the closest distance into a new group, calculating the distance between the new group and other groups, repeating the merging of the two groups with the closest distance, reducing one group each time until the current variables of all the units are merged into one group, finally forming a clustering tree diagram, and acquiring the information of the units which are to be divided into several groups and each group from the clustering tree diagram;
in hierarchical clustering, G is used to represent cluster, and there are m sets in G, i.e. m sets of current vectors, represented by column vector x i Where i is 1,2, …, m; d ij Represents the element x i And x j A distance between, D KL Then it represents the cluster G K And a cluster G L The distance between the current points is defined in a mode of a complete track of a current vector, and the mean value of the square distance between sampling points at each moment is defined by a mean-like law, so that G K And G L Square distance between them
Comprises the following steps:
if group G K And G L Form a new group, denoted as G M Then G is M And any original group G J Square distance between them
The recurrence formula of (c) is:
wherein n corresponds to the number of sets in the group, by defining a grouping threshold
n K 、n L 、n M Respectively represent a cluster G K 、G L 、G M The number of units contained; by deducing the above formula, the recursive formula of the square distance between clusters can be obtained as follows:
and 6, based on the grouping result, adopting a capacity weighting method to complete the calculation of the system equivalent unit parameters.
The equivalent parameters are calculated as follows:
wherein A is the wind sweeping area of the equivalent machine blade; a. the i 、c pi 、v i Respectively the swept area, the wind energy utilization coefficient and the input wind speed of the ith unit in the cluster; m is the number of units in the machine group; s i 、Z Gi 、H ti 、H gi 、K i 、D i Rated capacity, generator impedance, wind turbine inertia time constant, generator rotor inertia time constant, shafting stiffness coefficient and damping coefficient of the ith unit are respectively set; s Ti 、Z Ti Rated capacity and impedance of the machine-end transformer of the ith unit; equivalent impedance Z of current collection network eq In the formula, Z li The line impedance of the branch of the ith unit; p Zi To flow through impedance Z li Total power of (d); p Zs To flow through an equivalent impedance Z eq Total power of (d); s. the eq 、S T_eq 、H t_eq 、H g_eq 、K eq 、D eq 、Z G_eq 、Z T_eq Respectively representing the equivalent rated capacity of the equivalent unit, the equivalent rated capacity of a generator-end transformer, an equivalent wind turbine inertia time constant, an equivalent generator rotor inertia time constant, an equivalent shafting stiffness coefficient, a damping coefficient, the equivalent generator impedance and the equivalent generator-end transformer impedance; v. of eq 、c p_eq Respectively representing the input wind speed and the equivalent wind energy utilization coefficient of the equivalent machine; z is a linear or branched member eq Is the equivalent impedance of the collector network.
Examples
Taking a large wind farm in a certain mountain area as an example, the wind resource management software WAsP is subjected to site selection and modeling, and is shown in FIG. 3. The double-feed power generation system comprises 4 power collection circuits and 16 double-feed units, wherein each unit is connected into a power collection network through a machine-end boosting transformer, and every 4 units are connected to one group of feeder lines. And 4 feeder lines are connected to the PCC bus and then connected with the infinite system through two step-up transformers and double return lines.
The system parameters are as follows:
all wind turbine generators adopt a Bonus 1.5MW double-fed type, the transformation ratio of a terminal transformer is 575V/25kV, the resistance of a feeder cable is 0.1153 omega/km, the reactance is 0.3958 omega/km, a constant power factor control strategy is adopted for the wind turbine generators WT 1-WT 8, and a constant voltage control strategy is adopted for the WT 9-WT 16; the unit connection mode is as shown in fig. 4, a doubly-fed wind turbine model on a current collecting line is built in the MATLAB, simulation analysis is carried out on a dynamic process under large disturbance, and simulation analysis results are as shown in (a) - (b) in fig. 5;
solving characteristic equation of electromagnetic system of doubly-fed wind generator
Analyzing the leading mode of the method, and judging the basis of coherence:
TABLE 1 System eigenvalue results for doubly-fed wind generator
The eigenvalue results of the calculation of the eigenvalue matrix a are shown in table 1, where: lambda is a characteristic value; σ and ω are the real and imaginary parts of the eigenvalues, respectively. As can be seen from Table 1, the model has three oscillation modes and two attenuation modes, wherein the mode λ 5,6 The damping of the system is smaller and is the dominant mode of the system, the damping of other modes is larger and the damping is fast and is the non-dominant mode, therefore, the state quantity i influencing the dominant mode is needed in the dynamic grouping ds ,i qs ,i dr ,i qr As a coherent observation. The rotor-side current is selected here as the observed quantity.
The characteristic quantity obtained by the homodyne discrimination is taken as a wind turbine generator grouping basis, the homodyne grouping is carried out on the wind turbine generators in the wind farm by adopting a hierarchical clustering algorithm, and a tree-shaped result diagram obtained after the hierarchical clustering calculation is carried out on the wind turbine generators in the wind farm is shown in fig. 6.
Based on the grouping result, the capacity weighting method is adopted to complete the calculation of the system equivalent unit parameters
TABLE 2 results of equivalent machine calculations
The result of calculating the equivalent parameters for the wind farm of the embodiment is shown in table 2. The equivalent effect is shown in fig. 7 (a) - (b) compared with the conventional method.
TABLE 3 example parameters relevant to wind farm
Parameters such as input wind speed and feeder cable length of each unit at a certain time under the complex terrain are obtained by simulating the wind power plant through WAsP software and are shown in table 3.
Aiming at the problem of low equivalence precision caused by the fact that the influence of terrain factors is not considered in the traditional wind power plant equivalence method, the influence of actual terrain on input wind speed and the effect of current collection network impedance in a dynamic process are effectively designed, and therefore the accuracy of equivalence calculation is improved; dominant characteristic quantities of the dynamic process of the doubly-fed wind generator are calculated and analyzed, so that the obtained rotor current is used as a basis for judging a coherent unit, and the grouping effectiveness is improved; and a hierarchical clustering algorithm is adopted, so that the units in the same group have higher similarity, and the different groups show difference, and the method has certain guiding significance for site selection planning and simplified calculation of the wind power plant.
Claims (6)
1. A dynamic equivalence method for a wind power plant based on coherent unit grouping is characterized by comprising the following steps:
step 1, modeling environmental wind speed distribution;
step 2, establishing a wake effect model according to mutual interference of input wind speeds when the units are irregularly arranged;
step 3, analyzing the influence of the dynamic characteristics caused by unequal lengths of the connecting cables aiming at the unit in irregular arrangement;
step 4, solving a characteristic equation of the electromagnetic system of the doubly-fed wind generator, analyzing a dominant mode of the equation, and judging a homodyne basis;
step 5, taking the characteristic quantity obtained by the homodyne discrimination as a wind turbine generator grouping basis, and carrying out homodyne grouping on the wind turbine generators in the farm by adopting a hierarchical clustering algorithm, wherein the method specifically comprises the following steps:
step 5.1, acquiring complete dynamic tracks of leading feature vectors of all wind generation sets in a set time period by using offline data of a wind power plant;
step 5.2, calculating a correlation coefficient for each group of characteristic quantity tracks according to a coherence discrimination principle;
variable x i And x j Coefficient of correlation C ij Is defined as:
where n represents the number of samples in the variable, k represents the kth sample in the variable, p represents the number of groups of variables, x ki 、x kj Respectively representing the kth sample in the ith group of variables and the kth sample in the jth group of variables;
step 5.3, hierarchical clustering is carried out, wherein current variable sample points of all the units are initially classified into a group, and the distance between variables and the distance between groups are specified;
distance d between variables ij Defined by the correlation coefficient as follows:
d ij ＝1-C ij ,i＝1,2,…,p；j＝1,2,…,p
step 5.4, merging the two groups with the closest distance into a new group, calculating the distance between the new group and other groups, repeating the merging of the two groups with the closest distance, reducing one group each time until the current variables of all the units are merged into one group, finally forming a clustering tree diagram, and determining the groups to be divided into several groups and the unit information contained in each group according to the clustering tree diagram;
in hierarchical clustering, G is used to represent cluster, and there are m sets in G, i.e. m sets of current vectors, represented by column vector x i Where i is 1,2, …, m; d ij Represents the element x i And x j A distance between, D KL Then it represents the cluster G K And a cluster G L The distance between the current vector and the current vector is defined in a mode of complete track, and the mean value of the square distance between sampling points at each moment is defined by adopting a mean-like law, so that G K And G L Square distance between them
Comprises the following steps:
if group G K And G L Form a new group, denoted as G M Then G is M And any original group G J Square distance between them
The recurrence formula of (c) is:
wherein, by defining a clustering threshold
n K 、n L 、n M Respectively represent a cluster G K 、G L 、G M The number of units contained; deducing the above formula to obtain a recurrence formula of the square distance between clusters as follows:
and 6, based on the grouping result, calculating the system equivalent unit parameters by adopting a capacity weighting method.
2. The coherent unit clustering-based wind farm dynamic equivalence method according to claim 1, wherein the modeling of the ambient wind speed distribution in step 1 is specifically as follows:
the wind speed statistical law is close to Weibull distribution, and the statistical probability density function f (v) and the distribution function F (v) of the wind speed v are as follows:
wherein v is the wind speed, k is the shape parameter, and c is the scale parameter;
the wind speed change model is established according to the terrain as follows:
in the formula, v H Is the wind speed, v, over the height H 0 Is a reference height H 0 The upper wind speed and the length d are barrier shielding coefficients, and if the ground surface barriers are scattered, the value of d is 0.
3. The dynamic equivalence method for the wind farm based on the coherent unit clustering as claimed in claim 1 or 2, wherein the step 2 is to establish a wake effect model according to the mutual interference of the input wind speeds when the units are irregularly arranged, specifically:
wherein, i, j are upstream and downstream units respectively, x ij Is the horizontal distance of upstream and downstream units, h i 、h j Altitude, R, of upstream and downstream units, respectively i 、R j Radius of impeller of upstream and downstream wind turbine, R i (x ij ) For the wake effect radius of an upstream wind turbine at a downstream wind turbine position, A rotor ＝πR j 2 For the swept area of the wind wheel blades, A shadow,ij Is the wake overlap area;
area A of the wake overlap shadow,ij The calculation formula of (a) is as follows:
wherein d is ij Is the distance between the horizontal central axes of the upstream wind turbine and the downstream wind turbine, and delta h is | h j -h i And | is the altitude difference between the two units, and when Δ h is 0, the model is the multi-wake effect model under the flat ground.
4. The dynamic equivalence method for the wind farm based on the coherent unit clustering, according to claim 1, characterized in that, aiming at the units under irregular arrangement, the influence of dynamic characteristics caused by unequal lengths of connecting cables is analyzed in step 3, specifically as follows:
in order to analyze the influence of unequal lengths of unit connecting cables under irregular arrangement on dynamic operating characteristics, a doubly-fed fan model on a current collecting line is built in MATLAB, and simulation analysis is carried out on a dynamic process under large disturbance.
5. The wind farm dynamic equivalence method based on coherent unit clustering according to claim 1 or 2, characterized in that the step 4 of solving the doubly-fed wind generator electromagnetic system characteristic equation, analyzing the dominant mode thereof, and discriminating the basis of coherence is as follows:
the characteristic equation of the electromagnetic system of the doubly-fed wind generator is as follows:
judging the dominant mode and observed quantity on which the coherence should be based by adopting a single-machine multi-order dynamic model to obtain the optimal dominant observed quantity as the coherent observed quantity; wherein Δ x ═ Δ i qs ,Δi ds ,Δi qr ,Δi dr ,Δi qg ,Δi dg ,Δω r ,Δv dc ] T ，Δi qs And Δ i ds D-axis and q-axis components of the stator current, respectively; Δ i qr And Δ i dr D and q axis components of the rotor current respectively; Δ i qg And Δ i dg D and q axis components of the network side controller current respectively; Δ ω r Is the generator rotor speed; Δ v dc Is a direct current capacitor voltage; a is a characteristic matrix of the system;
characteristic equation of electromagnetic system of doubly-fed wind generator
And calculating a characteristic root of the system, calculating a damping ratio according to a real part and an imaginary part of the characteristic root, and judging a dominant mode.
6. The dynamic equivalence method for the wind power plant based on the coherent unit clustering as claimed in claim 1, wherein the clustering result based on step 6 is adopted to complete the system equivalence unit parameter calculation by adopting a capacity weighting method, specifically as follows:
the equivalent parameters are calculated as follows:
wherein A is the wind sweeping area of the equivalent machine blade; a. the i 、c pi 、v i Respectively the swept area, the wind energy utilization coefficient and the input wind speed of the ith unit in the cluster; m is the number of units in the machine group;S i 、Z Gi 、H ti 、H gi 、K i 、D i rated capacity, generator impedance, wind turbine inertia time constant, generator rotor inertia time constant, shafting stiffness coefficient and damping coefficient of the ith unit are respectively set; s Ti 、Z Ti Rated capacity and impedance of a machine-end transformer of the ith unit; equivalent impedance Z of current collection network eq In the formula, Z li The line impedance of the branch of the ith unit; p Zi To flow through impedance Z li Total power of (d); p Zs To flow through an equivalent impedance Z eq Total power of (d); s eq 、S T_eq 、H t_eq 、H g_eq 、K eq 、D eq 、Z G_eq 、Z T_eq Respectively representing the equivalent rated capacity of the equivalent unit, the equivalent rated capacity of a generator-end transformer, an equivalent wind turbine inertia time constant, an equivalent generator rotor inertia time constant, an equivalent shafting stiffness coefficient, a damping coefficient, the equivalent generator impedance and the equivalent generator-end transformer impedance; v. of eq 、c p_eq Respectively representing the input wind speed and the equivalent wind energy utilization coefficient of the equivalent machine; z eq Is the equivalent impedance of the collector network.
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