CN109638892A - A kind of photovoltaic plant equivalent modeling method based on improvement fuzzy clustering algorithm - Google Patents
A kind of photovoltaic plant equivalent modeling method based on improvement fuzzy clustering algorithm Download PDFInfo
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Abstract
The invention discloses a kind of based on the photovoltaic plant equivalent modeling method for improving fuzzy clustering algorithm, and step includes: 1 determining each photovoltaic generation unit clustering target and is standardized；2 setting clustering parameters, initialize subordinated-degree matrix；3 carry out Clustering to photovoltaic generation unit by improving fuzzy clustering algorithm；4, according to cluster result, calculate equivalent parameters, merge photovoltaic generation unit；5 pass through the correctness of verification of error analysis Equivalent Model.The present invention can carry out scientificlly and effectively grouping equivalence to numerous photovoltaic generation units, so as to improve the precision of large-scale photovoltaic power station Equivalent Model.
Description
Technical field
The present invention relates to electric system simulation analysis field, specifically a kind of equivalence of large-scale grid connection photovoltaic plant
Modeling method.
Background technique
With petering out for global fossil energy, photovoltaic power generation with its cleanliness without any pollution, that renewable, reserves are huge etc. is excellent
Point is rapidly developed in countries in the world.In recent years, grid-connected simulation analysis becomes the research hotspot of field of power system.It passes
The emulation mode of system establishes detailed simulation model to all grid-connected photovoltaic power generation units, to realize to grid-connected temporarily stability
The accurate simulation of energy.However, for a large amount of grid-connected units of centralization, being adopted with the continuous expansion of photovoltaic plant scale
With traditional modeling method not only labor intensive, the system scale of emulation also will increase, increase simulation time, reduce emulation effect
Rate.Therefore, photovoltaic generation unit similar in dynamic property is subjected to the grid-connected model that cluster is equivalent, after establishing equivalence,
Guarantee to improve simulation efficiency under the premise of simulation accuracy, is the effective means of large-scale distributed power grid simulation analysis.
Fuzzy C-Means Cluster Algorithm is a kind of clustering algorithm based on division, suitable to its research theoretically
It is perfect.In FCM, it is 1 that the same sample, which belongs to the sum of degree of membership of all classes, this make it to noise and outlier very
It is sensitive；The algorithm for the iteration decline that FCM is used, it is sensitive to the cluster centre or subordinated-degree matrix of initialization, it cannot be guaranteed that
Converge to globally optimal solution, it is possible to converge to local extremum or saddle point.
Summary of the invention
The present invention is provided a kind of based on improvement fuzzy clustering calculation to avoid above-mentioned existing deficiencies in the technology
The photovoltaic plant equivalent modeling method of method, it is equivalent to which can numerous photovoltaic generation units be carried out with scientificlly and effectively grouping, thus
Achieve the purpose that improve large-scale photovoltaic power station Equivalent Model precision.
In order to achieve the above object, the technical scheme adopted by the invention is as follows:
A kind of the characteristics of photovoltaic plant equivalent modeling method based on improvement fuzzy clustering algorithm of the invention is by following step
It is rapid to carry out:
Step 1: determining each photovoltaic generation unit clustering target and being standardized:
Step 1.1 establishes the grid-connected simulation model of photovoltaic generation unit, and different photovoltaic array parameter and grid-connected inverse is arranged
Become device parameter；Then fault point is set at each grid-connected side bus respectively, to obtain each grid-connected photovoltaic unit
Dynamic characteristic；
Step 1.2, the control parameter vector for enabling photovoltaic DC-to-AC converter are [KUP,KUI,KQP,KQI] and as photovoltaic intra-cluster
Indicator vector, wherein KUP,KUIIt is voltage-controlled proportionality coefficient and integral coefficient, K in outer loop control respectivelyQP,KQIIt is respectively
The proportionality coefficient and integral coefficient of Reactive Power Control in outer loop control；
Enabling photovoltaic cluster external indicator vector is [P0,tp0,Q0,tq0], wherein P0For active power first pendulum peak value,
tp0Start for simulation model dynamic process to active first pendulum peak value required time, Q0First for reactive power puts peak value, tq0
The time required to starting for simulation model dynamic process to idle first pendulum peak value；
Step 1.3, by clustering target vector [K inside any j-th of photovoltaic cellsUP,KUI,KQP,KQI] successively it is denoted as [xj (1),xj (2),xj (3),xj (4)], by clustering target vector [P outside j-th of photovoltaic cells0,tp0,Q0,tq0] successively it is denoted as [xj (5),xj (6),xj (7),xj (8)], and any t-th of the index of j-th of photovoltaic cells is denoted as xj (t), t=1,2 ..., 8；J=1,2 ..., n；n
For the quantity of photovoltaic generation unit；
Step 1.4, to j-th of photovoltaic cells, t-th of index xj (t)It is standardized, the index after being standardizedThe clustering target vector x of j-th of photovoltaic generation unit is obtained using formula (1)j, to obtain n photovoltaic generation unit
Clustering target vector X={ x1,x2,…,xj,…,xn}:
Step 2: the clustering target vector of photovoltaic generation unit is mapped to feature space H from original data space Rs
In, establish the objective function and degree of membership iterative formula of feature space H:
Step 2.1 constructs original cluster data space R using the clustering target vector Xs；Recycle function K (xα,xβ)
=< φ (xα),φ(xβ) > calculate any two points x in luv space RsαWith xβInner product after mapping in feature space H, from
And original data space RsIt is mapped to feature space H, and obtains eigenmatrixWherein, s is the dimension of sample space；φ () is indicated from original data
Space RsTo the mapping of feature space H,<,>indicate inner product operation in feature space H；And 1≤α, β≤n；
Step 2.2, to set initialization cluster number c be 2, and enabling maximum cluster number is cmax；Enable W=[ω1,
ω2,...,ωi,...,ωc] indicate feature space in cluster centre, wherein ωiExpression ith cluster center, 1≤i≤
c；
Enabling current iteration number is k, and initializes k=0；Set maximum number of iterations as M, iteration convergence precision be ε, and
ε > 0；
Enable the degree of membership Iterative Matrix of kth time iterationWherein,It is
The clustering target vector x of j-th of photovoltaic generation unit of k iterationjBelong to the i-th class cluster centre ω after φ mapsiBe subordinate to
Angle value；
Step 2.3 utilizes the i-th class cluster centre when formula (2) update kth time iterationMapping matrix
In formula (2), T represents the transposition of matrix；
Ith cluster center when step 2.4, using formula (3) that kth is secondary iterationIt is write as after mapping in feature space H
The linear combination of point:
In formula (5), φ (X) indicates the mapping to vector X, and φ (X)=(φ (x1),φ(x2),...,φ(xn))；
Step 2.5, the clustering target vector x that j-th of photovoltaic generation unit when kth time iteration is obtained using formula (4)jThrough φ
After mapping with ith cluster centerDistance in feature space H
Step 2.6, setting fuzzy coefficient are m, and with the clustering target of j-th of photovoltaic generation unit when kth time iteration to
Measure xjAfter φ maps with the i-th class cluster centreDistance in feature space HThe minimum target of summation is established such as formula
(5) objective function shown in:
Step 2.7, setting subordinated-degree matrix constraint condition as shown in formula (6):
Step 2.8, using lagrange's method of multipliers, under the subordinated-degree matrix constraint condition shown in formula (6), seek formula
(5) extreme value of objective function shown in, to update the degree of membership Iterative Matrix U of kth time iteration(k), and obtain+1 iteration of kth
Degree of membership Iterative Matrix U(k+1)；
Step 2.8.1, logical expression is enabledJudgementIt is whether true, if so,
Then the clustering target vector x of j-th of photovoltaic generation unit when+1 iteration of kth is obtained using formula (7)jBelong in the i-th class cluster
The heartBe subordinate to angle valueOtherwise, step 2.8.2 is executed；
Step 2.8.2, j is judged whether there is to have any iIf
It is then to obtain the clustering target vector x of j-th of photovoltaic generation unit when+1 iteration of kth using formula (8)jBelong to the i-th class cluster
CenterBe subordinate to angle valueIf it is not, thening follow the steps 2.8.3；
Step 2.8.3, i is judged whether there is to have any jIf depositing
Then the clustering target vector x of j-th of photovoltaic generation unit when+1 iteration of kth is being obtained using formula (9)jBelong to the i-th class cluster
CenterBe subordinate to angle valueOtherwise, j-th photovoltaic generation unit is poly- when obtaining+1 iteration of kth using formula (10)
Class indicator vector xjBelong to the i-th class cluster centreBe subordinate to angle value
Step 2.9, judgement | | U(k+1)-U(k)| | whether≤ε or k > M is true, if so, when then obtaining kth time iteration
Cluster centre W(k)With degree of membership Iterative Matrix U(k)And as the photovoltaic cluster result under current cluster number c, then execute step
Three；Otherwise, k+1 is enabled to be assigned to k, and return step 2.3 sequentially executes；
Step 3: changing photovoltaic plant cluster number c step 2 to be repeated, to obtain next cluster number after c+1
The corresponding photovoltaic cluster result of c；
Photovoltaic cluster result each time is analyzed using Validity Function shown in formula (11), determines best available property
Index VbestCorresponding photovoltaic plant clusters number cbestWith corresponding subordinated-degree matrix Ubest, and as final cluster result:
In formula (11), determinant function, F are sought in det () expressioniIndicate the fuzzy covariance square of the i-th class cluster centre
Battle array, and
Step 4: according to shown final cluster result, by best available property index VbestCorresponding photovoltaic plant cluster
Number cbestIn the corresponding photovoltaic generation unit of same category of each number be merged into an equivalent photovoltaic generation unit, thus
To photovoltaic plant multimachine Equivalent Model；
Step 4.1 obtains ith cluster center ωiCorresponding photovoltaic DC-to-AC converter control parameter, 1≤i≤cbest, and utilize
Weighted average method shown in formula (12) seeks the value of i-th of equivalent photovoltaic combining inverter, t-th of control parameter1≤t
≤ 4, thus after being clustered in i-th of equivalent photovoltaic combining inverter photovoltaic DC-to-AC converter 4 internal parameter controls:
In formula (12), λiIndicate the number for the photovoltaic cells for including in ith cluster；It indicates to wrap in ith cluster
T-th of control parameter of m-th of the photovoltaic cells contained；
Step 4.2 sets cbestAny ith cluster shares ψ in a clusteriA photovoltaic generation unit, respectively using formula (13)
Obtain the capacity parameter of the equivalent photovoltaic array of ith clusterVoltage parameterAnd current parameters1≤i≤cbest:
In formula (13),Indicate the capacity of m-th of photovoltaic generation unit in ith cluster,It indicates in ith cluster
ψiA photovoltaic generation unit exit potential average value；Indicate the output electricity of m-th of photovoltaic generation unit in ith cluster
Stream；
Step 4.3, the filter inductance that side is exchanged ith cluster medium value photovoltaic combining inverter using formula (14)Filter capacitorWith DC side filter capacitorIt carries out equivalent:
In formula (14), Lf、Cf、CdcThe respectively ψ of ith cluster medium value photovoltaic combining inverteriA photovoltaic generation unit
Ac filter inductance average value, ac filter condenser paper mean value, DC side filter capacitor average value；
Step 4.4 obtains current collection equivalent line impedance in ith cluster using formula (15)
In formula (15), PZsTo flow through ith cluster medium value current collection line impedanceGeneral power；PZmTo flow through i-th
ψ in a clusteriThe current collection line impedance Z of m-th of photovoltaic generation unit of a photovoltaic generation unitimPower, ZimIt is poly- for i-th
ψ in classiThe current collection line impedance of m-th of photovoltaic generation unit of a photovoltaic generation unit, 1≤m≤ψi；
Step 5: being missed using the active power that formula (16) and formula (17) obtain the photovoltaic plant multimachine Equivalent Model respectively
Poor EpWith reactive power error Qp, and with the active power error EpWith reactive power error QpTo the photovoltaic plant multimachine
Equivalent Model is evaluated:
In formula (16) and formula (17), τ is the sampling number in wanted analysis time section；Pλ、QλRespectively photovoltaic plant is detailed
The sampled value of active power and reactive power of the model at points of common connection PCC；Respectively photovoltaic plant multimachine etc.
It is worth the sampled value of active power and reactive power of the model at points of common connection PCC.
Compared with the prior art, the beneficial effects of the present invention are embodied in:
1, the present invention will be divided with the photovoltaic generation unit of similar operation characteristic at one using fuzzy clustering algorithm is improved
In group, same group of photovoltaic generation unit is merged into an equivalent photovoltaic generation unit, the multimachine etc. of photovoltaic plant is completed in building
It is worth model, to realize the simplification depression of order of the large-scale photovoltaic power station under the conditions of simulation accuracy is subjected to.
2, the present invention considers that photovoltaic power generation when short circuit occurs for grid-connected photovoltaic power generation unit inverter control parameter and grid entry point
Inside and outside characterisitic parameter is combined together as the clustering target vector of photovoltaic generation unit by the external characteristics parameter of unit, thus
Making the Clustering of photovoltaic generation unit has higher accuracy and reliability.
3, improvement FCM clustering algorithm proposed by the present invention, relaxes the constraint to subordinating degree function, by clustering target vector
It is mapped to feature space and carries out Clustering, improve traditional FCM algorithm defect sensitive to noise or outlier, have more preferable
Robustness so that photovoltaic generation unit have good grouping effect.
4, the present invention proposes new Validity Index for improved FCM algorithm.With traditional division factor (PC) and
Cluster entropy (PE) compare, Validity Index proposed by the present invention is not only related with fuzzy membership, also with the geometry of data
There is close connection, by seeking the extreme value of this Validity Index, available ideal clustering.
Detailed description of the invention
Fig. 1 is that photovoltaic active power of the present invention disturbs curve graph；
Fig. 2 is that photovoltaic generation unit improves FCM Cluster Evaluation flow chart in large-scale photovoltaic power station of the present invention.
Specific embodiment
In the present embodiment, as shown in Fig. 2, a kind of be based on the photovoltaic plant equivalent modeling method for improving fuzzy clustering algorithm
It carries out as follows:
Step 1: determining each photovoltaic generation unit clustering target and being standardized:
Step 1.1 establishes the grid-connected simulation model of photovoltaic generation unit, and different photovoltaic array parameter and grid-connected inverse is arranged
Become device parameter；Then fault point is set at each grid-connected side bus respectively, to obtain each grid-connected photovoltaic unit
Dynamic characteristic；
Step 1.2, the grid-connected transient characterisitics of region centralization photovoltaic generating system mainly determine by gird-connected inverter, photovoltaic
Inverter control parameter vector is [KUP,KUI,KQP,KQI,KIP,KII], parameter KUP,KUIInfluence to the active output characteristics of photovoltaic
It is bigger, parameter KQP,KQIInfluence to the idle output characteristics of photovoltaic is bigger, and ignoring influences lesser parameter KIP,KII.It takes
KUP,KUI,KQP,KQIAs photovoltaic intra-cluster index.The control parameter vector for enabling photovoltaic DC-to-AC converter is [KUP,KUI,KQP,KQI]
And as photovoltaic intra-cluster indicator vector, wherein KUP,KUIIt is voltage-controlled proportionality coefficient and product in outer loop control respectively
Divide coefficient, KQP,KQIIt is the proportionality coefficient and integral coefficient of Reactive Power Control in outer loop control, K respectivelyIP,KIIIt is electric current respectively
Proportionality coefficient and integral coefficient in inner loop control；
The capacity of photovoltaic system, the position of photovoltaic system, disturbance type etc. are also all to influence photovoltaic system dynamic characteristic
Factor comprehensively considers various external factor, herein by the characteristic point conduct extracted on step 1.1 photovoltaic system disturbance curve
Photovoltaic clusters external indicator, determines that the first pendulum peak value of active power and system dynamic course start to wattful power as shown in Figure 1
The time required to rate first puts peak value, determine that the first pendulum peak value of reactive power and system dynamic course start after the same method
The time required to putting peak value to reactive power first, enabling photovoltaic cluster external indicator vector is [P0,tp0,Q0,tq0], wherein P0For
First pendulum peak value, t of active powerp0Start for simulation model dynamic process to active first pendulum peak value required time, Q0For nothing
First pendulum peak value, t of function powerq0The time required to starting for simulation model dynamic process to idle first pendulum peak value；
Step 1.3, by clustering target vector [K inside any j-th of photovoltaic cellsUP,KUI,KQP,KQI] successively it is denoted as [xj (1),xj (2),xj (3),xj (4)], by clustering target vector [P outside j-th of photovoltaic cells0,tp0,Q0,tq0] successively it is denoted as [xj (5),xj (6),xj (7),xj (8)], and any t-th of the index of j-th of photovoltaic cells is denoted as xj (t), t=1,2 ..., 8；J=1,2 ..., n；n
For the quantity of photovoltaic generation unit；
Step 1.4, to j-th of photovoltaic cells, t-th of index xj (t)It is standardized, the index after being standardizedThe clustering target vector x of j-th of photovoltaic generation unit is obtained using formula (1)j, to obtain n photovoltaic generation unit
Clustering target vector X={ x1,x2,…,xj,…,xn}:
Step 2: the clustering target vector of photovoltaic generation unit is mapped to feature space H from original data space Rs
In, establish the objective function and degree of membership iterative formula of feature space H:
Step 2.1 constructs original cluster data space R using the clustering target vector Xs；Recycle function K (xα,xβ)
=< φ (xα),φ(xβ) > calculate luv space RsMiddle any two points xαWith xβInner product after mapping in feature space H, thus
Original data space RsIt is mapped to feature space H, and obtains eigenmatrixWherein, s is the dimension of sample space；φ () is indicated from original number
According to space Rs to the mapping of feature space H,<,>indicate inner product operation in feature space H；And 1≤α, β≤n；It herein can
It takesWherein σ is bandwidth parameter；
Step 2.2, to set initialization cluster number c be 2, and enabling maximum cluster number is cmax；Enable W=[ω1,
ω2,...,ωi,...,ωc] indicate feature space in cluster centre, wherein ωiExpression ith cluster center, 1≤i≤
c；
Enabling current iteration number is k, and initializes k=0；Set maximum number of iterations as M, iteration convergence precision be ε, and
ε > 0；
Enable the degree of membership Iterative Matrix of kth time iterationWherein,It is
The clustering target vector x of j-th of photovoltaic generation unit of k iterationjBelong to the i-th class cluster centre ω after φ mapsiBe subordinate to
Angle value；
Step 2.3 utilizes the i-th class cluster centre when formula (2) update kth time iterationMapping matrix
In formula (2), T represents the transposition of matrix；
Ith cluster center when step 2.4, using formula (3) that kth is secondary iterationIt is write as after mapping in feature space H
The linear combination of point:
In formula (5), φ (X) indicates the mapping to vector X, and φ (X)=(φ (x1),φ(x2),...,φ(xn))；
Step 2.5, the clustering target vector x that j-th of photovoltaic generation unit when kth time iteration is obtained using formula (4)jThrough φ
After mapping with ith cluster centerDistance in feature space H
Step 2.6, setting fuzzy coefficient are m, and with the clustering target of j-th of photovoltaic generation unit when kth time iteration to
Measure xjAfter φ maps with the i-th class cluster centreDistance in feature space HThe minimum target of summation is established such as formula
(5) objective function shown in:
Step 2.7 relaxes constraint of traditional FCM algorithm to subordinated-degree matrix, and the subordinated-degree matrix as shown in formula (6) is arranged
Constraint condition:
Step 2.8, using lagrange's method of multipliers, under the subordinated-degree matrix constraint condition shown in formula (6), seek formula
(5) extreme value of objective function shown in, to update the degree of membership Iterative Matrix U of kth time iteration(k), and obtain+1 iteration of kth
Degree of membership Iterative Matrix U(k+1)；
Step 2.8.1, logical expression is enabledJudgementIt is whether true, if at
It is vertical, then the clustering target vector x of j-th of photovoltaic generation unit when+1 iteration of kth is obtained using formula (7)jBelong to the i-th class cluster
CenterBe subordinate to angle valueOtherwise, step 2.8.2 is executed；
Step 2.8.2, j is judged whether there is to have any iIf
It is then to obtain the clustering target vector x of j-th of photovoltaic generation unit when+1 iteration of kth using formula (8)jBelong to the i-th class cluster
CenterBe subordinate to angle valueIf it is not, thening follow the steps 2.8.3；
Step 2.8.3, i is judged whether there is to have any jIf depositing
Then the clustering target vector x of j-th of photovoltaic generation unit when+1 iteration of kth is being obtained using formula (9)jBelong to the i-th class cluster
CenterBe subordinate to angle valueOtherwise, j-th photovoltaic generation unit is poly- when obtaining+1 iteration of kth using formula (10)
Class indicator vector xj belongs to the i-th class cluster centreBe subordinate to angle value
Step 2.9, judgement | | U(k+1)-U(k)| | whether≤ε or k > M is true, if so, when then obtaining kth time iteration
Cluster centre W(k)With degree of membership Iterative Matrix U(k)And as the photovoltaic cluster result under current cluster number c, then execute step
Three；Otherwise, k+1 is enabled to be assigned to k, and return step 2.3 sequentially executes；
Step 3: changing photovoltaic plant cluster number c step 2 to be repeated, to obtain next cluster number after c+1
C corresponding photovoltaic cluster result；
Photovoltaic cluster result each time is analyzed using Validity Function shown in formula (11), determines best available property
Index VbestCorresponding photovoltaic plant clusters number cbestWith corresponding subordinated-degree matrix Ubest, and as final cluster result:
In formula (11), determinant function, F are sought in det () expressioniIndicate the fuzzy covariance square of the i-th class cluster centre
Battle array, andIf a fuzzy division be it is fine and close, it has a low V value, this
The extreme value of index corresponds to an ideal division；
Step 4: according to shown final cluster result, by best available property index VbestCorresponding photovoltaic plant cluster
Number cbestIn the corresponding photovoltaic generation unit of same category of each number be merged into an equivalent photovoltaic generation unit, thus
To photovoltaic plant multimachine Equivalent Model；
Step 4.1 obtains ith cluster center ωiCorresponding photovoltaic DC-to-AC converter control parameter, 1≤i≤cbest, and utilize
Weighted average method shown in formula (12) seeks the value of i-th of equivalent photovoltaic combining inverter, t-th of control parameter1≤t
≤ 4, thus after being clustered in i-th of equivalent photovoltaic combining inverter photovoltaic DC-to-AC converter 4 internal parameter controls:
In formula (12), λiIndicate the number for the photovoltaic cells for including in ith cluster；It indicates to wrap in ith cluster
T-th of control parameter of m-th of the photovoltaic cells contained；
Step 4.2 follows equivalence front and back photovoltaic array total capacity and output voltage, exports the constant principle of electric current, if
cbestAny ith cluster shares ψ in a clusteriA photovoltaic generation unit, obtained respectively using formula (13) ith cluster etc.
It is worth the capacity parameter of photovoltaic arrayVoltage parameterAnd current parameters1≤i≤cbest:
In formula (13),Indicate the capacity of m-th of photovoltaic generation unit in ith cluster,It indicates in ith cluster
ψiA photovoltaic generation unit exit potential average value；Indicate the output electricity of m-th of photovoltaic generation unit in ith cluster
Stream；
Step 4.3 follows the principle that the check-ins such as same multiply unit number represented by equivalence again, using formula (14) to i-th
Cluster the filter inductance of medium value photovoltaic combining inverter exchange sideFilter capacitorWith DC side filter capacitorIt carries out equivalent:
In formula (14), Lf、Cf、CdcThe respectively ψ of ith cluster medium value photovoltaic combining inverteriA photovoltaic generation unit
Ac filter inductance average value, ac filter condenser paper mean value, DC side filter capacitor average value；
Step 4.4 obtains current collection equivalent line impedance in ith cluster using formula (15)
In formula (15), PZsTo flow through ith cluster medium value current collection line impedanceGeneral power；PZmTo flow through i-th
ψ in a clusteriThe current collection line impedance Z of m-th of photovoltaic generation unit of a photovoltaic generation unitimPower, ZimIt is poly- for i-th
ψ in classiThe current collection line impedance of m-th of photovoltaic generation unit of a photovoltaic generation unit, 1≤m≤ψi；
Step 5: dynamic simulation is carried out according to above-mentioned clustering method and as a result, establish photovoltaic plant multimachine Equivalent Model,
Simulation result is compared with photovoltaic plant detailed model.The photovoltaic plant multimachine is obtained respectively using formula (16) and formula (17)
The active power error E of Equivalent ModelpWith reactive power error Qp, and with the active power error EpAnd reactive power error
QpThe photovoltaic plant multimachine Equivalent Model is evaluated:
In formula (16) and formula (17), τ is the sampling number in wanted analysis time section, and sampled point interval is walked with dynamic simulation
Length is unit, primary every 10 simulation step length samplings, to obtain error assessment data as complete as possible；Pλ、QλRespectively light
The sampled value of active power and reactive power of the overhead utility detailed model at points of common connection PCC；Respectively photovoltaic
The sampled value of active power and reactive power of the power station multimachine Equivalent Model at points of common connection PCC.
Modeling and simulating is carried out to the equivalent front and back photovoltaic plant model of cluster, short trouble is set in grid entry point, detects photovoltaic
Generating state obtains the dynamic changing curve of active power and reactive power, passes through active power and reactive power relative error
Photovoltaic generation unit cluster result is evaluated, with the accuracy and validity for examining cluster equivalent.
The present invention can improve the traditional fuzzy C means clustering algorithm defect sensitive to noise and outlier, guarantee to imitate
Under the premise of true precision, reduce the simulation scale of photovoltaic generating system, shorten simulation time, improves simulation efficiency, be extensive
The transient performance analysis of power distribution network provides premise and theoretical basis after photovoltaic access.
Claims (1)
1. it is a kind of based on the photovoltaic plant equivalent modeling method for improving fuzzy clustering algorithm, it is characterized in that carrying out as follows:
Step 1: determining each photovoltaic generation unit clustering target and being standardized:
Step 1.1 establishes the grid-connected simulation model of photovoltaic generation unit, and different photovoltaic array parameter and gird-connected inverter is arranged
Parameter；Then fault point is set at each grid-connected side bus respectively, to obtain the dynamic of each grid-connected photovoltaic unit
Characteristic curve；
Step 1.2, the control parameter vector for enabling photovoltaic DC-to-AC converter are [KUP,KUI,KQP,KQI] and as photovoltaic intra-cluster index
Vector, wherein KUP,KUIIt is voltage-controlled proportionality coefficient and integral coefficient, K in outer loop control respectivelyQP,KQIIt is outer ring respectively
The proportionality coefficient and integral coefficient of Reactive Power Control in control；
Enabling photovoltaic cluster external indicator vector is [P0,tp0,Q0,tq0], wherein P0First for active power puts peak value, tp0For
Simulation model dynamic process starts to active first pendulum peak value required time, Q0First for reactive power puts peak value, tq0It is imitative
The time required to true mode dynamic process starts to idle first pendulum peak value；
Step 1.3, by clustering target vector [K inside any j-th of photovoltaic cellsUP,KUI,KQP,KQI] successively it is denoted as [xj (1),xj (2),xj (3),xj (4)], by clustering target vector [P outside j-th of photovoltaic cells0,tp0,Q0,tq0] successively it is denoted as [xj (5),xj (6),xj (7),xj (8)], and any t-th of the index of j-th of photovoltaic cells is denoted as xj (t), t=1,2 ..., 8；J=1,2 ..., n；N is light
Lie prostrate the quantity of generator unit；
Step 1.4, to j-th of photovoltaic cells, t-th of index xj (t)It is standardized, the index after being standardized
The clustering target vector x of j-th of photovoltaic generation unit is obtained using formula (1)j, to obtain the cluster of n photovoltaic generation unit
Indicator vector X={ x1,x2,…,xj,…,xn}:
Step 2: by the clustering target vector of photovoltaic generation unit from original data space RsIt is mapped in feature space H, builds
The objective function and degree of membership iterative formula of vertical feature space H:
Step 2.1 constructs original cluster data space R using the clustering target vector Xs；Recycle function K (xα,xβ)=<
φ(xα),φ(xβ) > calculate any two points x in luv space RsαWith xβInner product after mapping in feature space H, thus handle
Original data space RsIt is mapped to feature space H, and obtains eigenmatrix
Wherein, s is the dimension of sample space；φ () is indicated from original data space RsTo the mapping of feature space H,<,>
Indicate the inner product operation in feature space H；And 1≤α, β≤n；
Step 2.2, to set initialization cluster number c be 2, and enabling maximum cluster number is cmax；Enable W=[ω1,ω2,...,
ωi,...,ωc] indicate feature space in cluster centre, wherein ωiIndicate ith cluster center, 1≤i≤c；
Enabling current iteration number is k, and initializes k=0；Set maximum number of iterations as M, iteration convergence precision be ε, and ε >
0；
Enable the degree of membership Iterative Matrix of kth time iterationWherein,It is kth time
The clustering target vector x of j-th of photovoltaic generation unit of iterationjBelong to the i-th class cluster centre ω after φ mapsiDegree of membership
Value；
Step 2.3 utilizes the i-th class cluster centre when formula (2) update kth time iterationMapping matrix
In formula (2), T represents the transposition of matrix；
Ith cluster center when step 2.4, using formula (3) that kth is secondary iterationWrite as the midpoint feature space H after mapping
Linear combination:
In formula (5), φ (X) indicates the mapping to vector X, and φ (X)=(φ (x1),φ(x2),...,φ(xn))；
Step 2.5, the clustering target vector x that j-th of photovoltaic generation unit when kth time iteration is obtained using formula (4)jIt is mapped through φ
Afterwards with ith cluster centerDistance in feature space H
Step 2.6, setting fuzzy coefficient are m, and with the clustering target vector x of j-th of photovoltaic generation unit when kth time iterationjThrough
φ mapping after with the i-th class cluster centreDistance in feature space HThe minimum target of summation is established such as formula (5) institute
Show objective function:
Step 2.7, setting subordinated-degree matrix constraint condition as shown in formula (6):
Step 2.8, using lagrange's method of multipliers, under the subordinated-degree matrix constraint condition shown in formula (6), seek formula (5) institute
Show the extreme value of objective function, to update the degree of membership Iterative Matrix U of kth time iteration(k), and obtain being subordinate to for+1 iteration of kth
Spend Iterative Matrix U(k+1)；
Step 2.8.1, logical expression is enabled
JudgementIt is whether true, if so, then the cluster of j-th of photovoltaic generation unit when+1 iteration of kth is obtained using formula (7)
Indicator vector xjBelong to the i-th class cluster centreBe subordinate to angle valueOtherwise, step 2.8.2 is executed；
Step 2.8.2, j is judged whether there is to have any iIf so, sharp
The clustering target vector x of j-th of photovoltaic generation unit when obtaining+1 iteration of kth with formula (8)jBelong to the i-th class cluster centre
Be subordinate to angle valueIf it is not, thening follow the steps 2.8.3；
Step 2.8.3, i is judged whether there is to have any jIf it exists, then
The clustering target vector x of j-th of photovoltaic generation unit when obtaining+1 iteration of kth using formula (9)jBelong to the i-th class cluster centreBe subordinate to angle valueOtherwise, the cluster of j-th of photovoltaic generation unit refers to when obtaining+1 iteration of kth using formula (10)
Mark vector xjBelong to the i-th class cluster centreBe subordinate to angle value
Step 2.9, judgement | | U(k+1)-U(k)| | whether≤ε or k > M is true, if so, then obtain cluster when kth time iteration
Center W(k)With degree of membership Iterative Matrix U(k)And as the photovoltaic cluster result under current cluster number c, then execute step 3；It is no
Then, k+1 is enabled to be assigned to k, and return step 2.3 sequentially executes；
Step 3: changing photovoltaic plant cluster number c step 2 to be repeated, to obtain c pairs of number of next cluster after c+1
The photovoltaic cluster result answered；
Photovoltaic cluster result each time is analyzed using Validity Function shown in formula (11), determines best available property index
VbestCorresponding photovoltaic plant clusters number cbestWith corresponding subordinated-degree matrix Ubest, and as final cluster result:
In formula (11), determinant function, F are sought in det () expressioniIndicate the fuzzy covariance matrix of the i-th class cluster centre, and
Step 4: according to shown final cluster result, by best available property index VbestCorresponding photovoltaic plant clusters number cbest
In the corresponding photovoltaic generation unit of same category of each number be merged into an equivalent photovoltaic generation unit, to obtain photovoltaic
Power station multimachine Equivalent Model；
Step 4.1 obtains ith cluster center ωiCorresponding photovoltaic DC-to-AC converter control parameter, 1≤i≤cbest, and utilize formula
(12) weighted average method shown in seeks the value of i-th of equivalent photovoltaic combining inverter, t-th of control parameterSo that 4 internal controls of photovoltaic DC-to-AC converter are joined in i-th of equivalent photovoltaic combining inverter after being clustered
Number:
In formula (12), λiIndicate the number for the photovoltaic cells for including in ith cluster；Include in expression ith cluster
T-th of control parameter of m-th of photovoltaic cells；
Step 4.2 sets cbestAny ith cluster shares ψ in a clusteriA photovoltaic generation unit is obtained respectively using formula (13)
The capacity parameter of the equivalent photovoltaic array of ith clusterVoltage parameterAnd current parameters
In formula (13),Indicate the capacity of m-th of photovoltaic generation unit in ith cluster,Indicate ψ in ith clusteriIt is a
Photovoltaic generation unit exit potential average value；Indicate the output electric current of m-th of photovoltaic generation unit in ith cluster；
Step 4.3, the filter inductance that side is exchanged ith cluster medium value photovoltaic combining inverter using formula (14)Filter
Wave capacitorWith DC side filter capacitorIt carries out equivalent:
In formula (14), Lf、Cf、CdcThe respectively ψ of ith cluster medium value photovoltaic combining inverteriThe friendship of a photovoltaic generation unit
Flow filter inductance average value, ac filter condenser paper mean value, DC side filter capacitor average value；
Step 4.4 obtains current collection equivalent line impedance in ith cluster using formula (15)
In formula (15), PZsTo flow through ith cluster medium value current collection line impedanceGeneral power；PZmTo flow through ith cluster
Middle ψiThe current collection line impedance Z of m-th of photovoltaic generation unit of a photovoltaic generation unitimPower, ZimFor ψ in ith clusteri
The current collection line impedance of m-th of photovoltaic generation unit of a photovoltaic generation unit, 1≤m≤ψi；
Step 5: obtaining the active power error E of the photovoltaic plant multimachine Equivalent Model respectively using formula (16) and formula (17)p
With reactive power error Qp, and with the active power error EpWith reactive power error QpIt is equivalent to the photovoltaic plant multimachine
Model is evaluated:
In formula (16) and formula (17), τ is the sampling number in wanted analysis time section；Pλ、QλRespectively photovoltaic plant detailed model
The sampled value of active power and reactive power at points of common connection PCC；Respectively photovoltaic plant multimachine equivalence mould
The sampled value of active power and reactive power of the type at points of common connection PCC.
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