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energies Article

Correlation Analysis between Wind Speed/Voltage Clusters and Oscillation Modes of Doubly-Fed Induction Generators Jierong Miao 1 , Da Xie 1, *, Chenghong Gu 2 and Xitian Wang 1 1 2

*

School of Electronic Information and Electrical Engineering, Shanghai JiaoTong University, Shanghai 200240, China; [email protected] (J.M.); [email protected] (X.W.) Department of Electronic and Electrical Engineering, University of Bath, Bath BA2 7AY, UK; [email protected] Correspondence: [email protected]; Tel.: +86-156-1866-9531

Received: 13 August 2018; Accepted: 5 September 2018; Published: 8 September 2018







Abstract: Potential machine-grid interactions caused by large-scale wind farms have drawn much attention in recent years. Previous work has been done by analyzing the small–signal modeling of doubly-fed induction generators (DFIGs) to obtain the oscillation modes. This paper, by making use of the metered power data of wind generating sets, studies the correlation between oscillation modes of the DFIG system and influence factors which includes wind speed and grid voltage. After the metered data is segmented, the Prony algorithm is used to analyze the oscillation modes contained in the active power. Then, the relevant oscillation modes are extracted in accordance with the small-signal analysis results. Meanwhile, data segments are clustered according to wind speed and grid voltage. The Apriori algorithm is finally used to discuss the association rules. By training the mass of data of wind generating sets, the inevitable association rules between oscillation modes and influence factors can be mined. Therefore, the prediction of oscillation modes can be achieved based on the rules. The results show that the clustering number quite affects the association rules. When the optimal cluster number is adopted, part of the wind speed/voltage clusters can analyze the certain oscillation modes. The predicted results are quite consistent with the practical data. Keywords: wind power; oscillation mode; correlation analysis; Apriori algorithm

1. Introduction According to the 2016 Global Wind Power Development Outlook Report, the wind power market will reach 100 GW by 2020, and the cumulative wind power market will reach 879 GW [1]. With the continuous increase of wind power penetration, the machine-grid interaction has attracted increasing attention. It is found that the interaction is usually reflected in the oscillation of active power [2]. The oscillation modes can be divided into sub-synchronous interaction and low frequency oscillation. The former can be categorized into sub-synchronous control interaction (SSCI) and sub-synchronous torque interaction (SSTI). SSTI includes sub-synchronous oscillation (SSO) [3] and sub-synchronous resonance (SSR) [4]. Since the 1960s, accidents caused by machine-grid interactions have occurred in Europe, America and other countries. The first SSCI accident caused by an interaction between the rotor-side converter and the fixed string compensation system of the doubly-fed induction generator (DFIG) happened in Texas (USA). It resulted in damage to the wind turbines and internal lever circuits [5]. At present, research on the machine-grid interaction is mainly based on modeling and simulation. For instance, Reference [6] proposes a unified modularized small signal dynamic model of wind farm based on an induction motor. It can simulate a random number of fixed speeds, some variable speed

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(doubly-fed) induction motor wind turbine, providing a lot of flexibility for wind turbines and their controllers. In [7], a small-signal model of the direct-drive permanent magnet synchronous generator is established to study the stability of the grid-connected wind generating sets after the small disturbance, and the parameters of the controller are designed effectively. Reference [8] aimed at the suppression of torsional vibrations caused by small electrical disturbances from the grid side in a DFIG-based wind turbine system. The Prony algorithm is a complementary method used in the time-domain model system. It decomposes time-domain signals into damped sinusoids with four parameters per mode: frequency, damping, amplitude and phase. Compared with small-signal analysis, the Prony analysis shows an advantage when the system turns complicated because the former has difficulty solving high-order matrix [9,10]. All the papers above investigated the wind power oscillation mechanism and suppression method by modeling methods. However, the operation of wind generating sets is affected by factors which are more complex than the modeling simulation. A more direct and convenient way is to directly use the metered data. With the advent of the big data era, the vast amounts of data collected from wind farms conceals vast information [11]. Data mining and machine learning theory including correlation analysis, cluster analysis, classification analysis, have brought new ideas to power research [12]. Among them, the Apriori algorithm, one of the correlation algorithms, provides an effective solution for exploring the association relationship between large data item-sets. In the power industry, correlation analysis is mainly used for transformer fault diagnosis. The Apriori algorithm is a common tool of correlation analysis. The Apriori algorithm is a hierarchical algorithm, which seeks frequent item-sets in the increasing item number order. The algorithm can be divided into two steps. The first step is to generate frequent item-sets with minimum support condition. The second step is to produce association rules with minimum confidence condition [13,14]. In [15], a data-driven method of association rule mining for transformer state parameters is proposed by combining the Apriori algorithm and probabilistic graphical model. Paper [16] proposes a new fault diagnosis method based on Set Pair Analysis and association rules. Via analyzing the relationship of fault symptoms and fault types, the corresponding association rules are established. In addition, cluster analysis, as an unsupervised classification method, provides a solution for the information mining of large quantity unknown data [17]. Reference [18] clusters the photovoltaic power station according to the geographical space and analyzes the evolution characteristics of cluster center and cluster radius to predict the spatio-temporal expansion of photovoltaic power supply. Based on new wind pattern recognition technologies, Reference [19] proposes a short-term wind power predicting method for a wind power farm. The correlation between wind power data and numerical weather prediction is used to cluster the meteorological grid data first, and then to construct artificial neural network and support vector machine model for each cluster to improve the accuracy of prediction. However, limited research has been done into the oscillation of wind generating sets through big data technology. In this paper, metered actual output power data of wind generating sets will be used to mine the association rules between oscillation modes and influence factors. Based on the mode analyzing results via the small-signal modeling of DFIG, the information of the machine-grid interaction embedded in the actual operation data will be mined. The Prony algorithm will be used as the fundamental signal analysis method to do the preliminary signal decomposition. As a big data analysis technology, the Apriori algorithm will be introduced to make further efforts on the association rules mining and oscillation prediction. The association rules between clusters and oscillation modes through the analysis of metered data will be obtained. The prediction reveals the comprehensive impact of wind speed and voltage factors on the oscillation modes that may be contained in wind power. The novelty of this paper is that it: (i) combines the modeling method and data analysis method to mine the oscillation information in the practical data of wind power; (ii) establishes the association analyzing modeling based on the Apriori algorithm to analyze the association rules between wind speed/voltage fluctuation clusters and oscillation modes; (iii) proposes a prediction method for the wind power oscillation modes.

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The rest of the paper is organized as follows: Section 2 introduces the research methods of the The rest of the paper is organized as follows: Section 2 introduces the research methods of the oscillation modes of wind generating sets from two aspects: modeling and data analysis. Section 3 oscillation modes of wind generating sets from two aspects: modeling and data analysis. Section 3 establishes the data correlation analysis model of the wind generating sets. The data is segmented by establishes the data correlation analysis model of the wind generating sets. The data is segmented the wind speed and the segments are clustered according to the wind speed and the voltage by the wind speed and the segments are clustered according to the wind speed and the voltage fluctuation. Section 4 is a case analysis, where the impact of cluster number set on association rules fluctuation. Section 4 is a case analysis, where the impact of cluster number set on association rules is is analyzed, and the predict is done according to the association rules between wind power and wind analyzed, and the predict is done according to the association rules between wind power and wind speed/voltage clusters, and the conclusion is given finally. speed/voltage clusters, and the conclusion is given finally. 2. Study of Oscillation Modes of Grid-Connected DFIG System 2. Study of Oscillation Modes of Grid-Connected DFIG System Based on the structure of a grid-connected DFIG system, the small-signal system of DFIG has Based on the structure of a grid-connected DFIG system, the small-signal system of DFIG has been been established and used to analyze the oscillation modes to obtain the results of the modeling established and used to analyze the oscillation modes to obtain the results of the modeling analysis. analysis. Meanwhile, the Prony algorithm is introduced to analyze the metered power data and the Meanwhile, the Prony algorithm is introduced to analyze the metered power data and the result is result is compared with the characteristic frequencies obtained from the modeling analysis. compared with the characteristic frequencies obtained from the modeling analysis. 2.1. 2.1. Oscillation OscillationModes ModesAnalysis Analysis Based Based on on the the Small-Signal Small-Signal Model Model The The detailed detailed structure structure of of the the grid-connected grid-connected DFIG DFIG system system is is shown shown in in Figure Figure 1. 1. Ps Qs

us

is

DFIG

AC/DC/AC inverter

ωr θ

ir

ωr ωr _ ref

Kp0 +

Ki0 s

Ps*

K i1 s i qr _ ref

K p3 +

Qs _ ref

K p2 +

i dr

Ps Ki 3 s

Grid-side converter control

s r X m ids

i qr K p1 +

ig

u dc Rotor-side converter control

uqr Ki 2 s sr X rridr sr X rr iqr

idr_ref K p4 +

u dr

Ki 4 s

u DC

i dg ∗ u dg

u

∗ qg

K p6 +

K p7 +

Ki 6 s

Ki7 s

idg _ ref

K p5 +

i qg

uDC_ ref

Ki 5 s

i qg _ ref

sr X miqs

Qs

Legend inverter

Q s transformer

Gearbox

K p2 +

Ki 2 PI controller s

transformation of coordinates

DFIG

Double-fed asynchronous induction generator

Blade

grid

Figure1. 1.The Thestructure structureof ofgrid-connected grid-connected DFIG DFIG system. system. Subscript Subscript ss and and rrisisthe themark markof ofthe thestator statorside side Figure parameter and and the therotor rotor side siderespectively. respectively. Subscript Subscript gg is is the themark markof ofthe thegrid gridside sideparameter. parameter.Subscript Subscript parameter and qq is is the the mark mark of of dd axis axis parameter parameter and and qq axis axis respectively. respectively. dd and

Three-mass block blockmodel, model,which whichis is more suitable dynamic analysis, is applied Three-mass more suitable for for dynamic analysis, is applied here. here. The The mechanical rotation system of the DFIG can be divided into three parts namely blade, low-speed mechanical rotation system of the DFIG can be divided into three parts namely blade, low-speed shaft shafthigh-speed and high-speed The low-speed connects blades gearbox,and andthe thehigh-speed high-speed and shaft.shaft. The low-speed shaftshaft connects thethe blades to to thethe gearbox, shaft connects the gearbox to the induction generator unit. In addition, the output of the rotor circuit shaft connects the gearbox to the induction generator unit. In addition, the output of the rotor circuit enters the power grid via the converter device, while the stator circuit is directly connected to the the enters the power grid via the converter device, while the stator circuit is directly connected to external power power grid grid [8,20]. [8,20]. external The main objective of the the machine-side machine-side converter converter control control isis to to stabilize stabilize the the active active power power and and The main objective of machine voltage of DFIG. Vector control is adopted based on stator flux orientation, and the coordinate machine voltage of DFIG. Vector control is adopted based on stator flux orientation, and the system of which and d-axis stator flux coincident introduced. The active power and power voltageand are coordinate systemd-axis of which and are stator flux are is coincident is introduced. The active controlled by u and u , respectively. The control goal of the network-side converter is to stabilize qr dr uqr and udr, respectively. The control goal of the network-side converter is to voltage are controlled by the DC side voltage and reactive power.power. The current component idg and to realize the qg are stabilize the DC side voltage and reactive The current component idg iand iqg used are used to realize control respectively by the grid-side converter. The rotating coordinate system is consistent with the the control respectively by the grid-side converter. The rotating coordinate system is consistent with generator. The symbols of electric parameters do not make a distinction in the coordinate system. the generator. The symbols of electric parameters do not make a distinction in the coordinate system.

The control block diagrams of the machine-side converter and network-side converter are shown in

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The control blockon diagrams of the machine-side and network-side converter are shown Figure 1. Based the system structure above,converter the small-signal model of grid-connected DFIGinis Figure 1. Based on the system structure above, the small-signal model of grid-connected DFIG is shown in Figure 2. shown in Figure 2. ΔU b = 0

induction generator

ΔU s

ΔI r

ΔI s

ΔU r

ΔI pc

Capacitance shunt to ground

line

ΔI L

-

ΔU g

ΔU s Transmission

+

ΔTe

Δωr

-+

Δ Tw

Threemass model

ΔU r

ΔU r

ΔI s ΔI r ΔU s

ΔU g

ΔU g

Grid-side

DC side ΔVDC Converter

Rotor-side Controller

ΔI g inductance

Grid-side Controller

ΔVDC _ ref

and transformer of converter

Δiqg _ ref

Δωr _ ref ΔQs _ ref

Figure 2. Small-signal model of DFIG connected to grid. Figure 2. Small-signal model of DFIG connected to grid.

By using the small-signal model, the distribution of the system eigenvalue can be analyzed. By using the small-signal model, thetodistribution of theform system can beresonance analyzed. are The The characteristic values corresponding non-oscillatory andeigenvalue high-frequency characteristic values to interaction. non-oscillatory and high-frequency resonance eliminated to focus on corresponding the machine-grid The form characteristic frequency to be reservedare is eliminated to focus on the machine-grid interaction. The characteristic frequency to be reserved is between 0 and 100 Hz. The result is shown in Table 1 [20]. between 0 and 100 Hz. The result is shown in Table 1 [20]. Table 1. Eigenvalues of DFIG connected to grid. Table 1. Eigenvalues of DFIG connected to grid. Eigenvalues Mode Frequency (Hz) Eigenvalues Mode79.25 Frequency (Hz) −23.63 ± 498i

Type Type SSR SSR SSO SSO

SSCI SSCI Low frequency oscillation Low frequency oscillation

−23.63 ± 498i −16.75 ± 147i −16.75 ± 147i −1.477 −1.477±± 77.97i 77.97i −11.72 −11.72±± 12.08i −51.17±± 285.1i 285.1i −51.17 −8.91 ± 27.45i −8.91 ± 27.45i −0.319 ± 3.177i −0.319 ± 3.177i

79.25 23.40 23.40 12.41 12.41 1.921.92 45.37 45.37 4.37 4.37 0.51 0.51

Damping Ratio Damping Ratio 0.0474

0.0474 0.1132 0.1132 0.0189 0.0189 0.6963 0.6963 0.1767 0.1767 0.3087 0.3087 0.1 0.1

In the analysis below, these mode frequencies will be used as reference values for frequency In theto analysis these mode frequencies will be used as reference values for frequency screening classifybelow, metered data. screening to classify metered data. 2.2. Study of Oscillation Modes Based on Metered Data 2.2. Study of Oscillation Modes Based on Metered Data 2.2.1. Prony Algorithm 2.2.1. Prony Algorithm For time series generated by interval sampling, Prony algorithm is commonly used for curve For time series generated by interval sampling, Prony algorithm is commonly used for curve fitting with the linear combination of exponent items [10]. Its discretization expression is: fitting with the linear combination of exponent items [10]. Its discretization expression is: p

in which: in which:

p

n p  bi zi =p Ai exp(α i n ) sin(2π f i n + ϕ i ) xˆ ( n ) = n i = 1 xˆ (n) = ∑ bi zi = ∑i =1Ai exp(αi n) sin(2π f i n + ϕi )

(1) (1)

(  b = A exp( jϕ ) i i i  bi = Ai exp( jϕi ) exp[( j 2πf f)i ∆t ) Δ]t ] i =exp zi z= [(ααi i++ j2π i

(2) (2)

i =1

i =1

where, Ai, αi, fi, ϕi (i = 1, 2, …, n) respectively represent the amplitude, attenuation factor, frequency and initial phase Angle of the ith fitting component; p is the component number of fitting functions; n = 1, 2, ..., N − 1, N is the number of fitting points.

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where, Ai , αi , fi , φi (i = 1, 2, . . . , n) respectively represent the amplitude, attenuation factor, frequency Energies 2018, 11, x FOR PEER REVIEW of 20 and initial phase Angle of the ith fitting component; p is the component number of fitting 5functions; n = 1, 2, ...,The N Prony − 1, Nalgorithm is the number of fitting points. is a fitting algorithm, and the objective function is the error function shown The Prony algorithm is a fitting algorithm, and the objective function is the error function shown in (3): in (3): "  # N −1 2 1 min ε N x ( n ) − xˆ ( n ) 2 =− (3) min ε = (3)  ∑n = 0| x (n) − xˆ (n)| n =0

Using the least squares method, the value of the unknown parameter in Equation (1) can be Using the The leastoriginal squaressequence method,can the be value of the unknown parameter in Equation can be obtained. decomposed into attenuation components and(1)DC obtained. The original sequence can be decomposed into attenuation components and DC components. components.

2.2.2. 2.2.2. The Oscillation Modes Analysis SpeedUsing Usingthe the Prony Algorithm The Oscillation Modes Analysisunder underFixed Fixed Wind Wind Speed Prony Algorithm Based on the metered data ofofthe sets,the theoutput output power curve is plotted Based on the metered data thewind windgenerating generating sets, power curve is plotted in in Figure Figure 3. 3.

Figure3.3.Operation Operation data data of Figure ofthe theDFIG. DFIG.

The analysis results Pronyalgorithm algorithm are are shown shown in oscillation frequencies The analysis results of of thethe Prony inTable Table2.2.The The oscillation frequencies higher than 100 Hz are eliminated for exceeding the frequency range between 0 and 100 100 Hz of higher than 100 Hz are eliminated for exceeding the frequency range between 0 and Hz of machine-grid interactions. machine-grid interactions. Table 2. Results of the Prony analysis.

Table 2. Results of the Prony analysis. Amplitude

Amplitude 190,696 75,562 190,696 63,194 75,562 62,034 63,194 36,437 62,034 34,919 36,437 28,455 34,919 26,792 28,455 24,909 26,792 24,175 24,909 22,959 24,175 16,312 22,959 14,049 16,312 13,875 14,049 12,269 13,875 11,490 12,269 10,384 11,490 9987 10,384 9528 9987 9465

9528 9465

Frequency (Hz)

(Hz) 0.143 Frequency (low-frequency oscillation) 19.466 0.143 (low-frequency oscillation) 40.545 19.466 50.307 40.545 0 50.307 35.2 0 6.748 35.2 20.582 6.748 10.449 20.582 40.556 10.449 15.242 40.556 8.433 15.242 26.189 8.433 17.107 26.189 32.948 17.107 63.518 32.948 68.174 63.518 3.107 68.174 23.523 (SSR) 3.107 12.404 (SSO) 23.523 (SSR) 12.404 (SSO)

Damping Ratio (%)

Damping Ratio −37.127(%) 3.712 −37.127 3.7124.535 4.5356.586 6.586100 100 2.06 2.066.501 6.5011.218 11.286 1.218 11.2861.65 1.652.607 2.6075.332 5.3322.883 −0.473 2.883 0.082 −0.473 0.154 0.082 1.121 0.154 −2.071 1.121 0.008 −2.071 0.865 0.008 0.865

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It can be concluded from the above data that the low frequency oscillation, SSCI, SSO, and SSR exist in the process of actual system operation. However, the frequencies obtained by the metered data slightly deviate from the characteristic frequency calculated by the small-signal model. Therefore, frequency filtrating rules are designed in Table 3. Table 3. Frequency filtrating rules. Machine-Grid Interaction Type

Oscillation Modes from Small Signal Model (Hz)

Filtrate Range of Prony Analysis Result (Hz)

Correlation Analysis Mark Tag

Low-frequency oscillation

0.1–1.8 Hz

[0.1, 1.8] other

1 0

[4.17, 4.57] other [44.57, 46.17] other

1 0 1 0

[11.91, 12.91] other [1.82, 2.02] other

1 0 1 0

[77.5, 80.5] other [22.4, 23.6] other

1 0 1 0

4.37 Hz SSCI 45.37 Hz 12.41 Hz SSO 1.92 Hz 79 Hz SSR 23 Hz

When the oscillation frequency in the Prony analysis result appears in a certain screening range in Table 3, it can be considered that the analyzed object contains the corresponding oscillation mode component. 3. Modeling of the Correlation Analysis of Wind Speed/Voltage Factors and Oscillation Modes 3.1. K-Means Clustering According to the project observation, the machine-grid interaction of the wind turbine often occurs at low wind speeds. Meanwhile, the voltage change at the PCC point also has the same effect. Thus, the K-Means algorithm is used to find out the influence of both two factors on the oscillation mode by clustering the metered data according to wind speed and voltage. As a result, influence factors in the same cluster have the same characteristics. The K-Means algorithm is an iterative clustering algorithm. The given data set is divided into the specified k clusters [11]. In the data transformation process, influencing factors include wind speed and three-phase voltage fluctuation. To explore the effects of these whole factors on the oscillation modes, clustering can be done first for the same cluster has the same characteristics and influence on the oscillation modes. When the factors number to be considered is d, the input object is the d-dimensional point set and the output is to assign each point to one cluster. The entire analysis object can be represented by the set C, and one element in C can be expressed as (4): C (i ) = c( xi1 , xi2 , · · · , xid )

(4)

in which, xij (j = 1, 2, . . . , d) represents wind speed, three-phase voltage fluctuation and so on. The Euclidean distance between two d-dimensional vectors is shown in (5):

d12

v u d u = t ∑ ( x1k − x2k )2 k =1

(5)

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The K-Means algorithm minimizes the total Euclidean distance between each point and the cluster center. In this paper, the optimal cluster number is first selected with fewer sampling data. It is necessary to record the cluster center of the optimal cluster number to be set as the initial cluster center in the later analysis, which ensures the consistency of clustering results. 3.2. Association Rules and the Improved Apriori Algorithm Assume that set D represents the wind power data set, which is the input data of the correlation analysis. If there is association rule “Cluster1→SSTI”, it means that when the influencing factors are clustered in cluster 1, it is very likely that the output power oscillation mode contains “SSTI”. “Cluster1” and “SSTI” are both wind power data item set. The item set is also likely to be the clustering combination like “Cluster1& Cluster2” or oscillation modes like “SSR”. According to [14,15], for the association rule “Cluster1→SSTI”, the support degree “support(Cluster1→SSTI)” is the percentage of transactions that “Cluster1” and “SSTI” occurs at the same time to the total transactions, shown in (6): support(Cluster1 → SSTI) =

count(Cluster1 ∩ SSTI) count(D)

(6)

Confidence coefficient confidence(Cluster1→SSTI) is the proportion of appearance of “SSTI” given that “Cluster1” happens, shown in (7): confidence(Cluster1 → SSTI) =

support(Cluster1 ∩ SSTI) support(Cluster1)

(7)

In transaction set D, the rule satisfying the minimum support condition minsup and the minimum confidence condition minconf is the strong association rule. In this paper, the time cost of scanning can be reduced because the preceding item is limited in the cluster item-set and the subsequent item is limited in oscillating mode item-set. The first step is to use the hierarchical sequential search method which is the same as the Apriori algorithm. The difference is that the frequent 1 item-set is searched in the oscillating modes, while from frequent 2 item-set, the search area is reduced to the cluster item-set. The frequent k item-set are then used to generate frequent (k + 1) item-set. The circulation is done until the new frequent sets cannot be found. When producing frequent k item-set, Apriori mainly accomplishes two tasks, connecting and cutting. The connection process happens when a candidate item-set is generated by connecting the frequent k − 1 item-sets. The cutting process is to get rid of nonfrequent item-set according to the minimum support threshold. Thus, the frequent k item-set is obtained. Due to the limitation in the first step, the frequent item set contains only one oscillation mode as consequent denoted by q. After all the frequent item-sets are found, the second step is to generate association rules by corresponding the different subset pji (i = 1, 2, ..., n) of frequent preceding item-set pj (j = 1, 2, ... m) with q exclusive to different subsequent item-set qj , and then calculating the confidence level by (8): support(q j ) ≥ mincon f (8) support( p ji ) when the inequality is satisfied, the rule “ p ji → qi ”can be output. The improved algorithm flow is shown in Figure 4. To show the advantages of the Improved algorithm more clearly, comparison tabulation between ‘Improved Apriori Algorithm’ and ‘Apriori algorithm’ is given by Table 4.

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Step1 produce frequency item-set Generating frequent 1 item-set by the oscillation mode term-set Minimum support linking

Searching for frequent 2 candidate item-sets

Generating frequency 2 item-set pruning

Linking

Searching for frequent 3 candidate item-sets

Generating frequency 3 item-set pruning

Searching for frequent 2n-1-1 candidate item-sets

Generating frequency 2n-1-1 item-set pruning

Step2 produce association rules Minimum confidence Preceding frequent item-set p11

consequent item-set q1

Association rule p11

q1

Preceding frequent item-set p12

consequent item-set q1

Association rule p12

q1

Preceding frequent item-set p1n

consequent item-set q1

Association rule p1n

q1

Preceding frequent item-set p21

consequent item-set q2

Association rule p21

q2

Preceding frequent item-set pmn

consequent item-set qm

Association rule pmn

qm

Figure4.4.The Theflowchart flowchartof ofthe theimproved improvedApriori Apriorialgorithm. algorithm. Figure Table 4. Comparison between ‘Improved Apriori Algorithm’ and ‘Apriori algorithm’. Table 4. Comparison between ‘Improved Apriori Algorithm’ and ‘Apriori algorithm’. Comparison Item Search Method Item Restriction Time Cost Comparison Item Search Method Item Restriction Time Cost The preceding item and The preceding item and subsequent Apriori Algorithm Traverse Traverse data High Apriori Algorithm thethe data set set High subsequent are unrestricted item item are unrestricted Improved Apriori Search in the The preceding item and Improved Apriori Search in the appointed The preceding item and subsequent Low Algorithm appointed data set subsequent item are restricted Low Algorithm data set item are restricted

3.3.Modeling Modelingofofthe theCorrelation CorrelationAnalysis Analysis 3.3. Basedon onthe thealgorithm algorithmabove, above, the the correlation correlation analysis analysis model model of of wind wind speed/voltage speed/voltagefluctuation fluctuation Based clustersand andoscillation oscillationmodes modesisisestablished. established. The Themodeling modelingprocess process is is shown shown in in Figure Figure 5. 5. clusters In this paper, the data wind generating sets of is based on the sampling frequency of 4000 Hz, including wind speed, grid-connected voltage and current information. Firstly, the raw data is cleaned, and then the original data is clustered by K-Means cluster algorithm to find out and eliminate the noise data. Then, the mean of the data before and after the vacant is used to fill the empty data. To study the influence of wind speed and voltage on the oscillation modes of wind generating sets, the preprocessed data was firstly divided into segments according to the wind speed, and the sectional flow chart is shown in Figure 6.

Obtaining cleaned data

Wind speed Grid-voltage

Dividing data Data Energies 2018, 11, 2370 segment by transforming wind speed

Energies 2018, 11, x FOR PEER REVIEW Output power

Data cleaning

Clustering the cleaned data considering average wind speed and grid-voltage using k-means method

Wind speed/voltage cluster record

Analyzing output power of each segment via Prony algorithm and transferring the frequency to tag data

Oscillation mode tag record

Eliminating noise data with clustering method

Association rules mining Data transforming

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Filling vacancy data with the mean of the adjacent data

Obtaining input data of association analysis Obtaining cleaned data

Determining the optimal cluster number

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Doing association analysis with different cluster number

Comparing the quality of the rules from different k

Wind speed Grid-voltage

Clustering the cleaned data Wind speed/voltage considering averagesupport wind speed and Acquiring frequent item-set Minimum cluster record grid-voltage using k-means method

Output power

Analyzing output power of each Minimum confidence Obtaining association Oscillation moderules segment via Prony algorithm and tag record transferring the frequency to tag data

Dividing data Mining association rules of“wind segment by speed/voltage—>oscillation mode” wind speed

Figure 5. Correlation Analysis Modeling Process. Obtaining input data of association analysis

In this paper, the data wind generating sets of is based on the samplingComparing frequency of 4000 Hz, the quality Doing association analysis of the rules from Determining the optimal cluster number with different information. cluster number including wind speed, grid-connected voltage and current different k Association Firstly, the raw data is cleaned, and then the original data is clustered by K-Means cluster rules mining Minimum support frequent item-set algorithm to find Mining out and eliminate the noise data. Then, the mean of theAcquiring data before and after the association rules of“wind speed/voltage—>oscillation vacant is used to fill the empty data. mode” Minimum confidence Obtaining association rules To study the influence of wind speed and voltage on the oscillation modes of wind generating sets, the preprocessed data was firstly divided into segments according to the wind speed, and the Figure Correlation Analysis Modeling sectional flow chart is shown in Figure 6. Figure 5.5.Correlation Analysis ModelingProcess. Process. In this paper, the data wind generating sets of is based on the sampling frequency of 4000 Hz, Begin including wind speed, grid-connected voltage and current information. Firstly, the raw data is cleaned, and then the original data is clustered by K-Means cluster a new data algorithm to find out and eliminate the noise data. Then, the meanCreate of the data before and after the Write into data segment to store the vacant is used to fill the empty data. segment original data To study the influence of wind speed and voltage on the oscillation modes of wind generating Yes sets, the preprocessed data was firstly divided into segments according to the wind speed, and the Read6.original data sectional flow chart is shown in Figure No Value change > 0.05 m/s

by sampling sequence Begin

Subsection finished

Yes

No Create aWind new data value segment to store the original data

Data read finished Write into data segment

Yes Figure Figure6.6.Flowchart Flowchartof ofdata datadivision divisionby bywind windspeed. speed. Read original data

No

Value change > 0.05 m/s value by sampling Original aadata to speed Originaldata dataisisread readand andwritten writteninto into datasegment segmentaccording according towind wind speed valuein insampling sampling sequence sequence. When wind speed change rate is more than 0.05 m/s, a new data segment is built and sequence. When wind speed change rate is more than 0.05 m/s, a new data segment is built and used used to record the subsequent circulation is done until the final data segment is obtained. to record the subsequent data.data. This This circulation is done until No the final data segment is obtained. The The sampling point of each data segment is approximately 4000. Thesampling sampling data in in the Yes sampling point of each data segment is approximately 4000. The data the same same data data Subsection Wind Data read finished finished value segment is analyzed. Records can be extracted from each data segment time sequence, and segment is analyzed. Records can be extracted from each data segment time sequence, andact actas asthe the input inputof ofcorrelation correlationanalysis. analysis.After Afterthe thedata dataisissegmented segmentedaccording accordingto towind windspeed, speed,the themean meanof ofwind wind Figure 6. Flowchart of data division by wind speed. speed inin the record. speedin ineach eachsegment segmentisisrecorded recorded thecorresponding corresponding record. The voltage effective value is calculated according to the sliding window principle. The influence Original data is read and written into a data segment according to wind speed value in sampling of voltage fluctuation on the power oscillation modes is required to be observed, so in each data sequence. When wind speed change rate is more than 0.05 m/s, a new data segment is built and used segment, the difference between the maximum and the minimum of the three phase rms voltage is to record the subsequent data. This circulation is done until the final data segment is obtained. The sampling point of each data segment is approximately 4000. The sampling data in the same data segment is analyzed. Records can be extracted from each data segment time sequence, and act as the input of correlation analysis. After the data is segmented according to wind speed, the mean of wind speed in each segment is recorded in the corresponding record.

average of three phase fluctuations as is shown in (10):

ΔVA = VA rms max − VA rms min  ΔVB = VB rms max − VB rms min ΔV = V C rms max − VC rms min  C

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(9)

used as the indicator of the voltage fluctuations is shown in (9). Total voltage fluctuation takes the average of three phase fluctuations as Δ isV shown = ΔVin (10): +ΔV +ΔV / 3

(10)

Energies 2018, 11, 2370

(

A

B

C

)

  A = VArmsmax − VArmsmin  ∆V Thus, each data segment record stores a wind speed value, three phase voltage fluctuation (9) ∆VB = VBrmsmax − VBrmsmin   ∆V value. indicators, and a total voltage fluctuation In order to study the combined effects of these factors, = V − V C Crmsmax Crmsmin

the data segments studied were clustered according to wind speed, ΔVA , ΔVB , ΔVC , and Δ V . The

(10) segment (∆VA + ∆VB + ∆Vdata clustering results are recorded in are∆V the=corresponding C ) /3 segment. When k = 6, if a data is clusteredThus, in cluster 1, the clusterrecord tag of this adata is [cluster 1, cluster 2, fluctuation cluster 3, cluster 4, each data segment stores windsegment speed value, three phase voltage cluster indicators, 5, cluster and 6] = a[1, 0, 0, 0, 0, 0]. total voltage fluctuation value. In order to study the combined effects of these factors, the data segments studied were clustered wind speed, ∆Vmode ∆VC , and results ∆V. A , ∆VB ,analysis Meanwhile, Prony analysis is performed on according each datatosegment. The of the The clustering results are recorded in are the corresponding data segment. When k = 6, if a data small-signal model in the second part are used to filtrate oscillation frequency within a certain error segment is clustered in cluster 1, the cluster tag of this data segment is [cluster 1, cluster 2, cluster 3, range and the filtering rules are shown in Table 3. cluster 4, cluster 5, cluster 6] = [1, 0, 0, 0, 0, 0]. The oscillation datais and the cluster are The summarized to results be theofinput Meanwhile,mode Prony tag analysis performed on eachtag datadata segment. mode analysis the data of correlation analysis. Then thesecond association be analyzed. Finally, within the association rules can be small-signal model in the part are rules used tocan filtrate oscillation frequency a certain error range and the filtering rules are shown in Table 3. obtained. The oscillation mode tag data and the cluster tag data are summarized to be the input data of correlation analysis. Then the association rules can be analyzed. Finally, the association rules can 4. Correlation Analysis between Wind Speed/Voltage Cluster and Oscillation Modes of Wind be obtained.

Generating Sets

4. Correlation Analysis between Wind Speed/Voltage Cluster and Oscillation Modes of Wind

In Generating this part, Sets 807 data segments are chosen to be the sampling segments to select an optimal clustering number. Association results using different k values are compared first and the optimal In this part, 807 data segments are chosen to be the sampling segments to select an optimal one is chosen fornumber. further analysis.results using different k values are compared first and the optimal one clustering Association is chosen for further analysis.

4.1. Influence of Cluster Number k on Correlation Analysis Result 4.1. Influence of Cluster Number k on Correlation Analysis Result

Total voltage fluctuation (V)

807 data segments are used as a sample to seek the optimal k value. The data segments are 807 data segments are used as a sample to seek the optimal k value. The data segments are clustered by different k values namely = 6, 6,kk==8,8,and and = The 10. The clustering are clustered by different k values namely k k= k =k10. clustering results results are shown in shown in 7 below. Figure Figure 7 below. 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

Cluster1 Cluster2 Cluster3 Cluster4 Cluster5 Cluster6

1

2

3

4

5

Wind speed (m/s)

(a) Figure 7. Cont.

6

7

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Cluster1 Cluster2 Cluster3 Cluster4 Cluster5 Cluster1 Cluster6 Cluster2 Cluster7 Cluster3 Cluster8 Cluster4 6.5

Cluster5 Cluster6 Cluster7 Cluster8

7.0

Wind speed (m/s)

0.4 0.2 0.0 1.5

2.0

2.5

3.0

(b)4.0

3.5

4.5

5.0

5.5

voltage Total voltage Total fluctuation (V) fluctuation (V)

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3.0 2.8 2.6 Energies 2018, 11, x FOR PEER REVIEW 2.4 2.2 2.0 3.0 1.8 2.8 1.6 2.6 1.4 2.4 2.2 1.2 2.0 1.0 1.8 0.8 1.6 0.6 1.4 0.4 1.2 0.2 1.0 0.0 0.8 1.5 0.62.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

Total voltage fluctuation (V)

Total voltage fluctuation (V)

Energies 2018, 11, x FOR PEER REVIEW

6.0

6.5

3.0 2.8 2.6 2.4 2.2 2.0 3.0 1.8 2.8 1.6 2.6 1.4 2.4 2.2 1.2 2.0 1.0 1.8 0.8 1.6 0.6 1.4 0.4 1.2 0.2 1.0 0.0 0.8 0.6 0.4 0.2 0.0

11 of 20 Cluster1 Cluster2 Cluster3 Cluster4 Cluster5 Cluster1 Cluster6 Cluster2 Cluster7 Cluster3 Cluster8 Cluster4 Cluster9 Cluster5 Cluster10 Cluster6 1.5

2.5

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Cluster7

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6.5Cluster8 7.0

Cluster9 Cluster10

Wind speed (m/s) 1.5

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(c)5.0

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Wind speed (m/s)

Wind speed (m/s)

Figure 7. Clustering results with different k values. (a) k = 6; (b) k = 8; (c) k = 10. (b) (c) Figure 7. Clustering results with different k values. (a) k = 6; (b) k = 8; (c) k = 10.

3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

Total voltage fluctuation (V)

Total voltage fluctuation (V)

When k = 6, it can be seen from Figure 7a that the 807 5-dimensional data points are divided Figure results with different k 807 values. (a) k = 6; (b) k =data 8; (c) k =the 10. characteristics k = 6, itCluster can be7.seen from Figure 7apoint that the 5-dimensional points are divided into into When six clusters. 1Clustering is the black data set in the graph, which has of six Cluster 1 is the1.7~2.5 black data point set influctuation. the graph, which 3~5 3~5clusters. m/s wind speed and V total voltage Clusterhas 2 isthe thecharacteristics red data pointofset inm/s the When k = 6, it can be seen from Figure 7a that the 807 5-dimensional data points are divided into wind speed V total voltage fluctuation. 2 isspeed the red point set in fluctuation. the figure, figure, whichand has1.7~2.5 the characteristics of more than 3.5 Cluster m/s wind anddata 0~0.8 V voltage six clusters. Cluster 1 is the black data point set in the graph, which has the characteristics of 3~5 m/s which has the characteristics more than 3.5 m/s wind speed V voltage fluctuation. Cluster Cluster 3 is the green data point set in thefluctuation. graph. This cluster the data characteristics speed wind speed and 1.7~2.5 Vof total voltage Cluster 2 and is has the0~0.8 red point set in of thewind figure, 3greater is the green data point set in the graph. This cluster has the characteristics of wind speed greater than 5 m/s and the voltage fluctuation greater than 2 V. Cluster 4 is the dark blue data which has the characteristics of more than 3.5 m/s wind speed and 0~0.8 V voltage fluctuation. Clusterpoint than m/s and thedata voltage greater than 2 V. Cluster 4 isisthe blue data point set in the set in53 the picture, andpoint it isfluctuation also abundant cluster thedark stateof that occurs most often. is the green set inthe the most graph. This cluster has theand characteristics wind speed greater than 5speed m/s and the voltage greater 2voltage V.isCluster 4 is the dark blue data point setCluster in thewind picture, and it is also the most abundant cluster thefluctuation state that occurs most often. The The wind of cluster 4 isfluctuation 3.5~4.5 m/s, andthan theand is normal 1~1.7 V. 5 is picture, also set them/s, most abundant cluster and is theofstate that occurs most often. speed of cluster 4itisis 3.5~4.5 and the voltage fluctuation isthe normal 1~1.7 V. than Cluster 5m/s iswind the light the light blueand data point in the figure. The wind speed cluster is less 3.5The and the speed of cluster 4 is 3.5~4.5 m/s, and the voltage fluctuation is normal 1~1.7 V. Cluster 5 is the light blue data point set is inbetween the figure. TheV.wind speed of the is less 3.5graph. m/s and voltage voltage fluctuation 1~1.7 Cluster 6 is the redcluster data point setthan in the Thethe cluster has blue data point set in the figure. The wind speed of the cluster is less than 3.5 m/s and the voltage fluctuation is between 1~1.7 V. Cluster 6greater is the red point in the graph. The m/s. cluster has the the characteristics of voltage fluctuation thandata 2.2 V and set wind speed of 4~5.5 Therefore, fluctuation is between 1~1.7 V. Cluster 6 is the red data point set in the graph. The cluster has the characteristics ofdata voltage fluctuation than 2.2 V andofwind 4~5.5 m/s. Therefore, after after clustering, points with thegreater same characteristics windspeed speedofand voltage fluctuation are characteristics of voltage fluctuation greater than 2.2 V and wind speed of 4~5.5 m/s. Therefore, after clustering, data points with the same characteristics of wind speed and voltage fluctuation are clustered into the same cluster. clustering, data points with the same characteristics of wind speed and voltage fluctuation are clustered into the same cluster. When k = 8, as shown in Figure 7b, clusters 1, 3, and 6 in Figure 7a are subdivided into 4 clusters. clustered into the same cluster. WhenWhen k4=and 8,k as in Figure 7b,7b,clusters in Figure7a7a are subdivided clusters. The cluster in 7aFigure are subdivided into three clusters. And when k = 10, as is4shown in =58,shown asFigure shown in clusters1, 1,3, 3, and and 66 in Figure are subdivided intointo 4 clusters. The cluster 4 and 5 in52Figure 7a 7a are subdivided into clusters. And when = 10, is shown Figure 7c,cluster the cluster inFigure Figure 7b issubdivided further subdivided into two clusters, 2asshown and cluster The 4 and in are into three three clusters. And when kclusters =k10, as is in in3 Figure 7c, the cluster in Figure subdivided two clusters, clusters 2 and cluster 3 Figure 7c, the cluster in2 Figure 7b7b is isfurther subdivided into twofluctuation clusters, clusters 2 and 3 respectively. There are2only three points infurther cluster 3, and theinto voltage is less than 0.4 cluster V, which respectively. There are only three points in cluster 3, and the voltage fluctuation is less than 0.4 V, respectively. Thereasare three points in cluster and the fluctuation is less 0.4 V, can be considered theonly abnormal data point. These3,points are voltage filtered out and ignored in than subsequent which canconsidered be considered as abnormal data point. point.In These points are filtered andand ignored in in which can be thethe abnormal These points are filtered ignored correlation analysis under as minimal support data condition. addition, the cluster 9out inout Figure 7b is further subsequent correlation analysis under minimal support condition. In addition, the cluster 9 in Figure subsequent minimal support condition. In 8addition, cluster 9 The in Figure subdivided correlation into clustersanalysis 8 and 9under in Figure 7c, and the range of cluster and 9 is the intersected. wind 7b is further subdivided into clusters 8 and 9 in Figure 7c, and the range of cluster 8 and 9 is 7b is further subdivided clusters and 8 and 9 voltage in Figure 7c, and the of cluster and 9 is speed, three-phase voltageinto fluctuation total fluctuation are range considered in the8clustering, intersected. The wind speed, three-phase voltage fluctuation and total voltage fluctuation are intersected. Theinwind speed, three-phase voltage fluctuation andin total voltage fluctuation are but the subdivision is not necessary terms of the total fluctuation and wind Therefore, considered the clustering, butinthe subdivision is voltage not necessary terms of the speed. total voltage considered inscene the but the subdivision is not necessary of is theclustered total nine clusters iswind likely to be the best case the clustering result. The fluctuation andclustering, speed. Therefore, ninefrom clusters scene is likely toinbeterms the data best case from voltage theagain fluctuation andresult. wind speed. Therefore, nine clusters scene is likelyresults to beare theshown best in case from with k = 9 and the clustering areagain shown inkFigure 8. clustering The data isresults clustered with = 9 and the clustering Figure 8. the clustering result. The data is clustered again with k = 9 and the clustering results are shown in Figure 8. 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

Cluster1 Cluster2 Cluster3 Cluster1 Cluster4 Cluster2 Cluster5 Cluster3 Cluster6 Cluster4 Cluster7 Cluster5 Cluster8 Cluster9 Cluster6 1.5

2.0

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Wind speed (m/s) 1.5

Cluster7 Cluster8 Cluster9

2.0Figure 2.5 8. 3.0 3.5 clustering 4.0 4.5 5.0result 5.5 (k 6.0 6.59).7.0 8.The The clustering Figure result (k= =9).

Wind speed (m/s)

Figure 8. The clustering result (k = 9).

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To further determine the optimal cluster number, a new comparison is made by comparing the correlation analysis results of different k values namely k = 8, k = 9 and k = 10. 4.1.1. The Same Data Segment Correspondence To study the effect of wind speed and voltage fluctuation on the oscillation frequency in the same data segment, the cluster tag data is set as input and the oscillation mode tag in the same data segment is the target. Different clustering numbers namely k = 8, k = 9 and k = 10 achieve different association rules as is shown in Table 5. Table 5. Association rules (the same data segment correspondence). k

No.

Preceding Item

Subsequent Item

Support (%)

Confidence (%)

8

1 2 3 4 5 6 7 8 9 10 11 12

0.1–1.8 Hz 23 Hz 45.37 Hz 12.41 Hz 45.37 Hz 23 Hz 45.37 Hz 23 Hz 0.1–1.8 Hz 23 Hz 0.1–1.8 Hz 45.37 Hz

cluster 3 cluster 4 cluster 7 cluster 3 cluster 1 cluster 8 cluster 8 cluster 3 cluster 4 cluster 7 cluster 5 cluster 5

6.1958 18.0917 9.7893 6.1958 4.9566 42.2553 42.2553 6.1958 18.0917 9.7893 4.2131 4.2131

42.0000 41.0959 39.2405 38.0000 37.5000 36.9501 36.6569 36.0000 34.9315 34.1772 32.3529 32.3529

9

1 2 3 4 5 6 7 8 9 10 11 12

0.1–1.8 Hz 23 Hz 45.37 Hz 12.41 Hz 45.37 Hz 23 Hz 45.37 Hz 23 Hz 23 Hz 0.1–1.8 Hz 45.37 Hz 23 Hz

cluster 6 cluster 5 cluster 7 cluster 6 cluster 2 cluster 7 cluster 3 cluster 3 cluster 6 cluster 5 cluster 4 cluster 4

6.0719 20.4461 9.4176 6.0719 4.9566 9.4176 37.6704 37.6704 6.0719 20.4461 6.9393 6.9393

42.8571 41.8182 40.7895 38.7755 37.5000 36.8421 35.8553 35.8553 34.6939 34.5455 33.9286 30.3571

10

1 2 3 4 5

45.37 Hz 23 Hz 45.37 Hz 23 Hz 0.1–1.8 Hz

cluster 5 cluster 1 cluster 4 cluster 5 cluster 1

8.4263 20.4461 4.9566 8.4263 20.4461

42.6471 41.8182 37.5000 36.7647 34.5455

The threshold is adjusted so that the associated rules of output will have higher confidence and support. The support value should not be set too large, or it will result in missing some strong association rules. Therefore, a small support threshold is set at first, and the output rules are sorted by confidence level. The rules with high confidence level are selected and the lowest support value among them is chosen as the support threshold. And the confidence threshold can be set as the minimum confidence value among the selected rules. After the adjusting, the minsup is set as 4, and minconf is 30. For comparison convenience, the main parameters of the rules with different k are presented in Table 6, including the number of rules, minimum support and confidence, maximum support and confidence, mean percentage of support and confidence, the standard deviation percentage of support and confidence, and so on.

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Table 6. Statistics comparison of association rules with different k values (the same data segment correspondence). Comparison Item

k=8

k=9

k = 10

Rule number Minimum support Maximum support Average support (%) the standard deviation of support Mid-value of support Minimum confidence Maximum confidence Average confidence (%) standard deviation of confidence Mid-value of confidence

12 4.213% 42.255% 14.3536 13.8834 7.9926 32.353% 42.0% 36.7715 3.0745 36.8035

12 4.957% 37.67% 14.3432 12.1143 8.1784 30.357% 42.857% 36.9848 3.6034 36.3487

5 4.957% 20.446% 12.5403 7.3547 8.4263 34.545% 42.647% 38.6551 3.4546 37.5000

From the view of the rule number, both k = 8 and k = 9 can produce 12 rules, involving the relationship between multiple frequency components and speed as well as voltage. When the cluster number is 10, there are only five rules, and these five rules only involve three frequency components. Therefore, k = 10 is excluded. Then k = 8 and k = 9 are compared. From the perspective of the support level, their statistical indicators are very close, and their standard deviations are large too which means both of them are not centralized. From the point of confidence level, compared with k = 8, k = 9 has smaller minimum confidence, almost the same maximum confidence and a larger standard deviation. This indicates that considering rules with a confidence level, k = 9 has a higher confidence level than k = 8. Hence, k = 9 brings higher quality association rules. 4.1.2. The Adjacent Data Segments Correspondence (for Prediction) When studying the factor influence of the previous data segment on the oscillation mode of the next data segment, the target data becomes the oscillation modes in the next segment. Input data is still the cluster tag. Like the analysis of the same segment, correlation analysis is done under different clustering numbers, namely k = 8, k = 9 and k = 10. After adjusting, the minsup is set as 6, and the minconf is 29. Results are shown in Table 7. Table 7. Association rules (the adjacent data segments correspondence). k

No.

Preceding Item

Subsequent Item

Support (%)

Confidence (%)

8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

45.37 Hz 12.41 Hz 23 Hz 23 Hz 23 Hz 45.37 Hz 45.37 Hz 23 Hz 45.37 Hz 45.37 Hz 45.37 Hz 23 Hz 45.37 Hz 23 Hz 12.41 Hz 23 Hz

cluster 4 & cluster 8 cluster 4 & cluster 8 cluster 4 & cluster 8 cluster 4 cluster 8 cluster 8 cluster 4 cluster 7 cluster 1 cluster 7 cluster 5 cluster 5 cluster 3 cluster 3 cluster 6 cluster 1

4.71464 4.71464 4.71464 18.1141 42.1836 42.1836 18.1141 9.8015 4.9628 9.8015 4.2184 4.21836 6.2035 6.2035 10.67 4.9628

47.3684 42.1053 42.1053 37.6712 37.0588 36.4706 35.6164 35.4430 35 32.9114 32.3529 32.3529 32 32 31.3953 30

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Table 7. Cont. k

No.

Preceding Item

Subsequent Item

Support (%)

Confidence (%)

9

1 2 3 4 5 6 7 8 9 10 11 12 13

23 Hz 23 Hz 23 Hz 45.37 Hz 45.37 Hz 45.37 Hz 45.37 Hz 23 Hz 45.37 Hz 12.41 Hz 45.37 Hz 12.41 Hz 23 Hz

cluster 5 cluster 3 cluster 7 cluster 4 cluster 2 cluster 5 cluster 7 cluster 6 cluster 3 cluster 1 cluster 6 cluster 5 cluster 2

20.4715 37.7171 9.4293 6.9479 4.9628 20.4715 9.4293 6.0794 37.7171 10.6700 6.0794 20.4715 4.9628

38.7879 38.1579 36.8421 35.7143 35 33.9394 32.8947 32.6531 32.5658 31.3953 30.6122 30.3030 30

10

1 2 3 4 5 6 7 8

23 Hz 23 Hz 45.37 Hz 45.37 Hz 45.37 Hz 12.41 Hz 12.41 Hz 23 Hz

cluster 1 cluster 5 cluster 4 cluster 1 cluster 5 cluster 1 cluster 6 cluster 4

20.4715 8.43672 4.9628 20.4715 8.4367 20.4715 10.6700 4.9628

38.7879 38.2353 35 33.9394 33.8235 30.3030 30.2326 30

The same comparison is given in Table 8. Table 8. Statistics comparison of association rules with different k values (the adjacent data segments correspondence). Comparison Item

k=8

Rule number Minimum support Maximum support Average support (%) the standard deviation of support Mid-value of support Minimum confidence Maximum confidence Average confidence (%) the standard deviation of confidence Mid-value of confidence

16 4.218% 42.184% 12.2364 12.5273 6.2035 30.0% 47.368% 35.7407 4.7163 35.2215

k=9

k = 10

13 8 4.963% 4.963% 37.717% 20.471% 15.0315 12.3604 11.6484 6.9741 9.4293 9.5533 30.0% 30.0% 38.788% 38.788% 33.7589 33.7902 2.9510 3.4930 32.8947 33.8815

From the view of rule number, k = 10 produces the least number of rules and can be excluded; k = 8 can generate 16 rules, where the first three rules both have the previous item with two Clusters; k = 9 produces 13 association rules, less than k = 8, and the statistics of the rule confidence are all less than k = 8. Therefore, in the adjacent segment analysis, k = 8 brings higher quality association rules. 4.2. Association Rule Analysis of Wind Speed/Voltage Cluster And Oscillation Modes Further analysis of the association rules between wind speed/voltage clusters and oscillation modes of wind generating sets is carried out with 1500 data segments. According to the analysis in Section 4.1.1, k = 9 is taken. The clustering results are shown in Figure 9.

Total voltage fluctuation (V)

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3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

Cluster1 Cluster2 Cluster3 Cluster4 Cluster5 Cluster6 Cluster7 Cluster8 Cluster9 1.5

2.0

2.5

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3.5

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4.5

5.0

5.5

6.0

6.5

7.0

Wind speed (m/s)

Figure Figure9.9.The Theclustering clusteringresult resultwith with1500 1500data datasegments segments(k(k==9). 9).

The clustering result is basically consistent with 807 points. The cluster center parameters of these Table 9. Cluster center (k = 9). nine clusters are shown in Table 9. The clustering center will affect the result of clustering. In the Cluster analysis Wind V-A V-C Voltage subsequent withSpeed more data segments, theV-B initial values of the cluster centerFluctuation should be set cluster 1 5.3710 2.2746 2.1476 2.1994 2.2072 consistently to achieve the same clustering effect. cluster 2 4.1656 0.4119 0.3693 0.4125 0.3979 cluster 3 5.0864 2.7239 2.5850 Table 9. Cluster2.5004 center (k = 9).2.5306 cluster 4 2.1246 1.3252 1.2975 1.3173 1.3133 Cluster Wind Speed V-A V-B V-C Voltage Fluctuation cluster 5 4.0849 1.1553 1.1468 1.1374 1.1465 2.2746 2.1476 2.1994 2.2072 2.1732 cluster 6 cluster 1 4.46255.3710 2.2289 2.1224 2.1684 0.4119 0.3693 0.4125 0.3979 1.4302 cluster 7 cluster 2 4.32264.1656 1.4596 1.4068 1.4241 cluster 3 5.0864 2.7239 2.5004 2.5306 2.5850 cluster 8 cluster 4 3.23412.1246 1.4214 1.3658 1.3975 1.3252 1.2975 1.3173 1.3133 1.3949 cluster 9 cluster 5 6.15924.0849 2.4109 2.3131 2.3499 1.1553 1.1468 1.1374 1.1465 2.3580 cluster 6

4.4625

2.2289

2.1224

2.1684

2.1732

The clustering are transformed tag data,1.4241 and the final association input data is cluster 7 results4.3226 1.4596 into1.4068 1.4302 cluster 1.3658 1.3975 1.3949 and are shown in obtained. After the8Apriori3.2341 correlation 1.4214 analysis, the association rules are achieved 6.1592 2.4109 2.3131 2.3499 2.3580 Table 10. cluster 9 10. Association rules of and 1500the datafinal segments. The clustering results areTable transformed into tag data, association input data is obtained. After the Apriori correlation analysis, the association rules are achieved and are shown in Table 10. No. Preceding Item Subsequent Item Support (%) Confidence (%) 1 45.37 Hz cluster 9 8.1142 41.6667 Table 10. Association rules of 1500 data segments. 2 12.41 Hz cluster 3 6.7618 41.1111 No.45.37Preceding Item Subsequent Support (%) Confidence (%) 3 Hz cluster 8 Item 15.9279 40.0943 4 cluster 6.7618 10.1–1.8 Hz 45.37 Hz cluster39 8.1142 41.6667 36.6667 2 23 Hz12.41 Hz cluster73 6.7618 41.1111 35.7143 5 cluster 15.7776 3 45.37 Hz 45.37 Hz cluster58 15.9279 40.0943 35.2025 6 cluster 24.1172 4 0.1–1.8 Hz cluster 3 6.7618 36.6667 7 23 Hz cluster 5 24.1172 34.5794 5 23 Hz cluster 7 15.7776 35.7143 8 23 Hz cluster 3 6.7618 6 45.37 Hz cluster 5 24.1172 35.2025 34.4444 9 cluster 8.6401 7 23 Hz 23 Hz cluster65 24.1172 34.5794 33.9130 8 45.37 Hz23 Hz cluster63 6.7618 34.4444 33.0435 10 cluster 8.6401 9 23 Hz cluster 6 8.6401 33.9130 11 45.37 Hz cluster 1 13.7491 32.2404 10 45.37 Hz cluster 6 8.6401 33.0435 12 cluster 13.7491 11 23 Hz45.37 Hz cluster11 13.7491 32.2404 30.6011 13 cluster 8.1142 12 23 Hz 23 Hz cluster91 13.7491 30.6011 30.5556 1345.37 Hz23 Hz cluster79 8.1142 30.5556 30.4762 14 cluster 15.7776 14

45.37 Hz

cluster 7

15.7776

30.4762

As Table 10 indicates, the association rules are mainly concentrated in the three modes: 45.37 Hz, 23 Hz and 12.41 Hz. In the correlation analysis results, there is no association rule of 1.92 Hz, 79 Hz and 4.37 Hz. It shows that in the output power of the wind generating sets, the oscillation components of these three frequencies occupy less.

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Total voltage fluctuation(V)

Among the 14 association rules, rule “cluster 9 → 45.37 Hz” has the maximum confidence level which2018, is 41.67%. 5.5~6.75 Energies 11, 2370 According to the clustering results, the “cluster 9” has the characteristics of 16 of 21 m/s wind speed and 2.0~2.6 V voltage fluctuation. This rule indicates that the wind speed and voltage fluctuation cluster will rapidly cause the 45.37 Hz frequency component, and the probability of As Tableis10over indicates, the association the three 45.37 Hz, occurrence 40%. The confidencerules levelare of mainly the ruleconcentrated “cluster 3 →in12.41 Hz” modes: ranks the second, 2341.11%. Hz andThe 12.41 Hz. In the correlation analysis results, there is no association rule of 1.92 Hz, 79 Hz clustering results show that the “cluster 3” has the characteristics of high voltage and 4.37 Hz. and It shows that in wind the output of the wind generating sets, the oscillation components fluctuation 4~5.75 m/s speed.power The rule states that such a combination will quickly lead to a of12.41 theseHz three frequencies occupy less. frequency component, and the probability of occurrence is over 40%. The confidence level Among 14 association rule reaches “cluster over 9→45.37 has the maximum confidence level of the rule the “cluster 8 → 45.37rules, Hz” also 40%.Hz” According to the clustering results, the which is 41.67%. According to the clustering results, the “cluster 9” has the characteristics of “cluster 8” has the characteristics of 1~1.8 m/s voltage fluctuation and the 2.5~3.5m/s wind speed. The 5.5~6.75 m/sthat wind speed and 2.0~2.6 Vwill voltage fluctuation. This ruleHz indicates that the wind speed and rule states such a combination quickly cause the 45.37 frequency component, and the voltage fluctuation cluster will rapidly cause the 45.37 Hz frequency component, and the probability of probability of occurrence is up to 40%. Meanwhile, the rules with anterior “cluster 4” with the occurrence is over The confidence rulevoltage “clusterfluctuation 3→12.41 Hz” ranks the second, 41.11%. characteristics of40%. the wind speed lesslevel thanof 2.5the m/s, among 1~1.6 m/s never show The clustering results show that the “cluster 3” has the characteristics of high voltage fluctuation up in the result. and 4~5.75 m/s wind speed. The rule states that such a combination will quickly lead to a 12.41 Hz frequency component, and the probability is over 40%. The confidence level of the rule 4.3. Prediction of Oscillation Mode Based on of theoccurrence Apriori Algorithm “cluster 8→45.37 Hz” also reaches over 40%. According to the clustering results, the “cluster 8” has To predict the oscillation mode, input becomes the combination of the clustering tag data in the the characteristics of 1~1.8 m/s voltage fluctuation and the 2.5~3.5m/s wind speed. The rule states previous data segment corresponding to the oscillation frequency tag segment in the next. 1500 data that such a combination will quickly cause the 45.37 Hz frequency component, and the probability of segments are taken for analysis. According to the above analysis in 4.1.2, k is given the value of 8, occurrence is up to 40%. Meanwhile, the rules with anterior “cluster 4” with the characteristics of the and the clustering result is shown in Figure 10. wind speed less than 2.5 m/s, voltage fluctuation among 1~1.6 m/s never show up in the result. The clustering result is consistent with 807 points. Among all the clusters, cluster 2 is the largest and cluster the smallest, is different the result in part A above because different 4.3. Prediction 4ofisOscillation Modewhich Based on the Apriorifrom Algorithm cluster centers are selected. When cluster centers are chosen like Figure 10, the elements of cluster 4 To predict the oscillation mode, input becomes the combination of the clustering tag data in the can be considered as outliers and will be ignored by the minimum support condition in the previous data segment corresponding to the oscillation frequency tag segment in the next. 1500 data correlation analysis. segments are taken for analysis. According to the above analysis in 4.1.2, k is given the value of 8, and the clustering result is shown in Figure 10. 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

Cluster1 Cluster2 Cluster3 Cluster4 Cluster5 Cluster6 Cluster7 Cluster8 1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

wind speed(m/s)

Figure data segments (k(k = =8).8). Figure10. 10.Clustering Clusteringresult resultwith with1500 1500 data segments

The result is consistent with8807 points. Amonginall the 11. clusters, 2 is the Theclustering cluster center parameters of these clusters are shown Table In thiscluster part, the cluster largest 4 is result the smallest, which which is different from the affects result in abovejudgment. because center and willcluster affect the of the cluster means it also thepart finalA mode different cluster centers are selected. When cluster centers are chosen like Figure 10, the elements Therefore, when the association rules are applied to oscillation mode prediction, initial values of of the cluster can bemust considered as outliers be ignored by the minimum condition in the cluster4 center be consistent withand thewill training condition to achieve thesupport same clustering effect. correlation analysis. The cluster center parameters of these 8 clusters are shown in Table 11. In this part, the cluster center will affect the result of the cluster which means it also affects the final mode judgment. Therefore, when the association rules are applied to oscillation mode prediction, initial values of the cluster center must be consistent with the training condition to achieve the same clustering effect.

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Table 11. Cluster center (k = 8). Cluster

Wind Speed

V-A

V-B

V-C

Voltage Fluctuation

cluster 1 cluster 2 cluster 3 cluster 4 cluster 5 cluster 6 cluster 7 cluster 8 cluster 9

2.42045 1.25799 2.24225 0.26148 2.68967 1.38416 2.00854 0.46793 2.42045

2.28851 1.23799 2.14732 0.2329 2.48604 1.33245 1.87115 0.41485 2.28851

2.30949 1.23884 2.20835 0.27851 2.52175 1.36456 1.91066 0.44918 2.30949

2.33949 1.24494 2.19931 0.25763 2.56582 1.36039 1.93011 0.44399 2.33949

6.04808 4.14762 5.17199 5.67557 4.97684 2.92717 4.14033 3.90241 6.04808

The clustering result is tag-converted to obtain the final associated input data. After correlation analysis, the association rules are shown in Table 12. Table 12. Association rules of 1500 data segments (the adjacent data segments correspondence). No.

Preceding Item

Subsequent Item

Support (%)

Confidence (%)

1 2 3 4 5 6 7 8 9 10 11

45.37 Hz 23 Hz 45.37 Hz 45.37 Hz 23 Hz 23 Hz 12.41 Hz 23 Hz 12.41 Hz 23 Hz 45.37 Hz

cluster 8 cluster 5 cluster 5 cluster 6 cluster 6 cluster 7 cluster 1 cluster 1 cluster 7 cluster 3 cluster 7

15.9398 24.1353 24.1353 8.6466 8.6466 15.7895 13.7594 13.7594 15.7895 6.6917 15.7895

41.5094 37.3832 34.2679 33.9130 33.9130 33.8095 32.7869 30.6011 30.4762 30.3371 29.5238

From the results in Table 12, the wind speed and voltage fluctuation of the previous data segment mainly affect partial oscillation modes of the next data segment, including 45.37 Hz, 23 Hz, and 12.41 Hz. As the same with the result in the same data segment analysis, the wind speed and voltage fluctuation of the previous data segment are irrespective with mode 1.92 Hz, 79 Hz, and 4.37 Hz of the next data segment. Different from the same data segment analysis result, the association between the wind speed and voltage of the previous data segment and the low-frequency oscillation mode of the next data segment is weakened, indicating that the two factors have less influence on the low-frequency oscillation mode of the next data segment. The support degree is related to the number of clusters, so we use it only as a threshold for rule screening. The analysis of rules mainly depends on the confidence level. Among all the rules, rule “cluster 8→45.37 Hz” has the highest confidence level of 41.5%. As can be seen from Figure 10, the wind speed of the cluster 8 is between 3.2 m/s and 4.5 m/s, and the voltage fluctuation is low. Meanwhile, the mode 45.37 Hz is a SSCI mode, which means the controller acts to stable the output power but at the same time interacts with the fixed series compensation, resulting in the SSCI mode in the next data segment. Then, 200 data segments are selected to predict the three modes of 45.37 Hz, 23 Hz, and 12.41 Hz. These 200 points are clustered in the same cluster center of Table 10. Most of these points belong to clusters 2, 3, 6, and 7. Rules 4, 5, 6 and 9, 10, 11 can be extracted from Table 11 as the oscillation mode prediction result, namely “cluster 6→45.37 Hz”, “cluster 6→23 Hz”, “clustering” 7→23Hz”, “cluster 7→12.41Hz”, “cluster 3→23Hz”, “cluster 7→45.37 Hz”. The confidence levels of these six rules are taken as the predicted value, which means that when the previous item occurs, the occurrence probability of the latter item is the corresponding confidence value. Prony analysis is performed on the

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performed on the actual power curve of the 200 data segments to obtain the actual oscillation modes. The actual is of thethe segment number percentage. Statistical prediction errors are obtained in value Table 13. actual powervalue curve 200 data segments to obtain the actual oscillation modes. The actual is the segment number percentage. Statistical prediction errors are obtained in Table 13. Table 13. Confidence level analysis of prediction and reality. No.

Preceding Item

1 No. 2 1 23 34 45 56 6

23 HzItem Preceding 45.37 Hz 23 Hz 23 Hz 45.37 Hz 45.37 23 HzHz 23 Hz 45.37 Hz 23 HzHz 12.41 12.41 Hz

Table 13. Confidence level analysis of prediction and reality. Subsequent Item Predict Confidence (%) Actual Confidence (%)

cluster 6Item Subsequent cluster 7 cluster 6 cluster cluster 37 cluster cluster 63 cluster cluster 76 cluster 77 cluster cluster 7

33.91 Predict Confidence (%) 29.52 33.91 30.34 29.52 33.91 30.34 33.81 33.91 33.81 30.48 30.48

38.98 Actual Confidence (%) 36.97 38.98 33.33 36.97 32.20 33.33 28.57 32.20 28.57 26.89 26.89

Error 5.07 Error 7.45 5.07 2.99 7.45 −1.71 2.99 −−5.24 1.71 −−3.59 5.24 −3.59

Figure 11 is a line graph comparing the confidence level of predicted results and practical results. Figure 11 is a line graph comparing the confidence level of predicted results and practical results. 100

predicted practical

confidence level%

80

60

40

20

0 1

2

3

4

5

6

rule number

Figure 11. The comparison of the results. Figure 11. The comparison of the results.

From the prediction results, the maximum confidence level error between the predicted value From thevalue prediction results, the8%, maximum confidence rules level related error between the predicted value and the actual does not exceed and the association to the clustering results of and the actual value does not exceed 8%, and the association rules related to the clustering results 200 predicted data segments are all confirmed, indicating that prediction rules obtained by trainingof 200 data predicted dataare segments all confirmed, indicating that prediction rules6→ obtained by has training 1500 segments alreadyare highly credible. Among them, the rule “cluster 45.37 Hz” the 1500 data segments are already highly credible. Among them, the rule “cluster 6 45.37 Hz” has the → smallest error, which means the probability that the wind speed/voltage combination of cluster 6 smallest error, which means the probability that the wind speed/voltage combination of cluster induces the 45.37 Hz mode is very close to 0.3391; the rule “cluster 7→45.37 Hz” has the largest error,6 induces the 45.37 mode is very to 0.3391; the rule “cluster 7 → 45.37 Hz” has the largest error, indicating that the Hz probability that close the wind speed/voltage combination of the cluster 7 induces the indicating that the probability that the wind speed/voltage combination of the cluster 7 induces the 45.37 Hz mode is around 0.2952. The prediction and actual confidence percentage here are statistical 45.37 Hz mode is around 0.2952. The prediction and actual confidence percentage here are statistical values. As the sample size increases, the statistical value will be close to the probability value, and the values. Asresult the sample size increases, the statistical value will be close to the probability value, and prediction will have higher credibility. the prediction result will have higher credibility. 5. Conclusions 5. Conclusions In this paper, association analyzing model of correlation between wind speed/voltage fluctuation In and thisoscillation paper, association analyzing model of correlation wind speed/voltage clusters modes is established. The traditional power between signal processing method is fluctuation clusters and oscillation modes is established. The traditional power signal processing combined with a data mining algorithm to mine association rules between the oscillation modes and method is combined with a data mining algorithm mine association betweenare theasoscillation main influencing factors, using metered data of windto generating sets. Therules conclusions follows. modes and main influencing factors, using metered data of wind generating sets. The conclusions are •as follows. The association rules between clusters and oscillation modes can be obtained by analyzing the metered data via improved Apriori algorithm. The rules are denoted by “Wind speed/voltage • fluctuation The association rules→between clusters and oscillation modes can belevel obtained analyzing the clustering oscillation mode”. The higher the confidence of an by association rule datathe viaprobability improved of Apriori algorithm. The rulesmodes are denoted by “Wind speed/voltage is,metered the greater corresponding oscillation occurrence is. fluctuation clustering → oscillation mode”. The higher the confidence level of an association rule • In association rule analysis, support level does not need to be set too high. Low support and is, the greater the probability of corresponding oscillation modes occurrence is. high confidence can reflect the strong correlation between a cluster and the corresponding mode. • In association rule analysis, support level does not need to be set too high. Low support and high confidence can reflect the strong correlation between a cluster and the corresponding mode.

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•

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Even when the cluster contains few elements, it is also easy to cause the corresponding oscillation mode in the power. Wind speed/voltage fluctuation cluster number has a great influence on association rules. Optimal cluster number corresponds to highest support and confidence level. The results of correlation analysis show that different clusters can lead to different oscillation components, and large voltage fluctuation may quickly induce SSCI component in power. The association rule of adjacent data segments can be used to predict the oscillating mode of the wind generating sets. The error between the prediction result and the actual situation is small, indicating that the confidence level is very close to the probability value. As the sample capacity increases, the statistical value will be close to the probability value, and the prediction result will be more credible.

Based on the result, it is possible to directly judge whether there is an oscillation mode under the corresponding conditions directly from the clustering category of voltage fluctuation and wind speed, which provides convenience for the monitor of the wind farm. Besides, the proposed correlation analysis model is also universal and can also be used to analyze oscillation problems of other systems, or harmonic problems, which means the model has a certain reference value for the scientific community too. Author Contributions: Conceptualization, J.M. and D.X.; Methodology, J.M. and D.X.; Software, J.M.; Validation, D.X., C.G. and X.W.; Formal Analysis, J.M.; Investigation, J.M.; Resources, D.X. and X.W.; Data Curation, J.M.; Writing-Original Draft Preparation, J.M.; Writing-Review & Editing, J.M.; Visualization, J.M.; Supervision, D.X., C.G. and X.W.; Project Administration, D.X.; Funding Acquisition, D.X. and X.W. Acknowledgments: This work was supported in part by the National Natural Science Foundation of China (51677114) & State Grid project (SGTYHT/16-JS-198). Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature DFIG SSR SSO SSTI SSCI DC SVPWM Subscript s Subscript r Subscript g Subscript d Subscript q Confidence Support Cluster i minsup minconf Ai αi fi ϕi p N

i = 1, 2, 3, . . .

w dimensionless Hz rad 1 1

Doubly-fed Induction Generator Sub-Synchronous Resonance Sub-Synchronous Oscillation Sub-Synchronous Torque Interaction Sub-Synchronous Control Interaction Direct Current Space Vector Pulse Width Modulation The mark of stator side parameter The mark of rotor side parameter The mark of grid side parameter The mark of d axis parameter The mark of q axis parameter The confidence level in the Apriori algorithm The support level in the Apriori algorithm The ith cluster in the k-means result The minimum support in the Apriori algorithm The minimum confidence in the Apriori algorithm The amplitude The attenuation factor The frequency The initial phase angle of the ith fitting component The component number of fitting functions The number of fitting points

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pj pji qj ∆V A V Armsmax V Armsmin ∆V k (in Section 4)

V V V V

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The jth frequent preceding item-set The ith subset of the jth frequent preceding item-set The jth subsequent item-set corresponding to Pj The voltage fluctuation of phase A The minimum rms voltage of phase A The minimum rms voltage of phase A The total voltage fluctuation The cluster number

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