International Conference on Embedded Systems in Telecommunications and Instrumentation (ICESTI'16), Annaba, Algeria, October, 24-26, 2016
Fault detection in solar photovoltaic arrays using principal component analysis and outlier detection rules S.AOUABDI1,2 1-
Dept. Electrotechnique-UBMA Faculté des sciences de l’ingénieur, Annaba, Algérie 2Research Centre in industrial technologies CRTI, B.P. 64, Cheraga, Algeria (
[email protected])
M.TAIBI Dept. Electronique – UBMA Faculté des sciences de l’ingénieur, Annaba, Algérie (
[email protected])
N.BOUTASSETA1,2 1-
Dept. Electrotechnique-UBMA Faculté des sciences de l’ingénieur, Annaba, Algérie 2Research Centre in industrial technologies CRTI, B.P. 64, Cheraga, Algeria (
[email protected])
Abstract— This paper presents a new method for the detection of different types of faults in photovoltaic arrays. The operation of photovoltaic arrays in outdoor areas requires additional supervision algorithms to be implemented in order to prevent unnecessary energy loss. The proposed method approach allows the detection of the most frequent faults that may arise in any photovoltaic installation. We used the principal component analysis decomposition to extract the main characteristics of the raw data. Outliers detection rules are used consequently to detect a fault occurrence by analyzing the measured current on the strings of the photovoltaic array. Simulation results show the effectiveness of the proposed approach in detecting most common faults in photovoltaic arrays. Keywords— Photovoltaic (PV) arrays, fault detection, principal component analysis (PCA), outlier detection rules, maximum power point tracking. I. INTRODUCTION Solar photovoltaic technologies are receiving more attention due to the deceasing cost of photovoltaic (PV) panels, the expansion of its market and the increasing efficiency of the PV cell contributed by the advances in materials sciences. A better management of the energy of photovoltaic installations increases the efficiency of photovoltaic systems and allows a considerable cost reduction. The energy management software allows also the supervision of the PV installation by analyzing the process variables and detecting abnormal values. Some fault detection methods have been proposed to monitor the state of PV systems. The method used in [1] requires the
measurement of the actual weather conditions, which are not always available and that may bring additional complexity to the fault diagnosis procedure. The fault detection method proposed in [2] used a simple approach based on the evaluation of statistical indicators at each iteration to detect outliers. In this work, we have improved the diagnosis technique proposed in [2] by adding a principal component analysis PCA [5] of the raw data before passing to the calculation of outlier detection rules. Such approach will allow additional robustness to noise and reduces the amount of data to be processed by considering the main component of the original signal. This paper is organized as follows: In the following section we present the analytical model of the photovoltaic array. Section 3 briefly introduces the most common faults in PV installations. In Section 4, we present the proposed approach to fault diagnosis of PV arrays. Simulation results are given in Section 5. Conclusions are given at the end. II. MODEL OF THE PV ARRAY The equivalent electric circuit of a photovoltaic cell is given in Fig.1. The circuit consists of a controlled current source Iph, a diode traversed by a current Id and a series and shunt resistances Rs and Rsh respectively. The controlled current source Iph is dependent on the level of solar irradiation G and the temperature of the photovoltaic cell surface: G I ph = I ph ,n + K I ∆ T (1) Gn
(
)
International Conference on Embedded Systems in Telecommunications and Instrumentation (ICESTI'16), Annaba, Algeria, October, 24-26, 2016
Rs
Iph
Id
Rsh
The partial shading fault is the most frequent fault in PV installation due to the conditions leading to its occurrence [9]. It may be caused by shading of adjacent buildings, leaf drops, soiling, …etc. Fig.2 (d) gives an example of a partial shading of 10 panels of the total 25 panels.
I
V
I
Figure 1. Equivalent circuit of a PV cell.
V
Where Iph,n is the nominal generated current (given at nominal conditions: T=25°C and G=1000W/m²), KI is the short-circuit current/temperature coefficient, ∆T=T-Tn (T and Tn are the current and nominal temperatures), G and Gn are the current and nominal irradiations. The current in the diode Id is given by: V + RsI − 1 I d = I 0 exp (2) aVt I0 the saturation current of the diode is given as follows: I sc,n + K I ∆ T I0 = (3) Voc,n + K V ∆ T −1 exp aVt Where Isc,n is the nominal short-circuit current, Voc,n is the nominal open-circuit voltage. KV is the open-circuit voltage/temperature coefficient, a is a diode constant, Vt is the thermal voltage of the array: Vt=NskT/q, with Ns cells connected in series. k is the Boltzmann constant and q is the electron charge. Rs is the series resistance which depends on the material used to construct the PV cell and its effect is stronger in the voltage source operating region. Rsh is the shunt resistance, its effect is stronger in the current source operating region [3]. For a PV array with Npp parallel panels and Nss series panels, the equivalent circuit is given in figure Fig.2, its output current is given as follows:
(a)
I = I ph N pp
(4)
III. COMMON FAULTS IN PHOTOVOLTAIC ARRAYS In this work, we consider the most common faults that affect the normal operation of photovoltaic arrays. The Line-Ground fault is a short circuit between a live line of a string and the ground (Fig.2 (a)) [6]. Line-Line fault is a short circuit between the strings of a PV array [7]. Mismatch fault arises when one photovoltaic panel or more have electrical characteristics different from that of the rest of the installation [8].
V
(b) I
I
V
(c)
V
(d)
Figure 2. Common faults in photovoltaic installations. IV. FAULT DETECTION USING PCA AND OUTLIER DETECTION RULES
The following section describes the principal component analysis procedure. A. Principal component analysis: Principal component analysis (PCA) is used to reduce noise effects and extract the main components of the signal [4]. A sample vector of n variables is denoted as x ∈ℜ . If we assume that there are m samples, we can construct a data n
matrix N N V + R s ss I V + R s ss I N pp N pp −1 − − I0 N pp exp aVt N ss N ss R sh N pp
I
X ∈ℜm×n in which each row represents a sample [10].
xT (1) T x (2) X = ... T x (m)
(5)
The sample mean and covariance of the variables are calculated from the data matrix X and used to scale the data to zero mean and unit variance. The covariance of x is approximated by the sample covariance matrix
S≅
1 XT X m −1
(6)
International Conference on Embedded Systems in Telecommunications and Instrumentation (ICESTI'16), Annaba, Algeria, October, 24-26, 2016
Principal component analysis (PCA) performs eigendecomposition of the covariance matrix to obtain the n×l
~
n×(n−l )
principal and residual loadings, P ∈ℜ and P ∈ℜ , where l is the number of principal components (PCs) retained in the model.
~ Λ 0 ~T ~~ ~ S = PΛP T = [P P] [P P] = PΛPT + PΛPT (7) 0 Λ The diagonal matrix Λ contains the principal eigenvalues and ~ the diagonal matrix Λ contains the residual eigenvalues. x = xˆ + ~ x (8) Where
t = PT x ∈ ℜl xˆ = PPT x = Pt
(9) (10)
Are the scores and the projection to the PCs, respectively. The
PPT is the projection matrix of the PCs and will be ~ denoted as C . The RS projection matrix will be denoted as C and the projection of x to the RS is defined as matrix
~ ~~ ~ x = PPT x = Cx
(11)
τ 2 = xα2 (l) With (1 − α ) ×100% confidence level. • Combined index ϕ [10]:
(18)
The combined index combines the SPE and T2 indices into one single index as follows:
ϕ=
SPE
δ
+
2
T2
τ
2
= x T φx
(19)
Where
φ=
~ C
δ
2
+
D
(20)
τ2
The process is considered normal if
ϕ ≤ ζ 2 , where the
ζ 2 is ζ 2 = g ϕ xα2 (hϕ )
control limit
(21)
Where
lδ 2 l θ l θ lδ 4 gϕ = 4 + 24 / 2 + 12 = 4 +θ2 / δ 2 2 +θ1 τ δ τ δ τ τ
(22)
θ l θ l hϕ = 2 + 12 / 4 + 24 δ τ δ τ 2
2
B. Fault Detection indices : The most popular statistical indices used for fault detection are SPE and T2 and a combination of the two. • Squared prediction error SPE [10]: 2 ~ ~~ SPE = ~ x = xT PPT x = xT Cx
With a control limit
δ =g 2
SPE 2
δ
2
(12)
as
SPE
xα (h ) With (1 − α ) ×100% confidence level and
θ2 θ1 θ2 h SPE = 1 θ2 g SPE =
(14)
(15) n
Where
(13)
n
θ1 = ∑λi , θ 2 = ∑λ2i i =l +1
and
i =l +1
λi
is the
i th eigenvalue
of the covariance S . • Hotelling’s T2 statistic [10]: The variation of a process in the PCs is measured by the T2 index and it is defined as :
T 2 = t T Λ−1t = xT PΛ−1 PT x = xT Dx T ≤τ
And the control limit
τ
β2 g ϕ = + θ 2 / δ 2 (β + θ1 ) l 2 2 β hϕ = (β + θ1 ) / + θ 2 l With (1 − α ) ×100% confidence level.
τ
is
(25)
In this work, we use outlier detection rules to detect abnormal values of the current variables, it indicate that a fault has occurred in the PV installation. The 3-sigma rule is firstly used to detect outliers that are located outside the range of 3 times the standard deviation of the mean: |x-µ|>3σ
(26)
The second rule is the Hample identifier. It uses the sample median s as a reference value:
(17) 2
(24)
C. Outlier detection rules :
|x-s|>αS
2
(23)
(16)
The process is normal if 2
lδ 2 lδ 4 = 2 + θ1 / 4 + θ 2 τ τ 2 lδ We put = β and after we obtain : 2
S=
1 median ( x − s ) 0.6745
(27) (28)
International Conference on Embedded Systems in Telecommunications and Instrumentation (ICESTI'16), Annaba, Algeria, October, 24-26, 2016
Where s is the sample median, α is a threshold parameter, S is a scale estimator.
The fault detection procedure starts by measuring the current variable in each string of the PV array. The acquired values are passed through a linear transformation (PCA) to extract their main components and reduce the measurement noise (Fig. 3). Outlier detection statistics are then calculated to monitor the current variable for abnormal values. A fault is detected if one of the bounds is bypassed (Fig. 3). Is1
Is2
Is3
Is4
Fault detection using the 3σ rule:
The bounds of the 3σ rule includes the current signal until when the fault is introduced in the time instant (t=5s) where we notice a clear bypass of the bounds of the 3σ rule which indicates an occurrence of a fault. Results 3σ under (faults-1- :Line-line)
-9
3
x 10
Upper bound 3σ Lower bound 3σ PCA(IPV)
2
1
Upper bound of 3 Sigma rule
Normalized string current
V. FAULT DETECTION PROCEDURE
A.
Is5
0
Lower bound of 3 Sigma rule
time of fault
-1
-2
Data acquisition
-3
-4 0
1
2
3
4
5 Data points
6
7
8
9
10 4
x 10
Figure 5. Line-Line fault detection using 3σ rule.
PCA decomposition
Results 3σ rule under fault-2- ( Ground fault)
-8
8
x 10
Upper Bound 3σ Lower bound 3σ PCA(Ipv)
6
Outlier Detection Rules Normalized string current
4
Fault Detection
2
0
-2
time of fault
-4
-6
Figure 3. Proposed fault detection flowchart.
-8 0
1
2
3
4
5 Data points
6
5 Data points
6
7
8
if(i,j) (A)
0
2
3
4
7
8
1
2
3
4
5 Data points
6
5 Data points
6
7
8
0
1
2
3
4
7
8
3.5
1
2
3
4
5 Data points
9 Fault* 1* Line-line Fault* 2* Ground faults Fault* 3* Mismatch faults Faults* 4* Partial shadings
if(i,j) (A) if(i,j) (A)
4
0
9 Fault* 1* Line-line Fault* 2* Ground faults Fault* 3* Mismatch faults Faults* 4* Partial shadings
4
3
4
0
-0.5
time of fault
-1 0
10
1
2
3
4
5 Data points
6
7
8
9
10 4
x 10
Figure 7. Mismatch fault detection using 3σ rule.
4
x 10
Results 3σ rule under fault-4- partial shadings
x 10
Upper bound Lower bound PCA(IPV)
10 4
x 10
6
4
0
3.5
3
9 Fault* 1* Line-line Fault* 2* Ground faults Fault* 3* Mismatch faults Faults* 4* Partial shadings
3.5
3
x 10
-16
1
10 x 10
0.5
8
0
4
if(i,j) (A)
9 Fault* 1* Line-line Fault* 2* Ground faults Fault* 3* Mismatch faults Faults* 4* Partial shadings
5
-5
9
1
6
7
Figure 4. PV Current IPV in the strings.
8
9
10 4
x 10
10
Normalizedstringcurrent
if(i,j) (A)
4
3.5
3
8
Upper bound Lower bound PCA(IPV)
Fault* 1* Line-line Fault* 2* Ground faults Fault* 3* Mismatch faults Faults* 4* Partial shadings
i=1:5; j=1:5
2
7
1.5
Normalizedstringcurrent
In order to validate the proposed approach, we have introduced different types of faults on a 5x5 MSX60 photovoltaic array. The simulations were carried out in STC conditions (T=25°C & G=1000W/m²). Fig.4 presents the current in each string (the PV array has 5 strings), where a fault is introduced in the string at the time instant (t=5s) for each case.
1
6
Results 3σ rule under fault-3-(Mismatch fault)
-9
2
0
5 Data points
Figure 6. Line-Ground fault detection using 3σ rule.
VI. SIMULATION RESULTS
3
4
2
0
-2
4
x 10
time of fault
-4
10 4
x 10
-6 0
1
2
3
4
5 Data points
6
7
8
9
10 4
x 10
Figure 8. Partial shading fault detection using 3σ rule.
International Conference on Embedded Systems in Telecommunications and Instrumentation (ICESTI'16), Annaba, Algeria, October, 24-26, 2016
B. Fault detection using the Hampel identifier rule
6
x 10
-9
4
upper and lower bound of 3 Sigma rule ( faults-Line -line) 2 Normalized string current
The Hampel identifier fixes upper and lower bounds according to the sample median of the original signal. The major inconvenient of such fault detection technique is the need for a stabilization time as in Fig.11, where the bounds are adjusted in real time with the processed signal.
Upper bound of 3 sigma rule (Mismatch faults)
0
upper and lower bound of 3 Sigma rule ( partial shadings) -2
Lower bound of 3 Sigma rule (ground faults)
-4
-6 -9
6
0
1
2
3
4
5 Data points
Results Hampel identifier under fault-1- (Line-line)
x 10
7
8
9
10 4
x 10
Figure 13.The envelop simulation result : faults –Line-line, Mismatch faults, Partial shadings and ground faults .
PCA(IPV) Upper bound Lower bound
4
6
Norm alizedstringcurrent
2 Hampel identifier
-8
0
2
Hampel identifier
x 10
time of fault
-2
1
-4
1
2
3
4
5 Data points
6
7
8
9
10 4
x 10
Figure 9. Line-line fault detection using Hampel identifier rule. -8
Hampel identifier ( Partial shadings)
Normalizedstring current
-6 0
8
Hampel identifier ( ground faults)
1.5
0.5 Hampel identifier ( Mismatch fault)
0
-0.5
-1
Results Hampel identifier under fault-2- Ground faults
x 10
PCA(IPV) Upper bound Lower bound
-1.5
6
-2
Normalized stringcurrent
4
0
1
2
3
4
5 Data points
6
7
8
9
10 4
x 10
Hampel identifier
2
Figure 14.The envelop simulation result : faults –Line-line, Mismatch faults, Partial shadings and ground faults .
0
-2
time of fault
-4
-9
Hampel identifier (Zoom)
x 10 5
-6 0
1
2
3
4
5 Data points
6
7
8
9
10 4
x 10
Hampel identifier (Mismatch faults) 4
Figure 10. Line-ground fault detection using Hampel identifier rule. -9
x 10
Normalized string current
8
PCA(IPV) Upper bound Lower bound
time of fault
Hampel identifier
6
4
Normalized string current
3
Results Hampel identifier under fault-3-Mismatch faults
2
0
2
Hampel identifier ( Partial shadings) 1
Hampel identifier (Line -line ) 0
-1
-2
-2
-3 -4
-4 -6 0
1
2
3
4
5 Data points
6
7
8
9
10 4
x 10
-15
Results under fault-4- Partial shadings
x 10
PCA(IPV) Time of fault
Upper bound Lower bound
Hampel identifier
8
8.5
9
Data points
Figure 11. Mismatch fault detection using Hampel identifier rule. 3
7.5
9.5
10 4
x 10
Figure 15. Zoom on the envelop simulation result : faults – Line-line, Mismatch faults, Partial shadings and ground faults .
2
VII. CONCLUSIONS
Normalizedstringcurrent
1
0
-1
-2
-3 0
1
2
3
4
5 Data points
6
7
8
9
10 4
x 10
Figure 12. Partial shading fault detection using Hampel identifier rule
In this paper, we have considered the problem of detecting faults in photovoltaic installations. The nonlinear nature of the power-voltage characteristic curve of the PV cell has made the diagnosis procedure more difficult. For such Most of the existing methods consider only the problem of fault detection without the possibility to isolate the nature of the fault, and use costly sensors in order to achieve fault detection. The proposed fault detection method uses only current sensors. It
International Conference on Embedded Systems in Telecommunications and Instrumentation (ICESTI'16), Annaba, Algeria, October, 24-26, 2016
is based on the extraction of the main component of the current signal by the PCA method and the calculation of statistical indicators that allow the detection of outliers. Simulation results show the effectiveness of the proposed method in the detection of faults in most of the cases. Further developments can be made to adjust the detection bounds according to the nature of the fault. REFERENCES [1] S. Vergura, G. Acciani, V. Amoruso, G. E. Patrono, and F. Vacca, "A simple model of PV system performance and its use in fault detection", Solar Energy, vol. 84, pp. 624-635, 2010. [2] Y. Zhao, B. Lehman, R. Ball, J. Mosesian, and J.-F. de Palma, "Outlier detection rules for fault detection in solar photovoltaic arrays", in 2013 Twenty-Eighth Annual IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 2913–2920, 2013. [3] M. G. Villalva, J. R. Gazoli, and E. R. Filho, “Comprehensive Approach to Modeling and Simulation of Photovoltaic Arrays,” IEEE Transactions on Power Electronics, vol. 24, no. 5, pp. 1198–1208, May 2009. [4] H. Abdi & L. J. Williams, "Principal component analysis", Wiley Interdisciplinary Reviews: Computational Statistics, vol. 2, no. 4, pp. 433-459, 2010. [5] Jolliffe, Ian. Principal component analysis. John Wiley & Sons, Ltd, 2005. [6] N.Boutasseta, M. Ramdani, and S. Aouabdi, "Performance evaluation of photovoltaic arrays subject to a Line-Ground fault", in 3rd International Conference on Systems and Control, pp. 83–86, 2013.
[7] Y. Zhao, J.-F. de Palma, J. Mosesian, R. Lyons, and B. Lehman, "Line–Line Fault Analysis and Protection Challenges in Solar Photovoltaic Arrays," IEEE Transactions on Industrial Electronics, vol. 60, no. 9, pp. 3784–3795, Sep. 2013. [8] J. D. Bastidas, E. Franco, G. Petrone, C. a. RamosPaja, and G. Spagnuolo, "A model of photovoltaic fields in mismatching conditions featuring an improved calculation speed", Electric Power Systems Research, vol. 96, pp. 81– 90, Mar. 2013. [9] Y.-J. Wang and P.-C. Hsu, "An investigation on partial shading of PV modules with different connection configurations of PV cells," Energy, vol. 36, no. 5, pp. 3069–3078, May 2011. [10] Carlos Alcala and S.Joe Qin, "Reconstruction- based Contribution for Process Monitoring," Proceedings of the 17 th world congress, the IFAC,Seoul? Korea, July 611,2008.
