Case Study: Condition Assessment of a Photovoltaic Power Plant using

Change-point Analysis

Steffen Dienst

, Johannes Schmidt

and Stefan K

uhne

Institute of Computer Science, University of Leipzig, Leipzig, Germany

Institute for Applied Informatics (InfAI) e.V., Leipzig, Germany

Keywords:

Data Mining, Renewable Energy, Condition Monitoring, Photovoltaics, Multivariate Time Series.

Abstract:

Today, the operation of sustainable power plants mainly relies on visualization of power production. Measure-

ment data of such power plants are often discarded. We show the idle potential of such data by applying a

state of the art algorithm to recognize malfunctions in a photovoltaic power plant. Up to now, these failures

could only be found by manual inspection of the power plant every six weeks. Our results show a substantial

ﬁnancial beneﬁt: power outages of power plant components due to fuse failures often can be recognized within

days. This fact results in a reduction of ﬁnancial losses up to at least 63% by being able to schedule repairs

faster.

1 INTRODUCTION

Germany is currently changing the national electricity

production from fossil and nuclear energy to renew-

able energy. This process led to a massive increase of

installed sustainable power plants in Germany within

the last years. According to (Wirth, 2013) there are

currently about 1.200.000 photovoltaic (pv) power

plants in operation in Germany, two thirds of them are

operated by individuals. Since these power plants are

operated by thousands of individuals with a varying

degree of understanding of underlying technical pro-

cesses and mechanisms, there is a necessity of better

tool support.

Typically several sensors are installed which pro-

vide a wide range of measurement data. According to

our experience as well as published case studies like

(Moore and Post, 2008) or (Oozeki et al., 2010), oper-

ators often just visualize the daily gain of the plant to

get an impression of the amount of energy produced.

Even dedicated software systems for monitoring re-

newable power plants, for example as described in

(Papadakis et al., 2005), are often limited to features

like storing and visualizing measurement data. Anal-

ysis algorithms used in practice often are just simple

threshold calculations. Therefore, any malfunctions

in the PV power plant that does not lead to an immedi-

ate total power loss may go unnoticed for a long time.

Such failure conditions might be broken pv modules,

broken cables to individual modules, reduced power

output from inverters etc. Specialized data analysis

software is not widely use in the context of pv power

plant operation, so data often is discarded.

We argue that this data can be used as-is to tell the

operators more about the state of their power plants

and thereby boost the economic gain without any ad-

ditional investments, for example in sensors. We want

to show how to use available algorithms applicable

to pv plant monitoring to detect and thereby miti-

gate the economic losses originating from these fail-

ures. To do so, we are mainly interested in algorithms

that need as little conﬁguration settings as possible to

be able to apply them automatically to many power

plants without customization overheads.

Section 2 presents the subject of this case study: a

pv power plant with two-axis trackers, and the prob-

lems observed when operating this power plant. Sec-

tion 3 shows our reasoning for selecting an applicable

algorithm from the scientiﬁc literature and explains

our application to the problem at hand. The last sec-

tion 4 will present our ﬁndings as well as a discussion.

2 CASE STUDY: TWO AXIS

TRACKER

We have access to the measurement data in 2012 of

a PV power plant with an installed peak power of

2.15MW. It consists of two separate ﬁelds. Each ﬁeld

159

Dienst S., Schmidt J. and Kühne S..

Case Study: Condition Assessment of a Photovoltaic Power Plant using Change-point Analysis.

DOI: 10.5220/0004406801590164

In Proceedings of the 2nd International Conference on Smart Grids and Green IT Systems (SMARTGREENS-2013), pages 159-164

ISBN: 978-989-8565-55-6

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

contains one inverter, which is responsible for con-

verting direct current (DC) power produced by PV

modules into alternating current (AC) power (which

gets fed into the electrical grid). One inverter has two

internal inverter subsystems, the other one has four.

Each inverter subsystem has four distinct inputs for

DC power (in total 24 inputs).

The PV modules in the two ﬁelds are installed on

431 two-axis trackers, that means, the modules are

not mounted on rigid stands but get moved throughout

the day to stay perpendicular to the sun at all times.

For a demonstration of their working principle refer

to (Abdallah and Nijmeh, 2004). Trackers combine

their individual power outputs in so called combiner

boxes which feed their outputs into DC inputs of the

inverter subsystems. That means, the measurements

available in the inverters are the sum of groups of 12

to 24 individual trackers.

Trackers are mechanical devices, meaning they

tend to fail or work sub optimally due to wind, dust

or bird droppings. The most serious failures are fuses

failues. In contrast to a mere reduction of power pro-

duction, if a fuse is open, this tracker will not produce

any power at all. Our dataset contains the dates of

routine six-weekly inspections and the names of the

trackers with failed fuses. If a fuse failes within this

inspection interval it goes unnoticed until six weeks

later.

2.1 Problem Statement

There are no hardware sensors installed on the track-

ers that would allow us to learn about their individual

state of operation remotely. The only data we have

about the condition of any tracker is the accumulated

generated power fed into the inverters (as measured

within the inverters), one insolation sensor per ﬁeld

and maintenance data that shows the dates of fuse re-

pairs per tracker. So, the problem can be stated as the

following: how can we recognize malfunctions in in-

dividual trackers just by using data we can measure in

an inverter?

Figure 1 shows a plot of the DC power input of

a sunny day showing the effects for a fuse failure

around noon. This line chart shows the ratio of in-

solation power to DC current as measured on one DC

input string. After sunrise, around 7am, there were

some clouds which lead to different insolations at the

PV modules and the insolation sensor. These dif-

ferences result in an increased volatility in the chart.

Starting from 7:30am, the rest of the day is sunny.

Around 11am the plot shows the effect of a failed

tracker fuse: the ratio drops visibly. Henceforth the

power production of this string is reduced.

Figure 1: Plot of the DC currents curve of one inverter input,

showing a failing fuse around noon on a cloud free day.

3 METHODOLOGY

We reviewed literature about data mining algorithms

(Gaber et al., 2005), time series analysis (Fu, 2011)

and process control statistics (Venkatasubramanian

et al., 2003) to identify appropriate algorithms that

can help to gain insight about the state of the trackers

described in the use case in section 2. We identiﬁed

three major groups of algorithms appropriate for our

problem:

Simulation Models create a model/simulation of the

inner operations and use its predictions to identify

deviations of behaviour from the predictions, like

(Perpian, 2009).

Anomaly Recognition ﬁnd anomalous behaviour by

various metrics. For an overview we recommend

(Chandola et al., 2012).

Statistical Time Series Analysis apply statistical

measures to time series to distinguish between

normal and anormal behaviour (Hill and Lewicki,

2005).

Creating a model for the whole PV power plant

proved to be not feasible as well as potentially dif-

ﬁcult to transfer to other scenarios. Anomaly recog-

nition, especially conﬁguration free algorithms as

demonstrated in (Keogh et al., 2005), showed some

potential in our pre-study. The effects of fuse fail-

ures and repairs on the shape of the measurement data

curves are very similar to the effects of a cloudy sky.

Both lead to sudden jumps in the power output of

each pv module. Anomaly recognition algorithms,

at least unparametrized instances, tend to mark too

many days of data with bad weather as to be useful

for ﬁnding fuse failures and repairs.

We looked for appropriate algorithms in the re-

search ﬁeld of statistical time series analysis and set-

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tled on change-point analysis as a promising tool for

the problem at hand.

3.1 Change-point Analysis

Change-points describe discrete points in a time series

where the mean of the values changes, i.e. the mean

prior to the change-point is signiﬁcantly (according to

a given conﬁdence value) higher or lower than after

it. This technique is useful for ﬁnding changes at an

unknown point in time. It was described as early as

1971 by (Hinkley, 1971).

Literature discusses a variety of metrics that can

be used to ﬁnd change-points. One of the most

straight forward metric is taking the global maximum

or minimum of the cumulative sum of differences be-

tween the values of the time series from its mean

value. We used the algorithm described by (Wayne,

2000) to ﬁnd change-points in the hourly ratio time

series as described in the last section. As we did not

enhance the algorithm itself but rather focus on its ap-

plication to our use case, we will not give a thorough

description of it but refer to the detailled description

of the author (Wayne, 2000).

The only parameter we varied in our implementa-

tion of the change-point algorithm is the minimal con-

ﬁdence. It determines the probability that the change-

point found is not just due to chance.

3.2 Data Preparation

The data recorded by the inverter represents natural

processes, that is, it depends on the sun light available

at any time. This fact means, we have to deal with

volatile time series. On a sunny day, the power pro-

duction of every given tracker follows a smooth curve

(ﬁgure 2) while on cloudy or rainy days, the shape of

the curve is ragged. Furthermore, the power produc-

tion is not stationary; its value depends on the sun’s

position and therefore on the time of day. We had

to ﬁnd a derived metric that has to have two essen-

tial properties: it has to be stationary (see (Hill and

Lewicki, 2005) for details) and it has to be robust in

spite of different weather conditions.

Our dataset contains direct currents measured on

each inverter input, as described in section 2. Also,

each PV ﬁeld has a single insolation sensors. These

sensors measure the insolation power of the sun on an

area of one square meter. Each sensor, DC as well as

insolation, is averaged every minute, giving 1440 data

points per day. For each DC input, we derive a time

series by dividing the current value by the insolation

value. As the ratio between insolation and absorbed

power should be constant, these derived time series

Figure 2: Zoomed plot of DC/insolation ratios on a sunny

day, showing the change over the day.

are expected to be constant and therefore stationary.

Figure 2 shows that the ratio is not constant but

rather changes throughout the day. The bend of this

curve changes over the year, too. To mitigate this

non-stationarity property, we do not look for change-

points within these intra-day ratios themselves, but

rather on time series derived by taking the average

per hour. That means, for each DC input of each in-

verter, we get get 8 different time series, one for each

hour from 9am to 4pm (ensuring we have sun shine

for every day of the year during this time of day). The

results are several new time series (one per hour of

the sun day, visualized in ﬁgure 3) that have just one

data point per calendar day. These series are station-

ary and can thus be passed into the change-point al-

gorithm used in this case study.

As the raw ratios tend to vary a lot, we also con-

sidered to use not only these values as-is but also

their derived ranked values. To get this data, we sort

all unique values and gave them an index each, ef-

fectively enumerating all distinct values. This proce-

dure is recommended, if data contain outliers (Draper,

1988).

The data preparation process comprises in sum-

mary:

1. ∀ DC sensors ﬁnd the closest insolation sensor

2. Calculate ratios

Insolation

, i = 1..24, j = 1..2 (up

to 24 DC inputs per inverter, up to two insolation

sensors per PV ﬁeld)

3. Derive time series from these ratios by averaging

the ratios per hour between sunrise and sunset

4. Order each time series in ascending order and use

the ranks of each value in place of the raw value

4 EVALUATION

Since a change-point just designates a change in the

CaseStudy:ConditionAssessmentofaPhotovoltaicPowerPlantusingChange-pointAnalysis

161

average of a time series, the algorithm does not distin-

guish between increases and decreases of the mean.

This property allows us to evaluate the feasibility of

applying the change-point algorithm to our problem

of ﬁnding open fuses by looking not for these failure

events but rather for repairs. We do not know when

each fuse failed exactly, but we do know the repair

times. Because of the symmetric behaviour of our al-

gorithm, we can use the results of ﬁnding fuse repairs

to estimate the time required to ﬁnd fuse failures.

We ran the change-point analysis for each ratio of

DC and insolation for the two month period around

repair times. We varied the number of days after a

fuse repair event from 1 to 21 days. Regular mainte-

nance of the PV power plant in our use case is sched-

uled for every six weeks, so we assume that in average

after 21 days (50% of 6 weeks) a failed fuse will be

found manually. We tested different minimal conﬁ-

dences for the changepoints (0.80, 0.90, 0.95, 0.99)

and ran on raw as well as on ranked ratios.

From an algorithmic point of view, our problem

is an information retrieval problem: We know when

fuses were repaired and we are trying to ﬁnd these

events using only the measurement data available.

To evaluate the quality of the results, two metrics

are typically used: precision and recall (Makhoul

et al., 1999). Precision, in our case, is the ratio of

repair events f ound

all repair events

. If the algorithm would mark more

false events than correct repair events, the ratio would

be close to zero. If, on the other hand, approximately

all repair events are found, the ratio would be close

to one. Recall is the fraction of relevant events of all

events returned. Here, recall tells us, what fraction of

all fuse repairs the algorithm can correctly be identify.

Because we only know about repair times of fuses,

we are not able to determine in every instance whether

a change-point that looks like a repair is valid or not.

It could be due to another repair or mere coincidence

(a tracker that gets unstuck by itself). Therefore, in

the results chapter and in the result tables in the ap-

pendix we only provide the recall values and not the

precision.

4.1 Results

Our annotated dataset comprises 41 different fuse re-

pairs in 2012. Each repair affected one up to six fuses

per DC input of an inverter in a given day. The al-

gorithm performed best on the derived time series of

ranked ratios in the hours 1pm to 2pm. We are able to

ﬁnd 36 out of the 41 repair events when assuming a

minimal conﬁdence of 0.95, 1000 bootstrap samples

and a maximal recursion depth of 2. The algorithm

marks all events where more than one fuse were re-

paired at the same time. If only one fuse (out of up

to 24) was repaired, we can still identify 22 out of 27

distinct events. Finding single repairs of single fuses

is the most important case, because we are interested

in applying the algorithm to fuse failures which hap-

pen individually. The recall for ranked ratios in this

case is higher than for raw ratios (0.81 versus 0.59),

please see the details in the result table 1 .

Figure 3 shows a visualization of the results of the

algorithm on one fuse repair in October 9

. It shows

the ranked ratios for the time interval June to Novem-

ber and the sliding average of these ratios as a human

readable indicator. The red vertical lines are change-

points automatically marked by the algorithm. We

can see the fuse repair in October (the ratios jump up)

as well as at least two suspected fuse failures in July.

For economic reasons operators are interested in

being notiﬁed about failures as quickly as possible.

We had a look at how many days the algorithm needs

to mark a change-point after the occurrence happens.

In this case, the results are the other way around: Run-

ning the algorithm on raw ratios ﬁnds single fuse re-

pair events quicker (5.31 days) than on the ranked ra-

tios (9.26 days). The detailed results can be found in

table 1. The table shows, dependent on the conﬁdence

value and the hour of the day, how many days on av-

erage after a fuse got repaired did the algorithm mark

the repair day and what is the recall (percentage of

fuse repairs found).

As we wrote in section 4, we can’t give precision

values or the F1 measure (Sundheim, 1992), because

we don’t have data about every single repair that oc-

curred in this PV power plant in 2012. We only know

about fuse repair dates. If the algorithm marks a data

point as a change-point with a positive change of the

mean, it could be a repair we do not know about, a

tracker that gets unstuck by itself, or it could be due to

too few bootstrap samples or too low minimum con-

ﬁdence.

It is probably not possible to reduce the number

of days needed to recognize failures/repairs signiﬁ-

cantly. The reason is the reduced recognition power of

Figure 3: Plot of ranks of the DC/insolation ratios, showing

one repair on Oct. 9

as well as several potential failures.

Parameters used: conﬁdence=0.99, maxlevel=2.

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Table 1: What is the recall per hour and conﬁdence and how many days does it take to ﬁnd one open fuse (using ranked or

raw ratios)?

Hour

Conﬁdence

0.80 0.90 0.95 0.99

ranked raw ranked raw ranked raw ranked raw

recall days recall days recall days recall days recall days recall days recall days recall days

9 0.70 0.44 10.78 12.58 0.67 0.37 11.81 13.80 0.67 0.33 12.30 13.89 0.56 0.22 14.04 14.00

10 0.70 0.33 9.93 10.33 0.70 0.33 10.48 10.44 0.63 0.33 12.04 11.11 0.59 0.33 13.85 11.78

11 0.85 0.41 8.56 4.91 0.81 0.37 9.70 4.20 0.74 0.37 11.37 4.60 0.67 0.37 13.74 5.10

12 0.81 0.74 8.52 5.50 0.81 0.63 9.48 5.12 0.81 0.56 10.15 5.87 0.78 0.48 12.33 5.31

13 0.85 0.67 7.30 4.89 0.85 0.59 7.96 4.38 0.81 0.59 9.26 5.31 0.81 0.59 11.41 5.94

14 0.85 0.63 7.48 4.82 0.81 0.63 8.93 5.41 0.78 0.52 9.63 5.71 0.74 0.41 11.89 4.36

15 0.89 0.70 6.89 5.68 0.85 0.63 7.81 5.18 0.81 0.59 8.89 5.13 0.81 0.56 10.04 4.93

16 0.89 0.59 7.89 6.75 0.81 0.56 8.89 7.07 0.81 0.56 9.52 7.87 0.74 0.48 11.33 8.38

the cusum metric within the change-point algorithm

we used, see ﬁgure 1 in (Robbins et al., 2011) for de-

tails. Change-points are generally easier to ﬁnd in the

middle of a time windows than on its boundaries.

4.2 Economic Gains

We have reason to believe that the algorithm used

gives equally sound results for fuse failures as it does

for fuse repairs. The economic gains are twofold: We

reduce the outage time per failed fuse/tracker and we

need less time to ﬁnd the failed fuse.

At least 81% of all single fuse failures can be rec-

ognized automatically after in average 9.26 days (us-

ing 0.95 conﬁdence). Assuming that our results do

apply to fuse failures, we could reduce power losses

by up to 63.1% (0.81·(7 weeks - 9.26 days)=26 days

earlier than by regular inspection) if the fuses get re-

paired at the day of failure recognition.

Furthermore, the technician can be advised to in-

spect only a subset of all trackers. If a potential fail-

ure is detected on the measurements of one DC cur-

rent input, then it will be possible to send a technician

directly to the part of the PV power plant where the

trackers are located that feed their power into this in-

put. As there are 12-24 trackers connected to each

DC input, only between 2.8% and 5.6% (

431

)

of the PV power plant has to be inspected, reducing

the expenditure of time by up to 97.2%.

We did not include the recognition time for the

cases where more than one fuse was repaired at the

same time, because we have reasons to believe that

each fuse failes individually, not in bulk. Multiple

fuses failing on the same day on trackers connected

to the same DC input seem unlikely. Given this as-

sumption we can only take the single fuse cases as an

estimation for the economic loss reduction that seems

plausible.

4.3 Related Work

There are several groups working on applying state

of the art machine learning algorithms on the task of

identifying machine failures. These groups use for

example support vector machines (Widodo and Yang,

2007), neural networks (Saravanan et al., 2010), mod-

eling of the machine inner workings (Toliyat et al.,

2012) or wavelet decompositions (Peng and Chu,

2004). On the domain of monitoring pv plants there

are works on predicting failing power electronics

(Middendorf et al., 2011) and (Guenther et al., May).

A system based on a combination of dynamic re-

gression and neural networks for anomaly recognition

speciﬁcally on pv power plant data was presented by

(Sanz-Bobi et al., 2012). The authors of this pv spe-

ciﬁc paper do not give numeric results for the recog-

nition power of their method.

All these sophisticated analysis methods require

elaborate data preparation, models of the working

principles of the machines that get monitored, as well

as ﬁne tuned parameter sets to give sufﬁcient results.

Our attempt, on the other hand, strives to use as lit-

tle parameters as possible to be usable by domain ex-

perts in pv monitoring, not machine learning special-

ists. Other monitoring solutions also often on training

data, needing a perfectly working power plant. We

do not have such a time range. The algorithm used in

this case study has to work reasonably well without

reference/training data.

4.4 Outlook

We strive to apply the algorithm used in this paper

to ﬁnd fuse failures throughout 2013. After a change-

point designating a failing fuse is found we will verify

if this is indeed the case. This procedure will allow us

to collect reliable data about the precision and there-

fore of the applicability of the change-point algorithm

to our problem as stated initially in section 2.1.

ACKNOWLEDGEMENTS

This work presented in this paper was undertaken as

part of the project EUMONIS

(01IS10033K and

http://www.eumonis.org

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163

01IS10033D), funded by the German Federal Min-

istry of Education and Research.

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