Solar Panel Data Analysis

Gao, Xiang

August 6, 2013

1 Introduction

Solar energy is being revisited as an important sustainable alternative to fossilfuel, and is receiving increasing attention recently. In fact, the annual installedcapacity was about 29.6 Gigawatts (GW) in 2011 and approximately 31 GW in2012[2]. Especially, following the nuclear disaster in Japan, people tend to relyon more secure power, and the potential now is believed to install an additional100 gigawatts (GW) of PV by 2015[12]. Many countries now heavily reply onsolar photovoltaic (PV) as a large proportion in their power supply. For exam-ple, by June 6th, 2013, PV electricity production in Germany reached 23.4 GW,which meets 39% of national peak electricity needs[13].

However, unlike fossil fuel, solar energy is vulnerable to external factors suchas inclement weather, clouds, shadows, and dust. For instance, studies by Salimet al.[14] and Wakim[15] indicate that there is 32% reduction in solar panelperformance after eight months accumulation in Riyadh, and 17% after six daysin Kuwait city, respectively. Moreover, with increases in solar module efficiency,the area required for installation has decreased, which results in an increasingimportance for detecting and removing anomalies that affect efficiency.

Since manually observe solar panels to detect and identify anomalies is notpractical, not only because it is laborious but also many large scale deployedsolar panels are very far away from cities. To achieve this goal solely basedon the power output data, time series analysis is adequate[3]. However, thoseanomalies detected by time series analysis includes many anomalies caused byweather condition, such as cloud and sudden overcast, which cannot be elimi-nated. Worse still, anomalies due to weather can be noise making identificationof removable anomalies, such snow, dust, and shadows, more difficult.

Our method focuses on the identification to removable anomalies, which isreasonable because we have on solution to adverse weather effect on solar pan-els, but we can take corresponding actions after identifying certain removableanomalies. We address the need for simple detection and interpretable classifi-cation of anomalies by using reference, the theoretical power output, to detectthese anomalies and employing profiling method to classify anomalies. Ourspecific contributions are:

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• We develop a method to find an equation fitting local horizontal solarirradiance, which can be used to predict the theoretical maximum solarpower .

• We develop a simple model to calculate the in-plane irradiance accordingto the horizontal irradiance, which outperforms the conventional modelboth in usability and precision. The conventional model is highly depen-dent on local data , while our model requires only some known parameters.

• We Fit the efficiency, function of temperature and irradiance, with theirradiance value we can calculate the theoretical maximum power yield ona panel of a particular size.

• Our detection procedure has two steps; the first step identifies weatheranomalies, while the second identifies anomalies that can be eliminatedmanually. This separation, at an early stage, is beneficial to increaseaccuracy in the following classification of the anomalies.

• We develop a method to detect anomalies, first detect single time pointanomaly, then glue them up and form a physical anomaly.

• We evaluate and select useful characteristics from profiled original anomalydata.

• We develop a classfier to classify the three removable anomalies, and theaccuracy reaches 95% .

• Our experience in processing data quality issues and alignment.

• Other discoveries in our experiment, anomaly effect w.r.t its relative posi-tion on a string; anomaly mainly decreases the current rather than voltage.

The rest of this report is organized as follows: the next section introduces therelated models for calculating theoretical irradiance, related work on anomalyeffect and classification research. Section 3 discusses how to build the modelused for reference, and its evaluation. Section 4 describes the procedure ofdetecting anomalies, criteria for profiling data and data quality issues as well.Section 5 discusses anomaly attributes selection and classification. Sections 6presents two feasible applications to utilize out approach, and the conclusion isin Section 7.

2 Related Work

We use solar irradiance to indicate the density of solar radiation, solar irradianceis defined as the power of solar radiation incident on unit area surface.In-planeirradiance is the irradiance arrives on a inclined surface, and horizontal irradi-ance is the irradiance arrives on a horizontal surface.

There are verified theories and approaches for modelling solar irradiance onhorizontal and inclined surfaces.

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2.1 Modelling Theoretical Solar Irradiance on HorizontalSurfaces

Luque, et al.,[1] give basic physical concepts for computing theoretical solarirradiance: Imagine putting a solar panel just outside of the atmosphere, whichmeans there is no detrimental effects by air, then the resulting solar irradiationreceived by unit area perpendicular to the beam is named solar constant B0 =1367W/m2.

Air mass is employed to describe the cleanness of the atmosphere on cleardays, AM = 0 indicates exoatmosphere while AM = 1 represents the situationin which a beam lies perpendicularly on the surface of the earth(impacted onlyby air mass, but without incident angle). The solar radiation w.r.t AM = 1is 1000W/m2, which is just the value used for standard tests to PV devices.In general, increasing air mass displaces the solar spectrum towards the red.In most situations, there is an angle θzs between the zenith and the beamincidence, and the air mass can be represented by θzs . Intuitively, AM = 1when θzs = 0, which indicates perpendicularly incident beams, and incidentbeams travel longer distance and scatters more in the condition of larger cosθzs.Therefore, Luque, et al.,[1] give the following formula for computing AM:

AM =1

cosθzs(1)

The track in which the earth travels around the sun is not a strictly circularorbit, which results in the variation in distance between the sun and panels fora whole year, so that the solar irradiance varies w.r.t. date. In engineering, auseful expression for the so-called eccentricity correction factor given by Luque,et al.,[1] is

ε0 = 1 + 0.33cos

(360dn365

)(2)

where dn is the sequence number of the particular day in one year.Solar declination δ, which indicates the angle between the equatorial plane

and the line connected the center of the Earth and the center of the sun, isutilized in computing the angle θzs.δ can also be regarded as the latitude atwhich the sun beams lie perpendicularly on particular days, for instance, δ = 0on spring equinox (20th/21st March) and autumn equinox (22nd/23rd Septem-ber), and δ = 23.5 on summer solstice. Luque, et al.,[1] give the followingformula for computing δ:

δ = 23.45o[

360(dn + 284)

365

](3)

Above all, at any given moment, the angular coordinates(θzs) of the sunwith respect to geographic latitude φ are calculated from the equation given byLuque, et al.,[1]:

cosθzs = sinδsinφ+ cosδcosφcosω (4)

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Figure 1: Relationships between angles and EarthSun position at solar noon

where φ is latitude and ω is true solar time, which is the difference betweensolar noon and a particular moment of the day in terms of a 360o rotation. Inpractice, ω is defined based on this principle but customized to meet differentgranularity requirements. For instance, if the time is graduated by minutein calculation, let T is the current solar time expressed in minute(e.g. 9:00represented by540 = 9 ∗ 60 minutes ), so the current ω is expressed in

ω =T − 720

720∗ π (5)

Figure 1 depicts these useful angles at solar noon[1].Notice the celestial poleis perpendicular with the equator, and angle φ(represents geographic latitude)has inverse direction w.r.t angle δ(represents solar declination). So the incidenceangle θzs at solar noon is expressed by φ− δ.

The sunrise angle, ωs, can be derived from equation 5. At sunrise, θzs isa rectangle(sun beam is at the same plane as the horizon) such as cosθzs = 0.Intuitively, −ωs can represent sunset time.

Meinel A[9] gives an empirical formula to compute the global solar irradianceG on a horizontal surface for clear days with general air mass values, which isa regression of irradiance data collected in the desert in California. Note thatsince ω is involved in this formula, it can plot the theoretical irradiance for theentire daytime.

G = B0ε0 × 0.7AM0.678

× cosθzs (6)

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Figure 2: Different components of solar radiation

2.2 Modelling Theoretical Solar Irradiance on Inclined Surfaces(In-plane irradiance)

In practice, solar panels are usually mounted with a slope(β) to increase equiv-alent irradiation area and reduce rain or snow accumulation as well, and thereis an orientation angle(α) in many cases due to construction or landform limi-tation.

As solar radiation passes through the atmosphere, it is modified by interac-tion with the components there. Some of them such as clouds, reflect radiation.Others such as ozone, oxygen, carbon dioxide and water vapour, have signifi-cant absorption at several specific spectral bands. Water droplets and suspendeddust also cause scattering. All these processes result in that the solar radiationincident on the panel is decomposed into three components: direct radiation,diffuse radiation and albedo radiation. Direct radiation is made up of beamsreaching the surface in a straight line from the sun. Diffuse radiation is ra-diation scattered towards the receiver. Albedo radiation is radiation reflectedfrom the ground. The sum of these three components is named global radiationgenerally.

Figure 2 from Handbook of Photovoltaic Science and Engineering[1] depictsthe components of the solar radiation.

The conventional procedure for calculating the global irradiance on an in-clined surface, G(β,α), is given by Luque et al.[1](in Northern Hemisphere,αis negative if towards east). The first phase is to divide the direct, diffuse

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Figure 3: Receiver position (slope β, orientation angle α) and sun beam inci-dence angle θs

and albedo components in horizontal global irradiance, respectively. Next theycompute the irradiance of the three components on inclined surface using cor-responding formula. Finally sum them up to obtain the global irradiance on aninclined surface. They also introduced the angle between solar incidence andnormal to panels,θs, and corresponding calculating method.

cosθs = sinδsinφcosβ − sinδcosφsinβcosα+ cosδcosφcosβcosω

+cosδsinφsinβcosαcosω + cosδsinαsinωsinβ(7)

In many cases that panels orient to due south(in Northern Hemisphere),α = 0 , hence the expression will be simplified. Figure 3[1] depicts the angleswe use in the model.

Global irradiance on an horizontal surface can be calculated in last subsec-tion, and there are models to compute the three components on inclined surfacefrom horizontal surface[1]. Yang et al.[6] and N.Z. Al Rawahi. et al.[7] use thisapproach to calculate the local global irradiance on inclined surfaces. Virtually,since the energy concentrates in the direct and diffuse components(above 99%),the common method is to extract the direct or diffuse part from the global ir-radiance and omit the albedo part. Therefore, either diffuse fraction derivedfrom regression of local irradiance data or the average diffuse irradiance valuederived from local history data can be used for this purpose. However, theseapproaches are heavily dependent on the local historical irradiance data andthe data may be unavailable or in coarse granularity(e.g. monthly). Moreover,the irradiance data may varies in different years and may be non-stationary inthe long run(e.g. small glacial time). Above all, it is not appropriate to detect

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anomalies on daily basis with this approach.

2.3 Anomaly effects

Following researches are focused on correlate the anomaly effects with externalfactors, their experiment results are useful to the attribute selections.

2.3.1 shadows

Shadow effects have been investigated by physical experiments or computersimulations. Ramaprabha Ramabadran et al.[16], Mohammed Qasim Taha etal.[17], Chris Deline et al.[18] investigated the effects of shadows on solar panelsby simulating the anomaly using models, and their aim is to find a versatilemodel that can simulate random shading scenarios. Basically, by-dioxides areused to simulate the sheltered cells. However, the results has not been validated.

2.3.2 dust

Dust may diminish the performance of the solar panels by decreasing the trans-mittance of the glass cover of panels, and thereby influencing energy yield.Factors that determine to what extend dust affects solar panels performanceinclude types of dust, density of dust, distribution of the dust on panels, rateof accumulation, humidity, panels tilting angles, rainfall interval, wind speed,direction and panel orientation angles.

Basically, most of the dust related work are based on physical experimentand focus on the correlation between dust property and energy loss. ShaharinA. Sulaiman et. al[19] conducted an in door experiment and recorded that theenergy loss due to two different types of dust, mud and talcum, with quantifieddust thickness, is up to 20%. The advantage for indoor experiment is inter-ference free, but spot lights using in such experiments cannot provide enoughirradiance(< 500) in some cases, which will degrade the efficiency slightly.

Outdoor experiments are all based on natural dust accumulation. J. Zorrilla-Casanova et. al’s experiments in Mlaga indicates following conclusions[20]: thedirty panels can recover with even light rain, below 1 mm; daily energy lossis negatively related with the sun height, which means dust affect performancemore in the morning and afternoon than at noon; the maximum energy loss is25% after one month’s accumulation, and most are below 20%. In Bangladesh,Mizanur Rahman et. al observed that the panel performance drops in the morn-ing by 35% and 20% at noon after one month[21].

For other impacting factors, it is found that smaller size of particles will leadto more significant degradation in PV panels by Dirk Goosen et. al[22] and El-Shobokshy et. al[23]. Google discovered that dust has only 2% impact on tilted

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panels while 50% on flat ones[24]. Garg’s[25] experiment also verifies this con-clusion. Hamdy K. Elminir et al.[26] quantified the deposition density on panelstilted by different angles and orientations after 6 months, and the results showthat the density drops nearly linearly with the tilting degree increase. Moreover,they fit the regression of the transmittance loss against the deposition amount.The advantageous condition for their experiment is that there are only two rain-falls during the six months. The variation effects by different orientation angleshave greatly relation with the prevailing wind which will bring dust particles[26].

To maintain the performance of the panels, Ali Omar Mohamed and Ab-dulazez Hasan’s experiment in Libya shows that periodically weekly cleaningmaintains the PV performance losses between 2 2.5%[27], but the interval maychange in other environment.

2.3.3 snow

Snowing accumulation on panels is complicated, which is mainly affected by theambient temperature, wind speeds, tilting angles, and surface properties[28].Once a snow layer is formed, light penetrate snow pack and reach the panelshas an exponential relationship with the depth. Approximately 20% of incidentradiation will be available at 2cm snow depth, and 3-4% is available at 10cmdepth[29].These correlations have been demonstrated empirically by O’Neill etal.[30] and Curl et al.[31].

Brench[32] performed the first snow effect experiment with different angles,the results show that with 30o tilting angle, average daily energy loss is 45% ifthe snow depth is greater than 1 inch, and 11% if the snow depth less than 1inch; on panels with 40o angle the number decreases to 26% and 5%, respectively.Rob W. Andrewsa et al.[33] built a model to predict energy loss due to snowon panels by time series analysis. Rob W. Andrews et al.[34] and G. Becker etal.[35] built models and predicted yearly energy loss percentage is up to 3.5% and2.7% , respectively, based on experimental data and meteorology information.However, their conclusion is not fine enough to detect and identify snow on dailybasis.

2.4 Anomaly classifications

While there are several mechanisms for detecting anomalies in solar power out-put, these solutions are either too complicated to interpret or highly dependenton local data. For example, H. Bo and S. Keshav[3] detected anomalies by build-ing a time series model, and using the statistical characteristics for classifying.However, the computing process is complex and the characteristics derived fromanomaly samples are difficult to understand.

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3 Modelling

A reference is required to detect anomalies in our approach, since the detectionprocedure is simply compare whether the real power output is lower than athreshold. Hence, the best reference is an anomaly free panel with same param-eters at the same location, but it is usually unavailable in practice. Thereby, weintroduce a method for calculating the reference power output by our irradiancemodel and efficiency equation.

3.1 Data description

Two sets of solar panels power output data are referenced in this project. Dataset 1 is from one string of solar panels deployed in Toronto from December,2011 to December, 2012, together with the ambient temperature and in-planeirradiance data. It contains pictures recording ground truth on panels in 5minutes interval . Data set 2 is from several strings of solar panels deployed onthe roof of a building in University of Waterloo(UW), the data is solely poweroutput, so we refer the meteorology data from weather station of UW. Thepower output data in both datasets are in one minute granularity.

3.2 Modelling Local Theoretical Solar Irradiance on Hor-izontal Surfaces

Ideal theoretical solar irradiance is a perfect fitting to locally measured irra-diance values, which forms a cosine shape through a sunny day without anyweather anomalies. Since equation 6 is a curve fitting irradiance data collectedin California, it is necessary to adjust the two constants, 0.7 and 0.678 to fitother locations.

Mathematically, the effect of alteration to the exponent from 0.1 to 0.9 (0.1interval) on a selected day (3.11.2012) is depicted by figure 4 (the base numberis fixed as 0.8). Moreover, the the effect of alteration to the base from 0.1 to0.9 (0.1 interval) is depicted by figure 5 (the exponent is fixed as 0.41).

To determine the corresponding parameters reflecting theoretical irradiancein Toronto, we conducted the following steps:

• First we select sunny days in the year according to daily radiation, theintegration of irradiance in an entire day.Intuitively, high solar radiationis a necessary condition of sunny days. However, radiation on summerdays is higher than in winter, due to higher incidence angles. Therefore,we choose the top 10% of days with the highest solar radiation from eachmonth as candidate days. Next, we visually inspect the measured solarirradiance from these days, as any types of anomaly will deform the ir-radiance curve, and classify them into completely sunny days and sunnydays with occasional weather anomalies.

• We use irradiance data from the 11 completely sunny days for fitting andverification, which distribute evenly in spring, summer, and autumn. For

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Figure 4: alteration to the exponent from 0.1 to 0.9

Figure 5: alteration to the base from 0.1 to 0.9

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each single day, we use minimum mean square error (MMSE) as criteriaand exhaust the exponent with an interval of 0.001. According the sensi-tivity analysis, each 0.1 alteration to the base value causes average 38%change in the mean square error (MSE). Hence, the base value shouldbe selected carefully. After removing the obvious outliers (0.9, 0.88, dueto measurement errors in the radiation meter), rest base values are quitestable(average 0.80, standard deviation 1.7%).

• After the determination of the base value, we can exhaust the exponentwith an interval of 0.001 to find the optimal value (0.410) achieves MMSEfor all the 11 days as a whole. The exponent value effect is negligible sinceaccording to the sensitivity analysis, each 0.1 alteration to the exponentcauses a maximum 3.8% change in the mean square error. The originalparameter combination (0.7,0.678) obtains 344.69% MSE, compared withthe global optimal(0.8,0.410) constants.

Therefore, the optimal equation with MMSE is:

G = B0ε0 × 0.8AM0.41

× cosθzs (8)

However, in some cases the measured irradiance may exceed this formula,which makes it unreliable. To ensure that the theoretical model always gener-ate the theoretical maximum irradiance value, we choose the highest constantcombination for the equation below(omit the outliers). This combination has5.7% more MSE compared with the optimal one.

G = B0ε0 × 0.831AM0.549

× cosθzs (9)

3.3 A simple method to model the in-plane Irradiance

The conventional method is highly dependent on local historical data or empir-ical formula to separate the three components of solar irradiance. This step willgenerate certain errors. Virtually, even though we can exactly obtain the threecomponents, the following computing procedure is still quite complex and timeconsuming. Hence, without loss of generality, we develop a simple model to cal-culate the global irradiance on inclined surfaces w.r.t. the known parameters,θs.

Suppose we project the horizontal surface to the plane whose normal parallelswith the solar beam, the equivalent area Sh is cosθzs times of original area S;similarly, the equivalent area of an inclined surface after projection is cosθstimes of S. Since the panels with the same size ought to receive same amountof irradiance at optimal angles, the irradiance on an inclined surface can becalculated by the following equation:

GI =Gcosθscosθzs

(10)

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Figure 6: Measured horizontal solar irradiance

This formula is reasonable in geometrics and enable us to calculate the in-plane irradiance in only one step, instead of by the conventional complicatedprocedures.

3.4 Measurement values of Solar Irradiance

In general, local weather stations have solar irradiance data but the granularityvaries. Solar measurement can be achieved by installing pyranometers on thesame rack of solar panels or nearby. Note that shortwave radiation includesmost of the solar irradiance (0.3 to 3 micrometers), which can be used as solarirradiance value.

Environmental factors may affect the precision of measurement. For in-stance, the pyranometers located by Columbia Lake is mounted horizontally,but there is a tower in the south, which will project a shadow on the incomingsolar radiation gauge. This effect is seen from about January 9th to March 7thand then again from October 5th to November 21st, accounting for the dip insolar radiation readings.

External effects should be taken into account when using the measured ir-radiance data. Figure 6 is the measured horizontal solar irradiance at the U.W.campus on Nov. 8, 2012. The fluctuation reflects the polytropic weather condi-tion.

3.5 Calculation of Measured In-plane Irradiance

In-plane Irradiance is the total irradiance that arrives on an inclined surface.Sometimes there is only local horizontal measured irradiance data available,

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hence we develop an intuitive approach to derive in-plane irradiance with theaid of the theoretical model.

First we calculate theoretical horizontal irradiance and retrieve horizontalirradiance data for the same day. Next, we calculate ratios between measuredvalues and theoretical horizontal irradiance. Ratios below certain threshold canbe regarded as anomalies caused by weather, since measured data will be im-pacted by weather while theoretical irradiance will not. Finally, we use oursimple model to calculate theoretical in-plane irradiance. Notice that this irra-diance is also anomaly-free. Multiply theoretical in-plane irradiance with theratio derived in the first step to obtain measured in-plane irradiance.

3.6 Efficiency

Efficiency describes the ratio between energy outputs and inputs, in PV area,efficiency η is described by following equation[36]:

η =Pmax

I ∗A(11)

where Pmax is the maximum electricity power output, I is the irradiance withunit W/m2 and A is the solar panel surface area. In practice, the efficiency ofsingle cell is named cell efficiency, which mainly depend on material technology;while the efficiency of whole panel is named module efficiency, which is alsorelated to interconnection craft[36]. Hence, the module efficiency is slightlylower than cell efficiency. Module efficiency is more suitable in our approachsince we are detecting anomalies on panel basis.

Generally, the cell efficiency and module efficiency are available in manu-facturer’s manual. However, the data is collected in standard test conditions(STC: Air mass AM 1.5, irradiation 1000 W/m2, Cell temperature 25C), somemanufacturers also provide another reference which is collected in nominal op-erating cell temperature (NOCT: Cell temperature 45C, irradiation 800 W/m2,ambient temperature 20C, Wind speed 1m/s). Therefore, neither the precisionor the rangeability of the data from manufacturer meets the requirement fordetecting anomalies at any condition, so a process to verify the reference dataand fitting changing conditions is necessary.

J. Michael ,et al.,[5] proved that there is little impact on the efficiency bywind speed, which only impacts ambient temperature, so we omit the windspeed impact here since we have the panel temperature data.

To obtain the efficiency formula w.r.t. our experimental panels in Toronto,first we compute the efficiency of the five strings of solar panels during the day-time w.r.t. the sunny days, respectively. Of the five strings, the standard moduleefficiency can be derived from manuals. Next, we observe that efficiency is quitestable during a single day whereas varies slightly on different days. Figure 7depicts the efficiency on different days on panel 3. Furthermore, temperatureaccounts for these small changes. Notice that temperature varies as much as40C, such that its impact should not be ignored. From regression analysis re-

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Figure 7: Efficiency on different days on panel 3

sults, we obtained a theoretical efficiency formula w.r.t current temperature,which is a revision of E. Skoplaki’s engineering formula[4]:

ηc = ηTref[1− βref (Tc − Tref )]− 0.06 (12)

where Tref is the reference temperature, 25◦ C; ηTrefis the efficiency at the

reference temperature; βref is the coefficient determined by material properties,and is given by the manuals, usually it varies from 0.0044 to 0.0047 per C. Notethat where Tc is current temperature, ηc is current efficiency. Evaluation resultsshow that this formula fits up to two decimal places with measurement, whichis precise enough for anomaly detections.

Figure 8 depicts the correlation between temperature and power efficiencyon panel 5.

Besides, the efficiency could also be affected by irradiance, for some pan-els, it decreases linearly by 5% when the irradiance decreases from 500 to 200W/m2. So we correct the efficiency equation when irradiance drops into thisrange to diminish inaccurate detection in the morning and afternoon. In thedust related research[20], people find that the dust affect when incident angleis large(sunrise and sunset), but the low irradiance at that time could accountfor it.

Conditions that irradiance is below 200W/m2 are seldom researched due toits high uncertainty and very low profits. Finally, the panel efficiency does notdegrade due to materials for 10 years in modern technology[11].

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Figure 8: Correlation between temperature and power efficiency on panel 5

3.7 Evaluation

3.8 calculation of theoretical in-plane irradiance

Figure 9 and 10 depict the theoretical in-plane irradiance on Mar.11,2012 andSep. 16,2012 respectively(panel slope β = 15o, orientation angle α = 23.11o)in UW campus using our simple model and conventional model as well, theexternal data used in conventional model is retrieved from[10]. Notice that thepanels in UW campus are facing south by west, so the peak irradiance appearsat afternoon.

Figure 11 and 12 depict the theoretical gin-plane irradiance on Mar.11,2012and Sep. 16,2012 respectively(panel slope β = 30o, orientation angle α = 0o)in Toronto using our simple model and conventional model as well, the externaldata used in conventional model is retrieved from[10]. Since we also have first-hand measured in-plane irradiance data in this case, we also plot the measuredin-plane irradiance as reference.

We can see that our model fit the real horizontal solar irradiance curve wellon arbitrary days and different locations, and for in-plane irradiance, our simplemodel achieves comparable results with the conventional one. Moreover, in mostcases the measured irradiance curves are under the theoretical curves.

3.9 calculation of theoretical power output

Since the in-plane irradiance already contains the weather impacts no matterit is measured directly or derived from horizontal measured irradiance. Anygap between the theoretical power output and the real power output over athreshold should be regarded as anomaly.

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Figure 9: Theoretical in-plane irradiance on Mar.11,2012, UW

Figure 10: Theoretical in-plane irradiance on Sep.16,2012, UW

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Figure 11: Theoretical in-plane irradiance on Mar.11,2012, Toronto

Figure 12: Theoretical in-plane irradiance on Sep.16,2012, Toronto

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Figure 13: Compare between the theoretical power output with the real one,UW

Figure 13 depicts the theoretical power output at UW on Nov. 29,2012based on the calculated in-plane irradiance, we also plot the real power out-put(measured) as reference.The anomaly in the morning could be caused byshadows due to the low solar altitude in winter while the anomaly at nooncould be accumulated snow(A decrease in irradiance can be observed in earliertime, which means overcast or snowy).

Figure 14 and 15 depict the theoretical power output at Toronto on Sep.16,2012 and Mar. 11, 2012, respectively based on the measured in-plane irradi-ance. No removable anomaly has been observed.

4 Data-Driven Anomaly Detection

Anomalies can be divided into two categories: weather and removable. It isnot possible to eliminated the former one manually, which can be detected bycomparing theoretical in-plane irradiance and the measured.

However, anomalies that can be removed are those worth focusing on. Afterobtaining the in-plane irradiance and the efficiency, we calculate theoreticalpower output and compare it with the measured. Any significant decrease in thereal power output is due to the anomalies, and there should be an explanationto that.

4.1 Detection

We only check the irradiance greater than 200 W/m2, since the efficiency withirradiance below 200 is not given by the manufacturer, and it is trivial comparedwith the major power period. It is general in solar energy analysis, [20] analyzedthe dust anomaly by checking only the efficiency greater than 200 W/m2.

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Figure 14: Compare between the theoretical power output with the real one,Toronto, 2012-11-29

Figure 15: Compare between the theoretical power output with the real one,Toronto, 2012-03-11

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This threshold may delay the anomaly discovery occasionally. For instance,if it continues to be overcast after snowing, no warning will emerge since theirradiance is very low on overcast days in winter. According to the detectionresults and camera pictures, it began to snow at 16:00pm, Jan. 26th, 2012 inToronto, but this anomaly cannot be detected due to the very low irradiance,so we find it at 11:00, Jan 27, when the irradiance is high enough.

The detection procedure is described as following:

Algorithm 1 Framework of detecting anomalies

Require:The set of real power output of panels, P ;The set of irradiance, Ir;The set of temperature, T ;The sampling time, t;The panel number, panel;

for all sampling time doif (Ir >= 200) then

for all panels docalculate theoretical efficiency, Teff = func(panel,Ir,T )calculate theoretical power output, Tp = Teff * Ircalculate ratio between real power output and theoretical, rif (r < 0.95) then

store panel anomaly dataset, ArrayListanopanel ← (t, r, P )end if

end forend if

end forthe single time point anomaly data of each panel is collectedfor all panels do

glue the single time point anomaly together with interval in 5 minutesend forif ( any panel has anomaly longer than 20 minutes ) then

store all the anomaly data into a map struct (panel, anopanel)end if

In this project we examine the sampling time on daily basis (daytime from8:00 to 18:00, 600 minutes) , usually there is only one anomaly happens withduration longer than 20 minutes per day. For real time detecting, a struct ismaintained for all panels anomaly data, and a profiling and classification processwill be conducted every 30 minutes, which will be discussed in next section.

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4.2 Data quality

Data quality is essential in our approach since several datasets are referenced,there are four issues basically :

availability : The best reference is an anomaly free solar panel in same modeland mounted on same site, but this is usually unrealistic unless manual su-pervising. The alternative is irradiance data, horizontal or in-plane, should beavailable on site. Since pyranometers are small, many material technology canbe applied to isolate anomaly, for example, electrostatic anti-dust glass andheater for melting snow. Otherwise it can be found in local weather station,but the data precision may diminish based on the distance. Sometimes thein-plane temperature is unavailable, we had to use the ambient temperaturefrom weather station, notice this could bring inaccuracy in computing efficiencysince in-plane temperature differs largely from in-plane temperature due to in-sulation[33] and wind effects.

granularity: Note that it is essential for the irradiance data has fine enoughgranularity(e.g. 1 minute), otherwise some anomalies may be missed. For in-stance, the radiation data from the weather station of UW is with a 15 minutesinterval while the interval of power output data is 1 minute, therefore, transientanomalies such as sudden clouds will be missed by weather station but captureby the power meter, and it is nor possible to explain the gap correctly.

alignment: Discontinuous data is very common due to sensors or collectionsystem errors. Therefore, align the data in each step based on its timestamp isnecessary. For missing data, it is better to discard than try to interpolate it.

extreme values: Extreme data values should also be detected and processedbefore applying. In this project, we meet −850C in-plane temperature, negativecurrent values and negative irradiance values. Although negative irradiancevalue has its physical meaning, surface giving more than receiving, we shoulddiscard these values anyway.

4.3 Profiling

Profiling the raw anomaly data is essential to interpret the classification pro-cedure. For the map struct containing anomaly data for all panels, earliestbeginning time on all panel is the beginning time of this anomaly, and theanomaly duration is the difference of the beginning time and the ending time.For average remaining percentage, we take the average remaining percentageweighted by the duration of each panel anomaly. Coefficient of variation (COV:std/mean) reflects the deviation degree, so it only derived from those panelanomalies whose duration is longer than 30 minutes. We talk about COV indetail next section.

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Figure 16: two types of COV Figure 17: Dist. of remainingpower percentage

5 Classification

5.1 Attribution selection

According to the data collected on EV3, shadows lead to relatively stable lowpower output, which can be explained by the constant diffusing component ofirradiance, assuming the air mass is not changing in short time. Another phys-ical truth is that the effect of shadows spreading on several panels cannot beobserved, that is, all panels on which the shadow is traveling generate samepower. The diffusing component dominates the irradiance during large incidentangle, low irradiance in sunrise, may account for this phenomenon.

This truth inspire us to use coefficient of variation (COV: std/mean) as animportant attribute. Particularly, a panel has shadow on it in morning, but dueto the relatively constant diffusing part in the irradiance, the absolute poweroutput does not fluctuate a lot. Consequently, for contactless anomalies, suchas shadows, their COV of absolute power output is low, usually less than 1.However, power generated by anomaly free panels is very sensitive to the directpart of irradiance, which is impacted by polytropic weather condition, thereby,COV of the ratio between real power and theoretical power( remaining powerpercentage) should be relatively large.

Figure 16 depicts the two types of COV. Notice that there is a clear bound-ary line between these two sets of COV, in other words, panels with shadowanomaly does not track the performance of anomaly free panels. This point isimportant because contact anomalies,such as snow or dust, will not stop thetracking.

Another feature is the distribution of mean remaining power percentage(power output on anomaly panel/reference power output), the results show thatit is usually keep a fair value, greater than 40%, which can be explained by thefair proportion of diffusing component irradiance, too. Figure 17 depicts the

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distribution of residual power percentage for two weeks.

Beside COV, several attributes have been considered for classifying theseanomalies :

Duration According to the data with pictures from Toronto, snow will existfor 1 - 3 days; duration for dust is highly relied on precipitation interval; shadowlasts for 6 hours at most, unless it is mounted facing north in north sphere, whichis unrealistic. At last, transient anomalies, such as dew or frost, disappears in20 minutes based on the data.

TimeIn practice, solar panel deployment will avoid facing a high block inright south, so shadows occur in the morning (building located on the east) inour experiment or in the sunset (building located on the west). The discoverytime for dust anomaly can be arbitrary. For snow, it happens at night in mostcases so that the discovery time is morning. It also snows in the morning andin the afternoon.

Affected panel number For dust and snow, all panels will be affected. Butfor shadow, several or all panel can be affected.

Average remaining power percentage The average remaining power percent-age is usually high for dust, due to its long accumulation. But it is low(lowerthan 0.4) for snow based on the data in Toronto, this attribute should be cus-tomized based on local climate.

Average power output value In our evaluation this attribute does not con-tribute a lot to the classification, that is because this value is greatly related tothe irradiance, which fluctuates largely.

Season It is mainly employed for snow identification, and can be replacedby month if finer category is needed. In Canada, winter usually covers fromDecember to March.

5.2 Experimental Data Description

There are challenges for building a general classifier :

Lacks of data Anomalies are not common in solar panel operations, especially shadows.For dust data, it is difficult to observe in South Ontario, because of itsevenly distributed 60mm precipitation per month.

Labels Due to the lacks of ground truth, the detected anomaly is unlabeled.Camera may solve this problem to some extent, but some ground truth isstill ignored due to its resolution and shooting interval.

Representativeness Due to the limitation of physical condition, the patterns of shadow anoma-lies is relatively fixed. Moreover, the forming of dust is highly location andclimate orientated.

Because of the data limitation, we use synthetic data to evaluate our method.Of the data collected in Toronto across 2012, we have 20 detected and labeledsnow anomalies. Since our experimental solar panels are mounted on the roof of

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a building in UW campus, we can only conduct a two weeks experiment due toregulation. We derive 15 natural shadow anomalies by a wall on the roof, butthese anomalies are highly similar since they are generated by the same blockand repeated every day. We don’t observe the natural dust anomalies becauseof the clean air and rainy climate in South Ontario.

Based on the real data we augment our data set reasonably to improve thegenerality and representativeness.

For shadow data, we change the beginning time, average power output andcorresponding characteristics based on season. For instance, in summer theshadow begins earlier than in winter, and so as its duration. Moreover, since theDIF(diffuse) can become a higher proportion(90%) compared to summer(40%),the impact of shadows is much smaller in winter. Thus, we change average re-maining percentage based on season, too.

For dust, we change the duration corresponding to the average rainfall in-terval based on the season. The dust anomaly disappears after rainfall(even alight rain below than 1 mm is enough to clean[20]) or strong wind(depend onthe humidity, wind direction and panel orientation). When the rainfall begins,the irradiance drops while the efficiency of the dirty panel rises. Usually it takesless than 10 minutes to recover the efficiency for a medium rainfall, but it takeslonger time for light rain. We normalize the distribution of the different amountrainfalls based on precipitation data[8]. The energy loss percentage due to nat-ural dust varies from 4% to 30%, according to the related research around theworld[14][15][19][20][21].

For snow data, all the average remaining percentage drops in the range from20% to 50%. Still concentrating in winter, redistribution has been applied toseveral attributes, such as beginning time, duration, average remaining percent-age, to make the situation more polytropic.

Based on the description, we obtain a synthetic data set containing 1000labelled anomalies. It is composed by three types of anomalies with randomproportions, and it has better generality and can represent these three types ofnormal anomalies in South Ontario.

5.3 Classification results

We apply C 4.5 Decision Tree algorithm to the test dataset and run cross val-idation for 10 folds. 10 folds validation means the data set is divided into 10parts, and conduct 10 rounds test. For each round, 9 parts are used for trainingand 1 part is used for test alternately. The final precise rate is the average valueof the 10 round test.

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Figure 18: first classification

Figure 19: second classification

The result for the cross validation achieves 98% precise rate. The classi-fication is simple since there are clear characteristics among these anomalies.Figure 18 depicts the generated decision tree.

We find that in the previous classification,number of panels plays a key rolein classifying shadow and the other two. So we ignore the panel number at-tribute and run classification again. A precise rate of 97% has been achievedand other attributes can also help classification effectively. Figure 19 depict thegenerated decision tree.

Hence, our attribution selection and classifier is robust and effective.

6 Applications

6.1 Anomaly Warning

Anomaly warning can be sent to the maintainer when anomaly is classified, andthey will handle the specific anomaly according to the warning. For the longdistance location, they can customize the remaining percentage threshold and

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affected number of panels to decide under which situation a warning will betriggered.

6.2 Energy loss estimation

Energy loss estimation will interest many solar panel investors. Based on ourapproach, we can give the estimation of energy loss due to weather factor andremovable factors. If the energy loss is too great due to weather factors, maybea new location should be taken into consideration. Whereas, by analysing re-movable anomaly causing energy loss, they can adjust the deployment of panels,install necessary maintaining equipment, or refine the management.

7 Conclusion and future work

We develop an easy-understanding data-driven approach to detect the anomaliesin the solar power output. With the support of measure irradiance, we can derivethe theoretical power output and detect anomalies by comparing the real poweroutput with theoretical one. Our method can be utilized generally to obtainlocal irradiance by adjusting the constants in equation 6, and our model tocalculate in-plane irradiance on inclined surface is worth popularizing, too. Thedetection , profiling and classification method can be referenced based on localcondition. Abundant data is beneficial to the representativeness and precisionof the classification.

For the future work, we are going to collect more data and try to fit theefficiency in low irradiance condition, thereby to detect anomalies in earliertime. Additionally, a methodology for identifying several anomalies from thecombination is also worthy to dig. Finally, a mechanism with user involvementcould be developed, which lets user label in real time to strengthen the classifier.

8 In the Wild

8.1 Quantitative results in anomaly experiment in UW

• An A4 size paper will drop the power output by 20%, which is in accor-dance with Bo’s experiment. The effect is nearly linear with the increaseof papers.

• Each panel consists of 72 cells: covering half (36 cells) stops power gener-ation; covering 16 cells drops the performance to 12%−14%, 5 cells dropsto 20%− 25%. In size, an A4 size paper equal to about 3 cells. However,in covering cells experiment we use package paper, which is much thickerthan A4 print paper.

• Sometimes the real power is even higher than the theoretical power (max-imum 10%), to avoid this situation, we can increase the efficiency andlower the anomaly threshold.

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Figure 20: distribution of the difference due to postion

8.2 Different efficiency on different panels

There is a constant difference(10 watts) between the power output of panel10 and panels on string 50. Sometimes the gap disappears for a certain time,though both are anomaly free. Thus, the assertion that efficiency is differentfor panel 10 and others does not hold. Still, we can use it as reference with themean gap value as compensation.

8.3 Central panel temperature higher

There is no obvious temperature difference between the central panels with theedge panels based on the data collected in Toronto. On average, the differencesare greater than -0.5 and less than 1 degree during daytime on 70% days in2012, and the maximum difference is 1.5. Figure 20 depicts the distribution ofthe difference between the panel in the center and a panel in the corner on thesame string.

8.4 Anomaly impact w.r.t. position

According to the experiment results, anomalies have bigger impact on one sidethan the other side. In this project, both panels are covered by a A4 size paper,but the performance of the panel on west edge is deteriorated more than theone mounted on east edge.

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