Australasian Universities Power Engineering Conference, AUPEC 2013, Hobart, T AS, Australia, 29 September - 3 October 2013

Variability and Performance Analysis of the PV Plant at The University of Queensland

Saeid Veysi Raygani*, Rahul Sharma, Tapan Kumar Saha School of Information Technology and Electrical Engineering, The University of Queensland

Brisbane, Australia

Abstract-Variability in the output of photovoltaic (PV)

power plants continues to hinder their interconnection to

power systems. Consequently, available PV plant data should

be carefully analysed so that appropriate strategies can be

developed to mitigate effects associated with variability in PV

output. This paper constructively illustrates the

characterisation of the variability and evaluates performance

of the 1.2MW PV plant at The University of Queensland. The

characterisation is based on some of the recently proposed

indices and utilises I-minute resolution data captured over a

2I-month period.

Keywords-Variability; photovoltaic power plant; indices;

I. [NTRODUCTION

Photovoltaic (PV) capacity is increasing on utility systems, As a result, potential impacts of PV output variability caused by transient clouds concerns utility planners and grid operators, Utilities and control system operators need to adapt day ahead scheduling, load following, and second to minute's regulation to accommodate this variability while at the same time maintaining existing standards of reliability, So far, there are no standard indices to characterise variability and performance of PV power plants.

The existing standard for reporting individual power plant performance, [EEE Std. 762-2006, defines reliability, availability, and productivity indices to report conventional controllable power plant performance [[]. The standard assumes fuel is available and indicates to what extent the rest of the plant performs relative to its rating and availability. In contrast to conventional plants, for PV plants, performance indices must consider variability of fuel, input. This contrast between traditional dispatchable generation and emerging variable PVs, has limited incorporating solar plants into a conventional generation fleet. Therefore, indices compatible with the traditional generation are needed allowing easy comparison between new generation options. When indices are defined and adopted into standards such as IEEE, appraisals of bringing solar PV into a traditional generation fleet can be more reliable. Authors in [2] have proposed indices with generalisation capabilities to evaluate the performance and quantify output variability for any given PV plant.

The objective of this paper is to provide insight into the performance of The University of Queensland (UQ) PV

system. The data available at two UQ PV sites is used to evaluate the PV performance and output variability indices introduced in [2]. Daily variability and daily clearness indices are utilised to categorise days based on the level of variability. Performance of the two sites is evaluated in terms of the capacity factor and the energy performance factor. The season-wise variability corresponding to the one-minute power ramp rate is characterised in terms of probability distribution functions. The three-sigma rule is used as a confidence interval for PV ramp rates because it covers 99.73% of the PV output changes. Based on this analysis, guidelines are developed to establish the required level of the spinning reserves to balance the PV variability at the UQ sites. Furthermore, correlation in the outputs of the two PV sites are evaluated and discussed.

Specification of the two sites is listed in Table I. One­minute resolution data were available over a 21-month period from Sep 20 [ [ to May 2013. Fig. 1 shows a view of site 1 PV plant. Data collected from this site includes the ac power, temperature, and irradiance measurements. The site's irradiance instrumentation is a pyranometer located on the roof of the UQ centre building and it is horizontal.

The rest of this paper is organized as follows. The defmition of irradiance and insolation are presented in Section [I. [n Section III, variability and performance indices are defined. Analyses of UQ power plant performance and variability are presented in Section [V, and Section V presents the conclusions of this work.

Fig. l. Overview of site 1 PV arrays.

Australasian Universities Power Engineering Conference, AUPEC 2013, Hobart, T AS, Australia, 29 September - 3 October 2013 2

TABLE I. UQ PLANT SPECIFICATION Site Name site 1 site 2 DC Ratinf{ 433.44 kW 338.9 kW Modules TSM 240-PC/PAI4: 240 W dc at STC"

Number of modules 1806 1412 Ground mounted, Ground mounted,

average fixed 3.710 ti It, average fixed 3.660 tilt, Mount Oriented due to 200 Oriented due to 200 East

East of North of North Commission date 2011

a Standard test conditions (1.5 air mass , 1000 w/m2 irradiance, and 25°C module temperature)

II, IRRADIANCE AND INSOLATION

Tn this section, irradiance and insolation are defined to help quantify variability and performance indices, Because PV plant instantaneous power output is generally proportional to irradiance, variability in irradiance is a measure of the variability in plant output power [2-4]. Thus, understanding the behaviour of solar resources is the first step to study PV power outputs, Two common and well­defined measures of solar resource are Global horizontal irradiance (CHI) and insolation, Both these measures are used to define the variability indices and performance indices and, thus, should be determined with precision and accuracy.

A. CHI CHI is a measure of solar power on a given horizontal

surface, and is usually expressed in W/m2. CHI is the sum of the diffuse radiation incident on a horizontal surface plus the direct normal irradiance (DNl) projected onto the horizontal surface (i.e., CHI = DNlxcos(z)+Diffuse) where z denotes the zenith angle. CHI is highly dependent on the position of the sun in the sky relative to the observer on the Earth's surface. At higher z angles, the light goes through more atmosphere than when the sun is directly overhead. Thus, all GHI clear sky models require geometric inputs describing the solar zenith angle throughout the year.

GHI models of varying complexities exist in the literature. The simplest models are the functions of z angle only. Haurwitz model (1946) [5, 6], Daneshyar-Paltridge­Proctor model (1978) [7, 8], Kasten-Czeplak model (1980) [9], Berger-Duffie model (1997) [10] are some of the published clear sky models which lack high accuracy, since they are solely based on the zenith angle and do not take into account the site altitude and atmospheric conditions. Accuracy improvements are obtained through the inclusion of the dependence on some basic parameters such as air pressure, temperature, relative humidity, aerosol content, and Rayleigh scattering in GHI modelling. Nevertheless, these improvements are achieved at the expense of the increased model complexity. The Ineichen and Perez' clear sky model [11] is a trade-off between complexity and accuracy [12]. This model is given as follows:

GHI = c,/o cos(z) x exp( -cg2 x AM X (fh] + 1;'2 (� - I))) x exp(O.O 1 x AM18);

(1)

where,

cos(z) = cos(¢!) cos( 0) cos( OJ) + sine¢!) sine 0) cg] =5.0ge-5xh+0.868 and C,2 =3.92e-5xh+0.0387

2Jr 10 = 1367.7x(l +0.033xcos(-x DOy))

365

1;,] = exp( -h I 8000) and 1;'2 = exp( -h 11250).

(2)

where, DOYand h are the day of year and height of the site. ¢! , 0, and OJ are latitude of the site, declination angle, and

solar time in degree, respectively. For more information please refer to [12, 13]. This model is also highly dependent on Linke turbidity, TL, which expresses the total optical thickness of a cloudless atmosphere relative to the optical thickness of a water and aerosol free atmosphere [12, 14]. The magnitude of this factor ranges between 1 and 8, is heavily reliant on the atmospheric conditions, and must be chosen correctly to predict the exact amount of irradiance [ 15].

B. Insolation

Insolation is defined as the solar energy received over time, and is computed as the integration of irradiance over the specified duration (usually the daylight hours). Clearly, the magnitude of insolation depends on location, the time of year, tilt angle and weather. For UQ PV system, the typical daily values range from 1.2-kWh/m2 in overcast days to 7-kWh/m2 in high variability days. Because insolation quantifies solar energy over a period of time, it is roughly proportional to the expected plant electrical energy output for the same period of time.

III. VARIABILITY AND PERFROMANCE INDICES

In this section, variability and perfonnance indices are presented. Quantifying variability of fleet of PV plants and classifying days as having a specific variability helps power system operators to make decision to set the level of regulating reserves and detennine how many times variable day occurs. Furthermore, defining performance indices can facilitate the comparison of the performance of PV plants and with conventional power plants.

A. Daily Variability and Daily Clearness Indices

Variability in irradiance can be qualitatively categorised using combinations of daily clearness index (DCI) and daily variability index (DVI). Using combination of DC I and DVI in a method could be useful to classify and determine variability for a certain location. Distinguishing variability in this manner can be used by utility generation planners or grid operators to know about typical variability days. DCI is the ratio of solar energy measured on a given surface to the calculated maximum energy on that same surface during a clear sky day [2]:

Australasian Universities Power Engineering Conference, AUPEC 2013, Hobart, T AS, Australia, 29 September - 3 October 2013 3

f Measured solar irradiation DC! = (3) f Calculated clear sky solar irradiation

The clear sky solar insolation should be calculated from an accurate clear sky modeL The accurate typical values for the daily clearness index range from 0.0 to 1.0. Values greater than 1.0 can be obtained if a calculated clear-sky model does not correctly predict the real GHI.

DVI is the ratio of variability in measured irradiance to the variability of the calculated clear sky irradiance. Both of them are quantified by the length of the plot of irradiance versus time for the day, where the curve length between two measurements is determined using a line segment. Typical values for daily variability index range from 1 to 30 and are detennined using (4) [2, 16]:

I�(GHlk -GHlk_Y +M2 D VI =

..::;.k=�2----;========­I�(CSlk -CSlk_1)2 +M2 k=2

(4)

where, GHI is a vector of length n of global horizontal irradiance values at time interval in minutes, M, CSI is a vector of calculated clear sky irradiance (horizontal) values for the same times as the GH I data. In this paper, the clear sky model developed by Ineichen and Perez [11] is used.

B. Capacity Factor and Energy Performance Factor

Capacity factor (CF) is normally defmed as the ratio of actual output of a plant over a period of time relative to the rated output, if operating at nameplate capacity over the same period [1] as shown in (5). For example, in Australia, coal plants operate at about 85%, wind power at around 35%, hydro power at about 17.4% capacity factor (i.e., if they are used for peak power). Gas power station capacity factors vary from as high as 85% to less than 10% (i.e., if they are designed only for peak power) [17-19].

Total Energy Produced (kWh) CF=----------��---------------

System Rating (kW) x Time Interval (hours) (5)

To calculate capacity factor of PV plants, the choice of system rating and economic advantage in over-sizing or under-sizing the inverter ratings should be considered. The utility industry uses the inverter ac rating to calculate capacity factor, whereas the PV industry is using the dc rating of arrays. While more PV s are integrated into the fleet, using ac rating as the system rating would be desirable. From the economic point of view, designing the size of dc arrays relative to the ac inverter capacity would affect the capacity factor significantly. As an example, for 2 UQ PV sites, the ac ratings are 392.5 kW and 310 kW, while dc ratings are 433.5 and 338.9 and if the ac rating is chosen in the denominator instead of dc rating, CF increases

significantly.

On the other hand, the time period for the capacity factor is another important issue. PV plants generate power during daytime hours, whereas conventional plants are available 24 hours a day. For dispatchable plants, the capacity factor can be a good indicator of how often a plant is economically dispatched and how frequently it is kept in reserve. On the other hand, for solar plants, the capacity factor and efficiency of the plant are playing the second fiddle because the output is dependent on solar resources. Therefore, another PV performance indicator, which takes into account the level of solar irradiance, is needed to enable fair comparison of various PV plants located at different sites and of different capacities. This factor can be considered in future revisions of IEEE Std. 762. Energy performance factor (EPF) specific to PV plants and with respect to sunlight can be expressed as (6):

where,

Performance Factor (PF) EPF=------------------

Sun Factor (SF)

Total Energy Produced (kWh) PF=------------�----------�-----

plant ratingirr�/oOo (kW) x Time Interval (hours)

Total insolation (kWh) SF=------------------------

Irradiance,Tc x Time Interval (hours)

(6)

(7)

where, PF is the production factor and SF is the sun factor. The plant rating is in terms of the array (dc rating) at standard test conditions (STC). Sun factor is the insolation normalized to a value representing STC (1000 W/m2) times the daytime hours. Energy performance factor is dimensionless and can be used to compare performance of different PV plants. Values of EPF are usually lower than l .0. They can be computed over any time period, usually over month, seasons, or annual periods. Lower values indicate lower performing systems.

IV. UQ PV PLANT DATA ANALYSIS

In this section, daily variability and daily clearness indices are utilised to categorise variability of days for UQ PV plant. By fitting the ramp rate of PV output instantaneous power to the normal distribution function, 1-minute variability in power ramp rate is characterised. In addition, using capacity factor and energy performance factor, performance of the UQ Centre, site 1, and Car-Park, site 2, is evaluated. The temperature and irradiance are measured at the roof of site 1. PV output is directly proportional to variability in irradiance. To quantify irradiance variability, Ineichen and Perez GHI clear sky model is used as a clear sky model to compare different irradiance of variable days.

Australasian Universities Power Engineering Conference, AUPEC 2013, Hobart, T AS, Australia, 29 September - 3 October 2013 4

A. Defining daily variability at the UQ PV sites

In terms of variability, days would fall into five categories: clear, overcast, high variability, moderate variability and mild variability days based on the values of DVI and DCI indices as follow:

• If lSDVI<2 and O.5<DCI<S1, the day is named clear day;

• Extremely overcast or rainy conditions have low DVI values too. So, if 1 <DVI<2 and DCI<s0.5 the day is categorized as the overcast day;

• The day with the DVI value greater than 10 can be called a high variability day;

• Moderate variability days are categorized by 5 <DVI<S10;

• The days with 2<DVI<s5 are named mild variability days.

Examples of each type of days with a corresponding value for DVI and DCI are shown in Fig. 2. The measured irradiance is collected from site I. Based on some trial and error, Tr = 5.5 was found to yield a good approximation for GHI. This value is consistent with the typical values of TL which ranges between 4 and 6 for warm and moist atmospheric conditions [15], as is typically the case in November for Brisbane. For a clear day, theoretically, the calculated clear sky model is perfectly matched to measurements. Thus, DVI and DCI are equal to 1. However, in reality, the D VI value for a clear day is not exactly I because of uncertainty of clear sky model and natural and random variability of irradiance.

B. Performance Factors

Fig. 3 shows the monthly capacity factor for the two sites of UQ PV plant based on PV dc rating. The trends for both sites are almost the same. The monthly capacity factors for these two sites range from about 10% to 22%. Average day-time hours for each month are given in the background to show relation between the CF and daytime hours. As can be seen, the capacity factor is the highest during October­December due to long daytime hours. The graphs also show that CF is lowest during May-July because of the low daytime hours.

Besides the daytime hours, the CF also depends on many factors such as the plant efficiency, location, tilt angle, shading of building and trees, and weather parameters like irradiance and temperature. For example, for two sites in a close geographical location, the tilt angle of arrays and number of modules of two sites leads to difference in capacity factors. The average tilt angle of site 1 is 3.77° due to 20° East of North (EON) while this value for site 2 is 3.66° due to 20° EON. If the tilt angle reduces amount of irradiance over the plain of arrays, in turn, the total energy generated by PV plant will be reduced and consequently CF reduces. In addition, whether the dc arrays rating or ac inverter rating is considered also has a significant effect on the value of the CF (as discussed section III-B).

6/11/2012, High Variability Day � 2000 . ,. DVI = 22, DCI= 0.9 : 'ff : .� 1 000 ..................... r\t':.lPlrlfH\;;ftJ1Hl!�"" ] ro

a rtl 10 15

1011 1/2012, Overcast Day

1-c.o'""'1 -- Me!: .. J,f�

20

1611112012. Clear Day

f ' :::EZ/fmR=1 C/O 5 10 15 20

17/1112012, Moderate Variability Day

22/1112012, Mild Variability Day � 2000 . ,. DVI = 5, DCI= 0.8 : -g : t 1000 ........................ "'".!�. ---....!I...c

10 Time (hour)

15

1-,,-,rul""'1 --!Il"....;;1J,f�

20

Fig. 2. Clear, overcast, high variability, moderate variability, and mild variability days based on the defined DVI and DCI indices.

0.25

0.2 � & 0.15 '" � 0.1 0-II

0.05

0.25

0.2 � � 0.15 '" ! 0.1

0.05

a) Capacity Factor for Site 1

.CE •• AvHours 1 =�

--..--.. _i--" ----......... 1

5

II 0 Sep OctNovDec Jan FebMarAptMayJun Jul AugSepOctNovDec Jan FebMarAprMay

b) Capacity Factor for Site 2

.CE "

Av Hours 1 =�

"'-. ......... .. c.c,l

.1 5

II 0 Sep OctNovDec Jan FebMarAprMayJun Jul AugSepOcrNovDec Jan FebMarAprMay

Fig. 3. Capacity factor and average working hours per month.

000 " a

I

Fig. 4 shows the PF and SF for site 1 and site 2 evaluated on a monthly basis. Ambient temperature, measured by the sensor at the roof of site I, is shown in the background of each plot. The PF and CF follow the same trend. The PF is

Australasian Universities Power Engineering Conference, AUPEC 2013, Hobart, T AS, Australia, 29 September - 3 October 2013 5

calculated for daytime hours, whereas CF is calculated for 24 hours. EPF is shown in Fig. 5. Since the efficiency of the PV modules is negatively influenced with temperature, the performance of the PV array (and hence the magnitude of EPF) generally decreases with a rise in temperature, and vice versa. There is a slight variation in the monthly performance of the two sites, mainly due to the different tilt angles and the number of arrays. It should be mentioned that the corresponding results for the month of March are of relatively low accuracy since only two days' worth of data were available.

Fig. 4. Sun factor and perforemance factor for two sites.

� 08 LL m

g 06

� � 04

2i � 02 w

� 08 LL m � 0_6

§ � 04 a.

2i l' 0 w

2

j

r-'"

IJ

f\ \!

r-'-II' I""

-'-

y:'\ a) Energy Performance Factor for Site 1

-

\. \ I

1\

.1. Q-'- '- .J... � � r- r'- \.:

/ / i\

1\

1\

2

2

2

2 1 I\.. V ' .. � �1

c::::J EPF 1 b) Energy Performance Factor for Site 2

r 26 � r-,. . : ;--\ .... r- r-'-[-\ . r'-

1/ 1'-- 24

1\ 1\ V

II 1\

I\. V I""

1\ 1\

1\

22 � 20 � � 1 E 8�

l� 1 c::::J EPF 1

Fig. 5. Energy perforemance factor for two sites for 21- month period.

C. Seasonal Ramp Rates Ramp rate can be fitted to Gaussian Probability function.

So, to analyse variability of PV output, ramp rate data (i.e., ramp rate (kW) per minute, !J.PIM, for four seasons during I year) is fitted to normal distribution function. The probability distribution functions (PDF) of ramp rates of the PV sites are shown in Fig. 6. For site 1, the probability of having zero ramp rates in one-minute time scale is 0.015, while this value for site 2 is higher because of its lower standard deviation and lower dc rating. Standard deviation of ramp rate regarding cumulative instantaneous power of two sites (Fig. 6-c)) is higher because of higher range of variation and correlation between outputs of two sites. As it can be seen, variability of ramp rates is lowest in winter, whereas this amount for summer is the highest. In winter, usually the weather is much clearer than other seasons. On the other hand, the cloudiest days are in summer. The ramp rates during spring and autumn have close standard deviations. The ramp rate in site I is higher than site 2 because of the high number of modules and consequently higher rating.

This information is also useful to interconnect the UQ PV plant to the grid with respect to the 99.7 percentile rule. This rule, known as the three-sigma rule, states that nearly all values lies within 3 standard deviations, (J, of the mean, f-J in a normal distribution function, (i.e., P (f-J-3(J :s x :s f-J+ 3(J) ;:::: 99.73%). Planners could apply the desired confidence level (e.g., they may choose three-sigma of ramp rate) to accommodate variability by using variability spinning reserves. As it can be concluded, there is a need to clarify ramp rates in a normalised way.

The normalised three-sigma ramp-rate for the two sites is shown in Table II (i.e., three-sigma ramp rate divided by the corresponding dc rating). For both sites, in the same season, the normalised values have close numbers. The maximum difference between values is 1.2% calculated in spring. In addition, in the case of electrical interconnection of the two sites, again the lowest value is in winter and the highest value is in summer. As it can be seen, the cumulative three-sigma ramp rate of the two sites is lower. There are two reasons for this: 1) aggregate of the two sites dc ratings used in denominator as reference value; 2) the output of sites are correlated.

The correlation between the variability in power outputs of the two sites is shown in Table II and is expressed in terms of the correlation coefficient, p. In order to determine p, the standard deviations in the ramp rates of the power outputs in the two sites, (Jx and (Jy, are evaluated. Then, covariance, cov, is calculated using (8):

COV(x,y)= Ii' [var(x+y)-var(x)-var(y)] (8)

where, var is the variance which is equal to (J2

. Therefore, p can be calculated using p=cov(x,y)/(Jx(Jy' These values show the correlation between ramp rates of two sites affecting their total power ramp rate. Correlation coefficient in winter, 0.11, is the highest which indicates that the

Australasian Universities Power Engineering Conference, AUPEC 2013, Hobart, T AS, Australia, 29 September - 3 October 2013 6

variability of two sites is the most correlated during this season, potentially due to the lowest weather variability. On the other hand, the correlation coefficient for more variable months is lower. The low negative correlation coefficient indicates that in fall, PV outputs counteract variability in a small number.

a) PDF for Site 1 0. 02,-----:-------:-------:-----;=======::::;]

0.015

LL o 0.01 c..

0.005

------------- r-------------- r------------, . , , -- Winter, Sigma = 26.2 kW - -Spring, Sigma = 34.6 kW ----- Summer, Sigma =44 _ 1 kW -------, Autumn, Sigma = 37.3 kW

-100 -50 0 50 100 150

b) PDF for Site 2 0. 025,-----:-------:-------:-----;=======::::;] -- Winter, Sigma = 19.9 k\V

0.02 ....... - -Spnng, Sigma - 28.4 kW

LL 0.015 o c.. 0.01

0.005

----- Summer, Sigma - 34.8 kW ------- Aurumn, Sigma = 30.4 kW

-?50 o 50 100 150

c) PDF for two Sites 0.015 ,-----:-------:-------:-----;===:=======::::;] -- Winter, Sigma'" 34.6 kW

LL o c..

0,01

0.005

- -Spring. Sigma � 46.S kW ----- Summer, Sigma = 56.6 kW ------- Autumn, Sigma = 47.6 kW

--------------r - ------------

___ - --�L:-:;:;:� ':' , �'----: -- ! '-...:..':':.:::::�� �-

-?50·- -- --100 -50 0 50 100 150

Ramp Rate (kW)

Fig. 6. PDF for ramp rate of each site and cumulative power of two sites.

TABLE II. THREE-SIGMA RAMP RATE AND CORRELATION COEFFICIENT Normalised Three-Sigma Ramp Rate Correlation Coefficient

(%) Season Site Site

1 2 Winter 18.1 17.6 Spring 23.9 25. 1

Summer 30.5 30.8 Autumn 25.8 26.9

Site 1 & Site 2 13.5 18.2 22

18. 5

V. CONCLUSION

(p) Site 1 & Site 2

0.1 1 0.09 0.01

-0.02

New variability and performance indices are analysed using l -minute resolution data collected from an operating PV system in The University of Queensland. Based on the level of variability in the level of irradiance, variability in days is categorised as high, low, mild, overcast and clear sky. Furthermore, the capacity factor and the energy performance factor are evaluated to determine PV plants' performance.

One-minute instantaneous power ramp rates of the two

sites are fitted to the normal distribution function. As expected, the variability is found to be the lowest in winter and the highest in summer. In particular, the standard deviations in the power ramp rates in summer are found to be 1.69 and 1.75 times the standard deviation in winter for the sites I and 2, respectively. The three-sigma rule is used as a confidence interval for PV ramp rate. Their normalised values are used to develop guidelines for establishment of the required level of the spinning reserves to balance the PV variability at the UQ PV plant. To analyse effects of PV plant geographical locations on variability and correlation of changes in power output, various time scales will be the subject of our future studies.

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