A Method to Estimate the Location and Orientation of Distributed Photovoltaic Systems from their Generation Output Data Navid Haghdadia,c, Jessie Coppera, Anna Brucea,c, Iain MacGillb,c a
School of Photovoltaic and Renewable Energy Engineering, UNSW Australia, Sydney 2052, Australia. School of Electrical Engineering and Telecommunications, UNSW Australia, Sydney 2052, Australia. c Centre for Energy and Environmental Markets, UNSW Australia, Sydney 2052, Australia. Corresponding author is Navid Haghdadi, Email:
[email protected], b
Abstract: Distributed PV systems, mostly on household, commercial and industrial rooftops, represent around half of global PV capacity. Their orientation (tilt and azimuth) often depends on the particular rooftop on which they are installed, rather than being designed for optimal performance. Furthermore, data collection, and particularly validation, of their configurations is often lacking. However, their generation output is usually well monitored given this determines cashflows. Rooftop PV systems therefore pose important performance assessment challenges. Large databases of distributed PV generation performance now exist. However, there is often little information on the actual system installation, or quality checks on provided information, which is a major problem for performance assessment. We therefore present a method for estimating tilt, azimuth, and even location for PV plants by fitting a model to their time-series generation. The method is tested for three case studies: (1) simulated generation of a theoretical PV system using weather data; (2) measured generation of PV systems with validated location and orientation; and (3) measured generation from PV systems with self-reported information. Results suggest that the proposed method can estimate array tilt, azimuth, longitude, and latitude with Mean Absolute Deviations of 2.75°, 5.85°, 0.2°, and 4.08° respectively, for a typical PV system. Keywords: PV orientation, PV location estimation, PV performance analysis
1 Introduction Global installed Photovoltaic (PV) capacity has grown from 5.1GW to 227GW over the past decade, and represented some 34% of total renewable generation capacity added in 2015, and 20% of all added capacity including coal, gas and nuclear [1]. Unlike almost all other generation options, PV is highly scalable and around half of global PV capacity consists of distributed PV systems installed, largely, on household, commercial and industrial roofs [2, 3]. In some jurisdictions, the great proportion of PV generation is from small (less than 10kW) PV systems on housing. For example, as of June 2016, 83% of Australia’s 5.3GW of PV capacity is from some 1.5 million household systems [4]. The performance of PV systems depends on a wide range of factors. These include the locational solar resource and system components, of course, but also the orientation of the PV modules. While these characteristics are carefully chosen for utility PV plants, the location, tilt and azimuth of small-scale PV systems are often determined by energy consumers and their available roof characteristics. Given Preprint submitted to Renewable Energy (http://dx.doi.org/10.1016/j.renene.2017.02.080 )
that these systems are so small yet numerous, data collection on their tilt and azimuth, and sometimes even their location, is often not undertaken, or poorly executed in practice. For example in Australia, the address, date of installation and inverter and/or array capacity are recorded as part of the policy support incentives provided for deployment, or as a requirement for network connections [4], but no data is collected on tilt or azimuth. By comparison, metered generation data from these systems determines system revenue and is therefore generally far better managed; including by the utility, using specified metering equipment and data collection processes. While arrangements vary, both gross and, particularly, net-metering tariff arrangements will often involve interval metering – typically at half hour resolution. This data may not separate generation from load in the case of net metering, and it will often not be publicly available except, sometimes, under strict confidentiality requirements that limit information about the actual systems. However, interval generation output data is collected in many cases from PV system inverters and made available to system owners and in some cases system installers and the inverter vendor. In some circumstances, system owners will even make this data freely available in crowd sourced on-line databases [5, 6]. Although PV generation output data, alone, can be used for assessing the historical performance of PV systems, it is less useful for assessing whether a particular PV system is performing as expected. For such assessments, location and orientation are key modelling inputs. Unfortunately, orientation data is not typically collected by utilities, while publicly available inverter data that can often be accessed by researchers and other stakeholders for performance analysis usually cannot be linked to databases of PV system specification data (such as capacity and specific location) even if available, again due to confidentiality requirements [7]. Some public data sources attempt to record these parameters at the system design stage, or by having the installer or system owner enter the information. However, certainly in the latter case, there is rarely an automatic process to collect these parameters, and experience has highlighted the often poor quality of such ‘self-reporting’ for rooftop PV systems. For instance, based on the analysis conducted on the self-reported information of tilt and azimuth of the largest publicly available PV performance database in Australia, PVOutput.org [5], about 10% of the 5000 PV systems contributing data did not report the tilt angle of PV array and another 32% have reported the clearly wrong value. This would normally suggest that 42% of the systems should be excluded before conducting performance analysis due to this missing necessary metadata. Similarly, other self-reported system parameters such as the panel azimuth angle and its location may also be missing or deviate markedly from their correct value. This information matters for analysis. As an example, about half of the PV systems with likely valid self-reported information in the PVOutput.org database have a tilt more than 10% lower than the optimal angle (assuming optimal is the latitude angle), with 10% of systems having a tilt more than 20° lower than optimal. About half of the systems are reported to be installed with an azimuth 45° or more away from optimal (due north) [8]. There are, of course, many reasons for the high variability seen in distributed PV system performance beyond tilt and azimuth, including, for example, micro-climate impacts, inappropriate string configurations, poor maintenance and shading. Correcting for tilt and azimuth if possible could greatly
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assist in performance assessments seeking to determine whether some of these other issues might be reducing performance, and what performance equivalent PV systems might be expected to achieve. This paper therefore presents a novel method to estimate the location and orientation of small-scale distributed Photovoltaic (PV) systems based only upon generation data. The basis of the proposed method is to express the normalized PV output as a function of latitude, longitude, tilt, and azimuth, and to estimate the missing or incorrectly identified parameters using non-linear least squares. The rest of the paper is structured as follows. Section 2 presents a literature review of the general topic, while Section 3 describes the impacts of location and orientation on PV generation output. Our proposed method is presented in Section 4, while the case studies used to assess its performance and the results of these studies are described in Sections 5 and 6 respectively. The performance of the method is then discussed in Section 7 while Section 8 offers some brief conclusions regarding the work.
2 Literature Review The effect of different orientations on the total energy generation of PV systems has been extensively investigated in studies including [9-12] and is incorporated into standard PV system modelling tools. In general, the optimal tilt and azimuth for maximum PV generation is approximately equal to the location’s latitude and direction to the equator respectively. In practice, different climatic patterns and other impacts can slightly change these [13-17]. However, the identification of a PV system’s location and orientation from performance data has received limited attention. The authors of [18] introduced a method for doing this, which consisted of two parts; firstly the identification of PV system location and then secondly the identification of system’s orientation. Two solution approaches were assessed for each of these two parts; specifically, a network and simulation-based approach for the identification of location, and an astronomical and simulation-based approach for the identification of orientations. To detect the location, the first approach in [18] uses generation data from a network of existing PV systems to identify the most correlated system to the particular PV system under investigation. This approach is not practical in all circumstances given its reliance on data from an existing network of PV systems whose locations and configurations span the possible location and configuration of the system being assessed. To address this limitation, the second approach involved simulating the PV system’s performance for all possible latitude and longitude combinations to find the best correlation with actual performance. To detect the PV system tilt and azimuth, the astronomical approach uses the sun position to predict the azimuth angle. Without knowledge of the tilt angle, however, it is impossible to calculate the azimuth with this method since the proposed value of “skew”, which is used to predict the azimuth, is dependent on the tilt angle. The second approach is to use a network of so-called virtual PV systems, iterating thorough different pairs of tilt and azimuth angles to find the best fit to actual system performance.
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Although simulation of virtual PV systems for all possible locations and then all combinations of tilt and azimuths, as per the second approach seems to achieve better results, it is unable to detect both location and tilt and azimuth simultaneously. In other words, for the identification of either location or system orientation, the methodology in [18] requires the knowledge of the other parameter, limiting the usefulness of the method. The method proposed in this paper solves the limitations of the approaches introduced in [18], enabling the detection of all four parameters (latitude, longitude, tilt and azimuth) simultaneously. The proposed method also reduces the computational requirements, as it uses a model-based optimisation method to identify the unknown parameters rather than simulating all possible combinations of location, tilt and azimuth. Furthermore, the method presented in this paper does not require any additional parameters, such as PV system module and inverter specifications or meteorological data, enabling it to work for almost all PV system with recorded generation data.
3 Influence of location and orientation on PV output power The radiant energy absorbed by PV systems depends on both the intensity and incident angle of the solar radiation. The intensity of irradiance falling on the plane of array (POA) can be estimated by using a solar transposition algorithm such as the Perez model [19] which uses inputs of Global Horizontal Irradiance (GHI), Diffuse Horizontal Irradiance (DHI) and the tilt and azimuth angles of the plane. The accuracy of the various transposition models presented within the existing literature have been extensively studied [19-26], indicating that the Perez model has a comparable level of accuracy to other models. Further, confidence in the accuracy of this transposition model is confirmed via industry wide utilisation of this model within standard PV modelling packages like PVSyst [27] and NREL’s System Advisor Model [28]. PV generation is a function of the Plane of Array (POA) irradiance, ambient temperature and PV module rated power [29], in conjunction with derating factors to account for different losses, where 𝑃𝑚𝑝 = 𝑃𝑂𝐴/1000 × 𝑃𝑚𝑝0 × [1 + 𝛾𝑡 (𝑇𝑐 − 25)] (1) 𝜂𝑓𝑖𝑛𝑎𝑙 = 𝜂𝑖𝑛𝑣 × 𝛾𝐴𝐶 × 𝛾𝐴𝐺𝐸 × 𝛾𝐷𝐶
(2)
𝑃𝑎𝑐 = 𝑃𝑚𝑝 × 𝜂𝑓𝑖𝑛𝑎𝑙
(3)
𝑃𝑎𝑐 is the PV generation. 𝜂𝑓𝑖𝑛𝑎𝑙 constitutes the combined total efficiency of the PV system including the efficiency of the Inverter (𝜂𝑖𝑛𝑣 ), the PV generation derate factor (𝛾𝐴𝐶 ), the DC power derate factor (𝛾𝐷𝐶 ), and a degradation rate due to the age of the system (𝛾𝐴𝐺𝐸 ). 𝛾𝑡 is the temperature coefficient (%/°C) for maximum power which takes into consideration power loss due to higher temperature. Tc is the PV cell temperature in °C calculated using the Sandia module and cell temperature models [30]. 𝑇𝐶 = 𝑃𝑂𝐴 × 𝑒 (𝛼+𝛽×𝑆𝑊 ) + 𝑇𝑎𝑚𝑏 + 𝑃𝑂𝐴/1000 × ∆𝑇 (4) Where 𝛼, 𝛽, and ∆𝑇 are coefficients of the Sandia module and cell temperature models, 𝑆𝑊 is the wind speed (m/s) and 𝑇𝑎𝑚𝑏 is ambient temperature (°C). Preprint submitted to Renewable Energy (http://dx.doi.org/10.1016/j.renene.2017.02.080 )
As a basis for this study, an initial investigation into the effect of varying the tilt and azimuth angles on the output power of a PV system was undertaken using measured weather data sourced from the Australian Bureau of Meteorology (BoM) [31] for the location of Wagga Wagga in New South Wales, Australia, including GHI, DHI, 𝑇𝑎𝑚𝑏 and 𝑆𝑊 . These parameters were used to calculate the POA irradiance and cell temperature for each possible combination of tilt (0 to 85° in 5° increments) and azimuth (0 to 360° in 15° increments). The PV system in Table I was modelled using one year of 1 minute meteorological data as input to Equations 1 to 3, based on the algorithms used within the NREL’s PVWatts model [29], which has been evaluated extensively, through comparisons of measured versus simulated output power [32, 33]. Table I Characteristics of the simulated PV system
PV Module MPP temperature coefficient (𝜸𝒕 ) STC power (𝑷𝒎𝒑𝟎 ) Cell temperature parameters
System parameter (𝜼𝒇𝒊𝒏𝒂𝒍)
SUNTECH POWER STP190S
-0.436 190.32 W 𝛼 -3.56 𝛽 -0.075 ∆𝑇 3 0.85
The influence of tilt and azimuth on the modelled PV generation of this PV system is depicted in Figure 1, which indicates that deviations within 10 ° from the optimal tilt angle or 15 from optimal azimuth angle result in a reduction in annual energy generation by approximately 5%. Therefore, models using values of PV system tilt and azimuth within 10° and 15° of actual, respectively, would result in estimations of energy generation within 5%, and hence allow reasonably accurate performance evaluations. Optimal tilt and azimuth angles of a PV system are easily calculated for a given location in order to maximise the total annual energy generation of a PV system. However, as noted earlier, most smallscale (i.e. residential) PV systems are installed at non-optimal angles due to factors including roof slope and orientation. Similarly, Figure 2 indicates that different months of the year are affected differently by changes in the tilt angle. Depending on the application, some PV system owners may wish to install their system at sub-optimal tilt angles to achieve higher energy outputs in specific months, or at suboptimal azimuth angles to generate more power at specific times of day (e.g. closer to peak load times).
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Figure 1. 3-D surface and contour plot for annual energy generated from a PV system in Wagga Wagga, for different tilt and azimuth angles, normalized to the annual optimum angle (30° tilt and 0° azimuth)
Tilt 0
Tilt 30
Tilt 60
Simulted Average Daily Output (kWh/kWp/day)
7 6 5 4 3 2 1 0
Figure 2. Simulated Energy for different tilt angles for different months of one sample year in Wagga Wagga Station
Moreover, the effect of tilt and azimuth on the PV output varies under different weather conditions due to the nonlinear effects of tilt and azimuth on the amount of diffuse irradiance absorbed by the PV panels. Figure 3 illustrates the effect of tilt and azimuth under four different weather conditions; a sunny day, a partly cloudy morning, a partly cloudy afternoon and a cloudy day. Measured GHI is shown via the line plots, whilst the simulated energy output for four different tilt and azimuth combinations (horizontal plane, 30° tilted toward north, 30° tilted toward northeast, and 30° tilted toward northwest) are represented by the bar charts, highlighting the effect of changing azimuth on the intra-daily weather pattern and energy generation. For example, whilst the output power of the simulated PV is almost the same when facing west or east on a sunny day, it differs significantly for a partly cloudy day. The level of dependence is a function of the patterns of cloud in the morning and afternoon. Preprint submitted to Renewable Energy (http://dx.doi.org/10.1016/j.renene.2017.02.080 )
Figure 3. Effect of tilt and azimuth on output power under different weather conditions. Line plots show the GHI (W/m2) and bar plots show the relative amount of PV power generated at different tilts and azimuths (horizontal being 1).
The effect of incorrectly identified tilt angles on PV system generation is discussed in more detail in [34]. In this work, the authors compared the performance of two systems with different tilt angles, validated the theoretical simulation results and highlighted the differences in output, concluding that even a slightly different tilt angle would change the annual energy generation as well as the pattern of generated energy in different times of year.
4 Method This paper proposes a new method for extracting the location, tilt and azimuth of PV systems from the measured generation data. The method consists of two steps. First, the longitude of the PV system is estimated using the time difference between solar noon (which can be extracted from the measured PV generation profile), and local noon. Second, the PV generation is expressed as a function of latitude, tilt and azimuth, enabling the estimation of any unknown parameters by fitting the measured data to the parametric curve that minimises the error. For simplicity, the effect of temperature and wind speed on PV power is not considered. Therefore, the method requires only PV output power as an input, without the need for meteorological data, which is often unavailable. Only periods of clear sky are considered, where GHI is predicted for each location using sun position formulas [35]. For DHI, a typical value for clear skies of 0.1 × GHI [36] is used. All steps of the methodology presented within this paper including POA estimation, modelling PV system output power, managing datasets and applying the parameter estimation, have been implemented within the MATLAB environment.
4.1 Estimation of Longitude The longitude of the PV system is estimated first, as it does not affect the estimation of the other variables. The primary effect of longitude on the PV output is on the position of solar noon. It can therefore be estimated using the time difference between solar noon, extracted from the available data, and local noon. In this method, longitude is calculated by using sunset/sunrise solar position Preprint submitted to Renewable Energy (http://dx.doi.org/10.1016/j.renene.2017.02.080 )
algorithms in conjunction with the Equation of Time (EoT) for the calculation of solar noon [35]. Solar noon can be estimated from the available PV output data by determining the midpoint of the available daylight hours, as per Equation 5 and 6. 𝑆𝑁(𝑑) = (𝑆𝑅(𝑑) + 𝑆𝑆(𝑑))/2
(5)
𝑇𝐶(𝑑) = 𝑆𝑁(𝑑) − 720
(6)
Where SR and SS are sunrise and sunset times in minutes extracted from observed start and end of PV power production, SN(d) is the estimated solar noon from SR and SS for day number d, TC(d) is time correction factor (in minutes) of day number d which is the difference between solar noon and local noon (i.e. 12 pm), d is the day number (1-365) starting from 1 Jan, and 720 is the conversion of local noon to minutes (12×60). For systems with more than one year of data, the maximum duration day from any year is selected to minimise the error introduced by clouds in the morning and afternoon. Finally, the longitude of the PV system can be calculated using Equations 7 to 10 [35], 𝐵(𝑑) = 360/365 × [𝑑 − 81]
(7)
𝐸𝑜𝑇(𝑑) = 9.87 × sin(2 × 𝐵(𝑑)) − 7.53 ∗ cos(𝐵(𝑑)) − 1.5sin(𝐵(𝑑))
(8)
𝐿𝑆𝑇𝑀 = 15 × ∆T𝐺𝑀𝑇
(9)
𝐿𝑜𝑛𝑔𝑖𝑡𝑢𝑑𝑒 = 𝑚𝑒𝑑𝑖𝑎𝑛(𝑇𝐶(𝑑)/4 − 𝐸𝑂𝑇(𝑑)/4) + 𝐿𝑆𝑇𝑀
(10)
The equation for EOT is derived empirically and is used to account for the eccentricity of the Earth’s orbit and tilt. LSTM is the Local Standard Time Meridian and ∆T𝐺𝑀𝑇 is the difference between Greenwich Mean Time (GMT) and local standard time. By using equations 5 to 10 the longitude of PV systems can be estimated.
4.2 Estimation of Latitude, tilt and azimuth The tilt, azimuth and latitude angles of a PV system have interdependent effects on the system output, and so need to be estimated simultaneously. The method presented here uses only clear sky conditions. Periods of cloudy and partially cloudy skies are detected in the measured PV system data and removed prior to the analysis. Prior to the curve fitting, an irradiance profile under clear sky conditions as a function of the PV system latitude is first estimated by using the ASHARE clear sky model [37], with the longitude estimated as per section 3.1, and based on attenuation factors and sun position algorithms [38]. Secondly, POA irradiance is defined as a function of the tilt, azimuth, and latitude angles using the clear sky irradiance and the Perez transposition model [19]. A best surface is then fitted to the clear sky data using the irradiance profile and the PV performance algorithms presented in Equations 1 to 4, with four unknown parameters of tilt, azimuth, latitude, and 𝜂𝑓𝑖𝑛𝑎𝑙 . During development of the method, we tested several surface fitting methods to fit the POA irradiance function to the dataset. The least squares method was selected, as it produced the best results in terms of accuracy and processing speed.
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The resulting method is relatively simple to implement, with minimal processing time required. It can therefore be used to quickly estimate parameters for a large number of PV systems. In order to accelerate the convergence of the fitting problem and to reduce the error for all estimated parameters, upper and lower boundaries were defined to limit the fitting to within the theoretical limits of each parameter. These boundaries are 0 and 360 for azimuth, 0 and 90 for tilt, 0 and -40 for latitude (to cover the entire region of Australia) and 0.6 and 1.3 for the combined system efficiency. This range was used to allow for situations of incorrectly reported systems sizes, underperforming systems (e.g., due to significant soiling). In addition, starting conditions for all parameters were set to zero. During the process of parameter estimation, it was observed that the fitting method was unable to estimate the azimuth of PV systems facing approximately south (azimuth angles around 180°). Under such scenarios, the fitting algorithm converged to an azimuth angle of zero degrees resulting in coefficient of determinations (R2) of the fit less than 0.9. When the fitted azimuth was observed to be less than ±15° with a fitted R2 less than 0.9, a second instance of the fitting procedure was undertaken using a starting condition of azimuth equal to 180°.
4.3 Clear Sky Timestamp Detection For the parameter estimation method described above, a method to extract clear sky periods was required. A number of existing methods for clear sky detection were reviewed in [39]. However, all of these were found to be dependent on measurements of GHI and prior knowledge of latitude and longitude, and hence not applicable where the location of PV systems are unknown and only PV output data are available. As a result, this paper introduces a new two-part method to detect periods of clear sky based on fluctuations in the PV output power and via the process of fitting a 3-d surface to the PV output data. The first part of the clear-sky extraction method assesses the fluctuation of output power between consecutive time stamps. Fluctuations greater than 30 Wh/kWp/minute are flagged as cloudy periods and this data is discarded. The second part of the method filters the measured data based on a theoretical profile of PV output under clear skies. Multiple years’ worth of data is used to select the 90th percentile from the measured PV output data, for each timestamp across the year, to represent the theoretical output. The entire profile is then smoothed and filled by fitting a 3rd order polynomial surface to the selected 90th percentile data. Figure 4 presents an example of the measured PV power and the fitted theoretical clear sky surface. This smoothing procedure removes any outliers and small power spikes due to cloud brightening effects. A 3-d surface is applied instead of a 2-d surface to take advantage of similar sun angles and therefore irradiance at both consecutive time intervals of each day and for the same time across consecutive days (the x and y axis of the 3d surface, respectively). After finding the clear sky profile, measured data from timestamps where the data fell within ±10% of the profile were retained in the final time series of clear sky data. A summary of the steps in the method is shown in Figure 5.
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Figure 4. Clear Sky fitted surface to one year data points of a sample PV system, blue dots are real measured power and surface is the clear sky pattern Measured PV output power
Daily pattern
Extracted sunrise, sunset and noon
Comparing with EOT and extract longitude
Longitude
3-D surface fit to data
Time series of clear sky data
Parameter Estimation P=ƒ(tilt,azimuth,lat,η) Clear sky model
GHI=ƒ1(lat)
Perez model
PVwatt model
POA=ƒ2(GHI,tilt,azimuth)
tilt
azimuth
P=ƒ3(POA,η)
lat
Figure 5. Steps of the method
5 Description of the case studies The method presented in this paper was tested via its application to three case studies namely simulated PV generation; measured PV with known tilt, azimuth and location; and measured PV systems with self-reported information. In all case studies, the temporal resolution of output power was 5 minutes. Figure 6 illustrates the geographical distribution of the PV systems used within this study. The three case studies are differentiated by colour.
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Figure 6. Geographical distribution of all case studies: 1- Weather stations (green markers); 2- Validated reported PV systems (blue markers); and 3- Measured self-reported PV Systems (red markers)
5.1 Case study 1: 2454 simulated PV systems using six weather stations For the first case study, the output of a typical PV system was simulated on the basis of measured irradiance, temperature and wind speed recorded by the BoM [31] for 6 meteorological weather stations located across Australia (Table II). The simulation was run for 2454 possible combinations of tilt (0 to 85° in 5° increments) and azimuth (0 to 345° in 15° increments), using two years of data from each location. POA irradiance was calculated using the Perez model [19] and cell temperature was calculated using measured values of ambient temperature as input to Equation 4. Finally, the PV generation was modelled using the NREL PVWatts model [29] using the typical PV module with characteristics listed in Table I, as described in section 3. Table II Weather stations of case study 1
Number
BOM Station ID
Station Name
State
Latitude
Longitude
1
008051
Geraldton Airport
WA
-28.7953
114.6975
2
014015
Darwin Airport
NT
-12.4239
130.8925
3
023034
Adelaide Airport
SA
-34.9524
138.5204
4
039083
Rockhampton Aero
QLD
-23.3753
150.4775
5
072150
Wagga wagga Station
NSW
-35.1583
147.4575
6
086282
Melbourne Airport
VIC
-37.6655
144.8321
5.2 Case Study 2: 31 PV systems with validated values for tilt, azimuth and location For the second case study, the parameter estimation method presented in this paper was tested on one year of measured data from 28 PV systems located at the Desert Knowledge Australia Solar Centre (DKASC) [40] in Alice Springs (case study 2-1) and three PV systems at the University of Queensland
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[41] (case study 2-2). Table III summarises the configurations and locations of these PV systems, which are well documented and are publicly available. Table III. PV systems of case study 2 Case study
2-1
2-2
Number of systems 24
Name or Technology
Location
Size
Tilt
Azimuth
Latitude Longitude
DK Solar Centre NT 0870 1.98 – 6.3 kW
20
0
-23.76
133.88
1
Multiple module and inverter technologies Solar Compass East BP Solar
DK Solar Centre NT 0878
1.98 kW
23
90
-23.76
133.88
1
Solar Compass North BP Solar
DK Solar Centre NT 0879
1.98 kW
23
0
-23.76
133.88
1
Solar Compass West BP Solar
DK Solar Centre NT 0880
1.98 kW
23
270
-23.76
133.88
1
Solar Compass Flat BP Solar
DK Solar Centre NT 0881
1.98 kW
0
0
-23.76
133.88
1
UQ St. Lucia Campus (MultiLevel Carpark) Heron Island Research Station
St. Lucia, Brisbane QLD 4067 Heron Island QLD 4680
338.9 kW
2-6
20
-27.49
153
25.2 kWp
10
30
-23.44
151.9
UQ St. Lucia Campus (Sir Llew Edwards Building )
St. Lucia, Brisbane QLD 40 67
89.76 kWp
3
280
-27.01
153.49
1 1
5.3 Case study 3: 939 PV system from PVoutput.org database For the third case study, the method was applied to PV generation data sourced from PVOutput.org [5], a publicly accessible PV data portal, for 939 PV systems located across Australia. PV system owners are able to set up automatic upload of their PV data into the PVOutput.org database, enter the tilt and azimuth of the PV system, and select the location postcode. The latitude and longitude are then by default set to the centre of the postcode, which can be later modified by the user, who can opt to find the exact latitude and longitude on the map. The azimuth angle can also be defined by the user more precisely, however the azimuth values collected from the database were mostly expressed in units of cardinal and inter-cardinal directions (i.e. North, North-East, etc.). Based on the user-reported values, the average tilt angle of the 939 PV systems was 22° with the majority of the tilt angles ranging between 20° and 30°. About half of the systems were reported as facing north and 32% were reported as facing either northwest or northeast. The average reported system size was 4.8 kWp and all systems were below 8 kWp, which is fairly typical for PV systems in Australia. A complete review of the specifications of PV systems in this sample was reported in [42].
5.3.1 Data Pre-processing Because real field data with incomplete information about the PV systems has been used for this case study, there are a range of unknown factors that could affect the PV system output, apart from the variables of interest, such as shading, power outages, variation of the system configuration (i.e. addition of new modules, upgrades to inverters etc.), inverter clipping and so on. Therefore prior to applying the parameter estimation method, the data was pre-processed. Only PV systems with greater than one year of available data, that displayed no significant deviation from the expected pattern of PV performance were selected. Any data identified as affected by shading or inverter clipping, and periods of power outage, where the output power of the PV system was identified as zero, were also removed from the dataset. PV system data reported in local time was converted to standard local time in order to correct for changes due to daylight savings.
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6 Results The accuracy achieved by using the method presented in this paper to estimate tilt, azimuth, latitude and longitude for the three case studies described above is reported in this section. For case study 11, the Mean Absolute Deviation (MAD) of estimating tilt, azimuth, latitude, and longitude are 6.7°, 10.89°, 0.23°, and 4.89° respectively. When considering only tilt and azimuth angles within a typical range seen in PV installations in Australia (10° ≤ tilt ≤ 35° and 240° ≤ azimuth ≤ 120°, case study 1-2), we see a significant reduction in the deviations for tilt and azimuth and a similar result for latitude and longitude, with MAD of 2.75°, 5.85°, 0.2°, and 4.08° respectively. The results for the three case studies are summarised in Table IV. Using the simulated PV system in Wagga Wagga presented in section 3 as an example, we assessed the effect of errors of this magnitude on annual energy generation estimates. For Wagga Wagga, the average change in annual generation per degree change in tilt angle is 0.69%, and per degree change in azimuth is 0.34% (i.e. a deviation of 10° from the optimal tilt angle or 15° from optimal azimuth angle results in a reduction in annual energy generation of approximately 5%). When considering only the more optimal range (as per case study 1-2), the impact on annual generation is 0.2% and 0.18% per degree of change in tilt and azimuth respectively. Therefore, a deviation of 6.7° and 10.89° (equal to the MADs for tilt and azimuth estimation across the entire range of tilt and azimuth angles) would result in an error in estimated annual energy generation of about 4.6% and 3.7%, respectively, while in the more optimal tilt and azimuth range, the MADs of 2.75° and 5.85° would result in annual generation errors of about 0.55% and 1.05% respectively. Hence we conclude that the method presented in this paper can be used to estimate missing system parameters which sufficient accuracy for PV system performance analyses, particularly where the PV system is tilted and oriented within a typical range. Table IV. Statistics of the results
Tilt (°) Case Study 1-1 Case Study 1-2 Case Study 2-1 Case Study 2-2 Case Study 3
Azimuth (°)
Latitude (°)
Longitude (°)
MBD
MAD
STD
MBD
MAD
STD
MBD
MAD
STD
MBD
MAD
STD
-4.47 -2.12 -1.13
6.70 2.75 5.26
11.43 2.93 4.21
-2.33 -0.83 7.80
10.89 5.85 9.84
27.12 4.07 6.84
2.42 3.97 4.44
4.84 4.08 5.84
3.42 2.12 3.42
-0.02 -0.01 -1.22
0.23 0.20 1.22
0.12 0.08 0.78
-4.18 -0.96
4.18 4.18
1.30 3.34
3.55
17.63
20.64
4.57 1.40
4.57 3.75
1.65 2.94
-0.52 -0.69
0.52 1.18
0.47 1.40
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Figure 7 shows the statistics for estimation of all parameters averaged across all weather stations in case study 1-1. The results show a fairly consistent level of deviation among almost all stations with minor variations from the average. 35 30
Deviation (°)
25 20 15 10 5 0 -5 -10 MBD
MAD Tilt
STD
MBD
MAD Azimuth
STD
MBD
MAD Latitude
STD
MBD
MAD
STD
Longitude
Figure 7. Statistics of case study 1 for all weather stations; solid lines are the average of all stations, circles represent the whole range and triangles are for near optimum range
The results from case study 2 (using data from real PV systems with known and validated tilt, azimuth and location) show good agreement with the results from case study 1 for systems within the same range of tilt and azimuth. The results for estimating the azimuth angles for case study 2-2 are not included, as the tilt angles of all 3 systems in this case study are very close to zero, so the method was unable to estimate the azimuth. It should be noted that the azimuth angle, when tilt angles are approximately zero, has a very minor impact on the annual energy production of a PV system. For instance, based on the results presented in Figure 1, changing azimuth by 45° when tilt angle is 5° would change the annual energy generation by less than 1.3%. Therefore, accurate estimation of azimuth for such systems may not be required for many applications of PV system performance analysis. For case study 3, the results show MAD values of 4.18° when estimating the tilt angle, 17.63° for the azimuth angle, 3.75° for latitude and 1.18° for longitude. However, the underlying reasons for the higher rates of MAD and STD of tilt and azimuth in the third case study are likely due to user error in the user reported information, rather than error in estimation of the parameters. The largest MAD for case study 3 occurs for the parameter of azimuth. This may be an artefact of the dataset used in case study 3, where the azimuth parameter is not classified as value from 0 to 360° but rather are classified into one of eight categories (i.e. N, NE, E, SE, S, SW, W, NW). Hence, the true azimuth of any PV system in the database is likely to be up to 22.5° different to the value recorded within the database. Similarly, the user reported tilt is likely to be approximated by the user within only 5°-10° of accuracy. The magnitude of MAD and STD for estimating latitude is within the expected range for this case study. The latitude and longitude values used to validate location estimates are likely to be quite accurate, because the majority of PV systems in this case study are located in major cities where postcodes (used by the users to report location) span small geographical areas. The larger error for longitude estimation in real PV systems with respect to simulated systems may result from typically more variable shading and weather conditions during mornings and evenings, which introduce error in extraction of the sunrise and sunset times used to estimate longitude. For example, the presence of
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shading due to neighbouring buildings during the initial period after sunrise could delay the rise of PV module output voltage and hence the start of PV inverter operation and system generation.
7 Discussion While the results obtained when applying the method presented in this paper under Australian conditions are promising, further validation is required using a larger set of field data where the system parameters are known, as well as over a broader range of locations around the world, since larger latitude angles or local weather or typical installation conditions may affect the error obtained using the method. In practice, field data may vary in temporal resolution and quality. In the remainder of this section we review some of the potential implications of these aspects of data availability on the resultant error and make recommendations about application of the method.
7.1 Effect of time resolution The majority of the PV systems within the PVOutput.org dataset used for case study 3 in this paper report data at 5 minute intervals, with some systems reporting at 10 or 15 minutes. In some PV datasets, in order to reduce data storage and communication requirements, the resolution of data may be lower. For instance, for most publicly available utility-metered load and PV datasets the resolution is 30 minutes (in accordance with electricity market dispatch). In other datasets or commercial PV simulation tools, such as PVWatts, the resolution is hourly. To assess the accuracy of the method under different time resolutions, we applied the method to case study 1 using 1 minute, 5 minute, 15 minute, 30 minute and 1 hour meteorological data. The PV output power was simulated using meteorological data recorded by the BoM for each minute and then averaged over the relevant time interval, resulting in a new PV generation data series. The MAD and STD for tilt, and azimuth increase slightly when data with lower temporal resolutions are used above 5 minutes (Figure 8), whereas decreasing temporal resolution from one minute to five minute decreased the error obtained for azimuth. The error observed for latitude does not change significantly across temporal resolutions. The increase in error with lower resolution data is more significant for longitude, with eight times higher MAD at hourly resolution and five times at the 30 minute resolution by comparison with one minute resolution data. Nevertheless, the MAD and STD for hourly resolution are still below 0.8° and 1.4° respectively, while for the other parameters, the change in MAD and STD for different time resolutions is modest, indicating that the method proposed within this paper can be used with data of up to 1 hour temporal resolution, depending on the level of acceptable estimation accuracy needed for the specific application.
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Tilt MAD and STD (°)
20 15 MAD
10
STD Average MAD
5
Average STD 0 1
5
15
30
60
Time Resolution
Azimuth 45 40
MAD and STD (°)
35
30 25
MAD
20
STD
15
Average MAD
10
Average STD
5 0 1
5
15
30
60
Time Resolution
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Latitude 8 7
MAD and STD (°)
6 5 MAD
4
STD
3
Average MAD
2
Average STD
1 0 1
5
15
30
60
Time Resolution
Longitude 2.0 1.8
MAD and STD (°)
1.6 1.4 1.2
MAD
1.0
STD
0.8
Average MAD
0.6
Average STD
0.4 0.2 0.0 1
5
15
30
60
Time Resolution Figure 8. MAD and STD of all parameters for different temporal resolution
7.2 Effect of total time period of data For the third case study the output data from 939 systems was used to estimate the parameters of location, tilt and azimuth. These PV systems were installed at different times and therefore the period of time for which data was available from each of the PV systems varied from one year up to four years. To investigate the effect of total time period of data used on the accuracy of the method, Figure 9 plots the MAD and STD per parameter (compared to the user reported values) sorted by period of time data was available for. The resultant error for estimation of parameters generally decreases with multiple years’ worth of data, likely due to better smoothing, reducing the effect of noise and occasional invalid data on estimating the parameters. In the case of latitude, no significant variation Preprint submitted to Renewable Energy (http://dx.doi.org/10.1016/j.renene.2017.02.080 )
Percentage of deviation from average
was observed for systems with less than 3 years of data, with an increase in MAD observed for systems with more than 3 years of data. The STD of longitude also increased for systems with more than three years of data, which is likely due to a small number of systems in this category. 120 110 100 90 80 70 60 MAD
STD
MAD
Tilt
STD
Azimuth
1-2 years
2-3 years
MAD
STD
Latitude >3 years
MAD
STD
Longitude Average
Figure 9. MAD and STD of systems with different available data
7.3 Effect of invalid data As discussed within the description of the pre-processing step for case study 3, a number of filtering methods were applied to the PVOutput.org dataset, such that systems that were identified as having a large numbers of invalid data points were excluded from the analysis. In order to evaluate the sensitivity of the method to the presence of invalid data, we reviewed the excluded data points, attempted to characterise their underlying causes and assess the impact of the invalid data on the results as follows: 1- Incorrect time stamps, including time shifts due to incorrect local clock or daylight savings time, lead to incorrect detection of the longitude parameter. For instance, an incorrect daylight savings time shift for a typical PV system introduced an error in the estimated longitude of approximately 7°. 2- Changes in the system size (due to module or inverter failure or by adding more modules or inverters) resulted in incorrectly identified latitude and tilt angles. Systems with changes in size that persisted for a significant period of operation resulted in an error in identification of tilt and latitude angles of up to 30°. 3- Total or partial shading, which occurs over a significant proportion of the year, resulted in errors within the identification of azimuth. 4- Undersized inverters which result in power trimming of PV systems especially on summer days resulted in incorrect tilt and latitude angle identification due to non-identical effects on summer and winter generation patterns. While working with the distributed PV field data from PVOutput.org, a large number of systems with invalid data were identified. For case study 3 in this paper, systems with changes in capacity, and data affected by time shifts, shading, and inverter clipping were removed from the dataset. Including the Preprint submitted to Renewable Energy (http://dx.doi.org/10.1016/j.renene.2017.02.080 )
invalid data points was shown to have a significant impact on the accuracy of the method, highlighting the importance of applying filtering methods before applying our parameter estimation method or analysing the performance of individual PV systems.
8 Conclusion This paper has presented a new automated method for identifying PV system location, tilt and azimuth. The longitude of a PV system’s location is identified by finding the difference between solar noon and local noon. Then data from clear sky timestamps is fit via least squares to the best surface using a model for PV system output with variables tilt, azimuth and latitude, in order to identify the parameters simultaneously. The method was tested via three case studies, using a combination of simulated and field data, and over a wide range of possible values of the parameters and different time resolutions. The results indicate good accuracy for the detection of location, tilt and azimuth, particularly for PV systems with tilt and azimuth angles within the typical installation range of these parameters. Further testing of the method should be conducted to ensure its validity under a wide range of locations and field conditions. Opportunities to improve the method in future work include the application of alternative optimisation algorithms to estimate the unknown parameters. The steps of the method could also be adjusted to enable the estimation of other parameters including the PV system efficiency, and in some cases, the identification of PV system technology.
Acknowledgment The work in this paper has been undertaken as part of the Australian PV Institute's Climate-based Performance and Reliability project, supported by the Australian Government through the Australian Renewable Energy Agency (ARENA). Responsibility for the views, information or advice expressed herein is not accepted by the Australian Government. Data has been kindly provided for this study by PVOutput.org, University of Queensland PV systems database and Desert Knowledge Australia Solar Centre (DKASC).
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