Forecasts of PV Power Output Using Measurements of PV Output of 100 Residential PV Installs

Vincent P. A. Lonij1, Vijai Thottathil Jayadevan1Jayadevan2 , Adria E. Brooks1, Kevin Koch3 2, Mike Leuthold4 3, and Alexander D. Cronin1

1University of Arizona, Physics, Tucson, AZ 857212 University of Arizona, ECE, Tucson, AZ 857213 2Technicians For Sustainability, Tucson, AZ 857054 3University of Arizona, Atmospheric Sciences, Tucson, AZ 85721

ABSTRACT

We report results of a new method to forecast variability in PV power output due to clouds using measurements from 100 residential rooftop PV systems. We will compare the performance of this method to results from a numerical weather model, and forecasts based on images from an all-sky camera. Our numerical weather model provides forecasts of irradiance up to several days in advance. Our network of PV systems can forecast output up to an hour in advance. Our images from an all-sky camera, and associated image analysis can be used to forecast 10 minutes in advance. We will show how using results from a numerical weather model as an input to the other forecasts improves accuracy of 45-minute ahead forecasts. We present animated (video) data for each of forecasting method.

INTRODUCTION

Solar power utilization at the utility-scale is a Grand Challenge. A major problem is the intermittent output of solar power plants due to passing clouds and nighttime. Intermittency limits the adoption solar power by utility companies and industry because they require reliable power.

Intermittency can be mitigated with energy storage, spinning reserves, or demand response. However, optimal

management of these three methods requires accurate forecasts of PV power output on several timescales.

Forecasting at all timescales is valuable for utility operators and plant owners. Day-ahead forecasts are needed to better determine pricing in the energy market. Hour-ahead and shorter time-scale forecast are valuable for electric grid operators to schedule spinning reserves.

Several methods exist to forecast PV power output [1,2] including

1. Numerical weather models,2. Measurements of PV power from a regional

network of PV systems,3. Block motion analysis of ground based camera

images.

We will discuss the advantages and drawbacks of each of these methods and we will show that combining these methods can improve the accuracy of our forecasts. In particular, using predicted wind speeds from a numerical weather model, or using cloud velocity measurements from an all-sky camera improve the forecasts that use measurements of a network of PV systems.

Figure 1: a) 30 hour ahead forecast of GHI in the Arizona region, b) DNI forecast, c) Satellite image of the same region. Movie available at [3].

NUMERICAL WEATHER MODEL

Numerical weather models can forecast up to several days in advance. Figure 1 shows forecasts of DNI and GHI based on our implementation of the WRF (Weather Research and Forecasting) numerical atmospheric model made 30 hours in advance. While Figure 1 shows excellent agreement with satellite images, forecasting the exact timing of cloud events is still challenging (see Figure 2). This implementation of the WRF utilizes a 448-node Beowolf cluster and requires 2 hours of computation to provide forecasts every 2 minutes on a 1.8KM gird across Arizona up to 50 hours in advance.

Figure 2: One-day ahead forecasts of Plane of array irradiance in a single location compared to measurements of PV power output. [WILL REMAKE FIGURE WITH HI-RES WRF RESULTS]

Figure 2 shows that the WRF model is able to predict large-scale cirrus clouds, as well as days that are entirely cloudy, but has difficulty with smaller scale clouds on partially cloudy days. This demonstrates the need for alternative forecasting methods.

Techniques that apply velocimetry to satellite images are able to forecast intermittency due to clouds on time scales ranging from 1 hour to 6 hours. For timescales less than one hour forecasts based on persistence outperform satellite-based forecasting methods. [1]

Next, we will discuss a new method create intra-hour forecast PV power intermittency due to clouds using measurements from a distributed network of ground-based PV systems.

MEASUREMENTS OF PV POWER FROM A REGIONAL NETWORK OF PV SYSTEMS.

We used measurements of PV power output from 100 residential rooftop systems distributed over a 100km x 100km area to forecast PV power output. Measurements are taken at 15-minute intervals (15 min. averages). Figure 3 shows final yield for 83 systems in the Tucson area plotted on a map for three different times. The dark points (indicating low output, due to a cloud) shift from the

southeast to the northwest of the Tucson valley over the course of 1 hour.

Figure 3: Measurements of PV power output from 83 systems at three different times, over the course of 1 hour. The dark points (indicating low output) indicate a cloud moving from the southeast of the Tucson valley to the northwest. A ground-based wind measurement indicates winds to the southwest. The two black

horizontal lines indicate two major streets in Tucson, one mile apart. A movie of this data is available at [4]. For this figure, the location of each of the systems has been offset by one mile in a random direction to preserve the anonymity of the system owners.

The ground sensor network presented here offers better spatial and temporal resolution than the GOES satellite images. An additional advantage of this method is that PV power output can be directly inferred from the output of other PV systems. That is, we do not need to know about the density, spectral properties or reflectivity of clouds, as we do in the other methods discussed in this paper. This leads to smaller errors in the forecasts of cloud cover opacity and POA irradiance.

The data presented here data is obtained using only existing infrastructure. Each of the PV systems used in this study use a SMA inverter with a data communications card installed to record data. This data is transmitted over the Internet using an SMA “Sunny Web-Box”.

Although the results we present here are based on historical measurements, no additional hardware is needed to make real time forecasts. Changing the operation of the hardware to provide real-time measurements of power output at 5 min. intervals can be done with a change to the software.

Once data is collected on a central server, PV output for each system can be forecast as follows. First we obtain a clear-sky expectation for the output of a system as described in [XXX]. Subsequently, We also correct for shading, outages and system orientation [XXX]. We then identify deviations from the clear-sky operation of the system due to clouds. We define the clear sky index as

K ≡ POA (t)POAClear (t)

where POA(t) indicates the Plane Of Array irradiance at time t and and POAClear(t) indicates the POA irradiance in the absence of clouds.

The output of any system is then given by

y f ( x , y , t )= y f −clear K where yf(t) is the yield (kW/kWpeak) at time t.

Once K has been determined for every system, we can forecast K at time t+dt, at location (x,y) from K at time t and location (x’,y’) = (x-vx*dt,y-vy*dt) using

K ( x , y , t+dt )=K (x−v x∗dt , y−v y∗dt , t)

(1)

where vx and vy are the x and y components of the cloud velocity vector respectively.

Values of K at locations between the points where PV systems are located are determined by interpolation as follows. For a location (x,y) we determine K for the four closest PV systems {Ki}, we then take K(x,y) = median({Ki})

The main challenge now is to determine the wind velocity at the altitude of the clouds. Ground based measurements of wind (also indicated in figure 3) are not an accurate measure of the velocity of clouds.

We examine three different ways of estimating cloud velocity:

1. we use wind velocity from a numerical weather model,

2. We infer cloud velocity from ground based irradiance measurements as well by finding the closest solution to y f ( x , y , t )= y (x−v x∗dt , y−v y∗dt ,t−dt )(2)

for vx and vy based on measurements of y for all systems.

3. For selected days we use a constant cloud velocity throughout the day, that was optimized (retrospectively) to give the best forecast for that day.

Table 1 shows RMS error using these three different cloud velocity estimates for time horizons ranging from 15 minutes to 75 minutes. Table 2 shows mean bias error (MBE) defined as Mean(yforecast-ymeasured). We show results for the period Aug1 through Oct 31. This period has a clearness index of 80%.

Both tables also list results from the persistence model. The persistence model assumes that the clear sky index at a future time t = t0 + dt is the same as the cloud index at t0. For time horizons larger than 30 minutes our forecast out-performs the persistence model.

On days that are entirely clear the output of a PV system is very predictable; the cloud index is always 0, and therefore the persistence model performs as well as our forecast. Similarly, on days that are entirely overcast, when the cloud index is constant close to 0.8, the persistence model also performs as well as our forecast. It is on days when the sky is partially or intermittently cloudy that PV power output is hard to forecast, and our algorithm outperforms the persistence model.

Table 1: RMS Errors for different cloud velocity estimates at different forecasting horizons for the period Aug 1 through Oct 31 2011.

RMS Error/Avg yield

Vc from WRF

Vc from Grnd. Sens.

Vc optimized

Persistence

15 min30 min45 min 0.38 0.37 0.25 0.4260 min75 minClearness Index

80%

Table 2: Mean Bias error for different cloud velocity estimates at different forecasting horizons for the period Aug 1 through Oct 31 2011.

MBE/Avg yield

Vc from WRF

Vc from Grnd. Sens.

Vc optimized

Persistence

15 min30 min45 min 0.006 0.005 0.005 0.00460 min75 min

Figure 4 shows the result of a forecast for one day in August of 2011 [TODO!!!], using each of the three cloud velocity estimates. The best result is obtained using method 3. For the data in figure 4, method three has an RMS error that is 40% smaller than methods 1 and 2. This suggests that better cloud velocity measurements or forecast are needed.

Figure 4: Forecasts of PV performance based on measurements of a network of 83 PV systems.

BLOCK MOTION ANALYSIS OF GROUND BASED CAMERA IMAGES.

Ground-based cloud imaging can be used to forecast intermittency due to clouds about 10 minutes in advance (the time it takes for a cloud to move from the edge of the frame to the center). Similar to [2] we used block-motion estimation to estimate the velocity of clouds in different parts of the image (see Fig 5) [6].

We use a wide-angle camera mounted on a dual axis equatorial tracker that follows the sun throughout the day. Using a block-motion estimation algorithm we determine the velocity of clouds in the image (in pixels/second). Using our knowledge of the orientation of the camera, we can convert the velocity of pixels in the image to estimates of cloud velocity in real-world coordinates (in meters/second), see figure XXX.

If we assume cloud velocity to be constant, we can forecast cloud position up to 10 minutes into the future. These forecasts can predict cloud arrival times with an accuracy of a few minutes. (see Figure 6).

Figure 5: Image taken with a camera mounted on a dual axis tracker pointed at the sun. Red arrows indicate motion vectors obtained from block motion estimation analysis. Movie available at [4].

Figure 6: Forecasts of cloud arrival time based on block-motion estimation. Cloud arrival times can be predicted with an accuracy of a few minutes.

In future work we will also incorporate these measurements of cloud velocity into the forecasting method that uses a network of distributed PV systems described in section XXX.

CONCLUSION

We presented results of a forecasting method that uses measurements from a network of residential PV systems. We compared results of this new forecasting technique to results of a WRF numerical weather model as well as forecasts using a images from a ground based camera.

Forecasts using 15-minute interval measurements from a network of distributed PV systems outperform the persistence model for forecast horizons larger than 30 minutes.

We observed that the main source of error in a forecast is an error in the estimation of the cloud velocity. Determining cloud velocity from measured PV data is challenging for our data set because the geographical area spanned by our dataset is small relative to the time resolution of our measurements. Using wind velocities obtained from numerical weather models gives improved results, however, because cloud edge velocity is not always the same as wind velocity, there is still significant error.

In future work we will therefore explore other techniques to determine cloud velocity, including image analysis of cloud images from satellites and from a ground based camera.

Using a ground based sun tracking camera we can also make forecasts with a temporal resolution of about 1 min,

however, these techniques are already affected by nonlinear cloud motion over the course of 5 to 10 minutes.

The three different forecasting methods we presented here have complementary characteristics. For example, the WRF model is better at forecasting cirrus clouds at forecast horizons of up to 50 hours, but has difficulty forecasting cumulus clouds with temporal resolution better than one hour. Our forecasting method using measurements from a network of distributed PV systems on the other hand has difficulty with slowly varying cirrus clouds but is able to provide intra-hour forecast of quickly varying cumulus clouds. This suggest a potential for hybrid forecasting systems that use input from distributed PV systems into WRF models and vice versa.

REFERNCES

[1] “Validation of short and medium term operational solar radiation forecasts in the US” Richard Perez, Sergey Kivalov, James Schlemmer, Karl Hemker Jr., David Renne, Thomas E. Hoff, Solar Energy 84, 2010, 2161–2172

[2] “Intra-hour forecasting with a total sky imager at the UC San Diego solar energy testbed“, Chi Wai Chow, Bryan Urquhart, Matthew Lave, Anthony Dominguez, Jan Kleissl, Janet Shields, Byron Washom, Solar Energy 85, 2011, 2881–2893

[3] http://www.atmo.arizona.edu/?section=weather&id=wrf

[4] http://www.uapv.org/

[5] “Performance Reviews from the Tucson Electric Power Solar Test Yard”, Alexander D. Cronin, Vincent P.A. Lonij, Garrett Hardesty, and Adria Brooks, IEEE Photovoltaic Specialist Conference, 2011.

[6] “Looking to the sky to predict PV output” , Vijai Thottathil Jayadevan, Alexander Cronin, Sarah Jones, Vincent Lonij, American Physical Society 4-corners meeting, 2011.