Today's snowy climate PV systems tend to be installed at angles shallow enough to make them prone to snow loss, and as large-scale PV installations become more widespread in snowy locations analytical models are needed to estimate the impact of snow on energy production.

Both weather and array design factors influence the amount of snow loss. Weather factors include the quantity and quality (moisture content) of the snow, the recurrence pattern of storms, and the post-storm pattern of temperature, irradiation, wind speed, wind direction, and relative humidity. Array design factors essentially boil down to orientation (fixed or tracking, tilt, azimuth, and tracker rotation limits) and the surrounding geometry (open rack or building-integrated). Building features can also either help (e.g. melt) or hinder (e.g. dam up or drift) natural snow shedding.

Nonetheless, a generalised monthly snow loss model is introduced here which, despite some limitations, appears to deliver good- quality, unbiased monthly loss estimates which can now be used as inputs to the simulation programs PV investors rely on for decision-making.

**Lake Tahoe Test Bed**

BEW Engineering, Inc - a DNV company - set up three pairs of 175 WP poly-silicon Mitsubishi model PV-UD175MF5 PV modules at fixed tilt angles of 0°, 24° and 39° on south-facing racks in Truckee, California, at the beginning of the 2009-2010 winter. The module pairs are spaced far enough apart to prevent row shading, even on the winter solstice.

Near Lake Tahoe, the station's latitude is 39° and its elevation is 5900 feet (1800 metres). The site receives an annual average of 200 inches (5 metres) of snow.

One module of each pair is manually cleaned and thermostatically heated. The three un-cleaned modules are allowed to shed or accumulate snow naturally and are bordered with two feet (0.6 metres) of similar material to minimise edge effects.

A datalogger saves hourly records of irradiance for the three tilt angles, short-circuit current and temperature for each module, along with air temperature and relative humidity. Meanwhile, an hourly webcam shot records snow depth and assists with quality checks. A second source of data is a 125 kWP Truckee Sanitary District (TSD) system located two miles (3.2 km) south of the BEW station and sitting at the same elevation.

For BEW's rig, snow losses are gauged as the difference in monthly amp-hours between the clean and uncleaned modules. For the TSD system, snow losses are gauged as the difference in measured energy and predicted energy for an always-cleaned array.

The TSD system faces south at a fixed 35° tilt, similar to one of the paired sets of BEW's test modules. The lowest edge of the 17 foot (5 metre) long rows are six feet (2 metres) above ground. While the District does not manually clean this array, they do regularly plough snow from between the rows to prevent snow from piling up. This maintenance practice proved to be especially valuable because snow is not removed from the array, yet ground interference does not occur. It is as if the array is very high above ground. Indeed, ground interference at the BEW site has resulted in twice the annual energy loss as the TSD site.

**Calculate Winter Losses**

Depending on tilt angle, wintertime energy losses of 40%-60% and annual energy losses from 12%-18% were noted in the first year of operation, though data from the TSD system were not included. The first winter was statistically very normal. The lost energy due to snow buildup in the seven-month winter season ranged from as little as 25% for the 39° tilt to as much as 42% for the flat orientation. The seasonal results project to losses in annual output of 12%, 15%, and 18% for the 39°, 24°, and 0° tilts, respectively.

While these results were hugely significant for this location, no attempt was made to project how the Truckee results would translate to other, less snowy locations based on the first year of measurements. The model development and fitting task was completed after the second year of measurements, after which BEW's generalised model was tuned enough to be provisionally applied to other locations. The current form of the model is:

Snow loss, % = C

_{1}*Se'*cos^{2}(T)*GIT*RH/T_{AIR}2/POA^{0.67}
Where:

C

Se = S (monthly snow, inches)*0.5*[1+1/N], where N is the number of snow events per month

GIT = ground interference term, defined in detail below

RH = average monthly relative humidity, %

TAIR = average monthly air temperature, C

POA = monthly plane of array insolation, kWh/m

_{1}is a fitted coefficient, 5.7x10^{4}Se' is the 6-week rolling average effective snowfall in inches, withSe = S (monthly snow, inches)*0.5*[1+1/N], where N is the number of snow events per month

GIT = ground interference term, defined in detail below

RH = average monthly relative humidity, %

TAIR = average monthly air temperature, C

POA = monthly plane of array insolation, kWh/m

^{2}
The GIT is further defined as:

GIT = 1-C

_{2}/exp(ϒ); C2 is fitted from data as 0.5; ϒ is the dimensionless ratio of snow received divided by snow dissipated, such that whenever the amount of snow received exceeds the ability of the array geometry to deposit it on the ground, shadow-like interference will quickly reduce array output by a factor of 2 to 1. BEW defines ϒ as:
R*cos(T)*Se'*2*tan(P)/(H

^{2}-Se'^{2})
Where:

R is the row plane of array dimension, inches

T is the tilt angle, degrees

P is the stabilised snow pile angle, nominally assumed to be 40 degrees

H is the drop height, inches

T is the tilt angle, degrees

P is the stabilised snow pile angle, nominally assumed to be 40 degrees

H is the drop height, inches

And Se', effective rolling-average snowfall, inches as defined above

For one of the US's snowiest urban areas, it was observed that annual losses of 12%-18% may be expected in a typical year for fixed tilt arrays mounted at tilt angles ranging from 39° to 0° (flat). However, monthly losses may be substantially higher; an entire month's output was lost for a shallow tilt angle unit when several feet of snow fell, for example.

On a rolling annual basis, the snow losses have averaged 6% for the TSD system, 13% for the 39° BEW module, 17% for the 24° BEW module, and 26% for the flat 0° BEW module. However, the principal use of this information is not necessarily to point out how much potential generation is sacrificed in a very snowy location, but to serve as a baseline for validating proposed snow loss models.

**Developing a Losses Model**

Key variables affecting generation might be supposed to include snowfall quantity, climate and weather factors such as temperature, radiation, relative humidity, wind speed/direction, and snow moisture content. Additional influences include array geometry such as tilt angle, row slant length and distance to ground as well as ground interference effects.

An equation that relates monthly energy loss to monthly snowfall in inches was developed with units of percentage loss per inch of snow. The final equation accounts for ground interference, air temperature, plane of array insolation and relative humidity. Terms such as wind and snow moisture content were not available in this test.

A promising simple annual snow loss relationship was posed, which suggests annual energy loss may be estimated as the product of a 0.1%/inch snow loss, multiplied by a tilt angle adjustment factor.

There is a clear relationship between tilt angle and energy loss, though the relationship will be influenced by other factors. However, the study only evaluated fixed-tilt configurations, and although tracking systems can be evaluated to some degree by the model, in practice the dynamic movement and vibration of tracking systems is likely to lessen the effect of snow even more than predicted.

The most encouraging findings are that the study shows annual energy predictions can be essentially unbiased when accounting for snow, and that the errors are well within the normal level attainable with simulation programs in general. Furthermore, these results can be obtained using measurements widely available in long-term climate databases, coupled with array-specific design geometries. Better estimates are possible if exact array geometry information is available to characterise ground interference effects. Indeed, the effect of ground interference is significant and was observed to have roughly a two-fold effect on typical snow loss for the specific array geometry used at the test station.

**Applying a General Model**

The Lake Tahoe area is not a prominent solar market, though the Truckee Sanitary District installed an array in 2009 and there are several other commercial PV installations in the region. However, well-established commercial solar markets (together with average annual snowfall) include Denver, 60 inches (152 cm); Milwaukee, 47 inches (119 cm); Boston/New England, 43+ inches (109+ cm); Detroit (and Ontario Canada), 42 inches (107 cm); Chicago, 38 inches (97 cm); and the Mid-Atlantic region with 20-30 inches (51-76 cm). Taking Philadelphia, Detroit and Denver, each city is at about the same latitude, roughly 40°, but their average annual snowfall varies smoothly from 20-60 inches (0.5-1.0 metres)/year, all well short of Truckee's normal total.

Each system is assumed to be south-facing, at a tilt angle equal to latitude minus 15°, with ground interference characteristic of common modules 2 metres long in portrait mode, mounted six inches (15 cm) above the roof.

Inputs needed to generate these estimates were readily obtained from the National Renewable Energy Laboratory's (NREL) solar radiation database and Wikipedia's climate data for each city. In addition to two fixed coefficients, the data needed to run the model are factors including site latitude, array geometry (tilt, row slant length, and height above ground), monthly snowfall and the number of snow events per month, average air temperature, plane of array insolation, and average relative humidity. The monthly loss estimates which result can be used directly as inputs to popular PV simulation programs such as PVSyst.

BEW is now concluding its third season of measurements at Truckee and plans to present its updated findings at the Solar Power International conference in Orlando, Florida this autumn. With such large amounts of money tied to performance, quantitative means of addressing snow loss risk are sorely needed. As this is the first published analytical model for snow loss estimation, the impact of applying it in this emerging market is potentially very large. The goal is to improve snow loss modelling and thereby improve the bankability of projects in snowy locations.

*Tim Townsend and Loren Powers are engineers at BEW Engineering, San Ramon, California. BEW is now part of DNV KEMA Energy & Sustainability. E-mail: tim.townsend@dnv.comor loren.powers@dnv.com*

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