Stochastic modelling and forecasting of solar radiation

Conway, Eunan Martin (1998) Stochastic modelling and forecasting of solar radiation. Doctoral thesis, University of Northumbria at Newcastle.

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Abstract

From a review of the existing literature it was evident that statistical analysis and stochastic modelling of solar radiation has been applied to horizontal data recorded at
sites remote from populated areas, in a deliberate attempt to eliminate the localised climatic effects of city centres. But both are very limited and unsophisticated. Various sampling intervals were adopted from 1 minute instantaneous values to hourly, daily and even monthly averages. In most other time series analysis applications the sampling frequency or sampling interval is set, for example annual crop yield, daily average temperature, monthly unemployment figures where a smaller sampling
interval would be meaningless and impractical to impose. To model solar irradiance at smaller sampling intervals within an urban environment could stimulate investment in large-scale Photovoltaic Systems, which could be incorporated into the urban / national grid to provide predictable levels of base load. Since solar cells respond almost instantaneously to variations in solar irradiance, the instantaneous variations in power from a photovoltaic system have design implications for devices that transfer
energy from the system to the grid. Being able to set a guaranteed low level of output from photovoltaic systems would be an important step forward in the integration of
solar energy into the urban / national power grid. Therefore an understanding of high frequency variation may be necesary. This in turn requires a short sampling interval. For other applications, such as solar water heating, high frequency variation may not be important. In such cases it is useful to know what the longest duration of sampling interval can be, or whether averaging the data over a sampling period would result in more predictable levels of base load. To this end the work reported in this thesis considered modelling solar irradiance in association with photovoltaic systems. Since solar cells respond almost instantaneously to variations in solar irradiance the major
part of this work was to assess the optimal sampling interval at which to record data, horizontal and vertical both summer and winter. Knowing horizontal and vertical
components the total on a plane normal to sun's rays can also be calculated (Chapter 2), also a possible application to panels that move so as to be normal at all times. The
optimal sampling interval must reduce the amount of information lost but still contain the essential characteristics of the past behaviour of solar irradiance at that location.
This work involved statistical analysis of solar radiation values recorded at a measuring station situated on the city campus at the University of Northumbria, Newcastle-upon-Tyne, England. The first part of this work involved recording 10, 20, 30 and 60 minute averaged horizontal and vertical solar irradiance data over 13-15 day periods for three winters and summers. This data was then used to derive and compare ARIMA models for 10,20,30 and 60 minute averaged horizontal and vertical solar irradiance data. The second part considered 1,5 and 10 minute instantaneous and 5
and 10 minute averaged horizontal and vertical solar irradiance data for one summer and one winter. This analysis modelled individual days separately with the days
categorised as good, average or overcast depending on the percentage sunshine recorded on that day.
In both cases the ARIMA models were derived for original data and log transformed data and compared via their %R2 value. The models produced during this work were 111 very good, giving %R2 values as high as 91% in some cases with the minimum of parameter estimates to be calculated.

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