Statistical Tools for Solar Resource

Forecasting

Vivek VijayIIT Jodhpur

Date: 16/12/2013

• Solar Resource Assessment

• Types of Data

• Regression Analysis – Modeling of Cross Sectional Data

• Statistical Tests

•Dimensionality Reduction

• Time Series Forecasting

• Learning Algorithm - ANN

Outline

Solar Resource Assessment (SRA) is a characterization of solar irradiance

available for energy conversion for a region or specific location over a

historical time period of interest.

Forecasting solar irradiance is an important first step toward predicting the

performance of a solar-energy conversion system and ensuring stable

operation of electricity grid.

PV plants are fairly linear in their conversion of solar power to electricity,

that is, their overall conversion efficiency during operation typically

changes less than 20%.

On the other hand, assessment of CSP production is more challenging due to

the non-linear nature of thermodynamic parameters.

Solar Resource Assessment

Cross Sectional Data

Multiple individuals at the same time

Time Series Data

Single individuals at multiple points in time

Panel or Longitudinal Data

Multiple individuals at multiple time periods

Types of Data

Problem – Estimation of Global Solar Radiation from

Meteorological Parameters (Air temperature, relative humidity etc.)

and Sunshine Duration

Angstrom-Prescott Model – A linear regression model (Monthly

average daily radiation at a particular location (H) v/s Monthly

average daily sunshine hours (S))

and can be obtained by using some other parameters.

Regression Analysis

• The accuracy of the estimated models must be judged by

statistical indicators, such as

• Correlation Coefficient

•Mean Bias Error

• Root Mean Square Error

• Percentage Error

• Coefficient of Determination

Statistical Test

The dimension of the data is the number of variables that are

measured on each observation. When the dataset is high-

dimensional, not all the measured variables are “important”. The

analysis also becomes computationally expensive. The removal of

“irrelevant” information is dimensionality reduction.

Given the dimensional random vector , the problem is to find a

lower dimensional representation of it, with that captures the

information in the original data, according to some criterion.

Dimensionality Reduction

Dimensionality ReductionThe techniques of dimensionality reduction are mainly

classified into

(a) Linear (PCA, Factor Analysis etc)

(b) Non-linear (Kernel PCA, MDS, Isomap etc)

Linear techniques result in each of the components of the new

variable being a linear combination of the original variables

Time Series Forecasting• Linear Time Series Models (Under Stationarity)

• Simple Autoregressive (AR) Models

• Simple Moving Average (MA) Models

•Mixed ARMA Models

• Seasonal Models

•AR (1) model

Where is assumed to be a white noise series with mean zero and

constant variance.

•Order Determination of AR

• Partial Autocorrelation Function

•AIC or BIC

• Parameter Estimation – Any AR(p) is similar to multiple

regression model and so least square method can be used to

estimate the parameters.

•Goodness of Fit

Some Measures

•Artificial Neural Networks – When the data is non-linear in

nature, ANN is a good methodology for forecasting. The

gradient decent algorithm can be used for updation.

• Issues

•How many number of hidden neurons?

•How many number of hidden layers?

•Overestimation

A Learning Algorithm - ANN

Thank You