What is the mathematics model to calculate daily, hourly, of wind speed and load demand data ..... when put the resource data input to HOMER program and then the plot button clicked ..... Can you make a description about the HOMER calculation process? 

The steps of the wind speed data synthesis algorithm are as follows:

1.       Generate a first-order autoregressive sequence with the desired degree of autocorrelation.  This data sequence has a normal distribution.

2.       Create a data sequence consisting of the desired 24-hour daily wind speed profile, repeated each day.

3.       Do a probability transformation on the sequence generated in step 2 so that it conforms to the same normal distribution as the sequence generated in step 1.

4.       Add this transformed sequence to the sequence generated in step 1.  Now you have a sequence with the desired autocorrelation and daily pattern, but it is normally distributed instead of Weibull distributed.

5.       Do a probability transformation on the sequence to give it the desired Weibull distribution.

We designed the algorithm to require as simple input parameters as possible.  It requires three pieces of information:

1.       The desired distribution, which you specify with an average wind speed and a Weibull k value.  Most wind speed distributions have Weibull k values between 1.5 and 2.5.  Look up "weibull k" in the index of the Help system for more information.

2.       The desired daily profile.  For interface simplicity HOMER forces you to specify a sinusoidal profile so you just enter the phase and amplitude.  HOMER calls those parameters the "hour of peak wind speed" and the "diurnal pattern strength", respectively.

3.       The autocorrelation factor.  That's the desired one-time-step autocorrelation coefficient, which is equivalent to the value of the parameter in the first-order autoregressive model.  The typical range for this parameter is 0.8 to 0.95, and it is somewhat related to the complexity of the surrounding topography.  Look up 'autocorrelation factor' in the Help system for more details and guidance.