Statistical

A statistical analysis allows you to examine the effect of uncertainty in the value of one or more input variables on an output metric. For example, you could use statistical analysis to explore how the degree of uncertainty in the installation cost of one or more system components might affect the system's levelized cost of energy over the project life.

In a statistical analysis, Solar Advisor runs several simulations for a distribution of values assigned to one or more input variables, and displays a histogram showing the frequency distribution of different output metric values over each input variable's distribution of values.

For an example of a Solar Advisor file with multiple systems, open the sample template Statistical Analysis Sample: On the File menu, click Open Sample Template and select the template from the list.

To display the statistical simulation setup options:

1.	On the Main window, click Configure Simulations to view the Configure Simulation page.

2.	On the Configure Simulations page, click Statistical to display the statistical simulation setup options.

SS_ConfigureSimulations-StatisticalClick

3.	Click Add Parametric Simulation to add a set of parametric simulation setup options. You can add as many parametric simulations as your analysis requires.

Click Remove Simulation to delete a simulation option.

Click Clear All to remove all simulation options from the case.

Contents

►	Page Reference describes the statistical simulation setup options.

►	Input Distribution Options describes the distribution parameters that you specify for each statistical variable.

►	Setting up a Statistical Analysis describes the steps for choosing an output metric, input variables, and distribution parameters for a statistical analysis.

►	Displaying Histograms for Statistical Variables describes the graphing options on the Results page available for statistical analyses.

Page Reference

The statistical Analysis Setup options allow you to select the output metric, add and remove variables from the list of statistiacl variables, and assign distribution parameters to the statistical variables.

SS_Statistical-Overview

Analysis Setup

Select an output metric	Choose the output metric for the statistical analysis.
Add	Choose one or more statistical variables from a list of available input variables.
Edit	Assign an input distribution for the analysis. See below for details.
Remove	Remove the highlighted variable from the statistical variable list.
Number of Monte Carlo Runs	Enter a value for the number of simulations to run for the analysis. The default value is 400.

Input Distribution Options

The edit distribution window allows you to define the type of distribution to use for the statistical analysis and to assign values to the statistical analysis parameters.

SS_Statistical-EditDistributionWindow

Choose an input distribution

Variable name	The name of the statistical variable. This the variable that was highlighted in the statistical variable list when you clicked Edit.
Current Value	The value of the statistical variable on the variable's input page.
Uniform Distribution	Solar Advisor randomly selects a value for each simulation between the minimum and maximum values that you specify.
Minimum	The minimum value of the statistical variable for the uniform distribution option.
Maximum	The maximum value of the statistical variable for the uniform distribution option.
Normal Distribution	Solar Advisor chooses a value for each simulation according to a standard bell curve defined by the mean and standard deviation values that you specify.
Mean (mu)	The expected value (in statistical terms) of the statistical variable.
Std. Dev. (sigma)	The variability or dispersion of the variable's probability distribution, defining the apparent width of the bell curve.

Setting up a Statistical Analysis

Once you have added a statistical simulation, you must choose an output metric for the analysis, add one or more statistical variables to the simulation, and edit the distribution parameters of each variable.

After setting up the optimization, click the Run All Simulations button, or click Run All Simulations on the Case menu to run the optimization and any other enabled simulations.

To set up a statistical analysis:

1.	Display the statistical simulation setup options as described above.

2.	Click Add to choose variables to which you want to assign a distribution from a list of available input variables. Solar Advisor adds the variables to the parametric variables list.

3.	Highlight each variable in the parametric variables list and click Edit to assign the distribution parameters.

4.	Enter a number of simulations for Number of Monte Carlo Runs. Solar Advisor will run this many simulations using variable values based on the distribution parameters you specify.

5.	Check Enable this simulation to include the optimization in simulation runs. You can save the optimization setup options and exclude the analysis from simulations by clearing the checkbox. Clearing the checkbox allows you to shorten simulation run times without losing the setup configuration.

SS_Parametrics-Enable

Displaying Histograms for Statistical Variables

After you run all simulations with one or more statistical simulations enabled, Solar Advisor allows you to view a histogram for each statistical variable on the Results page. To display a histogram, Solar Advisor sorts the values of the simulations into bins. The number of bins is specified in the graph setup.

For example, in the Statistical Analysis Sample file, the Inverter Cost histogram shows the number of occurrences of inverter cost that fall into each of the equally spaced bins, whose center values are shown along the x axis. The blue line is the estimated cumulative distribution function (CDF), labeled on the right axis from 0 to 1, and indicates the percentage of inverter cost values whose values fall below the corresponding x value.

SS_Statistical-InverterHistogramGraph

The histogram graph can only plot a single variable. Instead of plotting the inverter cost values, you could plot the levelized cost of energy, showing histogram of the 700 calculated LCOE values that correspond to the random values chosen for the Inverter costs. This way, given different amounts of uncertainty in your chosen inputs, you can visualize the effect and uncertainty on any of the single-valued output metrics.

SS_Statistical-LCOEHistogramGraph