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This report is available at no cost from the National Renewable Energy
Laboratory (NREL) at www.nrel.gov/publications.
Contract No. DE-AC36-08GO28308
Reference Manual for the
System Advisor Model
’s Wind
Power Performance Model
Janine Freeman
and Jennie Jorgenson
National Renewable Energy Laboratory
Paul Gilman and
Tom Ferguson
Independent Consultant
s
Technical Report
NREL/TP-6A20-60570
August 2014
NREL is a national laboratory of the U.S. Department of Energy
Office of Energy Efficiency & Renewable Energy
Operated by the Alliance for Sustainable Energy, LLC
This report is available at no cost from the National Renewable Energy
Laboratory (NREL) at www.nrel.gov/publications.
Contract No. DE-AC36-08GO28308
National Renewable Energy Laboratory
15013 Denver West Parkway
Golden, CO 80401
303-275-3000 • www.nrel.gov
Reference Manual for the
System Advisor Model’s Wind
Power Performance Model
Janine Freeman and Jennie Jorgenson
National Renewable Energy Laboratory
Paul Gilman and Tom Ferguson
Independent Consultants
Prepared under Task No. WE11.1214
Technical Report
NREL/TP-6A20-60570
August 2014
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iii
Table of Contents
List of Figures ................................................................................................................................ iv
List of Tables ................................................................................................................................. iv
1 Executive Summary ................................................................................................................. 1
2 Variables and Naming Conventions ........................................................................................ 1
2.1 Abbreviations ................................................................................................................ 1
2.2 Variable Names ............................................................................................................. 1
3 Introduction ............................................................................................................................. 4
3.1 SAM Overview ............................................................................................................. 4
3.2 SAM Simulation Core (SSC) ........................................................................................ 5
3.3 Model Applications and Limitations ............................................................................ 5
3.4 General Modeling Approach......................................................................................... 6
4 Wind Resource Data Options .................................................................................................. 6
4.1 Wind Resource Data from a Weather File .................................................................... 7
4.2 Wind Resource Data as a Weibull Distribution ............................................................ 7
5 Wind Turbine Model Options.................................................................................................. 9
5.1 Turbine Power Curve from the Library ........................................................................ 9
5.2 Turbine Power Curve from Characteristics ................................................................ 10
6 Wind Turbine Output from a Weibull Distribution ............................................................... 15
6.1 Wind Speed at Turbine Hub Height ............................................................................ 15
6.2 Wind Speed Probability .............................................................................................. 16
6.3 Turbine Output Probability ......................................................................................... 16
7 Wind Turbine Output from a Weather File ........................................................................... 17
7.1 Wind Speed at Turbine Hub Height ............................................................................ 17
7.2 Turbine Output at Hub Height Wind Speed ............................................................... 17
7.3 Turbine Output Adjusted for Air Density ................................................................... 18
8 Wind Farm Output from a Weather File ............................................................................... 18
8.1 Wind Farm Layout Matrix .......................................................................................... 19
8.2 Wake Effect Losses ..................................................................................................... 20
9 System Electrical Output and Capacity Factor ...................................................................... 23
9.1 Hourly Output from a Weather File ............................................................................ 23
9.2 Annual Output Energy from a Weibull Distribution .................................................. 24
9.3 Performance-Adjusted System Output ....................................................................... 24
9.4 System Annual Electrical Output (Annual Energy) .................................................... 25
9.5 Capacity factor ............................................................................................................ 25
10 Summary ................................................................................................................................ 25
11 Index of SAM and SSC Variable Names .............................................................................. 27
12 References ............................................................................................................................. 28
iv
List of Figures
Figure 1. Power Curve Diagram ................................................................................................... 11
Figure 2. Geometry of the Park Wake Model ............................................................................... 22
List of Tables
Table 1. Abbreviations used in this manual .................................................................................... 1
Table 2. Subscripts Used in Variable Names .................................................................................. 2
Table 3. Variable Names and Descriptions ..................................................................................... 3
Table 4. Wind Turbine Power Curve ............................................................................................ 10
Table 5. Drivetrain loss characteristics by drivetrain design ........................................................ 12
Table 6. Wake Effect Model Options in SAM User Interface and SSC Windpower Module ..... 20
1
1 Executive Summary
This manual describes the National Renewable Energy Laboratory's System Advisor Model
(SAM) wind power performance model. The model calculates the hourly electrical output of a
single wind turbine or of a wind farm. The wind power performance model requires information
about the wind resource, wind turbine specifications, wind farm layout (if applicable), and costs.
In SAM, the performance model can be coupled to one of the financial models to calculate
economic metrics for residential, commercial, or utility-scale wind projects. This manual
describes the algorithms used by the wind power performance model, which is available in the
SAM user interface and as part of the SAM Simulation Core (SSC) library, and is intended to
supplement the user documentation that comes with the software.
2 Variables and Naming Conventions
This chapter describes the abbreviations, variables, and naming conventions used in this manual.
2.1 Abbreviations
Table 1. Abbreviations used in this manual
Abbreviation Description
API application programming interface
NREL National Renewable Energy Laboratory
SAM System Advisor Model
SDK software development kit
SSC SAM Simulation Core
2.2 Variable Names
This manual describes three types of variables.
• Letters and subscripts to represent variables in equations in the algorithm descriptions.
• Variable names in bold font are names of inputs and results from the SAM user interface.
• Variable names in in Courier font are names of inputs and outputs in the SAM
Simulation Core (SSC).
Table 3 lists the variables used in this manual, and Table 2 lists the subscripts used with
variables.
2
Table 2. Subscripts Used in Variable Names
Subscript Description
h turbine hub height
i wind speed bin in the Weibull resource distribution
j hour in an 8760 hourly data set for one year
m power curve rated power point
The variable names in this document are described in Table 3. For those variables that appear in
the SAM user interface, their name appears in the table's "Name in SAM" column. Names of
variables that are either inputs or outputs to the SSC windpower module are listed under "Name
in SSC."
3
Table 3. Variable Names and Descriptions (For a complete list of SAM and SSC variables, see the variable index in Chapter 11 of this manual.)
Name Description Name in SAM Name in SSC Units
C

Maximum power coefficient Max Cp max_cp -
Wind turbulence coefficient Turbulence Coefficient turbul -
D
Rotor diameter User Defined Rotor Diameter rotor_di m
h
Hub height Hub Height hub_ht m
K
System capacity factor Capacity Factor - -
k
Weibull shape parameter Weibull K Factor weibullK -
L
Fixed loss factor Wind Farm Losses lossp %
(
)
Turbine rated power at wind speed
Turbine Output
(c)
pc_power kW
,
Wind farm hourly electrical output - farmpwr
(
)
Turbine electrical output at wind speed
Annual Energy @ wind speed
(kWh)
(c)
turbine_output kWh

System annual output after performance adjustments Annual Energy
(a)
annual_e_net_delivered kWh

Wind farm annual output before performance adjustments - farmpwr
V

Wind speed at 50 m Average Annual Wind Speed
(@ 50 meters)
resource_class m/s
Turbine power curve wind speed Wind Speed
(c)
pc_wind m/s
V
 
Maximum tip speed Max Tip Speed - m/s
Turbine power curve cut-in wind speed Cut-in Wind Speed cutin m/s
Wind shear coefficient Shear Coefficient shear -
Weibull scale parameter -
(b)
- m/s

Maximum tip speed ratio Max Tip Speed Ratio - -
Table 3 Notes:
(a) An output of the SSC annualoutput module.
(b) SAM calculates the Weibull scale parameter from the average annual wind speed at 50 meters input.
(c) These variables are available in SAM on the Results page,
Tables, Data: 161 values.
4
3 Introduction
This reference manual describes the wind power performance model in the National Renewable
Energy Laboratory's System Advisor Model (SAM) Version 2013.9.20 (SIL 3.0.1, SSC 33).
SAM is a desktop application designed for renewable energy analysts to evaluate system design
and project financial options. SAM's wind power performance model is also available to
software developers as the windpower module in the SAM Simulation Core (SSC) application
programming interface (API) included in the SAM software development kit (SDK).
NREL provides both the SAM application and SDK for free from the SAM website at
https://sam.nrel.gov/. More information about the software development tools can also be found
on the SAM website.
For SAM users, this reference manual supplements the SAM user documentation in SAM's Help
system.
1
For software programmers, it supports development of applications that use the API to
the windpower module.
3.1 SAM Overview
The System Advisor Model (SAM) is a desktop application designed to facilitate techno-
economic analysis of renewable energy projects. It is a decision-making tool for project
developers, financial analysts, policymakers, and energy researchers. SAM can model grid-
connected power systems that use wind, photovoltaic, concentrating solar power, solar hot water,
biopower, or geothermal electricity generation technologies.
To model a renewable energy project in SAM, you choose a performance model to represent the
system, and a financial model to represent the project's financial structure. You then specify
values on the input pages to describe the physical characteristics of the system and financial
parameters of the project. All of the input variables are populated with default values so that you
can start generating preliminary results before you have collected all of the data for your project.
After specifying inputs, you run a simulation and the performance model makes a series of 8,760
hour-by-hour calculations to calculate the system's hourly electrical output over a one-year
period
2
. The financial model uses the hourly electric generation profile and user inputs such as
installation and operating costs, electricity price, taxes and incentives, and debt parameters to
calculate the project's annual cash flows over a multi-year period [1]. SAM displays results from
both the performance and the financial models in tables and graphs, and provides options for
exporting the results for use in reports and presentations.
SAM's advanced simulation options facilitate parametric, sensitivity, and statistical studies that
involve multiple simulation runs. The SamUL scripting language is a built-in programming
language that makes it possible to automate repetitive or complex modeling tasks.
1
SAM's user documentation is available as a Help system in the user interface, and as both a web document and
PDF document on the SAM website at https://sam.nrel.gov/content/resources-learning-sam
(accessed October 11,
2013).
2
This description is generally true for SAM's performance models, with the exception of the wind power model's
Weibull distribution option for the wind resource which calculates a statistical distribution of the system's annual
output instead of time-series values (see Chapter 4.2).
5
SAM can model both distributed generation and central generation projects. The residential and
commercial financial models are for distributed generation projects that buy and sell electricity at
retail rates, and use renewable energy to supplement electricity from the grid to meet a building’s
or facility's electric load. The utility financial models are for central generation projects that sell
all of the electricity generated by the system at a price negotiated through a power purchase
agreement.
This manual describes SAM's wind power performance model. It does not describe the financial
models or other simulation options available in SAM. For an overview of SAM's financial
models, see the Financial Models topic in SAM's Help system
[https://www.nrel.gov/analysis/sam/help/html-php/index.html?fin_overview.htm].
3.2 SAM Simulation Core (SSC)
The SAM Simulation Core (SSC) is the library of software modules that SAM uses to run
simulations. The SSC's application programming interface (API) makes it possible for software
developers to develop their own applications using SAM's underlying performance and financial
models.
The SAM Software Development Kit (SDK) is a collection of software development tools that
make it possible to write programs in C++, C#, Java, MATLAB, or python that run SAM
Simulation Core (SSC) modules. The SDK includes the API to the
windpower simulation
module described here, and the APIs to SAM's other modules. Note that the SDK does not
provide access to the module's source code.
Table 3 and the Index of SAM and SSC Variable Names on Page 27 show where a specific
windpower module variable is mentioned in this manual.
3.3 Model Applications and Limitations
SAM's performance models are intended for project pre-feasibility level analysis. The wind
performance model can provide a very preliminary estimate of the expected hourly electricity
production and capacity factor over a one-year period for a single wind turbine, small wind
project, or large wind farm. The financial model uses the sum of the hourly values as an estimate
of the project's production in its first year, and extends the estimate over a period of several years
to calculate metrics such as levelized cost of energy, project net present value, power purchase
agreement (PPA) price and internal rate of return for utility projects, and total electricity savings
and payback period for residential and commercial projects.
SAM's wind performance model requires information that describes the wind resource at the
project location, a set of inputs to describe the wind turbine performance characteristics, and
inputs to describe the layout of the turbines for projects with more than one turbine. The quality
of the performance model's predictions depends on the quality of these inputs.
SAM's approach to modeling a wind farm includes a number of simplifying assumptions
described in Chapter 8. Although SAM does calculate wake effect losses due to the effect of
upwind turbines on their downwind neighbors, more detailed wind analysis models are better
suited than SAM for detailed analysis of the impact of farm layout, topography and terrain on
wind farm performance.
6
SAM's hourly simulation time step provides enough temporal resolution to offer insight into the
effect of daily and seasonal resource variation on the system's output with sufficient detail for
project techno-economic modeling, but not for detailed engineering design modeling such as
physical stresses on turbine components or electrical transients.
3.4 General Modeling Approach
The SAM wind performance model algorithm consists of the four primary steps described briefly
below and in more detail in the chapters that follow.
Step 1. Characterize the Wind Resource: The wind power model uses wind resource data
either from an hourly data file or defined as a Weibull statistical distribution.
Step 2. Specify the Wind Turbine's Power Curve: SAM models wind turbine performance
using a power curve- either a user-specified power curve table or one that SAM calculates from a
set of turbine characteristics.
Step 3. Define the Wind Farm Layout: The wind farm is a two-dimensional array of
coordinates for each turbine's location with additional inputs used to calculate wake effect losses.
Step 4. Calculate the Wind Farm Electrical Output: SAM's hour-by-hour simulation
calculates the system's electrical output in kWh for each of the 8,760 hours in one year.
3
SAM
reports the hourly values on the Results page along with monthly and annual totals in tables and
graphs that can be exported to other applications.
4 Wind Resource Data Options
The wind resource data provides information about the kinetic energy available in the wind at the
wind turbine's location and hub height. The amount of available energy depends on the wind
speed and air density and varies with time. The options on SAM's Wind Resource input page
determine how SAM characterizes the wind resource:
• Weather file (Wind Resource by Location), Chapter 4.1: The wind resource data comes
from a weather file with 8,760 hourly values for wind speed, direction, air temperature,
and air pressure at one or more turbine hub heights.
• Weibull distribution (
Wind Resource Characteristics), Chapter 4.2: The wind resource is
represented by a statistical distribution characterized by an annual average wind speed
value and Weibull K factor. This option only works with a single turbine because there is
insufficient data to model wind farm wake effects.
In the SSC
windpower module, variable model_choice = 0 is equivalent to the Wind
Resource by Location option in SAM, and model_choice = 1 is equivalent to the Weibull
distribution option.
3
The financial models assume that this annual generation profile applies to all years in the project life. They apply a
set of optional performance adjustment factors to account for system availability, curtailment, and any annual
decrease in system output. See the user documentation for details (or online at
https://www.nrel.gov/analysis/sam/help/html-php/index.html?fin_annual_performance.htm
, last visited October 10,
2013).
7
4.1 Wind Resource Data from a Weather File
When the option on SAM's Wind Resource input page is Wind Resource by Location, SAM reads
wind resource data from the weather file highlighted in the weather file list. The Folder Settings
options determine where on your computer SAM looks for the weather files.
In the SSC windpower module, the variable file_name stores the weather file’s complete path
and name, for example file_name = "c:\users\paul\weather
data\my_weather_file.srw"
refers to a weather file named my_weather_file.srw in the
c:\users\paul\weather\data folder.
4.1.1 The SRW Weather File Format
The wind performance model reads wind resource data from a weather file in the SRW format
4
,
which is a text format with comma-separated values. You can find examples SRW files in the
default weather file folder (c:\SAM\2013.9.20\weather in Windows), and a description of the
format in the "Weather File Formats" topic of SAM's help system [2].
The SRW file format is designed to be flexible enough to allow you to create files with your own
data. See the SAM help topic for more information on using or creating SRW files.
4.1.2 Representative Typical Weather Files
The SAM installation package includes a set of 39 weather files developed for NREL by AWS
Truepower that contain wind speed, wind direction, ambient temperature, and atmospheric
pressure data at 50, 80, and 110 meters above the ground. They are "representative" because they
are for locations with topography and weather combinations that represent regions of the U.S.
where large-scale wind farms are typically developed. The files are "typical" because they
represent the wind resource over a period of 14 years between 1997 and2010 [3].
4.1.3 Weather Files from the NREL Wind Integration Datasets
This data is available for 2004, 2005, and 2006 from different sources for the Western United
States and Eastern United States. The Western Wind Dataset has data developed by NREL and
3Tier for over 32,000 locations in the Western United States. The Eastern Wind Data set has data
developed by NREL and AWS Truepower for 1,326 locations in the Eastern United States.
When you download data from these datasets from within SAM, SAM converts the data into an
SRW file.
The Download weather file button on SAM's Wind Resource input page when it is in Wind
Resource by Location
mode automatically downloads files from the NREL Wind Integration
Datasets database. The SSC windpower module does not have a function for accessing this
database, but these files can be downloaded externally and used with the SSC module.
4.2 Wind Resource Data as a Weibull Distribution
For analyses that do not require the detail of time series wind resource data, SAM's Weibull
distribution option represents the wind resource as a statistical distribution characterized by a
single average annual wind speed and Weibull K factor. This option may be useful for very
4
Older versions of the model used a different file format than that used in the SRW file extension.
8
preliminary project feasibility studies before time series data is available, or for analyses
involving parametric studies on a single annual average wind speed value or the shape of wind
speed distribution over the year.
SAM disables the variables on SAM's Wind Farm input page with the Weibull Distribution wind
resource option because the option provides no information about wind direction that SAM
needs to model wake effect losses in a wind farm.
4.2.1 Weibull Distribution
The Weibull probability distribution function determines the probability that a given wind speed
value will occur over a given period:
(
)
=
×
(
)

×

( 1 )
where
() = Weibull wind speed probability distribution function
= wind speed
k =
dimensionless shape parameter, Weibull K Factor in SAM, weibullK in the SSC
windpower module
= scale parameter in m/s, Average Annual Wind Speed (@ 50 meters) in SAM,
resource_class in SSC
The turbine's elevation above sea level is an input for the "turbine power curve from
characteristics" option described in Chapter 5.2. It has no effect on the wind speed distribution
curve.
4.2.2 Wind Resource Curves
When the Wind Resource input page is in Wind Resource Characteristics mode, the graph shows
the Weibull wind speed distribution that SAM uses for simulations:
• Weibull wind speed distribution (Weibull): The wind speed probability distribution
function defined by the Weibull factors you specify on the Wind Resource input page (see
Equation 1). This is the distribution that SAM uses to calculate the turbine's total annual
electrical output.
The graph also shows two other reference probability distribution curves that SAM does not use
in simulations:
• Rayleigh wind speed distribution (Rayleigh): Another commonly-used probability
distribution function for wind resource analysis. The Weibull and Rayleigh distributions
are the same when = 2.
• Weibull Betz turbine electrical output distribution (Weibull Betz): This represents the
distribution of power for a theoretical "Betz turbine" as described in [4].
When you specify the turbine from characteristics (see Chapter 5.2), the graph displays three
additional curves from an implementation of the NREL Wind Turbine Design Cost and Scaling
Model described in Chapter 3.5 of [5]. This model is implemented in SAM's user interface and is
not available in SSC. SAM does not use these additional curves for simulations. In order to see
these curves, you must change the value of one of the input variables on the Wind Resource input
9
page because the graph will only refresh when an input value changes (this behavior may change
in future versions of SAM so that the graph updates automatically). The three curves are:
• Weibull coefficient of power turbine electrical output distribution (Weibull Cp):
Distribution of the modeled electrical output of the turbine with characteristics defined on
the Turbine input page.
• Turbine electrical output distribution (Turbine Energy): The product of the turbine power
and the Weibull probability.
• Hub efficiency distribution (Hub Eff/10): The conversion efficiency of the turbine with
characteristics defined on the Turbine input page. The efficiency value is divided by 10
so that it fits on the right-hand y-axis.
5 Wind Turbine Model Options
SAM uses a wind turbine power curve to calculate the turbine's electrical output in each time
step, given the resource characteristics as described above. The Turbine input page provides two
options for defining the power curve:
• Power curve library (Select turbine from a list), Chapter 5.1: A pre-defined table of wind
speed/turbine output value pairs represents the turbine's performance. When you choose a
turbine from the list on the Turbine input page, SAM displays the turbine's power curve
from the library.
• Turbine characteristics (Define the turbine characteristics below), Chapter 5.2: SAM
uses a set of user-specified turbine design parameters to calculate a turbine power curve.
You specify values for the parameters on the Turbine input page, and SAM calculates and
displays the power curve.
5.1 Turbine Power Curve from the Library
SAM's power curve library contains power curve data developed by NREL for the NREL Wind
Turbine Cost and Scaling Model described in [4]. NREL developed the power curves from
analysis of published performance data, so they do not represent manufacturer data.
The power curve library is not part of the SSC windpower module. In the windpower module,
you specify the wind turbine power curve using the pc_wind and pc_power input variables,
where pc_wind is a list of wind speed values included in the power curve in m/s, and
pc_power is a list of the same length containing the power curve output values in kW.
For most turbines in the library, SAM stores an array of 160 pairs of wind speed and power
output values, corresponding to wind speeds in 0.25 m/s increments from 0 to 40 m/s. Table 4
shows an example from the library for a small wind turbine's power curve (note that unlike most
turbines in the library, this turbine power curve has fewer than 160 value pairs).
10
Table 4. Wind Turbine Power Curve for the Bergey Excel S 60 Wind Turbine from the SAM Library..
Most turbines in the library have 160 data points instead of the 40 for this turbine. This small turbine is
nominally rated for 8.9 kW at 11 m/s
V P(V) V P(V)
0 0 21 3
1 0 22 3
2 0 23 3
3 0 24 3
4 0.25 25 3
5 0.8 26 0
6 1.65 27 0
7 2.55 28 0
8 3.65 29 0
9 4.85 30 0
10 6.15 31 0
11 7.5 32 0
12 9 33 0
13 9.5 34 0
14 10 35 0
15 8 36 0
16 6 37 0
17 2.7 38 0
18 3 39 0
19 3 40 0
20 3
It is possible to run SAM with a power curve for a turbine that is not included in the library by
creating a user library and adding power curve data for one or more turbines to the library.
SAM's library editor is described in the "Libraries" Help topic [5].
5.2 Turbine Power Curve from Characteristics
The Turbine Characteristics option uses a set of user-specified turbine characteristics to calculate
the turbine's power curve. SAM's algorithm, described below, is adapted from the method
described for the NREL Wind Turbine Design Cost and Scaling Model described in Chapter 3.5
of [4] and also in [8].
In Define the turbine characteristics below mode, SAM calculates the turbine power curve in the
user interface. These calculations are not part of the SSC windpower module.
The algorithm divides the power curve into the five regions shown in Figure 1, and uses
empirical equations to calculate the curve in each region.
11
Figure 1. Power Curve Diagram (Example from SAM)
Region 1: Below the cut-in wind speed. The point on the power curve at the boundary between
Regions 1 and 2 corresponds to the zero-torque point of the power curve (
,
).
Region 2: Above the cut-in wind speed but below the power curve transition point (
,
). In
this region, the turbine power increases with the cube of the wind speed, so Region 2 is
sometimes called the cubic region.
Region 2.5: The linear transition between Region 2 and Region 3. It begins at the power curve
transition point (see Figure 1) and ends at the rated power point (
,
). In an ideal power
curve, Region 2.5 would not exist, but real power curves behave slightly differently than the
ideal power curve, hence the introduction of an empirical Region 2.5. Note that this region is
called Region 2.5 following the convention of the Cost and Scaling Model.
Region 3: Above the rated wind speed but below the cut-out speed. The turbine operates at its
rated capacity in this region.
Region 4: Above the cut-out speed.
The drivetrain efficiency is the ratio of the turbine's AC electrical output to the mechanical
energy of the spinning rotor, as defined in Section 8.3.5 of [5]. The Cost and Scaling Model
algorithm defines the drivetrain efficiency as described on Page 8 of [8]:
=
(

)
( 2 )
12
where
= drivetrain efficiency
= constant turbine losses
= linear turbine losses
= quadratic turbine losses
= power ratio (ratio of produced power to rated power)
Constant losses are independent of power production and include transformer losses and other
electrical conversion losses. Linear losses scale directly with power production. Quadratic losses
depend on the square of the power production. The most common quadratic loss is copper losses
at constant voltage (resulting from the well-known =
equation, where is current and
is resistance). The losses are dependent on the type of drive train as shown in Table 5 [8].
The algorithm assumes an ideal power ratio of one,
= 1, so that Equation 2 simplifies to:
= 1 (+ + ) ( 3 )
Table 5. Drivetrain loss characteristics by drivetrain design
Drivetrain Design
C L Q
Total Losses
3 Stage Planetary 0.013 0.085 0 0.098
Single Stage 0.013 0.037 0.061 0.11
Multi-Generator 0.015 0.044 0.058 0.12
Direct Drive 0.010 0.020 0.069 0.099
The rated hub power is given by:
,
=
( 4 )
where
,
= calculated rated hub power in W
= turbine rated power in W, User Defined Rated Output on the Turbine input page
= drivetrain efficiency
And the rated hub rotor speed is:
=

 
( 5 )
where
= rated hub rotor speed in revolutions per second
 
= maximum tip speed in m/s, Max Tip Speed on the Turbine input page
= rotor diameter in m, User Defined Rotor Diameter in SAM
The rated torque
in N‐m is then:
=
,
( 6 )
13
The calculations for power curve regions 2.5, 3, and 4 require another parameter, the variable
speed torque constant [4]:
=




( 7 )
where
= variable speed torque constant in kg*m
2

= maximum turbine coefficient of power, Max Cp on the Turbine input page

= the maximum tip speed ratio, Max Tip Speed Ratio in SAM
= air density in kg/m
3
, from Equation 8
The air density at any altitude is:
=
×
×
×


×
(

×
)
( 8 )
where
= mean sea level atmospheric pressure (101,325 Pa)
= standard temperature lapse rate (‐0.0065 K/m)
= elevation above sea level in meters, either from the weather file, or
Elevation Above
Mean Sea Level
on the Wind Resource input page
= ICAO standard temperature (288.15 K)
= standard gravity (9.80665 m/s
2
)


The transition points between power curve regions are the zero torque point, power curve
transition point, rated power point, and cut-out wind speed (given in turbine specifications)
shown in Figure 1.
The Region 2 rotor speed where torque is zero is given by:
=


( 9 )
where
= rotor speed at zero torque
= rotor speed at rated torque, from Equation 5
= the slope of Region 2.5 of the power curve, assumed to be 5
The sloped sections of the power curve in Region 2 and Region 2.5 intersect at the power curve
transition point:
=



( 10 )
14
where
= rotor speed at transition point
= from Equation 7
=
 
=
 
The wind speed in m/s at the transition point is:
=


( 11 )
And the power in W at the transition point is:
=
( 12 )
The wind speed at the rated power point in m/s is given by:
=

,


/
+
.


× 
,
 
+
( 13 )
The derivation of Equation 13 is beyond the scope of this manual.
After calculating values for the transition points, the Cost and Scaling Model algorithm
calculates hub power and wind speed value pairs to define the entire power curve for wind
speeds between 0 and 40 m/s in increments of 0.25 m/s. The hub power calculation used at each
speed depends on the region in which that wind speed falls, which may be determined from
comparison to the transition points.
For Regions 1 and 4 (below cut-in speed and above cut-out speed, respectively), the hub power is
zero by definition:
= 0 ( 14 )
In Region 2, hub power is a cubic function of the wind speed:
=


( 15 )
where
= hub power at wind speed
= variable speed torque constant from Equation 7

= maximum tip speed ratio, Max Tip Speed Ratio from the Turbine input page
= rotor diameter, User Defined Rotor Diameter from SAM
In Region 2.5, the hub power at a given wind speed is interpolated linearly between
and
calculated in Equations 11 and 13, respectively:
=
(
)
(

)
(
,
 
) +
( 16 )
In Region 3, the hub power is equal to the rated power:
15
=
,
( 17 )
The Cost and Scaling Model algorithm can now calculate the actual drivetrain efficiency at
wind speed for non-zero hub power
using the actual power ratio, rather than the ideal power
ratio used in Equation 2:
=
,

,

,
,
( 18 )
Combining the appropriate equation from Equations 14-16 with Equation 18, the turbine power
at any wind speed is then:
=
( 19 )
SAM stores these turbine power values in an array of 160 points corresponding to their wind
speeds, similar to the power curve of a library turbine. The values are available in SAM after
running simulations on the Results page, in Tables, under Data: 161 values as Turbine Power
Curve - Rating (kW)
and Turbine Power Curve - Wind Speed (m/s).
6 Wind Turbine Output from a Weibull Distribution
When you run a simulation in SAM with the wind resource defined as a Weibull distribution or
the SSC
windpower module with model_choice = 1 (see Chapter 4), SAM does not perform
a time series simulation, but instead calculates the turbine's electrical output for a series of wind
speed “bins.” Each bin is a range of wind speeds on the turbine power curve from the current
wind speed (
) to the previous wind speed (

).
The number of bins depends on the wind turbine model. Most power curves in SAM's turbine
library have 160 wind speed points (every 0.25 m/s from 0-40 m/s), which corresponds to 160
wind speed bins. Some of the turbines in the library have fewer points. When SAM calculates the
power curve from turbine characteristics, it uses 160 points.
When you specify the wind resource as a Weibull distribution, there is no information about
wind direction, so SAM disables the wind farm inputs and models the system as a single turbine.
6.1 Wind Speed at Turbine Hub Height
To compute the power output for a given wind speed bin, SAM first determines the wind speed
at the turbine hub height:
=


( 20 )
16
where
= wind speed at the hub height in m/s

= wind speed at 50 m in m/s, Average Annual Wind Speed (@ 50 meters) on the Wind
Resource
input page
= hub height in m, Hub Height on the Turbine input page
= shear coefficient, Shear Coefficient
on the Turbine input page
The shear coefficient depends on the terrain, typically ranging from about 0.1 for open water to
about 0.3 for hills or mountains. Because
describes the average wind speed of the Weibull
distribution for the given hub height, the shape parameter for that hub height can be back-
calculated using the gamma function [6]:
=


( 21 )
where
= Weibull shape parameter (unitless) at hub height
= average wind speed in m/s at hub height
= Weibull
k
parameter, Weibull K Factor
on the Wind Resource
input page, WeibullK in
the SSC windpower module
6.2 Wind Speed Probability
Next, SAM uses the cumulative probability distribution function to predict the probability that
the turbine hub wind speed will be a positive number less than or equal to the wind speed
(note that the cumulative distribution function is different from the probability distribution
function in Equation 1):
(
)
= 1  
(
)
( 22 )
where
(
)
= Weibull cumulative probability distribution function for wind speed
= wind speed in m/s
= Weibull
k
factor, Weibull K Factor
on the Wind Resource
input page
= shape parameter at hub‐height from Equation 21
The probability that the hub wind speed will fall within the current wind speed bin is given by:
(

)
=
(
)
 (

) ( 23 )
where
(
)
and (

) = the cumulative probability function at the wind speed in the
current bin and previous bin, respectively.
6.3 Turbine Output Probability
Finally, to compute the contribution of this wind speed bin to the total annual electrical output,
SAM computes the power for wind speed bin i:
17
= (
) × () × 8760 ( 24 )
where
= contribution of wind speed
to turbine's total annual electrical output in Wh
(
) = power from the turbine power curve at the wind speed
in W
8760 = number of hours in a year
7 Wind Turbine Output from a Weather File
When you use a weather file with time series data for the wind resource data or the SSC
windpower module with model_choice = 0 (see Chapter 4.1), SAM calculates a single wind
turbine's hourly output using wind speed data from the weather file and the turbine's power curve
from either the turbine library (see Chapter 5.1), or calculated from wind turbine characteristics
(see Chapter 5.2). SAM then adjusts the turbine output using the air density data from the
weather file.
7.1 Wind Speed at Turbine Hub Height
SAM determines the wind speed at the turbine's hub height from the wind speed in the weather
file for the given hour. The weather file may contain wind speed data at one or more data
heights. If the turbine hub height is the same as one of the data heights in the weather file, SAM
uses that wind speed. Otherwise, it determines the data height nearest the hub height and uses the
shear coefficient to estimate the wind speed at the hub height:
,
=
,
×
( 25 )
where
,
= wind speed at turbine hub height for hour
,
= wind speed from weather file at data height nearest the turbine hub height for
hour
= turbine hub height
= data height (height at which wind speed in weather file was measured) nearest
the turbine hub height
= wind shear factor, Shear Coefficient on the Turbine input page, or shear in SSC
windpower module
7.2 Turbine Output at Hub Height Wind Speed
To determine the turbine's output in a given hour, SAM finds the hub height wind speed in the
turbine power curve table, and looks up the turbine output power for that wind speed. If the hub
height wind speed falls between two points in the power curve table, SAM uses linear
interpolation to estimate the output:
(
,
) =
(
)(
)

× (
,
 
) + (
) ( 26 )
18
where

,
= turbine output at hub height wind speed for hour
,
= hub height wind speed for hour
() = the turbine output at wind speed V from the power curve
and
= the next smallest and largest power curve wind speed to the hub height
wind speed, respectively
If the wind speed at hub height
,
for a given hour is less than the power curve cut-in speed,
or greater than the highest wind speed in the power curve, then the turbine output
is set to
zero. Note that for most of the turbines in SAM's turbine library, the maximum wind speed is 40
m/s, and the cut-out wind speed is between 20 m/s and 25 m/s. For typical wind project locations
in the United States, the maximum hourly average wind speed rarely exceeds 25 m/s.
7.3 Turbine Output Adjusted for Air Density
SAM assumes that the wind turbine power curve is for a turbine installed at sea level. The model
adjusts turbine output at hub height wind speed for a given hour to the air density at the turbine's
location in that hour. The hourly air density depends on the atmospheric pressure value from the
weather file:
=

×
( 27 )
where
= air density at the turbine location for hour
= atmospheric pressure at the turbine location from the weather file for hour
converted from atm to Pa


= temperature from weather file for hour j converted from °C to K
The adjusted wind turbine output in W in a given hour is:
P
= PV
,
×
( 28 )
where
= the wind speed at hour j from the weather file
(
,
) = the turbine output at wind speed
,
from the turbine's power curve
(calculated in Equation 26 above)
= the air density at hour j from the weather file
= the air density at sea level, 1.225 kg/m
3
at 15 °C
8 Wind Farm Output from a Weather File
When you use a weather file with time series data for the wind resource data, SAM can model
either a single wind turbine or a wind farm with two or more turbines.
19
Because SAM needs information about wind direction to calculate wake losses associated with a
wind farm, it cannot model a multi-turbine wind farm when the wind resource data is defined by
a Weibull distribution.
SAM makes the following simplifying assumptions about the wind farm:
• All turbines are at the same elevation above sea level so that the air density is constant
across the entire wind farm.
• The terrain type is the same across the entire wind farm so that the wind shear is the same
for all turbines.
When you model a wind farm with more than one turbine, SAM calculates the wind farm output
for each hour using an algorithm conceptually similar to these steps:
1) Calculate the output and thrust coefficient of the most upwind turbine in the wind
farm.
2) For each remaining turbine in the farm:
a) Determine the downwind and crosswind distance from the nearest upwind
turbine using wind direction data from the weather file and turbine
coordinates from the wind farm layout matrix.
b) Use the wake effect model to calculate the wind speed at the turbine using the
output wind speed from the neighboring upwind turbine.
c) Calculate the turbine's electrical output and thrust coefficient at the adjusted
wind speed.
3) Calculate the wind farm output by adding up the electrical output values of all the
turbines.
4) Adjust the wind farm output by the wind farm loss factor.
8.1 Wind Farm Layout Matrix
In order to identify the upwind and downwind turbines in the wind farm, SAM uses a simple
two-dimensional array to represent turbine locations. Each turbine location is an x,y coordinate
pair that defines the distance in meters of the turbine from an arbitrary origin (0,0) where the
smallest or most negative x and y values define the location of the southwest corner of a
cardinally-oriented rectangle enclosing the wind farm.
The
Wind Farm input page has a basic visual layout tool to help you specify the location of
turbines using a rectangular or triangular layout. The input page also allows you to import wind
turbine coordinates from a text file instead of using the layout tool. The layout tool and file
format are both described in the Help topic for the Wind Farm input page [9].
In the SSC windpower module, you specify the rectangular coordinates of the turbine locations
using two one-dimensional array variables: wt_x for the x-axis and wt_y for the y-axis location,
where wt_x = 0 and wt_y = 0 is the origin as defined above, with distance from the origin
measured in meters. The wind farm layout is independent of latitude and longitude information,
and does not check for reasonability with respect to bodies of water, etc.
20
8.2 Wake Effect Losses
SAM provides three options for modeling wake effect losses in a wind farm. Each option uses a
turbulence coefficient value as input to calculate losses due to disturbance of the wind flow to
downwind turbines by neighboring upwind turbines.
The Wake Model variable (wake_model in the SSC windpower module) on the Wind Farm
input page determines what wake effect model SAM uses. Table 1 summarizes the three wake
effect model options, described in more detail below.
Table 6. Wake Effect Model Options in SAM User Interface and SSC Windpower Module
Wake Model
(SAM)
wake_model
(SSC)
Description
Simple Wake Model 0 Uses wind speed deficit calculation
Park (WAsP) 1 Implementation of approach used for WAsP software
Eddy Viscosity 2 Represents wake profile as a Gaussian curve
The Simple Wake Model is an implementation of a model developed at NREL and adapted for
SAM. Park (WAsP) and Eddy Viscosity models are described briefly below with references to
documents that describe them in more detail. The Simple Wake Model is suitable for most
analyses in SAM. The Park (WAsP) and Eddy Viscosity wake effect models are provided to
allow for comparison with implementations in other software.
8.2.1 Turbine Output and Thrust Coefficient
SAM calculates the turbine output from the turbine power curve as described in Chapters 6 and
7.
The turbine thrust coefficient characterizes the thrust, or force on the turbine rotor. SAM uses a
numerical solution of the relationship between the thrust coefficient and the power coefficient to
calculate the thrust coefficient.
The theoretical power in the wind depends on density, wind speed, and rotor diameter:
=

V
( 29 )
where
= theoretical power in the wind in W
= air density in kg/m
3
= rotor diameter in m
= wind speed in m/s
The power coefficient
is then:
=
()
( 30 )
21
where
(
)
= Power at wind speed determined from the power curve
As shown in [6], the power coefficient
and the thrust coefficient
are given by:
= 4(1  )
( 31 )
= 4(1  ) ( 32 )
where
= axial induction factor (describing the wind speed drop across a turbine), which is
unknown.
Solving numerically for
in terms of
gives the following relationship when 0 <
< 0.6
(which is a sufficient range, since the Betz limit tells us that
< 0.59) [6]:
=  +
+
+
( 33 )
where
= ‐0.01453989
= 1.473506
= ‐2.330823
= 3.885123
8.2.2 Simple Wake Model
The Simple Wake Model [8, Chapter 3] is an adaptation of a model developed in 1996 at the
University of Wisconsin's Solar Energy Research Center for the TRNSYS [11] simulation
platform. The model uses the wind speed deficit factor to estimate the reduction in wind speed at
a downwind turbine due to the wake of an upwind turbine.
The turbulence intensity is:
=
× (1
× log (2 × ))
+
( 34 )
where
= turbine thrust coefficient
= crosswind distance between turbines in rotor radii
= wind turbulence coefficient, Turbulence Coefficient on the Wind Farm inputs page,
turbul in the SSC windpower module
The wind speed deficit factor

is:
f

=
×
×

×
×
( 35 )
22
where
C
= turbine power coefficient
= transverse turbulence intensity (Equation 37)
= downwind distance between turbines in number of rotor radii
= crosswind distance between turbines in number of rotor radii
The adjusted wind speed

is then:

= V × (1 f

) ( 36 )
where
= wind speed at neighboring upwind turbine

= wind speed deficit factor (Equation 40)
8.2.3 Park Wake Model
The Park wake model [12] assumes that a decrease in free-stream wind speed occurs
immediately behind the turbine, and that the turbine wake expands linearly downstream of the
turbine, with the magnitude of this expansion given by an empirically determined wake-decay
constant k. Given the geometry shown in Figure 2:
Figure 2. Geometry of the Park Wake Model
The radius
of the wake at the location of turbine 1 is computed using the wake-decay
constant:
=
+

( 37 )
where
= rotor diameter of the upstream turbine
k
= wake‐decay constant (in SAM, this is equal to 0.07, a typical value for this constant)

= horizontal distance between the upstream and downstream turbines

is then computed geometrically. The decrease in wind speed occurring at the
downstream turbine is then given by the wind speed deficit, calculated in the following:
= 1
1  



( 38 )
23
where
 = wind speed deficit at the downstream turbine
= thrust coefficient

= area of the overlap between the wake and the rotor swept area of the
downwind turbine as shown in Figure 2
= the swept area of the downstream turbine's rotor
The adjusted wind speed

at the downwind turbine is then:

= V × (1 

) ( 39 )
where
= wind speed at neighboring upwind turbine

= wind speed deficit factor (Equation 40)
In the case where a turbine is affected by more than one upstream turbine, the Park model
calculates the adjusted wind speed for each upstream turbine, and uses the minimum adjusted
wind speed value (i.e. the largest wake effect).
8.2.4 Eddy-Viscosity Wake Model
The Eddy-Viscosity wake model is an implementation of the numerical solution developed and
described in 1996 at Renewable Energy Systems, Ltd. It implements a solution of the Navier-
Stokes and continuity equations from fluid mechanics to predict the centerline velocity deficit
downstream of a turbine, which is then used to represent the initial wake profile behind a turbine
as a Gaussian curve. A detailed description of this model is beyond the scope of this manual, see
[13] for its documentation.
This model calculates the adjusted wind speed

of each downwind turbine in the farm based
on the wind speed at the nearest upwind turbine.
9 System Electrical Output and Capacity Factor
SAM models different kinds of renewable energy systems. For each kind of system, it calculates
the system's electrical output and reports it as hourly, monthly, and annual energy on the Results
page. For the wind performance model, the system electrical output is the wind farm's electrical
output (in some cases, the output of a single turbine). In SAM, the system's electrical output
(Annual Energy) is the wind farm output adjusted by optional performance adjustment factors.
9.1 Hourly Output from a Weather File
For simulations that use an hourly weather file as input, SAM calculates the output of each
turbine in the farm as described in Chapter 8. The wind farm's hourly electrical output is the sum
of all of the turbines' electrical output, adjusted by the wind farm loss factor:
,
=

×
,

( 40 )
24
where
,
= electrical output of wind farm in hour in kWh/h, in the SSC windpower
module, farmpwr. (This value is not displayed on SAM's Results page.)
= loss factor, Wind Farm Losses on the Wind Farm input page, lossp in the SSC
windpower module
,
= electrical output of turbine in hour in kWh/h
= number of turbines in the wind farm
The wind farm loss factor is intended to account for wiring and other losses associated with the
wind farm design. You can account for operational losses such as system availability,
curtailment, and degradation using the adjustment factors described in Section 9.3.
9.2 Annual Output Energy from a Weibull Distribution
For simulations based on a Weibull distribution of wind speed, SAM calculates each wind speed
bin's contribution to the annual electrical energy output of a single turbine as described in
Chapter 6. For a wind farm consisting of a single wind turbine, the annual electrical output is
then:

=

( 41 )
where

= annual output of a single turbine in kWh
= power output of the wind speed bin as shown in Equation 24 in kW
= number of wind speed bins in the Weibull distribution
Recall that
is already adjusted by the number of hours that it occurs per year, as shown in
Equation 24.
Because SAM's financial models require hourly electrical output values, SAM calculates the
values by dividing the annual electrical output by the number of hours in one year:
,
=


( 42 )
where
,
= electrical output of the turbine in hour in kWh/h

= annual output of a single turbine
8760 = number of hours in a year
9.3 Performance-Adjusted System Output
SAM applies a set of adjustment factors to the performance model's results to account for
operational losses due to maintenance downtimes, grid operator curtailment requirements, or
annual output degradation due to aging of system components. These factors are inputs on the
Performance Adjustment input page. In SSC, these adjustment factors are not part of the
windpower module. They are in the annualoutput module, and can use windpower module
outputs as inputs.
25
The performance adjustment factors are (see [14] for more details):
• The Percent of annual output factor (energy_availability in the SSC
annualoutput module) is applied to the wind farm (or turbine) annual output.
• The Year-to-year decline in output factor (energy_degradation in SSC) is applied to
the annual output in Years 2 and later of the project cash flow.
• The Hourly Factors (energy_curtailment in SSC) are applied to the hourly output.
SAM reports the hourly, monthly, and annual energy values in results both before and after the
performance adjustment factors.
9.4 System Annual Electrical Output (Annual Energy)
The system's annual electrical output is the sum of the turbines' output adjusted by the
performance adjustment factors described in Section 13.3. SAM reports this value on the Results
page as Annual Energy:

=

,
×
,


( 43 )
where

= adjusted annual electrical energy output of the system in kWh. (In SSC, this value
can be calculated using the annualoutput module.)
,
= electrical output of wind farm in hour in kWh/h, in the SSC windpower
module, farmpwr
,
= hourly adjustment factor defined on the Performance Adjustment input page in
SAM, and in the SSC annualoutput module
9.5 Capacity Factor
The system's capacity factor is the ratio of the system's annual electrical output to its potential
output at the wind farm's rated capacity:
=

×
( 44 )
where
= system capacity factor
= system's total annual electrical ouput in kWh after performance adjustments
= wind farm's rated capacity in kW, System Nameplate Capacity on the Wind Farm
input page
8760 = number of hours in one year
10 Summary
The wind power model described in this manual is an hourly simulation model developed and
distributed by the National Renewable Energy Laboratory that calculates a wind power system's
hourly electrical output. The model is available for project modelers as part of the System
26
Advisor Model, and for software developers as the windpower module in the SAM Simulation
Core software development kit. The model can simulate the performance of a single wind turbine
or wind farm using weather data from a weather file or specified as a Weibull distribution. The
model uses a wind turbine power curve to calculate the electrical output of a single turbine. For
simulations of a wind farm, the model adjusts the output of each turbine in the farm using a wake
effect model. A set of performance adjustment factors account for project operating losses.
27
11 Index of SAM and SSC Variable Names
This index lists the page numbers where SAM and SSC variables are discussed in this manual.
See Table 1 for a list of variable names used in the equations in the chapters above.
Annual Energy, 29
Average Annual Wind Speed (@ 50 meters),
12, 20
coefficient of power, 13, 17
Define the turbine characteristics below, 13
Elevation Above Mean Sea Level, 17
file_name, 11
Hub Eff/10, 13
hub height, 6, 20
hub_ht (hub height), 6, 20
lossp. See Wind Farm Losses
Max Cp, 17
Max Tip Speed, 16
Max Tip Speed Ratio, 17, 18
model_choice, 11, 19, 21
pc_power, 13
pc_wind, 13
Rayleigh, 12
resource_class. See Average Annual Wind
Speed (@ 50 meters)
Select turbine from a list, 13
shear, 21
shear coefficient, 20
Turbine Energy, 13
Turbine Power Curve - Rating (kW), 19
Turbine Power Curve - Wind Speed (m/s),
19
turbul. See Turbulence Coefficient
Turbulence Coefficient, 25
User Defined Rated Output, 16
User Defined Rotor Diameter, 16, 18
Weibull, 12
Weibull Betz, 12
Weibull Cp, 13
Weibull K Factor, 12, 20
weibullK. See Weibull K Factor
WeibullK. See Weibull K Factor
Wind Farm Losses, 28
Wind Resource by Location, 10, 11
Wind Resource Characteristics, 10
wt_x, 23
wt_y, 23
28
12 References
1. "System Advisor Model: Financial Models." National Renewable Energy Laboratory.
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