DEVELOPING WIND TURBINE MODULES FOR GRIDLAB-D
A Report
Presented to the Faculty of the Graduate School
of Cornell University
In Partial Fulfillment of the Requirements for the Degree of
Master of Engineering
by
Noah Benjamin Maze
January 2014
© 2014 Noah Benjamin Maze
ALL RIGHTS RESERVED
ABSTRACT
As modern energy production techniques move away from monolithic, fossilfuel-driven generation facilities, heuristics for the development and maintenance of
distributed renewable energy systems must be developed; furthermore, antiquated
heuristics undervalue renewable energy and ignore externalities.
The objective of this project was to facilitate the advancement of new decisionmaking paradigms by incorporating sustainable energy sources into distribution-level
simulation software.
Specifically, this report describes the development and
implementation of wind-turbine add-ons to an open-source distribution-network
simulation and analysis tool called Gridlab-D [1]. The additions include single- and
multiple-turbine simulation objects that estimate power generation based on climate
data (an existing part of the simulation tool) and user-defined turbine parameters.
The resulting software was verified by comparing the expected and observed
power output for each turbine model. These values were calculated externally in
MATLAB and then compared with the output of Gridlab-D for the same weather
information. Retrospective software validation was carried out by using real-world
turbine data from NREL, Weaver Wind, and Middelgrundens Wind Turbine
Cooperative to generate model parameters. The resulting parameters were plugged
into Gridlab-D (compiled with the new models) along with observed wind data, and
then the simulated output was compared to the observed wind power output.
Further work in this area could entail reproducing existing wind integration
studies on the Gridlab-D platform. This would allow researchers to directly compare
studies that were originally carried out in disparate simulation environments.
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ACKNOWLEDGMENTS
This work would not have been possible without the guidance and support of my
advisor, Dr. C. Lindsay Anderson. I would also like to thank Weaver Wind Energy,
the IU Offshore Wind Energy Measurements Project, and the National Renewable
Energy Laboratory for providing the turbine data used to verify and validate this work.
Personally, I am grateful for the kindness of my family and friends, and for the
unwavering support, love, and patience given to me by my wife, Elizabeth Ann Maze.
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TABLE OF CONTENTS
Chapter 1: Introduction .............................................................................................................. 1
The Power Grid........................................................................................................................... 2
History .................................................................................................................................... 2
Modern Consequences .......................................................................................................... 2
The Smart Grid ........................................................................................................................... 3
Transmission Level Advantages.............................................................................................. 3
Consumer Level Advantages .................................................................................................. 3
Distribution Level Advantages................................................................................................ 3
Modelling the Grid ..................................................................................................................... 5
Systems of Equations ............................................................................................................. 5
Optimal power flow solvers ................................................................................................... 5
Gridlab-D ................................................................................................................................ 6
Summary of Outcomes ............................................................................................................... 6
Chapter 2: Choosing a Wind Turbine Model .............................................................................. 8
Model Examples ......................................................................................................................... 8
Static Models .......................................................................................................................... 9
Dynamic Models ..................................................................................................................... 9
Data-Driven Models ............................................................................................................. 10
Chapter 3: Implementation ...................................................................................................... 14
Compiling Gridlab-D ................................................................................................................. 14
Adding a Gridlab-D Class .......................................................................................................... 15
Source Code Requirements .................................................................................................. 15
Auxiliary Functions ............................................................................................................... 15
Merging This Project with Gridlab-D .................................................................................... 16
Chapter 4: Verification, Validation, and Discussion ................................................................. 17
Software Verification................................................................................................................ 17
Software Validation .................................................................................................................. 19
Conclusion ................................................................................................................................ 22
References .................................................................................... Error! Bookmark not defined.
Appendix .................................................................................................................................. 28
v
Gridlab-D Prerequisites ........................................................................................................ 28
Gridlab-D Build Procedure.................................................................................................... 28
Table of Logistic Parameters ................................................................................................ 28
Gridlab-D Compatible Timestamped Weather CSV ............................................................. 29
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LIST OF FIGURES
Figure 1 GDP per capita versus Energy per capita worldwide [48] ............................... 1
Figure 2: Parts of a Wind Turbine .................................................................................. 8
Figure 3: Piecewise Linear Model Featuring the Model (blue) and Data-points (red) 11
Figure 4: Five-Parameter Logistice Model featuring Model (blue) and Data-points
(red) .............................................................................................................................. 12
Figure 5: Linear Piecewise (blue) and Aggregate power curves (green and red) ........ 13
Figure 6: System Load Time Series on a partly cloudy afternoon with (A) Low, (B)
Moderate, and (C) Pervasive Solar Penetration. Plot D illustrates the solar intensity
over this period. ............................................................................................................ 14
Figure 7: Static Model Verification—The original power curve (top left) is used to
generate linear and logistic models (bottom left). Synthetic wind data (top right) is
swept from low to high, creating the power output estimation shown (bottom right). 17
Figure 8: Multiple Turbine Model Verification--Observed and Nominal Power Curves
(top) and Power Output over Time (bottom). ............................................................... 18
Figure 9: Observed and Predicted Power Output of the NREL CART 3 Wind Turbine
...................................................................................................................................... 19
Figure 10: Distribution of Power Output for Denver, Seattle, and San Francisco ....... 20
Figure 11: Observed Data and Logistic Fit for Middelgrunden Turbine ..................... 21
Figure 12: Estimated and Observed Power Output at Middelgrunden ......................... 21
Figure 13: The impact of turbine downtime on power output estimation. ................... 22
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Chapter 1: Introduction
One of the most critical aspects of the challenges presented by carbon pollution
and rising energy demand is that reducing energy use is not a viable solution. Most of
the basic human necessities--food, water, and shelter--cost energy. Additionally, as a
country becomes more industrialized and better able to take care of its people, the
energy requirements per capita increase. Unlike many developmental problems that
eventually sort themselves out once the country becomes developed, per-capita power
consumption correlates positively with GDP throughout the entire development
process, as shown below.
Figure 1 GDP per capita versus Energy per capita worldwide [48]
In order to reduce the amount of carbon being released into the atmosphere,
carbon-polluting technologies must be replaced with renewable technologies like
solar, geothermal, hydroelectric, and wind power. However, the transition to these
technologies is not easy due to the fact that the many renewable power sources are not
easily dispatchable: they lack the stability and predictability of older technologies like
coal and natural gas.
Wind power, in particular, is subject to difficult-to-forecast meteorological
processes, as well as internal dynamics that complicate the estimation of the output of
the turbine even further. Mathematical models can be used to focus on particular
details to facilitate the design and analysis of a given generator, and they can also be
used to quantify the value of a generator given typical meteorological data for a given
site.
This project facilitates the simulation and analysis of wind turbine power
generation by adding single- and aggregate-turbine modules to a power distribution
network simulator. This addition allows users to contextualize wind power output
based on locally observed wind data, and to examine its impact on the overall
distribution grid. Wind energy can be unpredictable and unstable, but localized
simulations help system operators understand the challenges more clearly. The
1
modules were written in C++ and compiled alongside the original source for GridlabD.
The remainder of this chapter provides a brief overview of the power grid of
the United States, and a discussion about the benefits of locally relevant simulation.
Chapter 2 presents a collection of mathematical models for characterizing wind
turbines, and the motivation behind selecting four models. Chapter 3 outlines the
implementation of the chosen models and the process of creating and compiling a
module in Gridlab-D. Software verification, validation, and concluding remarks can
be found in Chapter 4.
The Power Grid
The power grid of the United States connects energy producers with consumers.
Large, gigawatt-scale generation facilities provide energy to vast areas via hundreds of
thousands of miles of high-voltage transmission lines [2]. Distribution networks
transform this voltage to lower levels and distribute it to energy consumers. Because
most renewable facilities are only megawatt scale, it can be challenging to incorporate
them into this arrangement. A variety of “Smart” technologies have been proposed to
help untangle the power grid from its historical roots.
History
The history of the power grid began in Manhattan in 1882 with Pearl Street
Station, a DC plant that powered Edison’s nearby electric lamps. In the next few
decades, small systems like this one sprung up all over the country. In the early
20th century governments began regulating and consolidating these systems, but
this effort could not prevent monopolies and unfair pricing.
In the 1930s, the whole system became a heavily regulated monopoly that
encompassed everything: generation, transmission, and distribution. A byproduct
of this arrangement was the increased prevalence of monolithic power plants and
larger, longer transmission lines.
In the 70s, legislation was passed that allowed private corporations to sell
energy alongside utilities. The existing monopolies fought back against this by
refusing to allow these private entities to use the lines. This resulted in a push for
energy market liberalization that is still ongoing today [3].
Modern Consequences
In short, the grid originated as a collection of incongruous small systems, and then
grew to alarming magnitudes due to vertically-integrated monopolies. This history
has produced a network with poor communication and control systems due to the
regional differences. And the history of gigawatt-scale power generation has led
to the creation of a grid that expects deterministic power sources and is sensitive to
stochastic processes.
The grid is lacking the communication and robustness that most modern
systems possess. These problems impact renewable energy incorporation severely.
As a result, the United States gets most of its power from the traditional
monolithic, carbon-heavy power plants [4].
2
The Smart Grid
Incorporating renewable energy is one of many technical challenges facing the power
grid. In [5], Beard et al stress that 1) emission-reducing strategies, 2) extreme weather
events, and 3) changes in governmental policy will also impact the generation,
transmission, and consumption of power. Power systems researchers from all over the
world have proposed countless “Smart Grid” systems, and they usually possess three
main qualities: integrated communication, improved interfaces and decision support,
and advanced control methods [6].
Transmission Level Advantages
At the transmission level, advanced sensing and control methods could facilitate
maintenance and improve response times to outages. Sensor data provided over
the integrated communication network could detect incipient failures early,
allowing engineers to repair faults before they precipitate into system failures. In
the event of an outage, the system could immediately recognize the affected area,
allowing crews to react swiftly. The changes brought by a smarter grid would
enable the transmission system to become more robust and reliable by facilitating
remedial actions and preventative measures.
Consumer Level Advantages
Integrated communication could bring real-time information to consumers, which
could help them make informed choices about their energy use. Previous research
indicates that consumers value renewable energy but these values are not being
acknowledged by utility companies because consumers do not have sufficient
bargaining power [3]. The Smart Grid could empower consumers by giving them
access to a wider variety of suppliers.
The Smart Grid could also supply consumers with information relating to their
own consumption, through Smart Meters. These meters could inform consumer
decisions by illustrating which devices were consuming the most power, and how
much this consumption was costing the consumer [7]. With better communication,
this cost could be changed dynamically to reflect the current cost of power
generation. The resulting peaks during heavy use could trigger consumers (and
automated devices) to minimize the amount of power they were consuming.
Overall, these impacts would reduce peak power usage and encourage utilities to
increase renewable power generation capacity.
Distribution Level Advantages
The distribution system would also benefit from the previously mentioned
advantages: a reduction in peak power demand would reduce generation costs
while lowering bills for consumers, and the enhancement of sensing and control
systems would increase the reliability of both the transmission and the distribution
network. On top of these perks, the Smart Grid could create more opportunities
for distributed power generation and storage facilities. These facilities could sink
and source demand as needed to offset deviations from generation and
consumption forecasts.
3
Like the transmission system, distribution-level security and reliability will be
enhanced by the Smart Grid. Dynamic network analysis, visualization, and
decision guidance will decrease reaction time and severity of distribution system
faults [8]. However, increased reliance on cyber-physical systems creates more
opportunities for network intrusions. Adversaries with access to distribution
system control networks could cause significant harm. The security of the
distribution system depends on the security of the devices, configurations, and
networks contained therein, so the Smart Grid must communicate securely,
mitigate possible security risks, and leverage known information flows [9]. In the
event of a successful intrusion, security systems will be able to use recorded
information to identify and attribute attacks.
In addition to security concerns, the reliability of the system is impacted by
unexpected changes in load and power generation. Demand response, alluded to
in the previous section, is defined by the Federal Regulatory Commission as
“changes in electric usage by end-use customers from their normal consumption
patterns in response to changes in the price of electricity over time, or to incentive
payments designed to induce lower electricity use at times of high wholesale
market prices or when system reliability is jeopardized [10].” As Demand
Response becomes a more prevalent mechanism among end-users, the resulting
load shifts could reduce power consumption significantly below forecasted values.
In [11], Medina et al assert that this growth in Demand Response management
could negatively impact grid health unless the load reduction of each end-user is
mapped to the grid model during forecasting.
Renewable power generation can also create unexpected deviations from
distribution forecasts. Photovoltaic systems that harvest solar energy possess both
long-term and short-term variations. Long-term solar energy variations due to
astronomical conditions are trivial to forecast, but fluctuations due to cloud cover
and related meteorological events can cause significant, unpredictable voltage
changes in the short term [12]. Wind power is also subject to stochastic
meteorological conditions.
The power output of wind turbines changes
nonlinearly with wind speed, and the wind itself is significantly more intermittent
and unpredictable than the sun. While short-term (15-minute timescale) wind
fluctuations contribute to power output variance, forecast error is the primary
source of imbalances [13].
To offset the stochastic nature of renewable power systems, the Smart Grid can
offset fluctuations with energy storage and generation systems [14]. These
systems can ramp up or reduce power output as needed, resulting in stable service
for end users. Smart Grid advancements will also encourage the creation of
distributed generation and storage units, designed to reside within the distribution
network, near the end-users (instead of on the transmission network, near the
natural resources). This shift towards smaller generation facilities will increase
energy market competition and reduce the environmental impact of energy
generation facilities [15].
The Smart Grid’s potential impact on power distribution systems is significant
and far-reaching, but the implementation of this vast collection of concepts is
4
nontrivial. The remainder of this section discusses existing Smart Grid simulation
methods and their relationship with the concepts described above.
Modelling the Grid
Implementing the changes discussed in the previous section is an expensive and timeconsuming process that leaves very little room for experimentation after the fact.
Instead, the research and development of the modern grid must be carried out within
software simulations; furthermore, system planners can use models to decide how to
address projected growth [6]. This section discusses a few common approaches to
modelling power networks.
Systems of Equations
Distribution systems can be modelled by systems of equations representing
network constraints and objectives. The primary advantage of this approach is that
it can be tailored to emphasize specific aspects of the grid. It can also abstract
irrelevant systems away from the model. The main disadvantage of this approach
is the amount of time that the original researchers and interested readers must
spend understanding the model before they can move on to understanding the
implementation thereof; additionally, it is challenging to compare solutions that
were simulated under different constraints.
An example of this approach can be found in “Learned Behaviors of Multiple
Autonomous Agents in Smart Grid Markets” by Reddy and Veloso [16]. In this
paper the authors introduce a distribution-level market simulation that simulates
market interaction between the transmission system, broker agents, and energy
consumers. The purpose of the model was to illustrate that autonomous broker
agents with relearning algorithms outperform those with greedy, fixed, balanced,
or random algorithms. This was accomplished by abstracting almost everything
about the distribution system, leaving only a tariff market, six broker actions, and a
stochastic customer allocation process.
Incorporating power markets into simulations is one of the most
computationally challenging aspects of smart grid research, but it is also extremely
important in order to determine best practices and policies for smart grid
implementation and participation. Broker agents that buy power from generators
and sell to consumers have been proposed in previous work as a method to model
market transactions and facilitate simulation in this area [17], but the efficacy of
the presented algorithms may change when subjected to power grid constraints. It
would be unreasonable to expect the authors to build an all-encompassing model,
but open-source Optimal Power Flow (OPF) solvers have been created to facilitate
more comprehensive power grid simulations. A more comprehensive model
would describe the impact that this broker algorithm could have on a real power
distribution system.
Optimal power flow solvers
Power system optimization has been an open problem for more than 50 years [18].
The combination of economic, electrical, and computational constraints create a
5
challenging non-linear and non-convex problem. Alternating current introduces
further challenges. MATPOWER and SuperOPF are two projects intended to
optimize power systems accessibly and comprehensively.
MATPOWER is a suite of MATLAB files designed to solve optimal power flow
problems at the transmission level [19]. Although it is primarily focused on
system hardware, the suite also allows users to extend the optimization to include
additional user-defined cost functions. In [20], Conley used this software suite to
explore the impact of introducing distributed power generation to existing (and
theoretical) bus networks, but a different tool, PLEXOS, was used to simulate the
economic dispatch.
In [21], Naama et al used MATPOWER to simulate an optimal power flow
problem on a 57-bus power system with economic and security constraints. The
simulation, which considered 7 generators attached to 42 loads, took 38 seconds to
arrive at a solution. When the authors compared this solution to the results of
other optimization heuristics (Genetic Algorithm, Quasi-Newton Method, and
Tabu Search [22]) it was found to produce the lowest cost, but the execution time
was an order-of-magnitude slower than the other heuristics.
Offloading
computation to Computational Unified Device Architecture (CUDA)-enabled
graphics processing units and decomposing matrices with multi-frontal sparse LU
factorization has been shown to reduce execution time [23].
SuperOPF is a comprehensive analysis tool that originated from work relating
to day-ahead and real-time electricity markets. Instead of breaking optimization
problems in to sub-problems, SuperOPF is designed to co-optimize the entire
system. This co-optimization considers power flow, single-element (N-1)
contingency [24], reactive power, pricing and dispatch.
Gridlab-D
Gridlab-D was designed with the future of the distribution system in mind. Like
SuperOPF, it is comprehensive—it currently has a solver and power system,
control system, building, and market modules—but it is also open-source and
extensible in a variety of ways. Users can use built-in functions to create userdefined systems or attach Gridlab-D to systems written in MATLAB or Java.
Because the source code is publicly available, users may also write their own
custom modules that can hook in to the existing network components.
The existing (incomplete) wind turbine module in Gridlab-D version 2.3.0
contains code for custom wind turbine parameters and a couple of commercial
turbine presets, but it does not function. As a result, when Trevor Williams et al
used Gridlab-D to investigate the impact of distributed wind generation, the
authors simulated the wind turbine portion of the system in M ATLAB and fed it
into the Gridlab-D simulation.
Summary of Outcomes
The goal of this project was to facilitate the advancement of new decision-making
paradigms by incorporating sustainable energy sources into distribution-level
simulation software. This goal was motivated by the fact that antiquated heuristics
6
undervalue sustainable energy and ignore externalities. To achieve this goal, a
selection of single and multiple- turbine models were chosen and implemented into the
source code of Gridlab-D. These models can be used alongside the existing Gridlab-D
climate and power-flow modules to simulate wind power output given local
meteorological data.
7
Chapter 2: Choosing a Wind Turbine Model
In search of a compromise between the simplicity of static wind turbine models, and
the overwhelming complexity of high-fidelity dynamic models, this section discusses
at length the current state of wind turbine modeling before focusing on a data-driven
approach to create a variety of power output estimators.
Wind turbines can be mathematically modelled in a wide variety of ways.
Aerodynamic models seek to facilitate the design and optimization of the blades of the
rotor and the shape of the nacelle, aiming to maximize converted power, and to tune
the turbine to work best within a specific, attainable wind speed. Mechanical models
can be used to design the moving parts of the turbine safely and efficiently. Noise
generation models simplify the process of site selection by reducing the necessary
“buffer” zone between the turbine and the general public. Economic models range
from simple statistical estimations of cost versus profits to incredibly complex systems
of equations that consider every imaginable loss, gain and outage. Esoteric bird
collision models can even allow engineers to minimize the chance of bird collisions
based on turbine design choices, which could result in a significant operating cost
reduction in places where protected bird species abound [25].
For this project many of these considerations are irrelevant. Aerodynamic and
mechanical outcomes are not the focus, so the parameters relating to them can be
abstracted, and economic simulation will be handled by an existing Gridlab-D module.
As far as increased renewable energy reliance goes, general models that estimate the
power output as a function of the turbine parameters and the weather are sufficient.
Model Examples
Mechanically and conceptually, wind turbines can be broken into four parts: the
turbine itself, the gearbox, the generator, and the control system, as shown in the
figure below.
Figure 2: Parts of a Wind Turbine
Each of these subsystems has a specific function and an opportunity for power
to be lost. For the turbine, power is lost by failing to convert the energy of the wind
into rotational mechanical energy. The absolute best efficiency by which this power
can be converted is known as the Betz Limit. It is equal to 16/27, and it corresponds to
the threshold wherein if any more wind energy was harnessed, the overall wind energy
gradient would suffer and the available energy to harness would decrease.
Once the wind energy is converted into mechanical energy, it must again be
transformed: the speed and torque of the wind does not usually match the desired
8
speed and torque of the generator, so the gearbox must transform the rotational energy
to maximize the efficiency of the gearbox. This conversion introduces additional
losses due to friction and the inertia of the gearbox. When the energy makes its way
to the generator, it is again transformed through a control system, into usable electrical
energy. The design and modeling of the generator within the turbine is complex
enough to merit a tremendous amount of academic investigation, and it is also
important enough to be directly relevant to the overall stability of the power system.
Static Models
Static models attempt to estimate the losses at each stage of the process based solely
on the current atmospheric conditions and known wind turbine parameters. Models
can be as simple as a linear piecewise equation relating wind speed and power output,
or as complex as a full-fledged electro-mechanical simulation.
An example of the latter approach can be found in [26]. Moriarty and
Butterfield outline an extremely fine-grain system for estimating the forces on a wind
turbine based on its dimensions and the impact of its environment. This overview
helps illustrate the potential benefits of an incredibly detailed model that considers
more than just wind speed. By considering the control systems of the turbine alongside
the environmental variables the model could produce a much more realistic estimation
of the power output of a wind generator. Unfortunately, this more realistic estimation
of wind events requires a huge amount of parameter estimation and many different
modeling suites.
The subsystems of a wind turbine are complex enough to merit modeling each
one independently, but static models that are willing to sacrifice the finer details to
address the big picture are more commonplace. In [27], Zaman et al use a more
generalized approach to estimating power output as part of a study investigating the
cost per kWh of wind power generation. The study optimized rotor and tower
construction options based on a simulated maximum power output objective that
depended solely on rotor height and turbine diameter.
Simulating a collection of turbines as a single entity can reduce execution time
and simulation complexity. Norgaard et al’s multi-turbine power curve approach is a
very widely used approach to estimating the output of a collection of wind turbines
based on scant data [28]. The estimated power output of a collection is determined by
relating the spatial and temporal distribution of the wind to geographically distributed
generation facilities. Aggregation of dispersed facilities has a well-known positive
”smoothing” impact on the chaotic output of wind farms, and this paper
mathematically quantifies this effect by essentially convolving a Gaussian distribution
(with parameters based on spatial and temporal distribution) with a piecewise-linear
power curve at each generator. This approach is valuable for extrapolating pointsource data about turbines and climate into estimations of wind farm output.
Dynamic Models
The main drawback of this simplified approach is its failure to consider the impact
of changing wind velocity and direction. For each subsystem’s coefficient of power,
the system is assumed to be at a steady state. To address the problems associated with
9
the simplified static models, many different dynamic models have been proposed. In
[29], Petru proposed an exhaustive approach that modeled the state vectors of every
imaginable moving part of a turbine system, culminating in a six equation model with
an enormous number of parameters that must be defined before simulation can take
place.
Henriksen created a simpler model to facilitate control system design, that
considers the coefficient of power as a dynamic quality that is driven by the tip-speedratio, a number that compares the current speed of the turbine, the wind and the
turbine’s inherent (static) rotor qualities [30]. Gyulai proposed a further simplified
model based around the same concept, but with fewer additional parameters [31].
Shafiu et al propose an excellent and incredibly detailed aggregated wind
generator model in [32] that is firmly rooted in the mechanical and electrical
engineering foundations of wind generating systems. Instead of using a more
conventional power curve with cut-in and cut-out, the authors created a higher-order
model whose power output is determined by not only the current state of the wind, but
also the previous states. This hysteresis is particularly important in locations where the
wind is very chaotic, i.e. wind turbines that are situated very low to the ground, but it
contributes a great deal of complexity that might not be necessary for wind farms with
higher rotors.
All of these models require a significant amount of information about the turbine
in question. Estimating the parameters in question is nontrivial, and requires a great
deal of data. Given that the audience for this project will likely consider various wind
turbines, a complicated list of parameters for each turbine option is far too
cumbersome. Simpler approximations of relevant power curves could provide enough
detail to inform the decision-making process without burdening the audience with
overwhelming parameter estimation requirements.
Data-Driven Models
In an effort to find a happy medium between simplistic and complex models, datadriven models were investigated. An ideal model would provide a high degree of
specificity—allowing users to discern subtle differences between turbines—while
minimizing necessary parameters to simplify estimation. The next section describes
the three data-driven static models illustrated in the following figure.
1. Linear Segmented Model
This model breaks the relationship between wind speed and power output into
a series of linearized estimations. These equations are defined by cut-in and
cut-out wind speeds and a series of ordered pairs, between which the output is
assumed to be linearly interpolated. These parameters can be approximated
visually, estimated based on observed data, or derived from manufacturer
specifications. The implementation described in the next chapter allows users
to naively scale the power output by defining the number of turbines onsite.
Computationally, this model can be estimated from training data by
creating an anonymous function in MATLAB that returns the estimated power
output given a series of wind speeds and linear segmented model parameters
and then executing a nonlinear solver like lsqcurvefit to find the model
10
parameters that best fit the training data. This optimization is not trivial; inputs
to the anonymous function must be sanitized to prevent lsqcurvefit from
settling on impossible curves. Advancements in machine learning have led to
more effective linear piecewise estimation techniques, if this method yields
poor results [33]. An example of this model is shown in the figure below.
Figure 3: Piecewise Linear Model Featuring the Model (blue) and Data-points (red)
2. Five-Parameter Logistic Model
The five-parameter logistic model is commonly used for curve-fitting in
biomedical applications because it mathematically characterizes the process of
interpolating between two levels [34]. It has not seen much use in terms of
estimating wind turbine power curves, but it provides an accurate,
continuously differentiable estimation that is easier to optimize
computationally. The output of the model is described by the following
equation.
The parameters for this model are not as intuitive as the piecewise linear
model, but they are much easier to estimate computationally based on observed
data. Additionally, because it is commonly used by biologists doing
immunoassays, users can compute these constants using conventional solvers,
a MATLAB add-on [35], a website [36], or proprietary software [37]. Unlike
immunoassay applications, cut-in and cut-out must be included for windturbine applications. An example of this model is shown in the figure below.
11
Figure 4: Five-Parameter Logistice Model featuring Model (blue) and Data-points (red)
Aggregate Model
The final model allows users to implement a group of turbines based on a
power curve from either of the previous models. Based on Nørgaard and
Holttinen’s multi-turbine power curve approach, this model takes spatial and
wind speed distribution into account [28]. The parameters for this model
include the length of the wind farm in meters, the shape and scale of the wind
speed (assuming Weibull distribution), the spatial standard deviation of the
wind, and the parameters of the chosen single-turbine model.
The original approach temporally smoothes the power output by
averaging the wind speed over a window determined by the size of the wind
farm and the average wind speed. To save memory, this implementation uses
an IIR filter to approximate a moving average. This approximation is
described in the equation below.
𝜇̂ 𝑣 (𝑡) = (𝛼 ∗ 𝑣𝑡 ) + ( (1 − 𝛼) ∗ 𝜇̂ 𝑣 (𝑡 − 1))
In this equation 𝜇̂ (𝑡) is the estimated moving average of the wind speed
at time 𝑡. The parameter 𝛼 is equal to 1/𝑁, where N is the window size
defined in the original approach as the number of observations per average
wind propagation time. Because the wind speed is provided as a data-stream,
the mean wind speed used to calculate mean wind propagation time is
estimated based on the user-provided shape and scale parameters. For a
Weibull distribution, the mean 𝜇 is described by the following equation [38].
1
𝜇 = 𝜆Γ (1 + )
𝑘
12
In this equation 𝜆 is the shape parameter and 𝑘 is the scale parameter,
both of which are supplied by the user. Because the gamma function contains
computationally expensive factorial terms, this implementation implemented
Stirling’s approximation to estimate this function [39].
The original approach also applies smoothing to the power curve to
simulate the impact of the spatial distribution of wind speed. Spatial
smoothing was implemented by calculating a weighted sum of power outputs
for wind speeds ranging from zero to three standard deviations away from the
observed moving average.
Figure 5: Linear Piecewise (blue) and Aggregate power curves (green and red)
In the above figure, three power curves are illustrated. The first curve is the
original curve of a single wind turbine. The second curve is a smoothed power
curve representing a collection of 330 turbines arranged in a box formation.
The final curve is the same collection of turbines arranged in a single-file line.
The aggregate graphs have been scaled down to facilitate comparison to the
original curve.
Based on the end-users of the wind turbine module, linear and logistic
data-driven models were selected for implementation. Gridlab-D users who
wish to quickly simulate turbines can approximate a linear model based on
observed data or manufacturer specifications. The logistic model offers more
precision and an easier optimization function to facilitate computerized curvefitting. Both models can be extended with Nørgaard and Holttinen’s multiturbine power curve approach [28].
13
Chapter 3: Implementation
Gridlab-D is made up of two primary components, the “Core” and the modules [1].
Modules are made up of classes that define different ways to analyze and describe
distribution systems. The currently supported modules include power-flow, market,
climate, and reliability. The Core connects these modules together, calculates their
interactions, and executes optimizations. Gridlab-D’s Core is written in C, while the
modules are written in C++.
End users create and modify distribution system models by creating and
connecting objects within plain-text GLM files. From the command line, users may
open these GLM files with Gridlab-D. The model is then simulated, and the resulting
output (if defined) is returned. The modelling language is very versatile; GLM files
can be used to simulate systems as small as a single house (complete with appliances)
or as large as an entire distribution system.
Figure 6: System Load Time Series on a partly cloudy afternoon with (A) Low, (B) Moderate, and (C)
Pervasive Solar Penetration. Plot D illustrates the solar intensity over this period.
In the figure above, simulation results for various levels of solar power
penetration within a neighborhood on a partly cloudy day are provided. This figure
was created based on data generated by Gridlab-D. The model that generated these
data contained a neighborhood of houses and solar panel objects, which are instances
of classes that can be found in the residential and generator modules.
In order to implement wind turbine models, a new class must be created within
the generators module that interacts with the climate module. This is accomplished by
creating new header and source files, modifying existing configuration and build files,
and then rebuilding Gridlab-D.
Compiling Gridlab-D
Software development was carried out on a fresh installation of Ubuntu 12.04 LTS.
The existing build process streamlines the compiling process on a variety of operating
systems. A detailed description of the components required to build Gridlab-D—as
well as build instructions—can be found in the Appendix. Once the automatic
configuration process generates new configuration settings based on the current
machine, automake compiles and installs the applications to the local machine.
14
Adding a Gridlab-D Class
In order to add a class to an existing Gridlab-D module, the class must first be
registered. Adding the class name to generators/Makefile.am ensures that it
will be compiled alongside existing classes. To link a new generator class to the core,
generators/init.cpp must be edited to include the new class as well. Finally,
generators/generators.h must be updated to include the header file for the new
class. After these steps are completed, work can begin on the source code of the class.
Source Code Requirements
The source code describes the calculations to be performed by the class, the ways
that users can interact with the class, and how these calculations and interactions
impact existing modules. The functions required by the Gridlab-D core are
enumerated below [40].
1. Create – This function is called once every time a new object (instance of a
class) is declared within the input GLM or XML file. It contains default values
for all user-defined parameters.
2. Init – This function is called after all objects have been created. When an
aggregate model is used, it estimates the mean wind speed based on the usersupplied shape and scale of the wind speed distribution, and then updates the
IIR weighted moving average filter parameter 𝛼.
3. Sync – This function is called after initialization, and repeatedly thereafter
while the simulation executes. The bulk of the computation takes place inside
of this function, and it returns a timestamp indicating when it should be called
again. This mechanism allows the wind turbine model to update as often or as
rarely as necessary.
Auxiliary Functions
The following auxiliary functions were created to supplement the functions
required by Gridlab-D
1. Init_climate – This function connects the wind turbine model to an existing
climate object.
2. Stir_gamma – This function is called from the Init function to approximate
the average wind speed for the supplied distribution.
3. Lin_pow – This function returns the estimated power output for a given wind
speed based on the user-supplied linear segmented model parameters.
4. Log_pow – This function returns the estimated power output for a given wind
speed based on the user-supplied five-variable logistic model parameters.
5. Agg_lin_pow – This function calls Lin_pow for a normal distribution of wind
speeds (based on user-supplied spatial standard deviation) and then combines
the results with weights based on their probabilities.
6. Agg_lin_pow – This function calls Lin_pow for a normal distribution of wind
speeds (based on user-supplied spatial standard deviation) and then combines
the results with weights based on their probabilities.
15
Merging This Project with Gridlab-D
The process for merging code changes with the source trunk involves contacting the
project administrator to request access to the issue-tracking sites and code repository.
Once write access is granted to the software management systems, a branch can be
created. The code can be uploaded to the branch and then merged with the trunk after
review.
Currently, a fork (a modified copy of the complete source code) of Gridlab-D
with the module described in this report resides in a public Github repository [41].
The fork can be compiled with the same build process as the original, because the
source code repository includes build scripts that have been modified to reflect the
additional wind turbine module.
16
Chapter 4: Verification, Validation, and Discussion
When contributing to an open-source project, it is important to ensure the quality of
the contribution. Validation and verification procedures must be followed in order to
avoid issues upstream. Software validation is the act of assuring that the software
fulfills its intended purpose, and software verification is the act of assuring that the
software was written correctly. Boehm summarized these concepts concisely: To
validate software, ask “Are we building the right product?” To verify is, ask “Are we
building the product right?” [42]
Software Verification
Software verification was carried out continuously during development with static
code analysis and unit testing. Once all functions were implemented, test models were
written that supplied a sweep from low wind speeds to high. Because the class is
composed of static models, this is sufficient to verify their functionality.
Figure 7: Static Model Verification—The original power curve (top left) is used to generate linear and
logistic models (bottom left). Synthetic wind data (top right) is swept from low to high, creating the power
output estimation shown (bottom right).
Starting with a 36-coordinate linear power curve from the National Renewable
Energy Laboratory (NREL), a linear model with fewer parameters was created
manually, as well as parameters for cut-in and cut-out. Shortly thereafter, a five
parameter logistic model was parameterized with MATLAB’s lsqcurvefit solver.
A function was designed that accepted five parameters and a vector of wind speeds.
This function returned a vector of power estimations based on the supplied data. The
parameters for this function were computed by passing the function to
17
lsqcurvefit alongside the existing pairs of wind-speed and power-output data
shown in Figure 7. The resulting parameters for this and other logistic curve-fittings
are available in the Appendix.
Because the single-turbine models are static, verifying their operation was
trivial. The multiple-turbine power curve approach discussed earlier does have a
moving-average component that introduces dynamic behavior into the system, so
verification of multiple-turbine power curves requires more realistic data.
The data used for this portion of the verification process came from NREL. It
was collected as part of the Eastern Wind dataset [43]. This data spans three years and
includes wind and modeled power-output data-points. Each file represents a MWscale wind farm based on a collection of turbines with the nominal power curve shown
in the previous example.
Simply scaling the previously-modeled power curve by the number of turbines
per farm would be a naïve way to estimate the power output, but the spatial and
temporal distribution of the turbines prevents them from being combined so easily.
The aggregate model compensates for this problem, at the cost of more parameters.
Figure 8: Multiple Turbine Model Verification--Observed and Nominal Power Curves (top) and Power
Output over Time (bottom).
The impact of multiple turbines is slight for this dataset due to the low spatial
standard deviation of wind (caused by low wind turbulence); however, the aggregate
model’s ability to smooth out high-frequency speed changes allows it to estimate the
18
power output more accurately than the linear model during turbulent periods, as shown
in Figure 8.
Software Validation
Because this project was added on to an existing platform, much of the software
validation had already been done. Gridlab-D is already designed to accommodate
users who design and operate distribution systems. While building the new wind
class, a conscious effort was made to continue this accommodation. This effort is
epitomized by the model selection process that focused on both ease of
implementation and specificity.
After the add-on was completed, retrospective validation was carried out by
taking wind turbine data through the entire process. To understand the experience of
an end-user, two tasks were undertaken. The first task was to extrapolate power
output elsewhere from data collected during testing of the NREL CART 3 turbine.
The data used in this portion of the validation process was provided by NREL,
and it pertains to a three-bladed, 600kW wind turbine in Denver, Colorado. The figure
below illustrates the observed data points and the results of a five-parameter logistic
curve fit. Note that the deviation of the data from the centerline is much lower on a
single turbine than it was on the previous multiple-turbine curve.
Figure 9: Observed and Predicted Power Output of the NREL CART 3 Wind Turbine
Once the parameters are defined, the system can be simulated as a part of Gridlab-D.
Initially, the original meteorological data recorded on-site in Colorado was used to
simulate data that would help contextualize other sites. This was accomplished by
declaring a GLM file that contained a small distribution system with a wind turbine
and a climate object. A logistic model was chosen for this wind turbine due to the
ease of fitting a curve to this distribution when compared to manually choosing a
linear representation.
An automated piecewise-linear-fitting sub-function was
19
designed to facilitate the use of computer-generated linear models, but it does not
converge as quickly as the logistic version. The climate object referenced a CSV file
of meteorological data. With these sources, Gridlab-D was able to simulate a year of
wind power generation. The result of this simulation was saved to disk and compared
to the results of similar simulations using typical meteorological year (TMY) data
from Seattle and San Francisco. The kernel-smoothed density estimation of the power
output in each city is shown in the figure below.
Figure 10: Distribution of Power Output for Denver, Seattle, and San Francisco
The second task was to use the aggregate turbine model on real wind farm
data. Dr. Barthelmie of the Indiana University Offshore Wind Energy Measurements
Project provided access to a cluster of off-shore wind turbines outside of Copenhagen,
Denmark. This wind farm, known as Middelgrunden, is home to 40 MW of power
generation. The data has a slight problem with consistency. The farm has 21 windspeed and power sensors, but only 65.76% of the data-points feature all sensors
reporting. The source of this reduction in information is unclear, but wind and power
sensors drop out in unison so it is likely that individual turbines are being shut down
and then brought back online.
Aggregate model simulation begins just like single-turbine models: a model is
chosen and then fitted to the existing data. For this task, the turbine with the highest
availability (86.71%) was isolated as the sole source of training data for the logistic
model. Despite this turbine’s high availability, the data has a few strange artifacts. In
Figure 11, there exist a few peculiar straight lines leading out from the center of the
linear region of the power curve. Because the power sensor maintains its level while
the wind speed changes, this could be the result of a temporary change in power level
or simply a sensor fault.
After the power curve is defined, some additional aggregate model parameters
must be defined. Nørgaard and Holttinen’s multi-turbine power curve approach
suggests that the output of the farm is affected by both spatial and temporal distances,
20
so the model needs parameters to determine these impacts. The size of the wind farm
is 3.457 km at its widest point. With this information and the average wind speed, this
number could be used to calculate the average temporal distance in between turbines.
The average wind speed is calculated based on shape and scale parameters supplied by
the user. For this data, a call to MATLAB’s wblfit function returned a shape
parameter of 2.0876 and a scale parameter of 7.343. The standard deviation of wind
spatially across the farm was calculated based on simultaneous wind-speed readings at
multiple nodes. Finally, the number of turbines (21) was added to the model.
Figure 11: Observed Data and Logistic Fit for Middelgrunden Turbine
.
Figure 12: Estimated and Observed Power Output at Middelgrunden
21
Once the simulation was executed on Gridlab-D, the problems associated with
middling availability began to become clearer. When all the turbines were up and
running, the models correctly estimated the power output, but moments of lucidity
would quickly fade as turbines were taken down and observed power output faded.
The figure below sums up this phenomenon nicely. When the system is available, the
aggregate model is an effective estimator, but the model does not consider system
availability in its current state.
Figure 13: The impact of turbine downtime on power output estimation.
Curiously, the scaled model performs closer to the observed truth in Figure 12.
The aggregate model is smoothing out the power curve too much, estimating too much
power at low wind speeds, and too little at higher speeds. This is likely caused by an
incorrect spatial standard deviation. The method mentioned at the beginning of this
section may have been measuring the deviation of the wind speed sensors themselves
instead of the variation of the wind. After all, the farm is situated on a broad, flat
surface with little in the way of aerodynamic obstruction. It stands to reason that the
variation of the wind across the entire farm is insignificant. A real-world investigation
of this magnitude would include tweaking of the aggregate model parameters supplied
to Gridlab-D (wind distribution and spatial deviation) to produce a more accurate
estimation of the wind farm’s power output.
Conclusion
This report began by introducing the present abundance of carbon pollution, and
acknowledging that a simple reduction in overall energy usage was not feasible
solution. After discussing the historical and modern power grid, a bevy of smart grid
concepts were introduced.
In an effort to facilitate the analysis and comparison of proposed smart grid
solutions that would encourage renewable energy production, wind turbine models
22
were investigated and four data-driven models were implemented in Gridlab-D: linearsegmented, five-variable logistic, aggregated linear-segmented, and aggregated fivevariable logistic. The linear segmented model was chosen to be human readable and
easy to approximate with back-of-the-envelope calculations, while the five-variable
logistic model facilitates computational estimation. The aggregate models applied
temporal and spatial smoothing based on Nørgaard and Holttinen’s multi-turbine
power curve approach, leading to a more accurate estimation of the power output of
large, dispersed wind farms.
Future work in this area could entail replicating existing distributed, renewable
power simulations on the Gridlab-D platform. This would provide a standard testing
ground for distribution grid solutions while informing the ongoing development of the
platform.
23
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27
Appendix
Gridlab-D Prerequisites
Before Gridlab-D can be compiled, the target system must have the following software
[44].
1. Autoconf
GNU Autoconf generates configuration scripts that are used to adjust compilation
based on detected system features [45]. Gridlab-D requires version 2.63 or higher.
2. Xerces-C
Xerces-C is an XML parser that simplifies software interaction with XML files [46].
This software can be found in the “third_party” folder of the source repository.
3. Curses
Curses is a control library that simplifies terminal interaction by standardizing the way
that software interacts with a broad variety of terminals [47]. It is preinstalled on most
linux systems.
4. Subversion
Subversion is a software revision control system. While not strictly required for the
build process, Gridlab-D’s source code is hosted on Sourceforge.com and managing
code with Subversion is the most efficient way to access it.
Gridlab-D Build Procedure
Once the prerequisites are installed, building Gridlab-D is straightforward. The build
must be reconfigured, compiled, and installed. The code below (reproduced from
[44]) summarizes this process.
host% svn checkout https://svn.code.sf.net/p/gridlab-d/code//tree workdir
host% cd workdir
host% autoreconf -isf
... a few messages ...
host% ./configure
... many messages followed by the installed component report ...
host% make
... huge number of messages ...
... *** will preceded final build error report ...
host% sudo make install
... lots of messages ...
host% gridlabd --version
... check the version ...
host% cd workdir
Table of Logistic Parameters
Generator
A
B
Nominal IEC
2.003
-13.684
Turbine
28
C
D
G
10.125
-0.013
0.228
Derived IEC
Turbine
Single Turbine
Middelgrunden
Weaver Wind
Turbine
NREL
Cart 3
0.1000
4.0958
11.2427
642.2300
2.9877
34511
-10.0072
11.1017
-376.8661
0.2845
1771.4
-150
19.4
-12.9
0.0000
565.3440
-8.2656
12.2358
-6.1141
0.3631
Gridlab-D Compatible Timestamped Weather CSV
#Wind Turbine Test Standard Weather File
$state_name=CO
$city_name=Denver
$lat_deg=12
$lat_min=34
$long_deg=12
$long_min=34
$timezone_offset=0
temperature,wind_speed,pressure
#month:day:hour:minute:second
10:12:16:06:05,32,9.707,1000
10:13:18:02:34,32,6.139,1000
10:13:18:52:34,32,10.735,1000
10:25:03:03:13,32,5.891,1000
10:25:03:13:13,32,5.572,1000
11:05:23:50:41,32,8.371,1000
11:15:04:18:12,32,11.869,1000
11:15:04:28:12,32,11.236,1000
11:22:20:52:05,32,9.366,1000
02:21:17:25:33,32,12.609,1000
02:21:17:35:33,32,12.640,1000
02:21:17:45:33,32,14.495,1000
03:12:17:17:03,32,11.683,1000
…etc…
29