POWER DEMAND CURVE MANAGEMENT BY
RESOURCE ALLOCATION PREDICTION MODELING
A Thesis
Presented to the faculty of the Department of Mechanical Engineering
California State University, Sacramento
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
Mechanical Engineering
by
Devin Swanick
SPRING
2016
© 2016
Devin Swanick
ALL RIGHTS RESERVED
ii
POWER DEMAND CURVE MANAGEMENT BY
RESOURCE ALLOCATION PREDICTION MODELING
A Thesis
by
Devin Swanick
Approved by:
__________________________________, Committee Chair
Dr. Rustin Vogt
__________________________________, Second Reader
Dr. Troy D. Topping
____________________________
Date
iii
Student: Devin Swanick
I certify that this student has met the requirements for format contained in the University
format manual, and that this thesis is suitable for shelving in the library and credit is to be
awarded for the thesis.
___________________________________, Graduate Coordinator ____________
Dr. Akihiko Kumagai
Date
Department of Mechanical Engineering
iv
Abstract
of
POWER DEMAND CURVE MANAGEMENT BY
RESOURCE ALLOCATION PREDICTION MODELING
by
Devin Swanick
The duck curve is a power demand curve that is named for its shape, and represents the
demand on utility power generation. Recently, the peaks and valleys of the duck curve
have been diverging. As more solar power is generated, mid-day supply becomes more
abundant, resulting in decreasing simultaneous demand on utilities. These sudden
changes in power availability can be damaging to the electrical infrastructure, e.g. by
desensitizing safety equipment or tripping breakers. By modeling these loads on a
computer and using predictive information on solar power availability, power loads can
be scheduled to more closely match supply. Scheduling power loads to times when power
is most abundant would shift those loads away from peak demand, both flattening the
duck curve and reducing risk to the utility infrastructure.
___________________________________, Committee Chair
Dr. Rustin Vogt
____________________
Date
v
TABLE OF CONTENTS
Page
List of Tables .................................................................................................................... vii
List of Figures .................................................................................................................. viii
INTRODUCTION: SOLAR EFFICIENCY AND THE DUCK CURVE .......................... 1
BACKGROUND: METHODS FOR SUPPLY AND DEMAND ALIGNMENT ............. 5
BUILDING THE TOOL: THE PROGRAM AND HOW IT WORKS .............................. 7
RESULTS: ANALYSIS OF THE DATA ........................................................................ 13
FINDINGS AND INTERPRETATIONS ......................................................................... 16
References ......................................................................................................................... 18
vi
LIST OF TABLES
Table
Page
1.
Organizatonal Variables ………………………………………………………… 8
2.
Configurable Variables …………………………………………………………. 8
vii
LIST OF FIGURES
Figure
Page
1.
The duck curve shows steep ramping needs and over generation risk .................. 1
2.
Daily Renewables Watch, April 6th, 2016 ............................................................ 3
3.
Comparing curves to ensure demand fits within supply ...................................... 10
4.
An idealized 4.5 kW solar array input with scheduled appliance loads. .............. 13
5.
A modified 4.5 kW solar array input with scheduled appliance loads. ................ 14
6.
Start times of demand loads on the standard (top) and modified (bottom) solar
input curves. ......................................................................................................... 15
viii
1
INTRODUCTION: SOLAR EFFICIENCY AND THE DUCK CURVE
Figure 1: The duck curve shows steep ramping needs and over generation risk (2).
Power demand curves have a very definite structure. Power usage by the California
population tends to rise sharply at about 7:00 a.m. when people are getting ready for
school and work and have various appliances on to make breakfast, take showers, or
otherwise get ready for the day. Power demand peaks at about 9:00 p.m. when people
have come home and are cooking and eating dinner, watching TV, and starting to turn on
lights and doing daily chores like laundry and the dishes. Combine these two elements
and the source of the duck curve begins to be understood.
2
The duck curve (Figure 1) is named for its shape, much like the back of a duck, the tail
being at about 7:00 a.m., and the head at 9:00 p.m. The curve represents the demand on
utility companies for electrical generation throughout an average day. The belly of the
duck is a result of solar power input to the utility grid, thus reducing that demand.
Figure 1, published in 2013 by California Independent Systems Operators (CAISO),
shows the expected deepening of the duck curve over the next several years out to 2020.
2012 and 2013 are known data, and all other lines are predicted based on usage patterns
in California.
Solar power generation is on the rise, having moved from 1.82% of California’s total
energy landscape in 2013 to 4.2% in 2014 (1). Solar power is a great way to reduce
dependence on other, less “green” forms of energy production, but has a problem that it is
rarely produced when, or where it is needed most. Solar production is most available at
mid-day, between about 7:00 a.m. and 4:00 p.m. on average (2). Outside of those times,
solar generation is negligible.
3
Figure 2: Daily Renewables Watch, April 6th, 2016 (3).
A daily graph of power usage taken on April 6, 2016 (Figure 2) shows that the lines are
holding true so far. The red line represents the total load on the California power grid on
an hour by hour basis, and the green line shows the net load on the utilities after wind and
solar, represented by the blue and yellow lines in the lower graph, have been accounted
for. The green line is a classic duck curve and clearly indicates that CAISO predictions
are holding true. Visual analysis indicates that the 2016 difference from the mid-day low
to the evening peak in Figure 1 is close to 10 GW, and the curve from April 6, 2016
shows a 9 GW swing.
In 2002, Gov. Gray Davis signed Senate Bill No. 1078 that would “require all retail
sellers of electricity, including electrical corporations, community choice aggregators,
and electric service providers, purchase a specified minimum percentage of electricity
generated by eligible renewable energy resources […] no later than December 31, 2017”
(3). This was one of the early steps in the green energy movement. It was followed the
4
next year by a California Energy Commission advisory to move the 2017 deadline up to
2010 (4), and a second advisory in 2004 to implement a goal for 2020 to move to 33%
renewable energy (5).
In 2008, Gov. Schwarzenegger made the 33% goal law with Executive Order S-14-08
(6), and the California Senate implemented the law irrevocably in Senate Bill X1-2 in
2011 (7). In 2015, the California Senate followed up with a second law requiring a 50%
commitment by 2030 (8).
The 2017 goal was never officially changed to 2010, but was met in 2014 with 20.1%
renewable energy in the California Power Mix (1).
With the duck curve and the encouragement toward renewable energy technologies by
the California governor’s office and legislature comes a whole host of other potential
problems. Solar power is unpredictable at best, and power production can change
suddenly with the movement of a cloud across the sun. These sudden changes can stress
infrastructure, either desensitizing safety systems or setting them off and causing
unexpected outages due to the sudden voltage spikes and drops on the grid (9). Both of
these scenarios are damaging to the safety equipment in question. If the demand were
able to adapt to those changes in supply these risks could be mitigated, at least in part.
5
BACKGROUND: METHODS FOR SUPPLY AND DEMAND ALIGNMENT
Research into the area of the duck curve has taken largely to two different approaches,
shifting supply, and shifting demand. Shifting supply requires the generation to be
changed or stored until the demand for that power exists. This is achieved by either
shifted in when or how the power is created or by using a storage solution such as
batteries or heat to keep the power available until a later time. Shifting demand has
everything to do with changing end point power usage.
In the category of shifting supply, Abengoa is a Spanish energy company who activated
Solana Generating Station in Gila Bend, Arizona in 2013. This project is a concentrated
solar thermal generation station that provides power to Arizona Public Services for use
across the state. Solana Generating Station utilizes the sun’s energy, reflected by
parabolic mirrors, to heat a synthetic oil that is then used to boil water and run steam
turbines. This plant also has the ability to store up to 6 hours of heat capacity in a molten
salt storage system, allowing up to a third of power generation to happen when solar
power cannot be generated directly. Solana was, at the time of its activation, the largest
such power plant in the world (10).
Pecan Street Research did research the summer of 2013 into the directionality of solar
panels. Taking a survey of 50 homes in Austin, Texas with a variety of west and south
facing solar panel arrays. The study found that during summer months, west facing
arrays produced more power, both in total, and specifically during peak hours. Between
the hours of 3:00 and 7 pm, these panels generated up to 49% more energy than their
south facing counterparts (11).
6
Looking into demand peak shifting, in the summer of 2014, the Sacramento Municipal
Utilities District (SMUD) looked into the power saving possibilities of radio controlled
thermostats. In a project titled “PowerStat Precooling Pilot,” 180 participant houses were
selected from volunteers and installed with a Honeywell smart thermostat. The
thermostat was dubbed a “3rd party load management system” and SMUD maintained the
ability to adjust the thermostat remotely via a one-way paging network. On days that the
utility expected especially high peak power usage, they would pre-cool the participant’s
residence to lower than normal temperatures and allow the interior temperature to rise
slightly above normal during peak times. Each time this event occurred, SMUD observed
a 1.0-1.3 kW reduction in power usage per household for the peak hours (12).
Tesla Motors has been working on improvements in the battery market, and one of their
big advances has been the introduction of the Tesla Powerwall. This home battery
system is designed to offset peak power usage by supplementing the grid power with
battery power that was stored at off peak times. This can be done for peak shifting
purposes, or simply to offset peak power pricing (13). Tesla’s batteries are advertised as
92% efficient, some of the best on the market, but this still requires a larger power
commitment at off peak times to produce peak power, and when combined with
installation and maintenance costs does not make fiscal sense for most homeowners.
And then there’s the granddaddy of all demand control mechanisms, price pressure.
There are many studies on how to use price pressure to adjust the power usage of a
household, a neighborhood, or an entire city, and a myriad of studies trying to predict
how those price changes will affect consumption. Only two things seem to come up
7
constant: rising prices will result in lower demand, and that it only works once the
consumer is informed of the changes in a timely manner. (14) (15) (16) (17)
This project will be falling into the demand shifting category, as supply shifting is
something that cannot be done in a small scale setting without significant investment into
power generation capabilities.
BUILDING THE TOOL: THE PROGRAM AND HOW IT WORKS
Controlling demand is often about factors of convenience, or the perception thereof.
Consider for a second the car cup holder. Most Americans think more about cup holders
than power when shopping for a new car, and cup holder placement and design can make
or break the sales of a specific car. This tool was designed to assist in the peak shifting of
power demands while maintaining convenience for the user. By producing a piece of
software that can easily and comfortably shift the power usage curve of an individual or a
household by increasing the convenience of household chores, i.e. scheduling such things
as the laundry machine or the dishwasher, its use becomes almost guaranteed.
To start any set of code requires several declarations and some basic organization. A lot
of these declarations and organization occur throughout the process of writing the code.
In the case of this tool, quite a variety of information had to be tracked, and specific
spaces had to be created to track each piece (Table 1).
8
Table 1: Organizational Variables
Solar Input
(7.5 minute intervals)
Load Requirements
(1 minute intervals)
Loads to be Scheduled
(List)
Current power utilization
(1 minute intervals)
Eight data points per hour over 24 hours indicating the
normalized solar power availability.
The power requirement curve over the runtime of each
appliance or load that needs to be scheduled.
A list of electrical loads the user has requested be run,
and their run modes.
Previously scheduled power loads over a 24 hour
timeframe.
In addition to basic organization, there are a variety of configurable elements within the
code which each require a variable and a human input (Table 2). These variables can be
changed within the code to direct it to do different things for demonstration purposes or
to ensure certain amounts of under- or over-utilization of resources.
Table 2: Configuration Variables
Automatic Mode
(Boolean)
Data locations
(String)
Allocation percentage
(Decimal)
Modified input mode
(Boolean)
Display Loads
(Boolean)
Use pre-defined data instead of user input to determine
which loads and run modes to schedule.
A filesystem location for both load and solar data files.
Amount of available solar input to be allocated to
scheduling loads. 1.0 is 100%.
Use a modified input file for solar data. Intended for
testing and demonstration.
Display scheduled power loads in the final output graphs.
Disabling this will show only the solar input curve in the
program output.
The filesystem location for solar and load data files.
Input File
(String)
Output File
The filesystem folder location in which produced graphs
(String)
and other outputs will be saved.
Solar panel area
Solar panel area in m3. For use in calculating total solar
(Decimal)
input of a specific system.
As soon as the variable data is defined and initialized the system begins to access the
files for input that have been defined, and inputting solar and load data. Solar data will
be read from the idealized data file or the modified data file based on the modified input
9
data variable. Which electrical loads will be considered will be determined by human
input unless the automatic mode is selected, in which case the information is already
programmed into the code. If the program requires human inputs, it will give options for
the electrical loads based on the information available in the load data file in the input file
location.
Once the solar data and load profiles are selected, input, and verified, we still have to
convert our solar data to minute increments, as it is input at 7.5 minute increments. This
was done using purely linear interpolation based on Equation 1.
𝐶𝑤 =
𝑁𝑤 −𝑃𝑤
𝑁𝑡 −𝑃𝑡
(𝐶𝑡 − 𝑃𝑡 ) + 𝑃𝑤
(Eq. 1)
𝐶𝑤 , 𝑃𝑤 , and 𝑁𝑤 are the wattages at the current minute, the previous known data point and
the next known data point. 𝐶𝑡 , 𝑃𝑡 , and 𝑁𝑡 are the time in minutes since midnight for the
same three points. Because all of the data on points 𝑃 and 𝑁 are provided within the raw
solar data, we simply have to provide a 𝐶𝑡 and the equation returns 𝐶𝑤 . This linear
interpolation allows our data to change from 8 times an hour to once a minute allowing it
to match frequency with the data available for power loads.
A configurable element was introduced at the beginning of this section called an
allocation percentage. This allocation number is there specifically to allow the user to
adjust the amount of available power that should be allocated to the requested loads. This
number is a decimal representing a percentage. 0.9 indicates that 90% of the available
power should be allocated to the schedulable loads when possible. The purpose of this
number is to allow for a buffer in power production over load to allow for sudden
changes in production, such as a cloud crossing the solar array, or unexpected loads on
10
the system. This allocation can also be set higher than 1.0, or above 100% to allow the
system to use more power than the system knows about, pulling power from the local
utility grid instead of just local, renewable sources for instance.
To schedule the electrical loads, the program does an element by element comparison of
the predicted power availability, and the known load requirements. Because the
information for the availability
and the load have been set to
the same information frequency
and power scales, units can be
entirely disregarded in the
comparison. For purposes of
this program, each box in Figure
3
represents one minute of time,
and the numbers represent a
Figure 3: Comparing curves to ensure demand fits within supply.
unit of power. This data is
fictional and used for demonstration purposes only. The shorter array of boxes indicates
the demand load from an appliance, and the larger array of boxes represents the predicted
power availability from the solar system. The illustration demonstrates the computer’s
comparison process. The computer aligns the first element of each curve, and compares
them. If the number indicating supply is larger or equal to the number indicating
demand, the second element is compared, but if not, as in [1], the demand is realigned
one element to the right, and the comparison restarted. The comparison continues
11
iteratively until every element in the demand is less than or equal to its corresponding
element in supply, as in [4], at which time the program has found a location where the
demand curve fits within the supply curve. By tracking how many times the demand is
moved right one element, the program can convert that number into time units (minutes
after midnight) and it becomes the scheduled start time of that power load. The demand,
as scheduled, must then be subtracted from the supply for the scheduled period before the
next load can be scheduled.
Once all of the curves have been correctly scheduled, the information is graphed, and
saved to a file in the computer’s memory. The save location is defined by the Output File
variable that is defined at the beginning of the code.
To implement this code as more than a model, several changes would have to be made.
If real-time data were to be incorporated in the model, a source would have to be found
and implemented as an input. The real time data could then be used to periodically recalculate the predicted supply curve based on observed availability, and load schedules
altered to fit the new prediction.
The model would also have to implement an activation scheme. Appliances today are
getting smarter, and many are a part of the “internet of things” which typically have
connections to smart phone apps or online interfaces. Leveraging some of that
connectivity, the program could easily utilize a network connection to remotely activate a
load, or a simple control unit could be wired to the appliance in question, for direct
activation. All of the loads scheduling would need to be done in a single location for the
program to be effective.
12
For the purposes of this model, I used the automatic data inputs, and a 90% allocation.
Solar data was procured from www.pveducation.org using a latitude of 39 degrees north,
and a date of March 20. Sacramento, California is located at 38.5816 degrees north, and
the site only allows whole degree increments. March 20 is at, or approximately the
vernal equinox, and was deemed a decent average input day for solar radiation. The
program will accept any supply curve from any source, both renewable and nonrenewable, but considering that solar power is at the root of the duck curve problem, it
was the supply chosen for this research.
Load data was acquired from research done at Virginia Tech (18). Records were made
of appliance power requirement data and several of those appliances were used as
demonstration loads for the model. Any load can be put into the model as long as it has a
known power demand profile and the information is properly formatted. This includes
charging electrical cars, the lighting for major buildings, or running an oven or television.
Not all of these loads should be scheduled, but any of them can be put into the program
as example loads.
13
RESULTS: ANALYSIS OF THE DATA
Figure 4: An idealized 4.5 kW solar array input with scheduled appliance loads.
Figure 1 shows a successful arrangement of loads beneath the solar availability curve.
This graph shows the arrangement of the loads as decided by the computer based on the
power and runtime requirements of each load. Both the GE and LG washers are running
at the same time quite early in the day, starting around 6:15 a.m. Each one draws little
enough power that the system decided to run them both at once, and add the dish washer
at about 6:30 a.m. All three devices were able to run at once. By 8:00 a.m., the LG dryer
was selected to run due to its slightly lower peak power usage than the GE dryer, and
14
finally the GE dryer turned on close to 8:30 a.m. In this example the loads are
appliances, and the power input is from an idealized 4.5 kW solar array, but the program
can easily handle any sources with correct data formatting. Wind power would be more
difficult to use predictively, but the program can be easily adjusted to determine when
there is enough power being generated to offset the demand in real time.
Figure 5: A modified 4.5 kW solar array input with scheduled appliance loads.
Figure 5 shows how the program adapts to changes in the input. A lower input early in
the day caused delays in several of the appliances, and required the Kenmore dishwasher
to run after the washing machines, and pushing the LG dryer back to after the GE. Each
starting time was pushed back to better accommodate the power availability (Figure 6),
15
and the dryers were both deemed to be low enough power draw to begin before the
dishwasher had completed its cycle. The GE dryer was selected to start before the LG
dryer due to its higher power requirements. This program runs predictively, but in a nonpredictive situation a choice like that gives the larger load a higher chance of completing
before power drops below the demand requirements.
Figure 6: Start times of demand loads on the standard (top) and modified (bottom) solar input curves.
16
FINDINGS AND INTERPRETATIONS
The tool is designed to shift peak power requirements of a system. By scheduling loads
of any kind, from as big as an industrial dryer to as small as a cell phone charger, to times
when power is most available the duck curve can be smoothed. Other solutions require
direct human intervention or dependence on the ability to change their habits. This
solution provides a means of selecting what needs to run, and then leaving the computer
to do the management until the end of the day.
As an additional benefit, this method of scheduling also reduces the need to store power,
either in a battery or by sending it to the grid just to draw from the grid again later. By
storing power by either of these methods, produced power suffers a 15% loss, on average.
Some of this loss is inescapable, as even a power inverter, required to convert DC solar to
AC grid compatible power, has an efficiency of less than perfect, but power grids have a
whole host of connections and voltage regulators that each produce a loss. Even the most
efficient batteries in the world, currently produced by Tesla, cannot reach a better
efficiency than 92%, which is dropped again once the battery sends the power back out
through the inverter.
As a result of using power closer to where it is generated the grid also suffers less stress.
Large voltage changes or unexpected shifts in current flow can cause unexpected breaker
trips or the desensitization of breakers altogether. As a solar panel drops in power
reduction due to a cloud crossing the sun, the grid may sense strange behavior and shut
down entirely, or become desensitized to such changes, so when a real threat is posed it is
less likely to shift to a safety mode.
17
While this program is far from a total solution, it is one other tool that can be added to a
tool box full of ingenious ideas like solar thermal storage and west facing solar panels.
With some work this program can be extended to cover entire neighborhoods ensuring
that while solar power is still sent to the grid, it will be used, as much as possible, locally,
and that each residence in the area still gets their laundry done, their dishes cleaned, and
their water heated before the sun ceases its assistance for the day. There is a requirement
that sources of electrical loads are adapted along with the means for control, to include
the ability for remote activation, but in a world that is increasingly connected by the
internet of things, this seems more like an inevitability than a challenge to forward
thinking.
18
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19
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20
19. California ISO. Renewables Watch. caiso.com. [Online] April 06, 2016. [Cited:
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