Summary: Modeling the Energy Consequences of the Cell Phone Revolution Introduction
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- Summary: Modeling the Energy Consequences of the Cell Phone Revolution Introduction
- Strengths and Weaknesses of the Model
- Modeling the Energy Consequences of the Cell Phone Revolution
- Table 1.1 - Usage Percentages by Phase
- Table 1.2 – Energy Consumption by Phase (watts) 2
- Table 1.1 and Table 1.2
- Table 1.3 - Weighted Average of Wattage by Phone Type
- Table 1.4 - Number of Phones Per Household by Type
- Table 1.4
- Table 1.3 and Table 1.4
- Figure 1.1
- Table 1.5 - List of Figures
- Table 1.5
- Partitioning Model
- Figure 1.3 and Figure 1.4
- Product (Off) Mean
- Total: 90.87
         
Summary: Modeling the Energy Consequences of the Cell Phone Revolution Introduction - The purpose of this study was to model the energy consequence of the wireless phone revolution. As this technology has continued to grow, the demand for electricity to charge cell phones has grown linearly. We decided to model the energy consumed by one cell phone, on an average day, and extrapolate this to encompass the energy demands of the entire U.S. population. We did this by breaking down the energy consumption of the cell phone into the following three parts: time during which cell phone battery is replenishing from the charger, the standby time where the phone battery is fully charged but still plugged in, and lastly the time which the phone is removed from the charger but the charger remains plugged into the wall. Together these times make up the typical day for the energy profile of each wireless phone. Model Approach - In order to be flexible, our model was created to handle various distributions of data. For example, we partitioned people into groups according to how much time they spend on their cell phones each day; this gave us a distribution on how much the phone battery had been drained throughout the day. However, to solve the many problems asked, we used several expected values to get the mean range to the solution. We also used several linear regressions, by Least Squared Estimates, to predict population trends in the future. Strengths and Weaknesses of the Model - The biggest strength of our model is that it encompasses many factors to accurately predict the amount of energy required to charge a cell phone battery. By partitioning people into subgroups of the population, and separating the typical day into distinct charging periods, our model gives a more accurate look at the energy consumption by cell phones. Likewise, our model has strength in its’ ability to forecast the future by extrapolating current trends in population and subscriptions to wireless phone service. The main weakness out our model is that it tends to predict average energy consumption and may not fully estimate the total energy consumption. Likewise, our models’ Achilles Heel is likely the research we found. Our research came from a large amount of resources, and some of it may not be as accurate as we hoped. Table of Contents
Energy Consumption.....................................................................................................11
Landlines or Cell Phones................................................................................................16
Households with Landlines............................................................................................41 Modeling the Energy Consequences of the Cell Phone Revolution: Introduction: The purpose of this study was to analyze the energy consequences of the cell phone revolution. As many people are choosing to become reliant on wireless phones, and to forgo the use of landline phones, the number of mobile phone and mobile phone chargers using electricity has dramatically increased. However, there still remain a large percentage of U.S. households that use landline services or a combination of landline and wireless services. Our first goal is to model the effects on energy consumption if the U.S. were to replace landline telephones with cellular phones. We will attempt to predict how this change will occur in order to analyze the transitional and steady state periods of this switch. Lastly, we will estimate the energy wasted by various household electronics in terms of barrels of oil per day. The second goal of this study is to consider a “Pseudo U.S.” which has comparable economic standing to the real United States, but has yet to provide any telephone service to its citizens. Our model will attempt to find an optimal way of choosing which phone service is the most energy efficient. Considering that populations do not remain constant, so we will also predict future growth of Pseudo U.S. and its impact on energy consumption in terms of barrels of oil per day. Finally, we will model how much energy is wasted by inefficient cell phone charging techniques such as daily battery charging, battery over-charging, and leaving the charger plugged when not charging.
Our model will attempt to estimate the costs of electricity consumption by cell phones in terms of barrels of oil per day. To do this we must consider several variables to use in our model. The change in population is one of the biggest factors, but we must also consider the following:
Developing our Model: Assuming mobile phones are plugged into their chargers for 8 hours, how long is battery being charged when it is full? -Consumes energy at rate of battery drainage. Assuming cell phone chargers are always left plugged in, they consume a phantom load for 16 hours of each day. -find phantom energy data on cell phone chargers. Finding average battery capacity consumed during day. -using data on avg. min. talked and avg. talk time of phone. Standby energy consumed by fully charged cell phone that remains plugged into charger. Phantom load: energy consumed by cell phone charger (cell phone not plugged in). Energy from charging cell phone. -based on percentage of battery capacity used. Initial Equation to model total energy consumed: E = Ec + Es + Ep -Ec = energy charging -Es = energy standby -Ep = phantom load
Population Growth: -calculating changing population of US and consumers with cell phones. Total Energy consumed per cell phone per day Total US energy consumption by cell phones, in terms of barrels of oil per day. Requirement One: Synopsis: The US currently has about 300 million people. These people have either chosen to continue using their existing landlines, adopt the wireless technology of cell phones, or use a combination of both. Our goal is to model the transition from landline usage to reliance on wireless phones. Our model will attempt to analyze the consequences of this change in electricity utilization by considering the amount of energy used to recharge the cell phone batteries versus using landline phones. We will look at both the transition period and the steady state of this change. Assumptions:
Analysis of Landline Telephone Usage and Energy Consumption:
Using the data from Table 1.1 and Table 1.2, it is possible compute the weighted averages of wattage usage for each type of landline telephone. This is done by taking the sum of the products of the percent of time spent in a particular phase and the energy consumed while in that phase for each of the applicable phases. Doing this yields the results in Table 1.3. These weighted averages tell us how much wattage is being used by each of the phone types, on average, at any given time.
Using the computed weighted averages, the assumptions presented in Table 1.4, household projections from the U.S. Bureau of the Census and the percent of households with landline telephones from the Centers for Disease Control (see Appendix C), it’s possible to calculate the total amount of energy consumed by landline telephones for a given year. For instance, in 2007 there were 111,162,259 households3, 81.9% of which had landline telephones3, which indicates that there were a total of 91,041,890 total households with landline telephones. The total wattage consumed by landline telephones in an average household can be computed by taking the sum of the products of the data in Table 1.3 and Table 1.4 for corresponding telephone types. This shows that the average household in the U.S. with landline telephones uses 10.48 watts exclusively for landline telephones, which is equivalent to 251.6Wh (watt-hours) per day. 91,041,890 households times 251.6Wh is equal to 22,906,139,524Wh per day, which is equivalent to 13,475 barrels of oil per day4. Figure 1.1 shows how the total amount of energy consumed by landline telephones is decreasing due to the decreasing number of households with landline telephones. Figure 1.1 shows that the amount of energy consumed by landline telephones peaked around the year 2001. This seems puzzling at first, but makes sense considering that prior to 2001 the number of households with landline telephones was increasing as the population (and correspondingly the number of housing units) was increasing. After 2001, some households began substituting landline telephones in favor of cellular phones. Analysis of Cellular Telephone Usage and Energy Consumption:
Throughout our research and analysis of data, we determined the values listed in Table 1.5 above. Using the figures from Table 1.5, population projections from the U.S. Bureau of the Census and the number of cell phone subscriptions in the U.S. from the Global Wireless Matrix 4Q07 Report (see Appendix D), it’s possible to calculate the total amount of energy consumed by cellular telephones for a given year. For instance, in 2007 there were 255 million cell phone subscriptions11 and 301,279,593 people in the U.S.11, assuming 10% of subscriptions are for people with multiple cell phones, we can calculate the total percentage of the U.S. population with cell phones by taking 90% of the 255 million subscriptions and dividing by the number of people in the United States, which gives us 76.2% or 22.95 million people. The total energy consumed by cellular telephones by an average person can be computed by the Partitioning Model below. Partitioning Model Methodology: Suppose each individual, 
where:
Calculating  :
Let 
where:
We constrict  , since the battery cannot be more than 100% drained. This is because  represents the percentage of battery drained while talking and  represents the percentage of battery drained while in standby. Adding these two percentages together yields the total percentage of the battery that was drained in an average day.
Then, the energy that a cell phone consumes in an average day is equal to the energy the battery consumes during a full recharging cycle scaled by the percentage drained: 
where:
 is the voltage of the battery (typically 3.7V)13.
 is the capacity of the battery in amp-hours (our data suggests an average of 935mAh)14.
Calculating  :
When the battery is fully charged, yet still plugged into the charger, we propose that the rate of energy being drawn from an outlet is equal to the rate that the battery drains while in standby. In this case, we can calculate 
where Calculating  :
We are assuming an 8 hour charge time with a corresponding 16 hour period where the charger is using energy but is not plugged in to the cell phone. This energy loss is known as a phantom load. The phantom energy consumed by cell phone chargers has been estimated by the University of Berkeley (0.14W)15. From this estimate, we conclude that 
Consider a full 24-hour day in which an individual has a cell phone. Assume that an individual charges his/her cell phone for 8 hours each night. Then, cell phone energy use can be modeled by considering the energy profile of every individual 
Estimating  :
Naturally, data on the energy profile for each cell phone user is unavailable. However, if something is known about the proportion of people that talk on their cell phones, we can estimate 
Where Note that, if Thus, the more partitions that are available, the better the estimate can be. Example: According to a survey of 2,011 cell phone users from Wirefly.com:
Convert this into a daily average:
Partition the group of 2,011 people as follows, based on the percentage of time they talk on a cell phone per day:
Now, the energy profile can be estimated by the methodology and estimates discussed above:
Now, suppose that this sample is representative of the current United States cell phone users. Then, if we scale this number by the number of cell phones users in the United States we can get an estimate of the total amount of energy consumed by cell phones. For instance, in 2007 there were 22.95 million16 cell phone users, which gives us 
or about 64.6 MWh. As the number of people surveyed and the distinctions among partitions increase, the model would more accurately describe the overall energy usage. Also, such a large population size plays an important role in this model; a change in even a tenth of a watt makes a tremendous difference. The model greatly depends on the fidelity of the data. Figure 1.2 shows that the rate at which the energy consumed by cellular telephones increases from year to year changes abruptly around 2013. This is because prior to 2013 the percentage of people with cell phones in the U.S. was increasing along with the population. After 2013, our model indicates that nearly 100% of people will have a cell phone, at which point the number of people with cell phones, and correspondingly the amount of energy consumed by cell phones, will increase only as the population increases. Analysis and of Both Landline and Cellular Telephone Usage and Energy Consumption: Figure 1.3 shows the total amount of energy used by all telephones broken up by type. Comparing the year 1990 (all landline phones) to 2034 (projected to be all cellular phones) it is clear that cell phones consume more energy than landline phones. The total energy consumed by all phones appears to level off around the year 2013. This is because prior to 2013 the percentage of people with cell phones in the U.S. was increasing along with the population. After 2013, our model indicates that nearly 100% of people will have a cell phone, at which point the number of people with cell phones, and correspondingly the amount of energy consumed by cell phones, will increase only as the population increases. Coincidently the population increases at about the same rate that households with landline phones decreases, causing the amount of energy consumed by all phones to appear to level off. After 2034, the energy consumed by all phones (at this point all cell phones) will begin to increase again as the population, and thus the number of cell phone users, increases. Figure 1.4 shows the total amount of energy used by all telephones broken up by type, assuming negligible phantom load. Comparing the year 1990 (all landline phones) to 2034 (projected to be all cellular phones), it appears from this figure that the energy amounts consumed are roughly equal. This figure is interesting because it indicates that the differences between Figure 1.3 and Figure 1.4 are caused exclusively by phantom load. That is to say, phantom load is the only thing that causes cell phones to use so much more energy than landline phones in Figure 1.4. Consider also that the population in 1990 was 247 million and the population in 2032 is projected to be 380 million. Roughly the same amount of energy could be used to provide telephone service to 133 million more people using cell phones rather than landlines, provided that phantom load could be eliminated. This suggests that if the phantom load could be eliminated (for example by removing the charger from the wall when it’s not being used), cell phones would actually consume less energy than landline phones. Requirement Two: Synopsis: “Pseudo U.S.” is a country very similar to the current US. It has approximately 300 million people and has a comparable economic standing. However, this developing country has neither landline phones nor cell phones. We will attempt to use our model to predict the optimal was of providing phone service to this emerging country. Although our model will purely consider this from and energy perspective, we will also briefly discuss the social and economic consequence of choosing landlines or cell phones. Assumptions:
Optimal way of providing phone service: Case 1: Cell phone users keep their chargers plugged in while not in use If all wireless users forgo conservative energy practices, than the sum of the energy wasted becomes so large that landlines are by far the optimal choice for providing cell phone service. This is so because of the phantom energy costs of leaving the phone chargers plugged in. Our model has shown these energy costs to be quite significant, and thus wireless phone service would cost much more in terms of energy. Therefore, we can conclude under these circumstances that “Pseudo U.S.” would adopt landlines as their primary means of communication. Case 2: Cell phone users practice energy efficient techniques and unplug chargers when not on. If the citizens of “Pseudo U.S.” adopted energy efficient techniques, then the optimal phone service would be wireless. Our model shows that without the phantom energy consumption, the amount of energy consumed by landline and wireless is nearly equal. Thus “Pseudo U.S.” could have either of the two. It is most likely they would choose a wireless phone service due to several factors. Such as cell phones are extremely convenient, portable, and provide users with entertainment.
Although under most conditions it is more energy efficient to use landlines, there are many social and economic advantages that come with the use of cell phones. The main advantage of cell phones, and a large reason they have become so popular in the current US, is their portability. Cell phones can not only be used at home, but can be used at work or when traveling. Studies have shown that 74% of Americans have used their cell phone in some sort of an emergency, and received help by doing so. Also, 41% of cell phone owners admit they use their wireless device to fill in their free time (Rainie). Clearly cell phones have transcended the levels of landline communications; offering multimedia messaging and round the clock access to people who carry them. These additional benefits, which could not be obtained by phonelines, are the reasons that people have chosen to accept the higher monetary costs of using wireless services. Yet, there still remains a small demographic in the current US that chooses to utilize the existing landline services. Their motives are most likely based on cost. As phone lines are already in place, and thus very cheap to use, many people still choose to use their existing landline phones. However, as the advantages of having cell phones continue to grow and become more appealing to Americans, we will continue to see growth in the number of cell phone users. Thus, the convenience of using cell phones, and the entertainment we receive from them, has trumped the cost and energy effectiveness of landlines. If current trends hold true, landlines will soon become obsolete; and the US will we become completely wireless. Requirement Three: Synopsis: Although cell phones do not need to be recharged every day, many people choose to do so. They may also choose to leave their chargers plugged in all day. These practices waste energy, and add to the overall energy consumption by cell phones. Our model will be used here to calculate the costs of this wasteful practice in terms of barrels of oil per day. Assumptions:
Figure 3.1 shows the changes in the amount of phantom energy consumed by cell phones by year. Cell phones did not become commercially viable at the retail level until around 1996, which is represented in the graph by the constant value of 0 barrels of oil per day being consumed by cell phones prior to 1996. This graph shows that the rate at which the energy consumed by cellular telephones increases from year to year changes abruptly around 2013. This is because prior to 2013 the percentage of people with cell phones in the U.S. was increasing along with the population. After 2013, our model indicates that nearly 100% of people will have a cell phone, at which point the number of people with cell phones, and correspondingly the amount of energy consumed by cell phones, will increase only as the population increases. The amount of energy consumed by cell phones that are plugged into chargers longer than necessary to fully charge the phone is not included in the above model. This exclusion results from our assumption that cell phones are left on 24 hours per day. This means that whether the phone is plugged into the charger or not the battery will drain at the same rate. If the cell phone were unplugged from the charger after fully charging, the battery would drain at the standby rate and would thus need to charge more the next night. If the cell phone were left plugged into the wall, the battery would still drain at the standby rate, but would instantaneously be recharged. The difference between unplugging the phone once it is fully charged compared to leaving the phone plugged in comes down to a question of when the battery is recharged, not how much energy it takes to do it. Note: If we include the amount of energy consumed by cell phones that are plugged into chargers longer than necessary to charge the phone in the above graph, the results change only slightly. That is to say that the amount of energy “wasted” in this way is essentially negligible. Requirement Four: Synopsis: Phantom loads are not only a concern while considering cell phone usage. All electrical appliances draw power, even while switched off. With this power drain continuously occurring in U.S. households, one might question how much energy is consumed from phantom loads alone. In this section, we will target this question and approximate how much energy phantom loads are responsible for in terms of barrels of oil. Analysis: A sample of phantom loads from common electronic devices was collected. These data were obtained from the Lawrence Berkeley National Laboratory. From this compilation, the authors selected a list of appliances to be a conservative estimate, representative of a typical household:
Suppose that each household has one of each of the above electronic devices and has a phantom load consumption of 90.87 Watts. We use this assumption, the same U.S. Census Bureau household data as discussed in Requirement 1, and the appropriate conversion for a barrel of oil into energy. We use these data to convert phantom load energy into its barrel of oil equivalent:  
Appendix E contains tabulated values for  .
The following figure shows According to the Energy Information Administration, the U.S. consumes 20,680,000 barrels of petroleum each day.18 Compared to this figure, daily phantom load consumption may not appear to amount to much daily, but suppose that U.S. households consume the amount of barrels predicted by A linear regression in Microsoft Excel provides the following function for 
Let
Where The sum, The energy withdrawal for phantom loads over time is considerable; if phantom loads could have been prevented from 1990 up to 2070, enough energy could be conserved to meet the oil provisions of the current United States for over 246 days. Recall that these figures are derived from conservative estimates of a household. If each household in the U.S. owned more than one TV, computer, sound system, etc., the phantom load consumption would be even more substantial (see Appendix E for data).
Even though cell phones are a considerable part of our economy right now, they will continue to expand and become an even larger factor for energy consumption in the future. Our model will attempt to predict the changes in population and economic growth over the next 50 years, and how this will impact energy consumption in terms of barrels of oil. Figure 5.1 shows the total energy consumed by telephones from 1990 to 2060. An abrupt shift in the rate of change of the amount of energy consumed first appears around 1996. This is because cell phones did not become commercially viable at the retail level until around 1996. As cell phones began to increase in popularity, the amount of energy consumed by all phones increased as well. The next abrupt change appears to occur around 2013. This is because, prior to 2013, the percentage of people with cell phones in the U.S. was increasing along with the population. After 2013, our model indicates that nearly 100% of people will have a cell phone, at which point the number of people with cell phones, and correspondingly the amount of energy consumed by cell phones, will increase only as the population increases. Coincidently, the population increases at about the same rate that the number of households with landline phones decreases, causing the amount of energy consumed by all phones to appear to level off (or slightly decrease). After 2034, the energy consumed by all phones (at this point, all cell phones) will begin to increase again as the population, and thus the number of cell phone users, increases. Summary and Evaluation: Brief Introduction: The purpose of this study was to model the energy consequence of the wireless phone revolution. As this technology has continued to grow, the demand for electricity to charge cell phones has grown linearly. We decided to model the energy consumed by one cell phone, on an average day, and extrapolate this to encompass the energy demands of the entire U.S. population. We did this by breaking down the energy consumption of the cell phone into the following three parts: time during which cell phone battery is replenishing from the charger, the standby time where the phone battery is fully charged but still plugged in, and lastly the time which the phone is removed from the charger but the charger remains plugged into the wall. Together, these times make up the typical day for the energy profile of each wireless phone. Strengths: The strength of our model comes from partitioning the population into subsets dependent on their usage of their cell phone. This allows us to include the varying amounts of energy needed to recharge the batteries in our model. This helped to get a more accurate estimate of the total energy consumption by cell phone chargers in the U.S. Similarly, we divided the energy profile of each cell phone into three time frames. First, the battery is partially or fully drained and it is recharged. Second, the battery is full but still plugged into the charger. Lastly, the phone is removed from the charger, but the charger remains plugged into the wall. This has helped us to accurately model the energy consumption by cell phone chargers. Weaknesses: The main weakness of our model is its’ tendency towards the average. Many of the data inputs we use in our calculations are averages of the data we found from our resources, and this may not fully represent the current trends in energy consumption. Our model most likely estimates the total energy consumption on the conservative side. Another weakness of the model is that we have assumed a perfectly efficient energy transfer from the charger to the battery. Realistically, some energy might be lost to resistance, and the total energy used to charge a cell phone would be higher. Problems: The biggest problem with our model will most likely be the accuracy and cohesiveness of the data. As our data was taken from so many different sources, some of varying credibility, tiny errors in their calculations could extrapolate to very large errors as we used our model to make projections into the future. Furthermore, some of the research was very hard to find during our short period of time we had to work on this problem. We have tried our hardest to find the most credible and accurate sources, and we have cited them throughout our solution. Conclusion: We found that the total energy consumption of cell phones is far greater than the total energy consumption of landline phones. This is partly due to the fact that people do not share their mobile phones, as they could with landline phones. So, there are a growing number of cell phones, and shortly in the future we expect there to be one wireless subscription for every person in the U.S. This has created a large increase in the consumption of energy (in terms of barrels of oil) by all phones. However, a very large part of this increase is wasted by inefficient cell phone charging techniques. Our model shows that phantom load, energy consumed by the charger itself plugged into the wall, plays a significant role in the overall levels of energy consumption. Thus, if the U.S. were able to adopt more energy efficient charging techniques, the costs of cell phones cut largely be cut. Works Cited: “Battery review – CNET.” Product reviews and Prices, Software downloads, and tech news – CNET. 07 Feb. 2009 Download 0.57 Mb. Share with your friends:
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, has an energy profile, 
. That is, an individual consumes a finite amount of power in a given day from cell phone use. Then, the energy that is consumed by a single individual can be modeled as follows:
be the percentage of the battery drained. Then, for an average day,
is the average talk time for an individual
is the total talk time a cell phone battery allows (
)12
is the total time the battery is away from the charger (
in our 8-hour charging assumption)
is the total standby time 
is the time it takes for a battery to become fully charged after having no charge 
15.
, the cell phone users of the United States. If we sum over all energy profiles in the United States, we could estimate how much energy is used from cell phones in the United States each day. Namely, if 
subsets. Place each individual in 
. Based on the percentage of time each person talks on his/her cell phone, we can generate an energy profile, 
for each group. Then, we have 
denotes the cardinality of subset 
.
, and each individual has a distinct energy profile,
for a number of years.
:
is the constant used to convert from watts to barrels of oil.
, computes the cumulative number of barrels of oil consumed by Americans at time 
, the number of days after 1990. The following plot of