3. Modeling
In addition to the general need to use a simulation tool, Voorspools and D’haeseleer (2000) also highlight the need for “instantaneous” rather than “linear” emission approximations (i.e. not using daily or annual average figures) to accurately determine GHG emissions under varying demand-supply scenarios (Voorspools and D’haeseleer 2000). Despite the need for a sufficiently resolved time-scale, the duration need not be exceptionally long. For example, Verhaegh et al (2010) elected to focus on one-week periods during different seasons (e.g. winter and summer), which suggests that this is a reasonable approach to avoid simulating an entire year’s worth of data.
This study included developing a model in Microsoft Excel, which allowed for the inclusion of a user-friendly interface as well as the ability to make alterations to the model as new types of data were included to increase the accuracy of the model. As a drawback, the Excel-based model could only handle a limited set of calculations before overwhelming the available computing facilities. In order to keep the size of the model within the limitations of the computing facilities available, this study allowed for a time resolution of 15 minute intervals but restricted the simulated time frame to a one-week period, which allowed for sufficient temporal resolution (i.e. as great or greater than that of models described in articles listed in the Reference section) and the inclusion of lower demand periods during the weekend.
In order to develop the model some basic assumptions (see section III.3.a.) were made based on the data gathered regarding ES technologies and electricity generating technologies and electricity consumption patterns in the model region. In some cases these assumptions were used to develop specific formulae that guided the manner in which electricity demand and generation and storage were represented (see section III.3.b.). In other cases these assumptions provided the parameters with which GHG emissions factors and other variables were determined (see section III.3.c.). Naturally, using such assumptions (and the modeling process in general) necessarily limits the accuracy and applicability of the results to real-life purposes (see section III.3.d.).
a. Assumptions
The first major assumption necessary to build an accurate grid simulation is that the simulated demand for electricity is consistent with actual electricity demand curves. A more accurate demand curve allows for a better understanding of the potential for ES deployment. Officially, PJM recognizes that its ‘on-peak period is all non-holiday weekdays from 7 a.m. until 11 pm and the off-peak is comprised of all other hours’ (PJM 2009). Thus, roughly speaking the demand should be relatively higher between 7 a.m. and 11 p.m. on weekdays than at other times. To simplify matters, this study assumes there all weekdays are non-holidays.
In order to determine the appropriate shape of the diurnal fluctuations and the relative difference between demand on a weekend and on a weekday, historical real-time data was observed on the PJM website (i.e. http://edata2007.pjm.com/eData/index.html). The data observed showed that during the week demand fluctuated between ~70 GW at night and ~120 GW during the day, and the curve appeared roughly sinusoidal reaching about ~90 GW at around roughly 8:30 a.m. and 11:00 p.m. each day. On the weekends, the demand curve showed a roughly similar shape during the night and day; however, the range of the demand was ~62 GW to ~110 GW.
It must be noted that the observation period was not exhaustive (covering only a few days in July). Thus, it is possible that the days observed were not especially ‘normal’; however, this use of real data means the example is not outside the realm of possibility. Furthermore, the observation period does not conflict with any of the other data or reports presented by PJM. As such, the observed data was used as a basis for simulating electric demand (see section III.3.b. for the exact formula used).
The second major assumption made in this study is that over the next two decades the use of bulk ES in the PJM territory is more likely to include a plethora of ES technologies rather than a single type or brand of ES. Therefore, it did not seem prudent to specifically restrict the model to match the exact characteristics of any particular type of ES. Instead, the model was set up to measure the potential for ES use as an output rather than an input. However, to make any useful calculations regarding the impact of ES on GHG emissions it is necessary to make an assumption about the average roundtrip cycle efficiency (i.e. the ratio of usable electricity retrieved divided by the electricity consumed during the storage process) of all the bulk ES in use on the grid.
Rather than speculating about the various proportions of the bulk ES technologies that may be installed over the next two decades, it was simply assumed that for all scenarios the average roundtrip cycle efficiency was 75%. This ratio was chosen because it fell safely within the range of roundtrip cycle efficiencies of all of the bulk ES technologies described in section II.2.a.
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