Energy-related activities are a major contributor of greenhouse gas (GHG) emissions. A growing body of knowledge clearly depicts the links between human activities and climate change. Over the last century the burning of fossil fuels such as coal and oil and other human activities has released carbon dioxide (CO2) emissions and other heat-trapping GHG emissions into the atmosphere and thus increased the concentration of atmospheric CO2 emissions. The main human activities that emit CO2 emissions are (1) the combustion of fossil fuels to generate electricity, accounting for about 37% of total U.S. CO2 emissions and 31% of total U.S. GHG emissions in 2013, (2) the combustion of fossil fuels such as gasoline and diesel to transport people and goods, accounting for about 31% of total U.S. CO2 emissions and 26% of total U.S. GHG emissions in 2013, and (3) industrial processes such as the production and consumption of minerals and chemicals, accounting for about 15% of total U.S. CO2 emissions and 12% of total U.S. GHG emissions in 2013. This is why the adoption of hybrid and all-electric vehicles (EVs) instead of conventional gasoline powered vehicles with renewable source of power has been identified as the most effective GHG emissions mitigation strategy. This strategy not only saves considerable amounts of transportation-related CO2, but also reduces the demand for electricity in buildings, which is mainly supplied by coal-fired generation. Since solar energy is the only source of renewable energy that can be applied at a small scale (e.g. directly to the roof decking or solar window), this paper focuses only on the mitigation strategies in which EVs are powered by solar energy. One reason mitigation strategies are having difficulty delivering the desired outcome sought by policy makers is that many factors that affect the success or scale of GHG emissions reductions are uncertain and complex. Vehicle's specification (e.g. battery capacity, weight, and optimal energy use), road type and driving behavior (e.g. average speed), and environmental conditions (e.g. temperature and sunlight) are among the many factors affecting either energy consumption or generation and characterized by a significant degree of uncertainty. Thus, urban community planners and policy makers are confounded with huge amounts of unknown parameters, in which they wish to find the best solution from all feasible solutions (e.g. the largest GHG emissions reduction that a mitigation strategy can achieve) in the presence of uncertainty. The objective of this paper is to develop a stochastic mathematical model for energy consumption and mitigation strategy analysis that maximizes GHG emissions reductions based on the current demand trend and market prices. In this model, we consider EV and solar system costs, as well as the human activities (e.g. time spent in the building, time spent driving, and distance traveled) and environmental impacts (e.g. temperature, humidity, and sunlight) under uncertain conditions. What makes this study different from previous energy management or GHG emissions mitigation research is its focus on small-scale energy system and its validation process. Although mitigation actions through large-scale changes in energy system (e.g. new renewable energy power plant) will undoubtedly result in the largest GHG emissions reductions, but they also require major changes in the generation part of the energy sector and definitely need more investment. One the other hand, small-scale GHG emissions mitigation actions (e.g. EVs powered by solar energy) can be accomplished by local communities and characterized by a short decision making cycle, need much less investment, and also eliminate electricity losses in transmission and distribution systems. These all make small-scale GHG emissions mitigation strategies more practical and feasible. Another principal problem with prior energy management or GHG emissions mitigation research is that optimization models have not been validated with real data. In contrast, the proposed optimization approach is validated by comparing the estimated values of the optimal decision and actual values as realizations of the uncertain elements become known. Problem Statement The use of hybrid or EVs alone does not necessarily reduce the transportation's GHG emissions and it depends on the energy source. A conventional gasoline powered vehicle with 30 miles per gallon (mpg) fuel efficiency emits about 0.65 pounds CO2 per mile driven. In contrast, an EV with an average energy use of 3 mile per kWh emits about 0.71 pounds CO2 per mile driven when coal-fired electricity is used, and it emits 0.40 pounds CO2 per mile driven when natural gas-fired electricity is used. In order to optimize the mitigation strategies in which EVs are powered by solar energy (EV + solar power strategy), both energy supply (electricity generation) and demand (electricity consumption) sides must be considered. Research Methodology There are three primary solar systems: off-grid, grid-tied, and hybrid. Off-grid solar systems feed the extra energy the solar panels produce into batteries, while grid-tied solar systems send excess power to the electrical grid. Both off-grid and grid-tied systems yield the same amount of CO2 emissions reduction when the solar panels produce enough power for charging EV's batteries. When the solar panels are not producing the power required for charging an EV (e.g. during cloudy weather or night), however, grid-tied systems use electricity from the grid but off-grid systems use electricity stored in batteries. Depending on the electrical grid energy source in this case, a mitigation strategy using grid-tied systems may add a significant amount of CO2 to the atmosphere. Hybrid solar systems offer the flexibility of using a battery backup and being connected to the grid. Therefore, the outcome of a mitigation strategy using hybrid systems depends largely on the power generation capacity of the solar system. The area of solar panels, the solar cell efficiency and temperature coefficient, irradiance of input light, and temperature are the main factors affecting the capacity of a solar system. In the present problem, the decisions variables are the type of EV, which determines the optimal EV's energy use, the capacity of the solar system in the case of grid-tied system as well as the solar system storage capacity in the case of off-grid and hybrid system. Under a pre-specified budget constraint, the objective is to find these decision variables in such way to maximize GHG emissions reductions. The present model starts the optimization process by identifying the energy source of electricity generation. The electrical grid energy source is determined by the electricity demand at time t, Load t, and the electric power plants generating capacity, PPCj. The time index t takes integer values between 1 and N, where N is the time horizon of the analysis and the units of time measurement are hours. For instance, Load30 indicates the electricity demand on day 2, 6 AM. Smaller time horizons for the analysis and the prediction require less computation efforts but they are less accurate. To obtain a perfect reference for the best possible GHG emissions mitigation strategy, we solve a stochastic optimization problem with a prediction horizon of 1 hour over a year, thus N is 1 ×  365 × 24 = 8760 hours. The power plant index j indicates the respective set of the renewable (j = 1), nuclear- (j = 2), natural-gas (j = 3), coal- (j = 4), and oil-fired (j = 5) power plant. Load t is a probabilistic variable because it is unknown at the time the decision should be made; however, PPCj is a deterministic variable and is known for the analysis region. It is assumed that the supply level is sufficient to meet peak demand. The CO2 emissions at time t are then calculated for each type of solar system. For a grid-tied system, the CO2 emissions (measured in lb or kg) are calculated which may be positive or negative. A Negative value indicates a reduction in the CO2 emissions. When an EV is charging at time t, the energy generated by solar panel will be used in transportation sector. However, when an EV is not charging, all the energy will be used in the building. For an off-grid system, the factor that can seriously affect the CO2 emissions is the solar battery's state of charge. This factor is a function of the solar system storage capacity, and the charging duration, which starts at the last prediction horizon, and ends at time t. Once the solar batteries are fully charged, the extra energy the solar panels produce will be used only in the building. Since off-grid solar systems are not connected to the electrical grid, the energy produced by the system can meet at most the building's demand (DB) and the rest is wasted. This happens when the solar batteries are fully charged and the system is producing more energy than building's load. In the off-grid system, the EV is charged using the electricity stored in batteries. When the energy required to fully charging the EV exceeds the electricity stored in batteries, the EV will be charging using both the batteries and the electrical grid. In contrast to an off-grid solar system, no extra power is wasted in hybrid systems because they can send excess power to the electrical grid. In order to reduce more GHG emissions, the energy generated by solar panel must preferably be used to charge EV's vehicle batteries. For a grid-tied system, this happens when the EV is charging right when the solar system is producing energy. Off-grid and hybrid solar systems offer the flexibility of using a battery backup to charge the EV even when the solar system is not producing enough energy, for example during cloudy weather or night. Thus, it is assumed that the power from the solar system is first used to charge the batteries and then excess power is used in the building or fed into the electrical grid. In order to estimate the electricity generated by solar system, the distributions of stochastic variables such as solar irradiance and temperature are obtained from the weather records over the last 20 years from 1994 to 2014. Also, a database of 46 solar panels from 15 manufacturers is used to obtain solar cell efficiency and temperature coefficient. The average efficiency of 15.86% and temperature coefficient of -0.44 %/°C are used in the analysis. In order to estimate the electricity demand at a given time, the distributions of hourly load are obtained from the operable electric generating plants with a combined rated capacity of 1 MW or more over the last 18 years from 1996 to 2014. The Energy Information Administration (EIA) was the primary sources of hourly load data. Results and Conclusions Results show that among three primary solar systems (i.e. off-grid, grid-tied, and hybrid), a hybrid system consists of 7 modules of solar panels with 6 kWh storage capacity was found to be the best solution. Hybrid solar systems overcome the disadvantage of off-grid solar systems by sending the excess power to the electrical grid and reduce more CO2 emissions than grid-tied solar systems by using the electricity stored in batteries in transportation sector instead of buildings. The presented model is also capable of estimating CO2 emissions reductions from mitigation strategies in which EVs are powered by solar energy. With this capability, urban community planners and policy makers will know how long it will take for their strategy to meet GHG emissions reduction targets. The stochastic optimization problem was solved with a prediction horizon of an hour over a month. Then, CO2 emissions reductions estimated by the presented stochastic model were compared with actual data collected on an hourly basis for the analysis period of one month (720 hours). The results showed an accuracy of about 4% when the EV is powered by a grid-tied or hybrid solar system. When applied to an EV + off-grid solar power strategy, the stochastic model estimated CO2 emissions reductions 11% lower than the actual reductions. Overall, the presented stochastic model had better performance than deterministic methods for different types of solar systems.

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