1. Introduction

In the context of global efforts to combat climate change, the promotion of renewable energy sources and energy storage technologies has become crucial. Solar home energy storage systems, which combine photovoltaic (PV) panels with energy storage devices, offer a sustainable solution for residential energy consumption. These systems not only enable homeowners to reduce their reliance on the traditional power grid but also contribute significantly to carbon emission reduction. To accurately assess the environmental benefits of solar home energy storage systems, a scientific and comprehensive carbon emission reduction benefit calculation model is necessary. This model can help policymakers, researchers, and homeowners understand the potential of these systems in mitigating climate change and making informed decisions regarding their adoption and promotion.

2. Components of the Calculation Model

2.1 Carbon Emission Factors

The foundation of the calculation model lies in the determination of carbon emission factors. These factors represent the amount of carbon dioxide equivalent (CO₂e) emissions associated with the generation, transmission, and consumption of electricity from different sources. For traditional grid - supplied electricity, the carbon emission factor varies depending on the energy mix of the local power grid. In regions where coal - fired power plants dominate the energy supply, the carbon emission factor can be relatively high, often ranging from 0.8 to 1.2 kilograms of CO₂e per kilowatt - hour (kg CO₂e/kWh). In contrast, regions with a higher proportion of renewable energy sources in their grid, such as hydro, wind, and solar, will have lower carbon emission factors, potentially as low as 0.1 to 0.3 kg CO₂e/kWh.

For solar home energy storage systems, the carbon emission factor during the operation phase is extremely low, close to zero, as solar energy is a clean and renewable energy source. However, there are still some embodied carbon emissions associated with the manufacturing, transportation, installation, and end - of - life disposal of the PV panels, batteries, and other components of the system. These embodied emissions need to be considered in the overall calculation. For example, the manufacturing of PV panels typically generates around 0.3 to 0.8 kg CO₂e per watt of installed capacity over the panel's lifespan, depending on the manufacturing process and the type of PV technology used (monocrystalline, polycrystalline, or thin - film). Lithium - ion batteries, commonly used in energy storage systems, have an embodied carbon emission of approximately 0.5 to 1.2 kg CO₂e per kWh of battery capacity, considering the extraction of raw materials, battery production, and transportation.

2.2 Energy Consumption and Generation Data

Accurate energy consumption and generation data are essential for the calculation model. For a solar home energy storage system, the amount of electricity generated by the PV panels can be measured using power meters installed on the panels. The generated electricity is either consumed directly by the household, stored in the battery for later use, or fed back into the grid (in the case of grid - connected systems with net metering). The energy consumption of the household can be monitored through smart meters or by analyzing historical electricity bills.

The battery's charging and discharging cycles also need to be recorded. The efficiency of the battery, which represents the ratio of the energy output to the energy input during charging and discharging, is an important parameter. A typical lithium - ion battery in a home energy storage system may have an efficiency of around 85% to 95%. By tracking the energy flows between the PV panels, the battery, and the household load, as well as the grid interactions, the model can accurately calculate the amount of electricity that would have been sourced from the grid if the solar home energy storage system were not in place.

2.3 System Lifespan and Degradation

The lifespan of the solar home energy storage system is a critical factor in the calculation model. PV panels typically have a lifespan of 25 to 30 years, while lithium - ion batteries may need to be replaced after 10 to 15 years, depending on their usage and maintenance. Over time, the performance of both the PV panels and the batteries will degrade. PV panels may experience a decrease in power output, with an average annual degradation rate of around 0.5% to 1% of their initial capacity. Batteries will gradually lose their storage capacity, with a decline in state - of - health (SOH) over each charging and discharging cycle.

These degradation factors need to be incorporated into the model to accurately estimate the long - term carbon emission reduction benefits. For example, as the PV panels degrade, the amount of electricity they generate will decrease, potentially increasing the reliance on the grid and reducing the carbon emission reduction. Similarly, as the battery's capacity declines, more frequent charging from the grid may be required, offsetting some of the environmental benefits.

3. Calculation Process

3.1 Baseline Scenario Calculation

The first step in the calculation process is to establish a baseline scenario, which represents the situation without the solar home energy storage system. In this scenario, the household's entire electricity consumption is assumed to be sourced from the grid. Using the local grid's carbon emission factor and the measured or estimated energy consumption data of the household, the annual carbon emissions of the baseline scenario can be calculated as follows:

\(

\text{Annual Carbon Emissions}_{baseline} = \text{Annual Energy Consumption} \times \text{Grid Carbon Emission Factor}

\)

3.2 Solar Home Energy Storage System Scenario Calculation

Next, the carbon emissions associated with the solar home energy storage system scenario need to be calculated. This includes two main components: the embodied carbon emissions of the system components and the operational carbon emissions.

The embodied carbon emissions are calculated based on the initial investment in the system. For the PV panels, if the installed capacity is \(P\) (in watts) and the embodied carbon emission factor per watt is \(E_{PV}\) (in kg CO₂e/W), the total embodied carbon emissions of the PV panels over their lifespan \(L_{PV}\) (in years) are \(P \times E_{PV}\). Similarly, for the battery with a capacity of \(C\) (in kWh) and an embodied carbon emission factor per kWh of \(E_{battery}\) (in kg CO₂e/kWh), the total embodied carbon emissions of the battery over its lifespan \(L_{battery}\) are \(C \times E_{battery}\). The total embodied carbon emissions of the entire system \(E_{embodied}\) are the sum of the embodied emissions of all components.

During the operation phase, the carbon emissions are mainly related to the electricity that still needs to be sourced from the grid when the solar energy generated is insufficient. If the annual electricity generated by the PV panels is \(E_{PV - generated}\), the annual electricity consumed by the household is \(E_{consumption}\), and the battery's efficiency is \(\eta\), the amount of electricity sourced from the grid \(E_{grid - sourced}\) can be calculated as:

\(

E_{grid - sourced} = \max\left(0, E_{consumption}-\frac{E_{PV - generated}}{\eta}\right)

\)

The annual operational carbon emissions \(E_{operational}\) are then calculated by multiplying \(E_{grid - sourced}\) by the grid carbon emission factor. The total annual carbon emissions of the solar home energy storage system scenario \(E_{system}\) are the sum of the embodied carbon emissions divided by the system lifespan and the operational carbon emissions:

\(

E_{system} = \frac{E_{embodied}}{L_{system}}+E_{operational}

\)

where \(L_{system}\) is the overall lifespan of the solar home energy storage system, which can be determined based on the shorter lifespan of its components (e.g., the battery lifespan if it is shorter than the PV panel lifespan).

3.3 Carbon Emission Reduction Calculation

Finally, the carbon emission reduction benefit of the solar home energy storage system can be calculated by subtracting the total annual carbon emissions of the system scenario from the annual carbon emissions of the baseline scenario:

\(

\text{Annual Carbon Emission Reduction} = \text{Annual Carbon Emissions}_{baseline}-E_{system}

\)

Over the lifespan of the system, the cumulative carbon emission reduction can be obtained by summing up the annual carbon emission reductions for each year, taking into account the degradation of the system components over time.

4. Sensitivity Analysis

4.1 Impact of Carbon Emission Factors

The carbon emission factors of the grid and the system components can have a significant impact on the calculated carbon emission reduction benefits. A small change in the grid carbon emission factor can alter the baseline scenario's carbon emissions and, consequently, the overall reduction amount. Similarly, variations in the embodied carbon emission factors of the PV panels and batteries can affect the system scenario's carbon emissions. Sensitivity analysis can be conducted to determine how sensitive the results are to changes in these factors. For example, increasing the grid carbon emission factor by 10% can be simulated to observe the corresponding increase in the calculated carbon emission reduction, indicating the importance of accurately determining these factors.

4.2 Influence of Energy Consumption and Generation Patterns

The energy consumption and generation patterns of the household also play a crucial role. If the household's electricity consumption increases over time or if the solar energy generation is affected by changes in weather conditions or shading, the carbon emission reduction benefits will be impacted. Sensitivity analysis can be used to model different consumption and generation scenarios, such as a 20% increase in energy consumption or a 15% decrease in solar generation due to shading, to understand how these changes affect the carbon emission reduction calculations.

4.3 Effect of System Lifespan and Degradation Rates

The lifespan and degradation rates of the system components are also sources of uncertainty in the calculation. A shorter lifespan or a higher degradation rate will lead to a decrease in the carbon emission reduction benefits over time. By varying these parameters in the sensitivity analysis, policymakers and homeowners can assess the robustness of the calculated benefits and make more informed decisions regarding system design, maintenance, and replacement strategies.

5. Case Study

5.1 Case Study Setup

To illustrate the application of the calculation model, a case study of a single - family home in [Region Name] is considered. The home has an annual electricity consumption of 5,000 kWh. A solar home energy storage system is installed, consisting of 20 PV panels with an installed capacity of 300 watts each (total capacity of 6 kW) and a 10 kWh lithium - ion battery. The local grid has a carbon emission factor of 0.9 kg CO₂e/kWh. The embodied carbon emission factor for the PV panels is assumed to be 0.6 kg CO₂e/W, and for the battery, it is 1.0 kg CO₂e/kWh. The PV panels have a lifespan of 25 years with an annual degradation rate of 0.8%, and the battery has a lifespan of 12 years with a capacity degradation rate of 3% per year.

5.2 Calculation Results

Using the calculation model, the baseline scenario's annual carbon emissions are \(5000 \times 0.9 = 4500\) kg CO₂e.

The embodied carbon emissions of the PV panels are \(6000 \times 0.6 = 3600\) kg CO₂e, and for the battery, they are \(10 \times 1.0 = 10\) kg CO₂e. The total embodied carbon emissions of the system are \(3600 + 10 = 3610\) kg CO₂e.

In the first year, the PV panels generate \(6 \times 1000 \times 365 \times 0.8 \) (assuming 8 hours of sunlight per day on average) \(= 1752\) kWh of electricity. After considering the battery's 90% efficiency, the amount of electricity sourced from the grid is \(\max\left(0, 5000-\frac{1752}{0.9}\right) = 3053.33\) kWh. The operational carbon emissions in the first year are \(3053.33 \times 0.9 = 2748\) kg CO₂e. The total annual carbon emissions of the system in the first year are \(\frac{3610}{25}+ 2748 = 2892.4\) kg CO₂e.

The annual carbon emission reduction in the first year is \(4500 - 2892.4 = 1607.6\) kg CO₂e. Over the 12 - year lifespan of the battery (the shorter lifespan of the components), the cumulative carbon emission reduction can be calculated by repeating the above calculations for each year, taking into account the degradation of the PV panels and the battery.

6. Conclusion

The solar home energy storage system carbon emission reduction benefit calculation model provides a systematic and scientific approach to evaluate the environmental benefits of these systems. By considering factors such as carbon emission factors, energy consumption and generation data, system lifespan, and degradation, the model can accurately calculate the carbon emission reduction achieved by solar home energy storage systems. Sensitivity analysis helps to understand the impact of various uncertainties on the calculation results, enabling more informed decision - making. Through case studies, the practical application of the model can be demonstrated, highlighting its importance in promoting the adoption of solar home energy storage systems and quantifying their contribution to carbon emission reduction and climate change mitigation. As the world continues to transition towards a low - carbon future, such calculation models will play an increasingly vital role in assessing the environmental performance of renewable energy technologies.