In recent years, energy storage has emerged as a critical complementary technology to enhance the utilization of solar energy resources, addressing the inherent intermittency and mismatch between supply and demand in renewable energy systems. The integration of storage solutions into solar power systems enables more reliable and efficient energy management, particularly in grid-connected photovoltaic (PV) setups. This paper presents a comprehensive decision-making tool designed to determine the optimal storage capacity for electricity demand during working hours in a solar power system. By leveraging optimization models, we analyze the interplay between solar generation, demand patterns, and storage dynamics to maximize system efficiency. Our findings demonstrate that a storage capacity of 231 kWh can achieve a solar power system efficiency of 0.292, highlighting the pivotal role of storage in improving the performance of solar power systems. Throughout this work, we emphasize the importance of tailored storage solutions for various applications, reinforcing the value of solar power systems in sustainable energy landscapes.
The growing adoption of solar power systems worldwide underscores the need for effective storage mechanisms to mitigate the variability of solar energy. Storage technologies, such as batteries, facilitate peak load shifting and energy arbitrage, allowing excess solar generation to be stored for later use. This is especially relevant for scenarios where demand is concentrated during specific periods, such as working hours in commercial or residential settings. In this context, we develop a decision tool that incorporates demand modeling, solar generation simulation, and storage optimization to guide the sizing of storage capacity. The tool is implemented using accessible software like Microsoft Excel, making it practical for real-world applications. By focusing on a case study of a workplace in the Southern Hemisphere, we illustrate how the tool can be applied to derive actionable insights. The subsequent sections detail the methodologies and models employed, with an emphasis on mathematical formulations and empirical data to support the decision-making process.
Demand Modeling for Solar Power Systems
Accurately modeling electricity demand is the foundation for determining the appropriate storage capacity in a solar power system. For a typical workplace, demand patterns are influenced by the operational schedules of various electrical appliances. We consider a scenario where demand occurs predominantly during working hours, defined as 8:00 AM to 5:00 PM on weekdays, with non-working hours encompassing evenings, nights, and weekends. To construct a demand profile, we treat each appliance as operating independently and account for their usage rates during different time periods. For instance, appliances like refrigerators may run continuously, while others, such as computers and air conditioners, are active primarily during working hours.
The total hourly electricity demand is computed by aggregating the power consumption of all appliances, considering their quantities and usage proportions. Let \( D(t) \) represent the demand at hour \( t \), where \( t = 1, 2, \ldots, 8760 \) for a full year. For each appliance \( i \), the power consumption is given by \( P_i \), the number of units is \( N_i \), and the usage rate during hour \( t \) is \( U_i(t) \). The demand can be expressed as:
$$ D(t) = \sum_{i} P_i \cdot N_i \cdot U_i(t) $$
where \( U_i(t) \) is derived from statistical data on appliance operation. The usage rates vary between working and non-working hours, reflecting typical behavior patterns. For example, during working hours, usage rates for computers might range from 50% to 70%, while at night, they drop to 10–20%. This approach allows us to generate a realistic demand curve that captures seasonal variations, such as higher demand in winter due to heating needs in the Southern Hemisphere.
To illustrate, we provide a table summarizing the appliance data used in our case study. This includes the power rating, quantity, and usage rates for each device, which are essential inputs for the demand model.
| Appliance | Power (W) | Quantity | Working Hours Usage Rate (%) | Non-Working Hours Usage Rate (%) |
|---|---|---|---|---|
| Air Conditioner (Cooling) | 1100 | 15 | 70–100 | 1–10 |
| Air Conditioner (Heating) | 2000 | 15 | 70–100 | 1–10 |
| Desktop Computer | 500 | 576 | 50–70 | 10–20 |
| Wall Lamp | 10 | 288 | 20–50 | 1–10 |
| Laptop | 120 | 576 | 50–70 | 10–20 |
| Refrigerator | 1200 | 6 | 20 | 20 |
| Fax Machine | 110 | 96 | 20–40 | 0–10 |
| Printer | 800 | 160 | 20–40 | 0–10 |
| Electric Kettle | 1500 | 144 | 3–5 | 0–1 |
| Water Purifier | 50 | 12 | 95–100 | 10–50 |
| Coffee Machine | 750 | 6 | 30–60 | 0–10 |
Using this data, we calculate the hourly demand over a year, resulting in a profile that peaks during winter months and dips in summer, consistent with the climatic conditions of the Southern Hemisphere location. This demand model serves as a critical input for the solar power system analysis, enabling us to assess how storage can bridge the gap between generation and consumption.
Solar Generation Modeling in Solar Power Systems
The solar generation component of the solar power system is modeled to estimate the electricity produced by PV panels based on local solar radiation data and system parameters. We employ a simplified approach that calculates the optimal tilt angle for the panels, the spacing between rows to avoid shading, and the total number of panels that can be installed on a given roof area. The model inputs include latitude, panel dimensions, power rating, roof dimensions, and hourly global horizontal irradiance (GHI) data.
First, the optimal tilt angle \( \beta \) for the PV panels is determined using a formula that relates it to the latitude \( \phi \). For the Southern Hemisphere, this can be approximated as:
$$ \beta = \phi + 10^\circ $$
where \( \phi \) is the latitude in degrees. For our case study, \( \phi = -34^\circ \) (South), so \( \beta = -24^\circ \). Next, the row spacing \( D \) between panel arrays is calculated to prevent shading, considering the solar altitude angle. The formula for spacing is:
$$ D = H \cdot \frac{\cos(\beta)}{\tan(\alpha)} $$
where \( H \) is the height of the panel row, and \( \alpha \) is the solar altitude angle at solar noon during the winter solstice. The solar altitude angle can be derived from the latitude and declination angle \( \delta \), which varies throughout the year. The declination angle is given by:
$$ \delta = 23.45^\circ \cdot \sin\left( \frac{360}{365} (284 + n) \right) $$
where \( n \) is the day of the year. The solar altitude angle \( \alpha \) at solar noon is:
$$ \alpha = 90^\circ – \phi + \delta $$
Using these calculations, we determine the maximum number of panels that can be installed on a roof with dimensions 50 m (north-south) and 40 m (east-west). For a panel of length \( L = 1.689 \) m and width \( W = 0.996 \) m, the area per panel is \( A_{\text{panel}} = L \times W \). The total roof area is \( A_{\text{roof}} = 50 \times 40 = 2000 \) m². The number of panels \( N_{\text{panels}} \) is limited by the row spacing and roof layout, and can be estimated as:
$$ N_{\text{panels}} = \frac{A_{\text{roof}}}{A_{\text{panel}} \cdot \text{spacing factor}} $$
where the spacing factor accounts for the row spacing and orientation. In our example, we use JAM60S10-320W/PR panels with a power rating of 320 W per panel, leading to a total system capacity \( C_{\text{system}} = N_{\text{panels}} \times 320 \) W.
The solar radiation on the tilted panels is computed from the horizontal radiation data. The ratio of tilted to horizontal radiation \( R_b \) depends on the tilt angle and the solar geometry. For a surface with tilt \( \beta \), the incident radiation \( G_t \) is:
$$ G_t = G_h \cdot R_b + G_d \cdot \left( \frac{1 + \cos(\beta)}{2} \right) + G_h \cdot \rho \cdot \left( \frac{1 – \cos(\beta)}{2} \right) $$
where \( G_h \) is the global horizontal irradiance, \( G_d \) is the diffuse horizontal irradiance, and \( \rho \) is the ground reflectance (albedo). The ratio \( R_b \) is calculated as:
$$ R_b = \frac{\cos(\theta)}{\cos(\theta_z)} $$
where \( \theta \) is the angle of incidence on the tilted surface, and \( \theta_z \) is the zenith angle. The hourly generation \( E_{\text{gen}}(t) \) is then:
$$ E_{\text{gen}}(t) = C_{\text{system}} \cdot \frac{G_t(t)}{G_{\text{std}}} \cdot \eta_{\text{system}} $$
where \( G_{\text{std}} = 1000 \) W/m² is the standard irradiance, and \( \eta_{\text{system}} \) is the system efficiency factor (e.g., inverter losses). Using实测 irradiance data from the Southern Hemisphere location, we generate an hourly production profile for the year. This model allows us to simulate the solar power system’s output under varying conditions, providing a basis for storage optimization.
Storage Optimization Model for Solar Power Systems
The storage component of the solar power system is optimized using a dynamic programming model that determines how stored energy can be used to meet demand during working hours. The goal is to find the storage capacity that maximizes the solar power system efficiency, defined as the proportion of solar generation that directly meets demand or is stored for later use. Let \( S_{\text{max}} \) denote the storage capacity in kWh, and \( S(t) \) the stored energy at hour \( t \). The state of charge evolves according to:
$$ S(t+1) = \min\left( S_{\text{max}}, \max\left( 0, S(t) + \eta_{\text{charge}} \cdot E_{\text{excess}}(t) – \frac{E_{\text{deficit}}(t)}{\eta_{\text{discharge}}} \right) \right) $$
where \( \eta_{\text{charge}} \) and \( \eta_{\text{discharge}} \) are the charging and discharging efficiencies (assumed to be 0.95 each), \( E_{\text{excess}}(t) = \max(0, E_{\text{gen}}(t) – D(t)) \) is the excess solar generation, and \( E_{\text{deficit}}(t) = \max(0, D(t) – E_{\text{gen}}(t)) \) is the energy deficit. The solar power system efficiency \( \eta_{\text{system}} \) is calculated as:
$$ \eta_{\text{system}} = \frac{\sum_{t} \left( \min(E_{\text{gen}}(t), D(t)) + \eta_{\text{discharge}} \cdot \Delta S_{\text{discharge}}(t) \right)}{\sum_{t} E_{\text{gen}}(t)} $$
where \( \Delta S_{\text{discharge}}(t) \) is the energy discharged from storage at time \( t \). The optimization involves iterating over different values of \( S_{\text{max}} \) from 1 kWh to a maximum practical value (e.g., 500 kWh) and computing \( \eta_{\text{system}} \) for each case. The relationship between storage capacity and efficiency typically shows diminishing returns, as illustrated in our results.
To evaluate the effectiveness of storage, we also define the storage capacity efficiency \( \eta_{\text{storage}} \) as the incremental gain in system efficiency per unit increase in storage capacity:
$$ \eta_{\text{storage}}(S) = \frac{\eta_{\text{system}}(S) – \eta_{\text{system}}(1)}{S – 1} $$
for \( S > 1 \). This metric helps identify the point where additional storage yields minimal improvements. The dynamic programming logic ensures that energy is stored during periods of excess generation and discharged during deficits, prioritizing working hours demand. This model is implemented in Excel, using the hourly demand and generation data to simulate annual performance.
Results and Analysis for Solar Power Systems
Applying the decision tool to the case study, we compute the solar power system efficiency for various storage capacities. The results indicate that efficiency increases with storage capacity up to a point, beyond which it plateaus. Specifically, for storage capacities below 231 kWh, efficiency rises steadily from approximately 0.2786 at 1 kWh to 0.2925 at 231 kWh. Beyond 231 kWh, efficiency remains constant at 0.2925, indicating that additional storage does not enhance utilization further. This behavior is consistent with the law of diminishing returns and is critical for economic decisions in solar power systems.
The storage capacity efficiency analysis reveals a declining trend, with \( \eta_{\text{storage}} \) starting at 0.000172 for small capacities and decreasing rapidly. For instance, at low storage levels, each additional kWh contributes significantly to efficiency, but as capacity grows, the marginal benefit diminishes. This is summarized in the table below, which shows selected values of storage capacity, system efficiency, and storage capacity efficiency.
| Storage Capacity (kWh) | Solar Power System Efficiency | Storage Capacity Efficiency |
|---|---|---|
| 1 | 0.2786 | — |
| 50 | 0.2850 | 0.000130 |
| 100 | 0.2885 | 0.000099 |
| 150 | 0.2902 | 0.000077 |
| 200 | 0.2915 | 0.000064 |
| 231 | 0.2925 | 0.000057 |
| 300 | 0.2925 | 0.000000 |
From a practical standpoint, the optimal storage capacity depends on factors such as cost, available space, and energy policies. While 1 kWh and 231 kWh both represent efficient solutions, the latter maximizes the solar power system’s performance. However, the slight efficiency gain from 0.2786 to 0.2925 must be weighed against the higher investment for larger storage. In many cases, a hybrid approach that combines storage with other demand-side management strategies may be beneficial for solar power systems.
Conclusion
This paper has introduced a decision-making tool for determining the storage capacity in solar power systems, focusing on demand during working hours. By integrating demand modeling, solar generation simulation, and storage optimization, the tool provides a systematic approach to enhance the efficiency of solar power systems. Our analysis demonstrates that a storage capacity of 231 kWh can achieve a system efficiency of 0.292, representing an optimal balance between performance and resource allocation. The models and methodologies presented here are adaptable to various contexts, underscoring the versatility of solar power systems in addressing energy challenges. Future work could explore the integration of advanced forecasting techniques or hybrid storage solutions to further improve the reliability and economics of solar power systems. Ultimately, this research contributes to the broader goal of maximizing the utilization of solar energy through intelligent storage design, reinforcing the critical role of solar power systems in the transition to sustainable energy.