# Strategic Resource Planning for Sustainable Biogas Integration in Hybrid Renewable Energy Systems
## 2 Materials and Methods
### Biogas Production and Management  
In this renewable energy system, the only controllable parameter is the biomass input to the biogas reactor, which is crucial for biogas production. This is because other energy sources, such as solar and wind, inherently depend on environmental conditions and are not directly controllable. Solar energy generation varies based on sunlight availability, which changes throughout the day and is influenced by weather conditions and seasonal patterns. Similarly, wind power generation depends on wind speed and is subject to fluctuations that cannot be regulated. The system incorporates a hydroelectric component as an energy storage mechanism to balance these fluctuations. When solar panels or wind turbines generate excess energy, this surplus pumps water from a lower reservoir to an upper reservoir. During higher energy demand, or when solar and wind resources are insufficient, the stored water is released from the upper to the lower reservoir, driving turbines to generate electricity. This energy storage capability helps smooth out the variability of renewable energy sources, reducing reliance on the external grid and ensuring that energy needs can be met consistently. However, the biomass input remains the most flexible and directly controllable parameter. By adjusting the amount of biomass fed into the biogas reactor, the system can ensure a steady production of biogas, producing electricity. This controllability allows for continuous energy generation even when solar and wind resources and hydroelectric storage are insufficient to meet demand. Biomass, therefore, plays a crucial role in maintaining the overall system's stability and reducing dependence on the grid. Since biogas production can be controlled by adjusting the biomass flow entering the digester, a more detailed analysis of the governing relationships is required. Understanding the dynamics between biomass input and biogas output is crucial for optimizing the system's performance, ensuring consistent energy generation, and maintaining the efficiency of the overall process. Biogas production in an anaerobic digestion system relies heavily on the quantity and characteristics of the biomass fed into the reactor. The total biomass input (\(m_{Biomass}\)) is a key factor, and only a fraction of that, known as volatile solids (\(f_{VS}\)), can be broken down by microbes to produce biogas. The percentage of \(f_{VS}\) in the biomass is 80%, indicating that 80% can be converted into biogas. Additionally, the conversion efficiency (\(\eta_{Conversation}\)), which is 75%, represents the proportion of volatile solids converted into biogas during digestion. The mass of volatile solids that are converted into biogas each day (\(m_{VS}\)) can be calculated using Equation (1):  
\[m_{VS}=m_{Biomass}\times f_{VS}\times\eta_{Conversation} \tag{1}\]  
From this, the daily biogas production rate is calculated by considering the methanogenic capacity (\(k_{Methanogenic}\)), representing the volume of biogas produced per kilogram of volatile solids. In this case, \(k_{Methanogenic}\) is estimated to be 0.228 Nm\({}^{3}\)/kg, meaning that 0.228 cubic meters of biogas is produced for every kilogram of volatile solids. The maximum potential biogas production rate can be calculated using Equation (2):  
\[Q_{max}=m_{VS}\times k_{Methanogenic} \tag{2}\]  
This gives the maximum potential biogas production rate at the start of the process on Day 1 (\(Q_{max}\)), reflecting the energy output when the system runs at full capacity. However, biogas production does not remain constant over time. As the microbes digest biomass, the rate of biogas production gradually decreases. This time-dependent decay in biogas production is often modeled using an exponential decay function.