# Assessment of Solar Energy Generation Toward Net-Zero Energy Buildings
## 2 System Models
### Proposal Optimization Framework  
The proposed optimization framework includes two major models: a prediction model of PV output power and a multi-objective optimization model for the operation of entire building systems. These models are interdependent, as the output of the prediction model serves as input for configuring the building's operational optimization. The prediction model produces a forecast of expected output from a PV system based on environmental factors. The detailed input/output for both prediction and optimization models are summarized in Table 1.  
First, three prediction models were assessed and analyzed on their performance on PV generation data from Berlin, Germany, using the PVWatts API [23]. The prediction models chosen were ARIMA, support vector regression (SVR), and a feedforward neural network (FNN). To maintain consistency and accurate comparisons, the same input data were used across all models. The input data used in the model were beam irradiance, diffuse irradiance, ambient temperature, wind speed, and date and time. The output parameter was the output power of the PV system.  
After testing the three chosen models and gathering their actual and predicted output, the following testing error metrics, including mean absolute error (MAE), root mean squared error (RMSE), and normalized root mean squared error (nRMSE), are calculated for each prediction model. To better evaluate the developed models, these metrics are also compared among one-day, three-day, and seven-day predictions. This study will concentrate on the results for the one and three-day models, as the seven-day model was included solely to demonstrate the scalability of the prediction and optimization model over a longer time frame.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model Type** & **Inputs** & **Outputs** \\ \hline \multirow{4}{*}{Prediction} & City’s PV site generation & \multirow{4}{*}{Predictions for 1, 3, and 7 days} \\  & Electric demands & & \\  & Cooling demands & & \\  & Heating demands & & \\ \hline \multirow{4}{*}{Optimization} & Operational cost of DGs & \multirow{4}{*}{Setpoint of DGs} \\  & Operation boundary of DGs & & \\ \cline{1-1}  & Load demand & & ESS \\ \hline \hline \end{tabular}
\end{table}
Table 1: Framework parameters.  
Figure 1: Energy building systems.  
Regarding the optimization model, we developed a MILP-based multi-objective optimization model to find the most efficient way to operate the energy system to minimize costs while at the same time ensuring that all energy demands from electricity, heating, and cooling are met. Decision variables such as the generation output of the boiler, heat pump, DGs, and chillers are the quantities that need to be optimized. To ensure that optimal results are achieved by the model, power constraints were implemented. To find the most efficient way to operate, the optimization model will explore many combinations of decision variable values to end up with the smallest possible cost.  
The project framework was developed to consider the variability present in environmental parameters across different locations and climate zones, making it adaptable for real-world applications. This adaptability allows the model to take in data specific to an environment, retrain, and produce updated predictions suited to the building or environment's unique conditions. Despite the uncertainty in climate and renewable energy generation, the option for continuous model retraining helps to increase the reliability of its predictions for both power generation and operational costs. This energy management framework would be particularly beneficial for commercial buildings, ideally the ones equipped with rooftop solar/PV panels. Due to the model's reasonable basis for scheduling energy coverage, the commercial buildings would gain important insights into efficiently meeting power demands.