# Day-Ahead PV Generation Scheduling in Incentive Program for Accurate Renewable Forecasting
## 3 Modeling of the PV Generation Scheduling Problem  
### Formulation of PV Generation Scheduling Problem  
This paper proposes a method to determine the optimal PV generation schedule based on characteristics of energy deviation, ESS operation, and PV curtailment. The main objective is to maximize the economic benefit from MP and incentives. Assuming that there are s PV scenarios, Equation (2) related to calculating the net PV generation is modified as follows:  
\[output^{s}_{t}=PV^{s}_{t}-curt^{s}_{t}-ess^{s}_{chg,t}+ess^{s}_{dis,t} \tag{4}\]  
where \(s\) is the number of PV scenarios. The PV curtailment should be determined to be less than PV generation and should not be negative. The physical constraint related to PV curtailment can be expressed as follows:  
\[0\;\leq\;curt^{s}_{t}\;\leq\;PV^{s}_{t} \tag{5}\]  
An hourly PV curtailment rate can be calculated as follows:  
\[r^{s}_{t}=\frac{curt^{s}_{t}}{PV^{s}_{t}}\times 100\% \tag{6}\]  
where \(r^{s}_{t}\) is the hourly PV curtailment rate, which varies by scenario and time. The constraint related to the state of charge (SOC) of ESS can be expressed as follows:  
\[soc^{s}_{t}=soc^{s}_{t-1}+\eta_{chg}\times ess^{s}_{chg,t}-\frac{ess^{s}_{dis, t}}{\eta_{dis}} \tag{7}\]  
where \(soc^{s}_{t}\) is an indicator of the remaining capacity of the ESS at the time \(t\) for scenario \(s\), \(\eta_{chg}\) and \(\eta_{dis}\) are charging and discharging efficiencies of the ESS, respectively. Equation (7) updates the SOC based on the ESS charge and discharge from the previous time step to the current time step. \[ess^{s}_{chg,t}\leq PCS_{max}\times s^{s}_{t} \tag{8}\]  
\[ess^{s}_{dis,t}\leq PCS_{max}\times(1-o^{s}_{t}) \tag{9}\]  
where \(PCS_{max}\) is the capacity of the power conversion system (PCS) of the ESS, and \(o^{s}_{t}\) is a binary variable that distinguishes between the charging and discharging operations of the ESS. Equations (8) and (9) restrict the ESS operation to charging or discharging during each time step. The physical constraints related to ESS operation can be expressed as follows:  
\[0\leq\mathit{ess}^{s}_{\mathit{chg,t}}\leq PV^{s}_{t} \tag{10}\] \[0\leq\mathit{soc}^{s}_{t}\leq SOC_{max}\] (11) \[0\leq\mathit{ess}^{s}_{\mathit{chg,t}}\] (12) \[0\leq\mathit{ess}^{s}_{\mathit{dis,t}} \tag{13}\]  
where \(SOC_{max}\) is the maximum storage capacity of ESS. Equation (10) restricts the ESS to prevent charging beyond the PV generation. Equation (11) imposes a physical constraint by setting the maximum ESS storage capacity as an upper bound for all scenarios and time steps. In addition, it assumes that the values of \(\mathit{ess}^{s}_{\mathit{chg,t}}\) and \(\mathit{ess}^{s}_{\mathit{dis,t}}\) are positive. The energy deviation considering scenarios can be calculated by modifying Equation (1) as follows:  
\[0\;\leq\;curt^{s}_{t}\;\leq\;PV^{s}_{t} \tag{5}\]0  
where \(a_{t}\) is a decision variable of the MILP model. By optimally adjusting the generation schedule to cover all scenarios, the energy deviation is moved within the available range for incentives. The incentive unit price in Figure 1 can be generalized as follows:  
\[i^{s}_{t}=\left\{ \begin{array}{ll}u_{1},&0\%\leq e^{s}_{t}\leq E_{1}\\ u_{2},&E_{1}<e^{s}_{t}\leq E_{2}\\ \vdots&\vdots\\ u_{k},&E_{k-1}<e^{s}_{t}\leq E_{k}\\ \vdots&\vdots\\ u_{K}&E_{K-1}<e^{s}_{t}\leq 100\%\end{array} \right. \tag{15}\]  
where \(u_{k}\) is the incentive unit price, \(E_{k-1}\) and \(E_{k}\) are the lower and upper limits of the energy deviation range corresponding to the incentive unit price. A parameter \(K\) divides the energy deviation (0-100%) into \(K\) intervals, which is the number of intervals in which the energy deviation is accumulated. The user can set parameters \(K\) according to the incentive program. The PV site's daily revenue consisted of energy market sales revenue, renewable energy certificates (REC) revenue, and incentives. The REC can be received when energy is generated from renewable energy sources.