## 2 Methods
### Two-Stage Risk-Benefit Hedging Calculation Considering Forecast Uncertainty  
In the normal operation of the reservoir, as long as the initial water level of the reservoir does not exceed the flood limit water level, the flood control safety of the reservoir itself and the upstream and downstream protected objects in the planning and design can be guaranteed without increasing the flood control risk. Therefore, the two-stage risk-benefit calculation method caused by forecast uncertainty should be considered in the joint operation of hydropower and photovoltaic. The hedging mechanism of hydropower and photovoltaic joint power generation is mainly reflected in the hedging variables, that is, the complex multi-objective conflict is processed and processed and the hedging relationship is generalized to form a mathematical expression, which provides a basis for the establishment of the hedging model. Taking a two-stage hydropower station and a photovoltaic electric field as an illustration, we illustrate the two-stage hedging dispatching mechanism of the multi-objective of hydropower and photovoltaic. The decision-making process and relevant conventions are shown in Figure 4 and Table 1 for the decision-making variable conventions of combined hydropower and photovoltaic power generation. Figure 3: Rolling updating mechanism of the hydropower and photovoltaic combined generation scheduling model. Combination Forecasting Model Based on VMD-ARMA-DBN Hedging Mechanism Design for Hydropower and Photovoltaic Joint Dispatch  
5.1 Initial Determination of VMD Mode Calculation of Profit and Benefit of Reservoir Pre-Storage Operation  
The advantages and disadvantages of the reservoir's profit goal are expressed by the benefit added value \(B^{-}=0\); the larger the value, the better the profit and benefit. The benefit added value \(B^{+}\) is determined by the size of the pre-storage water \(W\) and there is a direct proportional relationship between them. In order to facilitate the solution of the model, it is transformed into the benefit difference \(B^{-}\); the smaller the value, the better the benefit. At the same time, it is negatively correlated with the pre-storage water \(W\). The normalized calculation formula of the benefit difference \(B^{-}\) is as follows:  
\[B^{-}=\left(1-\frac{W}{W_{N}}\right)^{m} \tag{1}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Stage k** & **Stage 1: Decision Stage \(\Delta T\)** & **Stage 2: Remaining Stage \(\Delta T\)** \\ \hline Forecast water inflow \(Q\) & \(Q_{1}^{a},Q_{1}^{ab},Q_{1}^{b}\) & \(Q_{2}^{a},Q_{2}^{ab},Q_{2}^{b}\) \\ Regulatory decisions \(D\), \(N\) & Reservoir discharge \(D_{1}\) & Reservoir discharge \(D_{2}\), \\  & PV power generation \(N_{1}\) & PV power generation \(N_{2}\) \\ Pre-storage capacity \(W\) & Initial \(W_{0}\), end \(W_{1}\) & Initial \(W_{1}\), end \(W_{2}\) \\ Storage of reservoir \(V\) & Initial \(V_{0}\), end \(V_{1}\) & Initial \(V_{1}\), end \(V_{2}\) \\ Flood control objectives \(R\) & \(R_{1}^{b}\) & \(R_{2}^{b}\) \\ Profitable target \(B\) & \(B\) & \(B\) \\ Combined output target \(G\) & \(G_{1}\) & \(G_{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Decision variables of combined hydropower and photovoltaic power generation. Figure 4: Schematic diagram of multi-objective decision-making in the two-stage for hydropower and photovoltaic joint power generation. where m is the shape coefficient of the curve of the benefit difference \(B^{-}\) changing with pre-storage water \(W\). The difference in benefits between the first and second stages is as follows:  
\[B_{1}^{-}=\left(1-\frac{W_{1}}{W_{N}}\right)^{m} \tag{2}\]  
\[B_{2}^{-}=\left(1-\frac{W_{2}}{W_{N}}\right)^{m} \tag{3}\]  
The change in pre-storage volume \(W\) in the adjustment process is analyzed. If the pre-storage water of the first stage \(W_{1}>0\), the process changes as follows in this case:  
(1) In the future period \(T\), the forecast data do not show a large influx of water.