## 6 Case Studies
### Analysis of the Influence of Robust Model on System Reliability  
In order to analyze the impact of the robust planning model on system reliability in the planning stage, this paper introduces two evaluation indicators, namely, load shedding cost _C\({}_{LL}\)_ and discarding wind (discarding light) cost _C\({}_{LW}\)_. Because the influence of the fluctuation of light intensity on the system is similar to that of wind speed, this paper only takes wind speed fluctuation and load fluctuation as examples for analysis. The formulas of load shedding cost _C\({}_{LL}\)_ and discarding wind cost _C\({}_{LW}\)_ are as follows:  
\[C_{LL}=\sum_{s\in S}\sum_{t\in T}\Delta t\sum_{j\in B^{\text{load}}}c_{ENS}p_{ j,s,t}^{ENS} \tag{25}\]  
where \(S\) is the scene set. \(T\) is the planning period set. _B\({}_{load}\)_ is a collection of load nodes. _\(\Delta t\)_ is the time interval. _c\({}_{ENS}\)_ is the unit price of load loss penalty. _p\({}_{j,s,t}^{ENS}\)_ is the active power of load loss. \[C_{LW}=\sum_{s\in S}\sum_{t\in T}\Delta t\sum_{j\in B^{\text{wind}}}c_{WNS}p_{ j,s,t}^{WNS} \tag{26}\]  
where _B\({}_{wind}\)_ is a collection of nodes for installing fans; _c\({}_{WNS}\)_ is the penalty unit price for wind abandonment; _p\({}_{j,s,t}^{WNS}\)_ is the active power of abandoned wind. When the load and wind speed increase by 10%, 20% and 30%, respectively. The calculation results of _C\({}_{LL}\)_ and _C\({}_{LW}\)_ are shown in Table 2 (_c\({}_{ENS}\)_ is taken as 0.6 USD/(kW \(\bullet\) h), _c\({}_{WNS}\)_ as 0.4 USD/(kW \(\bullet\) h)). It can be seen from Table 2 that when the load fluctuates by 10%, 20% and 30%, respectively, the load loss costs of the robust planning model built in this paper are, respectively, USD 26,520,000, USD 520,000 and USD 770,000, which are correspondingly reduced by USD 2000, USD 3000, and USD 9000 compared with the deterministic planning model. It can be concluded that the robust programming model built in this paper can ensure that the system has higher security and reliability, can adapt to the impact of load fluctuation, and can ensure the safe use of power by the load. With the increase in load fluctuation, the advantages of the model against disturbance become more prominent. When the wind speed fluctuates by 10%, 20% and 30%, respectively, the wind abandonment cost of the robust planning model built is USD 64,000, USD 111,000, and USD 171,000, respectively. Compared with the deterministic planning model, the wind abandonment cost is significantly reduced, with a corresponding reduction of USD 445,000, USD 455,000, and USD 451,000. It can be concluded that the robust planning model built in this paper is more suitable for the characteristics of high penetration and large uncertainty of ADN clean energy, can use clean energy more efficiently, and conforms to the development trend of the future distribution network. In order to further verify the effectiveness of the proposed method, the computation time of a planning model for different cases is represented, which is shown in Table 3. \begin{table}
\begin{tabular}{c c c c c} \hline  & \multicolumn{2}{c}{**Load Shedding Cost**} & \multicolumn{2}{c}{**Discarding Wind Cost**} \\  & \multicolumn{2}{c}{**(10\({}^{4}\) USD)**} & \multicolumn{2}{c}{**(10\({}^{4}\) USD)**} \\ \hline
**Range** & **Robust Model** & **Deterministic Model** & **Robust Model** & **Deterministic Model** \\ \hline
10\% & 26.00 & 26.20 & 6.40 & 50.90 \\
20\% & 52.00 & 52.30 & 11.10 & 56.60 \\
30\% & 77.00 & 77.90 & 17.10 & 62.20 \\ \hline \end{tabular}
\end{table} 
Table 2: Cost under different load and wind speed fluctuation. It can be seen from Table 3 that the computation times of Case 1 and Case 2 are relatively short because both cases adopt deterministic models and only complete the planning under a basic scene of \"wind speed-light intensity-load\".