## 5 Simulation Examples
### Examples with No Consideration of Uncertainties
#### 5.1.3 Example 3--Response to Real Weather Forecast Data  
In this example, the integration of renewable energy sources and battery systems will be explored within a single network topology. It is important to note that renewable energy sources cannot consistently provide 100% of the required energy due to grid stability considerations and weather-related variations. Typically, renewables can cover approximately 30-40% of the total energy demand [29; 57]. The remaining energy can be stored in battery systems for later use. The types of generators in this topology are the same as in the previous case. A business case on energy network stability with renewable sources and BESS integration is addressed here. For simplicity, a maximum renewable energy coverage will be set as 30% of the total load (denoted as \(P_{\mathrm{D}}\)). Any excess production beyond this limit will be stored in BESS for future use. This condition corresponds to \(X_{\mathrm{level}}=30\%=0.3\), as discussed in Section 3. Figure 10 shows the network topology for this example. Vertices 1 and 2 are **Type I** generators. Vertex 3 is **Type II** generator, and vertex 4 is **Type III** generator. Vertex 5 denotes solar power plant. Vertex 6 represents the wind farm, and vertex 7 denotes BESS. The parameters of the generators remained unchanged again. The weight matrix \(W\) is set according to the Equation (29). The weather data stated in (40) were linearly interpolated to obtain 86,400 samples. Acquired data in this way were used as input for Sections 4.1.1 and 4.1.2 from which the actual power provided at a distinct moment was calculated. The BESS charge and discharge parameters are considered in the same way as in the previous Example 2 (Section 5.1.2). The initial battery capacity will be set as \(E_{b}^{0}=50\) kW again. Total demand was set as \(P_{\mathrm{D}}=1200\) kW. Table 5 described the initialization of the algorithm. Figure 9: Example 2 results for BESS capacity \(E_{b_{i}}(t)\) and fuel price \(\mu(t)\). Speed of the wind and sun power values from 24 h forecast were taken from [27]. \[ \begin{split} u&=[2.0,2.3,3.2,5.8,5.9,7.1,5.2,4.8,6.8,8.2,7.7,7.2,6.5\\ &\qquad 7.3,6.8,6.1,5.6,6.7,4.1,3.5,2.5,1.6,1.65,1.9,2.8]\text{m/s} \\ S_{t}&=[0,0,0,0,0,0,0,0.01,0.045,0.12,0.16,0.27,0.05,0.03\\ &\qquad 0.22,0.18,0.07,0.04,0.005,0.02,0.01,0,0,0,0,0]\text{kW/m}^{2} \end{split}  \tag{40}\]  
For a better illustration of this example, the fuel price for all sources \(\mu_{c_{i}}\), \(\mu_{s,w_{i}}\) and \(\mu_{b_{i}}\) will be constant throughout the simulation. However, it is not a problem to supplement this example with their changes like in the previous example. Figure 11 shows the reactions of the algorithm to incorporating renewable sources and BESS together. The first graph shows the estimated incremental cost \(\lambda_{i}\), the second output power \(P_{i}\), and the third battery system capacity status. The results indicate that maximizing the use of renewable sources in the network reduces the overall incremental price. The lowest price, 8.1801 USD/kWh, was observed during two periods: from \(k=30\),953 s to 41,176 s and then from \(k=48\),527 s to 54,455 s. In contrast, at the end of the simulation, when renewable resources were minimal and BESS was depleted, the price was 8.5476 USD/kWh. It is important to note that we evaluated steady-state values of the algorithm, excluding transient events during input changes as the minimum achieved values. Additionally, the BESS was in discharge mode until step \(k=17\),351 s. Subsequent discharge sequences occurred from \(k=41\),761 s to 48,522 s and then from \(k=54\),456 s to 64,159 s. Charging sequences for the BESS occurred from \(k=30\),947 s to 41,760 s and from \(k=48\),523 s to 54,455 s.  
This example confirmed the feasibility of applying the described algorithm using real weather forecast data.