# Potential of Onshore Wind Turbine Inertia in Decarbonising the Future Irish Energy System
## 4 Results
In the top subplot the first six hours of the day are characterised by minor RES feed-in. During these hours, demand is mainly covered by pump storage units, imports, natural gas fired power plants as well as an increasing share of onshore wind feed-in. Electric power flow imports and exports at the same time indicate that the Irish system in this case acts as a transfer system. In other words, electrical energy is transferred from France to Great Britain (or in opposite direction) using the Irish transmission capacities. With increasing onshore wind feed-in, a natural gas fired power plants gets disconnected from the system at a time of 04:00. This results in a downward step in the accumulated provided synchronous inertia by natural gas fired power plants area in the bottom subplot. While feed-in from solar PV and onshore WTs increases during the day and surpasses power demand, feed-in from pump storage units, hydro plants and gas fired power plants remain constant at minimum stable operation due to the minimum stable operation constraint described by Inequation (8). Inertia by such units is needed to satisfy the minimum system inertia constraint described by Inequation (7). Thus, to balance power generation and consumption, power is exported and energy is stored by pump storage units. With decreasing feed-in from solar PV, feed-in from storage units increases. However, since no additional synchronous generator is connected to the power system, provided inertia remains constant throughout the remaining time period. Since feed-in from WTs is high throughout the remaining day and power demand is surpassed by the accumulated feed-in, power exports remain high too. In conclusion, the before described base scenario demonstrates the influence of the minimum system inertia constraints (see Inequations (6) and (7)). While feed-in from WTs and PV is high throughout the second half of the example time series and surpassing power demand, feed-in from synchronously connected generators such as from gas fired power plants, hydro plants and pump storage units remain at their minimum stable operation  
Figure 3: Illustration of a 24 h time series of the base scenario. The top subplot depicts electric power flow results and the bottom subplot flow provided inertia  
points to provide sufficient inertia. This results in exports and electrical energy being stored in energy storage units. Figure 4 depicts results of the exact same time period as depicted in Figure 3, but for the parameter combination \(H_{dem}\) of 3.5 s and a ROCOF threshold of 2 Hz/s. Hence in this case, WTs provide SI. First 12 h of the time period are almost identical. Minor differences, compared to Figure 3, are visible in the bottom subplot since SI is provided by WTs in the time between 4:00 to 5:00 and 6:00 to 9:00. Moreover, SI provision increases from 11:00 onwards. To satisfy ther overall minimum system inertia constraint (see Inequation (7), natural gas fired power plants, hydro units and pump storage plants are connected to the power system and operate at minimum stable operation. At 12:00 wind SI provision increases significantly. Thus, SI provision from WTs increases. This results in the disconnection of gas fired power plants in the time between 12:00 to 15:00. The system synchronous inertia constraint (see Inequation (6)) is met by the pump storage plants and hydro units provided inertia as well as the provided inertia from gas fired power plants which are disconnected stepwise while feed-in from WTs increases. From 15:00 onwards, the minimum synchronous inertia constraint (see Inequation (6)) can solely be satisfied by the accumulated synchronous inertia from hydro and pump storage plants. Accompanied by sufficient SI from WTs, the overall system inertia constraint (see Inequation (7) is satisfied. Concluding the model outcome depicted in Figure 4, the beneficial influence of the SI provision by WTs is visible.