# Potential of Onshore Wind Turbine Inertia in Decarbonising the Future Irish Energy System
## 4 Results
By the second half of the depicted day, gas fired power plants are completely disconnected from the system, since feed-in from onshore WTs, pump storage units, hydro and offshore WTs is high enough to meet power demand. At the same time, the disconnection of the gas fired power plant is only realisable, due to the fact that overall system inertia constraint is satisfied by the provided wind SI. Figure 5 illustrates the provided SI (here represented by the synthetic moment of inertia in kg:m\({}^{2}\)) by dispatched WTs for the demanded inertia constant (\(H_{dem}\)) of 3.5 s and 5 s. The results are illustrated via a histogram plot, where the bars height depicts  
Figure 4: Illustration of a 24 h time series of the parameter combination: ROCOF threshold = 2 Hz/s and demanded inertia constant = 3.5 s. The top subplot depicts electric power flow results and the bottom subplot flow provided inertia. the frequency of occurrence and the x-axis depicts the provided SI. The frequency of occurrence is equal to the number of hours of the moddeled year. The green bars depict the synthetic moment of inertia provided by WTs considering the demanded inertia constant (\(H_{dem}\)) of 3.5 s and the red bars depict the synthetic moment of inertia provided by WTs considering the demanded inertia constant of 5 s. Obviously, for more then 4300 h of the modelled times series no or very little SI is provided. Thus, for the rest of the modelled time series (the accumulated number of the remaining bars), SI is provided by WT. A higher demanded inertia constant results in higher values for the provided synthetic moment of inertia (compare red bars (\(H_{dem}\) = 5 s) to green bars (\(H_{dem}\) = 3.5 s)). Table 4 shows the accumulated CO2 emissions and curtailment results per parameter combination. The second column, depicting the CO2 emissions, indicates that with increasing ROCOF thresholds and higher demanded inertia constants accumulated CO2 emissions decrease significantly. Equation (10) explains how emission savings in column three of Table 4 are calculated. The respective scenario (e.g., ROCOF = 1 Hz/s, \(H_{dem}\) = 3.5 s) results are applied in the numerator of Equation (10). The denominator input is always the result of the base scenario. Increasing the ROCOF threshold up to 2 Hz/s and combining this parameter with an higher \(H_{dem}\), e.g., 5 s, results in CO2 emission savings of 30.99% with respect to the base scenario. Column four in Table 4 shows accumulated WT and PV curtailment. Similar to the accumulated CO2 emission results, with increasing demand for WTs to provide SI by higher ROCOF thresholds, the curtailed energy decreases significantly. Equation (11) explains how curtailed energy reduction in column five of Table 4 is calculated. Curtailment reduction up to 39.72% for a demanded inertia constant of 3.5 s and 39.90% for a demanded inertia constant of 39.00% is achievable. \[reduction\_CO2\_emissions=\frac{overall\_CO2\_emissions_{scenario}}{overall\_CO2\_emissions_{base\_scenario}}\cdot 100 \tag{10}\]  
\[reduction\_curtailment=\frac{overall\_curtailed\_energy_{scenario}}{overall\_ curtailed\_energy_{base\_scenario}}\cdot 100 \tag{11}\]  
Figure 5: Depiction of the synthetic moment of inertia provided by WTs. The green bars depict the synthetic moment of inertia provided by WTs considering the demanded inertia constant (\(H_{dem}\)) of 3.5 s and the red bars depict the synthetic moment of inertia provided by WTs considering the demanded inertia constant of 5 s.  
Table 5 shows results of the overall system costs and cost savings with respect to the provided SI. With increasing demand for WTs to provide SI, accumulated system costs decrease significantly, since less feed-in from fossil power plants running at minimum stable operation (must-run capacities) is needed with the purpose to satisfy minimum system inertia constraints. Equation (12) illustrates how cost savings in column two of Table 4 are calculated.