# Potential of Onshore Wind Turbine Inertia in Decarbonising the Future Irish Energy System
## 2 Methodology
### Dispatch Model Formulation  
The hereafter presented methods are created applying the novel modelling tool Open Inertia Modelling (OpInMod) [20]. OpInMod is an open source modelling tool extending the basic functionalites of the open energy modeling framework (oemof) package solph [21; 22]. oemof is developed considering a strict open source and non-proprietary philosophy and is implemented in python [21]. Thus, scientific principles like reproducibility are transparency fulfilled [23; 24; 25; 26]. Additionally, comparing oemof to the proprietary software solutions which have been applied in the reviewed literature [13; 14; 15; 16], its free of charge availability makes it easy to access [21]. In general, oemof, and therefore OpInMod as well, allows for an easy representation of energy systems applying a graph structure consisting of buses and components [21]. Components are used to represent power plants, variable RES units or energy storage units in an energy system model [21]. Buses and components are connected via edges representing an energy flow [21]. Components hold basic attributes of the represented energy system component. For example, a representation of a power plant would hold attributes such as the variable costs, the installed capacity or the power plants efficiency. OpInMod extends oemof.solph functionality to depict different sources of inertia as well as creating additional constraints when modelling system inertia. The before example of a power plant representation would in OpInMod be extended by attributes such as the type of inertia source (synchronous inertia or SI), the generators inertia constant or costs associated with the provision of inertia. OpInMod is published under MIT License and available via Github [27] and zenodo [28]  
Figure 1 provides an schematic overview of the modelling process of a unit commitment and economic inertia dispatch model created with OpInMod. The process can be devided in three sub processes. In the first sub process, named preperation and initialisa  
tion, all packages needed are imported as well as the input files. Next, the energy system is created, using components and buses. In the modelling sub process the energy system representation is translated into an optmisation problem, including all sets of constraints, based on python's optmisation package pyomo [29]. The optimisation problem is solved by a freely selectable solver. In Figure 1 the COIN OR (CBC) solver, GNU Linear Programming Kit (GLPK) solver or gurobi solver are listed as examples. The post processing step of the solver results is the last in the modelling sub process. In the third and last sub process, the results are exported and can be further analysed. The optimisation function depicted in Equation (5) and created by OpInMod is set to minimise the overall system costs subjected to supply power demand for each time step. The first term describes the flow costs by the variable costs of the generator, \(c_{g}^{xc}\) and the flow variable, \(x_{g}^{flow}\)[22]. The second term of the function describes the inertia related costs. The generators moment of inertia is represented by \(x_{g}^{inettia}\), the costs of the generator  
Figure 1: Schematic overview of the full modelling process applying OpInMod. In the preperation and initialisation part of the process, necessary data is imported and the energy system is created using eomof.solph’s base components. The base components are extended by attributes and functions to depict synchronous and SI. In the modelling part of the process the optimisation problem, including OpInMod’s inertia constraints, is created, solved by an external solver and the results are processed and prepared for the output. In the last section of the process, results are exported and can be further analysed as needed. providing inertia by \(c_{g}^{ic}\). Traditionally, a synchronously connected rotating mass provides its full inertia to the power system as long as it is connected. This is reflected by the binary variable \(x_{g}^{source\_inertia}\).