Renewables in the European power system and the impact on system rotational inertia

Generation from synchronous machines in European power systems is decreasing as variable renewable energy penetration increases. Appropriate levels of system rotational inertia to ensure system stability, previously inherent in synchronous areas across Europe, can no longer be assumed. This work investi- gated the impact different levels of minimum inertia constraint have in Europe and in each synchronous area. Two scenarios with divergent decarbonisation ambitions were simulated for the year 2030 using a unit commitment and economic dispatch model. The key ﬁ ndings show that an increasing inertia constraint elevates total generation costs, variable renewable energy curtailment and carbon dioxide emissions across Europe for an ambitious decarbonisation scenario. When inertia constraints were applied to the contrasting scenario with a low decarbonisation ambition, decreases in carbon dioxide emissions of up to 49% were observed in some synchronous areas where the constraint was frequently active. The work also scrutinised the spread of inertia in the large synchronous area of Continental Europe. It emerged that some countries are likely to experience periods of low inertia even if an inertia constraint is applied at synchronous area level.


Introduction
The rapid and significant growth of renewable power capacity across the European Union (EU) over the last decade will continue even faster as Member States strive to reach 2030 and 2050 renewable energy and greenhouse gas emissions reductions targets [1,2]. This is forcing system operators to re-evaluate how power systems will be operated in the future as large inertia-providing synchronous machines are supplanted by variable renewable energy (VRE) sources. Intermittent sources such as wind and solar provide very limited to no rotational inertia depending on the device technology. 1 Without supplementary supports such as frequency triggered battery energy storage systems (BESS), insufficient rotational system inertia can lead to extreme frequency deviations including high rates of change of frequency (ROCOF) in the event of an imbalance between generation and demand. A high ROCOF event that exceeds the prescribed tolerances could lead to involuntary shedding of customer load, interconnectors and generation. This could ultimately result in a total system blackout.
Managing system frequency in the face of reducing rotational system inertia (i.e. low inertia systems) to avoid such high ROCOF events is considered one of the largest future challenges for power system operators [3,4].
Dynamic studies examining the impact of increased VRE on power system stability examine aspects such as frequency, voltage and angular stability in the immediate aftermath of a system disturbance. The output of an hourly dispatch model provided some of the inputs to the dynamic studies in Ireland (i.e. Republic of Ireland and Northern Ireland) [5] and Great Britain (GB) [6]. Another investigation utilised historical system data following disturbance events to tune the parameters of a dynamic model for the Nordic region [7]. The subsequent model output was compared to newly recorded disturbance events to evaluate its performance. Pagnier et al. investigated the locational aspect of inertia and the impact on fault propagation for Continental Europe [8]. These studies capture the stability effects of particular ROCOF levels or VRE penetration levels but they do not capture the economic and environmental impacts.
The use of a unit commitment and economic dispatch tool provides a complementary way to assess the broader impact of potential strategies to mitigate inertia decline as VRE penetration increases over a longer timeframe. Some studies have considered a constraint to ensure that at all times a certain percentage of generation is synchronous generation to address inertia concerns [9,10]. This type of constraint does not take into account the number and type of generation units required to be synchronised to provide inertia and therefore does not necessarily ensure frequency stability. Daly et al. adopt a more robust approach to determine the costs and impacts of maintaining minimum inertia levels on the Irish power system by determining the amount of rotational inertia required to limit ROCOF to a particular level [11]. By focusing only on Ireland, this work does not capture the impacts of neighbouring systems on each other. This may be significant when one considers the correlation between Ireland and GB's wind power production [12]. Similarly, Johnson et al. used a minimum inertia constraint to determine the impacts of plant closures with various levels of VRE penetration on the stability of the Electric Reliability Council of Texas (ERCOT) system [13]. As part of a broader analysis of EU policy, Collins et al. provided a high-level overview of the impact of inertia constraints at synchronous area level in Europe for one decarbonisation scenario and a single ROCOF level of 0.75 Hz/s [14]. Unlike this work, understanding the impacts of maintaining a minimum inertia level to limit ROCOF to a particular level was not the sole focus of that work and the depth of analysis reflects this.
This study adds to the literature by providing a detailed comparison of two different levels of ROCOF (0.5 Hz/s and 1 Hz/s) for a pair of contrasting decarbonisation scenarios. By considering Europe and each synchronous area in Europe, this work captures the effect neighbouring synchronous areas have on each other when the minimum inertia constraints are applied. Using a unit commitment and economic dispatch model, with constraints to limit ROCOF for prescribed contingency events, the impact on interchange, curtailment of VRE, carbon dioxide (CO2) emissions and production costs in each synchronous area and across Europe are assessed. The scenarios considered, based on the European Network of Transmission System Operators of Electricity's (ENTSO-E) official projections for long-term transmission capacity expansion in Europe, make this work representative of the range of challenges that will be encountered on the continent. The work also explored the distribution of inertia in the large synchronous area of Continental Europe (CE) revealing that some countries will Terawatt hour experience periods of no or very low inertia if regional mitigation strategies are not employed. This paper is organised in five sections. In section 2, the context and the progress made to date in addressing the inertia challenge is reviewed/summarised for Europe. In section 3, the methodology adopted and assumptions used for carrying out the studies are described. In section 4, the results are presented and analysed, followed by conclusions and future work in sections 5 and 6.

Context and progress to date
This section provides an overview of how inertia is currently being estimated/measured by ENTSOE members, the factors that can influence the level of inertia on a power system, possible solutions to the inertia challenge and the legislative efforts in Europe to address inertia concerns.

Inertia and how it is estimated currently
The stored kinetic energy in a synchronous machine's rotating mass provides inertia, which resists changes in the speed of the machine. The inertia constant of a synchronous machineH, measured in seconds, is given by the following equation: (1) where E k;m is the kinetic energy of the machine at rated speed in MWs (megawatt seconds) and S m is the generator rated power in MVA [15]. A power system can be considered to act similar to a giant synchronous machine where the inertia resists changes in frequency of the power system. Similar to equation (1) the system inertia constantH sys , is then the stored kinetic energy in the system divided by the apparent power in the system;S sys . The stored kinetic energy in the system can be approximated as the sum of the stored kinetic energy provided by each synchronous generator online in that system [3]. Using equation (1) the inertia constant of the system, measured in seconds (s), can be calculated as follows: For the purpose of this paper, it is appropriate to represent the inertia of a power system in megawatt seconds (i.e. the stored kinetic energy of the system) rather than seconds as per equation (2). For the rest of this paper when the term inertia is used it can be assumed that it refers to the meaning as per equation (3) measured in megawatt seconds.
The standard approach to estimating the inertia of a power system in real time has been to aggregate the inertia provided by each online synchronous machine. A list of some typical values are shown in Table 4 [16]. This is the approach taken by Transmission System Operators (TSO) in Ireland, Denmark, Finland, GB, Norway and Sweden. Some types of electrical load such as synchronous motors can also provide inertia. Generally, the inertial contribution from electrical load is ignored as system operators may not have telemetry on that load and it is normally relatively small [7].
Following a successful trial in 2017 in the United Kingdom (UK), National Grid UK (NGUK) is moving towards direct inertia measurement. This involves creating a miniscule frequency variation of 0.0005Hz, which is measured at various locations around the grid, and the results analysed in a cloud-based analytics server [17]. Other TSO may adopt a similar approach in time, as the estimation method based only on large synchronous generators becomes less relevant. With increasing levels of distributed generation, particularly behind the meter, or embedded in distribution systems, it is becoming increasingly difficult to fully assess which generators besides the large synchronous generators are contributing to system inertia [7]. This is likely to become even more challenging as consumers and prosumers assume a more active role within the electricity market [18].

Factors that can affect inertia
Generation mix and interconnection to other synchronous systems can all affect the inertia available within a synchronous system. A high percentage of renewable energy in the balancing mix does not automatically result in an inertia issue. This is evident in the Nordic synchronous area where a large amount of renewable energy is provided by hydro-generation. However, a high percentage of VRE can result in reducing inertia, as is the case on the island of Ireland. Interconnection to other jurisdictions also influences the inertia level. Imports via high voltage direct current (HVDC) interconnection can replace generation from synchronous machines, while exports can sometimes allow headroom for additional synchronous generation. To account for this an operational metric is utilised by the TSO in the Ireland synchronous area, which includes the Republic of Ireland and Northern Ireland, known as System Non-Synchronous Penetration (SNSP) [19].
where NSG is non-synchronous generation in MW, NI is net imports in MW, SD is system demand in MW, and NEis net exports in MW. Ireland, out of necessity, has been leading the way for Europe in identifying solutions to integrate higher levels of non-synchronous generation. This SNSP metric is used to identify the amount of nonsynchronous generation that can be permitted on the system at any one time while ensuring system stability. Following a successful trial period, the permitted SNSP in Ireland is currently 65% [20] making it the "first in the world to reach this level" [21]. There are plans to increase this by 5% each year to a maximum of 75% by 2020 [22]. Monitoring this metric alone is not sufficient to maintain stability so a minimum inertia requirement of 23,000 MW at all times is also in force in Ireland [20].

Solutions to the inertia challenge
In the 'System Needs Analysis' for the future European power system, ENTSOE highlights a number of areas that need further research that could mitigate the frequency management challenges as renewable penetration increases. It includes constraining generation from VRE to allow generation providing rotational inertia into the balancing mix, the limitation of cross border flows between small and large synchronous areas for dynamic reasons and using synchronous compensators, as well as grid forming converters and fast frequency response (FFR) amongst other solutions [4].
Provision of FFR from different technology types is discussed in depth by Karbouj et al. [23]. Fast frequency response and synthetic inertia are often conflated. While there is no consensus in the literature on the definition of synthetic inertia, a distinction between synthetic inertial response and FFR is made by Eriksson et al. [24] who also presents a strict definition of synthetic inertial response. Synthetic inertial response means a response that emulates synchronous inertia by responding in proportion to ROCOF and FFR is any other type of fast controlled response [24]. Technologies that have the capability to provide a synthetic inertial response as per Eriksson et al.'s definition are being developed but they have yet to reach maturity. Concerns remain regarding their ability to respond in the required timeframe after detecting a frequency event [25], although the recently concluded RESERVE project demonstrates that this is an active area of research [26e28]. This project also serves to highlight that with the growing amount of distributed generation inertia and control solutions may be provided at distribution level rather than transmission level, which has been the traditional approach.
Some TSO are examining and implementing alternative methods of minimising frequency disturbances. Common methods under investigation include energy storage, modifying system equipment and grid codes to tolerate higher ROCOF levels and incentivising more flexible operation of synchronous machines using ancillary services [25]. EirGrid, the TSO in Ireland, has introduced a new range of ancillary services that complement system rotational inertia to limit ROCOF to facilitate the high level of SNSP [29]. In GB energy storage has been introduced [30]. In Denmark, additional system rotational inertia is achieved by utilising synchronous condensers. These provide additional benefits in terms of reactive support and short circuit currents during faults. Furthermore, TSO are actively participating in research and trials through projects such as DINOSAURS [31], MIGRATE [32] and EU-SysFlex [33] to find workable solutions.

Forthcoming european legislation on inertia
The legislative package 'Clean Energy for all Europeans', also known as the 'Winter Package', provides for consumer and communities to be active participants that can buy from and sell to electricity markets [34]. It also introduces changes for TSO and how they interact and co-operate with each other on a range of issues including inertia. Members of ENTSO-E have prepared for these changes through amendments to network codes. Article 39 of the 'Network Code on System Operation' (NCSO) requires TSO to participate in a study of their relevant synchronous area(s) to determine if a minimum inertia level or an alternative should be prescribed. If a minimum inertia level is required, the relevant TSO must jointly agree a methodology for defining the minimum inertia level for that area, and each TSO is then responsible for maintaining the required proportion of that minimum inertia level within its area of control [35]. Table 1 below shows which synchronous areas in Europe require minimum inertia levels currently as indicated by their representatives to ENTSOE [36,37]. It should be noted that the assessment of the Baltic States (i.e. Estonia, Latvia and Lithuania) was based on the present strong interconnection with the Integrated/Unified Power System (IPS/UPS) of Russia and Belarus. There are plans by the European Commission (EC) to remove the energy isolation of the Baltic States from the Belarus, Russia, Estonia, Latvia and Lithuania (i.e. BRELL) ring and integrate the Baltic States to the CE synchronous area both in terms of technical standards and market frameworks [38].

Methodology
The methodology used in this study implemented minimum inertia constraints in Europe in order to explore the impact on total generation costs, VRE curtailment and CO 2 emissions. It is described in this section. This is one proven solution to address reducing inertia as VRE penetration increases that is readily implementable. The approach adopted in this study was to utilise a unit commitment and economic dispatch, set up for contrasting decarbonisation scenarios for the year 2030. The same method for estimating total system rotational inertia in real time operation in most power systems is used. The total system inertia is assumed to be the sum of rotational inertia available from each online synchronous generator. Static constraints to maintain the system rotational inertia for a synchronous area above the amounts required to ensure ROCOF is limited, as defined in Daly et al. [11], are then applied and the outcomes are then examined: Equation (5) where RI sys is the system rotational inertia,f 0 is the nominal system frequency P max is the largest infeed and Lim ROCOF is the ROCOF limit set for the synchronous area.

Pan european model
A pan-European electricity dispatch test system with hourly resolution developed in an Integrated Energy Model (IEM) for previous works [14,39] in PLEXOS ® Simulation Software [40] has provided the basis for this study. Each Member State is modelled as a node with transmission capacity between countries modified to the ENTSO-E's Reference Capacities for 2030 [41] similar to some of the other studies [14,39]. The objective function is set to minimize the overall generation cost across the EU to meet demand, subject to operational and technical characteristics, while co-optimising thermal and renewable generation. The objective function considers operational costs in the form of fuel costs, carbon costs, and fixed unit start-up costs; the model equations can be found in Refs. [39]. The optimization problem, in the form of a mixed integer linear programme (MILP), is solved for each hour of a 24-h rolling horizon with a 6-h look ahead for the year studied. An overview of the objective function with the main constraint under focus in this study is provided in Table 2.

Base case scenarios
The two base case scenarios considered in this study are informed by the ENTSO-E Visions for 2030 used to inform the 'ENTSO-E Ten-Year Network Development Plan', which represent a wide range of energy system decarbonisation with varying levels of electrification heating and transport sectors, and demand response [41]. The IEM model inputs of hourly electricity demand, installed generation capacity mix, and fuel and CO2 pricing in 2030 used to inform the two base case scenarios, Scenario 1 and 2, are taken from the ENTSO-E decarbonisation visions an overview of which is provided in Table 3.
As illustrated in Fig. 1 Vision 1 'Slowest Progress' and Vision 4 'European Green Revolution' contrast in terms of decarbonisation ambition [41]. In Scenario 1, nuclear still features strongly in many countries while in Scenario 2 nuclear capacity reduces in most countries with the exception of GB.

Renewable generation profiles
The VRE implemented in the IEM in the context of this work are wind and solar photovoltaic (PV) generation only. The synthesised hourly output from each Member States wind and solar PV generation portfolio derived from the EMHIRES dataset [42] for the year 1989 was chosen. This was found to be the best representative year for the long run average of European wind and solar profiles [43]. Historic hydro generation profiles with a monthly resolution for the year 2012 provided by ENTSO-E for each individual member state of the EU-28, Switzerland and Norway were scaled appropriately for this study.

Generator characteristics
The main generator characteristics used are detailed in Table 4, which are based on standard generator characteristics used in previous studies [14,39]. Each generator type was assigned a particular value for its stored rotational energy (MWs) [16].
For the purpose of this study, the contribution to inertia from wind turbines is considered to be zero.

Model runs
Three modelling run iterations were undertaken for each base case with different levels of constraints. Firstly, no minimum inertia constraints were applied. The purpose of this run, which effectively ignores the stability issues associated with low inertia systems, was to identify which synchronous areas would require constraints to limit ROCOF. In the second and third runs, constraints are applied to limit ROCOF to 0.5 Hz/s and 1 Hz/s respectively for the loss of the largest infeed for the relevant synchronous grids in Europe as identified by the first run. The synchronous grids in Europe considered were Ireland, GB (England, Scotland and Wales), the Baltic states (i.e. Estonia, Latvia and Lithuania), the Nordic states (i.e. Finland, Norway, and Sweden) and the CE grid (i.e. Austrian, Belgium, Bulgaria, Croatia, Czech Republic, Denmark, France, Germany, Greece, Hungary, Italy, Luxembourg, Netherlands, Poland, Portugal, Romania, Slovakia, Slovenia, and Spain). For most synchronous areas, the largest infeed is considered to be the maximum capacity of the largest generator or cross border interconnector. The exception to this is CE, where the largest loss is based on the ENTSO-E definition of the 'Reference Incident' of 3000 MW representing the loss of the two largest nuclear power units within the same power station that can cascade trip for a frequency disturbance [44]. The minimum static levels of inertia required to mitigate the loss of the largest infeed for the two ROCOF levels, calculated as per Equation (1), are provided in Table 5.
As can be seen in Table 5 a ROCOF tolerance of 1 Hz/s halves the required level of system inertia to offset the largest infeed compared to a ROCOF tolerance of 0.5 Hz/s. The selection of 0.5 Hz/s and 1 Hz/s was influenced by the situation in the synchronous grid in Ireland. The current ROCOF level for the Republic of Ireland is 0.5H/z. However, the TSO, EirGrid, had planned for the ROCOF level to be increased to 1 Hz/s by late 2017 [22], but this is not implemented yet [20].

Assumptions made in the analysis
This study is not intended to replace dynamic studies, rather this  work is intended to complement and provide insights into the impacts of applying inertia constraints over a longer time horizon.
Other issues that will arise from a lack of synchronous machines and a proliferation of inverter connected generation such as reactive support, short circuit currents, harmonics or blackstart capability are not considered. A perfect day-ahead market is assumed across the EU (i.e. no market power or anti-competitive bidding behaviour, thus power stations bid their short-run marginal cost (SRMC)) similar to Deane et al. [45]. The results then reflect the least cost generation dispatch based on marginal cost (MC) rather than the cost resulting from bidding behaviour. Standard generator classes with standard characteristics such as maximum capacities, minimum stable factors, startup costs and the inertia contribution for each generator type are considered. This eliminates the need to obtain detailed technical data for each generator within the countries studied. In this study, the power systems of Malta and Cyprus were excluded as the inertia constraints considered in this study would be overly onerous on such small systems. It was assumed that the power system of the Baltic States consists only of Latvia, Lithuania and Estonia for this study. This reflects the ambition to reduce dependence on the AC interconnectors to the Russian and Belarusian power systems by 2025. Interconnection between countries is included but no transmission network within a country is considered to keep simulation times reasonable. Hence, Denmark is considered to be wholly part of the CE synchronous area whereas in reality part of the Danish power system is within the Nordic synchronous area. Inertia from non-generating sources such as synchronous condensers has not been included as the focus was to ascertain how much inertia would be provided by conventional generation sources in the year 2030 in the absence of any shift in portfolios. Inertia provided by electrical load is ignored as it is normally relatively small.

Limitations
The scope of the study is limited to inertia from conventional generation sources only and thus the potential to provide synthetic inertia and fast frequency response is not included. Therefore, the results reflect a worst-case scenario in terms of inertia provision, albeit somewhat alleviated by the perfect foresight of the IEM model in PLEXOS. The results of this study, particularly in relation to VRE curtailment, are likely to be conservative, as effects caused by congestion due to bottlenecks in transmission systems within countries are not captured and the IEM resolution time may also have an affect. The study considers a static limit only for the minimum inertia requirement in each synchronous area. Daly et al. showed that applying a dynamic inertia requirement for the island of Ireland reduced costs compared to a static inertia requirement [11]. Furthermore, the provision of ancillary services that may reduce minimum inertia requirements has not been considered in the study.

Results & analyses
The scenarios offer divergent decarbonisation ambitions for the European power system and differ in a number of areas including levels of electricity demand, VRE generation capacity and fuel prices. The purpose of the analyses of the results is not to compare these base case scenarios to each other but rather to compare the effect of applying various minimum inertia constraints to each base case. The model is set up to optimise cost rather than VRE curtailment and CO 2 emissions. The CO 2 emissions are captured to some extent within the optimization problem, as the CO 2 price is included in the calculation of total generation costs.

Simulations without an inertia constraint applied
In Fig. 2, the inertia duration curves for each synchronous area in Europe for the unconstrained simulations for each base case scenario are presented. The reference lines show the minimum levels required to minimize ROCOF to 0.5 Hz/s and 1 Hz/s as per Table 5. The curves for the Nordic, CE and GB synchronous areas appear to be quite smooth compared to the curves for the Baltic and Ireland/ Northern Ireland systems, but this is simply due to the scaling of the y-axis.
The model uses perfect foresight and focuses on minimising  total generation costs across Europe as a whole. Therefore, the dispatch will change with the constraints applied. While only indicative as the optimization of constraints will result in a less severe outcome, it is clear from Fig. 2 (a)e(e) that the constraint is likely to have a significant effect on the Baltic states and Ireland synchronous areas and to a lesser extent on the synchronous area of GB. It also shows that the constraints will not be binding for the Nordic region and CE synchronous areas in either scenario. Examining the hourly contribution of kinetic energy from each generation type for the CE and Nordic systems for the base case scenarios provides more insights as shown in Fig. 3 (a) and (b). It is evident that in the Nordic synchronous area hydro generation alone is sufficient to meet the minimum inertia requirement for both Scenario 1 and Scenario 2. Due to the sheer size of the synchronous area and the volume and mix of generators required to meet the system demand, the CE synchronous area also easily surpasses the limits set out in Table 5. Due to these findings, the inertia constraints were applied to the Baltic states, GB and Ireland synchronous areas for subsequent model runs. After each simulation, the hourly stored kinetic energy for the CE and Nordic region was checked to ensure it did not breach the requirements in Table 5 due to the change in dispatch to meet the constraints in the other synchronous areas.

Simulations with inertia constraints to limit ROCOF
The changes in interchange between synchronous areas, total generation costs, VRE curtailment and CO2 emissions relative to the base case that result from applying the constraints are presented in Table 6 and Fig. 4 for Scenario 1 and Table 7 and Fig. 5 for Scenario 2. The results confirm that for the heavily decarbonised Scenario 2, the total generation costs, VRE curtailment and CO 2 emissions increase with increasing inertia constraint for the pan European power system. For a less ambitious scenario, Scenario 1, the results follow the trend for rising total generation costs and VRE curtailment, but a decreasing trend in emissions is observed. In this   scenario, coal is cheaper than gas but a Combined Cycle Gas Turbine (CCGT) contributes twice as much rotational kinetic energy as a solid fuel fired generator ( Table 4). The generation output from coal reduces to allow additional gas fired generation units synchronize for inertia provision to meet the constraint. Gas produces less CO 2 emissions than coal and thus a decrease, albeit small, in CO 2 emissions for this constraint is noted. This shows that minimum inertia constraints are a useful tool to have as the transition to higher penetrations of VREs and power electronic devices accelerates. There will come a point in the transition, however, where the inertia constraints impinge on progress towards a low carbon environment. Thus, better synthetic inertia technologies and the communications systems will support a quicker transition to a low carbon power system. Across Scenario 1 and 2, the trends for the CE and Nordic region are consistent; total generation costs and CO2 emissions reduce with the increasing inertia constraint. In the synchronous areas where the constraint is heavily binding, the constraint causes an increase in generation. Thus, the export required from the CE and Nordic region reduces and generation in the CE and Nordic region reduces. The generation reductions affects fossil fuel fired generation plant and results in reductions in CO 2 emissions in these areas. Curtailment in these areas also increases with the increasing inertia constraint as less power is exported so there is less headroom for VRE generation.
For Ireland, additional hydro and gas generation units mainly provide the additional inertia required to meet the minimum inertia constraint (Fig. 6).
The suggestions of EirGrid [46] and Cuffe et al. [47] hold true for Ireland in this study as total generation costs, VRE curtailment and CO2 emissions increase with increasing minimum inertia constraint in both scenarios. The doubling of minimum inertia constraint results in the total generation costs increasing from 9.7% to 43.4% for Scenario 1 and from 10.8% to 37.5% for Scenario 2, while CO2 emissions increase from 4.3% to 20.2% and from 11.1% to 28.1% for Scenario 1 and 2 respectively.
Due to the interconnected nature of the power systems within Europe, constraints in one synchronous area can affect others. In this work, GB benefits from the heavily binding constraints in Ireland due to the increased exports. Total generation costs, VRE curtailment and CO2 emissions increase in GB also but only for Scenario 2 the more heavily decarbonised scenario (Table 7). Even though the constraint is binding at times in the GB synchronous area in Scenario 1, the total generation costs decrease by 2.6% for the more severe constraint compared to the base case. The constraint in GB does not bind as often as it does in Ireland, GB's neighbour. It results in Ireland generating more electricity to meet this constraint and becoming a net exporter for the most severe constraint examined. The exports to GB from Ireland more than double and GB benefits from this. As shown in Fig. 4, there is a net increase in imports to GB. In fact, the yearly total generation in GB reduces thereby reducing the total generation costs and CO 2 emissions. This is due to reduced production from gas and solids fired generation. However, with Brexit and increased HVDC interconnection between France and Ireland, this may change, leaving GB more isolated and at risk. This is particularly relevant to GB in terms of future generation expansion planning and grid code modifications.
Earlier the analyses showed the availability of large quantities of hydro generation gave the Nordic region a weighty advantage in terms of inertia provision. Similarly, the advantages of generation mix is also observed when the results of the Baltic states are compared to Ireland in Figs. 6 and 7. In the Baltic states, as the constraint increases, additional hydro and gas generation units are synchronised at times to meet the inertia constraint requirement. The Baltic synchronous area has over 5 times the amount of hydro that Ireland has in both scenarios. In Scenario 1, nuclear generation and hydro provide the majority of the required inertia with the rest comprised of biomass and gas fired generation when required. In Scenario 2, nuclear does not form part of the generation mix. This highlights the pivotal role that generation capacity mix plays on the effect a minimum inertia constraint has in a power system.
The practical and grid code limits for ROCOF in the various synchronous areas in Europe vary from 0.25 Hz/s [49] up to 2.5 Hz/s [50]. This study focused on the levels currently set and proposed in Ireland. Increasing the minimum inertia requirement to meet a ROCOF level of 0.5 Hz/s has a considerable effect in Ireland and in the Baltic synchronous area. For example, in the Baltic synchronous area, relaxing the constraint from a 0.5 Hz/s limit to a 1 Hz/s limit would reduce the total generation costs by over 53% for Scenario 1 and 14% for Scenario 2 while CO 2 emissions would reduce by 49% and 11% respectively. The doubling of the inertia constraint had a significant influence in the areas where the constraint was binding in both scenarios. This emphasizes the importance of increasing ROCOF tolerance as much as possible in the path towards achieving cost effective decarbonisation and integration of VRE. Given that this study assumed that the Baltic synchronous area was comprised of Estonia, Latvia and Lithuania only, it emphasizes the importance of undertaking long-term inertia studies for this area. This would help identify if the ROCOF limit currently employed should remain at the same level when it is de-synchronised from the IPS/UPS of Russia and Belarus.
Adopting the same approach to determining the inertia constraint level across each synchronous area in Europe, has resulted in a situation where the constraint is most heavily binding in the smaller synchronous areas. Examining the results from a synchronous area level has revealed that when a constraint is more heavily binding in one synchronous area than its neighbour, it can have a positive outcome for its neighbours. In the next subsection, the results of per-country analyses of the CE synchronous area are presented.

Inertia distribution in the CE synchronous area
In the two base case scenarios considered, there is sufficient inertia within the CE synchronous area as a whole to limit ROCOF to  (Table 8) reveals that sufficient inertia at synchronous area level does not guarantee that sufficient inertia is maintained at a per-country basis at all times.
Countries such as France, with a large nuclear generation portfolio that features regularly in the balancing mix, have an automatic advantage due to the contribution of stored rotational energy per nuclear generation unit ( Table 4). The minimum hourly inertia level in France for all of 2030 in Scenario 1 exceeds the minimum inertia requirement for the entire CE area to limit ROCOF to 0.5 Hz/s. In Scenario 2, which is the more ambitious scenario in terms of the volume of VRE penetration, France also has the highest minimum inertia over the year albeit much lower than in Scenario 1.
As shown in Table 8 the gap between the maximum and minimum in countries such as Spain and Germany is stark. The period when inertia was at its lowest for CE for the entire year was examined to understand how vast the differences in inertia could be between neighbouring countries. Fig. 8 shows the distribution of inertia level by country for Scenario 1 and 2 for the hour where inertia across CE is at its lowest. The inertia from France alone in this period in Scenario 1 is more than sufficient to provide the inertia required for the CE synchronous area for the most severe constraint to limit ROCOF to 0.5 Hz/s. Germany, Portugal and Spain on the other hand provide no inertia. For the period where inertia is at its lowest across CE in Scenario 2, France is still the largest contributor of inertia, at approximately 52 GWs and Spain, Portugal, Italy, Denmark and Germany provide zero inertia.
An obvious area to focus on based on Fig. 8 is the Iberian Peninsula, which in both scenarios has zero inertia. Although there are plans to increase interconnection to France, the peninsula is still poorly interconnected. Bearing in mind that the major blackout experienced in Europe in 2006 was a result of the system splitting into smaller unbalanced isolated systems [48], system splits are credible contingencies. Without the application of a minimum inertia level on the Iberian Peninsula, such a contingency would have dire consequences. This scrutiny of the CE area revealed that even though the requirement at a synchronous area level was met, localised deficiencies could exist. Examining inertia at a more localised level in large synchronous areas such as CE is essential as the penetration of VRE increases. This demonstrates the limitations of considering a minimum inertia requirement at a synchronous area level as a proxy for system stability without having first conducted a complementary dynamic study of the area. The requirement alone does not consider the physical locations of the inertia providers within the synchronous area and therefore does not ensure frequency stability in the event of a contingency such as a system split.
The inertia providers considered in this piece of work were limited to large synchronous generators and did not capture the inertia from other sources similar to the inertia estimation methods employed by many TSO. Minimum inertia constraints provide a useful transition tool as confirmed by this study, however, to gain the highest benefit in terms of CO2 emissions reductions it is essential that the TSO utilise advanced methods of calculating or measuring real time inertia. Real time inertia monitoring would flag situations where there are inertia deficits. It would also ensure that the contribution to system inertia from all sources is captured thereby reducing the situations where synchronous generation is constrained on for inertia reasons. Furthermore, if the TSO provide transparent plans for funding future ancillary services it may result in the emergence of new inertia providers at a more rapid pace. In addition to inertia [11], explicit payments for ramping [51], balancing [52], primary frequency response [53], fast frequency response [54,55] may be necessary as the needs of the system evolves. EirGrid is the first system operator in Europe to design new ancillary services related to non-synchronous VG integration [56] but it is too early yet to determine how effective it will be.

Conclusion
The increase in renewable generation, particularly VRE, presents challenges in power system operation with decreasing levels of synchronous generation. One of the tools available to TSO is to ensure that there is a minimum level of inertia on the system at all times. Using a unit commitment and economic dispatch model for the year 2030, this work explored the impact of applying minimum inertia levels to five synchronous areas in Europe for two diverging decarbonisation scenarios for two ROCOF limits. The analyses found that the impact of minimum inertia levels were unique to each synchronous area depending on size, generation capacity mix, and interchange with neighbouring synchronous areas. This study Table 8 Minimum, maximum and average hourly inertia values in the CE synchronous area. highlighted the effect of ROCOF limits, the potential consequences of using a minimum inertia requirement at synchronous area level without a complementary dynamic stability study and the importance of TSO adopting real time inertia monitoring. It demonstrated that minimum inertia levels may be useful in the transition to higher penetration levels but will ultimately impede emissions reduction goals if not replaced in a timely manner. Finally, this work also shows the social benefits of coordinated balancing and planning of interconnection across the wider EU in terms of achieving EU emissions reduction and VRE deployment targets.

Future work
The model presented in this work could be extended by the inclusion of additional technology types such as concentrated solar power, energy storage and synchronous condensers. An examination of the technologies and associated costs that may enable a shift away from the use of minimum inertia levels to maintain ROCOF below certain values is also recommended. Additionally, the methodology followed in this study could be used to justify the retrospective application of more recent grid code requirements on ROCOF to older generators in Denmark and Spain for example. A fundamental finding of the work was that minimum inertia requirements should be complemented by dynamic stability studies, thus such a study of CE 'soft linked' to the outputs of this study to investigate further is a natural next step of this work.

CRediT (Contributor Role Taxonomy)
Laura Mehigan is a PhD student at University College Cork. This work forms part of a PhD in Energy Engineering investigating the role decentralization and interconnection in the evolution of future electricity systems.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.