Battery Energy Storage Contribution to System Adequacy

: The objective of this paper is to evaluate the contribution of energy storage systems to resource adequacy of power systems experiencing increased levels of renewables penetration. To this end, a coherent methodology for the assessment of system capacity adequacy and the calculation of energy storage capacity value is presented, utilizing the Monte Carlo technique. The main focus is on short-duration storage, mainly battery energy storage systems (BESS), whose capacity values are determined for different power and energy conﬁgurations. Alternative operating policies (OPs) are implemented, prioritizing system cost or reliability, to demonstrate the signiﬁcant effect storage management may have on its contribution to system adequacy. A medium-sized island system is used as a study case, applying a mixed integer linear programming (MILP) generation scheduling model to simulate BESS and system operation under each OP, in order to determine capacity contribution and overall performance in terms of renewable energy sources (RES) penetration, system operating cost and BESS lifetime expectancy. This study reveals that BESS contribution to system adequacy can be signiﬁcant (capacity credit values up to ~85%), with energy capacity proving to be the most signiﬁcant parameter. Energy storage may at the same time enhance system reliability, reduce generation cost and support RES integration, provided that it is appropriately managed; a combined reliability-oriented and cost-driven management approach is shown to yield optimal results.


Introduction
Future targets for operation of power systems foresee high penetration of renewable energy sources (RES) as well as gradual decarbonization of the electricity sector. Specifically, for the power systems of non-interconnected islands (NIIs), which are characterized by increased CO 2 emissions and operating costs due to their reliance on oil-fired generation, the elevation of renewables participation in their energy mix in place of existing thermal production is imperative. However, increased penetration of stochastic RES, such as wind and solar generation, substituting dispatchable units, may eventually compromise resource adequacy of these systems.
To date, energy storage introduction is a decisive factor to enable RES uptake in saturated small island grids, where absorption of renewable energy is impeded by technical and security constraints that eventually impose a ceiling to the renewable hosting capacity of such systems [1,2]. Multiple benefits associated with the introduction of storage include the mitigation of RES curtailments, the provision of ancillary services, the reduction in variable generation cost, etc. [3][4][5]. At the same time, energy storage systems (ESS) can become a key factor to support resource adequacy by extending their role into firm capacity providers.
Over recent years, a discussion has been initiated on the contribution of ESS to resource adequacy and the feasibility of substituting conventional thermal generation to address security of supply issues. The contribution of generation to system adequacy is typically evaluated using the concept of capacity value (or capacity credit) and the popular metric executing a peak shaving strategy. Alternative operating strategies for BESS are applied in [30], similar as in [25], from the perspective of both system and wind farm operators.
The majority of the existing literature investigates the contribution of energy storage facilities integrated into large interconnected continental power systems or elementary test power systems. Furthermore, most studies lack a balanced approach regarding the ESS operating policy, either adopting resource adequacy-oriented strategies that ignore other aspects of system performance or disregard their capacity contribution enhancement. ESS are often represented in an oversimplified manner in adequacy studies, disregarding their reliability characteristics and availability limitations and failing to account for the deterioration induced by the applied operating policies.
This paper primarily aims to shed light on energy storage contribution to capacity adequacy of island systems, giving due consideration to their operating strategies. Notably, in a competitive market environment, where storage would participate as an independent profit-driven entity, its operating pattern and resulting contribution to resource adequacy would be dictated by the prevailing market conditions and the participation strategies selected by its operators. In isolated island systems, however, lacking competitive generation markets, the operating strategy of centrally dispatched storage assets needs to be set by the system operator considering different and often conflicting objectives. To this end, alternative operating policies (OP) are developed and evaluated in terms of the achieved storage contribution to resource adequacy, but also as regards overall system performance, to validate the suitability of each policy and address the fundamental question of whether a storage operated in a realistic manner, i.e., enhancing system economics and supporting RES penetration, will contribute sufficiently to capacity adequacy. Three policies are evaluated in the paper: • OP1-Cost driven: BESS are operating in a market-oriented manner that maximizes economic benefits; • OP2-Reliability driven: BESS execute peak shaving on a daily basis throughout the year, in order to maximize resource adequacy contribution; • OP3-Hybrid policy: peak shaving is prioritized only on high demand days, while a cost-driven approach is adopted for the rest of the year.
A coherent methodology is developed for the assessment of resource adequacy and capacity value of energy storage, utilizing the Monte Carlo technique. Through a resource adequacy model (RAM), the well-established reliability metrics of Loss of Load Expectation (LOLE) and Expected Energy Not Supplied (EENS) are calculated and capacity value is assessed via the EFC and ECC metrics. The RAM employs an availability model for BESS within the Monte Carlo simulations (MCS) and utilizes annual storage operation profiles generated by a unit commitment and economic dispatch (UC-ED) model, which constitutes a detailed optimization methodology for the generation scheduling of the autonomous power system consisting of thermal units, RES and centrally managed BESS, built upon the mixed integer linear programming approach (MILP). The alternative policies are implemented inside the UC-ED model, which delivers the annual system operating and economic results. The OP-dependent impact on storage lifetime expectancy is evaluated ex-post, assuming Li-ion batteries.
The remainder of this paper is organized as follows. Section 2 describes in detail the rationale behind each operating policy and presents the UC-ED model formulation. In Section 3, the RAM model is developed and the applied BESS capacity value estimation method is outlined. The description of the case study follows in Section 4. Section 5 presents the results from the introduction of BESS on both adequacy and overall island system operation. The main conclusions are summarized in Section 6. OP1 is the baseline to create a realistic operating pattern of a BESS, driven by overall system operating cost and performance objectives, as are the variable generation cost of the system and RES energy absorption, both enhanced through energy arbitrage functionality and the provision of fast reserves, critical for the security of isolated system and the integration of stochastic RES. In this policy, batteries will operate in the market, aiming to provide flexibility and reduce system cost; however, BESS energy arbitrage and peak shaving functionality may be limited, as battery stations of limited energy capacity are primarily utilized as fast reserve-providing assets in island systems [31]. This is illustrated in Figure 1, where the residual system load (demand minus RES contribution) is shown when the alternative policies are applied. With OP1 (blue line in Figure 1a), demand peaks are only moderately mitigated, indicating that arbitrage is performed sparingly with this policy. method is outlined. The description of the case study follows in Section 4. Section 5 presents the results from the introduction of BESS on both adequacy and overall island system operation. The main conclusions are summarized in Section 6.

Operating Policy 1-Cost Driven
OP1 is the baseline to create a realistic operating pattern of a BESS, driven by overall system operating cost and performance objectives, as are the variable generation cost of the system and RES energy absorption, both enhanced through energy arbitrage functionality and the provision of fast reserves, critical for the security of isolated system and the integration of stochastic RES. In this policy, batteries will operate in the market, aiming to provide flexibility and reduce system cost; however, BESS energy arbitrage and peak shaving functionality may be limited, as battery stations of limited energy capacity are primarily utilized as fast reserve-providing assets in island systems [31]. This is illustrated in Figure 1, where the residual system load (demand minus RES contribution) is shown when the alternative policies are applied. With OP1 (blue line in Figure 1a), demand peaks are only moderately mitigated, indicating that arbitrage is performed sparingly with this policy.

Operating Policy 2-Reliability Driven
Given that high demand intervals are most critical for resource adequacy of a power system [32], this operating policy places emphasis on the elimination of peaks of the load curve, prioritizing the arbitrage functionality of the BESS on a daily basis seeking to maximize the capacity value of the storage asset. This is illustrated with the orange line in Figure 1a, where the difference in comparison to OP1 is apparent. Nevertheless, enforcing a daily peak shaving operation will prove non-optimal both for system economics and BESS degradation, as it will perform one full charge-discharge cycle per day, compromising the lifetime expectancy of the batteries.

Operating Policy 3-Hybrid Policy
OP3 aims at combining the advantages of the OP1 and OP2, in order to obtain a high capacity value out of storage, with a minimum burden on system operating cost and battery longevity. In this policy, peak shaving is performed only on high demand days, which are most crucial from a resource adequacy viewpoint. A simple criterion for selecting such days is the load exceeding a threshold value (P threshold ), determined by the system operator. Application of this strategy is illustrated in Figure 1b

Operating Policy 2-Reliability Driven
Given that high demand intervals are most critical for resource adequacy of a power system [32], this operating policy places emphasis on the elimination of peaks of the load curve, prioritizing the arbitrage functionality of the BESS on a daily basis seeking to maximize the capacity value of the storage asset. This is illustrated with the orange line in Figure 1a, where the difference in comparison to OP1 is apparent. Nevertheless, enforcing a daily peak shaving operation will prove non-optimal both for system economics and BESS degradation, as it will perform one full charge-discharge cycle per day, compromising the lifetime expectancy of the batteries.

Operating Policy 3-Hybrid Policy
OP3 aims at combining the advantages of the OP1 and OP2, in order to obtain a high capacity value out of storage, with a minimum burden on system operating cost and battery longevity. In this policy, peak shaving is performed only on high demand days, which are most crucial from a resource adequacy viewpoint. A simple criterion for selecting such days is the load exceeding a threshold value (P threshold ), determined by the system operator. Application of this strategy is illustrated in Figure 1b. The residual demand is shaped exactly in the same way as through OP1, except on high demand days where the performance resembles that of OP2.

UC-ED Model Fundamentals
A unit commitment and economic dispatch model is developed, incorporating the alternative policies considered, to reproduce the management of the island system in each case and capture the impact of each operating policy on system and BESS performance. The generation scheduling problem adopts a cost-optimal approach and is formulated as a MILP problem with a 24 h look-ahead horizon and hourly dispatch intervals, as explained in more detail in [2,33] and amended in [31] to integrate centrally dispatched energy storage. MILP is a state-of-the-art optimization method for modeling the generation scheduling problem of power systems, effectively handling both binary and continuous variables and tracing optimal solutions in reasonable computational times [34,35]. The UC-ED model incorporates all technical and economic characteristics of the thermal generation fleet and the storage, as well as system-level constraints, including reserve requirements and real-time management constraints for the production level of intermittent renewables.
The objective function (1) of the UC-ED model is composed of the variable generation cost (C p ), startup/shut down costs (C su/sd ) and operating/maintenance costs (C O&M ) of thermal units. The term of C peak is necessary for the activation of the peak shaving mode, as explained in more detail in the following, while the rightmost term of (1), C sl , stands for the cost of slack variables, allowing the relaxation of constraints to ensure a feasible solution of the optimization problem.
The active power equilibrium is presented in (2) and ensures that the output power of committed thermal units (P u, t ), distributed photovoltaics (P f PV, t ) and wind farms (WFs) after curtailments (P f W, t −X w,t ), the discharge of BESS (P d ξ, t ) and the energy not served (P ens, t ) equals the load demand (P L, t ) and BESS charging (P c ξ, t ) per time interval t.
Constraints (3) and (4) impose the commitment status (st u, t ) and the start-up and shut-down states (su u, t and sd u, t ) of each thermal unit. Constraints (5) and (6) ensure that minimum up (T run u ) and down (T stop u ) times of each unit are observed. Constraints (7) and (8) restrict the output power of each unit by its ramp rates (RU u , RD u , RSU u , RSD u ). Additionally, constraints (9) and (10) limit the output of conventional units by their maximum (P max u ) and minimum (P min u ) permissible loading, accounting for their contribution to positive and negative reserves (r up/dn u, t, r ) per reserve type and time interval.
The fundamental constraints related to the logical status of commitment of BESS are (11)- (14). Constraint (11) bounds the charge and discharge power of BESS to the maximum levels (P c/d ξ ), while (12)  charge (SoC ξ, t ) of BESS unit ξ, taking into consideration its charging and discharging efficiency, bound in (14) by its minimum (E ξ ) and maximum (E ξ ) levels.
Constraints (11)- (14) apply to all three operating policies; however, additional constraints apply when implementing OP2 and OP3. For OP2, the virtual cost term C peak , defined in (15), is introduced in (1) to penalize daily peaks (P peak, t ) and thus prioritize peak shaving functionality, depending on the value of penalty factor ϕ peak . Equations (16)- (17) are implemented for the identification of residual load peaks during one day period (T D ). The residual load P R,t includes demand and battery charging load, reduced by available RES generation and BESS discharging, as in Equation (22) below including BESS. The non-linear terms of (15) and (17) are properly linearized and incorporated in the MILP UC-ED model according to [36,37], respectively.
P peak, t = max P R,t , P avg (17) In OP3, BESS peak shaving operation is initiated only when the peak demand of the dispatch day exceeds a predefined threshold (P threshold ), (18), in which case ϕ peak receives the same value as in OP2, enforcing peak shaving through arbitrage. Otherwise, the system operates as in OP1. In (18), the residual load is used, before BESS action.
Additional UC-ED constraints, related to wind power limitations and the quantification of reserves requirements, are described in Appendix A and apply to all OPs.

Resource Adequacy Evaluation Methodology
Monte Carlo simulation is a state-of-the-art analysis technique for stochastic problems and the principal technique to address resource adequacy in power systems incorporating energy storage facilities [38]. MCS evaluates system adequacy through a sequence of annual simulations accounting for the stochastic nature of uncertainties impacting adequacy [39]. A dominant uncertainty is the full/partial unavailability of thermal units to deliver their rated capacity, modeled in this paper by a two-state model. The time duration that a unit is available until its next failure (TTF-time to failure) and the time for the unit to repair after a failure (TTR-time to repair) are random variables following exponential distributions, with means λ = 1/MTTF and µ = 1/MTTR, respectively, where the Mean Time to Failure (MTTF) and Mean Time to Repair (MTTR) are expressed in hours. Sampling sequential values of the TTF and the TTR random variables carried out by using Equations (19) and (20), where U and U' are sequences of random numbers uniformly distributed in [0,1] ( [39]): The standard reliability metric used for conventional units is the FOR (forced outage ratio) indicator, related to MTTF and MTTR as in (21) [32].
After generating annual availability histories with hourly resolution for each thermal unit, in the form of chronological up-down-up cycles, the cumulative available thermal capacity (ATC) of the system was obtained, combining the operating cycles of all units. This process is illustrated in Figure 2a. ATC will be compared to the residual load (P R ) that the dispatchable thermal generation is required to serve, given by the system load demand, incremented by BESS charging power and reduced by the available RES production and BESS discharge. The BESS operating profile was determined by the UC-ED model described in Section 2. The construction of P R,t,s timeseries for every sample year of the MCS is shown in Figure 2b.
The system reliability indices LOLE and EENS are estimated in (25) and (26) as the mean values of LLD s and ENS s over the ensemble of N MCS sampling years [39]. As the number of sample years increases in the MCS process, the target reliability indicators converge towards their final value. The convergence criterion used in this paper to terminate the MCS process was set at 1% and it was applied to the EENS, which has the lowest convergence speed compared to other indices [39]. The accuracy of the MCS is defined in (27), where σ is the standard deviation, obtained by the quadratic root of the EENS variance after N MCS samples, given by (28).

Capacity Value Assessment
The capacity value of BESS is typically quantified through the EFC and ECC metrics, providing the capacity of an "equivalent production asset" that brings about the same system adequacy enhancement as the introduction of storage in question. Whilst EFC refers to a perfectly reliable "equivalent production asset", ECC benchmarks storage against realistic conventional generation with a non-zero FOR.
An iterative process is implemented to calculate the EFC and ECC metrics. Generation capacity, with a zero FOR for the EFC and non-zero for the ECC, was gradually added  Same as for thermal units, BESS unavailability due to forced outages needs to also be accounted for. This is modeled on a daily basis, facilitating the inclusion of modified residual load profiles. When BESS is not available, based on its randomly generated availability intervals, its charging and discharging powers are excluded from residual load calculation, as in (22): for days that BESS is unavailable (22) The ATC and P R,t,s timeseries were then compared to identify capacity inadequacies (Figure 2c), i.e., intervals where P R,t,s exceeds ATC, allowing the evaluation of the appropriate reliability indices for the particular MCS sample year, specifically, the loss of load duration (LLD) and the energy not supplied (ENS). LLD in (23) is the annual number of hours that load curtailments have to be imposed (i.e., a generation inadequacy is noted), while ENS in (24) stands for the total load energy (MWh) curtailed on an annual basis for the specific sample year.
The system reliability indices LOLE and EENS are estimated in (25) and (26) as the mean values of LLD s and ENS s over the ensemble of N MCS sampling years [39].
As the number of sample years increases in the MCS process, the target reliability indicators converge towards their final value. The convergence criterion used in this paper to terminate the MCS process was set at 1% and it was applied to the EENS, which has the lowest convergence speed compared to other indices [39]. The accuracy of the MCS is defined in (27), where σ is the standard deviation, obtained by the quadratic root of the EENS variance after N MCS samples, given by (28).

Capacity Value Assessment
The capacity value of BESS is typically quantified through the EFC and ECC metrics, providing the capacity of an "equivalent production asset" that brings about the same system adequacy enhancement as the introduction of storage in question. Whilst EFC refers to a perfectly reliable "equivalent production asset", ECC benchmarks storage against realistic conventional generation with a non-zero FOR.
An iterative process is implemented to calculate the EFC and ECC metrics. Generation capacity, with a zero FOR for the EFC and non-zero for the ECC, was gradually added in increments (G step in MW) to the base case (BC) scenario, until the EENS reached the same level as the BESS configuration under investigation (EENS ESS ). Adequacy recalculation was performed at every increase in generation capacity. For EFC calculation, the capacity increment can be directly subtracted from demand, as it is always available. The procedure is illustrated in the flowcharts of Figure 3a,b. Both metrics are expressed in MW or normalized as ratios of calculated capacity value over the rated capacity of the ESS under study. in increments (G step in MW) to the base case (BC) scenario, until the EENS reached the same level as the BESS configuration under investigation (EENS ESS ). Adequacy recalculation was performed at every increase in generation capacity. For EFC calculation, the capacity increment can be directly subtracted from demand, as it is always available. The procedure is illustrated in the flowcharts of Figure 3a,b. Both metrics are expressed in MW or normalized as ratios of calculated capacity value over the rated capacity of the ESS under study.

Study Case NII System and Analysis Scenarios
The island power system described in [40] was selected as the study case, with certain modifications in the thermal fleet to serve the purposes of this study. Peak demand is 228.4 ΜW with a load factor of 44%. The system includes 13 heavy fuel oil (HFO) and 2 light fuel oil (LFO) units, whose basic technical and reliability characteristics are listed in Table  1. Additional data can be found in [40]. Installed PV and WF capacity values are 36 and 70 ΜW and the respective feed-in tariffs are 350 and 90 EUR/MWh. The crude oil price is USD 85/barrel, using an exchange rate of USD 1.10/EUR.
A centrally dispatched Li-ion battery system is considered, with a roundtrip efficiency of 85% and minimum and maximum SoC levels set at 15% and 95% of its installed energy capacity. A minimum energy reserve of 30 min of operation at rated BESS power was maintained on top of the minimum SoC level to ensure sustained provision of upward reserves. Similarly, a 5 min charging margin was maintained below maximum SoC to ensure provision of negative fast-response reserves. The FOR of the BESS was set at 2%, with an MTTR of 1 day per outage. The BESS configurations investigated include capacities from 10 to 40 MW, while installed energy capacity is 2/4/8 h expressed on rated BESS power base. As a result of the minimum and maximum SoC level restrictions and energy margins maintained for reserves provision, the exploitable capacity of 2, 4 and 8 h systems corresponds to 1, 2.6 and 5.8 h of operation at rated power.
RAM was developed in MATLAB [41]. The optimization UC-ED model was implemented in GAMS [42], using the CPLEX optimizer [43]. All simulations were performed on a 3.20 GHz Intel Core i7 processor with 16 GB of RAM, running 64-bit Windows.

Study Case NII System and Analysis Scenarios
The island power system described in [40] was selected as the study case, with certain modifications in the thermal fleet to serve the purposes of this study. Peak demand is 228.4 MW with a load factor of 44%. The system includes 13 heavy fuel oil (HFO) and 2 light fuel oil (LFO) units, whose basic technical and reliability characteristics are listed in Table 1. Additional data can be found in [40]. Installed PV and WF capacity values are 36 and 70 MW and the respective feed-in tariffs are 350 and 90 EUR/MWh. The crude oil price is USD 85/barrel, using an exchange rate of USD 1.10/EUR. A centrally dispatched Li-ion battery system is considered, with a roundtrip efficiency of 85% and minimum and maximum SoC levels set at 15% and 95% of its installed energy capacity. A minimum energy reserve of 30 min of operation at rated BESS power was maintained on top of the minimum SoC level to ensure sustained provision of upward reserves. Similarly, a 5 min charging margin was maintained below maximum SoC to ensure provision of negative fast-response reserves. The FOR of the BESS was set at 2%, with an MTTR of 1 day per outage. The BESS configurations investigated include capacities from 10 to 40 MW, while installed energy capacity is 2/4/8 h expressed on rated BESS power base. As a result of the minimum and maximum SoC level restrictions and energy margins maintained for reserves provision, the exploitable capacity of 2, 4 and 8 h systems corresponds to 1, 2.6 and 5.8 h of operation at rated power. RAM was developed in MATLAB [41]. The optimization UC-ED model was implemented in GAMS [42], using the CPLEX optimizer [43]. All simulations were performed on a 3.20 GHz Intel Core i7 processor with 16 GB of RAM, running 64-bit Windows.

System Operation under the Alternative Policies
A three-day period of high demand was used to demonstrate the operation of the island system and BESS using the three alternative operating policies. Operation without BESS and the coverage of the required primary reserves are illustrated in Figure 4. The same three-day period is presented in Figure 5 assuming the presence of a 30 MW/8 h BESS, for each OP. In Figures 4 and 5, Net Load represents the demand load, excluding any additional demand for BESS charging.
In the base-case (BC) scenario without storage, shown in Figure 4, the system cannot accommodate all available wind production and RES curtailments that take place on certain days, as thermal units need to operate above their minimum loading levels (TM) to provide down-regulation reserves (Figure 4a). In this scenario, primary reserves are only provided by thermal units. Upward reserves requirements are determined by the loss of the largest online unit (N-1 criterion) or the abrupt loss of RES generation [31]; downward requirements are set as a percentage of demand (Figure 4b).
In the presence of storage operated according to OP1, the BESS mainly contributes primary reserves to enhance RES penetration, without any substantial exchange of energy (Figure 5c), as this leads to minimum operating cost of the system. With OP2, on the other hand, the BESS is discharged on a daily basis, reducing demand peaks, as shown in Figure 5a, to achieve maximum benefits in terms of resource adequacy. BESS charging relies on wind power, but also on thermal generation in the valley hours, leading to an increase in conventional production compared to OP1, alongside the reduction observed in the peak hours, albeit at the expense of greatly increased BESS cycling. Under OP3, peak shaving takes place in the last two days, where the residual demand exceeds P threshold , here selected at 148 MW (70% of the annual peak thermal demand), while cost-driven operation was adopted on the first day. On an annual basis, the peak shaving mode was implemented on only 48 days, which of course depends on the selection of P threshold .

System Operation under the Alternative Policies
A three-day period of high demand was used to demonstrate the operation of the island system and BESS using the three alternative operating policies. Operation without BESS and the coverage of the required primary reserves are illustrated in Figure 4. The same three-day period is presented in Figure 5 assuming the presence of a 30 MW/8 h BESS, for each OP. In Figures 4 and 5, Net Load represents the demand load, excluding any additional demand for BESS charging.
In the base-case (BC) scenario without storage, shown in Figure 4, the system cannot accommodate all available wind production and RES curtailments that take place on certain days, as thermal units need to operate above their minimum loading levels (TM) to provide down-regulation reserves (Figure 4a). In this scenario, primary reserves are only provided by thermal units. Upward reserves requirements are determined by the loss of the largest online unit (N-1 criterion) or the abrupt loss of RES generation [31]; downward requirements are set as a percentage of demand (Figure 4b).  In the presence of storage operated according to OP1, the BESS mainly contributes primary reserves to enhance RES penetration, without any substantial exchange of energy (Figure 5c), as this leads to minimum operating cost of the system. With OP2, on the other hand, the BESS is discharged on a daily basis, reducing demand peaks, as shown in Figure  5a, to achieve maximum benefits in terms of resource adequacy. BESS charging relies on wind power, but also on thermal generation in the valley hours, leading to an increase in conventional production compared to OP1, alongside the reduction observed in the peak hours, albeit at the expense of greatly increased BESS cycling. Under OP3, peak shaving [   takes place in the last two days, where the residual demand exceeds P threshold , here selected at 148 MW (70% of the annual peak thermal demand), while cost-driven operation was adopted on the first day. On an annual basis, the peak shaving mode was implemented on only 48 days, which of course depends on the selection of P threshold .
(a) (b) (c)  Figure 6 presents the reliability indices EENS and LOLE calculated for different BESS configurations under the three alternative policies. Without any storage, the island system faces a resource adequacy deficit, with the LOLE reaching 9.87 h and EENS 112.6 MWh per annum. Applying OP1, where the storage operates without consideration of the reliability needs of the system, improvement in resource adequacy is minimal regardless of the BESS size, with a very modest reduction in LOLE, down by only 2.25 h even for the largest BESS considered and in spite of its substantial capacity. Under OP1, BESS capacity was utilized to provide fast response reserves, allowing a more efficient unit commitment and load dispatch for the thermal units, which in turn led to RES penetration uptake and a resulting reduction in generation cost. The level of energy arbitrage is very limited, as the conventional generation mix does not present any important spread in terms of its [ Figure 6 presents the reliability indices EENS and LOLE calculated for different BESS configurations under the three alternative policies. Without any storage, the island system faces a resource adequacy deficit, with the LOLE reaching 9.87 h and EENS 112.6 MWh per annum. Applying OP1, where the storage operates without consideration of the reliability needs of the system, improvement in resource adequacy is minimal regardless of the BESS size, with a very modest reduction in LOLE, down by only 2.25 h even for the largest BESS considered and in spite of its substantial capacity. Under OP1, BESS capacity was utilized to provide fast response reserves, allowing a more efficient unit commitment and load dispatch for the thermal units, which in turn led to RES penetration uptake and a resulting reduction in generation cost. The level of energy arbitrage is very limited, as the conventional generation mix does not present any important spread in terms of its variable cost between valley and peak hours, to balance the cost of cycling energy through the batteries.

BESS Contribution to Resource Adequacy
largest BESS configuration examined (40 MW/5.8 available hours), while storages of very modest capacities can achieve good results.
The results obtained by the hybrid policy OP3 indicate that targeted peak shaving in high demand days, as applied in this policy, practically achieves the same benefits for system adequacy as the reliability-oriented policy OP2 (reduction in EENS by 85.8% for the largest BESS considered), even though peak shaving only takes place on 48 days over the year, rather than on a daily basis. The necessary sample years for MCS to reach the desired level of convergence depends on the selected indicator, with EENS requiring more sample years to achieve the targeted accuracy level. The number of sample years needed for the results of Figure 6 ranged from ~10.000 to ~90.000 and the respective computational time ranged from ~3′ to ~20′. In Figure 7, the convergence of EENS is illustrated for one indicative scenario. On the other hand, OP2 is entirely reliability-oriented, disregarding any potential impact on system cost due to suboptimal BESS exploitation. As shown in Figure 6, the reliability indices improved substantially, with EENS decreasing by 86.3% for EENS the largest BESS configuration examined (40 MW/5.8 available hours), while storages of very modest capacities can achieve good results.
The results obtained by the hybrid policy OP3 indicate that targeted peak shaving in high demand days, as applied in this policy, practically achieves the same benefits for system adequacy as the reliability-oriented policy OP2 (reduction in EENS by 85.8% for the largest BESS considered), even though peak shaving only takes place on 48 days over the year, rather than on a daily basis.
The necessary sample years for MCS to reach the desired level of convergence depends on the selected indicator, with EENS requiring more sample years to achieve the targeted accuracy level. The number of sample years needed for the results of Figure 6 ranged from~10.000 to~90.000 and the respective computational time ranged from~3 to~20 . In Figure 7, the convergence of EENS is illustrated for one indicative scenario.
Energies 2021, 14, x FOR PEER REVIEW 12 of 23 variable cost between valley and peak hours, to balance the cost of cycling energy through the batteries. On the other hand, OP2 is entirely reliability-oriented, disregarding any potential impact on system cost due to suboptimal BESS exploitation. As shown in Figure 6, the reliability indices improved substantially, with EENS decreasing by 86.3% for EENS the largest BESS configuration examined (40 MW/5.8 available hours), while storages of very modest capacities can achieve good results.
The results obtained by the hybrid policy OP3 indicate that targeted peak shaving in high demand days, as applied in this policy, practically achieves the same benefits for system adequacy as the reliability-oriented policy OP2 (reduction in EENS by 85.8% for the largest BESS considered), even though peak shaving only takes place on 48 days over the year, rather than on a daily basis. The necessary sample years for MCS to reach the desired level of convergence depends on the selected indicator, with EENS requiring more sample years to achieve the targeted accuracy level. The number of sample years needed for the results of Figure 6 ranged from ~10.000 to ~90.000 and the respective computational time ranged from ~3′ to ~20′. In Figure 7, the convergence of EENS is illustrated for one indicative scenario.    The threshold value for OP3 was selected to avoid excessive peak shaving, without sacrificing the resource adequacy benefits from this functionality, as documented by the diagrams in Figure 9. The number of days per year with peak shaving activation for each P threshold is presented in Table 2.   The threshold value for OP3 was selected to avoid excessive peak shaving, without sacrificing the resource adequacy benefits from this functionality, as documented by the diagrams in Figure 9. The number of days per year with peak shaving activation for each P threshold is presented in Table 2.  The threshold value for OP3 was selected to avoid excessive peak shaving, without sacrificing the resource adequacy benefits from this functionality, as documented by the diagrams in Figure 9. The number of days per year with peak shaving activation for each P threshold is presented in Table 2.   Figure 9. Sensitivity analysis of LOLE results with respect to P threshold , for all BESS configurations considered: (a) 1 h; (b) 2.6; (c) 5.8 h.

BESS Capacity Value
The capacity value of the examined BESS configurations under the three policies is evaluated in Figures 10 and 11 using the EFC and ECC metrics. Capacity value is expressed in MW and normalized on the installed battery power. EENS is the system reliability index used to determine EFC and ECC, while a new Open Cycle Gas Turbine (OCGT) unit, with the characteristics given in [44], is the conventional generation benchmark for ECC calculations. ECC values are always greater than EFC, as EFC represents the capacity of an ideal, perfectly reliable conventional unit to achieve the same contribution in system adequacy. mark for ECC calculations. ECC values are always greater than EFC, as EFC represents the capacity of an ideal, perfectly reliable conventional unit to achieve the same contribution in system adequacy.
The capacity value of storage obtained under OP1 is very limited, not exceeding 15%, while the same BESS will achieve substantially higher contributions under the other two policies, confirming the fact that peak shaving is the primary mechanism for storage to support resource adequacy of the system. The results obtained with the other two policies are quite similar, with the daily peak shaving operation enforced in OP2 leading to insignificant gains in comparison to the more targeted functionality of OP3. From Figures 10 and 11, it is clear that, while the capacity value of storage is bound by its installed power capacity, the decisive factor determining its contribution to system adequacy is energy capacity, expressed by its duration. For example, the EFC of the 20 ΜW BESS varies between 18.8% and 67.8% with its duration, largely due to the fact that higher energy capacities allow more effective utilization of available BESS power for load leveling purposes. It is also noted that the normalized capacity contribution is reduced for storages of a higher rated power. In fact, the contribution of storage to the capacity adequacy of a specific system tends to saturate at higher capacities, reaching a maximum that reflects the limitations in achievable load leveling of a given daily load curve.
The significance of storage duration for the achieved peak reduction and therefore its contribution to system adequacy is easily understood through the simplified peak shaving functionality depicted in Figure 12, a deterministic approach often used to quan-  The capacity value of storage obtained under OP1 is very limited, not exceeding 15%, while the same BESS will achieve substantially higher contributions under the other two policies, confirming the fact that peak shaving is the primary mechanism for storage to support resource adequacy of the system. The results obtained with the other two policies are quite similar, with the daily peak shaving operation enforced in OP2 leading to insignificant gains in comparison to the more targeted functionality of OP3.
From Figures 10 and 11, it is clear that, while the capacity value of storage is bound by its installed power capacity, the decisive factor determining its contribution to system adequacy is energy capacity, expressed by its duration. For example, the EFC of the 20 MW BESS varies between 18.8% and 67.8% with its duration, largely due to the fact that higher energy capacities allow more effective utilization of available BESS power for load leveling purposes. It is also noted that the normalized capacity contribution is reduced for storages of a higher rated power. In fact, the contribution of storage to the capacity adequacy of a specific system tends to saturate at higher capacities, reaching a maximum that reflects the limitations in achievable load leveling of a given daily load curve.
The significance of storage duration for the achieved peak reduction and therefore its contribution to system adequacy is easily understood through the simplified peak shaving functionality depicted in Figure 12, a deterministic approach often used to quantify the capacity credit of storage [14,45]. Trimming of residual load peaks achieved by a 20 MW BESS becomes more effective as its energy capacity increases. BESS of low capacity, e.g., 1 or 2.6 h, even though they have sufficient power capability, do not have the necessary reserves to provide the energy in the load curve peak, as opposed to the larger BESS of 20 MW/5.8 available hours, which manages to fully utilize its rated power for peak shaving purposes. Notably, the duration required for a storage to claim its full capacity credit becomes higher as the rated power increases.

Impact of OPs on System and BESS Performance
The selection of a BESS operating policy for the island system would not rely solely on reliability considerations, but it should consider additional factors, primarily the impact on the generation cost of the system and the achieved enhancement of RES integration.
Τhe annual RES penetration level achieved with each operating policy is presented in Figure 13, with the three policies proving to be practically equivalent in this respect. The introduction of battery storage leads to a drastic increase in RES uptake, driven by BESS rated power, rather than its energy storage capacity. This increase is primarily related to the provision of fast reserves to cover system needs and saturates at a battery capacity of ~20 MW, regardless of its duration and system operating policy, as RES curtailments become fully exploited.
In Figure 14, the annual energy production of thermal units is presented for the same scenarios. The increased RES penetration leads to a reduction in thermal output; however this varies considerably by the operating policy selected. Whilst OP1 presents the largest gains, OP2 and OP3 are characterized by increased thermal outputs as a result of increased BESS charging needs and therefore losses to execute peak shaving. This is expectedly more pronounced in OP2, where arbitrage takes place on a regular basis.
With the remuneration of exploited RES energy curtailments being lower than the cost of substituted conventional energy (90 EUR/MWh wind energy tariff vs. 143.7  The last diagram on the right in Figure 12 explains the saturation that BESS contribution to peak reduction will eventually reach, beyond a capacity level. Assuming a BESS of 40 MW/5.8 available hours, a completely levelized residual load curve can be achieved utilizing only a fraction of the BESS full rated power (85% or 34 MW). In such a case, any further increase in the power or energy capacity of the batteries would not result in more effective peak reduction and hence increased BESS capacity value.
The impact of BESS duration on the capacity value of storage and its maximum contribution to capacity adequacy for a given system are strongly dependent on the characteristics of the residual load demand. In principle, the storage contribution will be enhanced for a peaky daily load curve shape, which in turn is created at increased PV penetration levels giving rise to the so-called "duck" curve shape [46].

Impact of OPs on System and BESS Performance
The selection of a BESS operating policy for the island system would not rely solely on reliability considerations, but it should consider additional factors, primarily the impact on the generation cost of the system and the achieved enhancement of RES integration. The annual RES penetration level achieved with each operating policy is presented in Figure 13, with the three policies proving to be practically equivalent in this respect. The introduction of battery storage leads to a drastic increase in RES uptake, driven by BESS rated power, rather than its energy storage capacity. This increase is primarily related to the provision of fast reserves to cover system needs and saturates at a battery capacity of~20 MW, regardless of its duration and system operating policy, as RES curtailments become fully exploited. In Figure 14, the annual energy production of thermal units is presented for the same scenarios. The increased RES penetration leads to a reduction in thermal output; however this varies considerably by the operating policy selected. Whilst OP1 presents the largest gains, OP2 and OP3 are characterized by increased thermal outputs as a result of increased BESS charging needs and therefore losses to execute peak shaving. This is expectedly more pronounced in OP2, where arbitrage takes place on a regular basis. With the remuneration of exploited RES energy curtailments being lower than the cost of substituted conventional energy (90 EUR/MWh wind energy tariff vs. 143.7 EUR/MWh average variable cost of thermal units), increases in RES penetration lead to decreased system costs in Figure 15 (consisting of the variable cost of conventional units plus the remuneration of RES). The increased output of thermal units in OP2 comes at the expense of a substantial increment in the generation cost of the system compared to OP1 (Figure 15b), unlike the hybrid policy OP3, which leads to a very moderate increase in system cost. The impact of the applied OP on batteries' lifetime expectations is illustrated in Figure 16, indicatively for one BESS duration (8 h installation), evaluated according to the methodology described in [47]. The nominal lifetime of BESS is assumed to be 15 years. As anticipated, the daily cycling of the batteries in OP2 drastically reduces its lifetime, which becomes prohibitively short for a realistic BESS investment. OP1 is the most advantageous, with OP3 inducing only a moderate deterioration in battery lifetime.

Conclusions
In this paper, the contribution of storage to resource adequacy of isolated power systems was investigated for a large array of BESS configurations, giving due consideration to the operating policy adopted by the system operator. The Monte Carlo technique was applied for resource adequacy assessment, while system operation, including storage, was determined using a UC-ED model built upon MILP approach. A medium sized island system with substantial RES installed capacity was used as a study case.
A salient conclusion of the investigation conducted is that storage may provide a substantial capacity contribution only when a reliability-driven operating policy is adopted, primarily through a peak shaving functionality, which may conflict with other objectives sought after via the introduction of storage. Hence, BESS capacity credit in the reliability-driven policy OP2 ranges from ca. 25% to 85%, depending on BESS power and capacity, the corresponding contribution is limited to only 5-15% with the cost-oriented OP1. At the same time, however, OP2 increases system cost by up to ~1 MEUR and reduces battery lifetime by up to 5 years compared to OP1, for the specific case study. The best compromise is achieved by combining a cost-oriented management approach with targeted load-leveling in high demand periods. This may maximize, at the same time, reliability and generation cost benefits, while avoiding an excessive impact on battery lifetime.
As far as BESS characteristics are concerned, energy capacity (duration) is most significant in achieving maximum resource adequacy contribution, which gradually diminishes as their power ratings increase. In terms of normalized capacity credit, values up to ~85% can be achieved with suitably sized and operated systems.

Conclusions
In this paper, the contribution of storage to resource adequacy of isolated power systems was investigated for a large array of BESS configurations, giving due consideration to the operating policy adopted by the system operator. The Monte Carlo technique was applied for resource adequacy assessment, while system operation, including storage, was determined using a UC-ED model built upon MILP approach. A medium sized island system with substantial RES installed capacity was used as a study case.
A salient conclusion of the investigation conducted is that storage may provide a substantial capacity contribution only when a reliability-driven operating policy is adopted, primarily through a peak shaving functionality, which may conflict with other objectives sought after via the introduction of storage. Hence, BESS capacity credit in the reliabilitydriven policy OP2 ranges from ca. 25% to 85%, depending on BESS power and capacity, the corresponding contribution is limited to only 5-15% with the cost-oriented OP1. At the same time, however, OP2 increases system cost by up to~1 MEUR and reduces battery lifetime by up to 5 years compared to OP1, for the specific case study. The best compromise is achieved by combining a cost-oriented management approach with targeted load-leveling in high demand periods. This may maximize, at the same time, reliability and generation cost benefits, while avoiding an excessive impact on battery lifetime.
As far as BESS characteristics are concerned, energy capacity (duration) is most significant in achieving maximum resource adequacy contribution, which gradually diminishes as their power ratings increase. In terms of normalized capacity credit, values up to~85% can be achieved with suitably sized and operated systems.

Conflicts of Interest:
The authors declare no conflict of interest. Step-value for EFC and ECC calculation (MW) l PV Coefficient quantifying proportion of PV power that may be suddenly lost l w Coefficient quantifying proportion of wind power that may be suddenly lost Wind generation operating in NII systems is subjected to output power curtailments via set-points dispatched to individual wind farms. No curtailments are imposed on PV generation due to the small scale and distributed nature of island PV facilities. Rejected wind energy is not compensated.

Abbreviations
Acceptable wind penetration is restricted by the minimum loading (P ML W max, t ) and dynamic limitations (P D W max, t ) [1], expressed through Equations (A1) and (A2). Equation (A1) ensures that the minimum loading levels of online thermal units are respected, taking into account the additional room created by the charging capability of ESSs. Non-linearities of (A1) are linearized according to [37]. P ML W max, t = P L, t + ∑ ξ (min{ P c ξ , E ξ − SoC ξ,t }) − P f PV, t − ∑ u (P min u ·st u, t ) (A1) The dynamic limitation (A2) maintains security of operation by ensuring that the primary reserves provided by online thermal units (R up u,pr ) and the ESS (R up ξ,pr ) suffice to cover any sudden loss of renewable generation, quantified in (A2) using the empirical coefficients l w and l PV [2]. P D W max, t = ∑ u R up u,pr · st u, t + ∑ ξ R up ξ,pr − l PV · P PV, t l w (A2) The wind energy absorption capability of the system is given by the minimum of P ML W max,t and P D W max,t and it is distributed to individual WFs in proportion to their installed capacities.

Appendix A.2 Operating Reserves
Active power reserves (r) are distinguished as primary, secondary and tertiary, depending on their deployment times. Primary reserves (r = pr) are activated within a few seconds, following disturbances in the active power equilibrium of the system. Secondary (r = sr) and tertiary (r = tr, spinning and non-spinning) reserves correspond to activation times of 5 and 20 min, respectively. Reserves are provided both by thermal units and energy storage systems, to meet the requirements of the system based on constraints (A3)-(A5), where reserve substitutability is assumed. The amounts of positive (r up ξ, t, sr ) and negative (r dn ξ, t, sr ) reserves provided by storage are subject to constraints (A6) and (A7). Slack variables X up/dn t, r in constraints (A3)-(A5) allow the relaxation of these constraints for the sake of feasibility of the solution.
∑ u r up/dn u, t, pr + ∑ u r up/dn