Enhanced Dynamic Control Strategy for Stacked Dynamic Regulation Frequency Response Services in Battery Energy Storage Systems

: Energy storage systems are undergoing a transformative role in the electrical grid, driven by the introduction of innovative frequency response services by system operators to unlock their full potential. However, the limited energy storage capacity of these systems necessitates the development of sophisticated energy management strategies. This paper investigates the newly introduced frequency response service, Dynamic Regulation, within the Great Britain electrical grid. Our study not only establishes control parameters but also demonstrates a novel approach to energy management that pushes the boundaries of the allowable service envelope. We present two distinctive control methods, the ﬁrst serving as a reference for standard response, and the second as a dynamic control approach, exploiting the extremities of the allowable service envelope. A comprehensive sensitivity analysis that considers availability, the number of equivalent full cycles, and cost–revenue analysis based on grouped dynamic control state of charge setpoints is carried out. Our results underscore that the optimization of average availability takes precedence over merely minimizing the number of cycles, which leads us to deﬁne a target state of charge range of between 40% and 45% for a 1-h battery to achieve an availability >95%. Furthermore, our study presents simulated results utilizing real-world frequency data, which reveal the transformative potential of the latter control method. By enhancing the availability of battery energy storage systems, this innovative approach promises not only higher revenues for the asset owner but also assists the system operator in managing frequency.


Introduction
The increase in the integration level of variable renewable energy resources (RES), such as wind and solar, into the power grid in the form of distributed generation (DG) has driven global efforts to reduce greenhouse gas emissions [1,2].These resources are considered as variable, independent, and intermittent by nature and can contribute to power quality, stability, and reliability issues [3,4].To mitigate these problems, excess energy can be stored when generation exceeds demand and then this stored energy can be used when demand exceeds supply such as at peak times [5].Grid-connected Energy Storage Systems (ESSs) are widely regarded as an enabler for RES [6][7][8].The stored energy can be used to improve power quality as well as to achieve better grid performance.In addition, energy storage can be used to mitigate energy security issues that result from intermittent renewable power.This will lead to a better contribution in the prediction response of such resources, while, at the same time, providing additional flexibility in the energy system [9].Integration of ESSs with the grid will enable the large-scale expansion of RES and lead to a faster transition to a low-carbon future energy system [10,11].ESSs can be realized using different technologies, which include battery, flywheel, pumped-storage hydropower, supercapacitor, compressed air, hydrogen, and thermal (including molten salt).There are many features of ESSs that relate to its electrical capacity, efficiency, charge/discharge behaviour, lifetime, cost, and environmental/location issues.Some of these characteristics are intimately related to each other [1].The operational capabilities of ESS types are, therefore, significantly different, with some being suitable to mitigate annual fluctuations, while others could be ideally used for very short peak power requirements [10,12,13].Pumped hydroelectric storage (PHS) is considered the most widely deployed energy storage technology to date; however, this type of ESS is constrained by geographical limitations [14].In [15], battery energy storage systems (BESSs) have been successfully demonstrated in grid applications to provide power-balancing services.BESSs are considered favorable because they have several advantages, which include high energy efficiency, good energy density, variable charging/discharging rates, faster response time compared to conventional energy generation sources, low self-discharge rates, and low maintenance [16].One commonly quoted use for a BESS is to provide ancillary services that are used to balance demand and supply; these include fast frequency response services, voltage support, and peak power lopping [17].In addition, in recent years, the cost of battery cells has declined, and this has led to increased profitability of BESSs for large-scale grid applications [18].In Great Britain (GB), in order to maintain frequency very close to 50 Hz, the National Grid Electricity System Operator (NGESO)-the primary electricity system network operator-has introduced various frequency response services to provide a real-time response to deviations in the grid frequency, and they include Enhanced Frequency Response (EFR), Dynamic Firm Frequency Response (DFR) and Static Firm Frequency Response (SFR), and new frequency response services, which include Dynamic Contaminant (DC), Dynamic Regulation (DR), and Dynamic Moderation (DM) [19][20][21].In this paper, one of the new frequency response services, DR, which contains two service conditions, Dynamic Regulation High-Frequency Response (DR-HF) and Dynamic Regulation Low-Frequency Response (DR-LF), has been modeled in MATLAB/Simulink using a generalized ESS and simulated against a realworld frequency data set obtained from NGESO [22].The paper investigates whether the allowable limits, as defined by NGESO, for the delivery parameters of the service could be exploited to manage the state of charge (SOC) of the BESS using a dynamic control strategy to achieve higher availability.This control offers either a fast or slow response to changes in frequency to minimize energy throughput.The service error calculation for contracted delivery is presented and used to demonstrate increased revenue through dynamic control.Two scenarios are investigated for comparison.The first scenario (S1) is a base case, where a stacked DR-HF and DR-LF service has been delivered without implementing the dynamic control.For the second scenario (S2), both services have been delivered using the dynamic control to assist with SOC management.To conclude, a sensitivity analysis is carried out to assess a stacked DR-HF and DR-LF service in terms of energy throughput, availability, penalty payment, and number of equivalent full cycles (EFCs).

Dynamic Regulation (DR)
DR is considered a pre-fault service that is designed to slowly correct continuous but small deviations in frequency.The DR contains two service conditions: Dynamic Regulation High-Frequency Response (DR-HF) and Dynamic Regulation Low-Frequency Response (DR-LF).The aim of such a service is to continually regulate frequency around the target of 50 Hz.In order to comply with the NGESO specifications, as shown in Table 1, an ESS must continually respond to the grid frequency deviation through increased or decreased import/export power.In this service, the deadband (DB) is considered as the area that is limited by frequency band ±0.015 Hz.For both DR-LF and DR-HF, there is no requirement to import/export power in the DB, but there is also no opportunity to charge/discharge the ESS to manage its SOC.From the edge of the DB to −0.2 Hz for DR-LF or +0.2 Hz for DR-HF, the DR power demand (P DR ) increases linearly to 100% of the contracted quantity.According to NGESO specifications, actual BESS power (P BESS ) needs to start responding to changes in P DR within 2 s and must deliver the full P DR no later than 10 s [23].Figure 1 illustrates a high-level block diagram of the DR model (DR-LF, DR-HF, or both services) as used in MATLAB/Simulink.The first block represents the real-time grid frequency (f) with a unit (Hz) that changes second by second and has been obtained from the national grid (NG) [22].The grid frequency is input into the second block, called a service power calculation block, that calculates P DR for the required frequency response service (DR-LF or DR-HF) or both services.The calculation of P DR is demonstrated in Table 2, where the required P DR envelope is calculated as a function of the desired limits according to NG specifications.The obtained P DR is measured in watts (W) and then converted to kilowatts (kW).It is also possible to convert the power unit to per unit (p.u),where 40 MW is equal to 1 p.u.

DR Service Specification
Table 2 and Figure 2 show the algorithm for the proposed model, which starts by detecting the position of the measured frequency in relation to the zones bounded by frequency values 'J' to 'P', as shown in Table 2.The P DR setpoint can be calculated using the appropriate equation to give P DR(LF or HF) or both services.According to NGESO [23], P BESS must be delivered as per the service envelope specification as previously described; if the power is delivered outside the agreed range, this will then cause a reduction in a metric called the Service Performance Measurement (SPM), resulting in a reduced payment for the contracted service.Contractual obligations require that power delivered to the grid is recorded at 20 Hz and must be provided as evidence of this operation to NGESO for the SPM to be calculated.In the DB, the required P DR = 0.The third block represents the dynamic control with SOC management, where the three inputs are included; SOC, power calculations P DR(LF or HF) or for both services, and ∆P DR(LF or HF) or for both services, while the output is the required P Demand , which is connected to the BESS block through the inverter, as illustrated in Figure 1.As we can see from Figure 3, the algorithm starts to measure P DR each second then calculates the ∆P DR ; this is based on the desired SOC limitations.Thus, if ∆P DR is equal to zero then the current ∆P DR will be equal to the previous ∆P DR .Whereas, if ∆P DR is negative or positive and SOC is in between the agreed limits, then P Demand will equal to the contracted power (P DR ).However, if SOC is greater than SOC high and ∆P DR is less than zero, then the slow response will be implemented, while, if ∆P DR is greater than zero, then the fast response will be implemented (and vice versa in the case where SOC is less than SOC low ).
The final blocks consist of an inverter and a battery energy storage model, both controlled by a BESS controller.The input to this controller is the dynamic control output, P Demand .The BESS controller manages the power delivered by the BESS based on P Demand , while adhering to any power and SOC limits.These SOC limits are defined as SOC low = 5% and SOC high = 95%.Consequently, if the battery's SOC reaches either the upper or lower limit, it will cease importing or exporting power.The SOC of the BESS is calculated, as described in [15], using the following equation: where SoC start , Q and P BESS represent initial SOC, Watt-hour capacity, and instantaneous P BESS , respectively.Also, in this block, the stored energy in the BESS has been calculated using a switch, where the input is the P Demand , which is the output power of the third block calculated, multiplied by the charge/discharge efficiency.The calculation of Stored Energy in the BESS, as in [19], is expressed in the following equations: where η D , η C , P t , and E t refer to the battery discharge efficiency, battery charge efficiency, battery power for charging or discharging at a specific hour (t), and stored energy in the battery at that hour (t).It is important to note that, if P t > 0 is positive, indicating that the system is exporting or discharging, Equation ( 2) can be used, whereas, if P t is negative, indicating that the system is importing or charging, Equation ( 3) can be used.

DR-LF or DR-HF Service Envelope
Figures 4 and 5 show the relationship between P DR and the frequency data for DR-LF and DR-HF service, respectively.In these services, the assets must respond to low or high-frequency events by exporting and importing power.

DR-LF and DR-HF Service Envelope
Figure 6 illustrates the relationship between frequency data obtained from NG and P DR for stacked DR-LF and DR-HF.In this service, the assets must respond to both lowand high-frequency events by exporting and importing power.The parameters used in the DR model are shown in Table 3.In this section, SOC start has been set to 5%, and the SOC limits for the BESS are indicated on the SOC plot by purple dashed lines: SOC high = 95% and SOC low = 5%.It is evident that SOC high is not breached in the simulation.If the BESS reaches the upper limit, as it does at 14.7 h, then the system can only export power, and P BESS will be set to zero.

Simulation Results of DR-LF Service Model
Figure 8 presents the simulation results of a BESS delivering DR-LF, contracted for 40 MW, for the first 9 h on January 2019 for frequency, P Demand , P BESS , and SOC.The plots include data for frequency, P Demand , P BESS , and SOC.The purple dashed lines on the frequency plot represent the DB (±0.015Hz).The P Demand and P BESS are represented by orange and blue colors, respectively.In this section, the SOC start has been set to 95%, and SOC limits for the BESS are indicated on the SOC plot by pink dashed lines and set as the same values as in DR-HF; it is clear that SOC low is not breached in the simulation.If the BESS reaches this limit, as it does at 7.4 h, then the system can only import power and P BESS will be set to zero.In this section, SOC start has been set to 50%, and the SOC limits for the BESS are indicated on the SOC plot by grey dashed lines: SOC high = 95% and SOC low = 5%.It can be seen that P Demand and P BESS are changing proportionally with change in the frequency data that are obtained from NG [22] second by second, and the deadband (DB) is shown with the limits (±0.015Hz); in this area, there is no opportunity for BESS to manage SOC, which means power is equal to zero.Also, it shows both SOC high and SOC low are not breached in the simulation.If the BESS reaches a higher limit, as is shown in this figure, then the system can only export power and BESS will be set to zero, whereas, if the BESS reaches the lower limit, as it does in this figure, then the system can only import power and P BESS will be set to zero.

Dynamic Control of DR-LF or DR-HF
The objective of implementing the dynamic control is that there is an opportunity to exploit the speed of the control response to assist with SOC management as there is no opportunity in the DB.In this section, we consider the ESS delivering either DR-LF or DR-HF and do not consider the case of delivering both in a stacked bid [23].The strategy in this work is to minimize the energy throughput for either service by responding quickly to decreases in P DR and slowly to increases in P DR , the sign of which depends on the service being delivered.The fast response will use a 100% p.u./s ramp rate for P Demand , resulting in the power being delivered within 1 s.The slow response follows the slower limits of the service specification, in that P DR must be delivered no later than 10 s, with a minimum delay period of 2 s.This is implemented using a fixed control delay of 2 s and a ramp rate of 12.5% p.u./s.

Dynamic Control of DR-HF
For DR-HF delivery, the SOC start will be set at the lower limit (SOC low = 5%).The fast response will be delivered if the change in DR-HF power ∆P (DR−HF) > 0, whereas the slow response is implemented if ∆P (DR−HF) < 0.
Figure 10 shows the simulation results of DR-HF for both fast and slow responses by using an illustrative example input which represents P (DR−HF) .It can be seen that, when P (DR−HF) increases (∆P (DR−HF) < 0), then the slow control response is applied, whereas, when (∆P (DR−HF) > 0), then a fast response is used.In this methodology for DR-HF, the control is switching between ramp rates and uses the maximum allowable delay to minimize the charging power.

Dynamic Control of DR-LF
For DR-LF, the SOC start will be set at a higher limit (SOC high = 95%).The fast response will be delivered if the change in DR-LF power ∆P (DR−LF) < 0, whereas a slow response could be implemented if ∆P (DR−HF) > 0.
Figure 11 illustrates the simulation results of DR-LF for both fast and slow responses again by using an illustrative example that represents P (DR−LF) .It can be seen that, when P (DR−LF) increases (∆P (DR−LF) > 0), a slow control response is applied; when (∆P (DR−LF) < 0), then the fast response is used.For DR-LF, this means that the discharging power is minimized.The result is that, for both DR-HF and DR-LF, the energy throughput is minimized over the service delivery with the aim of extending the time before the SOC limits are reached.

BESS Availability
In this work, the availability of the BESS is defined as the percentage of time that it can deliver P Demand ; it is considered unavailable when the SOC is at its limit and, therefore, unable to deliver P Demand .The availability of BESS can be calculated using Equation (4) [26]: In the results, 'avg.Availability' is presented; this is the average value of the BESS Availability for each month and includes the BESS being available when the P Demand = 0.

Number of Equivalent Full Cycles (EFCs)
In this paper, a method is used to calculate the number of Equivalent Full Cycles (EFCs) required to deliver a service over a time period.This is particularly important for a BESS, as the system will degrade (reduced capacity, for example) with increased cycles; Ref. [27] states that, in commercial documents such as warranties, an EFC is calculated using energy throughput, as shown in Equation ( 5):

EFCs =
Total o f Export and Import Energy o f ESS Total Energy throughput by Capacity /2 (5)

Penalty Payment
To define load profiles through the day, there are six Electricity Forward Agreement (EFA) blocks in 24 h, and each EFA block represents 4 h of the day [28].These are the minimum units of time an ESS can bid to deliver a service.Each half-hour period of the day is referred to as the Settlement Period (SP) and is used as a time unit for the purposes of energy trading and balancing.To calculate the penalty payment for the service, we need to define the upper and lower bounds of the service.Based on the scenarios presented in this paper, these correlate with the fast (P DR (upper) ) and slow (P DR (lower) ) control response.If the P BESS is on or between these bounds, then the error is calculated as zero.However, if P BESS is outside of these bounds, then the error can be calculated by taking the difference between P BESS and the upper or lower bounds [22,29].The error e m for one-time measurement and metered response (P BESS ) can be calculated using Equation ( 6) and implemented as shown in Figure 12.The scaled error (es m ) for one measurement is given by es m = e m P contract (7) where e m is the calculated error and P contract is the contracted quantity that the provider is contracted to deliver; in this work, the example is 40 MW.For each settlement period (SP), the performance score can be calculated using and the factor for each SP can be calculated as shown in Equation ( 9): where A = 0.03 and B = 0.07.For each contracted EFA block, the K e factor can be calculated as shown in Equation (10): The payment adjustment (K e factor) curve is shown in Figure 13.

Dynamic Control of DR-LF and DR-HF
In this section, BESS has been procured for staking DR-LF and DR-HF services.The SOC start is set at 50%, and fast and slow responses are delivered based on the dynamic control SOC higher & SOC lower setpoints.Therefore, four steps are taken into account: 1.
For DR-HF delivery, the slow response will be delivered if (∆P DR (t−1) > 0) && (∆P DR (t) > 0) && (SOC < SOC lower ), whereas the fast response is implemented if (∆P DR (t−1) < 0) && (∆P DR (t) < 0) && (SOC < SOC lower ), and the results are shown in Figure 14. Figure 14 presents the simulation results of DR-HF for both fast and slow responses by using an illustrative example input which represents the P (DR−HF) when SOC < SOC lower .
It can be noticed that, when P (DR−HF) decreases, which means (P DR−HF (t−1) > 0) && (∆P DR−HF ( t) > 0), a slow control response is applied, while, when (P DR−HF (t−1) < 0) and (∆P DR−HF (t) < 0), then the fast control response is applied.The aim of this methodology for DR-HF control is switching between ramp rates and using the maximum allowable delay to minimize the discharging power when SOC < SOC lower ; 3.
For DR-HF delivery, the slow response will be delivered if (∆P DR (t−1) < 0) && (∆P DR (t) < 0) && (SOC > SOC higher ), whereas the fast response is implemented if (∆P DR (t−1) > 0) && (∆P DR (t) > 0) && (SOC > SOC higher ), and the results are shown in Figure 11. Figure 11 shows the simulation results of DR-HF for both fast and slow responses by using an illustrative example input, which represents P (DR−HF) .
It can be seen that, when P (DR−HF) increases (∆P (DR−HF) < 0), then the slow control response is applied, whereas, when (∆P (DR−HF) > 0), then a fast response is used.In this methodology, the target of the dynamic control for DR-HF is to be used to minimize the charging power when SOC > SOC higher ; 4.
Figure 15 illustrates the simulation results of DR-LF for both fast and slow responses by using an illustrative example input, which represents P (DR−LF) when SOC> SOC higher .It is clear that, when P (DR−LF) increases (∆P (DR−HF) > 0), then the fast control response is implemented, whereas, when (∆P (DR−LF) < 0), then a slow response is used.The aim of this methodology is to exploit the dynamic control for DR-HF to minimize the charging power when SOC > SOC higher .

Analysis of the Availability of BESS Used to Deliver DR-LF and DR-HF Services Based on Grouped Dynamic Control SOC Setpoints
In this section, BESS availability has been calculated using Equation ( 4) in Section 2.7 and based on grouped dynamic control SOC setpoints (SOC higher ) and (SOC lower ), in order to select the optimum range of dynamic control SOC setpoints which will have high average availability.The SOC lower grouped as (10%, 15%, 20%, 25%, 30%, 35%, 40%, 45%, 50%), while SOC higher grouped as (45%, 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%), and the results are shown in Table 4 and Figure 16.From Table 4 and Figure 16, it is clear that, from 10-40% SOC lower range and at all ranges of SOC higher , the average availability increases by the increase in SOC lower and with the decrease in SOC higher , and vice versa.The highest value of average availability was at 45% SOC higher and 40% SOC lower , with a value equaling ∼ 90.49%.However, when SOC lower > 40% at all ranges of SOC higher , the average availability was decreased gradually compared to SOC lower when it was equal to 40%.Therefore, the suitable range of dynamic control SOC setpoint is 40%SOC lower -45% SOC higher .

Analysis of the EFCs of BESS Used to Deliver DR-LF and DR-HF Services Based on a Grouped Dynamic Control SOC Setpoints
In this section, the number of cycles has been obtained from the EFCs counting method using Equation ( 5) and based on grouped dynamic control SOC setpoints, which are demonstrated in Section 2.11, and the results are shown in Table 5 and Figure 17.From Table 5 and Figure 17, it can be seen that the number of equivalent full cycles is decreased with the increase in SOC lower and decrease in SOC higher , and vice versa.The highest number of full cycles was at SOC lower = 10% and SOC higher = 80%, 85%, and 90%, whereas the lowest number of full cycles was at SOC lower = 50% and SOC higher = 50%.However, based on the results that are obtained from Section 2.11, the availability of BESS in this region was lower compared to the region, which is SOC lower = 40% and SOC higher = 45%.
When it comes to the revenue, the higher availability is more important than the higher number of full cycles for example; if we have BESS (Li-ion) with a capacity of 40 MWh, a total number of cycles (10,000 cycles), and Purchase Cost (£200/kWh), this value includes the other costs such as battery inverter (£/kW), electrical balancing of the system (BOS) (£/kW), structural balancing of the system (BOS) (£/kW), amd operation and maintenance (O & M) (£/kW-yr).The BESS cost per cycle can be calculated using = £200/kWh × 40 MWh 10,000 cycle = £8,000,000 10,000 cycle As we discussed above, the highest number of cycles for the first 6 EFA blocks for November 2019 required 2.0559 cycles; therefore, the cost per cycle/day = £800/cycle × 2.0559 cycle = £1644.72.In case of availability, we assume that the capacity of BESS is still the same as in the above example, and it is used to deliver DR-HF and DR-LF services for the first 6 EFA blocks for November 2019; the DR service price for the year 2022 is £19.37/MW[30], so revenue can be calculated using Therefore, based on the obtained results, we can decide that the highest Avg.availability is more important than the highest number of cycles, so the range, which is SOC lower = 40% and SOC higher = 45%, is considered in this paper when it comes to calculating Avg.availability, number of cycles, and penalty payment.

Analysis of BESS Used to Deliver DR-LF & DR-HF Services
In this section, each service has been procured for six EFA blocks, and each two EFA blocks have been simulated back-to-back together.Two scenarios have been applied to examine the stacking of both services (DR-LF and DR-HF): • (S1)-The base case that uses a fixed delay (2 s) and maximum ramp rate; • (S2)-Using dynamic control, as previously described.
Each pair of EFA blocks has been simulated in MATLAB and, to illustrate the differences between the two scenarios, the SOC start for the stacking of DR-LF and DR-HF are set to different values (30%, 50%, 70%), and the dynamic control setpoints of the SOC are set to (SOC higher = 45%) and (SOC lower = 40%).The results are shown in Tables 6-8 and Figure 18. Figure 18 and Tables 6-8 present the simulation results that are obtained by implementing both DR-LF and DR-HF services for the first six EFA blocks in Dec-2019, based on the two different scenarios (S1&S2).From all these tables, it can be noticed that, in all scenarios, the penalty payment has not occurred at any EFA blocks because the K e factor is equal to 1, which means that the providers can receive a full payment.In addition to that, the obtained results that are shown in the EFA odd blocks (1, 3, and 5) for all different SOC start illustrate that, at S2, the total export/import energy is minimized over the time compared to S1, and this led to a decrease in the total number of cycles that are obtained from EFCs; the main reason behind this is that the implemented dynamic control has allowed more time for BESS to be charged or discharged.Moreover, from Table 6, the results show that, in all EFA odd blocks when the SOC start =50%, in both scenarios (S1&S2), the average availability of BESS is 100%, whereas, at the same EFA blocks and for SOC start = 30%, the average availability for BESS reaches 100% for the EFA blocks 3 and 5.However, for EFA block 1 at S1, it is almost 98.90%, and, for S2, it was increased to approximately 99.14%.When SOC start = 70%, the battery reached 100% average availability for both scenarios at EFA blocks (1 and 3), but, for block 5 at (S1), it was ∼97.29%, and it increased to almost 98.90% for S2.
In the EFA even blocks (2, 4, and 6) for SOC start = 50%, the average availability of BESS reached 100%, except for block 2 (with 99.58% for S1), and it increased to ∼99.72.However, for SOC start = 30%, the average availability reached 100% for both S1 and S2 for EFA blocks (4 and 6), but, for block 2, it equates to 95.89% for S1, and it increased to approximately 96.78%.For SOC start = 70%, BESS reached 100% average availability at only EFA block 2, and the main reason why BESS did not reach 100% average availability for the first and second EFA blocks, although a dynamic control had been applied, is that the battery reached SOC lower = 5%, which made it unavailable for a certain time.).From all these Tables, it can be noticed that, in all scenarios, the penalty payment has not occurred at any EFA blocks because the K e factor equates to (1), which means that the providers can get a full payment.In addition to that, the obtained results that are shown in the EFA odd blocks (1, 3, and 5) for all different SOC start illustrate that at S2, the total export/import energy is minimized over the time compared to S1, and this has led to decrease the total number of cycles that are obtained from EFCs, and the main reason behind this is that the implemented dynamic control has allowed more time for BESS to be charged or discharged.Moreover, from Table 5.6, the results show that in all EFA odd blocks where the SOC start =50% in both scenarios (S1&S2) the average availability of BESS is 100%, whereas, at the same EFA blocks and for SOC start =30%, the average availability for BESS reaches 100% for the EFA blocks 3 & 5 but for EFA block1 at S1, it equates to almost 98.90%, and for S2, it was increased to approximately 99.14%, when SOC start =70%, the battery reach 100% of average availability for both scenarios at EFA blocks (1 & 3) but for block5, at (S1) it was ∼ 97.29% and it increased to almost 98.90% for S2.
In the EFA even blocks (2, 4, and 6), for SOC start =50%, the average availability of BESS reached 100% except for block2 with 99.58% for S1, and it increased to ∼99.72, however, for SOC start =30%, the average availability reached 100% for both S1 & S2, for EFA blocks (4 & 6), but for block2, it equates to 95.89% for S1, and it increased to approximately 96.78%, and for SOC start =70%, BESS has reached 100% of average availability at only EFA block2 and the main reason why BESS did not reach 100% of average availability for the first and

Conclusions
The analysis of Battery Energy Storage Systems for delivering both DR-LF and DR-HF services has provided valuable insights into the dynamic control strategies and performance metrics of these systems.The study explored various scenarios, including fixed delay (S1) and dynamic control (S2) for SOC management.The findings reveal that the dynamic control strategy (S2) significantly improved the overall performance of BESS by minimizing the total import/export energy and the number of equivalent full cycles (EFCs).This reduction in energy throughput and EFCs indicates the potential for extending the operational life and reliability of the BESS, while still meeting the service demands effectively.
Furthermore, the analysis emphasized the importance of BESS availability, where a higher average availability of the system was considered more crucial than achieving a higher number of cycles.This is particularly relevant when considering the economics of BESS deployment and the associated cost per cycle.Overall, the study underscores the significance of dynamic control strategies in optimizing BESS performance for DR-LF and DR-HF services.These insights can be beneficial for decision-makers and stakeholders in the energy sector seeking to implement efficient and cost-effective energy storage solutions while enhancing grid stability and reliability.

Figure 1 .
Figure 1.Block diagram of DR Service model.

Figure 2 .
Figure 2. Implemented BESS power management strategy for DR service model.

Figure 3 .
Figure 3. Flow diagram of Dynamic Control Model.

Figure 6 .
Figure 6.Power vs. frequency for DR-HF and DR-LF service.

Figure 7
Figure 7 depicts the simulation results of a BESS delivering Demand Response with DR-HF, contracted for 40 MW, for the first 18 h of January 2019.The plots include data for frequency, P Demand , P BESS , and SOC.The blue dashed lines on the frequency plot represent the DB (±0.015Hz).The P Demand and P BESS are represented by orange and violet colors, respectively.

Figure 7 .
Figure 7. Simulation results of DR-HF service for the first 18 h on January 2019 (40 MW/40 MWh ESS).

Figure 9
Figure 9 presents the simulation results of a BESS delivering DR-HF and DR-LF, contracted for 40 MW, for the first 3 days of January 2019 for frequency, P Demand , P BESS , and SOC.The blue dashed lines on the frequency plot represent the DB (±0.015Hz).The P Demand and P BESS are represented by red and blue colors, respectively.

Figure 9 .
Figure 9. Simulation results of DR-HF and DR-LF Services for the first 3 days of January 2019 (40 MW/40 MWh BESS).

Figure 10 .
Figure 10.Simulation results of DR-HF with Dynamic Control using test inputs.

Figure 11 .
Figure 11.Simulation results of DR-LF with Dynamic Control using test inputs.

Figure 12 .
Figure 12.Implemented error calculation (e m ) for DR service model.

Figure 13 .
Figure 13.The payment adjustment (K e factor) curve.

Figure 14 .Figure 15 .
Figure 14.Simulation results of DR-HF with Dynamic Control (SOC < SOC lower ) using test inputs.

Figure 16 .
Figure 16.Simulation results of BESS used to deliver DR-HF and DR-LF with dynamic control for the first 6 EFA blocks for December 2019 frequency data (Avg.availability vs. Dynamic Control SOC setpoint).

Figure 17 .
Figure 17.The obtained number of cycles from EFCs for BESS used to deliver DR-HF and DR-LF with Dynamic Control, based on grouped dynamic control SOC setpoint for the first 6 EFA blocks for November 2019 frequency data.

Figure 18 .
Figure 18.Simulation results for battery SOC for different scenarios (S1&S2) for the first six EFA blocks of Dec-2019 frequency data, SOC start =50%.are obtained by implementing both DR-LF & DR-HF services for the first six EFA blocks of Dec-2019 based on the two different scenarios (S1 & S2).From all these Tables, it can be noticed that, in all scenarios, the penalty payment has not occurred at any EFA blocks because the K e factor equates to(1), which means that the providers can get a full payment.In addition to that, the obtained results that are shown in the EFA odd blocks (1, 3, and 5) for all different SOC start illustrate that at S2, the total export/import energy is minimized over the time compared to S1, and this has led to decrease the total number of cycles that are obtained from EFCs, and the main reason behind this is that the implemented dynamic control has allowed more time for BESS to be charged or discharged.Moreover, from Table5.6, the results show that in all EFA odd blocks where the SOC start =50% in both scenarios (S1&S2) the average availability of BESS is 100%, whereas, at the same EFA blocks and for SOC start =30%, the average availability for BESS reaches 100% for the EFA blocks 3 & 5 but for EFA block1 at S1, it equates to almost 98.90%, and for S2, it was increased to approximately 99.14%, when SOC start =70%, the battery reach 100% of average availability for both scenarios at EFA blocks (1 & 3) but for block5, at (S1) it was ∼ 97.29% and it increased to almost 98.90% for S2.In the EFA even blocks (2, 4, and 6), for SOC start =50%, the average availability of BESS reached 100% except for block2 with 99.58% for S1, and it increased to ∼99.72, however, for SOC start =30%, the average availability reached 100% for both S1 & S2, for EFA blocks(4  & 6), but for block2, it equates to 95.89% for S1, and it increased to approximately 96.78%, and for SOC start =70%, BESS has reached 100% of average availability at only EFA block2 and the main reason why BESS did not reach 100% of average availability for the first and

Figure 18 .
Figure 18.Simulation results for battery SOC for different scenarios (S1 and S2) for the first six EFA blocks of December 2019 frequency data, SOC start = 50%.

Table 2 .
P DR and frequency setpoints and calculations in the control algorithm.

Table 5 .
The number of cycles obtained from the EFCs counting method based on grouped dynamic control SOC setpoint using BESS used to deliver DR-LF and DR-HF services with implementing dynamic control for the first 6 EFA blocks for November 2019 frequency data.

Table 6 .
Simulation results of DR-HF and DR-LF services with the two different scenarios for the first 6 EFA blocks for December 2019 frequency data, SOC start = 50%.

Table 7 .
Simulation results of DR-HF and DR-LF services with the two different scenarios for the first 6 EFA blocks for December 2019 frequency data, SOC start = 30%.

Table 8 .
Simulation results of DR-HF and DR-LF services with the two different scenarios for the first 6 EFA blocks for December 2019 frequency data, SOC start = 70%.