Optimal Scheduling and Real-Time State-of-Charge Management of Energy Storage System for Frequency Regulation

Abstract

An energy storage system (ESS) in a power system facilitates tasks such as renewable integration, peak shaving, and the use of ancillary services. Among the various functions of an ESS, this study focused on frequency regulation (or secondary reserve). This paper presents an optimal scheduling algorithm for frequency regulation by an ESS. This algorithm determines the bidding capacity and base point of an ESS in each operational period to achieve the maximum profit within a stable state-of-charge (SOC) range. However, the charging/discharging efficiency of an ESS causes SOC errors whenever the ESS performs frequency regulation. With an increase in SOC errors, the ESS cannot respond to an automatic generation control (AGC) signal. This situation results in low ESS performance scores, and finally, the ESS is disqualified from performing frequency regulation. This paper also presents a real-time SOC management algorithm aimed at solving the SOC error problem in real-time operations. This algorithm compensates for SOC errors by changing the base point of the ESS. The optimal scheduling algorithm is implemented in MATLAB by using the particle swarm optimization (PSO) method. In addition, changes in the SOC when the ESS performs frequency regulation in a real-time operation are confirmed using the PSCAD/EMTDC tool. The simulation results show that the optimal scheduling algorithm manages the SOC more efficiently than a commonly employed planning method. In addition, the proposed real-time SOC management algorithm is confirmed to be capable of performing SOC recovery.

1. Introduction

Recent power systems are focusing on energy storage systems (ESSs) because of their ability to store energy. Many studies have examined ESSs to utilize renewable integration, peak shaving, ancillary services, and microgrids [1,2,3,4,5,6,7,8,9,10]. In [11], the authors presented the feasibility of an ESS for the operation of an island AC microgrid with photovoltaic generation. In [12], the authors proposed an ESS management algorithm for full renewable energy source (RES) exploitation. This algorithm was shown to minimize the curtailment of RES energy generation through energy buffering and forecasting error compensation by an ESS. A one-day-ahead scheduling procedure was combined with a real-time control strategy to improve RES generation and reliability. This study shows that excellent forecasting error compensation can be achieved even with ESSs of moderate size. In recent years, many studies have focused on the ability of ESSs to enable frequency regulation, given that its ramp rate is higher than that of conventional resources. In [13], the authors proposed an alternative market structure with the ability to efficiently demand response (DR) and automatic generation control (AGC) and accommodate the intermittency and uncertainty that are concomitant in renewable generation, thereby leading to the efficient integration of renewables at the market level and reduced regulation requirements at the AGC level. This paper proposed an integrated dynamic market mechanism (DMM) that combined a real-time market clearing procedure with AGC. DMM implementation enabled more frequent economic dispatch than the optimal power flow (OPF). Our proposed algorithm also reduces the root mean square error of the area control error by using an aggregate frequency error. In [14], the authors proposed a hybrid operation strategy for a wind energy conversion system with a battery energy storage system (BESS) to support frequency control. In their study, the output power command of the BESS was determined according to three factors: the state-of-charge (SOC), frequency deviation, and load variation. Their proposed operation strategy significantly improved the initial low-frequency response and provided a superior contribution to short-term frequency regulation. The research of [15] proposed an SOC feedback control scheme and investigated the performance of the grid frequency deviation response. The control was integrated with the widely used wind turbine blade pitch control and the speed governor control of a local synchronous generator. It was shown that the ESS helped supply power to wind farms to support frequency regulation and effectively regulated the battery SOC. An outcome of the increasing number of studies conducted on ESS frequency control is the proposal of a novel approach associated with the actual performance measurement of an ESS conducting frequency regulation [16]. This paper evaluated the current methods for procuring, dispatching, and compensating resources for frequency regulation. The authors also calculated the performance payment of the proposed novel approach by employing a sigmoid function. This approach influenced revenue by adjusting the calculation of the performance score. This approach will provide further insight into administrative price adjustment. The operator would be able to estimate the total mileage expected on an annual cost, and they would be able to calculate an administrative price that would reflect a fair compensation for the resources based on their actual frequency-regulation contribution and performance. In [17], the authors proposed a model that decided the optimal joint bidding strategy of battery storage in joint day-ahead energy, reserve, and regulation markets. Their novel algorithm considering the battery life cycle significantly improved a storage battery’s overall economics in performance-based regulation.

At present, an ESS participates in the frequency regulation market by bidding its maximum capacity. However, an ESS is unable to manage its SOC because the power system operator sends an AGC signal without considering the SOC of an ESS. If an ESS is unable to manage its SOC, it does not respond to the AGC signal; therefore, an ESS should be able to manage its SOC. Many studies have focused on SOC management via day-ahead scheduling or via compensation by renewable generation; however, management by these methods in a real-time operation is difficult.

This study proposes an optimal scheduling algorithm and a real-time SOC management algorithm for frequency regulation by an ESS. The optimal scheduling algorithm determines the bidding capacity and base point through the particle swarm optimization (PSO) method for achieving the maximum profit through SOC management. Further, the real-time SOC management algorithm recovers the SOC in a real-time operation via participation in the energy market. This algorithm manages the SOC of an ESS by rebidding the scheduled base point in the energy market. Furthermore, a simulation is performed using actual PJM (Monroe, MN, USA) operation data. This paper is organized as follows. Section 2 explains the frequency regulation service and frequency regulation market. Section 3 presents the optimal scheduling algorithm and compares it with a commonly employed planning method. Section 4 presents the proposed real-time SOC management algorithm. Section 5 presents simulation cases and discusses the simulation results. Section 6 summarizes the conclusions and suggests future work.

2. Frequency Regulation Market

In a power system, the frequency changes continuously because of an imbalance of supply and demand. The system operators conduct frequency regulation or secondary reserve to reduce the fluctuations and thereby provide stable and reliable system operation. Frequency regulation involves the injection or withdrawal of as much active power as the assigned regulation capacity of the resource [18]. Two types of frequency regulation market exist. The first frequency regulation market type is separated into regulation up and regulation down. Examples include New York Independent System Operator (NYISO, Rensselaer, NY, USA) and California Independent System Operator (CAISO, Folsom, CA, USA), and ISO of Europe. The second frequency regulation market type does not separate regulation up and regulation down and examples for this type include PJM and Midcontinent Independent System Operator (MISO, Carmel, CA, USA). The second frequency regulation market type was assumed in this study because PJM data were used; the frequency regulation market in PJM was selected as the test bed, and simulation was performed according to PJM frequency regulation market rules. To provide frequency regulation, resources bid on the frequency regulation market according to the requisite capacity in each operation time [19]. The resources provide as much active power as the AGC signal whenever the resources receive an AGC signal; this output point is called the “set point”. If the resources participate in the energy market, the resources provide as much active power as the bidding quantity every time; this output point is called the “base point”. The resources participating in both frequency regulation and the energy market provide as much active power as the base point and perform frequency regulation whenever the resources receive an AGC signal by additionally providing as much active power as the set point [20]. Figure 1 illustrates the concept of the set point and base point of an ESS.

An ESS always provides active power according to the base point with the assigned energy and provides active power according to the set point when the ESS receives an AGC signal. Therefore, an ESS provides as much active power as the output point. The data used in this paper consist of the actual operation data of the PJM region. The hourly averaged AGC signal, regulation market capacity clearing price, regulation market performance clearing price, and locational marginal price were used to plan the optimal scheduling [21,22,23]. A real-time operation simulation was performed using an actual AGC signal. The data were collected on 5 September 2013. Figure 2 shows the hourly market price data, hourly averaged AGC signal, and actual AGC signal.

3. Optimal Scheduling Algorithm

To provide frequency regulation, ESS owners bid the maximum capacity in the day-ahead market, but they do not manage the SOC in the same manner. The optimal scheduling algorithm schedules the bidding plan of an ESS to earn the maximum profit within a stable SOC range. When a schedule is determined, ESS owners bid on the frequency regulation market in day-ahead market according to the schedule. For a scheduling plan, this study chose 4 MW/2 MWh Li-ion batteries as the ESS and set the charging/discharging efficiency to 91%. The initial SOC was set at 60%. This section compares the SOC, frequency regulation profit, and scheduling results of the maximum-capacity bidding plan and the optimal scheduling algorithm.

3.1. Maximum-Capacity Bidding Plan

The maximum-capacity bidding plan is a conventional bidding method in the frequency regulation market. In this plan, the base point is set to zero. Therefore, the bidding capacity is 4 MW, and the base point is set to 0 p.u. The SOC changes are calculated as follows Equation (1):

$$\begin{gathered} \mathrm{If}\overline{AGC}\left(i\right)\le 0,SOC\left(i+1\right)=SOC\left(i\right)-\frac{c_{bid}\times \overline{AGC}\left(i\right)}{C_{rated}}\times {\mathsf{\eta }}_c\times \Delta t; \\ \mathrm{If}\overline{AGC}\left(i\right)>0,SOC\left(i+1\right)=SOC\left(i\right)-\frac{c_{bid}\times \overline{AGC}\left(i\right)}{C_{rated}}\times \frac{1}{{\mathsf{\eta }}_d}\times \Delta t \end{gathered}$$

(1)

where i is the index of time (h), SOC (i) is the SOC of the ESS at time i, $c_{bid}$ is the bidding capacity of ESS, $C_{rated}$ is the rated capacity of ESS, $\overline{AGC}\left(i\right)$ is the hourly averaged AGC signal, and ${\mathsf{\eta }}_c$ and ${\mathsf{\eta }}_d$ are the charging and discharging efficiencies of the ESS, respectively. Figure 3 presents the bidding capacity, base point, and SOC when the ESS is bid by the maximum-capacity bidding plan. In addition,

Table 1. Frequency regulation scheduling profits.

Method	Regulation Profit	Energy Profit	Total Profit
Maximum capacity bidding plan	$2773.4	$0	$2773.4
Optimal scheduling algorithm	$2483.1	$9.4	$2492.5

lists the frequency regulation profit.

3.2. Optimal Scheduling Algorithm

The optimal-scheduling algorithm is a method used to earn the maximum profit within a stable SOC using the PSO method. PSO is a widely used traditional method for solving problems in power systems [24,25,26,27]. PSO solves the optimization problem as follows:

$$x_{k+1}^j=x_k^j+v_{k+1}^j$$

(2)

$$v_{k+1}^j=w{v}_k^j+c_1{r}_1\left(P_k^j-x_k^j\right)+c_2{r}_2\left(P_k^g-x_k^j\right)$$

(3)

where $P_k^j$ and $P_k^g$ are the individual best position and the global best position, respectively; k and j represent the iteration number and particle number, respectively; x is the position of the particle; v is the velocity; w is the inertia weight; $c_1$ and $c_2$ are acceleration coefficients, and $r_1$ and $r_2$ are randomly generated numbers in the range of [0,1]. The PSO method finds a solution to minimize the cost function, F ($x_i$). To minimize the cost function F ($x_i$) in particle j, PSO calculates the individual best position of particle j using each x_i and updates each x_i position as much as the velocities to find the individual best position in each iteration k. Finally, PSO is used to compare the individual best position to update the global best position and determine a solution.

To plan the optimal scheduling, the cost function, F (x_i), was formulated as:

$$max{\displaystyle {\displaystyle \sum }_{i=1}^{24}}{C}_o\left(i\right)$$

(4)

$$C_o\left(i\right)=C_c\left(i\right)+C_p\left(i\right)-C_e\left(i\right)$$

(5)

$$C_c\left(i\right)=c\left(x_i\right)\times RMCCP\left(i\right)\times PS$$

(6)

$$C_p\left(i\right)=c\left(x_i\right)\times RMPCP\left(i\right)\times PS\times MR$$

(7)

$$C_e\left(i\right)=c\left(x_i\right)\times LMP\left(i\right)\times bp\left(x_i\right)$$

(8)

subject to the following constraints:

SOC (0) = SOC (24)

(9)

$$SO{C}_{\min }\le SOC\left(i\right)\le SO{C}_{\max }$$

(10)

$$\begin{gathered} \mathrm{If}\overline{AGC}\left(i\right)\le 0,SOC\left(i+1\right)=SOC\left(i\right)-\frac{c_{bid}\times \left[\overline{AGC}\left(i\right)+bp\left(x_i\right)\right]}{C_{rated}}\times {\mathsf{\eta }}_c\times \Delta t; \\ \mathrm{If}\overline{AGC}\left(i\right)>0,SOC\left(i+1\right)=SOC\left(i\right)-\frac{c_{bid}\times \left[\overline{AGC}\left(i\right)+bp\left(x_i\right)\right]}{C_{rated}}\times \frac{1}{{\mathsf{\eta }}_d}\times \Delta t \end{gathered}$$

(11)

$$c\left(x_i\right)+c\left(x_i\right)\times bp\left(x_i\right)\le Maximumcapacity$$

(12)

where $C_o\left(i\right)$ is the operation profit, $C_c\left(i\right)$ and $C_p\left(i\right)$ are the regulation capability credit and regulation performance credit, respectively; $C_e\left(i\right)$ is the cost by bidding in the energy market; $c\left(x_i\right)$ and $bp\left(x_i\right)$ are the scheduled bidding capacity and base point in the energy market by PSO, respectively; RMCCP (i), RMPCP (i), and LMP (i) are the hourly regulation market capability clearing price, the hourly regulation market performance clearing price, and the hourly locational marginal pricing, respectively. PS and MR are the performance score and mileage ratio, respectively. Note that the initial SOC and final SOC are considered in constraint Equation (9). For operation within a stable SOC range, the SOC management constraint is set as in Equation (10). The SOC was calculated using constraint Equation (11). Constraint Equation (12) manages the bidding capacity up to the maximum capacity. For the optimal scheduling algorithm, the upper and lower limits of the stable SOC range, S_min and S_max, are set to 40% and 80%, respectively. Typically, ESSs achieve a performance score of 0.95; thus, PS was assumed to be 0.95. In addition, the MR on 5 September 2013 was 3. To perform optimal scheduling, the data described in Section 3 were used, and Equations (4)–(12) were solved in MATLAB/Simulink (MathWorks, Natick, MA, USA). Figure 3 shows the changes in the bidding capacity, base point, and SOC. Table 1 lists the frequency regulation profits. Regulation profit is the benefit participating frequency regulation market, and energy profit is the cost participating energy market. As shown in Table 1, the maximum-capacity bidding plan earned higher frequency regulation profit than that of the optimal scheduling algorithm. On the other hand, the optimal scheduling algorithm was advantageous in terms of SOC management. The maximum-capacity bidding plan did not manage the SOC, which can cause problems in the operation the next day; in contrast, the optimal scheduling algorithm did manage the SOC by using constraints Equations (9) and (10), which ensured stable operation every day.

4. Real-Time State-of-Charge Management Algorithm

In a real-time operation, the ESS performs frequency regulation in response to an AGC signal every two seconds. The charging/discharging efficiency of the ESS causes an SOC error whenever the ESS provides frequency regulation. Because the SOC error would prevent the ESS from providing frequency regulation, a novel SOC management algorithm is proposed. In a real-time operation, the SOC is calculated as follows:

$$\begin{gathered} \mathrm{If}AGC(z)\le 0,SOC\left(z+1\right)=SOC\left(z\right)-\frac{c\left(x_i\right)\times \left[AGC\left(z\right)+bp\left(x_i\right)\right]}{C_{rated}}\times {\mathsf{\eta }}_c\times \Delta t; \\ \mathrm{If}AGC(z)>0,SOC\left(z+1\right)=SOC\left(z\right)-\frac{c\left(x_i\right)\times \left[AGC\left(z\right)+bp\left(x_i\right)\right]}{C_{rated}}\times \frac{1}{{\mathsf{\eta }}_d}\times \Delta t \end{gathered}$$

(13)

where AGC (z) is the actual AGC signal, and z is the frequency regulation interval. To solve the SOC error, this study presents a real-time SOC management algorithm. This algorithm changes the base point through hysteresis loop according to the SOC range. Figure 4 illustrates the concept of a real-time SOC management algorithm. When the SOC is between SOC_{min_limit} and SOC_{max_limit}, the base point is set to $bp\left(x_i\right)$. The ESS then operates according to the optimal scheduling algorithm. When the SOC is above SOC_{max_limit} because of the accumulation of SOC errors, $bp\left(x_i+2\right)$ is set to $B{P}_{dis}$ by rebidding the base point after two hours’ operation according to PJM market rules. Owing to the changing base point, the ESS provides as much additional active power in the energy market as $B{P}_{dis}$ until the SOC crosses SOC_{max_end}. When the SOC crosses SOC_{max_end}, the ESS bids the base point as $bp\left(x_i+2\right)$ in the optimal scheduling algorithm results. When the SOC is below SOC_{min_limit}, bp (x_i + 2) is set to $B{P}_{ch}$ by rebidding the base point, and the ESS provides as much additional active power in the energy market as $B{P}_{ch}$ until the SOC crosses SOC_{min_end}. When the SOC crosses SOC_{min_end}, the ESS bids the base point as $bp\left(x_i+2\right)$ in the optimal scheduling algorithm results.

Table 2. Simulation case results.

Case	Regulation Profit	Energy Profit	Total Profit	SOC
Case 1	$911.8	$0	$911.8	10%
Case 2	$1116.2	$−10.4	$1105.8	10%
Case 3 (0.05 p.u)	$2630.3	$−147.4	$2482.9	39.9%
Case 3 (0.1 p.u)	$2555.5	$−159.7	$2395.8	48.9%
Case 3 (0.15 p.u)	$2506.2	$−157.2	$2349	37.4%

lists the parameters selected to maintain a stable SOC range for real-time SOC management. SOC_{min_limit} and SOC_{max_limit} was set to 45% and 75%, respectively. SOC_{min_end} and SOC_{max_end} was set to 50% and 70% respectively. The stable SOC range was set from 40% to 80%.

5. Simulation Results

This section reports the simulation results to evaluate the performance of the proposed algorithm using a real operation parameter. In the first case, the maximum-capacity bidding plan was performed, the second case used the optimal scheduling algorithm, and the third case applied the real-time SOC management algorithm to the optimal scheduling algorithm. The PSCAD/EMTDC (Manitoba HVDC Research Centre, Winnipeg, MB, Canada) was used to confirm the SOC changes using Equation (12) when the ESS performed frequency regulation in a real-time operation. The actual AGC signal data in the PJM on 5 September 2013 were used to calculate the SOC in real-time. Because the AGC cycle of the PJM is 2 s, the SOC was calculated every 2 s. For the simulation, the scheduling was set as described in Section 4. To protect the ESS, the operational SOC range was set between 10% and 90%. Therefore, the ESS will shut down to protect itself when the SOC exceeds the operational SOC range. Case 1 is result by maximum capacity bidding plan, case 2 is result by optimal scheduling algorithm and case 3 is result by optimal scheduling algorithm with real-time SOC management by various base point. Cases 1 and 2 were compared to evaluate the optimal scheduling algorithm, which was confirmed by the frequency regulation profit change and increased operation time. In addition, Case 2 was compared with Case 3 to evaluate the real-time SOC management algorithm by changing the base point. Table 2 shows total case results.

5.1. Case 1

Figure 5 shows the SOC changes when the ESS performed frequency regulation through the maximum-capacity bidding plan. In a real-time operation, the ESS performs frequency regulation by charging and discharging in response to an AGC signal. At 1 a.m., the SOC difference between the real-time operation SOC (55.8%) and maximum-capacity bidding plan (59.8%) was 4% because of the charging/discharging efficiency. This SOC difference increased consistently when the ESS performed the frequency regulation in a real-time operation. At 10 a.m., the SOC reached 10%, and the ESS was shut down. When the ESS performed frequency regulation according to the maximum-capacity bidding plan, the performance score decreased because the ESS does not perform frequency regulation when the SOC reaches 10%. According to the decreasing performance score, the frequency regulation profit decreased from $2773.40 to $911.80.

5.2. Case 2

Figure 6 shows the SOC changes when the ESS performed frequency regulation through the optimal scheduling algorithm of Section 4. The SOC decreased consistently when the ESS performed frequency regulation. According to the optimal scheduling algorithm, the base point of the ESS was set to −0.1 p.u for charging the SOC at 6 a.m. By changing the base point, the ESS recovered the SOC. Nevertheless, the real-time SOC reached 10% at 1 p.m., and the ESS was shut down. On the other hand, the simulation result of the optimal scheduling algorithm operated 3 h longer than the maximum-capacity bidding plan because the optimal scheduling algorithm managed the SOC by constraint in Equation (10). In the planning step, the maximum-capacity bidding plan earned more frequency regulation profit than the optimal scheduling algorithm (more than $280.90); however, in the real-time operation, the optimal scheduling algorithm earned more frequency regulation profit than the maximum-capacity bidding plan (as much as $194.00) through its scheduling capacity and base point. This result means that the optimal scheduling algorithm can increase the operation time of the ESS and earn more frequency regulation profit.

5.3. Case 3

Figure 7 presents the SOC changes when the ESS performed frequency regulation through the optimal scheduling algorithm and real-time SOC management algorithm by various base points. In the 0.05-p.u case, at 3 a.m., the SOC reached 43.7%. Consequently, the bidding schedule of the base point was changed to −0.05 p.u through the real-time SOC management algorithm after 2 h according to the PJM market rules until 9 a.m., when the SOC reaches more than 50%. The bidding schedule can change 1 h before the operation time according to PJM market rules, thus, the bidding schedule was changed at 4 a.m. because the bidding schedule of 3 a.m. had already been submitted. Although the SOC reached more than 50% at 3 p.m., the bidding schedule was not changed until 4 p.m. for the same reason. Owing to the changed base point, the bidding capacity was also changed to 3.8 MW by constraint Equation (12). In this case, the ESS maintained recovery time for 16 h because 0.05 p.u was not enough for SOC recovery. The SOC reached 39.9% when the ESS finished operating. The frequency regulation earned a profit of $2482.90. In the 0.1-p.u case, the ESS maintained the recovery time for 8 h, and the 0.1-p.u case recovery was more rapid and stable than that of the 0.05-p.u case. The SOC reached 48.9% in the stable range, and the frequency regulation earned a profit of $2395.80. In the 0.15-p.u case, the ESS recovery was more rapid than that of the 0.1-p.u case; however, the 0.15-p.u case recovered too much because the SOC reached 81.7% at 5 p.m. The SOC management algorithm changed the base point to 0.15 p.u, causing the SOC to escape the stable range again. In this case, the ESS maintained the recovery time for 9 h, and the SOC reached 37.4%. The frequency regulation earned a profit of $2349. The ESS of Case 3 used the optimal scheduling algorithm and real-time SOC management algorithm to perform frequency regulation for a day. In contrast, Case 2, which used only the optimal scheduling algorithm, did not perform for a day. This result shows that when an ESS performs frequency regulation without an additional SOC management algorithm, the ESS does not perform for a day, and the proposed SOC management algorithm successfully managed the SOC of the ESS. Moreover, the base point is a significant factor in this algorithm because the base point determines the recovery quantity.

Table 3. Additional simulation case results.

Optimal Scheduling & Real-Time SOC Managment	Base Point	Profit	SOC
2013.06.10	0.05	$1254.2 → $211.7	10%
	0.1	$1254.2 → $948.4	25.61%
	0.15	$1254.2 → $953.6	40.60%
2013.12.2	0.05	$2232.4 → $1857.1	51.42%
	0.1	$2232.4 → $1815.1	37.89%
	0.15	$2232.4 → $1778.1	42.32%
2014.03.10	0.05	$4024.3 → $3536.8	52.12%
	0.1	$4024.3 → $3301.4	65.56%
	0.15	$4024.3 → $3475.8	41.21%

lists simulation results for different day. As shown Table 3, the base point is an important factor in this algorithm because the base point determines the recovery quantity of the SOC. Furthermore, for the determination base point, real-time SOC management algorithm should use accurate forecasting information.

6. Conclusions

This study proposed an optimal scheduling algorithm for frequency regulation by an ESS to ensure the realization of maximum profit within a stable SOC range. The maximum-capacity bidding plan is the best method for realizing frequency regulation profit, but it does not manage the SOC. The optimal scheduling algorithm schedules a bidding plan using the PSO method to realize the maximum frequency regulation profit within a stable SOC range. Although the optimal scheduling algorithm provides less frequency regulation profit than the maximum-capacity bidding plan, the former maintains stable operation through SOC management. The proposed algorithm was evaluated through simulation of three cases by means of the PSCAD/EMTDC tool in a real-time operation. The simulation results show that the optimal scheduling algorithm increases the duration of real-time operation and results in higher profits in comparison to the conventional bidding plan without SOC management. While the conventional maximum-capacity bidding plan provides more profit than the optimal scheduling algorithm in the planning step, the optimal scheduling algorithm provides more profit in real-time operations.

This study also proposed a real-time SOC management algorithm. The ESS constantly performs frequency regulation using this algorithm by which the ESS changes the base point to recover the SOC in a real-time operation. In the case where the real-time SOC management algorithm was applied in the PJM regulation market, it effectively recovered the SOC when the base point was changed to 0.1 p.u. The proposed real-time SOC management algorithm can be applied to various regulation market environments by changing the base point. This algorithm is expected to promote the participation of ESSs in various regulation markets.

Future work will deal with the forecasting error. The cases in this study were simulated using actual operation data, but the ESS uses forecast data during actual operation. Accordingly, the proposed algorithm should consider ESS potential forecasting error.