As the energy development strategy of our country continues to advance, renewable energy devices primarily based on wind and solar power are increasingly being integrated into power grids. However, these renewable energy devices do not possess the capability to actively participate in frequency response, which significantly reduces system inertia. Moreover, their output is highly uncertain and fluctuating, making it difficult for traditional thermal power units and other frequency regulation units to meet the system’s frequency regulation demands. Battery Energy Storage Systems (BESS) exhibit characteristics such as fast response speed, high control accuracy, and flexible configuration, making them an excellent frequency regulation resource. In recent years, the application of battery energy storage systems in frequency control has garnered widespread attention, and many engineering projects involving energy storage participation in frequency regulation have been implemented in our country.
To date, scholars both domestically and internationally have conducted in-depth research on control strategies for battery energy storage systems participating in primary frequency regulation (PFR). Some studies have considered the limitations of virtual droop control in the initial stage of frequency disturbances and introduced virtual inertia control to effectively reduce the rate of change of frequency (ROCOF) during the initial disturbance. Other research has shown that while virtual inertia control can reduce the speed of frequency drop, it also hinders frequency recovery. Therefore, a negative virtual inertia control was designed, switching control modes in different frequency intervals to meet the system’s frequency regulation needs. Further analysis of the regulation requirements at different frequency regulation stages has been performed to optimize the action timing and depth of virtual droop and virtual inertia control, achieving complementary advantages between the two controls. Additionally, based on the state of charge (SOC), the output of battery energy storage systems is constrained to prevent overcharging and overdischarging. Fuzzy control strategies have been adopted to achieve smooth switching between the two typical control modes, and feedback coefficients are designed using logistic regression functions to prevent SOC from exceeding limits.
The setting of the frequency regulation dead band also affects the response timing and action depth of battery energy storage systems in primary frequency regulation. Some studies have set the dead band range of battery energy storage systems to be smaller than that of traditional synchronous units, thereby improving the frequency regulation capability of the energy storage system while reducing the number of actions of synchronous units, effectively enhancing system frequency quality. Others have analyzed the influence mechanism of the dead band of renewable energy units and proposed a frequency regulation coefficient correction strategy to reduce the adverse effects of the dead band on system stability. Several approaches have been implemented to restore the SOC of battery energy storage systems within the dead band range, improving the frequency regulation effect while adjusting the SOC to an ideal state. A joint wind-storage control strategy considering the dead band has also been proposed, manually setting the dead bands of wind turbines and battery energy storage systems to achieve better control performance.
In summary, most existing research on battery energy storage systems participating in frequency control focuses on how to achieve complementary advantages between the two typical control modes and constraining control coefficients through SOC to prevent overcharging and overdischarging. However, the setting of the frequency regulation dead band and control coefficients often does not fully consider the frequency regulation requirements of the power system, making them unable to adapt to different load disturbance conditions. To address this problem, this paper proposes an adaptive frequency control strategy for battery energy storage systems considering the frequency regulation dead band, achieving adaptive adjustment of the dead band range and control coefficients, aiming to optimize the dynamic frequency regulation performance of battery energy storage systems under different operating conditions. The superiority of the proposed control strategy is verified through simulation.
1. Primary Frequency Regulation Model of Power System with Battery Energy Storage Systems
To analyze the influence of the frequency regulation dead band and control coefficients of battery energy storage systems on their frequency regulation capability, a dynamic primary frequency regulation model of a power system containing battery energy storage systems is established, as shown in the following figure.
In the model, \( s \) is the Laplace operator, \( H \) and \( D \) are the equivalent inertia and damping coefficients of the system, respectively, \( K_g \) is the power regulation coefficient of synchronous units, \( \Delta f(s) \) is the system frequency deviation, \( \Delta P_g(s) \) and \( \Delta P_b(s) \) are the frequency regulation outputs of synchronous units and battery energy storage systems, respectively, \( \Delta P_L(s) \) is the load disturbance, and \( G_g(s) \) and \( G_b(s) \) are the transfer functions of synchronous units and battery energy storage systems, respectively.
$$ G_g(s) = \frac{1 + F_H T_{RH} s}{(1 + T_G s)(1 + T_{CH})(1 + T_{RH} s)} $$
$$ G_b(s) = \frac{1}{1 + T_{PCS} s} $$
where \( F_H \) is the reheater gain; \( T_G \), \( T_{CH} \), and \( T_{RH} \) are the time constants of the governor, turbine, and reheat turbine, respectively; \( T_{PCS} \) is the time constant of the power conversion system of battery energy storage systems.
To improve the stability of units under small frequency fluctuations, a frequency regulation dead band is set. The traditional setting method for the dead band is shown in the following conceptual description: \( \Delta f_{in} \) is the frequency deviation input to the dead band, \( \Delta f_{out} \) is the frequency deviation after passing through the dead band, and \( D_{th} \) is the boundary value of the frequency regulation dead band. The dead band only outputs the frequency regulation reference signal when the frequency deviation exceeds \( D_{th} \). If \( D_{th} \) is set too large, although it reduces the number of actions of battery energy storage systems, it also slows down the response speed and reduces the frequency regulation performance; if \( D_{th} \) is set too small, it causes frequent starts of battery energy storage systems, reducing their service life. Therefore, it is necessary to set the dead band range reasonably to improve the frequency regulation effect of battery energy storage systems under different operating conditions.
Based on the model, the dynamic response equation of system frequency is established:
$$ 2H \frac{d \Delta f(t)}{dt} + D \Delta f(t) = \Delta P_g(t) + \Delta P_b(t) – \Delta P_L(t) $$
When battery energy storage systems participate in frequency regulation through virtual inertia control or virtual droop control, the output power expressions are:
$$ \Delta P_{ME}(s) = -M_E s \Delta f(s) G_b(s) $$
$$ \Delta P_{KE}(s) = -K_E \Delta f(s) G_b(s) $$
where \( \Delta P_{ME}(s) \) and \( \Delta P_{KE}(s) \) are the output powers of battery energy storage systems under virtual inertia control and virtual droop control, respectively; \( M_E \) and \( K_E \) are the virtual inertia coefficient and virtual droop coefficient, respectively.
From the above equations, we can derive the frequency deviations under different control modes:
$$ \Delta f_I(s) = \frac{-\Delta P_L(s)}{2Hs + D – K_g G_g(s) – M_E s G_b(s)} $$
$$ \Delta f_D(s) = \frac{-\Delta P_L(s)}{2Hs + D – K_g G_g(s) – K_E G_b(s)} $$
Virtual inertia control can effectively slow down the speed of frequency drop but has little effect on the frequency deviation magnitude. Once the frequency reaches its nadir, it reverses the output direction, affecting the speed of frequency recovery. Virtual droop control can effectively reduce the magnitude of frequency deviation but cannot slow down the speed of frequency drop. Therefore, a reasonable allocation of \( M_E \) and \( K_E \) can significantly improve the frequency regulation effect of battery energy storage systems. If \( M_E \) and \( K_E \) remain constant during the control process, the battery energy storage systems will quickly release stored energy to suppress the frequency drop, but this will also cause the SOC to change too rapidly, leading to overcharging or overdischarging. To further analyze the impact of different magnitudes of \( M_E \) and \( K_E \) on the frequency regulation effect of battery energy storage systems, the following two cases are considered:
Case 1: \( M_{E1} \) and \( K_{E1} \) are both constant values of 1. The system frequency is given by:
$$ \Delta F_1(s) = \frac{\Delta P_L(s)}{K_g G_g(s) + (M_{E1}s + K_{E1}) G_b(s) – 2Hs – D} $$
Case 2: \( M_{E2} \) and \( K_{E2} \) are constrained by SOC. When SOC is low, both \( M_{E2} \) and \( K_{E2} \) are less than 1. The system frequency is:
$$ \Delta F_2(s) = \frac{\Delta P_L(s)}{K_g G_g(s) + (M_{E2}s + K_{E2}) G_b(s) – 2Hs – D} $$
Comparing the two equations, when \( M_E \) and \( K_E \) are low, \( |\Delta F_1(s)| < |\Delta F_2(s)| \), indicating that reducing \( M_E \) and \( K_E \) weakens the frequency regulation capability of battery energy storage systems. However, too high values of \( M_E \) and \( K_E \) accelerate the decrease of SOC. To improve the frequency regulation effect of battery energy storage systems under different operating conditions, it is necessary to set \( M_E \) and \( K_E \) appropriately.
2. Adaptive Frequency Control Strategy Considering Frequency Regulation Dead Band
The proposed adaptive frequency control strategy for battery energy storage systems considering the frequency regulation dead band is illustrated in the block diagram described below. In the strategy, \( M_{E0} \) and \( K_{E0} \) are the initial values of the virtual inertia coefficient and virtual droop coefficient, respectively. \( K_1 \) and \( K_{SOC1} \) are the input coefficient and feedback coefficient of the virtual inertia control, while \( K_2 \) and \( K_{SOC2} \) are the input coefficient and feedback coefficient of the virtual droop control. The condition \( K_1 + K_2 = 1 \) always holds. \( f \) is the system frequency, \( t \) is the frequency regulation time, and \( \alpha \) is the ratio between the feedback coefficients of the two control modes.
The output power of battery energy storage systems \( \Delta P_b(s) \) is determined jointly by virtual inertia control and virtual droop control, with \( W_1 \) and \( W_2 \) as the output coefficients of the two typical controls:
$$ \Delta P_b(s) = -(W_1 M_{E0} s + W_2 K_{E0}) \Delta f(s) G_b(s) $$
$$ W_1 = K_1 \cdot K_{SOC1} $$
$$ W_2 = K_2 \cdot K_{SOC2} $$
2.1 Adaptive Adjustment of the Frequency Regulation Dead Band
The traditional frequency regulation dead band is set to a fixed range, which cannot meet the frequency regulation requirements under different operating conditions. Therefore, this paper proposes a method that adaptively adjusts the dead band range based on frequency signals and SOC.
Since \( \Delta f \) has a lagging characteristic and cannot promptly reflect the degree of power imbalance in the system, linearization of the dynamic response equation yields the initial rate of change of frequency:
$$ F(t_0) = \left. \frac{d \Delta f}{dt} \right|_{t = t_0} = -\frac{\Delta P}{2H} $$
where \( \Delta P \) is the power imbalance and \( F(t_0) \) is the rate of change of frequency at time \( t_0 \), which is proportional to the power imbalance.
To meet the frequency regulation requirements under different operating conditions, the dead band range of battery energy storage systems is adaptively adjusted by combining ROCOF and SOC:
$$ D_{th} = \begin{cases}
0.033, & F_{\max}(t) < \delta \cup SOC \not\subset (SOC_{\min}, SOC_{\max}) \\
0.02, & F_{\max}(t) < \delta \cup SOC \subset (SOC_{\min}, SOC_{\max}) \\
& \quad / \quad F_{\max}(t) > \delta \cup SOC \not\subset (SOC_{\min}, SOC_{\max}) \\
0, & F_{\max}(t) > \delta \cup SOC \subset (SOC_{\min}, SOC_{\max})
\end{cases} $$
where \( F_{\max}(t) \) is the maximum ROCOF during system operation; \( \delta \) is the constraint value of ROCOF, which can be set according to actual engineering requirements; \( SOC \) is the state of charge of battery energy storage systems; \( SOC_{\max} \) and \( SOC_{\min} \) are the upper and lower limits of SOC, respectively.
The adaptive adjustment flow of the frequency regulation dead band is described as follows. The dead band is set with three boundary values: 0.033 Hz, 0.02 Hz, and 0 Hz. Among them, 0.033 Hz is the traditional dead band boundary, and 0.02 Hz is the optimal dead band boundary. The proposed adaptive method considers the frequency regulation requirements under different operating conditions. Taking the case of battery energy storage systems discharging (when the system frequency deviation \( \Delta f < 0 \)) as an example, four scenarios are considered:
| Scenario | Power imbalance | SOC status | Dead band \( D_{th} \) |
|---|---|---|---|
| 1 | Small | Low SOC | 0.033 Hz |
| 2 | Large | Low SOC | 0.02 Hz |
| 3 | Small | High SOC | 0.02 Hz |
| 4 | Large | High SOC | 0 Hz |
2.2 Adaptive Adjustment of Control Coefficients
To further optimize the frequency regulation effect of battery energy storage systems under different operating conditions, the input coefficients and feedback coefficients are adaptively adjusted.
2.2.1 Adaptive Adjustment of Input Coefficients
By adjusting the input coefficients, the contribution ratio of the two typical control modes in the primary frequency regulation process can be modified, fully leveraging the advantages of each control in different frequency intervals. Fuzzy control, compared to traditional control, can effectively solve nonlinear problems and has good robustness. Therefore, a fuzzy logic controller (FLC) is used to adaptively adjust the input coefficients of the two typical controls.
The first fuzzy logic controller (FLC1) has two input variables: \( df/dt \) and \( \Delta f \), and one output variable \( K_1 \). The universes of the input variables are both \([-0.5, 0.5]\), and the universe of the output variable is \([-1, 1]\). All universes are divided into seven levels: NL (negative large), NM (negative medium), NS (negative small), ZR (zero), PS (positive small), PM (positive medium), PL (positive large). The membership functions of the input and output variables are trapezoidal and triangular membership functions.
The input coefficients must satisfy the following requirements:
- During the frequency drop period, to prevent further deterioration of frequency, the input coefficient of virtual inertia control decreases from the maximum value 1 as \(\Delta f\) increases, while the input coefficient of virtual droop control increases from the minimum value 0 as \(\Delta f\) increases. When ROCOF is zero, the input coefficient of virtual inertia control should be 0, and that of virtual droop control should be 1.
- During the frequency recovery period, ROCOF is negative. If the input coefficient of virtual inertia control continues to be positive, it will reduce the efficiency of frequency recovery. To improve the recovery speed, negative virtual inertia control should be used. Therefore, during this period, the input coefficient of virtual inertia control first decreases from 0 and then increases as ROCOF increases, becoming 0 again when frequency returns to the stable value; the input coefficient of virtual droop control also first decreases and then increases, becoming 1 when frequency is stable.
The fuzzy control rules of FLC1 are established as shown in Table 2. The Mamdani algorithm is used to solve for the input coefficients.
| \(\Delta f\) | \(df/dt\) | ||||||
|---|---|---|---|---|---|---|---|
| NL | NM | NS | ZR | PS | PM | PL | |
| NL | PL | PL | PM | PL | NM | NL | NL |
| NM | PM | PM | PM | PM | NM | NM | NM |
| NS | PM | PS | PS | PS | NS | NS | NM |
| ZR | ZR | ZR | ZR | ZR | ZR | ZR | ZR |
| PS | NM | NS | NS | PS | PS | PS | PM |
| PM | NM | NM | NM | PM | PM | PM | PM |
| PL | NL | NL | NM | PL | PM | PL | PL |
2.2.2 Adaptive Adjustment of Feedback Coefficients
Adaptive adjustment of input coefficients can achieve effective coordination between virtual droop control and virtual inertia control. However, if the SOC of battery energy storage systems is not considered during the frequency regulation process, the SOC may become too high or too low, affecting subsequent frequency regulation effects, and in severe cases, may cause overcharging or overdischarging, leading to lifespan loss. Therefore, to prevent overcharging and overdischarging and to reasonably regulate the output power of battery energy storage systems according to the SOC, the feedback coefficients are adaptively adjusted in combination with the system frequency and the SOC of battery energy storage systems. The block diagram of the feedback coefficient adaptive control strategy is described.
Traditional constraints using a linear function can suppress overcharging and overdischarging, but they may cause secondary disturbance problems at the critical points and also weaken the fast response capability of battery energy storage systems. Therefore, a fuzzy controller is still used to achieve adaptive adjustment of feedback coefficients. The second fuzzy logic controller (FLC2) has input variables \( SOC \) and \( \Delta f \), with universes of \([0, 1]\) and \([-0.2, 0.2]\), respectively, and output variable \( K_3 \) with universe \([0, 1]\). The membership functions of the input and output variables are trapezoidal. The input variable \( SOC \) is characterized by three states: L (low), M (medium), H (high); the other input variable \( \Delta f \) is characterized by two states: N (negative), P (positive); the feedback coefficient \( K_3 \) is represented by two states: L (low), H (high). The fuzzy control rules are shown in Table 3.
| \(\Delta f\) | SOC | ||
|---|---|---|---|
| L | M | H | |
| N | L | H | H |
| P | H | H | L |
The meaning of the FLC2 fuzzy control rules: when the frequency deviation is negative (positive) and the SOC of battery energy storage systems is high (low), the system can provide high active power; to fully release the frequency regulation capability, the feedback coefficient \( K_3 \) is set to the maximum value 1. Conversely, when the frequency deviation is negative (positive) and the SOC is low (high), the ability to provide active power is limited, so the feedback coefficient should be reduced to prevent overcharging or overdischarging; \( K_3 \) decreases as SOC decreases, and becomes 0 when SOC reaches the lower limit.
Since FLC2 does not fully combine frequency and SOC to optimize the output power of battery energy storage systems to meet the frequency regulation requirements under different operating conditions, a third fuzzy logic controller (FLC3) is used to correct FLC2. In FLC3, the input variable \( SOC \) has universe \([0, 1]\) and is represented by five states: NL (small), NM (relatively small), ZR (medium), PM (relatively large), PL (large); the other input variable \( \Delta f \) has universe \([-0.2, 0.2]\) and is also represented by five states: NL (negative large), NM (negative small), ZR (zero), PM (positive small), PL (positive large); the correction coefficient \( K_4 \) has universe \([0, 0.5]\) and is represented by four states: ZR (zero), L (low), M (medium), H (high). The membership functions are trapezoidal and triangular. The fuzzy control rules are shown in Table 4.
| \(\Delta f\) | SOC | ||||
|---|---|---|---|---|---|
| NL | NM | ZR | PM | PL | |
| NL | ZR | ZR | ZR | H | H |
| NM | L | ZR | ZR | M | H |
| ZR | M | L | ZR | L | M |
| PM | H | M | ZR | ZR | L |
| PL | H | H | ZR | ZR | ZR |
The meaning of the FLC3 rules: when the frequency deviation is positive (negative) and the SOC of battery energy storage systems is low (high), increasing the feedback coefficient to raise the output power not only benefits frequency stability but also helps adjust the SOC to a better state for subsequent frequency regulation; therefore, the correction value \( K_4 \) is set relatively large. When the frequency deviation is negative (positive) and the SOC is low (high), while meeting the frequency regulation requirements, the SOC constraints must still be considered; thus, \( K_4 \) is relatively small.
The feedback coefficients for virtual inertia control and virtual droop control are given by:
$$ K_{SOC1} = K_3 + K_4 $$
$$ K_{SOC2} = \alpha \cdot K_{SOC1} $$
where \( \alpha \) is taken as 0.35 to make the outputs of the two controls appropriate.
2.3 Control Strategy Flow
The specific control flow of the proposed adaptive frequency control strategy considering the frequency regulation dead band is as follows. First, battery energy storage systems acquire information such as frequency and SOC, adjust the dead band range, and determine whether the frequency is within the dead band to decide whether to participate in the current frequency regulation. Then, the input coefficients and feedback coefficients are calculated comprehensively based on frequency and SOC, and the final output power of battery energy storage systems is determined using the equations above.
3. Simulation Analysis
Based on reference literature, a primary frequency regulation dynamic model as shown earlier is established in MATLAB/Simulink. The rated capacity of traditional synchronous units is 150 MW, the coefficient of battery energy storage systems is 15 MW/10 MW·min, and the traditional frequency regulation dead band of synchronous units is set to ±0.033 Hz. Other simulation parameters are given in Table 5.
| Parameter | Value |
|---|---|
| \( T_G \) | 0.08 s |
| \( T_{CH} \) | 0.3 s |
| \( T_{RH} \) | 10 s |
| \( F_H \) | 0.5 |
| \( K_g \) | 17 |
| \( T_b \) | 0.1 s |
| \( D \) | 1 |
| \( H \) | 10 s |
| \( M_{E0} \) | 6 |
| \( K_{E0} \) | 4 |
| \( SOC_{\min} \) | 0.3 |
| \( SOC_{\max} \) | 0.7 |
3.1 Comparison under Step Load Disturbance
Under step load disturbance, three indicators are used to evaluate the control strategies: maximum frequency deviation \( \Delta f_{\max} \), steady-state frequency deviation \( \Delta f_s \), and time to reach peak frequency deviation \( t_m \). A step disturbance with an amplitude of 10 MW is added after 1 s of system operation. Two cases are compared: initial SOC of 0.8 and initial SOC of 0.3. Simulation duration is 80 s.
Case 1: Initial SOC = 0.8
The proposed control strategy shows superior frequency regulation performance compared to the fixed-coefficient direct switching control and the variable-coefficient adaptive control. The maximum frequency deviation is reduced by about 11.2% relative to the fixed-coefficient control and by about 2.9% relative to the variable-coefficient control. The time to reach peak frequency deviation is also shorter. Since the initial SOC is high, the proposed strategy increases the output of battery energy storage systems, effectively improving the frequency regulation effect and helping to adjust the SOC to a better state.
| Control strategy | \( \Delta f_{\max} \) (Hz) | \( \Delta f_s \) (Hz) | \( t_m \) (s) |
|---|---|---|---|
| Proposed adaptive control | 0.167 | 0.134 | 2.23 |
| Fixed-coefficient direct switching | 0.188 | 0.135 | 2.45 |
| Variable-coefficient adaptive control | 0.172 | 0.135 | 2.29 |
Case 2: Initial SOC = 0.3
When the initial SOC is low, the proposed control strategy reduces the control coefficients to avoid secondary frequency drop and better meets the frequency regulation requirements, effectively suppressing the frequency drop. The maximum frequency deviation is reduced by about 7.4% relative to the fixed-coefficient control and by about 7% relative to the variable-coefficient control. The SOC decline speed of the proposed strategy is faster than that of the variable-coefficient control but still prevents the SOC from reaching the lower limit, indicating that the strategy comprehensively considers the frequency regulation requirements under different conditions, avoiding secondary frequency drops while achieving better frequency regulation effects.
| Control strategy | \( \Delta f_{\max} \) (Hz) | \( \Delta f_s \) (Hz) | \( t_m \) (s) |
|---|---|---|---|
| Proposed adaptive control | 0.174 | 0.144 | 2.24 |
| Fixed-coefficient direct switching | 0.188 | 0.135 | 2.45 |
| Variable-coefficient adaptive control | 0.187 | 0.141 | 2.29 |
3.2 Comparison under Continuous Load Disturbance
Under continuous load disturbance, three indicators are used: root mean square frequency deviation \( \Delta f_{\text{rms}} \), root mean square SOC \( Q_{\text{SOC\_rms}} \), and peak-to-valley frequency deviation \( \Delta f_{p-v} \). A continuous load disturbance is added after the system starts, with an initial SOC of 0.5 and a simulation duration of 1800 s. The disturbance curve is as shown in the following data series.
The proposed control strategy demonstrates a stronger ability to suppress frequency fluctuations. The peak-to-valley frequency deviation is reduced by about 13.6% relative to the fixed-coefficient control and by about 9% relative to the variable-coefficient control. The root mean square frequency deviation is also lower than that of the other two strategies, indicating better frequency stability. Due to the comprehensive adjustment of the dead band and control coefficients based on frequency signals and SOC, the proposed strategy shows superior SOC maintenance performance. The SOC root mean square value is 0.4701, which is closer to the initial value of 0.5 compared to the other two strategies, proving that under continuous load disturbance, the proposed strategy has better SOC maintenance effect.
| Control strategy | \( \Delta f_{\text{rms}} \) (Hz) | \( Q_{\text{SOC\_rms}} \) (%) | \( \Delta f_{p-v} \) (Hz) |
|---|---|---|---|
| Proposed adaptive control | 0.0450 | 0.4701 | 0.155 |
| Fixed-coefficient direct switching | 0.0468 | 0.4241 | 0.179 |
| Variable-coefficient adaptive control | 0.0458 | 0.4659 | 0.171 |
4. Conclusion
To improve the frequency regulation effect of battery energy storage systems under different operating conditions, an adaptive frequency control strategy considering the frequency regulation dead band is designed and validated through simulation. The following conclusions are obtained:
- Under step load disturbance, compared with traditional frequency control strategies, the proposed control strategy can adaptively adjust the frequency regulation dead band range and control coefficients according to the real-time system frequency and the SOC of battery energy storage systems, better meeting the frequency regulation requirements of the power system.
- Under step load disturbance, the proposed strategy comprehensively considers the SOC status of battery energy storage systems, not only avoiding insufficient frequency regulation capability when SOC is too low or too high but also effectively preventing SOC from exceeding limits and causing lifespan loss.
- Under continuous load disturbance, the proposed strategy has a stronger ability to suppress frequency fluctuations and achieves better SOC maintenance, providing a guarantee for further improvement of subsequent frequency regulation effects.
In summary, the proposed adaptive frequency control strategy for battery energy storage systems considering the frequency regulation dead band can maintain the SOC within a reasonable range while achieving superior frequency regulation performance under both step and continuous load disturbances.