With the continuous advancement of energy development strategies in our region, renewable energy sources such as wind and solar power are being integrated into the power grid at an increasing rate. However, these renewable energy devices lack the inherent capability to actively participate in frequency response, which significantly reduces the system inertia. Moreover, their output power is highly uncertain and fluctuating, making it difficult for traditional thermal power and other frequency regulation units to meet the system’s frequency regulation demands. The battery energy storage system, with its fast response speed, high control accuracy, and flexible configuration, has emerged as an excellent resource for frequency regulation. In recent years, the application of battery energy storage systems in frequency control has garnered widespread attention, and numerous engineering projects involving energy storage for frequency regulation have been implemented in various regions.
To date, researchers both domestically and internationally have conducted extensive studies on control strategies for battery energy storage systems participating in primary frequency regulation. Some studies have considered the limitations of virtual droop control in the initial stage of frequency disturbance and introduced virtual inertia control to effectively reduce the rate of change of frequency (RoCoF) during the early disturbance period. Other works have shown that while virtual inertia control can decrease the frequency drop rate, it may also hinder frequency recovery. Therefore, a negative virtual inertia control was designed, switching between different frequency intervals to meet the regulation demands. Several researchers have optimized the action timing and depth of virtual droop and virtual inertia controls by analyzing the regulation requirements of each frequency regulation stage, achieving complementary advantages between the two controls. They also constrained the energy storage output based on the state of charge (SOC) to prevent overcharging or over-discharging. Fuzzy control strategies have been employed to achieve smooth switching between these two typical controls, and a feedback coefficient based on logistic regression function was designed to prevent SOC from exceeding limits.
The setting of the frequency regulation dead band also significantly affects the response timing and action depth of the battery energy storage system in primary frequency regulation. Some studies have set the dead band of the energy storage system 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. The influence mechanism of the dead band in renewable energy units has also been analyzed, and a correction strategy for frequency regulation coefficients was proposed to mitigate the adverse effects of the dead band on system stability. Other works have restored the SOC of the energy storage system within the dead band range, improving the frequency regulation effect while adjusting the SOC to an ideal state. A combined wind-storage control strategy considering the frequency regulation dead band was proposed, manually setting the dead bands of wind turbines and the energy storage system to obtain better control performance.
In summary, existing research on energy storage participating in frequency control mostly focuses on how to achieve complementary advantages between the two typical control modes and using SOC constraints to prevent overcharging or over-discharging. However, the setting of the dead band and control coefficients often does not fully consider the actual regulation needs of the power system, making it difficult to adapt to different load disturbance conditions. To address this issue, this paper proposes an adaptive frequency control strategy for battery energy storage systems that considers the frequency regulation dead band. The proposed strategy enables adaptive adjustment of the dead band range and control coefficients, aiming to optimize the dynamic frequency regulation performance of the energy storage system under various operating conditions. The superiority of the proposed control strategy is verified through simulations.
1. Primary Frequency Regulation Model of Power System with Battery Energy Storage System
In order to analyze the influence of the frequency regulation dead band and control coefficients on the frequency regulation capability of the battery energy storage system, we establish a dynamic model of primary frequency regulation for a power system incorporating a battery energy storage system. The model is represented by the following block diagram (conceptual description without figure number). The system equivalent inertia and damping coefficients are denoted by H and D, respectively. The power regulation coefficient of the synchronous unit is Kg. The frequency deviation Δf(s) is the system output. The output powers of the synchronous unit and the battery energy storage system are ΔPg(s) and ΔPb(s), respectively. The load disturbance is ΔPL(s). The transfer functions of the synchronous unit and the energy storage system are Gg(s) and Gb(s).
The transfer function of the synchronous unit is given by:
$$
G_{g}(s) = \frac{1 + F_{H} T_{RH} s}{(1 + T_{G} s)(1 + T_{CH})(1 + T_{RH} s)}
$$
The transfer function of the energy storage power conversion system is:
$$
G_{b}(s) = \frac{1}{1 + T_{PCS} s}
$$
where FH is the reheater gain; TG, TCH, and TRH are the time constants of the governor, steam turbine, and reheat turbine, respectively; and TPCS is the time constant of the energy storage power conversion system.
To improve the stability of the unit during small frequency fluctuations, a frequency regulation dead band is set. Traditionally, the dead band is implemented as a fixed threshold. The input frequency deviation to the dead band is Δfin, and the output after the dead band is Δfout. The dead band boundary value is Dth. The dead band only outputs a reference signal when the frequency deviation exceeds Dth. If Dth is set too large, although the number of actions of the battery energy storage system is reduced, the response speed is slowed down, degrading the frequency regulation performance. If Dth is set too small, the energy storage system may start frequently, reducing its service life. Therefore, the dead band range must be set reasonably to enhance the frequency regulation effect under different operating conditions.
Based on the dynamic model, the system frequency dynamic response equation can be expressed as:
$$
2H \frac{d \Delta f(t)}{dt} + D \Delta f(t) = \Delta P_{g}(t) + \Delta P_{b}(t) – \Delta P_{L}(t)
$$
Introducing the battery energy storage system can improve the stability of the power system frequency. When the storage unit participates in frequency regulation through virtual droop control or virtual inertia 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 ΔPME(s) and ΔPKE(s) are the output powers under virtual inertia and virtual droop control, respectively; ME and KE are the virtual inertia and virtual droop coefficients, respectively.
From the above equations, we can derive the frequency deviations under each control mode:
$$
\Delta f_{I}(s) = \frac{-\Delta P_{L}(s)}{2Hs + D – K_{g}G_{g}(s) – M_{E}sG_{b}(s)}
$$
$$
\Delta f_{D}(s) = \frac{-\Delta P_{L}(s)}{2Hs + D – K_{g}G_{g}(s) – K_{E}G_{b}(s)}
$$
Virtual inertia control can effectively slow down the speed of frequency drop but has limited effect on the magnitude of frequency deviation. Moreover, once the frequency reaches its lowest point, the control output direction changes, and continuing with this control affects the frequency recovery speed. Virtual droop control can effectively reduce the amplitude of frequency deviation but cannot slow down the rate of frequency drop. Therefore, a reasonable allocation of the virtual inertia coefficient ME and the virtual droop coefficient KE can significantly improve the frequency regulation performance of the battery energy storage system. If ME and KE remain constant during the control process, the storage system will quickly release stored energy to suppress frequency drop, but this also causes the SOC to change too rapidly, leading to overcharging or over-discharging.
To further analyze the impact of different magnitudes of ME and KE, we consider two cases. In the first case, both ME1 and KE1 are fixed at 1. In the second case, ME2 and KE2 are constrained by SOC: when SOC is low, both coefficients are less than 1. The resulting frequency deviations are:
$$
\Delta F_{1}(s) = \frac{\Delta P_{L}(s)}{K_{g}G_{g}(s) + (M_{E1}s + K_{E1})G_{b}(s) – 2Hs – D}
$$
$$
\Delta F_{2}(s) = \frac{\Delta P_{L}(s)}{K_{g}G_{g}(s) + (M_{E2}s + K_{E2})G_{b}(s) – 2Hs – D}
$$
Comparing these two expressions, we observe that when ME and KE are low, we have |ΔF1(s)| < |ΔF2(s)|, meaning that reducing the coefficients weakens the frequency regulation capability. However, if the coefficients are too high, the SOC decreases rapidly. Therefore, a proper setting of ME and KE is essential to improve the frequency regulation effect under different operating conditions.
2. Adaptive Frequency Control Strategy Considering Frequency Regulation Dead Band
We design an adaptive frequency control strategy for battery energy storage systems that considers the frequency regulation dead band. The control block diagram is shown conceptually. The output power of the battery energy storage system ΔPb(s) is determined by both virtual inertia control and virtual droop control. The parameters are defined as follows: ME0 and KE0 are the initial values of the virtual inertia and virtual droop coefficients; K1 and KSOC1 are the input coefficient and feedback coefficient for virtual inertia control; K2 and KSOC2 are the corresponding coefficients for virtual droop control; we always have K1 + K2 = 1; α is the ratio between the two feedback coefficients. The output power expression is:
$$
\Delta P_{b}(s) = -(W_{1} M_{E0} s + W_{2} K_{E0}) \Delta f(s) G_{b}(s)
$$
$$
W_{1} = K_{1} \cdot K_{SOC1}
$$
$$
W_{2} = K_{2} \cdot K_{SOC2}
$$
2.1 Adaptive Adjustment of Frequency Regulation Dead Band
The traditional fixed dead band cannot meet the frequency regulation requirements under different operating conditions. Therefore, we propose a method that adaptively adjusts the dead band range based on frequency signals and SOC. Since Δf has a lagging characteristic and cannot promptly reflect the degree of power imbalance, we linearize the dynamic equation to obtain the initial RoCoF:
$$
F(t_{0}) = \left. \frac{d \Delta f}{dt} \right|_{t = t_{0}} = -\frac{\Delta P}{2H}
$$
where ΔP is the power imbalance quantity, and F(t0) is the RoCoF at time t0, which is proportional to the power imbalance. To meet the regulation needs under various conditions, we adjust the dead band range Dth according to the maximum RoCoF and SOC:
$$
D_{th} =
\begin{cases}
0.033, & F_{max}(t) < \delta \ \cup \ SOC \not\subset (SOC_{min}, SOC_{max}) \\
0.02, & F_{max}(t) < \delta \ \cup \ SOC \subset (SOC_{min}, SOC_{max}) \ / \ F_{max}(t) > \delta \ \cup \ SOC \not\subset (SOC_{min}, SOC_{max}) \\
0, & F_{max}(t) > \delta \ \cup \ SOC \subset (SOC_{min}, SOC_{max})
\end{cases}
$$
Here, Fmax(t) is the maximum RoCoF during system operation; δ is the RoCoF constraint value that can be set according to practical engineering needs; SOC is the state of charge; SOCmax and SOCmin are the upper and lower limits of SOC. The dead band has three boundary values: 0.033 Hz (traditional value), 0.02 Hz (optimal value), and 0 Hz. The adaptive setting process considers four cases with the battery discharging (when frequency deviation is negative). For example, when the power imbalance is small and SOC is low, Dth is set to 0.033 Hz to reduce the number of actions and prolong battery life. When the power imbalance is large and SOC is low, Dth is set to 0.02 Hz to meet regulation demands while preventing over-discharge. When the power imbalance is small and SOC is high, Dth = 0.02 Hz to maintain SOC and frequency stability. When the power imbalance is large and SOC is high, Dth = 0 Hz to allow immediate participation.
2.2 Adaptive Adjustment of Control Coefficients
To further optimize the frequency regulation effect under different operating conditions, we adaptively adjust the input coefficients and feedback coefficients.
2.2.1 Adaptive Adjustment of Input Coefficients
The input coefficients regulate the contribution of the two typical control modes during the frequency regulation process, taking advantage of their respective benefits in different frequency intervals. Fuzzy logic control is robust for nonlinear problems, so we use a fuzzy logic controller (FLC1) to adaptively adjust the input coefficient K1 (with K2 = 1 – K1). The two inputs of FLC1 are df/dt and Δf, and the output is K1. The universes of the inputs are [-0.5, 0.5] and the output universe is [-1, 1], each divided into seven levels: NL, NM, NS, ZR, PS, PM, PL. The membership functions are trapezoidal and triangular. The control rules are established in Table 1.
| Δf | 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 |
The rules are designed to satisfy: (1) During frequency drop, the virtual inertia coefficient should gradually decrease from 1 as Δf increases, while the virtual droop coefficient increases from 0. When RoCoF = 0, the virtual inertia coefficient becomes 0 and the virtual droop coefficient becomes 1. (2) During frequency recovery, RoCoF is negative; if the virtual inertia coefficient remains positive, it will hinder recovery. Therefore, negative virtual inertia is used, and the coefficient changes accordingly. The Mamdani inference method is used to compute K1.
2.2.2 Adaptive Adjustment of Feedback Coefficients
Adaptive adjustment of input coefficients enables effective coordination between the two controls. However, without considering SOC, the SOC may become too high or too low, affecting subsequent frequency regulation and potentially causing overcharging or over-discharging, leading to battery life loss. Therefore, we combine system frequency and SOC to adaptively adjust the feedback coefficients. The block diagram of the feedback coefficient adaptive control strategy is shown conceptually. We introduce a second fuzzy logic controller FLC2 and a third FLC3. The output of FLC2 is K3, and the output of FLC3 is a correction coefficient K4.
FLC2 takes SOC and Δf as inputs. The universe of SOC is [0, 1] with three states: L, M, H. The universe of Δf is [-0.2, 0.2] with two states: N, P. The output K3 has two states: L, H. The membership functions are trapezoidal. The fuzzy control rules are given in Table 2.
| Δf | SOC | ||
|---|---|---|---|
| L | M | H | |
| N | L | H | H |
| P | H | H | L |
The rules imply: when the frequency deviation is negative (positive) and SOC is high (low), the energy storage can provide high active power; thus K3 is set to H (1). Conversely, when frequency deviation is negative (positive) and SOC is low (high), the available power is limited; K3 is set to L and decreases as SOC approaches the limit.
Since FLC2 does not fully couple frequency and SOC to optimize output power for different conditions, we use FLC3 to correct K3. The inputs of FLC3 are SOC (universe [0,1] with five states: NL, NM, ZR, PM, PL) and Δf (universe [-0.2,0.2] with five states: NL, NM, ZR, PM, PL). The output K4 (universe [0,0.5]) has four states: ZR, L, M, H. Membership functions are trapezoidal and triangular. The control rules are given in Table 3.
| Δf | 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 rules are designed to enhance the output when the frequency deviation direction aligns with SOC recovery. For instance, when frequency deviation is positive (negative) and SOC is low (high), a larger correction K4 is applied to increase output, which helps both frequency stability and SOC recovery. Conversely, when they are opposite, the correction is smaller.
The final feedback coefficients are given by:
$$
K_{SOC1} = K_{3} + K_{4}
$$
$$
K_{SOC2} = \alpha \cdot K_{SOC1}
$$
where α is set to 0.35 to ensure appropriate power sharing between the two controls.
2.3 Control Strategy Flow
The overall flow of the proposed adaptive frequency control strategy considering the dead band is as follows. First, the battery energy storage system acquires frequency and SOC information. It adaptively adjusts the frequency regulation dead band range and determines whether the frequency is within the dead band, thereby deciding whether the energy storage should participate. If participation is required, the system calculates input coefficients and feedback coefficients based on frequency and SOC using the fuzzy logic controllers, and then computes the final output power of the energy storage system according to the earlier expressions.
3. Simulation Analysis
We built a primary frequency regulation dynamic model in MATLAB/Simulink, referring to typical parameters from existing literature. The rated capacity of the traditional synchronous unit is 150 MW, and the battery energy storage system has a capacity of 15 MW/10 MW·min. The dead band of the synchronous unit is set to ±0.033 Hz. Other simulation parameters are listed in Table 4.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| TG (s) | 0.08 | D | 1 |
| TCH (s) | 0.3 | H (s) | 10 |
| TRH (s) | 10 | ME0 | 6 |
| FH | 0.5 | KE0 | 4 |
| Kg | 17 | SOCmin | 0.3 |
| Tb (s) | 0.1 | SOCmax | 0.7 |
We compared three control strategies under step load disturbance and continuous load disturbance conditions: (1) fixed-coefficient direct switching control (fixed k switching), (2) variable-coefficient adaptive control (variable k adaptive), both with a fixed dead band of 0.02 Hz, and (3) the proposed adaptive frequency control strategy considering dead band (proposed strategy).
3.1 Step Load Disturbance
We considered a step disturbance of 10 MW at t = 1 s. Two initial SOC values were tested: 0.8 and 0.3. The simulation time was 80 s. The frequency deviation and SOC curves for initial SOC = 0.8 are shown in the simulation results (without figure numbers). The key frequency regulation indices are summarized in Table 5.
| Control strategy | Δfmax (Hz) | Δfs (Hz) | tm (s) |
|---|---|---|---|
| Proposed strategy | 0.167 | 0.134 | 2.23 |
| Fixed k switching | 0.188 | 0.135 | 2.45 |
| Variable k adaptive | 0.172 | 0.135 | 2.29 |
For initial SOC = 0.8, the proposed strategy reduced the maximum frequency deviation by about 11.2% compared to fixed k switching, and by about 2.9% compared to variable k adaptive. The time to reach peak frequency deviation tm was also shorter. The SOC variation shows that the proposed strategy effectively utilized the high SOC to improve frequency regulation and also helped adjust SOC to a better state.
For initial SOC = 0.3, the results are shown in Table 6.
| Control strategy | Δfmax (Hz) | Δfs (Hz) | tm (s) |
|---|---|---|---|
| Proposed strategy | 0.174 | 0.144 | 2.24 |
| Fixed k switching | 0.188 | 0.135 | 2.45 |
| Variable k adaptive | 0.187 | 0.141 | 2.29 |
When the initial SOC was low (0.3), the proposed strategy still achieved a 7.4% reduction in Δfmax compared to fixed k switching, and about 7% compared to variable k adaptive. The time to peak was still shorter. The SOC trajectory shows that the proposed strategy prevented the SOC from reaching the lower limit while maintaining good frequency response, avoiding secondary frequency dips. This demonstrates the effectiveness of the adaptive dead band and coefficient adjustment in considering both frequency and SOC constraints.
3.2 Continuous Load Disturbance
We applied a continuous load disturbance profile over 1800 s, as shown in the simulation curves. The initial SOC was set to 0.5. The performance is evaluated using three indices: root mean square of frequency deviation (Δfrms), root mean square of SOC (QSOC_rms), and peak-to-valley difference of frequency deviation (Δfp-v). The frequency deviation and SOC variations were recorded. The indices are summarized in Table 7.
| Control strategy | Δfrms (Hz) | QSOC_rms (%) | Δfp-v (Hz) |
|---|---|---|---|
| Proposed strategy | 0.0450 | 0.4701 | 0.155 |
| Fixed k switching | 0.0468 | 0.4241 | 0.179 |
| Variable k adaptive | 0.0458 | 0.4659 | 0.171 |
The peak-to-valley difference Δfp-v with the proposed strategy was reduced by about 13.6% compared to fixed k switching and by about 9% compared to variable k adaptive, indicating stronger suppression of frequency fluctuations. The Δfrms was also the smallest, showing better overall frequency stability. The QSOC_rms value (0.4701) was closest to the initial SOC of 0.5, demonstrating superior SOC maintenance capability, which is beneficial for subsequent frequency regulation performance.
These results confirm that the proposed adaptive frequency control strategy for battery energy storage systems, which considers the frequency regulation dead band, effectively improves frequency quality under various operating conditions while maintaining SOC within a reasonable range.
4. Conclusion
In this paper, we proposed an adaptive frequency control strategy for battery energy storage systems that takes into account the frequency regulation dead band. The key findings are as follows:
1) Under step load disturbance, compared with traditional fixed-coefficient strategies, the proposed strategy adaptively adjusts the dead band range and control coefficients based on real-time frequency and SOC, better meeting the frequency regulation requirements of the power system. The maximum frequency deviation is significantly reduced, and the time to reach peak frequency is shortened.
2) The proposed strategy comprehensively considers the SOC condition of the battery energy storage system. It not only avoids the situation where the regulation capability is insufficient when SOC is too low or too high, but also effectively prevents SOC from exceeding limits, thereby prolonging battery life.
3) Under continuous load disturbance, the proposed strategy exhibits stronger capability in suppressing frequency fluctuations, as evidenced by smaller root mean square frequency deviation and peak-to-valley difference. Moreover, it achieves better SOC maintenance, providing a solid foundation for further improvement of subsequent frequency regulation performance.
In summary, the adaptive frequency control strategy for battery energy storage systems considering the frequency regulation dead band demonstrates superior performance in both step and continuous disturbance scenarios, enhancing grid frequency quality and ensuring safe operation of the energy storage system.