In modern power systems, the integration of renewable energy sources and fluctuating loads has increased the demand for rapid and precise frequency regulation. The battery energy storage system (BESS) has emerged as a critical solution due to its fast response, accurate power tracking, and bidirectional power flow capabilities. However, the lifespan of the battery energy storage system remains a significant constraint, as frequent charge-discharge cycles and extreme operating conditions can lead to accelerated degradation. This paper proposes an adaptive frequency modulation strategy that leverages state-of-charge (SOC) feedback to optimize the participation of the battery energy storage system in grid frequency regulation. By dynamically adjusting the power output between virtual inertia control and virtual droop control, the strategy aims to enhance grid stability while extending the operational life of the battery energy storage system. The approach incorporates a fuzzy logic controller to smooth transitions between control modes and a SOC-based feedback mechanism to prevent over-charging or over-discharging. Simulations conducted using real-world data from a power plant demonstrate the effectiveness of the proposed method in improving the longevity of the battery energy storage system compared to conventional strategies.
The core of the adaptive strategy lies in the integration of virtual inertia and virtual droop control, which complement each other in suppressing frequency deviations and stabilizing the grid. The frequency deviation $\Delta f$ is calculated as:
$$\Delta f = \frac{\Delta P_b + \Delta P_g – \Delta P_{agc}}{H_s s + D}$$
where $\Delta P_b$ represents the change in active power output from the battery energy storage system, $\Delta P_g$ is the change in thermal power generation (assumed known for simplicity), $\Delta P_{agc}$ denotes the variation in automatic generation control (AGC) commands, $H_s$ is the generator inertia constant, and $D$ is the damping coefficient. The total power output from the battery energy storage system is composed of contributions from virtual inertia control ($\Delta P_{b,I}$) and virtual droop control ($\Delta P_{b,D}$), expressed as:
$$\Delta P_b = \Delta P_{b,I} + \Delta P_{b,D}$$
$$\Delta P_{b,I} = \mu_1 \cdot M_b \cdot \frac{d\Delta f}{dt} \cdot G_{bess}(s)$$
$$\Delta P_{b,D} = \mu_2 \cdot K_b \cdot \Delta f \cdot G_{bess}(s)$$
Here, $\mu_1$ and $\mu_2$ are adaptive factors for virtual inertia and virtual droop control, respectively, $M_b$ and $K_b$ are power regulation coefficients, and $G_{bess}(s) = \frac{1}{T_b s + 1}$ is the transfer function of the battery energy storage system with time constant $T_b$. The adaptive factors are determined by input coefficients ($\alpha_1$, $\alpha_2$) and feedback coefficients ($\beta_1$, $\beta_2$) as follows:
$$\mu_1 = \alpha_1 \cdot \beta_1$$
$$\mu_2 = \alpha_2 \cdot \beta_2$$
with $\alpha_1 + \alpha_2 = 1$ to ensure balanced control. The input coefficient $\alpha_1$ is regulated by a fuzzy logic controller that processes frequency deviation ($\Delta f$) and its rate of change ($d\Delta f/dt$), eliminating the need for hard thresholds and enabling smooth mode transitions. The fuzzy controller uses triangular membership functions and rules summarized in Table 1 to map inputs to $\alpha_1$, with output levels ranging from zero (Z) to very large (VB).
| $d\Delta f/dt$ | $\Delta f$ | ||||||
|---|---|---|---|---|---|---|---|
| NB | NM | NS | Z | PS | PM | PB | |
| NB | VB | B | B | VB | Z | Z | Z |
| NM | B | B | M | B | Z | Z | S |
| NS | M | M | M | M | Z | S | S |
| Z | Z | S | Z | Z | Z | S | Z |
| PS | S | S | Z | M | M | M | M |
| PM | S | Z | Z | B | M | B | B |
| PB | Z | Z | Z | VB | B | B | VB |
The feedback coefficients $\beta_1$ and $\beta_2$ are derived from the SOC of the battery energy storage system to prevent operational limits. Using a segmented Logistic function, the charging coefficient $K_c$ and discharging coefficient $K_d$ are defined for the SOC range [0.23, 0.8], with $K_{\text{max}} = 1$:
$$K_c = \frac{P_0 \cdot K_{\text{max}} \cdot \exp\left[v_0 \cdot \frac{0.8 – S_{SOC}}{(0.8 – 0.23)/2}\right]}{K_{\text{max}} + P_0 \cdot \left(\exp\left[v_0 \cdot \frac{0.8 – S_{SOC}}{(0.8 – 0.23)/2}\right] – 1\right)}$$
$$K_d = \frac{P_0 \cdot K_{\text{max}} \cdot \exp\left[v_0 \cdot \frac{S_{SOC} – 0.23}{(0.8 – 0.23)/2}\right]}{K_{\text{max}} + P_0 \cdot \left(\exp\left[v_0 \cdot \frac{S_{SOC} – 0.23}{(0.8 – 0.23)/2}\right] – 1\right)}$$
where $P_0 = 0.01$ and $v_0 = 15$ are constants. For SOC values outside [0.23, 0.8], $K_c$ and $K_d$ are set to 0 or $K_{\text{max}}$ to enforce unilateral charging or discharging. The feedback coefficients are then computed as:
$$\beta_1 = \begin{cases}
\lambda \cdot K_c & \text{if } \frac{d\Delta f}{dt} \geq 0 \\
\lambda \cdot K_d & \text{if } \frac{d\Delta f}{dt} < 0
\end{cases}$$
$$\beta_2 = \begin{cases}
K_c & \text{if } \Delta f \geq 0 \\
K_d & \text{if } \Delta f < 0
\end{cases}$$
with $\lambda = \frac{1}{3}$ to balance the domains of frequency deviation and its rate of change. The final power output coefficients for virtual droop control ($K$) and virtual inertia control ($K’$) are given by:
$$K = \mu_2 \cdot K_b = (1 – \alpha_1) \cdot \beta_2 \cdot K_b$$
$$K’ = \mu_1 \cdot M_b = \alpha_1 \cdot \beta_1 \cdot M_b$$
This adaptive framework allows the battery energy storage system to respond dynamically to grid conditions while maintaining SOC within safe bounds. To evaluate the strategy, I compared it with two conventional methods: the fixed-$K$ method, where $K$ is constant and SOC limits trigger disengagement, and the variable-$K$ method, where $K$ adjusts based on SOC but without fuzzy logic input. The simulation model was built in Matlab/Simulink using real operational data from a 330 MW thermal power plant coupled with a 10 MW/5 MWh battery energy storage system. The system parameters included a nominal frequency of 50 Hz, inertia constant $H_s = 5$ s, damping coefficient $D = 1$, and battery time constant $T_b = 0.1$ s. The AGC commands and frequency deviations from a typical day (August 20, 2023) were used as inputs.
The results demonstrated that the adaptive strategy effectively tracked AGC commands while minimizing power fluctuations. For instance, during periods of high power demand (e.g., 959–1027 s), all strategies prevented reverse power flow, but the adaptive approach reduced extreme charge-discharge cycles. The SOC profiles under each strategy are summarized in Table 2, highlighting the improved SOC maintenance of the adaptive method. The SOC maintenance metric $Q_{SOC}$ was calculated as:
$$Q_{SOC} = \frac{1}{n} \sum_{i=1}^{n} (Q_i – Q_{ref})^2$$
where $Q_i$ is the SOC at time $i$, $Q_{ref} = 0.55$ is the reference SOC, and $n$ is the number of samples. Lower $Q_{SOC}$ values indicate better SOC stability.
| Strategy | SOC Range | $Q_{SOC}$ | Improvement Over Variable-$K$ |
|---|---|---|---|
| Fixed-$K$ | [0.199, 0.701] | 0.045 | N/A |
| Variable-$K$ | [0.402, 0.781] | 0.032 | Baseline |
| Adaptive | [0.402, 0.781] | 0.030 | 5.91–7.78% |
The lifespan of the battery energy storage system was predicted using the rain-flow counting method, which analyzes charge-discharge cycles by extracting peaks and valleys from the SOC data. This method accounts for the cumulative damage from cycling at different depths of discharge (DOD). The number of equivalent cycles $R_{cyc}$ at each DOD level was recorded, and the total lifespan in years was estimated based on the average cycle life. The rain-flow algorithm involved data compression, peak-valley extraction, and cycle counting, as illustrated in the flowcharts. The results, shown in Table 3, indicate that the adaptive strategy significantly extends the battery life compared to other methods.
| Strategy | Maximum Cycles | Average Lifespan (Years) | Improvement Over Current Strategy |
|---|---|---|---|
| Fixed-$K$ | 6422 | 8.93 | -38.19% |
| Variable-$K$ | 5556 | 10.08 | -22.42% | Current Plant Strategy | N/A | 9.83 | Baseline |
| Adaptive | 8783 | 12.34 | 25.53% |
The adaptive strategy achieved a 25.53% increase in lifespan over the current plant strategy, underscoring its efficacy in protecting the battery energy storage system. The fuzzy logic controller enabled smooth transitions between virtual inertia and droop control, reducing stress on the battery, while the SOC feedback mechanism optimized power distribution. For example, when frequency deviation was small but its rate of change was large, the controller prioritized virtual inertia control to prevent further instability. Conversely, for large steady-state deviations, virtual droop control dominated to accelerate stabilization. This flexibility enhanced grid frequency response and reduced the risk of SOC limit violations.
In conclusion, the proposed adaptive frequency modulation strategy based on SOC feedback offers a robust solution for integrating battery energy storage systems into power grid frequency regulation. By leveraging fuzzy logic and Logistic functions, it dynamically adjusts control parameters to balance grid stability and battery longevity. Simulation results confirm that this approach not only improves SOC maintenance but also extends the operational life of the battery energy storage system by over 25% compared to conventional methods. Future work could explore real-time implementation and adaptability to varying renewable energy penetration levels. The battery energy storage system, with its rapid response and scalability, remains pivotal to modern power systems, and strategies like this one are essential for maximizing its economic and technical benefits.