In modern power systems, the integration of renewable energy sources has significantly increased the demand for fast and accurate frequency regulation. Battery energy storage systems (BESS) have emerged as a key technology due to their precise power output, rapid response, and bidirectional regulation capability. However, the service life of the energy storage cell remains a critical limitation. In this work, I propose an adaptive comprehensive frequency regulation strategy based on state-of-charge (SOC) feedback, aiming to extend the lifetime of the energy storage cell while maintaining grid frequency stability. I employ a fuzzy controller to adjust the input coefficient and a SOC-based feedback coefficient to determine the adaptive factor, which optimally distributes the output between virtual inertia control and virtual droop control. Using actual operational data from a power plant, I simulate different control strategies on the Matlab/Simulink platform and apply the rain-flow counting method to predict the lifetime of the energy storage cell. The proposed strategy demonstrates a 25.53% improvement in battery life compared to the current plant strategy, outperforming both the fixed K and variable K methods by 38.19% and 22.42%, respectively.
Introduction
The frequency stability of power systems is increasingly challenged by the variability of renewable generation. Battery energy storage systems offer an ideal solution for secondary frequency regulation due to their fast response and bidirectional power flow. However, frequent charge-discharge cycles, especially deep cycles, degrade the energy storage cell and shorten its operational life. Traditional frequency regulation strategies often rely on a fixed combination of virtual inertia control and virtual droop control, which may lead to excessive SOC excursions and accelerated aging. To address this, I develop an adaptive strategy that continuously adjusts the power sharing between the two control modes based on real-time frequency deviations and SOC of the energy storage cell. This approach not only maintains frequency within acceptable limits but also minimizes unnecessary stress on the energy storage cell.
The key contributions of my work include:
- Design of a fuzzy logic controller to dynamically determine the input coefficient for virtual inertia control based on frequency deviation and its rate of change.
- Development of a SOC feedback coefficient using a logistic function to prevent overcharge and over-discharge of the energy storage cell.
- Integration of the above two coefficients into an adaptive factor that smoothly regulates the output of the energy storage cell.
- Application of the rain-flow counting method to accurately estimate the equivalent cycle life of the energy storage cell under different strategies.
Frequency Regulation Control Strategy
Model of BESS Participating in Frequency Regulation
The frequency deviation Δf in the power system can be described by:
$$ \Delta f = \frac{\Delta P_b + \Delta P_g – \Delta P_{agc}}{H_s + D} $$
where ΔPb is the active power change of the BESS, ΔPg is the change from thermal units (treated as known in this study), ΔPagc is the AGC dispatch command variation, Hs is the inertia constant, and D is the damping coefficient. The total output of the BESS is the sum of virtual inertia control and virtual droop control:
$$ \Delta P_b = \Delta P_{b,I} + \Delta P_{b,D} $$
$$ \Delta P_{b,I} = K’ \frac{d\Delta f}{dt} G_{bess}(s) = \mu_1 \cdot M_b \cdot \frac{d\Delta f}{dt} G_{bess}(s) $$
$$ \Delta P_{b,D} = K \cdot \Delta f \cdot G_{bess}(s) = \mu_2 \cdot K_b \cdot \Delta f \cdot G_{bess}(s) $$
Here, Gbess(s) is the transfer function of the energy storage cell system:
$$ G_{bess}(s) = \frac{1}{T_b s + 1} $$
where Tb is the time constant. The adaptive factors μ1 and μ2 are determined by the product of the input coefficient α and the feedback coefficient β:
$$ \mu_1 = \alpha_1 \cdot \beta_1 $$
$$ \mu_2 = \alpha_2 \cdot \beta_2 $$
with α1 + α2 = 1.
Input Coefficient α via Fuzzy Logic
The fuzzy controller takes frequency deviation Δf and rate of change dΔf/dt as inputs, and outputs α1 (the weight of virtual inertia control). The universe of discourse for Δf is [-0.5, 0.5] Hz, and for dΔf/dt is [-1, 1] Hz/s. The output α1 ranges between 0 and 1. Seven linguistic variables (NB, NM, NS, Z, PS, PM, PB) are used for inputs, and five (Z, S, M, B, VB) for the output. The fuzzy rules are designed based on engineering experience as summarized in Table 1.
| dΔf/dt | Δf | ||||||
|---|---|---|---|---|---|---|---|
| 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 |
Defuzzification is performed using the centroid method.
Feedback Coefficient β Based on SOC
The SOC of the energy storage cell must be maintained within a safe range to avoid degradation. According to the battery manufacturer, the allowed operating SOC range for the energy storage cell is [0.23, 0.8]. Within this range, I use a logistic function to determine the charging/discharging coefficients Kc and Kd:
$$ K_c = \frac{P_0 K_{max} \exp\left( \frac{v_0 (0.8 – S_{SOC})}{(0.8-0.23)/2} \right)}{ K_{max} + P_0 \left[ \exp\left( \frac{v_0 (0.8 – S_{SOC})}{(0.8-0.23)/2} \right) – 1 \right] } $$
$$ K_d = \frac{P_0 K_{max} \exp\left( \frac{v_0 (S_{SOC} – 0.23)}{(0.8-0.23)/2} \right)}{ K_{max} + P_0 \left[ \exp\left( \frac{v_0 (S_{SOC} – 0.23)}{(0.8-0.23)/2} \right) – 1 \right] } $$
where P0 = 0.01, v0 = 15, and Kmax = 1. The feedback coefficients are then:
$$ \beta_1 = \begin{cases} \lambda K_c, & \frac{d\Delta f}{dt} \geq 0 \\ \lambda K_d, & \frac{d\Delta f}{dt} < 0 \end{cases} $$
$$ \beta_2 = \begin{cases} K_c, & \Delta f \geq 0 \\ K_d, & \Delta f < 0 \end{cases} $$
The factor λ = 1/3 is used to balance the different physical ranges of dΔf/dt and Δf. The final virtual droop control coefficient K is:
$$ K = \mu_2 K_b = (1 – \alpha_1) \cdot \beta_2 \cdot K_b $$
Similarly, the virtual inertia coefficient K’ = α1·β1·Mb. The complete control flow is illustrated in the following figure.
Control Strategies for Comparison
To evaluate the proposed adaptive integrated frequency regulation strategy, I compare it with three other methods:
- Fixed K method: K = Kb constant, with SOC limits [0.23, 0.8] for enabling/disabling the energy storage cell.
- Variable K method: K = β2·Kb, i.e., only SOC feedback is considered, without fuzzy input coefficient.
- Adaptive integrated method: K = α2·β2·Kb, which incorporates both fuzzy logic and SOC feedback.
Simulation Results and Analysis
I built a simulation model in Matlab/Simulink based on a 330 MW thermal unit paired with a 10 MW / 5 MWh BESS (nominal capacity). The grid frequency is 50 Hz. I used actual operational data from a power plant on August 20, 2023. The simulation time window is 55000 seconds to cover one full day of operation.
Active Power Output Comparison
The active power output of the energy storage cell under the three strategies is compared. The fixed K method tracks the planned AGC power closely but often forces the energy storage cell to operate at extreme SOC, leading to over-discharge. The variable K method avoids extreme SOC but still lacks smooth transition between control modes. The adaptive integrated strategy achieves a good balance: it tracks the planned output with reasonable accuracy while maintaining SOC within a safe range and reducing sudden power swings.
SOC Behavior and Metrics
The SOC evolution over the day is shown in Figure 4 of the original work. The fixed K method frequently hits the lower limit (0.23) and even goes below (0.199), which is prohibited in practice. The variable K method keeps SOC within [0.23,0.8], while the adaptive method maintains SOC within [0.402,0.781], a narrower and healthier band. I define a SOC maintenance index:
$$ Q_{SOC} = \frac{1}{n} \sum_{i=1}^n (Q_i – Q_{ref})^2 $$
where Qref = 0.55. The adaptive method achieves a QSOC improvement of 5.91%–7.78% over the variable K method, indicating better SOC stability and prolonged life of the energy storage cell.
Lifetime Prediction of the Energy Storage Cell
Rain-Flow Counting Method
To estimate the battery life, I use the rain-flow counting algorithm, which extracts cycles from the SOC time series. The method identifies full and half cycles characterized by their depth of discharge (DOD) and mean SOC. The algorithm proceeds as follows:
- Compress the data by removing small amplitude fluctuations and extracting only peaks and valleys.
- Identify cycles by matching rain-flow patterns.
- Count the number of cycles for each DOD bin.
The equivalent cycle life is then computed based on the cycle-count histogram. The rain-flow algorithm is implemented in Matlab.
Cycle Count Histograms
Applying the rain-flow method to the SOC traces from the three strategies yields the cycle count distributions. The fixed K method shows a maximum cycle count of 6422, but this occurs at an SOC of 0.22, violating the allowable range. The variable K method yields a maximum of 5556 cycles. In contrast, the adaptive integrated method achieves a maximum of 8783 cycles with the peak occurring at a moderate SOC. The average cycle count over all depth bins is also highest for the adaptive method.
| Control Strategy | Average Life (years) | Life Improvement vs. Current Plant Strategy |
|---|---|---|
| Current plant strategy (actual operation) | 9.83 | – |
| Fixed K method | 8.93 | -9.16% (lower) |
| Variable K method | 10.08 | +2.54% |
| Adaptive integrated method (proposed) | 12.34 | +25.53% |
The average service life of the energy storage cell under the adaptive strategy is 12.34 years, which is 25.53% higher than the current plant operation (9.83 years). Compared to the fixed K method and the variable K method, the adaptive method extends life by 38.19% and 22.42%, respectively. This demonstrates the effectiveness of the proposed approach in preserving the health of the energy storage cell.
Additional Discussion
The adaptive strategy operates the energy storage cell with a shallower depth of discharge on average, reducing wear. The fuzzy controller prevents unnecessary power surges by prioritizing virtual inertia control when frequency deviation is small, and virtual droop control when deviation is large. The SOC feedback ensures that the energy storage cell is not overstressed near its limits. The combination yields a win-win scenario: better frequency regulation and longer battery life.
Conclusion
In this work, I developed an adaptive comprehensive frequency regulation strategy for BESS that integrates fuzzy logic control and SOC-based feedback. The key conclusions are:
- The fuzzy controller dynamically allocates the output ratio between virtual inertia and virtual droop control, avoiding abrupt switching and reducing frequency oscillations.
- The SOC feedback coefficient, derived from a logistic function, effectively prevents overcharge and over-discharge of the energy storage cell.
- Using actual power plant data, the proposed strategy demonstrates excellent tracking performance and maintains SOC within [0.402, 0.781], a healthier range than the fixed or variable K methods.
- The rain-flow counting method reveals that the adaptive strategy extends the average service life of the energy storage cell to 12.34 years, a 25.53% improvement over the current plant strategy. It also outperforms the fixed K and variable K methods by 38.19% and 22.42%, respectively.
These findings highlight the importance of intelligent control in battery energy storage applications and provide a practical solution for power plant operators seeking to maximize both performance and longevity of the energy storage cell.