In modern power systems, energy storage cells have emerged as critical components for frequency regulation due to their rapid response, precise power output, and bidirectional adjustment capabilities. However, the service life of energy storage cells remains a significant constraint, as frequent charging and discharging cycles can lead to degradation. This article presents an adaptive frequency modulation strategy that integrates state-of-charge (SOC) feedback to optimize the participation of energy storage cells in grid frequency regulation. By dynamically adjusting the power output between virtual inertial control and virtual droop control, the strategy aims to enhance grid stability while prolonging the lifespan of energy storage cells. The approach employs a fuzzy controller to determine input coefficients and SOC-based feedback coefficients, forming an adaptive factor that ensures smooth transitions between control modes without predefined thresholds. Simulation models built on Matlab/Simulink, using real-world data from a power plant, demonstrate the effectiveness of this strategy. Furthermore, the rain-flow counting method is utilized to predict the cycle life of energy storage cells, comparing the proposed method with fixed-K and variable-K strategies. Results indicate a substantial improvement in battery longevity, underscoring the practical benefits of this adaptive approach for power plant operations.
The integration of energy storage cells into frequency regulation addresses the limitations of conventional thermal power units, which exhibit slower response times and reduced accuracy. Virtual inertial control and virtual droop control are two primary methods for energy storage participation, each with distinct advantages. Virtual inertial control suppresses the rate of frequency deviation changes, while virtual droop control reduces steady-state frequency deviations. The adaptive strategy combines these methods by introducing an adaptive factor, μ, which allocates the power output proportion between them based on real-time frequency parameters and SOC levels. This not only stabilizes grid frequency but also mitigates over-charging and over-discharging of energy storage cells, thereby extending their operational life. The core of this strategy lies in its ability to adapt to varying grid conditions without requiring explicit threshold values, thus avoiding secondary frequency disturbances and minimizing stress on energy storage cells.
The frequency deviation Δf in a power system can be modeled as follows, considering the contributions from energy storage cells, thermal units, and automatic generation control (AGC):
$$ \Delta f = \frac{\Delta P_b + \Delta P_g – \Delta P_{agc}}{H_s s + D} $$
where ΔP_b represents the change in active power output from energy storage cells, ΔP_g denotes the change from thermal units (treated as a known input in this context), ΔP_agc is the AGC dispatch instruction change, H_s is the generator inertia constant, and D is the damping coefficient. The energy storage system’s output is composed of virtual inertial control and virtual droop control components, expressed as:
$$ \Delta P_b = \Delta P_{b,I} + \Delta P_{b,D} $$
$$ \Delta P_{b,I} = K’ \frac{d\Delta f}{dt} G_{bess}(s) = \mu_1 \cdot M_b \cdot \frac{d\Delta f}{dt} G_{bess}(s) $$
$$ \Delta P_{b,D} = K \cdot \Delta f \cdot G_{bess}(s) = \mu_2 \cdot K_b \cdot \Delta f \cdot G_{bess}(s) $$
Here, K’ and K are the output proportion coefficients for virtual inertial and droop control, respectively; M_b and K_b are the power regulation coefficients; and G_bess(s) is the transfer function of the energy storage system, given by:
$$ G_{bess}(s) = \frac{1}{T_b s + 1} $$
where T_b is the time constant of the energy storage system. The adaptive factors μ_1 and μ_2 are derived from input coefficients (α_1, α_2) and feedback coefficients (β_1, β_2), satisfying α_1 + α_2 = 1 and μ_1 = α_1 β_1, μ_2 = α_2 β_2. The input coefficient α_1, which determines the proportion of virtual inertial control, is adjusted using a fuzzy controller that processes frequency deviation and its rate of change. This eliminates the need for critical value quantification, enhancing robustness. The fuzzy controller defines input ranges for frequency deviation ([-0.5, 0.5] Hz) and its derivative ([-1, 1] Hz/s), with output α_1 in [0, 1]. Membership functions and rules, such as those prioritizing virtual inertial control for large derivative values, ensure optimal performance.
The feedback coefficients β_1 and β_2 are based on the SOC of energy storage cells, using a logistic function to prevent SOC limits from being exceeded. For SOC within [0.23, 0.8], the charging and discharging coefficients K_c and K_d are defined as:
$$ K_c = \frac{P_0 \cdot K_{max} \cdot \exp\left[v_0 \cdot \frac{0.8 – S_{SOC}}{(0.8 – 0.23)/2}\right]}{K_{max} + P_0 \cdot \left( \exp\left[v_0 \cdot \frac{0.8 – S_{SOC}}{(0.8 – 0.23)/2}\right] – 1 \right)} $$
$$ K_d = \frac{P_0 \cdot K_{max} \cdot \exp\left[v_0 \cdot \frac{S_{SOC} – 0.23}{(0.8 – 0.23)/2}\right]}{K_{max} + P_0 \cdot \left( \exp\left[v_0 \cdot \frac{S_{SOC} – 0.23}{(0.8 – 0.23)/2}\right] – 1 \right)} $$
where K_max = 1, P_0 = 0.01, and v_0 = 15. For SOC outside this range, K_c and K_d are set to 0 or K_max to enforce unilateral charging or discharging. The feedback coefficients are then calculated as β_1 = λ K_c or λ K_d (depending on the sign of dΔf/dt) and β_2 = K_c or K_d (based on Δf), with λ = 1/3 to balance the control modes. This SOC feedback mechanism ensures that energy storage cells operate within safe limits, reducing degradation.
The adaptive factor ultimately determines the output proportion coefficients K and K’ as follows:
$$ K’ = \mu_1 \cdot M_b = \alpha_1 \cdot \beta_1 \cdot M_b $$
$$ K = \mu_2 \cdot K_b = (1 – \alpha_1) \cdot \beta_2 \cdot K_b $$
This formulation allows the strategy to dynamically adjust to grid disturbances and SOC conditions, optimizing the performance of energy storage cells. To evaluate the strategy, simulations were conducted using data from a 330 MW thermal unit coupled with a 10 MW/5 MWh energy storage system. The results compare three methods: fixed-K (constant K), variable-K (K adjusted based on SOC), and the adaptive comprehensive strategy (incorporating both fuzzy control and SOC feedback).
The simulation outcomes demonstrate that the adaptive strategy effectively tracks AGC instructions while minimizing SOC fluctuations. For instance, over a 55,000-second operational period, the adaptive method maintains SOC within [0.402, 0.781], compared to [0.199, 0.701] for the fixed-K approach, indicating better SOC maintenance. The SOC sustainability metric Q_SOC, defined as the mean squared deviation from a reference value (0.55), shows improvements of 5.91% to 7.78% over the variable-K method. This highlights the adaptive strategy’s ability to keep energy storage cells in an optimal state, reducing wear and tear.
To quantify the impact on energy storage cell life, the rain-flow counting method is applied to analyze charge-discharge cycles. This method counts cycles based on SOC peak-valley differences, providing insights into degradation. The results for each strategy are summarized in the table below, which includes the maximum cycle count, average cycle count, and predicted service life in years. The service life is calculated based on the average cycle count and typical degradation models for lithium iron phosphate energy storage cells operating at 25°C with a 2C rate.
| Strategy | Maximum Cycle Count | Average Cycle Count | Predicted Service Life (Years) |
|---|---|---|---|
| Fixed-K | 6422 | — | 8.93 |
| Variable-K | 5556 | — | 10.08 |
| Adaptive Comprehensive | 8783 | — | 12.34 |
Note: The average cycle count is derived from the rain-flow analysis, and service life assumes a linear relationship with cycle count. The adaptive strategy achieves a 25.53% increase in service life compared to the current plant strategy (9.83 years), and outperforms fixed-K and variable-K by 38.19% and 22.42%, respectively. This underscores the importance of adaptive control in prolonging energy storage cell longevity.
The rain-flow counting process involves compressing SOC data, extracting peak-valley points, and counting cycles based on amplitude and mean values. For example, the algorithm identifies cycles where the SOC swings exceed certain thresholds, and the cumulative effect of these cycles determines the overall life consumption. The mathematical representation of the rain-flow method can be expressed as:
$$ R_{cyc} = \sum_{i=1}^{n} f(DDOD_i) $$
where R_cyc is the equivalent cycle count, DDOD_i is the depth of discharge for cycle i, and f is a function mapping DDOD to cycle life. In this study, the adaptive strategy results in a higher number of cycles with moderate discharge depths, reducing the degradation rate of energy storage cells.
In conclusion, the adaptive frequency modulation strategy based on SOC feedback offers a comprehensive solution for enhancing grid frequency stability while extending the life of energy storage cells. By leveraging fuzzy logic and real-time SOC adjustments, it dynamically balances virtual inertial and droop control, avoiding the pitfalls of traditional methods. The simulations and life prediction models confirm its superiority, making it a viable approach for power plants seeking to optimize energy storage cell utilization. Future work could explore integration with renewable energy sources and advanced machine learning techniques for further improvements.
The effectiveness of this strategy is further validated through additional analyses, such as sensitivity to frequency disturbances and long-term reliability. For instance, the adaptive factor μ responds to changes in grid conditions, ensuring that energy storage cells contribute optimally without excessive strain. The table below compares key performance metrics across the three strategies, including frequency deviation suppression and SOC maintenance.
| Metric | Fixed-K | Variable-K | Adaptive Comprehensive |
|---|---|---|---|
| Frequency Deviation RMS (Hz) | 0.12 | 0.09 | 0.07 |
| SOC Range | [0.199, 0.701] | [0.350, 0.750] | [0.402, 0.781] |
| Cycle Life (Years) | 8.93 | 10.08 | 12.34 |
These results highlight the adaptive strategy’s ability to maintain tighter frequency control and better SOC management, directly contributing to the prolonged life of energy storage cells. The integration of such strategies into power plant operations can lead to significant economic benefits, as reduced replacement costs for energy storage cells offset initial investments in control systems.
In summary, the proposed adaptive frequency modulation strategy represents a significant advancement in the use of energy storage cells for grid support. By addressing both performance and longevity, it aligns with the growing demand for sustainable and reliable power systems. Continued research in this area will further enhance the role of energy storage cells in the energy transition, ensuring their viability as key components in modern grids.