I propose a comprehensive adaptive primary frequency control strategy for grid-connected battery energy storage systems. Traditional control methods for battery energy storage systems often suffer from poor adaptability and low state of charge estimation accuracy, which limits their performance in primary frequency regulation. My approach integrates a novel trend control strategy with conventional inertia and droop control, while implementing adaptive coefficient determination and a multi-source SOC estimation method to enhance both frequency support capability and battery protection.
This research is motivated by the increasing penetration of renewable energy sources in modern power systems, which leads to reduced system inertia and greater frequency deviations. Battery energy storage systems, with their fast response characteristics, are ideal candidates for providing primary frequency regulation. However, existing control strategies either constrain the output based on fixed SOC thresholds or use simple linear adjustments, failing to fully exploit the potential of battery energy storage systems. My proposed strategy addresses these limitations by dynamically adjusting control coefficients based on real-time grid conditions and improving SOC estimation accuracy to prevent overcharging and overdischarging.
1. Introduction
In the context of carbon peak and carbon neutrality, the proportion of renewable energy connected to the power grid continues to increase, resulting in lower inertia in new power systems. With the release of the ’14th Five-Year’ new energy storage development implementation plan, battery energy storage systems have been comprehensively developed to participate in primary frequency regulation. Due to the fast response and flexibility of battery energy storage systems, grid stability has been improved. However, conventional inertia-droop control strategies often neglect the acceleration of frequency deviation, which can exacerbate frequency deterioration during the initial stage of disturbances. Moreover, fixed coefficient settings or simple SOC-based adjustments limit the adaptive capability of battery energy storage systems. Additionally, inaccurate SOC estimation may lead to overcharging or overdischarging, accelerating battery degradation.
To overcome these challenges, I combine a trend control strategy with inertia and droop control. The trend control utilizes the frequency acceleration to provide an additional power component that counters rapid frequency changes. I also propose adaptive determination of the trend coefficient, inertia coefficient, and droop coefficient based on real-time grid signals. Furthermore, a multi-source adaptive SOC estimation method is introduced to improve accuracy by combining the ampere-hour integration method and the unscented Kalman filter with adaptive weight correction.
2. Model of Battery Energy Storage Systems Participating in Primary Frequency Control
The battery energy storage system considered in this work consists of lithium-ion batteries. A simplified model for primary frequency regulation is established as shown in the block diagram below. The figure is inserted at this point.
The transfer functions of the thermal power unit governor and reheat turbine are given as:
$$ G_g(s) = \frac{1}{1 + s T_g} $$
$$ G_{en}(s) = \frac{1 + s F_{HP} T_{RH}}{(1 + s T_{CH})(1 + s T_{RH})} $$
The battery energy storage system transfer function is:
$$ G_E(s) = \frac{1}{1 + s T_E} $$
When load disturbances occur, the battery energy storage system works together with the thermal power unit to provide primary frequency regulation. Due to the fast response speed, battery energy storage systems can effectively reduce grid frequency deviations.
3. Comprehensive Adaptive Primary Frequency Control Strategy
3.1 Combined Control Strategy
The traditional inertia-droop control strategy for battery energy storage systems can be expressed as:
$$ P_E = M_b \frac{\Delta f}{\Delta t} + K_b \Delta f $$
I propose adding a trend compensation term to this structure. The trend output is defined as:
$$ a = T_b \frac{d^2 f}{dt^2} $$
The trend coefficient \( T_b \) is adaptively determined based on the frequency acceleration. The relationship among frequency deviation, frequency change rate, and frequency acceleration is illustrated conceptually: the slope of the frequency deviation curve is the frequency change rate, and the slope of the frequency change rate curve is the frequency acceleration. During the initial decline phase, both frequency acceleration and frequency deviation have the same sign, so the trend term provides additional support. During the recovery phase, the signs become opposite, preventing the trend output from hindering frequency restoration.
3.2 Adaptive Coefficient Determination
To improve the adaptability of battery energy storage systems, I define the three control coefficients as functions of real-time grid signals and SOC constraints.
Trend coefficient:
$$ T_b = \begin{cases}
T_0 + T_a + P_c & f > 50\,\text{Hz} \\
T_0 + T_a + P_d & f < 50\,\text{Hz}
\end{cases} $$
where the adaptive term \( T_a = T_1 \cdot \frac{d^2 f}{dt^2} \), and \( P_c, P_d \) are charge/discharge constraint coefficients derived from logistic functions of SOC.
Inertia coefficient:
$$ M_b = \begin{cases}
M_0 + M_a + P_c & f > 50\,\text{Hz} \\
M_0 + M_a + P_d & f < 50\,\text{Hz}
\end{cases} $$
with \( M_a = M_1 \cdot \frac{df}{dt} \).
Droop coefficient:
$$ K_b = \begin{cases}
K_0 + K_a + P_c & f > 50\,\text{Hz} \\
K_0 + K_a + P_d & f < 50\,\text{Hz}
\end{cases} $$
with \( K_a = K_1 \cdot \Delta f \).
The charge and discharge constraint coefficients are defined as:
$$ P_c = \begin{cases}
0 & S_{OC} \leq 0.7 \\
\frac{P_0}{e^{n(S_{OC}-0.8)/0.1} + 1} & 0.7 < S_{OC} < 0.8 \\
P_0 & S_{OC} \geq 0.8
\end{cases} $$
$$ P_d = \begin{cases}
P_0 & S_{OC} \leq 0.2 \\
\frac{P_0}{e^{n(0.2-S_{OC})/0.1} + 1} & 0.2 < S_{OC} < 0.3 \\
0 & S_{OC} \geq 0.3
\end{cases} $$
These logistic curves provide smooth transitions near the SOC limits, preventing abrupt power changes that could stress the battery. The SOC regions are defined as:
| SOC Region | Discharge | Charge |
|---|---|---|
| Safe | SOC > 0.3 | SOC < 0.7 |
| Warning | 0.2 ≤ SOC ≤ 0.3 | 0.7 ≤ SOC ≤ 0.8 |
| Danger | SOC < 0.2 | SOC > 0.8 |
3.3 Multi-Source Adaptive SOC Estimation
Accurate SOC estimation is critical to prevent overcharging and overdischarging of battery energy storage systems. I propose a method that combines the ampere-hour integration method and the unscented Kalman filter with adaptive weight adjustment.
The ampere-hour integration method with SOH correction is:
$$ S_{ah} = S_0 – \frac{\eta \int I_t dt}{S_{rated} \cdot S_{OH}} $$
The unscented Kalman filter uses the following state and observation equations:
$$ \begin{bmatrix} S_{k+1} \\ U_{1,k+1} \\ U_{2,k+1} \end{bmatrix} = \mathbf{A} \begin{bmatrix} S_k \\ U_{1,k} \\ U_{2,k} \end{bmatrix} + \mathbf{B} I_{t,k} + w_k $$
$$ \mathbf{A} = \begin{bmatrix} 1 & 0 & 0 \\ 0 & e^{-\Delta t / (R_1 C_1)} & 0 \\ 0 & 0 & e^{-\Delta t / (R_2 C_2)} \end{bmatrix} $$
$$ \mathbf{B} = \begin{bmatrix} -\eta \Delta t / (S_{rated} S_{OH}) \\ R_1 (1 – e^{-\Delta t / (R_1 C_1)}) \\ R_2 (1 – e^{-\Delta t / (R_2 C_2)}) \end{bmatrix} $$
$$ U_{t,k} = U_{oc,k} – I_{t,k} R_0 – U_{1,k} – U_{2,k} $$
The final SOC estimate is obtained by adaptively combining the two methods:
$$ S_{OC} = \begin{cases}
b S_{ah} + c S_{ukf} & \Delta U_{ah} \cdot \Delta U_{ukf} < 0 \\
b S_{ah} – c S_{ukf} & \Delta U_{ah} \cdot \Delta U_{ukf} > 0
\end{cases} $$
where \( c = \frac{\Delta t}{60} \) and \( b = 1 – c \). \(\Delta t\) starts counting after the disturbance occurs. The weights are initialized with higher emphasis on the ampere-hour method and gradually shift to the Kalman filter as time progresses, reducing the initial large error of the UKF.
4. Simulation Results and Analysis
4.1 Simulation Setup
The thermal power unit is rated at 1000 MW (maximum frequency regulation power limited to 60 MW). The battery energy storage system is rated at 30 MW / 10 MWh. The deadband for thermal units is 0.033 Hz, and for battery energy storage systems it is 0.6 times that of thermal units. The simulations are performed using Simulink with the parameters listed below.
| Parameter | Value |
|---|---|
| \( F_{HP} \) (pu) | 0.5 |
| \( T_{RH} \) (s) | 10 |
| \( T_{CH} \) (s) | 0.3 |
| \( T_g \) (s) | 0.08 |
| \( K_g \) | 20 |
| \( D \) | 1 |
| \( M \) | 10 |
| \( T_E \) (s) | 0.1 |
| \( P_0 \) | 0.01 |
| \( n \) | 15 |
4.2 Step Load Disturbance
A step load increase of 60 MW is applied at t = 10 s. The frequency deviation responses are compared between no energy storage, variable K method, adaptive method, and my proposed method. The key metrics are shown in the table.
| Method | Maximum Frequency Deviation (Hz) | Steady-State Frequency Deviation (Hz) |
|---|---|---|
| No storage | -0.096 | -0.063 |
| Variable K | -0.082 | -0.058 |
| Adaptive | -0.067 | -0.053 |
| Proposed | -0.061 | -0.049 |
My proposed method achieves the smallest maximum and steady-state frequency deviations. Compared with the adaptive method, the maximum deviation is reduced by 9% and the steady-state deviation by 8%. The improvement is attributed to the trend control which slows the initial frequency deterioration and accelerates recovery, combined with adaptive coefficients that respond to real-time grid conditions.
The SOC estimation accuracy is also evaluated. The following table compares the errors.
| Method | Maximum Error (%) | Average Error (%) |
|---|---|---|
| Ah integral | 0.42 | 0.21 |
| UKF | 0.88 | 0.13 |
| Neural network | 0.13 | 0.04 |
| Proposed | 0.09 | 0.01 |
The multi-source adaptive method yields the best accuracy, with a maximum error of only 0.09% and average error of 0.01%, significantly outperforming individual methods.
4.3 Short-Term Continuous Load Disturbance (10 min)
In this scenario, the initial SOC is 0.5. The performance metrics are:
| Method | Average Frequency Deviation (Hz) | Peak-to-Peak Frequency Deviation (Hz) | Average SOC | Peak-to-Peak SOC |
|---|---|---|---|---|
| No storage | 0.048 | 0.197 | — | — |
| Variable K | 0.044 | 0.170 | 0.490 | 0.021 |
| Adaptive | 0.041 | 0.140 | 0.482 | 0.037 |
| Proposed | 0.038 | 0.126 | 0.474 | 0.052 |
My proposed method achieves the smallest average and peak-to-peak frequency deviations, at 0.038 Hz and 0.126 Hz respectively, which are 7% and 10% lower than the adaptive method. The SOC variation is larger because the trend control increases the total energy exchange of the battery energy storage systems, but the enhanced SOC estimation prevents reaching dangerous limits.
4.4 Long-Term Continuous Load Disturbance (30 min)
| Method | Average Frequency Deviation (Hz) | Peak-to-Peak Frequency Deviation (Hz) |
|---|---|---|
| No storage | 0.044 | 0.205 |
| Variable K | 0.041 | 0.172 |
| Adaptive | 0.038 | 0.140 |
| Proposed | 0.035 | 0.126 |
Under prolonged disturbance, the proposed method still outperforms others, with an average frequency deviation of 0.035 Hz and peak-to-peak of 0.126 Hz, reductions of 8% and 10% compared to the adaptive method.
5. Conclusion
I have developed a comprehensive adaptive primary frequency control strategy for battery energy storage systems. The key contributions are:
- A novel trend control strategy that uses frequency acceleration to slow frequency deterioration and accelerate recovery, reducing the maximum frequency deviation of the power grid.
- Adaptive determination of the trend, inertia, and droop coefficients based on real-time grid signals, improving the flexibility and performance of battery energy storage systems in primary frequency regulation.
- A multi-source adaptive SOC estimation method that starts with ampere-hour integration and gradually transitions to unscented Kalman filtering, achieving a maximum error of 0.09% and average error of 0.01%, effectively preventing overcharging and overdischarging.
- Simulation results demonstrate that under step disturbance, the maximum and steady-state frequency deviations are reduced by 9% and 8% compared to the adaptive method. Under continuous disturbances, the average frequency deviation and peak-to-peak value are reduced by 7%–10%.
Future work will focus on further optimizing the weight allocation strategy for SOC estimation and extending the control framework to hybrid energy storage systems combining batteries with supercapacitors.