With the rapid development of renewable energy sources, the large-scale integration of intermittent and fluctuating power into the grid poses significant challenges to system stability. Frequency regulation becomes critical to maintain grid reliability. Conventional thermal power units, while capable of providing frequency regulation, suffer from slow response times due to mechanical inertia. Energy storage batteries, particularly lithium-ion batteries, offer fast response and high power density, making them ideal partners for thermal units in automatic generation control (AGC). However, improper control strategies can lead to overcharging or over-discharging of the energy storage battery, reducing its lifespan. To address this issue, we propose a dynamic droop coefficient control strategy for an energy storage battery assisting a thermal power unit in secondary frequency regulation. This strategy adaptively adjusts the power output of the energy storage battery based on its state of charge (SOC), thereby improving both frequency regulation performance and battery longevity. In this paper, we present a detailed model of the combined system, derive the control law, and validate its effectiveness through simulations under step and continuous load disturbances. The results demonstrate that the proposed dynamic droop coefficient control outperforms fixed droop coefficient control and conventional strategies without energy storage, achieving lower frequency deviations and better SOC maintenance.
1. Introduction
The increasing penetration of renewable energy sources such as wind and solar has intensified the need for flexible and fast-acting frequency regulation resources. Traditional thermal power units, with their slow governor and turbine responses, cannot adequately track high-frequency components of area control error (ACE) signals. Energy storage batteries, on the other hand, possess rapid ramping capabilities and can compensate for the deficiencies of thermal units. Numerous studies have explored various power allocation strategies between thermal units and energy storage batteries, including proportional allocation, frequency-based allocation, and deviation-based allocation. However, most of these strategies focus solely on frequency regulation performance and neglect the SOC state of the energy storage battery, which directly affects its service life and operational safety. Overcharging or deep discharging accelerates degradation. Therefore, it is essential to design a control strategy that balances frequency regulation effectiveness with SOC preservation. In this work, we propose a dynamic droop coefficient control strategy that continuously adjusts the droop gain of the energy storage battery as a function of its SOC. This prevents extreme SOC excursions while still providing effective frequency support. We build a simulation model in MATLAB/Simulink and compare our strategy with no-storage and fixed-droop strategies under both step and continuous load disturbances.
2. System Model
2.1 Overall Structure
The block diagram of the secondary frequency regulation system with an energy storage battery assisting a thermal power unit is shown in the following. The system consists of a thermal power unit (including governor and reheat steam turbine), a battery energy storage system (BESS), the power system inertia and load, and a power allocation module based on a low-pass filter.
The ACE signal is split into low-frequency and high-frequency components using a first-order low-pass filter. The low-frequency part is sent to the thermal unit, and the high-frequency part is sent to the energy storage battery. The dynamics of each component are described below.
2.2 Thermal Power Unit Model
The governor dynamics are represented by a first-order lag:
$$ G_{gov}(s) = \frac{1}{1 + s T_g} $$
where \(T_g\) is the governor time constant. The reheat steam turbine is modeled as:
$$ G_{gen}(s) = \frac{1 + s F_{HP} T_{RH}}{(1 + s T_{CH})(1 + s T_{RH})} $$
where \(T_{CH}\) is the high-pressure steam time constant, \(T_{RH}\) is the reheat time constant, and \(F_{HP}\) is the fraction of power from the high-pressure stage. The overall thermal unit transfer function from control signal to mechanical power output is \(G_{gov}(s) G_{gen}(s)\).
2.3 Power System Inertia and Load
The swing equation of the power system gives the relation between power imbalance and frequency deviation:
$$ G_{sys}(s) = \frac{1}{D + s M} $$
where \(D\) is the damping coefficient and \(M\) is the inertia constant.
2.4 Energy Storage Battery Model
We employ a second-order RC equivalent circuit model for the lithium-ion battery:
$$
\begin{cases}
U_b = U_{OC} – U_1 – U_2 – I_{Li} R_s \\
\dot{U}_1 = -\frac{1}{R_1 C_1} U_1 + \frac{I_{Li}}{C_1} \\
\dot{U}_2 = -\frac{1}{R_2 C_2} U_2 + \frac{I_{Li}}{C_2} \\
SOC(t) = SOC_0 – \frac{1}{C_{Li}} \int_0^t \eta I_{Li} d\tau
\end{cases}
$$
Here, \(U_{OC}\) is the open-circuit voltage (a function of SOC), \(R_s\) is internal resistance, \(R_1, C_1\) and \(R_2, C_2\) represent electrochemical and concentration polarization, \(\eta\) is the charging/discharging efficiency, and \(C_{Li}\) is the battery capacity. The battery output power is \(P_b = U_b I_{Li}\). For the frequency regulation simulation, the battery is modeled as a controllable power source that responds to the power command from the controller.
3. Power Allocation and Control Strategy
3.1 ACE Signal Splitting
The ACE signal is filtered using a low-pass filter with time constant \(T_f\) to separate low-frequency components for the thermal unit and high-frequency components for the energy storage battery:
$$
P_{ACE,G}(s) = \frac{1}{1 + s T_f} P_{ACE}(s) $$
$$ P_{ACE,B}(s) = \left(1 – \frac{1}{1 + s T_f}\right) P_{ACE}(s)
$$
The thermal unit responds slowly and thus receives the low-frequency part, while the energy storage battery handles the high-frequency part.
3.2 Dynamic Droop Coefficient Control
Conventional fixed-droop control applies a constant gain \(K_{fix}\) to the frequency deviation to determine the battery power:
$$ \Delta P_{B,fix}(s) = -K_{fix} \Delta f(s) $$
This can cause rapid SOC variation, leading to overcharging or deep discharging. To mitigate this, we propose a dynamic droop coefficient \(K(t)\) that adapts based on the current SOC. The charging droop coefficient \(K_c\) and discharging droop coefficient \(K_d\) are defined as follows.
When the frequency deviation \(\Delta f > 0\) (indicating a need to charge the energy storage battery), the charging droop coefficient is:
$$
K_c =
\begin{cases}
K_{max}, & 0 < SOC \leq SOC_{high} \\
\frac{K_{max} P_0 e^{n (SOC_{max} – SOC) / (SOC_{max} – SOC_{high})}}{K_{max} + P_0 \left(e^{n (SOC_{max} – SOC) / (SOC_{max} – SOC_{high})} – 1\right)}, & SOC_{high} < SOC < SOC_{max} \\
0, & SOC_{max} \leq SOC < 1
\end{cases}
$$
When \(\Delta f < 0\) (discharge required), the discharging droop coefficient is:
$$
K_d =
\begin{cases}
0, & 0 < SOC \leq SOC_{min} \\
\frac{K_{max} P_0 e^{n (SOC – SOC_{min}) / (SOC_{low} – SOC_{min})}}{K_{max} + P_0 \left(e^{n (SOC – SOC_{min}) / (SOC_{low} – SOC_{min})} – 1\right)}, & SOC_{min} < SOC < SOC_{low} \\
K_{max}, & SOC_{low} \leq SOC < 1
\end{cases}
$$
Here, \(K_{max}\) is the maximum droop gain, \(P_0\) and \(n\) are fitting parameters, \(SOC_{min}\) and \(SOC_{max}\) are the lower and upper limits, and \(SOC_{low}\) and \(SOC_{high}\) are thresholds where the gain starts to decrease. The actual power command to the energy storage battery is then:
$$
\Delta P_B(s) = -K_c \Delta f(s) \quad (\text{if } \Delta f > 0) $$
$$ \Delta P_B(s) = -K_d \Delta f(s) \quad (\text{if } \Delta f < 0)
$$
This ensures that when SOC approaches its limits, the battery output is gradually reduced or stopped, preventing overcharge/discharge.
4. Simulation Parameters and Evaluation Metrics
4.1 System Parameters
The simulation model is built using the per-unit system. The thermal unit is a 660 MW unit, and the energy storage battery is rated at 10 MW / 5 MWh. Key parameters are listed in Table 1.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| \(B\) (frequency bias) | 21 | \(SOC_0\) | 0.5 |
| \(K_G\) (unit regulation) | 25 | \(SOC_{min}\) | 0.2 |
| \(K_p\) (PI proportional) | -0.82 | \(SOC_{low}\) | 0.45 |
| \(K_i\) (PI integral) | -0.16 | \(SOC_{high}\) | 0.55 |
| \(T_g\) (governor time constant, s) | 0.1 | \(SOC_{max}\) | 0.8 |
| \(T_{RH}\) (reheat time constant, s) | 10 | \(\eta\) (efficiency, %) | 85 |
| \(T_{CH}\) (high-pressure time constant, s) | 0.3 | \(f_{max}\) (deadband, Hz) | 0.00066 |
| \(F_{HP}\) (high-pressure fraction) | 0.5 | \(f_{min}\) (deadband, Hz) | -0.00066 |
| \(M\) (inertia constant) | 10 | \(R_s\) (battery internal resistance, Ω) | 0.0252 |
| \(D\) (damping) | 2 | \(R_1\) (Ω) | 0.0087 |
| \(T_f\) (filter time constant, s) | 0.6 | \(R_2\) (Ω) | 0.0301 |
| \(K_{max}\) (max droop gain) | 24 | \(C_1\) (F) | 41.72 |
| \(P_0\) (curve fitting) | 0.01 | \(C_2\) (F) | 1437 |
| \(n\) (curve fitting) | 20 |
4.2 Evaluation Metrics
For step load disturbance, we use the maximum frequency deviation \(\Delta f_m\) and the frequency deterioration rate \(v_m\) defined as:
$$ v_m = \frac{|\Delta f_m|}{t_m – t_0} $$
where \(t_m\) is the time at which the maximum deviation occurs, and \(t_0\) is the start of the disturbance. Smaller values indicate better performance.
For continuous load disturbance, we use the root mean square (RMS) of frequency deviation and RMS of SOC deviation:
$$
\text{RMS}_f = \sqrt{\frac{1}{N} \sum_{i=1}^{N} \Delta f_i^2} $$
$$ \text{RMS}_{SOC} = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (SOC_i – SOC_0)^2}
$$
where \(N\) is the number of sampling points. Lower RMS values indicate better frequency regulation and SOC maintenance.
5. Simulation Results and Analysis
5.1 Step Load Disturbance
A step load increase of 0.05 p.u. is applied at \(t=1\) s. The frequency deviation responses for the three strategies (no energy storage, fixed-droop, and dynamic-droop) are compared in Table 2 and the following results.
| Control strategy | \(\Delta f_m\) (Hz) | \(t_m\) (s) | \(\Delta t_m\) (s) | \(v_m\) (Hz/s) |
|---|---|---|---|---|
| No storage | -0.2807 | 2.862 | 1.862 | 0.1508 |
| Fixed-droop | -0.0803 | 1.729 | 0.729 | 0.1102 |
| Dynamic-droop | -0.0551 | 1.507 | 0.507 | 0.1087 |
The dynamic-droop strategy yields the smallest maximum frequency deviation of -0.0551 Hz, which is an improvement of 0.2256 Hz over no storage and 0.0252 Hz over fixed-droop. The time to reach the maximum deviation is also the shortest (0.507 s), and the frequency deterioration rate is the smallest (0.1087 Hz/s). This demonstrates that the proposed dynamic-droop control effectively mitigates the impact of sudden load changes.
5.2 Continuous Load Disturbance
A 30-minute continuous load disturbance profile (shown in the original paper) is applied. The frequency deviation curves and SOC evolution are compared. The RMS values are listed in Table 3.
| Control strategy | \(\Delta f_m\) (Hz) | \(\text{RMS}_f\) | \(\text{RMS}_{SOC}\) |
|---|---|---|---|
| No storage | 0.2309 | 0.0625 | – |
| Fixed-droop | 0.1313 | 0.0271 | 0.0245 |
| Dynamic-droop | 0.1295 | 0.0257 | 0.0147 |
Under continuous disturbances, the dynamic-droop strategy achieves the lowest \(\text{RMS}_f\) of 0.0257, which is 0.0368 lower than no storage and 0.0014 lower than fixed-droop. Moreover, the \(\text{RMS}_{SOC}\) for dynamic-droop is 0.0147, a reduction of 0.0098 compared to fixed-droop, indicating significantly better SOC preservation. This confirms that the dynamic-droop control not only improves frequency regulation but also effectively prevents the energy storage battery from reaching extreme SOC levels, thereby prolonging its life.
6. Conclusion
In this paper, we propose a dynamic droop coefficient control strategy for an energy storage battery assisting a thermal power unit in secondary frequency regulation. By adaptively adjusting the droop gain based on the battery’s state of charge, the strategy simultaneously enhances frequency regulation performance and protects the energy storage battery from overcharging or deep discharging. Simulation results under step and continuous load disturbances demonstrate that the proposed strategy outperforms fixed-droop control and the case without energy storage. Specifically, the maximum frequency deviation under a step disturbance is reduced by 0.2256 Hz compared to no storage, and the RMS of frequency deviation under continuous disturbance is reduced by 0.0368. Additionally, the SOC deviation RMS is improved by 0.0098 relative to fixed-droop control. These findings validate the effectiveness of the dynamic-droop approach for energy storage battery integrated frequency regulation. Future work will consider multi-battery coordination and real-time implementation.