In recent years, the large-scale integration of renewable energy sources such as wind and solar power has gradually reduced the proportion of conventional thermal generating units in the power system. This change indirectly affects the stability of power system frequency. Therefore, it has become a research hotspot to find new frequency regulation methods to assist traditional units in quickly suppressing frequency fluctuations and improving overall regulation capability. Energy storage technology is widely recognized as an effective means to solve the frequency regulation problem. With the continuous breakthroughs in energy storage technology and decreasing costs, battery energy storage systems have been increasingly applied. Among them, lithium-ion battery energy storage is one of the key technologies, known for its fast response speed and high accuracy. Many studies have been conducted on applying battery energy storage to optimize primary frequency regulation. However, existing research has some shortcomings: 1) Some studies do not consider the impact of the state of charge (SOC) of the energy storage battery on primary frequency regulation stability and use a single control method; 2) Comprehensive control methods that consider SOC lack an effective proportional relationship to combine different control strategies; 3) The dead-band range of the energy storage battery system is not optimized for economic benefits. To address these issues, this paper proposes a comprehensive control strategy for the energy storage battery participating in primary frequency regulation of the power grid. First, we design SOC-based virtual droop and virtual inertia coefficients to prevent overcharging or over-discharging. Second, we set reasonable weighting coefficients to combine virtual droop control and virtual inertia control, allowing the grid to obtain the optimal frequency regulation under different frequency deviations. Third, we set an appropriate dead-band range for the energy storage battery to improve economic operation. Finally, we build a simulation model in Matlab/Simulink to verify the effectiveness of the proposed strategy.
1. Model Construction
1.1 Traditional Primary Frequency Regulation Model of Power System
The traditional primary frequency regulation model of a power system mainly consists of a turbine governor model, a turbine model, and a generator-load model. The turbine governor adjusts the frequency by controlling the steam flow, and its transfer function is given by:
$$ \Delta P_v(s) = \frac{1}{1+\tau_g s} \Delta P_n(s) $$
$$ \Delta P_n(s) = \Delta P_c(s) – \frac{1}{R} \Delta f(s) $$
where \(\Delta P_v\) is the power change corresponding to the valve opening (MW), \(\Delta P_n\) is the electromagnetic power change (MW), \(\Delta P_c\) is the control signal of the power system (MW), \(\tau_g\) is the inertia time constant of the governor (s), \(R\) is the droop coefficient of the governor, and \(\Delta f\) is the frequency deviation (Hz).
The transfer function of a reheat steam turbine is:
$$ G_T(s) = \frac{\Delta P_m(s)}{\Delta P_v(s)} = \frac{1+K_r \tau_r s}{(1+\tau_T s)(1+\tau_r s)} $$
where \(\tau_T\) is the time constant of the prime mover, \(\tau_r\) is the reheat time constant, and \(K_r\) is the reheat coefficient.
The generator-load transfer function is expressed as:
$$ \frac{\Delta \omega(s)}{\Delta P_M(s) – \Delta P_L(s)} = \frac{1}{Ms + D} $$
where \(\Delta P_M\) is the mechanical power change (MW), \(\Delta P_L\) is the load change (MW), \(M = 2H\) (H is the grid inertia time constant), \(D\) is the load damping coefficient, and \(\Delta \omega\) is the angular speed change (rad/s). In synchronous AC power systems, grid frequency \(f\) and generator angular speed \(\omega\) satisfy \(f = \omega / (2\pi)\), and after per-unit normalization, \(\Delta f = \Delta \omega\).
1.2 Energy Storage Battery System Model
The energy storage battery system model mainly includes a dead-band limiter, a transfer function, and an SOC calculation unit. Ignoring the internal characteristics of the battery, we use a first-order inertial model, which ensures simulation accuracy and speed. The transfer function is:
$$ G_B(s) = \frac{1}{1+\tau_B s} $$
where \(\tau_B\) is the time constant of the energy storage battery (s).
When the load in the power system changes, the grid frequency also changes accordingly. The participation of the energy storage battery in primary frequency regulation means that when the frequency changes, the battery provides or absorbs power to compensate for the frequency deviation, thereby reducing frequency fluctuations and maintaining stable operation.
2. Control Strategy for Energy Storage Battery Participating in Primary Frequency Regulation
2.1 Virtual Droop and Virtual Inertia Control Strategies
The two main control strategies for the energy storage battery system in primary frequency regulation are virtual droop control and virtual inertia control. Virtual droop control simulates the droop characteristic of a generator unit:
$$ \Delta P_e(s) = -K_e \Delta f(s) $$
where \(\Delta P_e\) is the droop output (MW), \(K_e\) is the droop control coefficient.
Virtual inertia control simulates the inertial response of a generator unit:
$$ \Delta P_{ine}(s) = -K_{ine} \frac{d\Delta f}{dt} $$
where \(\Delta P_{ine}\) is the inertia output (MW), \(\frac{d\Delta f}{dt}\) is the rate of change of frequency, and \(K_{ine}\) is the inertia control coefficient.
2.2 SOC-Based Variable Coefficient Control Strategy
Since the capacity of an energy storage battery participating in primary frequency regulation is much smaller than that of the power system, using constant control coefficients may lead to overcharging or over-discharging, and even cause frequency oscillations. To prevent this, we design a variable coefficient strategy based on SOC. Taking virtual droop control as an example, we divide the SOC into five intervals and adjust the droop coefficient according to the SOC state. The piecewise function for the virtual droop coefficient is:
| Charging case | \( K_{e,c} = \begin{cases} K_{e,\max} & Q_{SOC} \in [0, Q_3] \\ K_{e,\max}\left(\frac{Q_{SOC}-Q_4}{Q_4-Q_3}\right)^n & Q_{SOC} \in (Q_3, Q_4] \\ 0 & Q_{SOC} \in (Q_4, 1] \end{cases} \) |
|---|---|
| Discharging case | \( K_{e,f} = \begin{cases} 0 & Q_{SOC} \in [0, Q_1] \\ K_{e,\max}\left(\frac{Q_{SOC}-Q_1}{Q_2-Q_1}\right)^n & Q_{SOC} \in (Q_1, Q_2] \\ K_{e,\max} & Q_{SOC} \in (Q_2, 1] \end{cases} \) |
Here, \(K_{e,c}\) and \(K_{e,f}\) are the droop coefficients during charging and discharging, respectively; \(K_{e,\max}\) is the maximum droop coefficient; \(Q_{SOC}\) is the SOC value, and the normal working range of the energy storage battery is set to [0.1, 0.9]; \(Q_1\), \(Q_2\), \(Q_3\), \(Q_4\) are different SOC thresholds, taken as 0.1, 0.3, 0.7, 0.9, respectively. The exponent \(n\) is set to 2 in this work.
Similarly, the virtual inertia coefficient is defined as:
$$ \begin{cases}
K_{ine,c} = k_{ine/e} K_{e,c} \\
K_{ine,f} = k_{ine/e} K_{e,f}
\end{cases} $$
where \(k_{ine/e}\) is the ratio between the virtual inertia coefficient and the virtual droop coefficient, ensuring that the outputs of both strategies are comparable under similar conditions.
The virtual droop control is effective for frequency deviation \(\Delta f\), while virtual inertia control is effective for the rate of change of frequency. Combining both strategies, the total output of the energy storage battery is:
$$ \Delta P_B(s) = \lambda \Delta P_e(s) + (1-\lambda) \Delta P_{ine}(s) $$
where \(\lambda\) is the output coefficient for virtual inertia control, which is defined as a function of frequency deviation \(\Delta f\):
$$ \lambda = \begin{cases}
0.25 + \frac{|\Delta f|}{4\Delta f_s} & 0 \le |\Delta f| \le \Delta f_s \\
0.5 + \frac{|\Delta f|}{4\Delta f_s} & \Delta f_s < |\Delta f| \le 2\Delta f_s \\
0.75 & |\Delta f| > 2\Delta f_s
\end{cases} $$
Here, \(\Delta f_s\) is a set critical frequency deviation. When the frequency deviation is small, the proportion of virtual inertia output is increased to reduce the rate of change; when the frequency deviation is large, the proportion of virtual droop output is increased to suppress the large deviation.
2.3 Frequency Deviation Dead-Band Control Strategy
To prolong the life of the energy storage battery, we set a dead-band range. The conventional primary frequency regulation dead-band of thermal units is usually \([-0.033\,\text{Hz}, 0.033\,\text{Hz}]\). To improve overall economic efficiency, we set the dead-band of the energy storage battery system to 60% of that of thermal units, i.e., \([-0.0198\,\text{Hz}, 0.0198\,\text{Hz}]\). When the frequency deviation is within this range, the energy storage battery does not act; otherwise, it charges or discharges.
2.4 Comprehensive Control Strategy Based on SOC
Based on the above analysis, we propose a comprehensive control strategy for the energy storage battery participating in primary frequency regulation, considering SOC. The strategy is summarized as follows:
- If \(|\Delta f| \le 0.0198\,\text{Hz}\), the grid frequency is relatively stable, and the energy storage battery does not act.
- If \(|\Delta f| > 0.0198\,\text{Hz}\), the energy storage battery assists thermal units in primary frequency regulation. Based on the current \(Q_{SOC}\), calculate the charging/discharging droop and inertia coefficients using the piecewise functions, determine the droop and inertia outputs, and then compute the actual total output using the combination formula with the weighting factor \(\lambda\).
- If \(0.0198\,\text{Hz} < |\Delta f| \le \Delta f_s\), virtual inertia output dominates (with varying coefficients).
- If \(\Delta f_s < |\Delta f| \le 2\Delta f_s\), virtual droop output dominates (with varying coefficients).
- If \(|\Delta f| > 2\Delta f_s\), the energy storage battery outputs the maximum virtual droop power.
3. Simulation Analysis
We take a 1000 MW thermal unit from a power plant in Fujian as the research object and perform simulations on Matlab/Simulink. The turbine is manufactured by Harbin Turbine Company. To observe the impact of battery capacity on frequency regulation performance, we set the parameters of the energy storage battery to 10 MW/1 MWh. The base values are 1000 MW and 50 Hz, and all parameters are in per-unit values. The simulation parameters are listed in Table 1.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| \(M\) | 10 | \(k_{ine/e}\) | 4 |
| \(D\) | 2 | \(\tau_r\) (s) | 10 |
| \(R\) | 0.05 | \(\tau_T\) (s) | 0.3 |
| \(K_r\) | 0.3 | \(\tau_g\) (s) | 0.08 |
| \(K_{e,\max}\) | 10 | \(\Delta f_s\) (Hz) | 0.001 |
3.1 Step Load Disturbance
We evaluate the performance under a step load disturbance using the following metrics: maximum frequency deviation \(\Delta f_{jy,\max}\), steady-state frequency deviation \(\Delta f_w\), and SOC change after 300 s, \(\Delta Q_{SOC}\). Smaller values indicate better performance. When a step disturbance of \(\Delta P_L = 0.05\) (p.u.) is applied, the initial SOC is set to 0.5. We compare the proposed comprehensive control strategy with variable droop control, fixed droop control, and no energy storage. The results are shown in Table 2 and Figure 3 (simulation results omitted for brevity).
| Control Strategy | \(\Delta f_{jy,\max}\) (p.u.) | \(\Delta f_w\) (p.u.) | \(\Delta Q_{SOC}\) |
|---|---|---|---|
| No energy storage | 0.00578 | 0.00287 | – |
| Fixed droop | 0.00473 | 0.00242 | 0.5 |
| Variable droop | 0.00473 | 0.00242 | 0.376 |
| Proposed strategy | 0.00473 | 0.00242 | 0.369 |
Under the large step disturbance, all control strategies with energy storage battery output limited to 10 MW show similar maximum and steady-state deviations. However, compared to no energy storage, the maximum frequency deviation decreases by 18.17%, and the steady-state deviation decreases by 15.68%. As simulation time increases, the SOC gradually decreases. The fixed droop strategy eventually depletes the SOC to zero, causing a sudden frequency drop. The proposed strategy consumes the least SOC after 300 s: 0.369, which is 1.86% lower than variable droop and 26.2% lower than fixed droop, demonstrating better SOC maintenance.
3.2 Continuous Load Disturbance
For continuous load disturbance, we use metrics: peak-to-valley frequency difference \(\Delta f_{lx,\max}\), root-mean-square average frequency deviation \(\Delta f_{pj}\), and average SOC over 300 s \(SOC_{pj}\). Smaller \(\Delta f_{lx,\max}\) and \(\Delta f_{pj}\) indicate better performance, and \(SOC_{pj}\) closer to 0.5 indicates better SOC retention. A random continuous disturbance of amplitude \([-0.05, 0.05]\) (p.u.) is applied. The results are summarized in Table 3.
| Control Strategy | \(\Delta f_{lx,\max}\) (p.u.) | \(\Delta f_{pj}\) (p.u.) | \(SOC_{pj}\) |
|---|---|---|---|
| No energy storage | 0.00532 | 0.000811 | – |
| Fixed droop | 0.00550 | 0.000829 | 0.495 |
| Variable droop | 0.00439 | 0.000613 | 0.503 |
| Proposed strategy | 0.00380 | 0.000601 | 0.501 |
The proposed strategy reduces the peak-to-valley frequency difference by 13.4% compared to variable droop, 30.9% compared to fixed droop, and 28.6% compared to no energy storage. The average frequency deviation is also the smallest, with reductions of 25.9%, 27.5%, and 1.96% compared to no storage, fixed droop, and variable droop, respectively. Moreover, the average SOC under the proposed strategy (0.501) is closest to the initial set value of 0.5, demonstrating superior SOC maintenance. This indicates that our control strategy effectively improves frequency stability while preserving the battery’s health.
4. Conclusion
In this paper, we propose a comprehensive control strategy for the energy storage battery participating in primary frequency regulation, combining SOC-based virtual droop and virtual inertia control with an adaptive weighting factor. We also set an optimized dead-band to improve economic efficiency. The simulation results lead to the following conclusions:
- By setting appropriate variable output coefficients, the virtual inertia and virtual droop control strategies are effectively combined, allowing the energy storage battery to respond quickly to frequency changes while smoothing its output, avoiding secondary frequency fluctuations, and contributing to grid frequency stability.
- The proposed strategy considers both the output and the SOC of the energy storage battery. The SOC-dependent control coefficients prevent overcharging or over-discharging, prolonging the battery’s service life.
- The strategy achieves good control performance in terms of frequency regulation and SOC maintenance, making it a practical reference for real-world applications.