To enhance the performance of an energy storage cell in primary frequency modulation of the power grid, we propose a comprehensive control strategy that balances grid frequency stability with the state of charge of the energy storage cell. By setting an appropriate output coefficient, we integrate a virtual inertia control strategy with a virtual droop control strategy. We control the total output of the energy storage cell based on its SOC and adjust the proportion of virtual droop output to virtual inertia output according to the frequency deviation. Additionally, we set an optimal frequency dead-band for the energy storage cell to improve the economic efficiency of the unit. Our simulation results demonstrate that under step load disturbances, the proposed comprehensive control strategy reduces the energy consumption of the energy storage cell by at least 1.86% compared to other control methods, effectively improving the maintenance of the SOC. Under continuous load disturbances, the maximum frequency peak-to-valley difference is reduced by at least 13.4%. After a continuous simulation of 300 seconds, the SOC of the energy storage cell is also closest to the set value. These findings show that our comprehensive control strategy can effectively enhance the primary frequency modulation effect of the power system and maintain the SOC of the energy storage cell within a reasonable range.
In recent years, the expanding integration of renewable energy sources such as wind and solar power has led to a decrease in the proportion of conventional generating units like thermal power. This shift indirectly impacts the stability of power system frequency. Therefore, seeking novel frequency modulation methods to assist traditional generators in rapidly suppressing frequency fluctuations and improving the overall frequency regulation capability of the grid has become a current research hotspot. Energy storage technology is widely recognized as an effective solution to grid frequency regulation problems. With continuous breakthroughs in energy storage technology, costs are decreasing, making it widely applicable. The battery energy storage cell, particularly lithium-ion types, is a key technology known for its fast response and high precision. Several studies have explored the use of battery energy storage cell technology to optimize primary frequency regulation capability. Previous research on the primary frequency regulation design of lithium-ion energy storage power stations indicates that these stations can smooth grid frequency fluctuations and reduce the number of operations of generating units, providing a direction for our study. Regarding methods for an energy storage cell to participate in primary frequency modulation, the use of a droop control strategy has been proposed. This method can improve system frequency stability, but it does not consider the battery capacity or SOC, which may lead to overcharging or over-discharging in practice, affecting the life of the energy storage cell and even damaging grid frequency stability. Other comprehensive control methods based on SOC have been proposed, combining virtual droop control with virtual inertia control. These methods can control the total output of the energy storage cell in real-time based on changes in frequency deviation. Simulation results show good effectiveness in primary frequency modulation and SOC maintenance. However, these methods simply add virtual inertia output and virtual droop output without considering their proportional relationship.
Summarizing the existing research, we identify the following deficiencies: 1) Some studies do not consider the impact of the SOC of the energy storage cell on primary frequency modulation stability, and their control methods are single; 2) Comprehensive control methods that do consider the SOC fail to establish an effective proportional relationship to combine the control methods; 3) Furthermore, the frequency dead-band of the battery energy storage system should be smaller than that of traditional units to improve economic benefits, a factor not considered in the aforementioned studies. To address these issues, we propose a comprehensive control strategy for an energy storage cell participating in primary frequency modulation of the grid. First, we set virtual droop coefficients and virtual inertia coefficients based on SOC to prevent overcharging or over-discharging of the energy storage cell, thereby extending its service life. Second, for the comprehensive control method combining virtual droop and virtual inertia control, we set reasonable weighting coefficients to enable the grid to achieve the optimal frequency regulation mode under different frequency fluctuations. Subsequently, we set an appropriate frequency dead-band for the energy storage cell to improve the operational economy of the unit. Finally, we build a simulation model using the Matlab/Simulink platform to verify the effectiveness of our proposed comprehensive strategy.
1. Model Construction
1.1 Traditional Power System Primary Frequency Modulation Model
The traditional model for primary frequency modulation of a power system mainly consists of a steam turbine governor model, a steam turbine model, and a generator-load model, as shown conceptually. The transfer function for the steam turbine governor, which controls steam flow to regulate frequency, is:
$$ \Delta P_v(s) = \frac{1}{1+\tau_g s} \Delta P_n(s) $$
$$ \Delta P_n(s) = \Delta P_c(s) – \frac{1}{R} \Delta f(s) $$
Here, $\Delta P_v$ is the power change corresponding to the valve position change (MW), $\Delta P_n$ is the change in electromagnetic power (MW), $\Delta P_c$ is the control signal (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 for a reheat steam turbine is:
$$ G_T(s) = \frac{\Delta P_m(s)}{\Delta P_v(s)} = \frac{1+K_r \tau_r s}{(1+\tau_T s)(1+\tau_r s)} $$
Here, $G_T$ is the transfer function of the prime mover, $\tau_T$ is the time constant of the prime mover (s), $\tau_r$ is the reheat time constant (s), and $K_r$ is the reheat coefficient. The generator-load transfer function is given by the following equation, where $\Delta P_m$ is the change in mechanical power input to the generator (MW), $\Delta P_L$ is the change in load (MW), $M = 2H$ (with $H$ being the grid inertia time constant in seconds), $D$ is the load damping coefficient, and $\Delta \omega$ is the change in angular velocity (rad/s). In a synchronous AC power system, the relationship between grid frequency $f$ and generator angular velocity $\omega$ is $f = \omega/(2\pi)$. After per-unit conversion, we obtain $\Delta f = \Delta \omega$.
1.2 Model of the Energy Storage Cell System
The model of the energy storage cell system includes elements such as a dead-band limiter, the transfer function of the energy storage system, and the SOC calculation module. The transfer function of the battery energy storage cell system, modeled as a first-order inertial element to ensure simulation accuracy and speed while ignoring internal characteristics, is:
$$ G_B(s) = \frac{1}{1+\tau_B s} $$
Where $\tau_B$ is the time constant (s) of the energy storage cell system.
2. Control Strategy for an Energy Storage Cell in Primary Frequency Modulation
When the load in the power system changes, the grid frequency also changes. An energy storage cell participating in primary frequency modulation provides or absorbs power to compensate for this frequency change, thereby reducing frequency fluctuations and maintaining stable grid operation.
2.1 Virtual Droop and Virtual Inertia Control Strategies
Currently, the main control strategies for an energy storage cell system in primary frequency modulation are virtual droop control and virtual inertia control. The principle of virtual droop control is to simulate the droop characteristic of a generator unit to control the energy storage cell’s participation. Its expression is:
$$ \Delta P_e(s) = -K_e \Delta f $$
Here, $\Delta P_e$ is the droop output (MW), $\Delta f$ is the system frequency deviation (Hz), and $K_e$ is the droop control coefficient. The principle of virtual inertia control is to simulate the inertial response characteristic of a generator unit. Its expression is:
$$ \Delta P_{ine}(s) = -K_{ine} \frac{d\Delta f}{dt} $$
Here, $\Delta P_{ine}$ is the inertia output (MW), $\frac{d\Delta f}{dt}$ is the system frequency rate of change, and $K_{ine}$ is the inertia control coefficient.
2.2 Primary Frequency Modulation Strategy for an Energy Storage Cell System Based on SOC
Since the capacity of an energy storage cell system participating in primary frequency modulation is much smaller than that of the power system, using a fixed control coefficient for charging and discharging can lead to prolonged overcharging or over-discharging, potentially causing grid frequency oscillations. To prevent this, we design a variable control coefficient strategy based on SOC. Taking virtual droop control as an example, we divide the SOC of the energy storage cell into five intervals. The system adjusts the droop coefficient based on the SOC state to control the input and output power, thereby assisting the thermal power unit in primary frequency modulation. The piecewise function for the virtual droop control coefficient concerning SOC is:
$$ K_{e,c} = \begin{cases}
K_{e,max} & Q_{SOC} \in [0, Q_3] \\
K_{e,max} \left( \frac{Q_{SOC} – Q_4}{Q_4 – Q_3} \right)^n & Q_{SOC} \in (Q_3, Q_4] \\
0 & Q_{SOC} \in (Q_4, 1]
\end{cases} $$
$$ K_{e,f} = \begin{cases}
0 & Q_{SOC} \in [0, Q_1] \\
K_{e,max} \left( \frac{Q_{SOC} – Q_1}{Q_2 – Q_1} \right)^n & Q_{SOC} \in (Q_1, Q_2] \\
K_{e,max} & Q_{SOC} \in (Q_2, 1]
\end{cases} $$
Where $K_{e,c}$ is the droop coefficient during charging, $K_{e,f}$ is the droop coefficient during discharging, $K_{e,max}$ is the maximum droop coefficient, and $Q_{SOC}$ is the SOC value, with the normal operating range of the energy storage cell set to [0.1, 0.9]. $Q_1$, $Q_2$, $Q_3$, and $Q_4$ represent different SOC states of the energy storage cell, set to 0.1, 0.3, 0.7, and 0.9 respectively. Different values of $n$ lead to different adaptive curves for the droop coefficient; we select $n=2$.
Due to the similar nature of the virtual inertia coefficient and the virtual droop coefficient, we set the virtual inertia coefficient as:
$$ \begin{cases}
K_{ine,c} = k_{ine/e} K_{e,c} \\
K_{ine,f} = k_{ine/e} K_{e,f}
\end{cases} $$
Here, $K_{ine,c}$ and $K_{ine,f}$ are the virtual inertia coefficients during charging and discharging, respectively. $k_{ine/e}$ is the ratio of the virtual inertia coefficient to the virtual droop coefficient, used to equalize the output of these two control strategies. Given that virtual droop control has a better effect on the frequency deviation $\Delta f$, while virtual inertia control better suppresses the rate of change of frequency deviation $\frac{d\Delta f}{dt}$, we combine their advantages. The expression for the total power response of the energy storage cell, combining virtual droop and virtual inertia control strategies, is:
$$ \Delta P_B(s) = \lambda \Delta P_e(s) + (1-\lambda) \Delta P_{ine}(s) $$
Where $\Delta P_B$ is the total output (MW) of the energy storage cell, and $\lambda$ is the output coefficient for virtual inertia control. To allow the proportion of the energy storage cell’s output to vary flexibly with the frequency deviation, we define $\lambda$ as a function of the 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 the set critical value of the frequency deviation. When the frequency deviation is small, we increase the proportion of virtual inertia output to reduce the rate of change of frequency. When the frequency deviation is large, we increase the proportion of virtual droop output to suppress the larger frequency deviation.
2.3 Frequency Deviation Control Strategy
When a frequency deviation occurs in the power system, the energy storage system adjusts its output to suppress the change. However, due to the complex nature of grid frequency variations, the charging and discharging frequency of the energy storage cell can be very high, which damages its service life. Therefore, it is necessary to classify the grid frequency deviation to extend the operational life of the energy storage cell. The primary frequency modulation dead-band for conventional thermal power units is typically set to [–0.033 Hz, 0.033 Hz]. To increase the service life of the steam turbine unit and improve overall economic efficiency, we set the primary frequency modulation dead-band of the battery energy storage system to 60% of that of the thermal power unit, i.e., [–0.0198 Hz, 0.0198 Hz]. When the frequency deviation is within this dead-band, the energy storage cell does not operate. When the frequency deviation exceeds the dead-band, the energy storage cell operates, either by discharging or charging.
2.4 Comprehensive Control Strategy for an Energy Storage Cell System in Primary Frequency Modulation Based on SOC
Based on the above analysis, we propose a comprehensive control strategy for an energy storage cell system participating in primary frequency modulation based on SOC. The specific control strategy is as follows:
1) When $|\Delta f| \le 0.0198$ Hz, the grid frequency is relatively stable, and the energy storage system does not operate.
2) When $|\Delta f| > 0.0198$ Hz, the energy storage system needs to assist the thermal power unit in primary frequency modulation. Based on $Q_{SOC}$, we calculate the charging and discharging droop coefficients and inertia coefficients of the energy storage system using the equations provided, determine the droop output and inertia output, and finally determine the actual output of the energy storage cell using the equation for $\Delta P_B(s)$.
3) When $0.0198$ Hz $< |\Delta f| \le \Delta f_s$, the energy storage system primarily uses variable virtual inertia output.
4) When $\Delta f_s < |\Delta f| \le 2\Delta f_s$, the energy storage system primarily uses variable virtual droop output.
5) When $|\Delta f| > 2\Delta f_s$, the energy storage system operates with maximum virtual droop output.
3. Simulation Analysis
We conducted simulation analysis on the Matlab/Simulink platform using a 1000 MW steam turbine unit from a power plant in Fujian as the research object. To better observe the impact of battery capacity on frequency regulation performance, we set the parameters of the energy storage cell to 10 MW/1 MWh. Based on 1000 MW and 50 Hz as the base values, relevant parameters were converted to per-unit values. The parameters for the simulation model are shown in Table 1.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| M | 10 | k_{ine/e} | 4 |
| D | 2 | τ_r (s) | 10 |
| R | 0.05 | τ_T (s) | 0.3 |
| K_r | 0.3 | τ_g (s) | 0.08 |
| K_{e,max} | 10 | Δf_s (Hz) | 0.001 |
3.1 Step Load Disturbance Scenario
For the step load disturbance scenario, we used the maximum frequency deviation ($\Delta f_{jy,max}$) and the steady-state frequency deviation ($\Delta f_w$) as evaluation indices for the battery energy storage system’s primary frequency modulation. The evaluation index for the SOC of the energy storage cell was the change in SOC ($\Delta Q_{SOC}$) after a 300-second simulation. Smaller values of $\Delta f_{jy,max}$, $\Delta f_w$, and $\Delta Q_{SOC}$ indicate a better control strategy. With an initial SOC of 0.5 and a step disturbance of $\Delta P_L = 0.05$ (p.u.), we compared our comprehensive control strategy against variable droop control, fixed droop control, and a no-storage scenario. The results for frequency deviation and SOC are summarized in Table 2.
| Control Strategy | Δf_{jy,max} (p.u.) | Δf_w (p.u.) | ΔQ_{SOC} |
|---|---|---|---|
| No Energy Storage | 0.00578 | 0.00287 | – |
| Fixed Droop Coefficient | 0.00473 | 0.00242 | 0.5 |
| Variable Droop Coefficient | 0.00473 | 0.00242 | 0.376 |
| Proposed Strategy | 0.00473 | 0.00242 | 0.369 |
Our analysis indicates that when the power system is subjected to a step load disturbance at a high SOC, the maximum frequency deviation and steady-state deviation under our control strategy are consistent with those of the fixed and variable droop coefficient strategies. This is because the step load disturbance is large, and the battery output calculated by all strategies exceeds 10 MW. Due to the output limit of the energy storage cell, all strategies maintain output at 10 MW, resulting in no significant difference in these metrics. However, compared to the no-storage scenario, the maximum frequency deviation decreased by 18.17%, and the steady-state deviation decreased by 15.68%, demonstrating a clear improvement.
As the simulation time progresses, the SOC under all strategies gradually decreases. The fixed droop coefficient strategy, which does not consider SOC, maintains a high output state, leading to a gradual decrease in SOC to 0 and a sudden large frequency drop later in the simulation. Compared to the variable droop coefficient strategy, our strategy slows the frequency decline more effectively because the virtual inertia output hinders the rapid frequency drop. As shown in Table 2, after a 300-second simulation, the change in $Q_{SOC}$ under our strategy was 0.369. This is 1.86% less than that of the variable droop coefficient strategy and 26.2% less than that of the fixed droop coefficient strategy. Our strategy consumes the least power and achieves the best SOC maintenance effect.
3.2 Continuous Load Disturbance Scenario
For the continuous load disturbance scenario, we used the frequency peak-to-valley difference ($\Delta f_{lx,max}$) and the root mean square average of the frequency deviation ($\Delta f_{pj}$) as evaluation indices. The evaluation index for the SOC of the energy storage cell was the average SOC ($SOC_{pj}$) over the 300-second simulation. Smaller values of $\Delta f_{lx,max}$ and $\Delta f_{pj}$ indicate a better strategy, and a $SOC_{pj}$ closer to 0.5 indicates a better strategy. We added a continuous load disturbance in the range of [–0.05, 0.05] to the simulation model, set the initial SOC to 0.5, and compared our comprehensive control strategy against the variable droop control, fixed droop control, and no-storage scenarios. The results are summarized in Table 3.
| Control Strategy | Δf_{lx,max} (p.u.) | Δf_{pj} (p.u.) | SOC_{pj} |
|---|---|---|---|
| No Energy Storage | 0.00532 | 0.000811 | – |
| Fixed Droop Coefficient | 0.00550 | 0.000829 | 0.495 |
| Variable Droop Coefficient | 0.00439 | 0.000613 | 0.503 |
| Proposed Strategy | 0.00380 | 0.000601 | 0.501 |
Our analysis shows that under continuous load disturbance, the peak-to-valley difference ($\Delta f_{lx,max}$) with our strategy was reduced by 13.4% compared to the variable droop coefficient strategy, by 30.9% compared to the fixed droop coefficient strategy, and by 28.6% compared to the no-storage scenario. The root mean square average of the frequency deviation ($\Delta f_{pj}$) under our strategy was also smaller than for other strategies, reduced by 25.9%, 27.5%, and 1.96% compared to the no-storage, fixed droop, and variable droop scenarios, respectively. This demonstrates our strategy’s superiority in maintaining frequency stability. Furthermore, the average SOC ($SOC_{pj}$) over the 300-second simulation under our strategy was closer to the initial set value of 0.5, indicating that our control strategy also provides the best SOC maintenance effect, thereby extending the service life of the energy storage cell and improving operational economy. In summary, our proposed control strategy exhibits excellent performance in maintaining grid frequency stability and keeping the SOC within the optimal range.
4. Conclusion
To effectively suppress grid frequency fluctuations in practical applications, we have proposed a comprehensive control strategy that combines virtual droop control and virtual inertia control based on the SOC of the energy storage cell, with a reasonable output ratio. To improve the economic performance of the unit, we set the primary frequency modulation dead-band of the energy storage cell to 60% of that of the thermal power unit. Through simulation analysis, we draw the following conclusions: 1) Setting an appropriate variable output coefficient effectively combines the virtual inertia and virtual droop control strategies. This allows the energy storage cell system to respond quickly to frequency changes while making its output smoother, avoiding secondary frequency fluctuations and promoting grid frequency stability. 2) Our control strategy considers both the output of the energy storage cell and its SOC by setting control coefficients that vary with SOC, effectively preventing overcharging or over-discharging of the energy storage cell. 3) Our control strategy balances the output and SOC of the energy storage cell, achieving satisfactory control effects in both aspects, and can be a reference for practical applications.