The increasing global integration of renewable energy sources, characterized by inherent intermittency and volatility, presents significant challenges to power grid stability, particularly in maintaining system frequency. Traditional thermal power units, while forming the backbone of grid frequency regulation, suffer from inherent mechanical delays in their governor and turbine systems, limiting their ability to respond swiftly to rapid frequency deviations. This gap necessitates the incorporation of fast-responding resources. Among various options, the battery energy storage system (BESS), especially lithium-ion-based systems, has emerged as a superior solution due to its high power density, rapid response (within milliseconds), and improving cost-effectiveness. This article delves into a sophisticated control strategy where a battery energy storage system is deployed to assist thermal power units in secondary frequency regulation (Automatic Generation Control – AGC), with a specific focus on maintaining the battery’s State of Charge (SOC) to enhance system performance and longevity.
1. System Modeling for BESS-Assisted Frequency Regulation
The effectiveness of any control strategy hinges on an accurate mathematical representation of the integrated system. The model for a battery energy storage system assisting a thermal power unit in secondary frequency regulation primarily consists of three interconnected components: the thermal power plant model, the battery energy storage system model, and the overall grid frequency response model.
1.1 Thermal Power Unit Model
A thermal power unit is fundamentally comprised of a speed governor and a turbine. The governor, which regulates steam flow, can be modeled with a first-order lag. Its transfer function \( G_{gov}(s) \) is given by:
$$ G_{gov}(s) = \frac{1}{1 + sT_g} $$
where \( T_g \) is the governor time constant. For improved efficiency, a reheat-type turbine model is typically used. Its transfer function \( G_{tur}(s) \) approximates the dynamics of high-pressure and reheat stages:
$$ G_{tur}(s) \approx \frac{1 + sF_{HP}T_{RH}}{(1 + sT_{CH})(1 + sT_{RH})} $$
where \( T_{CH} \) and \( T_{RH} \) are the high-pressure and reheat time constants, and \( F_{HP} \) is the high-pressure turbine power fraction.
1.2 Battery Energy Storage System (BESS) Model
To accurately simulate the dynamic behavior of a lithium-ion battery energy storage system, an equivalent circuit model (ECM) is employed. This model captures key characteristics such as open-circuit voltage, internal resistance, and polarization effects. A second-order RC model is widely used for its balance of accuracy and simplicity.
The core equations governing this battery energy storage system model are:
$$
\begin{aligned}
U_b &= U_{OC}(SOC) – U_1 – U_2 – I_{Li}R_s \\
\dot{U_1} &= -\frac{1}{R_1 C_1}U_1 + \frac{I_{Li}}{C_1} \\
\dot{U_2} &= -\frac{1}{R_2 C_2}U_2 + \frac{I_{Li}}{C_2} \\
SOC(t) &= SOC_0 – \frac{\eta}{C_{Li}} \int_0^t I_{Li} \, d\tau
\end{aligned}
$$
Here, \( U_b \) is the terminal voltage, \( U_{OC} \) is the open-circuit voltage (a function of SOC), \( U_1 \) and \( U_2 \) represent polarization voltages, \( R_s \) is the ohmic resistance, \( R_1,C_1 \) and \( R_2,C_2 \) model the electrochemical and concentration polarization, \( I_{Li} \) is the battery current, \( \eta \) is the charge/discharge efficiency, and \( C_{Li} \) is the battery capacity. This model allows the battery energy storage system’s power output to be dynamically linked to its internal state, particularly the SOC.
1.3 Integrated Frequency Response Model
The complete system, combining the thermal unit, the battery energy storage system, and the grid’s inertial response, can be represented in a block diagram. The Area Control Error (ACE), a key signal in secondary frequency regulation defined as \( ACE = B\Delta f + \Delta P_{tie} \), is the primary input. For an isolated system study, the tie-line power deviation \( \Delta P_{tie} \) is often considered zero, simplifying ACE to \( B\Delta f \), where \( B \) is the frequency bias factor and \( \Delta f \) is the frequency deviation.
The power imbalance equation governing the system frequency is:
$$ \Delta P_m(s) + \Delta P_{BESS}(s) – \Delta P_L(s) = (D + sM)\Delta f(s) $$
where \( \Delta P_m \) is the mechanical power change from the thermal unit, \( \Delta P_{BESS} \) is the power from the battery energy storage system, \( \Delta P_L \) is the load disturbance, \( D \) is the load damping constant, and \( M \) is the system inertia constant. The total generation response is the sum of the primary response from the thermal unit’s governor \( (\Delta P_{G,F}) \), the secondary (AGC) response from the thermal unit \( (\Delta P_{G,S}) \), and the secondary response from the battery energy storage system \( (\Delta P_{B,S}) \).
2. Power Allocation and the Proposed Dynamic Droop Control Strategy
2.1 Frequency-Based Signal Allocation
A critical step is intelligently splitting the ACE signal between the slow thermal unit and the fast battery energy storage system. This is achieved using a frequency-domain allocation strategy. A first-order low-pass filter is applied to the ACE signal. The low-frequency component is dispatched to the thermal unit, while the complementary high-frequency component is assigned to the battery energy storage system. This leverages the respective strengths of each resource.
$$
\begin{aligned}
P_{ACE,G}(s) &= \frac{1}{1 + sT_f} P_{ACE}(s) \\
P_{ACE,B}(s) &= \left(1 – \frac{1}{1 + sT_f}\right) P_{ACE}(s) = \frac{sT_f}{1 + sT_f} P_{ACE}(s)
\end{aligned}
$$
where \( T_f \) is the filter time constant, \( P_{ACE,G} \) is the ACE component for the thermal generator, and \( P_{ACE,B} \) is the component for the battery energy storage system.
2.2 Dynamic Droop Control for the Battery Energy Storage System
While the allocated signal dictates when the BESS should act, the how much is determined by its droop control. Traditional fixed-droop control for a battery energy storage system, given by \( \Delta P_{BESS} = -K \cdot \Delta f \), has a major drawback: it does not consider the battery’s SOC. This can lead to deep discharge or overcharge, stressing the battery and reducing its lifespan, and may eventually remove the BESS from service when SOC limits are reached, degrading frequency regulation.
To address this, a Dynamic Droop Coefficient Control Strategy is proposed. The core idea is to modulate the droop coefficient \( K \) in real-time based on the instantaneous SOC of the battery energy storage system. The coefficient is maximized when SOC is in a safe, central range and is smoothly reduced to zero as SOC approaches predefined upper or lower limits. This prioritizes BESS participation when it is most effective and protects it from harmful states.
The dynamic droop coefficient \( K(t) \) follows a general form:
$$ K(t) = \frac{K_{max} P_0 e^{nt}}{K_{max} + P_0(e^{nt} – 1)} $$
where \( K_{max} \) is the maximum droop coefficient, and \( P_0 \) and \( n \) are shaping parameters. This function is adapted specifically for charge and discharge modes relative to SOC zones.
For Charging \( (\Delta f > 0) \):
$$
K_c =
\begin{cases}
K_{max}, & 0 < SOC \leq SOC_{high} \\[8pt]
\displaystyle \frac{K_{max} P_0 \exp\left( \frac{n(SOC_{max} – SOC)}{SOC_{max} – SOC_{high}} \right)}{K_{max} + P_0 \left[ \exp\left( \frac{n(SOC_{max} – SOC)}{SOC_{max} – SOC_{high}} \right) – 1 \right]}, & SOC_{high} < SOC < SOC_{max} \\[8pt]
0, & SOC_{max} \leq SOC < 1
\end{cases}
$$
For Discharging \( (\Delta f < 0) \):
$$
K_d =
\begin{cases}
0, & 0 < SOC \leq SOC_{min} \\[8pt]
\displaystyle \frac{K_{max} P_0 \exp\left( \frac{n(SOC – SOC_{min})}{SOC_{low} – SOC_{min}} \right)}{K_{max} + P_0 \left[ \exp\left( \frac{n(SOC – SOC_{min})}{SOC_{low} – SOC_{min}} \right) – 1 \right]}, & SOC_{min} < SOC < SOC_{low} \\[8pt]
K_{max}, & SOC_{low} \leq SOC < 1
\end{cases}
$$
Here, \( SOC_{min} \) and \( SOC_{max} \) are the absolute operational limits, while \( SOC_{low} \) and \( SOC_{high} \) define the beginning of the tapering zones. The final power command for the battery energy storage system is:
$$
\Delta P_{BESS}(s) = -K_{c/d}(SOC) \cdot \Delta f(s)
$$
This strategy ensures the battery energy storage system aggressively supports frequency regulation when its SOC is in the nominal zone (e.g., 45%-55%) but gracefully reduces its participation as SOC moves towards extremes, thus actively maintaining the SOC within a safer band and extending the useful service life of the BESS asset.
3. Simulation Analysis and Performance Evaluation
To validate the proposed dynamic droop control strategy for the battery energy storage system, a simulation model was built in Matlab/Simulink. A 660 MW thermal unit was modeled, assisted by a 10 MW / 5 MWh lithium-ion battery energy storage system. All parameters were per-unitized. Three scenarios were compared:
- No BESS Control: Base case with only the thermal unit performing frequency regulation.
- Fixed Droop BESS Control: The battery energy storage system uses a constant droop coefficient.
- Dynamic Droop BESS Control: The proposed strategy where the BESS droop coefficient varies with SOC.
Performance was evaluated under two types of disturbances: a step load change and a continuous random load variation.
3.1 Performance under Step Load Disturbance
A 0.05 p.u. step increase in load was applied at t=1 second. Key metrics are the maximum frequency deviation \( \Delta f_{max} \) and the rate of frequency decline \( v_m = \Delta f_{max} / (t_m – t_0) \), where \( t_m \) is the time at which the maximum deviation occurs.
| Control Strategy | \(\Delta f_{max}\) (Hz) | \(t_m\) (s) | \(v_m\) (Hz/s) |
|---|---|---|---|
| No BESS Control | -0.2807 | 2.862 | 0.1508 |
| Fixed Droop BESS Control | -0.0803 | 1.729 | 0.1102 |
| Dynamic Droop BESS Control | -0.0551 | 1.507 | 0.1087 |
The results clearly demonstrate the superiority of integrating a battery energy storage system. The dynamic droop strategy achieved the smallest frequency nadir (-0.0551 Hz), representing an improvement of 0.2256 Hz over the no-BESS case and 0.0252 Hz over the fixed-droop BESS case. It also reached the nadir fastest and had the lowest rate of frequency decline, indicating the most stable and effective response.
3.2 Performance under Continuous Load Disturbance
A 30-minute profile of random load variations was applied to test the strategy under more realistic, sustained conditions. The key metrics here are the Root Mean Square (RMS) of the frequency deviation \( RMS_f \) (measuring overall regulation quality) and the RMS of the SOC deviation from its initial setpoint \( RMS_{SOC} \) (measuring SOC maintenance).
| Control Strategy | \(\Delta f_{max}\) (Hz) | \(RMS_f\) | \(RMS_{SOC}\) |
|---|---|---|---|
| No BESS Control | 0.2309 | 0.0625 | – |
| Fixed Droop BESS Control | 0.1313 | 0.0271 | 0.0245 |
| Dynamic Droop BESS Control | 0.1295 | 0.0257 | 0.0147 |
Again, the battery energy storage system significantly improves frequency stability. The dynamic droop control yielded the best overall frequency regulation, with the lowest \( RMS_f \) value. Crucially, its \( RMS_{SOC} \) value of 0.0147 is substantially lower than the 0.0245 of the fixed droop strategy—an improvement of approximately 40%. This quantitatively proves that the dynamic droop strategy is highly effective in maintaining the SOC of the battery energy storage system closer to its desired setpoint, preventing drift towards the boundaries and ensuring the BESS remains available for frequency support over longer durations.
4. Conclusion
The integration of a battery energy storage system with conventional thermal power plants presents a potent solution to the growing frequency regulation challenges in modern power grids with high renewable penetration. This article has presented and validated an advanced control strategy that goes beyond simply using the BESS for fast power injection/absorption. The proposed Dynamic Droop Coefficient Control Strategy intelligently governs the participation of the battery energy storage system based on real-time frequency deviation and, more importantly, its own State of Charge.
Simulation results under both step and continuous disturbances confirm the dual advantages of this strategy:
- Enhanced Frequency Regulation: It delivers superior performance in minimizing frequency deviations and improving dynamic stability compared to both the baseline (no BESS) and a conventional fixed-droop BESS control.
- Effective SOC Maintenance: It actively manages the energy state of the battery energy storage system, significantly reducing SOC drift and keeping it within a safer operating range. This is critical for prolonging the cycle life of the expensive battery asset, reducing degradation, and ensuring its long-term economic viability and readiness for grid services.
In summary, the dynamic control of the battery energy storage system’s droop coefficient as a function of SOC represents a significant step towards smarter, more sustainable, and more reliable hybrid frequency regulation systems. Future work could explore the optimization of the SOC zone parameters (\( SOC_{low}, SOC_{high} \)) and the tairing function shape (\( n, P_0 \)) based on specific battery chemistry degradation models and grid service market signals, further refining the economic and technical benefits of deploying battery energy storage systems for grid support.