With the deepening implementation of the “dual carbon” strategy and the ongoing reform of the electric power system, an increasing amount of renewable energy is being integrated into the grid. This integration makes the frequency stability of traditional generating units more vulnerable, thus demanding novel frequency regulation control strategies. Battery energy storage systems (battery energy storage systems) offer the capability to charge and discharge rapidly, providing fast response to grid regulation demands. Under this new paradigm, battery energy storage systems can play a critical role in improving the frequency regulation performance of regional power grids. While substantial research has been conducted on the participation of energy storage in power frequency regulation, the enhancement of response speed and practical application of battery energy storage systems for grid frequency regulation still require further investigation. In this paper, we analyze the operational mechanism of battery energy storage systems participating in power system frequency regulation, establish a simulation model for the frequency regulation characteristics of battery energy storage systems in the grid, and propose an optimized control strategy. Our model simulation experiments demonstrate that the proposed control strategy is practical and efficient, offering valuable insights for the control strategy and practical application of battery energy storage systems in grid frequency regulation.
Modeling of Power System Frequency Control
Traditional Frequency Control Process
Grid frequency regulation is typically divided into primary frequency control and secondary frequency control. When the active power balance of the grid is disturbed by load changes, the primary frequency control of the generator governor is activated. It adjusts the turbine valve opening based on the frequency deviation to modify the active power output of the unit. Primary frequency control requires a fast response to frequency disturbances, typically on the order of seconds. However, due to the inherent characteristics of generators, it is difficult to achieve zero-error regulation, necessitating secondary frequency control to further correct the power signal. The block diagram of the traditional unit frequency control is well established and includes the governor model, turbine model, and generator-load model.
Equivalent Model for Battery Energy Storage Systems
In the traditional frequency regulation process, the power output change of a generator is relatively slow. With the integration of battery energy storage systems, the active power can be controlled rapidly, enabling fast response. The typical frequency control model includes several modules: the governor, the turbine, and the generator-load. Their transfer functions are well-defined. We focus here on the equivalent model of the battery energy storage systems. Following common practice, we model the battery energy storage systems using a first-order inertia link:
$$
G_B(s) = \frac{1}{1 + s T_B}
$$
where \(T_B\) is the time response constant of the battery energy storage systems output. The state of charge (SOC) dynamics are given by:
$$
\frac{dS(t)}{dt} = -\frac{P_B(t)}{E_B}, \quad S(0) = S_0
$$
Here, \(S(t)\) denotes the ratio of remaining energy to rated capacity of the battery energy storage systems, \(S_0\) is the initial SOC, \(E_B\) is the rated energy capacity, and \(P_B(t)\) is the discharge (or charge) power of the battery energy storage systems. Combining these, the overall frequency control model with battery energy storage systems is shown in the following diagram.
Two-Layer Distributed Frequency Regulation Control Strategy
Control Framework
Considering the frequency regulation requirements, the fast response advantage of battery energy storage systems, and the coordination among multiple battery energy storage systems, we propose a two-layer distributed frequency regulation control strategy. The upper layer (area dispatch layer) is responsible for the coordinated allocation of the regulation signal between conventional units and battery energy storage systems. The lower layer (battery energy storage system control layer) handles the communication and control among multiple distributed battery energy storage systems.
Upper Layer: Area Dispatch Control Strategy
The role of the area dispatch layer is to partition the area control error (ACE) signal into different regulation zones and to determine the reference power output for each zone using a coordinated control strategy. The structure is illustrated conceptually.
Dead Zone and Emergency Zone Control: When the ACE signal falls within the dead zone of the units, the external disturbance is small. The control objective is to restore the SOC of the battery energy storage systems to the rated state as quickly as possible. When the ACE signal falls into the emergency zone, the reference power for battery energy storage systems is set as:
$$
\Delta P_{B,ref} = \text{sgn}(\Delta P_{AGC}) \cdot \min\left( |\Delta P_{AGC}|, \Delta P_{B,max}^{ch/dis} \right)
$$
where \(\Delta P_{AGC}\) is the total frequency regulation control demand from the grid, and \(\Delta P_{B,max}^{ch}\) and \(\Delta P_{B,max}^{dis}\) are the maximum charging and discharging powers of the battery energy storage systems (positive for discharge, negative for charge).
Normal Regulation Zone Control: When the ACE signal lies in the normal regulation zone, the control logic is as follows: if the SOC of the battery energy storage systems is within the ideal range, the battery energy storage systems respond to the regulation signal with priority. If the SOC is outside the ideal range and the current power demand helps restore the SOC to the ideal state, the battery energy storage systems participate in regulation at maximum charge/discharge power. Otherwise, to protect the battery energy storage systems, they do not participate in this regulation event. The decision rules are:
$$
\begin{cases}
\Delta P_{B,ref} = \Delta P_{AGC}, & \text{if } SOC_0 \le S \le SOC_1 \\
\Delta P_{B,ref} = \text{sgn}(\Delta P_{AGC}) \cdot P_{B,max}^{ch/dis}, & \text{if } (S < SOC_0 \text{ and } \Delta P_{AGC} < 0) \text{ or } (S > SOC_1 \text{ and } \Delta P_{AGC} > 0) \\
\Delta P_{B,ref} = 0, & \text{otherwise}
\end{cases}
$$
where \(SOC_0\) and \(SOC_1\) are the lower and upper thresholds defining the ideal SOC range for the battery energy storage systems.
Lower Layer: Distributed Battery Energy Storage System Control Strategy
After the area dispatch layer determines whether battery energy storage systems should participate and the reference power, the next step is coordinated control among the distributed battery energy storage systems. We propose a control approach based on a distributed consensus algorithm, aiming to reduce the overall operation cost while fulfilling the frequency regulation task. The cost function for the \(i\)-th battery energy storage system in frequency regulation is defined as:
$$
C_i(P_{Bi,k}) = a_i P_{Bi,k}^2 + b_i (S_{bi,k} – S_{bi}^*)^2
$$
where \(a_i\) and \(b_i\) are weighting factors for the power output and SOC deviation, respectively; \(P_{Bi,k}\) is the regulation power output of the \(i\)-th battery energy storage system at time step \(k\); \(E_{BN,i}\) is the rated energy capacity; \(S_{bi,k}\) is the SOC at time \(k\); and \(S_{bi}^*\) is the optimal SOC for the \(i\)-th battery energy storage system.
To incorporate battery degradation, we introduce the depth of discharge (DOD) indicator. The battery life loss associated with DOD is modeled as:
$$
L_{DOD,i} = \delta \cdot \frac{E_{0,i}}{E_{B,N,i}} \cdot (\lambda_1 + \lambda_2 \cdot DOD)
$$
where \(E_{0,i}\) is the initial energy capacity of the \(i\)-th battery energy storage system, \(\delta\) is the cycle life of the battery, and \(\lambda_1, \lambda_2\) are life calculation coefficients. The energy output related loss is then given by:
$$
C_{loss,i} = C_{0,i} \cdot \frac{E_{Bi,k}}{E_{Bi,N}}
$$
with \(C_{0,i}\) being the initial investment cost of the \(i\)-th battery energy storage system. The total comprehensive cost for the battery energy storage system to participate in frequency regulation is:
$$
C_{total,i} = C_i(P_{Bi,k}) + C_{loss,i}
$$
The problem of distributed battery energy storage systems participating in grid frequency regulation is thus transformed into minimizing the sum of total costs subject to the power balance constraint. We apply the Lagrange multiplier method to solve for the optimal solution. The Lagrangian is:
$$
\mathcal{L} = \sum_{i=1}^n C_{total,i} + \lambda \left( \Delta P_{AGC} – \sum_{i=1}^n P_{Bi,k} \right)
$$
The optimality condition requires:
$$
\frac{\partial C_{total,i}}{\partial P_{Bi,k}} = \lambda, \quad \forall i
$$
Given the complexity of battery energy storage systems, we treat the partial derivative of the cost function with respect to power as the consensus variable. Based on the distributed consensus algorithm theory, we design an iterative update scheme for this variable:
$$
\lambda_i(k+1) = \lambda_i(k) + \epsilon \sum_{j \in \mathcal{N}_i} a_{ij} (\lambda_j(k) – \lambda_i(k))
$$
where \(\lambda_i\) is the incremental cost for the \(i\)-th battery energy storage system, \(\epsilon\) is the step size, \(\mathcal{N}_i\) is the set of neighbors of node \(i\), and \(a_{ij}\) are the adjacency weights. This iterative process ensures that all battery energy storage systems converge to the same incremental cost, thereby achieving economic dispatch while maintaining the power output balance.
Simulink Simulation and Analysis
We built the simulation model of the proposed two-layer distributed control strategy for battery energy storage systems participating in grid frequency regulation using Simulink. The parameters for four distributed battery energy storage systems are listed in the table below.
| BESS Index | Power Rating (MW) | Rated Capacity (MWh) | Charging/Discharging Efficiency | Time Constant | Power Cost Coefficient \(a_i\) | SOC Deviation Cost Coefficient \(b_i\) |
|---|---|---|---|---|---|---|
| 1 | ±15 | 3.5 | 0.90 / 0.90 | 0.01 | 0.90 | 0.65 |
| 2 | ±14 | 3.0 | 0.95 / 0.90 | 0.01 | 0.90 | 0.73 |
| 3 | ±13 | 2.5 | 0.90 / 0.85 | 0.01 | 0.90 | 0.86 |
| 4 | ±12 | 2.2 | 0.90 / 0.90 | 0.01 | 0.85 | 1.35 |
The initial SOC of each battery energy storage system is set to 0.6, and the rated SOC is also 0.6. The initial investment cost is 3000 RMB/(kWh). The convergence tolerance is set to 0.01. We simulate a step load disturbance of 0.2 pu applied at t = 5 s. We compare the proposed control strategy with a conventional grid frequency control model without battery energy storage systems.
The simulation results are analyzed in terms of frequency deviation, power output, and SOC evolution. The frequency deviation curves clearly show that the system with battery energy storage systems achieves faster response, smaller overshoot, and shorter settling time compared to the conventional system without battery energy storage systems. The power output plot illustrates that the battery energy storage systems provide immediate active power support, whereas the conventional units ramp up slowly. The SOC trajectories of the four battery energy storage systems demonstrate that the proposed distributed coordination strategy prevents any single battery energy storage system from reaching extreme SOC levels, ensuring consistent participation throughout the regulation event.
Quantitative performance metrics are summarized in the table below.
| Performance Metric | Conventional Control | With BESS (Proposed) |
|---|---|---|
| Maximum Frequency Deviation (Hz) | 0.45 | 0.28 |
| Settling Time (s) | 12.5 | 6.8 |
| Steady-State Error (Hz) | 0.02 | 0.01 |
| Peak Power from Conventional Units (pu) | 0.35 | 0.20 |
Further analysis of the SOC evolution for the four battery energy storage systems is given below. The SOC values remain within the safe operating range (0.2 to 0.9) throughout the simulation, and the consensus algorithm ensures that the incremental costs converge, leading to an economically optimal distribution of power among the battery energy storage systems.
| Time (s) | BESS 1 SOC | BESS 2 SOC | BESS 3 SOC | BESS 4 SOC |
|---|---|---|---|---|
| 0 | 0.60 | 0.60 | 0.60 | 0.60 |
| 5 | 0.58 | 0.59 | 0.59 | 0.58 |
| 10 | 0.55 | 0.57 | 0.58 | 0.56 |
| 15 | 0.56 | 0.58 | 0.59 | 0.57 |
| 20 | 0.59 | 0.60 | 0.60 | 0.59 |
Conclusion
In this work, we addressed the problem of how distributed battery energy storage systems can effectively participate in grid frequency regulation by proposing a two-layer distributed control strategy. The upper layer (area dispatch layer) allocates the regulation signal between conventional units and battery energy storage systems based on the ACE signal zone and battery SOC conditions. The lower layer (battery energy storage system layer) employs a distributed consensus algorithm to coordinate the power output among multiple battery energy storage systems, minimizing the total operation cost while considering battery degradation. Simulation results in Simulink validate that the proposed control strategy significantly improves the frequency regulation performance: it reduces maximum frequency deviation by 38%, shortens settling time by 46%, and decreases the peak power burden on conventional units by 43%. Moreover, the SOC of all battery energy storage systems remains within safe limits, and the consensus algorithm ensures economic fairness. This study demonstrates that battery energy storage systems, when properly controlled, serve as a powerful supplement to traditional frequency regulation, and the proposed hierarchical coordination approach provides a practical and efficient solution for integrating battery energy storage systems into future low-carbon power grids.