In modern power systems, the integration of renewable energy sources has introduced significant challenges to frequency stability due to their intermittent and variable nature. As a pivotal solution, battery energy storage systems have emerged as a key technology for providing fast and flexible frequency regulation services. Their unique characteristics, such as high ramp rates, precise power control, and bidirectional energy flow, make them ideal for supporting grid frequency within tight tolerances. However, the effective utilization of multiple distributed battery energy storage systems in a coordinated manner remains an underexplored area. This study addresses this gap by proposing an improved control strategy and algorithm optimization that enhances the coordination and economic efficiency of distributed battery energy storage systems participating in grid frequency regulation. The approach constructs an accurate load frequency control model and implements a two-layer distributed control framework, which not only improves the frequency response speed and efficiency but also optimizes the operational cost and battery life degradation, thereby providing a cost-effective and sustainable solution for power system frequency regulation.
Battery energy storage systems have been widely studied for their application in primary and secondary frequency regulation. Existing research focuses on strategies such as using electric vehicles for frequency regulation, robust control based on sparse communication networks, and two-layer frequency regulation control. While these studies demonstrate the feasibility and benefits of battery energy storage systems, they often treat the entire energy storage fleet as a single aggregated unit, neglecting the practical need for coordinated operation among geographically dispersed distributed battery energy storage systems. This oversight can lead to suboptimal power sharing, accelerated battery degradation, and reduced economic returns. To overcome these limitations, we propose a novel control framework that leverages graph theory and multi-agent consensus algorithms to achieve optimal power allocation among distributed battery energy storage systems while considering their state of charge and operating costs.
Load Frequency Control Model with Battery Energy Storage Systems
The core of our approach is a load frequency control model that incorporates the dynamic behavior of battery energy storage systems. In a conventional power system, secondary frequency control is responsible for restoring the system frequency to its nominal value after a disturbance. Traditional generators have limited ramp rates, which delay frequency recovery. By integrating battery energy storage systems, we can provide rapid power injection or absorption to counteract frequency deviations. The transfer function of a battery energy storage system can be approximated by a first-order lag:
$$
G_{B}(s) = \frac{1}{1 + s T_{B}}
$$
where \(T_{B}\) is the time constant representing the response delay of the battery energy storage system. This model captures the inherent latency in power electronics and battery management systems. To manage both conventional generators and multiple distributed battery energy storage systems, we design a two-layer distributed control architecture.
The upper layer, known as the regional dispatch layer, aggregates the total frequency regulation demand based on the Area Control Error (ACE) signal. It partitions the regulation range into different zones: emergency regulation zone, normal regulation zone, and dead zone. In each zone, specific control objectives are assigned. For instance, in the emergency zone, fast-acting resources including battery energy storage systems are used to quickly reduce ACE. In the normal zone, the goal is to eliminate ACE while gradually restoring the state of charge of battery energy storage systems without causing frequency deterioration. In the dead zone, battery energy storage systems perform self-recovery of their state of charge without triggering further frequency deviations. This layered approach ensures that the limited energy capacity of battery energy storage systems is used efficiently and their longevity is preserved.
The lower layer implements a consensus-based distributed control among multiple battery energy storage systems. Using graph theory, each battery energy storage system communicates with its neighbors to iteratively update its power output reference. The consensus algorithm ensures that the total power command from the upper layer is distributed among the battery energy storage systems in a way that minimizes the overall operational cost, which includes the cost of power deviation, state of charge deviation, and battery degradation. The update rule for each battery energy storage system \(i\) can be expressed as:
$$
P_{B,i}^{(k+1)} = \sum_{j \in N_i} w_{ij} P_{B,j}^{(k)} + \epsilon_i \cdot (P_{B,ref} – \sum_{j=1}^{n} P_{B,j}^{(k)})
$$
where \(N_i\) is the set of neighbors of node \(i\), \(w_{ij}\) are the consensus weights, \(\epsilon_i\) is a convergence parameter, and \(P_{B,ref}\) is the total reference power from the upper layer. This approach ensures that the sum of outputs converges to the required value while achieving economic optimality.
Regional Dispatch Layer Frequency Regulation Strategy
The regional dispatch layer determines the initial power allocation between conventional generators and the aggregated battery energy storage system. The optimization problem is formulated to minimize the total regulation cost over each control interval, subject to constraints such as available reserve capacity, ramp rate limits, state of charge limits, and charging/discharging efficiency. The objective function is:
$$
\min \quad C_{total} = C_{gen} + C_{B} + C_{deg}
$$
where \(C_{gen}\) is the cost of conventional generation, \(C_{B}\) is the operating cost of the battery energy storage system (including energy cost and SOC deviation penalty), and \(C_{deg}\) represents the battery degradation cost. The degradation model accounts for the cycle life reduction caused by depth of discharge and number of cycles. A typical life model can be expressed as:
$$
L_{loss} = \alpha \cdot (DOD)^{\beta} \cdot (N_{cycle})^{\gamma}
$$
where \(DOD\) is depth of discharge, \(N_{cycle}\) is the number of cycles, and \(\alpha, \beta, \gamma\) are empirical parameters. The degradation cost is then translated into a per-unit power cost. By incorporating this into the optimization, the battery energy storage system’s participation in frequency regulation becomes economically sustainable.
The control structure of the regional dispatch layer is summarized in Table 1, showing the key parameters and their roles.
| Parameter | Symbol | Value | Description |
|---|---|---|---|
| System frequency | f | 50 Hz | Nominal frequency |
| Speed droop coefficient | R | 0.05 | Governor droop |
| Frequency bias factor | B | 21 | Frequency bias for ACE |
| Governor time constant | t_g | 0.08 s | Turbine governor time constant |
| Steam turbine time constant | t_ch | 0.3 s | Reheat time constant |
| Generator inertia constant | M | 10 s | Swing equation inertia |
| Load damping coefficient | D | 1 | Frequency-dependent load damping |
| Battery response time constant | T_B | 0.1 s | First-order lag for BESS |
| Weight coefficient 1 | τ1 | 0.02 | Cost weight for SOC deviation |
| Weight coefficient 2 | τ2 | 1.55 | Cost weight for power deviation |
| AGC sampling interval | Δt | 4 s | Sampling time for AGC |
| Convergence tolerance | ε | 0.01 | Consensus convergence threshold |
| Initial SOC of BESS | SOC_0 | 50% | Optimal initial state of charge |
Simulation and Discussion
To validate the proposed control strategy, a simulation model of a regional power grid with multiple distributed battery energy storage systems was built in MATLAB/Simulink. The system base power is 4000 MVA, with a conventional thermal generator rated at 1000 MW. Five battery energy storage units with different capacities (ranging from 50 MWh to 200 MWh) are connected at various nodes. A load disturbance of 0.2 p.u. is applied at t = 5 seconds. We compare three scenarios: (1) no battery energy storage system (only conventional generator), (2) fixed proportion allocation among battery energy storage systems, and (3) the proposed two-layer distributed control with consensus optimization.
The simulation results are presented in Tables 2 and 3, which compare key performance metrics.
| Control Scenario | Maximum Frequency Deviation (Hz) | Frequency Nadir Time (s) | Settling Time (s) | Steady-State Error (mHz) |
|---|---|---|---|---|
| No BESS | 0.85 | 3.2 | 18.5 | 5.0 |
| Fixed Proportion BESS | 0.42 | 2.1 | 8.2 | 1.2 |
| Proposed Two-Layer Control | 0.28 | 1.5 | 5.6 | 0.8 |
From Table 2, it is evident that the inclusion of battery energy storage systems significantly improves frequency response. The proposed two-layer control achieves the smallest maximum deviation (0.28 Hz) and the fastest settling time (5.6 s), outperforming both the scenario without battery energy storage systems and the fixed proportion strategy. This improvement is due to the coordinated and optimized power sharing among distributed battery energy storage systems, which avoids overloading any single unit and maintains adequate headroom for further disturbances.
| Scenario | Final SOC of Unit 1 (50 MWh) | Final SOC of Unit 5 (200 MWh) | Total Degradation Cost ($) | Operational Cost ($) |
|---|---|---|---|---|
| Fixed Proportion | 32% | 45% | 1200 | 3500 |
| Proposed Control | 42% | 47% | 680 | 2800 |
Table 3 shows the state of charge of the smallest and largest battery energy storage systems at the end of the simulation, along with the estimated total degradation and operational costs. In the fixed proportion allocation, the small battery energy storage system (50 MWh) discharges rapidly, reaching a final SOC of 32%, which is below the safety threshold and may cause premature wear. In contrast, the proposed control maintains a balanced SOC across all units, with the small unit ending at 42%, still within safe limits. Consequently, the total degradation cost is reduced from $1200 to $680, and the overall operational cost (including energy and penalty) decreases by 20%. These results confirm that the proposed strategy effectively extends battery life while improving economic efficiency.
Furthermore, the dynamic behavior of the state of charge of each battery energy storage system under the proposed control was analyzed. Unlike the fixed proportion approach where the smallest battery energy storage system experienced a rapid SOC decline and had to be disconnected, our method allowed all battery energy storage systems to maintain their SOC above 35% throughout the operation. This is achieved by the consensus-based algorithm that dynamically adjusts power outputs based on the SOC levels, giving higher priority to units with higher SOC to supply power, and reducing the burden on units with lower SOC. Additionally, the upper layer ensures that during normal regulation, the battery energy storage systems are allowed to recover their SOC when the ACE is within the dead zone, further preventing deep discharges.
The scalability of the proposed control was also tested by increasing the number of distributed battery energy storage systems to 20. The consensus algorithm converged within 20 iterations (80 seconds), and the overall performance remained consistent with the 5-unit case. This demonstrates that the algorithm is suitable for large-scale deployment in real power systems with hundreds of distributed battery energy storage systems.
Conclusion
This paper presents a comprehensive control strategy for integrating distributed battery energy storage systems into power system frequency regulation. By constructing a load frequency control model and implementing a two-layer distributed framework, we achieve both fast response and economic optimization. The regional dispatch layer optimally allocates power between conventional generation and aggregated battery energy storage systems, while the lower layer uses consensus-based coordination to distribute power among individual battery energy storage systems, minimizing degradation and operating costs. Simulation results confirm that the proposed method outperforms conventional fixed proportion strategies in reducing frequency deviation, improving settling time, and prolonging battery life. The incorporation of battery energy storage systems into the frequency regulation market thus becomes more feasible and profitable. Future work will focus on real-time implementation challenges such as communication delays and cybersecurity, as well as the integration of heterogeneous energy storage technologies like flow batteries and supercapacitors.