With the accelerating transition of the global energy structure towards low carbon, renewable energy sources connected via power electronic devices are continuously increasing their penetration in power systems. The inherent volatility and intermittency of renewable energy output exacerbate the mismatch between supply and load. Meanwhile, the gradual replacement of synchronous generators by renewable energy weakens system inertia and damping, threatening the security and stability of system frequency across multiple timescales. This paper focuses on the transient frequency response process from the occurrence of a frequency event to the quasi-steady state, which includes inertial response and primary frequency regulation.
Due to the delayed response of synchronous generators, relying solely on them for high-quality transient frequency regulation becomes increasingly difficult after large-scale integration of renewable energy. There is an urgent need to explore new frequency regulation resources and approaches. The distributed battery energy storage system (BESS) in the grid, with its advantages of precise controllability, fast response, and flexible regulation, can support various auxiliary services such as frequency regulation and voltage regulation for systems with high renewable penetration, and has attracted widespread attention in recent years.
Conventional transient frequency regulation strategies for the battery energy storage system are generally based on the frequency regulation characteristics of synchronous generators, including virtual inertia control, damping control, and synthetic inertia control (SIC). While these strategies are autonomous and highly reliable, they fail to consider the influence on other power sources in the system and the actual frequency regulation demand, making it difficult to fully exploit the active support capability of the battery energy storage system under different operating conditions.
In contrast, with its fast power response capability, the battery energy storage system can also improve the frequency regulation characteristics of other power sources. In scenarios where synchronous generators and battery energy storage system jointly participate in transient frequency regulation, the battery energy storage system is mainly used to compensate for the response delay of synchronous generators. However, existing studies often integrate the battery energy storage system with specific source types (e.g., only wind turbines or only thermal units), leading to highly model-dependent and customized strategies that lack universality for complex systems with multiple heterogeneous sources.
To address these limitations, this paper proposes a novel transient frequency regulation strategy based on frequency regulation characteristic compensation. First, the energy dynamic model of the battery energy storage system is derived in the transient timescale, and a linearized frequency regulation transfer function is adopted to uniformly describe the frequency regulation characteristics of multiple types of power sources. A system transient frequency response model incorporating multiple battery energy storage systems is established to accurately reflect the contribution of the battery energy storage system during transients. Then, a universal compensation strategy for the delay in frequency regulation characteristics is proposed. With the goal of maximizing the utilization of battery energy storage system reserve energy, the power distribution coefficient and initial inertia coefficient in the strategy are configured to enhance the active frequency support capability of the battery energy storage system under different operating conditions. Finally, the effectiveness and superiority of the proposed strategy are verified through theoretical analysis and simulation on a modified IEEE 39-bus system.
We first present the model of the battery energy storage system for transient frequency regulation. The grid-connected model of the battery energy storage system unit includes a circuit part and a control part. The circuit consists of a battery, a DC bus capacitor, a bidirectional converter, an output RL filter, and a step-up transformer. The battery can be equivalently represented as a DC voltage source with open-circuit voltage ui in series with internal resistance ri. Neglecting temperature variations during transient frequency regulation, the voltage is a function of the state of charge (SOC) si:
$$u_i = f(s_i)$$
The SOC dynamics are described by the coulomb counting method:
$$s_i(t) = s_i^{\text{ini}} – \frac{1}{q_i^{\text{nom}}} \int_{t_0}^{t} i_i(\tau) d\tau$$
where siini is the initial SOC at time t0, qinom is the rated charge capacity, and ii is the battery current. Assuming the charging and discharging efficiency is close to 100% for simplicity, the output power Pi of the battery energy storage system unit approximately equals the battery power:
$$P_i \approx u_i i_i S_i^{\text{nom}}$$
where Sinom is the rated capacity of the converter. Combining the above, the energy dynamic model of the battery energy storage system unit i in the transient time scale is derived as:
$$\dot{E}_i = -\Delta P_i^{\text{ref}}$$
where Ei is defined as the energy of the battery energy storage system unit, calculated from the integral of voltage with respect to charge:
$$E_i = \frac{q_i^{\text{nom}}}{S_i^{\text{nom}}} \int f(s_i) ds_i$$
For simplicity, if the SOC operating point is far from the boundaries, the function f(·) can be approximated linearly:
$$f(s_i) = k_i^{\text{su}} (s_i – s_i^{\text{nom}}) + u_i^{\text{nom}}$$
where kisu is the SOC-voltage slope, and sinom, uinom are nominal values. The SOC operating constraints are divided into normal operation (within [siopt,min, siopt,max]) and transient frequency regulation (within [simin, simax]), which are mapped to energy constraints [Eiopt,min, Eiopt,max] and [Eimin, Eimax].
Next, we establish the system transient frequency response model with multiple battery energy storage systems. The power sources in a modern power system include synchronous generators and converter-interfaced non-synchronous sources (wind turbines, photovoltaic). Their frequency regulation processes are represented by linearized transfer functions. For synchronous generators, the speed governor and reheat turbine model gives:
$$\Delta P_g(s) = -\rho_{\text{sg}} \cdot D_{\text{sg}} \cdot \Delta \omega_{\text{sys}}(s) \cdot G_{\text{sg}}(s)$$
where ρsg is the power gain coefficient, Dsg is the damping coefficient, and Gsg(s) is the combined governor-turbine transfer function with time constants τg, τch, τrh, τco. For wind turbines with SIC, the output power Pwtg consists of deloaded power and SIC power:
$$\Delta P_{\text{wtg}}(s) = -\rho_{\text{wtg}} \cdot \left( 2H_{\text{wtg}}^{\text{sic}} s + D_{\text{wtg}}^{\text{sic}} \right) \cdot \Delta \omega_{\text{sys}}(s) \cdot \frac{B_{\text{wtg}}s + A_{\text{wtg}}}{B_{\text{wtg}}s + A_{\text{wtg}} + C_{\text{wtg}}}$$
where Hwtgsic, Dwtgsic are the virtual inertia and damping coefficients, and A, B, C are linearization parameters derived from the rotor dynamics and deloading factor. For photovoltaic systems with SIC:
$$\Delta P_{\text{pv}}(s) = -\rho_{\text{pv}} \cdot D_{\text{pv}}^{\text{sic}} \cdot \Delta \omega_{\text{sys}}(s)$$
where Dpvsic is the damping coefficient. The overall system frequency dynamics satisfy the swing equation:
$$\sum_j \rho_j \Delta P_j(s) – \Delta P_d(s) = (2H_{\text{sg}} s + D) \Delta \omega_{\text{sys}}(s) + \sum_{i \in \mathcal{B}} \rho_i \Delta P_i(s)$$
where Hsg is the system inertia from synchronous generators, D is the load damping, ΔPd is the disturbance power, and B is the set of battery energy storage system units. To unify the representation, we define the frequency regulation transfer function for each source type j (j = sg, wtg, pv) and for battery energy storage system unit i as:
$$F_j(s) = -\Delta P_j(s) / \Delta \omega_{\text{sys}}(s), \quad F_i(s) = -\Delta P_i(s) / \Delta \omega_{\text{sys}}(s)$$
The system transfer function becomes:
$$F_{\text{sys}}(s) = \sum_{j \in \hat{\mathcal{B}}} \rho_j F_j(s) + \sum_{i \in \mathcal{B}} \rho_i F_i(s) – D$$
where B̂ = {sg, wtg, pv}.
We now propose the transient frequency regulation strategy based on characteristic compensation. The key idea is to make the battery energy storage system compensate the delays of other sources rather than mimicking synchronous generators. The desired system transient frequency response should be overdamped, corresponding to a delay-free inertial-damping transfer function:
$$F_{\text{sys}}^!(s) = -(2H_{\text{sys}} s + D_{\text{sys}})$$
where Hsys and Dsys are the target system inertia and damping. Equating the actual Fsys(s) with the desired form yields the total compensation required from the battery energy storage system. By setting the quasi-steady-state damping contribution of the battery energy storage system to zero (to avoid persistent energy drain), the total expected compensation from all battery energy storage system units is:
$$\sum_{i \in \mathcal{B}} \rho_i F_i(s) = \sum_{j \in \hat{\mathcal{B}}} \rho_j \left[ 2H_j^{\text{ini}} s + D_j^{\text{qs}} – F_j(s) \right] + \sum_{i \in \mathcal{B}} \rho_i \cdot 2H_i^{\text{ini}} s$$
where Hjini = lims→∞ 0.5 Fj(s)/s and Djqs = Fj(0). This total is then distributed among the battery energy storage system units via power distribution coefficients γi (∑γi = 1):
$$F_i(s) = \frac{\gamma_i}{\rho_i} \left[ \sum_{j \in \hat{\mathcal{B}}} \rho_j \left( 2H_j^{\text{ini}} s + D_j^{\text{qs}} – F_j(s) \right) \right] + 2H_i^{\text{ini}} s$$
The first part compensates the characteristic delays of other sources, and the second part provides additional inertia support.
To configure the parameters, we define the reserve energy Eires for each battery energy storage system unit and the critical energy Ebesscri required to achieve full compensation. The critical energy is estimated from the energy deviation due to the compensation term:
$$\Delta E_{\text{bess}}^{\text{com}}(t) = \int_0^t \mathcal{L}^{-1}\left[ \sum_{j \in \hat{\mathcal{B}}} \rho_j \left( D_j^{\text{qs}} – F_j(s) \right) \cdot \Delta \omega_{\text{sys}}(s) \right] d\tau$$
Applying the final value theorem, the quasi-steady-state energy deviation is:
$$\Delta E_{\text{bess}}^{\text{com,qs}} = \sum_{j \in \hat{\mathcal{B}}} \rho_j \tau_j \cdot \Delta \omega_{\text{sys}}^{\text{qs}} \cdot D_{\text{sys}}$$
where τj = lims→0 (Fj(s)/s + 2Hjini) is the equivalent time constant of source j. For a known disturbance ΔPd, we estimate Ebesscri = max(|ΔEbesscom|, |ΔEbesscom,qs|). The power distribution coefficient γi is set as the proportion of reserve energy of unit i to the maximum of total reserve and critical energy:
$$\gamma_i = \frac{\rho_i E_i^{\text{res}}}{\max(E_{\text{bess}}^{\text{res}}, E_{\text{bess}}^{\text{cri}})}$$
Then the remaining energy Eirem after compensation is used for additional inertia, with the initial inertia coefficient Hiini configured as:
$$H_i^{\text{ini}} = \min\left(0.5 \frac{E_i^{\text{rem}}}{\Delta \omega_{\text{sys}}^{\text{max}}}, H_i^{\text{max}}\right)$$
where Δωsysmax is the frequency deviation threshold for system protection, and Himax is the upper bound for stability.
| Parameter | Value |
|---|---|
| Rated capacity Sjnom (MVA) | 1000 |
| Inertia constant Hj (s) | 4 |
| Damping coefficient Dj | 20 |
| Time constants (s): τg, τch, τrh, τco | 0.075, 0.3, 10.0, 0.6 |
| Parameter | Wind 1 | Wind 2 | PV1 | PV2 |
|---|---|---|---|---|
| Rated capacity (MVA) | 700 | 630 | 700 | 630 |
| Inertia constant H (s) | 2.5 | 2.5 | – | – |
| Virtual inertia Hsic (s) | 20 | 20 | 0 | 0 |
| Damping Dsic | 10 | 10 | 10 | 10 |
| Deloading factor k | 0.9 | 0.9 | 0.9 | 0.9 |
| Parameter | B1 | B2 | B3 |
|---|---|---|---|
| Rated capacity Snom (MVA) | 320 | 400 | 480 |
| Rated charge qnom (MAs) | 18 | 15 | 12 |
| SOC range [min, max] | [0.1, 0.9] | [0.1, 0.9] | [0.1, 0.9] |
| Initial SOC (pu) | 0.5 | 0.5 | 0.5 |
| Open-circuit voltage unom (V) | 500 | 500 | 500 |
| SOC-voltage slope ksu | 0.236 | 0.236 | 0.236 |
| Reserve energy Eres (s) | 8.438 | 5.625 | 3.750 |
| Max inertia Hmax (s) | 24.58 | 19.66 | 16.38 |
The reference power generation loop of each battery energy storage system unit includes an optimal state tracking term for normal operation and a transient frequency regulation term. The optimal tracking power adjusts the energy back to the normal range when it deviates, using a spring-like force function:
$$\Delta P_i^{\text{ost}} = \begin{cases} k_i^{\text{ost}}(E_i – E_i^{\text{opt,max}}), & E_i > E_i^{\text{opt,max}} \\ 0, & E_i \in [E_i^{\text{opt,min}}, E_i^{\text{opt,max}}] \\ k_i^{\text{ost}}(E_i – E_i^{\text{opt,min}}), & E_i < E_i^{\text{opt,min}} \end{cases}$$
The transient frequency regulation term is given by the designed Fi(s). The start signal e0 is a dead-zone function of frequency deviation:
$$e_0 = u(|\Delta \omega_{\text{sys}}| – \Delta \omega_{\text{sys}}^{\text{db}})$$
The total reference power is the sum of the optimal tracking power and the transient frequency regulation power, with the latter gated by e0:
$$\Delta P_i^{\text{ref}} = \Delta P_i^{\text{ost}} + e_0 \cdot \Delta P_i^{\text{tfr}}$$
where ΔPitfr is obtained from the inverse Laplace transform of Fi(s)Δωsys(s).
We theoretically analyze the control performance. With the proposed strategy, if the reserve energy is sufficient for full compensation (i.e., Ebessres ≥ Ebesscri), the system transfer function becomes exactly the desired delay-free form:
$$F_{\text{sys}}(s) = -(2H_{\text{sys}} s + D_{\text{sys}})$$
The resulting frequency response to a step disturbance ΔPd/s is:
$$\Delta \omega_{\text{sys}}(t) = -\frac{\Delta P_d}{D_{\text{sys}}} \left( 1 – e^{-(D_{\text{sys}} / (2H_{\text{sys}})) t} \right)$$
This is an overdamped response, eliminating oscillations and significantly reducing frequency nadir. If the reserve energy is insufficient (Ebessres < Ebesscri), the compensation is partial, and the frequency response remains underdamped but still improved compared to conventional strategies.
We also analyze the energy utilization of the battery energy storage system. The energy deviation of unit i during the transient is:
$$\Delta E_i(t) = \gamma_i \cdot \Delta E_{\text{bess}}^{\text{com}}(t) + \rho_i \cdot 2H_i^{\text{ini}} \cdot \Delta \omega_{\text{sys}}(t)$$
By construction, the total energy consumed by each unit never exceeds its reserve energy, ensuring safe operation. When the disturbance is small, the remaining energy after compensation can be fully used for inertial support, achieving high energy utilization. When the disturbance is large, all reserve energy is dedicated to compensation, also achieving near full utilization.
To validate the proposed strategy, we conduct simulations on a modified IEEE 39-bus system with three battery energy storage system units (B1-B3) connected at different nodes. We compare five strategies: No Frequency Regulation (NFR), Synthetic Inertia Control (SIC), Adaptive SIC (ASIC), Constant Frequency Control (CFC), and the proposed Frequency Regulation Characteristic Compensation (FRCC). Two scenarios are considered: Scenario 1 (only synchronous generators G7-G10 and BESS) and Scenario 2 (wind turbines W1-W2, PV P1-P2, and BESS). Two disturbance levels are tested: ΔPd = 600 MW (10% load increase) and 1200 MW (20% load increase).
| Scenario | Disturbance | NFR | SIC | ASIC | CFC | FRCC |
|---|---|---|---|---|---|---|
| 1 (Gen only) | 600 MW | -0.505 | -0.342 | -0.351 | -0.337 | -0.151 |
| 1 (Gen only) | 1200 MW | -1.048 | -0.694 | -0.734 | -0.683 | -0.417 |
| 2 (Wind+PV) | 600 MW | -0.401 | -0.318 | -0.323 | -0.278 | -0.199 |
| 2 (Wind+PV) | 1200 MW | -0.804 | -0.627 | -0.648 | -0.555 | -0.439 |
In Scenario 1 with 600 MW disturbance, the proposed FRCC strategy achieves an overdamped response with the frequency nadir very close to the quasi-steady-state value (-0.151 Hz), far better than other strategies. The energy utilization of B2 in FRCC is 75.4%, which is higher than SIC/ASIC (about 30%) and lower than CFC (100% but causing secondary frequency drop). For the 1200 MW disturbance, FRCC uses all reserve energy for compensation, achieving 95.8% utilization and still maintaining frequency above -0.5 Hz threshold, while others fall below. In Scenario 2, the presence of wind turbines with smaller equivalent time constants reduces the required compensation energy, and FRCC still outperforms others, achieving -0.199 Hz nadir for 600 MW disturbance (overdamped) and -0.439 Hz for 1200 MW disturbance.
These results confirm that the proposed frequency regulation characteristic compensation strategy effectively adapts to different disturbance magnitudes and system compositions, maximizing the use of battery energy storage system reserve energy to improve the frequency nadir. The strategy is universal and does not rely on specific source models.
In conclusion, this paper proposes a novel transient frequency regulation strategy for the battery energy storage system based on compensating the frequency regulation characteristics of other power sources. The main contributions are: (1) A unified transient frequency response model with multiple battery energy storage systems is established using linearized transfer functions. (2) The compensation strategy parameterized by power distribution coefficients and initial inertia coefficients is designed to achieve an overdamped frequency response when energy is sufficient, or to fully utilize the reserve energy otherwise. (3) Theoretical analysis proves that the energy consumption of each battery energy storage system unit never exceeds its reserve, ensuring operational safety. (4) Simulation results on a modified IEEE 39-bus system demonstrate that the proposed strategy outperforms conventional SIC, adaptive SIC, and constant frequency control in terms of both frequency quality and energy utilization, and it remains effective under varying system conditions and renewable penetration levels.