In modern power systems with high penetration of renewable energy, the displacement of synchronous generators reduces system inertia and damping, threatening frequency security. Distributed battery energy storage systems (BESSs) offer fast and precise control, making them ideal for transient frequency regulation. However, conventional strategies that mimic synchronous generator behavior fail to fully exploit the potential of energy storage. To address this, I propose a novel transient frequency regulation strategy for battery energy storage systems based on compensation of the delayed frequency regulation characteristics of other power sources. This approach achieves an overdamped transient frequency response and maximizes the utilization of BESS reserve energy under diverse disturbance scenarios.
1. System Model for Battery Energy Storage Systems in Transient Frequency Regulation
1.1 Energy Dynamics of BESS Units
Consider a set of BESS units indexed by \( i \in \mathcal{B} \). Each BESS unit consists of a battery, a DC-link capacitor, a bidirectional converter, and an output filter. The battery is modeled as a voltage source \( u_i = f(s_i) \) dependent on the state of charge \( s_i \), with internal resistance \( r_i \). Neglecting losses, the output power \( P_i \) approximately equals the battery charging/discharging power:
$$ P_i \approx u_i i_i = S_i^{\text{nom}} \Delta P_i^{\text{ref}} $$
where \( S_i^{\text{nom}} \) is the rated capacity. The SOC dynamics follow Coulomb counting:
$$ s_i(t) = s_i^{\text{ini}} – \frac{1}{q_i^{\text{nom}}} \int_{t_0}^t i_i(\tau) d\tau $$
Defining the energy \( E_i = \int (q_i^{\text{nom}} / S_i^{\text{nom}}) f(s_i)\, ds_i \), the dominant dynamics become:
$$ \dot{E}_i = -\Delta P_i^{\text{ref}} $$
This energy variable directly reflects the effect of reference power on the BESS state. Under normal operating conditions, each BESS maintains energy within the optimal range \( [E_i^{\text{opt,min}}, E_i^{\text{opt,max}}] \). During transient events, a wider range \( [E_i^{\text{min}}, E_i^{\text{max}}] \) is allowed. The reserve energy for transient frequency regulation is \( E_i^{\text{res}} \).
| Parameter | Symbol | Description |
|---|---|---|
| Battery voltage | \( u_i = f(s_i) \) | Function of SOC |
| Rated charge | \( q_i^{\text{nom}} \) | Battery rated ampere-hour |
| Rated capacity | \( S_i^{\text{nom}} \) | Converter rated power |
| Energy | \( E_i \) | Aggregated state variable |
| Reserve energy | \( E_i^{\text{res}} \) | Energy reserved for frequency support |
1.2 System Transient Frequency Response Model with Multiple BESSs
The power system includes synchronous generators (SG), wind turbines (WT), photovoltaic (PV), and battery energy storage systems. Each non-BESS frequency regulation unit is represented by a transfer function \( F_j(s) \) relating its power increment \( \Delta P_j(s) \) to the frequency deviation \( \Delta \omega_{\text{sys}}(s) \):
- Synchronous generator: \( \Delta P_{\text{sg}}(s) = F_{\text{sg}}(s) \Delta \omega_{\text{sys}}(s) \) with \( F_{\text{sg}}(s) = -2H_{\text{sg}} s – D_{\text{sg}} G_{\text{sg}}(s) \), where \( G_{\text{sg}}(s) \) includes governor and turbine dynamics.
- Wind turbine: \( F_{\text{wtg}}(s) = -2H_{\text{wtg}}^{\text{sic}} s – D_{\text{wtg}}^{\text{sic}} + \frac{B_{\text{wtg}} s + A_{\text{wtg}}}{B_{\text{wtg}} s + A_{\text{wtg}} + C_{\text{wtg}}} \).
- Photovoltaic: \( F_{\text{pv}}(s) = -D_{\text{pv}}^{\text{sic}} \) (no delay).
The overall system frequency dynamics are:
$$ \left( \sum_j \rho_j F_j(s) + \sum_i \rho_i F_i(s) – D \right) \Delta \omega_{\text{sys}}(s) = \Delta P_d(s) $$
where \( \rho_j \) and \( \rho_i \) are power gain coefficients, \( D \) is load damping, and \( \Delta P_d(s) \) is the disturbance. The BESS units contribute through their own transfer functions \( F_i(s) \) defined by the proposed strategy.
2. Proposed Transient Frequency Regulation Strategy Based on Characteristic Compensation
2.1 Compensation Strategy Design
The frequency regulation characteristic of a unit is defined by its transfer function. To quantify its ability to regulate rate of change of frequency (RoCoF) and frequency deviation, I define the initial inertia coefficient \( H_j^{\text{ini}} \) and quasi-steady damping coefficient \( D_j^{\text{qs}} \):
$$ H_j^{\text{ini}} = \lim_{s \to \infty} \left[ -0.5\, F_j(s)/s \right], \quad D_j^{\text{qs}} = -F_j(0) $$
Most power sources exhibit phase lag (e.g., synchronous generators), causing an underdamped transient response. Instead of mimicking synchronous behavior, I propose that battery energy storage systems compensate for the delay of other units, forcing the overall system response to be overdamped. The desired system transfer function is a delay-free inertia-damping block:
$$ F_{\text{sys}}^{\text{des}}(s) = -2H_{\text{sys}} s – D_{\text{sys}} $$
Equating this with the actual system transfer function yields:
$$ \sum_i \rho_i F_i(s) = \sum_j \rho_j \left[ -2H_j^{\text{ini}} s – D_j^{\text{qs}} – F_j(s) \right] + \sum_i \rho_i (-2H_i^{\text{ini}} s) $$
The total compensation power is decomposed among BESS units via power distribution coefficients \( \gamma_i \) satisfying \( \sum_i \gamma_i = 1 \):
$$ \rho_i F_i(s) = \gamma_i \left( \sum_j \rho_j \left[ -2H_j^{\text{ini}} s – D_j^{\text{qs}} – F_j(s) \right] \right) + \rho_i (-2H_i^{\text{ini}} s) $$
The first term compensates for delays; the second term provides additional inertia support.
2.2 Parameter Tuning
The distribution coefficients are tuned based on the required critical energy to achieve overdamped response. Let \( \tau_j \) be the equivalent time constant of \( F_j(s) \). The total energy deviation caused by compensation is:
$$ \Delta E_{\text{bess}}^{\text{com}} = \sum_j \rho_j \tau_j \Delta P_d / D_{\text{sys}} $$
The critical energy \( E_{\text{bess}}^{\text{cri}} \) is estimated as:
$$ E_{\text{bess}}^{\text{cri}} = \max \left( \Delta E_{\text{bess}}^{\text{com,qs}}, \Delta E_{\text{bess}}^{\text{com}} \right) $$
where \( \Delta E_{\text{bess}}^{\text{com,qs}} \) is the quasi-steady value. The distribution coefficient for each BESS unit is:
$$ \gamma_i = \frac{\rho_i E_i^{\text{res}}}{\max \left( E_{\text{bess}}^{\text{res}}, E_{\text{bess}}^{\text{cri}} \right)} $$
If reserve energy exceeds critical energy, the remaining energy is used for inertia support. The initial inertia coefficient \( H_i^{\text{ini}} \) is set as:
$$ H_i^{\text{ini}} = \min \left( \frac{0.5 E_i^{\text{rem}}}{\Delta \omega_{\text{sys}}^{\max}}, H_i^{\max} \right) $$
where \( E_i^{\text{rem}} = \rho_i E_i^{\text{res}} – \gamma_i \left( \sum_j \rho_j \tau_j \Delta P_d / D_{\text{sys}} \right) \). This ensures that energy is fully utilized under severe disturbances while respecting hardware limits.
| Parameter | Symbol | Formula |
|---|---|---|
| Distribution coefficient | \( \gamma_i \) | \( \frac{\rho_i E_i^{\text{res}}}{\max(E_{\text{bess}}^{\text{res}}, E_{\text{bess}}^{\text{cri}})} \) |
| Initial inertia coefficient | \( H_i^{\text{ini}} \) | \( \min\left( \frac{0.5 E_i^{\text{rem}}}{\Delta \omega_{\text{sys}}^{\max}}, H_i^{\max} \right) \) |
| Critical energy | \( E_{\text{bess}}^{\text{cri}} \) | \( \max\left( \sum_j \rho_j \tau_j \frac{\Delta P_d}{D_{\text{sys}}}, \Delta E_{\text{bess}}^{\text{com}} \right) \) |
2.3 Reference Power Generation Loop
The reference power for each BESS unit is:
$$ \Delta P_i^{\text{ref}} = e_0 \cdot \Delta P_i^{\text{tfr}} + (1 – e_0) \cdot \Delta P_i^{\text{ost}} $$
where \( e_0 = u(|\Delta \omega_{\text{sys}}| – \Delta \omega_{\text{sys}}^{\text{db}}) \) is a start-up signal based on frequency deadband, \( \Delta P_i^{\text{ost}} \) is the optimal state tracking power defined as a spring-like function of energy deviation from the optimal range, and \( \Delta P_i^{\text{tfr}} \) is the transient frequency regulation power derived from the compensation strategy.
3. Performance Analysis
3.1 Theoretical Improvement of Transient Response
When the reserve energy of all battery energy storage systems is sufficient to fully compensate for delays (\( \sum_i \gamma_i = 1 \)), the system transfer function becomes exactly \( -2H_{\text{sys}} s – D_{\text{sys}} \). The time-domain response under a step disturbance \( \Delta P_d \) is:
$$ \Delta \omega_{\text{sys}}(t) = -\frac{\Delta P_d}{D_{\text{sys}}} \left( 1 – e^{- \frac{D_{\text{sys}}}{2 H_{\text{sys}}} t} \right) $$
This is a purely exponential, overdamped response with no overshoot or oscillation. The frequency nadir approaches the quasi-steady value, eliminating the risk of under-frequency load shedding. If reserve energy is insufficient, partial compensation still yields an improved but underdamped response.
3.2 Energy Utilization Analysis
The energy deviation of BESS unit \( i \) during the transient period is:
$$ \Delta E_i(t) = \gamma_i \Delta E_{\text{bess}}^{\text{com}}(t) + \rho_i H_i^{\text{ini}} \Delta \omega_{\text{sys}}(t) $$
It can be proven that under all conditions, \( |\Delta E_i| \leq \rho_i E_i^{\text{res}} \), ensuring that the SOC never exceeds its limits. The utilization rate of reserve energy is maximized because the strategy first allocates energy to characteristic compensation, which directly improves damping, and only uses residual energy for inertia. The maximum achievable energy utilization approaches 100% under large disturbances.
4. Case Studies
4.1 Simulation Setup
I implemented the modified IEEE 39-bus system in MATLAB/Simulink with three BESS units (B1–B3) connected at different nodes. The system includes 10 synchronous generators (G1–G10), two wind farms (W1, W2), and two PV plants (P1, P2). A load increase of 600 MW (10% of total load) or 1200 MW (20%) is applied at node 18 at t=10 s. Five frequency regulation strategies for battery energy storage systems are compared:
- NFR: BESS not participating.
- SIC: Synthetic inertia control with fixed coefficients.
- ASIC: Adaptive synthetic inertia control with SOC-dependent coefficients.
- CFC: Constant frequency control with integral term.
- FRCC: The proposed frequency regulation characteristic compensation strategy.
Key parameters of the power sources are summarized below:
| Unit | Rated power (MVA) | Inertia (s) | Damping (pu) | Remarks |
|---|---|---|---|---|
| G1–G10 | 1000 | 4 | 20 | Reheat turbine, \( \tau_{\text{sg}} = 172.3 \) s |
| W1,W2 | 700,630 | 2.5 | 10 | De-loading 0.9 pu, SIC enabled |
| P1,P2 | 700,630 | / | 10 | De-loading 0.9 pu, no virtual inertia |
| B1–B3 | 320,400,480 | 19.66–24.58 | 20 | Reserve energies: 8.438, 5.625, 3.750 s |
4.2 Scenario 1: Only Synchronous Generators and BESSs
When G7–G10 are replaced by the three battery energy storage systems, I test two disturbance levels. Under a 600 MW load increase, the proposed FRCC strategy achieves an overdamped transient response with a frequency nadir of –0.151 Hz, far smaller than the –0.342 Hz of SIC or –0.337 Hz of CFC. The energy utilization of B2 reaches 75.4% (4.239 s out of 5.625 s reserve). Under a 1200 MW disturbance, the reserve energy is insufficient for full compensation; FRCC still produces the best nadir (–0.417 Hz) compared to –0.694 Hz (SIC) and –0.683 Hz (CFC). The energy utilization increases to 95.8%, demonstrating efficient use of stored energy.
4.3 Scenario 2: Hybrid System with Renewables
In this scenario, G7–G10 are replaced by W1, W2, P1, and P2. The wind turbines have an equivalent time constant of 13.86 s, much smaller than synchronous generators. Thus, the compensation energy required for WTs is less than 5% of that for SGs. Under a 600 MW disturbance, FRCC achieves a nadir of –0.199 Hz, again the best among all strategies. The energy utilization of B2 is 60.3%, lower than in Scenario 1 because the critical energy is reduced due to faster wind turbine response. Under 1200 MW, the nadir is –0.439 Hz (vs. –0.627 Hz for SIC) and energy utilization reaches 95.0%. These results confirm that the proposed strategy remains effective regardless of system inertia and damping variations.
5. Conclusion
In this work, I have developed a novel transient frequency regulation strategy for battery energy storage systems based on compensation of frequency regulation characteristic delays of other power sources. By constructing compensation power from the frequency regulation transfer functions of heterogeneous sources and using residual energy for inertia support, the strategy achieves an overdamped transient frequency response under small disturbances and maximizes the utilization of BESS reserve energy under large disturbances. Theoretical analysis and IEEE 39-bus simulations demonstrate the following key findings:
- The proposed FRCC strategy is adaptive and significantly outperforms conventional SIC, adaptive SIC, and constant frequency control in terms of frequency nadir improvement and energy utilization continuity.
- With small disturbances, the system response becomes overdamped, eliminating oscillations and frequency overshoot. With large disturbances, all reserve energy is efficiently used for characteristic compensation, providing the best possible frequency support while respecting operational limits.
- As renewable energy replaces synchronous generators, the energy required for full compensation decreases, making it easier to achieve optimal transient frequency regulation using the proposed strategy.
Future work will focus on balancing energy utilization among multiple BESS units through inter-unit communication and extending the proposed framework to other types of energy storage systems.