We propose an optimal capacity allocation strategy for a hybrid energy storage system (HESS) designed to smooth the power fluctuations from wind generation and reduce the impact on the power system. The HESS consists of a battery energy storage system (BESS) and a supercapacitor energy storage system (SC). The battery energy storage system handles low-frequency power fluctuations, while the supercapacitor addresses high-frequency components. We employ a moving average control method to filter the wind power output and meet grid integration requirements. The fluctuating component is then decomposed into high- and low-frequency parts using spectrum analysis. An optimized charge/discharge control strategy based on the state of charge (SOC) of each storage device is developed to prevent overcharge and overdischarge, thereby prolonging the cycle life of the battery energy storage system. A cost model considering the cycle life of the battery energy storage system is established, with the objective of minimizing the annualized total cost. Simulation results demonstrate that the proposed method effectively smooths power fluctuations, optimally allocates power between storage devices, maintains SOC within reasonable bounds, and achieves economic superiority.
Wind power is inherently intermittent, random, and uncertain. Directly connecting raw wind power to the grid can compromise system stability and reliability. Energy storage technologies, particularly hybrid configurations, enhance the regulation capability of microgrids, enable temporal and spatial shifting of energy, and improve the acceptability of wind power. In this work, we focus on a hybrid system combining a battery energy storage system (BESS) and a supercapacitor (SC). The BESS provides high energy density but suffers from limited cycle life under frequent charging/discharging. The supercapacitor offers high power density and long cycle life but low energy density. By allocating frequency components appropriately, we exploit the complementary characteristics of both technologies.
System Model
The wind-storage system consists of a wind turbine generator, the hybrid energy storage system, a power controller, and the grid. The power balance at any time t is:
$$
P_w(t) = P_{\text{grid}}(t) + P_{\text{HESS}}(t) = P_{\text{grid}}(t) + P_{\text{SC}}(t) + P_{\text{BAT}}(t)
$$
where Pw is the wind power output, Pgrid is the grid-connected power, PHESS is the total power exchanged with the HESS, PSC is the supercapacitor power, and PBAT is the battery energy storage system power. Positive values indicate charging, negative values indicate discharging.
To ensure grid code compliance, we apply two time‑scale constraints: the maximum power fluctuation over 1 min and over 10 min must be within limits. For a wind farm capacity between 30 MW and 150 MW, the limits are 10 % and 33.3 %, respectively. The fluctuation rates are defined as:
$$
\delta_{t,1} = \frac{\max[P_1(t)] – \min[P_1(t)]}{P_0} \times 100\%
$$
$$
\delta_{t,10} = \frac{\max[P_{10}(t)] – \min[P_{10}(t)]}{P_0} \times 100\%
$$
where P0 is the rated capacity.
Power Allocation between Battery and Supercapacitor
We use a moving average filter to derive the grid-connected power Pgrid from the raw wind power Pw. The window length T is chosen as the smallest value that satisfies both 1‑min and 10‑min fluctuation constraints. A longer window yields a smoother grid power but increases the required energy storage capacity. The grid power is:
$$
P_{\text{grid}}(t) = \frac{1}{T} \sum_{k=t-\frac{T}{2}+1}^{t+\frac{T}{2}} P_w(k)
$$
for t = T/2, T/2+1, …, N‑T/2, where N is the total number of samples. The HESS power is then:
$$
P_{\text{HESS}}(t) = P_w(t) – P_{\text{grid}}(t)
$$
We perform spectrum analysis on PHESS using Discrete Fourier Transform (DFT). The amplitude spectrum SHESS and frequency vector fHESS are obtained. A cut‑off frequency of 1.67 mHz separates the high‑frequency component (handled by the supercapacitor) from the low‑frequency one (handled by the battery energy storage system). The supercapacitor power is recovered by inverse DFT of the high‑frequency amplitudes:
$$
P_{\text{SC}} = \text{IDFT}(S_{\text{SC}})
$$
Consequently, the battery energy storage system power is:
$$
P_{\text{BAT}}(t) = P_{\text{HESS}}(t) – P_{\text{SC}}(t)
$$
State of Charge Control Strategy
We define five SOC zones for each storage device: overcharge zone (SOC ≥ SOCm), high zone (SOCm > SOC ≥ SOCh), normal zone (SOCh > SOC > SOCl), low zone (SOCl ≥ SOC > SOCn), and overdischarge zone (SOCn ≥ SOC). The control rules are as follows:
- In the overcharge zone, the device is forced to discharge only (no charging allowed).
- In the high zone, charging power is reduced using a sigmoid‑based correction coefficient to slow the SOC rise.
- In the normal zone, normal operation is permitted.
- In the low zone, discharging power is reduced to slow the SOC decline.
- In the overdischarge zone, the device is forced to charge only (no discharging allowed).
The corrected charging power Pc and discharging power Pd are given by sigmoid functions:
$$
P_c(t) = \frac{P(t)}{1 + \exp[-10 \times (x_{\text{ch}} – 0.5)]}
$$
$$
x_{\text{ch}} = \frac{SOC(t) – SOC_m}{SOC_h – SOC_m}
$$
$$
P_d(t) = \frac{P(t)}{1 + \exp[-10 \times (x_{\text{dis}} – 0.5)]}
$$
$$
x_{\text{dis}} = \frac{SOC(t) – SOC_n}{SOC_l – SOC_n}
$$
The above SOC‑based control prevents the battery energy storage system from operating in extreme SOC regions, thereby reducing capacity degradation and extending its cycle life.
Capacity Sizing and Cost Model
The rated power of each storage device is defined as the maximum absolute value of its power during the study period:
$$
P_x = \max |P_{x,n}| \quad (n=1,2,\dots,N)
$$
where x = SC (supercapacitor) or BAT (battery energy storage system). The energy capacity is determined from the cumulative energy profile:
$$
E_{x,n} = E_{x,n-1} + P_{x,n} \eta_{x,1} \Delta t \quad (P_{x,n} \ge 0)
$$
$$
E_{x,n} = E_{x,n-1} + P_{x,n} \Delta t / \eta_{x,2} \quad (P_{x,n} < 0)
$$
$$
E_x = \frac{2 \max(|E_{x,n}|)}{SOC_{\max} – SOC_{\min}}
$$
where ηx,1 and ηx,2 are charging and discharging efficiencies, and SOCmax, SOCmin are the upper and lower SOC limits.
We construct a comprehensive cost model including capital costs, operation & maintenance (O&M) costs, and battery energy storage system life‑dependent replacement cost. The annualized total cost C is:
$$
C = C_{\text{SC,cap}} + C_{\text{BAT,cap}} + C_{\text{O\&M}} + C_{\text{loss}}
$$
The capital cost for the supercapacitor is:
$$
C_{\text{SC,cap}} = \alpha_{\text{SC}} P_{\text{SC}} + \beta_{\text{SC}} E_{\text{SC}}
$$
For the battery energy storage system:
$$
C_{\text{BAT,cap}} = \alpha_{\text{BAT}} P_{\text{BAT}} + \beta_{\text{BAT}} E_{\text{BAT}}
$$
The O&M cost is proportional to energy capacity:
$$
C_{\text{O\&M}} = \phi_{\text{SC}} E_{\text{SC}} + \phi_{\text{BAT}} E_{\text{BAT}}
$$
The battery energy storage system replacement cost is based on the cycle life model. The number of cycles to failure at depth of discharge Di is:
$$
Q_i = \delta_1 + \delta_2 e^{\delta_3 D_i} + \delta_4 e^{\delta_5 D_i}
$$
where δ1–δ5 are empirical parameters. The expected life Fy of the battery energy storage system in years is:
$$
F_y = \frac{T_c}{T_y} \sum_{i=1}^{Q_d} Q_i^{-1}
$$
with Tc the study period duration and Ty one year. The annual depreciation cost is then:
$$
C_{\text{loss}} = \frac{T_y}{T_c} \sum_{i=1}^{N_d} Q_i^{-1} C_{\text{BAT,cap}}
$$
where Nd is the number of discharge events in the study period.
Simulation Data and Parameters
We use historical wind power data from an 80 MW wind farm with a 1‑min sampling interval, totaling 1440 samples. The simulation parameters are listed in Table 1.
| Device | Parameter | Value |
|---|---|---|
| Supercapacitor | Power cost coefficient (¥/kW) | 1500 |
| Energy cost coefficient (¥/kWh) | 27000 | |
| O&M cost coefficient (¥/kWh) | 0.05 | |
| Charge/discharge efficiency | 95% | |
| SOCmax | 90% | |
| SOCh | 80% | |
| SOCl / SOCmin | 20% / 10% | |
| Battery energy storage system | Power cost coefficient (¥/kW) | 2700 |
| Energy cost coefficient (¥/kWh) | 640 | |
| O&M cost coefficient (¥/kWh) | 0.05 | |
| Charge/discharge efficiency | 80% | |
| SOCmax | 80% | |
| SOCh | 70% | |
| SOCl | 30% | |
| SOCmin | 20% |
Results and Discussion
We first determine the moving average window length. Figure 4 (not shown here) indicates that a window length of 16 satisfies both 1‑min and 10‑min fluctuation constraints (1‑min: 9.635 % < 10 %, 10‑min: 32.56 % < 33.3 %). This window achieves a good balance between smoothness and storage capacity requirement.
The raw wind power and the grid‑connected power after moving average are plotted in Fig. 5 (qualitatively described). The fluctuating component is then decomposed. The supercapacitor absorbs high‑frequency variations (above 1.67 mHz) and the battery energy storage system handles low‑frequency variations. Without SOC control, both storage devices would violate their SOC limits (e.g., SOC of the battery energy storage system exceeds 80 % or drops below 20 %). With the proposed control, the SOC of each device stays strictly within the allowed range, preventing overcharge and overdischarge.
We compare four scenarios:
- Our proposed scheme: supercapacitor + battery energy storage system with SOC‑based control
- Scheme 1: supercapacitor alone
- Scheme 2: battery energy storage system alone
- Scheme 3: supercapacitor + battery energy storage system without SOC control
The optimal configuration results are summarized in Table 2.
| Metric | Our scheme | Scheme 1 (SC only) | Scheme 2 (BAT only) | Scheme 3 (uncontrolled HESS) |
|---|---|---|---|---|
| SC rated power (MW) | 4.709 | 12.381 | — | 4.709 |
| SC rated energy (MWh) | 1.337 | 35.642 | — | 1.486 |
| BAT rated power (MW) | 8.452 | — | 12.381 | 8.452 |
| BAT rated energy (MWh) | 38.307 | — | 42.192 | 40.129 |
| BAT cycle life (years) | 4.39 | — | 2.25 | 3.89 |
| Annualized total cost (¥100 million) | 1.109 | 2.371 | 1.621 | 1.227 |
The results demonstrate that our proposed scheme achieves the lowest annualized cost of ¥1.109 × 108. Compared to Scheme 1 (pure supercapacitor), the cost is reduced by 53.23 %—the high energy‑cost coefficient of supercapacitors makes exclusive use prohibitively expensive. Relative to Scheme 2 (pure battery energy storage system), the cost is 31.59 % lower because the battery energy storage system alone suffers from frequent deep cycling and shortened life. Compared to Scheme 3 (uncontrolled HESS), our scheme yields a 9.62 % cost reduction, attributable to the SOC‑based control that extends the battery energy storage system life from 3.89 years to 4.39 years.
The proposed SOC control effectively mitigates overcharge and overdischarge, keeping the battery energy storage system operating in a more favorable SOC window. This prolongs cycle life and reduces replacement costs. Meanwhile, the supercapacitor handles rapid power excursions, protecting the battery energy storage system from stress.
Conclusion
We have developed a capacity optimization framework for a hybrid energy storage system that combines a supercapacitor and a battery energy storage system. The key contributions are:
- A moving average filter and spectrum analysis to allocate high‑ and low‑frequency fluctuating power to the supercapacitor and battery energy storage system, respectively.
- An SOC‑based control strategy that adaptively adjusts charge/discharge power to keep SOC within safe limits, preventing overcharge and overdischarge.
- A comprehensive cost model incorporating the cycle‑life‑dependent replacement cost of the battery energy storage system.
Simulation results confirm that the proposed method meets grid‑code fluctuation limits, prolongs the battery energy storage system lifetime, and reduces the annualized total cost compared to standalone storage or uncontrolled hybrid configurations. This work provides a practical and economical solution for integrating large‑scale wind power into the grid. Future research may extend the approach to multi‑energy systems including photovoltaic, hydropower, and other renewable sources.