In the context of rapidly increasing global energy demand, wind power has emerged as a prominent renewable resource due to its abundant availability and environmental benefits. However, the inherent intermittency, randomness, and uncertainty of wind power generation pose significant challenges to the stable and reliable operation of power systems. To address these issues, I have developed an optimal control strategy for the capacity configuration of a hybrid energy storage system (HESS) that explicitly considers the state of charge (SOC) of each storage component. This work integrates moving average filtering, spectral analysis, and a SOC-based power distribution method to effectively smooth wind power fluctuations while minimizing the total annualized cost. The proposed approach targets the frequent overcharge and over-discharge problems that degrade battery lifetime, thereby improving both technical performance and economic viability.
My research focuses on a wind-farm–battery energy storage system configuration, where the battery energy storage system (BESS) is combined with a supercapacitor (SC) to form a hybrid storage solution. The battery energy storage system is well-suited for handling low-frequency power variations due to its high energy density, while the SC excels at managing high-frequency fluctuations owing to its high power density and rapid response. By decomposing the fluctuating wind power into high- and low-frequency components via spectral analysis, I allocate these components to the respective storage devices. Furthermore, I design a SOC-based optimization control strategy that partitions the SOC range into five distinct zones, applying sigmoid-function-derived power correction factors to prevent operation in overcharge and over-discharge regions. This strategy prolongs the cycle life of the battery energy storage system, reduces replacement costs, and enhances overall economic efficiency. The capacity optimization model is formulated as a cost-minimization problem that includes acquisition, operation and maintenance, and battery degradation costs. Simulation results using real 80 MW wind farm data demonstrate that my method satisfies grid-connection fluctuation limits at both 1-minute and 10-minute timescales, maintains SOC within safe bounds, and achieves a 9.62% reduction in annualized cost compared to a non-optimized HESS.
System Architecture and Power Fluctuation Modeling
I consider a typical wind–storage system composed of a wind turbine generator, a hybrid energy storage system (battery energy storage system alongside a supercapacitor), an energy controller, and the utility grid. The power balance at any time instant \(t\) is given by:
$$P_{\mathrm{w}}(t) = P_{\mathrm{grid}}(t) + P_{\mathrm{HESS}}(t) = P_{\mathrm{grid}}(t) + P_{\mathrm{bat}}(t) + P_{\mathrm{cap}}(t)$$
where \(P_{\mathrm{w}}(t)\) is the raw wind power output, \(P_{\mathrm{grid}}(t)\) is the power injected into the grid, and \(P_{\mathrm{bat}}(t)\) and \(P_{\mathrm{cap}}(t)\) are the powers of the battery energy storage system and supercapacitor, respectively. Positive values indicate charging, and negative values indicate discharging.
To ensure grid stability, national standards impose maximum power fluctuation limits over 1-minute and 10-minute windows. For a wind farm with capacity between 30 MW and 150 MW, the 1-minute and 10-minute maximum fluctuation rates must not exceed 10% and 33.3%, respectively, as summarized in Table 1.
| Wind Farm Capacity (MW) | Max 10-min Fluctuation (MW) | Max 1-min Fluctuation (MW) |
|---|---|---|
| >150 | 50 | 15 |
| 30–150 | 10–50 | 3–15 |
| <30 | 10 | 3 |
Corresponding 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 \(P_{1}(t)\) and \(P_{10}(t)\) are the wind power values over the respective windows, and \(P_{0}\) is the rated capacity.
Power Decomposition Using Moving Average and Spectral Analysis
To extract the smooth grid-connected power, I apply a moving average filter with window length \(T\). The grid power is computed as:
$$P_{\mathrm{grid}}(t) = \frac{1}{T} \sum_{k=t-(T/2-1)}^{t+T/2} P_{\mathrm{w}}(k), \quad t = \frac{T}{2}, \frac{T}{2}+1, \dots, N – \frac{T}{2}$$
The fluctuating component that must be compensated by the HESS is:
$$P_{\mathrm{HESS}}(t) = P_{\mathrm{w}}(t) – P_{\mathrm{grid}}(t)$$
I then perform discrete Fourier transform (DFT) on \(P_{\mathrm{HESS}}(t)\) to obtain its amplitude spectrum \(S_{\mathrm{HESS}}\) and frequency vector \(f_{\mathrm{HESS}}\). By selecting a cutoff frequency \(f_{\mathrm{cut}}\) (here 1.67 mHz), the spectrum is split into high-frequency (allocated to the supercapacitor) and low-frequency (allocated to the battery energy storage system) components. The inverse DFT is applied to each part to reconstruct the time-domain power commands:
$$P_{\mathrm{cap}} = \mathrm{IDFT}(S_{\mathrm{cap}})$$
$$P_{\mathrm{bat}}(t) = P_{\mathrm{HESS}}(t) – P_{\mathrm{cap}}(t)$$
The rated power of each storage device is taken as the maximum absolute value of its power command over the entire simulation horizon:
$$P_{x} = \max|P_{x,n}|, \quad n = 1,2,\dots,N$$
The energy capacity is derived from the cumulative energy trajectory:
$$E_{x,n} = E_{x,n-1} + P_{x,n} \, \eta_{x,1} \, \Delta t \quad (P_{x,n} \geq 0)$$
$$E_{x,n} = E_{x,n-1} + P_{x,n} \, \Delta t / \eta_{x,2} \quad (P_{x,n} < 0)$$
where \(\eta_{x,1}\) and \(\eta_{x,2}\) are charging and discharging efficiencies. The required capacity is:
$$E_{x} = \frac{2 \, \max(|E_{x,n}|)}{\mathrm{SOC}_{\max} – \mathrm{SOC}_{\min}}$$
SOC-Based Power Control Strategy
To protect the battery energy storage system from accelerated degradation due to overcharge and deep discharge, I partition the SOC range into five zones, as shown conceptually in Figure 2 (not reproduced here): overcharge, high-limit, normal, low-limit, and over-discharge. The control rules are:
- Overcharge zone (SOC ≥ SOCm): Only discharge allowed; charging is prohibited.
- High-limit zone (SOCm > SOC ≥ SOCh): Priority to discharge; charging power is reduced.
- Normal zone (SOCh > SOC > SOCl): Normal charging/discharging allowed.
- Low-limit zone (SOCl ≥ SOC > SOCn): Priority to charge; discharging power is reduced.
- Over-discharge zone (SOC ≤ SOCn): Only charging allowed; discharging is prohibited.
I use a sigmoid function to smoothly scale the charge/discharge power commands. For charging power correction when SOC is in the high-limit zone:
$$P_{\mathrm{c}}(t) = \frac{P(t)}{1 + \exp[-10 \times (x_{\mathrm{ch}} – 0.5)]}, \quad x_{\mathrm{ch}} = \frac{\mathrm{SOC}(t) – \mathrm{SOC}_{m}}{\mathrm{SOC}_{h} – \mathrm{SOC}_{m}}$$
For discharging power correction in the low-limit zone:
$$P_{\mathrm{d}}(t) = \frac{P(t)}{1 + \exp[-10 \times (x_{\mathrm{dis}} – 0.5)]}, \quad x_{\mathrm{dis}} = \frac{\mathrm{SOC}(t) – \mathrm{SOC}_{n}}{\mathrm{SOC}_{l} – \mathrm{SOC}_{n}}$$
This strategy ensures that the battery energy storage system operates predominantly in the normal SOC range, thereby extending its cycle life.
Cycle Life and Cost Model of the Battery Energy Storage System
The supercapacitor has a very long cycle life (treated as constant), but the battery energy storage system degrades with each discharge cycle. The number of cycles to failure as a function of depth of discharge (DOD) \(D_i\) is given by the fitted relationship:
$$Q_i = \delta_1 + \delta_2 e^{\delta_3 D_i} + \delta_4 e^{\delta_5 D_i}$$
where \(\delta_1\) through \(\delta_5\) are parameters specific to the battery chemistry. I estimate the lifetime \(F_y\) (in years) as:
$$F_y = \frac{T_c}{T_y \sum_{i=1}^{Q_d} Q_i^{-1}}$$
where \(T_c\) is the total simulation time (e.g., one day), \(T_y\) is the number of hours in a year, and \(Q_d\) is the number of discharge events during the simulation.
The total annualized cost includes:
- Acquisition cost: \(C_{\mathrm{cin}} = \alpha_{\mathrm{cin}} P_{\mathrm{cap}} + \beta_{\mathrm{cin}} E_{\mathrm{cap}}\) for supercapacitor; \(C_{\mathrm{bin}} = \alpha_{\mathrm{bin}} P_{\mathrm{bat}} + \beta_{\mathrm{bin}} E_{\mathrm{bat}}\) for battery energy storage system.
- Operation and maintenance cost: \(C_{\mathrm{om}} = \phi_{\mathrm{cap}} E_{\mathrm{cap}} + \phi_{\mathrm{bat}} E_{\mathrm{bat}}\).
- Battery degradation cost: \(C_{\mathrm{dep}} = \frac{T_y}{T_c} \sum_{i=1}^{N_d} Q_i^{-1} C_{\mathrm{bin}}\).
Total annual cost: \(C = C_{\mathrm{cin}} + C_{\mathrm{bin}} + C_{\mathrm{om}} + C_{\mathrm{dep}}\).
The parameters used in my simulation are listed in Table 2.
| Component | Parameter | Value |
|---|---|---|
| Supercapacitor | Power cost (yuan/kW) | 1500 |
| Energy cost (yuan/kWh) | 27000 | |
| O&M cost (yuan/kWh) | 0.05 | |
| Charge/discharge efficiency (%) | 95 | |
| SOCmax (%) | 90 | |
| SOCh (%) | 80 | |
| SOCl (%) | 20 | |
| Battery energy storage system | Power cost (yuan/kW) | 2700 |
| Energy cost (yuan/kWh) | 640 | |
| O&M cost (yuan/kWh) | 0.05 | |
| Charge/discharge efficiency (%) | 80 | |
| SOCmax (%) | 80 | |
| SOCh (%) | 70 | |
| SOCl (%) | 30 | |
| SOCmin (%) | 20 |
Simulation Setup and Results
I used historical wind power data from an 80 MW wind farm with a 1-minute resolution over 1440 samples (one day). The moving average window length was selected by evaluating the maximum fluctuation rates at 1-minute and 10-minute timescales. As shown in Figure 4 (not reproduced), a window length of 16 was found to satisfy both constraints: 1-min fluctuation rate = 9.635% (<10%), 10-min fluctuation rate = 32.56% (<33.3%). This window minimizes the required HESS power while meeting grid codes.
The raw and smoothed grid power are compared in Figure 5 (not reproduced). With the moving average window applied, the grid-connected power is effectively smoothed. The fluctuating power is then decomposed via spectral analysis at a cutoff frequency of 1.67 mHz. The resulting power commands for the battery energy storage system (low frequency) and supercapacitor (high frequency) are plotted in Figure 6 (not reproduced).
Applying the SOC-based control strategy, the SOC trajectories of both devices are shown in Figure 7 (not reproduced). Without optimization, the supercapacitor SOC exceeds 0.9 and the battery SOC falls below 0.2, leading to overcharge and deep discharge. With my control, the SOC remains within the safe bands (0.1–0.9 for SC, 0.2–0.8 for battery), thus protecting the battery energy storage system.
I compared four configurations:
- Case 1: Supercapacitor only.
- Case 2: Battery energy storage system only.
- Case 3: Hybrid SC + battery without SOC optimization (uncontrolled).
- Proposed: Hybrid SC + battery with SOC optimization.
The configuration results are summarized in Table 3.
| Metric | Proposed | Case 1 (SC only) | Case 2 (Battery only) | Case 3 (Hybrid no SOC opt.) |
|---|---|---|---|---|
| SC rated power (MW) | 4.709 | 12.381 | — | 4.709 |
| SC capacity (MWh) | 1.337 | 35.642 | — | 1.486 |
| Battery rated power (MW) | 8.452 | — | 12.381 | 8.452 |
| Battery capacity (MWh) | 38.307 | — | 42.192 | 40.129 |
| Battery lifetime (years) | 4.39 | — | 2.25 | 3.89 |
| Annualized total cost (100 million yuan) | 1.109 | 2.371 | 1.621 | 1.227 |
From the table, my proposed method yields the lowest annualized cost (1.109 × 10⁸ yuan). Compared to the supercapacitor-only case, the cost is reduced by 53.23% because the large capacity of SCs is extremely expensive. Compared to the battery-only case, the cost is reduced by 31.59% because the battery alone suffers frequent deep cycles, drastically shortening its life. Compared to the unoptimized hybrid, my SOC optimization improves battery lifetime from 3.89 years to 4.39 years, yielding a 9.62% cost reduction.
These results clearly demonstrate that the SOC-aware control strategy effectively prevents overcharge and over-discharge of the battery energy storage system, extending its operational life and significantly lowering total cost.
Discussion and Economic Implications
The key contributions of my work are as follows:
- Power decomposition and allocation: By combining moving average filtering with spectral analysis, the fluctuating wind power is split into high- and low-frequency components, which are respectively handled by the supercapacitor and the battery energy storage system. This exploits the complementary characteristics of both storage technologies and reduces the stress on the battery energy storage system.
- SOC-based optimization: The five-zone SOC control with sigmoid-based power correction ensures that the battery energy storage system remains in its safe operating region. This minimizes deep discharges and overcharges, which are the dominant causes of accelerated aging. The control is simple, robust, and easy to implement in real-time energy management systems.
- Lifecycle cost model: I explicitly incorporate battery degradation cost based on cycle count and depth-of-discharge. This allows the optimization to trade off between energy capacity and battery wear, leading to a more realistic and economically superior design.
- Compliance with grid codes: The method guarantees that both 1-minute and 10-minute power fluctuation limits are satisfied, ensuring seamless integration of wind power into the grid.
The proposed approach can be extended to other renewable energy sources such as solar and hydro, and to multi-energy systems where multiple storage technologies coexist. Future work may include stochastic optimization to account for forecast uncertainty, as well as online adaptive tuning of the SOC thresholds based on real-time battery health.
Conclusion
In this paper, I have developed an optimal capacity configuration strategy for a hybrid energy storage system comprising a supercapacitor and a battery energy storage system, specifically designed to smooth wind power fluctuations. The strategy uses a moving average filter to obtain grid-compliant power, spectral decomposition to assign high- and low-frequency components to the appropriate storage devices, and a state-of-charge-based control to prevent overcharge and deep discharge of the battery energy storage system. The cost model integrates acquisition, operation, maintenance, and battery degradation costs. Simulation results on an 80 MW wind farm dataset confirm that the proposed method satisfies grid fluctuation limits at both 1-minute and 10-minute timescales, maintains SOC within safe bounds, and achieves a 9.62% reduction in annualized cost compared to a non-optimized hybrid system. The work demonstrates that intelligent SOC management is a critical lever for extending battery energy storage system lifetime and improving the economic viability of wind power integration. The proposed framework is practical, scalable, and can be adapted to other hybrid energy storage applications.