In the rapid evolution of modern power systems, the integration of renewable energy sources such as wind power introduces significant challenges due to their inherent intermittency, randomness, and uncertainty. To mitigate the adverse impacts of wind power fluctuations on grid stability, we propose an optimal capacity configuration strategy for a hybrid energy storage system (HESS) that explicitly considers the state of charge (SOC) of each storage component. Our approach employs a moving average control method to smooth the wind power output fluctuations, followed by spectrum analysis to decompose the fluctuating power into high-frequency and low-frequency components. These components are then absorbed by supercapacitors and battery energy storage systems, respectively, based on their complementary characteristics. Furthermore, we design an adaptive charge/discharge power control strategy that adjusts the power output according to the SOC intervals of the storage devices, thereby preventing overcharging and overdischarging. A comprehensive cost model incorporating the cycle life of battery energy storage systems is established with the objective of minimizing the annualized total cost. Simulation results demonstrate that the proposed method achieves smooth power fluctuation control, optimal power allocation between storage units, and significant economic benefits.
Introduction
The increasing global demand for clean energy has accelerated the deployment of wind power generation. However, the stochastic nature of wind leads to severe power fluctuations that can jeopardize power system reliability and power quality. Energy storage technologies, particularly battery energy storage systems, offer a viable solution by enabling temporal energy shifting and providing fast response to smooth power variations. Among various storage configurations, hybrid energy storage systems combining supercapacitors and battery energy storage systems leverage the high power density of supercapacitors for high-frequency fluctuations and the high energy density of battery energy storage systems for low-frequency components. This synergy reduces the stress on batteries, prolongs their cycle life, and minimizes overall system cost.
Existing studies have explored different decomposition methods such as empirical mode decomposition, wavelet packet decomposition, and moving average filters to allocate power between storage units. However, most approaches overlook the impact of the SOC on the operational efficiency and lifespan of battery energy storage systems. The charge/discharge behavior significantly influences the aging process of batteries, and improper SOC management can lead to premature failure. In this paper, we propose a novel SOC-aware control strategy that partitions the SOC range into five distinct zones and applies sigmoid-based correction functions to modulate the power exchange. By maintaining the SOC within safe boundaries, we enhance the service life of battery energy storage systems and improve economic performance. A detailed cost model accounting for battery degradation is formulated, and a case study based on a 80 MW wind farm confirms the effectiveness and superiority of our method.
System Model of Wind-Storage Hybrid System
The investigated wind-storage system comprises a wind farm, a hybrid energy storage system (supercapacitors and battery energy storage systems), an energy management controller, and the grid connection point. The power balance at the point of common coupling is given by:
$$P_w(t) = P_{grid}(t) + P_{HESS}(t) = P_{grid}(t) + P_{cap}(t) + P_{bat}(t)$$
where \(P_w(t)\) is the wind power output, \(P_{grid}(t)\) is the grid-injected power, and \(P_{cap}(t)\) and \(P_{bat}(t)\) are the powers of the supercapacitor and battery energy storage systems, respectively. Positive values indicate charging, and negative values indicate discharging.
To meet grid code requirements, the power fluctuation must be limited. According to national standards for wind farm integration, the maximum allowed power fluctuations over 1-minute and 10-minute intervals depend on the installed capacity. For a 30–150 MW wind farm, the 1-minute and 10-minute fluctuation rates must not exceed 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 \(P_0\) is the rated capacity, and \(P_1(t)\), \(P_{10}(t)\) are the power values within the respective time windows.
Hybrid Energy Storage System Model
Power Allocation Methodology
We first apply a moving average filter to the original wind power data to obtain the grid-connected power. The window length \(T\) is a critical parameter: a too small window fails to suppress fluctuations, while a too large window results in oversized storage requirements. We choose the minimum window length that satisfies both 1-minute and 10-minute fluctuation constraints. The grid-connected power is:
$$P_{grid}(t) = \frac{1}{T} \sum_{k=t-T/2+1}^{t+T/2} P_w(k), \quad t = T/2, T/2+1, \dots, N-T/2$$
The fluctuating power to be absorbed by the HESS is then:
$$P_{HESS}(t) = P_w(t) – P_{grid}(t)$$
Next, we perform a discrete Fourier transform (DFT) on \(P_{HESS}(t)\) to decompose it into frequency components. The magnitude spectrum \(S_{HESS}\) and frequency vector \(f_{HESS}\) are obtained. A cutoff frequency \(f_c = 1.67\) mHz is selected to separate high-frequency and low-frequency parts. The high-frequency components are assigned to the supercapacitor, and the low-frequency components are assigned to battery energy storage systems. The supercapacitor power is obtained by inverse DFT of the high-frequency magnitude:
$$P_{cap}(t) = \text{IDFT}(S_{cap})$$
Consequently, the power of battery energy storage systems is:
$$P_{bat}(t) = P_{HESS}(t) – P_{cap}(t)$$
Capacity Sizing of Storage Units
The rated power of each storage device is the maximum absolute value of its power over the entire period:
$$P_x = \max_{n} |P_{x,n}|, \quad x \in \{cap, bat\}$$
The accumulated energy at each time step is computed considering charging/discharging efficiencies:
$$E_{x,n} = E_{x,n-1} + P_{x,n} \eta_{x,1} \Delta t \quad \text{if } P_{x,n} \ge 0$$
$$E_{x,n} = E_{x,n-1} + \frac{P_{x,n} \Delta t}{\eta_{x,2}} \quad \text{if } P_{x,n} < 0$$
where \(\eta_{x,1}\) and \(\eta_{x,2}\) are charging and discharging efficiencies, and \(\Delta t\) is the sampling interval. The required energy capacity is:
$$E_x = \frac{2 \max(|E_{x,n}|)}{SOC_{max} – SOC_{min}}$$
State-of-Charge Based Control Strategy
To prevent premature aging of battery energy storage systems and maintain operational safety, we design a SOC-aware control strategy that divides the SOC range into five zones: overcharge zone (\(SOC \ge SOC_{max}\)), high limit zone (\(SOC_{max} > SOC \ge SOC_h\)), normal zone (\(SOC_h > SOC > SOC_l\)), low limit zone (\(SOC_l \ge SOC > SOC_n\)), and overdischarge zone (\(SOC_n \ge SOC\)). The control rules are:
- Overcharge: only discharging allowed, no charging.
- High limit: prioritize discharging, restrict charging power to reduce SOC rise rate.
- Normal: normal operation with no restriction.
- Low limit: prioritize charging, restrict discharging power to reduce SOC decline rate.
- Overdischarge: only charging allowed, no discharging.
The power correction is implemented using a sigmoid function. For charging, the corrected power is:
$$P_c(t) = \frac{P(t)}{1 + \exp[-10 \times (x_{ch} – 0.5)]}$$
$$x_{ch} = \frac{SOC(t) – SOC_m}{SOC_h – SOC_m}$$
For discharging:
$$P_d(t) = \frac{P(t)}{1 + \exp[-10 \times (x_{dis} – 0.5)]}$$
$$x_{dis} = \frac{SOC(t) – SOC_n}{SOC_l – SOC_n}$$
This control strategy ensures that the SOC remains within the allowable limits and extends the cycle life of battery energy storage systems.
Cost Model Including Battery Cycle Life
The total annualized cost of the HESS consists of capital costs, operation and maintenance costs, and battery degradation cost. The cycle life of battery energy storage systems is modeled as a function of depth of discharge (DoD):
$$Q_i = \delta_1 + \delta_2 e^{\delta_3 D_i} + \delta_4 e^{\delta_5 D_i}$$
where \(D_i\) is the DoD of the \(i\)-th cycle, and \(\delta_1\) to \(\delta_5\) are parameters. The expected lifetime of the battery in years is:
$$F_y = \frac{T_c}{T_y} \sum_{i=1}^{Q_d} Q_i^{-1}$$
where \(T_c\) is the total period considered, \(T_y\) is one year, and \(Q_d\) is the number of cycles during the period.
The cost components are:
- Capital cost of supercapacitor: \(C_{cin} = \alpha_{cin} P_{cap} + \beta_{cin} E_{cap}\)
- Capital cost of battery energy storage systems: \(C_{bin} = \alpha_{bin} P_{bat} + \beta_{bin} E_{bat}\)
- Operation and maintenance cost: \(C_{om} = \phi_{cap} E_{cap} + \phi_{bat} E_{bat}\)
- Battery degradation cost: \(C_{dep} = \frac{T_y}{T_c} \sum_{i=1}^{N_d} Q_i^{-1} C_{bin}\)
Total annualized cost: \(C = C_{cin} + C_{bin} + C_{om} + C_{dep}\).
Simulation Results and Analysis
We use historical wind power data from an 80 MW wind farm with a 1-minute sampling interval over 1440 minutes. The system parameters are listed in Table 1.
| Component | Parameter | Value |
|---|---|---|
| Supercapacitor | Power cost coefficient (CNY/kW) | 1500 |
| Capacity cost coefficient (CNY/kWh) | 27000 | |
| O&M cost coefficient (CNY/kWh) | 0.05 | |
| Charge/discharge efficiency | 95% | |
| SOC_max | 90% | |
| SOC_h / SOC_l / SOC_min | 80% / 20% / 10% | |
| Battery energy storage systems | Power cost coefficient (CNY/kW) | 2700 |
| Capacity cost coefficient (CNY/kWh) | 640 | |
| O&M cost coefficient (CNY/kWh) | 0.05 | |
| Charge/discharge efficiency | 80% | |
| SOC_max | 80% | |
| SOC_h / SOC_l / SOC_min | 70% / 30% / 20% | |
| Cycle life parameters | \(\delta_1=695, \delta_2=-435, \delta_3=17.3, \delta_4=735, \delta_5=-14.5\) |
We determine the optimal moving average window length by evaluating fluctuation rates. As shown in Figure 1 (not displayed here), a window length of 16 satisfies both 1-minute (9.635% < 10%) and 10-minute (32.56% < 33.3%) constraints. Thus, \(T=16\) is selected.
The original wind power and the smoothed grid-connected power are plotted. The fluctuating power is decomposed via DFT with a cutoff frequency of 1.67 mHz. The resulting power allocation between supercapacitor and battery energy storage systems is shown in Figure 2 (not displayed).
Applying the SOC-based control strategy, we compare the SOC trajectories with and without optimization. Without control, the SOC of both the supercapacitor and battery energy storage systems exceeds their allowable limits. With the proposed strategy, the SOC remains within the safe zones (0.2–0.8 for battery, 0.1–0.9 for supercapacitor), as illustrated in Figure 3 (not displayed).
We evaluate four configurations:
- Proposed: hybrid with SOC control
- Scheme 1: supercapacitor only
- Scheme 2: battery energy storage systems only
- Scheme 3: hybrid without SOC control
Table 2 summarizes the sizing results and annualized costs.
| Index | Proposed | Scheme 1 | Scheme 2 | Scheme 3 |
|---|---|---|---|---|
| Supercapacitor rated power (MW) | 4.709 | 12.381 | — | 4.709 |
| Supercapacitor rated capacity (MWh) | 1.337 | 35.642 | — | 1.486 |
| Battery rated power (MW) | 8.452 | — | 12.381 | 8.452 |
| Battery rated capacity (MWh) | 38.307 | — | 42.192 | 40.129 |
| Battery lifetime (years) | 4.39 | — | 2.25 | 3.89 |
| Annualized total cost (billion CNY) | 1.109 | 2.371 | 1.621 | 1.227 |
The results reveal that the proposed method reduces annual cost by 53.23% compared to supercapacitor-only, 31.59% compared to battery-only, and 9.62% compared to hybrid without SOC control. The improvement stems from the extended cycle life of battery energy storage systems achieved through SOC regulation. The supercapacitor-only scheme suffers from high capacity cost, while the battery-only scheme suffers from frequent deep cycles causing rapid degradation. Our hybrid with SOC control balances these issues and yields the lowest economic burden.
Conclusion
We have presented an optimal capacity configuration strategy for a hybrid energy storage system that integrates supercapacitors and battery energy storage systems for wind power smoothing. The moving average filter combined with spectrum analysis effectively separates power fluctuations into high- and low-frequency components. A novel SOC-aware control strategy partitions the SOC range and applies sigmoid-based power corrections to keep the storage devices within safe operating limits, thereby enhancing the cycle life of battery energy storage systems. The comprehensive cost model, which includes battery degradation, demonstrates the economic viability of the proposal. Simulation results confirm that the proposed method achieves superior fluctuation mitigation, improved SOC management, and a 9.62% reduction in annualized cost compared to a non-optimized hybrid system. This work provides a practical framework for the deployment of hybrid storage in renewable energy applications, with potential extensions to multi-source systems such as wind-solar-hydro hybrids.