In my research, I focus on the power balancing allocation method for hybrid energy storage systems that integrate lithium batteries and supercapacitors. The combination of these two technologies leverages the high energy density of lithium batteries and the high power density of supercapacitors, ensuring stable energy output. However, the hybrid energy storage system faces power balancing issues due to differing response speeds and charge-discharge characteristics. To address this, I propose a method that prioritizes the supercapacitor’s response to power fluctuations and adjusts the power output of the lithium battery accordingly, achieving effective power balancing for the overall system. This approach significantly reduces the burden on battery energy storage systems, prolongs their lifespan, and enhances the stability of the power grid.
The hybrid energy storage system structure I analyze consists of a lithium battery bank and a supercapacitor bank connected through a common DC bus. The lithium battery is modeled as a controlled voltage source in series with a constant resistance, with state of charge (SOC) as the state variable. The output voltage of the lithium battery model is given by:
$$
U_b = E_0 – K \frac{Q_b}{Q_b – \int I_b dt} + \Phi \exp\left(-\Gamma \int I_b dt\right) – R_\gamma I_b
$$
where $E_0$ is the internal potential, $Q_b$ is the rated capacity, $\int I_b dt$ is the cumulative charge/discharge amount, $\Phi$ is the voltage sag in the exponential zone, $\Gamma$ is the reciprocal of the capacity in the exponential zone, $K$ is the polarization voltage, $R_\gamma$ is the equivalent internal resistance, and $I_b$ is the current. When $I_b > 0$, the battery is discharging; conversely, it is charging.
The supercapacitor is modeled using an RC series circuit, consisting of an ideal capacitor $C$ and a series resistance $R_e$. The terminal voltage $U_{sc}$ and current $I_{sc}$ satisfy:
$$
U_{sc} = \frac{1}{C} \int I_{sc} dt + R_e I_{sc}
$$
The stored energy $J_{SC}$ in the supercapacitor is expressed as:
$$
J_{SC} = \frac{1}{2} C \left(U_{\max}^2 – U_{\min}^2\right)
$$
where $U_{\max}$ and $U_{\min}$ are the maximum and minimum operating voltages, respectively.
In my power balancing allocation method, I first apply a first-order low-pass filter to perform initial power allocation for the hybrid energy storage system. The reference power for the lithium battery and supercapacitor is calculated as:
$$
P_{b\_ref} = \frac{1}{1 + t\sigma} P_{Hess}, \quad P_{sc\_ref} = \frac{t\sigma}{1 + t\sigma} P_{Hess}
$$
where $P_{Hess}$ is the total hybrid energy storage system power demand, $t$ is the filter time constant, and $\sigma$ is the differential operator. When $P_{x\_ref} > 0$, the component is in a discharging state; when $P_{x\_ref} < 0$, it is charging.
Based on the initial allocation, I divide the supercapacitor’s SOC into five distinct regions to perform secondary power allocation. The regions are defined by thresholds: $SOC_{sc\_min}$ (minimum safe SOC), $SOC_{sc\_L}$ (low warning), $SOC_{sc\_H}$ (high warning), and $SOC_{sc\_max}$ (maximum safe SOC). The following table summarizes the control actions for each region:
| Region | SOC Range | Supercapacitor Power Adjustment ($P_{sc\_sec}$) |
|---|---|---|
| Over-discharge | $SOC_{sc} < SOC_{sc\_min}$ | Stop discharging; charge at $2 \times P_{sc\_ref}$ if $P_{sc\_ref} < 0$; else $P_{sc\_sec}=0$ |
| Over-discharge warning | $SOC_{sc\_min} \le SOC_{sc} < SOC_{sc\_L}$ | Limit discharging; boost charging rate. If $P_{sc\_ref} > 0$, then $P_{sc\_sec}=0$; if $P_{sc\_ref} < 0$, then $P_{sc\_sec} = 2 \times P_{sc\_ref}$ |
| Normal operation | $SOC_{sc\_L} \le SOC_{sc} \le SOC_{sc\_H}$ | $P_{sc\_sec} = P_{sc\_ref}$ (no adjustment) |
| Over-charge warning | $SOC_{sc\_H} < SOC_{sc} \le SOC_{sc\_max}$ | Limit charging; boost discharging rate. If $P_{sc\_ref} > 0$, then $P_{sc\_sec} = 2 \times P_{sc\_ref}$; if $P_{sc\_ref} < 0$, then $P_{sc\_sec}=0$ |
| Over-charge | $SOC_{sc} > SOC_{sc\_max}$ | Stop charging; discharge at $2 \times P_{sc\_ref}$ if $P_{sc\_ref} > 0$; else $P_{sc\_sec}=0$ |
The secondary allocation for the lithium battery is then determined by the power balance equation:
$$
P_{b\_sec} = P_{Hess} – P_{sc\_sec}
$$
This ensures that any power surplus or deficit that the supercapacitor cannot handle is absorbed by the lithium battery. The overall goal is to minimize the direct response burden on the lithium battery, leveraging the supercapacitor’s fast response capability to smooth power fluctuations. By doing so, I effectively enhance the power balancing performance of battery energy storage systems in hybrid configurations.
To validate the proposed method, I conducted experiments on a wind-solar hybrid power station equipped with a hybrid energy storage system consisting of lithium batteries and supercapacitors. The station has a total area of 80,000 m², with solar panels occupying 50,000 m². The rated power output of the renewable generation is 30 kW. The load demand varies over a 2.5-hour period: 25 kW for the first 0.5 hours, 40 kW from 0.5 to 1.5 hours, and 35 kW from 1.5 to 2.5 hours. I compared the system performance with and without applying my power balancing method. The results are summarized in the following table:
| Parameter | Before Applying Method | After Applying Method |
|---|---|---|
| Lithium battery power fluctuation | Severe fluctuations, large peaks | Stable, smooth transitions |
| Supercapacitor power fluctuation | Erratic, high-frequency variations | Controlled, rapid but limited amplitude |
| DC bus voltage variation | Voltage dips and spikes up to 15% | Minimal variation (< 3%) |
| Circulating current between components | Observed during 0.5–1.5 h interval | No circulating current |
| SOC decline trend | Rapid decline, uneven | Gradual and uniform decline |
| Final SOC after 2.5 h | ~45% for lithium battery | ~62% for lithium battery |
The experimental data clearly demonstrate that my method effectively achieves power balancing for the hybrid energy storage system. The lithium battery and supercapacitor operate with stable power output, the bus voltage is well regulated, and the SOC decreases uniformly without over-charge or over-discharge conditions. Furthermore, the absence of circulating currents protects the battery energy storage systems from accelerated aging.
To further evaluate the long-term reliability of my method, I monitored the hybrid energy storage system over a 12-month period for unplanned outages caused by over-charge or over-discharge. The results are presented below:
| Month | Outages Due to Over-charge | Outages Due to Over-discharge |
|---|---|---|
| 1 | 0 | 0 |
| 2 | 1 | 0 |
| 3 | 0 | 1 |
| 4 | 0 | 0 |
| 5 | 0 | 0 |
| 6 | 0 | 1 |
| 7 | 0 | 0 |
| 8 | 1 | 0 |
| 9 | 0 | 0 |
| 10 | 1 | 1 |
| 11 | 0 | 1 |
| 12 | 0 | 0 |
| Total | 3 | 4 |
The total number of unplanned stoppages over 12 months was only 7, indicating that my power balancing allocation method significantly reduces the risk of over-charge and over-discharge events. This demonstrates the robustness and reliability of the approach for long-term operation of battery energy storage systems in hybrid configurations.
In conclusion, I have developed a practical and effective power balancing allocation method for hybrid energy storage systems that combine lithium batteries and supercapacitors. By prioritizing the supercapacitor’s fast response and adjusting the lithium battery power based on the supercapacitor’s SOC regions, the system achieves stable power output, minimal bus voltage variation, and improved SOC management. The method not only enhances the performance of battery energy storage systems but also extends their operational life by avoiding extreme charge/discharge states and circulating currents. My research provides a valuable solution for modern energy systems that require high efficiency, stability, and reliability.