As a researcher deeply involved in the field of power system operation and optimization, I have dedicated significant effort to investigating how a battery energy storage system can effectively assist thermal power units in secondary frequency regulation. The integration of a battery energy storage system offers the advantages of rapid response and high tracking accuracy. However, improper power allocation can accelerate battery degradation, increase operational costs, and reduce economic benefits. Therefore, it is crucial to develop a reasonable power allocation strategy that not only ensures excellent frequency regulation performance but also extends the lifespan of the battery energy storage system and improves overall economic returns. In this work, I present a comprehensive analysis of three typical power allocation strategies, including proportional allocation, differential allocation, and frequency-based allocation, considering the dynamic model of a lithium-ion battery energy storage system, its aging characteristics, and the actual operational data from a 660 MW thermal power unit in Jiangsu Province.
The remainder of this article is organized as follows. First, I establish a mathematical model for the battery energy storage system using a second-order RC equivalent circuit and identify the model parameters via a limited memory recursive least squares algorithm. Second, I introduce the coordinated frequency regulation framework and detail the three power allocation strategies. Then, I evaluate the frequency regulation performance, battery life, and economic benefits through simulations driven by real AGC data. Finally, I compare the results and draw conclusions.
1. Modeling of the Battery Energy Storage System
To accurately represent the dynamic behavior of the battery energy storage system, I employed a second-order RC equivalent circuit model, as shown in Figure 1. This model captures both the ohmic resistance and the polarization effects through two RC networks. The circuit consists of an ohmic internal resistance $R_0$, a charge transfer resistance $R_1$ with capacitance $C_1$, and a concentration resistance $R_2$ with capacitance $C_2$. The open-circuit voltage $U_{oc}$ is related to the terminal voltage $U$ and current $I$ by:
$$
U_{oc} = \left( \frac{R_1}{R_1 C_1 s + 1} + \frac{R_2}{R_2 C_2 s + 1} + R_0 \right) I + U
$$
where $s$ is the frequency variable. I selected a lithium iron phosphate (LiFePO₄) battery with a rated capacity of 3.3 Ah and a rated voltage of 3.6 V. The experimental data were sourced from a public dataset from the University of Maryland. Using the limited memory least squares recursive algorithm, I identified the parameters at a state of charge (SOC) of 50%: $R_0 = 0.0253\ \Omega$, $R_1 = 0.0087\ \Omega$, $R_2 = 0.0318\ \Omega$, $C_1 = 43.79\ \text{F}$, $C_2 = 1480\ \text{F}$. The model validation showed that the simulation voltage deviates from the experimental voltage by only 0.0524%, confirming its accuracy.
To construct a practical battery energy storage system for a 660 MW thermal unit, I connected multiple cells in series ($M=375$) and parallel ($N=4480$) to achieve the required voltage and capacity. The rated power of the battery energy storage system was set to 3% of the thermal unit’s capacity, i.e., $P_c = 19.8\ \text{MW}$. The initial SOC was set to 80% to ensure both charging and discharging capabilities. The transfer function model of the entire battery energy storage system is illustrated in Figure 3 of the original work.
2. Coordinated Frequency Regulation Framework and Power Allocation Strategies
In the coordinated frequency regulation framework, the automatic generation control (AGC) signal is distributed between the thermal unit and the battery energy storage system. The thermal unit responds to low-frequency components, while the battery energy storage system handles high-frequency components, thereby improving overall tracking performance. I analyzed the following three strategies:
2.1 Proportional Allocation Strategy
This strategy distributes the AGC power instruction $P_{AGC}$ in proportion to the rated powers of the thermal unit ($P_g$) and the battery energy storage system ($P_c$):
$$
P_{g, AGC} = \frac{P_g}{P_g + P_c} P_{AGC}, \quad P_{c, AGC} = \frac{P_c}{P_g + P_c} P_{AGC}
$$
This method is simple but often results in poor frequency regulation performance because it does not account for the dynamic response characteristics of the thermal unit.
2.2 Differential Allocation Strategy
In this strategy, the thermal unit receives the full AGC signal first. Then, the difference between the AGC instruction and the actual thermal output is assigned to the battery energy storage system. If the thermal unit lags, the battery energy storage system discharges to compensate; if it overshoots, the battery energy storage system charges. This approach ensures high tracking accuracy but leads to frequent and high-rate charge/discharge cycles, which accelerate battery aging.
2.3 Frequency-Based Allocation Strategy
This strategy uses a digital filter (Finite Impulse Response filter, 200th order, sampling frequency 1 Hz, cutoff frequency 0.007 Hz) to decompose the AGC signal into low-frequency and high-frequency components. The low-frequency part is sent to the thermal unit, and the high-frequency part is sent to the battery energy storage system. This leverages the fast response of the battery energy storage system for high-frequency fluctuations while protecting the battery from excessive deep cycles. The signal decomposition is illustrated in Figure 7 of the original study.
The following table summarizes the key characteristics of the three strategies:
| Strategy | Operation Scenario | Advantages | Disadvantages |
|---|---|---|---|
| Proportional | Suitable for small frequency deviations | Simple logic, easy implementation | Poor regulation performance, low economic benefit |
| Differential | When thermal unit and BESS handle different frequencies | High tracking accuracy, minimal impact on thermal unit | Frequent charging/discharging, fast battery degradation |
| Frequency-based | Complex regulation tasks requiring precise signal splitting | Excellent performance, extends battery life | Dependence on filter technology, more complex implementation |
3. Evaluation of Frequency Regulation Performance and Battery Life
I conducted simulations using actual AGC command data from a 660 MW thermal unit in Jiangsu. The frequency regulation performance was evaluated using the metric $K_P$, which accounts for both regulation speed and accuracy, as defined by the Jiangsu power ancillary service market rules. The regulation speed $V_i$ and accuracy $A_i$ for the $i$-th AGC event are calculated as:
$$
V_i = \frac{P_g(t_2) – P_g(t_1)}{t_2 – t_1}, \quad A_i = \frac{\int |P_g(t) – P_{agc}(t_i)| dt}{t_0 – t_2}
$$
The overall $K_P$ is the weighted average over all events, with weights being the positive regulation mileage $D^+$.
The simulation results in Figure 8 of the original work show that the differential strategy yields the best tracking performance, followed by the frequency-based strategy, while the proportional strategy is only slightly better than the thermal unit alone. The daily $K_P$ values are summarized below:
| Strategy | Thermal Only | Proportional | Differential | Frequency-based |
|---|---|---|---|---|
| $K_P$ | ~0.95 | ~0.96 | ~1.85 | ~1.60 |
Battery life was assessed using a capacity fade model based on the HRL laboratory’s empirical equation:
$$
Q_{loss} = B \exp\left( \frac{-31700 + 370.3 C_{rate}}{RT} \right) A_h^{0.55}
$$
where $Q_{loss}$ is the capacity loss percentage, $B$ is the pre-exponential factor depending on the discharge rate $C_{rate}$, $R$ is the gas constant, $T$ is the absolute temperature, and $A_h$ is the ampere-hour throughput. For non-constant current profiles, I discretized the operation into intervals and summed the contributions. Assuming a constant temperature of 298 K, I calculated the time for capacity to decay from 100% to 80% (end of life) under each strategy. The results are shown in Table 3.
| Strategy | Proportional | Differential | Frequency-based |
|---|---|---|---|
| Battery life (days) | 269 | 554 | 681 |
It is evident that the proportional strategy not only yields the worst regulation performance but also accelerates battery aging. The differential strategy provides excellent regulation but shortens battery life. The frequency-based strategy strikes a good balance, achieving satisfactory regulation while significantly prolonging the battery energy storage system lifespan.
4. Economic Benefit Analysis
To compare the economic viability, I considered costs and revenues over a 9-year project lifetime with 300 operating days per year. The costs include equipment cost $C_d$, construction cost $C_e$, and operation and maintenance cost $C_f$, defined as:
$$
C_d = K_a E_c + K_b P_c + K_c E_c, \quad C_e = K_e E_c, \quad C_f = K_f P_c
$$
where $K_a = 0.95\ \text{million RMB/MWh}$, $K_b = 0.32\ \text{million RMB/MW}$, $K_c = 0.48\ \text{million RMB/MWh}$, $K_e = 0.95\ \text{million RMB/MWh}$, $K_f = 0.05\ \text{million RMB/MW}$. Revenues consist of basic compensation $F$ and dispatch compensation $F_D$, given by:
$$
F = K_{agc} P_{agc} L_{agc} \min(K_P, 2), \quad F_D = D K_P B_{agc}
$$
where $K_{agc} = 2\ \text{RMB/MW}$, $P_{agc} = 0.5P_g + P_c$, $L_{agc} = 100\%$, $B_{agc} = 1\ \text{RMB/MW}$, and the effective mileage $D = D^+ – D^-$ (with penalty factor $K_d = 1$). Battery replacement costs were included based on the calculated lifetimes. The differential strategy requires 5 battery replacements, while the frequency-based strategy requires 4. The costs and net benefits are summarized in Table 4 and Table 5.
| Strategy | $C_d$ | $C_e$ | $C_f$ | Total Cost |
|---|---|---|---|---|
| Differential | 10,989 | 297 | 891 | 12,177 |
| Frequency-based | 9,108 | 297 | 891 | 10,296 |
| Strategy | $F$ | $F_D$ | Total Revenue | Net Benefit |
|---|---|---|---|---|
| Differential | 5,951 | 16,138 | 22,089 | 9,912 |
| Frequency-based | 5,652 | 15,150 | 20,802 | 10,506 |
Although the differential strategy generates slightly higher revenue due to better $K_P$, its higher replacement costs result in a net benefit of 9,912 million RMB, whereas the frequency-based strategy yields a net benefit of 10,506 million RMB — an advantage of 594 million RMB. This demonstrates that the frequency-based allocation strategy not only improves frequency regulation performance but also maximizes the economic return by extending the battery energy storage system life.
5. Conclusion
Through this investigation, I have reached the following conclusions:
- The second-order RC equivalent circuit model for the battery energy storage system was accurately identified using limited memory least squares, with simulation errors below 0.06%.
- Among the three power allocation strategies, the proportional strategy yields the worst frequency regulation performance and the fastest battery degradation. The differential strategy achieves the best tracking but leads to a battery life of only 554 days. The frequency-based strategy provides good regulation performance while extending battery life to 681 days.
- Economic analysis over a 9-year horizon reveals that the frequency-based strategy offers a net benefit of 10,506 million RMB, which is 594 million RMB higher than the differential strategy, despite slightly lower revenue. This is primarily due to reduced battery replacement costs.
- The frequency-based power allocation strategy is recommended for battery energy storage system applications in secondary frequency regulation, as it effectively balances frequency regulation performance, battery longevity, and economic benefits.
Future work will focus on optimizing the capacity configuration of the battery energy storage system and further refining the control strategies to adapt to varying grid conditions and market rules.