In recent years, the rapid rise of the global energy internet, centered on “smart grid + ultra-high voltage grid + clean energy,” has highlighted the importance of integrating renewable sources like wind and solar power. However, the output of these clean energy sources is characterized by volatility and uncertainty, which, when connected to the grid on a large scale, increases the pressure on frequency regulation. Insufficient frequency regulation capacity also limits the grid’s ability to absorb clean energy. Energy storage batteries, with their fast response speed and flexible regulation methods, offer a promising solution for assisting grid frequency regulation, effectively improving grid frequency performance. Among the theoretical and technical issues to be addressed in applying energy storage batteries to grid auxiliary frequency regulation, capacity configuration is a key focus. This article proposes a capacity optimization method for energy storage batteries that considers rate characteristics, aiming to minimize the configured capacity and power while meeting high-power frequency regulation demands during low-probability step disturbances in the grid.
Currently, research on capacity configuration for energy storage batteries participating in grid frequency regulation primarily focuses on control strategies or evaluation metrics. However, during small-probability emergency (extreme) accidents, such as step disturbances, the grid’s frequency regulation capacity demand is significant. Using conventional methods for capacity configuration may lead to insufficient frequency regulation capacity or high opportunity costs and idle waste of frequency regulation capacity to ensure regulation effectiveness. By considering the rate characteristics of energy storage batteries and controlling them to charge/discharge at high rates during step disturbances, this issue can be effectively addressed. Frequency regulation applications for energy storage mainly balance power fluctuations lasting from tens of seconds to several minutes, featuring short duration, high power demand, and low energy demand. Considering rate characteristics in capacity configuration for frequency regulation energy storage batteries can effectively reduce the rated power configured to meet larger regulation demands in small-probability emergency accidents, lowering the opportunity cost of frequency regulation capacity. Moreover, high-rate charging/discharging of lithium batteries results in minimal capacity degradation. Therefore, fully leveraging the potential of rate characteristics to reduce the capacity/power demand of energy storage batteries is crucial for improving the economic benefits of energy storage battery applications and promoting their entry into the frequency regulation market. Against this background, this article investigates the capacity configuration of frequency regulation energy storage batteries considering rate characteristics. Using a single-area grid model, capacity optimization and comparative analysis are conducted based on frequency regulation demands for actual grid accident scenarios.
The charging/discharging rate of an energy storage battery, often referred to as the C-rate, is an important parameter characterizing its charging/discharging performance, commonly expressed in terms of time rate or multiple rate. The time rate indicates the discharging time at a specific current to a specified terminal voltage, while the multiple rate refers to the multiple of the discharging current value relative to the rated value. A higher multiple rate implies a faster charging/discharging rate, making it more suitable for responding to and tracking power command signals, thereby maintaining power system frequency stability. The higher the multiple rate, the greater the current borne by the energy storage battery. Under constant charging/discharging voltage, the multiple rate also refers to the overload multiple of the battery, i.e., the multiple of actual active output to rated power. The multiple rate discussed in this article refers to the overload multiple of the energy storage battery. When participating in grid frequency regulation, energy storage batteries charge/discharge at high multiple rates, meeting the grid’s high instantaneous power demand with a lower configured rated power.
Under ideal conditions, an energy storage battery charging/discharging at 1C can sustain for 1 hour, while at 2C, it can sustain for 0.5 hours. However, in actual charging/discharging processes, the sustainable charging/discharging capacity varies with the multiple rate. The specific relationship between multiple rate and sustainable time is determined by the corresponding battery’s charging/discharging curve, summarized as follows:
$$ T(N) = \begin{cases} t_1, & N \leq N_1 \\ \vdots & \\ t_i, & N \leq N_i \\ \vdots & \\ t_n, & N \leq N_n \end{cases} $$
where \( T(N) \) is the sustainable overload time, \( N \) is the battery’s charging/discharging multiple rate \( C \), with \( N_1 > \cdots > N_i > \cdots > N_n \), and \( t_i \) is the sustainable charging/discharging time corresponding to \( N_i \) obtained from the charging/discharging curve, with \( t_1 < \cdots < t_i < \cdots < t_n \). The specific variation pattern depends on the charging/discharging curves of various types of energy storage batteries.
Based on experimental data provided by some battery manufacturers for charging/discharging at different multiple rates, after fitting processing, the charging/discharging rate characteristic curves (partial) for lithium titanate batteries, lithium iron phosphate batteries, and lead-acid batteries are shown above. From the figure, it is evident that the sustainable time of an energy storage battery is inversely related to the charging/discharging multiple rate: the higher the multiple rate, the shorter the corresponding sustainable charging/discharging time. Lead-acid batteries exhibit significantly shorter sustainable charging/discharging times at high multiple rates compared to ideal conditions, due to severe capacity degradation during high-rate charging/discharging. In contrast, lithium batteries have better rate characteristics, with minimal capacity degradation at high rates, so their sustainable charging/discharging times are close to ideal.
Building on the described rate characteristics of energy storage batteries, a capacity optimization method for energy storage batteries assisting grid primary frequency regulation is proposed. The basic idea is as follows: First, determine the power response characteristics to frequency deviations under the corresponding control strategy. Then, based on constraints related to sustainable charging/discharging times at different multiple rates, select the multiple rate to determine the minimized rated power/capacity of the energy storage that meets the requirements. Finally, verify the frequency regulation effectiveness achieved by the determined configuration scheme. The optimization configuration model and method corresponding to this basic idea are described below.
The objective is to minimize the battery’s rated energy \( E_{\text{rate}} \) and rated power \( P_{\text{rate}} \) for capacity configuration optimization, with the objective function as follows:
$$ \min\{ P_{\text{rate}}, E_{\text{rate}} \} $$
In the objective function given above, \( E_{\text{rate}} \) and \( P_{\text{rate}} \) should satisfy the constraints of the energy storage battery’s charging/discharging rate characteristics and control strategy, as shown in the following equations:
$$ \begin{cases} P_{\text{rate}} \leq |P(N)| \\ N_b < N_{\text{max}} \\ T_b > T(N) \end{cases} $$
$$ \begin{cases} P_{0-\text{dis}} = P_{b-\text{dis}} N_{i-\text{dis}} \\ P_{0-\text{ch}} = P_{b-\text{ch}} N_{i-\text{ch}} \end{cases} $$
$$ P_{\text{rate}} = \max\left\{ \frac{P_{0-\text{dis}}}{\eta_{\text{dis}}}, P_{0-\text{ch}} \cdot \eta_{\text{ch}} \right\} $$
$$ \text{SOC}(t) = \text{SOC}_0 + \frac{\int_0^t \Delta P_k(t) dt}{E_{\text{rate}}} $$
$$ E_{\text{rate}} = \max \left\{ \frac{\max_{t \in D} \left[ \int_0^t \Delta P_k(t) dt \right]}{\text{SOC}_{\text{max}} – \text{SOC}_0}, \frac{-\min_{t \in D} \left[ \int_0^t \Delta P_k(t) dt \right]}{\text{SOC}_0 – \text{SOC}_{\text{min}}} \right\} $$
where \( P(N) \) is the output power limit of the energy storage battery at charging/discharging multiple rate \( N \), \( N_{\text{max}} \) is the maximum charging/discharging multiple rate value of the energy storage battery, \( N_b \) is the selected charging/discharging multiple rate value of the energy storage battery, \( P_{0-\text{dis}} \) (\( P_{0-\text{ch}} \)) is the discharging (charging) power of the energy storage battery at the corresponding multiple rate, \( P_{b-\text{dis}} \) (\( P_{b-\text{ch}} \)) is the grid’s active discharging (charging) demand power under load disturbance, \( N_{i-\text{dis}} \) (\( N_{i-\text{ch}} \)) is the discharging (charging) multiple rate of the energy storage battery under load disturbance, \( \eta_{\text{dis}} \) (\( \eta_{\text{ch}} \)) is the discharging (charging) efficiency of the energy storage battery (including conversion efficiency of DC/DC, DC/AC, and storage equipment), \( \Delta P_k \) is the real-time output of the energy storage battery determined by the primary frequency regulation control strategy (positive for charging, negative for discharging), the study duration is set as \( D \), \( \text{SOC}_0 \) is the initial state of charge, generally set to 0.5, and \( \text{SOC}_{\text{max}} \), \( \text{SOC}_{\text{min}} \) are the upper and lower limits of the state of charge of the energy storage battery, respectively.
According to the optimization configuration model given by the equations above, capacity optimization configuration for energy storage batteries participating in grid frequency regulation considering rate characteristics is performed. The specific steps are as follows:
1. Select the maximum allowable charging/discharging multiple rate \( N_i \) (\( N_i = N_{i-\text{dis}} \) or \( N_{i-\text{ch}} \)) for the energy storage battery. Simulate the energy storage battery’s participation in frequency regulation according to the control strategy to obtain the real-time output curve \( \Delta P_k(t) \), and configure the capacity using the equation for \( E_{\text{rate}} \).
2. Based on the selected multiple rate, combine with the relationship in equation \( T(N) \) to obtain the theoretical sustainable time \( T \) (the time the configured energy storage battery can sustain charging/discharging at multiple rate \( N \)).
3. According to the obtained real-time output curve of the energy storage battery, combined with its charging/discharging multiple rate-time relationship, obtain the actual sustainable time \( T’ \). Compare the theoretical sustainable time \( T \) with the actual sustainable time \( T’ \) from simulation. If \( T > T’ \), it indicates that the energy storage battery meets the frequency regulation demand at this multiple rate. Then, determine the rated power \( P_{\text{rate}} \) and rated energy \( E_{\text{rate}} \) of the energy storage battery based on the equations for \( P_{\text{rate}} \) and \( E_{\text{rate}} \) (both rated power and rated energy are obtained based on the energy storage output curve under corresponding conditions). Otherwise, reduce the charging/discharging multiple rate (extend the overload sustainable time) and return to step 2 until the condition is met and the frequency regulation effect is verified, completing the optimization configuration of the energy storage.
It should be noted that the output and sustainable charging/discharging time of the energy storage battery depend on the output process determined by the control strategy, which may not necessarily match the charging/discharging power and sustainable time corresponding to the rate characteristics. For ease of comparison, the actual sustainable time of the output under the corresponding control strategy should be converted to an equivalent sustainable time based on rate characteristic constraints. This article refers to the rainflow counting method for charging/discharging cycle conversion and proposes a method to convert the actual charging/discharging time of the energy storage battery to an equivalent sustainable time. The conversion process is as follows: define the time equivalent coefficient \( \alpha \) for the energy storage battery, as shown in the equation below, where \( T(N_i) \) is the sustainable charging/discharging time corresponding to the real-time charging/discharging multiple rate \( N_i \) of the energy storage battery, and \( T(N_n) \) is the sustainable charging/discharging time related to the maximum charging/discharging multiple rate \( N_n \) determined by the control strategy output. \( \alpha(t_{n_i}) \) is the equivalent time conversion coefficient for the charging/discharging process at multiple rate \( N_i \) converted to multiple rate \( N_n \).
$$ \alpha(t_{n_i}) = \frac{T(N_n)}{T(N_i)} $$
For the actual output variation curve of the energy storage battery during the action time, use the equivalent coefficient to perform equivalent conversion of the actual sustainable time \( T’ \), as shown in the equation below, where \( \Delta T_i \) is the actual action time of the energy storage battery at multiple rate \( N_i \).
$$ T’ = \sum_{i=1}^n \alpha(t_{n_i}) \cdot \Delta T_i $$
It should be noted that the evaluation indicators for frequency regulation effectiveness are usually related to load disturbance characteristics. This article focuses on step load disturbance situations and uses time-domain evaluation indicators such as \( \Delta f_m \), \( \Delta f_s \), and \( \Delta o_m \) to quantitatively evaluate the effectiveness of energy storage batteries participating in rapid grid frequency regulation. Here, \( \Delta f_m \) and \( \Delta f_s \) are the maximum frequency deviation and steady-state frequency deviation after disturbance, respectively, and \( \Delta o_m \) is the maximum rate of change of frequency deviation. These indicators reflect the main characteristics of the grid frequency change trajectory during frequency regulation, where smaller values of \( \Delta f_m \) and \( \Delta f_s \) indicate more significant frequency regulation effectiveness, and a smaller \( \Delta o_m \) indicates stronger grid frequency regulation capability and faster frequency response, i.e., better grid frequency stability.
To verify the effectiveness and adaptability of the proposed method, a single-area equivalent model of an actual grid is constructed, and simulations are conducted based on typical non-peak load and peak load conditions. Corresponding grid parameters and frequency regulation effectiveness indicator requirements are shown in Table 1 below. First, the capacity configuration results considering and not considering rate characteristics are compared to verify the method’s effectiveness. On this basis, capacity configuration results for different types of energy storage batteries and under different control strategies considering rate characteristics are compared. The basic parameters of the energy storage battery are set as shown in Table 1 (setting energy storage conversion efficiencies \( \eta_{\text{dis}} \), \( \eta_{\text{ch}} \) as 1).
| Index | Condition 1 (Non-Peak Load) | Condition 2 (Peak Load) |
|---|---|---|
| \( S_B \) (MVA) | 150 | 250 |
| \( \Delta p_{L_{\text{max}}} \) (pu·MW) | 0.2 | 0.12 |
| \( K_G \) (pu·MW·pu·Hz⁻¹) | 23.34 | 20 |
| \( M \) (s) | 7 | 9 |
| \( D \) (pu·MW·pu·Hz⁻¹) | 1 | 1 |
| \( \Delta o_m \) (pu·Hz·s⁻¹) | 0.024 | -0.012 |
| \( \Delta f_m \) (pu·Hz) | 0.02 | -0.013 |
| \( \Delta f_s \) (pu·Hz) | 0.0072 | -0.005 |
To analyze the advantages of considering rate characteristics in configuring frequency regulation energy storage battery capacity, this article ignores the configuration specifications of capacity and power in actual battery production and compares the capacity configuration of lithium iron phosphate batteries considering and not considering rate characteristics (where energy storage batteries charge/discharge at conventional rates) under inertial-droop control in two conditions. According to the proposed capacity configuration method, with the relationship of the lithium iron phosphate battery’s charging/discharging rate characteristic curve as constraints and minimizing the configured rated power as the objective, capacity configuration under inertial-droop control for two conditions is performed. The constraint conditions corresponding to the lithium iron phosphate battery’s rate characteristic curve are as shown in the figure above, with the objective function same as before, and the configuration results calculated according to the equations are shown in Table 2 below.
| Condition | Control Strategy | \( P_{\text{rate}} \) (MW) | \( E_{\text{rate}} \) (kWh) |
|---|---|---|---|
| 1 | Without Considering Rate Characteristics | 11.54 | 13.3 |
| Considering Rate Characteristics | 0.8244 | ||
| 2 | Without Considering Rate Characteristics | 5.85 | 6.6 |
| Considering Rate Characteristics | 0.4877 |
From Table 2, it can be seen that under the premise of meeting grid frequency regulation indicator requirements, the lithium iron phosphate battery under this control strategy, when considering rate characteristics, requires a significantly lower configured rated power value compared to not considering rate characteristics, with no change in rated energy (determined by the control strategy and grid power demand). At present, the application of energy storage in the grid is mainly limited by economic factors. The better the rate characteristics of the energy storage battery, the smaller the required rated power value under the same demand scenario, generally resulting in lower opportunity costs for frequency regulation capacity. This helps improve the economic feasibility of energy storage applications and address issues of insufficient grid frequency regulation capacity.
To study the impact of rate characteristics of different types of energy storage batteries on frequency regulation capacity configuration, using the method in this article, capacity optimization under inertial-droop control is performed for lithium iron phosphate batteries, lithium titanate batteries, and lead-acid batteries under the conditions listed in Table 1, with results shown in Tables 3 and 4 below.
| Battery Type | Overload Multiple Rate | \( P_{\text{rate}} \) (kW) | \( E_{\text{rate}} \) (kWh) |
|---|---|---|---|
| Lithium Titanate | 20 | 577.1 | 13.3 |
| Lithium Iron Phosphate | 14 | 824.4 | |
| Lead-Acid | 2 | 5771.0 |
| Battery Type | Overload Multiple Rate | \( P_{\text{rate}} \) (kW) | \( E_{\text{rate}} \) (kWh) |
|---|---|---|---|
| Lithium Titanate | 17 | 344.3 | 6.6 |
| Lithium Iron Phosphate | 12 | 487.7 | |
| Lead-Acid | 3 | 1950.9 |
From Table 3, for different types of energy storage batteries under the same control strategy, lithium titanate batteries have superior high-rate charging/discharging performance, requiring the smallest configured rated power value under Condition 1, followed by lithium iron phosphate batteries, and lead-acid batteries the largest, with lithium titanate batteries requiring the smallest power/capacity configuration under inertial-droop control. Although lead-acid batteries are mature and low-cost, they suffer severe capacity degradation at high rates, so rate characteristics are generally not considered in their use.
From Table 4, under Condition 2, the configuration results are basically similar to Condition 1. Under the premise of meeting grid frequency regulation indicator requirements, lithium titanate batteries considering rate characteristics under inertial-droop control strategy charge/discharge at high rates with lower rated power values. The charging/discharging multiple rates of lead-acid batteries are much lower than those of lithium titanate and lithium iron phosphate batteries, with lithium titanate batteries having slightly better rate characteristics than lithium iron phosphate batteries. Fully utilizing the good rate characteristics of lithium batteries (lithium titanate or lithium iron phosphate) can effectively reduce the required rated power of energy storage batteries, thereby lowering the opportunity cost of energy storage battery configuration. If considering the production configuration specifications of energy storage batteries in engineering practice, the rated power can be prioritized, and then the minimum rated energy matching production technology capabilities can be selected based on actual specifications.
To study the impact of considering energy storage battery rate characteristics under different control strategies on frequency regulation capacity configuration, taking lithium iron phosphate batteries as an example, capacity configuration is performed based on three control methods: power-droop control, inertial-droop control, and typical fixed-droop control, combined with their rate characteristics. Inertial-droop control involves the energy storage battery outputting according to virtual inertial control (output proportional to the rate of change of frequency deviation) at the moment of engagement, switching to droop control (output proportional to frequency deviation) when the frequency deviation reaches its maximum. Constant power-droop control involves the energy storage battery outputting at maximum power (rated power \( P_{\text{rate}} \)) at the moment of disturbance, switching to droop control when the frequency deviation is maximum. Both methods control and switch energy storage battery output based on the rate of change of frequency deviation and frequency deviation. Fixed-droop control uses frequency deviation as the decision variable, always controlling energy storage battery output with a constant regulation coefficient.
| Condition | Control Strategy | Overload Multiple Rate | \( P_{\text{rate}} \) (kW) | \( E_{\text{rate}} \) (kWh) |
|---|---|---|---|---|
| 1 | Inertial-Droop | 14 | 824.4 | 13.3 |
| Fixed-Droop | 10 | 888.3 | 14.9 | |
| Power-Droop | 8 | 1068.8 | 15.9 | |
| 2 | Inertial-Droop | 12 | 487.7 | 6.6 |
| Fixed-Droop | 9 | 531.8 | 8.6 | |
| Power-Droop | 7 | 666.4 | 9.5 |
From Table 5, in both conditions, when considering the rate characteristics of lithium iron phosphate batteries under different control strategies, under the premise of meeting frequency regulation indicator requirements, inertial-droop control allows the highest battery multiple rate, followed by fixed-droop control, and power-droop control the smallest. That is, in this step disturbance scenario, inertial-droop control requires the smallest configured rated power value, followed by fixed-droop control, and power-droop control has the highest power demand. Under all three control strategies, lithium iron phosphate batteries have relatively high multiple rates, verifying their good charging/discharging rate characteristics.
In summary, this article investigates capacity optimization configuration for frequency regulation energy storage batteries considering rate characteristics, with main conclusions as follows:
1. The capacity configuration method for frequency regulation energy storage batteries considering rate characteristics takes the battery’s own rate characteristics as the main constraint and aims to minimize the required configured capacity/power for optimization configuration. It can address issues of insufficient frequency regulation capacity or high opportunity costs due to large instantaneous power demands during low-probability step disturbances.
2. For the same type of energy storage battery, the configuration scheme is related to the control strategy. When considering rate characteristics, inertial-droop control requires the smallest configured rated power for the energy storage battery, followed by fixed-droop control, and power-droop control the largest.
3. For the same control strategy, the configuration scheme is related to the type of energy storage battery. When considering rate characteristics, lithium titanate batteries show the most significant reduction in required configured power demand, followed by lithium iron phosphate batteries, while considering lead-acid battery rate characteristics shows no significant improvement in configuration results.
The proposed method provides some reference for the selection and control strategy of energy storage batteries applied in other grid scenarios. Future research needs to further investigate the impact of rate characteristics on the lifespan of energy storage batteries and the techno-economic comparison of high-rate charging/discharging applications for energy storage batteries.
Throughout this discussion, the importance of energy storage batteries in modern power systems cannot be overstated. The integration of energy storage batteries into frequency regulation services not only enhances grid stability but also facilitates the adoption of renewable energy sources. By optimizing the configuration of energy storage batteries with consideration of their rate characteristics, we can achieve more efficient and cost-effective solutions for grid management. The energy storage battery technology continues to evolve, and with advancements in materials and control algorithms, the potential for these systems to contribute to grid services will only increase. Therefore, ongoing research and development in this area are essential for realizing the full benefits of energy storage batteries in the energy landscape. The energy storage battery represents a key component in the transition towards a more resilient and sustainable power system, and its role in frequency regulation is a critical application that warrants further exploration and investment. As we move forward, the continued focus on improving the performance and reducing the costs of energy storage batteries will be paramount in ensuring their widespread deployment and integration into the grid. The energy storage battery is not just a tool for frequency regulation but a versatile asset that can provide multiple services, including peak shaving, load leveling, and backup power, making it a cornerstone of future smart grids. The optimization of energy storage battery configuration, particularly when considering rate characteristics, is therefore a vital area of study that bridges technical challenges and economic considerations, paving the way for more robust and adaptive power systems worldwide.