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A cost accounting method of the Liion battery energy storage system for frequency regulation considering the effect of life degradation
Protection and Control of Modern Power Systems volume 3, Article number: 4 (2018)
Abstract
The cost of Energy Storage System (ESS) for frequency regulation is difficult to calculate due to battery’s degradation when an ESS is in gridconnected operation. To solve this problem, the influence mechanism of actual operating conditions on the life degradation of Liion battery energy storage is analyzed. A control strategy of Liion ESS participating in grid frequency regulation is constructed and a cost accounting model for frequency regulation considering the effect of battery life degradation is established. The estimated operating life and annual average cost of the Liion ESS under different dead bands and SOC setpoints are calculated. The case studies show that the estimated operating life of the Liion ESS under the actual operating condition differs significantly from the nominal life provided by the manufacturer under the standard condition and the full discharge mode. This paper provides an accurate costing method for the ESS participating in grid frequency regulation to help the promotion of the ESS to participate in the ancillary service market.
Introduction
Fossil fuelbased energy model has caused serious environmental problems whereas wind power development has gradually become an important way to push lowcarbon energy transition. However, with increased largescale wind power being centrally connected to the grid and replacing traditional frequency regulation units, power systems with high wind power penetration are facing a severe frequency regulation issue. In addition, the high randomness and variation of wind power lead to frequent action of traditional frequency regulation units resulting in increased abrasion of the mechanical devices and reduced operating life. Therefore, it is urgent to develop a new frequency regulation method for power systems.
The Liion ESS has flexibility and fast response characteristic, and largescale application of Liion ESS has attracted extensive attention. However, current energy storage costs are relatively high and there is no effective frequency regulation compensation mechanism for ESSs in China. Therefore, the incentive for ESS to participate in power system frequency regulation has not been established. Consequently, some energy storage stations have not been fully utilized, resulting in a waste of resources. Accounting the cost of energy storage for frequency regulation is an important step for the development of energysaving frequency regulation compensation strategy, which can help to promote the development of ESS to participate in the frequency regulation service market.
Energy storage frequency regulation cost is related to not only the technology and economy of the ESS itself but also energy storage frequency regulation strategy, system frequency fluctuation characteristics etc. Previous researches have provided useful insights in these respects. The cost of ESS is closely related to its operating life which is affected by the operating conditions (chargedischarge power, depth of discharge) [1, 2], ambient temperature and other factors. The nominal life given by the manufacturers is the test result in a specific chargedischarge mode measured by the cycle chargedischarge time. When an ESS participates in grid frequency regulation, the chargedischarge mode will not be the same as the test conditions, resulting in the ESS operating life under frequency regulation mode being very different from the data given by manufacturers. Previous cost accounting method is based on the average cost of nominal life, which is very different from the actual cost. Therefore, it is an urgent need to develop a cost accounting method for frequency regulation of ESS considering the effect of life degradation.
Some domestic researchers have proposed a method that the ESS life is expressed as a sum of the available throughputs (A·h). This method introduces the grid’s previous scheduling function to build a dynamic optimization model to calculate the cost and economic aspect [3, 4]. Overseas researchers tend to convert energy storage life into a percentage to combine with the control strategy for participation in frequency regulation to calculate its economic aspect [5,6,7]. Realtime price of energy storage market should be considered for cost calculation. The current market price of the Liion ESS is 2500–4500 (yuan / kWh), which has gone down by 60% compared to 2010 [8, 9]. Taking primary frequency regulation as an example, references [10, 11] analyzed the model combining wind power and energy storage, and proposed an ESS’s control strategy to reduce wind curtailment and to participate in primary frequency regulation. With the maximum profit of windstorage combination as the objective, an optimization model of ESS was established. For secondary frequency regulation, references [12,13,14] drew a conclusion that the annual investment cost of one ESS is 2.7–4.7 times as a heatengine plant. However, the ESS is superior in the operation and maintenance costs. Existing researches have focused on the optimization of control strategies and the economic benefits, while the degradation of life was only considered under a given control strategy and given frequency regulation modes [15,16,17,18]. Therefore, current studies are short of a comprehensive and effective cost accounting method, which does not encourage the formation of ancillary service compensation mechanism, restrict the development of the ESS, and even hamper the grid integration of largescale wind power.
This paper focuses on the cost accounting of the ESS to participate in power system frequency regulation. In Section 2, Liion battery life degradation model is constructed. Section 3 shows the influence mechanism of actual operating conditions on energy storage life degradation. A frequency regulation control strategy and an ESS frequency regulation cost accounting model considering life degradation are established in Section 4. The estimated operating life and the annual cost of the ESS under different frequency dead bands and SOC setpoints are analyzed in Section 5, whereas Section 6 draws the conclusions.
Methods
Liion battery life degradation model
Under given chargedischarge mode and ambient temperature, the Liion battery cycle life refers to the cycle chargedischarge time until the battery capacity retention rate drops down to the specified nominal capacity value.
The Liion energy storage life degradation refers to life loss caused by the deterioration of battery functional properties and changes of working conditions. The life degradation is closely related to battery cycle time, chargedischarge status, temperature and other factors. It is expressed as a percentage reduction of Liion battery cycle life, and includes static degradation and dynamic degradation as:
The static degradation X_{ S } is caused by the degradation of functional properties of the Liion battery, including the thickening of the electrolyte interface film, the oxidation of electrolyte and the loss of electrode active material. Such functional property degradation will increase the internal resistance of the storage battery and lead to capacity reduction. Since X_{ S } is independent of the operating condition, it is generally considered to be linear with shelf life of the battery. The yearly static degradation can be expressed as:
where T represents the battery shelf life/year. For example, if the Liion battery shelf life is 20 years, one year’s static degradation is 1/20 = 5%.
The dynamic degradation X_{ D } corresponds to the degradation caused by changes in the operating status of the Liion battery. Operating conditions include the depth of discharge and the chargedischarge rate, corresponding to the battery’s chargedischarge process. As actual chargedischarge cycles are aperiodic, the dynamic life degradation is nonlinear. Therefore, actual operating conditions should be considered to calculate the dynamic degradation given by:
where k refers to the kth chargedischarge interval, i and j represent the start and end of chargedischarge with the SOC values being SOC_{i} and SOC_{j}, respectively. n is the number of chargedischarge cycles in the sampling time. C_{k (ij)} is the number of cycles when the Liion ESS’s SOC charges and discharges between i and j until the actual capacity of the storage battery drops down to 60% of its nominal capacity, and is given by:
where, as regards to the kth interval, C_{ k(i) } and C_{ k(j) } are the cycle numbers when the SOC charges and discharges from SOC_{ i } and SOC_{ j } to 100%, respectively, until the actual capacity of the storage battery drops down to 60% of its nominal capacity. 1/C_{ k(i) } and 1/C_{ k(j) } are the dynamic cycle degradation that the SOC charges and discharges between SOC_{ i } and SOC_{100%}, and SOC_{ j } and SOC_{100%}, respectively. The derivation of (4) can be explained by considering the dynamic degradation (1/C_{ k(ij) }) to be the dynamic degradation of SOC from SOC_{ i } to SOC_{ j } which equals half the value of the cycle dynamic degradation between SOC_{ i } and SOC_{100%} minus that between SOC_{ j } and SOC_{100%}.
Since the Liion battery life is measured by the number of cycles, the static degradation and the dynamic degradation need to be equivalent to the reduction of the number of cycles. Assuming the lithium battery cycle life is 4500 times under a given condition (80% DOD), and at this time, the capacity retention rate drop to 60%. Similarly, if the Liion battery idles for 20 years, the capacity retention rate will also drop to 60%. As the static degradation is linear, it can be considered that it will consume 4500 × 5% = 225 cycle times if the Liion battery remains idle for one year. So the percentage of life degradation caused by the static degradation and dynamic degradation can be considered in a similar process causing the Liion battery capacity retention rate to drop to 60%.
In summary, the Liion battery life degradation mode under actual operating conditions is given by:
Therefore, it is only necessary to analyze the relationship between the cycles of Liion ESS and the state of charge (SOC) or the depth of discharge (DOD). Thus, the Liion ESS life degradation of any chargedischarge interval under actual operating conditions can be calculated and the operating life of energy storage battery can be estimated.
Influence of depth of discharge on Liion ESS operating life
Liion batteries are tested at normal room temperature (20 ± 5 °C), and are charged and discharged with constant current and constant voltage (1C model). Using different depth of discharge as each chargedischarge indicator, Liion battery cycle life refers to the number of cycles until the actual capacity of the battery drops down to 60% nominal capacity.
The measured data of the LiFePO4 battery (one kind of Liion battery) shown in Fig. 1 is given by manufacturers. Under standard conditions, with different DOD as each chargedischarge indicator, it shows the variations of the LiFePO4 battery actual capacity retention rate as the number of cycles changes.
It can be seen from Fig. 1 that the relationship between battery capacity retention rate and the number of cycles is analogously parabolic. The deterioration rate of the battery is reflected in two stages. In the first stage, the battery decay rate gradually decreases, indicating that the battery tends to selfstabilize its state. In the second stage, the battery decay rate increases, indicating that the battery begins to accelerate its aging. It can also be seen from Fig. 1 that the higher the DOD value is, the faster aging rate of the battery becomes, and the fewer the cycle is. The relationship between the discharge depth and the cycle life is approximately exponential [3] and for the LiFePO4 battery it can be fitted as:
where C_{ i } is the number of cycles when the depth of discharge is DOD_{ i }.
Fig. 2 shows the relationship between DOD and cycle life calculated using (6). For other kinds of batteries similar fitting methods can also be used.
The formula DOD_{ i } = 1SOC_{ i } means that battery charges and discharges repeatedly between SOC_{ i } and SOC_{100%} at DOD_{ i }. According to DOD_{ i } = 1SOC_{ i } and (6), the relationship between the cycle life and SOC can be expressed as:
In summary, combing with the depth of discharge and state of charge, the annual life degradation model of energy storage battery under actual operating conditions is given as:
The cost accounting model for the frequency regulation of the Liion ESS considering the effect of life degradation
The cost accounting model
The cost accounting model of the Liion ESS is determined by the total initial investment cost, estimated operating life, operation and maintenance costs, and is give as:
where C_{ A } is the annual cost of the Liion ESS, C_{ INV } is the total cost of the initial investment of the Liion ESS, T_{ LC } is the estimated operating life (in years) of the Liion ESS considering the life degradation. C_{O&M} is the annual operation and maintenance cost. Because the Liion ESS C_{O&M} is much less than the initial investment, it is considered to be fixed in the case setting. The total cost of the initial investment of the Liion ESS is given by
where P_{ ESS } and E_{ ESS } are the respective rated power and capacity of the Liion ESS, λ_{P} is the unit price of the Liion ESS power, and λ_{E} is the unit price of the Liion ESS capacity. These parameters are given in Table 1 of the case setting.
The control strategy of the Liion ESS participating in power grid frequency regulation
(1) Energy storage power output constraints
where P_{ t } is the chargedischarge power of the Liion ESS. The ESS works in the charge state when P_{ t } > 0, and in the discharge state when P_{ t } < 0.

(2)
Storage SOC constraints
where w_{ fr } is the energy of the Liion ESS participating in the grid frequency regulation, ƞ is the efficiency of the Liion ESS. Because manufacturers usually only provide the total efficiency (ƞ) of ESSs, it is considered as the balanced result of charge and discharge efficiency in this paper. SOC^{min} and SOC^{max} are the minimum and maximum values of allowed ESS’s SOC.
The ESS utilizes the bidirectional flow of the battery energy to support network frequency to prevent it from deviating the standard range. The ESS charging and discharging power is given as [2]:
When the power supply is higher than the load demand, the system frequency rises above f_{ ref1 }. The ESS charges and absorbs power from the power grid until the system frequency drops down to f_{ ref1. } When the power supply is less than the load demand and the system frequency drops below f_{ ref2 }, the ESS discharges and releases power to the power grid until the system frequency moves up to f_{ ref2 }. The ESS’s unit adjustment power K_{ ESS } is directly related to the effect of the control strategy. Because of the limitation of energy storage capacity, this control strategy is only suitable for the primary frequency regulation of an interconnected system.
It can be seen from (14) that the frequency regulation dead band (f_{ ref1 }, f_{ ref2 }) directly affects the chargedischarge power (p_{ t }) of the ESS, and its life degradation and operating life T_{ LC }.
The calculation of the ESS frequency regulation power
The main benefit of the Liion ESS for frequency regulation is from frequency regulation energy w_{ fr }. As for the frequency regulation period from t_{ i } to t_{ j }, the frequency regulation energy w_{ fr } is given as:
where p_{ t } is the chargedischarge power of the Liion ESS in the period from t_{ i } to t_{ j }.
Calculation of the ESS estimated operating life T _{ LC }
As for the energy storage frequency regulation period t_{ i } to t_{ j }, the change of the ESS SOC is:
According to SOC(t_{ j }) and SOC(t_{ i }), and combining (4) and (7), the dynamic degradation X_{ D } can be obtained. As previously described, the static degradation X_{S} of the period is calculated according to (2). In summary, the life degradation of the frequency regulation period (t_{ i }, t_{ j }) is calculated as (17).
Similarly, according to the given frequency curve and dead band, ΔSOC changes within one year can be calculated. Combining with the life degradation model of the energy battery in (8), oneyear life degradation (X_{ y }) of the Liion ESS is expressed as:
where n is the number of chargedischarge cycles in one year. Fig. 3 shows the calculation flowchart to obtain Xy.
It can be assumed that the annual demand for frequency regulation in late years is similar to the demand of the first year. The actual capacity of the Liion ESS at the end of the first year is the rated capacity of the Liion ESS at the second year. So the Liion ESS life degradation of the second year can be calculated and so on for the rest years. When the Liion ESS operation life degradation process reaches 100% as shown in (19), the estimated operating life (T_{ LC }) under the corresponding dead band can be obtained.
According to different estimated operating life T_{ LC } of the Liion ESS under different dead bands, the average cost C_{ A } can be calculated according to (9) and (10).
Results and discussion
Case analysis
Case setting
The selected case is a wind farm with an ESS in Liaoning power grid, which is an interconnected system. In 2015, the installed capacity of the Liaoning power grid was 4.32 × 10^{4} MW, and the maximum load was 2.34 × 10^{4} MW. The wind farm is rated at 54.4 MW (P_{ NWF }) and equipped with 64 G58850 kW doublyfed asynchronous wind generators, whereas the rated power of the ESS is 5 MW. In order to achieve similar effect as synchronous generator frequency regulation, the frequency coefficient of the Liion ESS is set the same as the synchronous generators, i.e. K_{ ESS } = 0.4 × P_{NWF} = 21.76 MW/Hz. According to the power system frequency regulation need (including the primary frequency regulation and the secondary frequency regulation), the regulation time is about 30 min. Thus, the storage system capacity E_{ ESS } is set as 5 MW × 0.5 h = 2.5MWh. In the case study, the ESS is only used for frequency regulation. The LiFePO4 battery energy storage system is chosen as it has the best prospect of the current market application. The unit ESS price is shown in Table 1, the sampling period of the wind farm frequency is 1 min and the data amount is 525,600.
Calculation results and analysis
In this study, the frequency of the wind farm is used as the frequency regulation target, and f_{ref (1,2)} = 50 ± x Hz is selected as the frequency regulation dead band. When the system frequency offset exceeds the rated frequency by ±x Hz, the ESS will participate in system frequency regulation.
Frequency regulation cost accounting under the given dead band

(1)
The sharing cost accounting without considering the impact of life degradation
When the impact of ESS life degradation is not taken into account, traditional storage cost accounting is just a sharing accounting method, which uses the nominal life provided by the manufacturers. The initial investment of the Liion ESS is 970× 10^{4} yuan, and the Liion ESS nominal life is 15 years from manufacturers. The average life degradation is 6.67%. The annual sharing cost equals 76.7 × 10^{4} yuan (including the cost of operation and maintenance). If the given discharge depth is 80% DOD, the nominal life of the energy storage battery is 4500 times and the annual sharing number is 300 times, equivalent to the ESS being fully charged approximately once a day.

(2)
The annual average cost accounting considering the impact of energy storage life degradation under the given frequency regulation dead band.
The given frequency regulation dead band is 50 ± 0.04 Hz and when the system frequency offset exceeds the rated frequency by ±0.04 Hz, the ESS will participate in the system frequency regulation. Fig. 4 shows the calculated variations of the Liion ESS chargedischarge power and the SOC in a typical day. As seen, the Liion ESS is charged fully twice a day. One day’s frequency regulation power and life degradation are 3.297MWh and 0.0359%, respectively. According to the actual annual frequency curve of the wind farm, this model can be applied to calculate the annual life degradation of the Liion ESS, and the result is 11.59%. The annual frequency regulation power is 1175.9MWh. This indicates that the ESS is fully charged 432 times within one year, and the estimated operating life is 8.6 years, representing a significant reduction from the nominal life of 15 years. The annual average cost is thus 124.4 × 10^{4} yuan, higher than 76.7 × 10^{4} yuan from the traditional sharing accounting.
The annual average cost accounting under different frequency regulation dead bands
Using different frequency regulation dead bands, the estimated operating life and annual average cost of the Liion ESS are compared in Table 2.
As can be seen from Table 2, if the frequency regulation dead band is ±0.06 Hz, the annual average cost is 72.4 × 10^{4} yuan, which is close to the 76.7 × 10^{4} yuan according to the nominal 15year life provided by manufacturers. When the frequency regulation dead band is ±0.033 Hz, the estimated operating life of the energy storage is reduced to 5.95 years and its annual average cost is increased to 175 × 10^{4} yuan. It can be concluded that smaller frequency regulation dead band results in more frequent Liion ESS operation, leading to shorter battery operating life and higher average annual cost.
The above example was analyzed when the SOC setpoint is 50%. Analyzing data reveals that the SOC is usually in the range of 30 to 100% when the energy storage participates in frequency regulation. Therefore, it is necessary to analyze whether SOC setpoint of 50% is the optimal condition.
Fig. 5 shows the statistics histogram of the occurrence of different system frequency whereas Fig. 6 illustrates the annual duration of the energy storage frequency regulation power for different frequency dead bands. From Figs. 5 and 6, it can be seen that overfrequency occurs 70.19% in one year and the duration of charge is longer than that of discharge. Therefore, the choice of SOC setpoint is very important and affects the number of energy storage fully charging times and life degradation.
The annual average cost accounting under different SOC setpoints and different frequency regulation dead bands
If the SOC setpoint is reduced, the number of the ESS’s fully charging times can be reduced. However, the deep chargedischarge mode will increase the life degradation of the Liion ESS. Fig. 7 and Fig. 8 show the life degradation and estimated operating life of the energy storage under different SOC setpoints and frequency regulation dead bands. It is shown that under the same frequency regulation dead band, the smaller the SOC setpoint is, the higher the annual life degradation and the shorter of estimated operating life of the energy storage are. For example, when the SOC setpoint is 20% (deep chargedischarge state) and the frequency regulation dead band is ±0.033 Hz, the estimated operating life of the storage is the shortest, only 4.3 years, and the annual average cost is the largest at 237.6 × 10^{4} yuan. This compares to 16.05 years and 72.4 × 10^{4} yuan with the SOC setpoint of 50% and the frequency regulation dead band of ±0.06 Hz as previously discussed.
As small SOC setpoint leads to high frequency regulation power and thus, it is necessary to assess the life degradation caused by the unit frequency regulation power to determine the optimal SOC setpoint. Fig. 9 shows the life degradation of unit frequency regulation power under different SOC setpoints and different frequency regulation dead bands. It shows that when the frequency regulation dead band is ±0.033 Hz and the SOC setpoint is 50%, the ESS life degradation of the unit frequency regulation power is the smallest. The estimated operating life of the Liion ESS is 5.95 years and the annual average cost is 175 × 10^{4} yuan. In this case, it will consume relatively little life to complete more frequency regulation tasks.
Conclusions
In order to improve the accuracy of the cost accounting method for frequency regulation of the Liion battery energy storage system, a model of Liion battery life degradation is developed in this paper. The influence of DOD on the Liion ESS operating life is analyzed and the ESS life degradation in any frequency regulation period under actual operating conditions are obtained. Finally, an effective frequency regulation cost accounting method is proposed to calculate the annual average cost and the estimated operating life of the Liion ESS under different frequency regulation dead bands and SOC setpoints, which are significantly different from the sharing cost calculated by traditional method and the nominal life. The proposed method provides an accurate annual average cost of the ESS and is thus of great significance to accelerate the construction of the pricing mechanism of the frequency regulation ancillary service.
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Acknowledgements
This work is supported in part by Industrial Innovation of Jilin Province Development and Reform Commission (2017C0172), Science & Technology Project of SGCC (Key technology and application of super large capacity battery energy storage system),and Jilin Provincial “13th FiveYear Plan” Science and Technology Project ([2016] 88).
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GG. Y contributed to design and analysis of the study and drafted the manuscript; DY. L carried out the studies about the influence mechanism of actual operating conditions on the Liion battery energy storage life degradation; JH. L worked on the cost accounting model for frequency regulation of Liion battery energy storage system considering the effect of life degradation; MG contributed to the revision of the manuscript. All authors have read and approved the final manuscript.
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Correspondence to Gangui Yan.
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Yan, G., Liu, D., Li, J. et al. A cost accounting method of the Liion battery energy storage system for frequency regulation considering the effect of life degradation. Prot Control Mod Power Syst 3, 4 (2018) doi:10.1186/s4160101800762
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Keywords
 Energy storage system
 Estimated operating life
 Cost accounting method
 Frequency regulation
 Dead band