# A cost accounting method of the Li-ion battery energy storage system for frequency regulation considering the effect of life degradation

- Gangui Yan
^{1}Email author, - Dongyuan Liu
^{1}, - Junhui Li
^{1}and - Gang Mu
^{1}

**3**:4

https://doi.org/10.1186/s41601-018-0076-2

© The Author(s) 2018

**Received: **31 May 2017

**Accepted: **9 January 2018

**Published: **5 February 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 grid-connected operation. To solve this problem, the influence mechanism of actual operating conditions on the life degradation of Li-ion battery energy storage is analyzed. A control strategy of Li-ion 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 Li-ion ESS under different dead bands and SOC set-points are calculated. The case studies show that the estimated operating life of the Li-ion 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.

## Keywords

## 1 Introduction

Fossil fuel-based energy model has caused serious environmental problems whereas wind power development has gradually become an important way to push low-carbon energy transition. However, with increased large-scale 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 Li-ion ESS has flexibility and fast response characteristic, and large-scale application of Li-ion 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 energy-saving 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 (charge-discharge 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 charge-discharge mode measured by the cycle charge-discharge time. When an ESS participates in grid frequency regulation, the charge-discharge 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 [5–7]. Real-time price of energy storage market should be considered for cost calculation. The current market price of the Li-ion 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 wind-storage combination as the objective, an optimization model of ESS was established. For secondary frequency regulation, references [12–14] drew a conclusion that the annual investment cost of one ESS is 2.7–4.7 times as a heat-engine 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 [15–18]. 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 large-scale wind power.

This paper focuses on the cost accounting of the ESS to participate in power system frequency regulation. In Section 2, Li-ion 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 set-points are analyzed in Section 5, whereas Section 6 draws the conclusions.

## 2 Methods

### 2.1 Li-ion battery life degradation model

Under given charge-discharge mode and ambient temperature, the Li-ion battery cycle life refers to the cycle charge-discharge time until the battery capacity retention rate drops down to the specified nominal capacity value.

*X*

_{ S }is caused by the degradation of functional properties of the Li-ion 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:

*T*represents the battery shelf life/year. For example, if the Li-ion battery shelf life is 20 years, one year’s static degradation is 1/20 = 5%.

*X*

_{ D }corresponds to the degradation caused by changes in the operating status of the Li-ion battery. Operating conditions include the depth of discharge and the charge-discharge rate, corresponding to the battery’s charge-discharge process. As actual charge-discharge cycles are aperiodic, the dynamic life degradation is non-linear. Therefore, actual operating conditions should be considered to calculate the dynamic degradation given by:

*k*refers to the

*k*th charge-discharge interval,

*i*and

*j*represent the start and end of charge-discharge with the SOC values being SOC

_{i}and SOC

_{j}, respectively.

*n*is the number of charge-discharge cycles in the sampling time.

*C*

_{k (ij)}is the number of cycles when the Li-ion 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:

*k*th 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 Li-ion 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 Li-ion 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 Li-ion 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 Li-ion battery capacity retention rate to drop to 60%.

Therefore, it is only necessary to analyze the relationship between the cycles of Li-ion ESS and the state of charge (SOC) or the depth of discharge (DOD). Thus, the Li-ion ESS life degradation of any charge-discharge interval under actual operating conditions can be calculated and the operating life of energy storage battery can be estimated.

### 2.2 Influence of depth of discharge on Li-ion ESS operating life

Li-ion 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 charge-discharge indicator, Li-ion battery cycle life refers to the number of cycles until the actual capacity of the battery drops down to 60% nominal capacity.

*C*

_{ i }is the number of cycles when the depth of discharge is

*DOD*

_{ i }.

*DOD*

_{ i }= 1-

*SOC*

_{ i }means that battery charges and discharges repeatedly between

*SOC*

_{ i }and

*SOC*

_{100%}at

*DOD*

_{ i }. According to

*DOD*

_{ i }= 1-

*SOC*

_{ i }and (6), the relationship between the cycle life and SOC can be expressed as:

### 2.3 The cost accounting model for the frequency regulation of the Li-ion ESS considering the effect of life degradation

#### 2.3.1 The cost accounting model

*C*

_{ A }is the annual cost of the Li-ion ESS,

*C*

_{ INV }is the total cost of the initial investment of the Li-ion ESS,

*T*

_{ LC }is the estimated operating life (in years) of the Li-ion ESS considering the life degradation. C

_{O&M}is the annual operation and maintenance cost. Because the Li-ion 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 Li-ion ESS is given by

*P*

_{ ESS }and

*E*

_{ ESS }are the respective rated power and capacity of the Li-ion ESS, λ

_{P}is the unit price of the Li-ion ESS power, and λ

_{E}is the unit price of the Li-ion ESS capacity. These parameters are given in Table 1 of the case setting.

The LiFePO4 battery ESS System installed capacity and the power/capacity parameters

Parameter | Number |
---|---|

P | 54.4 |

P | 5 |

E | 2.5 |

λ | 1000 |

λ | 1880 |

C | 24 |

SOC | 0.5 |

SOC | 0.1 |

SOC | 1 |

#### 2.3.2 The control strategy of the Li-ion ESS participating in power grid frequency regulation

*P*

_{ t }is the charge-discharge power of the Li-ion 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

*w*

_{ fr }is the energy of the Li-ion ESS participating in the grid frequency regulation,

*ƞ*is the efficiency of the Li-ion 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.

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 charge-discharge power (*p*_{
t
}) of the ESS, and its life degradation and operating life *T*_{
LC
}.

#### 2.3.3 The calculation of the ESS frequency regulation power

*w*

_{ fr }. As for the frequency regulation period from

*t*

_{ i }to

*t*

_{ j }, the frequency regulation energy

*w*

_{ fr }is given as:

*p*

_{ t }is the charge-discharge power of the Li-ion ESS in the period from

*t*

_{ i }to

*t*

_{ j }.

#### 2.3.4 Calculation of the ESS estimated operating life *T*
_{
LC
}

*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).

*X*

_{ y }) of the Li-ion ESS is expressed as:

*Xy*.

*T*

_{ LC }) under the corresponding dead band can be obtained.

According to different estimated operating life *T*_{
LC
} of the Li-ion ESS under different dead bands, the average cost *C*_{
A
} can be calculated according to (9) and (10).

## 3 Results and discussion

### 3.1 Case analysis

#### 3.1.1 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 G58-850 kW doubly-fed 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 Li-ion 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.

#### 3.1.2 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.

#### 3.1.3 Frequency regulation cost accounting under the given dead band

- (1)
The sharing cost accounting without considering the impact of life degradation

^{4}yuan, and the Li-ion 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.

^{4}yuan, higher than 76.7 × 10

^{4}yuan from the traditional sharing accounting.

#### 3.1.4 The annual average cost accounting under different frequency regulation dead bands

Estimated operating life and annual average cost of the Li-ion ESS under different frequency regulation dead bands

frequency regulation dead bands /Hz | ±0.033 | ±0.04 | ±0.05 | ±0.06 | nominal life(15y) |
---|---|---|---|---|---|

| 189.62 | 117.59 | 54.34 | 21.14 | – |

Annual life degradation/% | 16.81 | 11.59 | 8. 21 | 6.23 | 6.67 |

| 5.95 | 8.63 | 12.18 | 16.05 | 15 |

| 175.0 | 124.4 | 91.6 | 72.4 | 76.7 |

Fully charging cycle | 696 | 432 | 201 | 78 | – |

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 15-year 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 Li-ion ESS operation, leading to shorter battery operating life and higher average annual cost.

The above example was analyzed when the SOC set-point 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 set-point of 50% is the optimal condition.

#### 3.1.5 The annual average cost accounting under different SOC set-points and different frequency regulation dead bands

^{4}yuan. This compares to 16.05 years and 72.4 × 10

^{4}yuan with the SOC set-point of 50% and the frequency regulation dead band of ±0.06 Hz as previously discussed.

^{4}yuan. In this case, it will consume relatively little life to complete more frequency regulation tasks.

## 4 Conclusions

In order to improve the accuracy of the cost accounting method for frequency regulation of the Li-ion battery energy storage system, a model of Li-ion battery life degradation is developed in this paper. The influence of DOD on the Li-ion 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 Li-ion ESS under different frequency regulation dead bands and SOC set-points, 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.

## Declarations

### Acknowledgements

This work is supported in part by Industrial Innovation of Jilin Province Development and Reform Commission (2017C017-2), Science & Technology Project of SGCC (Key technology and application of super large capac-ity battery energy storage system),and Jilin Provincial “13th Five-Year Plan” Science and Technology Project ([2016] 88).

### Authors’ contributions

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 Li-ion battery energy storage life degradation; JH. L worked on the cost accounting model for frequency regulation of Li-ion 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.

### Competing interests

The authors declare that they have no competing interests.

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## Authors’ Affiliations

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