# Optimization of Battery Energy Storage System Capacity for Wind Farm with Considering Auxiliary Services Compensation

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## Abstract

**:**

## 1. Introduction

## 2. Problem Formulation

#### 2.1. Wind Output Characteristics

#### 2.1.1. Variability

#### 2.1.2. Uncertainty

#### 2.2. Auxiliary Services Eased by BESS

#### 2.2.1. BESS Participation in the Scheduling Plan

_{net}and P

^{’}

_{net}with considering a certain confidence interval. BESS provides a good choose for wind farm to handle with the forecast error by leaving some reserve capacity. By comparing Figure 4a,b, it is corresponding to the lower peaking capacity of conventional units by increasing BESS reserve capacity P

_{cap}, which can effectively improve the economics operation of conventional units.

#### 2.2.2. Quantification the Ancillary Services Cost

#### 2.3. Mathematical Description of BESS

#### 2.3.1. Equivalent Loss of Cycle Life

#### 2.3.2. Constraints of BESS Accounting to the Scheduling

_{s,t}> 0 refers to charging, and P

_{s,t}$<$ 0 refers to discharging.

_{load,t}need to be retained in the Equation (3) given in Section 2.1.2.

## 3. Optimal Model

#### 3.1. Objective Function

_{ost}

_{ave}

_{serve}

#### 3.2. Constraints

#### 3.3. System Performance Indices

_{g}

## 4. Case Study

#### 4.1. Basic Data

_{OM}is taken as 26 $/kW·h/year [24]. The on grid price of wind power ${\rho}^{w}$ is 0.084 $/kW·h (0.54 ¥/kW·h). The computation for all cases are carried out using YALMP toolbox and CPLEX solver [27].

#### 4.2. Operation Results Without BESS

- Case 1: The optimal scheduling results of systems without wind power integration is calculated.
- Case 2: With allowing wind power curtailment, the scheduling results with wind power integration is considered.

#### 4.3. Operation Results with BESS

- Case 3: both the auxiliary service compensation and BESS reserve wind forecast error are considered, that is, the proposed model;
- Case 4: without auxiliary service compensation and with BESS reserve wind uncertainty;
- Case 5: with auxiliary service compensation, and without BESS reserve wind uncertainty; and,
- Case 6: neither auxiliary service compensation nor BESS reserve wind uncertainty is considered.

_{g}of Case 3~Case 6 with BESS is significantly smaller than that of case2 without BESS (21.534 $/MW·h). It is reasonable that BESS mitigate the operational cost of conventional units caused by the wind anti-peaking characteristics through transferring the wind power in the time and space. c

_{g}of the proposed model Case 3 (c

_{g}= 21.236 $/MW·h) is close to the results of Case 1 without wind power integration. It means that with taking both the ancillary services compensation and BESS reserve wind uncertainty into account, wind-energy union system can achieve the “wind power friendly integration” and the economy operation of systems.

_{g}of Case 3 with Case 4 in Table 4, it can be seen that the economical operation of conventional units is further improved with BESS keeping reserve capacity for the wind uncertainty. From the benefits f of the wind energy union system in the Case 4, it can be seen that even if the unit investment cost of BESS is assumed as 250 $/kWh, the positive income will not be realized without considering the ancillary services compensation for BESS. That is, ignoring this part benefit of the BESS adapting to scheduling will seriously hinder the enthusiasm of wind farm configuring BESS and further harmful to the large-scale wind power integration.

_{g}is also failed to be improved in Case 6.

#### 4.4. Sensitivity Analysis

#### 4.4.1. On-grid Price of Wind Power

#### 4.4.2. Investment Cost and Cycle Life of BESS

_{E}being 250 $/kW·h and L

_{cyc,N}being 4000 times. In other words, the additional benefits for wind farm configuration BESS is greater than the additional investment costs. To find the balance point of the additional benefits and costs with C

_{E}and L

_{cyc,N}varying, the impact of C

_{E}and L

_{cyc,N}on the optimization results is shown in Figure 8 and Figure 9, respectively.

_{cyc,N}being 4000 times, if BESS can be provided a certain compensation for participating in the scheduling, the wind-energy union system will reach the payment balance with C

_{E}being 360 $/kW·h. That is to say, C

_{E}< 360 $/kW·h can guarantee the positive benefits of this wind farm. The auxiliary service compensation for BESS is more effective to stimulate the wind farm configuring BESS and promote the early arrival of the “BESS generation”.

_{cyc,N}reducing to 2800 times under the condition of C

_{E}= 250 $/kW·h. In other words, compared to the above mentioned in Section 2.3, the cycle life should being more than 4000 times in large-scale BESS application, it will be more effective to incentive wind farm configuring BESS with taking the auxiliary service compensation of BESS into account.

#### 4.4.3. Reserve Level of BESS

_{g}, and q) are small with the reserve level between 40% and 60%. It means that the installed power of BESS being 68.75–76.8 $/MW·h and the installed capacity of BESS between 30.2 and 32.8MW can realize the operation efficiency of BESS and conventional units in this wind farm.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

P_{net,t} | net load of systems with wind power integration in hour t |

P_{load,t} | forecast value of load demand in hour t |

P_{wind,t} | forecast output of wind farm in hour t |

${R}_{amp,t}^{up}/{R}_{amp,t}^{dn}$ | up/down ramp demand of the net load in hour t |

${P}_{gi}^{\mathrm{max}}/{P}_{gi}^{\mathrm{min}}$ | maximum/minimum output of unit i |

u_{i,t} | on-off state of unit i in hour t |

P_{gi,t} | output of unit i in hour t |

△P_{load,t} | spinning reserve demand of the load demand in hour t |

$\Delta {P}_{wind,t}^{up}/\Delta {P}_{wind,t}^{dn}$ | upper and down limitation of wind prediction interval |

N_{g} | number of conventional units |

P_{online,max}/P_{online,min} | upper/lower limitation of the online units |

P_{online,total} | total output of the online conventional units |

P^{’}_{net} | net load of systems with wind farm configuration BESS |

R | total spinning reserve capacity required by the system |

P_{cap} | rated power of BESS |

S_{cap} | rate capacity of BESS |

C_{serve} | difference auxiliary service cost of systems with and without BESS |

C_{fixed} | fixed cost item of auxiliary service |

C_{vary} | variable cost item of auxiliary service |

C_{AI} | daily investment cost per capacity of conventional units |

${P}_{gi}^{N}$ | rated power of the conventional unit i |

${P}_{gi,t}^{B}$ | output of unit i with configuration BESS in hour t |

M^{BESS}/M | number of units participating the auxiliary service with/without BESS |

${c}_{g}^{BESS}/{c}_{g}^{Wind}$ | unit coal cost of conventional units with/without BESS |

T | one scheduling period |

D | charge/discharge depth of BESS |

L_{cyc,D} | cycle life of BESS under the charge/discharge depth of D |

L_{cyc,N} | cycle life of BESS with fully charge/discharge |

N_{B} | charge/discharge number of BESS though the life cycle |

T_{life} | equivalent operation years of BESS |

P_{s,t} | output of BESS in hour t |

P_{union,t} | output of wind energy union system in hour t |

S_{soc,t} | state of charge (SOC) of BESS in hour t |

△t | scheduled interval |

${\lambda}_{t}$ | charge/discharge status of BESS at time t |

${\eta}_{s}$ | charge/discharge effectiveness of BESS |

C_{ost} | total investment cost of BESS |

S_{ave} | directly benefit from saving wind curtailed energy |

C_{c}(p,n) | capital recovery factor with annual interest rate p |

C_{E} | unit capacity cost of BESS |

C_{OM} | unit operation and maintenance cost of BESS |

${\alpha}^{s}$ | amortized power cost per year |

${\beta}^{s}$ | amortized capacity cost per year |

r | kW·h/kW cost ratio of BESS |

${\rho}^{w}$ | on-grid price of wind power |

P_{wloss,t}/P^{B}_{wloss,t} | curtailed wind energy with and without BESS in hour t |

${C}_{serve}^{Wind}/{C}_{serve}^{BESS}$ | auxiliary service cost caused by wind power with/without BESS |

R_{i} | ramping ability of unit i |

${T}_{i,\mathrm{max}}^{\mathrm{on}}/{T}_{i,\mathrm{min}}^{\mathrm{on}}$ | maximum/minimum online time of unit i |

C_{Gen} | operating cost function of conventional units |

f(P_{gi,t}) | quadratic fuel cost function with coefficients a_{i}, b_{i}, c_{i} |

S_{i} | on-off cost of unit i |

q | curtailed rate of wind power |

N_{cyc} | equivalent cycle numbers of BESS though a scheduling period |

${\epsilon}_{s}$ | reserve level provided by BESS for the uncertainty of wind power |

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**Figure 1.**Load demand/wind output under four seasons; (

**a**) net load fluctuation with and without wind power integration; and, (

**b**) ramping demand of systems with and without wind power.

**Figure 3.**Schematic diagram of battery energy storage system (BESS) participating in the scheduling; (

**a**) wind power integration without BESS; and, (

**b**) wind power integration with BESS. BEES: battery energy storage system; WPC: wind power curtailment.

**Figure 4.**Schematic diagram of BESS making up the sparing reserve of the wind power uncertainty; (

**a**) wind power integration without BESS; and, (

**b**) wind power integration with BESS.

**Figure 6.**Scheduling results of systems without BESS; (

**a**) Case1 results without wind power integration; and, (

**b**) Case 2 results with wind power integration.

**Figure 8.**Optimal results under different investment costs of BESS. C

_{E}: unit capacity cost of BESS.

**Figure 9.**Optimal results under different cycle life of BESS. L

_{cyc,N}: cycle life of BESS with fully charge/discharge.

**Table 1.**Relationship between the charge/discharge depth and cycle life of Lithium-ion battery system.

Discharge Depth (%) | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 |
---|---|---|---|---|---|

Cycle (time) | 9000 | 7200 | 5700 | 5200 | 4500 |

Units | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

P_{max} (MW) | 455 | 455 | 130 | 130 | 162 | 80 | 85 | 55 | 55 | 55 |

P_{min} (MW) | 150 | 150 | 20 | 20 | 25 | 20 | 25 | 10 | 10 | 10 |

c ($/h) | 1000 | 970 | 700 | 680 | 450 | 370 | 480 | 660 | 665 | 670 |

b ($/MW·h^{2}) | 16.19 | 17.26 | 16.60 | 16.50 | 19.70 | 22.26 | 26.74 | 25.92 | 27.27 | 27.29 |

a (10^{−3} $/MW·h^{2}) | 0. 48 | 0.31 | 2.0 | 2.1 | 3.98 | 7.12 | 7.9 | 4.13 | 2.22 | 1.73 |

R_{i} (MW/h) | 130 | 130 | 60 | 60 | 90 | 40 | 40 | 20 | 20 | 20 |

S_{i} ($) | 4500 | 5000 | 550 | 560 | 900 | 170 | 260 | 30 | 30 | 30 |

Initial status (h) | 8 | −8 | −5 | −5 | −5 | −3 | −3 | −1 | −1 | −1 |

Case | c_{g} ($/MW·h) | q (%) | $\sum {\mathit{P}}_{\mathit{g}\mathit{i}}^{\mathit{N}}}\text{}\left(\mathbf{MW}\right)$ |
---|---|---|---|

1 | 21.201 | - | 382 |

2 | 21.579 | 6.09% | 437 |

Case | c_{g} ($/MW·h) | f ($) | q (%) | P_{cap} (MW) | S_{cap} (MW·h) | N_{cyc} (time) |
---|---|---|---|---|---|---|

Case 3 | 21.238 | 2990 | 0.0% | 58 | 122.4 | 1.73 |

Case 4 | 21.305 | −1540 | 0.64% | 55 | 88.9 | 1.71 |

Case 5 | 21.290 | 1790 | 3.61% | 27.75 | 60.25 | 1.85 |

Case 6 | 21.544 | 1050 | 4.32% | 7.15 | 35.75 | 1.56 |

On-Grid Price ($/kW·h) | f ($) | P_{cap} (MW·h) | S_{cap} (MW·h) |
---|---|---|---|

0.084 | 2990 | 58 | 122.4 |

0.080 | 2321 | 54 | 102.4 |

0.076 | 1845 | 35.25 | 63.25 |

0.072 | 740 | 27.75 | 60.25 |

0.068 | 322 | 7.15 | 14.25 |

0.064 | 0 | 0 | 0 |

${\mathit{\epsilon}}_{\mathit{s}}$ | c_{g} ($/MW·h) | f ($) | q (%) | P_{cap} (MW·h) | S_{cap} (MW·h) |
---|---|---|---|---|---|

100% | 21.238 | 2990 | 0.0% | 58 | 122.4 |

80% | 21.324 | 3160 | 1.10% | 44.8 | 95.2 |

60% | 21.323 | 3930 | 1.84% | 34.8 | 79.6 |

40% | 21.312 | 3560 | 2.54% | 31.2 | 70.35 |

20% | 21.307 | 2910 | 3.23% | 29.5 | 61.25 |

0% | 21.290 | 1790 | 3.61% | 27.75 | 60.25 |

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## Share and Cite

**MDPI and ACS Style**

Jiang, X.; Nan, G.; Liu, H.; Guo, Z.; Zeng, Q.; Jin, Y.
Optimization of Battery Energy Storage System Capacity for Wind Farm with Considering Auxiliary Services Compensation. *Appl. Sci.* **2018**, *8*, 1957.
https://doi.org/10.3390/app8101957

**AMA Style**

Jiang X, Nan G, Liu H, Guo Z, Zeng Q, Jin Y.
Optimization of Battery Energy Storage System Capacity for Wind Farm with Considering Auxiliary Services Compensation. *Applied Sciences*. 2018; 8(10):1957.
https://doi.org/10.3390/app8101957

**Chicago/Turabian Style**

Jiang, Xin, Guoliang Nan, Hao Liu, Zhimin Guo, Qingshan Zeng, and Yang Jin.
2018. "Optimization of Battery Energy Storage System Capacity for Wind Farm with Considering Auxiliary Services Compensation" *Applied Sciences* 8, no. 10: 1957.
https://doi.org/10.3390/app8101957