# Two-Stage Multi-Objective Collaborative Scheduling for Wind Farm and Battery Switch Station

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## Abstract

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## 1. Introduction

- (1)
- A two-stage multi-objective collaborative scheduling model was proposed based on the dependent chance programming theory. Since the decision-makers care more about operating risk, the model aimed at maximizing the realization probabilities of the three operating indices rather than optimizing the indices themselves.
- (2)
- The decision variable in the first stage was the stored energy rather than the charging/discharging power of BSS so as to provide effective guidance on further adjustment of BSS in the hour-ahead stage.
- (3)
- Different from other research, the adjustment procedure of the BSS within each hour was considered in the day-ahead stage in order to explore the capability of BSS as reserve.

## 2. Operating Indices of the Integrated System

#### 2.1. Index of Battery Swapping Demand Curtailment

_{t}is the number of time interval related to the day-ahead collaborative scheduling, and ${Q}_{\mathrm{q}}^{t}$ is the battery swapping demand curtailment at time interval t.

#### 2.2. Index of Wind Curtailment

#### 2.3. Index of Generation Schedule Tracking

## 3. Dependent Chance Programming

_{j}(x,y) ≤ 0, j = 1,2,…,p}, while Equation (5) refers to the uncertain environment at which the event is situated.

## 4. Day-Ahead Collaborative Scheduling Model

_{exmin}{·} is the minimized target vector in lexicographical order; the decision variable x is the stored energy ${Q}_{\mathrm{ev}}^{t}$ of BSS at diverse time frames; the random variable y includes the real power ${P}_{\mathrm{wn}}^{t}$ of a wind farm and the actual battery swapping demand ${Q}_{\mathrm{dn}}^{t}$ of EV users at each time frame; P

_{r}{·} is the realization probabilities of events; h

_{1}(x,y), h

_{2}(x,y) and h

_{3}(x,y,t) stand for the battery swapping demand curtailment in the BSS, the wind curtailment in the wind farm, and absolute value of relative error between output power of the integrated system and its generation schedule, respectively. In Equations (7)–(9), the first term on the left side of each equation represents the realization probability of battery swapping demand index, the realization probability of wind curtailment index, and the mean value of realization probabilities for generation schedule tracking indices at all time frames, respectively. Besides, P

_{Qds}, P

_{Qws}and P

_{δ}are target values for realization probabilities of the three indices, which are determine by decision-makers according to their risk preferences. ${d}_{i}^{+}$ and ${d}_{i}^{-}$ are positive and negative deviations for target i deviating from the its target value. They are nonnegative numbers. h

_{1}(x,y), h

_{2}(x,y) and h

_{3}(x,y,t) are expressed in Equations (12)–(14):

- BSS Storage Capacity Constraint$${Q}^{\mathrm{min}}\le {Q}_{\mathrm{ev}}^{t}\le {Q}^{\mathrm{max}}$$
^{max}and Q^{min}are maximum and minimum energy storage of the BSS. In order to prevent battery lift shortening from over discharge, 10%–30% of the maximum capacity of the station is usually taken as Q^{min}. - Energy Storage Constraint at the End of Decision-making Cycle of BSS$${Q}_{\mathrm{ev}}^{{N}_{t}}\ge {Q}^{\mathrm{end}}$$
^{end}refers to the minimum energy storage of the BSS required at the end of the decision-making cycle. Without prejudice to the battery swapping services at the next decision-making cycle, Q^{end}is generally required to be equal to the initial energy storage denoted by Q^{ini}. - Energy Storage Ramping Constraint for BSS$$-{P}_{d}^{\mathrm{max}}\Delta t/{\mathsf{\eta}}_{\mathrm{d}}\le {Q}_{\mathrm{ev}}^{t+1}-({Q}_{\mathrm{ev}}^{t}-{Q}_{\mathrm{dn}}^{t}+{Q}_{\mathrm{q}}^{t})\le {P}_{\mathrm{c}}^{t,\mathrm{max}}{\mathsf{\eta}}_{\mathrm{c}}\Delta t$$
_{c}and η_{d}denotes the efficiency of charging and discharging, respectively. ${P}_{d}^{\mathrm{max}}$ is the maximum discharge power of the BSS; and ${P}_{c}^{t,\mathrm{max}}$ is the maximum permissible charge power for the BSS at time t, and it can be expressed as:$${P}_{\mathrm{c}}^{t,\mathrm{max}}=\mathrm{min}\left\{{P}_{\mathrm{c}}^{\mathrm{max}},{P}_{\mathrm{wn}}^{t}\right\}$$

_{τ}time intervals. According to the day-ahead prediction of wind power and battery swapping demand as well as the probability distribution of their prediction error, m groups of scenarios are generated randomly to simulate the fluctuations of wind power and battery swapping demand. In addition, the hour-ahead optimization decision model is employed to calculate the optimization solution. In line with the law of large numbers, when m is large enough, the probability satisfied by such an operating index can be approximately replaced by the proportion taken by the number of scenarios satisfying the operating index in the total quantity of simulation scenarios.

## 5. Hour-Ahead Optimization Decision Model

_{τ}is the number of time intervals for each hour during ultra-short term prediction; Δτ is the time interval; and ρ

_{1}, ρ

_{2}and ρ

_{3}are weighting factors. The decision variables include the battery swapping demand curtailment ${Q}_{\mathrm{q}}^{t}$, wind curtailment power ${P}_{\mathrm{wq}}^{t,\tau}$, charge power ${P}_{\mathrm{c}}^{t,\tau}$ and the discharge power ${P}_{\mathrm{d}}^{t,\tau}$.

- Constraints on storage capacity in the BSS$${Q}^{\mathrm{min}}\le {Q}_{\mathrm{ev}}^{t,\mathsf{\tau}}\le {Q}^{\mathrm{max}}$$
- Constraints on energy storage in the BSS at the end of an hour$${Q}_{\mathrm{ev}}^{t,{N}_{\mathsf{\tau}}}={Q}_{\mathrm{ev}}^{t+1}$$
- Constraints on battery swapping demand curtailment$$0\le {Q}_{\mathrm{q}}^{t}\le {\displaystyle \sum _{\mathsf{\tau}=1}^{{N}_{\mathsf{\tau}}}{Q}_{\mathrm{dn}}^{t,\mathsf{\tau}}}$$
- Constraints on wind curtailment power$$0\le {P}_{\mathrm{wq}}^{t,\mathsf{\tau}}\le {P}_{\mathrm{wn}}^{t,\mathsf{\tau}}$$
- Constraints on charging/discharging power$$0\le {P}_{\mathrm{c}}^{t,\mathsf{\tau}}\le {U}_{\mathrm{c}}^{t,\mathsf{\tau}}{P}_{\mathrm{c}}^{\mathrm{max}}$$$${U}_{\mathrm{c}}^{t,\mathsf{\tau}}+{U}_{\mathrm{d}}^{t,\mathsf{\tau}}\le 1$$$${P}_{\mathrm{c}}^{t,\mathsf{\tau}}\le {P}_{\mathrm{wn}}^{t,\mathsf{\tau}}-{P}_{\mathrm{wq}}^{t,\mathsf{\tau}}$$

- Constraints on the maximum relative error between output power of the integrated system and generation schedule.$$\mathrm{abs}\left({P}_{\mathrm{wn}}^{t,\mathsf{\tau}}-{P}_{\mathrm{wq}}^{t,\mathsf{\tau}}-{P}_{\mathrm{c}}^{t,\mathsf{\tau}}+{P}_{\mathrm{d}}^{t,\mathsf{\tau}}-{P}_{\mathrm{Plan}}^{t}\right)/{P}_{\mathrm{Plan}}^{t}\le \mathsf{\alpha}$$

## 6. Simulation Analysis

^{ini}and Q

^{end}are set as 50% of the maximum storage capacity of the BSS.

^{2}), where the probability in [3σ, −3σ] is 99.73%. Based on the historical data, we found that the relative prediction error of wind power and battery switch demand is no more than 30%. Therefore, we assume that the relative prediction error of day-ahead prediction for wind power and battery swapping demand all follow the normal distribution of N(0, 0.1

^{2}). It should be noted that the distribution of the prediction error will not affect the use of the model proposed in this paper, what we need to do is just modify the stochastic simulation process in Section 4 accordingly.

_{ds}is 0.1 MW·h, 1‰ of cumulative daily battery swapping demand. The maximum wind curtailment Q

_{ws}, which takes 1‰ of the cumulative daily generated energy of a wind farm, is 1.2 MW·h. δ and α are 10% and 20%, respectively. In addition, the priority order and target values for realization probabilities of three operating indices should be reasonably set according to the decision-maker’s preference to different indices and the level of risk tolerance as well. In this paper, the priority ranking of the operating indices from high to low is the index of battery swapping demand curtailment, wind curtailment and generation schedule tracking. Target values for their realization probabilities are 97%, 90% and 90% respectively.

_{ws}(1.2 MW·h). Consequently, the second operating index is not satisfied. As for wind curtailment for all intervals, please refer to Figure 12. The actual output power of the integrated system is given in Figure 13.

## 7. Conclusions

- (1)
- The integrated system constituted by a wind farm and EVBSS can be adopted to utilize their complementary efficiency so as to exert a synergistic effect. On the one hand, the BSS is able to utilize wind power to perform battery charging and satisfy the battery swapping demands of EV users. On the other hand, the wind power can track the generation schedule better based on the reserve provided by the BSS.
- (2)
- The model give consideration to multiple operating indices according to decision-makers’ requirements. On the premise that both battery swapping demand curtailment index and wind curtailment index are met, the output power of integrated system can better follow the relevant generation schedule.
- (3)
- Based on the proposed model, configuration optimization is carried out for the adjustment capability of BSS from an overall view, so the premature exhaustion of its regulation capability can be avoided.
- (4)
- Compared to a day-ahead scheduling model without the readjustment process of charging/discharging power, the proposed two-stage collaborative scheduling model is more beneficial to explore the regulation capability of BSS, improve the capability of integrated system to track the generation schedule, and satisfy the three operating indices in a more preferable way.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

N_{t} | Number of time interval related to the day-ahead collaborative scheduling |

N_{τ} | Number of time interval related to the hour-ahead optimization |

$\Delta t$ | Length of a single time interval of the day-ahead collaborative scheduling |

$\Delta \mathsf{\tau}$ | Length of a single time interval of the hour-ahead optimization |

x | Decision variable |

y | Random variable |

p | Number of event of dependent chance programming model |

q | Number of constraint conditions of dependent chance programming model |

L_{exmin}{·} | Minimize target vector in lexicographical order |

P_{r}{·} | Realization probabilities of events |

${h}_{1}(x,y)$ | Battery swapping demand curtailment in the BSS |

${h}_{2}(x,y)$ | Wind curtailment in the wind farm |

${h}_{3}(x,y,t)$ | Absolute value of relative error between output power of the integrated system and its generation schedule |

${P}_{\mathrm{wq}}^{t}$ | Wind curtailment power at time t |

${P}_{\mathrm{wn}}^{t}$ | Actual power of wind farm at time t |

${P}_{\mathrm{Plan}}^{t}$ | Generation schedule at time t |

${P}_{\mathrm{ev}}^{t}$ | Charging/discharging power of BSS at time t |

${\mathsf{\eta}}_{\mathrm{c}}$ | Charging efficiency of the BSS |

${\mathsf{\eta}}_{\mathrm{d}}$ | Discharging efficiency of the BSS |

${P}_{\mathrm{c}}^{\mathrm{max}}$ | Maximum charge power of the BSS |

${P}_{\mathrm{d}}^{\mathrm{max}}$ | Maximum discharge power of the BSS |

${P}_{\mathrm{c}}^{t,\mathrm{max}}$ | Maximum permissible charge power for the BSS at time t |

${Q}_{\mathrm{ev}}^{t}$ | Stored energy of BSS at time interval t |

${Q}_{\mathrm{dn}}^{t}$ | Actual battery swapping demand at time interval t |

Q^{max} | Maximum energy storage of the BSS |

Q^{min} | Minimum energy storage of the BSS |

Q^{ini} | Initial energy storage of the BSS |

Q^{end} | Minimum energy storage of the BSS required at the end of the decision-making cycle |

${\mathsf{\rho}}_{1}$ | Weighting factor of battery swapping demand curtailment |

${\mathsf{\rho}}_{2}$ | Weighting factor of wind curtailment |

${\mathsf{\rho}}_{3}$ | Weighting factor of output power deviation |

${P}_{\mathrm{wn}}^{t,\mathsf{\tau}}$ | Wind power at time τ within the hour t |

${P}_{\mathrm{wq}}^{t,\mathsf{\tau}}$ | Wind curtailment power at time τ within the hour t |

${P}_{\mathrm{c}}^{t,\mathsf{\tau}}$ | Charging power at time τ within the hour t |

${P}_{\mathrm{d}}^{t,\mathsf{\tau}}$ | Discharging power at time τ within the hour t |

${Q}_{\mathrm{ev}}^{t,0}$ | Initial energy storage of the BSS within the hour t |

${Q}_{\mathrm{dn}}^{t,\mathsf{\tau}}$ | Battery swapping demand at time interval τ within the hour t |

${Q}_{\mathrm{ev}}^{t,\mathsf{\tau}}$ | Stored energy of the BSS at time interval τ within the hour t |

${U}_{\mathrm{c}}^{t,\mathsf{\tau}}$ | Charging flag of BSS at time τ within the hour t, binary variable |

${U}_{\mathrm{d}}^{t,\mathsf{\tau}}$ | Discharging flag of BSS at time τ within the hour t, binary variable |

$\mathsf{\delta}$ | permissible absolute value of relative error of the integrated system and generation schedule |

$\mathsf{\alpha}$ | maximum permissible absolute value of relative error of the integrated system and generation schedule |

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**Figure 5.**Probabilities for battery swapping demand curtailment, wind curtailment and integrated system output power threshold-crossing.

**Figure 13.**Actual output power of the integrated system in model without considering charging/discharging power readjustment.

Q^{max} | Q^{min} | ${\mathit{P}}_{\mathbf{c}}^{\mathbf{max}}$ | ${\mathit{P}}_{\mathbf{d}}^{\mathbf{max}}$ | ${{\eta}}_{{c}}$ | ${{\eta}}_{{d}}$ |
---|---|---|---|---|---|

55 MW·h | 5.5 MW·h | 11 MW | 7 MW | 0.95 | 0.92 |

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## Share and Cite

**MDPI and ACS Style**

Jiang, Z.; Han, X.; Li, Z.; Li, W.; Wang, M.; Wang, M.
Two-Stage Multi-Objective Collaborative Scheduling for Wind Farm and Battery Switch Station. *Energies* **2016**, *9*, 886.
https://doi.org/10.3390/en9110886

**AMA Style**

Jiang Z, Han X, Li Z, Li W, Wang M, Wang M.
Two-Stage Multi-Objective Collaborative Scheduling for Wind Farm and Battery Switch Station. *Energies*. 2016; 9(11):886.
https://doi.org/10.3390/en9110886

**Chicago/Turabian Style**

Jiang, Zhe, Xueshan Han, Zhimin Li, Wenbo Li, Mengxia Wang, and Mingqiang Wang.
2016. "Two-Stage Multi-Objective Collaborative Scheduling for Wind Farm and Battery Switch Station" *Energies* 9, no. 11: 886.
https://doi.org/10.3390/en9110886