Day-ahead battery scheduling in microgrid considering wind power

Day-ahead Battery Scheduling in Microgrid Considering Wind Power Uncertainty Using Ordinal Optimization Ruoyang Wang, Jiangran Wang, Zhengpai Cui and Zhigang Yang State Grid Jibei Electric Power Company Beijing, China

Qianyao Xu, Ning Zhang, and Chongqing Kang State Key Lab of Power Systems, Dept. of Electrical Engineering, Tsinghua University Beijing, China [email protected]

Abstract—This paper introduces the Ordinal Optimization (OO) theory into the microgrid operation, considering the wind power uncertainty. An energy balance model is established to obtain a day-ahead battery scheduling. Comparing with the stochastic optimization and the robust optimization, the OO method has the advantages of neither requiring a huge computation burden, nor resulting in an unexpectedly high operating cost. Case studies on different algorithms have been done in the paper. The results show that the OO method outperforms the stochastic and robust solutions, with a more reasonable operating cost while without compromising the microgrid reliability.

𝑊(𝑤, 𝑡) 𝐶(𝑤, 𝑡) 𝐿(𝑛, 𝑡)

Index Terms—Microgrid, day-ahead battery scheduling, wind power uncertainty, ordinal optimization.

𝑆(𝑏), 𝑆(𝑏)

I. Subscript t ΩB , ΩT , ΩW , ΩU , ΩL 𝑔(∙) 𝑝𝑖(𝑡) 𝐼(𝑡)

𝑝𝑐(𝑏) 𝑝𝑑(𝑏) 𝑝𝑠(𝑡) 𝐶(𝑏, 𝑡) 𝐷(𝑏, 𝑡) 𝑃(𝑘, 𝑡)

NOMENCLATURE

Value of a variable at the time t Set of batteries, time segments, wind turbines, generating units and system nodes, respectively Unit operation cost function ($) Electricity price charged by the main grid at time t ($/kWh) Interchange power between the main grid and the microgrid at time t, when the microgrid is receiving electricity, 𝐼(𝑡) is positive (kW) Cost to charge battery b ($/kWh) Cost to discharge battery b ($/kWh) Reward for islanding state ($/kWh) Charging power of battery b at time t (kW) Discharging power of battery b at time t (kW) Scheduled power of unit k at time t (kW)

This work was supported in part by National Science Fund for Distinguished Young Scholars (No.51325702) and the National High Technology Research and Development Program of China (863 Program No.2011AA05A101).

978-1-4799-5904-4/14/$31.00 ©2014 IEEE

𝑃(𝑘), 𝑃(𝑘) 𝐶(𝑏), 𝐶(𝑏) 𝐷(𝑏), 𝐷(𝑏)

𝐼(𝑡), 𝐼(𝑡) 𝑆(𝑏) 𝑈(𝑘, 𝑡) 𝐼𝐶(𝑏, 𝑡) 𝐼𝐷(𝑏, 𝑡) 𝐼𝐵(𝑡)

𝐼𝑆(𝑡), 𝐼𝐸(𝑡)

up

𝑅𝑘 , 𝑅𝑘down up

𝑅𝑏 , 𝑅𝑏down

Forecasted output of wind turbine w (kW) Curtailment of wind turbine w (kW) The forecasted load of bus n at time t Technical maximum and minimum power output of unit k (kW) Maximum and minimum charging power of battery 𝑏 (kW) Maximum and minimum discharging power of battery 𝑏 (kW) Technical maximum and minimum stored energy of battery 𝑏 (kW) Upper and lower bound of interchange power (kW) Initial stored energy in battery b (kW) Binary decision variable: “1” if unit k is on at time t; “0” otherwise Binary decision variable: “1” if battery 𝑏 is charging at time t; “0” otherwise Binary decision variable: “1” if battery 𝑏 is discharging at time t; “0” otherwise Binary decision variable: “1” if the microgrid is under islanding state at time t; “0” otherwise Binary decision variable: “1” if the microgrid start/end islanding state at time t; “0” otherwise Ramp-up/ramp-down rate limit for unit k (kW) Ramp-up/ramp-down rate limit for battery b (kW)

Positive and negative reserve rate (%) Weight coefficient for the objective function, x=1,2,3,4

𝛾𝑢 , 𝛾𝑑 𝜆𝑥

II.

INTRODUCTION

Recently, the microgrid has been one of the important solutions to deal with the uncertainty and fluctuation brought about by the renewable energy, namely wind and photovoltaic. By 2013, the world market for microgrid had reached around $10 billion, and it is expected to continue growing with the rapid growth of renewable energy [1]. However, because of the fluctuating nature of renewable energy [2-3], proper scheduling of generation units in microgrid is always difficult to obtain. The practice tends to equip microgrids with additional storage devices and sufficient spinning reserve. Stochastic optimization and robust optimization have been recently studied to handle with the uncertainty in power systems. [4-10]. However, both approaches suffer from several drawbacks. From one side, the high computing requirements resulting from the large sets of generated scenarios prevent the real application of stochastic optimization. Even though different scenario reduction approaches have been proposed, in order to obtain a reliable and feasible operation solution, the selected scenario set is still too large to be fully calculated nowadays. From the other side, robust optimization faces the challenges of conservatism because its objective function is to minimize the worst-case cost, while the worst case happens rarely. To address the above shortages of each approach (stochastic or robust optimization approach), the OO theory is applied in this paper to solve the microgrid day-ahead battery scheduling (MDBS) problem considering wind power uncertainty. OO theory was proposed by Y.C He in 1992 [11], and has been applied to many different fields [12-14]. It works well especially for the complex system optimization and computation-intensive models. The remainder of this paper is organized as follows: Section III presents the formation of day-ahead scheduling problem; Section IV proposes the ordinal optimization theory, Section V provides and analyzes case studies; finally, Section VI concludes the paper. III.

MICROGRID DAY-AHEAD BATTERY SCHEDULING MODEL

A. The Framework of the Proposed MDBS Model The microgrid considered in this paper contains four major components, i.e. loads, wind turbines, batteries and conventional units, shown in Fig. 1. Loads

Wind Turbines

Batteries

Units

Main Grid

Figure 1. Microgrid illustration and major components

The primary objective of microgrid operation is to promise a sufficient power delivery to the consumer. Meanwhile, the microgrid should purchase as less electricity as possible from the main grid, especially during peak hours with a higher electricity price. In addition, a sustainable microgrid operation is also supposed to consider the limitation of the battery life. Finally, the wind power uncertainty also needs to be covered in the model. Considering all the above factors, the structure of MDBS model used in this paper is shown in Fig. 2.

Inputs

Constraints Battery Ramp Constraints

Battery Parameters

Battery Storage Constraints

Battery Charge and Discharge Constraints

Forecasted Load

Power Balance and Reserve Constraints

Unit Parameters

Forecasted Wind Power Output

Operation Constraints of Units and Wind Farms

Main Grid Interchange Power Limit

Interchange Constraints between Microgrid and Main Grid

Objective Function

Battery Charging and discharging Punishment Wind Curtailment Punishment

Unit Operation Cost

Interchange Cost

Figure 2. MDBS model structure

B. The Formulation of the MDBS Model The objective of MDBS is to minimize operation cost expectation while considering wind production uncertainty, analytically: min C1  C2  C3  C4 

4 1 n   lim    Pr(W (i ))  j C j   n  n j 1    i 1 

  pi(t )  I (t )  ps(t )  IB(t )

tT

   pc(b)C (b, t )  pd (b) D(b, t )

(1)

tT bB

  g( P(k , t ))

tT k  U

  C (w, t )

tT w W

In (1), 𝑊(𝑖) represents the ith wind power output scenario, Pr (𝑊(𝑖)) is the accordant probability of the scenario, and ∑4𝑗=1 𝜆𝑗 𝐶𝑗 is the total cost of the corresponding scenario. ∑𝑚 𝑡∈ΩT [𝑝𝑖(𝑡) ∙ 𝐼(𝑡)] represents the interchange cost that the microgrid has to pay for receiving electricity from the main grid; − ∑𝑚 𝑡∈ΩT [𝑝𝑠(𝑡) ∙ 𝐼𝐵(𝑡)] represents the reward for islanding state. 𝐶2 represents the penalty for using batteries to charge or discharge, and it usually means the energy loss and storage life loss. 𝐶3 represents the system operation cost, 𝑃(𝑘, 𝑡) is the kth unit generation at time t, and 𝑔(∙) is the unit cost function in quadratic form. 𝐶4 represents the wind power curtailment penalty, and 𝐶(𝑤, 𝑡) is the wind power curtailment of the wth wind turbine at time t.

The constraints of MDBS are divided into five groups corresponding to Fig. 1:

(1  IB(t ))  I (t )  I (t )  (1  IB(t ))  I (t ) , t T

1) Power balance and reserve constraints Power balance



P(k , t ) +

k U



W (w, t ) - C (w, t ) 



L(n, t ) 

wW

 I (t ) 



niL

 C (b, t ) ,

 IE (t  1)  IB(t  1)  IB(t )  IS (t  1) , t T

(15)

 IS (t )  1

(16)

 IE (t )  1

(17)

(2)

t  T

tT

bB

Reserve

tT

Equations (6) and (7) restrict that the microgrid can start or end islanding state for only one time during the day.

 U (k , t ) P(k ) +  W (w, t )   D(b, t )

k U

w W

 (1   u )  L(n, t )  nD

bB



(3)

C (b, t ), t  T

bB

 U (k , t ) P(k )   D(b, t )

k U

bB

 (1   d )  L(n, t )  nD



It should be noted that 𝑈(𝑘, 𝑡), 𝐼𝐶(𝑏, 𝑡), 𝐼𝐷(𝑏, 𝑡), 𝐼𝐵(𝑡), 𝐼𝑆(𝑡) and 𝐼𝐸(𝑡) are binary variables; 𝐶(𝑏, 𝑡), 𝐷(𝑏, 𝑡), 𝑃(𝑘, 𝑡) and 𝐶(𝑤, 𝑡) are continuous variables. They are all decision variables of the MDBS model, and the value of other variables are appointed before optimization.

(4) C (b, t ), t  T

bB

2) Wind turbines

0  C (w, t )  W (w, t ), w W

, t T

3) Unit constraints Maximum and minimum power U (k , t ) P(k )  P(k , t )  U (k , t ) P(k ), k U , t T

(5)

(6)

Ramping up and down constraint P(k , t  1)  P(k , t )  (2  U (k , t )  U (k , t  1)) P(k )  (1  U (k , t )  U (k , t  1)) Rkup , k   U , t  T

(7)

P(k , t )  P(k , t  1)  (2  U (k , t )  U (k , t  1)) P(k )  (1  U (k , t )  U (k , t  1)) Rkdown , k   U , t  T

(14)

Islanding start and end times constraint

D(b, t )

bB

5) Interchange constraints Maximum and minimum interchange power

(8)

It is worth noting that (7) and (8) not only restrict ramping up and down speed, but also restrict the unit power right after starting up and before shutting down. 4) Batterie constraints Maximum and minimum charging/discharging power IC (b, t )  C (b)  C (b, t )  (9) IC (b, t )  C (b), b  B , t  T

IV.

ORDINAL OPTIMIZATION THEORY

A. Introduction of Ordinal Optimization The basic idea of OO is shown as Fig. 3. ΘS , is the search space of OO and Θ𝐺 is assumed as the set of good enough solutions of the optimization problem. Defining a certain alignment level, OO aims to capture the good enough solutions in ΘS with the probability satisfying the appointed level. The optimization guarantees that there is enough probability that at least k good enough solutions are in ΘS (represented by the dotted area in Fig. 2 below). k is called the alignment level, and this number quantifies how a crude model can help to assure the determination of “good enough” solutions. OO defines five types of problems [15], and all problems could be classified into one of them, shown as Fig. 4. The OPC curve could be obtained by ordering the objective values of N solutions in Θ𝑁 via a crude model. After determining the OPC type, the final result of a good enough solution could be achieved with high probability with the following steps [15]: 1) 2) 3) 4)

Specify the size of 𝛩𝐺 and the alignment level k Estimate the noise level of the crude model Determine the size s of 𝛩𝑆 Obtaining the good enough solution

ID(b, t )  D(b)  D(b, t )  ID(b, t )  D(b), b  B , t  T

State constraint IC(b, t )  ID(b, t )  1, b B , t T

(10)

(11)

Stored energy constraints j 1

ΘN : Search Space ΘG : Good enough Set ΘS

ΘG ΘG ∩ ΘS

t

S (b)  S (b)   C (b, j )  D(b, j ) 

ΘN

ΘS : Selected Set ● : Truly Optimum

(12)

○ : Estimated Optimum

 S (b), b  B , t  T Ramping up and down constraint

 Rbdown  C (b, t  1)  C(b, t )  Rbup

, b B , t T

(13)

Figure 3. Graphical illustration of the basic idea of OO

The wind power forecast output is shown as the black curve in Fig. 5. We sample 1000 curves considering the normally distributed forecast error, and then use the scenario reduction technique to extract 20 scenarios, shown in Fig. 5.

Figure 4. Types of ordinal performance curves

B. Apply OO theory to solve the MDBS model Based on the wind power forecast output curve, we assume that the forecast error follows normal distribution and cope with the uncertainty by extracting 20 typical output curves using the scenario reduction technique. Hence, the best schedule should have a minimum average objective value of the MDBS model with each wind power output curve. In order to reduce computation burden, this paper uses the OO theory to obtain a good enough schedule. Thus, a crude MDBS model is proposed. It is composing of (1), (2), (5)-(6), (9)-(17) and ignores wind power forecast error. V.

CASE STUDY

A. Basic parameters In this section, a case study based on Fig. 1 is carried out to verify the feasibility and validity of the proposed model. For simplicity, the microgrid has only one generating unit, one wind turbine, one load zone, and two batteries. Basic parameters are shown in Table I. TABLE I.

BASIC PARAMETERS OF THE MODEL

Parameter

Value

𝑝𝑐(𝑏), 𝑝𝑑(𝑏), ($/kWh)

125, 75

𝑝𝑖(𝑡) ($/kWh) 𝑝𝑠(𝑡) ($/h)

0.001𝑝2 + 0.04𝑝

Wind turbine capacity (kW) Wind power forecast error standard deviation 𝐶(1), 𝐶(1), 𝐶(2), 𝐶(2) (kW)

60 10% of capacity

𝐷(1), 𝐷(1), 𝐷(2), 𝐷(2) (kW)

120, 0, 75, 0

𝑆(1), 𝑆(1) (kWh)

600, 25

100, 0, 50, 0

300, 25

Peak hour

16:00~20:00

𝐼(𝑡) (kW)

10 200 (normal hours) 40 (peak hours) 30, 40

𝛾𝑢 , 𝛾𝑑 (%)

Additionally, we assume that set Θ𝐺 is composed by the top 1% of schedules, and the alignment level k is set at 1. Therefore, the actual good enough schedule number g in Θ𝐺 equals 1000 × 1% = 10.

350, 250

𝑆(2), 𝑆(2) (kWh)

𝐼(𝑡) (kW)

B. Estimate the OPC type, specify the size of good enough set and the alignment level The crude MDBS model is used here to estimate the objective values of N schedules in Θ𝑁 , and we can obtain the OPC shown in Fig. 6. The OPC curve shape fits the Flat type in Fig. 6. Hence, the MDBS is considered as a flat-type OO problem.

100 (normal hours) 400 (peak hours) 2000 (normal hours) 7000 (peak hours)

𝑔(𝑝) ($) ̅̅̅̅̅̅ 𝑃(𝑘), 𝑃(𝑘) (kW)

up 𝑅𝑏 , 𝑅𝑏down (kW/hour) up 𝑅𝑘 , 𝑅𝑘down (%/hour)

Figure 5. Wind power forecast output and the extracted output scenarios

100 5, 5

𝐼𝑆(𝑡), 𝐼𝐸(𝑡)

1, 1

𝜆1~𝜆4

1, 1, 1, 10

Figure 6. Estimated OPC by ordering the rough evaluated objective values

C. The noise level of the crude MDBS model It is assumed that the error of the estimated value using the crude MDBS model follows a uniform distribution u(-w, w) [15], we estimate w, the standard deviation of errors, by comparing the precise value with the rough estimated value of 25 schedules. Comparison on the results shows that w is 0.2060. The estimation value of w based on such a small number of samples is multiplied by 2 here to approximate the real value, and the final w equals 0.4119. Thus w falls into the interval [-0.5, 0.5], and it will be used in the following process to determine the size of ΘS .

D. Determine the size s According to the regression table at the page 475 of [15], the constants of 𝑍0 , 𝜌, 𝛾, 𝜂 equals 8.1378, 0.8974, -1.2058 and 6.00 respectively. In (18), ∥∙∥ returns the size of a set;  returns the minimum integer greater than the inside value. We can get the size of Θ𝑆 by (18), and s equals 220. s  S  eZ k  g      220

(18)

E. Obtain the good enough schedule We select the first 220 solutions in Θ𝑁 by estimated value in ascending order, and calculate the precise value using MDBS model. The interchange power curve of the final schedule is shown in Fig. 7. The microgrid will be in islanding state just during peak hours from 16:00 to 20:00.

Figure 9. SoC curves of the two batteries

Wind power generation output is smoothed partly by the battery charging and discharging to satisfy the microgrid energy balance. When the charging and discharging penalty is less than the profit derived from wind power curtailment reduction and islanding state reward, the batteries would be employed.

Figure 7. Microgrid islanding state and the interchange power with the main grid

Fig. 8 shows the day-ahead battery scheduling and Fig. 9 shows the stored energy of batteries at each time period. The state of charge (SoC) changes with the load tendency: charging when the load goes down and discharging when the load goes up. F. Wind Power Curtailment Situation For the final achieved day-ahead battery scheduling scheme, the average wind power curtailment is shown as Fig. 10. There is wind power curtailment during morning from 3:00 to 6:30, which is the low load demand time duration, and the average daily curtailment rate is 2.02%.

Figure 10. Wind power curtailment and load demand

G. Comparison with Robust Optimization and Stochastic Optimization In comparison, we run the same case by using robust optimization and stochastic optimization as well. The robust optimization uses the upper and lower boundary of the 20 curves in Fig. 5 as the wind power uncertainty bound. The results are shown in Table II. It shows that OO has the minimum objective value, and has a moderate-length islanding period of time. The schedule obtained by robust optimization is conservative and the microgrid only has one-hour islanding period of time. The schedule obtained by stochastic optimization has the longest islanding period but medium objective value because of the larger wind power curtailment than that of OO method. TABLE II.

Figure 8. Microgrid day-ahead battery scheduling

MDBS SOVED BY ROBUST OPTIMIZATION AND STOCHASTIC OPTIMIZATION

Method

Objective Value

Islanding Period

Ordinal Optimization

32,728 $

16:00~20:00

Robust Optimization

56,435 $

17:30~18:30

Stochastic Optimization

34,761 $

16:00~20:30

VI.

CONCLUSION

This paper establishes a microgrid day-ahead battery scheduling model and applies the Ordinal Optimization theory to solve this problem. Wind power uncertainty is considered in the model by establishing several wind power output scenarios. The crude MDBS model is used to identify the problem type and select out the potential good enough solutions. Furthermore, the precise MDBS model is used to estimate and find out the best one in the solutions. Case study and comparison with the robust optimization and stochastic optimization are carried out. The results show that the proposed model is valid and efficient, and the wind power uncertainty is well considered to obtain a relatively low curtailment rate.

[5]

[6]

[7]

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