The Optimal Allocation of Pumped Storage Station in Wind Farm

DING Li-jie ， WANG Biao, ZHANG Hua Sichuan Electric power Research Institute

Chengdu, China E-mail:ding_lijie@163.com

REN Zeng, QIU Xiao-yan School of Electrical Engineering and Information

Sichuan University Chengdu, China

E-mail: ren_zeng@126.com, cd_qxy@sina.com

Abstract—To solve peak shaving and abandoning the wind problems caused by the integrate wind generation capacity which is more than certain percentage, and improve the output characteristics of wind power, the mode of constructing the supporting pumped storage power station with wind farm can be adopted. This work is based on modeling the wind farm and pumped storage power plant operation, targets at the hybrid wind power and pumped hydro storage systems (WP-PHS) economic benefits. The stochastic nature of load and wind energy is addressed using scenarios developed through fuzzy clustering. Finally, a practical example simulation results showed that the combined revenues of wind farm can be improved by the proper capacity allocation of pumped storage power station.

Keywords--wind power generation; WP-PHS; optimal allocation; fuzzy clustering

I. INTRODUCTION Wind power is viewed as an important form of

developing renewable energy [1-3], when the power grid integrate wind power capacity which is more than certain percentage, grid security will be influenced definitely [4], such as the amount of spilled wind energy is wasted because of peak shaving in off-peak period when wind speed is high and loads are light , obviously,it is unfavorable for the wind power manufacturers. In order to maximize make use of wind power, at present, the feasible mode is to use energy storage system store the wind power which can not be transferred to the grid for various reasons [5],the wind power which was stored is transferred to the grid in the on-peak or other periods.Current storage devices contain pumped storage, super capacitor, battery, etc.Compared to other storage methods, pumped storage power station has large storage and conversion capacity, high efficiency, mature construction technology, relatively low cost; higher quality of power supply characteristic.Therefore, WP-PHS which is wind farm supporting the pumped storage station is considered to be the most feasible program.

The economic operation model of WP-PHS was established and the feasibility was analyzed [6]. The best installed capacity of pumped storage station and allocation of reservoir capacity were discussed in the optimal allocation model of WP-PHS [7],but this model only use a small amount of certainty data that can not response seasonal wind speed

and does not consider the investment cost, the power accepted by grid and specific operation mode of WP-PHS as well.Therefore, based on investment cost, wind power access limits and different operation strategies of WP-PHS are considered in this paper, the fuzzy clustering theory is applicated to process wind speed data and the acceptable power of grid data in area, the overall economic benefits of WP-PHS were consdered as the target for setting up optimization mathematical model, a new adaptive genetic algorithm is adopted to solve optimal allocation of the installed reservoir capacity of pumped storage station [8]. Finally, a practical example proves that this method is feasible and effective.

II. PROBLEM FOMULATION The identification of its storage capacity is a key problem

and is addressed as an optimization problem that is formulated as a single-objective constrained linear programming optimization problem. The wind farm electricity sale revenues and pumped storage power station operation costs are considered in the model, the maximum annualized economic benefit of WP-PHS is treated as the objective function.

A. Objective Function The objective function to be maximized is the annualized

economic benefits of WP-PHS

( )1 1

max max max max

m n

k wk k gk p PkD k

E P g

MaxF t C P C P C P

aC E aC P= =

⎡ ⎤= + −⎢ ⎥⎣ ⎦

− −

∑ ∑ （1）

In the objective function (1), the sum in the first line is the

electricity sale revenues, the second line corresponds to the annualized installment costs of energy and power capacity.

B. Constraint The equality and inequality constraints of the problem are

in (2)–(8). max0 kE E≤ ≤ （2） max0 pk pP P≤ ≤ （3） max0 gk gP P≤ ≤ （4）

Project Supported by Sichuan Electric Power Corporation (No.11H0892), Project Supported by Science and Technology Department of Sichuan (No.2011GZ0036).

978-1-4577-0547-2/12/$31.00 ©2012 IEEE

1gk

k k p pk dumpg

PE E t P t Eη

η+ = + − − （5）

vk wk pk dkP P P P= + + （6）

0dkP ≥ （7）

ck wk gkP P P= + （8）

C. Problem Variables and Parameters k is used to index periods during the day.

maxE (MWh) is the maximum amount of energy that the system can store.

maxgP (MWh) is the power rating of the power storage station while in generating mode.

maxpP (MWh) is the power rating of the storage station while in pumping mode.

vkP (MW) is the amount of output power of wind farm of

time period k .

gkP (MW) is the amount of power of time period

k generated by the pumped storage station in generating mode.

pkP (MW) is the amount of power of time period k consumed by the pumped storage station in pumping mode.

dkP (MW) is the amount of renewable power of time

period k that could be produced but has been curtailed.

kE (MWh) is the energy balance of storage. This represents the reservoir’s level at the beginning of time period k .

dumpE (MWh) is energy in the storage device that is dumped.

wkP (MW) is the amount of wind power that is transported to the grid directly.

ckP (MW) is the amount of power of time period k which accepted by grid.

maxEC (RMB/MWh) is the constant incremental cost of installing reservoir capacity.

maxPC (RMB /MW) is the constant incremental cost of installing pumping station power capacity.

kC (RMB /KWh) is electricity price of wind power of time

period k during day.

pC (RMB /MW) is pumping costs. a is a dimensionless annualization parameter.

pη is the efficiency of the pumping cycle of the pumped storage station.

gη is the efficiency of the generating cycle of the pumped storage station.

t (h) is the length of each time period. m is the days of a year. Based on the mathematical model and constraints, a new

adaptive genetic algorithm is adopted to achieve optimal allocation of pumped storage power station .

III. APPLICATION OF FUZZY CLUSTERING In order to obtain the better allocation results of pumped

storage station, all possible combinations of wind farm output and certain power constraints shoud be considered in the optimization process, the difficulty of this solution increased yet. For the test system used in this study, three years of hourly wind speed data and the acceptable power of grid data are available. Fuzzy clustering algorithms were chosen as a good approach to analysis this amount of detailed data, a small amount of typical data which reflects the overall characteristics of this data can be generated by clustering, then the typical prediction curves of wind farm output power and acceptable power of grid can be obtained easily. Fuzzy clustering is the classification through fuzzy mathematics method is used to study and deal with the given objects to discover natural groupings that exist in the data set.Fuzzy C-means(FCM) clustering algorithm is one of the most typical clustering algorithms [10], [11]. The objective function of FCM is the following:

( ) ( ) ( )2

1 1,

c N m

m iki k

J U V dikμ= =

=∑∑ （9）

Where,22

ik k i Ad x v i= − , ikμ is the resulting degrees of

membership betwin the sample point kx and the i class prototype of a sample, dik is the distance norm, represents distanc betwin the sample point kx and cluster centers vi .

( )1,m∈ +∞ is fuzzy weighted index, and A is the norm-

inducing matrix used in the distance calculation.

IV. CASE STUDY

A. Wind Speed and Acceptable power of grid According to the three years (2004-2006) of history wind

speed data of wind farm in the U.S. east [12], obviously, the wind farm output power can be obtained. The number of scenarios is determined by doing fuzzy clustering analysis using various numbers of clusters ranging from two to twenty, ten is chosen as the number of scenarios to use in this work. Clustering results of the historical wind speed and the acceptable power of grid are shown in Fig. 1.

2 4 6 8 10 12 14 16 18 20 22 240

2

4

6

8

10

12

Time of day(hour)

Wind

Spe

ed(m

/s)

1

23

4

56

789

10

2 4 6 8 10 12 14 16 18 20 22 246

8

10

12

14

16

18

Time of day(hour)

Acc

epta

ble

Pow

er o

f G

rid(M

W)

12

3

4

56

7

8

910

Fig.1 FCM clustering resrults of wind speed and the acceptable

power of grid

B. Determining Values for model Parameters The formulation of the optimization problem as described

above includes some parameters that must be defined. The installed capacity of wind turbine is 40 MW, cut-in

wind speed is 2.5 m/s, rated wind speed is 14 m/s, and cut-out wind speed is 25 m/s.

Reference to other relevant papers, approximate costs for installing pumped storage are CEmax= 129358 RMB /MWh and CPmax=3541945 RMB/MW.The constant a is an annualization

factor and is chosen to be 0.000174. The constants pηand

gηare the efficiencies of pumping and generating,

respectively, both of its are given values of 0.9. E0 is the initial capacity of the reservoir and is taken as 0. Pumping costs is Cp between which the relationship and Ck that is electricity price of wind power is Cp=0.25Ck. The relationship between Pgmax

and Ppmax is Ppmax=CgPgmax , Cg is scale factor which is generally 1.0 to 1.2.The constant n is the number of time periods in each scenario, a daily cycle composed of 24 one-hour periods is chosen, so n=24 and t=1. The annualized economic benefits of this model should be obtained, so m=365. Real-time electricity price of wind power during day are shown in Table 1.

TABLE 1. PRICES OF WIND POWER DURING DAY

Period（h） 0～6 6～10 10～22 22～24

Price（RMB/KWh） 680 827.5 1182 827.5

V. RESRUTS According to the actual role of WP-PHS in the power

system, the following two kinds of optimal strategies are used to analyse operation of WP-PHS.

The first optimization strategy is described as follows: On the premise of the acceptable power of grid as load demand, wind power and pumped storage power station must to meet needs of the grid load preferentially, but not more than. That is, when wind farm output is more than the grid load, pumping or abandoning wind can be happened; when wind power output is less than the load, the pumped storage power units should be given priority to generate, and the sum of pumped storage units output and wind farm output should be equal to or less than the load demand. Table 2 shows the four better cases of the first strategy, the case 1 is reckoned to be the best optimal solution, the optimization results shown in Fig. 2.

TABLE 2. BETTER CASES OF THE FIRST STRATEGY

2 4 6 8 10 12 14 16 18 20 22 240

20

40

60

80

100

Time of day(hour)

Res

ervi

or L

evel

(MW

h)

2 4 6 8 10 12 14 16 18 20 22 240

5

10

15

20

25

30

Time of day(hour)

Pow

er(M

W)

Pumping power

Generating powerOutput of WP-PHS

Fig. 2 Optimization results: Case 1 of the first optimization strategy

The second optimization strategy is described as follows: Output of wind farm and pumped storage power station is given a maximum output limit off-peak period in which the load are low, while given a maximum output limit in other periods. That is, all output of wind power can be uesd to pump in off-peak period, wind power field and pumped storage power station must reach a certain output, on the basis of this, and the grid can accept if the output increased. Table 3 shows the four better cases of the second strategy, the case 1 is deemed to be the best optimal solution, the optimization results shown in Fig. 3.

TABLE 3. BETTER CASES OF THE SECOND STRATEGY

The better cases

Revenues（RMBW）

Reservoir capacity（MWh）

Units capacity（MW）

Scale factor

1 11265.14 145 17 1.04

The better cases

Revenues（RMBW）

Reservoir capacity（MWh）

Units capacity（MW）

Scale factor

1 10741.68 79 16 1.04

2 10727.13 78 10 1.19

3 10715.41 79 11 1.20

4 10708.70 80 11 1.08

2 11264.52 142 17 1.19

3 11264.27 151 17 1.20

4 11263.75 137 15 1.08

2 4 6 8 10 12 14 16 18 20 22 240

50

100

150

Time of day(hour)

Res

ervi

or L

evel

(MW

h)

2 4 6 8 10 12 14 16 18 20 22 240

10

20

30

40

50

Time of day(hour)

Pow

er(M

W)

Pumping power

Output of WP-PHS

Generating power

Fig.3 Optimization results: Case 1 of optimization the second strategy

The relationship WP-PHS between profits and reservoir capacity is showed as Fig. 4 when the unit capacity is 16 MW and the scale factor is 1.0 .

30 40 50 60 70 80 90 100 110 1207500

8000

8500

9000

9500

10000

10500

11000

Reservoir Level(MWh)

Pro

fit(R

MBW

)

Fig.4 The relationship between WP-PHS profit and reservior capatity The relationship between WP-PHS profits and hydro-

power units capacity is showed as Fig. 5 when the reservoir capacity is 100MWh and the scale factor is 1.0.

0 5 10 15 20 25 30 35 401

1.01

1.02

1.03

1.04

1.05

1.06

1.07x 10

4

Rydro-power Units Capacity(MW)

Pro

fit(R

MBW

)

Fig.5 The relationship between WP-PHS profit and hydro-power

units capacity

VI. CONCLUSIONS

Considering wind power intermittent and random features in this work, a joint WP-PHS model is constructed, two kinds of optimization strategies are proposed to analys the sizing and allocation form of pumped storage power station, and the overall economic efficiency of wind farm analysis is included. The application of FCM for wind speed and acceptable power of grid clustering, the clustering results could reflect both the objectivity and representative.

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