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Determination of the Optimal Battery Capacity Based on a Life Time Cost Function in Wind Farm Cong-Long Nguyen

Tae-Won Chun

Hong-Hee Lee

School of Electrical Engineering University of Ulsan Ulsan, South Korea [email protected]



introduced [5]. In this method, the WT rotor speed is controlled to leveling the output power but it makes the system become more complex and the wind farm (WF) might not capture the maximum wind power [6]. Recently, utilizing a battery as an energy buffer to compensate the wind power fluctuation and to meet a scheduled dispatching power for WF has been introduced and getting attention in several literatures [7]-[11]. Compared with the previous method, existence of the battery helps the wind system be able to harness the maximum power available in wind, which is an essential demand in all renewable energy conversion systems. However, a large-scale battery is rather expensive thus use of an optimal battery capacity is indispensable to reduce the system cost [7].

Abstract—Use of the battery energy storage system (BESS) as a power buffer becomes a feasible solution to mitigate the intermittent wind power characteristic. Due to the cost, utilizing an economical battery capacity is a crucial requirement of the system design. In this paper, dispatch power strategies are overviewed and the min-max method is selected as the most suitable one for integrating the wind power to grid. A lifetime cost function, which indicates the BESS cost spent to dispatch 1kWh, is defined with the dispatch principle so that the battery capacity can be optimized. With using the optimal capacity, the minimum system operation cost is achieved and the dispatched power is able to satisfy its scheduled reference in any dispatching time period. Moreover, the battery state of charge (SOC) is also managed to be in a safe range so as to guarantee the system undamaged. In order to clarify the proposed determination method, a case study with a 3MW permanent magnet synchronous generator (PMSG) wind turbine model is investigated.

I.

Cooperating between BESS and WT to dispatch a stable power to grid results in a wind-battery hybrid power system, in which the power flow of BESS influences on the dispatched power. Therefore, in order to determine battery energy storage capacity, principle of dispatching power needs to be identified primarily. In [7], the dispatched power in a day is set at a constant level and the optimal battery capacity is obtained by varying the dispatched power within WT rating. With the optimal capacity, the WF achieves maximum income but the assigned capacity is not unique since the method depends on the day of wind studied. Another common dispatch method is use of a low-pass filter to smoothen the output WT power [8]. However, this paper just concentrates on control of the system in order to guarantee the battery state of charge within an unharmed range and do not mentions how determine the battery capacity. In [9], during charging the battery, the dispatched power is set at the minimum available wind power in the dispatching time interval, meanwhile the dispatched power is allocated at the maximum wind power range if the battery switches to discharging status. Based on this dispatching principle and an index function that indicates a trade-off between the battery lifetime and cost, the economical battery capacity is obtained. A large wind data and a complicated

INTRODUCTION

To solve the energy crisis and the environmental pollution problem, utilizing the renewable sources including wind, solar, or tidal energy has become urgent [1]. Amongst these energy resources, electricity generation produced from wind turbines (WT) is the leading candidate because of its lower investment cost compared with the photovoltaic or tidal system [2]. In addition, the well-developed technology of manufacturing high-power WT results in the harnessed wind power capacity grew rapidly year after year: from 159 GW in 2009 to 238 GW in 2011 [3]. However, similarly to the other renewable resources, wind generation is unsteady and uncontrollable because wind speed depends on natural and meteorological condition. Moreover, high penetration of intermittent power to the grid can introduce serious technical challenges related to the grid interconnection, power quality, and system reliability [4]. Therefore, the wind energy system developers need to overcome the problem before intending to dispatch high wind power level to the grid. In order to mitigate the wind power fluctuation, pitch angle control for a variable-speed WT generator is

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program are required to find out the function seem to be the disadvantage of such method. In this paper, an alternative determination method of the optimal battery capacity is proposed. By defining a lifetime cost function and using the min-max dispatching power strategy, the battery capacity is determined after two steps. First, the minimum battery capacity, which is capable of compensating wind power fluctuation in any dispatch time interval, is defined and considered as a basic capacity. The lifetime cost function indicating how much money spent for BESS to integrate 1kWh of electricity to grid is defined. Subsequently, in second step, by varying the battery capacity increasingly from the basic capacity, the minimum lifetime cost function value is achieved and hence the optimal battery capacity is designated. To clarify the proposed determination method, a numerical example with 3MW permanent magnet synchronous generator (PMSG) WT model is examined by a MATLAB program. II.

(a)

BATTERY ENERGY STORAGE SYSTEM IN WIND FARM

Fig. 1 shows the typical output power profile of a 3MWWT for a week period. It is recognized that wind power can increase rapidly to reach the rated level or drop suddenly to be zero during a day, so that wind is considered as a nonintegrated energy resource to dispatch directly into the grid [4]. In addition, battery technologies have been developed firmly and its cost is decreasing significantly in recent years. Therefore, using the battery energy storage to handle the wind intermittent behavior becomes a feasible solution. It is similar to an energy buffer, the battery absorbs the remained power once the wind power is larger a threshold and releases power on the contrary situation, resulting in a stable power integrated to grid [11].

(b) Figure 2. Configurations of hybrid BESS and WT system. (a) The BESS connnected to the dc-link. (b) the BESS connected directly to grid at PCC.

to discharge or charge the BESS. In Fig. 2(b), the BESS and the WT generator are independently connected to grid at the point of common coupling (PCC) through the power converter systems PCS1 and PCS2, respectively. Among many kinds of WT generators, the permanent magnet synchronous generator (PMSG) and the doubly fed induction generator (DFIG) are the most popular types in the industrial WF [12]. To integrate the BESS to the PMSG-based system, the configuration shown in Fig. 2(a) is usually employed. Meanwhile, the other configuration is recommended for the hybrid BESS and DFIG-based WT system.

A. Configurations of Wind-Battery Hybrid Power System Fig. 2 illustrates two common configurations of a hybrid wind and battery power system. In Fig. 2(a), a back-to-back converter is adopted to provide the grid connection capability. The output of the generator is rectified and stored in the dc-link where the BESS is also connected via a bidirectional dc to dc converter. This bidirectional converter is capable of delivering a negative or positive power in order

B. BESS Power and Energy Ratings The BESS capacity, which is normally specified in term of energy rating Ebrat and power rating Pbrat , is determined based on the dispatched power and the WT output power profiles [7], [13]. If assumption that the power losses in the system is negligible, the BESS power is an outcome of subtracting the dispatched power from the wind power or

Pb = Pw − Pd .

(1)

Considering that the system is operating in a time period T , the BESS power rating is defined as Pbrat = MAX | Pb (t ) |= MAX | Pw (t ) − Pd (t ) | . 0≤ t ≤T

0≤ t ≤T

(2)

To detail this definition, Fig. 3(a) shows a BESS power profile when the wind and dispatched power are given. During the considered time interval T , the BESS power is maximal at instant t1 hence this power value is identified as

Figure 1. The typical output power of 3MW-WT.

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the BESS power rating. By integrating the BESS power with respect to time yields the net energy injected into or drawn from the storage up to time t , t

t

0

0

Eb (t ) = ∫ Pb (τ )dτ = ∫ [ Pw (τ ) − Pd (τ )]dτ .

III.

It would be the most desirable if the wind-battery hybrid power system is designed to dispatch the wind power to the grid as a conventional generation station working, i.e., the dispatched power is able to commit a power scheduled in advance. Actually, power dispatching strategy determines the way of WTG-BESS delivering power to the grid and it decides the way of the renewable system operation regarding the efficiency and cooperation with the transmission system operator (TSO). In the view of WF planner, the power dispatching strategy should be decided prior to determination of the BESS capacity as well as the scheduled time for the BESS maintenance or replacement. This section attempts to overview three power dispatching methods with taking into account the simplicity, the ability of working with TSO and setting the maintenance plan, and impacting on the battery power converter operation.

(3)

It is similar to the power rating, the energy rating is the maximum energy which can be stored or released by the BESS while system operation in T and is defined as following Ebrat = MAX | Eb (t ) | . 0≤ t ≤T

OVERVIEW OF POWER DISPATCHING METHOD

(4)

Fig. 3(b) illustrates the BESS energy response, in which the energy capacity is designated at instant t0 when the storage stores the biggest energy quantity.

By utilizing a low-pass filter, the wind power is smoothened to create a reference Pdref of the dispatch power and then the difference between the reference and the wind power is a command power Pbref for the battery power converter (PCS) as shown in Fig. 4(a). If the power loss in the hybrid power system is negligible and the PCS satisfies its command, the dispatched power value is exactly equal to the output of the low-pass filter. Fig. 4(b) gives an example of the dispatching method where the wind and dispatched powers are plotted. Actually, this dispatching method is simple implementation because it does not require predicting the wind data. In addition, SOC of the BESS can be expressed mathematically in term of the smoothing time constant and hence the system controller is capable of

C. State of Charger of Battery Operating cost of the system does depend not only on the BESS capacity but also on the way of utilizing the storage [14]. During the system operation, the BESS technical information needs to be strictly considered, which includes state of charge (SOC) and deep of discharge (DOD). The SOC of a battery is a percentage indicating available energy capacity being stored by the battery compared with its rated capacity. In order to prevent the battery overcharged, the system controller should keep the SOC within a proper limit (usually, 20% to 90%). Moreover, a high DOD causes a significant degradation of the battery cycle life, so that a limitation of DOD needs to be set during discharging the battery; and the maximum DOD is 80% [10].

(a)

(a)

(b)

(b)

Figure 3. (a) The BESS power flow. (b) The BESS energy determined by integrating the BESS power with respect to time.

Figure 4. Dispatching power to grid based on a low-pass filter. (a) Overall system configuration. (b) Wind Power and dispatched power.

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battery results in the dispatched power smaller than the wind power. In order to make the hybrid power system operate effectively, the dispatched power should be assigned to the minimum level of the wind power. In this dispatching principle, it is clear that the battery is managed to be only charged or discharged status during each dispatching time Td so that the total number of deep charge/discharge cycle can be counted. Furthermore, to support the BESS maintenance and replacement task, the battery manufacturers usually give their customers a specification, in which a relationship between the number of charge/discharge deep cycles and its DOD is indicated. Therefore, in this method, the battery state of health is observed easily and system supervisors can decide a proper time for replacing the BESS. IV.

OPTIMIZATION OF BESS CAPACITY As a vital part of the system planning and design, determination of the BESS capacity means deciding how large battery needs to be utilized with taking into account not only be sufficient to compensate the unsteady wind power but also minimize the system operating cost. Thanks to several advantageous outcomes including communication with TSO, ease of controlling the BESS converter and planning the storage replacement or maintenance, and improving the BESS life time, the min-max dispatch strategy is selected as a modern dispatching method to integrate the wind power into grid. To determine the optimal BESS capacity for the wind farm in agreement with this dispatching method, firstly, the basic battery capacity is identified, then, the most valuable BESS capacity is determined so as to minimize the system operation cost. In this study, it is reasonable to assume that a historical longterm wind speed data at the wind farm located is known because this data must have been collected in order to evaluate the wind power availability and its variation characteristic before making any investment or design decision.

Figure 5. The min-max dispatching power strategy. (a) Wind power and dispatched power. (b) The battery SOC performance.

managing BESS effectively [8]. However, it is recognized that the dispatching power strategy does not consider the cooperation with TSO. In the modern power market rule, all generation units have to submit their output powers schedule to the TSO in a day or so ahead and then they have to commit the powers scheduled in all next dispatching time intervals Td , usually Td = 0.5h or 1h. In [7], the dispatching power is determined by mean of averaging the wind power for Td . In order to work together with TSO, the wind speed needs to be predicted and the forecast error should be considered. Similarly to the previous method, in a dispatching time interval Td , the BESS power flow is alternated from charge to discharge or against influencing on the variation of wind power. This causes degradation of the battery lifetime and challenges to control the PCS in the practical system.

A. The Basic Level of BESS Capacity As shown in Fig. 5, the BESS is only charged and discharged in each time interval Td to compensate the difference between the wind power and the dispatched power. Therefore, the BESS capacity must be sufficient to guarantee that at any time the battery is not overcharged or exhausted. In other words, the minimum BESS capacity defined as a basic volume should be determined primarily. Based on the given long-term wind speed data in a period T and under assumption that the WT capturing maximum power available in wind, the wind power profile can be specified [15]. Following three steps show procedure how to determine the basic BESS capacity:

An enhanced dispatching method is introduced in [9], which is capable of removing the battery power flow changing direction problem and helps the wind farm owner be able to schedule the BESS maintenance and replacement easily. As illustrated in Fig. 5(a), the dispatched power to grid is assigned as maximum or minimum value of the wind power in a dispatching time Td . When the dispatched power is set at the maximum wind power, the BESS power is always negative or the battery always discharges to fulfill a gap between the dispatched power Pd and the wind power Pw . In other words, the power flow through PCS is kept only one direction from the storage to the dc-link or to the PCC (Fig. 2). This process continues until the battery SOC decreasing to a lower limit (20%) shown in Fig. 5(b) and then the BESS needs to be charged immediately to avoid deterioration of battery inside structure. Once the battery status is shifted to the charging phase, a part of wind power used to charge the

1. Dividing the wind power profile into N sets and each set contains wind power for a time interval Td . In i th set,

wind power is denoted Pwi (t ) , where 1 ≤ i ≤ N and (i − 1)Td ≤ t < iTd . Noted that T = NTd .

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interval is the bigger one when we compare the battery discharge capacity calculated in (7)-(8) and the charge capacity computed in (11)-(12). In other words, the basic BESS capacity in the i th interval time is determined as following

2. For i th interval Td , the BESS can be charged or discharged according to the SOC status. If the BESS is being discharged then the dispatched power is assigned at the maximum value of wind power data in i th set. From (1), the battery discharge power in i th set can be expressed as

{ }

i Pdis (t ) = Pwi (t ) − MAX Pwi .

t

∫

( P (τ ) − MAX {P })dτ . i w

( i −1)Td

i w

{ }

rat [i ] = Edis

(6)

{ },

consider that the BESS is being charged for i th interval Td so that the dispatch power specifies at the minimum value in i th set wind powers. Similarly to the discharge phase, the battery charge power and charge energy up to time t can be expressed as

{ }

i Ech (t ) =

t

∫

( P (τ ) − MIN {P })dτ . i w

( i −1)Td

i w

(14)

{ }

(15)

{ }

(16)

The three main steps presented above to determine the basic BESS capacity can be summarized in flowchart shown in Fig. 6. Initially, key variables including Pbbasic , Ebbasic , and index i are set to be zero and unity; and the number of wind power set N is computed from the given dispatched time interval Td and the system operation period T . By increasing the index i one by one, the minimum requirement of BESS capacity in each interval Td is calculated based on (5)-(14). When the index i reaches to N , all wind power data sets were considered and the BESS basic capacity is eventually determined by using (15)-(16).

where η represents the SOC range e.g., if SOC of battery is managed to be in 20% to 90% then η = 0.7 . Next, we

Pchi (t ) = Pwi (t ) − MIN Pwi ,

}

Ebbasic = MAX Ebrat .

(8)

η

{

Pbbasic = MAX Pbrat ,

(7)

i MAX Edis

(13)

3. After determining the minimum requirement of BESS capacity in each interval Td , the biggest one in these data is defined as the basic BESS capacity to carry out successfully the min-max dispatching method for all time:

Based on the battery discharge power and energy profiles in i th interval Td , the battery capacity in term of discharge power rating and discharge energy rating need to be rat i Pdis [i ] = MAX Pdis ,

}

rat rat Ebrat [i ] = MAX Edis [i ], Ech [i ] .

By integrating the discharge power, the battery discharge energy up to time t in i th interval Td is calculated as following i Edis (t ) =

{

rat Pbrat [i ] = MAX Pdis [i ], Pchrat [i ] ,

(5)

(9) (10)

The maximum level of the battery charge power and energy profiles in i th interval Td are defined as the charge power rating and charge energy rating of the battery, respectively:

{ }

Pchrat [i ] = MAX Pchi ,

rat [i ] = Ech

{ }.

i MAX Ech

η

(11)

(12)

Because the BESS can be charged or discharged for i th interval Td , the minimum BESS capacity required in this

Figure 6. Flowchart of process for calculating the basic BESS capacity.

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B. The Optimal BESS Capacity The basic capacity guarantees that the wind-battery hybrid system is able to integrate power into the grid complying with the min-max dispatching strategy. However, it does not make the system operating optimally or does not ensure that the system obtains the maximum income. Because the electricity price sold to grid is fixed, the system achieves the maximum income when we minimize the system operation cost which depends only on the BESS spend cost for a given WF specification. To clarify the relation of BESS capacity with the system operation cost, we set A as a total energy ( kWh ) that the hybrid wind-battery system integrates into grid in T period and the BESS cost ($) including the initial investment and the maintain cost is denoted by M ; so the system operation cost ($ / kWh ) can be defined as M Sc = . (17) A

Figure 7. Flowchart of process for determining the optimal BESS capacity.

The system, which operates with a small cost Sc , will perform a high income. Under this definition, in order to reduce the system cost, we should use a small BESS capacity so as to lessen the cost M and needs to dispatch a high energy A to grid.

when the battery charges and discharges with an 80% DOD, it can carry out about 750 deep-cycles or Cr = 750 . Once the battery capacity is given and the wind power integrated into grid follows the min-max dispatching method, all components in (18) can be defined and then the LTC is computed. Therefore, by increasing the battery capacity from the basic level, it is able to identify the optimal BESS capacity which allocates the LTC at the minimum value.

However, not only in the min-max dispatching strategy but also in the other dispatching methods, they causes a tradeoff between dispatch energy and the BESS cost. Particularly, as shown in Fig. 5, once the battery capacity increases, time spending in discharge and charge phase is prolonged hence the battery life span is extended obviously. However, this increase results in an expensive battery cost. In other words, the bigger BESS capacity, the longer time to utilize the storage or the higher dispatch energy obtained but the more expensive BESS cost required. Therefore, the design objective should find out an optimal BESS capacity so as to minimize the system operating cost or make the wind farm work economically. In this study, a lifetime cost function (LTC) is introduced as an alternative system cost definition expressed in (17) to take the role of searching the optimal battery capacity suitably for the min-max dispatching method:

LTC =

α Eb

c . ∑ Pd Td Cr

Fig. 7 shows the flowchart of process for determining the optimal BESS capacity, where calculating components in (18) is the key task. In the process, k is a normalized ratio between BESS capacity and its basic value, so that we set k = 1 at the first iterative step to compute LTC of system with the basic BESS capacity. The LTC opt and Ebopt variables, which store the smallest LTC and the optimal BESS capacity, are initially set at a positive infinity and at zero values, respectively. Noted that after each iterative step, the normalized ratio k is increased 10% or step = 0.1 until it exceeds a upper limit k max . V.

In order to illustrate the BESS capacity determination method for the hybrid wind-battery system, several numerical examples are made by using MATLAB program. The wind speed profile in two years 2009 and 2010 is taken from [16] and converted into power data by using a 3MW PMSG-WT model [17]. This means the system is evaluated in a time interval T = 2 years with the dispatching time Td = 1 hour and the rated wind power 1p.u = 3MW . Deepcycle technique is adopted here and the battery SOC is controlled within a safe range 20% to 90%. It is assumed that the system utilizes Li-Ion battery whose specification in connection with the price and the lifelong charge/discharge cycles are α = 685.5 ($/kWh) and Cr = 1500 (cycles), respectively [18].

(18)

T

where α is the battery energy cost ($/kWh) and is used to calculate the total cost of the BESS by mean of multiplying with the capacity Eb ; considering the system operated in a time period of T , the term

∑P T

d d

NUMERICAL EXAMPLES

in the denominator

T

means the total energy delivered to the grid; and c denotes the total charge/discharge cycles of the battery. In addition, with given DOD, the rated charge/discharge deep cycles that the battery can be handled in its lifespan is defined as Cr . For example, the recent lead-acid battery technology shows that

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A. Determination of Basic BESS Capacity For ease of explaining the steps to decide the basic BESS capacity, we just consider wind power within a first twelve hours of a day. During discharge phase, dispatched power is set at the maximum wind power for each Td (i.e., each hour) as shown in Fig. 8(a). Based on (5) and (6), BESS discharge power and energy in each Td can be assigned and they are plotted in Fig. 8(b) and Fig. 8(c), where the discharged power and discharged energy ratings in first, second, and ninth dispatch time interval are also pointed out. Because the BESS is discharged, its power and energy profiles are negative values but we take into account only the magnitudes to determine the basic BESS capacity. By comparing all discharge power ratings in the considered window time (twelve hours), the biggest one is the basic BESS power rating during discharge phase; and it is obviously assigned at Pdisrat [9] or 1275kW. Similarly to the power rating, the basic BESS energy rating required in discharge stage is the biggest rat one within the energy rating set, which is defined at Edis [ 2] element or 450kWh. In Fig. 9, charge phase performances are depicted, where the dispatched power is assigned at the minimum wind power in each dispatch interval. Using (9) and (10), the BESS charge power and energy are computed in order to determine the basic BESS power and energy ratings. As

(a)

(b)

(c) Figure 9. Charge phase. (a) Wind power and dispatched power. (b) BESS charge power. (c) BESS charge energy.

shown in Fig. 9(b), the basic BESS power rating required in the charge stage is specified to 1285kW by the ninth dispatch Pchrat [9] which is the biggest value among the other power

ratings such as Pchrat [1] or Pchrat [ 2] . From Fig. 9(c), it is recognized that the BESS charge energy rating in the ninth dispatch is the biggest value compared with that in the other dispatches, thus Echrat [9] or 850kWh is defined as the basic BESS energy rating for charge phase. The minimum BESS capacity to be able to handle successfully the min-max dispatching method in the considered twelve hours is the bigger one of the capacities in charge and discharge phases. In term of power rating, the basic BESS capacity is defined by Pchrat [9] or 1285kW

(a)

because it is bigger than Pdisrat [9] =1275kW; and the basic

(b)

BESS energy rating is selected at Echrat [9] or 850kWh that is bigger than the energy rating in discharge phase defined at rat Edis [ 2] requiring only 450kWh. For general, running the proposed process with the two years wind speed data, we obtain the basic BESS capacity as Pbbasic = 1300 kW and Ebbasic = 875 kWh. B. Determination of the optimal BESS capacity As discussed in Section IV.B, the battery capacity is increased from its basic level to identify how BESS large for

(c) Figure 8. Discharge phase. (a) Wind power and dispatched power. (b) BESS discharge power. (c) BESS discharge energy.

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Government (2013R1A2A2A01016398) and the Networkbased Automation Research Center (NARC) funded by the Ministry of Trade, Industry & Energy. REFERENCES [1]

[2] [3]

Figure 10. Lifetime cost function versus the normalized capacity.

[4]

[5]

[6]

[7] Figure 11. SOC of BESS with its optimal capacity.

[8]

obtaining the minimum LTC function, where allocates the optimal capacity of BESS. Fig. 10 shows the LTC function value corresponding with the normalized ratio k. It is recognized that the optimal BESS capacity is defined at four times of the basic capacity level or 4x875=3500kWh and the minimum LTC value is 4.27 cents/kWh. The program carrying out the process depicted in Fig. 7 records 15.84 GWh of total energy integrating to grid and 424 deep-cycles that the battery has to execute in the two years associated with the optimal BESS capacity. In addition, using the optimal capacity, the system is also evaluated and the SOC of battery is managed and kept successfully in a safe range of 0.2-0.9 as illustrated in Fig.11. VI.

[9]

[10]

[11]

[12]

CONCLUSIONS

Dispatch power strategies are overviewed in order to select the most advantageous one for integrating the intermittent wind energy to grid. The min-max method poses several values and is proper to cooperate with TSO in the modern electricity system. The main contribution of this paper is introducing a method to determine the optimal BESS capacity by means of minimizing a lifetime cost function. In this method, the basic capacity of BESS is considered first to ensure the battery enough size to handle the min-max dispatch strategy. Subsequently, by increasing the BESS capacity from its basic volume, the lifetime cost of system is computed. The capacity making the lifetime cost minimum is the optimal one. A numerical example is carried out to demonstrate the proposed determination method.

[13]

[14]

[15]

[16] [17] [18]

ACKNOWLEDGMENT This work was partly supported by the National Research Foundation of Korea Grant funded by the Korean

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