1

Abstract—Distributed generation (DG) and microgrid will play

important roles in the future electric network operations. They could improve energy efficiency, minimize environmental impacts and enhance power system reliability. A power scheduling approach considering load/generation changes and time of use (TOU) tariff for a low voltage DC microgrid incorporating energy storage battery, fuel cell and photovoltaic power generations, is presented in this paper. The problem is solved by a multi path dynamic programming (MPDP) approach. Simulation results illustrate the benefits of DG and energy storage integrations in reducing electricity bill for customers adopting DC distribution system.

Index Terms—Smart grid, distributed generation, DC micro grid, dynamic programming

I. Introduction n current applications, most of the DG outputs would require two or three power conversions before power

reaches the loads. If energy from DG could be utilized in DC form and properly controlled, the loss could be minimized and energy efficiency is improved. A power network interconnected low voltage dc microgrid has many advantages over a conventional ac distribution system, such as: 1) Power resources can be easily operated cooperatively and the imbalance in the power generation and load in the dc network can be taken care by controlling dc bus voltage only through DC/AC inverter connecting the mains and dc grid. 2) When there are abnormal or fault conditions in the interconnected AC network, the dc-grid system can be switched to stand-alone operation where all or partial loads are served by local power resources. 3) The system cost and loss can be reduced because only one ac grid connected inverter is needed.

An autonomous-control method for a dc micro-grid system was proposed in [1] to suppress circulating currents in the dc grid which consists of a solar-cell generation unit, a wind-turbine generation unit, a battery energy-storage unit, a flywheel power-leveling unit, and an ac grid-connected power control unit. Each unit could be controlled autonomously without communicating each other. It shows that a dc microgrid provides a better scheme for dc generation output sources connections. If loads in the system are supplied by dc power, the conversion losses from sources to loads can be reduced.

To satisfy high efficiency and high-quality power supply, a low-voltage bipolar-type dc microgrid was proposed The authors are with Department of Electric Engineering, National Sun Yat-sen University, Kaohsiung, Taiwan, ROC. This work was support by National Science Council of Taiwan under contract NSC 100-3113-p-110-004.

in [2]. In this system, dc power is distributed through three-wire lines, and it is converted to required ac or dc voltages by load-side converters. With the progress of high power electronics technology, control efficiency and costs of small-scale dc power generation systems are improved.

In [3], a voltage control scheme performed by a power electronic building block (PEBB) for a dc microgrid with fuel cell, energy storage battery, photovoltaic shown in Fig. 1 has been reported by the authors. Experimental results shown in Fig. 2 illustrate the effectiveness of the dc bus voltage and power controls during different stages of operations. Fig. 2a shows the dc bus voltage and power flow changes at each stage of operation. In stage 1, PEBB is started and takes over the dc bus voltage control. In stage 2, a 2 kW load drawing power from the dc microgrid is connected to the system. The power at this stage is from the mains to the dc grid. In stages 3 and 4, PV and fuel cell power outputs are integrated into the system. A lower power demand from the mains can be seen. As shown in Fig. 2f, a 180 degree shift in the phase current angle due to a load reduction that causes a reverse power from the dc grid to the mains in stage 5.

Fig. 1 The studied DC Microgrid

(a)

DC Microgrid Operation Planning

Ching-Chih Huang, Student Member, Min-Jui Chen, Yung-Tang Liao, Chan-Nan Lu, Fellow, IEEE

I

2

(b)

(c)

(d)

(e)

(f)

Fig. 2 Experimental results As has shown in [3], with a suitable AC/DC inverter

controller design, the dc bus voltage and power flow can be

properly controlled. In this paper, a power dispatch strategy for the dc microgrid to determine the optimal contract capacity of the system in order to reduce electricity bill is presented. Power scheduling of an energy storage system and a fuel cell power with consideration of contract capacity and TOU charges, load and generation variations are investigated. The problem is solved by a multi path dynamic programming approach.

II. MODELING METHOD AND PROBLEM FORMULATION

The sample dc system used in this study is shown in Fig. 3. The system includes a 30 kW PV module, 5 kW fuel cell, 25Ah energy storage system, EV charging loads and 50 kW other loads. The mathematical models of PV, fuel cell, energy storage systems and AC/DC load variations are described in the followings.

tpvP t

FuelP tB

P +t

BP −

tLoadP

tgridP

tEVP

Fig. 3 A sample dc microgrid

A. PV power generation model

An illumination randomly selected from a normal distribution of illumination can be expressed as:

),()1()0(pvpvpv NkL σμ∈+ (1)

The accumulated solar illumination and estimated PV power output variation are calculated from the following equations

)1()()1( )0()1()1( ++=+ kLkLkL pvpvpv (2)

)(ˆ)1(ˆ)1(ˆ )1()1()0( kPkPkP pvpvpv −+=+ (3) Using the gray theory presented in [4], the power output estimation at each time interval can be estimated by

)1()1()1()1(ˆ )1()1()0()1(0, ++⎟

⎠⎞

⎜⎝⎛ +−=+ − kL

abekL

abPkP pv

atpvpvpv

(4)

Where a and b are derived from gray differential equation [4] 21,...,2;)()()( )1()1(

1)0( ==+ kkbLkazkP pvpv (5)

2;)1(5.0)(5.0)( )1()1()1(1 ≥−+= kkPkPkz pvpv (6)

a and b can be calculated by the least square method based on historical data. B. Fuel cell production cost modeling

Fig. 4 shows the required hydrogen flow volume for a Proton Exchange Membrane Fuel Cell (PEMFC) to generate electric power outputs. Multiplied by the price of hydrogen ($3.5/kg) and divided by a weight factor of 11200 l/kg, the

3

regression curve equation of the production cost curve shown in Fig. 5 is as follow.

904.0)(702.2)(9542.0 2 ++= t

fueltfuelfuel PPC (7)

Fig. 4 Hydrogen requirements for power generations by a PEMFC [5]

Fig. 5 The production cost function of a PEMFC used in this study

C. Battery energy storage system charging/discharging

operation cost model Modified from the battery model used in Matlab [6], the

battery terminal voltage variations during charging and discharging periods are described in the followings. Before battery state of charge (SOC) reaches 0.8, constant current mode is used to charge the battery and after that a constant voltage mode is used. The charging/discharging current should be lower than the max. charging/discharging current of the battery.

In charging period

)exp(

||)||(

||)||(1.0

)(110

usetB

usetB

usetB

tBrate

ratetB

usetB

tBrate

ratetB

tbattery

tiBA

titiQQ

QKi

tiQQQ

RViV

⋅⋅−−

⋅⋅⋅+−

+⋅⋅++

⋅−=−−

(8)

When SOC reaches 80%, a constant voltage charging mode is used, i.e., ViV t

Bt

battery 400)( =

In discharging period

)exp(

)()()(

110

usetB

usetB

usetB

tBrate

ratetB

usetB

tBrate

ratetB

tbattery

tiBA

titiQQ

QKi

tiQQQ

RViV

⋅⋅−+

⋅⋅⋅+−

−⋅⋅+−

⋅−=−−

(9)

Where Vt

battery is the battery terminal voltage at time interval t, V0 is the battery nominal terminal voltage, Qrate is the battery capacity (Ah), R is the polarization resistance (Ohms), K is the polarization constant (Ah-1), A is called the exponential voltage (V) and B is the exponential capacity (Ah-1). The

exponential voltage and the exponential capacity are corresponding to those at the end of the exponential zone. The voltage should be within acceptable and rated voltage. The capacity should be between 0 and nominal capacity. it

B is the charging/discharging current at time interval t, |it

B|*tuse is the battery energy used (Ah), Qt-1

B is the battery remaining energy (Ah) at time interval t-1 (Ah), tuse is the battery discharging duration starting at time interval t. Power output of the energy storage system is:

tB

tB

tB

tbatery

tB iiQVP ⋅= ))((

⎪⎩

⎪⎨⎧

<

>

0

0

tB

tB

iCharging

igDischargin

(10)

Power storage capacity constraint at each time interval is

max1 )(0 QiQtiQ t

BtBuse

tB

tB ≤=⋅+≤ −

(11) Where Qmax is the energy storage system capacity. The charging /discharging constraints are as follows:

tgdischarginB,

tB

tBQbt

BusetB

tB

tB

tB

ingchBtBuse

tB

tB

tB

tB

ii

gDischargin

aeiQtiQiQ

iiQtiQiQ

Charging

≤

≤>⋅+=

≤≤⋅+=

×−

−

- *8.0)(

*8.0)(

max1

arg,max1

，

，

(12)

Where

)]8.0*max*1[ln( QbrateCea −=

maxmax 8.0*)20/ln()1ln(

QQCCb raterate

−−=

Crate is current rating signifying a discharge/charge rate relative to the capacity of a battery in one hour.

Battery voltage

Charging current

80% SOC

1C/ 20

100% SOC Fig. 6 Battery voltage, charging current and SOC variations during constant current/ voltage charging schemes D. Battery operation costs

It is assumed that the charging/discharging cycle life of each type of battery depends on the depth of discharging (DOD). Table I shows the cycle life of different DOD for Lithium-ion battery. K is depth level of discharge.

Table II TABLE II shows the investment costs of different sizes

of Lithium-ion battery. By using the data shown in Tables I

4

and II, the daily battery operation costs can be estimated by the following calculation. Battery cycle cost (CycleCost(k)) = Battery investment cost / number of cycles life Battery daily operation cost is as follow:

∑=

=96

1

)(),cos (t

tt kCycleCostBCtBattery

(13)

TABLE I BATTERY CYCLE LIFE UNDER DIFFERENT DOD

k Depth of Discharge Batter cycle life

1 DOD<=20% 13750

2 20%<DOD<=50% 10000

3 50%<DOD<=80% 6250

4 80%<DOD<=100% 3750

TABLE II BATTERY COSTS OF DIFFERENT CAPACITIES

Battery Cap. (Ah) Costs (NT$) Battery Cap. (Ah)Costs (NT$)

25 (9kWh) 220,500 150 (54kWh) 1,688,500

50 (18kWh) 463,050 175 (63kWh) 2,068,400

75 (27kWh) 729,300 200 (72kWh) 2,482,100

100 (36kWh) 1,021,000 225 (81kWh) 2,932,000

125 (45kWh) 1,340,000 250 (90kWh) 3,420,700

E. EV charging load modeling

The dc bus has ac (through dc/ac inverter) and dc loads (through dc/dc converter). In addition to the non-EV loads, it is assumed that there are EV charging loads. The maximum charging capacity per charging pole is 19.2 kW. Assuming a minimum load of 10kW and considering different SOC of EV battery, the EV charging load at time interval t is calculated by

))(102.19(*()10, kWrandPt

kEV −+= (14)

where rand() is a random number. The total EV charging load of the dc system with N charging poles is

∑=

=N

k

tkEV

tEV PP

1 ,

(15)

According to the daily activities in a business area, the probability of the EV charging pole usage is shown in Fig. 7.

Fig. 7 Probability of EV charging pole usage

F. Time of use tariff and customer capacity charges

The capacity charge is assumed to be 89.44NT$/kW(between 100% and 110% of the contract capacity) and 134.16NT$/kW(higher than 110% of the contract capacity). The penalty incurred due to the power use exceeding the contract capacity is calculated by the followings:

⎪⎪

⎩

⎪⎪

⎨

⎧

−

>−

+−−

≥−

=

72.44*2*)(

0)(

72.44*} 2**1.03*]*1.0)[ {

*1.0)(

lim

lim

limlimlim

limlim

itt

grid

itt

grid

itititt

grid

ititt

grid

CP

CPif

CCCP

CCPif

Cpenalty(16)

Where Pt

grid is the power delivered from the grid to the DC

microgrid and Climit

is the contract demand. Fig. 8 and 9 show two different tariffs aiming at shaving peak load.

Fig. 8 TOU tariff of Taiwan Power Company

Fig. 9 Tariff structure for a demand response program

G. DC microgrid power scheduling problem formulation

The aim of the dc microgrid power scheduling problem is to minimize the daily operation costs of the system which is formulated as:

CrebateCbaseCpenaltyBC

pGPCCpGYt

tPVEVLt

tgrid

tpricefuelPVEVLt

−+++

⋅+=∑=

96

1,,

t,,cos )]~,(

41[)~,(min (17)

At each time interval t, in the state combinations Gt ∈{Q

B,

Pfuel

}, QB is the battery SOC and P

fuel is the fuel cell power

output. Ctfuel and Ct

price are fuel cell production cost and TOU price at time interval t. The regular and EV loads, and the PV power output are considered as random variables and given as, t

PVEVLp ,,~ ∈ )~,~,~( t

PVtEV

tL ppp Cpenalty is the penalty of

exceeding contract capacity usage. Cbase is the charge of the contract capacity. Crebate is the rebate of participating demand response program

The operation constraints considered in this study include:

5

Rampfuel

tfuel

tfuel PPP +<−< )(P 1--Ramp

fuel (18)

tfuel

tfuel

tfuel PPP max,min, << (19)

max1)(0 QtiQiQ use

tB

tB

tB

tB ≤⋅+=≤ − (20)

Where

⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪

⎨

⎧

≤

>

≥>⋅+=

≥≤⋅+=

<

×−

−

tgdischarginB,

tB

tB

tBQbt

BusetB

tB

tB

tB

ingchBtBuse

tB

tB

tB

tB

tB

ii

i ; gdischarginbattery if

aeiQtiQiQ

iiQtiQiQ

i ; chargingbattery if

0

- *8.0)(

*8.0)(

0

max1

arg,max1

，

，

(21) tBi is battery charging/discharging current (A)

tfuelP is fuel cell output power at time t (kW) tLp~ is non-EV load (kW) tEVp~ is EV charging load at time t (kW) tPVp~ is PV output power at time t (kW) tBQ is the battery SOC at time t (Ah)

maxQ is battery maximum capacity (Ah)

uset is battery charging/discharging time t

chargingB,i is the maximum charging current (A) t

gdischarginB,i is the maximum discharging current (A) -RampfuelP is fuel cell maximum decrease ramp rate (kW/15min)

RampfuelP + is fuel cell maximum increase ramp rate (kW/15min) t

minfuel,P is fuel cell minimum output (kW) t

maxfuel,P is fuel cell maximum output (kW)

III. SOLUTION METHODS For a time stage power scheduling problem, dynamic

programming (DP) would have many advantages over the enumeration scheme, the chief advantage being a reduction in the dimensionality of the problem. If the state switch cost is a function of the time, then a forward dynamic program approach is suitable since the previous history of the unit can be computed at each stage. A forward dynamic-programming recursive algorithm to compute the minimum cost in time interval K with state combination I is as follow:

)],1(),:,1(),([),( coscoscos}{cos LKFIKLKSIKPMinIKF tttJt −+−+=

(22)

Where Fcost(K,I) is the least total cost to arrive at state (K,I) Pcost(K,I) is the production/operation cost for state (K,I) Scost(K-1,L:K,I) is the transition cost from state (K-1,L) to state(K,I)

The solution procedure used to solve the problem is shown Fig. 10. Based on the discrete states of the battery capacity and fuel cell output, the number of state combinations is determined for each time interval. Feasible transitions from state (K-1,L) to state(K,I) are determined and transition and interval operations cost are then calculated. For each state in a

time interval the total power from the ac power grid is determined and the cost of power supply from the ac grid, including the penalty due to power usage exceeding the contact capacity, is calculated. Optimal path, the least total cost to arrive at state (K, I) is then determined.

Start

Input battery, fuel cell, contract, capacity, Ini_QB ,Ini_Pfuel , Climit

Sorting possible state combinations, {L}�{QB , Pfuel}

t=1

Calculate No. of discrete states count(QB) and count(Pfuel)

k=1

Compute battery and fuel cell operation costs

No. of feasible states at time interval t=0

n=1

No. of feasible fuel cell operation path=0

Calculate over usage penalty by (16)

Find feasible path based on (18)

n=count(Pfuel)?

k=count(QB)?

t=TDiv?

n=n+1

k=k+1

t=t+1

Stop

No

Yes

Calculate power from mains Pgrid(St)

Ptgrid>Cdeal(t-1,L)

Cdeal(t-1,I)>optimal path Ptgrid

Cdeal(t,I)=optimal path Pt

grid

No

Input battery parameters, time interval(TDiv), and p̃L , p̃EV , p̃PV

Storage optimal path at each time interval and the overall optimal operation strategy

),(cos LITtZ t ∈∀∈∀

Set 0),(cos =∈∀∈∀ LITtZ Divt

itDivdeal CLITtC lim),( =∈∀∈∀

Calculate charging/discharging current to reach Qt

B(k) from Qt-1B

{ })(Q }{Q 41 t

B1-t

B ki tB －=

Determine feasible path by (21)

Calculate battery voltage and charging/discharging current by (8), (9), (10)

Calculate fuel cell ramp rate}{ (n) 1t-

fueltfuel

Rampfuel PPP －=

Compute and store optimal path and state

},{

)},1()],(:),1[({min),(11

coscos}{cos

−−=

−+−=tfuel

tB

ttLt

PQL

LtZItLtYItZ

Yes

Find feasible states at time interval t)}(),({ nPkQS t

fueltB

t =

Yes

No

Yes

No

NoYes

Yes

No

No

Yes

Fig. 10 The proposed solution method

Multi Pass Dynamic Programming

In the conventional dynamic programming, without any solution efficiency enhancement strategy, the minimum cost-to-target is computed at each discrete time stage for every passible state at the stage. The cost-to-target from each of these states to every state of the next time stage must be calculated and the one optimal control policy which gives the lowest cost is selected. This process is repeated stage by stage, with large number of states, computational demands and memory would be unreasonably high. A multi-pass dynamic programming approach (MPDP) [7] is developed in this study in order to improve the computational efficiency.

Fig. 11 shows the concept of the proposed MPDP approach. It is an iterative procedure beginning with a coarse time and state grid and refining the grid pass by pass. In the first pass, a two-stage decision process is used to find a very coarse optimal control policy. The optimal trajectory of the first pass is then used as the nominal trajectory for the second pass. In the second pass, a finer four-stage decision process is used to find the optimal policy. Admissible state values during this pass include values on the nominal trajectory plus the states with finer units above and below the nominal values. The coarseness of the time and state increments is thus reduced. The process continues until the optimal trajectory of a pass remains unchanged. When this condition is reached by all states, the solution has converged to the true optimal within

6

the coarseness of one state increment. Fig. 12 shows the flow diagram of the proposed method.

Fig. 12 Multi-pass dynamic programming concept

Use flow diagram in fig.10

Start

Stop

pass=1

pass=3?

t=0

TDiv(1)=24、TDiv(2)=48、TDiv(3)=96

Find battery cap. states fuel cell states{L}={QB , Pfuel}

Calculate battery cap. states No. count(QB)fuel cell output states No. count(Pfuel)

Set battery parameters pL , p EV , p pv

Refine time intervals and find feasible path at t+1 St+1={Qt+1

B,Pt+1fuel}

pass=1?

t=TDiv?

Use flow diagram in fig.10

No Yes

Yes

pass=pass+1

No

Yes

t=t+1 No

Fig. 13 Flow diagram of the multi-pass dynamic programming technique Golden Section Search

The golden section search method is often used to find the maximum or minimum of a unimodal function. (A unimodal function contains only one minimum or maximum on the interval [a,b]) [8]. To start a search, choosing three independent bariables xL, x1 and xU (xL<x1<xU) with corresponding values of the objective function f(xL), f(x1), and f(xU), respectively. If f(x1)<f(xL) and f(x1)<f(xU), the minimum must lie between xL and xU. Now a fourth point denoted by x2 is chosen to be between the smaller of the two intervals of [x1, xU] and [x1, xL]. Assuming that the interval [x1, xU] is smaller than [xL, x1], we would chose [x1, xU] as the interval in which x2 is chosen. If f(x2)<f(x1) then the new three point would be x1<x2<xU; else if f(x2)>f(x1) then the new three point are

xL<x1<x2. This process is continued until the distance between the outer points is sufficiently small.

IV. NUMERICAL RESULTS DC microgrid power scheduling Stochastic models are used to generate PV power outputs, EV and non EV charging loads. Fig. 14 shows the randomly generated EV charging loads during a day for cases with 5, 10 and 15 charging poles. The average load or maximum load can be used for power schedule. The PV output, non-EV and EV charging loads shown in Fig. 15 and 16 are used in this test case. Fig. 15 and 16 show the average PV output and loads that are used for energy storage system and fuel cell power scheduling for minimizing the daily operation costs. The tariff structure shown in Fig. 9 is used for electricity bill calculations.

Fig. 14 100 randomly generated EV charging load scenarios

Fig. 15 Average load profile of non EV load and PV output

Fig. 16 EV charging load scenarios used in the study

Traditional DP and the MPDP approaches are used to solve the problem. Fig. 17 and 18 show the power scheduling results for the dc microgrid without and with EV charging (5 poles) loads. In these cases the contract capacities are assumed to be 34 and 98 kW respectively. It can be seen in Fig. 17 and 18, and Table III that power scheduling results obtained from DP and MPDP are similar. However, the memory space and execution time of the MPDP is much lower than those of traditional DP approach.

(a) Energy storage system

7

(b) Fuel cell

Fig. 17 Power scheduling result without EV charging load

(a) Energy storage system

(b) Fuel cell

Fig. 18 Power scheduling result with 5 EV charging poles

TABLE III Comparison of DP and MPDP results (DC microgrid daily operation costs (NT$))

No. of Charging poles DP results MPDP results

0 4,222 4,499

5 7,435 8,193

10 10,584 11,719

15 13,682 15,124

Optimal contract capacity for the DC microgrid

In this study the golden section search technique is used to find the optimal contract capacity for the dc microgrid under study. In this test case the following assumptions are made. The non-EV peak load is 50kW, maximum fuel cell, energy storage system and PV outputs are 5 kW, 9kW(25AH) and 30 kW respectively. The maximum EV load is 19.2x5 kW for a 5 pole case. The procedure shown in Fig. 10 for optimal power scheduling in conjunction with the golden section search procedure is used to determine the optimal contract capacity for the dc microgrid. To start the search, it is assumed that Climit,U=50+19.2*5(kW) and Climit,L=0(kW) are the high and low capacities that are used to start the search. Table IV and Fig. 19 show the changes of operation costs corresponding to different contract capacities. As shown, after 8 iterations, the variation of operation cost is lower than 0.1 kW.

V. CONCLUSION An efficient and reliable voltage and power controls would

provide a justification for adopting dc microgrid operations. This paper presents modeling methods for different elements in the microgrid operations. A MPDP method in conjunction

with a golden section search is adopted for daily energy storage system and fuel cell scheduling. Study results indicate that MPDP can solve the problem effectively and can be used to determine the optimal contract capacity for dc microgrid operations.

TABLE IV Operation costs during optimal contract capacity search

Operation cost (NT$) Contract capacity (kW)

17591.14 0(Climit,L)

8422.084 146(Climit,U)

10961.94 55.76704

8126.357 90.23296

8165.198 111.5341

8819.057 77.06815

8080.613 98.36926

8104.768 103.3978

8082.577 95.26147

Fig. 19 Determination of optimal contract capacity for the DC microgrid

operations

ACKNOWLEDGEMENTS The authors gratefully acknowledge the financial support

from National Science Council of Taiwan under contract NSC 100-3113-p-110-004.

REFERENCES [1] Y. Ito, Z. Yang and H. Akagi, "DC microgrid based distribution power

generation system," Proceedings of The 4th International Power Electronics and Motion Control Conference, IPEMC 2004, Aug. 2004.

[2] H. Kakigano, Y. Miura and T. Ise, “Low-Voltage Bipolar-Type DC Microgrid for Super,” IEEE Transactions on Power Electronics, Vol. 25, No. 12, Dec. 2010.

[3] C.-C. Huang, C.-H. Lin, M-J. Chen and C.-N. Lu, “DC microgrid voltage control,” Proceedings of the 11th Taiwan Power Electronics Conference and Exhibition, Hsinchu, Taiwan 2012, (in Chinese).

[4] Y. Li, R. Luan and J. Niu, "Forecast of power generation for grid-connected photovoltaic system based on grey model and Markov chain, "Industrial Electronics and Applications, 2008. ICIEA 2008. 3rd IEEE Conference on, vol., no., pp.1729-1733, 3-5 June 2008.

[5] Data sheet of a PEMFC of Horizon Co., available on-line http://www.horizonfuelcell.com/

[6] Battery model used in MATLab, available on-line http://www.mathworks.com/help/toolbox/physmod/powersys/ref/battery.html

[7] J. Yang and N. Chen, "Short term hydrothermal coordination using multi-pass dynamic programming," IEEE Transactions on Power Systems, vol.4, no.3, pp.1050-1056, Aug 1989.

[8] A. Yalcin and A. Kaw, “Golden Section Search Method, “http://numericalmethods.eng.usf.edu, August 17, 2011.