Optimal Sizing Of Battery Energy Storage System For An ...

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Optimal Sizing Of Battery Energy Storage System ForAn Islaned Microgrid

Pham Minh Cong, Tran Quoc Tuan, Ahmad Hably, Seddik Bacha, Luu NgocAn

To cite this version:Pham Minh Cong, Tran Quoc Tuan, Ahmad Hably, Seddik Bacha, Luu Ngoc An. Optimal Sizing OfBattery Energy Storage System For An Islaned Microgrid. IECON 2018 - 44th Annual Conference ofthe IEEE Industrial Electronics Society, Oct 2018, Washington, DC, United States. �hal-01895350�

https://hal.archives-ouvertes.fr/hal-01895350

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OPTIMAL SIZING OF BATTERY ENERGY STORAGE SYSTEM FORAN ISLANED MICROGRID

M.C. Pham �,∗, T. Q. Tran ∗, A. Hably �, S. Bacha �, Luu Ngoc An •

Abstract— This paper demonstrates a double layer optimiza-tion strategy to determine the optimum size of battery energystorage system (BESS) considering the EMS of a microgrid(MG). In the developed model, the BESS sizing problem isviewed as the outer optimal loop and the economic dispatch ofMG based on BESS data from the outer loop is considered asinner loop. An iterative method and a dynamic programming(DP) method are utilized to solve the optimal problems for outerand inner models respectively. A simulator is built in MATLABenvironment for an island microgrid is used to evaluate theefficiency of the proposed method.

I. INTRODUCTION

In order to minimize the use of fossil fuel production andto limit their impact on the global warming, grid operatorstires to maximize of the integration of renewable energysources (RESs). A microgrid (MG) is a small-scale powersupply network with loads, renewable energy sources (RES),distributed generation (DG), and energy storage systems(ESS). Two different modes of operation: the isolated modeand the grid-connected mode [1]. In this present paper, wewill focus on a isolated mode MG power system integratingRESs also know as islanded microgrid. One of the mostsignificant challenges in islanded MG is balancing the energybetween customers demand and the intermittent suppliers.A Battery ESS (BESS) with the abilities of mitigatingload mismatch and easing the integration of renewableenergy (RE) can be considered from the best choicesfor maintaining stability and enhancing power quality inislanded system [2]. However, the main drawback of BESSis the high investment cost and short life cycle. Thus, sizingthe BESS respecting both technical and economic constrainsis very crucial in a real implementation.There are three popular approaches to deal with sizingBESS [3]: energy balance approach, fluctuations stabilizeapproach, and the economic optimization approach. In[4], the authors follow the first approach by using theLoss of Power Supply Probability (LPSP), which ensuresthe power reliability of the system. In addition, in [3], aDiscrete Fourier Transform is used for sizing BESS in orderto compensate the imbalance power in the microgrid. Toreduce the mismatch between load and wind generationin an islanded system, a Probabilistic approach is used in[5]. On the other side, in [6], the optimal size of BESS isdetermined by Frequency Containment Reserve (FCR). The

�,� Univ. Grenoble Alpes, CNRS, Grenoble INP, G2elab, GIPSA-lab,38000 Grenoble, France [email protected]

∗ Alternative Energies and Atomic Energy Commission (CEA), Grenoble,France

• Danang University of Science and Technology, Da Nang, Viet Nam

BESS provides the service for reducing frequency deviation.Moreover, in order to maintain the specific tolerance (±0.05pu of error for 90% of the time) in the system with highwind energy penetration, the authors [7] have used a methodcalled Predictive Controller for optimizing the size ofBESS. An economic approach is also recommended in thebefore-mentioned paper. In [8], and by using ImprovedHarmony Search Algorithm (IHSA), the size of BESS isdesigned to optimize the total annual operating cost ofthe MG, with the moderating of state of charge (SOC)limitation. [3] presented a twostage strategy for sizing theBESS with respecting to optimal MG operation by applyingMesh Adaptive Direct Search (MADS) and an improvedparticle swarm optimization (IPSO) algorithm.Following the economic optimization approach, the mainpurpose is to evaluate the optimum BESS size, consideringthe energy management system of the islanded microgrid.

This present paper is organized as follows. First, theresearched microgrid is defined and modeled in SectionII. Next, in Section III, the optimization problems areformulated. Subsequently, suitable methodologies areproposed in Section IV. Section V indicates the results forthe simulation and concluding remarks are presented inSection VI.

II. CONFIGURATION OF THE SYSTEM

The microgrid model studied in this paper represents ahybrid system with different elements (see Figure 1). Themicrogrid system comprises distibuted DERs as a Photo-voltaic (PV) system and a Wind farm (Wind). Furthermore,the system will have a backup diesel generator for coveringsurplus power.


A model in Figure 1 mimics a hybrid system which will be developed in Con Dao island, Viet Nam. The microgrid system comprise such DERs as a Photovoltaic (PV) system and a Wind farm. Furthermore, the system also has a backup diesel generator for covering surpuls power from load.

Figure 1. The illustrated isolated MG system

A. Photovoltaic system The hourly data of the photovoltaic system is forecasted in

Figure 2. The peak of PV production is around 6 MW.

Figure 2. The daily PV production curve

B. Wind system Similarity with PV system, the predicted of Wind

production is indicated below. The maximum power point of Wind farm production is exactly 2.5 MW.

Figure 3. The daily Wind farm production curve

C. BESS The battery energy storage system is sized as the outer

optimization with the iterative method and the capacity fo r BESS capacity is simulated from the minimum to the maximum value. In order to satisfy the energy balance in the MG, BESS not only be be able to provide deficient the demand energy from the load when the power from DERs is not enough but also can absorb the surplus energy. In this paper, Lead – Acid battery is used as BESS. From [1], the minimum capacity for BESS (𝐸𝐵𝐸𝑆𝑆

𝑀𝑖𝑛 ) is determined as below:

𝐸𝐵𝐸𝑆𝑆

𝑀𝑖𝑛 = Max { 𝐸𝑑𝑖𝑠𝑀𝑖𝑛 , 𝐸𝑐ℎ

𝑀𝑖𝑛} (1)

Where:

𝐸𝑑𝑖𝑠𝑀𝑖𝑛 = ∫ (𝑃𝐿 − 𝑃𝑀𝐺

𝑀𝑎𝑥 )𝑑𝑡𝑇

0 if 𝑃𝑀 𝐺𝑀𝑎𝑥 < 𝑃𝐿 (2)

𝐸𝑐ℎ𝑀𝑖𝑛 = ∫ (𝑃𝑀 𝐺

𝑀𝑎𝑥 − 𝑃𝐿 )𝑑𝑡𝑇

0 if 𝑃𝑀 𝐺𝑀𝑎𝑥 ≥ 𝑃𝐿 (3)

𝐸𝑑𝑖𝑠

𝑀𝑖𝑛 𝑎𝑛𝑑 𝐸𝑐ℎ𝑀𝑖𝑛 are the minimum energy providing provided

by the BESS and the minimum energy absorbed by BESS respectively. 𝑃𝑀𝐺

𝑀𝑎𝑥 is the maximum production in the MG.Therefore, following the equation 1, the minimum capacity of BESS in the MG system is 7.8 MWh and the maximum capacity for BESS is 117 MWh which is enough to cover the load for 1 day without any RES. Thus, the optimum value of capacity of BESS will be located between 7.8 MWh and 117 MWh. The state of charge (SOC) of BESS can be calculated as follows:

𝑆𝑂𝐶 = 𝐶(𝑡)

𝐶𝑅𝑒𝑓(𝑡)

(4)

Where 𝐶(𝑡) is the capacity at each instant and 𝐶𝑅𝑒𝑓(𝑡 ) is the reference capacity of BESS. Furthermore, the SOC at time “t” can be formulated:

𝑆𝑂𝐶(𝑡) = 𝑆𝑂𝐶(𝑡 − 1) +

𝑃𝑀𝐺(𝑡)−𝑃𝐿(𝑡)

𝐶𝑅𝑒𝑓 (𝑡). ∆𝑡 (5)

D. Load The load profile utilized in this paper is based on daily load curve as shown in Figure 4.

Figure 4. The daily load curve

Fig. 1. The illustrated isolated MG system.

A. Photovoltaic system

The hourly data of the photovoltaic system is forecasted isshown on Figure 2. As it is shown, the peak of PV productionreaches around 6 MW in the middle of the day. It is also clearthat there is no production at night.















𝑀𝑖𝑛} (1)

Where:







𝐸𝑑𝑖𝑠






(4)


𝑆𝑂𝐶(𝑡) = 𝑆𝑂𝐶(𝑡 − 1) +


𝐶𝑅𝑒𝑓 (𝑡). ∆𝑡 (5)



Fig. 2. The daily PV production curve.

B. Wind system

The predicted of Wind production is indicated Figure 3.The maximum power point of Wind farm production is 2.5MW. The variability of the production is also taken intoaccount.















𝑀𝑖𝑛} (1)

Where:







𝐸𝑑𝑖𝑠






(4)


𝑆𝑂𝐶(𝑡) = 𝑆𝑂𝐶(𝑡 − 1) +


𝐶𝑅𝑒𝑓 (𝑡). ∆𝑡 (5)



Fig. 3. The daily Wind farm production curve.

C. The battery energy storage systes

The battery energy storage system (BESS) size will beevaluated in the outer optimization level as it will be shownlater in the iterative method. The capacity for BESS capacityis simulated from the minimum to the maximum value. Inorder to satisfy the energy balance in the microgrid, BESSnot only has to be able to provide deficient of the demandenergy from the load when the power from DERs is notenough but also it has to be able absorb the surplus energy.In this present paper, LeadAcid battery is used as BESS.

From [3], the minimum capacity for BESS (EMinBESS) can

be determined as:

EMinBESS = max{EMin

dis , EMinch } (1)

where

EMindis =

∫ T

0

(PL − PMaxMG ) if PMax

MG < PL (2)

and

EMindis =

∫ T

0

(PMaxMG − PL) if PMax

MG ≥ PL (3)

with EdisM in and Ech

M in are respectively the minimumenergy providing provided by the BESS and the minimumenergy absorbed by BESS. PMax

MG is the maximum pro-duction in the MG. Therefore, following equation 1, theminimum capacity of BESS in the MG system is estimated to7.8 MWh and the maximum capacity for BESS is 117 MWhwhich is enough to cover the load for one day without anyRES. Thus, the optimum value of capacity of BESS will betaken between 7.8 MWh and 117 MWh.The state of charge (SOC) of BESS can be calculated asfollows:

SOC =C(t)

CRef (t)(4)

where C(t) is the capacity at each instant and CRef (t) is thereference capacity of BESS. Furthermore, the SOC at timet can be formulated by the discrete equation:

SOC(t) = SOC(t− 1) +PMG(t)− PL(t)

CRef (t).∆t (5)

D. Loads profile

The load profile utilized in this present paper is based on adaily load curve as shown in Figure 4. As it is shown, thereis a consumption peak around noon.















𝑀𝑖𝑛} (1)

Where:







𝐸𝑑𝑖𝑠






(4)


𝑆𝑂𝐶(𝑡) = 𝑆𝑂𝐶(𝑡 − 1) +


𝐶𝑅𝑒𝑓 (𝑡). ∆𝑡 (5)


Figure 4. The daily load curve Fig. 4. The daily load curve.

E. Diesel generator

The diesel generator to be used has to cover the entire loaddemand in the case of unavailability of RESs and BESS.

III. PROBLEM FORMULATION

The relationship between the optimal capacity of BESSand the optimal energy management in MG is tricky mission.Thus, in this section, the problems will be separated intotwo parts represented in two loops in Figure 5. In the innerloop, the energy management system using the dynamicprogramming (DP). The operation cost is minimized in theouter loop. As mentioned above, the objective is to minimize

E. Diesel The diesel generator is applied used to cover the entire load

in case ofwhen insufficient RESs system and BESS productionare insufficient. Diesel is opened to meet the load demand and may be turn off whenever the RESs system and BESS production are enough to feed the load.

III. PROBLEM FORMULATION

The relationship between the optimal capacity of BESS and the optimal energy management in MG is very complex. Thus, in this section, the problems will be separated into two layers as in Figure 5.

Figure 5. The flowchart of the proposed method

On the one hand, in the inner layer, the objective is to minimize the cost of MG operation (CS) [4]:

min(CO) = min (∑ FC(t) + EC(t) + BrC (t))T

1

(6)

As shown in Equation 6, the cost of MG operation (CO) not only comprises the cost of fuel (FC) and emission cost (EC) but also includes the battery replacement cost (BrC). We have:

TABLE 1. The objective function factors Formulation Explaination

FC= ∑ Cf .F(t)T

t=1

Cf : the fuel cost per liter F(t) : the hourly consumption of diesel generator

F(t) = (0.246. PDG (t) + 0.08415. PR )

PR: the rated power of diesel generators. PDG (t): the diesel power at time t

EC= ∑Ef.Ecf PDG (t)

1000

T

t=1

Ef: the emission function (kg/kWh) Ecf : the emission cost factor

BrC(t)= BiC 'SOH(t)1-SOHmin

SOH : State Of Health of the BESS BiC: the batteries’ investment cost

'SOH ( t)= Z.(SOCxi (t-∆t)-SOCxj (t))

Z: the linear ageing coefficient: 3.10-4

Finally, the objective function in Equation 6 can be expanded: Subsequently, the constraints in the system are presented in Table 2:

TABLE 2. The constrains of the system Constraints Formulations

Power balance constraints

PL(t)=PPV(t) + PB(t) + PDG(t) + PWind(t)

BESS constraints 'SOC min ≤ 'SOC (t) ≤ 'SOCmax SOC min ≤ SOC (t) ≤ SOCmax SOH(t) ≥ SOHmin

Diesel generator constrain

PDG_min ≤ PD (t) ≤ PDG_max

On the other hand, the outer stage layer is use an iterative method. The values of BESS capacity are varied in the a predefined range and will be used as the input for the first node in the inner optimization layer as shown in Figure 5. After that, the optimal of capacity of BESS, following with the operation cost of MG and the energy schedule will be figured out.

IV. METHODOLOGIES

With the outer layer, the capacity of BESS is provided. In this layer, the iterative method is used to modify the value of capacity which is limited in Section II. With each value of capacity of BESS, we will have a different input for the inner layer, that will lead to different scenarios for energy schedule and the cost of operation. The most appropriate capacity will be the one that establish the minimum cost of operation.

With the inner layer, the idea is to describe the optimization problem of EMS through SOC of BESS, with the use of Dynamic Programming with Bellman algorthim. Thanks to power balance constrain, we have:

PB(t) = PL(t) - PPV(t) - PWind(t) - PDG(t) (7)

From the equation 7, we transform it into the energy balance formula:

SOC(t)=SOC(t-1)+ PPV(t)+ PDG(t)+PWind(t)–PL(t)

Cref.∆t

(8)

Where the state of charge is defined:

𝐶𝑂𝑖

EMS (DP)

Yes

No

𝐶𝑅𝑒𝑓𝑖

i = i +1

𝐸𝐵𝐸𝑆𝑆𝑀𝑖𝑛 ≤ 𝐶𝑅𝑒𝑓

𝑖 ≤ 𝐸𝐵𝐸𝑆𝑆𝑀𝑎𝑥

Minimization 𝐶𝑆𝑂𝑝𝑡𝑖𝑚𝑎𝑙

𝐸𝐵𝐸𝑆𝑆𝑂𝑝𝑡𝑖𝑚𝑎𝑙

Power schedule

Inner loop

Outer loop min(CS) = min ∑ Cf.F(t)+ Ef.Ecf.PDG(t)

1000+BrCT

t=1 (t) (7)

Fig. 5. The flowchart of the proposed method.

the cost of MG operation (CO) as the one used in [9]:

min(CO) = min(

T∑1

FC(t) + EC(t) +BrC(t)) (6)

As shown in Equation 6, the cost of MG operation (CO)does comprise not only the cost of fuel (FC) and emissioncost (EC) but also does include the battery replacementcost (BrC). Here, we will list the details of elements ofthe objective function. First, we have

FC =

T∑t=1

Cf .F (t) (7)

where Cf is the fuel cost per liter and F (t) is the hourly con-sumption of diesel generator. Second, F (t) can be calculatedas following:

F (t) = (0.246PDG(t) + 0.08415PR) (8)

with PR is the rated power of diesel generators and PDG(t)the diesel power at time instant t. The second element ofobjective function, emission cost, EC(t) can be expressedby the following equation:

EC =

T∑t=1

EfEcfPDG(t)

1000(9)

where Ef is the emission function (kg/kWh) and Ecf rep-resents the emission cost factor. Finally, the last element ofthe objective function BrC(t) is expressed by:

BrC(t) = BiC∆SOH(t)

1− SOHmin(10)

with SOH is the State Of Health of the BESS and BiC isthe batteries investment cost.

Subsequently, the constraints in the system are presented bythe following :

• Power balance constraints:

PL(t) = PPV (t) + PB(t) + PDG(t) + PWind(t) (11)

• BESS constraints:

∆SOCmin ≤ ∆SOC(t) ≤ ∆SOCmax (12)SOCmin ≤ SOC(t) ≤ SOCmax (13)SOH(t) ≥ SOHmin (14)

• Diesel generator constraint:

PDGmin ≤ PD(t)(t) ≤ PDGmax (15)

On the other hand, the outer loop uses an iterative method.The values of BESS capacity are varied in a predefinedrange and will be used as the input for the first node in theinner optimization loop as shown in Figure 5. After that, theoptimal of capacity of BESS, following with the operationcost of MG and the energy schedule can be figured out.

IV. METHODOLOGIES

Within the outer loop, the capacity of BESS is provided.In this layer, the iterative method is used to modify the valueof capacity which is limited in Section II. With each value ofcapacity of BESS, we will have a different input for the innerloop, that will lead to different scenarios for energy scheduleand the cost of operation. The most appropriate capacitywill be the one that establish the minimum cost of operation.

With the inner loop, the idea is to describe the optimizationproblem of EMS through SOC of BESS, with the use ofDynamic Programming with Bellman algorithm. Thanks topower balance constraint, one has:

PB(t) = PL(t)− PPV (t)− PWind(t)− PDG(t) (16)

From the above equation, we transform it into the energybalance formula:

SOC(t) = SOC(t− 1) + (17)−PL(t) + PPV (t) + PWind(t) + PDG(t)

Cref∆t

Where the state of charge is defined as in Equation 4 withC(t) and Cref are respectively the BESS capacity at timet and the reference capacity. ∆t is is a unit time periodwhich is chosen here to be equal to 1 hour. From Equation18, we can see that, by controlling the SOC of BESS, wecan control the PDG with the forecasted energy profiles of

RES and loads. Thus, we can find the best SOC profile inorder to minimize the operation cost of the system. Now,the SOC is illustrate as Figure 6. The purpose of the inneroptimization loop is to find the flow from the initial node tothe end node. As we can see that the structure of the systemcan be modeled by a graph. Now, we calculate the weight ofeach node in the first layer, which receives the informationfrom the beginning node. On the other hand, in order tocalculate the weight of each node in the second layer, whichreceives the information from all nodes in the first layer bydetermining the minimization of the CO from the beginningnode. Repeat this concept until the weights of nodes in thelast layer are obtained. Then, we aim to calculate the weightof the end node that receives the information from all nodesat the last layer by defining the the minimization of the cashflow from the beginning node. And finally, we can determinethe minimization of the flow from the beginning node to finalnode. Therefore, this method can be applied to determine theoptimal the cost of MG operation.

𝑆𝑂𝐶𝑚𝑖𝑛 𝑆𝑂𝐶𝑚𝑖𝑛 𝑆𝑂𝐶𝑚𝑖𝑛

𝑆𝑂𝐶1

𝑆𝑂𝐶2

𝑆𝑂𝐶𝑀𝐴𝑋 𝑆𝑂𝐶𝑀𝐴𝑋 𝑆𝑂𝐶𝑀𝐴𝑋

𝑆𝑂𝐶2

𝑆𝑂𝐶1

𝑆𝑂𝐶𝑇 𝑆𝑂𝐶0

SOC(t)= C(t)Cref

(9)

C(t) and Cref are the BESS capacity at time t and the reference capacity, respectively. ∆t is is a unit time period, we choose ∆t equal to 1 hour.

From Equation 8, we can see that, by controlling the SOC of BESS, we can control the PDG with the forecasted energy profiles of RES and load. Thus, we can find the best SOC profile in order to minimize the operation cost of the system. Now, the SOC is illustrate as Figure 6.

The purpose of the inner optimization is to find the cash flow from the beginning node to the end node. As we can see that the structure of the system can be modeled by a graph. Now, we calculate the weight of each node in the first layer, which receives the information from the beginning node. On the other hand, in order to calculate the weight of each node in the second layer, which receives the information from all nodes in the first layer by determining the minimization of the CO from the beginning node. Repeat this concept until the weights of nodes in the last layer are obtained. Then, we aim to calculate the weight of the end node that receives the information from all nodes at the last layer by defining the the minimization of the cash flow from the beginning node. And finally, we can determine the minimization of the cash flow from the beginning node to final node. Therefore, this method can be applied to dertimine the optimal the cost of MG operation.

Figure 6. Dynamic Programming for energy management based on SOC of BESS

V. SIMULATION AND RESULTS

Firstly, the input parameters for the microgrid system is set up in Table 3. The maximum and minimum capacity for the BESS are predefined in Section II. In addition, in order to preserve the battery, the maximum values state of charge and

discharge for BESS are 0.9 and 0.2 pu respectively. The initial and the final values of SOC of BESS are set at 0.5, which is the most sufficient rate for absorbing or providing energy for the system in term of next day preparation.

TABLE 3. The input values for the simulation Name Value Unit

𝐸𝐵𝐸𝑆𝑆𝑀𝑖𝑛 7.8 MWh

𝐸𝐵𝐸𝑆𝑆𝑀𝑎𝑥 117 MWh

𝑆𝑂𝐶0 0.5 pu 𝑆𝑂𝐶𝑇 0.5 pu 𝑆𝑂𝐶𝑚𝑖𝑛 0.2 pu 𝑆𝑂𝐶𝑚𝑎𝑥 0.9 pu 𝑆𝑂𝐻𝑚𝑖𝑛 0.7 pu δSOC 0.001 pu ΔSOC -0.7 ÷ 0.7 pu Cost of battery bank (US$/kWh)

200 (US$/kWh)

Minimum power of diesel

5.15 MWh

Maximum power of diesel

1.55 MWh

Fuel cost 0.7 (US$/l) δSOC is set to 0.001, thus, the number of state (N) at each period:

N= SOCmax -SOCmin

δSOC

(8)

Following the equation 8:

N= 0.9 - 0 .2

0.001= 700 𝑠𝑡𝑎𝑡𝑒𝑠

Running the proposed algorithm with the input values in Table 3, we have the optimal capacity for BESS, the optimal cost of the operation presented in Table 4 and the optimal power schedule shown in Figure 7.

TABLE 4. The optimal results

Name Value Unit 𝐸𝐵𝐸𝑆𝑆

𝑂𝑝𝑡𝑖𝑚𝑎𝑙 8 MWh

𝐶𝑂 𝑂𝑝𝑡𝑖𝑚𝑎𝑙 11115 USD It can be seen that the load demand is satisfied by the DERs. As illustrated in the Figure 7, at the beginning of the day, the load is not fully covered by the wind farm so the diesel generator is activated to compensate the deficit energy. In contrast, from 6 a.m to 8 a.m, under the proposed methodology, in order to achieve the optimum cost of operation, the diesel generator is turn off to make a way for BESS system. Moreover, from 10 a.m to 5 p.m, when the production from Photovoltaic and Wind reach the highest values, the BESS ingests the surplus energy. Therefore, the BESS not only charge and discharge to keep the power balance in the system but also to minimize the operation cost of the

0

ΔSOC

Initial State

State 1

δSOC

State 2 2

State n n

Final State

Time (h)

T (24)

Fig. 6. Dynamic Programming for energy management based on SOC ofBESS.

V. SIMULATION RESULTS

Firstly, the input parameters for the microgrid system isset up in Table I. The maximum and minimum capacity forthe BESS are predefined in Section II. In addition, in order topreserve the battery, the maximum values of state of chargeand discharge for BESS are respectively 0.9 and 0.2 pu. Theinitial and the final values of SOC of BESS are set at 0.5,which is the most sufficient rate for absorbing or providingenergy for the system in term of next day preparation. Thenumber of state (N ) at each period can be calculated:

N =S0Cmax − S0Cmin

δS0C(18)

Following the above equation we get that N is equal to 700states. Running the proposed algorithm with the input valuesin Table I, we get the optimal power schedule shown inFigure 7. Also we get the optimal capacity for BESS which

TABLE ITHE INPUT VALUES FOR THE SIMULATION STUDY

Name Value UnitEMin

BESS 7.8 MWhEMax

BESS 117 MWhS0C0 0.5 puS0CT 0.5 puS0Cmin 0.2 puS0Cmax 0.9 puSOHmin 0.7 puδS0C 0.001 pu∆SOC puCost of battery bank 200 $ per kWhMinimum power of dieselgenerator

1.55 MWh

Maximum power of dieselgenerator

5.15 MWh

Fuel cost 0.7 $ per l

is equal to 8 MWh and the optimal cost of the operationwhich is evaluated to $11115.

It can be seen that the load demand is satisfied by theDERs. As illustrated in Figure 7, at the beginning of theday, the load is not fully covered by the wind farm sothe diesel generator is activated to compensate the deficitenergy. In contrast, from 6 a.m to 8 a.m, under the proposedmethodology, in order to achieve the optimum cost of op-eration, the diesel generator is turn off to make a way forBESS system. Moreover, from 10 a.m to 5 p.m, when theproduction from Photovoltaic and Wind reaches the highestvalues, the BESS ingests the surplus energy. Therefore, theBESS is not only providing charge and discharge to keepthe power balance in the system but also the operation costof the MG is minimized. The diesel generator rests for 11hours/day, which is a very good operating condition andreduces a lot of CO2 emissions. Figure 8 suggests the state

MG. The diesel generator rests for 11 hours/day, which is a very good operating condition and reduces a lot of CO2 emission.

Figure 7. The optimal power schedule of the islanded

microgrid

Figure 8. The optimal SOC curve of BESS

Figure 8 suggests the state of charge curve for the BESS in a day ahead schedule. The SOC of BESS at the beginning and at the end of the day is successfully fixed at 0.5, which is accomplished by dynamic programming method.

VI. CONCLUSIONS

In this paper, the BESS sizing problem and the optimal energy management for islanded MG are both taken into account. The model for double layers optimization problem is developed and the Dynamic Programming with the iterative outer loop is utilized to solve the model. The proposed method give the best value for BESS capacity for the system and introduce the power schedule which are able to achieve global energy optimization.

REFERENCES [1] H. Xiao, W. Pei, Y. Yang, and L. Kong, ‘Sizing of battery energy storage

for micro-grid considering optimal operation management’, in 2014 International Conference on Power System Technology, 2014, pp. 3162–3169.

[2] I. Sansa, R. Villafafila, and N. M. Bellaaj, ‘Optimal sizing design of an isolated microgrid using loss of power supply probability’, in IREC2015 The Sixth International Renewable Energy Congress, 2015, pp. 1–7.

[3] I. Naziri Moghaddam, B. Chowdhury, and S. Mohajeryami, ‘Predictive Operation and Optimal Sizing of Battery Energy Storage with High

Wind Energy Penetration’, IEEE Trans. Ind. Electron., vol. PP, no. 99, pp. 1–1, 2017.

[4] ‘Luu Ngoc An “Control and management strategies for a Microgrid”. Grenoble University, France. PhD Thesis, December 2014’.

[5] R. Leon Vasquez-Arnez, D. Ramos, and T . Elena Del Carpio-Huayllas, Microgrid dynamic response during the pre-planned and forced islanding processes involving DFIG and synchronous generators, vol. 62. 2014.

[6] J. Xiao, L. Bai, F. Li, H. Liang, and C. Wang, ‘Sizing of Energy Storage and Diesel Generators in an Isolated Microgrid Using Discrete Fourier Transform (DFT)’, IEEE Trans. Sustain. Energy, vol. 5, no. 3, pp. 907–916, Jul. 2014.

[7] L. Cupelli, N. Barve, and A. Monti, ‘Optimal sizing of data center battery energy storage system for provision of frequency containment reserve’, in IECON 2017 - 43rd Annual Conference of the IEEE Industrial Electronics Society, 2017, pp. 7185–7190.

[8] C. K. Nayak and M. R. Nayak, ‘Optimal design of battery energy storage system for peak load shaving and time of use pricing’, in 2017 Second International Conference on Electrical, Computer and Communication Technologies (ICECCT), 2017, pp. 1–7.

[9] T . M. Masaud, O. Oyebanjo, and P. K. Sen, ‘Sizing of large-scale battery storage for off-grid wind power plant considering a flexible wind supply–demand balance’, IET Renew. Power Gener., vol. 11, no. 13, pp. 1625–1632, 15 2017.

Fig. 7. The optimal power schedule of the islanded microgrid.

of charge curve for the BESS in a day ahead schedule. TheSOC of BESS at the beginning and at the end of the day issuccessfully fixed at 0.5, which is accomplished by DynamicProgramming algorithm.

MG. The diesel generator rests for 11 hours/day, which is a very good operating condition and reduces a lot of CO2 emission.

Figure 7. The optimal power schedule of the islanded

microgrid

Figure 8. The optimal SOC curve of BESS

Figure 8 suggests the state of charge curve for the BESS in a day ahead schedule. The SOC of BESS at the beginning and at the end of the day is successfully fixed at 0.5, which is accomplished by dynamic programming method.

VI. CONCLUSIONS

In this paper, the BESS sizing problem and the optimal energy management for islanded MG are both taken into account. The model for double layers optimization problem is developed and the Dynamic Programming with the iterative outer loop is utilized to solve the model. The proposed method give the best value for BESS capacity for the system and introduce the power schedule which are able to achieve global energy optimization.

REFERENCES [1] H. Xiao, W. Pei, Y. Yang, and L. Kong, ‘Sizing of battery energy storage

for micro-grid considering optimal operation management’, in 2014 International Conference on Power System Technology, 2014, pp. 3162–3169.

[2] I. Sansa, R. Villafafila, and N. M. Bellaaj, ‘Optimal sizing design of an isolated microgrid using loss of power supply probability’, in IREC2015 The Sixth International Renewable Energy Congress, 2015, pp. 1–7.

[3] I. Naziri Moghaddam, B. Chowdhury, and S. Mohajeryami, ‘Predictive Operation and Optimal Sizing of Battery Energy Storage with High

Wind Energy Penetration’, IEEE Trans. Ind. Electron., vol. PP, no. 99, pp. 1–1, 2017.

[4] ‘Luu Ngoc An “Control and management strategies for a Microgrid”. Grenoble University, France. PhD Thesis, December 2014’.

[5] R. Leon Vasquez-Arnez, D. Ramos, and T . Elena Del Carpio-Huayllas, Microgrid dynamic response during the pre-planned and forced islanding processes involving DFIG and synchronous generators, vol. 62. 2014.

[6] J. Xiao, L. Bai, F. Li, H. Liang, and C. Wang, ‘Sizing of Energy Storage and Diesel Generators in an Isolated Microgrid Using Discrete Fourier Transform (DFT)’, IEEE Trans. Sustain. Energy, vol. 5, no. 3, pp. 907–916, Jul. 2014.

[7] L. Cupelli, N. Barve, and A. Monti, ‘Optimal sizing of data center battery energy storage system for provision of frequency containment reserve’, in IECON 2017 - 43rd Annual Conference of the IEEE Industrial Electronics Society, 2017, pp. 7185–7190.

[8] C. K. Nayak and M. R. Nayak, ‘Optimal design of battery energy storage system for peak load shaving and time of use pricing’, in 2017 Second International Conference on Electrical, Computer and Communication Technologies (ICECCT), 2017, pp. 1–7.

[9] T . M. Masaud, O. Oyebanjo, and P. K. Sen, ‘Sizing of large-scale battery storage for off-grid wind power plant considering a flexible wind supply–demand balance’, IET Renew. Power Gener., vol. 11, no. 13, pp. 1625–1632, 15 2017.

Fig. 8. The optimal SOC curve of BESS.

VI. CONCLUSIONS

In this paper, the BESS sizing problem and the optimalenergy management for islanded MG have been taken intoaccount. The model for optimization problem is developedand the Dynamic Programming with the iterative outer loopis utilized to find the optimal values. The proposed methodgives the best value for BESS capacity for the systemand introduces the power schedule achieves global energyoptimization.

REFERENCES

[1] H. Al-Nasseri, M. Redfern, and R. O’Gorman, “Protecting micro-gridsystems containing solid-state converter generation,” in Future PowerSystems, 2005 International Conference on. IEEE, 2005, pp. 5–pp.

[2] R. L. Vasquez-Arnez, D. S. Ramos, and T. E. Del Carpio-Huayllas,“Microgrid dynamic response during the pre-planned and forced island-ing processes involving dfig and synchronous generators,” InternationalJournal of Electrical Power & Energy Systems, vol. 62, pp. 175–182,2014.

[3] H. Xiao, W. Pei, Y. Yang, and L. Kong, “Sizing of battery energy storagefor micro-grid considering optimal operation management,” in PowerSystem Technology (POWERCON), 2014 International Conference on.IEEE, 2014, pp. 3162–3169.

[4] I. Sansa, R. Villafafila, and N. M. Bellaaj, “Optimal sizing design of anisolated microgrid using loss of power supply probability,” in RenewableEnergy Congress (IREC), 2015 6th International. IEEE, 2015, pp. 1–7.

[5] T. M. Masaud, O. Oyebanjo, and P. Sen, “Sizing of large-scale batterystorage for off-grid wind power plant considering a flexible windsupply–demand balance,” IET Renewable Power Generation, vol. 11,no. 13, pp. 1625–1632, 2017.

[6] L. Cupelli, N. Barve, and A. Monti, “Optimal sizing of data centerbattery energy storage system for provision of frequency containmentreserve,” in Industrial Electronics Society, IECON 2017-43rd AnnualConference of the IEEE. IEEE, 2017, pp. 7185–7190.

[7] I. N. Moghaddam, B. H. Chowdhury, and S. Mohajeryami, “Predictiveoperation and optimal sizing of battery energy storage with highwind energy penetration,” IEEE Transactions on Industrial Electronics,vol. 65, no. 8, pp. 6686–6695, 2018.

[8] C. K. Nayak and M. R. Nayak, “Optimal design of battery energy stor-age system for peak load shaving and time of use pricing,” in Electrical,Computer and Communication Technologies (ICECCT), 2017 SecondInternational Conference on. IEEE, 2017, pp. 1–7.

[9] N. A. Luu, “Control and management strategies for a microgrid,” Ph.D.dissertation, Universite Grenoble Alpes, 2014.

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