Impact of Advanced Load-Frequency Control on Optimal Size of Battery Energy Storage in Islanded Microgrid System

The application of battery energy storage (BES) in microgrid systems has attracted much attention in recent years. It is because the BES is able to store excess power and discharge its power when needed. In islanded microgrid systems, BES is starting to be considered as a unit that can regulate the system frequency. The control used in the BES to display frequency regulation performance is called load-frequency control (LFC). However, this participation resulted in the large size of the battery and high expansion planning cost. In this paper, an advanced LFC control that has frequency limitation compared to traditional LFC is proposed. The proposed control implies droop control as the base and has frequency limitations. Compared to the traditional LFC, the proposed control can reduce the system expansion planning costs. A performance simulation was done to validate battery performance. The results of the numerical simulation showed that the proposed control participated in reducing the operation cost. It directly led to a reduction in the expansion planning cost. A study of battery selection was conducted to draw the practicality of the BES sizing solutions.


Introduction
Electricity has become a basic necessity in human life. Every place inhabited by humans needs electricity to support their life, including isolated islands. Electricity should also be accessible for islands isolated from the utility grid [1]. A hybrid electricity system (HES) is often used to satisfy the power demand on the island. This system usually consists of main synchronous generators, such as diesel generators; renewable energy sources (RESs); and energy storage devices. Such a system installed in an isolated system is often called islanded microgrid system [2].
Islanded microgrid systems may impose several issues, such as limited generation, intermittency output power from RES, lack of inertia system, and fluctuating loads. Those issues may impact the system power quality, either in terms of voltage or frequency deviation. Deviation of the frequency can cause stability and power quality problems. The problem has resulted in many related studies that have been carried out, such as demand response, generation limitation, microgrid clusters, temporary microgrids, and energy storage deployments [3][4][5][6].
One of the most challenging issues is frequency regulation. Frequency issues mainly occur due to fluctuating loads and intermittent RES output power. The power balance between sources and load must be satisfied to keep the frequency grid [4][5][6]. Synchronous generators carry out frequency regulation. Nevertheless, they may impose limitations such as reserve power that must be available and slow generator response. [6][7][8][9]. Other works regarding microgrid control have also been carried out [10,11]. Author [10] introduced the optimal power flow between components in the microgrid. This management is realized using a distributed scheme in which one sensor broadcasts scalar variables over a wireless communication network. A total-sliding-mode-control (TSMC)-based droop control has The rest of the paper is organized as follows: Section 2 describes the structure of BES. Section 3 outlines the proposed LFC operation. Section 4 describes the optimization model to find the optimal battery capacity. The optimization results and the discussion on the proposed model are provided in Section 5 to demonstrate the proposed LFC benefits and validate its applicability. The conclusion is provided in Section 6.

Battery Energy Storage (BES) System
Battery energy storage consists of several components: the battery bank, the power conditioning system (PCS) as converter, the direct current (DC) and alternating current (AC) filters, the protection circuits, and the step-up transformer shown in Figure 1 [22]. The battery serves as the primary unit of BES. Researchers have developed different types of batteries. However, some are ready to be commercialized, while some are still in the experimental stage. [21]. To date, lead-acid, lithium-ion (Li-ion), sodium-sulfur (NaS), nickel-cadmium (NiCd), and vanadium redox (VR) are examples of technologically mature and marketed batteries [23]. Each type of battery has different characteristics. Besides the price difference, each battery technology can be implemented into a power system due to its unique features and characteristics. There are several BES applications in microgrids such as peak shaving, home energy management, load leveling, power fluctuations, transmission and distribution upgrade deferral, frequency regulation, low voltage ride through, and loss minimization. Peak shaving is the technique to reduce electricity consumption when the electricity demand is at a peak, usually during the daytime in summer and the nighttime in winters. A battery energy storage is deployed in the houses to provide a power supply during power interruptions. The batteries are often used with an uninterruptable power supply (UPS) to protect the equipment during load leveling. It involves storing energy when the grid load is light and delivering it back during high spikes of loads. Energy storage systems have effectively reduced fluctuations by shifting the load from the peak periods to off-peak periods. The electrical distribution system's radial structure has a large current to voltage ratio, which results in a high quantity of power losses in a distribution system [24][25][26].
Battery energy storage systems in microgrids are used to retain the power balance between the load demand and generation, ensuring grid frequency regulation. This function extends the capabilities of the battery to become a source of energy that helps other sources. However, continuous participation leads to battery cycle aging. the cycle aging mainly comes from BES depth of discharge (DoD) and the number of cycles [27,28]. The number of cycles and DoD determine whether a BES replacement is needed along the considered project lifetime. Neglecting those matters in expansion planning results in an inaccurate economic assessment. Figure 2 shows the typical battery life cycle model versus the DoD that the manufacturers usually provide [17,29]. Several studies to estimate the battery lifecycle have already been proposed. Those studies exhibited an exponential form of the relationship [30][31][32]. There are several BES applications in microgrids such as peak shaving, home energy management, load leveling, power fluctuations, transmission and distribution upgrade deferral, frequency regulation, low voltage ride through, and loss minimization. Peak shaving is the technique to reduce electricity consumption when the electricity demand is at a peak, usually during the daytime in summer and the nighttime in winters. A battery energy storage is deployed in the houses to provide a power supply during power interruptions. The batteries are often used with an uninterruptable power supply (UPS) to protect the equipment during load leveling. It involves storing energy when the grid load is light and delivering it back during high spikes of loads. Energy storage systems have effectively reduced fluctuations by shifting the load from the peak periods to off-peak periods. The electrical distribution system's radial structure has a large current to voltage ratio, which results in a high quantity of power losses in a distribution system [24][25][26].
Battery energy storage systems in microgrids are used to retain the power balance between the load demand and generation, ensuring grid frequency regulation. This function extends the capabilities of the battery to become a source of energy that helps other sources. However, continuous participation leads to battery cycle aging. the cycle aging mainly comes from BES depth of discharge (DoD) and the number of cycles [27,28]. The number of cycles and DoD determine whether a BES replacement is needed along the considered project lifetime. Neglecting those matters in expansion planning results in an inaccurate economic assessment. Figure 2 shows the typical battery life cycle model versus the DoD that the manufacturers usually provide [17,29]. Several studies to estimate the battery lifecycle have already been proposed. Those studies exhibited an exponential form of the relationship [30][31][32].
The BES investment/capital cost mainly depends on battery size, in terms of both power and energy rating. The increase in the investment cost of BES is proportional to the addition of the total expansion planning cost. Figure 3 shows the expansion cost as a function of BES size [33]. Expansion planning costs consist of the battery capital cost and the microgrid operation cost. The battery capital cost is proportionally linear with the battery size. However, as the battery size is increased, the microgrid operation is reduced. The lowest point of the expansion planning cost is the optimal point. This point shows the highest BES capital cost and the cheapest operation cost that can be achieved together. This curve shows that the active participation of the battery can lower the operating costs of the microgrid. If the correct battery size matches this participation, we can get the lowest expansion planning cost. This point can be called the optimal size point [34]. The BES investment/capital cost mainly depends on battery size, in terms of power and energy rating. The increase in the investment cost of BES is proportional t addition of the total expansion planning cost. Figure 3 shows the expansion cost as a tion of BES size [33]. Expansion planning costs consist of the battery capital cost an microgrid operation cost. The battery capital cost is proportionally linear with the ba size. However, as the battery size is increased, the microgrid operation is reduced lowest point of the expansion planning cost is the optimal point. This point show highest BES capital cost and the cheapest operation cost that can be achieved toge This curve shows that the active participation of the battery can lower the operating of the microgrid. If the correct battery size matches this participation, we can get the est expansion planning cost. This point can be called the optimal size point [34].

BES Advanced Load-Frequency Control Operation
LFC serves to suppress the grid frequency within a specified range by regulatin BES active power utilizing droop control. [35]. In this paper, an advanced LFC config  The BES investment/capital cost mainly depends on battery size, in terms of b power and energy rating. The increase in the investment cost of BES is proportional to addition of the total expansion planning cost. Figure 3 shows the expansion cost as a fu tion of BES size [33]. Expansion planning costs consist of the battery capital cost and microgrid operation cost. The battery capital cost is proportionally linear with the bat size. However, as the battery size is increased, the microgrid operation is reduced. lowest point of the expansion planning cost is the optimal point. This point shows highest BES capital cost and the cheapest operation cost that can be achieved toget This curve shows that the active participation of the battery can lower the operating c of the microgrid. If the correct battery size matches this participation, we can get the l est expansion planning cost. This point can be called the optimal size point [34].

BES Advanced Load-Frequency Control Operation
LFC serves to suppress the grid frequency within a specified range by regulating BES active power utilizing droop control. [35]. In this paper, an advanced LFC config BES output power using the multiregion P-f curve shown in Figure 4.

BES Advanced Load-Frequency Control Operation
LFC serves to suppress the grid frequency within a specified range by regulating the BES active power utilizing droop control. [35]. In this paper, an advanced LFC configures BES output power using the multiregion P-f curve shown in Figure 4. Figure 4 shows the BES power and frequency relation according to the droop characteristics. The frequency may vary between f max and f min , respectively the maximum and minimum values, f 0 is the vertical axis nominal frequency. The maximum and minimum frequencies are determined according to the IEEE standard in operating an islanded system. These frequencies must be within a predetermined range so that the system can be ascertained to operate within the allowable range [36]. On the horizontal axis, P b R shows the battery maximum output power both for discharging and charging modes. This power is determined based on the battery power capacity that can be delivered at one time. The maximum power supplied to the system includes the efficiency of the battery. The control is separated into three regions based on the frequency level. They are named  Figure 4 shows the BES power and frequency relation according to the droop ch acteristics. The frequency may vary between f max and f min , respectively the maximum a minimum values, f 0 is the vertical axis nominal frequency. The maximum and minimu frequencies are determined according to the IEEE standard in operating an islanded sy tem. These frequencies must be within a predetermined range so that the system can ascertained to operate within the allowable range [36]. On the horizontal axis, Pb R sho the battery maximum output power both for discharging and charging modes. This pow is determined based on the battery power capacity that can be delivered at one time. T maximum power supplied to the system includes the efficiency of the battery. The cont is separated into three regions based on the frequency level. They are named Region Region 2, and Region 3, and all of the regions determine BES operation. Region 1 rep sents linear operation, where the BES power is proportional to the droop curve. Region and Region 3 represent frequency saturation regions, where f max and f min point out the s urated frequency [37].

Region 1 (Droop Control with Deadband)
The control in Region 1 allows the BES power variation according to the droop equ tion expressed in (1) [38]: where fdh represents the grid frequency, f 0 as the droop reference, Kb acts as the BES dro gain, Pbdh is the BES power, and Pb 0 indicates the BES power at nominal frequency. In t region, a deadband area (Δf s ) is introduced. The droop reference shifts into f 0 +Δf s for B charging mode, while it shifts into f 0 -Δf s for discharging modes. In some references, Equ tion 1 is called the traditional LFC [13,35,[39][40][41].

Region 2 (Lower-Frequency Saturation)
In Region 2, BES power is regulated from Pb 1 to Pb R at saturated frequency f min , show in Figure 4. The grid frequency comes from the synchronous generator output. When B operates in this region, it makes the generator works at f min .

Region 1 (Droop Control with Deadband)
The control in Region 1 allows the BES power variation according to the droop equation expressed in (1) [38]: where f dh represents the grid frequency, f 0 as the droop reference, K b acts as the BES droop gain, P bdh is the BES power, and P b 0 indicates the BES power at nominal frequency. In this region, a deadband area (∆f s ) is introduced. The droop reference shifts into f 0 +∆f s for BES charging mode, while it shifts into f 0 -∆f s for discharging modes. In some references, Equation 1 is called the traditional LFC [13,35,[39][40][41].

Region 2 (Lower-Frequency Saturation)
In Region 2, BES power is regulated from P b 1 to P b R at saturated frequency f min , shown in Figure 4. The grid frequency comes from the synchronous generator output. When BES operates in this region, it makes the generator works at f min .

Region 3 (Upper-Frequency Saturation)
For Region 3, BES delivers its output power only at flat frequency f max from -P b 1 to its maximum charge power -P b R . This operation shows the ability of BES to meet load requirements when the generator operation always stays at f max .

Expansion Planning Cost
In the optimization model, the cost of expansion planning when BES operates in the system must be calculated. To get optimal results, the installed BES must be able to provide minimum expansion costs. Thus, the expansion planning cost equation can be written as: As explained in Section 2, expansion planning costs are divided into microgrid operating costs and BES investment costs. The equation can be written as: min Microgrid operation cost + BES investment cost$. (3) Energies 2021, 14, 2213 The microgrid operation cost is composed of the fuel needed by the generator during its operation and the value of lost load (VOLL). The needed fuel is determined according to the power supplied P gdh by the generator to the system. The generator is assumed to be a thermal unit generator that transforms the fuel-based energy source into electricity. Hence, the fuel needed is a quadratic function of the generated power. The process is imposed by the cost coefficients a, b, and c. Since the quadratic function defines the amount of fuel, a multiplier fuel cost Q must be included. An islanded microgrid operation is likely to have unserved energy due to the limited generation. VOLL calculates the amount of unserved energy, represents the customer's compliance to compensate for reliable energy that is defined by the amount of lost load LL dh at each hour, and R is the price of lost load. Hence, the microgrid operation cost can be written as: BES investment cost mainly depends on its size, both in terms of power rating P b R and energy rating E b R . In the practice, the BES investment cost mainly consists of power rating CP and energy rating capital costs CE, annual maintenance cost CM, and installation cost CI. PCS is assumed to be included in the power rating capital cost. Typically, annual maintenance costs are calculated based on the BES power rating, and installation costs are calculated based on the BES energy rating [17,18,39]. Hence, the BES investment cost can be represented as: However, the unit in maintenance costs with other costs is not the same. Maintenance costs are determined per year, while other costs are paid for one project lifetime T. Thus, the capital and installation costs must be annualized by the interest rate r, using the Equation (6): After determining the microgrid operation cost and BES investment cost equations, the expansion planning cost equation can be defined by substituting Equations (4) and (5) into Equation (3). The expression for final expansion planning cost can be written as: The objective function is modeled in a mixed-integer program (MIP) problem. By using this model, the problem can be assumed to be convex and have a unique single optimal point [42]. Several software tools are available to solve MIP problems, such as CPLEX, Xpress-MP, and SYMPHONEY. These tools are powerful in solving MIP problems quickly, so it is possible to do it on a personal computer [43,44]. In this paper, the software used to solve expansion planning problems was the IBM ILOG CPLEX Optimization Studio or CPLEX.

Microgrid Constraints
Microgrid constraints include the power balance, and grid limitation is shown in (8)-(10). ∑ i∈{G} P gidh + P bidh + ∑ i∈{W} P ridh + LL dh = P Ldh ∀d, ∀h The power balance (8) ensures that the power generated from all generators, RESs, and the BES equals the load demand at one time. Equality is used because the calculation of battery size requires a strict calculation. Power delivered by resources and the power from (or to) the BES are assumed to satisfy the load demand in each hour. The BES power and generator power are determined based on the LFC calculation. BES is discharging when the power is positive and charging when negative. The linear equation model is necessary to solve the model without introducing nonlinear equations. Hence, the power losses are ignored. The generator acts as the system backbone. Both the grid voltage and frequency are determined based on the generator output. In islanded microgrid systems, droop control applications are widely used. It allows the system to operate outside the nominal frequency. By applying the droop control, the grid frequency is determined based on the droop slope and the generator output power at each time interval in Equation (9). The frequency is limited by maximum and minimum value. It is represented by Equation (10).

Generator Constraints
The generator power is limited by maximum and minimum capacities illustrated in Equation (11). Moreover, the ramp-up and ramp-down limitations, (12) and (13), are also included in the constraints.

BES Constraints
In this study, as the proposed LFC is installed on BES, the BES constraints must be included in the optimization model. The following equations model the constraint.
ρ min = f min − f 0 P pu f pu K g Equation (14) represents the output power of BES. This equation is represented in two parts to determine the BES charging/discharging mode. The first part of the equation illustrates the discharging mode, and the second one illustrates the charging mode. When BES is in discharge mode, the output power is determined based on Region 1, representing the deadband droop, and Region 2, representing the lower frequency saturation area. In Region 1, when BES is in the deadband, the output power is zero.
On the other hand, the output power is following the droop equation, which ∆f s has shifted. When BES is in Region 2, the output power compensates for the difference between the load demand, the RES output power, and generator power at f max . This power is represented by the equation ρ max (15). In charging mode, the output power is determined according to Region 1 and Region 3. In Region 3, the output power comes from the load demand, the RES power, and the generator power at f min . This power is represented by the equation ρ min (16).
The charging/discharging powers of the BES are limited by its power rating, in which the negative power illustrates the charging mode and positive power illustrates the discharging mode. The charging/discharging powers are illustrated in (17). The energy rating is correlated to the power rating, which is illustrated with a ratio that determines the maximum discharge time at rated power (18). Equation (19) describes the energy stored in BES at each time interval. Stored energy is calculated based on the previously stored energy minus the energy discharged or charged. The stored energy cannot exceed the maximum value. Also, the stored energy cannot be less than the minimum value. The minimum and maximum values are defined by the determined maximum depth of discharge and charge to keep the stored energy or SoC within a determined range (20). This equation leads to the depth of discharge estimation of the battery, for which β max and β min , respectively, describe the maximum and minimum depth of discharge. Equation (21) is used to describe the BES cycles. The binary variable u dh represents the BES operation state. Status u dh counts 1 when the discharge mode operates and 0 when the charge mode takes over. The operation status calculation is summed over the project's life and must not exceed the specified number of cycles (22).

Simulation Result and Discussion
An islanded microgrid that contains a diesel generator, a solar photovoltaic (PV) unit, and a BES unit was used to study the proposed BES control [45]. Table 1 represents the characteristics of the source units in the microgrid. The PV and load hourly data are illustrated in Figure 5a,b obtained in [46] and [47], with the load factor for each month represented in Figure 6 [48]. The PV data are historical data obtained from NREL's PVwatt calculator [46]. In December and January, the targeted location experienced high rainfall, so the curves are relatively low. Factors such as passing clouds can influence this curve's formation but were not listed in detail by the data source. The fuel cost was assumed 0.9 $/L, borrowed from [49], and the VOLL was assumed to be 50 $/MWh, borrowed from [17]. The generator and BES parameters are shown in Table 2. Four battery technologies were used in this study. The characteristics of used BES were borrowed from [17] and are shown in Table 3. Table 4, which borrowed from [17,[50][51][52][53], shows the number of cycles that apply to each battery technology with various DoD. formation but were not listed in detail by the data source. The fuel cost was assumed 0. $/L, borrowed from [49], and the VOLL was assumed to be 50 $/MWh, borrowed from [17]. The generator and BES parameters are shown in Table 2. Four battery technologie were used in this study. The characteristics of used BES were borrowed from [17] and ar shown in Table 3. Table 4, which borrowed from [17,[50][51][52][53], shows the number of cycle that apply to each battery technology with various DoD.
(a) (b)    were used in this study. The characteristics of used BES were borrowed fro shown in Table 3. Table 4, which borrowed from [17,[50][51][52][53], shows the nu that apply to each battery technology with various DoD.

Implementation of Proposed Control
In order to show the effect of the proposed control in the system, three scenarios were studied in this paper: Case 1: Microgrid system optimal scheduling without BES installation. Case 2: BES installation in microgrid system with traditional LFC. Case 3: BES installation in microgrid system with the proposed control (advanced LFC).
Case 1: Table 5 shows the operating system's results without using a battery, where the generator compensates for all changes in the load and PV power. The absence of a battery makes expansion costs equal to microgrid operating costs. When the frequency cap is not in place, frequencies operate between 59.28-60.63 Hz at an expansion cost of $484,591/year. However, when the system imposes frequency limits, the expansion costs are even higher. The tighter the frequency limit, the more expensive the operation cost is due to the generator's operation limits. Thus, the VOLL of the system is getting higher. This result shows that the lowest cost of expansion is obtained when the frequency limitation is neglected. Case 2: Table 6 shows the operation of a system that implements the traditional LFC on the battery, with a considered project lifetime of 10 years and an interest rate r 4%. The optimization results with the droop gain variation were conducted to show their effect on expansion costs. Traditional LFC has no frequency limitation, so the system operates according to a load-sharing mechanism between the generator and battery. The results show that the greater the battery's droop gain, the greater the frequency deviation from the nominal value. Even with −0.08, the system operates in the 59. 45-60.34 Hz range, outside the value recommended by the manual. The choice of droop gain affects the amount of power capacity and battery energy, causing changes in the cost of expansion to the droop gain. The greater the droop gain, the lower the expansion costs required. Due to the battery's small participation, the generator must compensate for any changes in the system. This operation causes the battery's cost to be smaller, and the system frequency deviates from the nominal value. Case 3: Table 7 shows the results of operating a system that implements advanced LFC on the battery. Optimization with droop gain variation was carried out in order to show its effect on expansion costs. Besides, investigations were also carried out by varying the operating ranges of f max and f min . In general, larger droop gain contributes to lower expansion costs. The frequency limitation contributes to holding the generator from operating outside the specified range. It causes the diesel operation to be suppressed so that the battery's power compensation increases the size of the battery. The large size of the battery was confirmed by the table showing the low cost of expansion. However, the limit of frequency should be kept in mind because a broader range tends to provide lower costs than a narrow range (59.85-60.15 Hz). It is closely related to VOLL, which is getting higher. In general, Case 1, the diesel-only operation, offers the cheapest expansion cost. However, the resulted grid frequency was found to be outside the allowed range. The second-cheapest expansion cost was found to be Case 3 for every droop gain. Additionally, in the Case 3 results, the grid operated on the allowed frequency range. The proposed control can lower the expansion cost without violating the power quality. It is realized because the control can maintain the generator output, impacting the amount of fuel needed. Figure 7 shows the comparison of operations for each case for one week. This figure illustrates that when the battery is not implemented, the grid frequency fluctuates within 59.8-60.63 Hz. In terms of power quality, this result is still outside the allowed range in [36]. Thus, the use of a battery with a deadband droop was introduced. The utilization of deadband droop control keeps the frequency within 59.69-60.28 Hz due to the load sharing between the generator and the battery. It reduces the grid operation cost. The proposed control introduces a broader range of active-frequency control capabilities. This control ensures that the frequency is maintained within 59.8-60.2 Hz. This control expands the battery ability to regulate the grid frequency in the desired range. Hence, it causes the generator output to be maintained at these points, affecting the grid operation cost.
illustrates that when the battery is not implemented, the grid fre 59. 8-60.63 Hz. In terms of power quality, this result is still outs [36]. Thus, the use of a battery with a deadband droop was intro deadband droop control keeps the frequency within 59.69-60.28 ing between the generator and the battery. It reduces the grid posed control introduces a broader range of active-frequency control ensures that the frequency is maintained within 59.8-6 pands the battery ability to regulate the grid frequency in the causes the generator output to be maintained at these points, aff cost.

Selection of BES Technology Installed Proposed Control
The previous subsection estimated that the maximum DoD of BES using LFC, which was found to be 80% in a one-year operation. It shows unrealistic results since the installed BES is estimated to display 621 cycles per year. By referring to Table 4, it can be estimated that in about 8.5 months or less than 1 year, the battery must be replaced. The BES replacement certainly causes additional planning costs and is unattractive economically. Thus, a discussion of whether the proposed control is applicable for various battery types must be performed to draw the control capability. Each battery technology's simulation results are shown in Table 8, assuming each battery has a maximum DoD of 80%. These results indicate that the Li-ion battery can perform the proposed control. With an installed 2.5 MWh/59.44 kW, the total expansion cost becomes $4,630,710 per year. During one year of operation, BES is estimated to perform 1002 cycles per year. However, it is estimated the battery replacement still needs to be done after operating for about 4.5 years for a 10-year project.
The optimal results for each battery type are described in Table 9, where each maximum DoD for each battery is distinguished. The lead-acid battery delivers the total expansion cost of $3,689,075 per year at a 31.31 MWh/164.65 kW with a maximum DoD of 50%. Compared with the DoD calculation result of 80%, the expansion cost increases due to the battery operation restriction. Hence, the power difference must be satisfied by the grid. It increases the microgrid operation cost. In one year, the lead-acid battery operates 688 cycles. However, after a one-year operation, the battery replacement must be carried out due to the cycle limitation. A similar result was also found in the NiCd battery. At a total cost of $4,406,673 per year, size of 15.61 MWh/89.71 kW, and a maximum DoD of 65%, the battery performs 848 cycles per year. The battery can operate for one year without a replacement. However, assuming a 10-year project, around nine replacements would be required, leading to the additional cost of battery replacement. Li-ion battery shows an installed battery of 2.54 MWh/59.45 kW, a total expansion cost of $4,630,710 per year, and a maximum DoD of 80%. The battery is estimated to operate for 4.5 years without a battery replacement. By assuming a 10-year project, battery replacements would be required. The best result was obtained with a NaS battery. The operation cost incurred is $4,194,552 per year, with a 42.89 MWh/120.18 kW, and a maximum DoD of 75%. In one year of operation, the battery operates 628 cycles, where a replacement battery is not needed. Assuming the project period is 10 years, the battery cycle is still below the operating cycle limit. This shows that the NaS battery is able to perform the proposed control. Moreover, NaS battery is the second cheapest option after lead acid when compared to other technologies. It shows that selecting a suitable battery and the proposed control can reduce the expansion cost without relinquishing the system power quality.
These results indicate the proposed method has limitations that must be satisfied for battery implementation. This method only applies to a battery technology that has a high energy density or high capacity. A sensitivity analysis of battery size for each type was performed, which is shown in Figure 8a-d. The relation between battery capacity, expansion cost, and some battery replacements can be seen by varying the battery energy capacity. These results indicate the proposed method has limitations that must be satisfied for battery implementation. This method only applies to a battery technology that has a high energy density or high capacity. A sensitivity analysis of battery size for each type was performed, which is shown in Figure 8a-d. The relation between battery capacity, expansion cost, and some battery replacements can be seen by varying the battery energy capacity.
The number of battery replacements tends to decrease for all battery technologies as the battery capacity is increasing. The higher capacity causes lower DoD, which leads to a higher operation cycle. Thus, the higher capacity battery can operate much longer due to the allowed operating cycles. However, it leads to an increasing expansion cost, which was the objective function of this study due to the higher BES investment cost.

Conclusions
In this paper, advanced LFC implementation for BES optimization in microgrid systems has been introduced. In optimizing the size of BES, the expansion planning cost, which includes grid operation cost and BES investment cost, is the determining variable. The number of battery replacements tends to decrease for all battery technologies as the battery capacity is increasing. The higher capacity causes lower DoD, which leads to a higher operation cycle. Thus, the higher capacity battery can operate much longer due to the allowed operating cycles. However, it leads to an increasing expansion cost, which was the objective function of this study due to the higher BES investment cost.

Conclusions
In this paper, advanced LFC implementation for BES optimization in microgrid systems has been introduced. In optimizing the size of BES, the expansion planning cost, which includes grid operation cost and BES investment cost, is the determining variable. A one-year operation was simulated to evaluate the grid performance. A set of operation cases were simulated in the model to assess the BES operation.
It was found that the proposed LFC reduces the expansion planning cost. The frequency limitations in the LFC cause the operation of the generator to be restricted. The operation restrictions ultimately lead to reduced grid operation costs. Hence, it is concluded that the proposed LFC can reduce the expansion cost and keep the grid power quality.
In choosing a battery to implement, it is necessary to consider the degradation factor or battery life cycle. The factor illustrates that the BES operation affects the lifetime of the BES itself. By comparing the four battery types, it was found that the proposed control applies only to high-density or high-capacity batteries. Hence, this is the limitation in implementing the proposed control.
A follow-on work of this research will focus on studying the impact of multiple BES applications. A comprehensive discussion, such as calculating voltage and angle magnitude, might be developed to draw the proposed LFC applicability.

Conflicts of Interest:
The authors declare no conflict of interest.