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

Abstract

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.

1. 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 been introduced [11]. The proposed control successfully realized accurate power sharing and high voltage quality for the parallel-connected inverter system.

Nowadays, the world recognizes electrical energy storage has great potential to meet these challenges as an underlying technology [12]. The system response to load variations is swift due to the power electronics-based topology for battery energy storage (BES) [13]. Besides, many studies on BES have been carried out, so its ability to regulate frequency is more robust with greater capacity and lower self-discharge rates. In [14], the study reviewed a technical summary of battery energy storage systems and an instance of various operation modes for BES. Moreover, research related to BES frequency regulation is becoming an emerging research line due to increasing research in microgrid systems and RES fields [13,14,15,16].

On the other hand, BES has several issues of its own. The battery contributes to the highest price of components. Battery prices are getting higher as designers apply oversized batteries to guarantee system reliability. Several studies have conducted sizing of BES in microgrid application. An emergency resistor is used to optimize BES with frequency regulation when overfrequency occurs. This method considers the state-of-charge (SoC) limits [3]. This method has a limitation that the emergency resistor may not apply in general. Some operators cannot afford the use of an emergency resistor because it can affect the system’s cost and reliability. Research by [17] proposed a comprehensive BES sizing. This method was tested on a microgrid system by applying several operation scenarios. Although this study described the BES method in detail, this method only applies to grid-connected microgrids. Thus, it is necessary to control the BES frequency if the islanding operation is carried out and the participation of BES is required. A control scheme using the optimal sizing of BES-based particle swarm optimization (PSO) with a load shedding scheme to improve the grid frequency after islanding occurred was proposed [18]. This method introduces the optimal relationship of BES sizing with frequency control. However, the case used was still a grid-connected microgrid that changed to an islanded microgrid. In addition, frequency improvements were carried out based on the load shedding scheme.

A different approach was proposed in [19]. This method proposed the implementation of BES inertia control to assist system frequency regulation. The effect of the BES size was investigated to reduce the size of the battery. However, this method is very limited in short-term operation, so that the size of the battery does not ensure that the BES can continue to regulate the system frequency. A more complex study was carried out in [20]. This study focused not only on determining BES size but also on the BES placement in a location. Each placement will affect the effect of BES on the system. This study did not discuss more advanced BES controls, so that the role of BES has not been expanded. In [21], a new approach for determining optimal size of BES for primary frequency regulation in microgrid was introduced. The approach taken has proven the relationship between the BES frequency regulation function and its capacity. However, this method proposes the role of the BES as a reference for voltage and frequency control. The method only applies if the BES has been designed to have such a function from the start. Besides, in an islanded system, it is perilous to rely on the backbone of the system’s responsibility for energy storage, which may not be operational. From the references obtained, it is necessary to study the frequency control contained in BES in the islanded microgrid scope and aims to show the method can bring merits to the operation cost and BES size.

This paper proposes a BES sizing that implements a frequency regulation function by utilizing advanced load-frequency control (LFC). The control employs a droop control method that allows BES to supply power based on system frequency deviation. Also, advanced LFC implements frequency limiting controls to maintain system frequencies within a specific range. Investigation of the effect of advanced LFC on the size of BES is carried out by optimizing system performance both economically and technically. Besides, this paper also discusses the effect of advanced LFC on battery technology choice.

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.

2. 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].

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].

3. 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, f⁰ 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 Region 1, Region 2, and Region 3, and all of the regions determine BES operation. Region 1 represents linear operation, where the BES power is proportional to the droop curve. Region 2 and Region 3 represent frequency saturation regions, where f^max and f^min point out the saturated frequency [37].

3.1. 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]:

$$f_{dh}-(f^0\pm \Delta f^s)=K_b(P_{bdh}-P_b^0)$$

(1)

where f_dh represents the grid frequency, f⁰ as the droop reference, K_b acts as the BES droop gain, P_bdh is the BES power, and P_b⁰ indicates the BES power at nominal frequency. In this region, a deadband area (Δf^s) is introduced. The droop reference shifts into f⁰ +Δf^s for BES charging mode, while it shifts into f⁰-Δf^s for discharging modes. In some references, Equation 1 is called the traditional LFC [13,35,39,40,41].

3.2. Region 2 (Lower-Frequency Saturation)

In Region 2, BES power is regulated from P_b¹ 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.

3.3. Region 3 (Upper-Frequency Saturation)

For Region 3, BES delivers its output power only at flat frequency f^max from –P_b¹ 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.

4. Optimization Model

4.1. 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:

$$\min \mathrm{ExpansionCost}\$.$$

(2)

As explained in Section 2, expansion planning costs are divided into microgrid operating costs and BES investment costs. The equation can be written as:

$$\min \mathrm{Microgrid}\mathrm{operation}\mathrm{cost}+\mathrm{BES}\mathrm{investment}\mathrm{cost}\$.$$

(3)

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:

$$\mathrm{Microgrid}\mathrm{operation}\mathrm{cost}={\displaystyle \sum _d{\displaystyle \sum _{h}Q\left(a{P}_{gdh}{}^2+b{P}_{gdh}+c\right)+R}}{\displaystyle \sum _d{\displaystyle \sum _{h}L{L}_{dh}}}\$$$

(4)

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:

$$\mathrm{BES}\mathrm{investment}\mathrm{cost}=P_b^R\left(CP+CM\right)+E_b^R\left(CE+CI\right).$$

(5)

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):

$$\mathrm{Annualized}\mathrm{cost}=\frac{r{\left(1+r\right)}^T}{{\left(1+r\right)}^T-1}\times \mathrm{one}\mathrm{time}\mathrm{cost}\$.$$

(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:

$$\min {\displaystyle \sum _d{\displaystyle \sum _{h}Q\left(a{P}_{gdh}{}^2+b{P}_{gdh}+c\right)+R}}{\displaystyle \sum _d{\displaystyle \sum _{h}L{L}_{dh}}}+\left[P_b^R\left(CP+CM\right)+E_b^R\left(CE+CI\right)\right]\$$$

(7)

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.

4.2. Microgrid Constraints

Microgrid constraints include the power balance, and grid limitation is shown in (8)–(10).

$${\displaystyle \sum _{i\in \left\{G\right\}}{P}_{gidh}+P_{bidh}}+{\displaystyle \sum _{i\in \left\{W\right\}}{P}_{ridh}+L{L}_{dh}}=P_{Ldh}\hspace{1em}\forall d,\forall h$$

(8)

$$f_{dh}=K_g\left[\frac{\left(P_{gidh}-P_g^0\right)}{P^{pu}}\right]f^{pu}+f^0\hspace{1em}\forall i\in G,\forall d,\forall h$$

(9)

$$f^{\min }\le f_{dh}\le f^{\max }\hspace{1em}\forall d,\forall h$$

(10)

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).

4.3. 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.

$$P_{gi}{}^{\min }\le P_{gidh}\le P_{gi}{}^{\max }\hspace{1em}\forall i\in G,\forall d,\forall h$$

(11)

$$P_{gidh}-P_{gid\left(h-1\right)}\le R{U}_i\hspace{1em}\forall i\in G,\forall d,\forall h$$

(12)

$$P_{gid\left(h-1\right)}-P_{gidh}\le R{D}_i\hspace{1em}\forall i\in G,\forall d,\forall h.$$

(13)

4.4. 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.

$$\begin{gathered} P_{bdh}=\max \left(P_{Ldh}-P_{ridh}-{\rho }^{\min },\max \left(0,\frac{\left(K_b{P}_{Ldh}-K_b{P}_{ridh}+K_g{P}_g^0-K_{b}L{L}_{dh}\right)}{K_g+K_b}-\frac{\left(\frac{\Delta f^s}{f^{pu}}\right)P^{pu}}{K_g+K_b}\right)\right) \\ +\min \left(P_{Ldh}-P_{ridh}-{\rho }^{\max },\min \left(0,\frac{\left(K_b{P}_{Ldh}-K_b{P}_{ridh}+K_g{P}_g^0-K_{b}L{L}_{dh}\right)}{K_g+K_b}+\frac{\left(\frac{\Delta f^s}{f^{pu}}\right)P^{pu}}{K_g+K_b}\right)\right)\forall i\in W,\forall d,\forall h \end{gathered}$$

(14)

$${\rho }^{\max }=\frac{\left(f^{\max }-f^0\right)P^{pu}}{f^{pu}{K}_g}+P_g^0$$

(15)

$${\rho }^{\min }=\frac{\left(f^{\min }-f^0\right)P^{pu}}{f^{pu}{K}_g}+P_g^0$$

(16)

$$-P_b{}^R\le P_{bdh}\le P_b{}^R\hspace{1em}\forall d,\forall h$$

(17)

$${\alpha }^{\min }{P}_b{}^R\le E_b^R\le {\alpha }^{\max }{P}_b{}^R\hspace{1em}\forall d,\forall h$$

(18)

$$E_{bdh}=E_{bd\left(h-1\right)}-\frac{P_{bdh}^{dch}h}{{\eta }^{dch}}-P_{bdh}^{ch}{\eta }^{ch}h\hspace{1em}\forall d,\forall h$$

(19)

$$\left(1-\beta \right)E_b^R\le E_{bdh}\le E_b^R\hspace{1em}\forall d,\forall h$$

(20)

$${\zeta }_{bdh}=\left(u_{dh}-u_{d\left(h-1\right)}\right)u_{dh}\hspace{1em}\forall d,\forall h$$

(21)

$${\displaystyle \sum _d{\displaystyle \sum _h{\zeta }_{dh}}}\le \frac{1}{T}e\hspace{1em}\forall d,\forall h.$$

(22)

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 Δf^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).

5. 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. Source units characteristic.

Type	Cost Coefficient			Capacity
	a	b	c
	(L/kWh2)	(L/kWh)	(L)
Diesel unit	0.00009	0.2406	11.7	400 kW
PV	–	–	–	100 kWp

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. System parameters.

Parameter		Value
Generator droop gain	$K_g$	−0.0298 pu
Generator droop power reference	$P_g^0$	200 kW
Droop frequency reference	$f^0$	60 Hz
Base power	$P^{pu}$	400 kW
Base frequency	$f^{pu}$	60 Hz
BES droop power reference	$P_b^0$	0 kW
Maximum depth of discharge	$\beta$	80%

. Four battery technologies were used in this study. The characteristics of used BES were borrowed from [17] and are shown in

Table 3. BES technologies [17].

Technology	Power Rating Cost	Energy Rating Cost	Maintenance Cost	Installation Cost	η
	($/kW)	($/kWh)	($/kW/yr)	($/kWh)	(%)
Lead-acid	200	200	50	20	70
NiCd	500	400	20	12	85
Li-ion	950	600	–	3.6	98
NaS	350	300	80	8	95

.

Table 4. BES lifecycle for various depth of discharge values [17].

Depth of Discharge	Number of Cycles
(%)	Lead Acid	NiCd	Li-ion	Nas
10	8000	7900	–	100,000
20	2500	5800	–	60,000
30	1500	3400	–	30,000
40	950	2000	–	15,000
50	700	1200	8000	10,000
55	645	1050	7500	9500
60	590	900	6900	9000
65	545	950	6200	8000
70	500	800	5800	7000
75	475	850	5000	6500
80	450	700	4500	6000
85	420	650	4100	5500
90	390	600	3700	5000
100	350	500	3000	4000

, which borrowed from [17,50,51,52,53], shows the number of cycles that apply to each battery technology with various DoD.

5.1. 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. Optimization result for case 1.

Operating Frequency	Microgrid Operation Cost	Total Expansion Cost
(Hz)	($/year)	($/year)
59.28–60.63	484,591	484,591
59.5–60.5	759,188	759,188
59.6–60.4	1,641,050	1,641,050
59.7–60.3	3,556,352	3,556,352
59.8–60.2	7,075,788	7,075,788
59.85–60.15	9,696,305	9,696,305

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. Optimization result for case 2.

Droop Gain	Operation Range	Battery Capacity	Microgrid Operation Cost	BES Investment Cost	Expansion Cost
	(Hz)	(MWh/kW)	($/year)	($/year)	($/year)
−0.015	59.69–60.21	22.57/130.78	4,668,919	621,868	5,290,787
−0.02	59.65–60.23	20.3/117.65	4,668,990	559,431	5,228,422
−0.03	59.59–60.26	16.9/97.98	4,669,107	465,881	5,134,988
−0.04	59.55–60.29	14.45/83.94	4,669,198	399,136	5,068,334
−0.06	59.49–60.31	11.26/65.25	4,669,330	310,242	4,979,571
−0.08	59.45–60.34	9.21/53.61	4,669,419	253,731	4,923,150

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. Optimization result for case 3.

Droop Gain	Operation Range	Battery Capacity	Microgrid Operation Cost	BES Investment Cost	Expansion Cost
	(Hz)	(MWh/kW)	($/year)	($/year)	($/year)
−0.015	59.8–60.2	104.73/164.65	1,060,442	2,852,941	3,913,383
	59.85–60.15	50.19/180.63	3,040,992	1,374,837	4,415,829
−0.02	59.8–60.2	81.86/164.65	1,524,755	2,232,710	3,757,465
	59.85–60.15	27.79/180.63	3,600,879	767,340	4,368,219
−0.03	59.8–60.2	50.71/164.65	2,163,021	1,387,708	3,350,729
	59.85–60.15	13.9/94.87	4,875,732	384,112	5,259,844
−0.04	59.8–60.2	31.77/164.65	2,560,896	873,942	3,434,838
	59.85–60.15	9.175/94.35	5,762,704	255,924	6,018,627
−0.06	59.7–60.3	49.81/132.69	1,048,955	1,361,071	2,410,026
	59.8–60.2	14.57/95.43	3,338,498	402,203	3,740,701
	59.85–60.15	131.80/180.63	466,105	3,588,302	4,054,407
−0.08	59.7–60.3	36.25/132.69	1,261,462	993,057	2,254,519
	59.8–60.2	10.44/65.99	4,050,660	287,974	4,338,635
	59.85–60.15	130.88/180.63	465,976	3,563,400	4,029,376

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.

5.2. 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. Optimization results based on BES technologies (same maximum depth of discharge (DoD)).

Battery Type	Total Cost	Operation Cost	BES Investment Cost	Energy Rating	Power Rating	Maximum DoD	Number of Cycles
	($/year)	($/year)	($/year)	(MWh)	(kW)	(%)	(Cycles/year)
Lead acid	3,413,552	2,552,140	861,412	31.31	164.65	80	621
NiCd	4,377,500	3,973,638	403,862	7.81	89.71	80	870
Li-ion	4,630,710	4,435,223	195,488	2.54	59.45	80	1002
NaS	4,195,552	2,567,113	1,628,439	42.49	121.32	80	636

, 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. Optimization results based on BES technologies (different maximum DoD).

Type	Total Expansion Cost	Operation Cost	BES Investment Cost	Energy Rating	Power Rating	Maximum DoD	Number of Cycles	Expected End of Lifetime
	($/year)	($/year)	($/year)	(MWh)	(kW)	(%)	(Cycles/year)	(years)
Lead acid	3,689,075	2,827,663	861,412	31.31	164.65	50	688	1
NiCd	4,406,673	3,606,274	800,399	15.61	89.71	65	848	1
Li-ion	4,630,710	4,435,223	195,488	2.54	59.45	80	1002	4.5
NaS	4,180,408	2,552,140	1,628,268	42.89	120.18	75	628	10

, 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.

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.

6. 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.