Energy Storage System Sizing for Grid-Tied PV System: Case Study in Malaysia

Abstract

Energy storage systems (ESSs) have recently emerged as a common solution for mitigating the variability of intermittent renewable energy sources. A major challenge linked to ESSs is their expense. This study focuses on investigating techniques to decrease the size of an ESS while maintaining its performance levels. Data were gathered from a grid-connected 2MW PV system in Malaysia over multiple days, with numerous variables showing considerable hour-to-hour variations from hour to hour due to solar irradiation. A Python code was created to examine the impact of different ESS sizes on power grid stabilization utilizing the power conservation technique. The suggested ESS size derived from the program outcomes was evaluated utilizing a hybrid ESS, incorporating a vanadium redox battery (VRB) as the high-energy-density component and supercapacitors (SCs) as the high-power-density component. The effects of altering the output period lengths were examined. The result must stay consistent for at least five minutes as the minimum required duration. The findings show that an ESS capacity of approximately 10% of the overall produced power can meet the above duration requirement. A straightforward test was employed in the system to assess the power generation level in the upcoming time period. Simulink was employed to model the produced system, and the outcomes met the ESS requirements, enhancing efficiency and extending the battery lifespan.

1. Introduction

Malaysia’s average solar radiation remains consistent across various scenarios. However, climate change can affect solar performance and infrastructure during the daytime due to extreme temperatures and precipitation [1]. Solar systems, like other natural resources, are heavily influenced by weather and seasonal changes [2], with Large-Scale Energy Systems (LESSs) being more significantly impacted than Small-Scale Energy Systems (SLESs). Conventional power plants are based on synchronous generators which are affected by sudden frequency changes; this increases the chance of grid instability. In recent years, energy storage systems have been employed to address the intermittent nature of renewable energy resources, particularly when these are integrated with the power grid. These systems can be categorized as mechanical or electrochemical batteries [3], with the latter being the primary focus of this article. The cost of implementing battery energy storage systems (BESSs) remains the most significant challenge [4]. The approach proposed in this article aims to minimize the size of the BESS while maintaining the performance and efficiency of the LESS in managing intermittency.

Grid sizing of ESSs is crucial in grid planning due to the high capital costs involved and their significant impact on grid stability and efficiency [5]. Various methodologies can be employed to determine ESS sizing, depending on the specific objectives. Optimization techniques, probabilistic approaches, analytical models, and data-driven methods can be complex, largely due to the unpredictable nature of weather changes. However, data analysis has the potential to yield effective solutions. Several factors influence ESS sizing for renewable resources, including system characteristics, costs, grid stability and reliability requirements, and environmental impacts. Batteries are the most popular high-energy-density devices, while flywheels and SCs are commonly utilized as high-power-density devices.

Many studies have attempted to address ESS sizing. For example, in [6,7], the optimal ESS size in a microgrid was calculated with a focus on cost. Reference [8] concentrated on automatic generation control based on finite ramp rate control of PV peak, especially looking at ramp smoothing. Other studies have approached sizing from different perspectives, such as [9,10], which aimed to solve the issue of peak demand. Additionally, studies such as [11] have explored the probability of determining ESS sizing, while the study in [12] merged renewable source sizing with ESS sizing. Reference [13] combined optimizing the sizing with power management. Previous studies have primarily examined sizing from a financial perspective; however, this study adopts an electrical engineering viewpoint and is based on real data and instruments in a hybrid system combining VRB with SCs, which offers numerous advantages [14,15]. Successive processes are also considered in this topology; testing and simulation determine the state of the ESS over several consecutive days, addressing the problem at the unit level. A case based on data collected from tropical Malaysia is presented in this study, featuring thirty days of data arranged as three sets of ten days each as an example. These durations were chosen to demonstrate that tropical climates tend to exhibit repetitive daily patterns, which poses challenges due to rapid changes throughout the day.

This topology illustrates the process of ESS sizing based on collected data. The flowcharts outline the steps, using a hybrid VRB/SC as an example of an ESS. The type of ESS determines its limitations in real-world applications, and both reducing the ESS size without compromising energy efficiency and integrating ESSs with renewable resources presents a significant challenge. A straightforward control method, employing filtering and effective averaging, supports size reduction alongside other more efficient control techniques. However, the averaging technique used in this control method can also be applied using other modern or advanced controllers. This study employs a simple and effective control method to maintain focus on size reduction, ensuring that the ESS size is suitable for widespread use.

The topology was developed based on testing real data collected from an actual renewable energy plant. A Python program processes this data and determines the minimum ESS size required to achieve smoothing over a specified period. In the code the type of ESS is considered and its limitations based on market availability are determined after evaluating its advantages. Finally, an ESS of the proposed size is simulated using MATLAB 2025a Simulink to verify its effectiveness. A simple and efficient control method was also developed in MATLAB Simulink to optimize storage system performance for grid stability. This is achieved by regulating the grid generator during the subsequent settlement period to an appropriate level, enabling the ESS to maintain power output despite fluctuations in PV generation.

2. System Analysis

The system studied in this research consists of five parts as shown in Figure 1: (a) a PV solar energy system, which includes PV panels and inverters connected to the grid; (b) the grid (a generator with a droop controller); (c) an energy storage system ESS (vanadium redox battery VRB and supercapacitors); (d) converters (bidirectional DC-DC and AC-DC); and (e) the load (residential network).

2.1. Collected Data

The data collected for this case study came from a 30 MW PV plant in Malaysia. However, the data was collected using a Fluke meter from a 2 MW plant inverter. Significant variables from the output side of the three-phase inverter include current, voltage, and power. While voltage changes are limited, the current exhibits large fluctuations which result in power changes.

Three different periods during the year were chosen for testing, each lasting about 10 days. The first period was from 30 June to 8 July 2021; the second from 22 December to 1 January 2022; and the third from 10 February to 19 February 2022. The first period is presented across all time intervals and different settlement times, while the results from the second and third periods are combined into one figure to ensure validity across different times of the year.

A Python program was used to read power data as in [16]. Figure 2 summarizes (a) the power generated by the PV system between 30 June and 8 July 2021, (b) the increase in generated power on 3 July, and (c) the average power generated within an 8 h period. The total power generated was 98.3 MW, with an average power of 501.2 kW, and an average power of 1.503 MW/h over an effective 8 h period each day. On 2 July 2021, the maximum daily power generated was 16.0 MW, while the minimum was 9.1 MW.

During the generation period, the peak power was 2790.0 kW at 12:43 pm on 5 July 2021, the maximum increase within a minute was = 1437.0 kW at 11:49 am on 1 July 2021, and the maximum decrease was 1350.0 kW at 11:08 am on 1 July 2021. Changes greater than 420 kW did not exceed 1%. The maximum gap within six minutes was 2142.0 kW at 3:25 on 1 July 2021.

During the peak power generation period of 2790.0 kW at 12:43 pm on 5 July 2021, the maximum increase within a minute was = 1437.0 kW at 11:49 am on 1 July 2021, and the maximum decrease was 1350.0 kW at 11:08 am on 1 July 2021. Less than 1% of changes were greater than 420 kW. The maximum gap within six minutes was 2142.0 kW at 3:25 on 1 July 2021.

2.2. Storage System

Batteries are versatile and widely used for electrical storage due to their high energy density, rapid response time, and scalability. Lithium-ion batteries are the most popular; however, the VRBs offer several advantages for large-scale energy storage systems and are often used with SCs as hybrid storage systems.

2.2.1. Vanadium Redox Flow Batteries (VRFBs)

VRFBs (vanadium redox flow batteries) are a promising energy storage technology due to their design flexibility, low manufacturing costs, long lifespan, and recyclable electrolytes [17]. VRBs have a long service life, which means that their chemical aging process is relatively slow compared to those of alternative battery technologies. Figure 3 illustrates the VRB structure [18]. A VRFB’s cell membrane undergoes oxidation and reduction reactions during charging and discharging:

$$V^{4+}\to V^{5+}+e^{-}$$

(1)

$$V^{3+}+e^{-}\to V^{2+}$$

(2)

Figure 4 illustrates the equivalent circuit model. In this model, the voltage source is a stack voltage, a controlled current source is the current source, and the fixed loss resistance represents the parasitic losses of the pumps. Based on Randles’ circuit, which describes a battery’s electrochemical properties [19], the terms “Resistive” and “Reaction” indicate the electrolyte solution resistance and the charge transfer resistance, respectively. Figure 4 illustrates the equivalent circuit for the VRB [20].

The state of charge (SOC) refers to the ratio of battery charge to its fully charged state [18,19]. It provides a direct indicator of the state of energy (SOE) stored in a battery. When the SOC reaches its upper or lower limits, typically defined as 80% and 20%, respectively [11], the inverter considers battery lifetime and deterioration mitigation. Other researchers may extend this range to 10–90% [12], and these limitations should match the size of the batteries.

The VRB model can be derived as shown in [16]. E_stack, which determines the battery voltage, can be estimated using

$$E_{stack\left(OCV\right)}=n\times \left\{E_{{cell}_{\left(at 50\mathrm{\%} SOC\right)}}+{\displaystyle \frac{2RT}{F}}ln{\displaystyle \frac{SOC}{1-SOC}}\right\}$$

(3)

where n is the number of cells, R is the universal gas constant (8.144 JK⁻¹·mol⁻¹), T is the ambient temperature (K), F is Faraday’s number, and E_cell (at 50% SOC) is the cell equilibrium potential = 1.39 V.

The average DC output voltage from a three-phase full-wave rectifier is given by

$$V_{DC}={\displaystyle \frac{3\sqrt{3}}{\pi }}{V}_{rms}=400\times {\displaystyle \frac{3\sqrt{3}}{\pi }}=660V$$

(4)

The number of cells in the stack (n) at 660 V can be calculated as follows:

$$n={\displaystyle \frac{V_{DC}}{E_{{cell}_{\left(at 50\mathrm{\%} SOC\right)}}}}={\displaystyle \frac{660}{1.39}}\approx 476 cell$$

(5)

The constant at 30° can be calculated as

$${\displaystyle \frac{2RT}{F}}={\displaystyle \frac{2\times 8.144\times 303}{96485.3}}=0.051$$

(6)

The E_stack model in Figure 4 can be derived in Simulink by using (n) from Equation (5), and the constant E_stack in Equation (6) can be found on Simulink as shown in Figure 5.

The SOC can be estimated using the SOC calculation derived in [19] as

$$SOC={\displaystyle \frac{Current Energy in Battery}{Total Energy Capacity}}$$

(7)

$$SOC=SOC(t-1)+∆SOC$$

(8)

$$∆SOC={\displaystyle \frac{∆E}{E_{capacity}}}={\displaystyle \frac{P_{stack}{T}_{step}}{E_{capacity}}}={\displaystyle \frac{I_{stack}{V}_{stack}{T}_{step}}{P_{rating}{T}_{rating}}}$$

(9)

$$c={\displaystyle \frac{T_{step}}{P_{rate}{T}_{rate}}}$$

(10)

where c is the constant, T_step is the simulation step time, T_rate is the battery charge or discharge time, and P_rate is the battery power. From Equation (8) the SOC can be determined as the results of the ∆SOC integrator; the Simulink SOC Estimator is shown in Figure 6.

The Flow Pump model of the equivalent circuit in Figure 4 can be derived as shown in [19]; the electrolyte flow rate (Q) is

$$Q={\displaystyle \frac{I_{stack}}{N\times SOC}}{cm}^3{sec}^{-1}$$

(11)

where I_stack is the flow rate and is directly proportional to the stack current and inversely proportional to the SOC, and N is the electrolyte capacity.

The Flow Pump current can be derived as

$$I_{pump}=0.0096\left({\displaystyle \frac{I_{stack}}{SOC}}\right)$$

(12)

The pump loss can be represented by a controlled current source (I_parasitic), the shunt resistance (R_parasitic), and the combined resistance of the pump internal resistance and the auxiliary control circuit resistance (13.889Ω) [20].

The Flow Q Estimator of the VRB on Simulink is shown in Figure 7. Calculations of VRB parameters are based on an estimation of 15% internal losses and 6% parasitic losses. The cell stack output power should be [18].

$$P_s={\displaystyle \frac{P_n}{1-0.21}}$$

(13)

where P_n is the rated power. The fixed losses are represented as the fixed resistance and the variable losses are represented as the controlled current source. The losses are [18]

$$P_p=P_f+k\left({\displaystyle \frac{I_{stack}}{SOC}}\right)$$

(14)

where P_f is the parasitic loss and k is a constant value, assumed to be 1.011 in [18]. The losses are measured in kW. The 250 kWh product produced by the E22 Energy Storage Solutions Company can be considered a storage device. Its typical characteristic, as shown in

Table 1. Product specifications of the chosen VRB.

Power rating output	250 kW
Overload capability	Discharge: 30% 1 h, SOC > 60% Charge: 25% 45 min, SOC < 25%
Storage duration	2 to 8 h
DC bus voltage	300 to 800 V
Self-discharge %/day	0.05%

, is its overload capability: 30% discharge within one hour when the SOC exceeds 60% and 25% charge for 45 min when the SOC exceeds 25%; this means that 30% should be supplied or absorbed in one hour.

$$I_{Batt\_rms}=P_{Battary}/V_{rms}=250k/\sqrt{3}/400=360A$$

(15)

where P_Battary is the instantaneous power of the battery and V_rms is the nominal grid voltage.

This value is the current limitation of the charging and discharging current for the constant c in Equation (10), which depends on the total power of 250 kw, with a 5 ms sample, and a rate time of 4 h.

$$c=5\times {10}^{-2}/(250kw \times \left(4\times 3600\right))=1.389\times {10}^{-8}$$

(16)

The VRB model was simulated using Simulink, as shown in Figure 8. The charge and discharge result SOC change within 4 h for power and SOC is shown in Figure 9.

2.2.2. Super Capacitors (SCs)

SCs are energy storage devices that can store and deliver energy more rapidly than batteries. By integrating SCs into systems alongside batteries, transient energy peaks can be mitigated, and the lifespan of the batteries can be extended [20]. SCs offer several additional advantages, including a long lifespan characterized by numerous charge and discharge cycles. However, they also present two notable disadvantages: high costs and a tendency to self-discharge. This is why they are often utilized as secondary energy sources. Since SCs are responsible for managing the overcurrent problem in VRBs, they must handle significant current absorption or supply. The current should be approximately equal to the maximum PV supply current minus twice the maximum battery current

$$I_{SC\_max}=I_{PV\_max}-2I_{Batt\_max}$$

(17)

where I_{PV_max} is the maximum PV DC current peak supplied by the PV system and I_{Batt_max} maximum VRB DC current that can be supplied.

The Maxwell Technologies’ BMOD0165 P048 BXX model (San Diego, CA, USA) was selected as the SC storage battery, as shown in

Table 2. Product specifications of the SC.

Rated Capacitance	165 F
Maximum ESR DC, initial	6.3 mΩ
Rated Voltage	48 V
Absolute Maximum Current	1900 A
Maximum Series Voltage	750 V
Stored Energy	53 Wh

. To obtain a 660 V DC voltage, 14 cells needed to be connected in series. The 14 × 35 combination (490 cells) was selected to achieve 660 V and a capacitance of 412.5 F, or 490 × 53 = 26 kw.

2.2.3. Hybrid System (VRB) and (SC)

Hybrid systems, combining a VRB and SCs, may provide a comprehensive energy storage solution [21], combining the complementary advantages of both technologies. Each of the two systems should be provided with at least DC-DC bidirectional converters, and in the control process, these should be chosen between them for charging and discharging based on their basic function as high-energy- and high-power-density devices. The VRB serves as a long-term energy storage device, while the SC responds quickly due to its high power density [17,22].

2.2.4. System Economics

The cost of VRBs ranges from USD 600 to USD 800 per kWh, but future costs are estimated to decrease to USD 300 per kWh for a storage duration of 10 h [23]. VRBs have a long lifespan, exceeding 20 years. The unit price of the SC is USD 2500 per kWh [24]. In this study, the SC size is approximately 10% of the system capacity, resulting in a total hybrid system cost of USD 900 per kWh. Over a 20-year lifespan, the power savings from the hybrid ESS amount to less than 20% of the global average electricity price, which is USD 0.17 per kWh [25].

3. Renewable Energy Sources: Smooth Integration into the Grid

Various technical regulations and standards have been employed to ensure that electrical grids operate safely, reliably, and efficiently. Voltage, frequency, and harmonics must adhere to grid limitations. Variable Renewable Energy (VRE) generation forecasting helps address barriers to VRE grid integration. The National Electricity Market (NEM) adopts a five-minute dispatch period, the shortest possible timeframe. Due to limitations in metering and data processing, the AEMC adopts a 30 min settlement period (AEMC, 2017b) [21]. There is a regular change in the tuning coefficients of the droop controllers (e.g., every 5 min). This study focuses on the settlement periods of 5, 10, and 15 min and calculates the ESS size required to meet these periods.

4. Storage System Size

Even the largest PV generators can ramp down power from clear-sky nominal power to 20% in seconds, faster than required by grid codes [21]. Other studies have calculated the optimal ESS capacity to maintain grid stability at a minimum cost, such as [26]. However, in this study, we aim to optimize the ESS size so that it is less than 20% of generated power, as achieved in previous works.

Storage systems should be designed to absorb and supply energy during intermittent renewable energy sources to reduce these fluctuations and allow time for the groove controller to adjust and avoid network instability. Typically, at least five minutes is required in accordance with the electrical code; the Malaysian code follows the international code [27].

The ESS sizing strategy is based on the law of the conservation of energy. The ESS should be able to absorb all the energy above the expected average without reaching full charge, or, in practice, without reaching the limit of the maximum storage. Additionally, the ESS should be able to provide energy to cover the leakage of energy below the expected average without falling below the minimum storage energy limit.

The Python 3.11.9 program begins with the assumption that the SOC is 50% and that the size of the ESS is approximately only 5% of the renewable energy source produced. It calculates the losses by accumulating the energy that the ESS should absorb when its SOC is at a maximum, and the energy that the ESS should deliver when its SOC is at a minimum. In other words, the ESS must be able to help the system in providing the expected power. The program continues increasing the ESS size until the losses become less than 1% of the total energy produced.

The energy size, in kilowatt-hours (kWh), refers to the capacity of the ESS to supply power for a specified duration. Its unit is kilowatt-hours (kWh). In VRB systems, users can generally select a battery duration between 2 and 8 h. In the Python program used in this study, a four-hour battery life was chosen for comparison purposes. The total energy size of the ESS, as illustrated in Figure 10, is calculated by multiplying the rated power by four. If the user selects two hours, the ESS power is multiplied by two, and so on.

The energy losses were compared in ideal scenarios using Python code that excluded all electrical and chemical losses, as well as the battery size, from the collected data. The SOC was maintained between 20% and 85%. The strategy outlined in the flowchart of Figure 11 was implemented in the program; this satisfies battery limitations and ensures a simple, effective control method. Figure 10 illustrates the relationship between the storage system size and the percentage of energy loss in an ideal scenario for the data in Figure 2a.

Using 1% energy loss as a benchmark, Figure 10 shows that the minimum battery sizes for the intervals of 5, 10, and 15 min should be 135 kW, 255 kW, and 375 kW, respectively, where for Figure 2d,e the data was 130 kW, 251 kW, and 371 kW, and 115 kW, 224 kW, and 320 kW, respectively. Essentially, if the storage system is less than 135 kW, it cannot store ramp rates within 5 min. The VRB’s charging and discharging process should be regulated. As a result of the PV system generating the next power level, the system will not require intermittent power from the electricity network during charging and discharging, thus reducing the charging and discharging process. However, in practice, no exact expectation can be reached; thus, in this study, an easy-to-use low-pass filter to average the data is used; 15 min equals 900 s as the cutoff for this project. The filter is as follows:

$$F\left(s\right)={\displaystyle \frac{1}{900s+1}}$$

(18)

The discrete

$$F\left(z\right)={\displaystyle \frac{0.001111}{z-0.09989}}$$

(19)

where the input of this filter, $F\left(z\right)$, is the I_PV (PV system produced current).

The average of the last period of 5, 10, or 15 min of the I_PV gives the expected new level for the next period as

$$I_{avp}={\displaystyle \frac{{\sum }_{Period}\mathrm{F}\left(\mathrm{z}\right)}{Period}}$$

(20)

The summation is for discrete samples every one second and is divided by the number of samples, i.e., $Period$ in Equation (20).

The storage system should absorb any current from the PV system (I_PV) that exceeds this anticipated level. If the PV system cannot deliver the expected current, the storage system must compensate for the shortfall. However, two primary limitations restrict this process: I. the current limit of the battery, which in this case is approximately 380 A-, and II. and the battery’s SOC, which cannot absorb current when fully charged or produce current when empty. As recommended in [17], it is advisable to restrict SOC to between 20 and 85% to minimize issues with VRB charging and discharging and increase the lifespan. However, 0–90% SOC is acceptable in this case. The research controller chooses 10–90% limits as [26], forcing the SOC to be close to 50%. As illustrated in the Figure 11 flowchart, a simple method is to increase the expected level more than the expected level as the battery approaches full charge and to decrease the expected level less than the expected level as the battery approaches empty. This approach can achieve the Nash equilibrium by maintaining the (SOC) at approximately 50%. In other words, when the SOC decreases by 0.5 and a discharge occurs, the probability of charging increases inversely. To accomplish this, add 0.5 to the SOC and multiply the result by the expected level (I_avp)

$$I_{av}=I_{avp}\times (SOC+0.5)$$

(21)

where $I_{av}$ is the expected current level determined by Equation (20), in which the filter transfer function F averages the current generated by the PV system. This modified average current level is designed to maintain the SOC at approximately 50%.

The battery should be disconnected if the SOC exceeds 0.9 during charging or falls below 0.1 during discharging. In other words, the current should be zero. Additionally, the VRB must not exceed the maximum current rating.

Due to its limits, the battery cannot absorb or supply the necessary current. The sudden drop or rise in PV output causes a large change in currents, which exceeds the battery current and the network limit (−380, 380 A).

If the PV output is falling, the network will not be able to solve the leakage immediately, and if it is rising, the network will require more power. In either case, the frequency or voltage stability of the network may be affected. A hybrid system is one of the best current solutions for overcurrent problems.

Supercapacitors (SCs) were selected as storage aids in this study; (SOC_SC) the state of charge of capacitors ${SOC}_{SC}$ was chosen in the range [0–100%]. As illustrated in Figure 12, the hybrid SC and VRB storage systems are controlled as shown in the flowchart. As in [28], the new state of charge can be determined from merging the states of charge of the VRB and SC. Various methods can generate the SC state, but the simplest method is

$${SOC}_{SC}={\displaystyle \frac{V_{sc}^2}{V_{sc\_Max}^2}}$$

(22)

where V_SC is the instantaneous SC voltage and V_{SC_Max} is the maximum SC voltage, 660 V.

The new SOC is the summation of state of charges of the VRB and SC, where one of both is multiplied by weight (w₁: [0 − 1]) and the second is multiplied by (1 − w₁). The result will be increased by 0.5 to determine the new current average.

$$SOC=w_1\times {SOC}_{SC}+(1-w_1)\times {SOC}_{Batt}$$

(23)

As shown in Figure 12, the control strategy anticipates the new average of the predicted current according to the SOC in Equation (22). Since the SC can respond faster and its stored energy is lower, w₁ was chosen to be 20%, according to the current ratio; in addition, it can be observed that the SOC_SC is the output of the FIR filter with the same parameters as Equation (19), since it changes faster than SOC_Batt. In case of overcurrent in the battery—either supplying or charging—this can be covered by the SC; otherwise, the current will be divided between VRB and SC and is inversely proportional to SOC_SC as follows:

$$I_{Batt}={SOC}_{SC}\left(I_{pv}-I_{av}\right)$$

(24)

This equation determines the priority for charging or discharging to the capacitor if the SOC_SC is low. However, to avoid a full state being either charged or discharged in one of the storage systems when the second is in the opposite condition, the difference between SOC_Batt and SOC_SC is considered in the control process. The lower storage type will be charged more if the difference exceeds 30%, while the upper storage type will be discharged more. These rules should be added in game theory, and finally, the change should be limited to a maximum value to prevent rapid network changes and make both storage types better able to handle the change. As shown in Figure 13 and Figure 14, Simulink implements generation according to Equation (23).

5. Simulation Results

Figure 13 illustrates the simulation of the system using MATLAB Simulink. The system is a PV system that generates three-phase AC current from the stored data, and the generator is composed of a 250 kVA three-phase limited power source with a constant load of 220 kVA. The controller and Simulink have already been derived in the flowchart shown in Figure 11 and Figure 12 and Simulink in Figure 14 and Figure 15, respectively, and the SC and VRB have already been discussed. A bidirectional converter was used as an averaged inverter to speed up the system simulation, and the transient has been neglected as a result. As shown in Figure 16, the data collected during (3/7) represent the current absorbed or supplied by the VRB, which is limited by (−380, 380 A), as shown in the second row. The SC supplies or absorbs the current when the VRB current exceeds the limits, as shown in the third row. It is possible for the SC to absorb or supply a current up to 1200 A, but it does not exceed 1000 A in this experiment. PV, VRB, and SC supply the total current to the network in the fourth row, which appears to be a filtered current from the PV source. It does not change very much within 900 s. When the VRB and SC reach their limits within very short periods, some overcurrent remains in the grid.

As a general principle, this minimizes the large, rapid changes in energy that are supplied to the network and simplifies the generator’s groove control of the generator so that it can be applied with greater efficiency. Figure 17 shows the VRB and SC for the period (30/6–8/7), of which approximately 50% are within the 20–80% range, which ensures VRB stability and efficiency and increases its lifetime. Since the capacity of the VRB is a smaller than that of a supercapacitor and its job is to reserve fast changes in a short time, these changes almost disappear at low currents—the VRB can handle small changes.

A simulation was conducted for three settlement periods (5, 10, and 15 min) with battery storage capacities of 135 kWh, 255 kWh, and 375 kWh, respectively, as shown in Figure 10. Each battery is designed with a four-hour lifespan; for better evaluation, this value was multiplied by five, resulting in total energies of 675 kWh, 1275 kWh, and 1875 kWh. The system uses a 250 kWh battery for 3 h, 5 h, and 7 h durations corresponding to the three settlement periods of 5, 10, and 15 min-**, respectively. The SC size remained constant across all periods, as shown in Figure 17, Figure 18 and Figure 19 for the three datasets. Note that the currents vary with the battery sizes. The simulation outputs for the three settlement periods confirm that the state of charge (SOC) limitations minimize grid penetration. Figure 17, Figure 18 and Figure 19 illustrate the simulated system without losses, transient effects, or load changes. It is also assumed that the PV, ESS, and generator plants are connected regardless of their location, as discussed in [29,30,31]. Although these variables are important for determining system efficiency, they do not significantly affect the primary research objective, which is the size of the ESS. It is further assumed that inverter transient issues do not impact the ESS size as they exhibit minimal losses in batteries and SCs [32].

Figure 20 and Figure 21 illustrate the simulated system for the periods 22–24 December and 12–22 March, respectively. These figures demonstrate the improved effectiveness of that battery size during different times of the year.

Instead of direct communication between system parts, predicting grid stability regarding voltage and frequency can also be an excellent approach to changing sources. The load change has a clear effect, but it is assumed the grid was stable before adding the renewable source for future studies. Simply reducing the value of 0.5 added in Equation (21) to a smaller amount results in a higher average SOC, indicating that more energy is stored in the battery. This stored energy can be utilized during peak load periods to alleviate grid stress and provide economic power supply. For example, in the previous case, Figure 22 illustrates the modification of Equation (21) to include load feeding at night between 20:00 and 21:30, thereby minimizing the impact of peak load consumption on grid stability.

Comparing the summation of generated $I_{pv}$ power in Figure 17, Figure 18 and Figure 19 in part (a) to the summation of power supplied by PV and ESS to the grid, the difference was about 1% according to

$$P_{Losses of over charge or discharge}={\displaystyle \frac{\sum P_{PV}-\sum P_{Supplied to Grid}}{\sum P_{Supplied to Grid}}}\times 100\%\approx 1\%$$

(25)

6. Conclusions

The ESS size was determined using a simple Python program designed to reduce battery size and test whether it could accommodate the penetration of the PV source by analyzing historical data. The hybrid ESS was simulated using a high-power-density device, the VRB, and a high-energy-density device, the SC. The size of the storage system was determined through Python testing, representing 10% of the PV instantaneous power, achieving a five-minute settlement period. The total ESS capacity was approximately 5% of the energy generated throughout the day. However, other research suggests that this value should be approximately 20%. In this scenario, a battery with a capacity of 250 kWh and a lifetime of three hours, combined with supercapacitors with a storage capacity of 26 kWh, can support the PV system, which is capable of generating 2 MW of electricity in tropical climates. Settlement periods of 10 and 15 min were also tested using the same battery with lifetimes of five and seven hours, respectively. Many important factors were considered in the program development due to the limitations and lifespan of the VRB. In this simulation, a straightforward and effective control process was implemented. The SOC of both the VRB and SC remained within the optimal range by adding a simple factor derived from 0.5 to the SOC. The system effectively utilized the output from PV renewable resources based on the ESS size, determined using the Python code, adhering to the law of conservation of energy. The losses of the Simulink simulation are theoretically close to the Python outputs.

Furthermore, simulations were conducted for settlement periods of 10 and 15 min using actual data collected from a PV system in Malaysia. This method can be applied to any dataset by following the same steps; however, for non-tropical climates, different seasonal factors must be considered.