1 Introduction

The challenges in the operation of electrical power systems have grown in recent times owing to the increased utilization of energy and penetration of renewable energy sources [1]. Though the penetration has resulted in many positives like reduced carbon emissions, energy diversity, security, equity, decentralization of power generation, and economic development due to additional job creation [2], there have been several issues that are still being addressed [3]. The rate at which the renewable energy sector is growing and the very nature of power output from renewable energy sources have been of great concern and challenges for the concerned stakeholders. It is very difficult to correlate the demand and supply of energy from renewables due to the abrupt changes in the output power produced by renewables [4]. To overcome this problem, several types of solutions have been developed over time [2]. Using energy storage devices of different types and capacities has been one of the significant solutions to combat the variability in the output of renewable energy sources [5]. Proper selection and deployment of the right energy storage systems can effectually flatten the variations in the power [6], manage peak loads [7], make the energy time shifting possible [8], and ensure the proper supply of power to remote locations [9]. Among different energy storage mechanisms, electrochemical energy storage has found vast popularity due to its inherent advantages over its other counterparts like compressed air energy storage, and pumped hydro energy storage, [10]. Battery Energy Storage Systems (BESS) and supercapacitors (SC) fall under the category of electrochemical energy storage [11]. Superior energy density, longer life, modularity, scalability, and reduced cost are some of the inherent advantages of electrochemical energy storage over its counterparts [12]. These benefits make electrochemical energy storage systems suitable for different areas of application, like transportation using electric vehicles, integration of renewable energy sources, and energy storage at a grid scale. Perpetual progress and advances in electrochemical energy storage technologies hold the potential for further improvements in overall performance, cost reduction, and sustainability.

Further, the specific advantages again depend on the types of electrochemical energy storage systems. Though batteries have become a most common and versatile type of electrochemical energy storage system, they suffer from inferior power density. Moreover, due to chemical reactions, the possibility of environmental hazards is more which is a serious concern in the present situation [13]. The disposal of chemical waste in batteries has become a severe issue in the larger interest of protecting the environment. But so far as the load management is concerned the relatively slower time constant of the batteries poses a significant constraint on the battery performance during transient operations [14]. With frequent switching, the battery goes through cycles of discharge and recharge more often. This increases the average depth of discharge, which is the percentage of a battery's capacity that's used in a single cycle. A higher depth of discharge stresses the battery and reduces its overall lifespan [15]. Switching loads can cause fluctuations in the battery's current draw. Batteries are most efficient when delivering a steady current. Frequent changes can lead to higher internal resistance within the battery, reducing the amount of usable energy available. The internal resistance of a battery increases as it discharges and during current fluctuations caused by switching loads. This increased resistance can lead to heat generation within the battery. Heat is detrimental to battery health and can accelerate degradation [16]. Because of all these switching effects a suitable mitigation technique is required to be devised to enhance the battery performance during switching. There are different solutions to mitigate the effects of the switching transients on the performance of the battery. These generally include optimization of applications [17], choice of appropriate battery technology [18], choice of appropriate battery management system (BMS), and predictive management [19]. Yet, there is not a single solution available as these methods offer improvements but may not completely negate the impact of frequent switching. It's always a trade-off between functionality and battery life.

On the other side, supercapacitors which are the counterparts of BESS have grabbed a lot of research attention in recent times owing to their superior power density, quicker charging and discharging ability, good stability, ability to work at a wide range of temperatures, environment-friendly nature, safer operation, and lesser maintenance [20]. Supercapacitors also referred to as ultracapacitors are principally capacitors with larger charge storage capacity. The size and application make the constructional features of supercapacitors different from those of conventional capacitors. Accordingly, based on the fundamental principle of charge storage mechanisms, supercapacitors are further classified as Electrochemical double-layer capacitors (EDLC), pseudocapacitors, and hybrid supercapacitors. The details of the construction and operating principles of each type are well explained in the literature [21]. The inferior energy density of supercapacitors compared to batteries has resulted in the supercapacitor’s role in limited energy storage applications [22]. The short time constant of supercapacitors makes supercapacitors very effective in overcoming the negative effects of transients on battery performance. Supercapacitors excel at delivering very high bursts of power for short durations. During a transient event, when the load demand spikes, the supercapacitor can instantly deliver the required extra power. This takes the pressure off the battery, preventing large current surges and deep discharges. However, the battery remains the primary source of power for continuous operation. Once the transient passes, the battery can replenish the supercapacitor's charge and continue powering the system. By handling transients, the supercapacitor reduces the depth of discharge and current fluctuations experienced by the battery, extending its lifespan, and improving efficiency. Supercapacitors can react to transients much faster than batteries, ensuring uninterrupted power delivery during short spikes [23].

Several researchers have worked on assessing the role of supercapacitors in the energy storage scenario [24,25,26,27,28,29]. Mohammad Ahmed Zabera et.al have presented a semi-empirical modeling methodology is presented that can predict the current distribution and the voltage response of battery/supercapacitor hybrid systems under arbitrary charge/discharge profiles [30]. A solar photovoltaic (PV) powered battery-supercapacitor (SC) hybrid energy storage system has been proposed for electric vehicles and its modeling and numerical simulation have been carried out in MATLAB Simulink by Kiran Raut et.al [31]. A battery/supercapacitor hybrid energy storage system is proposed to improve battery lifetime in small-scale remote-area wind-power systems by diverting short-term charge/discharge cycles to a supercapacitor. Simulation and experimental results demonstrate the potential for improved battery lifetime and reduced project costs using this hybrid approach [32]. A hybrid energy storage system combining a supercapacitor and battery in parallel is proposed to enhance battery life by reducing heavy drainage during DC motor startup and overload periods. MATLAB simulations and experimental results demonstrate the effectiveness of this approach in improving power delivery and prolonging battery life[33]. Modeling and simulation of the energy storage system, combined with a converter system, is a cost-effective method to extend and enhance the life and operating range of hybrid and electric vehicles, and other battery-powered applications. Adding supercapacitors to the energy storage system improves energy delivery, increases efficiency, and extends battery life, especially during peak demands and low battery states [34]. A hybrid energy storage system (HESS) using a multi-input converter (MIC) and fuzzy logic control is proposed for electric vehicles, combining a battery and ultracapacitor (UC) to optimize energy flow and prolong battery life. The system is evaluated through simulation and experimental testing, demonstrating improved battery cycle life and a sustainable HESS solution [35]. Combining a battery with a super-capacitor can help meet the energy demands of Electric Vehicles (EVs) and mitigate the negative effects of non-monotonic energy consumption on battery lifespan. A novel system that starts a DC motor in parallel with a super-capacitor and battery is proposed, showing promise for uninterrupted power supply and extended battery life [36].

However, as per our understanding, none of the above-mentioned reports have addressed how the transient conditions affect the battery performance and how supercapacitors can quantitatively optimize the performance of the batteries by customizing the transient waveshapes. This reported work focuses on how the transient switching conditions affect the battery performance in the pertinent applications and the role of supercapacitors during transients. The following sections discuss the performance evaluation of supercapacitors with mathematical modeling, detrimental effects of frequent switching load on standalone batteries, method of supplementing the BESS with a supercapacitor, simulation of such system, and relevant experimentations to show how supercapacitor plays its role of ‘shock absorbing’ during the transient condition to optimize the battery performance and life.

1.1 Modelling and performance evaluation of supercapacitor

A supercapacitor is electrically represented as shown in Fig. 1a. The equivalent circuit consists of a constant capacitance Co and a variable capacitance xVc, which together represent the true capacitance of the supercapacitor. Rs is the series resistance of the supercapacitor which takes both internal resistance and lead resistance into account, while Rp represents the parallel resistance to determine the self-discharge characteristics of the supercapacitor.

Fig. 1
figure 1

a Electrical equivalent circuit of the supercapacitor, b Schematic representation of SC Battery charging system with recording mechanism Supercapacitor charging profile, c Experiment set up, d Supercapacitor voltage and current during charging e Supercapacitor charging profile at different charging currents and f Supercapacitor discharging profile at different load currents

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From the Fig. 1a, using KCL,

$${\text{Isc}}\, = \,{\text{Irp}}\, + \,{\text{Ic}}$$
(1)
$$\text{Cdiff}= C\text{o}+2xVc$$
(2)
$$Ic=(\text{Cdiff})\frac{dVc}{dt}$$
(3)
$$Irp=\frac{Vc}{Rp}$$
(4)
$$\text{Isc}=(\text{Cdiff})\frac{dVc}{dt}+\frac{Vc}{Rp}$$
(5)
$${\text{Vsc}}\, = \,{\text{Isc Rs}}\, + \,{\text{Vc}}$$
(6)
$$\text{Vsc}\hspace{0.17em}=\hspace{0.17em} \left[\left(\text{Cdiff}\right)\frac{dVc}{dt}+\frac{Vc}{Rp}\right]\text{Rs}\hspace{0.17em}+\hspace{0.17em}\text{Vc}$$
(7)

The series resistance Rs can be found our using two methods, one using the relationship.

$$Rs=\frac{\Delta Vsc}{\Delta Isc}$$
(8)

Another way of finding Rs is through the Electron Impedance spectroscopy (EIS) using Nyquist plots which is explained in our earlier research reports.

However, a DC load test was carried out to measure the voltage drop (ΔV) across the battery terminals with a known DC load current (I). Rs was calculated by taking the ratio of Δ V and current which also yielded the same value of Rs after the average value of three repeated readings was taken.

Rp is obtained by first charging the supercapacitor to its full capacity and then allowing it to self-discharge till Ic = 0. The time required for this phenomenon is noted and Rp is calculated using the relationship.

$$\left(\text{Cdiff}\right)\frac{dVc}{dt}+\frac{Vc}{Rp}=0$$
(9)

Figure 1b shows the schematic representation of the charging mechanism for both battery and supercapacitor. A supercapacitor with the specifications mentioned in Table 1 is considered for the analysis using the electrical analogy (Fig. 1a). To determine the values of x and Co, the tests on the charging and discharging patterns of supercapacitors were carried out. During charging the supercapacitor was allowed to get charged to the required voltage at different charging currents. Figure 1c shows the actual experimental setup and 1d shows the graph of the supercapacitor getting charged at its highest charging current. While discharging the discharge voltage was made zero at different load currents. Figures 1e and 1f show the charging and discharging profiles of the supercapacitor respectively. It was observed from the tests that the linear relationship between supercapacitor voltage (Vsc) and discharge time was maintained throughout. From these test results, using Eq. 6, the value of Vc is calculated. Since Rp is comparatively very high, Ip is negligible. Hence assuming Ic is equal to Isc, Cdiff was evaluated using Eq. 3. For the values of Cdiff obtained for each Isc, the values of x and Co were evaluated using Eq. 2. The value of Rs is taken as 3 mΩ from the datasheet which matched with the experimentally obtained value.

Table 1 Supercapacitor model parameters
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Thus, this experiment successfully validated the mathematical model of the supercapacitor such that the supercapacitor could be employed for further experimentation.

1.2 Battery performance during transient operation and supplementing battery using supercapacitor

Though the batteries are one of the most versatile and proven energy storage systems in the present scenario, the inherent slower time constant does not allow the batteries to reciprocate to the switching types of loads. This has posed a serious bottleneck in the effective utilization of the battery characteristics. Increased internal resistance [37], voltage dips [38], increased cycle count, heat generation, reduced charge acceptance, and degradation of electrodes [39] are some of the common problems in batteries due to switching loads. These effects can eventually reduce performance degradation and battery life.

In the case of an electric vehicle being supplied by an appropriately rated battery, peak power demand is significantly higher than the constant power needed for the steady operation of EVs. Designing the right size and achieving cost-effective advanced battery systems for electric vehicles (EVs) remains a significant challenge. Steady operation of EVs and accessories generally requires small amounts of power for long periods, thereby amounting to a large energy requirement. Conversely, acceleration requires large amounts of power for short periods, consuming less overall energy than an extended cruise but requiring the storage device to endure high power discharge. Unlike acceleration, deceleration which discharges the electric energy at a high rate, necessitates mechanisms that should be capable of absorbing the energy at a quicker rate. In power system operations where batteries are deployed for specific operations as a part of a hybrid system [40], are likely to be subjected to different power surges. To meet these requirements, the role of supercapacitors in supplementing the batteries during switching operations is analyzed.

Figure 2a shows a combination of battery and supercapacitor with a suitable power conditioning/switching circuit supplying a dynamic load (Table 2).

Fig. 2
figure 2

a Battery -supercapacitor-based system. b Motoring operation. c Braking operation

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Table 2 Specification details of the supercapacitor and battery
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The transient conditions in this case could be the switching ON and OFF of the load. The battery is supplemented by a supercapacitor of appropriate rating to supply the required transient energy to a load representing the frequent transient operations as shown in Fig. 2b, while Fig. 2c represents one more possible transient condition with the direction of power flow reversed shown electrically. An appropriately rated supercapacitor and BESS are chosen for simulation and consequent experimentation to supply the power to a load. Table 1 provides the specification details of the supercapacitor and battery for the chosen simulation and experiment. Since the supercapacitor’s role is the supply the required power only during the transients which are expected to be present for a relatively shorter duration, the rating of the supercapacitor is chosen as per the calculated values of the system requirement. Before performing simulation, the proposed system is electrically represented as shown in Fig. 3.

Fig. 3
figure 3

Electrical equivalent of the proposed system

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When the supercapacitor is connected in parallel with the battery to supply a switching type of load, electrically it acts as a low pass filter, that filters rapid voltage changes shaving the short duration high amplitude load spikes. However, the filtering effect depends on the value of the capacitance frequency of switching and the nature of the loads. The battery life can be further augmented by considering various effects during the switching.

The simulation of the proposed scheme is done using MATLAB Simulink. The schematic representation of the simulated model is shown in Fig. 4a. This simulation model represents the schematic diagram shown in Fig. 1a with the additional components required for the simulation. This is to illustrate the load shared by both the battery and supercapacitor at the instant of switching representing different transient conditions. Figure 4b shows the transient response of the proposed system. The battery takes its own time to supply the required load current due to the limitation of its slower time constant, while the supercapacitor takes the initial load quickly due to its superior time response. If the system is considered as a whole, the supercapacitor prevents the battery from being stressed at the instant of switching. However, the exact response of the system depends on the selection of the system components like battery, supercapacitor, and the nature of the load itself. To practically understand and validate the performance of the system, an experiment is conducted on an actual system as shown in Fig. 5a. The experimental setup of the same is shown in Fig. 5b.

Fig. 4
figure 4

a Simulink model of the proposed system. b Transient response of the proposed system using SIMULINK

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Fig. 5
figure 5

a Schematic diagram of Battery-SC circuit to supply a switching load. b Experiment to demonstrate Battery-SC circuit to supply a switching load. c Load current supplied to resistive load by Battery-SC system at different deliberate switching instances. d. Load current supplied by Battery-SC system to resistive load at switching instant (0 to 1 s). e Load current supplied to dynamic load by Battery-SC system at different deliberate switching instances. f Load current supplied by Battery-SC system to dynamic load at switching instant (0 to 1 s)

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1.3 Validation of the results using electrical experimentation

To validate the results obtained using simulation, an electric circuit has been rigged up. First, the supercapacitor is charged to understand the charging patterns and magnitudes of different quantities as a function of time. Since the initial charging current of the supercapacitor is very large, an Arduino-based recording mechanism is employed the details of which are provided in supplementary material (S1).

Further, a suitable switching load of appropriate rating (both resistive and dynamic type) is chosen to demonstrate the current supplied by the battery to the load both during switching and under steady state. The process of experimentation and the recording are explained in detail in supplementary material (S1). The required load current and current supplied by the battery and supercapacitor are shown in Fig. 5c. It can be noted from Fig. 5c that at different switching instances (at t = 0, 21 s, and 29 s) the required current is beyond the supplying capacity of the battery due to the inability of the battery to supply the required energy. Though it is momentary, the frequent switching results in considerable stress on the battery leading to an increase in the internal resistance, excessive heating, and consequent reduction in the battery life. Figure 5d shows the initial part of Fig. 5c for a better understanding of the phenomena at the time of switching and analytical calculations. Similar outcomes are shown in Figs. 5e, f respectively for the dynamic load (motor). Due to the very nature of the load, the initial current requirement is comparatively high which is met by the supercapacitor confirming its higher significance in the case of dynamic loads.

1.4 Analytical results

After successfully experimenting to show the relevance of supercapacitors to supply burst power under transient conditions, certain important parameters related to the battery performance are quantified. They mainly include transient response improvement (TRI), capacity fade factor (CFF), internal resistance increases factor (IRI), and stress reduction factor (SRF).

$$TRI\left(\%\right)=\frac{\text{trws}-\text{trs}}{\text{trws}}*100$$
(10)

where,trws= system response time without supercapacitortrs= system response time with supercapacitor

$$\text{CFF}=\Delta \text{C}= \alpha *(1-{e}^{-\beta *\text{t}})$$
(11)

where,

α and ꞵ are capacity fade constants that depend on battery type and chemistry.

t is the response time.

$$\text{IRI}=\Delta \text{R}=\lambda *(1-{e}^{-\beta *\text{t}})$$
(12)

where,

λ and δ are constants related to internal resistance that depend on battery type and chemistry.

Stress reduction factor (SRF) quantifies the reduction in battery stress, measured by the decrease in battery voltage sag or temperature rise during transient events. Peak Power Reduction (PPR) is another performance parameter that defines the reduction in peak power demand on the battery due to the supercapacitor's ability to provide instantaneous power. Equations 11 and 12 are the approximate relationship between the respective factors and battery response time, while the actual relationship varies depending on factors like battery chemistry, C cycles of the batteries, usage patterns, and environmental conditions where the batteries are deployed.

Table 3 below shows the values of the performance parameters calculated based on the experimental results of the proposed system by taking the suitable values of different constants [41, 42].

Table 3 Certain performance parameters of battery supplemented by supercapacitor
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It can be seen from the above table that there is a considerable improvement in the transient response of the system due to the presence of the supercapacitor. This further optimizes battery performance by reducing the change in internal resistance and capacity fade. Both the parameters are functions of response time. Though the exact quantification of the optimization of battery performance depends on several heterogeneous factors related to battery performance, the presence of the supercapacitor permits customizing the response curve of the system. Due to the large time constant, customization of the response curve is not possible by employing a battery alone. The presence of a supercapacitor makes it possible to push it beyond the capacity of the battery to obtain the required response during switching. The other conductive properties of the supercapacitors like the virtually unlimited number of charge /discharge cycles, ability to be able to charge and discharge quickly, ability to provide high current during transients, broad temperature range, and longer life make them more pertinent in these applications.

1.5 Performance optimization of supercapacitor with new materials

The higher energy density, power density, energy retention, and better cyclic stability imply that the battery will experience fewer stress events (due to less frequent load transitions) and the overall system will maintain its performance for a longer period. This results in a significant extension of battery life. Therefore, high-performance supercapacitors are always desirable in supplementing the batteries more effectively. Furthermore, to effectively deploy supercapacitors as the supplementary energy storage system with batteries, different shortcomings of the supercapacitors must be effectively addressed. Supercapacitors lack better energy density and ultralong cyclic stability is a very important desirable property. The optimization of the supercapacitor properties greatly depends on the materials used in the fabrication of electrodes and the process of fabrication. In our previously reported works, many attempts have been made to synthesize different types of electrode materials for obtaining optimized performance of supercapacitors in terms of enhanced energy density, cyclic stability, and sustainability. A technique was proposed to synthesize and characterize Silver-Zirconia nanocomposite material using green synthesis to address the issues of sustainable synthesis which has gained a lot of importance in the present context [43]. Using green synthesis, a method was proposed to synthesize zinc oxide and cobalt oxide nanocomposite to take advantage of their superior electrochemical properties and stability [44]. Evaluation of the morphological and electrochemical performance of the fabricated nanocomposite showed good results. Further, a method was proposed to fabricate a nickel cobaltite (NiCo2O4) nanomaterial for the construction of supercapacitor electrodes using green synthesis to take advantage of NiCo2O4. Extracts of Moringa oleifera (drumstick) leaves were used to synthesize nanoparticles [45]. Though green synthesis does not provide that high value of energy density compared to chemical methods of synthesis, it doesn't call for the requirements of high temperature and chemical-reducing agents. Furthermore, to take advantage of composite materials in optimizing the performance of electrodes, a Nickel Phosphide-Polyaniline (PANI) composite material was synthesized and characterized. Nickel phosphide nanoparticles are synthesized by hydrothermal method, while polyaniline is obtained through the polymerization of aniline to obtain a Nickel Phosphide-Polyaniline (PANI) composite [46]. A simple process for developing high-surface morphological nickel sulfide (NiS) nanostructures on commercial nickel foam at ambient temperature is developed in another study done by us [47]. A novel, simple, scalable, and low-cost fabrication technique to synthesize Nickel Cobalt Sulphide (NiCo2S4) nanostructures on commercial nickel foam was reported by us. Surface morphological and electrochemical experiments conducted, showed an energy density value of 62.8 Wh/kg and a retention capacity of 94% even after 8000 cycles. The electrochemical characteristics obtained in these reports were also validated using electrical experimentations. All these attempts have given satisfactory results in terms of enhanced energy density and ultralong cyclic stability as compared to the contemporary research outcomes listed in the respective reports. Hence attempts are going on to further optimize the operating performance of supercapacitors in terms of energy density and cyclic stability. These attempts are expected to provide an increased contribution to augment the characteristics and features of the supercapacitors in energy storage applications specifically to supplement batteries.

2 Conclusion

The present research report demonstrates a novel approach to improve system performance by using supercapacitors to complement batteries. This approach addresses the common limitation of batteries in handling instantaneous power surges, which is a significant issue in many energy storage applications. The development of a MATLAB Simulink model to illustrate the role of supercapacitors in reducing battery stress is demonstrated. This modeling helps visualize and quantify the benefits of integrating supercapacitors with batteries in real-time system simulations. The creation of an experimental setup to analyze system behavior during switching operations, involving resistive and dynamic loads, provides practical validation of the theoretical model. This includes using appropriately sized batteries and supercapacitors, which adds practical relevance to the work. Further, establishing and validating a mathematical model of the supercapacitor before experimentation is another novel aspect. It ensures that the supercapacitor's behavior is accurately represented and understood in the context of the overall system. The use of various performance evaluation parameters to quantify the effectiveness of the battery-supercapacitor system provides a comprehensive analysis. This quantitative assessment is crucial for understanding the practical benefits and potential improvements in system performance. The findings of this work suggest that high-performance supercapacitors are particularly well-suited for applications with frequent transient operations. This insight highlights the importance of developing superior supercapacitor technologies to enhance the performance of energy storage systems. The findings suggest that integrating high-performance supercapacitors can extend the life of existing lithium-ion batteries, which adds significant value to battery-supercapacitor hybrid systems in terms of durability and longevity. This provides further scope for developing high-performance supercapacitors that can augment the performance of hybrid energy storage systems that feature both battery and supercapacitors.