Integrated Control of EV Battery Chargers for Virtual Inertia and Vehicle-to-Grid Support Using Hybrid Energy Storage

Abstract

The increasing penetration of renewable energy sources and converter-interfaced loads has intensified the need for fast and reliable grid-support services. Although electric vehicle (EV) battery chargers have emerged as promising resources for Vehicle-to-Grid (V2G) applications, existing solutions typically focus on individual services such as virtual inertia or frequency regulation, while limited attention has been given to the coordinated provision of multiple ancillary services within a unified framework. Furthermore, the use of batteries alone for fast frequency support may accelerate battery degradation due to frequent high-power transients. To address these challenges, this paper proposes a hybrid energy storage-based EV battery charger architecture and a coordinated multi-timescale control strategy capable of simultaneously providing virtual inertia support, long-term frequency regulation, reactive power compensation, and harmonic mitigation. The proposed approach utilizes a DC-link capacitor to deliver fast inertial response while the battery supplies sustained frequency support, thereby reducing battery stress and improving energy management efficiency. An enhanced frequency estimation method based on a phase-locked loop combined with a low-pass filter is also introduced to improve dynamic performance. Simulation results demonstrate the effectiveness of the proposed strategy under various grid disturbances. The system achieves an equivalent virtual inertia constant of approximately 1.85 s and delivers up to 786 W of transient inertial support within 80 ms during frequency events. The enhanced frequency estimation method significantly reduces transient overshoot, while harmonic compensation limits the grid current and voltage total harmonic distortion to 1.50% and 3.23%, respectively. In addition, the controller provides up to 400 VAR of reactive power support during voltage disturbances while maintaining stable battery operation. These results demonstrate that the proposed EV battery charger can function as a multifunctional grid-support resource, enhancing frequency stability, voltage regulation, power quality, and overall V2G capability in future smart grids.

1. Introduction

As the global transition toward renewable energy accelerates, power systems face increasing challenges in maintaining frequency stability due to the declining presence of synchronous generators and the associated mechanical inertia. To address this issue, the concept of Grid-Forming and Grid-Following Virtual Inertia (GFL VI) has emerged as a critical solution. This paper presents a comprehensive study on the implementation of GFL VI in Electric Vehicle Battery Chargers (EVBCs) using a novel control strategy [1,2]. The approach leverages a hybrid energy storage system (HESS) composed of a DC-link capacitor and a battery to emulate virtual inertia and provide full Vehicle-to-Grid (V2G) functionality, including long-term frequency support, voltage regulation through reactive power compensation, and harmonic current filtering [3,4]. A two-stage AC–DC converter topology is proposed, integrating a three-phase Voltage Source Inverter (VSI) and a Dual Active Bridge (DAB) resonant DC–DC converter to interface with the grid and the EV battery, respectively. The control architecture is modular, incorporating fast, medium, and slow dynamic controllers to manage different timescale requirements efficiently [5,6,7]. Key innovations include an enhanced frequency estimation method using a phase-locked loop (PLL) with a low-pass filter (LPF) to minimize overshoot and improve transient response, and the strategic management of energy flow between the capacitor and battery to preserve battery life while ensuring rapid frequency response [8,9]. Most renewable energy systems are connected to the grid through inertialess power electronics converters, leading to a decrease in the overall system inertia and consequently to deviations of frequency beyond the acceptable range, resulting in undesirable load-shedding or even large-scale blackouts [10].

These frequency variations can be quantified by two parameters, the time derivative of the frequency, known as rate-of-change-of-frequency (ROCOF), and the minimum value of the frequency during the transient period, known as frequency nadir [11,12,13,14], which are shown in Figure 1. To overcome this problem, researchers have proposed the concept of virtual inertia (VI) [15] which consists of the integration of an energy storage system (ESS) into the grid to emulate the synchronous generator behavior [16,17] by grid-connected converters (GCCs), commonly called grid-forming converters (GFMs) [17,18,19,20]. However, since GCCs with GFM control strategies are controlled as a voltage source, the direct control of the AC voltage without an inner current control loop may lead to difficulties in dealing with voltage drop faults, generating over currents and stability problems, making these solutions challenging to integrate into distribution grids [21].

The proposed control strategy is validated through both analytical modeling and simulation results, demonstrating its efficacy in delivering robust frequency and voltage support under grid disturbances. This work offers a scalable, firmware-based upgrade path for existing EVBCs, supporting their role as active participants in modern, flexible power systems.

Table 1. Literature survey on hybrid energy storage systems.

Ref.	Title & Authors	Focus Area	Key Contributions	Applications	Challenges/Future Work
[22]	Abo-Khalil et al. (2023)—Advancements and Challenges in HESS	Topologies, control strategies, integration	Overview of ESS types, control techniques (e.g., MPC, fuzzy, SMC), design considerations	Renewable grids, microgrids	Standardization, interdisciplinary integration, reliability
[23]	Babu et al. (2020)—Comprehensive Review of HESS	Converter control strategies	Classification of HESS control methods (rule-based, fuzzy, predictive), limitations	Standalone/grid-connected microgrids	Unified control design, real-time validation
[24]	Schubert et al. (2023)—HESS with Redox-Flow Batteries	RFB-based HESS, EMS optimization	KPIs for battery–supercapacitor–RFB hybrids, optimal EMS designs	Stationary storage, grid applications	Advanced EMS algorithms, better RFB coupling
[25]	Cholidis et al. (2025)—Optimized Storage for Ports	HRES, EMS, GA-based optimization	Renewable-powered port energy systems, 54% cost reduction using HESS + EMS	Smart ports, maritime energy	Empirical EMS design, grid backup strategies
[26]	Reddy & Kumar (2024)—HESS for EV Drive Systems	EV power systems, control architecture	Feedback control circuit to isolate battery from regenerative braking	Electric vehicles (EVs)	Reducing EV energy loss, improving battery lifespan
[27,28]	Jiao (2022)—HESS Capacity Optimization and LCA	Optimization, environmental impact	LPF-based control to minimize capacity oversizing; LCA of HESS	100% RES integration	Environmental trade-offs, lifecycle emissions
[28]	Adeyinka et al. (2024)—HESS for Grid Integration	Grid stability and HESS	Review of HESS integration with variable renewables	Grid-connected RES	Demand forecasting, inverter coordination
[29]	Punyavathi et al. (2024)—LEV Power Management with ML	ML-based HESS control	ML ensures precise voltage, torque, and speed regulation	Light electric vehicles (LEVs)	Integration of AI into real-time drive control
Proposed	---	Virtual inertia, V2G support, HESS management, dual-converter architecture	Proposes a multi-timescale control strategy integrating virtual inertia, long-term frequency regulation, reactive power compensation, and harmonic mitigation using a HESS consisting of a DC-link capacitor and EV battery; introduces enhanced PLL-LPF-based frequency estimation and coordinated energy management through VSI–DAB converter architecture	Smart grids, V2G-enabled EV charging stations, renewable-rich distribution networks, ancillary grid services	Experimental validation under hardware implementation, scalability assessment for large EV fleets, cyber-secure V2G communication, and real-time field deployment

provides literature survey data on HESS technology.

In Table 1, existing studies primarily focus on hybrid energy storage configurations, energy management strategies, and renewable energy integration. However, limited attention has been given to the coordinated implementation of virtual inertia, long-term frequency regulation, reactive power support, and harmonic compensation within a unified EV battery charger architecture. Furthermore, most existing approaches either rely solely on DC-link capacitors for inertia emulation or employ hybrid energy storage systems without integrating comprehensive V2G ancillary services. To address these gaps, this work proposes a dual-converter EV battery charger equipped with a hybrid energy storage system and a multi-timescale control framework capable of delivering full V2G functionality while improving frequency stability, voltage support, and power quality.

The structure of the paper is organized into several key sections. It begins with the Abstract, providing a concise summary of the objectives, methodology, and findings of the study. The Introduction follows, highlighting the challenges posed by reduced system inertia due to renewable energy integration and introducing the concept of virtual inertia using EV battery chargers with a hybrid energy storage system (HESS). A literature review presents related work on HESS technologies, control strategies, and applications, summarizing gaps addressed by the proposed method. The Fundamentals of GFL Virtual Inertia section explains the theoretical basis, mathematical modeling, and limitations of conventional GFL VI implementations. The Proposed Control Strategy section outlines the two-stage power converter architecture and details the multi-timescale control scheme, dividing it into fast (AC current), medium (DC-link voltage, VI, battery current), and slow (power and droop) response controllers, along with enhanced PLL-based frequency estimation. The Simulation Results section validates the effectiveness of the proposed system through tests on harmonic compensation, virtual inertia performance, HESS dynamic response, and voltage support under different grid events. Finally, the Conclusion summarizes the benefits of the proposed strategy, including improved frequency stability, better harmonic performance, and enhanced suitability for future V2G applications, supported by a brief comparison with existing works and a comprehensive References section.

The main contribution of the paper is the development of a smart control strategy for Electric Vehicle Battery Chargers (EVBCs) that helps support the power grid by providing virtual inertia, frequency regulation, voltage support, and harmonic compensation. This is achieved using a hybrid energy storage system (HESS) that combines a fast-responding DC-link capacitor and a slower battery, allowing for efficient energy management. The paper introduces a two-stage converter system and designs a multi-level control scheme with fast, medium, and slow response times. It also improves frequency estimation by using a phase-locked loop (PLL) with a low-pass filter to reduce overshoot. Simulation results show that the proposed system can handle sudden changes in grid frequency, reduce power distortion, and support voltage during sags, making it a practical and scalable solution for enhancing the stability and flexibility of modern power grids through existing EV infrastructure.

Research Gap and Motivation

Despite significant advances in virtual inertia control, hybrid energy storage systems, and Vehicle-to-Grid technologies, several important challenges remain unresolved. Existing virtual inertia implementations commonly rely on either DC-link capacitors or battery energy storage systems alone. While DC-link capacitors can provide fast inertial response, their limited energy capacity restricts their ability to sustain grid-support services for extended periods. Conversely, battery-based inertia support can supply larger amounts of energy but may accelerate battery degradation due to frequent charge–discharge cycles associated with rapid frequency disturbances. Furthermore, most reported studies focus on a single ancillary service, such as virtual inertia or frequency regulation, without considering the simultaneous provision of reactive power support and harmonic compensation. In addition, coordinated energy management strategies capable of effectively distributing fast and slow dynamic responses among different storage elements remain limited.

Therefore, there exists a need for an integrated EV battery charger architecture that can simultaneously provide fast virtual inertia support, long-term frequency regulation, reactive power compensation, and harmonic mitigation while minimizing battery stress and improving overall grid-support capability. To address these challenges, this work proposes a hybrid energy storage-based EV battery charger employing a coordinated multi-timescale control framework in which the DC-link capacitor supplies rapid transient support and the battery delivers sustained energy support. The proposed approach enables comprehensive V2G functionality while enhancing grid stability, power quality, and energy management performance.

The main contributions of this work are summarized as follows:

• Development of a dual-converter EV battery charger architecture incorporating a hybrid energy storage system composed of a DC-link capacitor and battery.
• Design of a multi-timescale control framework that decouples fast virtual inertia support from long-term frequency regulation.
• Implementation of coordinated active and reactive power control for simultaneous frequency support and voltage regulation.
• Integration of harmonic compensation functionality to improve power quality at the grid interface.
• Validation of the proposed strategy through comprehensive simulation studies under frequency disturbances, voltage variations, and harmonic conditions.

2. Fundamentals of GFL VI

The GFL VI concept is based on the dynamics of the swing equation which is given by (1):

$$p_g- p_l= ∆p=2H{\displaystyle \frac{d}{dt}}∆f_{pu}$$

(1)

where

• ${\displaystyle \frac{d}{dt}}$—derivative of time;
• $∆f_{pu}$—frequency deviation;
• $∆p$—power difference for generated power and load power;
• H—inertia constant.

It can be easily followed that for a certain variation in power, inertia reduction in power systems leads to higher ROCOF and higher peak deviation of frequency. Hence, the concept of GLF VI consists of the integration of ESS for adding extra power to the system according to (2):

$$p_g- p_l+ p_{support }= ∆p+ p_{support}=2H{\displaystyle \frac{d}{dt}}∆f_{pu}^{\prime }$$

(2)

$$p_{support}-2H_v{\displaystyle \frac{d}{dt}}∆f_{pu}^{\prime }$$

(3)

where $∆f_{pu}^{\prime }$ is the instantaneous frequency of the system.

Then, substituting (3) into (2), the frequency dynamics of the system including the VI are given by the following:

$$∆p=2\left(H+H_V\right){\displaystyle \frac{d}{dt}}∆f_{pu}^{\prime }=2H^{\prime }{\displaystyle \frac{d}{dt}}∆f_{pu}^{\prime }$$

(4)

This way, the effective inertia constant is increased to $H^{\prime }=H+H_V$, increasing the frequency stability.

The implementation of the GFL VI approach in a VSI was introduced according to the functional diagram presented in Figure 2. Note that the GFL VI approach relates the frequency deviation $∆f_{PLL}$, measured by PLL, with a voltage deviation $∆V_{DC}$, in the DC-link voltage, according to a gain $K_{\omega }$. Moreover, the control strategy considers the well-known voltage and current control loops as presented in the block diagram of Figure 3.

Hence, a frequency deviation, $∆f_{PLL}$, generates a fast response of power through releasing/storing the energy in the DC-link capacitor CDC according to a “virtual inertia” (Hv) coefficient given by (5):

$$H_V= K_{\omega }{H}_C$$

(5)

$$H_C={\displaystyle \frac{C_{DC} V_{ref}^2}{2 P_o}}$$

(6)

where

• C_DC—capacitance;
• V_ref—rated voltage in DC link;
• P_o—nominal power

The gain $K_{\omega }$ in (5) is designed for the allowed maximum frequency deviation $∆f_{max}$ and a maximum voltage variation $∆V_{DC\_max}$ according to (7), where $f_b$ and $V_{ref}$ are the base grid frequency and the rated DC bus voltage, respectively:

$$K_{\omega }= {\displaystyle \frac{∆V_{DC\_max}}{∆f_{max}}} {\displaystyle \frac{f_b}{V_{ref}}}$$

(7)

Then, the dynamic response of DC-link voltage is related to the fast power response $∆P_{DC}$ (inertia response) according to the following:

$${∆P}_{DC}\left(s\right)\approx {\displaystyle \frac{2H_V{P}_o}{f_b}} \underset{R_o{C}_{o}F}{\underbrace{s∆f_{PLL}\left(s\right)}}$$

(8)

3. Measurement Limitations to Implementing GFL VI

3.1. Power Constraints for VI Supply

For a correct design of the converter, the extra power $∆P_{DC}$ for VI implementation must be considered as an overload. For instance, the relation between overloading capability $∆P_{DC}$, ROCOF and different inertia values is given in (8), considering a base frequency of 60 Hz. Note that for a ROCOF of 2 Hz/s and an inertia contribution of $H_V\approx 3.75$ s, an overloading capability of 25% is required. Moreover, considering $H_V=5$ s, for a ROCOF of 2 Hz/s, 33% of overloading capability is required. Whereas, for a ROCOF of 4 Hz/s and a $H_V=5$ s, the required overload is 66%. Hence, GFL VI implementation supporting high values of inertia and faster ROCOF constraints requires oversizing the AC–DC converter, which will increase the size and price of EVBCs.

3.2. Frequency Measurement from PLL

To analyze the influence of the PLL dynamic in VI power response, the block diagram of the frequency estimation of a typical second-order PLL, as shown in Figure 4, is considered.

Where $f_b$ is the grid frequency, while $K_p$ and $K_I$ are, respectively, the proportional and integral gains of the PI controller. Therefore, the closed-loop $G_f\left(s\right)$ transfer function (TF) for frequency estimation can be expressed by the following:

$$G_f\left(s\right)= {\displaystyle \frac{f_{PLL}}{f_{grid}}}= {\displaystyle \frac{{\omega }_b{K}_{p}s+ {\omega }_b{K}_I}{s^2+{\omega }_b{K}_{p}s+{\omega }_b{K}_I}}$$

(9)

The controller gains are then tuned. The $K_p$ gain is calculated to achieve the desired bandwidth ${\omega }_{bw}$ and the integral gain is tuned at $K_I=K_p{\displaystyle \frac{{\omega }_{bw}}{10}}$. Then, with the evaluation $G_{fCL}\left(s\right)$ for a unit ramp $f_{grid}\left(s\right)= {\displaystyle \frac{1}{s^2}}$, the ROCOF is calculated according to the following:

$$R_o{C}_{o}F\left(s\right)=s{f}_{PLL}\left(s\right)= {\displaystyle \frac{{\omega }_{bw}s+0.1 {\omega }_{bw}^2}{s^2+{\omega }_{bw}s+0.1 {\omega }_{bw}^2}} {\displaystyle \frac{1}{s}}$$

(10)

Thus, the maximum value of estimated ROCOF by PLL is 1.07 Hz/s. This means an overshoot of 7% that, according to (8), increases the transient peak power supplied by the converter $∆P_{DC}$. To overcome the above-mentioned issues, an enhanced design procedure along with a novel control strategy to implement VI, long-term frequency support, reactive power support, and harmonics correction is introduced in the following sections.

4. Proposed Control Strategy

The block diagram of the proposed control strategy and the scheme of the power stage are shown in Figure 5. Note that a two-stage AC–DC topology is adopted which is composed of a three-phase VSI to interface with the grid, and a Ddual Active Bridge series resonant DC–DC converter to interface with the EV battery.

In the proposed control strategy, different V2G functionalities are implemented through managing a HESS as shown in Figure 6. For this purpose, six controllers are designed: the AC current controller, the DC bus voltage controller, the DC current controller, the VI controller, the PQ controllers (active power P and reactive power Q controllers), and the droop controllers to compensate for frequency and voltage variations. In addition, a computational block to calculate active and reactive power (PQ block), a PLL, and transformation blocks complete the control strategy. The management of HESS allows to decouple the dynamics responses of active power as shown in Figure 6. Note that in front of a frequency variation increment $∆f_{PLL}$, the power delivered by the converter $P_g$ is given by the following:

$$P_g= P_c+ P_{EV}$$

(11)

where $P_c$ and $P_{EV}$ are active powers supplied by the DC-link capacitors and the EV battery, respectively. The power $P_c$ has a faster dynamic response compared to $P_{EV}$, and it is intended for VI support unlike $P_{EV}$ which is focused on long-term frequency support. For simplicity, no power losses are considered. Moreover, in the proposed control strategy, the controllers are classified according to timescale as fast, medium, and slow response. A fast response is required for the inner AC current controller on the AC–DC stage, with a timescale of around a few milliseconds. The medium response is related to DC-link voltage, VI, and DC current control, with a timescale of several milliseconds. Finally, the slow response corresponds to the PQ and droop controller with a timescale of several seconds. Since special care must be taken in choosing the bandwidth of medium response controllers to ensure system stability, the transfer functions and controller design are explained as follows.

4.1. Stability Analysis of the Proposed Control Strategy

The proposed EVBC-HESS controller adopts a hierarchical multi-timescale control architecture in which the individual control loops operate at different bandwidths. Such a design is widely used in power electronic systems to ensure dynamic decoupling and stable operation.

The AC current controller is designed as the fastest loop with a bandwidth of approximately 800 Hz, enabling rapid current tracking and disturbance rejection. The PLL and DC-link voltage controller operate at intermediate bandwidths of approximately 60 Hz and 30 Hz, respectively, while the battery current controller and active/reactive power controllers operate at slower timescales ranging from 5 Hz to 1 Hz. This bandwidth hierarchy ensures that the inner loops reach steady-state conditions before the outer loops respond, thereby minimizing dynamic interactions among controllers.

The ratio between adjacent control bandwidths is maintained above two, providing sufficient dynamic separation and reducing the possibility of control-loop coupling. In addition, the low-pass filter integrated into the frequency estimation mechanism suppresses high-frequency measurement noise and mitigates transient overshoot, thereby improving system damping characteristics.

The stability of the proposed framework is further verified through simulation studies under frequency disturbances of ±0.2 Hz, voltage variations of 17 V, and ROCOF conditions up to 3 Hz/s. In all cases, the system exhibits stable responses without sustained oscillations, divergence, or controller saturation. The DC-link voltage, battery current, and active/reactive power outputs remain within acceptable operating limits throughout the disturbances, confirming the effectiveness of the proposed control architecture.

Therefore, the combination of bandwidth separation, hierarchical control design, and coordinated energy management contributes to the stable operation of the proposed EVBC-HESS under a wide range of operating conditions.

4.2. Fast Response Control: The AC Current Controller

For AC current, proportional + resonant controllers in the stationary αβ frame are adopted. The TF from VSI voltage to AC current is given by (12) where $L_1, L_2, C_f and R_d$ are respectively the VSI side inductance, grid side inductance, filter capacitance, and damping resistance [29]:

$$G_{iv}= {\displaystyle \frac{i_{\propto }\left(s\right)}{v_{\propto }\left(s\right)}}= {\displaystyle \frac{R_d{C}_{f}s+1 }{C_f{L}_1{L}_2{s}^3+ R_d{C}_f\left(L_1+L_2\right)s^2+(L_1+L_2)s}}$$

(12)

The transfer function of the PR controllers with selective harmonic GPR(s) is defined in (13), where ${KP}_c$ is the proportional gain, ${Kr}_j$ (j = 13,57,9) are the gains for resonant components, and the term ξ is the damping factor which defines the bandwidth of the resonant components and the gain at each resonance frequency:

$$G_{PR}\left(s\right)= K_{PC}+ {\displaystyle {\sum }_{j-1}^n}{\displaystyle \frac{K{r}_{j}s}{s^2+2 \xi {\omega }_{o}s+ {\omega }_o^2}}$$

(13)

4.3. Medium Response Control

4.3.1. DC-Link Voltage Controller

The DC-link voltage controller is designed to provide the reference $I_{d\_ref}$ for the AC current controller according to the following equation:

$$G_{vi}\left(s\right)= {\displaystyle \frac{v_{DC}\left(s\right)}{i_d \left(s\right)}} \approx m {\displaystyle \frac{1}{C_{DC}s}}\mathrm{C}$$

(14)

where m is the modulation index.

Moreover, since the reference for the DC-link voltage $∆V_{DC}^{*}$ is provided by the VI controller, the dynamics of the VI controller should be slower to ensure the system stability.

4.3.2. Enhanced GFL VI Controller

As explained in the discussion on limitations of GFL VI, the traditional GFL VI approach generates an overshoot of 7% in the frequency estimation by the PLL. To reduce the overshoot, the estimated frequency $f_{PLL}$ is filtered by a first-order low-pass filter (LPF), as shown in Figure 6. The LPF must be tuned with a cutoff frequency lower than the DC-link voltage dynamic response to ensure stability. To evaluate the effectiveness on the resulting overshoot, the PLL response was evaluated with three different configurations: a PLL tuned at 10 Hz bandwidth without LPF, a PLL tuned at 60 Hz bandwidth without LPF, and a PLL tuned at 60 Hz bandwidth with an LPF tuned at 10 Hz. The PLL with LPF overshoot value can be obtained by evaluating the PLL TF $G_f\left(s\right)$, given by (9), including the LPF TF, leading to the following:

$$ROCOF\left(s\right)= {\displaystyle \frac{{\omega }_{bw}\left(s\right)+0.1 {\omega }_{bw}^2}{s^2+ {\omega }_{bw}s+0.1 {\omega }_{bw}^2}} {\displaystyle \frac{1}{s}} \left({\displaystyle \frac{\frac{{\omega }_{bw}}{6}}{s+\frac{{\omega }_{bw}}{6}}}\right)$$

(15)

With cutoff frequency of ${\displaystyle \raisebox{1ex}{${\omega }_{bw}$}\!\left/ \!\raisebox{-1ex}{$6$}\right.}$ for the LPF, following the procedure-detailed frequency measurement from PLL, a maximum ROCOF of 1.004 Hz/s is calculated. Hence, the overshoot in the estimated frequency has been considerably decreased, which leads lower transient peak deviation for both DC bus voltage and supplied power for VI.

4.3.3. Battery Current Controller

The equivalent circuit to control battery current I_o is shown in Figure 7 and Figure 8, where $L_0, C_0$ are the inductance and capacitance for the DC filter and $R_0$ is the inductor series resistance, whereas the averaged current source $\langle i_{ohf}\rangle$ is given by the following:

$$〈i_{oh f}〉= {\displaystyle \frac{8 n V_{DC}}{{\pi }^{2}Z(F-\frac{1}{F})}} \sin \left(\varnothing \right)$$

(16)

In (16), φ is the phase-shift angle, n is the turns ratio of HF transformer, $V_{DC}$ is the DC-link voltage, Z is the tank impedance, and F is the ratio between the switching frequency ${\omega }_s$ and the resonance frequency ${\omega }_r$. The parameters Z, F, and ${\omega }_r$ are defined in (17), where $L_s$ and $C_s$ are the inductance and capacitance of the resonant circuit:

$$Z= \sqrt{{\displaystyle \frac{L_s}{C_s}} }; F= {\displaystyle \frac{{\omega }_s}{{\omega }_r}} ; {\omega }_r= {\displaystyle \frac{1}{\sqrt{L_s{C}_s}}}$$

(17)

Then, according to Figure 7, the simplified TF for battery current $I_0$ is given by the following equation:

$$G_i= {\displaystyle \frac{I_o \left(s\right)}{〈i_{oh f}〉 \left(s\right)}}= {\displaystyle \frac{{\omega }_{LC}^2}{s^2+\frac{R_o}{L_o}s+ {\omega }_{LC}^2}}$$

(18)

where ${\omega }_{LC}$ is the cutoff frequency of the $L_0$, $C_0$ filter.

The block diagram of the proposed DC current controller is shown in Figure 8. The LPF is tuned at ${\omega }_c$ considering two decades lower than ${\omega }_{LC}$ to attenuate the resonance peak of $G_i\left(s\right)$. With this consideration, the loop-gain TF $\left(T_i\right)$ can be approximated according to (19), where $G_{i0}\left(s\right)$ is considered as unity since ${\omega }_c \ll {\omega }_{Lc}$. Then, the zero ${\omega }_i$ is tuned to eliminate the pole. Thus, the closed-loop TF $G_{iCL}\left(S\right)$ is given by (20):

$$G_{iOL}=PI\left(s\right)LPF\left(s\right)G_{io}\left(s\right)= k_{p }\left({\displaystyle \frac{s+ \frac{1}{T_i}}{s}}\right) {\displaystyle \frac{{\omega }_c}{(s+{\omega }_c)}}$$

(19)

$$G_{iCL}={\displaystyle \frac{G_{iOL}}{1+G_{i\_OL}}}={\displaystyle \frac{k_p{\omega }_c}{(s+k_p{\omega }_c)}}$$

(20)

4.3.4. Slow Response Controller

Instantaneous values of active power p and reactive power q are computed in the synchronous dq frame according to the following equations:

$$p= {\displaystyle \frac{3 }{2}}\left(v_d{i}_d+ v_q{i}_q\right)$$

(21)

$$q={\displaystyle \frac{3}{2}}\left(v_d{i}_q-v_q{i}_q\right)$$

(22)

Since $v_{q }$ is tracked by PLL synchronization, $v_q\approx 0$ and $v_{d }{v}_{m }$, where V_m is the amplitude of grid voltages. Therefore, TFs for p and q are given by the following:

$$G_{pq}\left(s\right)= {\displaystyle \frac{p}{i_d}}\left(s\right)= {\displaystyle \frac{q}{i_q}} \left(s\right)= {\displaystyle \frac{3}{2}}{V}_m$$

(23)

Then, integral controllers with gains K_p, K_q are adopted from Figure 5 and the closed-loop TFs $G_{pcL}$, $G_{qcL}$ are given by the following:

$$G_{pcL}\left(s\right)= G_{qcL}\left(s\right)= {\displaystyle \frac{1.5 V_m K_p}{s+1.5 V_m{K}_p}}= {\displaystyle \frac{1.5 V_m K_q}{s+1.5 V_m{K}_q}}$$

(24)

Finally, droop controllers are tuned through gains K_dP and K_dQ, according to the following equations:

$$P^{*}= P_{ref}+ K_{dP} ∆f_{PLL}$$

(25)

$$Q^{*}=Q_{ref}+K_{d Q}(V_d^{*}-v_d)$$

(26)

5. Validation of the Control Strategy

To validate the proposed control strategy, a MATLAB 2026a simulation is developed based on the parameters listed in

Table 2. Parameters of the EVBC simulation model.

Parameter	Variable	Value
Rated Power	$P_0\pm ∆P_{max}$	2.5 kW ± 500 W
Grid Frequency	$f_b\pm ∆f_{max}$	60 Hz ± 0.2 Hz
DC-Link Voltage	$V_{ref}\pm ∆V_{DCmax}$	425 V ± 25 V
Grid Voltage	$V_m\pm ∆V_m$	179 ± 17 Vp
Max. Considered ROCOF	${ROCOF}_{max}$	3 Hz/s
Battery Voltage	$V_b$	400 V
DAB Switching Frequency	$f_{sDC}$	100 kHz
VSI Switching Frequency	$f_{sAC}$	48 kHz
LCL Filter	$L_1, L_2, C_f and R_d$	900 µH, 250 µH, 15 µF and 2 Ω
Tank Impedance	$C_r, L_r$	10.2 nF, 300 µH
Transformer Turns Ratio	$n_t$	1
Battery Filter	$L_0, C_0, R_0$	300 µH, 16 µF, 0.2 Ω
DC- Link Capacitance	$C_{DC}$	2.9 mF

. For this $∆V_{DCmax}$ is limited to ensure the limited modulation, whereas the DC-link capacitance is sized considering the maximum allowed extra power $∆P_{max}$ for VI support. Therefore, $∆P_{DC}$, given by (8), must be limited to $∆P_{max}$, according to the following equation:

$$∆P\left(s\right)\approx {\displaystyle \frac{2 H_V P_O}{f_b}} R_o{C}_o{F}_{max } \le ∆P_{max}$$

(27)

Then, from (6), (7), and (27), the maximum allowable DC capacitance is calculated by the following:

$$C_{DC} \le {\displaystyle \frac{f_{b }∆ P_{max}}{K_{\omega } V_{ref}^2 R_o{C}_o{F}_{max}}}$$

(28)

Since ROCOF_max is an a priori known value defined by grid codes, the gain K_ω, given by (7), is calculated as K_ω = 17.65 from parameters of Table 2. Then, replacing values in (28), C_DC ≤ 3.13 mF is calculated. With this consideration, C_DC = 2.9 mF is adopted. Then, according to (5) and (6), an inertia of HV ≈ 1.85 is obtained; thus, the converter can provide VI in front of frequency variations up to 3 Hz/s without exceeding its limits. On the other side, according to constraints in the proposed control strategy, the chosen controller’s bandwidths are listed in Table 3.

Table 3. Bandwidths for the controller.

Fast	Medium				Slow
AC Current	PLL	Bus DC	Frequency LPF	Battery Current	P & Q
800 Hz	60 Hz	30 Hz	10 Hz	5 Hz	1 Hz

Note in Table 3 that the controllers are classified according to the dynamic response. The AC current controller is the fastest, whereas the active and reactive controllers (P&Q) are the slowest. Moreover, among the medium dynamic response controllers, the PLL is tuned considering a bandwidth equal to the grid frequency [9], whereas the DC-link voltage controller has a bandwidth higher than the battery current and the LPF cascaded to the PLL, which ensures the stability of the system [30]. Hence, considering the bandwidths of Table 2, the controller parameters are listed in Table 4.

Table 3. Bandwidths for the controller.

Fast	Medium				Slow
AC Current	PLL	Bus DC	Frequency LPF	Battery Current	P & Q
800 Hz	60 Hz	30 Hz	10 Hz	5 Hz	1 Hz

Note in Table 3 that the controllers are classified according to the dynamic response. The AC current controller is the fastest, whereas the active and reactive controllers (P&Q) are the slowest. Moreover, among the medium dynamic response controllers, the PLL is tuned considering a bandwidth equal to the grid frequency [9], whereas the DC-link voltage controller has a bandwidth higher than the battery current and the LPF cascaded to the PLL, which ensures the stability of the system [30]. Hence, considering the bandwidths of Table 2, the controller parameters are listed in Table 4.

Table 4. Controller gains of the EVBC.

Controller	Gains
AC Current	$K_{pc}=5.3, K_{ic}=2668, K_{r3}=889, K_{r5}=533, K_{r7}=381, K_{r9}=296$
Battery Current	$K_{pbc}=1, K_{lbc}=31.416$
PLL	$K_{ppll}=1, K_{ipll}=37.7$
DC-Link Voltage	$K_{pv}=0.6489, K_{iv}=4.8036$
Inertia	$K_{VI}=125$
Droop	$K_{dp}=2000, K_{dq}=23.53$
P—Q Controller	$K_p=0.0234$

Table 4. Controller gains of the EVBC.

Controller	Gains
AC Current	$K_{pc}=5.3, K_{ic}=2668, K_{r3}=889, K_{r5}=533, K_{r7}=381, K_{r9}=296$
Battery Current	$K_{pbc}=1, K_{lbc}=31.416$
PLL	$K_{ppll}=1, K_{ipll}=37.7$
DC-Link Voltage	$K_{pv}=0.6489, K_{iv}=4.8036$
Inertia	$K_{VI}=125$
Droop	$K_{dp}=2000, K_{dq}=23.53$
P—Q Controller	$K_p=0.0234$

The PLL, DC-link voltage, and AC current controller parameters are tuned following the methodology of a grid-connected converter. The battery current and P&Q controllers’ parameters are calculated according the first-order systems given by (20) and (24), respectively, and the desired bandwidth given in Table 3. Finally, the droop gains K_dP and K_dQ are calculated considering power deviations of $∆P_{ref}=400 \mathrm{W}$ and $∆{PQ}_{ref}=400 \mathrm{V}\mathrm{A}\mathrm{R}$ for frequency and voltage variations of 0.2 Hz and 17 V, respectively.

5.1. Stability and Robustness Considerations

The proposed control strategy employs a multi-timescale architecture in which the control loops are designed with well-separated bandwidths to reduce dynamic coupling and improve system stability. As shown in Table 3, the AC current controller operates with the highest bandwidth (800 Hz), followed by the PLL (60 Hz), DC-link voltage controller (30 Hz), low-pass filter (10 Hz), battery current controller (5 Hz), and active/reactive power controllers (1 Hz). This hierarchical arrangement ensures that faster loops reach steady-state operation before slower loops respond, thereby minimizing adverse interactions among the controllers.

The stability of the proposed framework can be qualitatively justified through the adopted bandwidth separation. The ratio between adjacent control bandwidths exceeds a factor of two, which is commonly employed in cascaded power electronic control systems to guarantee stable operation and sufficient dynamic decoupling. In addition, the LPF integrated with the PLL reduces frequency estimation overshoot and prevents oscillatory responses during transient grid events.

To assess robustness, the proposed system was subjected to several operating disturbances, including frequency variations of ±0.2 Hz, voltage amplitude reductions of 17 V, and ROCOF conditions up to 3 Hz/s. Under all tested conditions, the system maintained stable operation without sustained oscillations, controller saturation, or instability. The DC-link voltage remained within its designed operating range, the battery current remained properly regulated, and the active/reactive power support functions operated as intended.

These results indicate that the proposed multi-timescale control framework possesses satisfactory robustness against practical grid disturbances and parameter variations. Future work will focus on developing a detailed small-signal state-space model and performing eigenvalue, gain-margin, and phase-margin analyses to further quantify the stability characteristics of the proposed EVBC-HESS.

5.2. Dynamic Reactive Power Support Performance

To further evaluate the effectiveness of the proposed control strategy, a reactive power reference variation test was conducted. In this scenario, the reactive power reference was changed from 0 VAR to +400 VAR and subsequently returned to 0 VAR while the active power support and virtual inertia functions remained operational.

The results show that the reactive power controller successfully tracks the commanded reference with a fast transient response and negligible steady-state error. During the transition, the active power support function remained unaffected, demonstrating effective decoupling between active and reactive power control loops. In addition, the DC-link voltage remained within its operating limits and the battery current exhibited minimal variation, indicating that the reactive power compensation function does not impose significant additional stress on the energy storage system.

These observations confirm that the proposed EVBC-HESS architecture can reliably provide dynamic reactive power support while simultaneously maintaining frequency support and virtual inertia services. Therefore, the controller is suitable for practical grid-support applications where reactive power requirements may vary continuously due to changing load and network conditions.

6. Simulation Results

6.1. Harmonic Compensation

To test this functionality, the converter was connected to an AC grid with THDv = 3.19%. The corresponding voltage harmonic spectrum is presented in Figure 9. The test was performed considering a load of 1.6 kW (64% of the rated power). The resulting AC is presented in Figure 10 and Figure 11. Note that the main harmonics components of grid current and voltage have been suppressed and the obtained THD is only 1.50% and 3.23% respectively.

Figure 12 and Figure 13 present the Fast Fourier Transform (FFT) analysis of the grid current and voltage waveforms after the application of the proposed harmonic compensation strategy. The harmonic spectra demonstrate that the dominant low-order harmonic components are significantly attenuated through the action of the proportional–resonant controller and selective harmonic compensation loops.

From Figure 12, the grid current exhibits a total harmonic distortion (THD) of approximately 1.50%, which is well below the limits recommended by IEEE 519 standards for grid-connected power electronic systems. The suppression of the third, fifth, seventh, and ninth harmonic components confirms the effectiveness of the resonant control structure in tracking sinusoidal reference currents and mitigating harmonic injection into the utility grid.

Similarly, Figure 13 illustrates the FFT spectrum of the compensated grid voltage. The voltage THD is maintained at approximately 3.23%, indicating improved voltage quality at the point of common coupling. The results confirm that the proposed control framework not only provides virtual inertia and frequency support but also contributes to power quality enhancement through harmonic mitigation.

6.2. Enhanced VI Response

The dynamic response of the estimated frequency for a frequency step of 0.2 Hz is shown in Figure 14. Two cases are analyzed to estimate the grid frequency: using only a PLL and using a PLL cascaded to a first-order LPF. The bandwidth of the PLL is 60 Hz, whereas for the LPF it is 10 Hz. Then filtering the estimated frequency with an LPF allows to decrease the overshoot considerably which validates the analytic and simulation results of the proposed method shown in Figure 8.

The VI response was validated for “grid to vehicle” (G2V) mode at 1.1 kW. For this test, the droop controllers were disabled. The resulting waveforms are shown in Figure 15 and Figure 16, respectively. For a step-up frequency variation of +0.2 Hz, the measured RoCoF was 5.1 Hz/s. As frequency increases, DC voltage reference is increased proportionally to gain K_VI from 425 to 450 V. The DC-link capacitor current achieves a transient peak value of 3.6 A, increasing the grid current to 3 A. The fast dynamic response of active power for VI support achieves a transient peak of 786 W, according to (8), returning to the steady state of −1.1 kW after 80 ms. Note that the current consumed by the battery remains almost constant at 2.56 A but presents a little variation caused by DC-link voltage change. The obtained results are coherent with the estimations, where VI support is supplied by the DC-link capacitors, maintaining the battery current almost constant.

6.3. HESS Response in Front of Frequency Steps

The full control strategy was verified by a frequency step event of ±0.2 Hz in Figure 17 and Figure 18, respectively. In Figure 17 the EVBC initially extracts 1.1 Kw from the grid, working in G2V mode. The measured frequency by PLL is 60 Hz, the grid current peak value is 4.09 A, DC-link voltage takes its nominal value of 425 V, and the battery current is 2.56 A. Then, a frequency step of +0.2 Hz is applied.

The VI response is validated by the transient demand of 780 W since the DC-link voltage increases from 425 to 450 V, whereas the slower dynamic response for long-term frequency support is validated by the smooth variation from −1.1 to −1.5 kW. Note that the current of DC-link capacitors achieves its steady state 80 ms after the frequency event, whereas the battery current achieves its steady state after almost s, which means 12.5 times slower than the VI controller response. Next, a step of −0.2 Hz is applied, as shown in Figure 19 and Figure 20. The VI response is validated by the power transient of 760 W to decrease the DC-link voltage from 450 to 425 V. The slower dynamic response of active power is validated by the smooth variation of 400 W after 1 s. The results confirm that VI support is provided by DC-link capacitors whereas long-term frequency support with a slower dynamic is provided by batteries.

6.4. Voltage Support by Reactive Power

Main results of the voltage support in front of a grid voltage amplitude reduction are presented in Figure 21. Amplitude decreases linearly from 179 to 162 V (17 V) in 100 ms, producing a small decrease in the -link voltage, whereas the grid current increases from 4.09 to 4.53 A (peak). According to the voltage droop controller, since reactive power increases from 0 to +400 VAR, the grid current increases from 4.53 to 4.81 A (peak) after almost 673 ms. Note that the battery current remains constant at 2.56 A. In contrast, the DC-link capacitor current is slightly increased to supply reactive power support, validating the proposed control strategy to manage the HESS. The proposed control strategy is briefly compared with similar studies implementing VI and with experimental results, which are shown in Abo-Khalil

Table 5. Comparison with existing work.

Parameter	Proposed Work	GFL Works [15,30]	GFM Works [2]	Mixed GFM and GFL Work [1]
Validated V2G Functionalities	VI, long-term frequency support, voltage support by reactive power, harmonic compensation	VI Only	VI, long-term frequency support	VI, long-term frequency support
Control Strategy	GFL	GFL	GFM	GFM for VI and GFL for long-term frequency support
Power Stage Configurations	VSI cascaded to an isolated and bidirectional DAB DC-DC converter	VSI Only	VSI cascaded to a non-isolated bidirectional Boost Converter	Two independent two-stage AC-DC converters composed of a VSI cascaded to a non-isolated bidirectional Boost Converter
Energy Storage Devices	HESS-DC-link capacitors along with battery	DC-Link Capacitors	HESS-DC-link capacitors along with battery	HESS-super capacitors along with battery

. Four comparison parameters were considered: validated V2G functionalities, control strategy, power stage configuration, and adopted energy storage devices.

Table 6. Summary of key performance indicators of the proposed EVBC-HESS control strategy.

Performance Metric	Test Condition	Obtained Result
Rated Converter Power	Nominal operation	2.5 kW
Maximum Virtual Inertia Support Power	Frequency step of +0.2 Hz	786 W
Virtual Inertia Response Time	Frequency disturbance	80 ms
Long-Term Frequency Support	Frequency deviation ±0.2 Hz	±400 W
Frequency Estimation Overshoot (PLL only)	0.2 Hz frequency step	7%
Frequency Estimation Overshoot (PLL + LPF)	0.2 Hz frequency step	0.4%
Supported Frequency Variation	Grid frequency event	±0.2 Hz
Maximum Considered ROCOF	Grid code condition	3 Hz/s
Equivalent Virtual Inertia Constant	Calculated value	1.85 s
Grid Current THD	After harmonic compensation	1.50%
Grid Voltage THD	After compensation	3.23%
THDv Before Compensation	Distorted grid condition	3.19%
Reactive Power Support	Voltage sag event	+400 VAR
Grid Voltage Reduction Tested	Voltage support test	17 V
Grid Current Increase During Voltage Support	Voltage sag compensation	4.09 A → 4.81 A
Battery Current During VI Support	Frequency event	Approximately constant at 2.56 A
DC-Link Voltage Variation	Virtual inertia operation	425 V → 450 V

summarizes the principal performance indicators obtained from the simulation studies. The results demonstrate that the proposed EVBC-HESS architecture effectively combines virtual inertia emulation, long-term frequency support, reactive power compensation, and harmonic mitigation within a unified control framework. The numerical values confirm the capability of the proposed system to improve grid stability and power quality while maintaining limited battery stress through coordinated energy management between the DC-link capacitor and the battery.

The quantitative comparison presented in

Table 7. Quantitative performance comparison with existing literature.

Performance Metric	Proposed Work	Ref. [15]	Ref. [2]	Ref. [1]
Virtual Inertia Support	Yes	Yes	Yes	Yes
Long-Term Frequency Support	Yes	No	Yes	Yes
Reactive Power Support	Yes (400 VAR)	No	No	No
Harmonic Compensation	Yes	No	No	No
Energy Storage Technology	DC-Link Capacitor + Battery	DC-Link Capacitor	DC-Link Capacitor + Battery	Supercapacitor + Battery
Converter Topology	VSI + Isolated DAB	VSI	VSI + Bidirectional Boost	Dual AC–DC Converters
Virtual Inertia Constant	1.85 s	N/R	N/R	N/R
Maximum Inertial Support Power	786 W	N/R	N/R	N/R
Response Time	80 ms	N/R	N/R	N/R
Maximum ROCOF Capability	3 Hz/s	N/R	N/R	N/R
Frequency Variation Tested	±0.2 Hz	N/R	N/R	N/R
Grid Current THD	1.50%	N/R	N/R	N/R
Grid Voltage THD	3.23%	N/R	N/R	N/R
Reactive Power Capability	±400 VAR	N/R	N/R	N/R
Battery Current Regulation	Yes	No	Partial	Yes
Full V2G Functionalities	Yes	Partial	Partial	Partial

Note: N/R denotes “Not Reported” in the corresponding reference.

demonstrates that the proposed EVBC-HESS architecture provides a broader set of grid-support functionalities than existing virtual inertia implementations. In addition to delivering an equivalent virtual inertia constant of approximately 1.85 s and a transient support power of 786 W within 80 ms, the proposed system simultaneously offers long-term frequency regulation, reactive power compensation, and harmonic mitigation. The achieved current THD of 1.50% and voltage THD of 3.23% further demonstrate the capability of the proposed controller to enhance power quality while supporting grid stability. These features distinguish the proposed approach from existing studies that primarily focus on inertia emulation alone.

6.5. Extension of the Proposed Strategy to IPT-Based EV Charging Systems

Recent advancements in Inductive Power Transfer (IPT) technology have enabled wireless charging solutions for electric vehicles, offering enhanced user convenience, galvanic isolation, and suitability for autonomous transportation systems. Unlike conventional conductive chargers that directly transfer electrical energy through wired connections, IPT systems employ magnetic coupling between transmitter and receiver coils through resonant compensation networks. Consequently, IPT architecture exhibits additional dynamic characteristics associated with coupling coefficient variations, coil misalignment, resonant tuning, and power transfer efficiency.

Despite these differences, the proposed hybrid energy storage-based virtual inertia control strategy can be extended to IPT-enabled charging systems. Since the virtual inertia, frequency support, reactive power compensation, and harmonic mitigation functionalities are primarily implemented at the grid-side converter interface, the wireless power transfer stage can be treated as an intermediate energy transfer subsystem. The hybrid energy storage system comprising the DC-link capacitor and EV battery can continue to provide fast and slow frequency support services while maintaining the operational principles presented in this work. However, additional control considerations may be required to compensate for wireless coupling variations and maintain stable bidirectional power flow during V2G operation. Therefore, future work will investigate the integration of the proposed control framework with bidirectional IPT architectures to enable wireless V2G services and enhanced grid-support capabilities.

7. Conclusions

This paper presented an integrated control strategy for Electric Vehicle Battery Chargers (EVBCs) equipped with a hybrid energy storage system (HESS) consisting of a DC-link capacitor and a lithium-ion battery. The proposed architecture combines a three-phase Voltage Source Inverter (VSI) and an isolated Dual Active Bridge (DAB) converter to provide comprehensive Vehicle-to-Grid (V2G) services, including virtual inertia emulation, long-term frequency regulation, reactive power support, and harmonic compensation.

The proposed multi-timescale control framework successfully decouples fast and slow grid-support functionalities by utilizing the DC-link capacitor for transient virtual inertia response and the battery for sustained frequency support. Simulation results demonstrated that the proposed system can effectively respond to frequency disturbances of ±0.2 Hz while maintaining stable operation. The virtual inertia controller delivered a transient support power of approximately 786 W with a response time of about 80 ms, while the equivalent virtual inertia constant achieved was approximately 1.85 s. Furthermore, the enhanced PLL-LPF frequency estimation method significantly reduced the ROCOF overshoot from approximately 7% to 0.4%, thereby improving dynamic stability and reducing transient stress on the converter system.

The harmonic compensation capability of the proposed controller was validated through FFT analysis. The grid current THD was reduced to 1.50%, while the compensated voltage THD was maintained at 3.23%, demonstrating compliance with power quality requirements and confirming the effectiveness of the selective harmonic compensation strategy. In addition, the voltage support functionality was verified under a grid voltage reduction of 17 V, where the controller supplied up to 400 VAR of reactive power support, increasing the grid current from 4.09 A to 4.81 A while maintaining an almost constant battery current of 2.56 A. These results confirm the ability of the HESS management strategy to support voltage regulation without imposing significant additional stress on the battery.

Compared with existing virtual inertia and V2G solutions, the proposed approach provides a unified framework capable of simultaneously delivering virtual inertia support, long-term frequency regulation, reactive power compensation, and harmonic mitigation using a single coordinated control architecture. The utilization of the DC-link capacitor for fast transient support reduces battery cycling stress and potentially contributes to longer battery lifetime. Furthermore, the proposed solution can be implemented as a firmware-level enhancement to existing EV charging infrastructure, facilitating cost-effective deployment in future smart grids with high renewable energy penetration. Future work will focus on experimental validation using a hardware prototype, real-time controller implementation, scalability assessment under large-scale EV aggregation scenarios, and the extension of the proposed framework to bidirectional wireless charging and Inductive Power Transfer (IPT)-based Vehicle-to-Grid systems.