A Grid-Compatible Adaptive Charging Strategy for Bidirectional On-Board EV Chargers with SOC and Thermal Integration

Figure 1 illustrates the complete structure of a three-phase bidirectional EV charger system. It comprises a three-phase grid connection that delivers AC power through an LCL filter to eliminate harmonics. The filtered AC is then transformed to DC via a three-phase AC–DC converter. This DC power is stabilised by a DC link capacitor and then regulated by a bidirectional buck-boost DC–DC converter. The DC–DC stage charging and discharging of the battery is managed using an adaptive charging control technique with temperature and SOC-based regulation. Control systems are implemented for both converters to ensure regulated power flow, grid compliance, and support for G2V and V2G operation.

Figure 1.

Block diagram of three-phase bidirectional on-board charger. PLL, phase-locked loop.

The ideal grid source voltage and current are v_a, v_b, v_c and i_a,i_b,i_c, where L and R denote the circuit inductance and resistance. v_dc,i_dc,C is the DC link voltage, current and capacitance, respectively.

By applying KVL and KCL, the system model can be expressed as follows (Han et al., 2020): (1) va=Ldiadt+Ria+uan+unovb=Ldibdt+Rib+ubn+unovc=Ldicdt+Ric+ucn+unocdvdcdt=idc−iL \matrix{ {{v_a} = L{{d{i_a}} \over {dt}} + R{i_a} + {u_{an}} + {u_{no}}} \hfill \cr {{v_b} = L{{d{i_b}} \over {dt}} + R{i_b} + {u_{bn}} + {u_{no}}} \hfill \cr {{v_c} = L{{d{i_c}} \over {dt}} + R{i_c} + {u_{cn}} + {u_{no}}} \hfill \cr {c{{d{v_{dc}}} \over {dt}} = {i_{dc}} - {i_L}} \hfill \cr } where u_no is the voltage between N and O, and u_an, u_bn and u_cn are the voltages between the converter legs and neutral point O. Switching function is S_k = 1 when switches S_a1, S_b1, S_c1 are on and S_a2, S_b2, S_c2 are off, and S_k = 0 when switches S_a2, S_b2, S_c2 are on and S_a1, S_b1, S_c1 is off. Thus, u_k may be written as follows: (2) uk=ukn+uno=skudc+uno k=a,b,c {u_k} = {u_{kn}} + {u_{no}} = {s_k}{u_{dc}} + {u_{no}}\;\;\;\;\;\left( {k = a,b,c} \right) (3) va=Ldiadt+Ria+vdcsa−13sa+sb+scvb=Ldibdt+Rib+vdcsb−13sa+sb+scvc=Ldicdt+Ric+vdcsc−13sa+sb+scCdvdcdt=iasa+ibsb+icsc−iL \matrix{ {{v_a} = L{{d{i_a}} \over {dt}} + R{i_a} + {v_{dc}}\left[ {{s_a} - {1 \over 3}\left( {{s_a} + {s_b} + {s_c}} \right)} \right]} \hfill \cr {{v_b} = L{{d{i_b}} \over {dt}} + R{i_b} + {v_{dc}}\left[ {{s_b} - {1 \over 3}\left( {{s_a} + {s_b} + {s_c}} \right)} \right]} \hfill \cr {{v_c} = L{{d{i_c}} \over {dt}} + R{i_c} + {v_{dc}}\left[ {{s_c} - {1 \over 3}\left( {{s_a} + {s_b} + {s_c}} \right)} \right]} \hfill \cr {C{{d{v_{dc}}} \over {dt}} = {i_a}{s_a} + {i_b}{s_b} + {i_c}{s_c} - {i_L}} \hfill \cr }

The equation is shown in an a, b, c system, but it is more appropriate to represent it in a stationary reference α, β frame as follows: (4) vαvβ=Mvavbvc, \left[ {\matrix{ {{v_\alpha }} \cr {{v_\beta }} \cr } } \right] = \left[ M \right]\left[ {\matrix{ {{v_a}} \cr {{v_b}} \cr {{v_c}} \cr } } \right], (5) vavbvc=32MTvαvβ,32MT=10−1232−1232 \matrix{ {\left[ {\matrix{ {{v_a}} \cr {{v_b}} \cr {{v_c}} \cr } } \right] = {3 \over 2}{{\left[ M \right]}^T}\left[ {\matrix{ {{v_\alpha }} \cr {{v_\beta }} \cr } } \right],} \hfill \cr {{3 \over 2}{{\left[ M \right]}^T} = \left[ {\matrix{ 1 & 0 \cr { - {1 \over 2}} & {{{\sqrt 3 } \over 2}} \cr { - {1 \over 2}} & {{{\sqrt 3 } \over 2}} \cr } } \right]} \hfill \cr } where v_α, v_β are α, β frame quantities and v_a, v_b, v_c are stationary a, b and c frame quantities. The α, β frame is represented as follows: (6) vα=Ldiadt+Ria+savdcvβ=Ldibdt+Rib+sbvdccdvdcdt=32iasa+ibsb−iL \matrix{ {{v_\alpha } = L{{d{i_a}} \over {dt}} + R{i_a} + {s_a}{v_{dc}}} \hfill \cr {{v_\beta } = L{{d{i_b}} \over {dt}} + R{i_b} + {s_b}{v_{dc}}} \hfill \cr {c{{d{v_{dc}}} \over {dt}} = {3 \over 2}\left( {{i_a}{s_a} + {i_b}{s_b}} \right) - {i_L}} \hfill \cr }

The transition from the stationary (α, β) frame to the synchronous (d-q) frame, achieved through Park’s transformation, aligns the reference frame with the grid’s rotating magnetic field at angular frequency ω. This converts time-varying sinusoidal signals into steady-state DC signals, simplifying power control by decoupling active (d-axis) and reactive (q-axis) components and facilitating more effective voltage and current regulation as follows: (7) vdvq=Tvαvβ,T=coswotsinwot−sinwotcoswot, \matrix{ {\left[ {\matrix{ {{v_d}} \cr {{v_q}} \cr } } \right] = \left[ T \right]\left[ {\matrix{ {{v_\alpha }} \cr {{v_\beta }} \cr } } \right],} \hfill \cr {\left[ T \right] = \left[ {\matrix{ {\cos \left( {{w_o}t} \right)} & {\sin \left( {{w_o}t} \right)} \cr { - \sin \left( {{w_o}t} \right)} & {\cos \left( {{w_o}t} \right)} \cr } } \right],} \hfill \cr } (8) vαvβ=T−1vdvq,T−1=coswot−sinwotsinwotcoswot, \matrix{ {\left[ {\matrix{ {{v_\alpha }} \cr {{v_\beta }} \cr } } \right] = {{\left[ T \right]}^{ - 1}}\left[ {\matrix{ {{v_d}} \cr {{v_q}} \cr } } \right],} \hfill \cr {{{\left[ T \right]}^{ - 1}} = \left[ {\matrix{ {\cos \left( {{w_o}t} \right)} & { - \sin \left( {{w_o}t} \right)} \cr {\sin \left( {{w_o}t} \right)} & {\cos \left( {{w_o}t} \right)} \cr } } \right],} \hfill \cr }

Where v_d, v_q are synchronous d-q frame quantities. Using Eqs (6) and (7) we can simplify the model as follows: (9) vd=Ldiddt+Rid−woLiq+sdvdcvq=Ldiqdt+Riq−woLid+sqvdccdvdcdt=32idsd+iqsq−iL \matrix{ {{v_d} = L{{d{i_d}} \over {dt}} + R{i_d} - {w_o}L{i_q} + {s_d}{v_{dc}}} \hfill \cr {{v_q} = L{{d{i_q}} \over {dt}} + R{i_q} - {w_o}L{i_d} + {s_q}{v_{dc}}} \hfill \cr {c{{d{v_{dc}}} \over {dt}} = {3 \over 2}\left( {{i_d}{s_d} + {i_q}{s_q}} \right) - {i_L}} \hfill \cr }

Based on Eq. (9), Figure 2 represents a three-phase voltage source converter d-q synchronous reference model.

Figure 2.

Synchronous d-q frame model of a three-phase converter.

The design of the LCL filter is crucial for ensuring power quality in the bidirectional charger system. The LCL filter comprises the converter-side inductance, grid-side inductance and a filter capacitor, and it is responsible for attenuating high-frequency switching harmonics introduced by the power converter. The grid-side inductance (Lg) plays a specific role in limiting the high-frequency current injected into the grid. It acts as a buffer that smoothens the current waveform and reduces electromagnetic interference (EMI). Additionally, Lg helps improve the stability of the control system, particularly under weak grid conditions, and assists in suppressing resonance by interacting with the filter capacitor. Its value must be carefully chosen to balance the filtering effectiveness and avoid excessive reactive power injection or resonant oscillations. The design of the filter is as follows: (10) The base impedance zb=En2Pn {\rm{The}}\,{\rm{base}}\,{\rm{impedance}}\;{z_b} = {{E_n^2} \over {{P_n}}} (11) The base capacitance cb=1wgzb {\rm{The}}\,{\rm{base}}\,{\rm{capacitance}}\;{c_b} = {1 \over {{w_g}{z_b}}}

Where P_n, E_n and w_g denote rated power, rated voltage and angular grid frequency, respectively.

The product of the base capacitance of the converter and the rate of reactive power absorption yields the filter capacitance (Omkar and Vijaya Kumar, 2024) as follows: (12) cf=5% of cbCf=5%pn2πfgEn2 \matrix{ {{c_f} = 5\% \;of\;{c_b}} \hfill \cr {{C_f} = 5\% {{{p_n}} \over {2\pi {f_g}E_n^2}}} \hfill \cr } (13) The relation between the converter voltage and current is Vin=LidiindtThe maximum current ripple is Δimax=Vdc6LifswThe minimum value of the inductor on the converter side is Limin=Vdc6fswΔimax \matrix{ {{\rm{The}}\,{\rm{relation}}\,{\rm{between}}\,{\rm{the}}\,{\rm{converter}}\,{\rm{voltage}}\,{\rm{and}}\,{\rm{current}}\,{\rm{is}}\;{V_{in}} = {L_i}{{d{i_{in}}} \over {dt}}} \hfill \cr {{\rm{The}}\,{\rm{maximum}}\,{\rm{current}}\,{\rm{ripple}}\,{\rm{is}}\;\Delta {i_{\max \;}} = {{{V_{dc}}} \over {6{L_i}{f_{sw}}}}} \hfill \cr {{\rm{The}}\,{\rm{minimum}}\,{\rm{value}}\,{\rm{of}}\,{\rm{the}}\,{\rm{inductor}}\,{\rm{on}}\,{\rm{the}}\,{\rm{converter}}\,{\rm{side}}\,{\rm{is}}\;{L_{i\min \;}} = {{{V_{dc}}} \over {6{f_{sw}}\Delta {i_{\max}}}}} \hfill \cr } (14) The grid side inductance is Lg=1ka2+1CfW2sw {\rm{The\,grid\,side\,inductance\,is}}\;{L_g} = {{\sqrt {{1 \over {k_a^2}}} + 1} \over {{C_f}{W^2}sw}}

Where k_a is the attenuation factor and f_sw, f_g and f_res stand for switching, grid and resonant frequencies, respectively.

It is crucial to note that a lower harmonic attenuation level leads to a decrease in current harmonics. Consequently, reducing Ka leads to a decrease in the THD of the grid current. (15) The resonant frequency is wres=Li+LgLiLgcf {\rm{The\,resonant\,frequency\,is}}\;{w_{res}} = \sqrt {{{{L_i} + {L_g}} \over {{L_i}{L_g}{c_f}}}}

After determining all LCL filter parameters, it is crucial to verify the resonance frequency to ensure that it does not align with low-order or high-order harmonics. This satisfies Eq. (16): (16) 10fg≤fres≤fsw/2 10{f_g} \le {f_{res}} \le {f_{sw}}/2

If the resonance frequency is <10 times the grid frequency, the capacitor value should be reduced. If it goes beyond half that threshold, the switching frequency or capacitor value can be increased. The LCL filter parameters were optimised to minimise THD while ensuring resonance damping and grid compatibility. The phase delay introduced by the LCL filter is compensated by using a phase-locked loop (PLL) within the synchronous d-q frame control, which aligns the reference frame with the grid voltage phase, ensuring synchronisation. Additionally, feedforward compensation is used to decouple the d-q axis currents, while the PI controller parameters are tuned to compensate for the phase delay caused by the LCL filter. The filter was tuned to achieve sufficient harmonic suppression without introducing resonant peaks, based on LCL filter design and IEEE 519 standards.

The core control logic dynamically adjusts the charging mode based on real-time battery metrics, including temperature and SOC. The adaptive controller uses the Coulomb counting method for SOC estimation, integrating battery current with an initial SOC, calibrated periodically to minimise drift (Danko et al., 2019).

Figure 3 depicts an adaptive charging control system that receives inputs from the battery SOC and temperature. These inputs are processed by the adaptive controller, which generates optimised reference signals for current and voltage. The controller ensures safe and efficient charging by dynamically adjusting these references based on real-time battery conditions.

Figure 3.

An adaptive charging controller block diagram. SOC, state of charge.

Figure 4 illustrates a DC–DC adaptive controller that regulates battery charging using feedback from the output current. A PI controller processes the error between the reference and actual current, generating a PWM signal to drive either the buck or boost converter. The mode selection logic ensures appropriate operation based on current level comparisons, enabling efficient bidirectional energy flow. The Ziegler–Nichols tuning method is used to determine the PI controller parameters based on system oscillatory behaviour. (17) The PI controller transfer function is given as Gcs=Kp+Kis {\rm{The\,PI\,controller\,transfer\,function\,is\,given\,as}}\;Gc\left( s \right) = Kp + {{Ki} \over s} (18) Gcs=Kp1+1TisProportional gain is Kp=0.45kuIntegral time constant is Ti=Tu1.2Integral gain is Ki=KpTi \matrix{ {Gc\left( s \right) = Kp\left( {1 + {1 \over {{T_i}s}}} \right)} \hfill \cr {{\rm{Proportional\,gain\,is}}\;{K_p} = 0.45{k_u}} \hfill \cr {{\rm{Integral\,time\,constant\,is}}\;{T_i} = {{{T_u}} \over {1.2}}} \hfill \cr {{\rm{Integral\,gain\,is}}\;{K_i} = {{{K_p}} \over {{T_i}}}} \hfill \cr }

Where K_u = ultimate gain and T_u = ultimate period.

Figure 4.

Controller for the buck-boost DC–DC converter.

The battery’s temperature change is governed by a first-order thermal differential equation: (19) Cth⋅dTdt=I2⋅Rint−T−TambRth {C_{th}} \cdot {{dT} \over {dt}} = {I^2} \cdot {R_{int}} - {{T - {T_{amb}}} \over {{R_{th}}}}

Where: C_th = thermal capacitance (J/°C), R_int = internal resistance (Ω), R_th = thermal resistance (°C/W), T = battery temperature, T_amb = ambient temperature and I = battery current.

The internal resistance (R_int) is estimated using pulse current tests and voltage drop analysis across the battery terminals. Thermal capacitance (C_th) and thermal resistance (R_th) are derived from battery datasheet specifications.

Figure 5 illustrates the adaptive charging strategy for an EV battery system. It begins by measuring temperature and SOC. If SOC is <80%, the mode of constant current (CC) is activated; otherwise, mode of constant voltage (CV) is selected. In CC mode, the current is set to maximum unless the temperature exceeds the threshold, triggering current derating. The process continues to monitor SOC, and charging is terminated when 100% SOC is reached, ensuring safe and efficient battery operation.

Figure 5.

Flow chart for an adaptive controller. SOC, state of charge.

The proposed three-phase bidirectional on-board charger exhibits stable and efficient performance. The grid voltage (Figure 6a) maintains a smooth sinusoidal waveform with a 325 V peak (230 V RMS), indicating effective synchronisation. The grid current (Figure 6b) also shows sinusoidal waveforms with a balanced 25 A peak per phase, confirming harmonic mitigation and grid compliance.

Figure 6.

Three-phase bidirectional on-board charger performance during G2V mode: (a) Grid voltage, (b) Grid current, (c) Battery voltage, (d) Battery current, (e) Battery SOC and (f) Charging power. G2V, grid-to-vehicle; SOC, state of charge.

Battery voltage (Figure 6c) rises steadily during CC mode, transitioning to CV mode at 400 V. Charging current (Figure 6d) starts at 30 A in CC mode and decreases during CV mode to ensure safety. The SOC (Figure 6e) increases rapidly by up to 80% in CC mode and then gradually under CV, ensuring faster yet safe charging. Charging power (Figure 6f) peaks at 12 kW near 80% SOC, followed by a gradual decrease in CV mode. FFT analysis (Figure 7a) shows a grid current THD of 1.33%, FFT analysis (Figures 7b and 7c) reveals a grid current THD of 1.51% and 1.23% at a grid inductance value of 4.5 mH and 5.5 mH. FFT analysis (Figures 7d and 7e) indicates a grid current THD of 1.48% and 1.27% at a grid voltage of 370 V and 460 V. It shows high power quality, confirming compliance with IEEE 519 standards. These results validate the effectiveness of the adaptive charging algorithm in optimising charging speed, safety and grid performance.

Figure 7.

THD of grid current at different operating conditions in G2V mode: (a) at a grid inductance of Lg = 5 mH, (b) at a grid inductance of Lg = 4.5 mH, (c) at a grid inductance of Lg = 5.5 mH, (d) at a grid voltage of 370 V and (e) at a grid voltage of 460 V. G2V, grid-to-vehicle; THD, total harmonic distortion.

In V2G operation, the proposed bidirectional charger demonstrates stable and compliant power delivery. The voltage waveform (Figure 8a) and current waveform (Figure 8b) are sinusoidal with 325 V and 25 A peak, respectively, confirming proper synchronisation and low-distortion power injection into the grid. The battery voltage (Figure 8c) begins at 415 V and gradually decreases as discharging progresses, while the current (Figure 8d) remains steady at 30 A, ensuring consistent power transfer. The SOC (Figure 8e) exhibits a controlled linear decline, reflecting a safe and efficient discharge process governed by adaptive control logic. Discharging power (Figure 8f) shows initially peaking and then decreasing gradually with SOC, preventing deep discharge and preserving battery health. FFT analysis (Figure 9a) reveals a low THD of 1.7%; Figures 9b and 9c reveals a grid current THD of 2.10% and 1.62% at a grid inductance value of 4.5 mH and 5.5 mH; Figures 9d and 9e indicates a grid current THD of 1.92% and 1.65% at a grid voltage of 370 V and 460 V, indicating high power quality. These findings confirm the effectiveness of the suggested adaptive V2G technique to ensure efficient energy delivery, grid stability and battery longevity.

Figure 8.

Three-phase bidirectional on-board charger performance during V2G mode: (a) Grid voltage, (b) Grid current, (c) Battery voltage, (d) Battery current, (e) Battery SOC, and (f) Discharging power. SOC, state of charge.

Figure 9.

THD of grid current at different operating conditions in V2G mode: (a) at a grid inductance of Lg = 5 mH, (b) at a grid inductance of Lg = 4.5 mH, (c) at a grid inductance of Lg = 5.5 mH, (d) at a grid voltage of 370 V and (e) at a grid voltage of 460 V. THD, total harmonic distortion; V2G, vehicle-to-grid.

Table 3 shows a sensitivity analysis with parameter variation to assess the robustness of the proposed adaptive charging system by varying critical parameters such as grid-side inductance (Lg) and grid voltage levels. The THD was measured during both G2V and V2G operations under these variations. For Lg values ranging from 4.5 mH to 5.5 mH, the THD in G2V mode varied between 1.23% and 1.51%, while in V2G mode it ranged from 1.62% to 2.1%. Similarly, with grid voltage variations from 370 V to 460 V, the G2V THD remained within 1.27%–1.48%, and V2G THD ranged from 1.65% to 1.92%. These values are well within IEEE 519 harmonic limits, demonstrating that the system remains stable and grid-compliant even under significant variations, confirming its robustness to practical disturbances and parameter uncertainties.