A Novel Battery Self-Heating Method Based on Drive Circuit Reconfiguration Compatible with Both Preheating and On-Route Heating

Abstract

To reduce vehicular emission pollution in cold regions and maximize sustainable development of transportation, AC self-heating of electric vehicles is acknowledged as an efficient approach to mitigate the decline in Li-ion battery performance under low-temperature conditions. This paper introduces a novel battery self-heating approach based on reconfiguration of the drive circuit, which is compatible with both preheating and on-route heating. The undesired torque generated by the heating current can be inherently nullified regardless of the rotor position. The control of heating and driving currents is entirely decoupled, facilitating straightforward adaptation to a range of heating strategies. Furthermore, a battery electro-thermal model is proposed and integrated with the drive system model to estimate the battery temperature evolution. Comprehensive experiments are designed to validate the operating principle and the accuracy of battery temperature estimation under various working conditions. The results present a high fidelity between the experimental data and the simulation outcomes. The root mean square errors of the predicted battery temperature under all the constant and combined driving conditions are less than 1 °C.

1. Introduction

Vehicle electrification represents one of the most effective pathways to achieve sustainable development in the transportation sector. In the last decade, lithium-ion batteries (LiBs) have been recognized as the predominant power source for electric vehicles (EVs) due to their high power and energy density, extended cycle life, minimal environmental impact, and substantial capacity [1,2,3,4]. Numerous studies have concentrated on extending the driving range of LiB powered EVs, enhancing battery safety, and accurately estimating the state of health of LiBs. Collectively, this body of research highlights the strong temperature dependence of LiB energy storage performance. Consequently, battery thermal management has garnered increasing research attention, primarily focusing on preventing excessive temperatures and mitigating the risk of thermal runaway [5,6,7,8,9,10,11]. Conversely, LiBs exhibit significant degradation in charging and discharging capacity under extremely low-temperature conditions [2,12]. It has been observed that charging and discharging at low temperatures with unrestricted current can induce lithium-ion deposition and dendrite formation, which adversely affect battery capacity. Moreover, the presence of dendrites within the battery can penetrate the separator and lead to internal short circuit, triggering thermal runaway and other safety hazards [13]. Therefore, investigating battery heating approaches to enhance LiB performance in cold environments is important.

As illustrated in Figure 1, battery heating methods can be broadly categorized into external and internal heating based on the location of the heat source [14]. By employing approaches such as positive temperature coefficient (PTC) resistor, heat pump, and waste heat recovery, external heating is characterized by relatively lower system complexity; however, it presents notable limitations, including reduced efficiency and effect of non-uniform heating [15]. In contrast, internal heating inherently overcomes these disadvantages [16] and has gained widespread recognition for its considerable potential in LiB heating applications.

The current excitation-based battery self-heating represents the most prevalent technology for internal heating applications at present. This approach contributes to the decreased system complexity and cost observed with SHLB batteries [17,18,19], meanwhile avoiding the inconveniences linked to an external power sources [20]. Consequently, it has garnered significant interest among researchers [21]. In general, the on-board battery internal heating methods can be categorized by the on-board specific circuitry [22,23,24,25], integration in the battery management system (BMS) [26,27] or integration in the electric drive system (EDS) [28,29,30,31,32,33]. The on-board specific circuitry approach is recognized for its implementation flexibility. Various types of such heaters exist, primarily based on buck-boost circuits [22], H-bridge configurations [25], and LC resonators [23,24]. In comparison to their benefits, specific circuitry approaches necessitate increased installation space and higher hardware expenses. Meanwhile, key challenges for specific circuitry methods include the independent control of the amplitude and frequency of the heating current, as well as the capability of on-route heating. Alternatively, AC heater can be integrated with the equalizer circuit in BMS [26,27], thereby potentially decreasing hardware expenses and enhancing the power density of the battery system [21]. However, it should be noted that the equalizer circuit in BMS is not a standardized configuration across all EVs in the market.

Based on the integration in EDS, various heating methods have been explored and evaluated. Du et al. [28] propose a heating current control approach utilizing conventional EDS. This approach not only decreases hardware expenses but also gives the possibility of battery on-route heating. However, heating the rate of temperature rise is not sufficient. In addition, the research work does not deep dive into the on-route heating implementation. Li et al. [29,30] introduced the dual-/triple-module separated inverter (DMSI/TMSI) topology, facilitating rapid battery heating. The DMSI/TMSI approach significantly increases the root mean square (RMS) value of the heating current, compared with the conventional drive circuit heating approach. Zhu et al. [31] proposed an integrated battery self-heater (IBSH) together with a robust control method. A fast battery temperature rise can be achieved according to their experimental results. Despite the advantages of the above techniques, DMSI/TMSI and IBSH unfortunately lack the support for the functionality of battery on-route heating. Furthermore, the modification requirements for the battery pack architecture must also be considered when applying DMSI/TMSI. In the IBSH method, the undesired torque is nullified by adjusting the rotor permanent flux to the direction consistent with the excitation flux of the winding, which may restrict the applicability of IBSHs in certain scenarios.

Inspired by previous studies, a novel battery self-heating approach based on drive circuit reconfiguration is introduced in this paper. (1) The proposed neutral point battery heater (NPBH) is compatible with both the preheating mode and on-route heating mode, meanwhile significantly reducing the complexity, cost, and space requirement of the implementation. (2) The undesired torque caused by heating current can be inherently eliminated regardless of the rotor position. This does not necessitate a dedicated control algorithm or mechanical method. (3) The current control of the heating and the driving based on NPBH is fully decoupled. Thus, strategies dedicated to on-route heating can be easily implemented. (4) A significant rate of temperature rise (RTR) for the battery can be achieved using this method.

2. Proposed NPBH Method and Modeling Approach

2.1. Operating Principle

The circuit topology of NPBH is shown in Figure 2. E1 and E2 are two identical battery modules in series, providing the DC-bus voltage. C is the DC-bus capacitor of the inverter. Power electronic transistors Q1 and Q4 constitute the first bridge arm of the inverter, which is connected to the U phase of the electric motor (EM) winding. Similarly, transistors Q2 and Q5 comprise the second bridge arm, linked to the V phase of the EM winding. Lastly, transistors Q3 and Q6 form the third bridge arm, associated with the W phase of the EM winding. The neutral point of EM connects with the mid-point of the battery pack through switch SW.

When the battery temperature is low and heating is required, SW switches to on-state. The energy stored in E1, E2, and the windings of the EM is alternately charged and discharged by control. The common component of the current within each winding phase functions as the heating current, whereas the differential component of the current in each phase produces the driving torque. When the battery is warmed up, SW switches to off-state. The neutral point EM can be controlled as a normal motor.

Employing the NPBH circuit, the zero-axis current i₀ circulates continuously between EM windings and battery modules via the inverter and the EM neutral line. Within every switching cycle, the current evolution can be separated into different stages. Zero voltage vectors (Q1Q2Q3 command:000 or 111) are adopted for the synchronous control of the inverter arms to precisely regulate i₀ which serves as the heating current.

Figure 3 shows the four stages of the circulation of the heating and the driving current in a single operating cycle, given a rotor electrical angle of π/2. Figure 4 depicts the temporal relationship between the PWM signals and the zero-axis current i₀, where the positive direction of current flow is defined as originating from the U, V, and W phase terminals toward the motor neutral point. Since the PWM signals are generated center-symmetrically, it suffices to analyze half of the control cycle, which is divided into four stages with the current component of driving represented in blue and the component of heating represented in red. i₁ and i₂ represent the current component of heating passing through the upper battery module E1 and the lower battery module E2, respectively.

During Stage 1, Q1, Q2, and Q3 are in the on-state, resulting in a freewheeling state of the driving current. The torque gradually decreases while the heating current i₀ increases. The upper battery module is charged while the lower is discharged. The EM windings store the energy whereas the DC-bus capacitor releases the energy. In Stage 2, Q3 is turned off and Q6 is turned on, which leads to an increase in the driving torque while i₀ remains essentially constant. In Stage 3, Q1 is switched off and Q4 is switched on. Similar to Stage 2, the driving torque keeps increasing and the heating current remains largely unchanged. In Stage 4, Q2 turns off and Q5 turns on. The driving current is in the freewheeling state. Both the torque and i₀ decrease. The upper battery module is discharged while the lower is charged; the EM winding releases energy whereas the DC-bus capacitor stores energy.

In a close-loop operation, a reference of sinusoidal waveform is tracked by i₀ using the PI-based current controller. Since E1 and E2 have identical parameters, i₁ and i₂ have the same amplitude but opposite phases, as shown in Figure 5. The amplitude of the heating current I_heat can be obtained by (1), ignoring the losses of the wire and the inverter.

$$I_{heat}=\left|i_1\right|=\left|i_2\right|={\displaystyle \frac{3}{2}}\left|i_0\right|.$$

(1)

2.2. Control Method

The entire control logic of the NPBH contains the regulation of both heating and driving currents, as illustrated in Figure 6. A heating strategy determines the optimal amplitude I_heat and frequency f of the heating current, according to battery SOC and temperature T_b. When on-route heating is applied, I_heat and f can also be affected by driving torque T_em, battery pack voltage U_dc, as well as vehicle speed.

For heating current control, the duty cycle of PWMα_h can be obtained by Equation (2).

$${\alpha }_h={\displaystyle \frac{2}{U_{dc}}}\left[K_{0,P}\left(i_{0,ref}-i_0\right)+K_{0,I}{\displaystyle \int \left(i_{0,ref}-i_0\right)dt}\right],$$

(2)

where i_0,ref is the reference of i₀. K_0,P and K_0,I represent the factors of proportional and integral parts of the controller, respectively. The currents for driving, namely i_d and i_q, are regulated using the Field-Oriented Control (FOC). The duty cycles for driving, α_u,drv, α_v,drv and α_w,drv, can be determined by bipolar sinusoidal pulse width modulation (SPWM) according to the phase voltage calculated by FOC, as shown in Equation (3).

$$\left\{\begin{array}{c}{\alpha }_{u,drv}={\displaystyle \frac{\left|U_{s,drv}\right|·\cos \left(\angle U_{s,drv}\right)}{U_{dc}}}+0.5\\ {\alpha }_{v,drv}={\displaystyle \frac{\left|U_{s,drv}\right|·\cos \left(\angle U_{s,drv}-\frac{2}{3}\pi \right)}{U_{dc}}}+0.5\\ {\alpha }_{w,drv}={\displaystyle \frac{\left|U_{s,drv}\right|·\cos \left(\angle U_{s,drv}+\frac{2}{3}\pi \right)}{U_{dc}}}+0.5\end{array}\right.,$$

(3)

where |U_s,drv| and ∠U_s,drv are the module and phase angles of the phase voltage U_s,drv. The applied duty cycles for three inverter phases, namely α_u, α_v and α_w, are the superposition of the heating component and driving component, as presented in Equation (4).

$$\left\{\begin{array}{l}{\alpha }_u={\alpha }_{u,drv}+{\alpha }_h\\ {\alpha }_v={\alpha }_{v,drv}+{\alpha }_h\\ {\alpha }_w={\alpha }_{w,drv}+{\alpha }_h.\end{array}\right.$$

(4)

It should be noted that the driving current also contributes to warm the battery during the on-route heating process. This effect is considered in the heating strategy and will be discussed in the next subsection.

2.3. LiB Electro-Thermal Model

It is well established that the impedance characteristics of LiBs are influenced by temperature, SOC, and current frequency. These dependencies can be effectively captured through an equivalent circuit model (ECM) derived from the fitting of electrochemical impedance spectroscopy (EIS) test data. Figure 7 illustrates the second-order ECM employed in this study. U_OCV represents the open circuit voltage of the battery; R₀ is the ohmic resistance; R₁ and R₂ represent the equivalent resistance of the first and the second orders, respectively; C₁ and C₂ represent the corresponding capacity of the time constant for the first and the second orders. The battery impedance can be calculated by Equation (5):

$$\begin{array}{cc}\hfill Z\left(T_b,SOC,f\right)& =\left[R_0+{\displaystyle \frac{R_1}{1+{(2\pi f)}^2{R}_1^2{C}_1^2}}+{\displaystyle \frac{R_2}{1+{(2\pi f)}^2{R}_2^2{C}_2^2}}\right]\hfill \\ & \hspace{1em}-j\left[{\displaystyle \frac{2\pi f·R_1^2{C}_1}{1+{(2\pi f)}^2{R}_1^2{C}_1^2}}+{\displaystyle \frac{2\pi f·R_2^2{C}_2}{1+{(2\pi f)}^2{R}_2^2{C}_2^2}}\right]\hfill \end{array},$$

(5)

where f is the frequency of the current; Z represents the battery impedance. Since the internal heating has an excellent heating uniformity, it is reasonable to assume that no temperature gradient exists inside the battery. According to energy conservation, the temperature evolution of battery T_b can be expressed as follows.

$$m_b{C}_p{\displaystyle \frac{d{T}_b}{dt}}=q_h-q_d,$$

(6)

where m_b and C_p represent the cell mass and specific heat, respectively. q_h and q_d represent the heat generated and dissipated of the cell. Ignoring the impact of transient torque changes on the heat generation, q_h can be calculated by Equation (7).

$$\begin{array}{l}{q}_h=I_d^2\mathrm{Re}(Z){|}_{f=0}+I_h^2\mathrm{Re}(Z){|}_{f=f_h}\\ \mathrm{with}\\ I_d={\displaystyle \frac{3\left|U_{S,drv}\right|I_{drv}\cos \phi }{2U_{dc}{\eta }_e}},I_h={\displaystyle \frac{I_{heat}}{\sqrt{2}}}\end{array},$$

(7)

where I_d and I_h represent the RMS value corresponding to the driving current and the heating current, respectively, observed from the battery side; φ is the power factor of the EM. Re(Z) is the real part of battery impedance. It is the function of SOC, temperature, and current frequency. η_e represents the efficiency of EDS. The dissipated heat q_d can be expressed as follows.

$$q_d=h{A}_b(T_b-T_a),$$

(8)

where h is the heating transfer coefficient. A_b represents the heat exchange area of the battery. T_a represents the ambient temperature. Since the mean value of the heating current is zero, the SOC progression during on-route heating can be determined using the following calculation.

$${\displaystyle \frac{dSOC}{dt}}={\displaystyle \frac{I_d}{C_b}},$$

(9)

where C_b represents the nominal capacity of the battery.

2.4. Elimination of Undesired Torque

As is well known, the heating current through the windings of EM may generate undesired torque, resulting in the vibration or movement of the vehicle. Therefore, it is necessary to analyze the electromagnetic influence caused by the heating current. On neglecting the leakage inductance of the phase windings, the self and mutual inductance of the phase winding can be expressed as follows.

$$\begin{array}{cc}\left\{\begin{array}{c}{L}_{uu}=\frac{{\psi }_{uu}}{i_{u,h}}=L_{s0}+L_{s2}\cos 2\theta \\ L_{vv}=\frac{{\psi }_{vv}}{i_{v,h}}=L_{s0}+L_{s2}\cos 2(\theta -\frac{2}{3}\pi )\\ L_{ww}=\frac{{\psi }_{ww}}{i_{w,h}}=L_{s0}+L_{s2}\cos 2(\theta +\frac{2}{3}\pi )\\ L_{uv}=L_{vu}=-\frac{L_{s0}}{2}+L_{s2}\cos 2(\theta +\frac{2}{3}\pi )\\ L_{uw}=L_{wu}=-\frac{L_{s0}}{2}+L_{s2}\cos 2(\theta -\frac{2}{3}\pi )\\ L_{vw}=L_{wv}=-\frac{L_{s0}}{2}+L_{s2}\cos 2\theta \end{array}\right.& with\hspace{1em}\left\{\begin{array}{c}{L}_{s0}={(\frac{2}{\pi }{N}_{ph}{k}_w)}^2·\frac{\tau l}{p}·{\lambda }_{\delta 0}\\ L_{s2}=\frac{1}{2}{(\frac{2}{\pi }{N}_{ph}{k}_w)}^2{\lambda }_{\delta 2}\end{array}\right.,\hfill \end{array}$$

(10)

where L_xy represents the self of mutual inductance between the EM winding phases x and y. ψ_x is the flux linkage of the winding phase x. i_u,h, i_v,h, and i_w,h are the current components of heating flowing through each phase. θ is the rotor electrical angle. N_ph is the total winding turns of a single phase. k_w is the winding factor. τ denotes the pole pitch of the EM. l is the stack length of EM. λ_δ0 and λ_δ2 are the relative permeance of the air gap corresponding to the zero-order and the second-order harmonics, respectively. Therefore, the inductance matrix of the EM, namely L_S, can be expressed as follows.

$$L_s=\left[\begin{array}{ccc}{L}_{uu}& L_{uv}& L_{uw}\\ L_{vu}& L_{vv}& L_{vw}\\ L_{wu}& L_{wv}& L_{ww}\end{array}\right],$$

(11)

The electromagnetic torque T_em is calculated by Equation (12).

$$T_{em}=-p·{\left[\begin{array}{c}{i}_{u,h}\\ i_{v,h}\\ i_{w,h}\end{array}\right]}^T·\left(L_s·\left[\begin{array}{c}{i}_{u,h}\\ i_{v,h}\\ i_{w,h}\end{array}\right]-{\psi }_f·\left[\begin{array}{c}\sin \theta \\ \sin \left(\theta -{\displaystyle \frac{2\pi }{3}}\right)\\ \sin \left(\theta +{\displaystyle \frac{2\pi }{3}}\right)\end{array}\right]\right),$$

(12)

where p denotes the number of the pole pairs of the EM. ψ_f is the permanent flux linkage of the EM. Neglecting the harmonics caused by PWM modulation, the current component of heating in a single phase can be expressed as follows.

$$i_0=i_{u,h}=i_{v,h}=i_{w,h}={\displaystyle \frac{2}{3}}{I}_{heat}\sin (\omega t),$$

(13)

where ω is the angular velocity of the sinusoidal heating current. t represents the time. By substituting Equation (13) into Equation (12), the electromagnetic torque can be rewritten as follows.

$$T_{em}=p·i_0·\left\{\left.\begin{array}{c}{\psi }_f·[\sin \theta +\sin (\theta -{\displaystyle \frac{2}{3}}\pi )+\sin (\theta +{\displaystyle \frac{2}{3}}\pi )]\\ -\\ i_0·[L_{s2}\cos (2\theta )+L_{s2}\cos (2\theta -{\displaystyle \frac{4}{3}}\pi )+L_{s2}\cos (2\theta +{\displaystyle \frac{4}{3}}\pi )]\\ -\\ i_0·[L_{s2}\cos (2\theta -{\displaystyle \frac{4}{3}}\pi )+L_{s2}\cos (2\theta )+L_{s2}\cos (2\theta +{\displaystyle \frac{4}{3}}\pi )]\\ -\\ i_0·[L_{s2}\cos (2\theta +{\displaystyle \frac{4}{3}}\pi )+L_{s2}\cos (2\theta -{\displaystyle \frac{4}{3}}\pi )+L_{s2}\cos (2\theta )]\end{array}\right\}\right.=0.$$

(14)

According to Equation (14), it can be derived that the torque constantly equals zero regardless of rotor electric angle θ and current phase ωt. In other words, NPBH can inherently eliminate the undesired torque caused by the heating current.

2.5. Decoupling of Heating and Driving Currents

In on-route heating scenarios, it is essential to decouple the current control of heating and driving. Taking the driving current into consideration, the phase current can be reformulated as Equation (10):

$$\left\{\begin{array}{c}{i}_U=i_{u,h}+i_{u,drv}={\displaystyle \frac{2}{3}}{I}_{heat}\sin (\omega t)+I_{drv}\cos (\theta +\varphi )\\ i_V=i_{v,h}+i_{v,drv}={\displaystyle \frac{2}{3}}{I}_{heat}\sin (\omega t)+I_{drv}\cos (\theta -{\displaystyle \frac{2}{3}}\pi +\varphi )\\ i_W=i_{w,h}+i_{w,drv}={\displaystyle \frac{2}{3}}{I}_{heat}\sin (\omega t)+I_{drv}\cos (\theta +{\displaystyle \frac{2}{3}}\pi +\varphi )\end{array}\right.,$$

(15)

where i_U, i_V, i_W are the total current of each phase respectively. i_u,drv, i_v,drv, i_w,drv are the current components of driving for each phase respectively. I_drv is the amplitude of the driving current component. ϕ is the current advanced angle. Upon transforming from the stationary frame to the rotational frame, the currents can be represented as follows.

$$\left[\begin{array}{c}{i}_d\\ i_q\\ i_0\end{array}\right]=C\left[\begin{array}{c}{i}_U\\ i_V\\ i_W\end{array}\right]=\left[\begin{array}{c}{I}_{drv}\cos (\beta )\\ I_{drv}\sin (\beta )\\ {\displaystyle \frac{2}{3}}{I}_{heat}\sin (\omega t)\end{array}\right],\mathrm{with}\hspace{1em}C={\displaystyle \frac{2}{3}}\left[\begin{array}{ccc}\cos \theta & \cos (\theta -{\displaystyle \frac{2}{3}}\pi )& \cos (\theta +{\displaystyle \frac{2}{3}}\pi )\\ -\sin \theta & -\sin (\theta -{\displaystyle \frac{2}{3}}\pi )& -\sin (\theta +{\displaystyle \frac{2}{3}}\pi )\\ {\displaystyle \frac{1}{2}}& {\displaystyle \frac{1}{2}}& {\displaystyle \frac{1}{2}}\end{array}\right],$$

(16)

where i_d, i_q are the currents in the direct axis (D-axis) and quadrant axis (Q-axis) respectively. C represents the Clarke–Park transformation matrix. β is the phase angle of the driving current. According to Equation (12), the electromagnetic torque can be reformulated as follows.

$$T_{em}={\displaystyle \frac{3}{2}}p{i}_q\left[i_d(L_d-L_q)+{\psi }_f\right],\mathrm{with}\hspace{1em}\begin{array}{c}\left[\begin{array}{ccc}{L}_d& & \\ & L_q& \\ & & L_0\end{array}\right]\end{array}=C{L}_s{C}^{-1}$$

(17)

where L_d, L_q, and L₀ are the inductance in the D-axis, Q-axis, and Zero-axis respectively. ψ_f represents the permanent magnetic flux linkage. As can be noticed, i_d and i_q are determined by the amplitude I_drv and the phase angle β of driving current control according to Equation (16), while i₀ is determined by amplitude I_heat and the phase angle ωt of the heating current. There is no influence by i₀ on driving torque T_em according to Equation (14). Consequently, the controls of heating and driving are completely decoupled.

3. Experiment Design and Setup

3.1. Testbench Setup

As shown in Figure 8, an EDS testbench with a battery thermal chamber is built to validate the proposed NPBH working principle and the battery electro-thermal modeling approach. Given that the rated phase current of the EM on the testbench is 10 A, a cylindrical battery with capacity of 4 Ah is selected for the validation experiments of the on-route heating to achieve an observable temperature rise compared to the battery with large capacity. Conversely, a prismatic battery with a capacity of 58 Ah is utilized for the validation of preheating under large currents, as shown in Figure 9. Since no back electromotive force exists in the circuit during the preheating phase, three identical 10 uH discrete inductors with high current-through capability are employed to replace the EM, emulating the phase inductance of the windings. The parameters of the EM on the testbench and the batteries are shown in

Table 1. Parameters of EM.

Parameters	Value	Unit
Type	Surface mounted PMSM	-
Number of pole pairs	4	-
Stator inductance	3.21	mH
Phase resistance	1.38	Ω
Permanent flux linkage	0.1667	Wb
Rated current	10	A
Rated power	1	kW

and

Table 2. Parameters of batteries.

Parameters	Prismatic	Cylindrical	Unit
Electrode material	NMC-C	NMC-C	-
Nominal capacity	58	4	Ah
Charge cut-off voltage	4.25	4.2	V
Discharge cut-off voltage	2.2	2.5	V
Geometric dimensions	Width: 149 Height: 93 Thickness: 27	Diameter: 21 Height: 70 -	mm
Density	2333	2763.4	kg/m3
Specific heat	900	910	J/kg/K
Thermal conductivity	37.4	36	W/m/K

, respectively.

An assembled 24-Series battery pack is shelved in the thermal chamber with a constant ambient temperature. Before the beginning of each test, a 12 h rest duration for the battery is applied to ensure that the interior of each cell is completely frozen. A data collector is utilized to record the voltage of the upper and lower battery modules (1000 sample/s), the current-through battery pack positive wire, the negative wire, the EM neutral wire (1000 sample/s), and the temperatures of the cells (0.5 sample/s), respectively. The 3 K-type thermal couplers are mounted on the body and the tabs of each cell. Their average value is considered as the battery temperature.

3.2. Experimental Design

The experiments are primarily categorized into control validation for the NPBH and electro-thermal modeling validation for the battery, as illustrated in Figure 10. The control validation is further divided into the test groups of heating torque elimination and currents decoupling control. In the heating torque elimination test group, the torque is measured under various heating current amplitudes I_heat and rotor angles. In the current decoupling control test group, the independence of controlled variables and their dynamic responses are observed. On the other hand, the battery electro-thermal model is validated by observing the battery temperature rise under different conditions. Two distinct testing groups are included: (1) on-route heating tests; (2) preheating tests with the optimal strategy [33].

The experiments investigating the elimination of heating torque utilize the cylindrical battery as the power source. The torque is measured under different heating current amplitudes and rotor angles in the stationary state. The angular period of torque fluctuation can be determined by 360°/(4 pairs x 3 phases) = 30°. Detailed experimental conditions are shown in

Table 3. Experimental design of heating torque elimination.

Rotor Angle [°]	Iheat [C]	f [Hz]
0	0.75/1.5/3	100
0/7.5/15/22.5/30	1.5	100

.

The validation for decoupling control consists of four test groups. Each group varies a single variable across three different levels while keeping the other variables constant. Detailed experimental conditions are shown

Table 4. Experimental design of current decoupling control.

n [rpm]	Tem [Nm]	Iheat [C]	f [Hz]
100/150/200	2	1.5	50
100	0/3/6	1.5	50
100	4	0/1.125/2.25	50
100	4	1.5	10/30/50

.

The validation of on-route heating can be divided into the test group under fixed conditions and the test group under combined conditions. In the experimental design of on-route heating under fixed conditions, the rotor speed is maintained constant at 100 rpm. Since variations in either torque or speed will result in changes in I_d, only the influence of different torque levels on battery temperature is observed. Detailed experimental conditions are shown

Table 5. Experimental design of on-route heating under constant conditions.

n [rpm]	Tem [Nm]	Iheat [C]	f [Hz]
100	2/4/8	2	50
100	2	1/1.5/2/3	50
100	2	3	50/100/200

.

Two tests of combined conditions are designed to more realistically emulate the on-route heating scenarios since the rotational speed of the dynamometer on the testbench can be adjusted solely through manual control. The first emulates an aggressive driving behavior. The vehicle starts up with elevated torque, which progressively diminishes as the velocity increases. On the other hand, as the driving current decreases, more current is released to heating the battery. In the final stage of the combined conditions, the effect of current frequency adjusted by the heating strategy is emulated.

The second profile of combined conditions mimics a gentle driving style typical in urban areas. The vehicle starts up with low driving torque, so that more current can be released to heat the battery compared to the first profile. A higher frequency is applied at the beginning to prevent the battery’s terminal voltage from exceeding the cut-off threshold. As the battery temperature gradually rises, the frequency is gradually lowered down to achieve the heat generation as high as possible while maintaining the heating current amplitude. Detailed experimental conditions are shown

Table 6. Experimental design of on-route heating with combined driving conditions.

Driving Style	Stage	Duration [min]	n [rpm]	Tem [Nm]	Iheat [C]	f [Hz]
Aggressive	1	2	100	8	1.5	50
	2	2	200	6	2	50
	3	2	300	4	3	50
	4	2	300	4	3	200
Gentle	1	1	100	4	3	200
	2	1	200	4	3	200
	3	2	300	2	3.6	200
	4	2	300	2	3.6	100
	5	2	300	2	3.6	50

.

For the preheating validation, the heating process is evaluated at SOCs of 30%, 60% and 80%. To simplify the control, the amplitude and frequency of the optimal heating current according to the battery impedance characteristics are regulated with a temperature step of 5 °C [33]. The parameter values of set points for each temperature and SOC are listed in

Table 7. Control parameters of preheating under optimal strategy.

Tb [℃]	Iheat (30% SOC) [C]	f (30% SOC) [Hz]	Iheat (60% SOC) [C]	f (60% SOC) [Hz]	Iheat (80% SOC) [C]	f (80% SOC) [Hz]
−30	3.60	37	3.60	75	2.35	623
−25	3.60	22	3.60	45	2.83	584
−20	3.54	15	3.60	28	2.88	509
−15	3.51	11	3.60	20	3.17	506
−10	3.60	8	3.56	14	3.29	433
−5	3.54	6	3.54	9	3.57	400
0	3.56	2	3.54	3	3.60	303

. It should be noted that the heating current parameters here are optimized based on the EIS impedance characteristics of the fresh battery. As the battery degrades during usage, the heating current parameters should be periodically updated according to the battery’s SOH (state of health).

4. Results and Discussion

4.1. Validation of Torque Elimination

Figure 11 presents the current waveforms through phase and neutral wires with amplitudes of 3 C under preheating conditions. It is evident that the amplitude of the current in the neutral wire of EM is the sum of the current in each phase (three times i₀). Figure 12a illustrates the torque fluctuation at the heating current amplitudes of 0.75 C, 1.5 C, and 3 C, respectively. The result indicates that an increase in the heating current amplitude is associated with a deterioration in torque fluctuations. Additionally, Figure 12b presents the torque fluctuations at rotor angles of 0°, 7.5°, 15°, 22.5°, and 30°. It can be seen that their magnitudes demonstrate a periodic pattern. In both cases, the magnitude of torque fluctuations remains below 0.2 Nm, suggesting that the operational influence of NPBH on electromagnetic torque is acceptable. In practice, due to the constraints of the EM electromagnetic structure, rotor torque fluctuations cannot be completely eliminated; meanwhile, the alternating changes in radial magnetic flux density also cause vibration noise in the stator. Therefore, during long-term use, regular inspections are necessary to ensure that the mechanical connections in EDS remain secure, preventing loosening that could lead to accidents.

4.2. Validation of Decoupling Control of Current

Figure 13 presents the current waveforms through each phase and the neutral wire when the heating and driving components coexist. The picture from the oscilloscope distinctly reveals two eigen frequencies. One corresponds to the rotation speed at 6.67 Hz, and the other, at 50 Hz, is attributed to the heating. Notably, the current component associated with rotation in the neutral wire is nullified due to the displacement of 2π/3 among the three phases, resulting in the exclusive presence of the heating current. Consequently, the current in the neutral wire remains three times the magnitude of i₀.

The independence of the driving and heating controls when there is on-route heating is depicted in Figure 14. Specifically, Figure 14a presents stepwise changes in the rotational speed, increasing from 100 rpm to 150 rpm and subsequently to 200 rpm. Concurrently, Figure 14b illustrates stepwise changes in the torque, rising from 0 Nm to 3 Nm and then to 6 Nm. Notably, these variations in driving parameters do not give any affection to i₀. Similarly, Figure 14c depicts stepwise adjustments in I_heat, from 0 C to 1.125 C and then to 2.25 C, while Figure 14d shows stepwise reductions in f, decreasing from 50 Hz to 30 Hz and subsequently to 10 Hz. Importantly, these modifications in the heating current do not affect the driving torque.

To further demonstrate the decoupled control of driving and heating currents using the proposed heating approach under dynamic driving conditions, a simulation verification is carried out based on the WLTC driving cycle, as shown in Figure 15. The integrated model including the heating and driving control, battery, EDS and vehicle dynamics is built up. Within the first 10 min after vehicle startup, the amplitude of the heating current in the single phase i₀ starts at 50 A and increases stepwise by 10 A every 100 s. The frequency f is set to 50 Hz for the first 5 min and then 100 Hz for the following 5 min.

As shown in Figure 16a,b, during dynamic driving cycle, the proposed control method enables the vehicle to accurately follow the reference speed and torque profile. Meanwhile, the heating current is not affected by the control of the driving current. Throughout the on-route heating process, the current consistently maintains a rapid response to the changes in amplitudes and frequencies, as illustrated in Figure 17a,b.

4.3. Validation of NPBH Performance in On-Route Heating Mode

Figure 18 shows battery temperature variation under constant driving and heating conditions. The initial temperature of the battery is −20 °C and the heating process lasts 10 min for all tests. Specifically, Figure 18a illustrates the battery temperature rise corresponding to the driving torques of 2 Nm, 4 Nm, and 8 Nm, respectively. An increase in driving torque leads to a higher current output from the battery, which in turn elevates the heat generation and accelerates the temperature rise. The battery thermal model can accurately predict the temperature evolution of the battery under different torque levels, with RMS errors of 0.37 °C at 2 Nm, 0.33 °C at 4 Nm, and 0.75 °C at 8 Nm.

Figure 18b shows the temperature rise with different heating current amplitudes of 1 C, 1.5 C, 2 C, and 3 C. At the end of the heating process, the battery temperature reaches −17.39 °C, −14.47 °C, −11.19 °C, and 0.68 °C. The RMS errors between the temperature measured and the temperature calculated at different current amplitudes are only 0.19 °C at 1 C, 0.30 °C at 1.5 C, 0.28 °C at 2 C, and 0.25 °C at 3 C, respectively. Because the heat generation of the battery is proportional to the square of the current amplitude, the temperature at 3 C increases much faster than the others.

Figure 18c demonstrates the influence of heating current frequency on the battery temperature. At the end of the heating process, the temperature reaches 0.68 °C at 50 Hz, −2.94 °C at 100 Hz, and −4.04 °C at 200 Hz, respectively. The RMS errors between the temperature measured and the temperature calculated are 0.59 °C, 0.4 °C and 0.38 °C respectively.

The above results indicate that the battery thermal model can accurately predict the impact of current amplitude and frequency on battery temperature. A reduction in heating current frequency is associated with an increase in the real component of the battery impedance and consequently enhances the heat generation.

The results of the validation test for combined driving conditions are depicted in Figure 19. The RMS error for temperature prediction is 0.53 °C for the aggressive driving style and 0.82 °C for the gentle driving style. These results indicate that the battery electro-thermal model maintains a high fidelity in predicting battery temperature even for the real-world usage.

4.4. Validation of NPBH Performance in Preheating Mode

In this subsection, the preheating with optimal strategy is validated at SOC levels of 30%, 60%, and 80% with an initial temperature of −30 °C. Figure 20 represents the temperature rising processes with a current amplitude of 3.6 C. It can be seen that when the SOC level is at 30% or 60%, the temperature rise processes are quite similar. Their average RTR from −30 °C to 0 °C achieves 4.76 °C/min. However, when the battery SOC level increases to 80%, the temperature rise rate is significantly lower than the two formers. The reason is that EIS characteristics exhibit relatively minor variations within the mid-range of SOC compared to those observed at both high and low SOC. Specially, at high SOC levels, the battery OCV approaches the charging cut-off limit. Consequently, the frequency of heating current is substantially increased to reduce the impedance of the battery, ensuring the compliance with voltage constraints while maximizing the heat generation.

4.5. Comparison of Different Techniques

To demonstrate the benefits of the NPBH method, a systematic comparison of the existing technologies is presented in

Table 8. Comparison of existing technologies.

Method	RTR [°C/min]	Energy Consumption [%/°C]	Torque Elimination Method	On-Route Heating	Extra Components	Cost
Conventional Drive Circuit with Pulse Current [28]	2.88	-	Set Iq = 0	Support	None	Low
On-Board AC Heater [22]	3.39	0.25	No need	Not support	At least 1 switch per module and extra inductors	High
TMSI [30]	8.6	-	Set Iq = 0	Not support	2 switches	High
IBSH [31]	3.45	0.201	Rotor position θ = kπ (k = 0, 1, 2, …)	Not support	1 or 2 switches	Medium
NPBH [33]	4.76	0.2	No need	Support	1 switch	Medium

, evaluating heating performance, energy consumption, functional diversity, as well as complexity and cost. The NPBH demonstrates not only a high RTR but also a broader compatibility with the heating mode in comparison to alternative approaches. Furthermore, this new approach is easy to implement because it does not require specialized torque elimination control or the determination of a particular rotor stall position. Regarding the extra component required, the NPBH only adds one switch, which greatly reduces the system complexity as well as the modification cost.

5. Conclusions

This study proposes a novel battery self-heating method, known as the NPBH, which is compatible with both preheating and on-route heating, and delivers high-rate and uniform warming. It markedly reduces the complexity and cost of the battery on-board AC heater. An EDS testbench with a thermal chamber for the battery is built to validate the proposed method. The experimental results demonstrate the following:

• The proposed NPBH technique provides efficient heating for LiBs with rapid speed.
• The NPBH offers a simpler and more reliable approach in heating current control. The undesired electromagnetic torque caused by the heating current can be inherently eliminated regardless of the rotor position.
• The control of heating and driving is completely decoupled, which enables the NPBH to be compatible with both preheating and on-route heating modes, while also facilitating straightforward adaptation to a range of heating strategies.
• The proposed electro-thermal model can estimate the battery temperature with a high fidelity. The RMS errors of battery temperature under all the constant and combined driving conditions are less than 1 °C.

In summary, based on a comprehensive evaluation across distinct conditions, the NPBH demonstrates a great practical utility. A hybrid heating strategy combining preheating and on-route heating based on the NPBH method can further reduce the time consumed by heating while enhancing the battery performance on driving. In practice, inconsistencies in the switching transistor may cause unbalanced currents, leading to inverter degradation issues, which need to be paid attention. These will be the key focus of the future work in this article.