The circuit structure of the two-stage V2G vehicle-mounted bi-directional converter is shown in Fig. 1, composed of a filter, front-stage AC-DC converter, cascade bus capacitor, and post-stage DC-DC converter. The front AC-DC converter can convert the power grid voltage to the stable DC voltage of the system bus and carry out power factor correction (PFC). The post-stage DC-DC converter uses the system bus to adjust the voltage gain and realizes the charge and discharge management control according to the battery management system and V2G scheduling. This paper mainly studies the closed-loop control of the front-stage AC-DC converter of the V2G vehicle-mounted bi-directional converter constructed by totem-pole bridgeless PFC circuit topology.

As shown in Fig. 1, the totem-pole bridgeless PFC converter is composed of an inductor L_s, high-frequency switches S₁ and S₂, power frequency switches S₃ and S₄, and capacitor C₁. The converter operates in current continuous mode (CCM), which can reduce inductance current ripple and improve power factor.

High-frequency switch tubes S₁ and S₂ use switching frequency as the cycle to realize the storage of inductor L_s energy and load energy supply, while power frequency switch tubes S₃ and S₄ work at 50 Hz switching frequency to provide energy continuation channel.

According to the working state of the inductor and the working cycle of the input AC voltage, the working mode of the system in the CCM is analyzed as follows: the working mode of the energy storage of the inductor L_s when the grid voltage is positive is shown in Fig. 2a, at this time, switch tubes S₁ and S₃ are off, and the current passes through inductive L_s, switch tubes S₂ and S₄ to form a closed circuit for inductive energy storage. Load R is CLLC resonant converter powered by capacitor C₁.

Fig. 2b is a working mode diagram of the inductor L_s in the energy release stage in the positive half cycle. S₄ remains on during the positive half cycle of the grid, S₂ is off and S₁ is on, the inductor begins to release energy, and the energy released by the inductor supplies power to R and the capacitor through the AC grid. The voltage on the load side is a dual-frequency pulsating DC voltage.

Fig. 3 shows the working mode diagram of the negative half-cycle circuit. When the inductor stores energy, switches S₁ and S₃ are turned on, and current flows through switches S₁ and S₃ to form a closed loop for the inductor to store energy. When the inductor releases energy, switch S₁ is turned off, and S₂ is turned on, forming a closed loop for inductor energy release.

Take the energy storage and release state of the inductor as a switching cycle T. If the duty cycle is set as d and input voltage e is denoted as v_in, then the state equation of the circuit at the inductive energy storage stage is:

(1)[dis(t)|ddtdvBUS(t)|ddt]=d[000−1RC1][is(t)|dvBUS(t)|d]+d[1Ls0][vin(t)|d]

The circuit state equation of the energy release phase of the inductor in the 1-d control cycle is:

(2)[dis(t)|1−ddtdvBUS(t)|1−ddt]=(1−d){[0−1Ls1C1−1RC1][is(t)|1−dvBUS(t)|1−d]+[1Ls0][vin(t)|1−d]}

Combining Eqs. (1) and (2), a steady-state relationship expression between state vector and input vector in switching control cycle T is obtained:

(3)[dis(t)dtdvBUS(t)dt]=[0d−1Ls1−dC1−1RC1][is(t)vBUS(t)]+[1Ls0][vin(t)]

The small-signal disturbance is added to the input of the circuit and each state variable, and the small signal model is solved by the disturbance method. The expression of each disturbance is:

(4){is(t)=Is(t)+is(t)^vBUS(t)=VBUS(t)+vBUS(t)^d=D+d^vin(t)=Vin(t)+vin(t)^

In Eq. (4), I_s(t), V_BUS(t), D and V_in(t) are the direct current (DC) components of each state variable, is(t)^, vBUS(t)^, d^ and vin(t)^ are small signal disturbance components of each state variable. By introducing Eq. (4) into Eq. (3), we can get:

(5)[d(Is(t)+is(t)^)dtd(VBUS(t)+vBUS(t)^)dt]=[0(D+d^)−1Ls1−(D+d^)C1−1RC1][Is(t)+is(t)^VBUS(t)+vBUS(t)^]+[1Ls0][Vin(t)+vin(t)^]

Ignoring the high-order components and equivalently reducing the DC components at both ends in Eq. (5) according to the steady-state relationship, the equation expression of the final small-signal model can be obtained as:

(6){is(s)^=d−1LsvBUS(s)^+1Lsvin(s)^+1LsvBUSd(s)^vBUS(s)^=1−dC1is(s)^−1RC1vBUS(s)^−1C1Isd(s)^

From Eq. (6), the frequency domain equation of the system can be obtained as:

(7)is(s)^=(sC1+1R)vin(s)^+(sC1+1R)VBUSd(s)^+(1−d)Isd(s)^s2C1Ls+LsRs+(1−d)2vBUS(s)^=R(1−d)vin(s)^+R(1−d)VBUSd(s)^−sRLsIsd(s)^s2RC1Ls+sLs+R(1−d)2

According to Eq. (7), the transfer function expression between the output voltage, current, and duty cycle of the system can be obtained as follows:

(8){GidCCM(s)=is(s)^d(s)^=(1−d)RVBUS−sLsRIss2RC1Ls+Lss+R(1−d)2GvdCCM(s)=vBUS(s)^d(s)^=(sC1+1R)VBUS+(1−d)Iss2C1Ls+LsRs+(1−d)2

The front-stage circuit of the V2G bidirectional converter adopts double closed-loop control. The outer voltage loop stabilizes the output bus voltage, and the inner current loop realizes the function of the PFC. The structure of the double closed-loop controller is shown in Fig. 4. The flow chart of Fuzzy LADRC control is shown in Fig. 5. After sampling, the DC bus voltage v_BUS output by the totem-pole bridgeless PFC converter is subtracted from the reference voltage v_ref, and the error value v_err is obtained. The error value v_err passes through the control output control quantity of the voltage outer loop Fuzzy LADRC, The control quantity is multiplied with the AC sinusoidal half-wave to obtain the current reference quantity i_ref consistent with the phase of the input voltage. The reference value i_ref is subtracted from the sampling current i_s of the inductor to obtain the current error value. The current error value is input to the PI compensator of the inner current ring and output control quantity. After limiting the amplitude, the microprocessor generates pulse modulation waves to realize the control of switch tubes S₁~S₄ and finally realize the double closed-loop control of the V2G front-stage totem-pole bridgeless PFC converter.

The core idea of LADRC is to use LESO to estimate the internal disturbance caused by imprecise mathematical models and parasitic parameters of devices and the external disturbance caused by environmental factors. By estimating and compensating the total disturbance of the system in real-time, the controlled object is compensated as a linear integrator in series [25]. Fig. 6 is the structure diagram of the LADRC controller used in the system.

The differential equation of the LADRC second-order controlled object is:

(9)y..=bu+w−a0y−a1y.where, u and y are the input and output of the system respectively, w is the disturbance of the system and both a₁ and a₀ are unknowns, the known part of b is denoted as b₀.

Set the total disturbance of the system as:

(10)f=bu−b0u+w−a1y.−a0y

According to the totem-pole bridgeless PFC mathematical model and power balance equation, the following equation can be obtained [25]:

(11)vin⋅is=vBUS⋅C1dvBUSdt+vBUS2R

Let x₁ = vBUS2, then the following equation can be obtained according to Eq. (11):

(12)dx1dt=2vinCis−2x1RC1

Let b0=−2x1RC1, w=2vinC1; then we can find that load R is included in the system disturbance. When load R changes, LESO can estimate the system disturbance in real-time and effectively compensate for the impact of R change on the system. Taking the state variables x₁ = y, x₂ = y. and x₃ = f, the state equation expression of the system can be obtained as [26]:

(13){y=x1x˙1=x2x˙2=b0u+x3x˙3=h

According to Eq. (13), the expression of LESO is:

(14){z˙1=−β1(z1−y)+z2z˙2=−β2(z1−y)+z3+b0uz˙3=−β3(z1−y)where z₁~ z₃ are state variable matrices, then, as long as the appropriate observer gains β1, β2 and β3 are selected, the linear extended state observer can track each state variable in Eq. (13) in real-time. The disturbance compensation of the system is taken as:

(15)u=u0−z3b0

The expression of the proportional differential controller is:

(16)u0=kpr−kpz1−kdz2where r is the reference signal, k_p is the proportional gain of the controller, k_d is the differential gain of the controller.

According to Eqs. (9)–(16), the transfer function expression of LADRC control system can be obtained as follows:

(17)G(s)=kps2+kds+kp

According to Eq. (17), the parameter design of the controller and observer is completed by using the pole assignment method [27], and the characteristic equation and parameters of the state observer are obtained as follows:

(18){λ(s)=s3+β1s2+β2s+β3β1=3w0,β2=3w02,β2=w03kp=wc2,kd=2wcwhere w_o represents the observer bandwidth, w_c represents the controller bandwidth.

After the above analysis, because the totem-pole bridgeless PFC mathematical model makes some parameters of LADRC known, the parameters to be tuned for LADRC are only w_o and w_c. In engineering, w_o = (3~5) w_c is generally taken.

Electric vehicle batteries are easily affected by ambient temperature and SOC, which leads to significant changes in their electrochemical characteristics, and the performance of the system can be improved by adaptively adjusting the controller parameters. Therefore, in this paper, the LADRC proportional gain coefficient kp is changed timely by introducing fuzzy control. The proportional gain coefficient kp can compensate for the observation error of the state observer, thereby improving the system’s robustness. The method is to calculate the difference E between the output voltage and the given voltage and the change rate of the voltage difference ΔE as the input of the fuzzy controller, the proportional gain Δk_p as the output, and then according to the voltage difference E and the difference change rate ΔE adaptively adjust the proportional gain coefficient k_p. The principle is: the proportional gain coefficient at the time (T−1) is k_p (T−1), and the proportional gain adjustment value obtained by fuzzy reasoning is recorded as Δk_p. Then, the proportional gain coefficient of LADRC at time T can be obtained as k_p (T) = k_p (T−1) + Δk_p. The structure of the fuzzy controller is shown in Fig. 7.

According to the experience of simulation and debugging, the range of the DC bus voltage difference E and its difference rate of change ΔE is [−12, 12]. The range of the output Δk_p is [−6, 6]. The fuzzy subsets are taken as seven subsets such as NB (negative large), NM (negative medium), NS (negative small), Z0 (zero), PS (positive small), PM (positive medium), and PB (positive large).

The fuzzy rules formulated according to the experiment are shown in Table 1. Based on the fuzzy rules in Table 1, the relationship surface diagram with system error E and error change rate as input and KP as output can be obtained, as shown in Fig. 8.

The optimal parameters of PI controller are as follows: voltage outer loop K_p = 9.95, K_i = 10000, current inner loop K_p = 3.1, K_i = 30. The LADRC voltage outer loop parameters to be adjusted include observer bandwidth w_o and controller bandwidth w_c. Considering their optimal values, w_o is 6050 and w_c is 1600. The system simulation parameters are shown in Table 2.

In order to verify the robustness of the proposed control strategy and the effectiveness of reducing harmonic distortion rate, Fuzzy LADRC and PI algorithms are used to compare the simulation results of the system startup, load mutation, and reference voltage mutation, respectively. Figs. 9a–9c, respectively, show the amplitude waveforms of input voltage and current at the startup time of the system and the DC voltage output waveform under the Fuzzy LADRC and PI control strategy. We can find that the input current and the input voltage are always in the same phase, and the PFC is realized; Under the Fuzzy LADRC control strategy, the system can quickly reach a stable voltage of 400 V with a small overshoot. The control steady-state recovery time is 150.1 ms, less than the recovery time under PI control of 240.4 ms. The steady-state current THD of the totem-pole bridgeless PFC controlled by Fuzzy LADRC is 2.39%, and the steady-state current THD of PI control is 3.35%. The comparison of the startup performance of the system under the two control algorithms is shown in Table 3, which verifies that the steady-state performance of the Fuzzy LADRC algorithm is better than the PI algorithm.

In order to test the response capability of the system, the reference value of the system’s output voltage is reduced from 400 to 350 V at 0.5 s, and the simulation results are shown in Fig. 10.

We can see from Fig. 10a that at the moment of a sudden change of load voltage, the change amplitude of the input current of the system under the Fuzzy LADRC control strategy is small, which effectively avoids the impact of impulse current on the system. We can see from Figs. 10b and 10c that when the output reference voltage suddenly changes, the Fuzzy LADRC controller has a faster response speed and stronger anti-interference ability. Its steady-state time is 307.7 ms, and the output voltage oscillation range is 27.2 V, while the steady-state time under PI control is greater than 400 ms and the output voltage oscillation range is 31.91 V. According to Figs. 10d and 10e, we can see that under the Fuzzy LADRC control strategy, the THD of the input current in the steady state is 1.86%, and the THD of the input current in the steady state under the PI control strategy is 2.46%. The simulation results show that Fuzzy LADRC can effectively reduce the THD and steady-state recovery time. The system performance comparison when the system output voltage suddenly changes under the two control algorithms is shown in Table 4.

Fig. 11 shows the simulation waveform when the system's load is suddenly reduced from 40 to 20 Ω at 0.5 s. As can be seen from Fig. 11a, due to the observation and compensation effect of the Fuzzy LADRC on the load, the change of the system input current is gentler at the time of sudden load change, so the power fluctuation of the system is small. Figs. 11b and 11c show the output voltage waveform of the system when the load changes suddenly under the two control algorithms. It can be seen that the output voltage under the two control methods has an inevitable fluctuation; under the Fuzzy LADRC control strategy, the system reaches a steady state after 162.9 ms, and the output voltage oscillation range is 33.53 V. However, under PI control, the system needs 223.7 ms to reach a stable voltage output state, and the oscillation range of the output voltage is large, which is 45.9 V. Figs. 11d and 11e show the input current THD under Fuzzy LADRC control and PI control, respectively; we can see that the THD under Fuzzy LADRC control is only 1.66%, which is less than the value of PI control (2.67%). The system performance comparison of the two control algorithms in case of sudden load change is shown in Table 5.

According to the simulation results of the system under different working conditions, we can find that the Fuzzy LADRC control strategy can effectively improve the dynamic and steady-state performance of the totem-pole bridgeless PFC topology circuit and effectively reduce THD. Simulation results verify the effectiveness of this method.

Table 6 compares the inhibition ability of THD under recent research results. We can find that the method in this paper has a strong THD suppression ability, which plays a vital role in improving the performance of the V2G bidirectional converter.

We have developed a 3 kW V2G bidirectional converter to verify the control effect of the proposed method in practical application. The experimental platform and prototype are shown in Figs. 12 and 13, respectively, and the prototype parameters are shown in Table 7.

Fig. 14 is the waveform of the system input voltage and inductance current; we can find that the voltage and current remain in phase. Power factor correction is realized.

When the output DC voltage is 400 V, and the load changes from 200 to 100 Ω, the comparison of voltage and current under the two control methods is shown in Fig. 15. We can find that the voltage fluctuation range of the PI controller is 55 V, and the steady state is restored within 188 ms, while the voltage fluctuation range of the Fuzzy LADRC controller is only 28 V. The steady state is restored after 93 ms.

When the output voltage is 400 V and the load changes from 200 to 400 Ω, the experimental waveform is shown in Fig. 16. We can find that the voltage fluctuation amplitude of the Fuzzy LADRC control is 17 V, which is restored to the reference voltage after 91 ms, the voltage fluctuation amplitude of the PI control is 45 V, and the steady-state recovery time needs 152 ms. We can find that the Fuzzy LADRC has a faster adjustment time, can compensate for load disturbance, and has better robustness.

When the load is 100 Ω, the experimental waveform of the output voltage from 400 to 450 V is shown in Fig. 17. The experimental waveform of the output voltage from 400 to 350 V is shown in Fig. 18.

According to Figs. 17 and 18, We can see that the Fuzzy LADRC has faster regulation speed when the output voltage changes, which are 135 and 164 ms, respectively. Moreover, the voltage fluctuation is lower, 21 and 32 V, respectively. In contrast, the PI regulation time is relatively slow, and the voltage fluctuation is large; the regulation time is 284 and 272 ms, respectively. Moreover, the voltage fluctuation is 48 and 53 V, respectively.

The experimental results show that the control method in this paper has more robust adaptability, can compensate for the unknown disturbance in real-time, and the output voltage is smoother when the working condition changes.