https://doi.org/10.6113/JPE.2019.19.6.1393

ISSN(Print): 1598-2092 / ISSN(Online): 2093-4718

Power Flow Control of Four Channel Resonant Step-Down Converters

Lilla Litvani^* and Janos Hamar^†

^†,*Dept. of Automation and Applied Informatics, Budapest University of Technology and Economics, Budapest, Hungary

Abstract

This paper proposes a new power flow control method for soft-switched, four channel, five level resonant buck dc-dc converters. These converters have two input channels, which can be supplied from sources with identical or different voltages, and four output channels with arbitrary output voltages. They are specially designed to supply multilevel inverters. The design methodology for their power flow control has been developed considering a general case when the input voltages, output voltages and loads can be asymmetrical. A special emphasize is paid to the limitations and restrictions of operation. The theoretical studies are confirmed by numerical simulations and laboratory tests carried out at various operation points. Exploiting the advantages of the newly proposed power control strategy, the converter can supply five level inverters in dc microgrids, active filters, power factor correctors and electric drives. They can also play an interfacing role in renewable energy systems.

Key words: Design, Multichannel converter, Power flow control, Resonant converter, Soft switching, Step-down dc-dc converter

Manuscript received Feb. 6, 2019; accepted Jun. 27, 2019

Recommended for publication by Associate Editor Jae-Beum Lee.

^†Corresponding Author: litvani.lilla@aut.bme.hu Tel: +36 (1) 463-2337, Budapest University of Technology and Economics

^*Dept. Autom. Applied Inform., Budapest Univ. Tech. Economics, Hungary

Ⅰ. INTRODUCTION

Resonant DC/DC converters have recently drawn a lot of attention in various application fields due to their specific advantages. Among these advantages, zero voltage and zero current switching (ZVS and ZCS), high efficiency, low electromagnetic interference (EMI), improved performance and high power density make them popular in DC microgrids, renewable energy systems and switched mode power supplies. Several papers have been published on different converter topologies for electric vehicles [1]-[3]. In fuel cells, beside a simple control, the power semiconductors require a low voltage stress, while the DC bus needs a higher constant voltage. In order to achieve this, a three-level, H-type structural boost converter was created to provide a wide voltage-gain range [4]. For DC microgrid applications, voltage-balancing and battery state of charge adjusting are important requirements for an applied converter. Several control strategies have been proposed to ensure these criteria [5], [6]. For battery charging applications, a high efficiency design method has been proposed, where lithium-ion battery cells have been used due to their high current and voltage rates, which results in a high power density [7]. A parameter selection method was proposed to implement multi-element resonant converters after four design steps. The achieved converter allowed for an efficiency as high as 96.9% [8].

Since the application field of DC/DC converters is so wide, several different topologies have been presented with various additional advantages. Zero-voltage and zero-current switching topologies allow for a decrease of the switching losses [9]- [11]. In addition to ZVS, voltage regulation can be reached over a wide range of loads by the hybrid control of the frequency and duty ratio, which results in an enlarged conversion efficiency [12]. Using only one active switch, a leakage-energy recycling dual DC/DC flyback converter has been introduced [13]. Another single switch topology has been proposed, where the input source and the clamped capacitor are in series in order to transfer energy towards the load through dual voltage multiplier cells. As a result, the converter is able to produce a very high voltage while having a high conversion efficiency [14]. A reduced-size, two-switch converter was proposed with a non-isolated high voltage gain, which results in a very simple circuit with continuous input current and a small ripple [15]. A parallel loaded resonant converter providing a wide output voltage range was introduced in [16]. By modifying the transformer turns ratio, it can become applicable in high power environments. A two channel converter family was proposed, where the energy was able to flow from the input to the output within the channels, and also among the two channels. These converters were analyzed in both symmetrical and asymmetrical conditions [17], [18].

This paper proposes a new approach to control the power flow of the four channel buck converter introduced in [19]. Based on experience, the conventional duty ratio based control of this converter faces difficulties since changing the duty ratio of a single switch affects the power flow in multiple channels simultaneously. On the other hand, the newly proposed method enables the direct control of each channel’s power flow without any unwanted consequences for the rest of channels. In this paper, general cases of asymmetrical input voltages and output loads are assumed, and the aim is to produce predefined output voltages. This requires overall control of the power exchange among the converter channels. Efficient control strategies are presented for various use-cases. The presented method can be beneficially applied when using a converter to feed five level voltage source inverter (VSI) systems, which facilitates the reduction of their harmonic distortion.

The outline of the paper is as follows. Section II briefly summarizes the operation of a converter, which is crucial to understanding the control strategies. Section III derives a steady state analysis of the converter with energy equations for the discontinuous current conduction mode (DCM). Section IV presents a design method for power flow control. Section V concentrates on the proposed control in partially asymmetrical cases. Control characteristics are presented in Section VI. Section VII shows the simulation and experimental results. Finally, some conclusions are presented in Section VIII.

Ⅱ. BASIC OPERATION OF THE CONVERTER

A circuit diagram of a four-channel buck converter can be seen in Fig. 1. The operation of the converter is briefly summarized in this paper. Further information can be found in [19]. During the investigation of the lossless components, ripple free input and output voltages are presumed, and the commutation intervals are neglected among the switches. In the analytical study, one switching cycle is examined, which is built up from three time intervals (0p, 1p, 2p). T_s is the switching period, and is the resonant angular frequency. Steady-state operating waveforms of the converter in the DCM are shown in Fig. 2. They include the resonant currents i_Lp and i_Ln of both inductors and the resonant voltage of the switched capacitor v_c.

Fig. 1. Four-channel buck converter.

Fig. 2. Time function of the capacitor voltage and inductor current.

Interval 0p [0 ＜ ωt ＜ α_p] (see the red continuous line in Fig. 3). Here, the controlled switch S_p is turned on in order to charge the switched capacitor C and to energize the inductor L in the positive (p) channel. The switches S_cp1 and S_cp2 are turned off. The voltage of the capacitor v_c sinusoidally increases, while the sinusoidal current flows through the circuit V_ip-S_p-L-D_cp-V_op1-V_op2-C. The instantaneous value of the inductor current at the end of this interval is i_c(α_p)=i_Lp(α_p)=I_Lpa.

Fig. 3. Current paths during switching intervals.

Interval 1p [α_p ＜ ωt ＜ α_cp] (see the blue continuous line in Fig. 3). At the beginning of this interval, the controlled switch S_p is turned off, while S_cp1 is turned on using the energy of L to feed the output. V_c remains constant in this interval, while the current flows in the circuit L-D_cp-V_op1-S_cp1. As a result, i_Lp linearly decreases, and at the end of this interval i_Lp(α_cp)=I_Lpb.

Interval 2p [α_cp ＜ ωt ＜ α_ep] (see the green continuous line in Fig. 3). Both S_p and S_cp1 are turned off, and S_cp2 is turned on. When the current is flowing in the circuit L- S_cp2-V_op2-D_p, all of the energy of the inductor is depleted, and the current i_Lp becomes zero at the extinction angle α_ep, that is, i_Lp(α_ep)=I_Lpc=0. It remains in this state until the end of the period T_s. It is important to note, that this only holds true for the discontinuous conduction mode (DCM). In the continuous conduction mode (CCM), the inductor current cannot reach zero before the beginning of the next period.

Additionally, there is a special operational state of the converter, called the protection mode (see the purple continuous line in Fig. 4 for channel p, and the dashed line for channel n), which is due the voltage of the capacitor reaching the input voltage, V_cp=V_ip (or V_cn=-V_in). In this case, the diode D_p (or D_n) turns on making the inductor’s current flow in the circuit L- D_cp- V_op1-V_op2 -D_p. The purpose of this operation mode is to avoid overvoltage of the capacitor and to protect the switches in the circuit in case of a failure.

Fig. 4. Protection mode.

The operation intervals at the negative channel are the same as those written above (see the dashed lines in Fig. 3), only shifted by half a period, . The output voltages can be directly controlled by the switching frequency or the conduction angles of the controlled switches.

In the paper, positive and negative sequence symmetrical components are introduced, where x_p and x_n are the same kind of variables or parameters (e.g. voltages) in channels p and n, respectively. Examples of symmetrical components are as follows: positive sequence input voltage and negative sequence input voltage . Since V_cn＜0, the positive sequence capacitor voltage is , and the negative sequence capacitor voltage is . V_cp and V_cn are the peak values of the capacitor voltage time function (see Fig. 2).

Ⅲ. ANALYTICAL STUDY BASED ON ENERGY EQUATIONS

In this section, energy pulse equations are analyzed for one switching period, T_s. The equations are mostly derived for channel p, unless those for channel n are crucial for understanding. However, using the equations of channel p, the corresponding channel n equations can easily be produced by the following formal parameter substitutions: x_p ↔ x_n (except V_cp ↔ -V_cn ), x₁ ↔ x₁ and x₂ ↔ -x₂. During the analysis, the following per unit parameters are used: , , , , , , , , , , and , where is the resonant frequency, is the characteristic impedance and is the unit of the current. When R_p1=R_p2, R_p1^*=R_p2^*=R^* and when V_op1=V_op2, V_op1^*=V_op2^*=V_op1,2^*.

The total input energy w_ip is delivered by the current pulse i_cp = i_Lp feeding the converter, while 0 ＜ ωt ＜ α_p. The input energy taken from source p can be calculated from the capacitor current and voltage as follows:

                  (1)

Similarly:

                                    (2)

Supposing lossless operation, the total input energy is equal to the total output energy:

                                       (3)

Assuming the input voltages remain constant, V_c1 is a good candidate for controlling the input energy.

The switched capacitor plays an energy steering role among the input channels p and n.

                                           (4)

The energy that continues toward the output in channel p (n) and is dissipated on the loads is:

                (5)

               (6)

The ratio of the energy transferred in channel p, when compared to the total output energy, can be expressed by dividing (5) by (3) as follows:

           (7)

similarly:

           (8)

This shows that V_c2 is a good candidate for controlling the energy exchange among the input channels p and n.

In the DCM, the output energy pulses in channels p₁ and p₂ for the above described intervals, which can be calculated as follows:

0 ＜ ωt ＜ α_p

                                 (9)

                                  (10)

α_p ＜ ωt ＜ α_cp

                                 (11)

                                                                   (12)

α_cp ＜ ωt ＜ α_ep

                                                                   (13)

                                                   (14)

By adding equations (9), (11) and (13) and (10), (12) and (14), the energy transferred through channels p₁ and p₂ and dissipated on the loads can be calculated for one switching period.

                          (15)

                                    (16)

The total output energy of channel p can be calculated by adding equations (15) and (16). This is equal to the energy (w_op) supplied to channel p after deducting the capacitor’s energy change [see (5)]:

               (17)

From (17),  can be expressed as:

                                  (18)

Substituting (18) into (15), the following equation can be expressed for the output energy w_op1:

                    (19)

Equations (16) and (19) indicate that I_Lpb is a good candidate to control the energy exchange among output channels p₁ and p₂. Similarly, I_Lnb is a good candidate among channels n₁ and n₂.

V_op2 can be expressed from (16) as follows:

                              (20)

Substituting (20) into (19), V_op1 can be calculated as follows:

                               (21)

where:

                   (22)

Instead of energy pulses, average powers are used exclusively from now on, which can be directly calculated by multiplying the energy pulse values with the switching frequency so that: .

Based on (20) and (21), it can be concluded that the output voltages (and the powers) are determined by the inductor currents I_Lpb and I_Lnb as well as the positive and negative sequence switched capacitor peak voltages, V_c1 and V_c2. Consequently, these four parameters are considered as the control variables (f_s is kept constant).

Fig. 5 shows how they influence the power flow of the converter. Based on (3), V_c1 specifies the amount of power fed into the converter. V_c2 determines how this power is shared among input channels p and n (7) and (8). The inductor currents I_Lpb and I_Lnb enable the power exchange among output channels p₁, p₂ and n₁, n₂, respectively (16) and (19).

Fig. 5. Power flow from the inputs towards the outputs.

Ⅳ. DESIGN CONSIDERATIONS

This section discusses the procedure to design the power flow control. First, the calculation of the control variables V_c1, V_c2, I_Lpb and I_Lnb is introduced considering arbitrary steady-state operation points in the DCM. Afterwards, the steps are explained to decide if the operation point is feasible or not. Fig. 6 shows a circuit block diagram to generate the turn on and turn off signals of the controlled switches. The calculated values of the control parameters are denoted as reference values in the figure [V_c1,ref, V_c2,ref, I_Lpb,ref and I_Lnb,ref], which are compared to the instantaneous values of the respective variables during the operation [v_c(t), i_Lp(t) and i_Ln(t)]. Thus, the turn-on and turn-off intervals of the switches are indirectly controlled.

Fig. 6. Generating switching signals.

A. Calculation of Power Flow Control Parameters

The values of L and C determine the resonant frequency. Since the two input currents can only flow in separate intervals, the simultaneous turn-on of the controlled switches S_p and S_n must be avoided. This can be accomplished by choosing the switching frequency so that: . On the other hand, an increase of f_s is preferred to reduce the output voltage ripple and to avoid degradation of the dynamical performance of the converter. Hence, the switching frequency is chosen as: .

For the design, prior knowledge of the following parameters is assumed from the system specifications: V_ip, V_in, V_op1, V_op2, V_on1, V_on2, R_p1, R_p2, R_n1 and R_n2.

The four output powers can be easily calculated by using the well-known equation: .

Since lossless circuit components are assumed, the total input energy (average power) is equal to the total output energy (power), w_i=w_o and P_i=P_o. This power is determined by the control variable V_c1, which can be expressed from (3) as follows:

                                       (23)

The power exchange among the input channels p and n is controlled by the variable V_c2, which can be expressed from (7):

                                           (24)

The control parameter I_Lpb can be calculated from (16) using (3).

                                                       (25)

Similarly, I_Lnb is:

                                                       (26)

B. Operation Limits

Various operational limits need to be taken into consideration when designing the control. The peak voltages of the capacitor are limited by the available maximum commutation angles and . In this case, the capacitor current and the choke current waveforms are half sinusoidal. In addition, the instantaneous values of the currents I_Lpa and I_Lpb (and similarly I_Lna and I_Lnb) are zero (see Fig. 2). By substituting I_Lpa = I_Lpb =0 into (15) and (16) (and similarly I_Lna = I_Lnb =0 into the n channel equivalent equations), the capacitor voltage V_c1 is limited as follows:

                       (27)

By substituting I_Lpa=0 into (18) (and similarly I_Lna = 0 into the n channel equivalent equation), the limitations of V_c2 can be obtained as follows:

                       (28)

The inductor currents I_Lpb and I_Lnb have a limit since they cannot be higher than I_Lpa and I_Lna (see Fig. 2), respectively. From (18):

             &sp;           (29)

                         (30)

The converter operates in the protection mode when V_cp=V_ip or V_cn=-V_in. To allow for the proper control of the converter, the protection mode has to be avoided. Thus, and .

Ⅴ. SPECIAL ASYMMETRICAL CASES

To reveal the effects of control variables, the following special asymmetrical cases are examined: asymmetrical output voltages, asymmetrical loads and asymmetrical input voltages. At the same time, only one quantity is considered to be asymmetrical, while the remaining ones are considered to be symmetrical. The relating control characteristics are discussed in Section VI.

A. Asymmetrical Output Voltages

At this point, V_op1≠V_op2. However, V_op1=V_on1, V_op2=V_on2, V_ip=V_in and R_p1=R_p2=R_n1=R_n2. Substituting them into (7) and since V_ip=V_i1, it follows that V_c2=0. Substituting the per unit values into (16), I_Lpb^* in the function of V_op2^* can be calculated as:

                                              (31)

Substituting the per unit values into (21), I_Lpb^* can also be calculated in the function of V_op1^* as:

                                                      (32)

where: 

                                                      (33)

                 (34)

where:

                                                            (35)

B. Asymmetrical Loads

At this point, the case where R_p1≠R_p2, but R_p1=R_n1, R_p2=R_n2, V_ip=V_in=V_i1 and V_op1=V_op2=V_on1=V_on2 is investigated. Based on (7) V_c2=0.

Substituting the per unit values into (16), I_Lpb^* in function of R_p2^* can be calculated as:

                                           (36)

Similarly, I_Lpb^* as a function of R_p1^* can be expressed from (21) as:

                                    (37)

C. Asymmetrical Input Voltages

In this case, V_ip≠V_in, V_op1=V_op2=V_on1=V_on2, R_p1=R_p2=R_n1= R_n2 and all of the output powers are identical. At this point, is based on (7) and:

                                                                       (38)

This shows that the asymmetry in the input voltages can be efficiently compensated by V_c2.

The output power (and voltage) can be controlled by V_c1 [see (23)]:

                                                   (39)

I_Lpb and I_Lnb are determined by (25) and (26). As long as V_i1 remains constant, no adjustment is required at these control variables. If V_i1 changes, I_Lpb and I_Lnb need to be adjusted accordingly.

D. Symmetrical Operation Points

As a special case, symmetrical operation points can also be realized, by considering that all of the circuit and control parameters are identical in the p and n sides. V_c1 can be expressed using (23):

                                                         (40)

In symmetrical operation, all of the negative sequence components are zero. As a result, V_c2 is also zero. By subtracting (19) from (16), the control parameter I_Lpb^* can be calculated as follows:

                                         (41)

The ratio of the currents I_Lpb^* and I_Lpa^* can also be calculated. Squaring (41), dividing it by (18) and substituting the per unit values yields:

                                              (42)

As expected, this ratio gives 0.5 since half of the energy is delivered to the output p₁ and half to p₂. The situation is also the same in channel n.

Ⅵ. ASYMMETRICAL CONTROL CHARACTERISTICS

This section is concerned with the relationships among the output voltages, input voltages and control variables. As the steady state analysis pointed out, during asymmetrical conditions, the capacitor peak voltages V_c1^* and V_c2^* and the inductor currents I_Lpb^* and I_Lnb^* are appropriate parameters to control the output voltages and powers. Various scenarios are examined, including changes of the loads and the input voltages of the system. The characteristic curves were calculated in MATLAB R2018b. Numerous operation points were selected and marked with capital letters A-I, and simulations and laboratory measurements were carried (see Table I). In the characteristics, the green curves indicate symmetrical operation, while the black curves represent the protection mode and further operational limits. The continuous lines mark the channel p (or p1) parameters, while the dashed lines represent the channel n (or p2) parameters.

TABLE I SELECTED OPERATION POINTS FOR ASYMMETRICAL OPERATION, DCM, WHERE F_S^*=1

		Rp1*[pu]	Rp2*[pu]	Vip*[pu]	Vin*[pu]	Vc1*[pu]	Vc2*[pu]	ILpb*[pu]	ILnb*[pu]
A	asym load	6.0	3	1.00	1.00	0.10	0.00	0.40	0.40
B	asym load	1.5	3	1.00	1.00	0.20	0.00	0.26	0.26
C	asym outp. voltage	1.5	1.5	1.00	1.00	0.47	0.00	0.78	0.78
D, prot	asym outp. voltage	0.8	0.8	1.00	1.00	1.00	0.00	0.52	0.52
E	asym input	1.5	1.5	0.40	1.60	0.26	-0.60	0.51	0.51
F	asym input	1.5	1.5	1.30	0.67	0.26	0.33	0.51	0.51
G	sym	1.5	1.5	1.00	1.00	0.26	0.00	0.52	0.52
H	fully asym	0.6	0.8	0.86	1.14	0.30	-0.10	0.63	0.63

A. Change of the Output Voltage

Fig. 7 shows the effects of output voltage changes during constant and symmetrical loads and input voltages in the control plain set-up by V_c1 and I_Lpb. The point G represents a symmetrical operation point. Moving from G to C, V_op1^* remains constant, while V_op2^* increases by a factor of 1.6 when compared to its value at point G. By increasing both of the control variables, a new stable operation point is reached. Fig. 8 represents one of the advantages of the proposed control method. V_c1^*=1 is reached during operation that gives immediate information that protection mode is reached and V_c1^* cannot be increased any further as shown in point D. This also means that the total transferred power cannot be elevated any more.

Fig. 7. Control characteristics V_op1,2^*(V_c1^*,I_Lpb^*),R^*=1.5.

Fig. 8. Control characteristics V_op1,2^*(V_c1^*,I_Lpb^*),R^*=0.8.

B. Change of the Load

Fig. 9 represents the effects of load changes at a constant output voltage and input voltage. Assuming starting from the symmetrical operation point G, one of the load resistances, e.g. R_p2^* increases from 1.5 to 3. Although the operation becomes asymmetrical, by lowering the values of the control variables to and , the same output voltage can be maintained (B) like the original one. Here, due to the elevated resistance R_p2^* (note that V_op1,2^* is kept constant), the total output power is decreased, which was achieved by lowering V_c1. On the other hand, the ratio of the power balance is increased, which was achieved by lowering I_Lpb (see Fig. 5). At operation point A, the current of the inductor is close to the limitation.

Fig. 9. Control characteristics R_p1,2^*(V_c1^*,i_Lpb^*),V_o ^*=0.25.

C. Change of the Input Voltage

Fig. 10 shows how changes of the input voltage affect the control characteristics. Here the voltage of the capacitor reaches its maximum (V_c1^*max) before the protection mode. From the symmetrical operation mode G, if the voltage V_ip^* gets higher (or V_in^* lower), a stable operation point (F) with symmetrical output voltages (V_op1,2=V_on1,2) can be ensured by keeping V_c1^*=const.

Fig. 10. Control characteristics V_ip,n^*(V_c1^*,V_c2^*),V_o^*=0.25,R^*=1.5.

On the other hand, if V_ip^* gets smaller (or V_in^* gets larger), when V_c1^*=const., symmetrical output voltages can be accomplished with (operation point E). V_c2 controls the power flow among the input channels p and n.

Ⅶ. SIMULATION AND EXPERIMENTAL VERIFICATION

The considerations and analyses introduced above were tested in both simulation and laboratory environments.

The simulation was run in MATLAB Simulink 2018Rb. A 100W prototype of the converter was built with the following circuit parameters: C=1 µF, Ci=10 µF, Co=200 µF and L=10 µH. Here, the resonant frequency is fr=50.329 kHz. The input voltage range of the converter is 1-24V for both the p and n channels, the output voltage range of the converter is also the same. IRF530NPB MOSFETs and STTH802 diodes were used, while the open loop control was realized by a TMS320F283790 DSP. The asymmetrical operation of the converter was tested under numerous control parameter combinations considering changes of the load, input voltage and output voltage. The input voltage was chosen to be Vip=Vin=20V, except at operation points E (Vip=5V, Vin=20V) and F (Vip=20V, Vin=10V). A comparison of the theoretical, simulation and experimental results can be seen in Table II. Figs. 11-15 show steady-state waveforms of the capacitor voltage v_c(t), inductor currents i_Lp(t) and i_Ln(t), and capacitor current i_c(t). The red waveforms represent experimental results, while the blue ones show simulation outcomes. Fig. 11 shows the time functions at operation point A when the load is asymmetrical. Fig. 12. presents the effects of asymmetrical output voltages at operation point C. Fig. 13 represents operation point D, which is at the border of the protection mode. Consequently, the capacitor peak voltage just reaches the input voltage level. Fig. 14 demonstrates operation point E, where the input voltages are asymmetrical.

TABLE II COMPARISON OF THEORETICAL, SIMULATION AND EXPERIMENTAL RESULTS

	ILpb [A]			ILnb[A]			Vcp[V]			Vcn[V]			Vop1[V]			Vop2[V]
	Calc.	Sim.	Lab.	Calc.	Sim.	Lab.	Calc.	Sim.	Lab.	Calc.	Sim.	Lab.	Calc.	Sim.	Lab.	Calc.	Sim.	Lab.
A	2.55	2.55	2.52	2.55	2.55	2.47	1.97	1.98	2.35	-1.98	-1.98	-2.22	5.03	5.08	5.00	4.99	5.00	4.99
B	1.61	1.61	1.45	1.61	1.61	1.52	3.93	3.95	4.12	-3.93	-3.95	-4.30	4.98	4.99	4.90	5.00	5.01	4.90
C	4.91	4.91	5.10	4.91	4.91	4.08	9.38	9.40	8.88	-9.38	-9.40	-9.62	4.98	5.01	4.80	8.00	7.99	7.70
D	3.26	3.19	3.35	3.26	3.19	3.30	20.36	20.10	19.63	-20.36	-20.10	-20.50	8.00	7.93	6.70	6.20	6.15	4.70
E	2.02	2.02	1.95	2.02	2.02	1.98	-4.21	-4.20	-4.25	-10.79	-10.80	-11.25	3.14	3.15	2.90	3.13	3.13	2.80
F	2.43	2.43	2.40	2.43	2.43	2.38	8.95	8.97	9.31	1.05	1.04	1.00	3.76	3.78	3.50	3.76	3.76	3.50
G	3.26	3.25	2.80	3.26	3.26	2.78	5.28	5.30	5.38	-5.28	-5.30	-5.38	4.99	5.01	4.80	5.01	5.00	4.80
H	3.46	3.47	3.45	3.47	3.48	3.25	3.58	3.60	4.13	-7.12	-7.13	-8.13	2.80	2.81	2.67	3.50	3.50	3.70

Fig. 11. Time functions at operation point A, where the time unit is 2µsec/Div (blue: simulated; red: measured).

Fig. 12. Time functions at operation point C, where the time unit is 1µsec/Div (blue: simulated; red: measured).

Fig. 13. Time functions at operation point D, where the time unit is 2µsec/Div (blue: simulated; red: measured).

Fig. 14. Time functions at operation point E, where the time unit is 2µsec/Div (blue: simulated; red: measured).

Fig. 15. Time functions at operation point H, where the time unit is 2µsec/Div (blue: simulated; red: measured).

Consequently, , which means that . Fig. 15 illustrates fully asymmetrical operation at point H.

The compared theoretical and simulation results are practically the same. In addition, laboratory tests are also in good agreement. Small deviations of the latter were due to voltage drops of the real diodes, non-ideal circuit elements and non-linear behavior of the semiconductor switches and passive components.

Ⅷ. CONCLUSION

A new power flow control has been proposed for a four channel resonant buck converter, while operated in the zero current switching (ZCS) mode. Control of the output voltages and powers were achieved through control variables such as the inductor currents and the peak voltage levels of the capacitor. The switching frequency was fixed at its maximal value, which was determined by the resonant frequency. The new control strategy provides an excellent opportunity to control the total transferred power (by Vc1), the exchange of power among the input channels p and n (by Vc2) and the power exchange among the output channels p1 and p2 [n1 and n2] (by ILpb [ILnb]). Numerous operation points have been examined in order to verify the theory of the power flow control. Both tests and simulation results have been presented to confirm and verify the theoretical considerations.

ACKNOWLEDGMENT

Project no. FIEK_16-1-2016-0007 has been implemented with the support provided from the National Research, Development and Innovation Fund of Hungary, financed under the Centre for Higher Education and Industrial Cooperation - Research infrastructure development (FIEK_ 16) funding scheme. The research reported in this paper has also been supported by the National Research, Development and Innovation Fund (TUDFO/51757/2019-ITM, Thematic Excellence Program).

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Lilla Litvani received her M.S. degree in Electrical Engineering from the Budapest University of Technology and Economics, (BME), Budapest, Hungary, in 2015, where she is presently working towards her Ph.D. degree in the Department of Automation and Applied Informatics. Her current research interests include the modelling, analysis, control and optimization of power converters and DC microgrids.

Janos Hamar received his M.S. and Ph.D. degrees from the Budapest University of Technology and Economics, Budapest, Hungary, in 1998 and 2002, respectively. He was a Research Fellow at the Hungarian Academy of Sciences, Budapest, Hungary, from 1998 to 2001. Later, he worked as a Development Engineer for Exendis Industrie Automation GmbH, Freiburg, Germany. From 2004 to 2006, he was a Research Fellow at Utsunomiya University, Utsunomiya, Japan. He is presently working as an Associate Professor at the Budapest University of Technology and Economics. His current research interests include the modelling, analysis, control and optimization of power converters.