Analysis of a Series‑Parallel Resonant Converter for DC Microgrid Applications

Abstract

An input-series output-parallel soft switching resonant circuit with balance input voltage and primary-side current is studied and implemented for direct current (DC) microgrid system applications. Two resonant circuits are connected with input-series and output-parallel structure to have the advantages of low voltage stresses on active devices and low current stresses on power diodes. A balance capacitor is adopted on high voltage side to balance two input capacitor voltages. The LLC (inductor–inductor–capacitor) resonant circuit cells are employed in the converter to have soft switching operation for power semiconductors. The magnetic coupling component is adopted on the primary-side to automatically realize current balance of the two resonant circuits. In the end, a laboratory hardware circuit is built and tested. Experiments demonstrate and prove the validity of the resonant converter.

1. Introduction

High efficiency power converters were widely presented and discussed for modern industry products [1,2]. For high power demand, power converters with high input voltage have been proposed for DC microgrid systems and DC light rail transportation power units. The input voltage may be higher than 750 or 1500 V. The control strategies and basic circuit topologies in DC microgrid have been presented and discussed in detail in [3,4]. Power semiconductors with high voltage rating capability have high cost, low frequency operation and large conduction losses. Therefore, the circuit size cannot be reduced due to limited switching frequency. To overcome this problem, the circuit topologies with series-connected switches or converters [5,6,7,8,9,10,11,12] and multilevel converters [13,14,15,16,17,18,19,20] can adopt low voltage stress and high switching frequency operation power switches in high voltage input cases. Therefore, the voltage stress on active devices can be reduced in these circuit topologies. However, power switches may have an unbalanced voltage rating on these circuit topologies. Multilevel diode-clamped or flying circuit topologies have been developed for converters or inverters with balance voltage rating on power switches. The control scheme is usually based on duty cycle control [21,22] or variable frequency control [23,24] to regulate load voltage and implement soft switching operation on power devices. LLC (inductor–inductor–capacitor) resonant converters [25,26] have the benefits of high circuit efficiency and less switching loss. However, the main drawback of the parallel-connected resonant circuit is unbalanced resonant currents. Thus, the current stresses on input power switches and output diodes are different.

A series‑parallel resonant converter is presented and accomplished to achieve the advantages of the balanced input capacitor voltages and balance diode currents on two resonant circuits. The resonant converter presented has two LLC circuits with series–parallel connection. To balance input voltages, a flying capacitor is employed on high voltage side. A current balance component based on a magnetic-coupling core is used between two resonant circuits to achieve current sharing on power diodes. Therefore, the voltage and current balance issues on power semiconductors are all accomplished and achieved by using the voltage balance capacitor and magnetic-coupling component. Two resonant circuits are operated at inductive load. Thus, the soft switching operation on power semiconductors can be realized over the whole load range. Compared to past three-level circuit topologies in [13,19,21], this circuit topology has simpler control and less circuit components for high voltage input applications. Experiments of a laboratory circuit with 750~800 V input voltage, 24 V output voltage and 40 A load current are demonstrated to confirm the benefits of the circuit.

2. Presented Resonant Converter

Figure 1 gives the basic circuit diagram in a simplify DC microgrid. The input sources of the DC microgrid may be DC or AC utility systems and clean energy power systems such as solar power or wind power. The outputs of the DC microgrid may be the low or high power DC loads, AC motor drives, battery storage systems or light rail transit applications. For DC transportation or DC light rail transit system applications, the input DC bus voltage may be 750 or 1500 V. For local industry factory and residential house applications, the input DC bus voltage is 380 V. Thus, the DC bus voltage in the DC microgrid system may be 380, 750 and 1500 V for universal power demands. Therefore, the high voltage input DC–DC converters are needed for DC transportation or high power DC loads applications. The proposed converter is presented to meet the demand of these applications.

2.1. Circuit Characteristics of a Conventional Resonant Converter

Figure 2a provides the circuit structure of conventional LLC converter. L_m, L_r and C_r are the magnetizing inductance, series resonant inductance and series resonant capacitance, respectively. D_a and D_b are rectifier diodes and S_a and S_b are power switches. Frequency modulation with constant duty cycle is employed to regulate load voltage V_o and produce the gate signals for S_a and S_b. The basic circuit analysis of LLC converter can be analyzed using the fundamental harmonic approach in [27]. When a LLC converter is operated at series resonant frequency, the resonant converter likes a high frequency isolated DC transformer with zero-voltage switching (ZVS) turn-on operation on power switches and zero-current switching (ZCS) turn-off operation on rectifier didoes. Fundamental frequency harmonic approach is usually used to approximately derive voltage gain of the resonant circuit. The turn-on time of S_a and S_b equals half of the switching period so that a square signal with 0 and V_in voltage values are observed on v_ab. The root-mean-square fundamental voltage of v_ab can be calculated as $\sqrt{2}{V}_{in}/\pi$. However, the secondary winding current is a quasi-sinusoidal current so that v_Lm is a quasi-square voltage signal with nV_o and −nV_o voltage values. The root-mean-square value of v_Lm is derived as $2\sqrt{2}n{V}_o/\pi$. Figure 2b gives the ac equivalent circuit on the primary side. For high voltage applications, the Insulated Gate Bipolar Transistor (IGBT) devices with 1200 V voltage rating can be used for S_a and S_b, shown in Figure 2a. The switching frequency of IGBT devices, however, is normally less than 400 kHz, and IGBT devices have serious switching losses at turn-off instant.

2.2. Proposed LLC Resonant Converter

Figure 3 provides the circuit schematic of the LLC converter presented. The input voltage is about 750~800 V from DC microgrid or DC light rail power system. The converter developed has two LLC circuits with series–parallel structure. Thus, the voltage stress of S_a~S_d is reduced to V_in/2 and the average current of D_a~D_d is reduced to I_o/4. The first LLC circuit have components S_a, S_b, C_r,a, L_r,a, T_a, D_a and D_b. The circuit components of the second LLC circuit are S_c, S_d, C_r,b, L_r,b, T_b, D_c and D_d. D_a~D_d are rectifier diodes. C_r1 and C_r2 are the resonant capacitances, L_r,a and L_r,b are resonant inductors and L_m,a and L_m,b are the magnetizing inductors. C_o, C_in,a and C_in,b are output capacitor and input split capacitors. Capacitor C_f is connected between points b and c. If S_a and S_c are in the on-state and S_b and S_d are in the off-state, then V_Cf = V_Cin,a. If S_a and S_c are turned off and S_b and S_d are turned on, then V_Cf = V_Cin,b. Since the turn-on times of S_a~S_d are identical and equal T_s/2, the average capacitor voltages are derived as V_Cf = V_Cin,a = V_Cin,b = V_in/2. Therefore, input split DC voltages V_Cin,a and V_Cin,b are well balanced in each switching cycle. For achieving current balance of two LLC circuits, a magnetic-coupling (MC) component [28] is employed to achieve current sharing. If the inductor currents are well balanced (|i_Lr,a| = |i_Lr,b|), then the induced voltages V_La = V_Lb = 0. If the inductor currents are unbalanced (such as |i_Lr,a| > |i_Lr,b|), then V_L,a is decreased to reduce i_Lr,a and V_Lb is increased to increase i_Lr,b. After |i_Lr,a| = |i_Lr,b|, the voltages V_La and V_Lb are reduced to zero. Thus, i_Lr,a and i_Lr,b can be automatically balanced under steady state by using the MC component. The switching frequency is regulated to adjust voltage gain of the LLC presented. Therefore, V_o is regulated at the reference voltage value V_o,ref.

3. Principle of Operation

The circuit operations of the LLC converter presented are discussed from the following statements:

(1)

Transformers T_a and T_b have identical turn-ratio n_a = n_b = n_p/n_s;

(2)

Inductances L_m,a = L_m,b = L_m and L_r,a = L_r,b = L_r;

(3)

S_a~S_c have identical output capacitances C_Sa = C_Sb = C_Sc = C_Sd = C_S;

(4)

Capacitances C_in,a = C_in,b and C_r,a = C_r,b = C_r.

The gate singles of power switches and key current and voltage waveforms per every switching cycle are given in Figure 4. From the conducting states of power devices, it can be observed that the converter presented has six operating steps for every switching cycle. Figure 5 gives the topological circuits for the six operating steps.

Step 1 (t₀~t₁): At time t < t₀, S_a~S_d are all off and i_Lr,a > 0 and i_Lr,b < 0. Thus, i_Lr,a discharges C_Sa and charges C_Sb and i_Lr,b discharges C_Sc and charges C_Sd. Due to i_Lr,a < i_Lm,a and i_Lr,b > i_Lm,b, the diode currents i_Db and i_Dc are positive. After time t > t₀, v_CSa and v_CSc decrease to zero voltage. Due to i_Sa(t₀) < 0 and i_Sc(t₀) < 0, the body diodes of Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET) S_a and S_c conduct and v_Sa,ds and v_Sc,ds are zero voltage. Therefore, switches S_a and S_c can turn on to realize a soft switching characteristic. In step 1, i_Lr,a < i_Lm,a and i_Lr,b > i_Lm,b, the rectifier diodes D_c and D_d conduct, and V_Cf = V_Cin,a. Since the magnetizing voltages v_Lm,a = –nV_o and v_Lm,b = nV_o, the magnetizing currents i_Lm,a and i_Lm,b decrease and increase, respectively. Under steady state operation and |i_Lr,a| = |i_Lr,b| operation, the induced voltages V_La and V_Lb across the MC cell are equal to zero. (L_r,a and C_r,a) and (L_r,b and C_r,a) are naturally resonant in converters 1 and 2, respectively with frequency $f_r=1/2\pi \sqrt{L_r{C}_r}$. If f_s > f_r, then i_Db and i_Dc will decrease to zero before S_a and S_d turn off. After the step 1, circuit operation goes to step 2 when i_Db = i_Dc = 0. If f_s < f_r, then i_Db and i_Dc are still positive when S_a and S_c turn off. Under this condition, the circuit will go to step 3.

Step 2 (t₁~t₂): If f_s > f_r, then i_Lr,a = i_Lm,a and i_Lr,b = i_Lm,b at time t₁. Diodes D_a~D_d are turned off without reverse recovery current. (C_r,a, L_r,a and L_m,a) and (C_r,b, L_r,b and L_m,b) are resonant in circuits 1 and 2, respectively with frequency $f_p=1/2\pi \sqrt{(L_m+L_r)C_r}$.

Step 3 (t₂~t₃): At t₂, power devices S_a and S_c turn off. Due to i_Lr,a(t₂) < 0 and i_Lr,b(t₂) > 0, C_Sa (C_Sb) and C_Sc (C_Sd) are charged (discharged) in step 3. Diodes D_a and D_d are forward biased to conduct load current. If the energies on L_r,a and L_r,b are greater than the energies on C_Sa~C_Sd, then v_Sb,ds and v_Sd,ds will decrease to zero at t₃.

Step 4 (t₃~t₄): At time t₃, C_Sb and C_Sd discharge to zero voltage. Due to i_Lr,a(t₃) < 0 and i_Lr,b(t₃) > 0, the body diodes of S_b and S_d conduct and Thus, S_b and S_d can turn on to realize ZVS operation. Diodes D_a and D_d conduct, v_Lm,a = nV_o, v_Lm,b = −nV_o, i_Lm,a increases, and i_Lm,b decreases. (L_r,a and C_r,a) and (L_r,b and C_r,b) are naturally resonant in each LLC circuit.

Step 5 (t₄~t₅): At time t₄, the magnetizing currents i_Lm,a and i_Lm,b equal i_Lr,a and i_Lr,b, respectively. Thus, the secondary-side diodes D_a~D_d are turned off without reverse recovery current loss. (L_r,a, C_r,a and L_m,a) and (L_r,b, C_r,b and L_m,b) are naturally resonant in each circuit, respectively.

Step 6 (t₅~T_s + t₀): At time t₅, power devices S_b and S_d turn off. Due to i_Lr,a(t₅) > 0 and i_Lr,b(t₅) < 0, C_Sa (C_Sb) and C_Sc (C_Sd) are discharged (charged) in step 6. The diodes D_b and D_c are conducting. If the energies on L_r,a and L_r,b is greater than the energies on C_Sa~C_Sd, then v_Sa,ds and v_Sc,ds will be decreased to zero at T_s + t₀.

4. System Analysis and Design Example

Two LLC resonant circuits with series–parallel structure are adopted to decrease voltage stresses on power switches and current stresses on power diodes. A flying capacitor is employed to realize voltage balance on input capacitors. A magnetic-coupling component is connected between two LLC circuits to accomplish current sharing. In current balance condition and steady state operation, the primary and secondary voltages of the magnetic-coupling component equal zero. The magnetic-coupling component is ignored in the following discussion. Fundamental frequency analysis [27] is employed to obtain voltage gain of the converter presented. It is observed that v_ab and v_cd are square voltage waveforms. (L_r,a and C_r,a) and (L_r,b and C_r,b) are resonant on circuits 1 and 2 to generate two quasi-sinusoidal on i_Lr,a and i_Lr,b. The voltages v_ab and v_cd at the fundamental frequency are $v_{ab,f}=v_{cd,f}=V_{in}\sin (2\pi f_{s}t)/\pi$. If the circuit is operated at series resonant frequency, then the conducting time of D_a~D_d is equal to T_s/2. The secondary winding currents at fundamental frequency are derived as $i_{Ta,\sec }=i_{Tb,\sec }=\pi I_o\sin (2\pi f_{s}t-\theta )/4$. The fundamental magnetizing voltages are given as $v_{Lm,a,f}=v_{Lm,b,f}=4n{V}_o\sin (2\pi f_{s}t-\theta )/\pi$. The ac equivalent resistances R_ac,a and R_ac,b on primary-side of T_a and T_b are derived $R_{ac,a}=R_{ac,b}=\frac{v_{Lm,a,f}}{i_{Ta,\sec }/n}=16{(\frac{n}{\pi })}^2{R}_o$ (C_r,a, L_r,a, L_m,a and R_ac,a) and (C_r,b, L_r,b, L_m,b and R_ac,b) are resonant on each corresponding resonant tank. Figure 6a gives the resonant tank on the primary-side of resonant circuit 1. The ac voltage gain of the circuit developed can be expressed as.

$$|G(f_s)|=v_{Lm,a,f}/v_{ab,f}=1/\sqrt{{[1+\frac{1}{K_L}(1-\frac{1}{F^2})]}^2+{[Q(F-\frac{1}{F})]}^2}$$

(1)

where $f_r=1/2\pi \sqrt{L_r{C}_r}$, K_L = L_m,a/L_r,a, $Q=\sqrt{L_r/C_r}/R_{ac,a}$ and F = f_s/f_r. From Equation (1), the gain voltage between the different load (Q) and normalized switching frequency (F) under K_L = 8 is provided in Figure 6b.

The converter studied is proved by a prototype based on the following conditions: 750 V~800 V input voltage, 24 V output voltage, 40 A load current and 120 kHz series resonant frequency by C_r,a and L_r,a. T_a and T_b are implemented by magnetic cores TDK EER-42 with 24 primary winding turns and 3 secondary winding turns. Based on the turn-ratio of T_a and T_b, the maximum and minimum voltage gains of LLC converter are provided in (2).

$$G_{dc,\max }=\frac{4n(V_o+V_f)}{V_{in,\min }}\approx 1.06, G_{dc,\min }=\frac{4n(V_o+V_f)}{V_{in,\max }}\approx 1$$

(2)

where V_f = 0.8 V on D_a~D_d. At 100% output power, R_ac,a and R_ac,b are derived in (3).

$$R_{ac,a}=R_{ac,b}=16{(\frac{n}{\pi })}^2{R}_o\approx 62.25\mathsf{\Omega }$$

(3)

In the prototype, the selected Q is 0.3 to obtain the maximum gain at low voltage input under full load. The inductor ratio K_L is selected as 8 to reduce the circulating current losses on magnetizing inductor. With the given K_L, f_r and Q, the components L_r,a, L_r,b, C_r,a, C_r,b, L_m,a and L_m,b are derived:

$$L_{r,a}=L_{r,b}=\frac{Q{R}_{ac,a}}{2\pi f_r}\approx 25\mu H$$

(4)

$$C_{r,a}=C_{r,b}=\frac{1}{4{\pi }^2{L}_{r1}{f}_r^2}\approx 70nF$$

(5)

$$L_{m,a}=L_{m,b}=K_L{L}_{r,a}\approx 200\mu H$$

(6)

The root-mean-square magnetizing currents i_Lm,a,rms and i_Lm,a,rms at series resonant frequency 120 kHz are calculated as

$$i_{Lm,a,rms}=i_{Lm,b,rms}=\frac{1}{2\sqrt{3}}\frac{n{V}_o}{2f_s{L}_{m,a}}\approx 1.155A$$

(7)

The primary-side root-mean-square load currents at full load are expressed as

$$i_{Ta,pri,rms}=i_{Tb,pri,rms}=\frac{\pi }{4\sqrt{2}}\frac{I_o}{n}\approx 2.78A$$

(8)

Therefore, the root-mean-square resonant inductor currents are obtained as

$$i_{Lr,a,rms}=i_{Lr,b,rms}=\sqrt{i_{Lm,a,rms}^2+i_{Ta,pri,rms}^2}\approx 3A$$

(9)

Due the circuit structure, the voltage rating of power devices S_a~S_d is obtained as

$$v_{Sa,stress}=v_{Sb,stress}=v_{Sc,stress}=v_{Sd,stress}=V_{in,\max }/2=400V$$

(10)

The root-mean-square switch currents i_Sa,rms~i_Sd,rms are obtained in (11).

$$i_{S\mathrm{a},rms}=i_{Sd,rms}=i_{La,a,rms}^{}/\sqrt{2}\approx 2.13A$$

(11)

MOSFETs SIHG20N50C with 500 V/20 A rating are employed for power devices S_a~S_d. The voltage and average current ratings of diodes D_a~D_d are expressed as

$$v_{Da,stress}=v_{Db,stress}=v_{Dc,stress}=v_{Dd,stress}=2(V_o+V_f)\approx 49.6V$$

(12)

$$i_{Da,av}=i_{Db,av}=i_{Dc,av}=i_{Dd,av}=I_o/4=10A$$

(13)

MBR40100PT with 100 V/40 A ratings are employed for power diodes D_a~D_d. The input capacitances, voltage balance capacitance and output capacitances are C_in,a = C_in,b = 440 μF/450 V, C_f = 1 μF/630 V and C_o = 4400 μF/100 V.

5. Experimental Results

Experiments are given to confirm the circuit performance. The circuit components of the converter presented are derived in the previous section. Figure 7 demonstrates the test waveforms of S_a~S_d under 100% rated power. It is clear that S_a (S_b) and S_c (S_d) have the same gate signal. Therefore, the square voltage waveforms can be generated on voltages v_ab and v_cd. Due to the converter needing a higher voltage gain at V_in = 750 V than V_in = 800 V, the switching frequency of S_a~S_d at V_in = 750 V input (Figure 7a) is lower than the switching frequency at V_in = 800 V input (Figure 7b). Figure 8 provides the test waveforms of v_Sa,gs, v_Sa,ds and i_Sa at different input voltage and output power conditions. From the experimental results, one can observe that zero voltage switching of S_a is realized from 5% to 100% load over the whole input voltage range. Since the other switches S_c~S_d have the same circuit characteristics as switch S_a, it can be concluded that the soft switching operation of S_c~S_d is also accomplished from 5% load to full load. Figure 9 demonstrates the test results of v_Cr,a, v_Cr,b, i_Lr,a and i_Lr,b of two half-bridge resonant circuits at 100% rated power. The two currents i_Lr,a and i_Lr,b are well balanced for different input voltage cases. Figure 10 illustrates the experimental waveforms of i_Da~i_Dd under 100% rated power. The diode currents are also well balanced between two resonant circuits. Figure 11 gives the test results of V_Cin,a, V_Cin,b and V_Cf at 800 V input and 100% rated power. The voltage variation between V_Cin,a and V_Cin,b is 5 V under full load. The measured circuit efficiencies are 91.4%, 94.8% and 93.7% at 96, 480 and 960 W output power, respectively. The measured switching frequencies are 117 kHz (152 kHz), 110 kHz (135 kHz) and 99 kHz (120 kHz) at 96, 480 and 960 W output load under 750 V (800 V) input operation. Figure 12 provides the test waveforms of the load voltage and load current under load step response. It is clear that the load voltage is stable without serious voltage variation.

6. Conclusions

A series–parallel connected resonant circuit with the benefits of low current and voltage ratings, balance voltage on active switches, balance current on power components, and soft switching operation on power devices is proposed, discussed and implemented in this paper. The voltage balance of input split capacitors is achieved by a flying capacitor. The current sharing of two resonant tanks is realized by a magnetic-coupling core. Frequency-control modulation is used to adjust voltage gain of the LLC converter. Therefore, the load voltage is well controlled for different input voltage and output current. Since the resonant circuit is worked at the inductive impedance, power semiconductors can be controlled at soft switching operation. The converter presented can be applied in DC light rail vehicles and a DC microgrid bipolar voltage system with high voltage input applications. Finally, experimental tests are given and demonstrate the practicability of the proposed circuit.