Research on the Topology and Control Strategy of a Novel Three-Port Converter

Abstract

A novel three-port converter (TPC) is proposed to meet the diversity of demand for electrical equipment in this paper. It interfaces a single input power port and two output ports. The proposed TPC can be viewed as two bidirectional DC-DC converters. With a different operation mode, the proposed TPC can output two DC voltages or a single DC and a single AC voltage. The topology and operation principal of the TPC is analyzed in detail. Moreover, the mathematic model of the TPC is derived. Then, by considering the dynamic response and disturbance suppression, a step by step PI and PR controller design process for TPC is also presented. Both the simulation and the experimental results validate the proposed method.

1. Introduction

Sustainable energy is attracting more and more attention, due to environmental pollution and the shortage of fossil fuel, [1,2,3]. With the different demands of electrical equipment, the sustainable energy sources, such as photovoltaics, fuel cells, etc., [4,5,6], need to be converted to appropriate voltage sources. Hence, several separate DC-DC and DC-AC converters need to be used. However, multiple converters lead to high cost, low efficiency, and difficulty in achieving centralized control [7].

Compared to multiple separate converters, such as DC-DC, AC-DC and DC-AC converters, the three-port converter (TPC) has the advantages of fewer components, higher efficiency, higher power density and a multivoltage level output [8]. It has been widely used in industrial fields, such as aviation power supply [9], DC micro-grid [10] and electric vehicles [11,12]. Currently, a number of topologies and control strategies for TPC have been proposed. In [12], a TPC which consists of three bidirectional DC-DC converters is presented for fuel–cell-powered hybrid vehicles. It deals with the power flow from multisource on-board energy systems. Although the structure of the bidirectional DC-DC converter in [12] is independent, it still needs a lot of switches. In [13], a new DC-DC converter with three ports is proposed. Therein, only three controllable switches are used, which reduces the number of switches. In [14], a new single stage three-input DC-DC boost converter is proposed. It interfaces two unidirectional input ports and a bidirectional port. Although high integration and high efficiency are realized, the number of power devices is high and it needs bulky port filters. In [15], a three-port DC-DC converter is proposed with an integrated magnetic technique, where the port ripple cancellation and high-power density are realized by two magnetic devices. A three-port high-step-up/step-down bidirectional DC/DC converter is proposed in [16]. It combines a high-step-up converter by photovoltaic means and a battery charge/discharge bidirectional converter. In order to improve the efficiency of a two-stage AC-DC power system, a single-phase three-port PFC converter with sigma architecture is proposed in [17]. In addition, a novel three-port three-phase rectifier without isolation transformer is proposed in [18]. The TPC of [17,18] provides a low voltage DC load port, and a high voltage DC port. So far, nearly all the three-port converters are either dual input port and single DC output port or single input port and dual DC output port. It cannot supply AC and DC loads at the same time.

With the increase in electrical equipment demands, the DC and AC output hybrid system is more and more popular. Therefore, a novel three-port converter is proposed in this paper. The proposed TPC interfaces a single input power port and two output ports. With different operation modes, the proposed TPC can output two DC voltages or a single DC and a single AC voltage. The paper is organized as follows. In Section 2, the topology, operation principle and mode of the proposed TPC are analyzed in detail, and the simulation results of open-loop control are exhibited. In Section 3, the small-signal model and control strategy of the proposed TPC are investigated when it outputs DC voltage. In Section 4, the large signal model and the optimization design method for a PR controller are investigated when it outputs AC voltage. Finally, the simulation and experimental verification are completed in Section 5 and Section 6, respectively.

2. Topology and Operation Mode of Proposed TPC

The topology of the proposed TPC is shown in Figure 1. The DC-link capacitor is C_dc. u_dc is the input voltage. S₁–S₄ are four switch pairs which consist of an IGBT with anti-parallel diode. L_a and L_b are output filter inductors. C_a and C_b are output filter capacitors. There are two operation modes for the proposed TPC, namely dual DC output and single DC and single AC output. These are analyzed in the next subsection.

2.1. Dual DC Output Mode

In the dual-DC-output mode, Port 13 and Port 23 are two independent DC output ports. As each leg is combined with a set of LC filters, the proposed TPC can be viewed as two bidirectional DC-DC converters. Taking branch a as an example, the equivalent circuit under different switching states is shown in Figure 2. When S₁ is ON and S₄ is OFF, the DC load is supplied by the DC voltage source. Here, u_a equals u_dc. When S₁ is OFF and S₄ is ON, the DC load is supplied by inductor L_a and capacitor C_a, and u_a equals zero. Then, the u_a is a PWM voltage and its average value equals the out port voltage u₁₃.

Therefore, the output voltage of TPC in dual DC output mode is

$$\{\begin{array}{l}{u}_{13}^{}=u_{\mathrm{dc}}{d}_{\mathrm{a}}\\ u_{23}^{}=u_{\mathrm{dc}}{d}_{\mathrm{b}}\end{array}$$

(1)

where d_a and d_b represent the duty cycle of S₁ and S₃, respectively. Then Port 12 is also a DC voltage, and equals:

$$u_{12}^{}=u_{\mathrm{dc}}(d_{\mathrm{a}}-d_{\mathrm{b}})$$

(2)

where u₁₂, u₁₃ and u₂₃ are the voltage of the Port 12, Port 13 and Port 23, respectively. The two independent voltages can be obtained by controlling the duty cycles d_a and d_b.

2.2. Single DC and Single AC Output Mode

In single DC and single AC output mode, Port 23 and Port 12 are DC and AC output ports, respectively. As Port 23 is a DC port, then the duty cycle of S₃ needs to be controlled as a constant. Since the voltage of Port 12 is the voltage difference between Port 13 and Port 23, the duty cycle d_a should be controlled as follows:

$$d_{\mathrm{a}}=D+m\cos (\theta )$$

(3)

where D is a constant and equals d_b. m cos (θ) is the reference signal of Port 12. The range of m is:

$$m\in (0,\min (D,1-D))$$

(4)

Therefore, if the d_b is controlled as a constant and d_a is controlled as in (3), Port 23 and Port 12 can output a DC voltage and AC voltage, respectively.

2.3. Open Loop Simulation Results of TPC

In order to verify the voltage output capability of the TPC, the open loop simulation was carried out. The simulation parameters are shown in

Table 1. Simulation parameters.

Parameter	Value
Filter inductor La and Lb (mH)	2
Filter capacitor Ca and Cb (µF)	15
Voltage of DC-bus udc (V)	100
Switching frequency fsw (kHz)	10
Load of Port 12 R12 (Ω)	10
Load of Port 13 R13 (Ω)	20
Load of Port 23 R23 (Ω)	50

.

Firstly, in dual DC output mode, the duty cycles d_a and d_b are 0.7 and 0.4, respectively. The simulation results of output port voltages are shown in Figure 3. It is clear that each output port voltage is consistent with the results of (1) in steady state.

Next, in single DC and single AC output mode, the duty cycles d_a and d_b are:

$$\{\begin{array}{l}{d}_{\mathrm{a}}=0.5+0.3\cos (100\pi t)\\ d_{\mathrm{b}}=0.5\end{array}$$

(5)

The load of DC Port 23 R₂₃ is 20 Ω. The load of AC Port 12 R₁₂ is set as 1 Ω, 5 Ω and 10 Ω, respectively. Then the simulation results of u₂₃ and u₁₂ are shown in Figure 4. With the increase in AC load, a larger and larger AC component is superimposed on the DC output voltage u₂₃. Moreover, the amplitude and phase of the AC output voltage u₁₂ is affected by the change of AC load. Therefore, the controller should be carefully designed to eliminate the coupling between DC and AC output port. This is investigated in the next section.

3. Mathematical Modeling and Control Strategy of DC Output Port

As analyzed in Section 2, the DC output port of the TPC is actually the output of a bidirectional DC-DC converter whether in dual DC output mode or in single DC single AC mode. Taking DC Port 23 as an example, the corresponding circuit is the combination of branch b and the LC filter. When S₃ is turned on, the state equation of i_b, u₂₃ and the input current i_dc is as follows:

$$\{\begin{array}{l}L\frac{\mathrm{d}{i}_{\mathrm{b}}(t)}{\mathrm{d}t}=u_{\mathrm{dc}}(t)-u_{23}(t)\\ C\frac{\mathrm{d}{u}_{23}(t)}{\mathrm{d}t}=i_{\mathrm{b}}(t)-\frac{u_{23}(t)}{R}\\ i_{\mathrm{dc}}(t)=i_{\mathrm{b}}(t)\end{array}$$

(6)

where L, C, R represent the value of inductor, capacitor, and load of output port, respectively. When S₂ is turned on, the state equation is as follows:

$$\{\begin{array}{l}L\frac{\mathrm{d}{i}_{\mathrm{b}}(t)}{\mathrm{d}t}=-u_{23}(t)\\ C\frac{\mathrm{d}{u}_{23}(t)}{\mathrm{d}t}=i_{\mathrm{b}}(t)-\frac{u_{23}(t)}{R}\\ i_{\mathrm{dc}}(t)=0\end{array}$$

(7)

During a switching period, the average state equation is as follows:

$$\{\begin{array}{l}L\frac{\mathrm{d}{i}_{\mathrm{b}}(t)}{\mathrm{d}t}=d_{\mathrm{b}}(t)u_{\mathrm{dc}}(t)-u_{23}(t)\\ C\frac{\mathrm{d}{u}_{23}(t)}{\mathrm{d}t}=i_{\mathrm{b}}(t)-\frac{u_{23}(t)}{R}\\ i_{\mathrm{dc}}(t)=d_{\mathrm{b}}(t)i_{\mathrm{b}}(t)\end{array}$$

(8)

The average model in Formula (8) is equivalent to the superposition of the steady-state operating point and disturbed small signal, which includes the following forms:

$$\{\begin{array}{l}{i}_{\mathrm{b}}(t)=I_{\mathrm{b}}+{\widehat{i}}_{\mathrm{b}}\\ d_{\mathrm{b}}(t)=D_{\mathrm{b}}+{\widehat{d}}_{\mathrm{b}}\\ u_{\mathrm{dc}}(t)=U_{\mathrm{dc}}+{\widehat{u}}_{\mathrm{dc}}\\ u_{23}(t)=U_{23}+{\widehat{u}}_{23}\\ i_{\mathrm{dc}}(t)=I_{\mathrm{dc}}+{\widehat{i}}_{\mathrm{dc}}\end{array}$$

(9)

A small-signal state equation is constructed by substituting Equation (9) into Equation (7), which is shown as follows:

$$\{\begin{array}{l}L\frac{\mathrm{d}{\widehat{i}}_{\mathrm{b}}}{\mathrm{d}t}=D_{\mathrm{b}}{\widehat{u}}_{\mathrm{dc}}+U_{\mathrm{dc}}{\widehat{d}}_{\mathrm{b}}-{\widehat{u}}_{23}\\ C\frac{\mathrm{d}{\widehat{u}}_{23}}{\mathrm{d}t}={\widehat{i}}_{\mathrm{b}}-\frac{{\widehat{u}}_{23}}{R}\\ {\widehat{i}}_{\mathrm{dc}}=D_{\mathrm{b}}{\widehat{i}}_{\mathrm{b}}+I_{\mathrm{dc}}{\widehat{d}}_{\mathrm{b}}\end{array}$$

(10)

The small-signal equivalent circuit model of Formula (10) is shown in Figure 5.

From Figure 5, the expressions of duty ratio–output voltage transfer function G_d2u(s), input voltage output voltage transfer function G_u2u(s) and output impedance transfer function Z_out(s) are derived as follows:

$$\{\begin{array}{l}{G}_{\mathrm{d}2\mathrm{u}}(s)=\frac{U_{23}R}{D_{\mathrm{b}}(LCR{s}^2+Ls+R)}\\ G_{\mathrm{u}2\mathrm{u}}(s)=\frac{D_{\mathrm{b}}R}{LCR{s}^2+Ls+R}\\ Z_{\mathrm{out}}(s)=\frac{LRs}{LCR{s}^2+Ls+R}\end{array}$$

(11)

Then, a PI controller is used to regulate the voltage of Port 23; the control block diagram is shown in Figure 6.

The open loop transfer function H(s) can be derived as:

$$H(s)=\frac{U_{23}R(k_{\mathrm{p}1}s+k_{\mathrm{i}1})}{D_{\mathrm{b}}{U}_{\mathrm{dc}}s(LCR{s}^2+Ls+R)}$$

(12)

where k_p1 and k_i1 are the proportional and integral coefficients of PI controller, ${\widehat{u}}_{23}^{}$ can be expressed as:

$${\widehat{u}}_{23}(s)=\frac{H(s){\widehat{u}}_{23}^{*}(s)}{1+H(s)}+\frac{G_{\mathrm{u}2\mathrm{u}}(s){\widehat{u}}_{\mathrm{dc}}^{*}(s)}{1+H(s)}-\frac{Z_{\mathrm{out}}(s){\widehat{i}}_{23}^{*}(s)}{1+H(s)}$$

(13)

A series of steady-state operating points “U_dc = 100 V, D_b = 0.5, U₂₃ = 50 V, and R = 10 Ω”, and substituted into (12) and (13). Then, with the sisotool box of MATLAB, the PI controller parameters of TPC are determined by the following principles.

(1)

The cutoff frequency of H(s) is near one-tenth of the switching frequency. Then, the balance between steady-state performance and dynamic performance can be realized;

(2)

In the low frequency band, the amplitude of Z_out(s)/(1 + H(s)) should be below 0 dB;

(3)

In the low frequency band, the amplitude of G_u2u(s)/(1 + H(s)) should also be below 0 dB.

In this paper, k_p1 and k_i1 are 1.5 and 20, respectively. At same time, the bode plot of H(s) is shown as Figure 7. The cutoff frequency is 1.05 kHz, which satisfies the above principles. The phase margin is 35°. Then, the superior stability and disturbance rejection capability are realized.

The bode plots of Z_out(s)/(1 + H(s)) and G_u2u(s)/(1 + H(s)) are shown as Figure 8 and Figure 9, respectively. In the low frequency band, their amplitudes are all below the 0 dB, which satisfies the principle of design for PI controller parameters.

4. Control Strategy of AC Output Port

For the AC output port, the corresponding output voltage u₁₂ is affected by the AC load R₁₂. To solve this problem, the transfer function of AC output circuit is established in this section. Moreover, a proportional resonant (PR) controller is designed to regulate u₁₂. As analyzed in Section 2.2, the average value of PWM voltage u_ab equals the output voltage u₁₂ as in (2). Then, the output voltage can be controlled by adjusting the duty cycles d_a and d_b. Since the d_b has already been controlled by a PI controller, only d_a needs to be controlled for the AC port. Figure 10 shows the control block of the AC port.

The expression of the transform function of PR controller is shown as follows:

$$G_{\mathrm{PR}}(s)=k_{\mathrm{p}}+\frac{2k_{\mathrm{c}}\zeta {\omega }_{0}s}{s^2+2\zeta {\omega }_{0}s+{\omega }_0{}^2}$$

(14)

where ω₀ is the resonant frequency, and set to 100 π rad/s, ζ is the damping ratio and set as 0.5, k_p and k_c are proportional coefficients and resonance coefficients, respectively. From Figure 10, the u₁₂(s) can be expressed as:

$$u_{12}(s)=u_{12}^{*}(s)G_{\mathrm{close}}(s)+i_{12}(s)G_{\mathrm{i}2\mathrm{u}}(s)$$

(15)

where G_close(s) represents the closed-loop transfer function of the system, and G_i2u(s) represents the transfer function from load current to load voltage. The open loop transfer function G_open(s) can be derived as:

$$G_{\mathrm{open}}(s)=\frac{k_{\mathrm{p}}{s}^2+2\zeta {\omega }_0(k_{\mathrm{p}}+k_{\mathrm{c}})s+k_{\mathrm{p}}{\omega }_0{}^2}{(LC{s}^2+1)(s^2+2\zeta {\omega }_{0}s+{\omega }_0{}^2)(1+1.5T_{\mathrm{s}}s)}$$

(16)

The G_close(s) and G_i2u(s) can be rewritten as:

$$\{\begin{array}{l}{G}_{\mathrm{close}}(s)=\frac{G_{\mathrm{open}}(s)}{1+G_{\mathrm{open}}(s)}\\ G_{\mathrm{i}2\mathrm{u}}(s)=\frac{Ls}{[1+G_{\mathrm{open}}(s)](LC{s}^2+1)}\end{array}$$

(17)

The order of the transfer function is too high to directly obtain the coefficients in the PR controller. Therefore, to optimize the coefficients k_p and k_c, the amplitude–frequency characteristic curves of G_close(s) and G_i2u(s) under different values of k_p and k_c are plotted by MATLAB. Firstly, let k_p = 1 and k_c gradually increases from 1 to 30, and the amplitude–frequency characteristic curves of G_close(s) and G_i2u(s) are shown in Figure 11. With the increase in k_c, the amplitude of G_close(s) in the low frequency band gradually increases and approaches the 0 dB line. In the high frequency band, k_c has little influence on the amplitude of G_close(s). Meanwhile, the gain of G_i2u(s) at 50 Hz decreases with the increasing of k_c, which indicates that the increasing of k_c has a more obvious inhibition effect on the inhibition of port current.

Next, let k_c = 5 and k_p gradually increases from 1 to 30. The amplitude–frequency characteristic curves of G_close(s) and G_i2u(s) are shown in Figure 12. The following performance at low frequency improves with the increase in k_p, but the steady-state errors cannot be eliminated. Meanwhile, the cutoff frequency of G_close(s) increases as k_p increases. the amplitude of G_i2u(s) decreases as k_p increases.

Based on the independent analysis of k_p and k_c, the optimal parameters of the PR controller were obtained (k_p = 8 and k_c = 21) by using sisotool toolbox of MATLAB, and the Bode diagram of G_close(s) is shown in the Figure 13. It shows a good steady-state characteristic in the low frequency band, and the cutoff frequency is 1.2 kHz, which is near one-tenth of the switching frequency, a fast dynamic response can also be obtained.

5. Simulation Results

To verify the effectiveness of the proposed TPC and control strategy, simulations were carried out.

5.1. Simulation Results of Dual DC Output Mode

In dual DC output mode, the reference of u₁₂, u₁₃ and u₂₃ were 40, 90 and 50 V respectively. The simulation results of u₁₂, u₁₃ and u₂₃ are shown in Figure 14a. It is clear that the actual output voltage could accurately track the reference voltage without steady-state error, and the ripple of the voltage of all ports was within the range of [−1%, 1%].

Figure 14b shows the voltage of each output port when the input voltage u_dc step from 100 V to 120 V at the time of 10 ms. The results shown in Figure 14 demonstrate the effectiveness of the proposed controller.

5.2. Simulation Results of Single DC and Single AC Output Mode

In single DC and AC output mode, the reference of u₂₃ was 50 V, and the reference of amplitude and frequency of u₁₂ set as 25 V and 50 Hz, respectively. The corresponding results are shown in Figure 15 when the AC load was 5 Ω. Compared to the open loop results shown in Figure 4b, the amplitude of the 50 Hz AC component in u₂₃ reduced from 3.05 V to 0.03 V.

Figure 16 shows the simulation results of u₁₂ and i_a when AC load changed from 20 Ω to 5 Ω at the time of 0.03 s. It is obvious that a load step perturbation had no effect on u₁₂. When the reference of frequency dropped from 50 Hz to 25 Hz, the simulation result of u₁₂ is shown in Figure 17. From Figure 15, Figure 16 and Figure 17, it is clear that the coupling phenomenon between AC port and DC port was suppressed significantly with the proposed PR controller.

6. Experimental Results

The experiment was also carried out to validate the proposed TPC and its control strategy. The TPC prototype is shown in Figure 18 and its parameters are listed in

Table 2. Models and parameters of component and module.

Category	Part Number	Parameters
Filter inductor La, Lb	Custom-made	2 mH
Filter capacitor Ca, Cb	MKP1847610354P4	15 µF
DC-link capacitor Cdc	B435045477M000	720 µF
DC-link power supply	ITECH programmable power	100 V
Load	ITECH programmable load	Adjustable
IGBT modules	SKiip39AC066V4	600 V/150 A

. The controller is TMS320F28335.

6.1. Experimental Results under Dual DC Output Mode

Figure 19a shows the steady experimental results of u₁₂, u₁₃ and u₂₃ when their reference signals were 40, 90 and 50 V, respectively. When a step disturbance occurred in input voltage u_dc, the experimental results of u₂₃ are shown in Figure 19b. It is clear that the output of TPC in dual DC output mode had good steady and transient responses with the proposed controller from Figure 19.

6.2. Experimental Results under Single DC and Single AC Output Mode

Figure 20a shows the experimental results under single DC and single AC output mode. Therein, the reference signal of u₂₃ was 50 V, and the reference of amplitude and frequency of u₁₂ were 25 V and 50 Hz, respectively. The FFT results of u₁₂ are shown in Figure 20b. With the proposed PR controller, the THD of u₁₂ was only 2.86%. From Figure 20a, the DC output voltage u₂₃ did not contain the AC component. From Figure 20b, the low order harmonic component in AC output voltage u₁₂ was well suppressed with proposed PR controller. Figure 21 shows the experimental waveforms of u₁₂ and u₂₃ when the AC load R₁₂ changed from 20 Ω to 5 Ω. The results shown in Figure 20 and Figure 21 demonstrate that the output of TPC in single DC and single AC output mode had good steady and transient responses with the proposed controller.

7. Conclusions

The simulation and experimental results proved the feasibility and correctness of the topology and control strategy of the proposed TPC in this paper. Several conclusions are summarized as follows.

(1)

A novel and simple three-port converter is proposed. It interfaces a single input power port and two output ports.

(2)

The proposed TPC has two operation modes. It can output two DC voltages with different levels or output a single AC voltage and a single DC voltage at the same time.

(3)

With the proposed control scheme, the coupling between the DC and AC output ports in TPC could be suppressed, significantly.

(4)

In the single DC and single AC output mode, the maximum of AC output voltage is half of the input voltage.