Design and Implementation Procedure of a High-Gain Three-Input Step-Up 1 kW Converter

Abstract

The use of different sources to energize a load is convenient in many applications, particularly those where two or more renewable energy sources are employed, such as energy harvesting, hybrid vehicles, and off-grid systems. In these cases, a multi-input converter is able to admit sources with different characteristics and, if necessary, select the output power of each source. Several topologies of multi-input converters have been proposed to this aim; however, most of them are based on multistage designs, which decreases efficiency and increases control complexity, particularly when more than two sources are used. In this work, a three-input step-up converter, easy to control in open loop condition, is analyzed. A designed procedure is described, and experimental results are presented for a 1 kW power converter. The implemented converter results in a higher voltage gain and less storage element, keeping high efficiency compared to similar topologies. Using the procedure here proposed, this converter that was initially designed for photovoltaic applications is enabled to be used in medium- and high-power applications, for example, when renewable energy sources are used.

1. Introduction

An intense research effort has been made to increase the use of renewable energy in all human activities. Techniques to take advantage of solar [1], wind [2] and hydrogen-based energy [3], among other clean energies, have been developed. In some applications, it is necessary to jointly use several of these sources to feed a single load. Frequently, it is a convenient scheme where, if a single source is not enough, a second source may be used; if both are not sufficient, a third can be used, and so on. To make such scheme possible, a multi-input converter is necessary [4]. Among the applications where this scheme is used are energy harvesting for wireless sensors [5], smart buildings [6], hybrid and electric vehicles [7], off-grid systems in rural areas [8], etc.

Multi-input step-up converters have been reported in the literature; some of them are based on the boost converter. For example, experimental results for a multi-input multi-output step-up converter for a 1 kW prototype are presented in [9]; this topology presents some disadvantages, like a high number of energy storage elements and a low switching frequency operation, that increase the magnetic component’s size. In [10], a dual-input step-up converter is presented for a 125 W prototype with a high efficiency of 97%, but the number of switching power devices are two per input. The number of semiconductor devices increases severely in the dual step-up converter presented in [11] for a 200 W output power and an efficiency of 87%.

In [12], a model for the dual-input case of the topology proposed in [13] was derived and analyzed, and a 500 W converter was evaluated. However, the real difficulty with the existing multi-input converters arises when more than two inputs are used, and a higher power is required. In this context, to make sure that the model and design procedure match the experimental results, a 1 kW prototype for three input voltages is implemented in this work, considering an open loop control. Efficiency and reliability of the converter are also evaluated.

2. Principle of Operation

The converter analyzed in this paper is shown in Figure 1. It was first proposed in [13] for a low power application (100 W) for two inputs. The number of components is one MOSFET to each input source added; in this case, three input voltages are considered: V_in1, V_in2 and V_in3. Since the basic construction block is the boost converter, the only added component per input is a capacitor. To obtain the control switching signals, two basic conditions need to be considered: the phase shift in the control signals, φ = 360°/inputs = 360°/3 = 120°, and the minimum duty cycle, which is given by d_min = 1 − (1/inputs) = 0.66.

Figure 1. Operating modes of the three-input step-up converter: (a) Mode 1, S1 = S2 = S3 = On, (b) Mode 2, S1 = S3 = On, S2 = Off, (c) Mode 3, S1 = S2 = S3 = On, (d) Mode 4, S1 = S2 = On, S3 = Off, (e) Mode 5, S1 = S2 = S3 = On, (f) Mode 6, S2 = S3 = On, S1 = On.

The six operating modes are shown in Figure 1. The control signals that generate these modes (M1 to M6) are presented in Figure 2. The control signals for d_min are indicated in red; it can be observed that, at any timeframe, there are two switches in conduction, at most.

Figure 2. Control signals and operating modes in the three-input step-up converter.

To analyze the operation of each mode, the following initial conditions are considered: I_L1, I_L2 and I_L3 currents are greater than zero, and C₁ and C₂ are charged to +V_C1 and +V_C2. The conditions in each operating mode are as follows:

Mode 1, ∆t₁ (see Figure 1a): This mode starts by turning on switches S1, S2 and S3 at the same timeframe; diodes D₁, D₂ and D₃ are state–off. In this interval, inductors L₁, L₂ and L₃ are charged by V_in1, V_in2 and V_in3, respectively. Currents I_L1, I_L2 and I_L3 increase linearly from its minimum value to its maximum. Considering that the average currents through capacitor C₁, C₂ and C_o are zero, voltages V_C1, V_C2 and V_Co are constant. This mode ends when switch S2 is turned off at ∆t₂.

Mode 2, ∆t₂ (see Figure 1b). In this mode, S2 is turned off, and D₂ is activated, allowing current of inductor L₂ flows through C₁ and C₂. Thus, I_L2 decreases linearly and charges C₁ and C₂, increasing their voltages. This mode ends when switch S2 is turned on at ∆t₃.

Mode 3, ∆t₃ (see Figure 1c). This mode is the same as mode 1.

Mode 4, ∆t₄ (see Figure 1d). In this mode, S3 is turned off, and D₃ is activated, allowing the current of inductor L₃ flows through C₂. Thus, I_L3 decreases linearly and charges C₂. This mode ends when switch S3 is gated ON at ∆t₅.

Mode 5, ∆t₅ (see Figure 1e). This mode is the same as mode 1.

Mode 6, ∆t₆ (see Figure 1f). In this mode, S1 is turned off, and D₁ is activated, allowing the current of inductor L₁ flows through C₁ and C_o. Hence I_L1 decreases linearly and begins to charge C_o; at the same timeframe, C₁ is discharged to R_L. This mode ends when switch S1 is gated ON.

Although modes 1, 3 and 5 are the same, they are shown for completeness.

Converter stationary ideal waveforms obtained from analysis of its six operation modes are qualitative depicted in Figure 3.

Figure 3. Ideal waveforms of three-input step-up converter.

Model Based on a State Variable Equations

To obtain a model of the converter based on the state space analysis, the state variables are chosen according to:

$$x_1=I_{L_1},$$

(1)

$$x_2=I_{L_2},$$

(2)

$$x_3=I_{L_3},$$

(3)

$$x_4=V_{C_1},$$

(4)

$$x_5=V_{C_2},$$

(5)

$$x_6=V_{C_o}$$

(6)

According to the procedure described in [12], the state space equations for the six operating modes are shown in Table 1.

Table 1. State space equations.

Modes 1, 3, 5	Mode 2	Mode 4	Mode 6
${\dot{x}}_1=\frac{V_{in1}}{L_1}$	${\dot{x}}_1=\frac{V_{in1}}{L_1}$	${\dot{x}}_1=\frac{V_{in1}}{L_1}$	${\dot{x}}_1=\frac{V_{in1}}{L_1}+\frac{x_4}{L_1}-\frac{x_6}{L_1}$
${\dot{x}}_2=\frac{V_{i{n}_2}}{L_2}$	${\dot{x}}_2=\frac{V_{i{n}_2}}{L_2}-\frac{x_4}{L_2}+\frac{x_5}{L_2}$	${\dot{x}}_2=\frac{V_{i{n}_2}}{L_2}$	${\dot{x}}_2=\frac{V_{i{n}_2}}{L_2}$
${\dot{x}}_3=\frac{V_{i{n}_3}}{L_3}$	${\dot{x}}_3=\frac{V_{i{n}_3}}{L_3}$	${\dot{x}}_3=\frac{V_{i{n}_3}}{L_3}-\frac{x_5}{L_3}$	${\dot{x}}_3=\frac{V_{i{n}_3}}{L_3}$
${\dot{x}}_4=0$	${\dot{x}}_4=\frac{x_2}{C_1}$	${\dot{x}}_4=0$	${\dot{x}}_4=-\frac{x_1}{C_1}$
${\dot{x}}_5=0$	${\dot{x}}_5=-\frac{x_2}{C_2}$	${\dot{x}}_5=\frac{x_3}{C_2}$	${\dot{x}}_5=0$
${\dot{x}}_6=-\frac{x_6}{R_L{C}_o}$	${\dot{x}}_6=-\frac{x_6}{R_L{C}_o}$	${\dot{x}}_6=-\frac{x_6}{R_L{C}_o}$	${\dot{x}}_6=-\frac{x_1}{C_o}-\frac{x_6}{R_L{C}_o}$

Let us introduce the notation for every switch state:

$$u_n=\left\{\begin{array}{lll}1& if& s{w}_n=off\\ 0& if& s{w}_n=on\end{array}\right\},n=1,2,3$$

(7)

Then, the following general state space representation can be obtained:

$$\left[\begin{array}{c}\begin{array}{l}{\dot{x}}_1\\ \end{array}\\ \begin{array}{l}{\dot{x}}_2\\ \end{array}\\ \begin{array}{l}{\dot{x}}_3\\ \end{array}\\ \begin{array}{l}{\dot{x}}_4\\ \end{array}\\ \begin{array}{l}{\dot{x}}_5\\ \end{array}\\ {\dot{x}}_6\end{array}\right]=\left[\begin{array}{cccccc}0& 0& 0& \frac{u_1}{L_1}& 0& -\frac{u_1}{L_1}\\ 0& 0& 0& -\frac{u_2}{L_2}& \frac{u_2}{L_2}& 0\\ 0& 0& 0& 0& -\frac{u_3}{L_3}& 0\\ -\frac{u_1}{C_1}& \frac{u_2}{C_1}& 0& 0& 0& 0\\ 0& -\frac{u_2}{C_2}& \frac{u_3}{C_2}& 0& 0& 0\\ \frac{u_1}{C_o}& 0& 0& 0& 0& -\frac{1}{R_L{C}_o}\end{array}\right]\left[\begin{array}{c}\begin{array}{l}{x}_1\\ \end{array}\\ \begin{array}{l}{x}_2\\ \end{array}\\ \begin{array}{l}{x}_3\\ \end{array}\\ \begin{array}{l}{x}_4\\ \end{array}\\ \begin{array}{l}{x}_5\\ \end{array}\\ x_6\end{array}\right]+\left[\begin{array}{c}\begin{array}{l}\frac{V_{in1}}{L_1}\\ \end{array}\\ \begin{array}{l}\frac{V_{in2}}{L_2}\\ \end{array}\\ \frac{V_{in3}}{L_{\begin{array}{l}3\\ \end{array}}}\\ 0_{\begin{array}{l}\\ \end{array}}\\ 0_{\begin{array}{l}\\ \end{array}}\\ 0_{}\end{array}\right]$$

(8)

3. Design Procedure and Simulation Results

Although the converter uses three different input voltages, components are designed considering the lowest voltage, V_{in min}; due to inductors, current is maximum under this condition.

The complete development of the converter design equations was derived in [12] for the two-input case. Generalization of these equations was obtained from the operating modes described in the previous section. The gain for a three-input converter, M_VDC, is:

$$M_{VDC}=\frac{V_o}{V_{in}}=\frac{3}{1-d}=\frac{3I_{inn}}{I_o},$$

(9)

where d is the duty cycle of switching devices operation, and I_inn is the input current for each source. The duty cycle is determined according to an open loop control, where the output power or the voltage gain, M_VDC, are specified_. To calculate inductance values, note that the inputs of the converter are the same as the conventional boost converter, hence:

$$L_n=\frac{V_{in}d}{\Delta I_n{f}_s},$$

(10)

where $\Delta I_n$ is the ripple current of inductor, and $f_s$ is the switching frequency.

Capacitors C₁ and C₂ were carefully designed, since a small value may generate an inadequate conversion ratio, and a very large value will affect the time response and create output voltage oscillations. Note that voltage on capacitors C₁ and C₂ affect the output voltage only through inductor currents. This can be observed from state equations, particularly from the output voltage equation; the output voltage derivative only depends on the output voltage, itself, the current x1, the load and the output capacitor. Hence, ripple voltage in these capacitors can have a wide range, since this ripple is not reflected at the converter output. As it is proved in [12], the capacitors can be calculated according to:

$$C_1=\frac{I_o\left(1-d_1\right)}{d_2\Delta V_{c1}{f}_s},$$

(11)

$$C_2=\frac{I_o\left(1-d_2\right)}{d_3\Delta V_{c2}{f}_s}$$

(12)

$$C_o=\frac{I_o(1-d_1)}{\Delta V_o{f}_s}$$

(13)

where I_o is the output current and $\Delta V_{C1}, \Delta V_{C2}, \Delta V_{Co}$ are the ripple voltage of C₁, C₂ and C_o respectively.

The converter output voltage is given by:

$$V_o=\frac{V_{in1}}{1-d_1}+\frac{V_{in2}}{1-d_2}+\frac{V_{in3}}{1-d_3},$$

(14)

Using Equations (10)–(13), the final component values are obtained and listed in Table 2, together with the design conditions. A simulation was performed in Saber™ using ideal components to validate the design procedure and the correct operation of the three-input step-up converter.

Table 2. Test parameters and components.

Parameter	Value
Lowest input voltage, Vin min	12 V
First input voltage source, Vin1	12 V
Second input voltage source, Vin2	24 V
Third voltage source, Vin3	48 V
Output voltage, Vo	190 V
Output current, Io	5.2 A
Output power, Po	1000 W
Switching frequency, fs	100 kHz
Voltage gain, MVDC	15.7
Duty cycle, dn	0.66~0.8
Phase shift	120°
Voltage ripple in C1, ΔVcp1	50 V
Voltage ripple in C2, ΔVcp2	100 V
Output voltage ripple, ΔVo	2 V
Inductors, L1, L2, L3	47 µH
Capacitor C1	0.1 µF
Capacitor C2	0.2 µF
Capacitor Co	20 µF
Output load, Ro	33 Ω

Control signals S1, S2 and S3 are shown in Figure 4 with a phase shift φ = 120° and d = 0.72 The voltages V_L1, V_L2 and V_L3 and currents I_L1, I_L2 and I_L3 are shown in Figure 5, Figure 6 and Figure 7, respectively. They can be contrasted with the ideal waveforms of Figure 3 to verify the correct operation of the converter.

Figure 4. Simulation results for digital control signal S1, S2, S3 with φ = 120° and d = 0.72.

Figure 5. Simulation results for I_L1 and V_L1.

Figure 6. Simulation results for I_L2 and V_L2.

Figure 7. Simulation results for I_L3 and V_L3.

Simulation results for output voltage and current, V_o and I_o are shown in Figure 8 with DC (average) values V_ODC = 193.39 V and I_ODC = 5.52 A, getting an output power of P_o = 1.067 kW. The ripple voltage obtained ΔV_o = 951 mV.

Figure 8. Simulation results for V_o and I_o.

4. Experimental Results

Considering that the maximum drain-source voltage is the output voltage, SiC transistors CMF20120 and diodes C3 D06060 were employed to reduce switching losses in the implemented prototype. The NXP TWR−KV 58 F220 microcontroller was used to generate the PWM pulses with a phase shifted of 120°. Inductors were designed and constructed, following the methodology presented in [14].

The efficiency of the converter is determined by:

$$\eta =\frac{P_o}{P_{i{n}_1}+P_{i{n}_2}+P_{i{n}_3}},$$

(15)

The measure input current values were:

$$I_{i{n}_1}=12.5\mathrm{A}{,}^{}{I}_{i{n}_2}=18.5\mathrm{A}{,}^{}{I}_{i{n}_3}=11.5\mathrm{A}$$

(16)

$$V_{i{n}_1}=12\mathrm{V}{,}^{}{V}_{i{n}_2}=24\mathrm{V}{,}^{}{V}_{i{n}_3}=48\mathrm{V}$$

(17)

The implemented prototype can be seen in Figure 9, where the main components are indicated. Output voltage and current are shown in Figure 10; obtained multimeter measurements are 190.9 V_DC and 5.4 A_DC. In Figure 11, it can be seen that the output voltage is 192.09 V_DC, with ripple voltage of 1.005 V_RMS, resulting in an output power of P_o = 1.037 kW.

Figure 9. Implemented 1 kW prototype.

Figure 10. Implemented 1 kW prototype with voltage and current measurement.

Figure 11. Experimental results V_o = 192.09 V_DC, ΔV_o = 1.005 V.

In Figure 12, voltage and current waveforms of inductors L₁, L₂ and L₃ are shown. Positive amplitudes in voltage waveforms are approximately equal to the value of the corresponding input voltage supply. A comparison of these waveforms with the ideal waveforms of Figure 3 and Figure 5, Figure 6, Figure 7, Figure 8 shows their similarity, validating the experimental results. Spikes and high-amplitude ripples observed in the experimental waveforms show the existence of parasitic components that are not considered in simulation.

Figure 12. Experimental results: (a) V_L1 and I_L1, input voltage V_in1 = 12 V, (b) V_L2 and I_L2, input voltage V_in2 = 24 V, (c) V_L3 and I_L3, input voltage V_in2 = 48 V.

According to Equation (15), and using the input voltages and currents, the efficiency obtained is η = 90.51%. Figure 13 shows the experimental set up: (a) three-input step-up converter, (b) three input voltage sources, (c) the PWM signal generator and (d) the 33 Ω output load.

Figure 13. Experimental prototype with three input voltage sources, 33 Ω output load and the PWM signal generator.

A comparison between the proposed converter and similar topologies is summarized in Table 3. The implemented converter provides the highest output power, keeping a high efficiency, considering three voltage sources in its design. The number of energy storage elements is less than the converters proposed in [9,10,11,12,15,16]. The high switching frequency (100 kHz) is a factor to reduce its implementation size.

Table 3. A comparison between the proposed converter and similar topologies.

Factor/Topologies	Proposed High-Gain Three-Input Step-Up Converter	High Step-Up Multi-Input Multi-Output Converter [9]	Soft-Switched Step-Up Converter [10]	Modular Step-Up Converter [11]	High-Gain Two-Input Step-Up Converter [12]	Multiphase Buck Converter [15]	Multi-Input Multi-Output [16]
Open-loop current unbalance	Minimum	Minimum	Minimum	Medium	Minimum	Medium	Medium
Output power	1.037 kW	1 kW (divided in 2 outputs)	125 W	200 W	500 W	152 W	100 W
Efficiency	90.51%	75–96.8%	97%	87%	90–95%	87–95%	86%
Number of voltage sources	3	4	2	2	2	2	2
Input voltage	24 V, 12 V, 48 V	52 V, 40 V, 50 V,	24 V, 20 V	10 V, 10 V	24 V, 24 V	100 V, 50 V	60 V, 12 V
Output voltage	190 V	453 V, 322 V	200 V	250 V	186.6 V	18.5 V	48 V
Number of power switching devices	3	4	4	7	2	5	4
Number of diodes	3	7	4	1	2	2	6
Number of inductors	3	7	3	4	2	1	3
Number of capacitors	3	4	3	4	2	1	5
Switching frequency	100 kHz	40 kHz	100 kHz	25 kHz	100 kHz	10 kHz	100 kHz