Pre-Amplificador de potencia basado en conexión paralela de convertidores DC-DC para reducción de rizados de corriente e incremento de eficiencia

Eliana Arango¹, Carlos Ramos-Paja^*1, Carlos Carrejo², Roberto Giral³, Andres Saavedra-Montes¹

¹Universidad Nacional de Colombia. Carrera 80 N.° 65-223. Medellín, Colombia.

²Laboratoire d'Analyse et d'Architecture des Systèmes LAAS-CNRS. Toulouse, France.

³Universitat Rovira i Virgili, Avda. Països Catalans 26, 43007. Tarragona, España.

Abstract

Keywords: Pre-Amplifier, interleaved converters, efficiency improvement, ripple mitigation.

Resumen

Este artículo propone un pre-amplificador basado en convertidores DC-DC conectados en paralelo para la reducción de armónicos inyectados a fuentes de potencia. Las principales características del pre-amplificador son la reducción del rizado de corriente de entrada en convertidores de potencia, incrementado además la eficiencia del sistema de conversión. Se describe el cálculo de las condiciones óptimas de operación del pre-amplificador, así como su modelado matemático y control para operar en las condiciones seleccionadas. Así mismo, se analiza el pre-amplificador con un convertidor elevador clásico, obteniendo una reducción significativa en el rizado de corriente inyectado a la fuente, así como un incremento en la eficiencia del sistema. Finalmente, los análisis teóricos se confirman a través de simulaciones circuitales y resultados experimentales.

Palabras clave:Pre-Amplificador, conexión en paralelo, eficiencia, reducción de rizado.

Introduction

Considering the problematic that establishes the global warming, fossil fuel exhaustion and the need to reduce carbon dioxide emissions provided the stimulus to develop renewable energies sources as fuel cell and photovoltaic panels [1, 2]. These options have been outlined for being two of the most attractive since they are clean, pollution free, and inexhaustible. An important aspect to consider is that these options have a series of disadvantages as the high costs of installation and maintenance, low diffusion among the users and difficulties in the process of energy storage, and such characteristics maintain them non-competitive opposite to the option of fossil-based energy resources. The appearance of new types of semiconductors, control strategies and switched devices has raised the relation cost benefit for this type of applications [3-6]. Nevertheless, the interconnection with the utility grid continues to be a weak point to consider.

It is widely known that the current harmonics generated in source-power converter interaction can seriously affect the system integrity and performance. In fuel cell applications, the current harmonics are directly related to the Oxygen- starvation phenomena, which considerably increase the natural aging of the cell membranes [7]. As for the photovoltaic applications, the current harmonics affect the performance of the control strategy, like the Maximum Power Point Tracking (MPPT) controller, reducing its accuracy and decreasing the system efficiency [8]. In this paper, the current harmonic injection to power sources by power converters is addressed through an active cancelation. Nevertheless, low frequency oscillations at double of the grid frequency are not considered since they can be addressed by control approaches [9].
]]> This paper is based on the work "A Ripple- Mitigating Pre-filter Based on Interleaved DC- DC Boost Converters", developed by the authors, which appeared in the 36th Annual Conference of the IEEE Industrial Electronics Society (IECON-2010, © 2010 IEEE), and it is focused on the development of a power conversion system able to mitigate the high frequency current harmonics generated during the converter switching, which is traditionally addressed by the typical capacitor-filtering solution [10]. The proposed solution also reduces the input capacitor requirements, decreasing its cost and avoiding the use of non-reliable electrolytic capacitors.

The remain of the paper is organized as follows. The next section analyses a classical single boost converter considering power losses. Then, the novel pre-amplifier structure considering two boost converters in interleaved topology is introduced. Furthermore, the paper presents the proposed pre-amplifier operating with a boost converter, and compares it with the classical boost approach by analytical and PSIM simulation results. Moreover, the proposed solution is validated by means of experimental results. Finally, some conclusions of the work are given.

Single boost converter analysis

The design of a DC-DC converter, boost in this case, is performed to obtain the desired current and voltage ripples. Given the switching frequency, the input and output voltage, and ripples allowed, the capacitance and inductance are designed, which are largely responsible for the converter's size. The first step is to analyze the DC-DC boost converter efficiency considering the power losses lumped in a single inductor series-resistance as depicted in figure 1. Using the volt-second balance [11] (1), the relation between the input and output voltages (2) is obtained, where T is the switching period and D the steady-state duty cycle.

Pre-Amplifier topology and control

The pre-amplifier consists of two boost converters in parallel, analyzed by considering the power losses lumped in inductor series- resistances, which scheme is depicted in figure 2(a). The active switches, MOSFETs in this case, are controlled using complementary signals. This structure is called complementary interleaving and allows reducing the ripple of the input and output variables according to the specifications. The complementary activation of the switches in the boost converters cancels inductors current harmonics reducing the ripple in the input current [1].

Dynamic model

The state equations of the pre-amplifier circuit given in figure 2(a) can be expressed as:

where X and correspond to the state variables vector and its derivatives. The Y vector contains the system inputs, and A and B matrices depend on the converter parameters.

As is described in (9), the system states are the inductor currents i_L1 and i_L2, and the output capacitor voltage v. The inputs of the system are the input voltage V_g, and the load perturbation current i_O. In steady state, the derivatives of states are cero, and the vector X is obtained as:

In sake of simplicity, the losses of both converters are considered similar, R_L ≈ R_L1≈ R_L2, and expression (11) can be simplified as:

The relation between the input and output voltages, obtained from the volt-second balance is:
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Such a condition is valid for a duty cycle equal to 50 %, or D = 0.5. Otherwise, the pre-amplifier enters in Discontinuous Conduction Mode (DCM) preventing the cancelation of the current ripples. This conclusion is obtained by applying the volt-second balance in each inductor:

From equations (14) and (15) is concluded that the only condition that ensures a Continuous Conduction Mode (CCM) for the pre-amplifier is given by:

Simulations depicted in figure 3 corroborate the previous conclusion, where the inductor drove by the smallest duty cycle operates in DCM, and therefore the duty cycles of both converters must be D = 0.5 to operate in CCM and to obtain the desired current ripple reduction. Also, from equation (13), and considering a common relation between parasitic loss-resistance and load equal to 1%, the voltage conversion ratio of this pre-amplifier is approximately 2.

The current ripple magnitudes on the inductors are given by equations (17) and (18), obtained solving the charge balance (3) for each inductor in steady-state conditions:

Considering D = 0.5, the current ripple magnitudes (17) and (18) are equal but with opposite sign. This implies that the input current will have a small ripple, and in the ideal case, null ripple.
]]> For D ≠ 0.5 one inductor enters on DCM because the CCM conditions given by (14) and (16) are not fulfilled. The inductor drove by the smaller duty cycle, and therefore with lower steady- state current, enters on DCM. This illustrated in figure 3, where a duty cycle D = 0.7 causes a discontinuous L₂ current since it is driver by D', while D = 0.4 causes a discontinuous L₁ current.

The output voltage ripple, depicted in figure 4, is calculated by analyzing the current waveforms of the load i_O(t) and output capacitor i_C(t). Figure 4 shows that the output voltage ripple is small enough to consider the load current to be constant and equal to its steady-state value. The current ripple is a sawtooth waveform with a frequency equal to the double of the switching frequency.

The voltage ripple is obtained by integrating the current ripple on the capacitor in each semi-period. It is observed in figure 4 that in each T/4 seconds the capacitor current sign changes, hence the capacitor voltage waveform is a symmetric convex parabola with a maximum value of (2Vg + ΔV/3). Calculating the integral of i_C(t) through the triangular shaded area, the amplitude in absolute value of the output voltage ripple ΔV is calculated as:

From the inductors current ripple cancelation is expected a null input current ripple, but since in each switching interval the output port and the input source are connected through one inductor, L₂ during DT seconds and L₁ during D'T seconds, an input current ripple is generated by the output voltage ripple following the small-signal relation [12]:

Since the current ripple frequency in the output capacitor should be high, its losses are small enough to be neglected. Therefore, integrating the shaded area in capacitor voltage waveform of figure 4 and dividing it by L, the amplitude of the input current ripple ΔIg is obtained as follows:

In practical implementations, there is slightly different impedances in both pre-amplifier branches, which causes a difference between the DC current components of the inductors depending on its inductance and parasitic losses tolerances. This must be addressed to ensure the ripple reduction, and therefore a closed loop control system is required. Since the PWM technique requires an external periodic signal, the sliding-mode technique has been adopted due to its simpler implementation.

The first step in sliding-mode control consists in the design of the state space region to which the dynamic of the system must be restricted, being generally called sliding surfaces. One option is to choose hyperplanes [2], meaning linear combinations of the system state variables.

There are three state variables in the pre-amplifier. Two are the inductor currents and the last one is the voltage of the output capacitor. Although there are two switches, they are considered as a single control variable because they are activated by complementary signals, and therefore a single sliding surface S(x) is required to fulfill the desired condition D = 0.5:

The small-signal dynamics are defined by:

From the sliding-mode control theory [4] and the system description, matrices A, δ, B and γ are: ]]>

where the input voltage V_g is considered constant and positive, and the inductances are equal.

The equivalent control technique [2, 5] is used to calculate the continuous value u_eq to be taken by the control variable (22) if the conditions S(x) = 0 and dS(x) / dt = 0 are achieved. Such conditions guarantee that the system trajectory is tangent to S(x) and remain trapped into it. The expression for the equivalent control is described by equation (26). In the numerator of the equivalent control there is the vector field (Ax + δ) whose expression, in this case, is given by equation (27), and likewise the denominator vector field is described by (28).

The equivalent control expression depends on the parasitic losses and state variables, and also on the system inputs V_g and i_O. In sake of simplicity, the inductors parasitic losses are considered comparable, therefore R_L1 ≈ R_L2 ≈ R_L, and the equivalent control is simplified to:

Taking into account the transversality condition (v ≠ 0), if the system trajectory is on the surface {S(x) = 0, i_L1 = i_L2}, the equivalent control is constant and equal to 0.5 (30), while the switching frequency depends on the operating conditions.

The controller has been implemented using the structure described in figure 5, where u and are the complementary signals for activating   the MOSFETs, and Δi_Ls defines the maximum difference allowed between the inductor currents, therefore the width of the sliding surface. ]]>

To illustrate the controller behavior, figure 6 shows a transient simulation where also in such conditions the inductor currents are complementary and the input current is minimum. In the simulation the input current is shown divided by two to allow its visualization in the same scale.

Pre-Amplifier based system: classicalboost interaction

This section analyses the proposed Pre-Amplifier interacting with a classical boost converter as depicted in figura 7. The main objective of this structure is to reduce the current ripple injected to the source V_g without reducing the original power conversion efficiency. In this section, the input current ripple and the efficiency of both boost and boost with active pre-amplifier are contrasted.

Steady-state analysis of the pre-amplifier based system

By applying the volt-second balance, and considering R_L1 ≈ R_L2 ≈ R_L, the input-to-output voltage conversion ratio is:

Similarly, by applying the charge balance on the circuit, the steady-state input current is:
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Finally, the efficiency of the complete conversion system is:

Comparison between pre-amplifier based solution and classical single boost

To perform a fair comparison, the power converters must be analyzed in the same conversion ratio condition and under the same load and source characteristics. The pre-amplifier based system has a higher voltage conversion ratio M(D) than the typical boost under the same source and load characteristics for a given duty cycle D. This is observed in figura 8, where considering a losses ratio R_L/R = 0.005, or 0.5 %, a M(D) = 6 is obtained by operating the boost converter in the pre-amplifier based system at D = 0.72, while in single boost solution D = 0.88 is required. This is important since in boost converters the efficiency decrease with increments in D [11].

Experimental results

Experimental prototypes of the pre-amplifier based system, i.e. scheme of figura 7, and single boost solution, i.e. scheme of figura 1, have been developed to validate the analytical results. The inductors have been selected equal to 220 μH, the capacitors have been defined equal to 220 μF, obtaining a lumped parasitic resistances of 250 mΩ in each pre-amplifier branch and single boost converters. The load has been defined equal to 29.4 Ω, obtaining a parasitic losses ratio R_L/R = 0.0085, or 0.85 %, which is comparable with the one defined in the circuital simulations. The inductor and capacitor values have been designed to achieve switching frequencies below 100 kHz and avoid electrolytic capacitors. The operating conditions have been defined by the input and output voltages V_g = 12 V and V = 40 V, respectively.

Figura 12 shows the experimental waveforms of the inductors and input currents of the pre-amplifier converter. It is observed the opposite inductor currents slope as well as the small ripple in the input current, which corresponds to a 1.3 % of the DC component. In contrast, for the same operating conditions, the single boost solution produces an input current ripple equal to 12 % of the requested DC component.

Conclusions

This paper proposes a pre-amplifier aimed to reduce the current ripple injected to power sources by traditional DC/DC converters, being particularly analyzed with a boost converter. Besides, this solution improves the efficiency of the power conversion chain over the original system.

The proposed solution is based on interleaved boost converters, and it was analyzed in terms of efficiency and input current ripple. Its optimal operating conditions were calculated, and a sliding-mode controller was designed to ensure operation in such conditions.

The new power conversion chain, composed by the pre-amplifier and the original boost converter, was analyzed and contrasted with the original single boost solution. The theoretical analyses have been confirmed through PSIM circuital simulations, and experimental measurements validated the pre-amplifier benefits, obtaining a significant reduction up to 89 % of the original input current ripple, and an improvement on the efficiency between 7.7 % and 10.1 %.

Acknowledgments

This work was supported by GAUNAL and GITA research groups of the Universidad Nacional de Colombia (projects DACOGEN-PV and MECOVA-WIND), the Spanish Ministerio de Ciencia e Innovación (project TEC2009- 13172), and the Colombian Departamento Administrativo de Ciencia, Tecnología e Innovación COLCIENCIAS (scholarship 095-2005).

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(Recibido el 9 de diciembre de 2010. Aceptado el 20 de junio de 2011)

^*Autor de correspondencia: teléfono: + 57 + 4 + 425 53 45, fax: +57 + 4+ 234 10 02, correo electrónico: caramosp@unal.edu.co (C. Ramos)