STEP UP CONVERTER USING MATLAB-SIMULINK AND SIMPLORER PDF

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Page Proof January 21, 2016 17:28 WSPC/262-IJMSSC/S1793-9623 1650004 1 International Journal of Modeling, Simulation, 2 and Scientific Computing 3 Vol. 7, No. 3 (2016) 1650004 (13 pages) 4
c World Scientific Publishing Company 5 DOI: 10.1142/S1793962316500045 6 Analysis, modeling and simulation of st...

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1650004

International Journal of Modeling, Simulation, and Scientific Computing Vol. 7, No. 3 (2016) 1650004 (13 pages) c World Scientific Publishing Company
DOI: 10.1142/S1793962316500045

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Analysis, modeling and simulation of step up converter using Matlab–Simulink and simplorer

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Walid Emar

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Department of Electrical Engineering Isra University, Amman 11622, Jordan [email protected]

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Received 23 February 2015 Accepted 20 November 2015 Published

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The basic configuration of step up converter usually used in photovoltaic solar systems to increase the DC voltage generated at their outputs suffers from some drawbacks just like high ripple in the output voltage, greater losses in the system and unstable dynamic behavior. To eliminate these drawbacks, this paper introduces a two-phase connection of step up converter with uncoupled smoothing reactors. Detailed analysis, simulation and control strategy have been proposed in this paper to investigate the advantages of using such connection with uncoupled reactors. This paper is intended to prove that two-phase connection with uncoupled reactors helps increasing the output power of the converter, minimizing its output ripple and making its control easier and more efficient. It also increases the converter chopping frequency and consequently decreases the size of smoothing reactors and filters used in the system. Concerning the design of such converters, it requires a long working period of time with a significant cost and specific technical tests at nominal operating points. Therefore, simulation can essentially decrease economic and development costs. Using modulation and simulation software techniques (Simplorer, Simulink, and Matlab) throughout this paper helped simulation of very fast the converter behavior and accurate determination of its dynamic characteristics. Moreover, the paper deals with modulation of voltage control technique using Matlab and Simplorer, thus regulating the converter output current and voltage. Simulation results show that this control technique provides robust output current and voltage of step up converters and is more feasible for their chopper up conversion technique.

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Keywords: Step up converter; uncoupled smoothing reactors; two-phase and basic configuration; voltage mode control technique.

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1. Introduction

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One of the biggest problems in the power generation that meets the needs of world is the daily increase in the energy demands with the unavailability of the energy resources. With the development of industrial and commercial applications and

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technologies, the demand for alternative energy systems and power processors for efficiently controlling the efficiency and power conveyance of these systems has also dramatically increased. Furthermore, the fuel used for operating the fossil systems has dramatically reduced. This adversely affected the surrounding air and cumulatively increased the global warming of nature.1–3 Renewable energy sources such as solar panels and wind energy systems are being preferably used in this regard because they are environmentally friendly and cleaner for nature. However, they have some drawbacks since they usually produce a power of low voltage level which may not be sufficient for the electric network and power appliances.4,5 These drawbacks are usually overcome through the use of power electronic processors known as step up converters. The utilization of such processors improves the dynamic performance and efficiency of renewable energy sources. However, the continuous on–off switching process of these power electronic processors produces fluctuated waveforms in the input and output currents and voltages with certain harmonic content which increases the losses and makes their control more sophisticated and complex.1,2 In this paper, a step up converter with two channels connected in parallel is discussed. This solution may completely remove the ripple generated at the output, increases the power from the converter, improves efficiency and the overall dynamic behavior as well as increasing the switching frequency and consequent lower the size of reactors. The outputs of the two-phase step up converter are combined through uncoupled smoothing reactors.2,3 The equal division of the currents into the individual channels is achieved using voltage mode control which is developed in such a way just to yield a dynamic accuracy in the model and robustness in the load. Control algorithms of such converter are mainly used to determine the duty ratio and triggering pulse with modulation (PWM) signals required to operate the converter switches adequately in its both uninterrupted and interrupted regimes.3 This paper also proposes in addition to Simulink in Matlab a very specific technique for modulating and simulating the converter with Simplorer based on the static fixed topology approach where semiconductor characteristics are considered to be impedances with very low values in their on-state and very high values in their off-state. Therefore, the mathematical model of the system does not depend on the state of the semiconductors of the converter.1,5,8 Simplorer also provides a chance of using the so-called dynamic variable topology. The mathematical model of the converter then depends on the dynamic state characteristics of its semiconductors. Therefore, Simplorer helps improve converter modeling for Simulink control design and help design a better converter and controller by allowing the user to develop a design that combines predefined basic and industry-specific components with user-defined models. The user can create models in common programming languages or standard modeling languages such as VHDL-AMS.1,8 1650004-2

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Analysis, modeling and simulation of step up converter 1

2. Analysis of Two-Phase Step Up Converter

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This section deals with the analysis, simulation and modeling of two-phase step converter with linear components commonly encountered in the electrical energy conversion. In the topology of Fig. 1(a), the two-phase step up converter is usually employed in current–voltage conversion applications and to efficiently control the transfer of power between various types of electrical systems. This converter has two legs operating in parallel, S1 , D1 and S2 , D2 . It operates with a time period T where each switch is on for ton and off for the rest of this period (toff = T −ton ). The switching of individual switches is nonsimultaneouse and out of phase by a time T /n, where n is the number of phases. The load is considered to be an inductance La and resistor Ra .

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(a)

(b) Fig. 1. (a) Two-phase conventional step up converter with magnetically uncoupled smoothing reactors and (b) Two-phase step up converter model in SIMULINK. 1650004-3

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The output DC voltage generated from the solar panel, Vs is connected to the load via the converter phases through its magnetically uncoupled smoothing reactors. Each of these smoothing reactors is a passive electrical element from a coil of wire wrapped around solid magnetic core to concentrate the coil magnetic flux within its turns. This results in a much stronger magnetic field than that produced by a simple coil of wire without a magnetic core. The smoothing reactors also serve the purpose of storing energy during the on-mode of the switches and delivering it to the load during their off-mode just to increase voltage at the load.4,6,7

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2.1. Two-phase step up converter model in simplorer

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The most common strategy for controlling the switching technique of the semiconductor devices of the converter is by using PWM. A control voltage representing the desired output voltage is compared to a triangular voltage generated from a function generator of a high frequency representing the switching frequency of the converter.9–11 The currents and voltages of individual phases are then determined by a state of switching of the converter semiconductor devices that depends on the difference between the control voltage and the triangular voltage. Four cases can occur as explained in Fig. 1(b): (1) (2) (3) (4)

S1 S1 S1 S1

state state state state

off and S2 on and S2 on and S2 off and S2

state state state state

off, whereas D1 on, whereas D1 off, whereas D1 on, whereas D1

state on and D2 state off and D2 state off and D2 state on and D2

state state state state

on. off. on. off.

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Two operating modes are then counted: continuous conduction mode (CCM) and discontinuous conduction mode (DCM).

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2.1.1. Continuous conduction mode (CCM)

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Traditionally, the two-phase step up converter with magnetically uncoupled smoothing reactors, as shown in Fig. 1(a), highly reduces the total current peak-to-peak ripple flowing into the output capacitors and significantly increases the power as compared to the fundamental structure of this converter. So, assuming a CCM of operation and ideal switches, then the mathematical model describing the system when switch S1 is on is given as follows1,6 : i1 (t) = i1 (0) +

1 Vs ton . L1

(1)

In the off-state of switch S1 , the voltage across smoothing reactor L1 changes its polarity which causes diode D1 to turn on and to drive the smoothing reactor current, i1 , through the load. Assuming zero voltage drops across diode D2 , and large input output capacitive filters just enough to keep the supply voltage and the 1650004-4

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Analysis, modeling and simulation of step up converter

load voltage constants, Vs and Vo , then it yields: −Vs − L1

di1 L1 ∆i1 + Vo = 0 ⇒ toff = . dt Vo − Vs

(2)

Equation (2) indicates that the current through the smoothing reactor should decrease since the voltage across it has a reversed polarity compared to the switch on-state. Since the current instantaneous ripple in each phase is during the on-state of its active switch is equal to the ripple in the off-state of this switch, then the average output voltage of the load could be defined as Vo =

Vs ⇒ Vs = (1 − k)Vo . 1−k

(3)

The current peak-to-peak ripple of phase current i1 is given as: T = ton + toff , Vo = 1 2

Vs Vs (Vo − Vs ) k(1 − k)Vo ⇒ ∆i1 = = , (1 − k) f L1 Vo f L1

(4)

where k = ton /T respective T = 1/f are defined as the duty time ratio respective to the switching frequency of the controller. Provided that all smoothing reactors have identical design conditions whereas L1 = L2 = L3 = L, then the converter input current, is , is given as the sum of phase currents, i1 and i2 . Therefore, the peak-to-peak ripple of the input source current is of n-phase converter, may be determined for 0 ≤ k < 1/2 from the steep rise of this current during on-state of one switch and off-state of the remaining switch as shown in Fig. 2(a).3,6 Thus, when switch S1 is on,

 Vs (j − 1)T (j − 1t)T Vo − Vs ∆is = j ton − − (2 − j) ton − . (5) L 2 L 2 During the second time interval that occurs when 1/2 ≤ k < 1, the instantaneous ripple of current is may be determined from its steep fall when both switches are simultaneously on. This gives the following value for the current instantaneous ripple in this region:
 Vs T Vo (3k − 2k 2 − 1). (6) ∆is = 2 ton − = L 2 fL

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Equations (4) and (6) show that the peak-to-peak current ripple of the converter current is directly proportional to the supply voltage Vs or the output voltage vo and inversely proportional to the chopping frequency of the converter f and the smoothing reactor’s inductance L.1,5,7 The chopping frequency is a dynamic parameter which has an influence on the behavior of the converter and on its cost as well as on the cost of the supply. But it also has some drawbacks just like increasing the switching losses and decreasing the conversion ratio of the converter. Therefore, it is good to find a compromise between adding magnetically uncoupled smoothing reactors and using high frequency devices 1650004-5

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W. Emar Channel currents, i1 and i2 with input current and voltage, is and Vs

Converter input voltage and current, Vs and i1 200.00 180.00

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i1.I [A] i2.I [A] is.I [A] Vs.V [...

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Phase voltage, v1 with the output capacitive voltage and current, vo and ic

Phase voltage, v1 with the output capacitive voltage and current, vo and ic ic.I [A] vo.V [V] v1.V [V]

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Plot of converter input current, is versus its load current, ia

Plot of converter load current, ia versus its input current is= i1 ia.I [A]

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ic.I [A] vo.V [V] v1.V [V]

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Plot of converter output voltage, vo versus its input voltage, Vs

PLot of converter output voltage, vo versus its input voltage, Vs vo.V [V]

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Fig. 2. Current and voltage steady state and transient waveforms of step up converter for k = 1/2 in the continuous mode: (a) fundamental connection and (b) two-phase connection.

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just to achieve the above-mentioned advantages of the high frequency operating converter.11–13 The absolutely maximum instantaneous ripple value occurs at k = 1/4 for 0 ≤ k < 12 and at k = 3/4 for 1/2 ≤ k < 1. This maximum value is obtained 1650004-6

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Analysis, modeling and simulation of step up converter

by differentiating ∆is (t) in Eq. (6) with respect to duty time ratio k and making the result equal to zero which results in ∆is max = 1 2 3 4 5

Vs . 8f L(1 − k)

(7)

Equation (7) has a good practical significance, since it facilitates an approximate calculation of the current ripple and helps in the selection of the appropriate smoothing reactors for its reduction. Figure 2 illustrates the waveforms of the converter input and output voltage and currents in the continuous mode. The parameters used for simulation in Simplorer are switching frequency f = 250 Hz, reactor’s

Output voltage and load current, vo and ia with output capacitive filter current, ic in DC vo .V [V] ic.I [A] ia.I [A]

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Phase voltages v1, v2 with output voltage vo in DCM v1.V [V] v2.V [V] vo .V [V]

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Fig. 3. Current and voltage steady state waveforms of two-phase step up converter for k = 1/2 in discontinuous mode. 1650004-7

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inductance values L1 = L2 = 10 mH, load inductance La = 1 mH and load resistance Ra = 10 Ω. The supply voltage of the converter is about Vs = 55 V and it operates on a duty time ratio of k = 0.5.

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2.1.2. Discontinuous conduction mode (DCM)

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In the previous analysis, the inductance of the smoothing reactor was considered to be very large and due to the use of high frequency devices in the converter, all currents in the circuit have normal continuous waveform and they do not even touch the zero axis during the converter operating period as shown in Fig. 2. Otherwise, the source, the phase and the load currents are not sustained throughout the converter operating period as shown in Fig. 3.7–9 The parameters used for the simulation in the DCM are switching frequency f = 50 Hz, reactor’s inductance values L1 = L2 = 2 mH, load inductance, load resistance, duty time ratio and supply voltage of the converter have same values as in CCM. Therefore, during the on-state respective off-state of any phase, the discontinuous phase current is expressed as follows:

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i1 (t) =

Vs Vs Vo − Vs t respective i1 (t) = ton − (t − ton ), L L L

(8)

I1 lim =

Vo Vo (1 − k)k respective Is lim = n (1 − k)k. 2f L 2f L

(9)

However, if the source current also has a discontinuous waveform as shown in Fig. 3, then it would touch the limits of interruption exactly at tx = T /n. Therefore, the boundary condition for the source curr...