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Venkatesan et al., International Journal of Advanced Engineering Technology E-ISSN 0976-3945 Research Paper MODELING AND SIMULATION ANALYSIS OF SOLAR PV ENERGY…
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Venkatesan et al., International Journal of Advanced Engineering Technology E-ISSN 0976-3945 Research Paper MODELING AND SIMULATION ANALYSIS OF SOLAR PV ENERGY SYSTEM WITH LUO CONVERTER USING STATE-SPACE AVERAGING TECHNIQUE 1 Sundarrajan Venkatesan, 2Manimaran Saravanan Address for Correspondence 1 Assistant Professor, Alagappa chettiar College of Engineering and Technology, Karaikudi, Tamilnadu, India 2 Professor, Thiagarajar College of Engineering, Madurai, Tamilnadu, India. ABSTRACT This paper presents a modeling and simulation analysis of photovoltaic (PV) system with higher order DC-DC LUO converter using state-space averaging technique. The LUO converter has the non-inverting output and its output voltage can be more or less than input voltage with the input current being continuous. The inherent input filtering properties of LUO converter gives better output voltage and current with reduced ripples and increases the efficiency as compared to existing fundamental DC-DC converters. The state-space method is used to model the LUO converter. The PV panel simulink model is developed based on the single diode equivalent circuit of the PV module. The combined PV panel model and state-space model of LUO converter is simulated under varying environmental conditions using MATLAB SIMULINK. Incremental conductance maximum power point tracking (MPPT) algorithm is used to verify the performance of the LUO converter in a PV system. A circuitry simulation is performed under the same test conditions to validate the state-space model. The simulation result shows that state-space averaging technique yields similar performance as the result from circuitry model. The state-space technique is easier to implement as compared to circuit model. In addition, the controller design for converter in PV system with either simple or complex higher order system such as LUO converter is easily possible. KEY WORDS —Higher order power converter, incremental conductance, LUO, MPPT, and state-space averaging method. 1. INTRODUCTION: vehicles, and distributed DC systems such as space In recent year more attempts has been made to locate stations, ships, and airplanes, [15-17].Most of the renewable clean energies in the countries all over the applications need extremely low ripple in voltage and world to meet the energy demand. The solar energy current for battery operated portable devices. will play an important role in alleviating the energy Basic converters are not suitable for many crisis, it decreasing the environmental pollution and applications which required lowest ripple, higher and improving the green house effect, hence tremendous lower output voltage compared to input and high growth in the past decade. The significant research efficiency. The higher order converters such as attention on solar PV energy system is focused CUK,SEPIC and LUO converter is better one, but because of more reliable and easy to install [1-3]. CUK converter produces the output voltage higher or However, the solar PV energy system has low lower than the input voltage , with reverse polarity conversion efficiency, because of the output power of [18],[19]. The problem can be corrected easily, but solar cells mainly depends on factors such as this will inevitably lead to the increased in size and temperature and irradiance. To maximize the output cost of the converter. At the same time, the SEPIC power of PV and provide a constant or regulated and LUO converter does not suffer from this output voltage, there are a number of MPPT problem. The literature does not have sufficient techniques [4] and DC–DC converters are employed report of DC-DC LUO converter and its dynamic and play a vital role in solar PV system [5]. performance in conjunction with solar PV panel fed Different MPPT techniques have been developed and energy system. published such as hill climbing/ perturb and observe During the past two decades, different modeling of (P&O), incremental conductance (Inc-cond.) method, the DC-DC converters has been carried out by fractional open circuit voltage, fractional short circuit researchers to increase the power conversion current, Fuzzy logic and neural networks [6- efficiency in PV system [20-22]. The PWM and 11].These techniques differ in many aspects such as averaged switch model strategies are based on required sensors, time, complexity of the algorithm to equivalent circuit manipulation. The state-space track the MPP, implementation cost and the ease of model is the mathematical model that provides a implementation. Among these most suggested MPPT dynamic model of a physical system. In the state- algorithms hill climbing/ P&O and Inc-cond. space average (SSA) technique, differential equations algorithm are the center of attention because of their for a system are written in canonical form simplicity and ease of implementation. P&O (matrices).Hence, it is convenient for analyzing algorithm is not precise enough because it fails to complicated converter topologies through state space quickly track the MPP under fast varying modeling process of higher order converters. atmospheric conditions and they perform steady-state In this paper, Inc-cond. algorithm with fixed step size oscillations at MPP, which consequently waste the is used for simulation. DC-DC LUO converter energy [12]. The Inc-cond. method is the one which topology is considered for analysis and the state- exhibits better performance than other techniques space model for a non-isolated fourth-order DC-DC [13, 14]. In this algorithm, the array terminal voltage LUO converter is derived and the result comparisons is always adjusted according to its value relative to are made with circuit model in terms of PV and the MPP voltage by measuring the incremental and converter output voltage and current for various instantaneous array conductance of the PV module. irradiation conditions and at constant temperature. By In DC-DC converter perspective, all existing using this model, system matrices are derived, and a converter topology used in solar PV-based system MATLAB coding is written to extract the relevant such as buck, boost, buck-boost and higher order transfer functions particularly the audio susceptibility converters CUK,SEPIC converters have its own of the converter and control-to-output transfer unique characteristics and are employed in a number function of the DC-DC LUO converter and its of applications such as electric traction, electric stability is analyzed through bode plot. Int J AdvEngg Tech/Vol. VII/Issue II/April-June,2016/770-777 Venkatesan et al., International Journal of Advanced Engineering Technology E-ISSN 0976-3945 2. MATHEMATICAL MODEL FOR PV whose specification details are given in Table1. Fig.2 MODULE: (a) & (b) presents the current-voltage (I-V) and The basic structural unit of a solar module is the PV power-voltage (P-V) characteristics of the PV panel cells. It is an electrical device that converts the under different solar irradiation condition at a energy of light directly into electricity by the constant temperature of 25oC. photovoltaic effect. A single diode equivalent circuit model of a solar cell is shown in Fig.1. It is modeled by a current source, a diode and two resistors. The diode is connected in parallel to current source; the photon energy incident on the PV cell generates current. The current source (Iph) is proportional to the amount of energy incident on PV cell [23-25]. (a) Fig.1: Equivalent single diode model of a solar cell The I-V and PV curves of the PV are obtained by the equation (1-5). The PV cell light generated current Iph depends on the solar irradiation and temperature as given by (1) I ph  G k [ I sc  K i (Top  Tref )] (1) The PV module reverse saturation current is given by (b) I sc Fig 2. (a): I-V and (b) P-V characteristics of 40W solar I rs  panel under varying irradiation condition at 25oC. (Voc q N s KATop ) 1 e (2) Table 1 Electrical specification at 1000W/m2and 25oC The module diode saturation current Io varies with the (40-Watt solar panel) cell temperature and is given by (3) Parameter Value Top q * E go 1 1 Rated power 40W I o  I rs [ ]3 exp[ {  } Tref BK Tref Top Voltage at maximum Power(Vmp) 17.4V (3) Current at maximum Power(Imp) 2.29A The solar cell output current is given by Open circuit voltage(Voc) 21.8V I pv  I ph  I o  I sh (4) Short circuit current(Isc) 2.45A Equation (4) can be rewritten by substituting from 3. MAXIMUM POWER POINT (MPP) equation (1-3) and obtained as TRACKING: I pv  N P * I ph  N P I o [exp{ q * (V pv  I pv Rs )}  1] 3.1Basics and Load Matching of MPPT  (V pv  I pv Rs ) / Rsh Technique: (5) PV module has a maximum power point for a given where temperature and insolation. Fig.3 shows the PV Vpv :Output voltage of a PV module (V) module directly interfacing to load. If a load line Ipv :Output current of a PV module (A) crosses this point, maximum power would be Iph :Light generated current in a PV module (A) Gk :Constant which is equal to µ/1000; transferred to the load and it is well known that the P- µ :Irradiation( Irradiation level) (W/m2) V characteristics has only one point where power is IO :Diode saturation current (A) maximum, and the corresponding voltage is VMPP and q :Electron charge (1.6×10-19 C) current is IMPP. The optimum value of load resistance k :Boltzmann constant (1.38×10-23 J/K) is obtained by PV voltage and PV current at MPP and Ki :Temperature co-efficient at short-circuit current is given by equation (6). ISCr is 0.0017A / oC A=B :p-n junction ideality factor =1.6 Top :Cell operating temperature in ⁰C Tref :Cell reference temperature at 25⁰C Rs :Solar cell series resistance (Ω) Rsh :Solar cell shunt resistance (Ω) Fig.3: PV module directly interfacing to Load ISC :PV module short-circuit current at 25 oC The optimum resistance of PV module is described as and 1000W/m2 VMPP Ego :Band gap for silicon = 1.1 eV Ropt  Ns :Number of cells connected in series in the I MPP (6) module The load resistance of the circuit is, Np :Number of cells connected in parallel in the module VO The solar panel output power depends on the voltage RL  IO (7) and current obtained at its output terminals and there exists one operating voltage at which the solar panel where VMPP is the maximum PV voltage at MPP and can produce maximum power. A 40W PV module is IMPP is the maximum value of PV current at the MPP, taken as the reference model for simulation setup, Vo and Io are the converter output voltage and current Int J AdvEngg Tech/Vol. VII/Issue II/April-June,2016/770-777 Venkatesan et al., International Journal of Advanced Engineering Technology E-ISSN 0976-3945 respectively. reference voltage at which the PV array is forced to When the value of load resistance (RL) matches with operate. At the MPP, Vrefequals to VMPP. Once the that of Ropt maximum power transfer from MPP is reached, the operation of the PV array is photovoltaic panel to the load will occur. The maintained at this point unless a change in ΔI is objective of the MPPT is to make the load resistance noted, which is due to the change in atmospheric of the PV module to be equal to the optimal conditions. The algorithm decrements or increments resistance of the solar panel. Vref to track the new MPP. At the MPP, no control R opt  R L action is needed, therefore the adjustment stage will be bypassed and the algorithm will update the stored In order to achieve the above, and extract the parameters at the end of the cycle as usual. The Inc- maximum power from PV panel, DC-DC converter is Cond. technique is used the instantaneous inserted in between the PV panel and load and its conductance and the incremental conductance to duty cycle is varied. In this paper DC-DC LUO generate an error signal converter is used. The voltage gain of the higher order LUO converter = + (10) is given by From (10), we know that e goes to zero at the MPP, Vo D but it is rarely occurs in practical implementation,  Vin 1  D and a small error is usually acceptable. In this paper where “D” is the duty cycle of the converter. the error value e is taken as 0.02. Measurements of The variation of the duty cycle is not only regulating the instantaneous PV array voltage and current the output voltage but also can be used to vary the require two sensors, which can easily keep track of input side impedance of the converter. The DC-DC previous values of voltage and current and make all converter can be controlled to present optimum the decisions as per the flow chart; duty cycle is impedance at the PV array terminals which facilitate varied according to the algorithm. maximum power extraction from an array. This feature can be appreciated by inspecting the input side impedance (Rin) expressions for the converters. The input impedance of the higher order DC-DC LUO converter can be calculated by 2 2  1  D  V0  1  D  (8) Rin      RL  D  I0  D  The equation (8) indicates that by changing duty cycle, the input impedance (Rin) of converter should be equal to the optimum impedance (Ropt) at which the system is working at MPP. 3.2 Implementation of Inc-Cond. Method: The Inc-Cond. method is based on the fact that the slope of the PV array power curves as shown in Fig. 4. It is zero at the MPP, positive on the left of the MPP, and negative on the right, as given by Fig.5: Flowchart of Inc-Cond. algorithm MPPT 4. MODELING OF DC-DC LUO CONVERTER USING STATE-SPACE TECHNIQUE: The state-space-averaging approach [26] is widely used to derive the expressions and analysis for the small-signal characteristics of PWM-controlled DC- DC converters. It consists of state equation and output equation that reveals the characteristics of the particular physical system. It exhibits the dynamic behavior of a system or switching converter using computer simulations, which is very useful in the design of controllers. The operation of the state-space Fig.4: Basic of Inc-Cond. MPPT method model of the converters are described by the ( ) ∆ following basic state equations = = + = + (9) ∆ X (t )  Ax (t )  Bu (t ) The equation (9) can be rewritten by, ∆ Y (t )  Cx (t )  Du (t ) = − ;at MPP (11) ∆ ∆ where, − ;left of MPP ∆ x(t) = The state variable, u(t) = The input vector, ∆ − ;right of MPP parameter A is the state matrix, parameter B is the ∆ The MPP can thus be tracked by comparing the input matrix, C is output matrix and D is the instantaneous conductance (I/V) to the incremental transition matrix. conductance (ΔI/ΔV) as shown in flowchart as given In an electrical system, the method to identify the set in Fig.5 for Inc-Cond. algorithm MPPT. Vref is the of state variables is by identifying the number of Int J AdvEngg Tech/Vol. VII/Issue II/April-June,2016/770-777 Venkatesan et al., International Journal of Advanced Engineering Technology E-ISSN 0976-3945 energy storage elements. With that, the nth order of  . . the system can also be known. Using this state-space   1 average model of DC–DC converter, one can obtain  X 1  v in   L 1 the small signal model and transfer function of  X 2   1 v  1 v 1  C1 C2  v in converter, which will be very useful in the design of  L2 L2 L2 closed-loop controller using various control   1 techniques [27–28].  X 3  C iL2   1 The most superior advantages of DC-DC LUO  X 4  1 i  1 v converter is capacitor (C) assures the galvanic  C2 2 L RC 2 C2 insulation between input and output. The short circuit (12) or breakdowns of the load do not affect solar panels. 0 0 0 0  1 1 1 The additional filter elements in the LUO-converter  iL1  0 0     iL1   L    L2 L2    1  eliminate the output ripples and enhance the output d  iL2     iL2   1   1 voltage level effectively [29]. However, this type of dt  vC1  0 C 0 0   v    L  vin      C1   2  converter is still under research with regard to its 1 0 vC2  0 1  1  vC2    usage in industrial and domestic applications. 0   C2 RC2   0   4.1 States-Space Equation: (13) Fig.6(a) shows a higher order DC-DC LUO The output equation is expressed by (14), converter, which is used as the power stage interface  iL1  between the PV module and the load. The LUO i  converter can operate either in continuous conduction Vo   0 0 01 L2  vC1 mode (CCM) or discontinuous conduction mode   (DCM) depending on the current flowing through L1. v  C2  (14) In this paper CCM mode of operation is considered. During off state, the state equations are written by The DC-DC converter has two modes of operation. (15) using Fig 6(c), (i)When the switch S is closed (ON), in this mode,   1 the capacitor releases energy to the output. (ii) When  X 1   L vC 1 the switch S is in OFF, the current drawn from the  1 source becomes zero, and current iL1 flows through X 2   1 v C the diode to charge capacitor C1.The equivalent  L2 2  1 circuit of the LUO converter when switch is ON and X 3  iL OFF state as shown in Fig.6 (b)&(c).  C1 1   1 1 X4  iL  vC  C2 RC 2 2 2 (15)  1  0 0  L1 0   iL1    0 1  iL1  0   0 0      (a) d  iL2   L2   iL2  0    v     vin dt  vC1  1    0 0 0   C 1  0  vC 2  C  1  vC 2  0  1 1  0 0   C2 RC2  (16) The output equation, is expressed by  iL1  (b) i  Vo   0 0 01 L2  vC1   vC2  (17) The state-space equations have been implemented in MATLAB/Simulink, where the Simulink block is illustrated in Fig.7 (c) 5. SIMULATION RESULTS AND DISCUSSION: Fig.6: Circuit diagram of (a) LUO converter (b) Switch In order to validate the state-space model, a circuitry ON condition (c) Switch OFF condition simulation of the proposed PV system is connected in The fourth order elementary LUO converter made up parallel with the state-space model. Both the state- of two inductors and two capacitors and capable of space and circuitry models were developed in working in either step-up or step-down mode. The MATLAB/Simulink as shown in Fig. 8. state variables of the LUO converter (x1, x2, x3, x4) are The state-space model PV system was simulated considered as currents i L 1 and iL2 , voltages V c 1 and under different irradiance conditions. The function of the MPPT block is to ensure that the system delivers Vc 2 respectively. the maximum power to the load by varying the duty The state equation derivation for the LUO converter cycle of the higher order DC-DC LUO converter. for the ON and OFF state of the switch can be The LUO converter is fed by PV source and designed described by the following equations (13) and (16) for 40W/24 V, under the nominal maximum point respectively. These equations are expressed using the (irradiance G = 1000 W/ m2 and temperature T = switching function, when the switch is ON 25°C). This output value may change as the Int J AdvEngg Tech/Vol. VII/Issue II/April-June,2016/770-777 Venkatesan et al., International Journal of Advanced Engineering Technology E-ISSN 0976-3945 Vin, min I o  D max L1   D max ΔVC1  ΔI L1  f s C1  f S Selection of Selection of Inductors Vin, min Capacitors DmaxVin min L2   D max VC 2  ΔI L2  f s 8C 2 L2 f s2 (18) irradiance and temperature level of PV changes. The the MPPT controller tracks the new maximum component of the LUO converter used in the power point and the power output of the PV array simulation is calculated from the equation (18) and is which is 24W at 600W/m2 is increased to 40W at given in table 2.The DC-DC LUO converter was 1000W/m2. The voltage of the PV module is designed to operate at the switching frequency of 25 increased from 15.2V to 17.4V under that condition. kHz. Table 2 Specification of LUO Converter Components Specifications Inductor, L1& L2 69mH& 19mH Capacitor,C1&C2 220µF & 47µF Resistive load, R 15 ohm Switching frequency 25 kHz Input voltage 10.5V-17.5V Output voltage 24V at 1000W/m2 To test the effectiveness of proposed PV system, simulation is
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