Venkatesan et al., International Journal of Advanced Engineering Technology E-ISSN 0976-3945
Research Paper
1
Sundarrajan Venkatesan,
2
Manimaran 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:
In recent year more attempts has been made to locate renewable clean energies in the countries all over the world to meet the energy demand. The solar energy will play an important role in alleviating the energy crisis, it decreasing the environmental pollution and improving the green house effect, hence tremendous growth in the past decade. The significant research attention on solar PV energy system is focused because of more reliable and easy to install [1-3].
However, the solar PV energy system has low conversion efficiency, because of the output power of solar cells mainly depends on factors such as temperature and irradiance. To maximize the output power of PV and provide a constant or regulated output voltage, there are a number of MPPT techniques [4] and DC–DC converters are employed and play a vital role in solar PV system [5].
Different MPPT techniques have been developed and published such as hill climbing/ perturb and observe
(P&O), incremental conductance (Inc-cond.) method, fractional open circuit voltage, fractional short circuit current, Fuzzy logic and neural networks [6-
11].These techniques differ in many aspects such as required sensors, time, complexity of the algorithm to track the MPP, implementation cost and the ease of implementation. Among these most suggested MPPT algorithms hill climbing/ P&O and Inc-cond. algorithm are the center of attention because of their simplicity and ease of implementation. P&O algorithm is not precise enough because it fails to quickly track the MPP under fast varying atmospheric conditions and they perform steady-state oscillations at MPP, which consequently waste the energy [12]. The Inc-cond. method is the one which exhibits better performance than other techniques
[13, 14]. In this algorithm, the array terminal voltage is always adjusted according to its value relative to the MPP voltage by measuring the incremental and instantaneous array conductance of the PV module.
In DC-DC converter perspective, all existing converter topology used in solar PV-based system such as buck, boost, buck-boost and higher order converters CUK,SEPIC converters have its own unique characteristics and are employed in a number of applications such as electric traction, electric vehicles, and distributed DC systems such as space stations, ships, and airplanes, [15-17].Most of the applications need extremely low ripple in voltage and current for battery operated portable devices.
Basic converters are not suitable for many applications which required lowest ripple, higher and lower output voltage compared to input and high efficiency. The higher order converters such as
CUK,SEPIC and LUO converter is better one, but
CUK converter produces the output voltage higher or lower than the input voltage , with reverse polarity
[18],[19]. The problem can be corrected easily, but this will inevitably lead to the increased in size and cost of the converter. At the same time, the SEPIC and LUO converter does not suffer from this problem. The literature does not have sufficient report of DC-DC LUO converter and its dynamic performance in conjunction with solar PV panel fed energy system.
During the past two decades, different modeling of the DC-DC converters has been carried out by researchers to increase the power conversion efficiency in PV system [20-22]. The PWM and averaged switch model strategies are based on equivalent circuit manipulation. The state-space model is the mathematical model that provides a dynamic model of a physical system. In the statespace average (SSA) technique, differential equations for a system are written in canonical form
(matrices).Hence, it is convenient for analyzing complicated converter topologies through state space modeling process of higher order converters.
In this paper, Inc-cond. algorithm with fixed step size is used for simulation. DC-DC LUO converter topology is considered for analysis and the statespace model for a non-isolated fourth-order DC-DC
LUO converter is derived and the result comparisons are made with circuit model in terms of PV and converter output voltage and current for various irradiation conditions and at constant temperature. By using this model, system matrices are derived, and a
MATLAB coding is written to extract the relevant transfer functions particularly the audio susceptibility of the converter and control-to-output transfer function of the DC-DC LUO converter and its 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
MODULE:
The basic structural unit of a solar module is the PV cells. It is an electrical device that converts the energy of light directly into electricity by the 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 (I ph
) is proportional to the amount of energy incident on PV cell [23-25]. whose specification details are given in Table1. Fig.2
(a) & (b) presents the current-voltage (I-V) and power-voltage (P-V) characteristics of the PV panel under different solar irradiation condition at a constant temperature of 25 o
C.
(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 I ph
depends on the solar irradiation and temperature as given by (1)
I ph
 G k
[ I sc
 K i
( T op
 T ref
)]
(1)
The PV module reverse saturation current is given by
I rs

I sc e
(
V oc q
N s
KAT op
)  1
(2)
The module diode saturation current I o varies with the cell temperature and is given by (3)
I o
 I rs
T op
T ref
3
q
E
BK go
T ref

T op
(3)
The solar cell output current is given by
I pv
 I ph
 I o
 I sh
(4)
Equation (4) can be rewritten by substituting from equation (1-3) and obtained as
I pv
 N
P
* I ph
 N
P
I o
[exp{ q * ( V pv
 I pv
R s
)}  1 ]
 ( V pv
 I pv
R s
) / R sh (5) where
V pv
:Output voltage of a PV module (V)
I pv
:Output current of a PV module (A)
I ph
:Light generated current in a PV module (A)
G k
:Constant which is equal to µ/1000;
µ :Irradiation( Irradiation level) (W/m
2
)
I
O
:Diode saturation current (A) q :Electron charge (1.6×10
-19
C) k :Boltzmann constant (1.38×10
-23
J/K)
K i
:Temperature co-efficient at short-circuit current
I
SCr
is 0.0017A / o
C
A=B :p-n junction ideality factor =1.6
T op
:Cell operating temperature in ⁰ C
T ref
:Cell reference temperature at 25 ⁰ C
R s
:Solar cell series resistance (Ω)
R sh
:Solar cell shunt resistance (Ω)
I
SC
:PV module short-circuit current at 25
and 1000W/m 2 o
C
E go
:Band gap for silicon = 1.1 eV
Ns :Number of cells connected in series in the
module
Np :Number of cells connected in parallel in the
module
The solar panel output power depends on the voltage and current obtained at its output terminals and there exists one operating voltage at which the solar panel can produce maximum power. A 40W PV module is taken as the reference model for simulation setup,
Int J AdvEngg Tech/Vol. VII/Issue II/April-June,2016/770-777
(b)
Fig 2. (a): I-V and (b) P-V characteristics of 40W solar panel under varying irradiation condition at 25 o
C.
Table 1 Electrical specification at 1000W/m
2 and 25 o
C
(40-Watt solar panel)
Parameter Value
Rated power 40W
Voltage at maximum Power(Vmp) 17.4V
Current at maximum Power(Imp)
Open circuit voltage(Voc)
Short circuit current(Isc)
2.29A
21.8V
2.45A
3. MAXIMUM POWER POINT (MPP)
TRACKING:
3.1Basics and Load Matching of MPPT
Technique:
PV module has a maximum power point for a given temperature and insolation. Fig.3 shows the PV module directly interfacing to load. If a load line crosses this point, maximum power would be transferred to the load and it is well known that the P-
V characteristics has only one point where power is maximum, and the corresponding voltage is V
MPP
and current is I
MPP
. The optimum value of load resistance is obtained by PV voltage and PV current at MPP and is given by equation (6).
Fig.3: PV module directly interfacing to Load
The optimum resistance of PV module is described as
R  opt
V
MPP
I
MPP (6)
The load resistance of the circuit is,
R
L

V
O
I
O (7) where V
MPP
is the maximum PV voltage at MPP and
I
MPP is the maximum value of PV current at the MPP,
V o
and I o
are the converter output voltage and current

Venkatesan et al., International Journal of Advanced Engineering Technology E-ISSN 0976-3945 respectively.
When the value of load resistance (R
L
) matches with that of R opt
maximum power transfer from photovoltaic panel to the load will occur. The objective of the MPPT is to make the load resistance of the PV module to be equal to the optimal resistance of the solar panel.
R  R opt L
In order to achieve the above, and extract the maximum power from PV panel, DC-DC converter is inserted in between the PV panel and load and its duty cycle is varied. In this paper DC-DC LUO converter is used.
The voltage gain of the higher order LUO converter is given by
V o
V in

1
D
 D where “D” is the duty cycle of the converter.
The variation of the duty cycle is not only regulating the output voltage but also can be used to vary the input side impedance of the converter. The DC-DC converter can be controlled to present optimum impedance at the PV array terminals which facilitate maximum power extraction from an array. This feature can be appreciated by inspecting the input side impedance (R in
) expressions for the converters.
The input impedance of the higher order DC-DC
LUO converter can be calculated by



2



2
R in
 
 D
D V
I
0  

D
R
L
(8)
0
D
The equation (8) indicates that by changing duty cycle, the input impedance (R in
) of converter should be equal to the optimum impedance (R opt
) 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 reference voltage at which the PV array is forced to operate. At the MPP, V ref equals to V
MPP
. Once the
MPP is reached, the operation of the PV array is maintained at this point unless a change in ΔI is noted, which is due to the change in atmospheric conditions. The algorithm decrements or increments
V ref to track the new MPP. At the MPP, no control action is needed, therefore the adjustment stage will be bypassed and the algorithm will update the stored parameters at the end of the cycle as usual. The Inc-
Cond. technique is used the instantaneous conductance and the incremental conductance to generate an error signal
= + (10)
From (10), we know that e goes to zero at the MPP, but it is rarely occurs in practical implementation, and a small error is usually acceptable. In this paper the error value e is taken as 0.02. Measurements of the instantaneous PV array voltage and current require two sensors, which can easily keep track of previous values of voltage and current and make all the decisions as per the flow chart; duty cycle is varied according to the algorithm.
Fig.4: Basic of Inc-Cond. MPPT method
=
( )
= + = +
∆
∆
(9)
The equation (9) can be rewritten by,
∆
= − ;at MPP
∆
∆
> − ;left of MPP
∆
∆
< − ;right of MPP
∆
The MPP can thus be tracked by comparing the instantaneous conductance (I/V) to the incremental conductance (ΔI/ΔV) as shown in flowchart as given in Fig.5 for Inc-Cond. algorithm MPPT. V ref is the
Int J AdvEngg Tech/Vol. VII/Issue II/April-June,2016/770-777
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 model of the converters are described by the following basic state equations
X ( t )  Ax ( t )  Bu ( t )
Y ( t )  Cx ( t )  Du ( t )
(11) where, x(t) = The state variable, u(t) = The input vector, parameter A is the state matrix, parameter B is the input matrix, C is output matrix and D is the transition matrix.
In an electrical system, the method to identify the set of state variables is by identifying the number of

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 average model of DC–DC converter, one can obtain the small signal model and transfer function of converter, which will be very useful in the design of closed-loop controller using various control techniques [27–28].
The most superior advantages of DC-DC LUO converter is capacitor (C) assures the galvanic insulation between input and output. The short circuit or breakdowns of the load do not affect solar panels.
The additional filter elements in the LUO-converter eliminate the output ripples and enhance the output voltage level effectively [29]. However, this type of converter is still under research with regard to its usage in industrial and domestic applications.
4.1 States-Space Equation:
Fig.6(a) shows a higher order DC-DC LUO converter, which is used as the power stage interface between the PV module and the load. The LUO converter can operate either in continuous conduction mode (CCM) or discontinuous conduction mode
(DCM) depending on the current flowing through L
1.
In this paper CCM mode of operation is considered.
The DC-DC converter has two modes of operation.
(i)When the switch S is closed (ON), in this mode, the capacitor releases energy to the output. (ii) When the switch S is in OFF, the current drawn from the source becomes zero, and current i
L1 flows through the diode to charge capacitor C
1
.The equivalent circuit of the LUO converter when switch is ON and
OFF state as shown in Fig.6 (b)&(c).
(a)
(b)
(c)
Fig.6: Circuit diagram of (a) LUO converter (b) Switch
ON condition (c) Switch OFF condition
The fourth order elementary LUO converter made up of two inductors and two capacitors and capable of working in either step-up or step-down mode. The state variables of the LUO converter (x
1
, x
2, x
3, x
4
) are considered as currents i
L
1 and i
L
2
, voltages V c
1 and
V c
2 respectively.
The state equation derivation for the LUO converter for the ON and OFF state of the switch can be described by the following equations (13) and (16) respectively. These equations are expressed using the switching function, when the switch is ON











X

X

.
.
X

X

2
1
1
4
 v in
3
L
1




C
1 v
1
L
2 i
L
2 C
1
1 i
L
2
2
C
1


1
RC
1
L
2
2 v
C
2 v
C
2

1
L
2 v in
(12) d dt





 i i
L
1
L
2 v
C
1 v
C
2









0



0




0
0
0
0
1
C
1
1
C
2

0
1
L
2
0
0

0
1
L
2
0
 1
RC
2










 i
L
1



 v i v
L
2
C
1
C
2















1
L
1
L
2
0
0
1 






 v in
(13)
The output equation is expressed by (14),
   o
0 0 0 1



 i i
L
1
L
2
 v


 v
C
C
1
2






(14)
During off state, the state equations are written by
(15) using Fig 6(c),







X


X





X
3
1
2

X
4
1
 
L
1
1 v
C
1
  v
L
2
1


C
1
1
C
2 i
L
1 i
L
2
C
2

1
RC
2 v
C
2
(15) d dt





 i i v
L
1
L
 v
C
2
C
1
2









0




0
1





C
1
0
0
0
0
1
C
2
1

L
1
0
0
0


0
0
1
L
2
1
RC
2
















 i i
L
1
L
2 v
C
1 v
C
2









0

0





0

0


 v in
(16)
The output equation, is expressed by
   o
0 0 0 1






 i
L
1 i
L
2 v
C
1 v
C
2






(17)
The state-space equations have been implemented in
MATLAB/Simulink, where the Simulink block is illustrated in Fig.7
5. SIMULATION RESULTS AND DISCUSSION:
In order to validate the state-space model, a circuitry simulation of the proposed PV system is connected in parallel with the state-space model. Both the statespace and circuitry models were developed in
MATLAB/Simulink as shown in Fig. 8.
The state-space model PV system was simulated under different irradiance conditions. The function of the MPPT block is to ensure that the system delivers the maximum power to the load by varying the duty cycle of the higher order DC-DC LUO converter.
The LUO converter is fed by PV source and designed for 40W/24 V, under the nominal maximum point
(irradiance G = 1000 W/ m
2
and temperature T =
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
Selection of
Inductors
L
L
1
2
V in, min

ΔI
L
1
 f s
V in, min

ΔI
L
2
 f s
 D max
 D max irradiance and temperature level of PV changes. The component of the LUO converter used in the simulation is calculated from the equation (18) and is given in table 2.The DC-DC LUO converter was designed to operate at the switching frequency of 25 kHz.
Table 2 Specification of LUO Converter
Components Specifications
Inductor, L
1
& L
2
69mH& 19mH
Capacitor,C
1
&C
2
Resistive load, R
220µF & 47µF
15 ohm
Switching frequency
Input voltage
Output voltage
25 kHz
10.5V-17.5V
24V at 1000W/m 2
To test the effectiveness of proposed PV system, simulation is done for various environmental conditions. The results of both the state-space averaging and the circuit model provide very much close results. The MPPT tracking features of Inc-
Cond MPPT algorithm from 600 to1000 W/m
2
at
0.2sec is shown in Fig.9. As the irradiation varies,
ΔV
C1

I o
 D max
C
1
 f
S
Selection of
Capacitors
 V
C 2

8
D max
V in min
 C
2
L
2 f s
2
(18) the MPPT controller tracks the new maximum power point and the power output of the PV array which is 24W at 600W/m
2
is increased to 40W at
1000W/m
2
. The voltage of the PV module is increased from 15.2V to 17.4V under that condition.
Fig. 7:Open-loop state-space modeling of LUO DC-DC converter
Fig.8: Overall simulink model of the proposed system
X Y Plot
60
40
20
Max.Power at 1000w/m2 insolation = 40W
Max.Power at 600w/m2 insolation= 24W
0
0 10 20 30 40
PV Voltage (V)
50 60 70
Fig .9:MPPT tracking features of Inc-Cond. MPPT algorithm from 600 to1000W/m
2
at 0.2sec
Fig. 10: Simulation results of LUO converter on PV side at 1000W/m
2
PV panel 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
Fig.10 shows the simulation result of PV panel voltage and current at irradiation level of
1000W/m
2
.It is observed that PV voltage and current at MPP is 17.3V and 2.3 A respectively in steady state. The DC-DC LUO converter provides a dc voltage of 24V and current1.6A for the typical resistive load of 15 ohms as shown in Fig.11 (a) &
(b). The response time of both circuit and state-space model of the proposed system slightly differ, the state-space model is 0.02s faster than the circuit model.
(a)
(b)
Fig.11: The simulation results of LUO converter (irradiance 1000 W/m
2
) (a) converter output voltage (b) converter output current
(a)
(b)
Fig.12:The simulation results of LUO converter (irradiance 600 to 1000 W/m
2
) (a) converter output voltage (b) converter output current
Fig.13 Simulation results of the converter output voltage and current for the state space and circuit model for varying irradiation condition
Fig.14: Bode plot of control to output transfer function for LUO converter –For different value of duty cycle
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
For obtaining the dynamic response of the state-space model system, the irradiance, G, was initially set to
600 and varied to 1000 W/m
2
at 0.2sec as shown in
Fig.12 and Fig.13 shows the simulation results of the converter output voltage and current for the state space and circuit model for varying irradiation condition. It is observed that for all irradiation levels both converter output voltage and current in circuit and state-space model gives closer result.
5.1 Dynamic Function of the Converter:
The dynamic performance indices of the converter are audio susceptibility and control transfer function, where the audio susceptibility of the converter measures the amount of input variations that will reach the output as a function of frequency and the control transfer function describes gain between the control duty ratio and the output variable [30-32].
Audio susceptibility (F) of the LUO converter can be calculated by (19),
F
V o
( S )

V g
( S )
 q ( SI  A )  1 b
(19)
The most significant one is, duty cycle-to-output voltage transfer function (G
V
), which can be obtained by (20)
G
V

V o
( S ) d ( S )
 q ( SI  A )
 1 f  ( q
1
 q
2
) X
(20) where
A b q f



 (
A
1
D b
1
D  q
1
D
A
1


 A
2
( 1 b
2
( 1  q
2
( 1
A
2
) X


D

D
D
)
)
( b
)
1
 b
2
F
32 .
26 e 20 S

5765 e
12
S
4
 8178 e
15
S
3


6896 e
14
4 e
S
2
22
 6238 e
20
S  1063 e
23
) V in
The system matrices are derived, and a MATLAB Mfile coding is written to extract the relevant transfer functions and is given by equation (21) and (22) for
D=0.5.
The bode plot of control-to-output transfer function for different values of duty cycle D of the LUO converter is shown in Fig.14.The gain margin(GM) and phase margin(PM) are observed from the bode plot. For higher value of the duty cycle where D≥ 0.7, the system get stable as clearly shown in plot for the proposed system. Similarly the bode plot of audio susceptibility (F) of the LUO converter is generated with MATLAB as shown in Fig.15 and observed that for higher value of D is greater than 0.7 the system performance is good, which are significant for feedback control design purpose.
(21)
G
V

5765 e
12
S
4
 8178 e
15
35 .
6 e 8 S  3721 e 24
S
3
 6896 e
14
S
2
 6238 e
20
S  1063 e
23
(22)
Fig.15: Bode plot of audio susceptibility for LUO converter – For different value of duty cycle
6. CONCLUSION: REFERENCES
In order to help the researcher in choosing and analyzing the best converter for solar PV system, this paper reviewed state-space modeling of the nonisolated DC–DC LUO converter with MPPT algorithm. The simulation environment
MATLAB/SIMULINK is used to model the circuit, and learnt the dynamic behavior of converter for solar PV system. Simulation results confirmed the accuracy of the obtained model for this complex fourth order system and reduce the overall simulation convergence time as compared to circuit model simulation, since the state-space model does not include the effect of switching. The computation and plotting of typical transfer functions of a DC-DC
LUO converter provides ground work for controller design, and bode plots were presented to identify the stability region of the proposed PV system.
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