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Selection criteria of dc-dc converter based on load resistance powered by photovoltaic array
1Byamakesh Nayak, 2Tanmoy Roy Choudhury
1,2KIIT University, Bhubaneswar
Abstract: This paper deals with the selection of dc-dc converter and control variable required to track the maximum power of solar array, to optimize the utilization of solar power in cooking and heating. In order to reduce the maintenance cost and to simplify the model, battery has not been used in the proposed system. Since battery has not been used, selection of dc-dc converter is an important consideration of the model. Selection is based on maximum power transfer theorem which is dependent on load resistance. An effort has been made to choose the control variable which is the output signal of maximum power point (MPP) tracker. Control variable which is dependent on inputs of MPP tracker is decided based on stability.
Two MPP trackers designed by neural-network (NN) and perturb and observe (P&O) algorithms has been used to compare the tracking capabilities due to variation of insolation. The system is simulated using MATLAB/Simulink environment.
Key words: Photovoltaic power system, Power converter selection, Power converter control, maximum power point tracking (MPPT), Perturb and observe (P&O), Neural network (NN)
I. INTRODUCTION
Out of the total daily energy requirement of a household, about 7% of energy is required for cooking and heating purposes. Fossil fuel has been the major source of energy for cooking and heating. In order to avoid global warming, use of fossil fuel must be reduced.
Photovoltaic (PV) power generation system is the best alternative solution to meet the energy demand, because of its free availability and clean production.
There are two ways to use the solar energy for heating.
Direct heating requires radiator to absorb the solar energy falling on the radiator and used for heating of water. The best example is the solar cooker. The indirect method uses PV array for converting the solar energy into electrical energy, which can be utilized for any heating and cooking applications. The indirect method is expected to play an important role for cooking and heating application in near future because of its low cost compared to the direct method. A major problem of photovoltaic system is that power output is not constant and fluctuates with weather condition. To meet the constant voltage demand by the load and to manage the flow of power, the storage device like battery can be used across the load [1].The functions of battery are:
To keep the voltage across the load constant.
Depending on PV maximum power battery absorbs or discharges the power to keep the power demand by the load constant.
The additional cost of battery, maintenance thereof and the concern of environment while disposing are the major barrier to market the cooking PV module.
However for heating purpose (mainly household cooking), variation of maximum power of solar array due to change of insolation (G) and temperature (T) will not affect the reliability of the system. Hence for cooking purposes the solar power can be used without a battery. However, to harvest maximum solar power, maximum power point tracker must be incorporated in the PV system [2-3]. This requires selection of dc-dc converter, which is interfaced between the solar array and heating load [4]. The duty cycle of dc-dc converter can be controlled in such a way that the input voltage of dc-dc converter must be the voltage at maximum power point (VMPP), which changes with change of insolation and temperature. In order to achieve the VMPP point and to track the maximum power, the internal resistance of solar array at MPP must be equal to the equivalent load resistance (Load resistance referred to input side of chopper). Hence, the selection of chopper depends on load resistance.
Buck converter can be used if equivalent load resistance is greater than the load resistance.
Boost converter can be used if equivalent load resistance is less than the load resistance.
Buck-Boost converter can be used for any value of load resistance.
Several studies have been carried out for exact tracking of MPP and the control procedures are explained in detail by developing a transfer function model assuming the load voltage fixed as battery is incorporated across the load. The above control procedures are based on to control the duty cycle in such a manner that the solar voltage must be VMPP with a fixed battery voltage. Since only one parameter that is VMPP or current at maximum power (IMPP) is to be controlled, the control technique is simple and stability will not be affected whether VMPP or IMPP is chosen as control command.
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However the control problem has not been considered for tuning of MPPT in stand-alone mode without using battery. The control issue is somewhat difficult if battery has not been used across the load. In this case both input voltage and load voltage are to be adjusted to track the VMPP or IMPP point. Since two parameters are to be adjusted by the controller duty cycle, the controller design should be carefully considered otherwise it may lead to instability.
There are large numbers of control techniques (MPP Trackers) exist till date. Depending upon the inputs to MPP tracker, it can be classified as direct and indirect.
In direct control MPPT, the solar voltage or current or both may be inputs to the controller. Direct control MPPT can be named as feed forward method because inputs to this model are system parameters. If inputs to the MPPT tracker are not system parameters, but other external parameters such as insolation and temperature etc then the MPPT controller is called indirect MPP tracker.
II. EQUIVALENT CIRCUIT MODEL OF SOLAR ARRAY
The current-voltage characteristics of PV module shown in Figure 1 can be expressed as: [5]
s s
pv 0
s t p
V R I V R I
I I I exp 1
N V a R
(1)Where V and I are the output voltage and output current of PV module consisting of Ns number of cells connected in series. Ipv and I0 are the photovoltaic and saturation currents of the module respectively. Vt=kT/q is the thermal voltage of the PV cell, „q‟ is the charge of an electron, „k‟ is the Boltzmann constant, T in Kelvin (K) is the temperature of junction and „a‟ is the diode ideality constant. Rs and Rp are the equivalent series resistance and equivalent parallel resistance of the module respectively .The characteristics of PV module not only depends on the internal passive parameters of the device like RS and Rp, but also depends on external parameters like temperature and solar insolation (irradiance) level [6]. The change of temperature and irradiance has an effect on the PV module characteristics according to the following equations [7-8]
pv pv,n I n
n
I I K T T G
G
(2)
oc oc,n v n
V V K T T
(3)
sc,n I n
0
oc,n V n
s t
I K (T T )
I V K (T T )
exp 1
N aV
(4)
Here the subscript n represents the nominal condition (usually Tn= 25 °C and Gn=1000 W/m2). KI the short- circuit current/temperature coefficient and KV denote the open-circuit voltage/temperature coefficients of solar cell. The I-V characteristic of PV module at standard test condition (STC) is divided into three operating regions, such as voltage source region, power source region and current source region as shown in Figure 2.
STC means solar irradiance of
1000 W/m2 with a solar spectrum of 1.5 air mass (AM) at temperature of 25°C.
The variation of I-V and P-V characteristics for different insolation and different temperature for KC200GT solar panel are shown in Figures 3-6.The datasheet parameters of KC200GT PV module at STC used for MPP tracking and for analysis are given in Table 1.
III. SELECTION OF DC-DC CONVERTER
Solar radiation dramatically changes before it falls on PV array because of blocking and filtering nature of atmosphere and cloud cover. Change of insolation level with time, shifts the maximum power point as shown in Figures 3-4. Besides insolation, the variation of temperature also modifies the power-voltage and current-voltage characteristics of PV module as shown in Figures 5-6. Insolation has faster dynamics as compared to temperature. The design of MPP tracker must be based on the faster dynamic behavior of insolation in order to avoid the delay of maximum power point tracking. Maximum power point tracking demands the dc-dc converter in between PV array and load to keep the PV array voltage or current at MPP point for a given condition of insolation and temperature by controlling the duty ratio of dc-dc converter[9]. The MPP tracker decides the duty ratio of dc-dc converter.
3.1 Selection of dc-dc converter with battery Selection of dc-dc converter such as buck, boost and buck-boost converter depends on battery voltage if the battery is incorporated across the constant load .The boost converter is used to transfer the maximum available power on PV array to the load, if battery voltage is higher than VMPP in highest insolation and lowest temperature condition. The buck converter is used when the battery voltage is lower than VMPP in highest insolation and lowest temperature condition.
Buck-Boost converter can be used at any level of battery voltage. Further, charging and discharging of battery
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depends on the availability of maximum power of the PV array.
3.2 Selection of dc-dc converter without battery Selection of dc-dc converter without battery across the load is decided using maximum power transfer theorem.
To extract maximum power from the solar array the equivalent load resistance referred to the input terminals of dc-dc converter must be equal to internal resistance of solar array at MPP for a particular insolation and temperature level. The variation of internal resistance of KC200GT solar panel at MPP for different insolation level with fixed temperature of 25°C is shown in Figure 7. The curve is approximately exponential decay in nature and lowest at highest insolation level. Similarly, the variation of internal resistance of KC200GT solar panel at MPP for different temperature and fixed insolation of 1000 W/m2 is shown in Figure 8. It is a straight line and internal resistance decreases with increase in temperature but the range of decrease is small as compared to range of decrease of internal resistance for change of insolation. This concludes that the internal resistance at MPP is lowest at highest insolation and highest temperature.
3.2.1 Buck Converter
The relation between the output voltage (V0) and input voltage (V) of a buck converter under ideal condition (without parasitic elements) in steady-state can be expressed as:
V0
V D
(5) Using conservation of energy
0 0
2 2
0 0
0
l e l l e l
V I VI
V V V V
V V or,
R R R R
(6)
Where, Rl is the load resistance and Rel is the equivalent load resistance referred to input side of chopper respectively
l
e l 2
R R
D (7)
Since the range of duty ratio D is from 0 to 1 therefore,
l e l
R R
The above equation concludes that, buck converter must be used when the load resistance is less than or equal to internal resistance of solar array at MPP point in highest insolation and lowest temperature condition in order to track the maximum power. If the above condition is not fulfilled the maximum power point tracker fails to track the maximum power and tracking power at that time is
the power of solar array where the internal resistance of solar array is equal to load resistance by making duty ratio 1(dc-dc converter is always connected to load).
3.2.2 Boost Converter
The steady-state equation of boost converter under ideal condition in terms of load resistance and internal resistance can be expressed as:
2
e l l
R R 1 D (8)
Since the range of duty ratio is from 0 to 1therefore,
l e l
R R
So, boost converter is used when the load resistance is greater than or equal to internal resistance of solar array at MPP point in highest insolation and lowest temperature condition in order to track the maximum power. Like buck converter, the tracking of maximum power fails if the above condition is not satisfied and tracking power is the power of solar array where the internal resistance of solar array is equal to load resistance by making duty ratio 1.
3.2.3 Buck-Boost Converter
Buck-boost converter is used for any load resistance to track the maximum power by maximum power point tracker. The above point can be easily explained using steady-state equation of buck-boost converter under ideal condition in terms of load resistance and internal resistance which is expressed as:
2l
e l 2
R 1 D
R D
(9)
Equivalent load resistance at the input terminal of different dc-dc converters with respect to duty cycle for a load resistance of 1 ohm is shown in Figure 9. Buck converter is used to control when equivalent load resistance is greater than load resistance whereas boost converter is used to control when the equivalent load resistance is less than load resistance. Buck-boost converter is used to control when equivalent resistance varies from 0 to infinity and is independent upon load resistance.
IV. RESULTS AND DISCUSSION
To validate the effectiveness of choice of control variable, the data of KC200GT PV panel has been simulated by incorporating dc-dc buck converter. Two MPP trackers based on P&O and NN are used for comparisons. The MPP data of KC200GT solar panel‟s voltage, current and power at 1000 W/m2 and 600 W/m2 for fixed temperature of 25°C are tabulated in Table 2. A dc-dc buck converter is interfaced between the solar array model and the load resistance as shown in Figure 15. The value of load resistance is taken 1Ω which is less than the internal resistance at MPP of highest
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insolation and lowest temperature considered to be 1200 W/m2 and 25°C. From both the MPP tracker the MPP current command is generated which depends on insolation and temperature at that instant. This is compared with the actual solar input current sensed by current sensor by a hysteresis band controller to generate the pulse for control the duty cycle of chopper. The band width of hysteresis band controller is taken 0.002 units for both the MPP trackers for running of simulation in MATLAB environment. The control unit incorporating hysteresis band controller is shown in Figure 16.
At a fixed temperature of 25°C, step variation of insolation from 1000 W/m2 to 600 W/m2 at the instant of 1 second was considered to verify the tracking capability of MPP trackers. The tracking response is sluggish in nature when perturb and observe algorithm is used to design MPP tracker. The elapsed time is approximately 0.7second before coming to steady state which is shown in Figure 17. But, in NN MPP tracker, the elapsed time is very small and about 0.01second as shown in magnified sub plot of Figure 18.
The delay of tracking is the further drawback of P&O MPP tracker due to sudden fall of insolation. As shown in Figure.17, P&O MPP tracker fails to track the new maximum power point for some period of time, here, it is 0.3 second due to sudden fall of insolation from 1000W/m2 to 600W/m2.During this period of time the solar array is directly connected to load and the extracted power is the power of solar array whose internal resistance is equal to load resistance. Insolation variation has faster dynamic and may be the order of millisecond compared to temperature variation. Since, P&O MPP tracker posses slow dynamic (0.3 second delay) it may fails to track the rapid variation of insolation level which depends on climatic condition.
The delay time of NN MPP tracker is negligible and mainly depends on dynamics of pyranometer. However, the steady state error of both the tracker is small and is about 1%.
Using VMPP as control variable, same step variation of insolation is considered to study the tracking capabilities for both of the above MPP trackers. The control unit and tracking capabilities for both of the algorithms are shown in Figures 19-21. As shown in Figure 20, NN tracks the maximum power just like IMPP as control variable whereas P&O MPP tracker fails to track the maximum power which needs special attention for stability analysis before VMPP used as control variable.
The simulation result of P&O MPP tracker taking voltage as control variable is shown in Figure 21 which confirms the analysis discussed in control aspects of MPPT.
Figure 1. Equivalent circuit of PV module
Figure 2. I-V characteristic of PV module at STC of KC200GT solar panel
Figure 3. I-V curve of PV module influenced by different insolation levels with constant temperature of
25 °C
Figure 4. P-V curve of PV module influenced by different insolation levels with constant temperature of
25 °C
Figure 5. I-V curve of PV module influenced by different temperature levels with constant insolation of
1000 W/m2
0 5 10 15 20 25 30 35
0 2 4 6 8
Voltage in Volt.
Current in Amp. Current source region
Vmp=26.3 Imp=7.61
Power region MPP
Voltage source region Isc=8.21A
Voc=32.9
0 5 10 15 20 25 30 35
0 2 4 6 8 10 12
Voltage in Volt.
Current in Amp.
G=1000W/m2 G=800W/m2 G=500W/m2 G=200W/m2
MPP Point
0 5 10 15 20 25 30 35 40
0 2 4 6 8 10 12
Voltage in Volt.
Current in Amp
T=00C.
T=300C.
T=600C T=900C.
MPP Point
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Figure 6. P-V curve of PV module influenced by different temperature levels with constant insolation of
1000 W/m2
Figure 7.Internal resistance of PV module at MPP at different insolation level.
Figure 8. Internal resistance of PV module at MPP at different temperature
Figure 9. Equivalent load resistance of different types of dc-dc converter with duty ratio
Figure 10. Variation of PV voltage at MPP with insolation
Figure 11. Variation of PV current at MPP with Insolation
V. CONCLUSION
The variation of power of solar array due to variation of insolation and temperature because of climatic change is reviewed and analyzed by developing the mathematical model of solar array. Failure of tracking of maximum power occurs if chosen dc-dc converter is not matched with the load resistance connected directly to converter without battery. A mathematical analysis is provided based on maximum power transfer theorem for selecting dc-dc converter. A buck-boost converter will match for any load resistance for extracting the maximum power from PV array using any of the MPP trackers exist till date whereas use of buck and boost converter depends on load resistance. Buck converter is used when the load resistance is smaller than the internal resistance of PV array at MPP and Boost converter is used in vice-versa condition.
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0 200 400 600 800 1000 1200
0 5 10 15 20 25 30 35
Insolation in watt per square meter
Internal Resistance in ohm at MPP
25 30 35 40 45 50 55 60 65 70
2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5
Temp in degree centigrade
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Duty Ratio
Equivalent Load resistance in ohm
Buck-Boost Boost Buck
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0 1 2 3 4 5 6 7 8 9 10
Insolation in watt per square meter
Current in ampere at MPP
0 5 10 15 20 25 30 35 40
0 50 100 150 200 250
Voltage in Volt.
Power in Watt.
00C 300C 600C 900C
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