2011 IEEE Student Conference on Research and Development (SCOReD)
A Complete Model of Stand-alone Photovoltaic Array in MATLAB-Simulink Environment 1,3,4,5
R. Rahmani1, M. Fard2, A. A. Shojaei3, M. F. Othman4, R. Yusof5
Centre for Artificial Intelligence and Robotics, Universiti Teknologi Malaysia, Kuala Lumpur, 54100 Malaysia. 2 Electrical Power Department, Universiti Teknologi Malaysia, Skudai, 81310 Malaysia
[email protected] 1
Abstract— In this paper, a photovoltaic array has been modeled and developed for MATLAB-Simulink environment. The PVA model has been developed by basic circuitry equations of a photovoltaic array, considering the effects of ambient temperature, solar radiation and natural specifications of the photovoltaic cell. For evaluating the model, two different types of the loads have been utilized, a direct coupled DC load and an AC load via a three phase IGBT inverter. The proper matching circuits have been simulated and the output results and characteristics validate that the present study has higher quality in output waveforms. Index: Photovoltaic Array model; Total Harmonic Distortion; IGBT inverter; Power Generation; MATLAB-Simulink environment.
I. INTRODUCTION Photovoltaic System (PV) is getting popular by day as crude oil price increases, causing instability in the global market. Furthermore, green peace movement and the consciousness of mankind have heightened the importance of green energy. Photovoltaic may be one of the solutions for better, as well as cleaner energy, as it is naturally harnessed from the Sun. The technology is mainly well known in the space mission and is still alien for domestic usage. This is due to its high initial cost, generation efficiency and reliability [1-4]. On the other hand, the cry for alternative energy has made the PV system popular among researchers. Having said so, the rural areas where the grid connection is extremely expensive, PV Systems have been implied to give hope to these areas, while for urban life, the PV Water Heater is common and can be found on the roof of the houses [5-6]. Based on the report of the Earth Policy Institute (EPI) a record of 10,700 megawatts generated power was produced in 2009. Solar photovoltaic cells showed an impressive increment of 51 percent in power generation compared to 2008. Figure 1 shows the growth of solar energy production during the last three decades [7]. Currently PV cells are the world’s fastest growing electrical power technology and generate electrical power in more than 100 countries. More than 16,000 megawatts of PV arrays are installed in 2010 and Germany bears half of this capacity [7]. This fact clearly shows that this solar energy (photovoltaic) is very promising as the next generation energy source.
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Figure 1. World annual solar photovoltaic production from 1985 till 2009.
In this context, lots of research needs to be done in order to achieve a reliable and efficient energy. Looking at the grid connected system, whereby the system mainly consists of photovoltaic (PV) modules, inverter, battery, and switching point for the utility. Different types of photovoltaic cells will yield different energy output; meanwhile the controlling technique of inverter is very crucial in championing the PV system. Inverter design should consider the size and capacity of the plant. On the other hand, choosing the right controlling technique is needed as well in order to achieve an efficient renewable energy system. Ropp et al. [8] developed a MATLAB-Simulink model of a single-phase grid-connected photovoltaic system. In that model, a system for island-mode detection is implemented and a full gradient based MPPT model is also presented. Since the output power of a PV is related to the ambient temperature and solar irradiation, it is changed easily during a specific interval. Therefore, a complete and user friendly simulated model can help support work in Graphical User Interface (GUI) environment. While working in GUI environment is easier and more user friendly for normal users, developing a good model for such an environment helps the solar energy to be considered in simulations more than ever. There have been some works in this area, Altas et al. [9] developed a simulation model for stand-alone PV array, but they did not consider the complete equations and parameters. References [10-12] also modeled two different photovoltaic models in MATLAB but not in Simulink environment. Suntio et al. [13] also presented a model for solar generator with current-fed MPPT converters which is comprehensive and discussed the transient and steady state behaviors of a solar generator. Raju [14] presented a feasible PV array model for Simulink which is connected to a
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2011 IEEE Student Conference on Research and Development (SCOReD) permanent magnet DC motor (PMDC)) implementing a novel current rate control loop. In the present study, a PV system whicch has well defined parameters based on the real equations is developed and simulated with MATLAB-Simulink. Thee various types of loads are also applied to show the quality of o performance for the proposed model. G II. PV ARRAY MODELING
Generally, a photovoltaic cell model coonsists of a current source in parallel with a diode and the ouutput is in parallel with both of them through a series resistor. r Figure 2 demonstrates a simplified circuit equivalent e to a photovoltaic cell which is considered in thhe current study. A parallel resistor called Rp can be added rigght before Rs as it is considered in some cases [15-16].
Where NOCT is the Nominal Operating Cell Temperature which is equal to 45 and Kt is a regional coefficient indicating the monthly clearneess index and has a range of 0.2 to 0.8. Here, based on Malaaysian weather condition, it is considered equal to 0.45. So far the Iph can be realizeed by two main inputs Ta and G, but the ID is not determinedd yet. Equation (4) shows the equivalent equation for operatiion of the diode in the cell’s circuit [17].
⎡ ⎛ V I D = I 0 ⎢exp⎜⎜ D ⎣ ⎝ m.VT
⎞ ⎤ ⎟⎟ − 1⎥ ⎠ ⎦
⎡ ⎛ V + RS I C ⎞ ⎤ ⎟⎟ − 1⎥ = I 0 ⎢exp⎜⎜ C m V . T ⎠ ⎦ ⎣ ⎝
(4)
I0 is the diode reverse saturattion current which can be obtained from (5).
I0 =
Figure 2. Simplified equivalent circuit model of a photovoltaic cell.
Kirchhoff’s current law indicates that the output current of the cell can be obtained from (1).
I C = I ph − I D
(1)
Iph is called photocurrent which is the geenerated current by the influence of solar irradiation and cell’ss temperature. ID is the diode current that is in parallel withh Iph, and IC is the output current of the cell. Hence, for moodeling the IC, two other currents have to be modeled first. Iph depends on the ambient temperature and solar irradiaation of the sun. Equation (2) shows the equation which w leads the photocurrent of the photovoltaic cell [16].
I ph = (I ph ,n + K I ΔT )
G Gn
(2)
G is the received radiation from sunligght while Gn is the normal rated irradiation in the STC (standard testing ∆ is the difference condition) which is equal to 1 KW/m-2. ∆T between temperature of the cell (Tc) and the standard temperature (T0=25oc). Here KI is a factoor which indicates the impact of temperature on current and is equal to 4.42e-3 A/oc, while Iph,n is the normal current meeasured in standard condition. Hence, two inputs of G andd Tc generate the photocurrent of the photovoltaic cell. Buut Tc also depends upon the physic and dynamic characterristics of the cell. Equation (3) which is well known as Evan’s equation, shows how the cell’s temperature is relatted to the ambient temperature (Ta) and the cell’s properties.
⎛ NOCT − 20 ⎞ Tc = Ta + (219 + 832 K t )⎜ ⎟ 800 ⎝ ⎠
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(3)
I SCC ,n + K I ΔT + KV ΔT ⎞ ⎛V ⎟⎟ − 1 exp⎜⎜ OCC ,n m.VT ⎝ ⎠
(5)
In (5), ∆T is the difference bettween Tc and T0 while KV is a factor showing the impact of chhanges in temperature on the voltage of the cell. KI, m andd VT are the same as in the previous equations. While Isc,n (=5 ( A) and Voc,n (=240 V) are the short circuit current and oppen circuit voltage of the cell in STC respectively . Considering all the paraameters in the mentioned equations, (1) will be changed to t (6) which shows the output current of the cell [17].
⎡ ⎛ V + RS I C ⎞ ⎤ ⎟⎟ − 1⎥ I C = I ph − I 0 ⎢exp⎜⎜ C m V . T ⎝ ⎠ ⎦ ⎣
(6)
Equation (6) demonstrattes the relation between the cell’s current and all the possible parameters of a photovoltaic cell with two main m inputs of Ta and G. However, in practice we use sets s of cells in a module and sets of modules in an array whhich is modeled in the current study. We have to consider twoo other parameters as the total series number of cells (NSS) and a total parallel number of cells (NPP). The parallel currennts will be summed up while being divided by the series resiistance as well. So if we have RS for one cell the total resisstance of the system will be multiplied by NSS/NPP. III. SIMULATEED PV ARRAY Simulating the introduced eqquations in the last part will result in the general block diaggram of photovoltaic array to look as in Figure 3. The model of Figure 3 is the last step of the simulation and is called thhe “PVA model for Simulink environment”. It consists of thee total model of the PV array beside the three phase AC inverter and the said loads. The series diode in the simulation has been applied to prevent
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2011 IEEE Student Conference on Research and Development (SCOReD)
Figure 3. Functional block of the PV array model for Simulink environment.
the reverse current flow to the PV array. The system contains some sub-blocks to make the simulation easier to understand. The temperature block which is colored with cyan, and (3) is applied to the input ambient temperature. Figure 4 demonstrates the under mask of the temperature block with Ta as input and Tc as output temperatures in Celsius. Then the Tc generates an input for the PV array block. The yellow block is the main PV array which consists of four sub-blocks. For the PV array block simulation, (2), (4), (5) and (6) have been considered. Figure 6. Photocurrent of the PV.
Figure 4. Temperature block.
Figure 5 shows the simulation of the I0 as the reverse current saturation which is simulated from (5). The Iph has a subblock as shown in Figure 6, while Figure 7 illustrates the Im as the module’s total current. There, it can be observed that the series and parallel numbers of the cell of the simulated model.
Since the objective is to develop a model for Simulink environment, the sub-blocks are not going to be explained in more detail. In the main diagram, the modeled system supplies power to the DC and the AC loads. The AC load which is shown in orange color is connected to the system through a three phase IGBT inverter and an isolating transformer with turn ratio equal to 1. The inverter is in light blue and controlled with a discrete 6 pulses PWM generator. There is a RC filter block right after the diode and before the DC load which can be seen in magenta color in Figure 3. RC filter is used to make a better output power quality. The Ta is the ambient temperature in Celsius (oc) and is set to 32oC in this case but can be extended with another block if the weather changes. Irradiation is considered constant. However, considering the change in weather is not an objective of this current study, therefore it is not discussed here. IV. RESULT AND DISCUSSION
Figure 5. Reverse current saturation of the diode.
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The proposed PV array model uses the scheme as that shown in Figure 2, and supplies power to the DC and the AC loads. The DC load is mainly resistive so its voltage and current profile have the same waveforms. However, there is no problem with installing an inductive or capacitive load in DC part as well. But the reason for implementing a mainly resistive DC load is to show the quality of DC voltage before the IGBT inverter. The AC load is a RLC load with properties of 500 W, 200 VAr inductive and 500 VAr capacitive. The parameters for the AC load are considered
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2011 IEEE Student Conference on Research and Development (SCOReD)
Figure 7. Block diagram of the generated current by PV Array.
the same as [9] where also a model for MATLAB-Simulink environment of MATLAB-Simulink was proposed. However, no THD measurement was performed in that work and the results cannot be compared by numbers.
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Power output of the PV array (W)
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0
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Figure 9. The P-V characteristic for the proposed PV array.
750
625
P ower output of P V A rray (V )
Figures 8 and 9 show the I-V characteristic and P-V characteristic of the proposed PV array model respectively. Figure 10 depicts the time response of the total power output for the proposed PV Array model. Considering that the DC load is a 100 ohm resistive part, the power output range is acceptable because there is no control part or MPPT. However, power controlling parts are also simulated but not brought here in this paper. The voltage at the DC load is brought in Figure 11, because of being mainly resistive, there is no difference between current and voltage time response. That is why the current profile is not illustrated in a separate figure. Whereas there is an IGBT three phase inverter in the system, existing the harmonics looks inevitable. However, by having a good DC input profile the output AC will have less harmonic and better profile. Figure 12 illustrates the line to line output voltage of the PWM inverter. Implementing an isolation transformer will help the waveform to be the same as that depicted in Figure 13.
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Current of PV array (I)
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Figure 10. Time response of the PV Array power output. 0.5
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Figure 8. The I-V characteristic for the proposed PV array.
978-1-4673-0102-2/11/$26.00 ©2011 IEEE
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2011 IEEE Student Conference on Research and Development (SCOReD) Although the isolation transformer has turn ratio equal to 1 and does not increase the voltage, it has its winding characteristics. Table 1 shows the characteristics of the implemented transformer as the isolation transformer.
180
160
140
Voltage at DC load (V)
120
TABLE I PROPERTIES OF THE ISOLATION TRANSFORMER Feature value
100
Nominal Power (Sn) Frequency (f)
1000 KVA 60 Hz
Magnetization Resistance (Rm)
500 p.u.
Magnetization Reactance (Lm)
500 p.u.
Winding 1 Parameters [V1ph-ph(Vrms), R1(p.u.), L1 (p.u.)]
[ 350 , 0.002 , 0.08 ]
Winding 2 Parameters [V2ph-ph(Vrms), R2(p.u.), L2(p.u.)]
[ 350 , 0.002 , 0.08 ]
80
60
40
20
0
0
0.01
0.02
0.03
0.04
0.05 Time (sec.)
0.06
0.07
0.08
0.09
0.1
Figure 11. Voltage at the DC load.
200
150
O utput v oltage of the inv erter (V )
100
The line to line three phase voltage of the AC load is illustrated in Figure 13. It can be easily observed that current study has a better result when in the same condition with [9] without any necessity to have filtering in the AC part. The Total Harmonic Distortion (THD) of the voltage profile of the AC side is illustrated in Figure 14. The result shows that THD confirms to the requirements of IEEE std 519-1992.
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Figure 12. The output voltage of the IGBT inverter.
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112.5
V oltage at A C load with 500 V A r c apac itiv e (V )
0.16 The THD of three phas e AC v oltage
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0.25 Time (Sec.)
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0.5
Figure 14. the THD of voltage at the three phase AC side.
-37.5
-75
V. CONCLUSION
-112.5
-150
0
0.005
0.01
0.015
0.02 Time (sec.)
0.025
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0.035
0.04
Figure 13. Line to line three phase voltage at the AC load.
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A simulated model for photovoltaic arrays (PVA) is introduced in this paper. The proposed model is suitable for being used in MATLAB-Simulink environment. Having a generalized structure makes this model able to be used as a PV power source along with fuel cells, wind farms and etc. However, we must still consider some controller systems for the existing model in case of connection to the grid. Two different loads have been considered to show the ability of
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2011 IEEE Student Conference on Research and Development (SCOReD) the simulated model, besides high quality of output power wave form in AC part which satisfies the IEEE std 5191992, shows that the modeled system is capable to be connected to a grid system as well. On the other hand, a comparison is performed between the proposed model and one of the similar previous models. All in all, the proposed model has the ability to be considered as the part of the distributed power generation systems.
[6] [7] [8]
[9] [10]
ACKNOWLEDGEMENT The authors would like to thank Universiti Teknologi Malaysia and Centre for Artificial Intelligence & Robotics for their supports.
[11] [12] [13]
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