Modeling of Maximum Power Point Tracking Algorithm for Photovoltaic Systems Ioan Viorel Banu, Marcel Istrate “Gheorghe Asachi” Technical University of Iasi Faculty of Electrical Engineering Iasi, Romania
[email protected],
[email protected] Abstract—This paper presents a modeling method of photovoltaic (PV) systems and an implementation of the incremental conductance for maximum power point tracking (MPPT) algorithm. The method is used to study the influence of rapidly changing irradiance level concerning performance of photovoltaic systems. A simple circuit model of the dc/dc buck converter connected to the photovoltaic systems is used to easily simulate the incremental conductance MPPT method. The model has been implemented in MATLAB / Simulink. The simulation results are presented and analyzed to validate that the proposed simulation model is effective for MPPT control of the photovoltaic systems at rapidly changing irradiation condition. Keywords—modeling; photovoltaic systems; maximum power point tracking; incremental conductance; buck converter
I.
INTRODUCTION
The photovoltaic (PV) domain provide one of the most efficient ways of producing energy, with real perspectives in the future, considering the actual situation of the classical power resources around the world. It becomes a real problem the fact that we have insufficient supplies of this kind of power resources for insuring the world's needs. Usually, when a PV module is directly connected to a load, the operating point is rarely at the maximum power point or MPP [1]. The principle of maximum power point tracking (MPPT) is to place a convertor between the load and the PV array, as shown in Fig. 1 [1-4], to regulate the array output voltage (or current) so that the maximum available power is extracted [5]. A power converter is necessary to adjust the energy flow from the PV array to the load [1]. In the method described in [2], the power converter is controlled using the PV array output power [3]. Voltage and current sensing allow measuring the power. If the value of power is available can be decided if go up or down on the power curve [1]. The PV array is an unregulated dc power source, which has to be properly conditioned in order to interface it to the grid. The dc/dc converter is present at the PV array output for MPPT purposes, i.e. for extracting the maximum available power for a given insolation level [5]. The step-down dc/dc converter (buck converter) is used as a dc transformer which can match the PV array optimum load by changing its switching duty ratio (D) [6]. In general, the operation of an ideal buck converter [6-9] is described by (1).
Figure 1.
Block diagram of a PV array connected to the load [1].
Vout Vin = Iin I out = D ,
(1)
where Vin and I in are the voltage and current at the PV array side (i.e. the input of the buck converter), and Vout and I out are the voltage and current at the load side (i.e. the output of the buck converter). Multiple well-known direct control algorithms are used to perform the maximum power point tracking (MPPT) [1]. There are at least 19 distinct methods of MPPT control algorithms with different variations on implementation and performance [9]. One of the MPPT algorithms that are well known is the incremental conductance algorithm. The incremental conductance algorithm is based on the differentiation of the PV array power versus voltage curve as in (2) [1, 9].
dP d(VI) dV dI dI = =I +V = I+V dV dV dV dV dV
(2)
The MPP will be found when [1, 9]: dP dI I dI , = 0⇒ I+V =0⇒− = dV dV V dV
(3)
where I/V represent the instantaneous conductance of PV array and dI/dV is the incremental conductance (instantaneous
change in conductance). The comparison of those two quantities tells us on which side of the MPP we are currently operating [1]. The analysis of the derivative, presented in (4), can determine whether the PV array is operating at MPP or far from it, as is shown in Fig. 2 [9, 10]. ⎧dP/dV > 0, for V < VMPP ⎪ ⎨dP/dV = 0, for V = VMPP ⎪dP/dV < 0, for V > V MPP ⎩
Figure 2.
(4)
Figure 4.
Model of a PV solar panel connected to a load.
In Fig. 5 is shown the model of PV panel as a constant dc source created using the Lookup Table block from Simulink® as in [1, 13]. The model has two inputs an irradiance inputs coming from port 1 and respectively a voltage input that is coming as a feedback from the system and the output of the block is calculated the current. This model generated current and received voltage back from the circuit. The PV panel has 36 photovoltaic solar cells connected in series. The parameters of a single solar cell of PV panel model are listed in Table I.
Sign of the dP/dV at different positions on the P-V characteristic curve of a PV array [10, 11].
The principle of this algorithm [1, 9, 11, 12] is described in Flow chart presented in Fig. 3, where the triangle represent decision making [1].
Figure 5.
Block diagram of a PV panel connected to the load.
TABLE I. Table Head
Figure 3. Flow chart of the incremental conductance algorithm.
II.
SIMULINK MODEL OF PV SYSTEM WITH MPPT
The model shown in Fig. 4 represents a PV solar panel connected to resistive load through a dc/dc buck converter with MPPT controller.
THE PARAMETERS OF A SINGLE SOLAR CELL The Parameters of a Single Solar Cell Parameter
Value
1.
Short-circuit current (A )
I sc = 7.34
2.
Open-circuit voltage (V )
Voc = 0.6
3.
Quality factor
4.
Series resistance (Ω )
5.
First order temperature coefficient for I ph (1/K )
TIPH1 = 0.0008
6.
Temperature exponent for I s
TXIS1 = 3.3842
7.
Temperature exponent for R s
TRS1 = 0
8.
Parameter extraction temperature (°C )
TMEAS = 25
9.
Fixed circuit temperature (°C )
TFIXED = 25
N = 1.39989 R s = 0.00415132
Fig. 6 shows a Simulink® diagram of a buck converter in that can be seen its components parameters [1]. For the implementation of buck converter is used SimPowerSystems™, where can be built any custom structure. The buck converter has a voltage input from the PV solar panel and a reference command input from MPPT controller which command the power MOSFET transistor. At the output of the buck converter is connected a resistive load of 2 ohms.
Figure 6.
Diagram of a buck converter [1].
When the MOSFET is switched on, the current from the PV array can only flow through the inductor into the parallel RC combination of the capacitor C and of the resistive load R, where the capacitor voltage increases. When the MOSFET is off, current must remain flowing in the inductor, so the inductor current is now supplied by the capacitor through the diode, causing the capacitor to discharge. The extent to which the capacitor charges or discharges depends upon the duty cycle of the MOSFET. If the MOSFET is on continuously, the capacitor will charge to the array voltage. If the MOSFET is not on at all, the capacitor will not charge at all [8]. In Fig. 7 is implemented the MPPT controller using the Stateflow® from Simulink® library. Stateflow® chart is a very powerful tool that graphically allows to do state machines and logical event based controllers and can be created states and transitions. All of these transitions are based on decision based on measurement of system. It used a 100 kHz pulse-width modulation (PWM) driver for dynamics of the buck converter. The MPPT controller makes a step size in the duty cycle of the MOSFET [1]. The MPPT controller is realized using incremental conductance algorithm as in [1]. The graphics interface is shown in Fig. 8 in that can be visualized when the program running how is making the decision and how the system is moving from one state to another [1].
Figure 7.
Block diagram of the MPPT controller [1].
Figure 8. Stateflow® chart implementation of the incremental conductance algorithm [1].
III. RESULTS AND DISCUSSIONS The model shown in Fig. 4 was simulated using MATLAB® / Simulink®. The results obtained have been shown in Table II. Fig. 9 presents how the irradiance that falls on PV solar panel is changing. The voltage and the current vary depending on irradiance. The curve of variable irradiance is plotted using a signal builder, where the irradiance is not very realistic, because this are instantaneous changing irradiance, what will be equivalent to do very fast cloud moving for example [14], what allowing to the sun changing instantaneous which is not happen, but allow to give an idea of measure of how fast the controller responds [1]. In Fig. 10 is shown the V-P characteristics curve of the PV Solar Panel for different level of irradiance at temperature of 25°C.
Figure 9.
Variation of irradiance used in simulation.
Legend: Output of PV solar panel; Output of the buck converter.
─ ─
Figure 10. V-P characteristics for different irradiance levels.
The simulation was run with the MPPT controller using the incremental conductance algorithm. Fig. 11 presents the voltage, current and power coming out of the PV solar panel which is the magenta lines and the cyan lines which are the output of the buck converter. The voltage at the input of PV panel is stabilized at 17 V. As the irradiance is changing, the MPPT controller makes the power coming out of the PV array to be kept at maximum [1]. The PV solar panel generate 93.1 W maxim power and the power obtained at the output of buck converter was found to be around 87 W for a solar irradiation level of 800 W/m 2 (Fig. 11). The incremental conductance method has an efficiency of 93%. This suggests that the MPPT controller is doing a pretty good job.
Legend: Output of PV solar panel; Output of the buck converter.
─ ─
Figure 12. The simulation results of the PV system without MPPT controller.
From Table II result that the MPPT controller increasing the efficiency of the PV system as a whole. The loss of power from the available 93.1 W generated by the PV solar panel to 87 W at the output of buck converter can be explained by losses in coupling circuit (diode and capacitor), losses in the PWM circuit and the inductive and capacitive losses in the buck converter circuit. Therefore, it was seen that using the incremental conductance MPPT method increased the efficiency of the photovoltaic system, for a solar irradiation value of 800 W/m 2 , by approximately 26 % from an output power of 68.6 W to an obtained output power of 87 W. TABLE II.
POWER AS A FUNCTION OF IRRADIANCE MODIFICATION Power depending on irradiance (W)
Irradiance Maximum power (W/m²) from V-P curves
Figure 11. The simulation results of the PV system with MPPT controller.
The simulation was then run without the MPPT controller, under the same irradiance level. It was seen that when we do not use an MPPT algorithm, the power obtained at the load side, for a solar irradiation value of 800 W/m 2 , was around 68.6 W (Fig. 12). It must be noted that the PV solar panel generated 93.1 W maxim power (Fig. 10) for this irradiance level. Therefore, the output power is smaller.
With MPPT Output of buck converter
Output of PV panel
Without MPPT Output of buck converter
Output of PV panel
400
45. 2
45.2
41
19.5
17.2
600
69.5
69.5
64
42.3
38.7
800
93.1
93.1
87
73.3
68.6
1000
116.9
116.9
110
110
104.1
1200
140.6
140.6
134
140.6
134
The efficiency results for the incremental conductance algorithm and the case of directly connecting of PV array to the load are presented in Table III. TABLE III. Table Head 1.
EFFICIENCY OF THE MPPT ALGORITHM Efficiency of the MPPT algorithm (%) With MPPT
Without MPPT
0.93
0.7
In Table IV are presented the efficiency increase of the PV systems by using MPPT controller with incremental conductance algorithm against case without MPPT controller. TABLE IV.
EFFICIENCY INCREASE OF PV SYSTEM Efficiency increase of PV system
Table Head
Irradiance (W/m²)
Efficiency of PV System (%)
1.
400
138
2.
600
65
3.
800
26.82
4.
1000
5.66
5.
1200
0
Fig. 13 shows the step change response [15] of the MPPT controller under fast changing irradiance level. As can be seen from Fig 13 a), for a step size of duty cycle (Δd ) of 0.003 samples, the recovery step is 0.004 samples under increase step of irradiance of 200 W/m 2 and for decrease step of irradiance from 1200 W/m 2 to 600 W/m 2 the response of buck converter are 0.008 samples. As shown in figure 13 b), for a step size of duty cycle of 0.008 samples and the same irradiance step conditions stated above, the step change response is 0.002 and 0.004 respectively. Irradiance step between 800 W/m 2 and 1000 W/m 2
IV.
This paper discussed the implementation of a maximum power point tracking algorithm for a photovoltaic system that is used to evaluate the performance of the incremental conductance method under rapidly changing irradiance level. The algorithm was tested against fast change in irradiance (step change in irradiance). The simulation model includes the PV solar panel, the dc/dc buck converter and the MPPT controller. The modeling and simulation was done in MATLAB® / Simulink®. This simulation model enabled the analysis of the performance of PV systems. The simulation results were presented and analyzed to validate that the incremental conductance algorithm is effective at rapidly changing irradiance level. This model provides a good evaluation of performance of MPPT control for the PV systems. REFERENCES [1] [2]
[3]
[4]
[5]
Irradiance step between 1000 W/m 2 and 1200 W/m 2
[6]
[7] [8] Irradiance step between 1200 W/m 2 and 600 W/m 2
[9]
[10]
Irradiance step between 600 W/m 2 and 400 W/m 2
[11] [12]
[13]
Legend:
─ Output of PV solar panel; ─ Output of the buck converter. a)
b)
Figure 13. Step change response of power, for the two cases of step size for duty cycle change (Δd ) : a) Δd = 0.003 samples, b) Δd = 0.008 samples
CONCLUSIONS
[14] [15]
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