5.1 Simulation Results
5.1.1 PSIM Simulations
To verify the proposed maximum power point tracking algorithm and the overall PV system, PSIM simulation, for its simplicity and effectiveness, is used in the beginning. First of all, the nonlinear characteristic of the solar array has to be created to supply the necessary information for either the maximum power point tracker or the power converter stage. The characteristics of the solar array, however, are hard to predict and as a result the necessary parameters are also difficult to be identified. Eq. (5.1) revisits the formula discussed before. It reveals that the parameters mainly depend on the irradiation level and the ambient temperature.
parameters given in [37] and establishing the relationship to the irradiation and temperature, one can rephrase Eq. (5.1) into Eq. (5.2).
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photovoltaic voltage, VPV, the irradiation level, S, and the ambient temperature, T, is established. The PV current and PV voltage are obviously dependent on both the irradiation and the temperature. Fig. 5.1 shows the PSIM schematic for the PV array simulation under the condition of different irradiation levels. Eq. (5.2) is used here as a function block m to provide the transfer function for IPV.
Fig. 5.1 PSIM schematic of PV array with different solar irradiation levels.
Fig. 5.2 and Fig. 5.3 show the simulation results under different irradiation levels according to PV current and PV power respectively. Fig.
5.3 shows that the maximum power point increases along with the increase of the solar irradiation level. This proves one of the physical characteristics of solar array.
55 Different Irradiation Levels
Irradiation increases
Fig. 5.2 PV current vs. PV voltage with different irradiation levels.
Different Irradiation Levels MPP
MPP increases as irradiation increases
Fig. 5.3 PV power vs. PV voltage with different irradiation levels.
Temperature is another dominant factor that greatly affects the behavior of the solar array. Fig. 5.4 provides the PSIM schematic for simulating the PV characteristic curves under different temperature conditions. Similarly, the function block m here is provided by Eq. (5.2) as well.
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Fig. 5.4 PSIM schematic of PV array with different temperatures.
The following figures, Fig. 5.5 and Fig. 5.6, show the simulation results of the characteristic curves with respect to different environment temperatures. The results confirm that, as expected, the maximum power point is inverse proportional to the temperature. That is to say, the maximum power point decreases as the temperature increases, as shown in Fig. 5.6.
Different Temperatures
Temperature increases
Fig. 5.5 PV current vs. PV voltage with different temperatures.
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MPP
MPP decreases as temperature increases
Fig. 5.6 PV power vs. PV voltage with different temperatures.
Series- and parallel- connected solar arrays act basically like a battery or a large capacitor. For the convenience of the system simulation, a large capacitor is connected to the output node of the solar array simulator as an energy storage element. Fig. 5.7 shows the solar array simulator in PSIM.
Fig. 5.7 PSIM schematic for the solar array simulator.
Fig. 5.8 demonstrates the simulated behavior of solar array at temperature of 30oC and irradiance of 990 Watt/m2.
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MPP
VMPP
PMPP
VMPP
Fig. 5.8 PSIM simulated PV characteristic curves.
Fig. 5.9 shows the whole picture of the proposed maximum power point tracking technique in PSIM schematic. It can be roughly divided into four parts, as shown in Fig. 5.10 ~ Fig. 5.13.
The first part, Fig. 5.10, includes a solar array simulator and a boost converter. The solar array simulator is to provide the input current and voltage with the characteristics similar to a real solar array. The boost converter, in addition, is used to modulate the operating point and track the maximum power point.
The second part is about the slope detection tracking (SDT) circuit, as shown in Fig. 5.11. Sample-and-hold circuits here are used to sense the PV voltage and PV current information. Old voltage and current data are also stored for the use of slope calculation. In addition, arithmetic circuits, such as adder, subtractor, multiplier, are used to calculate the slope. The output of this circuit is an analog signal which indicates the value of the slope at that time instant.
The third part, shown in Fig. 5.12, is the circuit to determine the
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perturbation direction. The sensed slope information serves as an input for this circuit. Then it will be compared to the value ε according to the condition given in TABLE 5.1 to determine the new reference voltage for the boost converter so as the next move of the operating point. If the slope is positive and larger than the value ε, the next move of operating point will be in a positive direction. If the slope falls in the range between ε and –ε, the next reference voltage will remain the same. This means that the system is already operating on or near the maximum power point.
However, if the slope is smaller than –ε, it means the system needs to decreases the operating voltage to catch up the maximum power point. As a result, the operation will move in a negative direction. Fig. 5.13 shows the last part of the MPPT circuit which deals with the open-circuit detection (OCT) tracking. As mentioned before, OCT helps the system to locate the approximate maximum power point at the beginning. This circuit is only active during the system startup period. After the startup period, the SDT technique takes over the tracking control to track the maximum power point.
TABLE 5.1 Slope Condition vs. Perturbation Direction Slope Condition Perturbation Direction
Slope >
ε
Vref’ = Vref +ΔV-
ε
< Slope <ε
Vref’ = VrefSlope < -
ε
Vref’ = Vref -ΔV60
Fig. 5.9 PSIM schematic of the proposed maximum power point tracker.
Fig. 5.10 Solar array simulator along with boost converter.
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Fig. 5.11 PSIM schematic of the slope detection circuit.
Fig. 5.12 PSIM schematic of the perturbation circuit.
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Fig. 5.13 PSIM schematic of OCT circuit.
To verify the tracking efficiency of the proposed MPPT technique, the maximum power point voltage, current, and power of the solar array simulator at a given temperature and irradiation is first investigated and then compared to the measured result. Fig. 5.14 shows the simulated solar array output information. It shows that the output voltage at the maximum power point is around 24V at the temperature of 30oC and the irradiance of 990 Watt/m2. This means that under these environmental conditions the solar array can output its maximum power when the operating point is controlled around 24V. That is to say, the PV system needs to regulate the operating voltage around 24V to achieve a high tracking efficiency and high power conversion efficiency.
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VMPP=24V
MPP
Fig. 5.14 The output of solar array simulator at 30oC and 990 Watt/m2.
Fig. 5.15 shows the simulation waveforms of the proposed MPPT technique at the temperature of 30oC and the irradiance of 990 Watt/m2. The tracking procedure at first undergoes the OCT period. As mentioned before, during this period, the operating point voltage is set to be around the maximum power point, approximate 70% of the open-circuit voltage.
This increases the tracking speed during the system power-on period. After the OCT period, the SDT takes place the tracking control. SDT constantly detects the slope condition and changes the perturbation direction according to the polarity of the operating voltage to the maximum power point voltage. As the waveform indicated in Fig. 5.15, the settled PV voltage is around 24V, which agrees to the maximum power point voltage simulated by the solar array simulator in Fig. 5.14. This result concludes that the proposed system can effectively track the maximum power point as expected.
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VPV≈24V
OCT SDT
@30ºC, 990W/m²
Fig. 5.15 The MPP tracking waveforms at 30oC and 990 Watt/m2.
The solar irradiation is changed to 110 Watt/m2 to test the tracking efficiency under low irradiation level. The simulation in Fig. 5.16 shows that the maximum power voltage is regulated around 18V and this matches the maximum power point voltage given in a solar array simulator.
OCT SDT
VPV≈18V
@30ºC, 110W/m²
Fig. 5.16 The MPP tracking waveforms at 30oC and 110 Watt/m2.
The solar irradiation changes periodically during the day, a good MPP
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tracker needs to maintain a high performance, either fast tracking speed or high tracking accuracy, no matter the irradiation changes. The proposed tracking technique is put into an irradiation transition test in Fig. 5.17. The solar radiation changes from 990 Watt/m2 to 110 Watt/m2. As can be seen in the figure, the PV voltage successfully changes from 24V to 18V. This guarantees the universality of the proposed maximum power point tracking technique.
VPV≈18V VPV≈24V
Irradiation reduces
S=990W/m²
S=110W/m²
Fig. 5.17 The PSIM simulation waveforms under irradiation transition.
A versatile PV system needs to handle a wide temperature range as well, not only in a high temperature environment but also in a low temperature. Here both high temperature 50oC and low temperature 5oC are put into test, as shown in Fig. 18 and Fig. 19, respectively. The tracking undergoes the same tracking procedure as in previous examples. First is the OCT and then the SDT takes place. In either temperature, the high tracking efficiencies are both guaranteed. At high temperature 50oC, the PV voltage is controlled around 23.5V. And at low temperature 5oC, the PV
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voltage settles at around 25V. The solar irradiation in both cases is controlled as 990 Watt/m2.
OCT SDT
@50ºC, 990W/m² VPV≈23.5V
Fig. 5.18 The MPP tracking waveforms at 50oC and 990 Watt/m2.
OCT SDT
@5ºC, 990W/m² VPV≈25V
Fig. 5.19 The MPP tracking waveforms at 5oC and 990 Watt/m2.
The tracking performance during the temperature transition is examined in Fig. 5.20. As the temperature changes from high temperature of 50oC to low temperature of 5oC, the PV voltage changes from 23.5V to 25V with little time delay. The waveforms confirm the effectiveness of the
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proposed tracking technique and the circuit under the drastic temperature changes.
VPV≈25V VPV≈23.5V
Temperature reduces
T=50ºC
T=5ºC
Fig. 5.20 The PSIM simulation waveforms under temperature transition.
The PSIM simulations discussed in this section help confirm the effectiveness of the proposed maximum power point tracking algorithm and the robustness of the maximum power point tracking circuits. The simulation results show that the proposed maximum power point tracker can not only track the maximum power point accurately under varying solar irradiation but also work perfectly under the drastic temperature changes.