1. Introduction
Due to the global climate change issue [
1], every country is concerned with reducing carbon emissions and improving the greenhouse effect. First, the consumption of coal, natural gas, and other fossil fuels can be reduced significantly for power generation [
2] to achieve this goal. Second, people should reduce the use of fossil fuels in transportation [
3], and walking or riding bicycles can be preferred for shorter distances instead of driving. Furthermore, the government has already been promoting the utilization of renewable energy, such as wind power [
4], solar power [
5], hydroelectric power [
6], tidal power [
7], geothermal power [
8], and biomass power [
9], etc. Renewable energy is connected in parallel with the mains through power conversion technology and provides power to the demand side, as shown in
Figure 1. Electricity is supplied to the demand side, which includes residential buildings, industries, campuses, commercial applications, rail vehicles [
10], electric vehicles [
11], etc. It is obvious from the aforesaid uses that renewable energy has been integrated into people’s lives and has a wide range of applications.
Amongst the various renewable energy, the solar photovoltaic power system (SPPS) has drawn major attention of the researchers because SPPS does not generate noise during power generation and has a long service life [
12]. The small solar photovoltaic module (SPVM) can be carried around conveniently and used in watches, computers, backpacks, blankets, etc. [
13], which are more flexible in real life. Medium-sized solar photovoltaic arrays can be installed on rooftops to provide electricity for homes or farms [
14]. A large-scale solar photovoltaic array parallel grid can improve users’ stable power quality [
15].
The SPPS is a diverse field and could have different research areas, including SPPS fault diagnosis [
16], solar cell material upgrade [
17], SPPS microgrid technology [
18], and power electronics technology combined with the solar maximum power point tracking (MPPT) [
19], etc. This study focuses on improving the efficiency of SPPS by developing a new MPPT technique that can help achieve higher efficiency under both uniform irradiance conditions (UIC) and partial shading conditions (PSC). Numerous studies focusing on MPPT have been presented. Kumar et al. discussed that the perturbation and observation (P&O) algorithm architecture is simple, easy to implement, and widely used in SPPS. However, the P&O algorithm uses the perturbation characteristic to track the maximum power point (MPP), which causes a power loss during the MPPT process. Additionally, the MPP cannot be achieved under PSC, resulting in low system performance [
20]. Liu et al. examined the solar angle and horizon (SAH) algorithm to improve the performance of the hill−climbing algorithm. This SAH algorithm analyzes the solar angle and horizon with high efficiency under the UIC, but the efficiency decreases with environmental changes (as PSC) [
21]. Lu et al. used the solar photovoltaic module output power and load (SPMOPL) MPPT control method to capture the MPP effectively. However, this SPMOPL MPPT control method needs huge data analysis (such as irradiance level, temperature, SPVM output voltage, etc.), which will cause a system burden [
22]. Jagadeesan et al. proposed the right half−plane (RHP) MPPT control mechanism for tracking the MPP on the
Pspv−Vspv curve of SPVM to improve the system efficiency. This control mechanism reduces the MPPT range and thus reducing the system burden. However, the system efficiency will be low if the irradiance level and temperature change are high [
23]. Uno et al. discussed the dual MPPT control strategy, which analyzed the SPVM and power converter output voltage and current signals to estimate the best duty cycle and capturing MPP. The dual MPPT control strategy has high efficiency but requires multiple power MOSFETs and diodes, which increases the system cost [
24]. Mobarak et al. introduced the parabolic MPPT control strategy, which can make calculations quickly and accurately to improve SPPS efficiency. However, this control strategy must estimate multiple peak power points with the parabolic equations many times under the PSC and track the MPP. This will increase the system burden and the MPPT time [
25]. Zhu et al. discussed the finite−state−machine (FSM) MPPT that can improve the system efficiency under the UIC and PSC. However, the complicated control sequence increases the burden on the controller. Also, the system requires multiple power converters to be used in parallel, which increases the cost of the system [
26]. Kiran et al. introduced the variable step size artificial neural network (VSSANN) MPPT method that captures MPP through artificial intelligence training to improve system efficiency. However, the system requires the installation of an additional solar power meter and a thermometer, which makes the system costly [
27].
This study proposes a speed of light optical path difference measurement (SLOPDM) MPPT based on estimating optical path difference angle. The proposed method calculates the duty cycle for the boost converter to track the MPP by using the relationship between optical path difference angle, solar photovoltaic module impedance Rspv, and load Ro. The proposed SLOPDM control strategy helps achieve the high performance of the SPPS under both the UIC and PSC, verified by the experimental result. The proposed SLOPDM-based MPPT is fast, simple, low-cost, and does not cause a system burden.
Table 1 shows a comparison of various MPPT algorithms. The following points can be concluded from this table. First, the proposed SLOPDM algorithm is the least complex among the aforementioned algorithms. Second, the proposed algorithm performs better than the P&O and RHP MPPT algorithms. Last, the MPP tracking speed of the proposed algorithm is superior to the P&O, SAH, SPMOPL, dual MPPT, and FSM MPPT algorithms.
3. Proposed Speed of Light Optical Path Difference Measurement MPPT Control Strategy
Figure 6 is the schematic diagram showing the relationship between the sun, earth, and planets, where the sunlight shines on the planet and the planet reflects the light to the earth. However, the earth revolves around the sun. It leads to the position of the planet seen on the earth being different from the actual position of the planet due to the speed combination of the earth’s revolution and light. It is similar to being on a running train when it’s raining outside, and the rain looks like it is falling diagonally when observed from inside the train car.
In the 18th century, Prof. Bradley proposed the speed of light optical path difference measurement (SLOPDM) method to calculate the actual planetary position. The planetary position could be calculated accurately using this method [
35]. This study extends the use of the SLOPDM method for maximum power point tracking. So, the proposed MPPT method in this study is named SLOPDM MPPT. A detailed description of the proposed MPPT control strategy has been presented below.
In
Figure 6, the earth’s revolution speed is
, the speed of light reflected by the planet
is 3 × 10
5 km/s, and the angle of the optical path difference is
θ.
Figure 7 demonstrates a schematic diagram of the relationship between the earth’s revolution speed
, the light speed
, and the angle of the optical path difference
θ, which can also be represented by Equation (6).
where
is constant as 3 × 10
5 km/s,
changes with the distance between the sun and the earth.
becomes higher when the distance between the earth and the sun is reduced. Therefore,
is not constant.
Figure 8 is transformed from
Figure 7, which shows the relationship between angle
θ1 and its opposite
Y. In
Figure 8, the radius of the circle is regarded as 1 depending on the light speed
, which is a constant value; angle
θ1 corresponds to the angle of the optical path difference
θ. Using Equation (5),
Figure 7 and
Figure 8 and assuming that
Y is proportional to the
and
Rspv, the relationship between
,
Y,
Rspv,
Ro, and duty cycle
D are expressed as Equation (7).
When
θ1 = 0°,
is proportional to the radius (1). By substituting Equation (6) into (7), the relationship between tan
θ1,
Rspv,
Ro, and duty cycle
D can be obtained as follows:
When
θ1 = 45°, Equation (8) will be transformed into Equation (9).
If the value of Rspv and Ro are known, the duty cycle D at θ1 = 0° and θ1 = 45° can be calculated using Equations (8) and (9), respectively. Therefore, this study can estimate the MPPT’s duty cycle to achieve MPP using the relationship between tanθ1, Rspv, Ro, and duty cycle D.
Using the transformation of Equations (5)−(9), the relationship between
Rspv, angle
θ1, and duty cycle
D can be drawn, as shown in
Figure 9. In
Figure 9, the right
y−axis represents the impedance of SPVMs
Rspv; the left
y−axis represents the duty cycle
D; the
x−axis represents the angle; the straight blue line shows the results when
Rspv changes from 1 Ω to 46 Ω; and the brown curve shows the results when
D changes from 0 to 0.1. When load
Ro = 200 Ω,
Rspv = 34 Ω, angle = 34° using the Equations (5)–(9), 0.06 is the optimal duty cycle of the MPPT, because the proposed SLOPDM MPPT control strategy regards the optical path difference measurement of the light speed as the basis and considers the relationship between the load
Ro and
Rspv to calculate the MPPT duty cycle
D. Therefore, the proposed SLOPDM control strategy can capture the MPP rapidly and accurately.
Figure 10 shows the flowchart of the proposed SLOPDM MPPT control strategy. First, the system measures
Vspv,
Ispv,
Vo, and
Io. The
Rspv and
Ro will only be calculated when the boost converter’s output current
Io ≠ 0. Second, the
dPspv/
dVspv is the next parameter to be checked. If
dPspv/
dVspv = 0, the system is operating at MPP and the duty cycle
D is fixed. By contrast, if
dPspv/
dVspv ≠ 0, the proposed SLOPDM MPPT will be performed. Next, the system calculates the angel with
Rspv and
Ro (
Figure 9). Finally, the system substitutes
Rspv,
Ro, and angle
θ1 into Equation (8) to obtain the MPPT’s duty cycle
D, and drives the boost converter to capture the MPP.
Figure 11 displays the architecture diagram of the solar photovoltaic simulator that connects the boost converter and embeds the proposed SLOPDM MPPT control strategy. The solar photovoltaic simulator simulates two SPVMs connected in series whose total rated power is 430 W, and the specification of a single SPVM is shown in
Table 2. The specifications of the boost converter inductor
L1 and capacitor
C1, as well as the microcontroller unit (MCU), are shown in
Table 4. The control flow of the proposed SLOPDM MPPT strategy is explained as follows: First, the voltage and current sensors are employed at the solar photovoltaic simulator’s output
Vspv and
Ispv to capture the voltage
Vspv,ref and current
Ispv,ref signals to be transmitted to the MCU. Second, the boost converter’s output
Vo and
Io uses voltage and current sensors to catch the voltage
Vo,ref, and current
Io,ref signals transmitted to the MCU. Third, the
Vspv,ref,
Ispv,ref,
Vo,ref, and
Io,ref signals are utilized to calculate the MPPT duty cycle using the proposed SLOPDM MPPT control strategy, whose operating frequency is 50 kHz. Finally, the MCU generates the MPPT duty cycle to drive the power MOSFET SW
1 of the boost converter, thus tracking the MPP.
5. Conclusions
This research developed a novel SLOPDM MPPT control strategy for SPPS. The estimation of the optical path angle difference is used as the basis for the proposed control strategy. This is done by determining the relationship between the optical path angle difference, solar photovoltaic power impedance Rspv and load Ro, and then calculating the duty cycle corresponding to the MPP, which then drives the boost converter to capture the MPP. The proposed method can easily and rapidly achieve MPP. In this study, the experimental verification is carried out under both the UIC and PSC. The proposed SLOPDM algorithm performance is 99% under UIC, which is higher than that of the SAH and P&O algorithms. In addition, the proposed SLOPDM algorithm reached 99% under PSC with the irradiance level of 700 W/m2 and 65 W/m2, while the SAH algorithm efficiencies are 95% and 94%, and the P&O algorithm efficiencies are 52% and 35%, respectively. Under PSC, the proposed SLOPDM algorithm performed far better than the SAH and P&O algorithms. Finally, this novel control strategy does not need to change the hardware circuit design and requires any additional solar power meter. This reduces the cost and the complexity of the system significantly.
Future work can test and verify the proposed SLOPDM MPPT algorithm with multiple sets of SPPS. Furthermore, the related parameters can be modified to make it a faster MPPT control strategy, evaluate the period, and state that SPPS does not have to use MPPT, further improving SPPS efficiency.