Earthquake Algorithm-Based Voltage Referenced MPPT Implementation through a Standardized Validation Frame

Abstract

This paper presents a new direct maximum power point tracking (MPPT) with a reference voltage ($V_{ref}$) based on the metaheuristic earthquake algorithm (EA) where the optimization variable is the $V_{ref}$ for hard-switching converters. The efficiency and performance of EA-MPPT-$V_{ref}$ is compared with the perturb-and-observe (P&O) counterpart technique due to the fact that it is widely used for commercial products. Static and dynamic responses for both MPPT strategies are evaluated, which correspond to steady-state oscillations when they are near the maximum power point (MPP), and the tracking-speed, respectively. The efficiency was evaluated with the EN 50530 standard. The results show that the new MPPT proposed is a competitive method using the EA to obtain the optimal voltage reference. From static results, EA-MPPT VP presented a better efficiency of 5.13% and 3.23% for European and California energy commission (CEC) efficiency, respectively. Whereas, from dynamic results, MPPT-$V_{ref}$ techniques presented an efficiency from 95.13% to 99.91%, and 99.01% to 99.91% of the total power of the PV system for P&O and EA strategies, respectively.

1. Introduction

Since 1995, global energy demand has been increasing by 53% (according to the average annual growth rate of just 1.87∼2.1% of total energy supply and consumption). This high demand has generated a depletion of fuel resources, which supply about 80% of total energy consumed [1]. On the other hand, the use of fossil fuels deteriorates air quality, contributing to the global warming effects. For this reason, renewable energies have been adopted to reduce the use of fossil fuels to decrease carbon emissions [2].

Therefore, renewable energy has become more necessary than ever to discover the alternative of energy to supply the total energy demand. Between all renewable energies such as wind, geothermal, hydro, solar and biomass power, solar power is the most common for electricity generation, e.g., electric vehicles stations, energy storage systems, streetlights, heating equipment, home electricity, renewable energy hybrid system, etc. [3].

Generally, photovoltaic (PV) cells are the most used technology to convert solar energy into electricity due to advantages such as low maintenance cost, no fuel consumption (zero carbon emission), no moving parts and self-generated noise, and that they can be installed in many places. However, the limitations of PV system include low conversion efficiency and the searching for the maximum power point (MPP), determined by the surrounding environment [4,5]. To deal with the difficulties resulting from low-efficiency conversion, strategies have been developed to obtain the maximum power from PV systems. There are two main ways to track the solar energy: (1) mechanical, where the sun position is tracked, and (2) electrical, where the maximum point of voltage and current is searched for; this strategy is known as maximum power point tracking (MPPT) [6]. To find the MPP of PV systems is difficult due to its non-linear voltage-current (V-I) characteristic curve which can be modified by solar irradiance, ambient temperature, wind speed and other environment parameters [7]. Therefore, to operate in the MPP of the PV system, it is necessary to insert a converter direct current-direct current (DC/DC) or direct current-alternating current (DC/AC) between the PV and electric load. The MPPT algorithm must be embedded into the converter in order to continuously adapt the input load impedance of the PV system to track the instantaneous MPP [8].

According to [9], there are two main categories of MPPT techniques: (1) direct, and (2) indirect. Direct methods can work without any knowledge of PV system characteristics. By sensing the voltage and current of the PV system, it is possible to track the MPP. Sampling and modulation techniques are two kinds of direct control strategy. In sampling techniques, voltage and current are collected and compared with the present and past values in order to locate the MPP, while in modulation techniques, automatic oscillations are generated as a feedback signal to find the MPP. On the other hand, the indirect methods employ numerical estimation using technical data from the PV array and parameter values. Thus, they cannot precisely track the MPP of PV array at any irradiance and cell temperature of PV system given [10]. Similar classifications are presented in [10,11] where MPPT methods are classified into three groups: (1) conventional and direct control techniques, (2) indirect control methods, and (3) soft computing-based approaches. In [5], identical classification is presented: (1) conventional methods, (2) intelligent techniques, and (3) nature-inspired or metaheuristic algorithms.

Based on conventional/direct methods, the perturb and observe (P&O) technique is the most used due to its easy structure and implementation; several recent implementations and improvements are presented in the following studies [12,13,14,15,16,17,18,19,20,21,22]. This algorithm presents the following behaviors: first, the PV voltage is perturbed; then, the power of PV system is observed to compare with the previous one. If the power increases, it means that the operating point has moved toward the MPP, and the perturbation must be continued in the same direction. Otherwise, if the power from PV system decreases, the perturbation must be changed and reversed due the operating point moving away from the MPP. Nevertheless, the disadvantages of this method are: (1) when is near of the MPP presents steady-state oscillations, (2) poor efficiency in cloudy days, and (3) slow response to rapid changes in weather conditions. Another direct technique is the incremental conductance (IC) presented by [23,24,25,26,27,28,29] in recent years. This algorithm is based on the incremental ($dI/dV$) and instantaneous conductance ($I/V$) of the PV system in order to detect the slope of the power-voltage (P-V) curve. If the incremental is equal to the negative instantaneous conductance, it means that the algorithm reaches the MPP. On the other hand, if the incremental conductance is greater or less than instantaneous, the operating point is at the left and right side of the MPP, respectively. The main weakness of this algorithm is the uncertainties due to the noise of components and when the solar irradiation increases. For the fractional open-circuit voltage (FOCV) method [30,31], it is based on the relationship between the open-circuit voltage ($V_{oc}$) and the voltage at maximum power ($V_{mp}$) of the PV system. Commonly, a constant $K_{pv}$ is presented which is the voltage factor with the value in the range 0.7–0.9. The $V_{oc}$ is measured periodically disconnecting the load; then, the $V_{mp}$ is estimated using the $K_{pv}$ which is typically specified in the panel’s datasheet. However, the frequency and duration to estimate the $V_{mp}$ can be improved when it is high, but the power loss is increased.

Regarding the MPPT intelligent/indirect methods, the most used techniques (in recent years) for MPPTs are fuzzy-logic (FL) [32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51] controller, artificial neural networks (ANN) [52,53,54,55,56,57,58,59,60], and Kalman Filter (KF) [61]. In FL, the model of the system is not necessary and this is an important advantage due to the non-linearities and uncertainties presented in a model. Therefore, steady state and dynamical performance is improved by FL. However, the qualitative reaction of the system to different inputs must be prior known by the designer. Moreover, these implementation methods present lack for adaptivity with various operating points of PV systems [50]. On the other hand, ANN provides accurate and robust PV modeling and can deal with uncertain weather conditions if it is well trained. With these considerations, ANN provides a very fast and precise MPPT to locate and track the MPP. Nevertheless, the main drawback is that the ANN needs to be trained recurrently due to time/temperature variations of the PV arrays characteristics. Thus, the ANN accuracy depends on the ANN being comprehensively trained [62]. According to KF, this method applies two steps: (1) prediction and (2) correction. For MPPT application, the first step of KF is estimate the $V_{mp}$. The second step is to correct the estimation by calculating the error between the PV voltage measured and the estimated $V_{mp}$. This process is iterative until the error is close to 0. However, the main disadvantage is that KF uses the slope of P-V curve, and it is impossible to estimate the global MPP (GMPP) [11]. Moreover, implementation of these techniques in large-scale PV systems generates difficulties on the control system when it is implemented. Furthermore, the implementation of these techniques is very complex and demands high-level experience of user [63].

In [64], metaheuristic optimization algorithms supply a better switching between finding an approximate optimal solution and convergence speed using less hardware resources. Besides, these algorithms adopt strategies developed from artificial intelligence (AI), operation research, and soft-computing, which empower the optimization strategies that are convenient for conventional or high complex optimization problems [65]. According to [66], metaheuristic optimization algorithms provide a better trade-off. Moreover, [67] highlights that metaheuristic algorithms have been implemented to improve the performance to track the MPP in PV system. This can be useful to reduce the sensitivity of the algorithm to these parameters that do not allow reaching the global optimum or the solution stuck in a local optimum. Several metaheuristic MPPT methods are presented in the last year, such as particle swarm optimization (PSO) [68,69,70,71,72,73,74,75,76,77], genetic algorithm (GA) [78,79,80,81,82], differential evolution (DE) [27,83,84], cuckoo search optimization (CSO) [4,85,86], ant colony optimization (ACO) [87,88,89], firefly algorithm (FA) [90,91], chaotic search (CS) [92], artificial bee colony (ABC) [93], grey wolf optimizer (GWO) [94], bat algorithm (BA) [95], shuffled frog-leaping algorithm (SFLA) [96], monkey king evolution (MKE) [97], salp swarm algorithm (SSA) [98], remora optimization algorithm (ROA) [67], and EA [99]. Generally speaking, MPPT metaheuristic approach algorithms show improvement in tracking speed, tracking accuracy, and robustness. In addition, the speed of convergence and tracking accuracy can be improved by providing compensation using the exploration and exploitation features of metaheuristic algorithms. Furthermore, these algorithms do not need any pre-set configuration and can be applied directly to any PV system without having information about its characteristics. However, the main drawback of these algorithms is their higher probability of falling into a local optimum in the tracking process which results in the inability to reach the global peak. Figure 1 shows the chronology of the MPPT studies carried out in recent years, where metaheuristic algorithms were used in most cases.

Therefore, this work presents an MPPT strategy based on the EA metaheuristic optimization algorithm presented in [100]. In addition, to improve performance, a proportional-integral (PI) controller is integrated. First, the EA-MPPT estimates the optimal voltage that provides the maximum power of the photovoltaic system. Then, the optimum voltage is sent to a PI controller as a reference voltage ($V_{ref}$) which modifies the duty cycle of the DC/DC converter to achieve this voltage. Besides, in order to compare the efficiency of the proposed EA-MPPT, the P&O-MPPT strategy are implemented due that is the most MPPT used in commercial products with the IC algorithm, according to [11]. Aditionally, when P&O and IC are evaluated with EN50530 standard test, results indicate similar performance [17,18].

Another key factor to consider from the literature review is that many MPPT algorithms have been proposed with different techniques and strategies in order to improve the accuracy and performance of static and dynamic response. In addition, in some studies, different strategies of different classifications have been combined to hybridize the behavior between them. In these works, authors compared the MPPT algorithms using step changes in the irradiance or temperature of the PV systems. These steps are not standardized and it is difficult to compare their performance objectively [8]. Hence, in this work, the proposed EA-MPPT algorithm is evaluated with the standard test EN 50530 which is composed of two tests: static and dynamic. This test evaluates the efficiency of the MPPT algorithms analyzing the dynamic response which correspond to the performance of the tracking speed and the static response which is determined by the steady-state oscillations when they are near of the MPP. Moreover, the standard test EN 50530 evaluates the MPPT efficiency according to real-world weather conditions from different regions such as: (1) middle-Europe climate [101] and (2) US south-west regions [102].

The main contribution of this paper can be summarized as follows:

• A new MPPT based on EA algorithm is proposed with an improvement that integrates a PI controller.
• We evaluate the proposed EA-MPPT strategy with the EN 50530 standard test that uses real-world weather conditions.
• We implement the proposed EA-MPPT embedded into a LabVIEW-FPGA frame in order to explore computational parallelism and compare it with the P&O counterpart.

This paper is organized as follows: Section 2 explains the P&O-MPPT strategy with reference voltage, then Section 3 presents the proposed voltage reference-based MPPT based on EA. Additionally, Section 4 describes the experimental setup and Section 5 depicts the EN 50530 test to evaluate the efficiency of MPPT strategies in static and dynamic responses. Finally, Section 6 presents the results and Section 7 concludes this work.

2. Voltage Reference Based MPPT

Conventional MPPT methods are widely used due their simplicity to implement, low computational cost, and unnecessary prior knowledge of the PV system. However, these methods present disadvantages, such as the amount of perturbation which may produce lost energy when they are near of the MPP (by steady-state oscillations) or decrease tracking speed (by a small perturb step) when they are in the search of the MPP [11]. Furthermore, their performance decreases when a rapid change in irradiance occurs [62]. Therefore, variable or adaptive perturbance has been proposed to improve the performance and generate a good trade-off between faster response and steady-state oscillations [103]. Furthermore, P&O could not determine when the MPP is actually reached [104].

Figure 2a presents the basic topology for MPPT controller which is connected directly to the DC/DC converter. In this case, the duty cycle for pulse-width modulation (PWM) signal is adjusted by the MPPT controller. In contrast, Figure 2b shows the voltage-based MPPT method which estimates the voltage reference to be compared with the measured PV voltage. Then, the result of the comparison is used as an error signal to the PI controller which adjusts the duty cycle in order to find the MPP from PV system. It is important to mention that only the DC/DC converter is presented but it can be combined with more power electronic components to create specific power electronic devices such as inverters.

Voltage Reference Based P&O MPPT Method

The P&O technique is the most well-liked MPPT method due to its simple structure. Therefore, hardware implementation is easy and has low computational cost. This technique is an iterative approach, and each iteration perturbs the PV voltage system ($V_{pv}$), and the output power is compared with the previous one. If the power is increasing, the perturbation will continue, otherwise perturbation is reversed. These perturbations can be defined as a small variation of duty cycle which generates changes in the response of the PV system. The use of large or small step-size increases the power oscillations (which will result in loss energy) or decelerates the tracking speed, respectively, [8]. Another aspect to be considered is the sampling rate, which also contributes to the performance of MPPT [105]. In [106], it is suggested that the sampling rate should be selected by the dynamic response of the DC/DC converter.

According to [107], the issues mentioned above can be improved by implementing a reference voltage ($V_{ref}$) control. In this case, the MPPT algorithm estimate the disturbance signal ($V_{ref}$) to send through the PI controller as an input reference which regulates the manipulation variable (duty cycle) for the DC/DC converter. Moreover, Figure 3 depicts the flowchart of P&O based on $V_{ref}$. The strategy is similar to the original P&O, where voltage and current of PV system is measured to estimate the present power and compare it with the previous one. Then, the present PV voltage is compared with the last voltage to make a decision which consists of increasing or decreasing the $V_{ref}$. The $V_{ref}$ is the input reference to the PI controller in order to update the manipulation variable (duty cycle) to change the PV voltage with the DC/DC controller.

3. MPPT-EA Reference Voltage

3.1. Overview of EA

The EA algorithm is widely presented and implemented in many applications and platforms (as reported in [65]). Moreover, it is the first geological metaheuristic algorithm inspired by the earthquake phenomenon. The nature of earthquake is composed of P and S waves which the P-wave occurs first due to its higher speed than S-wave [100].

The P-wave is transmitted by any medium (solid, gas, and liquid) causing compression and tension of the medium and their velocity depends on earth material compressibility. Thus, volume changes occur when these characteristics are presented (Figure 4a). On the other hand, the transmission of the S-wave depends on rock elasticity. Its movement causes epicenters which are moved up and down perpendicular to the wave propagation direction (Figure 4b) [108].

Hence, mathematical estimation of P and S-wave is made in (1) and (2),

$$v_p=\sqrt{\frac{\lambda +2\mu }{\rho }},$$

(1)

$$v_s=\sqrt{\frac{\mu }{\rho }},$$

(2)

where $v_p$ and $v_s$ are the P- and S-wave, respectively; $\lambda$ and $\mu$ are the ground earth materials which are called Lamé parameters, and $\rho$ is the density of the earth material (according to [100]). Furthermore, the selected values from Lamé parameters for optimal performance are $\lambda =\mu =1.5$ GPa. Supplementary to the velocity’s estimation, the densities of earth materials are taken from a random value in a range between 2200 and 3300 kg m³ [65].

Considering the use of two different velocity equations in EA, in [100] introduces the concept of S-range (Sr) in order to define whether to use $v_p$ or $v_s$. The Sr parameter defines the range situated near the global best epicenter (solution). Therefore, each epicenter uses $v_p$ (exploration) or $v_s$ (exploitation) to update its position depending on which zone (in or out of Sr range) is located previously.

3.2. Proposed EA-MPPT-$V_{ref}$

In [99], a first MPPT adaption based on EA metaheuristic optimization was presented. The authors extrapolated the dynamic optimization behavior from original EA to generate a MPP tracker with the EA feature. In simple terms, to find the MPP, it is necessary that the epicenters are moving around to provide a good optimal solution near the MPP. Hence, in order to ensure this dynamic, a searching flag ($S_{flag}$) was implemented to introduce the duty cycle (the one that collects the most power) to the searching positions, achieving a trade-off between tracking speed and steady-state oscillations when the MPP is reached. Another important aspect for this adaptation is the use of the $v_s$ that is estimated with (2), to update the epicenter’s position which is the reference voltage ($V_{ref}$).

Regarding what is proposed in this work, the MPPT-EA algorithm estimates the optimal voltage located in $V_{mp}$ which, later, is the input for the PI controller as $V_{ref}$. The PI controller then modifies the duty cycle of the PWM signal which is the manipulation variable to eliminate any errors. Figure 5 depicts the flowchart of the proposed MPPT which estimates the $V_{ref}$ with the behavior of EA algorithm that is adapted to PV system requirements. Then, this algortihm returns the best global epicenter ($V_{ref}$) after evaluating the epicenter and analyzing the response of the PV systems before exploring the next epicenter.

4. Testbed System

The testbed system used for this work uses the platform for a request paten in [109]. This research facility was created to analyze energy consumption, storage, and generation patterns by conventional methods (i.e., fossil fuels) and renewable energies. Therefore, any energy consumption pattern can be reproduced and analyzed for distributed generation systems.

The experimental system for this work consists of four main blocks: (1) panel system, (2) DC/DC converter, (3) dynamic load, and (4) control and acquisition system. The PC host interacts with the acquisition and control systems, besides, sends virtual instrument software architecture (VISA) through standard commands for programmable instruments (SCPI) in order to change the parameterization of panel system (for the photovoltaic array simulator) and dynamic load. This interaction is achieved through a managed Ethernet switch which all devices are connected (as shown in Figure 6). The acquisition system captures five signals from the process system. The signals are: (1) voltage of the PV system, (2) current of the PV system, (3) voltage of load, (4) current of load, and (5) duty cycle. Moreover, the photovoltaic array simulator, when in the EN50530 test, storages the following data: (1) voltage at maximum power ($V_{mp}$), (2) current at maximum power ($I_{mp}$), (3) maximum power ($P_{mp}$), (4) PV voltage, (5) PV current, (6) PV power, (7) measured energy, (8) MPP energy, and (9) MPPT efficiency.

4.1. Solar Panel System

The experimental panel system is divided into two parts: (1) two monocrystalline solar panels and (2) photovoltaic array simulator. The monocrystalline solar panels consist of two-panel solar in series array of 5W each panel, with the following characteristics: open-circuit voltage ($V_{oc}$) = 6 V, short-circuit current ($I_{sc}$) = 1.1 A, voltage at max. power ($V_{mp}$) = 10 V, current at max power ($I_{mp}$) = 1 A, and maximum power ($P_{m}p$) = 10 W.

Figure 7 shows the implemented testbed to characterize the panel solar system. Four halogen lamps of 500 W each were used to emulate the solar irradiance. Moreover, a dynamic load was configured to sweep the load voltage to find the curves (I-V and P-V).

4.2. PV Array Simulator

To standardize the experiments, the photovoltaic array simulator (N8937APV, Keysight Technologies, Santa Rosa, CA, USA) was used to reproduce the output characteristics of a photovoltaic array allowing test maximum power point tracking (MPPT) algorithms and inverter efficiency (Figure 8). The photovoltaic array simulator has characterizations of photovoltaic panels with different standards such as: IEC60904, IEC61727, EN50530, and Sandia National Laboratories Photovoltaic Systems. Moreover, the software Keysight SAS control was used to manipulate the photovoltaic array simulator to evaluate the MPPT algorithms with the EN50530 dynamic and static test. In Section 5, the EN50530 standard test will be explained.

For this project, European Standard EN 50530 for solar array terrestrial model was selected to reproduce in the PV array simulator with the real characteristics from PV real system. This model is estimated by (3)–(5) and it can be found in [110]:

$$I_0=I_{sc}{(1-\frac{I_{mp}}{I_{sc}})}^{\frac{1}{1-\frac{V_{mp}}{V_{o}c}}},$$

(3)

$$C_{aq}=\frac{\frac{V_{mp}}{V_{oc}}-1}{ln(1-\frac{I_{mp}}{I_{sc}})},$$

(4)

$$I=I_{sc}-I_0(e^{\frac{V}{V_{oc}{C}_{aq}}}-1),$$

(5)

where $I_0$ and $C_{aq}$ are parameters used for this model and V and I are the estimated voltage and current of the PV system model. $I_{sc}$, $V_{oc}$, $V_{mp}$, $I_{mp}$ are parameters of the aforementioned characteristics of the PV system.

Figure 9a,b shows the comparison between the solar panel system (two monocrystalline solar panels) and the photovoltaic array simulator (PVsim).

Hence, Figure 10 presents the I-V and P-V curves from PVsim with different irradiances and temperatures.

4.3. DC/DC Converter

For this work, a DC/DC buck converter was used to evaluate the $V_{ref}$ MPPT. This buck converter was designed in [111] using EA optimization to generate a novel design methodology for inductance selection. The novel methodology and the implementable solution showed the feasibility of this approach. Moreover, the proposed solution reached the expected performance for fast voltage response with a low current slope with a low ripple inductor’s voltage and current.

4.4. LabVIEW FPGA

To understand the results and the implementation limitations from $V_{ref}$ MPPT-oriented study, it is important to emphasize the main features from the selected hardware for the embedded MPPT. Figure 11 depicts the main components of the cRIO-9030 hardware.

To exploit the parallel processing of FPGA, four loops were used (Figure 12, Figure 13, Figure 14 and Figure 15): (1) PWM signal generation, (2) data acquisition and MPPT-$V_{ref}$ execution, (3) PI controller for $V_{ref}$, and (4) sending data for data collection through FIFOs (First-In, First-Out).

Figure 12 shows the while loop used for PWM signal generation. In this case, a signal generation function from LabVIEW FPGA features was used for the PWM signal. Then, the signal value was transformed into Boolean value to send into one Digital Output (DO) channel from NI 9401 digital module.

Regarding data acquisition and MPPT-$V_{ref}$ execution, NI 9242 module was used to read the current from PV array or PV simulator and DC/DC buck converter output. The NI 9227 module reads the voltage from PV array or PV simulator and DC/DC converter output. Both modules have 24-bit ADC resolution and 50 kS/s sampling rate. In addition, for each signal, root mean square (RMS) function was applied to send to the MPPT-$V_{ref}$. When the MPPT starts, all variables are initialized to start the estimation of the first $V_{ref}$. The estimation begins when RMS function sends a boolean signal that its process has finished and $V_{ref}$ is estimated according to the MPPT algorithm flowchart (P&O and EA) as seen in Figure 13.

Once the $V_{ref}$ is estimated, the PI controller is responsible for rectifying the PV voltage with the $V_{ref}$. Figure 14 depicts the loop for control of referenced voltage. The duty cycle is estimated by the PI controller and send it to the loop for PWM signal generation.

Finally, a loop is necessary for sending data through FIFOs (LabVIEW FPGA) to the PC host in order to storage the following data: (1) PV voltage, (2) PV current, (3) load voltage, (4) load current, and (5) duty cycle.

5. EN50530 Test

To evaluate the performance of MPPT-$V_{ref}$ algorithms, an EN 50530 test was performed using the PV simulator and Keysight SAS Control^® software (Version 2021, Keysight Technologies, Santa Rosa, CA, USA). Figure 16 shows the interface for dynamic testing, which consists of 16 sub-tests with separate times of ramps and slopes; the total duration of the test is 6 h.

Regarding the static EN 50530 test, Figure 17 visualizes the interface where the current I-V and P-V curves and the present MPP is represented in a red circle. The total evaluation is composed of 24 sub-tests, which are divided by 3 MPP voltages: (1) 12.5 V, (2) 10 V, and (3) 8.4 V. These MPP voltages were selected according to the curves obtained in Figure 6, where irradiance is from 200 to 1000 W/m². The total duration of the static test is 6 h.

5.1. Dynamic Test

Figure 18 and Figure 19 depict the dynamic test for different ranges of irradiance. Each test starts with a waiting time of 300 s. After, a different number of ramps with dwell time of 10 s (up and down) and different slopes are defined as shown in Figure 18 where the irradiance range is from 100 to 500 W/m².

The second group for dynamic test is described by Figure 19, the irradiance range is from 300 to 1000 W/m². They have 10 ramps and dwell time is 10 s with different slopes.

Finally, Figure 20 depicts the last dynamic test, which is defined by one ramp with dwell time of 30 s, and slope of 0.1 W/m² per second.

5.2. Static Test

From the static test,

Table 1. Statistic test parameters.

MPP Voltage (V)	Irradiance (%)
12.5
10.0	5, 10, 20, 25, 30, 50, 75, 100
8.4

shows the MPP voltages selected (12.5, 10.0 and 8.4 V) for every test. Each MPP voltage is evaluated at different irradiances: 5, 10, 20, 25, 30, 50, 75, and 100%; and each sub-test has a duration of 600 s, with a setup time of 300 s.

6. Results

To compare both MPPT-$V_{ref}$ algorithms from EN 50530 standard test,

Table 2. EN 50530 static test report.

MPPT Algorithm	MPP Voltage	Irradiance (%)								European Efficiency	CEC Efficiency
		5	10	20	25	30	50	75	100
P&O	12.5	97.671	76.264	92.949	94.356	94.383	94.813	99.319	99.252	94.402	96.536
EA		98.489	98.095	96.813	99.743	99.774	99.689	99.975	99.868	99.249	99.652
P&O	10.0	91.469	77.385	75.210	81.177	97.992	99.392	98.901	97.325	94.452	96.771
EA		98.855	99.578	99.656	99.760	99.774	99.890	99.936	99.918	99.807	99.878
P&O	8.4	99.227	99.130	99.307	99.344	99.265	99.556	99.367	92.557	99.421	99.042
EA		99.117	99.499	99.812	99.859	99.840	98.948	99.704	99.962	99.340	99.572

and

Table 3. EN50530 dynamic test report.

Irradiance (W/m2)	No. of Ramps	Duration (s)	P&O Efficiency (%)	EA Efficiency (%)
100–500	2	1940	99.905	99.592
	3	1560	99.884	99.520
	4	1447	99.895	99.824
	6	1380	99.892	99.685
	8	1374	99.857	99.627
	10	1300	99.427	99.630
	10	1071	99.129	99.589
	10	900	99.039	99.497
	10	767	98.755	99.282
	10	660	98.325	99.066
300–1000	10	1900	99.571	99.905
	10	1500	99.665	99.884
	10	1200	99.745	99.895
	10	967	99.809	99.892
	10	780	99.762	99.857
	10	640	99.677	99.427
10–100	1	2320	95.129	99.093

present the MPPT efficiency for P&O and EA based on referenced voltage. In addition, Figure 21, Figure 22 and Figure 23 present the density plot for P&O and EA MPPT-$V_{ref}$ which represents the steady-state oscillations when the MPPT is near of the MPP.

6.1. Static Report

The static test evaluates the MPPT performance by measuring two efficiencies: European and CEC. The European efficiency is an averaged operating efficiency over a yearly power distribution corresponding to middle-Europe climate [101]. Meanwhile, CEC efficiency models the climates of higher isolations for US south-west regions, according to [102].

In the case of 12.5 V for MPP, EA-MPPT presents a better efficiency of 5.13% and 3.23% for European and CEC efficiency, respectively. For the MPP voltage of 10 V, EA-MPPT enhances the performance in 5.67% for European and 3.21% for CEC efficiency. Finally, in the specific case of 8.4 V for MPP, both efficiencies are similar (minor variations, <1%).

Density plots for 8.4 $V_{mp}$ are shown in Figure 21 with the objective of showing the steady-state oscillations. From the results, the $V_{ref}$ for each MPPT algorithm presents the following behavior: mean of 8.48 V and standard deviation of 0.1605 V and mean of 8.74 V and standard deviation of 0.1860, for EA and P&O, respectively.

At $V_{mp}$ of 10 V, steady-state oscillations at low irradiances are more remarkable for P&O strategy as seen in Figure 22. Results from static test shows that the mean and standard deviation for $V_{ref}$ estimation of P&O are 9.99 V and 1.28, respectively. Whereas, the EA strategy presents 9.98 V and 0.14 V, respectively.

In the case of 12.5 V for MPP (Figure 23), the average and standard deviation for P&O are 12.70 V and 1.15 V. On the other hand, EA-$V_{ref}$ strategy presents 12.32 V and 0.43 V, respectively. Likewise, the density plot depicts more steady-state oscillation for P&O strategy which is defined by the standard deviation aforementioned.

6.2. Dynamic Report

The dynamic test evaluates the tracking speed for MPP; in this case, $V_{ref}$ is estimated by the MPPT algorithm and it is regulated by the PI controller which determined the correct duty cycle for the DC/DC converter. The results in Table 3 indicate that both MPPT-$V_{ref}$ strategies present good performance and efficiency in dynamic responses. Hence, the MPPT tracking speed is well performed by the PI control loop and the FPGA implementation strategy.

7. Conclusions

In this work, a new direct EA-MPPT strategy based on the EA metaheuristic optimization algorithm is used to estimate the optimal voltage to reach the $V_{mp}$ of the PV system. Then, to reduce any error, a PI controller is integrated to rectify the optimal estimated EA-MPPT voltage, which is the $V_{ref}$ for the PI controller that changes the duty cycle to achieve this voltage.

To compare and evaluate the performance, the counterpart (direct) method such as P&O-$V_{ref}$ MPPT algorithm was implemented and tested because it is the most widely used for commercial products.

Moreover, a real PV system was experimentally characterized to reproduce the I-V and P-V curves into the NP8937APV Keysight^® PV array simulator to evaluate the MPPT efficiency using the EN50530 standard test. This standard test was executed to evaluate the static and dynamic responses of both MPPT direct strategies in real-world weather condition from different regions.

In addition, these strategies were embedded on an FPGA (cRIO-9030) using LabVIEW as a programming language and FPGA module to deploy into the device. The main structure of FPGA implementation consisted of four parallel loops: (1) PWM generation signal, (2) signal conditioning and MPPT-$Vref$ estimation, (3) duty cycle estimation from PI controller, and (4) sending data for data collection through FIFOs.

Overall results show the feasibility of both MPPT-$V_{ref}$ approach for LabVIEW FPGA hardware. Meanwhile, from static test results, EA-MPPT presented a better efficiency of 5.13% and 3.23% for European and CEC efficiency, respectively. Thus, EA-MPPT-$V_{ref}$ reduces the steady-state oscillations when it is near of the MPP. On the other hand, dynamic test results showed that P&O strategy obtained an efficiency from 95.13% to 99.91%, while EA strategy captured from 99.01% to 99.91% of the total power of the PV system.