Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2024. Universidad Tecnológica de Pereira. ISSN 0122-1701 y ISSN-e: 2344-7214
78
Abstract— This article presents an experimental analysis
of the conversion efficiency and total harmonic distortion
(THD) of two DC/AC converter prototypes designed for off-
grid photovoltaic generation systems (OPGS). The objective
is to determine the influence of two controllable factors; the
DC input voltage and the percentage of nominal load at the
output, on the converters’ performance. The prototypes,
based on unipolar SPWM modulation, were implemented
using simulation software, and tested under a factorial
experimental design. The study applied statistical methods,
including ANOVA, to analyze the effect of each factor and
their interaction on the two response variables: efficiency
and THD. Results showed that for the first prototype,
efficiency is independent of DC input voltage but dependent
on load, while THD is influenced by both factors. In the
second prototype, both efficiency and THD are affected by
variations in both factors, with THD showing instability due
to LC network resonance. The comparison reveals that
locating the LC filter after the transformer slightly
improves THD but reduces efficiency due to increased
harmonic losses. These findings are relevant for optimizing
inverter design in isolated PV systems.
Index Terms —Efficiency, Experimental Design, Inverter,
Photovoltaic System, Total Harmonic Distortion.
Resumen— Este artículo presenta un análisis experimental de la
eficiencia de conversión y la distorsión armónica total (THD) de
dos prototipos de convertidores DC/AC diseñados para sistemas
de generación fotovoltaica aislados de la red (OPGS). El objetivo
es determinar la influencia de dos factores controlables, el voltaje
DC de entrada y el porcentaje de carga nominal conectada a la
salida sobre el desempeño de los convertidores. Los prototipos,
basados en modulación SPWM unipolar, fueron implementados
Este manuscrito fue enviado el 30 de june, 2024, aceptado el 15 de Junio,
2025 y publicado 30 de junio 2025.
Elkin Wbeimar Suarez está con la empresa Future Solutions Development
S.A.S. Departamento de OTTIS HARDWARE. Sogamoso Colombia,
Colombia (e-mail: elkinsuarezews@gmail.com).
Johan Andrés Fernández está con la empresa Future Solutions Development
S.A.S. Departamento de OTTIS HARDWARE. Sogamoso Colombia,
Colombia (e-mail: andresjfz10@gmail.com).
Nairo Julián Rodríguez está con el SENA. Grupo de investigación
SENNOVA. Sogamoso Colombia, Colombia (e-mail:
njrodriguez43@misena.edu.co).
mediante software de simulación y evaluados bajo un diseño
experimental factorial. Se aplicaron métodos estadísticos,
incluyendo ANOVA, para analizar el efecto de cada factor y su
interacción sobre las dos variables de respuesta: eficiencia y THD.
Los resultados mostraron que, para el primer prototipo, la
eficiencia es independiente del voltaje DC de entrada pero
dependiente de la carga, mientras que la THD está influenciada
por ambos factores. En el segundo prototipo, tanto la eficiencia
como la THD se ven afectadas por las variaciones de ambos
factores, y la THD presenta inestabilidad debido a la resonancia
de la red LC. La comparación revela que ubicar el filtro LC
después del transformador mejora ligeramente la THD, pero
reduce la eficiencia debido a mayores pérdidas por armónicos.
Estos hallazgos son relevantes para optimizar el diseño de
inversores en sistemas fotovoltaicos aislados.
Palabras clave — Diseño experimental, Eficiencia, Inversor,
Sistema fotovoltaico, THD (Distorsión armónica total).
D
I.INTRODUCTION
C/AC converters, also called inverters, are subsystems
commonly used to convert direct current (DC) into
alternating current (AC), with applications in motor control,
energy conversion, and renewable energy systems [1].
Photovoltaic (PV) generation systems, whether grid-connected
or off-grid, rely on these converters to adapt solar energy to the
requirements of electrical loads and to enable efficient energy
management [2]. Due to increasing global energy demand and
the environmental impact of traditional power generation
methods, photovoltaic systems have become more relevant.
Since inverters are central to these systems, it is essential to
study their conversion efficiency and the quality of the output
power they deliver [3].
Recent studies have analyzed the performance of different
inverter topologies, considering aspects such as switching
techniques, filter configurations, and control strategies. For
instance, transformer-less designs and LC filter placement have
shown significant effects on total harmonic distortion (THD)
and energy losses [3][4]. Some authors have explored the
influence of DC input voltage and load variation on inverter
performance, highlighting the role of design parameters on
harmonic behavior and efficiency [5]. In particular, Rampinelli
et al. [7] proposed mathematical models that relate inverter
efficiency to input voltage and output power, demonstrating
Analysis of the conversion efficiency and THD of
DC/AC converters used in off-grid Photovoltaic
generation system
Análisis de la eficiencia de conversión y THD de convertidores DC/AC empleados en un
sistema de generación fotovoltaica aislado de la red
J. Fernández Zorro ; N. J. Rodríguez Ballesteros ; E. W. Suarez Chaparro
DOI: https://doi.org/10.22517/23447214.24807
Scientific and technological research paper
Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira
79
good accuracy for grid-connected PV systems. Similarly,
Farfán and Massen [15] evaluated two mathematical
approaches to model how variations in input voltage affect
conversion efficiency, supporting the importance of this
variable in experimental analysis. Likewise, Gallego-Gómez et
al. [8] analyzed conduction losses in SPWM-modulated
inverters, providing a mathematical formulation that links
internal power losses to efficiency degradation. Similarly,
Lázaro Campo [12] analyzed the performance of photovoltaic
installations in relation to inverter operation and final energy
yield, highlighting the importance of matching design
parameters to specific environmental conditions. Moreover,
comprehensive reviews have compared the behavior of single-
phase inverters in photovoltaic applications, providing insights
for optimizing topology selection based on THD limits and
energy quality standards [1][2]. Additionally, Beltrán Telles et
al. [9] carried out an experimental evaluation of H-bridge
inverters using SPWM, demonstrating that harmonic distortion
and waveform quality are significantly affected by switching
strategies and load variations—an aspect that closely aligns
with the objectives of this study.
Beyond mathematical modeling, experimental analysis remains
a fundamental tool for understanding system behavior under
controlled conditions. An experiment involves varying input
parameters to observe their influence on selected response
variables. However, many experimental efforts rely on trial-
and-error methods, which often lack the structure required for
drawing reliable and reproducible conclusions. A more rigorous
and effective approach involves the use of Experimental Design
[6][11], which offers a statistically supported framework for
identifying and quantifying the effects of key factors on system
performance.
This research applies an Experimental Design methodology to
analyze the conversion efficiency and THD of two unipolar
SPWM DC/AC converter prototypes implemented via
simulation software. Similar approaches have been used in
studies of converter performance for UPS applications, where
simulation environments enable detailed control and
comparison of circuit configurations [14]. The study considers
the DC input voltage and the percentage of nominal load at the
output as influencing factors. Based on these, null and
alternative hypotheses are formulated for each response
variable and evaluated through ANOVA statistical analysis..
This paper is organized as follows: Section II presents the
design and definition of factors; Section III details the
simulation methodology; Section IV discusses the results; and
finally, Section V provides the main conclusions.
II. CONSTRUCTION OF THE EXPERIMENTAL DESIGN
The Experimental Design is structured under the guidelines
shown in Fig. 1.
Fig. 1. General guidelines for designing an experiment [7].
A. Identify and state the problem
The problem consists in determining the influence of the DC
voltage applied to the inverter input and the percentage of
nominal load connected to its output, on the conversion
efficiency and the total harmonic distortion. For this, it is
essential to determine the set of tests to be applied, the way to
apply them, and the way to collect and analyze the data. Fig. 2,
presents the DC/AC converter under investigation, which
belongs to an OPGS and uses unipolar SPWM modulation.
Fig. 2. Block diagram of an OPGS. Source: own
B. Choose factors to control, their levels and ranges
Different types of variables or factors intervene in every
process, such as those shown in Fig. 3. The response variables
generally coincide with the output variables of the system and
are used to measure its performance and evaluate the effect of
the experiment. The controllable factors are the input variables
of the process, over which there is control, for this there must
be a mechanism that allows the experimenter to change or fix
their levels. The uncontrollable factors, also called noise,
correspond to those input variables over which there is no
control, such as physical, environmental or inherent phenomena
to the process and that appear randomly, affecting its behavior.
[8].
Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira.
80
Fig. 3. Variables involved in a process. Based on [8].
Table I shows the most relevant considerations when sizing
an OPGS. Taking into account that the DC / AC converter
(inverter) is the study center of this research, aspects such as the
voltage of the battery bank, the nominal power, the efficiency,
the THD and the type of load to be fed, are of great interest.
In accordance with [9], one of the most important parameters
and that best represents the operation of a PV inverter is its
efficiency curve. Efficiency (
), is the ratio between the
energy delivered to a load and the energy required by the
inverter. As the inverter is a central block in an OPGS, the
efficiency curve provides decisive information for its sizing.
THD is an important variable in electricity generation
systems, since it indicates the quality of the energy that is being
delivered to the load. The harmonics produced by PV inverters
can generate problems within an OPGS, reducing the useful life
of electronic devices, therefore, the study of harmonics from
THD measurements is crucial [10].
Inverter’s efficiency, lies according to operation point on it
works. Depending of supplied rated power (
) and (
),
we obtains the efficiency that is calculated through (1), where
is the power factor,
is the effective voltage of the
inverter,
is the effective current an
, is the average
current supplied for the DC source [9].
=
=
(1)
On an inverter, the THD of the voltage wave (
)
and of
the current wave (
) can be analyzed, these parameters
generally depend: of the type of inverter, of the filters used, of
the linearity of the load and of the rated power supplied, and it
is calculate using (2), where
, is the effective value of the
fundamental harmonic.
=
1
(2)
Table II, shows a resume of the variables that interact on a
DC/AC converter. Taking into account the information
provided on the Fig. 3, it can be considered as controllable
factors [11]: The DC voltage applied in the input, the load
connected on the output and the type of load. As response
variables, can be chosen: converter´s temperature, the
conversion efficiency and the THD on the voltage wave of the
output. Exist other no controllable variables as the
electromagnetic noise, generated both by the converter and by
external agents, and the climatic conditions.
For this research, the controllable factors chosen are: the DC
voltage applied on the input of the inverter and load´s
percentage connected on the output, considering for the analysis
purely resistive loads. For the first factor, 6 levels are chosen
and for the second 10 levels[3] [12]. On the other hand, no
controllable factors are neglected, and the efficiency and THD
of the voltage wave are considered as response variables.
C. Choose Experimental Design Type
There are many types of experimental designs to study
different problems or situations, however, there are five aspects
that influence when choosing one or the other, these are: the
objective of the experiment, the number of factors to study, the
number of levels that The effects to be investigated and the cost,
time and desired precision are tested on each factor [8].
For this research a factorial type experimental design are
choose, whose main characteristics are presented on Table III
Table IV shows the levels assigned to the controllable factors.
In the case of DC voltage, 6 voltage levels are proposed that are
within the expected range for the most common battery banks.
For the output load, 10 levels expressed as a percentage of the
nominal power of the inverter under test were established.
Taking in account that are raised a experimental design with
two controllable factors, we propose the next nulls hypotheses:
0
: The efficiency conversion, as well as the THD are
independents of DC voltage variation at input of the inverter.
0
: The efficiency conversion, as well as the THD are
TABLE I
CONSIDERATIONS WHEN SIZING AN OPGS
Variable
Characteristic
PV array
Morphology – Distribution – Angle of
incidence– Distance to battery bank
Battery Bank
Technology – Backup time – Voltage –
Connection
Commercial power grid
Availability – Voltage – Frecuency
Charge regulator
Availability – PWM – MPPT
Inverter
Type – Rated power – Temperature –
Efficiency – THD
Load
Type (R, C, L) – Linear - Nonlinear -
Consumption
Types of solar regulators: PWM = Pulse Width Modulation; MPPT =
Maximum Power Point Tracker.
Most common types of loads: R = Resistive; C = Capacitive; L = Inductive;
or combinations R-L-C.
Types of photovoltaic systems: GCPS = Grid Connected Photovoltaic
System; OPS = Off – Grid Photovoltaic System.
TABLE II
VARIABLES THAT INTERACT IN A DC/AC CONVERTER
Variable
Characteristic
Input DC Voltage (V)
Load connected to the output
(% of nominal)
Type of load R-L-C
Controllable Factors
Converter Temperature (°C)
Conversion Efficiency(%)
THD on output voltage (%)
Response Variables
Electromagnetic noise
Climatic conditions
Non Controllable Variables
Variables: DC = Direct Current; AC = Alternated Current; V = Voltage,
η = Conversion Efficiency; THD = Total Harmonic Distortion ; °C = Celsius
degrees, Load Types; R = Resistive; L = Inductive; C = Capacitive
Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira
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independent of nominal load percentage connected at the
inverter output.
0
: The efficiency conversion, as well as the THD are
independent of DC voltage variation at the inverter input and
the nominal load percentage connected at it’s output.
The same way, the following alternative hypotheses are
proposed:
: The efficiency conversion, as well as the THD are
dependents of DC voltage variation at inverter input.
: The efficiency conversion, as well as the THD are
dependent of nominal load percentage connected at the
inverter output
: La eficiencia de conversión, así como la THD son
dependientes de la variación del voltaje DC a la entrada del
inversor y del porcentaje de carga nominal conectada a su
salida.
In the next section the methodology employed for apply the
proposed experimental design are presented.
III. METHODOLOGY FOR EXPERIMENTAL DESIGN EXECUTION
For this research are proposed two DC/AC converters that’s use
unipolar SPWM modulation, and that are designed for a
nominal power of 2KVA. There block diagrams are shown in
the Fig. 4 and Fig.5, respectively.
Fig. 4. Block diagram of first prototype DC/AC converter. Source: own
Fig. 5. Block diagram of second prototype DC/AC converter. Source:
own
these prototypes were implemented using Matlab tool
simulink simulation software[13], taking in account real
parameters both in the Full bridge and in transformer , just with
difference of LC network positioning [14][15]. with this
prototypes ,are searching too , analyse the effect of LC network
positioning, about their performance and energy quality.
For apply the experimental design ,we follow the scheme
shown below, at Fig. 6.
Fig. 6. Employed method for experimental design validation. Source:own
First, the 120 random runs were obtained using the Minitab
software, taking into account that there are two controllable
factors each with 6 and 10 levels and two repetitions during the
experiment. Subsequently, a Matlab script was developed that
works in conjunction with Simulink, modifying the values of
each input factor according to the runs obtained in the previous
step and collecting the data referring to efficiency and THD for
each combination. Using the script, you get an array of data that
is then exported and organized in a spreadsheet. Finally, an
ANOVA analysis of variance is carried out and the main
TABLE III
CHARACTERISTICS OF PROPOSED EXPERIMENTAL DESIGN
Item
Value/Designation
Controllable Factors
2
Levels
6 y 10 respectively
Response Variable
2
Number of base runs
60
Specimens
Replicas
2
2
Randomness
Si
Number of total runs
240
Data to Collect
480
1. Controlable Factor: What can be varied during experiment
1. Level: Value that takes a controllable factor
2. Response Variable: what is case of study
3. Run: Combination of the factors
4. Specimens: Experimental unit
TABLE V
AVERAGE VALUES OF EFFICIENCY OF PROTOTYPE I
Factor A
Controllable
Factors
22
23.6
25.2
26.8
28.4
30
10
96.486
96.484
96.481
96.479
96.522
96.514
20
96.728
96.692
96.691
96.69
96.688
96.719
30
96.139
96.152
96.111
96.11
96.143
96.136
40
95.371
95.346
95.382
95.38
95.376
95.343
50
94.537
94.516
94.55
94.549
94.514
94.514
60
93.681
93.664
93.697
93.696
93.692
93.662
70
92.822
92.829
92.837
92.839
92.837
92.806
80
91.963
91.968
91.978
91.949
91.978
91.977
90
91.111
91.117
91.127
91.128
91.128
91.126
Factor
B
100
90.271
90.263
90.285
90.29
90.263
90.289
Media: 93.97
Standard Deviation: 2.2
Variance: 4.84
Controllable Factors: A = DC voltage at the input of the DC / AC Converter in volts
(V); B = Percentage of nominal load connected to the output of the DC / AC
Converter (%). Response variable: Conversion efficiency (%).
Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira.
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effects and interaction graphs for each response variable and the
normal probability graph are obtained. The results obtained are
examined in detail in the following Section.
IV. RESULTS
Table V, presents the average values of efficiency conversion
of the first prototype, related to each of the runs or combinations
that were applied during the experiment.
It can be seen that the average efficiency of this prototype is
93.97%, on the other hand, the standard deviation shows that
the data is relatively homogeneous, since there is a separation
from the mean. The Fig. 7, show the main effect of each of
the factors about conversion efficiency of prototype I.
Fig. 7. Main effects graph for the efficiency of the prototype I. Source: own
At first glance, the efficiency compartment is not affected by
variations in DC voltage, while the load percentage, if it has an
effect on it, and is as mentioned in Section II, since, depending
on the point inverter work, there is a different value for
efficiency. Efficiency presents this behavior, because, as the
load connected to the inverter increases, the current flowing
through the switches, conductors and transformer also
increases, the rising current increases the switching losses, due
to the joule effect and due to the harmonics present, and
according to the slope of the graph, these losses are not
negligible. The Fig. 8, shown the effect produce for interaction
of the both factors about efficiency.
Fig. 8. Efficiency curves of prototype I. Source: own
In this graph , can be noticed clearly, that’s DC voltage,
doesn’t have a significant effect over efficiency curve of the
DC/AC converter, this can be explained from harmonics point
of view, generated by used modulation required to obtain the
sinusoidal equivalent waveform at the output. The harmonics
generated in this type of systems, depends of many factors,
among them, DC input voltage, tuning of LC network [14] [15],
Switching frequency of full bridge, index amplitude modulation
among others. The harmonics in general produce power losses
in all elements that transport them, but for a OPGS, The power
losses increase in the isolation transformer [16],For this reason,
placing the LC filter behind the primary one prevents harmonics
from being conducted by the transformer, for this reason, when
the load remains constant and the DC voltage varies, the
amplitude of the harmonics may change; however, they are not
present at the transformer primary. As a result, the associated
power losses are not reflected in the efficiency.
On the other hand, the interaction graph drives that´s for a
nominal load of 100%, obtains a minimum efficiency of 90.5%
approximately, whereas a load of 20%, the efficiency reaches it
maximum value of 96.7% . the optimum operation point for this
system its located around 50% of load, at this point we can
extract the maximum power at a related good efficiency, this
information is useful for implement OPGS, and analyse the
different circumstances of operation of this important block.
Applying a statistical analysis ANOVA, can be determined
with certainty, if the null hypotheses, exposed on the Section II
are true and they must be accepted or, conversely, rejected.
Table VI, shows the ANOVA for the efficiency of the prototype
I.
Observing the values P, of each one of the factors of individual
way of each of the factors individually and their interaction, It
can be stated that the conversion efficiency of prototype I is
dependent on the percentage of nominal load connected to its
output and independent of the variation of the DC voltage
applied to the input, and also independent of their interaction.
Fig. 9, presents the graphic of normal probability of obtained
data for the efficiency. Considering a significance level of 0.05,
it can be said that most of the data follow the adjusted
distribution line and their behavior is normal.
TABLE VI
ANOVA FOR EFFICIENCY OF PROTOTYPE I
Source
DF
SS
MS
Valor F
Valor P
Inverter Load (%)
9
573.21
63.69
8246.5
0.000
DC Voltage (V)
5
0.002
0.0004
0.05
0.998
Inverter Load (%)
* DC Voltage (V)
45
0.145
0.0032
0.42
0.999
Error
60
0.463
0.0077
Total
119
573.82
Statistical Terms: DF = Degrees of Freedom; SS = Sum of Squares; MS = Mean
Square.
Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira
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Fig. 9. Normal probability plot for the efficiency of the prototype I. Source:
Own
Table VII, shows the average values of the THD of the
voltage wave of prototype I. According to international
standards such as IEEE519 or EN50160, the levels of total
harmonic distortion must be less than 8%, for systems whose
supply voltage is less than 1000V, in this way it is ensured that
harmonics do not cause considerable damage. sensitive
electronic devices. According to Table VII, the average THD
for prototype I is 0.0461%, which is much less than 1%, as
expected, when considering linear and purely resistive loads,
however, this information serves to check the waveform output
of prototype I.
Fig. 10, shows the response of the THD in front of
individual variations of the controllable factors. According to
this graphic, the THD depends both the DC voltage and the
percentage of connected load. It is observed that for a load level
between 10% and 90%, the THD varies proportionally with the
load, this behavior is due to the resonant effect of the LC
network, which causes an increase or decrease in harmonics,
close to the resonant frequency.
Fig. 10. Main effects plot for the THD of prototype I. Source: Own
Fig. 11 shows the interaction graph for the THD of the
prototype I. With this graph, it can be clearly seen that the DC
voltage has an influence on the THD response, since a
different curve is obtained for each value. It is observed that the
higher the DC voltage, the better the THD levels are obtained,
this is due to the fact that the latter is inversely proportional to
the amplitude of the fundamental harmonic, which is
proportional to the input voltage [1].
Fig. 11. THD Curves of prototype I. Source: Own
Table VIII, shows the ANOVA for THD of prototype I.
Observing the P values, of each of the factors individually and
their interaction, we can say, THD of prototype I, is dependent
of nominal load percentage connected to output and dependent
of variation of DC voltage applied to the input, but it also
depends of their interaction.
TABLE VIII
THD ANOVA FOR PROTOTYPE I
Source
DF
SS
MS
Value F
Valor P
Inverter Load (%)
9
0.027
0.003
77.36
0.000
DC Voltage (V)
5
0.05
0.010
251.14
0.000
Inverter Load (%)
* DC Voltage (V)
45
0.008
0.0002
4.68
0.000
Error
60
0.002
0.0000
Total
119
0.088
Statistical Terms: DF = Degrees of freedom; SS = Sum of squares; MS =
Middle Square.
TABLE VII
AVERAGE THD VALUES IN PROTOTYPE I
Factor A
Controllable
Factors
22
23.6
25.2
26.8
28.4
30
10
0.033
0.0012
0.01
0.001
0.004
0.001
20
0.058
0.005
0.051
0.003
0.002
0.002
30
0.059
0.064
0.055
0.028
0.016
0.003
40
0.062
0.063
0.064
0.039
0.023
0.004
50
0.069
0.06
0.069
0.045
0.021
0.005
60
0.077
0.057
0.074
0.05
0.033
0.006
70
0.078
0.063
0.079
0.056
0.034
0.007
80
0.074
0.067
0.076
0.053
0.037
0.018
90
0.078
0.065
0.075
0.064
0.042
0.016
Factor
B
100
0.077
0.058
0.068
0.064
0.036
0.029
Media: 0.0461
Desviación Estándar: 0.027
Varianza: 0.00072
Controllable Factors: A = DC voltage at the input of the DC / AC Converter in
volts (V); B = Percentage of nominal load connected to the output
of the DC / AC Converter (%).
Response variable: THD = Total Harmonic Distortion (%).
Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira.
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The Fig. 12, shows the normal probability graph of the THD
values obtained during the experiment. According to the chosen
level of significance, the experimental data behave according to
the normal distribution line, however, there is a variability in
the extremes that is common in this type of graph.
Fig. 12. Normal probability graph for THD of prototype I. Source: own
Next, the hypotheses raised in Section II are validated for this
particular prototype.
The hypotheses
0
, considers that’s the conversion
efficiency and the THD, are independents of the variation of
DC voltage, although, the results shown that’s efficiency are
independent of DC input voltage , but THD are dependent,
therefore must be rejected both hypotheses H0
1
and HA
1
The hypotheses
0
, establish that’s conversion efficiency
and THD, are independents of nominal load percentage
connected to the output inverter, however, the results shown
both efficiency and THD , are depend of load percentage, by
the arguments mentioned before the null hypotheses
0
are
rejected but the alternate hypotheses are confirm
The hypotheses
0
, assert efficiency conversion and THD,
are independents of interaction between DC voltage and load
percentage, however, the results allow assert efficiency is
independent of there interaction, but THD is dependent. En this
case, should be rejected both hypotheses, null
0
and alternate
.
Following, the same analysis is performed for conversion
efficiency and THD of prototype II
The Table IX, shows the average values of conversion
efficiency of prototype II, related with each combinations
applied during experiment.
According to the results, the prototype II has an average
efficiency of 93.73%, approximately 0.24% lower than that of
prototype I. This is explained by the additional losses caused by
high-frequency harmonics when the LC network is placed on
the secondary side of the transformer. This observation is
consistent with the findings of Gerardo and Miguel [10], who
reported that post-transformer LC filters improve harmonic
suppression but also introduce additional switching and
conduction losses, slightly reducing overall efficiency. It is also
observed that the data obtained are homogeneous, as in
prototype I, according to the standard deviation..
The Fig. 13, shows the individual effect of every factor over
conversion efficiency of prototype II.
Fig. 13. Main effects plot for the efficiency of the prototype II. Source: Own
According to this graphic, both the DC voltage and the load
percentage have an influence on the performance of the
converter. In the case of efficiency, the same thing happens as
in prototype I, since for each load value, there is a different
efficiency. According to Fig. 13, the lowest efficiency is
90.13% and occurs when 100% of the load is connected, on the
other hand, the maximum efficiency is 96.48% and like the
prototype I, occurs for a 20% load. It is also observed that the
DC voltage is inversely proportional to the efficiency, this is
due to the fact that when the DC voltage increases, the
mplitudes of the harmonics also increase, generating greater
losses in the transformer.
Fig. 14, shows the effect that have the interaction of the two
factors on the efficiency. According to this graphic, the effect
of the interaction is remarkable for load levels lower than 50%
, Despite of that, does not exist a big difference between one
curve and the other, the largest difference is 0.5% and occurs
for a 10% load, on the other hand, the maximum efficiency
occurs for a DC voltage of 22V and a load level of 20%, the
TABLE IX
EFFICIENCY AVERAGE VALUES OF PROTOTYPE II
Factor A
Controllable
Factors
22
23.6
25.2
26.8
28.4
30
10
96.081
95.971
95.861
95.752
95.644
95.536
20
96.486
96.43
96.374
96.317
96.262
96.207
30
95.971
95.933
95.895
95.858
95.821
95.784
40
95.231
95.207
95.179
95.151
95.122
95.095
50
94.422
94.399
94.374
94.356
94.329
94.311
60
93.58
93.56
93.535
93.523
93.504
93.487
70
92.727
92.713
92.693
92.665
92.666
92.65
80
91.872
91.86
91.846
91.814
91.816
91.806
90
91.025
91.01
91.002
90.991
90.979
90.968
Factor
B
100
90.186
90.179
90.169
90.159
90.147
90.13
Average: 93.73
Standard Deviation: 2.092
Variance: 4.38
Controllable Factors: A = DC voltage at input DC/AC converter, volts (V);
B = Nominal load Percentage connected to DC/AC Converter (%).
Response Variable: Efficiency conversion (%).
Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira
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worst efficiency occurs for a DC voltage of 30 V and a load
level of 100% and the optimum operating point appears around
50% of the load.
Fig. 14 Prototype II efficiency curves. Source: Own
Table X shows the ANOVA for the prototype II
conversion efficiency
Observing the P values of each of the factors individually and
their interaction, it can be ensured that the efficiency of the
prototype II is dependent on the percentage of load and the
variation of the DC voltage applied to the input, but it is
independent of their interaction, as shown in Fig. 14.
Fig. 15, shows the graphic of normal probability for the
efficiency of prototype II. Likewise, for a significance level of
0.05, it can be stated that the data follow the normal distribution
line and that its behavior is as expected.
Fig. 15. Normal probability plot for the efficiency of the prototype II. Source:
Own.
Tabla XI, presents the data of the THD produced by the
prototype II. This second prototype has an average THD of
0.019% and according to the standard deviation, the data is less
dispersed than in prototype I. Note that the amount of
harmonics generated by prototype II is relatively less than that
of prototype I, this is due to the location of the LC filter.
Fig. 16, presents the main effects plot for the prototype II
THD. The behavior of the THD against load variations is
different than in the prototype I, first, because its levels are
below 0.035% and second, because between 30% and 90%, it
is unstable. This unstable behavior is due to the resonance effect
of the LC filter, which depends on the connected load [14] [15].
Note that there is an inversely proportional relationship
between DC voltage and THD, for the same reason as in
prototype I.
Fig. 16. Main Effects Plot for Prototype II THD. Source: Own.
Fig. 17, shows the interaction graph between the factors,
where it can be clearly seen that both have an influence on the
THD response.
TABLE X
ANOVA FOR THE EFFICIENCY OF THE PROTOTYPE II
Source
DF
SS
MS
Value F
Value P
Inverter Load (%)
9
520
57.78
9146.89
0.000
DC Voltage (V)
5
0.387
0.0773
12.24
0.000
Inverter Load (%)
* DC Voltage (V)
45
0.329
0.0073
1.16
0.296
Error
60
0.379
0.0063
Total
119
521.16
Statistical Terms: DF = Degrees of Freedom; SS = Sum of Squares; MS = Mean
Square.
TABLA XII
ANOVA PARA LA EFICIENCIA DEL PROTOTIPO II
Fuente
DF
SS
MS
Valor F
Valor P
Inverter Load (%)
9
0.007
0.0008
1830.56
0.000
DC Voltage (V)
5
0.025
0.005
11346.6
0.000
Inverter Load (%)
* DC Voltage (V)
45
0.013
0.0003
658.1
0.000
Error
60
0.0003
0.0063
Total
119
0.045
Statistical Terms: DF= Degrees of Freedom; SS = Sum of Squares; MS = Mean
Square.
Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira.
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Fig. 17. THD curves of the prototype II. Source: Own
Similarly, it is observed that the THD presents an unstable
behavior, for load values between 30% and 90% of the nominal,
product of the resonant frequency of the LC filter. Note that for
a DC voltage of 30 V, lower THD values are obtained, while
for a voltage of 22 V, higher values are obtained. As future
work, it is proposed to find a solution to the instability of these
systems.
Table XII, shows the ANOVA for the THD of prototype II.
Observing the P values of each of the factors and their
interaction, it can be ensured that the THD of the prototype II is
dependent on both the load percentage and the DC voltage, and
also depends on their interaction, such as was shown in Fig. 17.
Fig. 18, shows the behavior of the collected data against the
normal distribution line. This graph shows how the data tries to
follow normality, but there is an oscillation, due to the
instability of the response.
Fig. 18. Normal probability plot for the prototype II THD. Source: Own
Next, the hypotheses raised in Section II are validated for this
particular prototype.
The hypothesis
0
, It considers that the conversion
efficiency and the THD are independent of the variation of the
DC voltage, however, the results show that both the efficiency
and the THD are dependent on the DC voltage. Therefore, the
null hypothesis
0
is rejected and the alternate
is
accepted.
The hypothesis
0
, establishes that conversion efficiency ,
such as the THD, are independent of load percentage,
nevertheless, the results show that both efficiency and THD, are
dependent of load percentage, for that reason, the null
hypothesis
0
is rejected and the alternate hypothesis
is
accepted.
The hypothesis
0
, affirms that conversion efficiency and
the THD,are independent of interaction between DC voltage
and load percentage, however, the results allow to affirm, that
efficiency is independent of their interaction, but the THD is
dependent. In this sense, both the null hypothesis
0
, and the
alternate hypothesis
are rejected.
The results obtained in this study align with and expand upon
recent findings in the literature related to inverter performance
in photovoltaic applications. For instance, the observation that
the THD is significantly affected by both DC input voltage and
output load is consistent with the analysis reported by
Bouzguenda and Selmi [4], who emphasized the sensitivity of
harmonic content to inverter design parameters and load
conditions. Similarly, the higher efficiency observed when the
LC filter is placed at the transformer’s primary supports the
conclusions of Shrestha et al. [3], who showed that minimizing
transformer-conducted harmonics is key to reducing losses in
transformer-based topologies.
Compared to the work of Albakri et al. [1], who provide a
comprehensive overview of inverter designs, this study adds
experimental insight by using a factorial design to quantify how
controllable factors affect efficiency and harmonic distortion.
Additionally, the THD levels achieved in both prototypes
(under 1%) are in line with international standards such as IEEE
519 and EN 50160, validating the models under linear and
resistive load assumptions —as also noted by Chaurasia and
Singh [5] in their work on multilevel inverters.
Moreover, the instability observed in the THD under certain
load conditions in prototype II may be associated with the
resonant behavior of LC filters, as discussed in previous studies
[2]. In particular, Horikoshi [13] examined how harmonic
components originate and propagate in grid-connected
photovoltaic inverters, emphasizing that both the selection and
positioning of filter elements significantly influence waveform
quality. This underscores the practical importance of not only
choosing appropriate filter components but also strategically
placing them within the circuit. The experimental methodology
applied in this study, grounded in statistical rigor through
ANOVA and controlled manipulation of input variables, offers
a structured and replicable approach that is rarely found in
similar simulation-based analyses, thereby enhancing the
study’s value in terms of reliability and applicability..
V. CONCLUSIONS
It was found that prototype I, the conversion efficiency is
dependent on the load variation and independent of the
variation of the DC voltage and its interaction, as an effect of
placing the LC filter in the primary of the transformer. It was
also observed that the THD is inversely proportional to the DC
voltage and directly proportional to the load percentage.
Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira
79
It was observed that in the prototype II, the conversion
efficiency is affected by the variations of the DC voltage and
the percentage of connected load, but it is independent of the
interaction of these two factors. On the other hand, the THD,
despite being dependent on the DC voltage and the connected
load, presents an unstable behavior for loads between 30% and
90% of the nominal power, due to the resonant effect of the LC
network.
It was found that by placing the LC filter on the secondary of
the transformer, the average efficiency of the converter is
reduced because the high frequency harmonics are not
attenuated and cause additional losses in the transformer, while
the THD levels are slightly reduced.
It was observed that the THD levels obtained with the
experiment, are much less than 1%, since during the
experiment, it just consider linear loads and purely resistive,
however, the analysis carried out provides an idea of how they
are going to behave prototypes in front of non-linear loads and
how they will affect the variation of the DC voltage and in the
percentage of the connected load.
The resonant effect of LC network, generates instability on
the response of the THD when it locates on the secondary of
transformer, This highlights the need to minimize this effect in
order to prevent high-power nonlinear loads from significantly
degrading inverter performance and waveform quality.
It was found that by placing the LC filter on the secondary of
the transformer, the average efficiency of the converter is
reduced because the high frequency harmonics are not
attenuated and cause additional losses in the transformer, while
the THD levels are slightly reduced. This behavior is consistent
with the findings of Gerardo and Miguel [16], who
demonstrated that filter location significantly impacts both the
harmonic suppression and energy losses in transformer-based
inverter configurations
VI. FUTURE WORK AND CONTRIBUTIONS
The findings of this study provide a solid foundation for future
developments in the design and optimization of DC/AC
converters for off-grid photovoltaic systems. First, the
experimental methodology used —based on factorial design
and statistical validation— can be replicated to evaluate other
converter topologies, modulation strategies (such as bipolar
SPWM, space vector PWM), or filtering techniques.
Additionally, the results highlight the importance of LC filter
positioning in harmonic mitigation and system efficiency,
offering practical guidance for designers seeking to optimize
inverter layouts.
In future work, the prototypes could be tested under nonlinear
and dynamic loads to simulate more realistic operating
conditions. Also, implementing physical prototypes in
laboratory settings will allow validation of the simulation
results and the quantification of real-world losses, including
thermal behavior and electromagnetic interference. Finally, this
study opens the door to developing intelligent control systems
that automatically adjust operating parameters (e.g., switching
frequency, modulation index) based on load conditions,
improving energy quality and system reliability in real-time.
By integrating these advances, the study contributes to the
continuous improvement of photovoltaic systems, enabling
more robust, efficient, and reliable off-grid energy solutions,
particularly relevant for rural or remote electrification projects.
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Scientia et Technica Año XXVIII, Vol. 30, No. 02, abril-junio de 2025. Universidad Tecnológica de Pereira.
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Johan Fernández Zorro. Sogamoso
native, Colombia. Received a degree in
Electronic Engineering from Universidad
Pedagógica y Tecnológica de Colombia,
located in Sogamoso, Colombia 2020. He
is teacher from Electronic Engineering
School from Universidad Pedagógica y
Tecnológica de Colombia. He works in
Future Solutions Development S.A.S
Company as research engineer.
https://orcid.org/0000-0003-2905-5438
Nairo Julian Rodriguez Ballesteros is
an junior researcher at the Sena centro
industrial de mantenimiento y
manufactura. He works as leader in
research group, innovation and applied
knowledge of boyaca (GICAB- SENA)
in reliability engineering. He received his
B.Sc. in electromechanical engineering
from Universidad pedagógica y
tecnológica de Colombia in 2009 and holds a M.Sc. in
engineering- mechanical from the Universidad Nacional de
Colombia, (2015). https://orcid.org/0000-0001-8471-1579
Elkin Wbeimar Suarez Chaparro
Sogamoso native, Colombia. Received a
degree in Electronic Engineering from
Universidad Pedagógica y Tecnológica de
Colombia, located in Sogamoso,
Colombia Colombia 2017. he is and
hardware developer , and amateur
embedded programmer , works in Power
electronics, oriented to photovoltaic
energy appliances, actually he works like senior research at
Future Solutions Development S.A.S company.
https://orcid.org/0000-0002-2721-5605