A Novel Harmonic Detection Method for Microgrids Based on Variational Mode Decomposition and Improved Harris Hawks Optimization Algorithm

Abstract

In the pursuit of enhancing harmonic detection precision within microgrids, this paper introduces a pioneering algorithm, VMD-DCHHO-HD, which amalgamates Variational Mode Decomposition (VMD) with an advanced Harris Hawk Optimization algorithm characterized by dynamic opposition-based learning and Cauchy mutation (DCHHO). This study establishes a fitness function based on Shannon entropy, thereby minimizing the Local Minimum Entropy (LME) as the optimization objective for DCHHO. Building upon this, the VMD crucial parameters are efficiently identified using the enhanced HHO algorithm (DCHHO), enabling precise decomposition of complex voltage signals. The proposed method effectively addresses issues commonly encountered in traditional Empirical Mode Decomposition (EMD) during harmonic analysis, such as mode mixing, endpoint effects, and significant errors. Notably, it adeptly captures harmonic components spanning diverse frequencies, offering a nuanced solution to common pitfalls in traditional methodologies. In simulation experiments, VMD-DCHHO-HD showcases remarkable proficiency in extracting microgrid voltage signals, excelling at discerning high-order, low-amplitude harmonic components amid noise. The algorithm’s superior precision and heightened reliability, as affirmed by comparative analyses against existing methods, position it as an advanced tool for precise and robust harmonic analysis in microgrid systems.

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1 VOLUME 1, 2024
Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.
Digital Object Identifier 10.1109/ACCESS.2022.Doi Number
A Novel Harmonic Detection Method for
Microgrids Based on Variational Mode
Decomposition and Improved Harris Hawks
Optimization Algorithm
XINCHEN WANG1, SHAORONG WANG1, JIAXUAN REN1, WEIWEI JING2, MINGMING SHI2,
AND XIAN ZHENG2
1School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
2State Grid Jiangsu Electric Power Co., Ltd., Nanjing 210024, China
Corresponding author: Xinchen Wang (m202271896@hust.edu.cn)
This work was supported by the State Grid Corporation of China Technologies Program under Grant 5700-202018485A-0-0-00.
ABSTRACT In the pursuit of enhancing harmonic detection precision within microgrids, this paper
introduces a pioneering algorithm, VMD-DCHHO-HD, which amalgamates Variational Mode
Decomposition (VMD) with an advanced Harris Hawk Optimization algorithm characterized by dynamic
opposition-based learning and Cauchy mutation (DCHHO). This study establishes a fitness function based
on Shannon entropy, thereby minimizing the Local Minimum Entropy (LME) as the optimization objective
for DCHHO. Building upon this, the VMD crucial parameters are efficiently identified using the enhanced
HHO algorithm (DCHHO), enabling precise decomposition of complex voltage signals. The proposed
method effectively addresses issues commonly encountered in traditional Empirical Mode Decomposition
(EMD) during harmonic analysis, such as mode mixing, endpoint effects, and significant errors. Notably, it
adeptly captures harmonic components spanning diverse frequencies, offering a nuanced solution to common
pitfalls in traditional methodologies. In simulation experiments, VMD-DCHHO-HD showcases remarkable
proficiency in extracting microgrid voltage signals, excelling at discerning high-order, low-amplitude
harmonic components amid noise. The algorithm's superior precision and heightened reliability, as affirmed
by comparative analyses against existing methods, position it as an advanced tool for precise and robust
harmonic analysis in microgrid systems.
INDEX TERMS Variational Modal Decomposition (VMD), harmonic detection, Harris Hawks
Optimization (HHO) algorithm, function optimization.
I. INTRODUCTION
With the ongoing development of the global economy and
society, the escalating environmental challenges associated
with fossil fuel usage have propelled a continual rise in
demand for various forms of distributed renewable energy
sources. The traditional centralized power supply model is
increasingly unable to meet the current societal requirements
for flexible, environmentally friendly, and efficient electricity
transmission. In response to these challenges, microgrid
technology has emerged, overcoming the drawbacks of
traditional power supply models by offering a flexible power
supply mode and effectively enhancing the overall resilience
and robustness of the power system [1-5].
While microgrids present various advantages, it is crucial
to tackle the related power quality challenges emerging during
their development. On the one hand, the increasing
incorporation of nonlinear loads into the grid has become a
prevailing trend. On the other hand, the utilization of inverter
control technology for diverse distributed energy sources
within microgrids introduces a substantial array of power
electronic devices. This presence contributes to distortions in
voltage waveforms and an increase in harmonic current levels.
Moreover, compared to traditional grid structures, the network
framework of microgrids is inherently more fragile,
highlighting the significance of harmonic issues [6-9].
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3394931
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X．Wang et al.: A Novel Harmonic Detection Method for Microgrids Based on VMD and Improved HHO algorithm
VOLUME 1, 2024 2
Analyzing harmonic content is not only the starting point
for studying harmonic issues but also a crucial basis for
formulating harmonic mitigation strategies [10]. Therefore,
finding a suitable and efficient algorithm to precisely analyze
harmonics in microgrids plays a pivotal role in enhancing the
quality of power supply in microgrids. In the quest for
effectively extracting features from harmonic signals in
microgrids, numerous efficient methods have been proposed,
with Fast Fourier Transform (FFT), Wavelet Transform (WT)
[11], and Empirical Mode Decomposition (EMD) [12]
standing out as chief among them.
FFT [13] is a widely employed and classical tool in time-
frequency analysis. However, the traditional FFT falls short in
capturing the local properties of signals in the time domain
and exhibits reduced effectiveness when dealing with signals
characterized by abrupt changes or non-stationarities. Unlike
the Fourier Transform, which employs monotonic sine waves,
the basis functions used for signal decomposition in WT are
diverse, featuring finite durations, abrupt changes in
frequency and amplitude, and the ability to scale and shift. On
one hand, the flexibility of these basis functions equips the
WT to handle abrupt signal changes and perform time-
frequency analysis. However, from another perspective, the
effectiveness of WT heavily relies on the selection of basis
functions. Currently, there is no universally accepted
quantifiable method for selecting wavelet bases, and it
predominantly depends on the experiential judgment of
researchers. While the Wavelet Packet Transform (WPT) [14]
surpasses the limitation of the WT by decomposing signals
beyond the low-frequency band, it remains powerless in
addressing the inherently subjective process of basis function
selection. In contrast to WT and WPT, which require the pre-
selection of wavelet basis functions, EMD [15] is an adaptive
signal analysis method. However, it is imperative to
acknowledge the presence of mode mixing and endpoint effect
[16]. To address these challenges, a series of refined
algorithms based on EMD has emerged, including the
Ensemble Empirical Mode Decomposition (EEMD) [17] and
the Complementary Ensemble Empirical Mode
Decomposition (CEEMD) [18]. However, it is noteworthy
that these algorithms incorporate white noise into the signal as
a means of mitigating mode mixing, inadvertently leading to
an expansion of errors.
In 2014, Konstantin et al. introduced Variational Mode
Decomposition (VMD), an adaptive and non-recursive
variational mode decomposition method [19]. VMD operates
by constructing and solving a variational problem, enabling
the decomposition of signals into modes with different central
frequencies. Unlike traditional methods like EMD, VMD
autonomously determines the number of decomposition
modes and adaptively matches optimal central frequencies
and finite bandwidths for each mode. VMD effectively
separates Intrinsic Mode Functions (IMFs), partitions signals
in the frequency domain, and yields efficient decomposed
components. It ultimately provides an optimal solution to the
variational problem, overcoming issues such as endpoint
effects and mode mixing present in methods like EMD.
Notably, VMD allows arbitrary specification of parameters
like the number of modes; however, imprudent parameter
settings can impact decomposition effectiveness in practical
applications.
To efficiently and precisely determine the optimal
parameters for VMD, maximizing its superiority in harmonic
detection, this paper combines an optimization algorithm with
VMD. Below are concise descriptions of widely-used
optimization algorithms. Compared to traditional gradient-
based optimization algorithms, which suffer from both low
efficiency and accuracy, Swarm Intelligence (SI) algorithms
have proven effective and robust [20-21]. The Ant Colony
Optimization (ACO) [22] algorithm draws inspiration from
the foraging behavior of ants to find the optimal path. While
robust, the algorithm suffers from slow convergence. Another
classic optimization method, the Particle Swarm Optimization
(PSO) [23] algorithm, simulates the collective behavior of bird
or fish swarms. It excels in requiring minimal parameter
configuration and boasts a simple algorithmic structure, but it
tends to get stuck in local optima. The Artificial Bee Colony
(ABC) [24] algorithm simulates honeybees' foraging behavior,
offering high flexibility. However, its processing speed often
disappoints when addressing specific problems. Moreover, in
recent years, several intriguing optimization algorithms have
emerged, including the Grey Wolf Optimization (GWO) [25]
algorithm, the Firefly Algorithm (FA) [26] and the Bat
Algorithm (BA). While these algorithms offer distinct
advantages, they share common limitations, including
challenges in handling complex scenarios and issues related to
global exploration.
In 2019, the Harris Hawk Optimization (HHO) algorithm
was introduced by the Iranian scholar Heidari et al. [27]. This
nature-inspired swarm intelligence approach, emulating the
hunting behavior of Harris hawks, is relatively straightforward
compared to other optimization algorithms. The HHO
algorithm adopts a parallel search strategy, significantly
accelerating the convergence speed. Additionally, the HHO
algorithm introduces competitive and search mechanisms,
allowing for adaptive adjustment of algorithm parameters,
showcasing high adaptability and robustness. Leveraging
these advantages, this paper opts to employ the HHO to
optimize the VMD. Furthermore, additional enhancements to
the HHO algorithm are discussed later in the paper, improving
algorithm performance.
This paper delves into the harmonic analysis of microgrids,
introducing the innovative VMD-DCHHO-HD algorithm to
overcome existing method limitations. This novel harmonic
detection algorithm effectively tackles the parameter selection
challenge in VMD. Importantly, it excels in extracting
harmonic signal characteristics within microgrid scenarios,
surpassing the performance of previous mainstream
algorithms and pushing the boundaries of the field. The
primary contributions of the paper can be summarized as
follows:
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3394931
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X．Wang et al.: A Novel Harmonic Detection Method for Microgrids Based on VMD and Improved HHO algorithm
3 VOLUME 1, 2024
1) Introduced an enhanced algorithm, DCHHO, based on
Harris Hawk Optimization, aiming to comprehensively
rectify its deficiencies and meticulously adapt it for the
determination of optimal algorithm parameters. The
detailed optimization strategy is outlined as follows:
⚫ Introduced Cauchy mutation to enable the HHO
algorithm to escape local optima during the
optimization process.
⚫ Introduced dynamic opposition-based learning to
enhance the optimization efficiency of the HHO
algorithm.
2) Incorporated DCHHO into VMD, adeptly identifying
the optimal combination of crucial parameters for
VMD. This integration resulted in the demonstration of
superior modal decomposition, highlighting its
effectiveness in harmonic detection within microgrid
scenarios.
3) Simulated a microgrid system in MATLAB, conducted
analysis and comparative experiments using the
simulated voltage signals, demonstrating the
effectiveness and engineering applicability of the
proposed novel algorithm.
II. PRINCIPLES OF MATHEMATICS
A. VMD
The VMD decomposition can be conceptually framed as an
optimization process for solving the following constrained
variational problem [28], as illustrated in (1).
2
( ) ( )
..
k
jt
tk
k
k
k
j
t u t e
t
s t u f


−




 + 







=


(1)
Where,
   
1,,
kk
u u u=
symbolizes the decomposed
Intrinsic Mode Function (IMF) component, while
   
1,,
kk
  
=
represents the central frequency of each
constituent part. Here,
()t

denotes the Dirac distribution, and
the symbol ∗ corresponds to the convolution operator.
By introducing the Lagrange multiplier operator λ,
transforming the constrained variational problem into an
unconstrained one. The augmented Lagrange expression is
obtained as (2):
   
( )
2
2
2
2
,,
( ) ( )
( ) ( ) ( ), ( ) ( )
k
kk
jt
tk
k
kk
kk
Lu
j
t u t e
t
f t u t t f t u t





−
=


 +  +




− + −


(2)
where,

serves as the quadratic penalty factor designed to
mitigate the interference of Gaussian noise. Subsequently,
utilizing the Alternating Direction Method of Multipliers
(ADMM), each component and its corresponding central
frequency are iteratively updated. Ultimately, this process
yields the saddle point of the unconstrained model,
representing the optimal solution to the original problem. The
specific steps and formulas are described as follows.
After initializing parameters
1 1 1
ˆkk
u

、 、
, iterative updates
are systematically carried out in accordance with (3), (4) and
(5).
1
2
ˆ ˆ ˆ
( ) ( ) ( ) / 2
ˆ() 1 2 ( )
i
nik
k
k
su
u
   
  
+
−+
=+−

(3)
2
1
10
2
1
0
ˆ()
ˆ()
n
k
n
kn
k
ud
ud
  

+
+
+
=

(4)
11
ˆ
ˆ ˆ ˆ
( ) ( ) ( ) ( )
n n n
k
k
fu
      
++

= + −



(5)
Repeating the steps until the iterative stopping condition
22
1
22
ˆ ˆ ˆ
/
n n n
k k k
k
u u u

+−

.
B. HHO
The Harris Hawk Optimization (HHO) algorithm is
renowned for robust global search and strong optimization
performance, organized into three distinct stages.
1) EXPLORATION PHASE
In this phase, the Harris hawks utilize two strategies for the
random search of prey within the spatial range [lb, ub].
Throughout iterations, the positions undergo updates guided
by q, as (6):
( ) ( )
12
34
( 1)
| ( ) 2 ( ) |, 0.5
( ) ( ) ( ) , 0.5
rand rand
rabbit m
Xt
X r X t r X t q
X t X t r lb r ub lb q
+=
− − 

− − + − 

(6)
Where
()
rabbit
Xt
represents the prey's position,
()Xt
denotes the Harris hawk's position,
()
rand
Xt
signifies the
randomly selected individual's position,
()
m
Xt
is the mean
position of individuals,
1 2 3 4
, , , ,q r r r r
are random numbers
within the range (0,1).
2) TRANSITION PHASE
In this phase, the escape energy equation for prey is defined,
as illustrated in (7), facilitating a suitable transition between
exploration and exploitation through the utilization of (7).
0
21
t
EE T

=−


(7)
Where E represents the escape energy of the prey, with
0
E
being the initial energy level. When
1E
, the Harris
Hawk algorithm conducts global exploration. Once
1E
,
the algorithm transitions into the local exploitation phase.
3) EXPLOITATION PHASE
In this phase, the algorithm employs four strategies to
simulate attacking behavior. Tab.1 outlines these strategies
employed by Harris hawks for capturing prey under different
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3394931
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. For more information, see https://creativecommons.org/licenses/by-nc-nd/4.0/

X．Wang et al.: A Novel Harmonic Detection Method for Microgrids Based on VMD and Improved HHO algorithm
VOLUME 1, 2024 4
conditions, providing a detailed description of their
respective position iteration equations.
TABLE 1. The Harris Hawk position iteration equation under different
conditions
Approach
Conditions
The Harris hawk position iteration
equation
Soft besiege
0.5
0.5
E






( 1)
( ) ( ) ( )
rabbit
Xt
X t E JX t X t
+
=  − −
( ) ( ) ( )
rabbit
X t X t X t = −
Hard
besiege
0.5
0.5
E






( 1) ( ) ( )
rabbit
X t X t E X t+ = − 
soft besiege
with
progressive
rapid dives
0.5
0.5
E






( 1)
, ( ) ( ( ))
, ( ) ( ( ))
Xt
Y F Y F X t
Z F Z F X t
+=




: ( ) ( ) ( )
: ( )
rabbit rabbit
Y X t E JX t X t
Z Y S LF Dim
−−
+
hard
besiege with
progressive
rapid dives
0.5
0.5
E






( 1)
, ( ) ( ( ))
, ( ) ( ( ))
Xt
Y F Y F X t
Z F Z F X t
+=




: ( ) ( ) ( )
: ( )
rabbit rabbit m
Y X t E JX t X t
Z Y S LF Dim
−−
+
III. ALGORITHMIC IMPROVEMENT MOTIVATIONS
While VMD and modal decomposition algorithms like EMD,
EEMD, and CEEMD share a common purpose, they exhibit
fundamental differences. VMD, in contrast to EMD and its
derivatives, offers the advantage of pre-specifying the number
of modes and the penalty parameter α. However, due to the
intricate nature of real-world signals, improper settings for
parameters k and α can potentially negate this advantage. An
excessively large k may result in over-decomposition problem,
while an excessively small one may lead to under-
decomposition problem. Similarly, an overly large α could
cause the loss of frequency band information, while an overly
small α may result in information redundancy [29-30].
Presently, the widely adopted method involves using the
central frequency observation approach to determine suitable
values for k and α. However, this method is highly subjective,
diminishing the VMD algorithm's fault tolerance and
providing insufficient determination of the penalty parameter
α. Consequently, the selection of an optimal parameter
combination is a critical and challenging aspect in applying
the VMD algorithm for harmonic information extraction.
In light of this, the study seamlessly integrates optimization
algorithms with VMD to precisely define its critical
parameters, effectively capitalizing on its strengths and
mitigating limitations for optimal performance in modal
decomposition. To better achieve this goal, this paper
enhances the Harris Hawk Optimization (HHO) algorithm,
significantly addressing its susceptibility to local optima and
thereby improving both algorithm accuracy and optimization
efficiency.
The overall system block diagram of the proposed VMD-
DCHHO-HD for microgrid harmonic detection is illustrated
in Fig.1.
FIGURE 1. Block diagram of the harmonic detection system
IV. A NOVEL HARMONIC DETECTION METHOD BASED
ON VMD AND IMPROVED HHO ALGORITHM (VMD-
DCHHO-HD)
A. OPTIMIZATION OF THE HHO ALGORITHM
The Harris Hawk Optimization (HHO) algorithm, drawing
inspiration from the hunting behavior of Harris hawks, is a
nature-inspired swarm intelligence algorithm recognized for
its robust global search capabilities and optimization
performance. However, it encounters challenges such as
susceptibility to local optima and low convergence accuracy.
This study enhances the HHO algorithm by introducing the
Cauchy operator and the dynamic opposition-based learning
strategy. The resulting refined algorithm exhibits improved
robustness and optimization performance, particularly
proving beneficial for addressing complex harmonic problems.
1) CAUCHY MUTATION
To alleviate the susceptibility of HHO algorithm to local
optima, drawing inspiration from the work referenced in [31-
32], this study incorporates optimization by integrating the
Cauchy distribution function. Harnessing the unique attributes
of the Cauchy distribution function, characterized by a smaller
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3394931
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. For more information, see https://creativecommons.org/licenses/by-nc-nd/4.0/

X．Wang et al.: A Novel Harmonic Detection Method for Microgrids Based on VMD and Improved HHO algorithm
5 VOLUME 1, 2024
peak at the origin and an extended distribution at both ends,
the inclusion of the Cauchy operator in the HHO algorithm
amplifies mutation effects at both ends during optimization,
yielding enhanced performance.
2
11
() 1
fx x


=
+

(8)
The update of the global optimum in each iteration of HHO
is determined using the standard Cauchy distribution function
(8), represented by (9). Leveraging the properties of the
Cauchy function, characterized by a moderate peak,
effectively reduces the exploration time spent by Harris hawks
in local intervals. Notably, the gradual decline at both ends of
the Cauchy function mitigates the algorithm's constraint force
on local extreme points, facilitating escape from local optima.
_(0,1)
new best best best
X X X Cauchy= + 
(9)
2) DYNAMIC OPPOSITION-BASED LEARNING
STRATEGY
Taking inspiration from prior studies [32], this research
integrates the dynamic opposition-based learning strategy to
improve the efficiency of acquiring optimal solutions. The
core principle of opposition-based learning entails generating
a solution derived from the current one. Simultaneous
searches are conducted at the present position and its opposite
counterpart, heightening the probability of attaining superior
solutions. The dynamic opposition-based learning introduces
a variable, denoted as r, which undergoes nonlinear evolution
with each iteration, more effectively steering the generation of
reverse solutions. This relationship is mathematically
expressed in (10) and (11).
( ) ( )
ii
X t lb ub rX t= + −
(10)
sin t
rT

=

(11)
In the search space
[ , ]lb ub
, where t represents the iteration
time,
()
i
Xt
denotes the position of individual i at time t,
()
i
Xt
represents its corresponding reverse solution, and r is
the dynamic coefficient.
B. CHOOSING THE FITNESS FUNCTION
In the process of optimizing the important parameters for the
VMD algorithm using the enhanced the Harris Hawk
Optimization algorithm, it is crucial to define a fitness
function [34-35]. This fitness function involves continuous
calculation and comparison of fitness values, leading to the
updating of the optimal position.
Drawing inspiration from the literature [36], this study
employs Shannon entropy to assess the sparsity characteristics
of the signal. The magnitude of entropy reflects the uniformity
of the probability distribution, with the highest entropy value
associated with the most uncertain probability distribution
[37]. Following this principle, the envelope signal obtained
through signal demodulation undergoes processing into a
probability distribution sequence pj. The resulting entropy
value Ep calculated from this sequence effectively captures the
sparsity characteristics of the original signal.
For each individual's position in the HHO algorithm, the
condition involves obtaining the envelope entropy values of
all IMF components after VMD processing. Among these
values, the minimum one is defined as the Local Minimum
Entropy (LME). Based on the definition of entropy, the less
noise contained in the IMF components, the more
characteristic information is present, and the signal exhibits
stronger sparsity characteristics, resulting in smaller envelope
entropy values. Therefore, this study minimizes the Local
Minimum Entropy value as the optimization objective, aiming
to optimize the values of k and α, as mathematically
formulated in (12).
min
min IMF
p
LE=
(12)
C. SPECIFIC STEPS OF THE VMD-DCHHO-HD
The process diagram of the enhanced harmonic analysis
algorithm, VMD-DCHHO-HD, resulting from the
aforementioned optimization innovations, is illustrated in
Fig.2.
FIGURE 2. The procedure for harmonic detection based on the VMD-
DCHHO-HD algorithm.
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3394931
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. For more information, see https://creativecommons.org/licenses/by-nc-nd/4.0/

X．Wang et al.: A Novel Harmonic Detection Method for Microgrids Based on VMD and Improved HHO algorithm
VOLUME 1, 2024 6
The specific steps of execution are outlined below：
Step 1: Initialization of the parameters to be determined in
the VMD algorithm, minimizing the local minimum entropy
as the optimization objective, and determining the fitness
function, as shown in (12).
Step 2: Initialize the whole population with parameter
combinations [k

] as individual positions, calculate the
fitness value for each individual, and determine the current
optimal individual.
Step 3: Calculate the initial energy and escape energy for
each individual, based on which determine whether the Harris
hawk individual is in the exploration phase or exploitation
phase. Continuously update individual positions accordingly.
Step 4: Apply Cauchy mutation to the optimal solution of
individuals in the capturing phase according to (9).
Step 5: Implement the dynamic opposition-based learning
operations on all individuals using (10). Combine the newly
acquired population with the original population, employing
the greedy strategy to select the top N individuals with the
highest fitness values for the new population.
Step 6: Continuously update the positions of Harris's hawk
and the global optimal solution.
Step 7: Check for convergence: if the maximum number of
iterations is not reached, continue the iterative process;
otherwise, report the final global optimal solution [
best
k
best

]
and its corresponding best fitness value.
Step 8: Apply the values
best
k
,
best

to the VMD algorithm
and perform modal decomposition.
V. SIMULATIONS AND RESULTS
A. MICROGRID VOLTAGE SIGNAL SIMULATION
To evaluate the practical applicability of the proposed
algorithm, this paper implemented a three-phase AC circuit
using MATLAB. The circuit configuration, illustrated in Fig.3,
simulates a DC Microgrid for Wind and Solar Power
Integration, demonstrating significant growth potential and
versatile applications. The microgrid includes components
such as Wind Turbine (WT) system, Photovoltaic (PV) system,
and Supercapacitor Energy Storage (SCES) system. These
components are connected to the DC bus using a DC-DC
converter. The transformed and filtered AC power is then
supplied to loads through the inverter [38-42]. Due to
constraints on the length of this paper, a detailed discussion of
each module's structure is beyond the scope.
In traditional power systems, sources of pollution mostly
arise from harmonics generated internally during the
processes of generation, transmission, and distribution
processes, as well as the connection of nonlinear loads such as
inverters, rectifiers, etc. In contrast to traditional power
systems, microgrid systems on the source side incorporate
numerous power electronic devices, further contributing to the
degradation of power quality. Therefore, harmonic
management is a crucial technical focus in microgrid planning.
1) SIMULATION PARAMETERS
To maximize the electric power generated from the wind, the
Wind Turbine (WT) system described in this paper is designed
based on the traditional Maximum Power Point Tracking
(MPPT) control strategy [43-44]. The system features a direct-
drive structure, where there is no transmission system between
the rotor and the generator, ensuring higher transmission
efficiency. Additionally, a Buck-Boost converter is integrated
before the load to address the low amplitude of the AC voltage
output. During operation, the system initiates with a pitch
angle set to 0 and a wind speed of 8 m/s. Tuning is performed
to validate the system's ability to swiftly attain the Maximum
Power Point shortly after the commencement of operation.
The PV system in this study employs the constant-step
Perturbation and Observation (P&O) MPPT algorithm [45].
Similarly, a Buck-Boost converter is introduced between the
output and the load. The system operates under a set solar
irradiance of
2
1200 /W cm
, showcasing commendable
response speed following tuning [46].
The energy storage system utilizes a supercapacitor to
output a vector containing measurement signals. Facilitated by
a bidirectional Buck-Boost converter, the energy storage
system achieves bidirectional charging and discharging
control of the supercapacitor. Integration of a Proportional-
Integral (PI) control system ensures the stable voltage and
current operation of the energy storage system [47-48].
FIGURE 3. Simulation of DC microgrid for wind and solar power
integration system
2) SIMULATION RESULTS OF THE VOLTAGE SIGNAL
The load side has
0.02R=
and
0.1mHL=
, and a 5 kW AC
load is connected before the system is operated. The output
three-phase AC voltage signals are shown in Fig.4.
FIGURE 4. Simulation results of three-phase AC voltage signals at the
load side of the microgrid
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3394931
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X．Wang et al.: A Novel Harmonic Detection Method for Microgrids Based on VMD and Improved HHO algorithm
7 VOLUME 1, 2024
From Fig.4, it can be observed that the simulated voltage
signals of the microgrid contain numerous harmonic
components with unknown frequencies and amplitudes. To
facilitate further analysis, the next step will involve harmonic
detection on the single-phase voltage signals extracted from
these signals.
B. ANALYSIS OF THE VMD PERFORMANCE OPTIMIZED
BY DCHHO
Setting the maximum iteration count to 30, using the
minimum envelope entropy as the fitness function, the
DCHHO algorithm efficiently obtains the optimal solution for
the important parameters of VMD. The optimization process
is illustrated in Fig.5.
FIGURE 5. The iterative process of utilizing the DCHHO algorithm to
find the optimal parameters for VMD
In Fig.5, it is evident that, with an increase in the number of
iterations, the optimal combination of [k α] stabilizes at [9
669]. This indicates that the optimal number of modes
obtained through DCHHO is 9, with the optimal penalty
parameter being 669. The corresponding optimal fitness value
for this combination is 6.2633. The decomposition result of
VMD-DCHHO-HD based on this optimal parameter set is
illustrated in Fig.6.
(a) IMF1
(b) IMF2
(c) IMF3
(d) IMF4
(e) IMF5
(f) IMF6
(g) IMF7
(h) IMF8
(i) IMF9
FIGURE 6. Results of modal decomposition of microgrid output voltage
signal using VMD-DCHHO-HD algorithm
Observing the IMFs depicted in Fig. 6, it is evident that
VMD-DCHHO-HD excels in achieving a remarkable modal
decomposition for the intricate voltage signals in the
microgrid. The algorithm precisely isolates harmonic signals
spanning various frequencies, effectively suppressing modal
aliasing and thereby facilitating a simplified yet
comprehensive harmonic analysis. To underscore the superior
performance of our novel harmonic detection algorithm, the
following section conducts a comparative analysis with
several widely adopted harmonic detection algorithms.
C. COMPARISONS AND ANALYSIS OF EXPERIMENTAL
RESULTS
Building upon the research content and objectives outlined in
the preceding section, this segment employs various
decomposition algorithms—EMD, EEMD, CEEMD, and
VMD-DCHHO-HD—to analyze the steady-state single-phase
voltage signals obtained from the simulation in Section A of
Phase V. The ensuing discussion involves a comparative
analysis of the effectiveness of these algorithms. Due to
constraints in space, a detailed presentation of the IMFs
obtained by each algorithm is omitted. Given that the
spectrogram provides ample information and visual clarity,
this paper will integrate the spectrogram along with metrics
such as Mutual Information (MI) and Root Mean Square Error
(RMSE) to illustrate the effects of modal decomposition.
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3394931
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. For more information, see https://creativecommons.org/licenses/by-nc-nd/4.0/

X．Wang et al.: A Novel Harmonic Detection Method for Microgrids Based on VMD and Improved HHO algorithm
VOLUME 1, 2024 8
01000 2000 3000 4000 5000
0
10
20
IMF1
01000 2000 3000 4000 5000
0
200
IMF2
01000 2000 3000 4000 5000
0
0.5
1
IMF3
01000 2000 3000 4000 5000
0
1
2
IMF4
01000 2000 3000 4000 5000
0
5
IMF5
Frequency(Hz)
(a) Spectrogram illustrating the results obtained from the decomposition of
the initial voltage signal using EMD.
0 1000 2000 3000 4000 5000
0
0.5
IMF1
01000 2000 3000 4000 5000
0
0.5
IMF2
0 1000 2000 3000 4000 5000
0
1
2
IMF3
01000 2000 3000 4000 5000
0
10
20
IMF4
01000 2000 3000 4000 5000
0
200
IMF5
Frequency(Hz)
(b) Spectrogram illustrating the results obtained from the decomposition of
the initial voltage signal using EEMD.
01000 2000 3000 4000 5000
0
0.1
0.2
IMF1
01000 2000 3000 4000 5000
0
0.5
1
IMF2
01000 2000 3000 4000 5000
0
5
IMF3
01000 2000 3000 4000 5000
0
10
20
IMF4
01000 2000 3000 4000 5000
0
200
IMF5
01000 2000 3000 4000 5000
0
5
10
IMF6
Frequency(Hz)
(c) Spectrogram illustrating the results obtained from the decomposition of
the initial voltage signal using CEEMD.
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
0
0.1
0.2
IMF1
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
0
0.2
0.4
IMF2
0500 1000 1500 2000 2500 3000 3500 4000 4500 5000
0
0.5
IMF3
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
0
1
2
IMF4
0500 1000 1500 2000 2500 3000 3500 4000 4500 5000
0
5
IMF5
0500 1000 1500 2000 2500 3000 3500 4000 4500 5000
0
5
10
IMF6
0500 1000 1500 2000 2500 3000 3500 4000 4500 5000
0
20
40
IMF7
0500 1000 1500 2000 2500 3000 3500 4000 4500 5000
0
100
200
IMF8
0500 1000 1500 2000 2500 3000 3500 4000 4500 5000
0
50
IMF9
Frequency(Hz)
(d) Spectrogram illustrating the results obtained from the decomposition of
the initial voltage signal using VMD-DCHHO-HD.
FIGURE 7. Spectrograms of decomposition results for each algorithm
Fig.7 illustrates the spectrograms of decomposition results
obtained by each algorithm. Based on Fig.7 (a), it is evident
that the EMD algorithm, applied to the voltage signal with
complex harmonic information obtained from the microgrid
simulation in this study, adaptively decomposes it into five
IMFs. However, the effectiveness of this decomposition is
suboptimal. The spectrogram clearly indicates a substantial
loss of high-frequency information after signal decomposition,
retaining only harmonic signals below 10f0 and the
fundamental frequency signal. Furthermore, the IMFs exhibit
pronounced mode mixing and noticeable endpoint effects,
highlighting the subpar performance of EMD in harmonic
analysis for the simulated voltage signal.
As depicted in Fig.7 (b) and (c), the enhanced versions of
EMD, namely EEMD and CEEMD, exhibit improvements in
mitigating endpoint effects and reducing the loss of high-
frequency signals compared to the original EMD. However,
despite addressing these issues, both modified algorithms still
suffer from mode mixing problems. Additionally, the
improvements come at a cost, as these enhanced algorithms
introduce white noise into the decomposition process. While
this helps suppress mode mixing, it simultaneously results in
the generation of numerous false components, leading to an
increase in errors.
In comparison to EMD, EEMD, and CEEMD, Fig.7 (d)
distinctly reveals the superior performance of VMD-
DCHHO-HD in resolving mode mixing and endpoint effects.
This is particularly notable for harmonics within the 20f0 range,
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3394931
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. For more information, see https://creativecommons.org/licenses/by-nc-nd/4.0/

X．Wang et al.: A Novel Harmonic Detection Method for Microgrids Based on VMD and Improved HHO algorithm
9 VOLUME 1, 2024
including 5f0, 7f0, 11f0, 13f0, 17f0, and 19f0, where the
algorithm exhibits exceptional separation capabilities.
To further elevate the precision of performance evaluation
in harmonic detection, this study introduces evaluation
metrics, including Mutual Information (MI) and Root Mean
Square Error (RMSE). Subsequently, a comparative table is
provided for a systematic analysis and comparison of these
algorithm.
Mutual Information (MI) serves as a non-parametric and
non-linear metric in information theory, offering a precise
quantification of the correlation between two random
variables[49-50]. In contrast to traditional correlation
coefficient methods, MI accurately reflects the coupling
degree between IMFs. Combining the analysis of MI and
spectrograms provides a clearer and more intuitive
understanding of an algorithm's ability to address mode
mixing. MI is defined by (13).
,( , )
MI(y ,y )=E log ( ) ( )
ij
j
i
yy
ij
ij y
y
ij
p y y
p y p y








(13)
Where yi represents the signal amplitude corresponding to
IMFi, yj represents the signal amplitude corresponding to IMFj,
pyi,yj(yi,yj) is the joint probability density function, pyi(yi) and
pyj(yj) are the marginal probability density functions.
Root Mean Square Error (RMSE) effectively reflects the
difference between the reconstructed signal and the initial
signal. A larger RMSE indicates a greater amount of error
introduced by the harmonic detection algorithm during the
modal decomposition process. RMSE is defined by (14).
2
1
1
ˆ ˆ
( , ) ( )
n
i
RMSE y y y y
N=
=−

(14)
Where
ˆ
y
represents the amplitude of the reconstructed
signal,
y
represents the amplitude of the initial signal and N
represents the number of sampling points.
Additionally, as the assessment of endpoint effects in the
initial signal decomposition process cannot be captured by a
specific metric, we will directly summarize based on
spectrograms. The findings will be presented and compared in
Tab.2.
TABLE 2. Comparison of multiple metrics
Indicators
EMD
EEMD
CEEMD
VMD-
DCHHO-HD
RMSE
5.4694
4.3877
1.9555
0.6998
MI between
IMFs
IMF1-2:0.2457
IMF2-3:0.3875
IMF3-4:0.5650
IMF4-5:0.6706
IMF1-2:0.2740
IMF2-3:0.1351
IMF3-4:0.2517
IMF4-5:0.3862
IMF1-2:0.2228
IMF2-3:0.2047
IMF3-4:0.3623
IMF4-5:0.2030
IMF5-6:0.2690
IMF1-2:0.0271
IMF2-3:0.0754
IMF3-4:0.0117
IMF4-5:0.0068
IMF5-6:0.0533
IMF6-7:0.2771
IMF7-8:0.1219
IMF8-9:0.0998
Occurrence
of Endpoint
Effects
(Yes/No)
Yes
No
No
No
Analyzing the metrics in Tab.2, it is evident that the RMSE
corresponding to VMD-DCHHO-HD is 0.6998, significantly
smaller than the other algorithms. This indicates that the
algorithm introduces minimal error and demonstrates high
precision. Furthermore, the MI between adjacent IMFs
obtained through VMD-DCHHO-HD is closest to 0.
Combining this with the spectrogram in Fig.7, it is evident that
the proposed method effectively eliminates redundant
components in each IMF, successfully overcoming the mode-
mixing problem. Additionally, the algorithm almost perfectly
eliminates endpoint effects.
In conclusion, the algorithm exhibits outstanding
performance in balancing decomposition effectiveness and
precision. It outperforms traditional harmonic detection
algorithms in various performance indicators.
CONCLUSION
This paper presents VMD-DCHHO-HD, a novel microgrid
harmonic detection algorithm integrating an improved HHO
algorithm with VMD. Comparative analysis with well-known
algorithms, such as EMD, EEMD, and CEEMD, highlights
the superior performance of VMD-DCHHO-HD in
overcoming endpoint effects and mode-mixing issues,
showcasing remarkable precision. The algorithm excels in
extracting microgrid fundamental signals, accurately
capturing high-order, low-amplitude harmonics amid noise.
Its effectiveness positions VMD-DCHHO-HD as a superior
choice for microgrid harmonic detection. Our future research
will explore harmonic source identification and suppression
strategies using this innovative detection method.
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X．Wang et al.: A Novel Harmonic Detection Method for Microgrids Based on VMD and Improved HHO algorithm
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content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3394931
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X．Wang et al.: A Novel Harmonic Detection Method for Microgrids Based on VMD and Improved HHO algorithm
11 VOLUME 1, 2024
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XINCHEN WANG was born in Xinyang, Henan,
China, in 1999. She received the B.E. degree in
electrical engineering and its automation from the
Huazhong University of Science and Technology,
in 2021. She is currently pursuing the master’s
degree with the same university.
She has two conference papers indexed in EI and
IEEE, respectively, in the fields of harmonic
detection and microgrid planning. Her research
interests include power quality, Multi-microgrid
Connect and harmonic mitigation.
.
SHAORONG WANG was born in 1960. He
received the B.E. degree in electrical engineering
from Zhejiang University, Hangzhou, China, in
1984, the M.E. degree in electrical engineering
from North China Electric Power University,
Baoding, China, in 1990, and the Ph.D. degree in
electrical engineering from the Huazhong
University of Science and Technology, Wuhan,
China, in 2004. He is currently a Professor with
the HUST. His current research interests include
smart grids, power system operation and control,
wind power and renewable energy.
JIAXUAN REN was born in Jinan, Shandong,
China, in 1999. He received the B.E. degree in
electrical engineering and its automation from
North China Electric Power University in 2022.
He is currently pursuing the master’s degree at
Huazhong University of Science and Technology.
He has two conference papers indexed in EI and
IEEE, in the fields of intelligent operation and
inspection of substations and harmonic coupling
characteristics. His current research interest is the
power quality in power systems.
WEIWEI JING was born in 1981. He is a senior
engineer and currently serves as the Deputy
Director of the Equipment Management
Department at State Grid Jiangsu Electric Power
Co., Ltd. Specializing in electric grid
development planning, production, and technical
management for operations and maintenance.
Moreover, he has successfully completed over 10
scientific and technological projects for the State
Grid Corporation of China.
MINGMING SHI was born in 1986. He is a
senior engineer and currently serves as the
Deputy Director of the Distribution Network
Technology Center at the Electric Power
Research Institute of State Grid Jiangsu Electric
Power Co., Ltd.
In recent years, he has focused on researching
power quality testing and analysis, along with
exploring the application of power electronic
technology in the power grid. He has published a
total of 15 papers indexed in SCI and EI databases.
XIAN ZHENG was born in 1995. She received
the Ph.D. degree in Sichuan University and
joined the Electric Power Research Institute of
State Grid Jiangsu Electric Power Co., Ltd. in
2021.
She is currently dedicated to research in the field
of power quality and harmonic analysis. She has
authored over 10 papers published in reputable
journals and presented 3 papers at major
international academic conferences, including
CIRED and ICHQP.
This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and
content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2024.3394931
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