Cloud Server-Assisted Remote Monitoring and Core Device Fault Identification for Dynamically Tuned Passive Power Filters

Abstract

Reliability and safety are crucial for the operation of a dynamically tuned passive power filter (DTPPF). Safe performance of DTTPFs implies complete normal filtering without failure within a specified period. To prevent potential disaster or economic loss, it is desirable to achieve early warning of any core device faults in a DTPPF based on its running state and to optimize its harmonic mitigation performance. In this paper, we explore effective methods for identifying core device faults in DTPPFs. First, we summarize the characteristic parameters of faults, running state parameters, parameters required for fault monitoring, and fault type parameters. Then, a cloud server-assisted remote monitoring and fault identification system for DTPPF is proposed, which consists of monitoring system’s architecture and cloud servers’ software architecture as well as software design of the back-end service layer and functional design of the front-end application layer. Our experiments demonstrate that the proposed system can monitor the real-time operational status of the DTPPF, enabling remote diagnosis and identification of core device faults. Moreover, it is user-friendly, as it is capable of optimizing equipment maintenance schedules and utilizing manufacturers’ service capacities. Therefore, this research provides a theoretical foundation for harmonic mitigation in low-voltage distribution networks and is valuable for practical engineering applications in industrial power grids.

1. Introduction

Electronic equipment used extensively in the power industry can generate electrical harmonics due to the presence of nonlinear loads. These electrical harmonics can cause a variety of negative effects. For example, they reduce the quality of power supply, increase power losses and load on power facilities, and have serious impacts on electronic devices, power capacitors, cables, relay protection, communication circuits, and more. These defects decrease the effective capacity and efficiency of electrical equipment and lead to unsafe production conditions and equipment shutdowns, resulting in significant economic losses [1,2,3].

Recently, researchers from both academia and industry have conducted in-depth analyses of the causes, effects, suppression methods, and related technologies of harmonics [4,5,6,7,8]. It is widely agreed that the optimal solution to harmonics is to install power filters at the source of harmonic generation and at the nearest end of the harmonic source. Currently, both passive power filters (PPFs) and active power filters (APFs) are widely used worldwide.

Passive power filters (PPFs) were developed earlier; they typically consist of passive components such as filter capacitors, inductors, and resistors. They are connected in parallel between the grid and ground. The principle is that they have low impedance to a specific harmonic, and can absorb the harmonics current. In this way, they reduce the corresponding harmonics current into the distribution network, achieving the purpose of filtering. PPFs are widely used in many industries because of their high reliability, simple structure, large capacity, and low costs. The filtering performance of PPFs depends on the parameters of the grid and the load. In contrast, active power filters (APFs) have complex structural and control requirements, making their operation conditions more demanding [8]. The main impediments for the development of PPF technology are the difficulty of continuously adjusting parameters, the need for a better understanding of the working mechanism of dynamic tuning, and challenges in optimizing the design and implementation of key components that cannot meet the requirements of practical engineering [9]. After ten years of research, the dynamic tuning power filter (DTPPF) was developed. DTPPFs consist of an electromagnetic coupling filtering inductor and multiple filter capacitors connected in series, which can effectively filter out the harmonics current. Recent studies have shown that DTPPFs are capable of harmonic suppression and energy saving. They can absorb the harmonics current and reduce the current RMS, thereby improving the power quality and the security of the power supply. DTPPFs can effectively achieve dynamic tuning and suppression of power harmonics in industrial applications [10,11,12]. However, long-term operation can affect the core devices of DTPPFs. For example, the harmonics current can cause aging or short-circuit failure of the filter capacitor, resulting in damage or reduced capacity. Additionally, it can lead to the breaking of the thyristor in the secondary winding of the electromagnetic coupling filter reactor (ECFR), rendering the primary-side inductance of the ECFR unable to be continuously adjusted. Both of these faults cause the resonant frequency of the DTPPF to deviate, resulting in a poor filtering effect.

There have been many studies on the capacitance and dielectric loss of capacitors [13,14]. The temperature of the capacitor case can be obtained by temperature sensors, while the temperature of the internal core can be inferred through estimation methods [15]. The equivalent series resistance of the filter capacitor can be obtained by measuring the dielectric loss angle of the capacitor, which can be calculated by the windowed Fourier transform, intelligent algorithm transform, or wavelet transform [16].

Infrared temperature sensors can only measure the temperature of the outermost winding of dry-type reactors [17]. Distributed optical fiber sensors can continuously measure the temperature of reactors to obtain the temperature distribution [18]. The inter-turn short-circuit fault status of the reactor can be judged by detecting the internal magnetic field signal of the coil. Iin the case of a short-circuit fault between turns, the magnetic field signal is no longer symmetrical [19]. If the reactor or capacitor of the PPF is abnormal (e.g., detuned), then the method of harmonic impedance identification can be used to analyze the changes in the harmonic impedance of the PPF. Additionally, a support vector machine algorithm can be applied to determine the faulty element based on the change rate of the harmonics current. Moreover, the detuning of the element can be determined by calculating the ratio of the variation rate of harmonics current [20,21].

Benefiting from the development of sensors, computer networks, and component technologies, researchers have proposed numerous techniques for monitoring and controlling industrial system operations. In recent years, numerous intelligent systems for diagnostic analysis have been studied and developed. The industrial remote monitoring system monitors the running state of industrial equipment through computer software and hardware. The existing remote monitoring system is not limited to the local area network. Industrial equipment can be connected to the internet to transmit data via the Internet of Things (IoT), enabling remote monitoring of industrial equipment through the internet. Elastic Compute Service has the advantages of high efficiency, reliability, and elastic scalability, and has consequently been widely deployed in remote monitoring systems. For example, Wu et al. [22] proposed a remote robot monitoring system which transmits image data to the Alibaba ECS via the TCP/IP protocol, enabling remote monitoring; the system can be accessed through a web interface. Mau et al. [23] proposed a panoramic monitoring system for start-up and debugging in substations. This system utilizes tunnel communication programs deployed on the ECS to monitor data from multiple substations.

Reliability and safety requirements are crucial to the operations of DTPPFs. To prevent potential disasters or economic losses, efforts have been devoted to supervising the running state of DTPPFs. At present, DTPPF performance is mainly measured and diagnosed by a combination of visual inspection and manual maintenance. However, this approach suffers from several shortcomings, such as high costs and imprecision. To address this issue, it is more desirable to explore an automated approach to monitor the running state of the DTPPF.

DTPPFs are incapable of maintaining the system on their own without technical support from the manufacturer. Consequently, a DTPPF manufacturer must provide technical support throughout the product lifecycle for routine operation. This study aims to meet DTPPF manufacturers’ needs and to improve the service quality of DTPPFs.

In general, most monitoring and fault diagnosis approaches are domain-specific and provide decision support to particular end users. Therefore, the study of monitoring and fault diagnosis is usually highly related to a specific application. In this paper, a more general fault identification method for the core devices of DTPPFs is proposed. A cloud server-assisted remote monitoring and fault identification system for DTPPFs is developed. This system enables fault alarms, fault recall, fault diagnosis, and real-time viewing of various states of the DTPPF via the internet.

The main contributions of this paper are as follows:

• We propose a method for identifying faults in DTPPF core devices based on the causes of core device faults. Through this method, characteristic parameters, operational status parameters, parameters required for fault detection, and fault type parameters are obtained.
• A monitoring system architecture and cloud server software architecture is constructed according to the design requirements of the cloud server-assisted remote monitoring and fault identification system for DTPPFs.
• The node.js development platform is used for the software design and functional realization of the back-end service layer according to the uniform interface and software architecture of this layer.
• A front-end application layer function page is designed.

The following is an outline of the subsequent sections. in Section 2, a DTPPF fault and identification method is proposed. Section 3 introduces the monitoring system architecture and software architecture. In Section 4, the functional design of the back-end service layer is introduced. Section 5 presents the design of the front-end application layer function page. Section 6 presents examples for verification of the proposed method. Finally, Section 7 concludes this paper.

2. DTPPF Fault Identification Method

2.1. Analysis of Fault Causes in DTPPFs

The structural topology of a DTPPF is shown in Figure 1.

In Figure 1, Q${}_{01}$ (

Table A1. Table of symbols in Text.

Number	Symbol	Description
1	$Q_{01}$	Circuit breaker
2	${\mathrm{KM}}_0$	Main contactoR
3	${\mathrm{FS}}_1$-${\mathrm{FS}}_n$	Fuse
4	${\mathrm{KM}}_1$-${\mathrm{KM}}_n$	Contactor
5	$C_s$	Equivalent capacitance of the filter capacitor bank(FCB)
6	L	equivalent inductance of the primary inductance winding of ECFR
7	$I_h$	Harmonics current generated by nonlinear loads
8	$I_f$	Harmonics current absorbed by the DTPPF
9	$X_{\left(h\right)}$	Impedance at the resonant frequency (h-th harmonic current)
10	Q	Quality factor of the ECFR
11	$Z_f$	Impedance at the resonant frequency (h-th harmonic current
12	$\omega$	Actual angular frequency of DTPPF
13	${\omega }_h$	Angular frequency of the h-th harmonic current
14	$\xi$	Resonant frequency shift
15	${\xi }_0$	Edge of the pass band-width of frequency
16	M	Highest harmonic order
17	$U_{1\left(h\right)}$	h-th harmonic voltage RMS at the power supply side
18	$U_{L\left(h\right)}$	h-th harmonic voltage RMS of the primary inductance winding of ECFR
19	$U_{C\left(h\right)}$	h-th harmonic voltage RMS of the filter capacitor
20	$U_{R\left(h\right)}$	h-th harmonic voltage RMS of the equivalent resistance of the primary inductance winding of ECFR
21	$I_{1\left(h\right)}$	h-th harmonic current RMS
22	${\theta }_{u\left(h\right)}$	Initial voltage phase angle at the power supply side
23	${\theta }_{i\left(h\right)}$	Initial current phase angle at the power supply side
24	${I_1}_{\mathrm{RMS}\left(x\right)}$	Current RMS in the filter capacitor
25	$K_{i\left(x\right)}$	Per unit value of the phase current at the power supply side
26	$I_{CN\left(x\right)}$	Rated current of the x-th filter capacitor
27	n	Number of filter capacitors
28	$f_0$	Fundamental frequency
29	$X_{f0}$	Fundamental reactance
30	$L_{\left(h\right)}$	Equivalent h-th harmonic inductance of the primary inductance winding of ECFR
31	$L_{\left(n\right)}$	Equivalent n-th harmonic inductance of the primary inductance winding of ECFR
32	$X_{L\left(n\right)}$	Equivalent n-th harmonic inductance reactance of the primary inductance winding of ECFR
33	$X_{L\left(h\right)}$	Equivalent h-th harmonic inductance reactance of the primary inductance winding of ECFR
34	$X_{C\left(n\right)}$	Equivalent n-th harmonic capacitive reactance of the filter capacitor
35	$X_{C\left(h\right)}$	Equivalent h-th harmonic capacitive reactance off the filter capacitor
36	$R_{\left(h\right)}$	Equivalent h-th harmonic resistance of the DTPPF
37	$U_{C\left(x\right)}$	Filter capacitor voltage RMS
38	$U_{C\left(1\right)}$	Voltage RMS of 1-th filter capacitor
39	$U_{C\left(n\right)}$	Voltage RMS of n-th filter capacitor
40	$U_{CN\left(x\right)}$	Rated voltage of the x-th filter capacitor
41	$K_{u\left(x\right)}$	Per unit value of the voltage for the filter capacitor
42	${\mathrm{THD}}_{\mathrm{act}}$	Total harmonic distortion caused by the even harmonic current during open-circuit fault of ECFR thyristor
43	$i_2$	Even harmonic current during DTPPF operation
44	$K_{eh}$	Per unit value of the total harmonic distortion caused by the even harmonic current
45	${\mathrm{THD}}_{\mathrm{avg}}$	Total harmonic distortion caused by the even harmonic current during normal operation of DTPPF

) is the circuit breaker, KM${}_0$ is the main contactor, FS${}_1$–FS${}_n$ are fuses, KM${}_1$–KM${}_n$ are contactors, $C_s$ is the equivalent capacitance of the filter capacitor bank(FCB), L is the equivalent inductance of the primary inductance winding of the electromagnetic coupling filter reactor (ECFR), $I_h$ is the harmonics current generated by nonlinear loads, and $I_f$ is the harmonics current absorbed by the DTPPF.

The DTPPF consists of a main circuit and a control system. The main circuit is composed of an electromagnetic coupling filter reactor (ECFR) and an FCB, forming a series filtering branch. The control system consists of a controller, trigger board (PTB), harmonic acquisition module (WD), and touch screen (TS), which are used to control the DTPPF and dynamically adjust the inductance L.

The ECFR consists of a primary inductance winding and a secondary inductance control winding connected to the thyristor PEIC. The primary inductance winding of the ECFR is connected in series with the FCB to form a filtering branch. When a certain frequency resonates (referred to as the “resonant frequency”), the harmonics current absorbed by the DTPPF is maximal, indicating the best filtering effect. The resonant frequency is equal to h times the fundamental frequency, where h is the harmonic order, and the corresponding harmonic current is called the h-th harmonic current.

Based on the h-th harmonics current and the total harmonic distortion (THD) as well as the designed absorption current, the controller determines the $C_s$ and then switches the filter capacitors on or off ($C_1$, $C_2$, …$C_x$). At the same time, the controller calculates the control signal $u_k$ through the control algorithm and outputs it to adjust L until the DTPPF resonates at the h-th frequency.

When the DTPPF operates at the rated load, the temperature increase of the filter capacitors remains within allowable limits. Nevertheless, any increase in the harmonics current accelerates this rise. When the temperature rise exceeds acceptable levels, the temperature of the insulation material increases as well, resulting in thermal aging. This causes a gradual decline in the capacitance value of the filter capacitors, ultimately shortening their lifespan. Typically, for every 7–8 °C increase in temperature, the lifespan is halved. When the filter capacitors are damaged or their capacitance decreases, the resonant frequency shifts, causing the DTPPF to become detuned, which in extreme circumstances can result in hazardous operating conditions such as burned out main contactors and fuses.

The presence of the harmonics current induces vibration in the core of the ECFR and deformation of its windings due to the resulting electromagnetic forces. In severe cases, the insulation material between windings may break down, resulting in short circuits between turns. An excessive harmonics current can cause the thyristor on the secondary side of the ECFR to break. Both phenomena impede continuous adjustment of the inductance of the primary side of the ECFR. When the thyristor on the secondary side of the ECFR fails, the resonant frequency shifts, causing the DTPPF to become detuned.

When the filter capacitors are damaged or their capacitance decreases, or when the thyristor on the secondary side of the ECFR fails, the resonant frequency shifts, causing the DTPPF to become detuned. This leads to deterioration of the filtering effect, and potentially to unsafe operation in severe cases.

2.2. Detuning Detection of DTPPF

The impedance at the resonant frequency (h-th harmonic current) and the quality factor of the ECFR are provided by

$$\left\{\begin{array}{c}{X}_{\left(h\right)}={\omega }_{h}L=\frac{1}{{\omega }_h{C}_s}=\sqrt{\frac{L}{C_s}}\\ Q=\frac{X_{\left(h\right)}}{R}=\frac{\sqrt{\frac{L}{C_s}}}{R}\end{array}\right.$$

(1)

where $X_{\left(h\right)}$ is the impedance at the resonant frequency (h-th harmonic current), Q is the quality factor, ${\omega }_h$ is the angular frequency of the h-th harmonic current, and R is the equivalent resistance of the DTPPF, the value of which is generally quite small.

The quality factor Q can characterize the sharpness of the impedance curve of the DTPPF, with the band-pass width of the frequency provided by

$$\left|Z_f\right|=\sqrt{2}R$$

(2)

where $Z_{\left(f\right)}$ is the impedance of the DTPPF and Q is the quality factor.

The resonant frequency shift is defined as

$$\xi =\frac{\omega -{\omega }_h}{{\omega }_h}$$

(3)

where $\xi$ is resonant frequency shift and $\omega$ is the actual angular frequency of the DTPPF.

Here, R is ignored because it is very small, meaning that the reactance of the DTPPF is

$$\left|X_f\right|=\left|\omega L-\frac{1}{\omega C_s}\right|$$

(4)

where $X_f$ is the inductive reactance of the DTPPF.

Substituting Equations (1) and (3) into Equation (4), we obtain

$$\left|X_f\right|=\left|\left(1+\frac{1}{1+\xi }\right)\zeta \right|X_{\left(h\right)}.$$

(5)

For $\left|\xi \right|\le 10\%$, Equation (5) can be simplified as follows:

$$\left|X_f\right|\approx 2\left|\xi \right|X_{\left(h\right)}.$$

(6)

When $|Z_f|=\sqrt{2}R$, i.e., $|X_f|=R=2\times (1/2Q)\times X_{\left(h\right)}$, the resonant frequency shift is

$${\xi }_0=\frac{1}{2}Q$$

(7)

where ${\xi }_0$ is the edge of the band-pass width frequency; when $\xi >{\xi }_0$, the DTPPF is out of resonance.

2.3. Method for Identifying Overcurrent Faults of Filter Capacitors

The overcurrent fault in the capacitors can be detected based on the magnitude of the per-unit value of the DTPPF phase current. Different combinations of filter capacitors in the DTPPF result in different allowable currents. From Equations (1) and (4), it can be observed that when a capacitor in the capacitor bank shorts, the reactance of the DTPPF decreases and the phase current increases. Therefore, by measuring the phase current of the DTPPF it is possible to identify whether the filter capacitor has experienced a short-circuit fault.

The phase voltage $u_1$ and phase current $i_1$ at the DTPPF power supply side (after FFT transformation) can yield the fundamental voltage and current as well as the harmonic voltage and current. Specifically,

$$\left\{\begin{array}{c}{u}_1=\sqrt{2}{\displaystyle \sum _{h=1}^M}{U_1}_{\left(h\right)}sin({\omega }_{\left(h\right)}t+{\theta }_{u\left(h\right)})\\ i_1=\sqrt{2}{\displaystyle \sum _{h=1}^M}{I_1}_{\left(h\right)}sin({\omega }_{\left(h\right)}t+{\theta }_{i\left(h\right)})\end{array}\right.$$

(8)

where M is the highest harmonic order and $U_{1\left(h\right)}$, $I_{1\left(h\right)}$, ${\theta }_{u\left(h\right)}$, and ${\theta }_{i\left(h\right)}$ are the h-th harmonic voltage RMS and current RMS, initial voltage phase angle, and initial current phase angle at the power supply side, respectively.

The current RMS in the filter capacitor is provided by

$${I_1}_{\mathrm{RMS}\left(x\right)}=\sqrt{\sum _{h=1}^M{I_1}_{\left(h\right)}^2}.$$

(9)

When the combination of filter capacitors ($C_1$-$C_x$) is connected, the per-unit value of the phase current at the power supply side can be obtained:

$$K_{i\left(x\right)}=\frac{{I_1}_{\mathrm{RMS}\left(x\right)}}{{\displaystyle \sum _{j=1}^n}{I}_{CN\left(x\right)}\left(j\right)}$$

(10)

where $I_{CN\left(x\right)}$ is the rated current of the x-th filter capacitor and n is the number of filter capacitors.

The steps for detecting overcurrent faults of the filter capacitors are as follows:

Step 1. Identify the overcurrent fault based on the per unit value $K_{i\left(x\right)}$; if the $K_{i\left(x\right)}$ is greater than 1, this indicates an overcurrent fault in the filter capacitors. In this case, proceed to Step 2 to identify the faulty capacitor. Otherwise, there is no overcurrent fault and the identification process ends.

Step 2. Use the elimination method to determine which capacitor has experienced an overcurrent fault. Check all the active filter capacitors one by one by disconnecting them one at a time one. For each disconnected capacitor, recalculate the per unit value $K_{i\left(x\right)}$ based on Equation (10). If the value is less than or equal to 1, this confirms that the disconnected capacitor has experienced an overcurrent fault.

2.4. Method for Identifying Overvoltage Faults of Filter Capacitors

The harmonic voltage vector of a DTPPF is shown in Figure 2.

In Figure 2, $U_{C\left(h\right)}$, $U_{L\left(h\right)}$, and $U_{R\left(h\right)}$ are h-th harmonic voltage RMS of the filter capacitors, ECFR primary reactance winding, and resistors, respectively.

The h-th harmonic voltage RMS on the power supply side is provided by

$${U_1}_{\left(h\right)}=U_{L\left(h\right)}+U_{C\left(h\right)}+U_{R\left(h\right)}.$$

(11)

The n-th harmonic inductive reactance and h-th harmonic inductive reactance are provided by

$$\left\{\begin{array}{c}{X}_{L\left(h\right)}=j2\pi h{f}_0{L}_{\left(h\right)}\\ X_{L\left(n\right)}=j2\pi n{f}_0{L}_{\left(n\right)}.\end{array}\right.$$

(12)

The fundamental inductive reactance is

$$\left\{\begin{array}{c}{X}_{f0}=2\pi f_0{L}_{\left(h\right)}=\frac{X_{L\left(h\right)}}{h}\\ X_{f0}=2\pi f_0{L}_{\left(n\right)}=\frac{X_{L\left(n\right)}}{n}.\end{array}\right.$$

(13)

From Equation (13), the h-th harmonic inductive reactance can be obtained:

$$X_{L\left(h\right)}=\frac{h}{n}{X}_{L\left(n\right)}.$$

(14)

Similarly, the h-th harmonic capacitive reactance of the filter capacitor can be obtained as follows:

$$X_{C\left(h\right)}=\frac{n}{h}{X}_{C\left(n\right)}.$$

(15)

Assuming that the resistance is a constant ($R_{\left(h\right)}=R$), according to the quality factor Q in Equation (1) the ratio of $U_{L\left(h\right)}$ to $U_{C\left(h\right)}$ and the ratio of $U_{R\left(h\right)}$ to $U_{C\left(h\right)}$ at the h-th harmonic can be calculated as follows:

$$\left\{\begin{array}{c}\left|\frac{U_{L\left(h\right)}}{U_{C\left(h\right)}}\right|=\frac{h^2}{n^2}\\ \frac{U_{R\left(h\right)}}{U_{C\left(h\right)}}=\frac{h}{n}\times \frac{1}{Q}=\frac{h}{nQ}.\end{array}\right.$$

(16)

Substituting Equation (16) into Equation (11), the relationship between $U_{1\left(h\right)}$ and $U_{C\left(h\right)}$ is obtained:

$$U_{1\left(h\right)}=U_{C\left(h\right)}-\frac{h^2}{n^2}{U}_{C\left(h\right)}+j\frac{h}{n}\frac{U_{C\left(h\right)}}{Q}.$$

(17)

The h-th harmonic voltage and phase of the filter capacitor can be derived from Equation (17):

$$\left\{\begin{array}{cc}& U_{C\left(h\right)}=\frac{U_{1\left(h\right)}}{\sqrt{{\left(1-\frac{h^2}{n^2}\right)}^2+{\left(\frac{h}{nQ}\right)}^2}}\\ & tan{{\theta }_u}_{\left(h\right)}=\frac{\left(n^2-h^2\right)Q}{nh}.\end{array}\right.$$

(18)

The filter capacitor voltage RMS is provided by

$$U_{C\left(x\right)}=\sqrt{U_{{}_{C\left(1\right)}}^2+U_{{}^{{}_{{}_{C\left(2\right)}}}}^2+U_{{}_{C\left(3\right)}}^2+\cdots +U_{C\left(n\right)}^2}.$$

(19)

Assuming the rated voltage $U_{CN\left(x\right)}$ of the x-th filter capacitor, the per unit value $K_{u\left(x\right)}$ of the voltage for the filter capacitor can be calculated by

$$K_{u\left(x\right)}=\frac{U_{C\left(x\right)}}{U_{CN\left(x\right)}}.$$

(20)

From Equation (20), it can be concluded that $U_{C\left(x\right)}$ is $K_{u\left(x\right)}$ times $U_{CN\left(x\right)}$.

Using $K_{u\left(x\right)}$, it is possible to determine whether the capacitor is overvoltage. When $K_{u\left(x\right)}>1$, the filter capacitor is overvoltage, while when $K_{u\left(x\right)}\le 1$ and $U_{C\left(x\right)}\le U_{CN\left(x\right)}$ the filter capacitor voltage is normal.

Filter capacitors can withstand overvoltage for a short period of time. However, if the duration of overvoltage exceeds the allowed value (see

Table 1. Allowable duration of filter capacitor under overvoltage.

Per Unit Value of Voltage	Allowable Duration
1.10	8 h/24 h
1.15	30 h/24 h
1.20	5 h/24 h
1.30	1 h/24 h

) this can lead to the breakdown of the filter capacitor.

2.5. Method for Identifying Open-Circuit Fault of ECFR Thyristor

When the thyristor on the secondary side of the ECFR is disconnected, the impedance of the positive and negative half cycles is unequal, resulting in an even harmonics current in the DTPPF phase current.

The total harmonic distortion caused by the even harmonics current during an open-circuit fault of the ECFR thyristor is

$${\mathrm{THD}}_{\mathrm{act}}=\frac{\sqrt{{\displaystyle \sum _{k=0}^q}{i}_{2\left(2k\right)}^2}}{{I_2}_{\mathrm{RMS}\left(x\right)}}\times 100$$

(21)

where q is a constant and takes the values 1, 2, ⋯.

The per-unit value of the total harmonic distortion caused by the even harmonics current is

$$K_{eh}=\frac{\mathrm{TH}{\mathrm{D}}_{\mathrm{act}}}{\mathrm{TH}{\mathrm{D}}_{\mathrm{avg}}}$$

(22)

where THD${}_{\mathrm{avg}}$ is the total harmonic distortion caused by the even harmonics current during normal operation of the DTPPF.

When $K_{eh}$ > THD${}_{\mathrm{avg}}$, this indicates an open-circuit fault in the ECFR thyristor. Otherwise, the thyristor is operating normally. On this basis, together with the magnitude of the $K_{eh}$, open-circuit faults in the thyristor can be identified.

2.6. Fault Characteristic Parameters of Core Devices

The fault characteristic parameters of the core devices are summarized based on the research results from Section 2.3, Section 2.4 and Section 2.5, as follows:

• The characteristic parameter of overcurrent faults of filter capacitors is the per-unit value of the phase current at the power supply side. If there is an overcurrent fault in the filter capacitors, $K_{i\left(x\right)}$ > 1; otherwise, $K_{i\left(x\right)}\le 1$.
• The characteristic parameter of overvoltage faults of filter capacitors is the the per-unit value of the voltage for the filter capacitors. If there is an overvoltage fault in the filter capacitors, $K_{u\left(x\right)}$ > 1; otherwise, $K_{u\left(x\right)}\le 1$.
• The characteristic parameter of open-circuit faults of the ECFR thyristor is the per-unit value of the total harmonic distortion caused by the even harmonics current. If there is an open-circuit fault in the ECFR thyristor, $K_{eh}>1$; otherwise, $K_{eh}\le 1$.

2.7. Monitoring Parameters of DTPPFs

2.7.1. Running State Parameters

The running state parameters of a DTPPF mainly include electrical parameters, operating parameters, running signals, control signals, and contact state signals, as listed in

Table 2. Running state parameters of DTPPFs.

Type of Parameter	Name of Parameter	Symbol
Electrical parameter	U-phase voltage/V	$U_u$
	V-phase voltage/V	$U_v$
	W-phase voltage/V	$U_w$
	THD${}_i$/%	$I_{rate}$
Operating parameter	Fundamental current/A	$I_{fmt}$
	U-phase h-th harmonics current/A	$I_{umain}$
	V-phase h-th harmonics current/A	$I_{vmain}$
	W-phase h-th harmonics current/A	$I_{wmain}$
Running signal	Power on	$S_{on}$
	Running	$S_{run}$
Temperature	ECFR temperature	$T_1$
	Filter capacitor C1 temperature	$T_2$
	Filter capacitor C2 temperature	$T_3$
	Filter capacitor C3 temperature	$T_4$
Control signal	Thyristor $u_k$	$L_{uk}$
Contact state signal	Switch on filter capacitor	$C_{use}$

.

2.7.2. Data for Monitoring Core Device Failure

In order to identify faults in the core devices of a DTPPF, it is necessary to first obtain the required data. These include the harmonic order of the current or voltage, which is set to 13 (h = 2–13).

Table 3. Data required for monitoring faults in the core devices of DTPPFs.

Fault Identification Algorithm	Name of Parameter	Symbol	Obtained by
Equation (9)	U-phase h-th harmonics current/A	$i_{u1}$(h)	Power supply current $i_1$
	V-phase h-th harmonics current/A	$i_{v1}$(h)
	W-phase h-th harmonics current/A	$i_{w1}$(h)
Equation (21)	U phase-h-th harmonics current/A	$i_{u2}$(h)	Filtering branch current $i_2$
	V-phase h-th harmonics current/A	$i_{v2}$(h)
	W-phase h-th harmonics current/A	$i_{w2}$(h)
Equation (18)	U-phase h-th harmonics voltage/V	$u_{u1}$(h)	Power supply voltage $u_1$
	V-phase h-th harmonics voltage/V	$u_{v1}$(h)
	W-phase h-th harmonics voltage/V	$u_{w1}$(h)
Equation (10)	Rated current of C1/A	$I_{CN1}$	Filter capacitor
	Rated current of C2/A	$I_{CN2}$
	Rated current of C3/A	$I_{CN3}$
	Rated current of C4/A	$I_{CN4}$
Equation (20)	Rated voltage of Filter capacitors/V	$U_{CN}$	Filter capacitor

reports the necessary data for monitoring faults in core devices.

2.7.3. Fault Type Parameters

Different types of faults in DTPPFs can be determined based on the real-time data from Table 3 and the fault characteristic parameters of the core devices mentioned in Section 2.6. In this study, the filter capacitors are divided into four groups, as shown in

Table 4. Fault type parameters of DTPPFs.

Fault Type	Fault Device	Symbol
Overcurrent fault	Filter capacitor C1	$F_{C1S}$
	Filter capacitor C2	$F_{C2S}$
	Filter capacitor C3	$F_{C3S}$
	Filter capacitor C4	$F_{C4S}$
Overvoltage fault	Filter capacitor C1	$F_{C1V}$
	Filter capacitor C2	$F_{C2V}$
	Filter capacitor C3	$F_{C3V}$
	Filter capacitor C4	$F_{C4V}$
Open-circuit fault	ECFR thyristor	$F_{L1S}$

.

3. Monitoring System Architecture and Software Architecture

3.1. Monitoring System Architecture

The proposed cloud server-assisted remote monitoring and fault identification system for DTPPF is mainly composed of monitoring terminals, a cloud server, and devices such as computers or cellphones. The system architecture is shown in Figure 3.

As shown in Figure 3, the monitoring terminal consists of DTPPF${}_1$–DTPPF${}_y$, ST${}_1$–ST${}_y$, and DC${}_1$–DC${}_y$. DTPPF${}_1$–DTPPF${}_y$ are the y installed DTPPFs, while ST${}_1$–ST${}_y$ are the temperature acquisition circuits of the core devices responsible for monitoring the temperatures of DTPPF${}_1$–DTPPF${}_y$; the data acquisition modules DC${}_1$–DC${}_y$ communicate with the controllers of PDF${}_1$–PDF${}_y$ to obtain their electrical parameters.

The data collected by DC${}_1$–DC${}_y$ are transmitted to the back-end service layer of the cloud server through a wireless communication network (WCN) and stored in a database after parsing. The front-end application layer of the cloud server uses a local computer to read data from the database and visualize these data to achieve human–machine interaction. In addition, users can browse the running state parameters of the DTPPF and the fault information of the core devices for further analysis.

Figure 4 presents the hardware used in the data acquisition module.

In Figure 4, adopted the microprocessor is of the STM32F405VGT6 type and the communication module is a GPRS communication module. The temperature is detected by LM75 temperature sensors, which have a measurement range of −55–125 °C and a measurement accuracy of 0.125 °C. These are responsible for obtaining the temperature signals T${}_1$ of the ECFR and T${}_2$–T${}_5$ of the filter capacitors.

3.2. Software Architecture of the Cloud Server

The cloud server consists of a front-end application layer, a back-end service layer, and a database. The workflow of the cloud server is shown in Figure 5.

As shown in Figure 5, the workflow of the cloud server is as follows:

Step 1. The software in the front-end application layer sends a request to the back-end service layer (1).

Step 2. The back-end service layer finds the corresponding method (2) to process the request (3) and executes the program. It then accesses the database through business logic to perform operations such as CRUD (create, read, update, and delete) (4).

Step 3. The back-end service layer retrieves the data (known as “dynamic resources”) from the database and processes them (5). It then encapsulates the database results (6) and returns them to the front-end application layer (7).

Step 4. The front-end application layer displays the results of the request in the form of charts (known as “static resources”).

3.2.1. Software Architecture of the Front-End Application Layer

A data module is designed to display the running state parameters and historical data. The web page information browsing service is used to display the running state parameter page and historical data monitoring page. The running state parameter page shows the running state parameters of the monitoring terminals (see Table 3). The historical data monitoring page displays the historical data of the user’s monitoring terminals in charts.

The functional modules of the front-end application layer are presented in Figure 6.

To ensure loose coupling, flexibility, and reusability of the frontend application layer, the MVVM design pattern is adopted to separate the view layer and the business logic layer. The software architecture of the front-end application layer is constructed as shown in Figure 7.

The view layer (View) serves as the entrance for users to interact with the cloud server, including a registration and login view, data module view, user management module view, fault alarm view, and log recording view. Among these, the user management module view is only accessible to administrators.

The business logic layer (ViewModel) is an intermediate layer and a key component of the front-end application layer. It orchestrates the interactions between the view layer and the model layer. It is responsible for logic control for users and permission control and logic control for administrators.

The model layer (Model) stores temporary data of front-end pages and interfaces with the ViewModel. It stores data from registration and login, data module, permission management module, fault alarm and log recording, etc., and processes the data of the ViewModel. When the ViewModel requests data from the back-end service layer, the model layer caches these data.

3.2.2. Software Architecture of the Back-End Service Layer

The back-end service layer can bind users with monitoring terminals, ensuring accurate retrieval of data from a specific monitoring terminal. To meet real-time data requirements, appropriate listening protocols are selected to provide uniform interface support for the front-end application layer and responsibility for requests. The back-end service layer handles the business logic processing of the functional modules shown in Figure 6 and access to the database through the corresponding business logic.

The uniform interface of the back-end service layer serves as the communication path for “sending requests” and “sending back results” between the front-end application layer and the back-end service layer. It plays a crucial role in connecting the two layers. In this study, the Express framework based on node.js is used to provide web services specifically for building single-page, multi-page, and hybrid modes. WebSocket, a full-duplex communication protocol, is used to listen to the parameters required for monitoring core device faults and diagnosing fault situations. Furthermore, HTTP, a reliable hypertext transfer protocol, is applied to listen to the running state parameters. Additionally, the WebService interface pushes fault information to users’ cellphones. The listening process of the back-end service layer parses the received data packets based on the respective protocols.

Figure 8 shows the software architecture of the back-end service layer.

3.2.3. Software Architecture of the Cloud Server

The software architecture of the cloud server was designed using the LAMJ architecture, and is depicted in Figure 9.

3.3. Data Block Design

To store the fault characteristic parameters and monitoring data of a DTPPF, it is necessary to design tables for the monitoring parameter data table, including the running state parameter table, core device fault monitoring data table, fault characteristic data table, and fault type table. Among these, the core device fault monitoring data table has too many fields, which can affect query efficiency. Therefore, it needs to be split into data tables for the power supply current, filtering branch current, power supply voltage, and rated current and nominal voltage of the filter capacitor according to different fault identification methods. In this paper, we designed a total of eleven main tables in the database, as shown in

Table 5. Information of the main tables included in the database.

Number	Table Name	Note
1	DTPPF_runpara	Running state parameter table
2	power_i	Power supply current data table
3	Filter _i	Filter branch current data table
4	power-u	Power supply voltage data table
5	capa-ui	Data table for rated current and voltage of filter capacitor
6	DTPPF_faultpara	Fault characteristic parameter table
7	DTPPF_faulttype	Fault type parameter table
8	user	User information data table
9	log	Log record data table
10	role_permissions	Role-based permission data table
11	monitor_terminal	Monitoring terminal data table

.

4. Function Design of the Back-End Service Layer

According to the uniform interface and software architecture of the back-end service layer, its software and functions are designed using the node.js development platform.

4.1. Uniform Interface of the Back-End Service Layer

The uniform interface of the back-end service layer is designed using the REST. The design process includes resource identification, resource representation, URI design, and HTTP methods. The design process is shown in Figure 10.

Resource identification refers to categorizing and identifying interactive resources to obtain monitoring terminal resources and user resources. Specifically, the monitoring terminal resources are obtained through the monitoring terminal interface (/device), abstracting the corresponding data of the monitoring terminal to support the business logic processing of the back-end service layer’s data module and fault alarm page. User resources are obtained via the user interface (/user), and mainly provide business logic processing functions for registration, login, permission management, and recording fault alarms and logs in the back-end service layer.

On the basis of resource identification, the JSON format is used as the form of resource representation to design the resource representation, including entity header design and representation format design. The entity header is the specific format that the browser uses to submit requests to the back-end service layer via Accept, while the representation format is the form in which the back-end service layer informs the browser about the representation of resources based on the content type.

The Uniform Resource Identifier (URI) identifies and specifies the location of resources, namely, the server address and port number. In this paper, Uniform Resource Locator (URL) is used to identify resources. URL is an application of URI that has the ability to identify resources such as URI and provides a special structure for locating resources.

The design of the URL structure is shown in Figure 11.

As shown in Figure 11, the URL mainly consists of the protocol name, server IP address or domain name, port number, one or multiple segments of paths, and query strings. The URL uses the forward slash separator to divide the hierarchy.

HTTP methods such as GET, POST, PUT, and DELETE are adopted to design interfaces to handle different resources, that is, to perform CRUD (create, read, update, delete) operations on the server’s resource data to ensure the consistency of the back-end interfaces.

Table 6. Commonly data retrieval interfaces used in the monitoring system.

Resource	URL	HTTP Method	Description
Homepage	*	GET	Home page
Login	*	POST	Login system
Registration	*	POST	Register an account
Running status	*	POST	Obtain running state parameters
Historical data	*	POST	btain historical monitoring data
Fault alarm	*	POST	Obtain fault alarm information
User management	*	GET	Query user information
Role management	*	GET	View user role
Permission management	*	GET	View user permission
Operation logs	*	GET	View user operation logs

* URL in table, the manufacturer does not agree to publish a valid website.

provides the most commonly used data retrieval interfaces in the monitoring system.

4.2. Router Management

Router management refers to handling of REST-style uniform interfaces and URL resource parsing based on requests from the front-end application layer. It is implemented using the Express application framework in the node.js development platform. All REST-style uniform interfaces are defined in the “routes” file of the project. The router finds the corresponding business logic processing based on the URL in the request from the front-end application layer.

The initial steps for building the router are as follows:

Step 1. Import the Express router module, then instantiate the router through the express.Router() method.

Step 2. Build the router table using the Express router mechanism. The routes are defined by the app.method(path, handler) method. Here, app is the cloud server object of Express, method is the HTTP request method, path is the URL resource accessed by the browser, and handler is the callback function when the router is triggered, which is responsible for executing the corresponding resource’s business logic.

After the router is initially built, whenever a user makes a request from the front-end, the URL resource in the request is parsed through the body-parser middleware. Then, the server IP address and target router information for processing the request are obtained and matched to the corresponding router. After receiving the resource, the router triggers the callback function to perform database operations, returns the results from the database, encapsulates the data in JSON format, and returns them to the front-end application layer.

4.3. Access Verification

When a user attempts to log in, they need to access the database and check the user table for user login permission. To this end, a class needs to be created to handle database connections. If the access path contains “login.html” or “/loginServlet”, the interceptor allows the user to access the login page. Otherwise, the user accesses a non-login page; in this case, it is necessary to check whether the Session object in the cloud server contains information about the accessing user. If the user logs in successfully and the Session object contains the user’s login information, the interceptor allows access. If the user has not logged in and the Session contains no user information, the page shows a “Please log in” prompt and then redirects the user to the login page.

Figure 12 shows the flowchart for access verification.

4.4. User and Monitoring Terminal Binding

(1) After the user successfully logs in, they enter their assigned term _id. The back-end service layer completes the binding process through the onBind() callback in the Bind script. This process involves querying the “monitor_terminal” table in the database to check whether the term_id is already bound to another user.

(2) If the query result is negative, the binding is successful and a prompt message saying “Binding succeeded” is displayed. If the query result is positive, the binding is canceled, and a prompt message saying “This monitoring terminal has been bound to another user” is displayed.

(3) After binding is completed, the monitoring terminal transmits monitoring data. When the cloud server detects data sent by the bound terminal on port 7201 through the WebSocket or HTTP protocol, the back-end service layer parses the data and stores them in the corresponding table in the database. Figure 13 illustrates the process of binding between the user and the monitoring terminal.

5. Design of Front-End Application Layer Function Pages

5.1. Registration and Login Page

The user account information for the monitoring system is stored in the “user” table. On the registration page, a Form is created through HTML language. To prevent repeated form submissions, a random captcha is generated through the MyCaptcha class.

After the user submits registration information, the front-end application layer sends the registration information to the back-end service layer interface to verify the captcha. If captcha verification fails, the user is redirected to the registration page. If captcha verification is successful, the back-end service layer checks the user table in the database for the existence of the user’s registration ID. If the user ID already exists, a prompt message “Current user ID already exists, please register again” is returned. If the user ID does not exist, the user information is written to the user table and a prompt message “Registration succeeded” is returned, followed by redirection to the homepage of the monitoring system.

Upon entering the login page, the user is prompted to enter their username (user_name) and password (user_pass). If the input is empty or does not meet the predefined conditions, the user is prompted to re-enter the information according to the requirements. The front-end application layer performs basic logic validation on the username and password to exclude invalid user access in advance, reducing the load on the database and preventing malicious attacks. When the basic validation is passed, the login request is sent to the back-end service layer, which then checks whether the username and password exist in the user table and whether they are correct. Finally, the result is returned.

5.2. Data Module Page

5.2.1. Running State Parameter Page

The running state parameter page includes a data table displaying the running state parameters of the DTPPF and a dropdown selection box to choose the monitoring terminal. The user can select the desired monitoring terminal from the dropdown box located in the top left corner. When the selection is made, View receives the status query command and sends the request to ViewModel. ViewModel encapsulates the request interface using Axios, which sends an ajax request to the backend service layer. After the request is triggered, ViewModel sends the request to the back-end service layer, where the interface parses the request, matches the specified route, processes the request through a callback function, and finally returns it to ViewModel. View then updates the running state parameters through two-way data binding.

The time sequence of the running state parameter operation is shown in Figure 14.

5.2.2. Historical Data Monitoring Page

The historical data monitoring page records the historical data of each parameter for each monitoring terminal. The data can be displayed in three different formats (table, line chart, and bar chart), which can be selected through the icon in the top right corner. These data are visualized by Apache E-Charts.

The process of querying the historical data of a monitoring terminal is shown in Figure 15.

5.3. User Management Page

The user management page includes user information, role management, and permission management. User information includes user ID, login name, user type, status, creation time, last update time, and operation.

When the administrator clicks on user information, the front-end application layer sends a request to the back-end service layer. Subsequently, the RoleController in the back-end service layer accesses the database and queries all users in the user table. The retrieved data are then returned to the front-end business logic layer for rendering and display in the user information page, and the administrator can perform operations such as querying, updating, and deleting users. User queries are submitted by clicking the button in the top right corner and submitting the query form. To delete a user, the user ID of the selected user is stored in the Session object. The front-end application layer requests the userDelete(userID) method in the back-end service layer to delete the user using the user_id field in the user table. The parameter userID represents the user_id in the Session object. If the user_role field in the user table is 0, this indicates that the user is an administrator; in this case, the deletion fails. The database has the ability to roll back to avoid dirty reads, repeated reads, and phantom reads, which could greatly decease the accuracy and integrity of the data.

In the role management page, the administrator can assign access permissions to users, such as the permission to view historical data. Unauthorized users cannot query the historical data of monitoring terminals. After clicking on assigning permissions, the Session object records the role type role_id and the front-end application layer sends a request. The back-end service layer then calls the searchRoleRoot(roleID) method and accesses the role_permissions table in the database. The root_num field is used to determine whether the permission belongs to a first-level permission or a second-level permission (the front-end application layer uses the ztree component to display the permission categories in a tree format). If the root_state is 1, this means that the permission is disabled. The query is performed through the intermediate table between the user table and the role_permissions table, and the result is returned to the front-end application layer for display.

The permissions of the entire monitoring system can be managed in the permission management page through CURD operations, facilitating subsequent system permission maintenance and upgrades. For example, when deleting the data module permission, the front-end application layer sends a request and the back-end service layer calls the deleteRoot(rootNum) method, checks the role_permissions table, and displays all permissions on the page. The Session object records the permission code role_num. The parameter rootNum is the same as role_num. When deleting the data module, parent_num is queried based on root_num. If parent_num%1000 = 0, this means that the permission belongs to a first-level permission, in which case the operation can only be performed after deleting all the second-level permissions it belongs to and cannot be deleted otherwise. When deleting the running state parameter, the back-end service layer calls the deleteRoot() method, checks whether it belongs to a second-level permission, directly deletes it, and returns a “Delete successful” prompt. If the root_state field is 1, this means that the permission is disabled.

5.4. Fault Alarm Page

The fault alarm page includes the display of the core device faults of the monitoring system and the remote control of DTPPF shutdown. The back-end service layer listens to the required parameters for device fault monitoring of the DTPPF via WebSocket. WebSocket calls the saveDeviceData() method in the back-end service layer with the corresponding field in the data and saves the parameters in the power_i, filter_i, power_u, and capa_ui tables. Then, the per-unit values of the core devices are calculated and stored in the DTPPF_faultpara table by calling the saveFaultPara() method in the back-end service layer. Based on these values, any faults in the core devices can be determined. When a fault occurs, the back-end service layer queries the user table to retrieve the user’s mobile number. It then uses a third-party WebService interface to push the fault information to the user’s mobile phone. The fault information is stored in the DTPPF_faulttype table for display in the front-end application layer. Users can remotely command the DTPPF to stop using the “stop device” button on the fault alarm page.

5.5. Log Recording Page

The log recording page is primarily used to define the operation type of each method before the method is used. After the method is called, the back-end service layer automatically records the user’s operation information, including the type name, method name, method parameters, etc. In addition, it records the CURD operations (login, delete, read, query) and time.

6. Experimental Verification

The proposed cloud server-assisted remote monitoring and fault identification system for DTPPFs consists of a monitoring system architecture and cloud server software architecture along with the software design of the back-end service layer and functionality design of the front-end application layer. It was successfully applied to monitoring of 25 DTPPFs to provide fault alarms, fault recall, and fault diagnosis while allowing users to view various DTPPF operating states through the internet in real time.

In our experiments, the monitoring object was the No. 1 medium-frequency furnace in a metal smelting plant in Nanjing City, China. The measured fundamental current and fifth harmonic current in the distribution room at a specific moment are shown in Figure 16.

6.1. Monitoring Example

Figure 17 shows photographs of DTPPF used in the experiments.

In Figure 17, the DTPPF core devices consist of four filter capacitors of 10 kVar, 20 kVar, 50 kVar, and 60 kVar along with an ECFR. The turn ratio between the primary winding and secondary winding of the ECFR is 1:5.

6.2. Monitoring Result Analysis

Users can browse the running state parameters and fault information of core devices of DTPPF and take appropriate actions via a computer or cellphone. Figure 18, Figure 19, Figure 20 and Figure 21 present examples of the page display results.

In Figure 18, 0 indicates no fault and 1 indicates a fault.

In Figure 19, the user selects the monitoring terminal to be viewed through the drop-down box in the upper left corner to display the running status parameters. Historical curves can be displayed as well.

In Figure 20, the orange broken line represents the fifth harmonic current at the load of the medium-frequency electric furnace and the blue broken line represents the fifth harmonic current injected into the distribution network.

In Figure 21, the user selects the monitoring terminal to be viewed through the drop-down box in the upper left corner and displays the fault device, fault type, and time when the fault occurs. The figure shows the fault alarms of No. 1 medium-frequency furnace.

The cloud server-assisted remote monitoring and fault identification system for DTPPFs succeeded in the experimental verification. The system was able to monitor the operation status of the DTPPF and effectively identify the faults in the DTPPF core devices.

7. Conclusions

DTPPFs are effective for the dynamic tuning and suppression of power harmonics in industrial applications. However, during long-term operation, faults or aging of core devices such as the filter capacitors and thyristors in the ECFR can lead to deteriorated filtering performance or even complete malfunction. Additionally, the electrical parameters and operational status of DTPPFs cannot currently be remotely operated or monitored, and there is no early warning system in place to promptly address such faults. To address these issues, the present paper focuses on methods for identifying faults in the core devices of DTPPFs. A cloud server-assisted remote monitoring and fault identification system for DTPPFs is developed that can effectively identifies faults in the core devices of DTPPFs. Our experimental results demonstrate that remote real-time monitoring of the operational status of DTPPFs can be achieved utilizing online monitoring technology and by designing a database to store the relevant operational parameters. Our research findings provide a theoretical foundation for harmonic mitigation in low-voltage distribution networks in industrial power grids. However, in this study we monitored only a few dozens DTPPFs. When monitoring hundreds of DTPPFs or more, the impact of high-concurrency data on the cloud server needs to be taken into consideration; we intend to investigate this topic in our future work.