**Fault Current Tracing and Identification via Machine Learning Considering Distributed Energy Resources in Distribution Networks †**

#### **Wanghao Fei and Paul Moses \***

School of Electrical and Computer Engineering, University of Oklahoma, Norman, OK 73019, USA; whf@ou.edu **\*** Correspondence: pmoses@ou.edu

† This paper is an extended version of our paper published in In Proceedings of the 2019 IEEE 7th International Conference on Smart Energy Grid Engineering (SEGE), Oshawa, ON, Canada, 12–14 August 2018; pp. 196–200.

Received: 11 October 2019; Accepted: 11 November 2019; Published: 14 November 2019

**Abstract:** The growth of intermittent distributed energy sources (DERs) in distribution grids is raising many new operational challenges for utilities. One major problem is the back feed power flows from DERs that complicate state estimation for practical problems, such as detection of lower level fault currents, that cause the poor accuracy of fault current identification for power system protection. Existing artificial intelligence (AI)-based methods, such as support vector machine (SVM), are unable to detect lower level faults especially from inverter-based DERs that offer limited fault currents. To solve this problem, a current tracing method (CTM) has been proposed to model the single distribution feeder as several independent parallel connected virtual lines that traces the detailed contribution of different current sources to the power line current. Moreover, for the first time, the enhanced current information is used as the expanded feature space of SVM to significantly improve fault current detection on the power line. The proposed method is shown to be sensitive to very low level fault currents which is validated through simulations.

**Keywords:** current tracing; fault current; distributed energy resources; network model

#### **1. Introduction**

Due to the increasing penetration rate of distributed energy sources (DERs), such as solar power injected at the distribution side of the power system, during the past decade, distribution grids have become large, complex, interconnected networks. The infusion of DERs onto distribution grids raises some new state estimation challenges, such as fault current identification, which was less of an issue in conventional distribution grids operating without DERs.

The traditional distribution grid was not affected by irregular back power feeds caused by intermittent DER activity, as it was originally designed for single direction power flow from the substation to the customers. The ordinary fault current identification process is based on the fault current threshold where no DERs are injected into the distribution grid. With DERs, excess power can be generated and consumed by the customer or feed back to the distribution feeder. This raises new challenges, especially in grid modeling methods for fault current identification, where the impact of back feed power flow has to be considered for determining the fault current threshold. Failure to do so may have far reaching and costly consequences such as inadvertent tripping of circuits or overlooking faults in the system.

Researchers have proposed many grid modeling methods for different types of power grids such as averaged models [1,2] and the port-Hamiltonian-based dynamic power system model [3]. Certain modeling methods are suited for specific parts of the grid such as cyber-physical power systems

framework modeling [4,5], topology modeling [6,7], load flow modeling [8,9], lightning protection models [10], and traveling wave modeling [11]. In [12,13], the author used pattern recognition to identify the fault current with the waveform data, which is an efficient tool for power transmission line fault detection. In addition, with the benefit of fast developing artificial intelligence (AI) technologies, many AI-based power system fault identification methods have been proposed as well, such as support vector machine (SVM) [14], k-nearest neighbors algorithm (KNN) [13], pattern recognition [15], and deep learning [16].

Although different AI methods have been used to improve the accuracy of power system fault identification, the approaches still heavily rely on grid modeling methods for some part of the power grid. Most importantly, almost all of these AI-based fault current identification methods based on existing grid modeling methods totally depend on the existing power line infrastructure, in that currents from different power sources are congested to one end of a single power line and flow towards the other end [17–19]. These methods are very effective when it comes to the identification of larger fault currents, but some detailed current information such as those from inverter-based DERs are difficult to detect. A much more detailed grid modeling method is needed to augment the AI method to be more sensitive to detect some lower level faults. This is particularly important in modern distribution grids, as inverter-based DERs are known to produce exceptionally small fault current contributions, due to inverter current limiting action, and are very difficult to detect through conventional means.

For addressing the aforementioned grid modeling problems, a detailed grid model (referred to herein as the CTM) was proposed by the authors in a companion paper [20], which has sufficient detail of the current flows on the power line from each individual DER connected to the grid. The main objectives of this paper are as follows. First, for the first time, it is shown how the accuracy of implementing AI algorithms on such a detailed grid model can be improved. Specifically, implementing SVM algorithm on the proposed CTM model is explored. Second, in addition to using fault current flows as the only input feature, the "traced" current information to expand the dimension of the feature space is exploited. That is, the traced current is used along with the power line current as the expanded feature space to identify the fault current which is a departure from existing methods. Finally, the performance of the combination of CTM with the SVM is demonstrated in the practical scenario of fault identification with DERs operating in distribution grids. Specifically, this work shows how applying this hybrid method can improve sensitivity in detecting very low level faults.

This paper is organized as follows. In Section 2, the weaknesses of using traditional grid models for fault current identification are pointed out, and applying CTM for multiple current sources of a distribution grid is proposed. The SVM method is implemented for fault current identification using the traced current in Section 3. Simulation results are presented in Section 4 and are discussed in Section 5, with concluding remarks given in Section 6.

#### **2. Proposed Tracing Method**

#### *2.1. Single Power Line Fault Current Threshold*

Consider the case where a DER group consists for example of solar and wind generation, a vehicle-to-grid support battery storage, and loads that are attached to bus 1 are connected to the end of the power distribution grid through a single power line as shown in Figure 1.

**Figure 1.** Single power line with distributed energy source (DER) customers.

In Figure 1, -*IL* represents the power line current, and *U*- <sup>1</sup> and *U*- <sup>2</sup> are the voltages on buses 1 and 2, respectively. The applied voltage difference angle of *U*- <sup>1</sup> <sup>−</sup> *<sup>U</sup>*- <sup>2</sup> is *ψ*. Without the impact of the DER group, -*IL* flows from bus 2 to bus 1 and the fault current can be easily identified by setting the fault current threshold. However, when the impact of renewable energy sources is considered, as in this case, the fault current threshold is difficult to determine, as the DERs may contribute to the fault current and the detection threshold varies. The power line's current value and direction may also vary with the impact of DERs, which complicates the discrimination of faults from the normal condition. It is therefore necessary to know significantly more details of the current to determine if there is a fault on the power line or at the load.

#### *2.2. Current Tracing*

Using Figure 1 to demonstrate the CTM deduction, without loss of generality, it is assumed that the power line impedance is

$$Z = R + jX,\tag{1}$$

where *R* > 0 and *X* > 0 are the resistance and reactance of the power line, respectively. An alternative case, when *X* < 0, is discussed in the companion conference paper [20]. In this paper, only the *X* > 0 case is considered. The impedance angle is *θ*. Based on Kirchhoff's current law, it follows that

$$I\_L = \sum I\_i e^{i\phi\_i}.\tag{2}$$

where -*Ii* = *Iie<sup>j</sup>φ<sup>i</sup>* is the current of the *i*th DER, and *Ii* > 0 and *φ<sup>i</sup>* are the magnitude and phase angle of -*Ii*, respectively.

Figure 1 can be expressed with an equivalent circuit as shown in Figure 2a. The equivalence holds as shown in Equations (3) and (4):

$$R\_E = \frac{R^2 + X^2}{R},\tag{3}$$

$$X\_E = \frac{R^2 + X^2}{X},\tag{4}$$

where *RE* > 0 and *XE* > 0 are the equivalent resistance and reactance respectively. Naturally, the equivalent circuit has the same total resistance, current, and power of the original circuit.

**Figure 2.** Equivalent circuit.

In the equivalent circuit, the power line current -*IL* is virtually split into two parts defined as active current -*ILR* and reactive current -*ILX*, which flows through *RE* and *XE*, respectively:

$$
\vec{I}\_L = \vec{I}\_{LR} + \vec{I}\_{LX\_Y} \tag{5}
$$

$$I\_{LR}' = I\_{LR}e^{j\psi} \, \_\prime \tag{6}$$

$$I\_{LR} = I\_L \cos(\theta),\tag{7}$$

$$\mathcal{I}\_{LX} = I\_{LX} e^{j(\psi - \frac{\pi}{2})},\tag{8}$$

$$I\_{LX} = I\_L \sin(\theta),\tag{9}$$

where *ILR* and *ILX* are the magnitude of the active current and reactive current, respectively. Likewise, all current sources attached to bus 1 follow the same rule:

$$
\vec{I}\_i = \vec{I}\_{Ri} + \vec{I}\_{Xi} = I\_{Ri}e^{j\psi} + I\_{Xi}e^{j\left(\psi - \frac{\mu}{2}\right)},\tag{10}
$$

$$I\_{Ri} = I\_{Li} \cos(\psi - \phi\_i),\tag{11}$$

$$I\_{Xi} = I\_{Li} \sin(\psi - \phi\_i),\tag{12}$$

where *IRi* and *IXi* are the magnitude of the active and reactive current from-*Ii*, respectively, which could either be positive or negative. From Kirchhoff's current law,

$$\sum\_{I\_{Ri}>0} \left(\check{I}\_{Ri}\right) + \sum\_{I\_{Ri}<0} \left(\check{I}\_{Ri}\right) = \sum \left(\check{I}\_{Ri}\right) = \check{I}\_{LR\prime} \tag{13}$$

$$\sum\_{I\_{Xi}>0} \left(\check{I}\_{Xi}\right) + \sum\_{I\_{Xi}<0} \left(\check{I}\_{Xi}\right) = \sum \left(\check{I}\_{Xi}\right) = \check{I}\_{LX} \tag{14}$$

where ∑ *IRi*>0 (-*IRi*) and ∑ *IRi*<0 (-*IRi*) stand for the positive and negative part of -*ILR*, respectively, and ∑ *IXi*>0 (-*IXi*) and ∑ *IXi*<0 (-*IXi*) represent the positive and negative part of -*ILX*, respectively. The positive part is responsible for supplying the load as well as feeding extra current to the power distribution grid. The negative part is responsible for absorbing current from positive part. The *j*th positive current source flowing through the power line is

$$I\_{LRj}^{+} = I\_{LRj}^{+} e^{j\psi},\tag{15}$$

$$I\_{LXj}^{+} = I\_{LXj}^{+} e^{j(\psi - \frac{\pi}{2})} \, , \tag{16}$$

$$I\_{LRj}^{+} = \frac{I\_{LR} I\_{Rj}}{\sum\_{I\_{Ri} > 0} (I\_{Ri})} \, ^{\prime} \tag{17}$$

$$I\_{LXj}^{+} = \frac{I\_{LX}I\_{Xj}}{\sum\_{I\_{Xi} > 0} (I\_{Xi})}.\tag{18}$$

where -*I* + *LRj* is the active part of the *j*th positive current source flowing through the power line with magnitude of *I* + *LRj*, and-*I* + *LXj* is the reactive part of the *j*th positive current source flowing through the power line with magnitude of *I* + *LXj*. Therefore, the distribution grid model where each of the currents are independent from one another can be shown in Figure 2b.

Combining the active and reactive components of the *j*th positive current source flowing through the power line, the equivalent circuit with part of the *j*th positive current source that flows through the power line can also be derived such that -*I* + *LZj* <sup>=</sup> -*I* + *LRj* <sup>+</sup>-*I* + *LXj*, with its impedance, *ZEj*, as shown in Figure 3. The complete derivation of this situation can be found in the companion paper [20].

**Figure 3.** Equivalent circuit of impedance lines.

#### **3. Support Vector Machine and Current Tracing Kernel**

#### *3.1. Binary Classification Problem Formation*

Given a set of power line current measurements *<sup>Z</sup>* <sup>=</sup> {*zi*, *<sup>i</sup>* <sup>=</sup> 1...*n*}, *zi* <sup>∈</sup> <sup>R</sup>*<sup>m</sup>* that may or may not contain fault current and the set of labels *Y* = {*yi*, *i* = 1...*n*}, *yi* ∈ {0, 1}, *m* stands for the dimension of the measurement, and *n* is the number of observations. The fault current identification problem can be modeled as a binary classification problem by establishing the connection between the above two sets such that

$$y\_i = \begin{cases} -1 & \text{if } a\_i = 0, \\ 1 & \text{if } a\_i \neq 0. \end{cases} \tag{19}$$

*yi* = 1 indicates that the *i*th current measurement is fault current, or, alternatively, there are no fault currents for *yi* = −1.

#### *3.2. Support Vector Classifiers*

The classification problem is reformatted into the optimization problem in [21]. The objective function can be defined as

$$\min \frac{1}{2} ||\omega||^2 + \mathbb{C} \sum\_{i=1}^{m} \xi\_{i\nu}^{\tau} \tag{20}$$

where *C* is used to control the penalty of the misclassification, *ω* is a constant such that *ω* = [*ω*0, *ω*1, ...*ωm*] *<sup>T</sup>*, and *ξ<sup>i</sup>* is the slack variable. The objective function is subject to the constraint that

$$
\omega\_0 + \omega^T z\_i \ge 1 - \zeta\_i \text{ if } y\_i = 1,\tag{21}
$$

$$
\omega\_0 + \omega^T z\_i \le \xi\_i - 1 \text{ if } y\_i = -1. \tag{22}
$$

#### *3.3. Support Vector Machines*

As an extension of the support vector classifier, SVM is established by enlarging the feature space using kernel. Kernel is a function that is used to quantify the similarity of two observations. A linear Kernel is defined as the inner product of two observations [21]:

$$K(z\_{i\prime}, z\_{i'}) = \sum\_{j=1}^{m} z\_{i,j} z\_{i',j\prime} \tag{23}$$

where *zi* and *zi* are the two observations, and *zi*,*<sup>j</sup>* and *zi*,*<sup>j</sup>* are the observations on *j*th dimension.

In addition, some commonly used kernels are [21]

• Polynomial kernel: *K*(*zi*, *zi*)=(1 + ∑*<sup>m</sup> <sup>j</sup>*=<sup>1</sup> *zi*,*jzi*,*j*)*<sup>d</sup>*

• Radial kernel: *<sup>K</sup>*(*zi*, *zi*) = *exp*(−*<sup>γ</sup>* <sup>∑</sup>*j*=<sup>1</sup> *<sup>m</sup>* (*xi*,*<sup>j</sup>* <sup>−</sup> *xi*,*j*)2)

where *γ* and *d* are positive constants and *r* is a constant.

#### *3.4. Current Tracing Kernel*

In [22], the author applied principle component analysis to select the best features with highest information content to identify faults. This study concluded that the top three features for fault identification were reactive power, real power, and angle of voltage. Interestingly, current is not one of them. The author concluded that with all of the three selected features, the accuracy of identification is almost 96%. With all of the six features, i.e., the above features plus magnitude and angle of current and magnitude of voltage, the accuracy of identification is no more than 97%. In the proposed approach, current is used as the only feature. Without current tracing, the feature space consists of only the line current magnitude and angle.

Based on Equations (15)–(18), the line current can be decomposed into several traced currents flowing through virtual impedance lines as shown in Figure 3. The feature space of line currents can be enlarged by using the traced currents:

$$K(I\iota, e^{j(\psi-\theta)}) = \vec{I}\_{LZj}^{+}.\tag{24}$$

where *K* represents the linear mapping from power line current to the traced current.

#### **4. Simulation Results**

#### *4.1. Current Tracing Kernel Results*

In this simulation, the proposed CTM is applied to the single line system of Figure 4. Both sides of the single line have a group of DERs and loads, and bus 2 is connected directly to the external distribution grid. All of the loads are of the constant power type, and the DERs are static generators.

**Figure 4.** Multiple source to multiple source on single power line.

The current sources parameters are listed in Table 1, which are given in the format of active and reactive power. DERs that connect to bus 1 cannot support the AC loads attached to bus 1 so that the currents flow from bus 2 to bus 1, which is opposite from the case shown in the companion paper [20]. Bus 2 is selected as the reference bus and the single power line is 20 km length with series impedance of 0.121 + j0.107 Ω/km.

**Table 1.** The current source parameters.


In Table 1, the positive elements indicate an absorption of power whereas negative elements represents generating power. The third current source attached to bus 2 is the external grid and is calculated by the power flow. Equations (15) and (16) are applied to find the traced current on the power line from each bus as shown in Table 2. All of the traced currents are listed in per unit value. The traced current magnitude and phase in radians are selected as the kernel for fault current identification.


**Table 2.** Current tracing results with Equations (15)–(18).

In Table 2, a zero value indicates that the corresponding current source does not contribute to the current on the power line. It can be observed that the zero value occurs at bus 1; labels 1 and 2; and bus 2, label 1. This does not violate common sense as these are all labeled as loads that are consuming active and reactive power and do not contribute to the power line current. Moreover, all of the traced active currents have the same phase angle regardless of how the current is traced from bus 1 or bus 2 in either direction. The same rationale applies to the reactive currents. This is also consistent with the fact that the voltages applied on the buses do not change when the current is decomposed into its traced components. The reactive current is 90 degrees out of phase from the active current, which complies with Equations (15) and (16).

It is observed that, if all of the traced currents from the same bus are summed, the result is equivalent to the total power line current. This proves the equivalence of the current tracing theory as the current tracing will not lose or generate new currents in addition to the line current.

#### *4.2. SVM Results*

In distribution systems with DERs, the fault current can be very small, as inverter-based DERs can only produce exceptionally small fault current contributions due to inverter current limiting action. Moreover, injected currents on different loads are continuously fluctuating in the normal condition. To obtain representative currents in the single line system, sample noises are injected to the specified load powers in Table 1 and the power flow is recalculated to obtain the traced current. This process is then repeated to obtain the load profile and a continuous currents curve. The injected noise follows the normal distribution such that,

$$X \sim N(\mu, \sigma^2),\tag{25}$$

where *X* represents active or reactive power sample noises; *μ* represents the average of the sample noises, which is set to 0; and *σ* stands for the standard deviation, which is set to 0.1. All the sample noises are independent from each other. The sample noises were injected cumulatively to the loads such that the *k*th point on the load profile is

$$P\_k = P + \sum\_{i=1}^k X p\_{i\prime} \tag{26}$$

$$Q\_k = Q + \sum\_{i=1}^k Xq\_{i\cdot} \tag{27}$$

where *Pk* and *Qk* represent the active and reactive power of the *k*th point of the load profile, respectively; *P* and *Q* represent the given active and reactive power (Table 1); and *X pi* and *Xqi* stand for the *i*th active or reactive power sample noises, respectively.

This process is repeated 500 times, and all of the parameters that are used for current tracing and SVM training purpose are recorded. In addition to sample noises, a small fault is also injected by increasing the active power consumption of bus 1, with current source 3 increased by 10% and decreasing the reactive power by 10% of the same current source. Again, the process is repeated 500 times, and all parameters are recorded. Only the traced current on the power line from bus 2 side is used as the current tracing kernel; however, it is the same as if the traced current from bus 1 side was used as the current tracing kernel, as in the conference paper [20]. The first 500 parameters are taken as normal condition, i.e., *yi* = −1, and the last 500 parameters are considered as fault condition, i.e., *yi* = 1. The penalty of misclassification *C* is set to be 1. Seventy percent of the parameters are randomly selected as the training data, and the remaining 30% are taken as the testing data. In this work, the non-waveform phasor current information is used for the fault identification problem. Other alternative measurement data have been considered in other research, such as exploiting sub-cycle waveform distortion features in pattern recognition algorithms as a part of the identification process [12,15].

The confusion matrix is used to represent the testing results as defined in [23]. The f-score, recall, and precision parameters are used to evaluate the performance of fault current identification based on the confusion matrix such that,

$$precc = \frac{tp}{tp + fp} \,\tag{28}$$

$$rec = \frac{tp}{tp + fn} \tag{29}$$

$$fs = 2\frac{prec \ast \text{rec}}{prec + rec} \,\text{s}\tag{30}$$

where *tp*, *fp*, *tn*, and *fn* represent true positive, false positive, true negative, and false negative, respectively.

To show the advantage of using the current tracing kernel, the fault current identification results using different feature spaces is compared. First, only the power line current -*IL* is used as the feature space. Then, the polynomial kernel, radial kernel, and current tracing kernel are added as the expanded feature space. All of the confusion matrices are calculated based on the same training and testing data. The confusion matrices and the performance based on the confusion matrices are shown in Tables 3 and 4, respectively.

**Table 3.** Confusion matrix using different feature space.


**Table 4.** Performance using different feature space.


It is clearly seen that among all the feature spaces used, the current tracing kernel has the best performance. All three performance parameters are significantly higher than the other feature spaces that were used. The recall value equals 1, which indicates that when there is a fault current on the power line; the SVM method using current tracing kernel will definitely detect it. In addition, the polynomial kernel and radial kernel have a better performance than if only -*IL* is used as feature space. However, the performance parameters do not increase significantly. When comparing with the results shown in [22], which have 97% overall accuracy, the overall current tracing kernel result in this paper has improved, i.e., an f1-score value of 98%.

#### **5. Discussion**

In the companion paper, it has been verified that the proposed tracing method is mathematically and physically identical to the original network. In this paper, the developed technique has been applied to a simple single power line system; however, it could be generalized to be as a part of a larger

distribution grid. Using the proposed CTM, pipelines of each current sources' contribution towards the fault currents were established in the form of virtually decomposed traced currents. The expanded features of the traced currents have the distinct advantage of containing more detailed information of the fault current, such as the change in contribution of each current source and the phase shift caused by the fault. These features can be exploited by the SVM algorithm for improved classification of faults, particularly where the fault levels are very low from the current limiting action of inverter-based DERs.

By choosing a large sample set of 1000 data points for faulted and normal cases, the proposed SVM method combined with the current tracing kernel is shown to be much more sensitive to very low-level faults on the power line compared to the polynomial and radial kernel methods, where the accuracy of detection was at most 74%. Compared to the other methods, such as the one in [22] where the accuracy of detection was at most 97%, the proposed method has improved accuracy of 98% while using significantly less measurement features.

These results are relevant in the context of smart grids aiming to improve distribution system state estimation, extending supervisory control and data acquisition processes beyond the substation domain as DERs proliferate. In these simulations, only the batch data is used for training and testing. However, the proposed model can be easily applied to practical streaming data obtained from intelligent electronic devices used in advanced metering infrastructure such as protection relays and phasor measurement units. With the enhanced features extracted through the proposed CTM, more intelligent protection relay coordination and fault isolation may be possible, particularly when considering multiple inverter-based DER operation from energy storage and renewable energy.

#### **6. Concluding Remarks**

In this paper, we propose a CTM augmented with SVM method to model and test a distribution feeder for power line fault current identification. The CTM modeled the distribution network by providing a detailed map of how current flows from each current source that is connected to one bus towards another source tied to a different bus. The proposed method does not violate any physical circuit laws. After applying the proposed current tracing, the virtual traced currents and the corresponding circuit are exactly equivalent to the original current and circuit. The traced current provides sufficient details and sensitivity for identifying faults and abnormal conditions in the distribution feeder. With these details, the feature space of the power line current is enlarged through the "current tracing kernel". In addition, the results proved and demonstrated the proposed method on a single power line distribution system, and the SVM method's performance was evaluated and compared by using different kernel methods. The results indicate that with the benefits of the proposed current tracing kernel, the SVM method is enhanced with more sensitivity to very low level faults compared to the commonly used kernel such as polynomial kernel and radial kernel.

The proposed method is a good fit for the distribution grid primary side overcurrent protection scheme. In the companion paper, the multicurrent sources to multicurrent source current tracing are already introduced, and they can be used to further expand the feature spaces of fault current. In the future, the authors will explore the implementation aspects of the proposed CTM described herein with the distribution grid backup protection scheme, especially the multicurrent sources to multicurrent sources case, which would undoubtedly occur with higher DER penetration in the future. Furthermore, in future work, the authors will explore how to implement and test this approach on a laboratory scale distribution test feeder to further verify the implementation of the SVM detection scheme using the proposed tracing method.

**Author Contributions:** Conceptualization, W.F.; methodology, W.F. and P.M.; software, W.F.; validation, W.F. and P.M.; formal analysis, W.F.; investigation, W.F.; resources, W.F.; data curation, W.F.; writing–original draft preparation, W.F.; writing–review and editing, P.M.; visualization, W.F.; supervision, P.M.; project administration, P.M.; funding acquisition, P.M.

**Funding:** This research was funded in part by the Oklahoma Center for the Advancement of Science and Technology (Project No. AR18-073) and the Oklahoma Gas & Electric Company (Project No. A18-0274).

**Conflicts of Interest:** The authors declare no conflicts of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript.


#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Comparison and Design of Resonant Network Considering the Characteristics of a Plasma Generator**

**Geun Wan Koo 1, Won-Young Sung <sup>2</sup> and Byoung Kuk Lee 1,\***


Received: 22 July 2019; Accepted: 15 August 2019; Published: 16 August 2019

**Abstract:** This paper presents a theoretical analysis and experimental study on the resonant network of the power conditioning system (PCS) for a plasma generator. In order to consider the characteristics of the plasma load, the resonant network of the DC-AC inverter is designed and analyzed. Specifically, the design of an LCL resonant network and an LCCL resonant network, which can satisfy the output current specification in consideration of plasma characteristics, is explained in detail. Moreover, the inverter current and phase angle between the inverter voltage and current is derived for evaluating inverter performance. Based on these analysis results, the DC-AC inverter can be designed for a plasma generator considering plasma load characteristics. The theoretical analysis of both networks is validated through the simulation and experimental results.

**Keywords:** plasma generator; LCL network; LCCL network; phase compensation; ZVS control

#### **1. Introduction**

Plasma generators are used in various industrial fields for display panels and in the wafer cleaning process of semiconductors. According to the growth in the display and semiconductor markets, plasma generators are becoming increasingly important in industrial fields [1,2]. These plasma generators are conventionally constructed as a power conditioning system (PCS) and a chamber for plasma generation. High frequency current must be supplied by the PCS to the reactor, which is a magnetic substance in the chamber for supply energy which is used to ionize the gas entering the chamber. The electric field for ionizing is generated according to the frequency, sinusoidal wave, and magnitude of the supplied current. Therefore, in order to effectively generate the electric field, the PCS should supply high switching frequency and low total harmonic distortion (THD) constant current [3,4].

Another characteristic of the PCS for a plasma generator is that the inverter of the PCS using zero voltage switching (ZVS) is conventionally adopted to decrease the switching losses. In order to implement ZVS, the phase shift technique or load resonant technique has been used in previous research on the inverter. In order to achieve ZVS, the inverter should be designed in consideration of the following load characteristics in the plasma load case [5]: (1) the resistance of the load is increased in proportion to the gas injected into the chamber; (2) the resistance of the load is changed in inverse proportion to the load current [6]; (3) a constant load current is recommended for maintaining the stable plasma state; (4) the THD of the load current should be low for effective plasma generation [7–9].

In the case of the conventional resistive load, the pulse frequency modulation (PFM) or phase shift control are applied for the ZVS operation of the inverter. In plasma load, applying the PFM to the control output current is difficult due to the characteristics of the plasma load mentioned above. When the PFM is used to vary the output current in the plasma load, the plasma load resistance is varied depending on the output current. If the output current for generating plasma is increased, the

resistance of the plasma load is decreased. When the output current for generating plasma is decreased, the resistance of the plasma load is decreased in an inversely proportional manner [6]. In addition, the designed initial Q-factor is varied rapidly due to changes in resistance. Because of the changed Q-factor, the resonant inverter cannot control the output current to the designed value.

Therefore, regulating the inverter output current using PFM is difficult because the plasma load resistance is changed again and the phenomena mentioned previously occur repeatedly. In order to solve these problems, the phase shift control should be used for the output current regulation. Conventionally, the phase shift full bridge inverter and load resonant inverter can solve the problem of using the phase shift control. In the plasma load case, the harmonics of the output current should be strictly regulated in order to satisfy plasma quality as characteristics of the plasma load [10–13]. Hence, it is difficult to adopt a phase shift full bridge inverter for the plasma system, and only the load resonant inverter using the phase shift method can be adopted. If a phase shift inverter is used for the plasma load, the filter with the ability to implement the sinewave of the load current is required for designing a phase shift inverter [14,15]. Using the additional filter on the phase shift inverter leads to increased system cost and volume. For this reason, the load resonant inverter using phase shift control is preferred for the plasma load system over the phase shift inverter with an additional filter [15].

In order to adopt a load resonant inverter in the plasma system, the effective resonant network design should be considered. There are two representative resonant networks for plasma systems: the structure of an LCL resonant network and the structure of an LCCL resonant network. These networks have different characteristics of the maximum inductor current and phase angle between inverter voltage (vo.inv) and inverter current (io.inv). In the resonant network design, the maximum inductor current and inverter phase are the factors that influence the conduction loss and the soft-switching range for phase shift control. Therefore, in order to design a resonant network that is suitable for a plasma generator, the characteristics of the LCL network and the LCCL network should be compared to select the optimal maximum inductor current and phase angle.

In this paper, in order to explain the specialty of plasma load to the design of the resonant network, both the LCL network and LCCL network, which are conventionally used for resonant inverter systems and satisfy the specification of the plasma load, are analyzed in detail. Based on the analysis, the LCL resonant network and LCCL network are designed in consideration of the characteristics of the plasma load and with the aim of preventing the drop-out phenomenon. In order to evaluate the designed networks, simulation and analysis are conducted. Finally, the experimental results based on a 1 kW plasma generator are presented to verify the performances of the LCCL and LCL resonant networks on the plasma generator.

#### **2. Control Scheme and Characteristics of the Plasma Load**

Figure 1 shows the conceptual circuit diagram of the plasma generation system that generates plasma by injecting gas into the reactor of the chamber. In Figure 1, Lr, Cr, Llkg, and Rplasma represent the resonant inductor, resonant capacitor, leakage inductor, and the equivalent resistance of the plasma load, respectively. The "Vin" represents the input voltage of the inverter. vo.inv, io.inv, and iplasma indicate the mean output voltage of the inverter, the output current of the inverter and the output current for generating plasma, respectively. In the plasma generation system, the injected gas affects the load. This plasma generator has unique features: (1) the impedance of the plasma load is proportionally decreased according to the increase in iplasma value [6] and (2) the sinusoidal wave is highly recommended for generating plasma [15]. These characteristics are an important consideration point for designing the power supply of the plasma system.

**Figure 1.** Conceptual circuit diagram of the plasma generation system.

#### *2.1. Chracteristics Analysis of the Plasma Load*

These characteristics cause a special issue in the plasma system. Among the above-mentioned plasma characteristics, the impedance of plasma load leads to a special issue when pulse frequency modulation is adopted for output current control. In Figure 2, in order to regulate the output current, the switching frequency (fsw) is changed to be above resonant frequency (fr). In the conventional gain curve of the resonant network shown in Figure 2, in order to regulate the output current, increasing or decreasing switching frequency is normally used in the resistive load.

**Figure 2.** Description diagram of plasma drop-out: (**a**) frequency control method in resistive load; (**b**) frequency control method in plasma load.

However, in the plasma load case, when increasing the switching frequency to reduce the output current the plasma load impedance is increased according to the reduced output current. The increased impedance changes the Q-factor of the network to make a sharp current gain curve. In addition, the output current is decreased again because of the change in the current output gain curve, as shown in Figure 2. These mechanisms progress repeatedly until the output current reaches zero. Therefore, using PFM to control the output current is difficult in the plasma load. This phenomenon is called drop-out and is observed when controlling output current using PFM in the plasma load. In order to solve the above-mentioned problems, the phase shift control scheme should be adopted for the resonant inverter to satisfy the output current control range. Moreover, the inverter should be operated at the resonant frequency to avoid plasma drop-out.

#### *2.2. Control Method Considering Characteristics of the Plasma Load*

In order to obtain various output current ranges with ZVS, the resonant network should be designed to consider the minimum phase shift angle which can control the minimum plasma current with ZVS operation. The minimum phase shift angle is calculated by Equation (1) [14], which represents the relation between the amplitude of the fundamental wave of the inverter output voltage (vo.inv.1) and the phase shift angle.

Figure 3 shows the phase shift control scheme for output current control in the resonant inverter. In this scheme, the inverter is operated in order to reduce the fundamental wave of the inverter output voltage (vo.inv.1) with increasing phase shift angle for reducing the width of the square wave (β). In this control scheme, the vo.inv.1 can be calculated using Equation (1) and the phase angle between the inverter output voltage and output current is the crucial factor during ZVS to obtain various output currents. According to Equation (1), vo.inv.1 can be controlled to adjust the phase shift angle at the fixed resonant frequency. The output current is obtained by the relationship between vo.inv.1 calculated using Equation (1) and the designed resonant network gain. Therefore, the maximum inverter current and phase angle between vo.inv and io.inv should be considered in designing the resonant network to achieve lower conduction loss and soft-switching.

$$\mathbf{v}\_{\rm o.inv.} = \frac{4\mathbf{V}\_{\rm in} \cdot \sin\left(\frac{\beta}{2}\right)}{\pi} \cos(\omega t - \frac{\beta}{2}) \tag{1}$$

**Figure 3.** Conceptual diagram of control method considering plasma drop-out: (**a**) full output current condition and (**b**) decreasing output current.

#### **3. Analysis of the Resonant Network for the Plasma Load**

The LCL network and the LCCL network are suitable structures for the resonant network for plasma generation. Depending on the network, the phase angle between the inverter maximum current and the plasma current has different characteristics. Therefore, impedance analysis is necessary for considering the different characteristics of the resonant network depending on variations in the values of passive elements. Using the results of impedance analysis, the maximum current of the inverter, plasma current at the resonant frequency, and the phase between the inverter voltage and the current can be calculated.

#### *3.1. Analysis of LCL Resonant Network*

The LC resonant network is suitable for satisfying the constant current output of the plasma inverter with just a few passive elements. However, the LC resonant network is constructed here as the LCL network because of the leakage inductance of the reactor which is used for plasma generation, as shown in Figure 4. Therefore, in order to design the power supply for the plasma generator, the characteristics of the LCL network should be analyzed mathematically. The first consideration point in designing the network using mathematical analysis is deriving the Lr and Cr values, which can regulate the constant output current of the inverter regardless of load variation.

**Figure 4.** Conceptual circuit diagram of the LCL resonant network.

In order to regulate the constant output current while preventing drop-out, the resonant frequency should be selected as an operating frequency of the inverter, and the output current can be derived from impedance analysis, as shown in Equation (2) [14]. Figure 5a presents the characteristics of output current through the impedance analysis according to frequency variation. As shown in Figure 5a, the output current changes with the load variation, except for the resonant frequency. Therefore, the resonant network should be designed to satisfy the maximum output current value at the resonant frequency in the plasma generation system.

**Figure 5.** Characteristics of LCL network for designing a power conditioning system (PCS): (**a**) output current characteristics of the LCL network and (**b**) phase angle characteristics of the LCL network.

After determining the maximum current, phase shift control is necessary for satisfying the minimum current of the load requirement and preventing drop-out. The phase shift angle for satisfying the minimum output current with phase shift control can be calculated using Equation (1). The consideration point for satisfying the phase shift angle which is calculated to regulate the minimum output current in the inverter is the phase difference between the inverter voltage and the current. When the phase difference is smaller than the phase shift angle, the inverter is operated in the hard-switching region. By contrast, when the phase difference is larger than phase shift angle, the inverter could be operated in the soft-switching region. The relationship between the phase shift angle and the phase difference is considered using Equation (3) [16]. If the calculation results of Equation (3) are larger than the required phase shift angle, the inverter could be operated in the soft-switching region at resonant frequency. Figure 5b shows the phase difference between the inverter voltage and the current according to load variation. When the inverter is operated at the resonant frequency to prevent drop-out and when the resistance of the load is small, the phase difference is large. Furthermore, the phase difference becomes small when the resistance of the load is large, as shown in Figure 5b.

*Energies* **2019**, *12*, 3156

Using the above-mentioned analysis, the inverter can control the output current, which is required for plasma generation. Regarding the other point of consideration aside from controlling load current in order to design the power supply for the plasma generator, the inverter current (io.inv) should be considered for the efficiency of the inverter. The inverter current, which is the main cause of inverter losses, can be calculated using Equation (4) [16]. This inverter current can be used for the index of the inverter efficiency. Therefore, in order to design a high efficiency inverter, the inverter current should be considered.

$$\mathbf{i}\_{\text{plasma.LCL}}(\mathbf{f}\_{\mathbf{r}}) = \frac{\mathbf{v}\_{\alpha \text{.inv.1}} \sqrt{\mathbf{C}\_{\mathbf{r}}}}{\sqrt{\mathbf{L}\_{\mathbf{r}}}} \tag{2}$$

$$\Theta\_{\rm LCL}(\mathbf{f\_r}) = \tan^{-1} \left[ \frac{(\mathbf{L\_r} - \mathbf{L\_{lkg}})}{\mathbf{R\_{plasma}} \sqrt{\mathbf{L\_r C\_r}}} \right] \tag{3}$$

$$\mathbf{i}\_{\rm o.inv.LCL}(\mathbf{f}\_{\rm r}) = \sqrt{\frac{\mathbf{C}\_{\rm r}}{\mathbf{L}\_{\rm r}}} \frac{1}{\mathbf{L}\_{\rm r}\sqrt{\frac{1}{\left(\mathbf{L}\_{\rm r} - \mathbf{L}\_{\rm lkg}\right)^2 + \mathbf{C}\_{\rm r}\mathbf{L}\_{\rm r}\mathbf{R}\_{\rm plosmu}^2}}} \tag{4}$$

#### *3.2. Analysis of LCCL Resonant Network*

The other structure of the resonant network for applying the plasma inverter is the LCCL network, as shown in Figure 6. Using the LCCL network, it is possible to compensate for the phase difference, which is not possible with the LCL network. In the case of the LCCL network design, it is necessary to use impedance analysis, as shown in Equation (5), to regulate the constant output current regardless of the load at the resonant frequency in order to prevent drop-out. Figure 7a shows the maximum current of the LCCL network according to load variation. Aside from the resonant frequency, the output current is changed with the load variation, as shown in Figure 7a.

**Figure 6.** Conceptual circuit diagram of the LCCL resonant network.

The phase shift control is also necessary for satisfying the minimum output current of the LCCL network. In this case, the phase shift angle satisfying the minimum output current can be calculated using Equation (1), and the phase shift angle is equal to the case of the LCL network case because both networks are designed for the same maximum current. In the case of the LCL network, designing the phase difference between the inverter voltage and current is difficult because the values of Lr, Cr, and Llkg are already fixed in order to satisfy the maximum output current. On the other hand, in the case of the LCCL network, the phase difference can be designed through the added compensation capacitor (Ccomp), as shown in Equation (6). Figure 7b shows the phase difference of the LCCL network according to the load variation at the resonant frequency. As shown in Figure 7b, the LCCL network can ensure a wider phase difference than the LCL network. Therefore, the LCCL network can be operated in a wider ZVS range than the LCL network. In the case of the LCCL network, the inverter current can be calculated using Equation (7), and the inverter current of the LCCL network is increased compared with the inverter current of the LCL network.

**Figure 7.** Characteristics of the LCCL network for designing a PCS: (**a**) output current characteristics of the LCCL network and (**b**) phase angle characteristics of the LCCL network.

Because of the compensation capacitor (Ccomp), as mentioned previously, the inverter current of the LCCL network is higher than that of the LCL network, and the LCCL network can extend the ZVS region due to the compensation capacitor. Therefore, considering the overall efficiency of the inverter, loss analysis is necessary to compare the efficiency of both networks.

$$\mathbf{i}\_{\text{plasma}.\text{L.C.L.}} (\mathbf{f}\_{\mathbf{r}}) = \frac{\mathbf{v}\_{\alpha \text{inv.}1} \sqrt{\mathbf{C}\_{\mathbf{r}}}}{\sqrt{\mathbf{L}\_{\mathbf{r}}}} \tag{5}$$

$$\theta\_{\rm L,CCL}(\mathbf{f\_{r}}) = \tan^{-1} \left[ \frac{\sqrt{\mathbf{L\_{r}C\_{r}}}}{R\_{\rm plasma}\mathbf{C\_{comp}}} + \frac{(\mathbf{L\_{r}} - \mathbf{L\_{lkg}})}{R\_{\rm plasma}\sqrt{\mathbf{L\_{r}C\_{r}}}} \right] \tag{6}$$

$$\mathbf{i}\_{\mathrm{o,inv.LCCL}}(\mathbf{f}\_{\mathrm{f}}) = \sqrt{\frac{\mathbf{C}\_{\mathrm{r}}}{\mathbf{L}\_{\mathrm{r}}}} \frac{1}{\mathbf{C}\_{\mathrm{comp}} \mathbf{L}\_{\mathrm{r}}} \frac{1}{\sqrt{\mathbf{C}\_{\mathrm{r}} \mathbf{L}\_{\mathrm{r}} \left[\mathbf{C}\_{\mathrm{r}} \mathbf{L}\_{\mathrm{r}} + \mathbf{C}\_{\mathrm{comp}}^{2} \mathbf{R}\_{\mathrm{plasma}}^{2} + 2 \mathbf{C}\_{\mathrm{comp}} (\mathbf{L}\_{\mathrm{r}} - \mathbf{L}\_{\mathrm{l} \mathrm{g}})\right] + \mathbf{C}\_{\mathrm{comp}}^{2} (\mathbf{L}\_{\mathrm{r}} - \mathbf{L}\_{\mathrm{l} \mathrm{g}})}} \tag{7}$$

#### **4. Simulation and Experimental Results**

The simulation and experimental results are presented for the purpose of verifying the analysis of the resonant network. The simulation has been conducted to describe the operation characteristics regarding the requirement and the phase shift angle. Finally, the applicability of the LCCL resonant network for the plasma generator is validated using experimental results. Figure 8 shows the simulation waveform about the LCL network and the LCCL network in the maximum current output condition. Both of the resonant networks can be operated to satisfy the maximum current output as shown in Figure 8a,b. When the LCL network is operated under the minimum current output conditions, the hard-switching region appears as is shown in Figure 8c. On the other hand, as shown in Figure 8d, the LCCL network can be operated with ZVS under the minimum load condition.

Loss analysis has been conducted to compare the efficiency of each resonant network [17]. In order to analyze the losses of the inverter, only the switch loss is considered, without any loss of resonant inductor, which consists of an air core inductor and a resonant capacitor. Regarding the analysis results, the loss of the LCL network is smaller than that of the LCCL network in the ZVS operation region under the 20 A output condition, as shown in Figure 9. In the non-ZVS operation region at the 20 A output condition, the loss of the LCL network is larger than that of the LCCL network. Beyond the 25 A output region, the loss of the LCCL network is larger than that of the LCL network because the large inverter current is required in the LCCL network.

**Figure 8.** Simulation waveform of each resonant network: (**a**) characteristics of the LCL network under the 9 Ω, 35 A output conditions; (**b**) characteristics of the LCCL network under the 9 Ω, 35 A output conditions; (**c**) characteristics of the LCL network under the 9 Ω, 20 A output conditions; and (**d**) characteristics of the LCCL network under the 9 Ω, 20 A output conditions.

**Figure 9.** Loss analysis of each resonant network: (**a**) loss according to load variation in the LCL network; (**b**) loss according to load variation in the LCCL network.

The experiment has been conducted based on the parameters listed in Table 1. Among these parameters, the input voltage 1/3 scale-down model has been used with consideration of the laboratory power distribution. The resonant network has been designed with Equation (2) considering switching frequency and maximum output current. Figure 10a shows the experimental waveform of the LCL network, which represents the narrow phase angle. In this case, it is impossible for iplasma to be controlled with the ZVS region using the phase shift control to obtain a minimum value, as shown in Figure 10a. On the other hand, a sufficient phase angle for the phase shift control in the ZVS region is obtained in the LCCL network, as shown in Figure 10b. In this result, the DC-AC inverter adopting the LCCL network can be operated with ZVS despite the worst case for obtaining the phase angle, as shown in Figure 10c.


**Table 1.** Parameters of the inverter and both resonant networks for simulation and experiment.

**Figure 10.** Feasibility test results of experimental waveform of each resonant network: (**a**) experimental waveform of the LCL network under the 9 Ω, 11.6 A conditions; (**b**) experimental waveform of the LCCL network under the 9 Ω, 11.6 A conditions; and (**c**) experimental waveform of the LCCL network under the 9 Ω, 6.6 A conditions.

The phase difference and soft-switching ability of the designed networks are verified through these experimental results. In the resonant inverter for using the plasma generator, the inverter loss is determined with the trade-off relationship between the conduction loss of the inverter current and the switching loss due to the phase difference. Therefore, the LCCL resonant network could be better performing than the LCL network under the large resistance of the plasma load and small plasma current conditions.

#### **5. Conclusions**

In this paper, the applicability of the LCL network and LCCL network for a plasma generator have been investigated with consideration of the characteristics of the plasma load. In particular, the drop-out phenomenon, which is substantially different from the resistive load, is considered for the design of an LCL network and an LCCL network. Considering the characteristics of the plasma load, an LCL network and an LCCL network are designed and analyzed. Based on the analysis, a simulation was conducted in order to verify the validity of the designed networks. Furthermore, the experiment was progressed while considering the laboratory power distribution level in order to verify the applicability of the networks.

**Author Contributions:** Conceptualization, G.W.K. and W.-Y.S.; methodology, G.W.K.; software, G.W.K. and W.-Y.S.; validation, G.W.K.; formal analysis, G.W.K.; investigation, G.W.K.; resources, B.K.L.; data curation, G.W.K.; writing—original draft preparation, G.W.K. and B.K.L.; writing—review and editing, G.W.K. and B.K.L.; visualization, G.W.K. and W.-Y.S.; supervision, B.K.L.; project administration, B.K.L.; funding acquisition, B.K.L. **Funding:** This work was supported by "Human Resources Program in Energy Technology" of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), granted financial resource from the Ministry of Trade, Industry & Energy, Korea. (No. 20184030202190); This work was supported by the Korea Institute of Energy.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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