*Article* **Consideration of Reactor Installation to Mitigate Voltage Rise Caused by the Connection of a Renewable Energy Generator**

#### **Yeonho Ok 1,2, Jaewon Lee <sup>1</sup> and Jaeho Choi 2,\***


Academic Editor: Birgitte Bak-Jensen Received: 13 January 2017; Accepted: 2 March 2017; Published: 10 March 2017

**Abstract:** This paper describes the detailed analysis of a reactor application for a power plant to mitigate the voltage rise of a distribution line (DL) caused by the connection of distributed resources (DRs). The maximum capacity of renewable energy generators (REGs) that meets the acceptable voltage rise of a DL and the necessary capacity of the reactor to mitigate that voltage rise according to the different types of REGs are analyzed. The re-coordination of a protection relay and the loss of generation revenue as well as the installation location of a reactor are described. Finally, the ON/OFF conditions of the reactor, such as the magnitudes of the grid voltage and generator voltage, and the duration time of the voltage rise are analyzed. As the voltage rise is mitigated and self-limited in small power plants, it is confirmed that the capacity of the DRs connected to the DL can be increased through a field demonstration.

**Keywords:** renewable energy; reactor; voltage rise; distribution line; distribution resource; grid connection; generator; power factor; coordination of protection relay

#### **1. Introduction**

The locations of power plants sourced by renewable energy, such as wind or solar power generation, are restricted by the applicable natural conditions. Therefore, it is necessary to consider how and where to connect them to the power grid. While the large-capacity power plants deliver power through a dedicated power line, the small-scale generators, such as distributed resources (DRs), are linked directly to the close distribution line (DL) to decrease the transmission loss and the construction cost. For example, in South Korea, a 10 MW or larger power plant has to be linked through a dedicated line [1]. On the other hand, renewable energy generators (REGs) which are generally smaller than 10 MW are connected to the DL directly. This paper describes what should be considered when connecting the small-scale REGs to the DL directly.

To connect REGs to the DL, a technological understanding of anti-islanding and power quality solutions against the harmonics and line voltage fluctuations, etc., are necessary [2]. When any faults occur in the grid, REGs should stop supplying power to the grid line using the appropriate anti-islanding method. Nevertheless, with the spread of microgrid technologies, the operation of REGs in stand-alone mode in all types of line fault conditions has attracted recent attention [3]. The voltage fluctuations are caused mostly by load variations in the grid, and the application of a static synchronous compensator (STATCOM) has been studied to improve voltage regulation [4–6]. Harmonics problems have become more serious with the increased use of power electronics equipment in power utility applications. The harmonic distortion of currents and voltages occurs at the Direct Current/Alternating

Current (DC/AC) inverter that feeds power from the REGs and the AC/DC converter that supplies power to the DC load. To reduce these harmonics problems, passive filters are installed conventionally as a simple method, but the active power filter (APF) has also been applied as an improved form of technology [7]. Although the performance of STATCOM and APF is good, the system is expensive and the controller is complicated.

The increase in REG output influences the voltage rise of the DL, and the voltage rise has a direct influence on the load linked to the DL. This voltage rise caused by the interconnection of DRs has been standardized by the IEEE Std. 1547 and there have been many studies aiming to solve grid voltage rise problems [8–11]. The rate of grid voltage rise related to DRs is limited to 2% in South Korea [1]. The allowable capacity of DRs for connecting to DL can be calculated, but it applies less capacity than the available renewable energy to meet the regulation of the voltage rise. Therefore, to maximize the utilization of renewable energy, it is important to suppress the voltage rise in accordance with the capacity increase of DRs using some technologies.

The grid voltage rise in the DL is dependent on the capacity of DRs, the characteristics of loads, and the line parameters of DL. The voltage rise of DL could be adjusted by controlling the load [12]. This was based on the policy that customers adjust loads themselves according to the voltage of the DL, with DRs to regulate the voltage, and the benefit of electricity charges was given to customers who accepted this policy. However, it was difficult to apply this system in a normal DL because of the separate electricity rate system. Some studies have been performed to mitigate the voltage rise with the tap changer of transformers of DL with DRs [13–16], but these are not directly applicable to systems that attempt to solve the voltage rise problems inside the power plant. Evaluations of the allowable REG capacities to connect to the DL have been carried out [17–21], but these studies were usually applied to take less capacity than the available energy. Therefore, they could not satisfy the original intention to use the available energy as much as possible.

To mitigate the voltage rise of the DL without downsizing the generating capacity, additional facilities, such as the Static Var Compensator (SVC) [22–24], STATCOM [25–28], and reactors, have been considered for installation in a power plant. The SVC and STATCOM are generally applied in large-capacity power plants over 60 MVA, but their system costs are expensive compared to the construction costs of small-capacity REGs [29,30]. A reactor has been installed in a small-capacity generator system, but a detailed study of the installation capacity, location, and coordination of protection relays has not been performed [31,32]. Therefore, its applications have been very limited in spite of its merits as a simple and cheap method.

This paper describes the detailed analyses of a reactor application of a power plant to mitigate the voltage rise due to the connection to DL of REGs. Firstly, the maximum capacity of REGs that meet the acceptable voltage rise of the DL without a reactor and the necessary capacity of the reactor to mitigate the voltage rise of the DL according to each type of REG is analyzed. Secondly, the installation locations of the reactor are examined by the comparative analysis of the advantages and disadvantages at each location considering the necessity of re-coordination of a protection relay and the loss of generation revenue according to the installation locations. Finally, the ON/OFF conditions of the reactor, such as the magnitude of the grid voltage and the generator output and the duration time of the set values, are investigated.

The effects of installing of the reactor are analyzed through field application tests by comparing the vector diagrams, the daily connection voltage data, and the monthly average grid voltage data before and after the installing the reactor.

#### **2. Considerations for Reactor Installation**

The voltage rise of DL with REGs depends on the load condition of DL. Therefore, the no load condition of DL is assumed in this study, which provides the maximum voltage rise with REGs [23].

#### *2.1. Capacity*

The capacity of REGs to be installed in DL is dependent on the capacity of the existing DRs in DL, the allowable load capacity of DL, the available voltage rise rate of DL, and the type of generators to be newly added. Figure 1 shows the single line and vector diagrams based on the connection point voltage when a REG is added to DL [5], and the voltage rise rate and DL voltage are described as Equations (1)–(4).

ͳΝΒΔΜ͙ͺʹͽΖΒΕ͚͑ͫ͑ͽΖΒΕΚΟΘ͑ΠΨΖΣ͑ͷΒΔΥΠΣ͑ΠΗ͑ΖΟΖΣΒΥΠΣ ͳΝΦΖ͙ͺʹ͚͑͑ͫ͑͑͢͢͟͡͡͡͡ΠΨΖΣ͑ͷΒΔΥΠΣ͑ΠΗ͑ΖΟΖΣΒΥΠΣ ΖΕ͙ͺʹͽΒΘ͚͑͑͑ͫ͑ͽΒΘΘΚΟΘ͑ΠΨΖΣ͑ͷΒΔΥΠΣ͑ΠΗ͑ΖΟΖΣΒΥΠΣ

**Figure 1.** Grid-connected renewable energy generators (REGs): (**a**) Single line diagram; (**b**) vector diagram. *VRated*: Rated voltage of DL (V); <sup>→</sup> *VCP*: Connection point voltage (V); <sup>→</sup> *I CP*: Connection point current (A); DL: Distribution line; <sup>→</sup> *VS*: Station voltage (V).

$$\%V\_{VRR} = \frac{V\_{CP} - V\_{S}}{V\_{Rated}} \times 100\tag{1}$$

$$
\stackrel{\rightarrow}{V}\_S = \stackrel{\rightarrow}{V}\_{CP} - \sqrt{3}\stackrel{\rightarrow}{I}\_{CP}(\mathbb{R} + jX) \tag{2}
$$

$$\stackrel{\rightarrow}{I}\_{CP} = I\_{CP}(\cos \theta\_{CP} \pm j \sin \theta\_{CP}) \tag{3}$$

$$\begin{split} V\_S &= \sqrt{\left\{V\_{CP} - \sqrt{3}I\_{CP}(R\cos\theta\_{CP} \mp X\sin\theta\_{CP})\right\}^2 + \left\{\sqrt{3}I\_{CP}(X\cos\theta\_{CP} \pm R\sin\theta\_{CP})\right\}^2} \\ &= \sqrt{V\_{CP}^2 + 3I\_{CP}^2(R^2 + X^2) - 2\sqrt{3}V\_{CP}I\_{CP}(R\cos\theta\_{CP} \mp X\sin\theta\_{CP})} \end{split} \tag{4}$$

where %*VVRR* is the voltage rise rate (%), *VRated* is the rated voltage of DL (V), <sup>→</sup> *I CP* is the connection point current (A), <sup>→</sup> *VCP* is the connection point voltage (V), cos *θCP* is the power factor of the connection point, *<sup>R</sup>* and *<sup>X</sup>* are the line parameters (Ω), and <sup>→</sup> *VS* is the station voltage (V).

According to Figure 1 and Equation (4), the voltage rise of DL is dependent on the power factor under the given value of the line constants of DL and the voltage and current of REG. The lower the generator lagging power factor, the higher the voltage rise, and the lower the generator leading power factor, the lower the voltage rise. In addition, the power factor of REGs that does not exceed the allowable voltage rise rate in DL can be calculated:

$$kVA\_R = kVA\_{REG}(\sin\theta\_1 - \sin\theta\_2) \tag{5}$$

On the other hand, the power factor of REGs is usually fixed excluding the synchronous generator, so it may be possible to calculate the capacity of the reactor to compensate for the power factor, as expressed in Equation (5), where *kVAR* is the capacity of the reactor, *kVAREG* is the capacity of REG, *θ*<sup>1</sup> is the tuned power factor angle, and *θ*<sup>2</sup> is the REG power factor angle.

Figure 2 presents the single line and vector diagrams of DL with the reactor, where the red parts show the changes after installing a reactor. The blue *θCPN* of Figure 2 corresponds to *θ*<sup>1</sup> in Equation (5). The limited values of *ICPN*, *VsN*, and *θCPN*, shown in blue in Figure 2 that do not exceed the allowable voltage rise rate in DL are then derived. If the reactor with the value calculated from Equation (5) is installed, *θCPN* is the same, but *ICPN* and *VsN* are different from *ICPR* and *VsR*, such as in the red parts in Figure 2. Therefore, the voltage rise in DL may be higher than the allowable voltage rise. A larger reactor should be installed to cover this additional voltage rise.

**Figure 2.** Grid-connected REG with reactor; (**a**) single line diagram; (**b**) vector diagram.

#### *2.2. Selection of Reactor Installing Location*

In this paper, the installation locations of the reactor are examined by the comparative analysis of the advantages and disadvantages at each location considering the necessity of re-coordination of a protection relay and the loss of generation revenue according to the installation locations. For these analyses, the reactor locations are selected firstly depending on where they are located, before or after CT1 or CT2. Therefore, there are only four locations where reactors can be installed in the plant as shown in Figure 3, and the most suitable place can be chosen among them after considering the coordination of the protective relays and economic issues. Table 1 lists the currents of CT1 and CT2 as the ON/OFF operation of reactor for each different location. The currents through CTs are not the same, so the protection relay must be coordinated differently according to the reactor ON/OFF condition. Figure 4 gives an example of the re-coordination for overcurrent relay (OCR) of CT2, when the reactor is installed at the location of -<sup>1</sup> , -<sup>2</sup> , or -<sup>3</sup> [33].

Location -<sup>1</sup> is between the generator and the generator CT. The reactor is installed to suppress the voltage rise, but the line voltage is decreased too much if the reactor is turned on when the line voltage is not high. Therefore, the reactor should be turned on or off considering the status of line voltage. For a small synchronous generator, CT1 is usually attached close to the generator; it is difficult to install the reactor between the generator and CT1 practically.

Location -<sup>2</sup> is between the generator CT and the low-voltage side of the transformer. When the reactor is turned on with the generator start-up, protection relay 1 will detect only the generator current but protection relay 2 will perform the summing current of the generator and reactor. Therefore, 51 (overcurrent) and 87 (percent differential) of protection relay 2 should be re-coordinated, considering the two elements carefully.

**Figure 3.** Candidate for location of the reactor.


**Table 1.** CT currents according to locations of the reactor.

a is the active current of generator; b is the reactive current of the generator; and c is the reactive current of the reactor.

**Figure 4.** Example of re-coordination of overcurrent relay (OCR) due to installing the reactor.

Location -<sup>3</sup> is between the high-voltage side of the transformer and the transformer CT. The re-coordination process should be applied, the same as for location -<sup>2</sup> . The more serious issue with respect to installing a reactor at this location is that the price of the reactor is about twice as much as that of reactors for locations -<sup>1</sup> or -2 .

Location -4 is at DL side of the transformer CT. If a reactor is installed at this location, then there is no difference at protection relays 1 and 2 as the reactor is in ON/OFF operation. Therefore, it is sufficient to consider the reactor ON/OFF conditions only.

#### **3. Design and Application of Reactors**

#### *3.1. Design of Reactor*

Figure 5 shows the single line diagram of the application site. Two 1.5-MVA small hydro synchronous generators are connected in the grid, of which the output powers are limited to two-thirds of the rated output power due to the voltage rise. To increase the generator output powers with the accessible voltage rise, two 215-kVA reactor banks are installed at each generator. As mentioned in Section 2, it is recommended to install the reactor at the DL side of the transformer CT (location -<sup>4</sup> ). However, they are installed between the generator CT and the low-voltage side of the transformer (location -<sup>2</sup> ), because there is no space for the reactor to be installed in location -4 .

Table 2 lists the voltage rise rate corresponding to the power factor of the generator. As shown in Table 2, the leading power factor to connect the 3-MVA generator to DL should be 0.9385 or less to meet the 2% permissible voltage rise rate in Korea. On the other hand, the leading power factor of the applied generators is 0.99 and the 3.79% voltage rise rate is more than the permissible range. Therefore, it is necessary to install reactors to make the leading power factor less than 0.9385. The required capacity of the reactor can be calculated from Equation (5) and Figure 2, as shown in Table 3. Table 3 shows the voltage rise rates depending on the capacity of the reactor.

**Figure 5.** Single line diagram of application site.



**Table 3.** Voltage rise rate according to reactor capacity.


In Table 3, the reference for all values is the point at which the REG is connected to the DL. A is the case when the synchronous generators are connected without any reactors. The voltage rise rate is 3.78%, so it is necessary to install a reactor. The maximum capacity of the grid-connected synchronous generator to guarantee the permissible voltage rise rate without installing a reactor can be calculated using Equation (4) and 1.55 MVA. B is the case when the 613-kVA reactor calculated using Equation (5) is installed. The voltage rise rate is 2.22%, so the capacity of the reactor should be increased to meet the 2% voltage rise rate. C is this case and a 705-kVA reactor is installed. D is the case for the real implementation in this paper, in which an 860-kVA reactor is installed considering the margin because the power factor of REG is not fixed.

The inductive generator does not have an excitation system and cannot control the power factor. The generator has a fixed leading power factor of approximately 0.9, so the reactor is not necessary, as

shown in Table 2. On the other hand, the solar generating system has a fixed unit power factor, so a 1144 kVA reactor calculated from Section 2.1 should be installed for the DL. The maximum capacity of the grid-connected solar generator to guarantee the permissible voltage rise rate without installing a reactor is calculated using Equation (5) and 1.21 MW.

#### *3.2. Operation of Reactor*

If the reactor is switched ON–OFF at once, the reactor current flows either fully or not. The grid voltage is then changed considerably and the peripheral equipment may be adversely affected due to the switching surge. Therefore, it would be better to install several small capacity reactors to decrease the abrupt voltage variation. Many divisions allow the system to be controlled linearly but this is not cost-effective. Therefore, it is recommended practically to operate the reactor in two steps. In addition, the duration (DT) must be set to avoid repeating ON and OFF of the reactor in a very short time.

Based on the following information on the generator ON or OFF condition (G = 0 or 1), the number of ON reactors (R = 0 or 1 or 2), the active power of the generator (PG), and the voltage of DL (VCP) are detected to operate the reactor. The reactor is ON only if both conditions of the active power of the generator and the voltage of the DL are met. On the other hand, if one of the conditions is not met after being an ON reactor, the reactor is set to be switched OFF to prevent the voltage of DL becoming worse due to the operation of the reactor. Figures 6 and 7 present the recommended set values for the ON and OFF of the reactor, respectively. The duration should be determined by the control speed of the output. Therefore, it is recommended that the duration of solar or wind with a quick control speed be five minutes, and hydro with the late control speed duration be one minute.

Figure 6 shows the voltage set criteria for the ON and OFF operation of the reactor, which are the permissible maximum (VPMax) and minimum (VPMin) voltages of the DL. The voltage condition (VSTRON), in which two reactors are switched ON is a value obtained by subtracting the permissible voltage rise rate (%VPVRR) from VPMax. The voltage condition (VSORON), in which one reactor is switched ON, is the value obtained by subtracting %VPVRR from VSTRON. The voltage condition for the reactor OFF will be the opposite of the ON condition.

**9ROWDJH**

**Figure 6.** Voltage set of DL for ON and OFF of reactors.

**Figure 7.** Output set of REG for ON and OFF of reactors.

Figure 7 presents the output set criteria of REG for the ON and OFF operation of the reactor. The output condition (PSTRON) in which two reactors are switched ON is 95% of the rated output (Prated) of the REG. Half of the value obtained by subtracting the reactor-free output (PRFree) of REG in Section 3.1 from Prated is subtracted from Prated. This is the output condition (PSORON), in which one reactor is switched ON. The output condition for OFF of the reactor is below 10%Prated of the ON condition.

Figures 8 and 9 present the flow chart for the ON and OFF operation of the reactor. If the voltage of DL exceeds VSORON and the generator output exceeds PSORON in the case of reactor OFF state, and if the duration time exceeds the setting value, one reactor is turned ON, as shown in the left part of Figure 8. If the voltage of DL exceeds VSTRON and the generator output exceeds PSTRON in case of one reactor ON state, and if the duration time exceeds the setting value, one reactor is additionally turned ON as shown in the right part of Figure 8. On the other hand, if the voltage of DL is lower than VSOROFF or the generator output is lower than PSOROFF in the case of two reactors in the ON state, and if the duration time exceeds the setting value, one reactor is turned OFF, as shown in the left part of Figure 9. If the voltage of DL is lower than VSTROFF or the generator output is lower than PSTROFF in case of one reactor ON state, and if the duration time exceeds the setting value, the reactors are all turned OFF, as shown in the right part of Figure 9.

**Figure 8.** Flow chart for ON operation of reactors.

**Figure 9.** Flow chart for OFF operation of reactors.

#### **4. Demonstration and Effectiveness**

To demonstrate the research results, the grid-connected synchronous generators shown in Figure 5 are selected. The field application result is different from the result calculated from the theoretical equations. This is because the latter calculation has been done under the assumption of a no-load condition where the voltage rise is maximized by the connection of a generator to the grid, but the no-load condition cannot be provided in a field test. The load condition of the DL before and after installing the reactor cannot be the same because of the frequent variations of the load, DL voltage, and output in grid-connected DRs. Therefore, the effects of field application are analyzed in the following three ways. The first test is conducted in the connection point of REG, but the second and third tests are added in the terminal of generators. The data from the second and third tests are per second from the Supervisory Control and Data Acquisition (SCADA) system.

Firstly, the vector diagram of the no reactor operation and two reactors operation are compared, as shown in Figures 10a–d and 11a–d. Tests are conducted at similar active outputs for a one-day interval to meet the same test conditions as much as possible. The vector diagram shows the phase voltages (*VCP*) and currents (*ICP*) at the connection point of the REG to the DL. Compared to Figure 10, Figure 11 shows that the magnitude and phase angle of the current vector are increased due to the reactor operation. The substation voltage (*VS*) is calculated because the substation is very far from the power plant. The test results are applied in Equations (1)–(4) and Table 4 lists the effectiveness of the reactor operation. The substation voltages are 22,459 V, 22,449 V, 22,435 V, 22,448 V from Equation (4) and the voltage rises due to the connection of REG in the two reactors OFF state are 539 V, 549 V, 542 V, 548 V, but the reactor is not switched ON because the DL voltage does not satisfy the condition of the reactor ON. The substation voltages are 23,125 V, 23,337 V, 23,324 V, 23,331 V using Equation (4) and the voltage rises due to the connection of REG in two reactors ON state are 1 V, 3 V, 3 V, 6 V. Accordingly, the mitigations of the voltage rise are 538 V, 546 V, 539 V, 536 V with the installation of the reactor under similar test conditions.


**Figure 10.** Non-reactor operations (**a**) first (**b**) second (**c**) third (**d**) fourth.

**Figure 11.** Two-reactor operations (**a**) first (**b**) second (**c**) third (**d**) fourth.

Secondly, the daily connection voltage data before and after installing the reactor are analyzed. To compare the test results before and after installing the reactor, tests are conducted on the daily-maximum generation day in the same season to provide the same condition. The excessive voltage rise occurs when the generator output is connected to the grid without a reactor so that the output-rise can be 1000 kW, which is two-thirds of the rated output. Table 5 and Figure 12a–c present the comparison data of the output active power and the daily grid voltage before and after installing the reactor. The voltage of the connection point increases with increasing the output of REGs. On the other hand, despite the increase in output, the voltage decreased due to the reactor operation. Figure 12a–c show that the generator outputs are increased by 455 kW and 494 kW on average, respectively, but the grid voltage is decreased by 56 V.

Thirdly, the monthly average grid voltage data before and after installing the reactor are analyzed. Similar to the second test, the same month is chosen to provide the same test condition. Figure 13a–c shows the monthly average grid voltage before and after installation of the reactor. The average grid voltage without the reactor is 23,279 V on average, whereas it is 23,047 V with the reactor, i.e., the reactor results in the voltage decrease of 233 V.


**Table 5.** Comparison of output active power and daily grid voltage before and after installing reactors.

**Figure 12.** Output active power and daily grid voltage before and after installing reactors; locations -2 , -<sup>3</sup> , -<sup>4</sup> , -<sup>5</sup> , -6 are same as in Table 5 (**a**) first (**b**) second (**c**) third.

**Figure 13.** Comparison of monthly average grid voltage before and after installing the reactor. (**a**) first (**b**) second (**c**) third.

#### **5. Conclusions**

To mitigate the voltage rise caused by the connection of synchronous generators of DRs to DL, the adoption of a reactor of a reactor was studied in this paper. From the vector analysis, it was verified that the capacity of the reactor depends on the power factor of the generator. Therefore, the maximum grid-connected capacity of the DRs without a reactor can be calculated if the power factor and line constant are pre-determined, and the necessary capacity of a reactor to mitigate the voltage rise of the DL can be derived. The advantages and disadvantages at each location considering the necessity of re-coordination of a protection relay and the loss of generation revenue according to the installation locations were analyzed comparatively. Among four candidates for a reactor location, it was verified that the reactor at the grid-connected point did not affect the coordination of the protection relay and no additional protection was necessary. It was found that the ON–OFF switching of the large reactor caused an abrupt rise and fall of the DL voltage. Therefore, dividing the reactor into a couple of small reactors to be switched ON–OFF in two steps was recommended. The adoption of more steps might allow the easy and smooth control of the DL voltage, but it incurs a higher cost. In addition, the reactor should be switched ON in the 'AND' condition, satisfying both the grid voltage and the generator output, and be switched OFF in the 'OR' condition in the case of not satisfying one of the conditions. Furthermore, the system must be set to avoid the reactor being switched ON–OFF repeatedly in a short time frame.

From the field application data for power plants with voltage rising problems, this study concludes that the generator output could be increased from 1000 kW to 1500 kW, and the daily average voltage and the monthly average voltage at the connection point could be reduced 300 V and 200 V, respectively.

**Acknowledgments:** This study was supported by the KETEP (Korea Institute of Energy Technology Evaluation and Planning) through the (*Development for Microgrid Common Platform Technology, 20141010501870*) project.

**Author Contributions:** Yeonho Ok and Jaewon Lee conceived and designed the tests; Yeonho Ok and Jaeho Choi analyzed the data and wrote the paper.

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

#### **References**


© 2017 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* **Power Quality Disturbance Classification Using the S-Transform and Probabilistic Neural Network**

**Huihui Wang 1,2,\*, Ping Wang <sup>1</sup> and Tao Liu <sup>3</sup>**


Academic Editor: Birgitte Bak-Jensen Received: 19 September 2016; Accepted: 9 January 2017; Published: 17 January 2017

**Abstract:** This paper presents a transient power quality (PQ) disturbance classification approach based on a generalized S-transform and probabilistic neural network (PNN). Specifically, the width factor used in the generalized S-transform is feature oriented. Depending on the specific feature to be extracted from the S-transform amplitude matrix, a favorable value is determined for the width factor, with which the S-transform is performed and the corresponding feature is extracted. Four features obtained this way are used as the inputs of a PNN trained for performing the classification of 8 disturbance signals and one normal sinusoidal signal. The key work of this research includes studying the influence of the width factor on the S-transform results, investigating the impacts of the width factor on the distribution behavior of features selected for disturbance classification, determining the favorable value for the width factor by evaluating the classification accuracy of PNN. Simulation results tell that the proposed approach significantly enhances the separation of the disturbance signals, improves the accuracy and generalization ability of the PNN, and exhibits the robustness of the PNN against noises. The proposed algorithm also shows good performance in comparison with other reported studies.

**Keywords:** transient power quality; S-transform; width factor; feature extraction; probabilistic neural network (PNN)

#### **1. Introduction**

In recent years, with the development and increasing implementation of distributed generation and micro-grids, large numbers of high-speed switching devices and non-linear converters are integrated into the power system. They are sources of power quality (PQ) disturbances such as sag, swell, interruption, flicker, harmonic, and oscillatory transients, etc. These voltage disturbances degrade the end user's experience, and more importantly, it may damage modern precision devices and seriously affect the production efficiency of the manufacturing industry. Owing to the facts above, the problem of PQ disturbance detection and classification has received the attention of many scholars [1].

To understand the PQ disturbance, the time-frequency characteristics of disturbances signals need to be extracted and analyzed. Various signal processing algorithms, for example, Fourier transform (FT), short time Fourier transform (STFT) [2], wavelet transform (WT) [3,4], and Stockwell transform (S-transform) [5,6] have been utilized for this purpose. FT has the advantages of requiring a relatively less amount of calculation and broad applicability, however it has the disadvantages of spectrum leakage and fence effect, and it is limited to only detecting steady state signals. STFT transforms a

signal into a two-dimensional complex function which reveals the frequency characteristics of the signal at each time instant, however its time window is relatively fixed and it is difficult to balance the frequency domain resolution and time domain resolution. WT can accurately detect the singular point and the time instant at which the PQ disturbance occurs, however it is time consuming and susceptible to noises. To overcome the disadvantages of the WT, Stockwell et al. [7] proposed the S-transform, which is conceptually a hybrid of STFT and WT. Compared with WT, S-transform can be treated as an extension of WT, on the other hand, S-transform can be treated as STFT with a variable window. S-transform has superior characteristics to WT and STFT, and it has good time-frequency focusing characteristics, satisfactory time-frequency resolution, and noise immunity. The features extracted with the S-transform of the disturbance signals are directly useable in intelligent algorithms for classification [8,9].

To make the S-transform more effective for different particular application focuses, various forms of S-transform have been proposed and examined. For example, to enable a flexible regulation of the time resolution and frequency resolution, a width factor is introduced into S-transform, which makes the width of Gaussian window adjustable. To have a better control over the scale and the shape of the analyzing window, a parameter P is introduced into the Gaussian window function [10–12]. Moreover, in [13], the frequency domain is segmented into domains of different frequencies, low, medium, and high. Within in different frequency domain, the width factor of the S-transform is different, which brings different time-frequency resolution the corresponding frequency domain, so the accuracy of PQ classification can be improved. In mechanical engineering, to analyze the vibration data, asymmetrical window function instead of the regular symmetrical one is used in S-transform [14]. To improve the ability for resolving signals whose frequency changes with time, a complex Gaussian window function is adopted in S-transform [15].

For PQ disturbance classification, it has been proven that S-transform-based approaches are effective, but efforts are needed to make them more favorable [16]. Conventionally, the S-transform used for this purpose takes its basic form—a symmetrical real Gaussian window function without a width factor or with a width factor but it takes a fixed value throughout. This paper studies how to make the S-transform more applicable to PQ disturbance classification by investigating its role in the S-transform-based classification approach. Specifically, an S-transform with a width factor is used; the determination of the value of the width factor is handled in a systemic view of the PQ disturbance classification problem itself. In other words, the width factor is treated as a variable. Its value is made to be feature oriented considering the fact that different features react to the time resolution or the frequency resolution differently.

As for the classification analysis, PNN is adopted in our study. The considerations are briefly given as follows. So far, various intelligent algorithms have been used to classify the PQ disturbances, for example, artificial neural network (ANN) [17], fuzzy logic [18], support vector machine (SVM) [19], etc. Artificial neural networks are mainly used for pattern matching, classification, function approximation, optimization, and data clustering. Neural networks have obvious advantages and have been widely used in PQ classification and fault diagnosis [20,21]. Multi-layer perceptron (MLP) and PNN are the typical forward neural network structures. Compared with MLP, PNN has many advantages such as simple structure, fast training rate, high accuracy, good generalization ability, and robustness, moreover, the training process of PNN is a single-pass network training stage without any iteration for weight adjustment, and it can be easily retrained to adapt to any network topology changes. In the comparison between PNN and the other two well-known neural networks i.e., feed forward multilayer (FFML) back propagation and learning vector quantization (LVQ), PNN provides better performance in terms of the classification results [16,19,22,23]. Based on the advantages of PNN and the characteristic of PQ disturbances, PNN is considered to be more favorable for PQ disturbances classification.

In summary, a PQ disturbance classification approach based on S-transform with a feature oriented regulatory and PNN is proposed and examined. Contents of sections below include: firstly, four features are selected through investigating the impacts of the width factor on the

S-transform-Amplitude matrix of eight disturbance signals and the behavior of signal separation based on the features extracted; secondly, favorable value of the width factor used to extract each of the four features from the S-transform-amplitude matrix of disturbance signals is determined by examining the impacts of the width factor on the performance of PNN used for disturbance classification, and finally the proposed approach is tested, showing that it has higher classification accuracy and performs well with and without the noises.

#### **2. Power Quality Disturbance Classification Based on Generalized S-Transform and Probabilistic Neural Network**

In this section, first, the PQ disturbance classification algorithm based on S-transform and PNN is briefly described. Then, details of each functional unit of the algorithm are given, including the definition of eight disturbance signal types and the normal sinusoidal signal used in this study, mathematic description of S-transform without and with a width factor, definition of signal features and corresponding extraction formulation, and PNN. Finally, work of the authors is briefly introduced. Specifically, it is the implementation of the S-transform with a feature oriented optimal width factor to realize effective classification of the nine types of signals with a PNN.

#### *2.1. Method Overview*

The PQ disturbance classification based on S-transform and PNN is illustrated in Figure 1. It contains three steps: (1) S-transform, by which the time and frequency information of the given PQ disturbance signal are obtained; (2) feature extraction, by which the customized feature vectors are further extracted from the time and frequency information obtained in step (1); (3) disturbance classification with PNN, the input of which is the feature vector of the PQ disturbance signal and the output of which is the disturbances classification result.

**Figure 1.** The schematic diagram of power quality (PQ) disturbance classification using S-transform and probabilistic neural network (PNN).

#### *2.2. Disturbance Signal Types*

IEEE Standard 1159 and the European standard EN50160 give definitions for various PQ disturbances and the corresponding suggested threshold settings [24,25]. For instance, Figure 2 shows the disturbance defined as a sag in the mentioned standards, which occurred to a normal sinusoidal voltage during the time approximately from 0.02 s to 0.14 s. The disturbance signal was captured on 21 March 2014 in Jurong East which located in the West Region of Singapore. The official source said it was due to a customer installation fault at Jurong Gateway Road. The PQ will be considered poor if the voltage magnitude is lower than the threshold set by the standard. In this specific case, the threshold should be 90% of the normal voltage magnitude.

**Figure 2.** The waveform of sag captured from actual power system [26].

Table 1 lists the PQ disturbance types considered in this paper. Each disturbance type is described with an equation with parameters, with which the disturbance generated comply with the corresponding disturbance defined in IEEE standard 1159-1995 [24]. S1, S2, ... , and S8 denote sag, swell, interruption, flicker, oscillatory transient, harmonic, sag & harmonic, and swell & harmonic, respectively, S9 denotes normal signal. Where *f* = 50 Hz; ω = 2π*f*; *T* = 1/*f*. The parameters for the equations such as α, α3, α5, α7, *t*1, *t*2, αf, β, τ, *fn* are determined randomly within the thresholds.


**Table 1.** Mathematical model of PQ disturbances.

#### *2.3. Generalized S-Transform and Feature Extraction*

#### 2.3.1. Generalized S-Transform

The continuous S-transform of signal *x*(*t*) is described as:

$$S(\pi, f) = \int\_{-\infty}^{\infty} x(t)w(\pi - t, f) \mathbf{e}^{-i2\pi ft} \,\mathrm{d}t \tag{1}$$

where *f* is the frequency of signal *x*(*t*). w(τ − *t*, *f*) is Gaussian window function, it is defined as:

$$w(\tau - t, f) = \frac{1}{\sigma \sqrt{2\pi}} \mathbf{e}^{\frac{-(\tau - t)^2}{2\sigma^2}} \tag{2}$$

The S-transform matrix is a complex matrix whose rows pertain to frequency and columns to time. According to the Heisenberg principle, the time and frequency resolution cannot be improved at the same time. The intent of using the Gaussian window function in Equation (1) is to allow a better balancing between the time resolution and the frequency resolution. In Equation (2), τ is the point at the time axis at which the center of *w*(τ − *t*, *f*) sits. σ is a scale factor, it is defined as:

$$
\sigma = 1/|f|\tag{3}
$$

To make the Gaussian window function more effective, a width factor λ is introduced to Equation (3):

$$
\sigma = \lambda / |f|\tag{4}
$$

Changing the value of λ adjusts the value of scale factor σ and therefore makes the width of Gaussian window function adjustable. If a value greater than 1 is assigned to λ, for the same frequency point, Gaussian window will be wider than in the case where λ takes a value of 1. Thus, higher frequency resolution can be achieved in time-frequency domain. Inversely, if a value less than 1 is assigned to λ, for the same frequency point, Gaussian window will be narrower than in the case where λ takes a value of 1. Thus, higher time resolution can be achieved in time-frequency domain.

For instance, Figure 3 shows the effect of width factor on the time-frequency analysis of S-transform. The source signal, as shown in Figure 3a consists of two sinusoidal signals of different frequencies, 50 Hz for the signal from time 0 to 0.1 s, 100 Hz for the signal from 0.1 to 0.2 s. Width factors under examination are 0.2 and 2.0. In the case of λ > 1.0, the Gaussian window will be wider and cover more line frequency cycles, and this will help to improve the accuracy of frequency analysis of the signal. However, a wider Gaussian window will not make it easy to identify the time instant at which the frequency of the signal changes. In the case of λ < 1.0, the Gaussian window will be narrower and cover fewer line frequency cycles, this will decrease the accuracy of frequency analysis of the signal, but a narrower Gaussian window will make it easy to identify the time instant at which the frequency of the signal changes.

The result presented in Figure 3b shows that by using a width factor greater than 1.0, the frequency of two sine signals can be satisfactorily identified, as seen the two thin frequency bands in sharp yellow, however, this brings more uncertainty on the time of the signal changes because the changing part of the two frequency bands is not clear. This indicates a width factor greater than 1.0 helps to achieve the better frequency resolution, but the time resolution will get worse. On the contrary, the result presented in Figure 3c shows that using a width factor less than 1.0, the frequency of two sine signals cannot be clearly identified, as seen the two thick frequency bands in sharp yellow, however, the changing part of the two frequency bands is clearly identified. This indicates a width factor less than 1.0 results unsatisfactory frequency resolution, but the time resolution will get better.

Substituting Equation (4) into Equation (1), the continuous generalized S-transform takes the form:

$$S(\mathbf{r}, f) = \int\_{-\infty}^{\infty} \mathbf{x}(t) \frac{|f|}{\lambda \sqrt{2\pi}} \mathbf{e}^{\frac{-(t-\tau)^2 f^2}{2\lambda^2}} \mathbf{e}^{-i2\pi ft} \mathbf{d}t \tag{5}$$

**Figure 3.** Time-frequency analysis results with different setting value of the width factor. (**a**) The comparison of the Gaussian windows with different width factor; (**b**) Time-frequency spectrum with λ = 2.0 and (**c**) Time-frequency spectrum with λ = 0.2.

Then, with the definition τ = *mT*, *f* = *n*/*NT*, the discrete generalized S-transform expression can be obtained:

$$\begin{cases} S[mT, \frac{n}{NT}] = \sum\_{k=0}^{N-1} X[\frac{k+n}{NT}] e^{-\frac{2\pi^2 k^2 k^2}{n^2}} e^{\frac{2\pi mk}{N}} & n \neq 0\\\ S[mT, 0] = \frac{1}{N} \sum\_{k=0}^{N-1} X[\frac{k}{NT}] & n = 0 \end{cases} \tag{6}$$

where *k*, *m*, *n* = 0, 1, ... , *N* − 1, *N* is the total number of sampling points. *T* is the time interval between two consecutive sampling points. *X* is the discrete Fourier transform.

Further, for the purpose of extracting the features of disturbance signals, the S-transform-Amplitude (STA) matrix is calculated as follows:

$$A[mT, \frac{n}{NT}] = \left| S[mT, \frac{n}{NT}] \right| \quad m, n = 0, 1, \dots, N - 1 \tag{7}$$

#### 2.3.2. Feature Extraction

Feature extraction is one of the essential steps of PQ disturbance classification. Below are definitions of 10 features extracted from STA matrix.

F1: maximum amplitude of *TmA*-plot (time-maximum amplitude plot), and it has:

$$\text{F1} = \max\{TmA(m)\}\tag{8}$$

where *TmA*-plot is maximum amplitude versus time by searching columns of STA matrix given in Equation (7) at every frequency, *TmA*(*m*) = max7 *A*[*mT*, *<sup>n</sup> NT* ] 8 .

F2: minimum amplitude of the *TmA*-plot:

$$\text{F2} = \min\{Tm A(m)\}\tag{9}$$

F3: mean value of the *TmA*-plot:

$$\text{F3} = \frac{1}{N} \sum\_{m=1}^{N} TmA(m) \tag{10}$$

F4: standard deviation of *TmA*-plot:

$$\text{F4} = \sqrt{\frac{1}{N} \sum\_{m=1}^{N} \left( TmA(m) - \text{F3} \right)^2} \tag{11}$$

F5: the summation of the maximum and minimum of the *TmA*-plot:

$$\mathbf{F5} = \mathbf{F1} + \mathbf{F2} \tag{12}$$

F6: the standard deviation of *FmA*-plot (frequency maximum amplitude plot, which is maximum amplitude versus frequency by searching the rows of STA matrix at each time instant) for frequencies above four times the line frequency. It has:

$$\text{F6} = \sqrt{\frac{1}{N} \sum\_{n=1}^{N} \left( FmA(n) - \overline{FmA(n)} \right)^2} \tag{13}$$

where *FmA*(*n*) = max7 *A*[*mT*, *<sup>n</sup> NT* ] 8 with *<sup>n</sup> NT* <sup>&</sup>gt; 200, *FmA*(*n*) is the mean value of *FmA*(*n*). F7: the subtraction of the maximum and minimum of the *FmA*(*n*):

$$F\mathbb{Z} = \max(FmA(n)) - \min(FmA(n))\tag{14}$$

F8: the Skewness of *FmA*-plot:

$$\text{F8} = \frac{1}{(N-1)\text{F6}^3} \sum\_{n=1}^{N} \left( FmA(n) - \overline{FmA(n)} \right)^3 \tag{15}$$

F9: the Kurtosis of *FmA*-plot:

$$\text{F9} = \frac{1}{(N-1)\text{F6}^4} \sum\_{n=1}^{N} \left(FmA(n) - \overline{FmA(n)}\right)^4 \tag{16}$$

F10: standard deviation of *mr* plot, where *mr* is time-amplitude plot determined by the frequency which has maximum amplitude in STA matrix above the frequency of 200 Hz, and it has

$$\text{F10} = \sqrt{\frac{1}{N} \sum\_{m=1}^{N} \left( mr(m) - \overline{mr(m)} \right)^2} \tag{17}$$

where *mr*(*m*) = *A*[*mT*, *nmr NT* ] 8 , and *nmr* <sup>=</sup> argmax *<sup>n</sup>* 7 *A*[*mT*, *<sup>n</sup> NT* ] 8 with *<sup>n</sup> NT* <sup>&</sup>gt; 200.

Apparently, when more features are used, a better classification effect may be expected. However, increasing the number of features results in a substantial increase of the calculation time as the scale of ANN used for disturbances classification will be increased. Therefore, the number of features used for the PQ disturbance classification should be as few as possible without obviously decreasing the classification accuracy. In this paper, four features are chosen according to the characteristic of disturbance and width factor, which are presented in Section 3.1.

#### *2.4. Probabilistic Neural Network*

As shown in Figure 1, a vector of features selected is used to be the input of PNN. The output of PNN will be the disturbance type. Figure 4 shows the schematic diagram of PNN. It contains four layers: input layer, pattern layer, summation layer, and competitive layer. The function of each layer is as follows.

*Energies* **2017**, *10*, 107

Pattern layer calculates Euclidean distance between the feature vectors of PQ disturbance testing sample *X* and every PQ disturbance training sample *Xij*, respectively. Below is the equation:

$$H\_{ij}(X) = \frac{1}{(2\pi)^{n/2}\delta^n} e^{-\frac{\|X - X\_{ij}\|^2}{2\delta^2}}\tag{18}$$

where *X* = [F1 F2 F3 ... F*n*] <sup>T</sup> is the feature vector of an PQ disturbance testing sample, and F1, F2, F3, ... , F*n* are the features as defined in Section 2.3; *n* is the dimension of the feature vector; *Xij* is the feature vector of *i*th training sample of PQ disturbance type *Sj*, *Sj*∈ {S1, S2, ... , S9}; δ is a smoothing parameter.

Summation layer makes summation of the results output from pattern layer, and the calculated conditional probability of *X* belonging to PQ disturbance type *Sj* is given below:

$$\mathbb{C}\_{j}(X) = \frac{1}{N\_{\restriction}} \sum\_{i=1}^{N\_{\restriction}} H\_{ij}(X) \tag{19}$$

where *Nj* is the number of training samples belonging to PQ disturbance type *Sj*.

In the competitive layer, *X* is assigned to the PQ disturbance type with maximum conditional probability. It has:

$$\text{type}(X) = \underset{j}{\text{argmax}} \left\{ \mathbb{C}\_{j}(X) \right\} \tag{20}$$

**Figure 4.** The schematic diagram of PNN.

#### **3. Power Quality Disturbance Classification Based on Generalized S-transform with Feature Oriented Width Factor and Probabilistic Neural Network**

The goal of this study is to realize an effective and efficient classification with high accuracy for eight types of disturbance signals plus the normal signal given in Section 2.2 using an approach based on the S-transform with a favorable width factor and PNN. Contents presented below include: selection of features used as inputs of PNN—four of ten are selected after examination; favorable value determination of the width factor for each of the four selected features by investigating the impacts of width factor on the PNN performance, and implementation of PNN for disturbance classification.

#### *3.1. Method Proposed—Considering the Width Factor to Be Feature Oriented*

In conventional PQ disturbance classification based on S-transform, the width factor λ is treated as a constant. In other words, all features interested are extracted from the S-transform matrix obtained with a width factor of the same value. Our studies, presented here, reveal that considering the width factor λ to be feature oriented renders a more satisfactory result. Implementation data and results presented below include: how does the STA-matrix of S-transform vary with λ, how does the effect of the feature separation behavior change with λ, and how does the classification accuracy of PNN vary with λ.

#### 3.1.1. Effect of Width Factor on S-Transform-Amplitude-Matrix

Figure 5a–h shows the 3D plots of the STA-matrix of eight disturbance signals, listed in Table 1. For each disturbance signal, there are three 3D plots, which are graphical presentation of the STA-matrix obtained with three different values of the width factor λ, respectively. The STA-matrix is obtained per Equations (6) and (7); three values of λ are 0.1, 1.0, and 3.0. The values of λ, 0.1, 1.0, and 3.0 are selected per what was presented in Section 2.3.1: One less than 1.0, 0.1, which is used to examine its impacts on the low frequency domain resolution; one greater than 1.0, 3.0, which is used to examine its impacts on the high frequency domain resolution, and the value of 1.0, which is used as the base for comparison purpose.

**Figure 5.** *Cont*.

**Figure 5.** *Cont*.

**Figure 5.** Disturbance signal and 3-D time-frequency magnitude spectrum. (**a**) sag; (**b**) swell; (**c**) interruption; (**d**) flicker; (**e**) oscillatory transient; (**f**) harmonic; (**g**) sag & harmonic; and (**h**) swell & harmonic.

3D plots in Figure 5 illustrate the behavior of the time-frequency characteristic of STA-matrix of each specific disturbance signal under the condition that different values of λ are used. This information helps to understand the advantages of introducing the width factor λ and the impacts of different λ values on distinguishing eight disturbance signals, S1 to S8.

Disturbance signals S1–S8 can be divided into three groups in terms of their characteristics: group 1 which has S1–S4, group 2 which has S5 and S6, and group 3 which has S7 and S8. The characteristic of group 1 is that the disturbances occur to the amplitude of the signals at the line frequency for a short period of time. Plots in Figure 5a, as an example, show the S-transform results of sag, and it can be seen that:


The characteristic of group 2 is that the disturbance appears to be the occurrence of harmonic components for a certain period of time or the harmonic components existing over the entire time range. The common feature of these two disturbance signal types is that the amplitude of the line frequency component of them stays unchanged. The difference between these two signals and the others are in the high-frequency domain. Plots in Figure 5e–f show the S-transform results of oscillatory transient and harmonic, and it can be seen that: (1) when the width factor takes a value less than 1.0, the frequency resolution of the STA matrix gets significantly reduced; High-frequency components which apparently do not belong to the original signals appear in the high-frequency domain; (2) these high frequency-components gradually fade away as λ increases. In the case when λ takes a value greater than 1.0, the high-frequency characteristics of the oscillatory transient and harmonic are well represented in the high-frequency domain.

Based on what are presented above, one can draw a conclusion that: A less than 1.0 value of λ results a better presentation of the behavior of the original signal at the line frequency, but distort the presentation of the behavior of the original signal in the high-frequency domain; A greater than 1.0 value of λ results a distorted presentation of the behavior of the original signal at the line frequency, but improves the presentation of the behavior of the original signal in the high-frequency domain. This indicates that combination of features is needed for the classification of different signals. As the signals of sag, swell, interruption, and flicker can be distinguished from others by the characteristic at the line frequency, a less than 1.0 value of λ is needed in the setting of the corresponding features; As the signals of oscillatory transient and harmonic can be distinguished from others by the characteristic in the high-frequency domain, a greater than 1.0 value of λ is needed in the setting of the corresponding features.

Characteristic of group 3 combines the characteristics of groups 1 and 2. Special attention needs to be paid to disturbance types S7 and S8, which are the combination of sag & harmonics and swell & harmonics, respectively. Investigation given above tells neither a value less than 1.0 nor a value greater than 1.0 ensures a successful separation of S7 or S8 form S1–S6, so in this condition, it needs combination of features to distinguish these disturbances from others.

In summary, to realize classification of the nine signal types defined in Table 1, a combination of features is needed; to make the classification more effective and efficient, making the width factor feature oriented may be considered.

#### 3.1.2. Effect of Width Factor on Feature Distribution Behavior

Different features represent different characteristics of signals. Among the 10 features defined in Section 2.3.2, features F1–F5, give an intuitive description of disturbance signals S1–S9 at the line frequency. Differently, features F6–F10, give an intuitive description of signals in the high-frequency domain. Specifically, F6–F9 expresses the frequency characteristic of signals in the high-frequency domain and F10 expresses the time characteristic of signals in the high-frequency domain. For a successful distinction of PQ disturbances S1–S9, commonly experienced in power system, a combination of features is needed per what are presented above. The goal is to use the least number of features to realize the classification with high accuracy. Various combination possibilities were examined. Combination of F2, F5, F7, and F10 was found to be the most applicable to our purpose:


Based on the features F2, F5, F7, F10 above, firstly, to get intuitionistic vision, the distributions of PQ disturbances are shown in plots with the features combination F5 & F7, F5 & F10, F2 & F10. By analyzing the separation degree of eight types of PQ disturbances and the normal signal with different setting of λ (λF2, λF5, λF7, λF10), the distributions of PQ disturbances are shown in Figures 6–8.

**Figure 6.** Comparison of F5 and F7 distribution behavior: (**a**) λF5 = 1.0, λF7 = 1.0; and (**b**) λF5 = 0.2, λF7 = 3.0.

**Figure 7.** Comparison of F5 and F10 distribution behavior: (**a**) λF10 = 1.0, λF5 = 1.0; and (**b**) λF10 = 3.0, λF5 = 0.2.

**Figure 8.** Comparison of F10 and F2 distribution behavior: (**a**) λF10 = 1.0, λF2 = 1.0; and (**b**) λF10 = 3.0, λF2 = 0.1.

Figure 6 shows distributions of F5 & F7 of signals S1–S9. Figure 6a is the distribution obtained with both λF5 and λF7 taking a value of 1.0, which is the case of the features extracted from traditional S-transform. It shows that there is obvious overlapping between areas taken by S1, S3, and S7, respectively. Also, the areas taken by S2 and S8 respectively are too close to be easily separated. This will reduce the accuracy of classification algorithm. For comparison, Figure 6b shows the results obtained with λF5 = 0.2 and λF7 = 3.0, determined per discussion above. It can be seen that areas taken by S1, S3, and S7 are nicely separated, and there appears a clear space between areas taken by S2 and

S8. Feature F7 is used to distinguish S1–S4 from S5–S6. Comparison between results obtained with λF7 = 1.0 and λF7 = 3.0, it can be seen the separation between S1–S4 and S5–S6 along the longitudinal axis (the direction of F7 axis) are much better in the case which λF7 is equal to 3.0.

Figure 7 shows distributions of F10 & F5 of signals S1–S9. Figure 7a is the distribution obtained with both λF10 and λF5 taking a value of 1.0. It shows that there are obvious overlapping between areas taken by S1, S3 and S7; Figure 7b shows the results obtained with λF10 = 3.0 and λF5 = 0.2. It shows that areas taken by S1, S2, S3, S7, S8 are nicely separated. F10 is used to separate transient oscillation S5 and harmonic S6, F2 and F10 distribution map given in Figure 7a shows that there is obvious overlapping between S5 and S6 along the horizontal axis (the direction of F10 axis) with λF10 = 1.0 while Figure 7b, there appears a clear space between areas taken by S5 and S6 with λF10 = 3.0.

Figure 8 shows distributions of F10 & F2 of signals S1–S9. Feature F2 contributes to the separation of normal signal, sag, swell and interruption. The result in Figure 8a shows that, along the longitudinal axis (the direction of F2 axis), there is obvious overlapping between areas taken by S1 and S3, and also some overlapping between areas taken by S2 and S4 with λF10 = 1.0; the result in Figure 8b shows that areas taken by S1 and S3, S2 and S4 are nicely separated with λF10 = 3.0. Moreover, comparison between Figure 8a,b says the S7 can be nicely separated from other signals with λF10 = 3.0, λF2 = 0.1.

In summary, results presented in Figures 6–8 confirm that a combination of features is needed to separate S1 to S9. The results also verify that making λ feature oriented and using a favorable value instead of 1.0 for λ helps to achieve a satisfactory separation of S1–S9. In addition, for features which work better with λ greater than 1.0, λ values greater than 3.0 were tested and the result tells the improvement of the separation of signals S1 to S9 is insignificant. Similar results were obtained if values less than 0.1 are applied to λ for those features which work better with λ less than 1.0. Therefore, the variation range of λ used in the PNN section below is set to be from 0.1 to 3.0.

#### **4. Determination of the Favorable Value of Feature Oriented Width Factor with the Use of Probabilistic Neural Network**

This section presents the determination of favorable width factor set (λF2, λF5, λF7, and λF10) with PNN. Inputs of PNN are features F2, F5, F7, and F10 of the signal being classified. F2, F5, F7, and F10 are calculated from the S-transform matrix generated with width factor (λF2, λF5, λF7, and λF10); output of PNN is the classification result. The objective is to obtain the favorable value of (λF2, λF5, λF7, and λF10), with which and a trained PNN the classification of disturbances which falls into S1–S9 can be achieved with high accuracy. Steps for finding the favorable width factor (λF2, λF5, λF7, and λF10) are given in Figure 9.

64 = 1296 combinations of width factor λF2 λF5 λF7 λF10, see the external loop of the flowchart in Figure 9, are examined, which are generated by assigning each element of [λF2 λF5 λF7 λF10] with 0.1, 0.3, 0.6 1.0, 2.0, and 3.0, respectively. For each width factor combination set [λF2 λF5 λF7 λF10]: (1) in PNN training, 900 samples of signals are used, which are obtained by randomly generating 100 signals for each of nine signal types; in PNN testing, similarly, 900 randomly generated samples of signals are used; (2) the feature vectors [F2 F5 F7 F10] are extracted from the 1800 samples of signals by using the S-transform with the corresponding width factor combination [λF2 λF5 λF7 λF10]; (3) the PNN are trained and tested with the feature vectors [F2 F5 F7 F10] (900 for training; 900 for testing), and the classification error for the corresponding width factor combination [λF2 λF5 λF7 λF10] is evaluated.

In the process explained above, the 200 signals (100 for PNN training; 100 for PNN testing) of each disturbance type are generated by randomly selecting the value of parameters used by each disturbance signal type, seen the parameter column of Table 1. To mitigate the possible randomicity-related classification error, the internal loop is repeated six times, *q* = 6, as shown in the flowchart in Figure 9. The classification errors of PNN are calculated six times, and the average of the obtained six classification errors is taken as testing error of the PNN. The obtained testing errors of PNN are presented in Figure 10 with spheres, the size of which is proportional to the value of the corresponding error.

**Figure 9.** The flow chart for the PNN classification error.

**Figure 10.** The error of PNN classification with the width factors combination [λF2 λF5 λF7 λF10] varying in the range of 0.1–3.0 (the smaller the radius of sphere, the smaller its corresponding classification error).

Firstly, take a look at Figure 10a. The size of spheres becomes smallest when λF2 takes the smallest value 0.1, λF7 and λF10 takes their greatest value 3.0. Similarity exists in Figure 10b–f. In other words, the smallest spheres on Figure 10a–f all locate at the lower right corner in the back. This tells us that favorable values for λF2, λF7 and λF10 are 0.1, 3.0, and 3.0, respectively. Then, comparing the size of the smallest sphere of each individual subfigure, one can see that the sphere at the lower right corner in the back of Figure 10a has the smallest size. This tells us that the PNN classification error becomes the least if λF5 takes a value of 0.1. Numbers in percentage format shown on the upper right corner in the back of each subfigure are the classification error of PNN corresponding to the sphere of the smallest size of each individual subfigure. It shows that the trained PNN will have the classification error be less than 1% (0.741% on Figure 10a) if λF2, λF5, λF7, and λF10 take their values to be 0.1, 0.1, 3.0, and 3.0, respectively. The trained PNN, with features F2, F5, F7, F10 as inputs, may provide a satisfactory classification of PQ disturbance S1 to S8 and the normal sinusoidal signal if F2, F5, F7, F10 are extracted from S-transform matrix obtained with width factors λF2, λF5, λF7, λF10 equal to 0.1, 0.1, 3.0, 3.0, respectively.

#### **5. Accuracy of the Proposed Power Quality Disturbance Classification Approach**

Without noise, classification results of PNN corresponding to the favorable width factor combination are shown in Table 2, and the classification accuracy is 99.259%. To analyze the effect of noise on the classification errors, different levels of noise are added to the nine types of signals. The results are listed in Table 3. The level of noise is expressed by the signal-to-noise ratio (*SNR*), and *SNR* = 20log10(*A*S/*A*N), where *A*<sup>S</sup> and *A*<sup>N</sup> are the maximum amplitude of the signal and noise, respectively.


**Table 2.** PNN classification results with the favorable width factor combination.

**Table 3.** PNN classification accuracy with noise conditions.


As can be seen from Table 3, for the PQ disturbances without noise, the classification accuracy corresponding to the optimal width factor is 1.84%–7.86% higher than that of other width factor settings. The favorable width factor still maintains a good classification accuracy under noise (20 dB) and the classification accuracy is 2.21%–8.31% higher than the other width factor settings, including the traditional width factor settings ([λF2 λF5 λF7 λF10] = [1.0, 1.0, 1.0, 1.0]).

#### **6. Performance Comparison**

In order to evaluate the effectiveness and feasibility of the proposed algorithm, Table 4 shows the comparison between the obtained results in this paper and the reported results by other studies [4,8,16,17].


**Table 4.** Performance comparison in terms of percentage of correct classification results.

In [8,16], the classification accuracy of each PQ disturbance is lower than that of the proposed algorithm. For [4], the classification accuracy of each PQ disturbance is lower than that of the proposed algorithm except S7. For [17], the classification accuracy of each PQ disturbance is lower than that of the proposed algorithm, except for S1 and S2. The average classification accuracy shows the ratio of correctly classified PQ disturbances to the total number of PQ disturbances, and the proposed method gives the best classification results for this case.

The classification accuracy comparison between the proposed algorithm and other reported studies is shown in Table 5. For the PQ disturbances without noise, the classification accuracy corresponding to the proposed algorithm is 99.26% higher than that of other algorithms. For the PQ disturbances with low level noise condition (40 dB), the classification accuracy corresponding to the proposed algorithm is 99.13% slightly lower than that of the algorithm in [27], but higher than that of other algorithms. For the PQ disturbances with high level noise condition (30 dB), the classification accuracy corresponding to the proposed algorithm is 98.63% higher than that of other algorithms.


**Table 5.** Comparison between the proposed algorithm and other algorithms with noise conditions.

#### **7. Conclusions**

This paper proposed a PQ disturbance classification approach based on S-transform with a feature-oriented width factor and PNN. By introducing a width factor into the conventional S-transform, the time resolution and the frequency resolution presented by the STA matrix of the signal being analyzed is made adjustable. In this way, the impact of the width factor on the 3D-STA time-frequency magnitude spectrum of eight disturbance signals are studied and the overall picture of how the regulator factor affects the description accuracy of the signal in the low frequency domain and

the high frequency domain is obtained. On the basis of this and according to the joint consideration of the characteristics of eight disturbance types in frequency domain and the definition of 10 features, four out of 10 features are selected to be used for the disturbance classification. Three combinations of four selected features are investigated in terms of the 2D distribution behavior of their values for the eight disturbance signal types; the influence of the width factor on the separation of data points denoting the values of each feature combination is presented. From there, association between each feature and the width factor value favorable for the corresponding feature is established. Further, it is verified with PNN by examining the classification accuracy with a wide variation range of each width factor, from 0.1 to 3.0. Furthermore, a PNN satisfactorily trained is obtained. Simulation tells it renders high classification accuracy (less than 1% error) for 8 type disturbance signals by using only four features as inputs, which are extracted from the S-transform amplitude matrix with corresponding favorable width factor. In addition, the obtained PNN shows satisfactory robustness under various noise conditions. Finally, the proposed algorithm shows better performance in comparison with those presented in other research studies.

**Acknowledgments:** The authors are grateful to the financial support from the Specialized Research Fund for National Key Research and Development Plan (No.2016YFB0900204), and doctoral Program of Higher Education of China (No. 20120032110070).

**Author Contributions:** The paper was collaborative effort among the authors. The authors contributed collectively to the theoretical analysis and manuscript preparations.

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

#### **References**


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