Abstract
Nowadays, integration of renewable sources into the local distribution system and the nonlinear behavior of advanced power electronic equipment have made a large impact on the power quality (PQ). The unified power quality conditioner (UPQC) is a multifunctional FACTS device, which is a combination of both shunt active filter and series active filters via a common DC link. Presently, the artificial intelligence is playing a vital role in the development of the intelligent control methods. Traditional training methods of artificial neural network (ANN) like back propagation and Levenberg-Marquardt may get stuck in local optimal solution which leads to the invention of ANN trained optimally by metaheuristic algorithms. This paper develops a firefly algorithm-trained ANN (FF-ANNC) controller for the shunt active filter and proportional integral controller (PI-C) for the series active filter of the UPQC integrated with the solar energy system and battery energy storage via boost converter (B-C) and buck boost converters (B-B-C). The main aim of the proposed FF-ANNC is to reduce the mean square error (MSE) thereby achieving the constant DC link capacitor voltage (DLCV) during load and irradiation variations, reduction of imperfections in current waveforms, improvement in power factor (PF), and mitigation of sag, swell, disturbances, and unbalances in the grid voltage. The working of developed FF-ANNC was tested on five test studies with different types of loads and source voltage balancing/unbalancing conditions. However, to demonstrate supremacy of the suggested FF-ANNC, a comparative study with the training methods like genetic algorithm (GA) and ant colony optimization (AC-O) and also with other methods that exist in literature like PI-C, fuzzy logic controller (FL-C), and artificial neuro fuzzy interface system (ANFI-S) was conducted. The proposed method reduces the total harmonic distortion to 2.39%, 2.32%, 2.27%, 2.45%, and 2.66% which are lower than the existing methods that are available in literature. The FF-ANNC shows an excellent performance in reducing voltage fluctuations and total harmonic distortion (THD) successfully and thereby improving PF.
1. Introduction
Nowadays, distribution network is prone to power quality (PQ) issues like interruptions, disturbances, flicker, sag/swell, harmonics, and PF due to the integration of inconsistent behavior solar, wind, tidal, and the large nonlinear and unbalanced loads with advanced power electronic equipment. Therefore, the maintenance of PQ has turned into the main challenge to the electrical engineers.
1.1. Motivation of the Research Work
The unified power quality conditioner (UPQC) pays more attention in microgrids and distributed generation due to the introduction power electronic devices. The combination of UPQC with a solar energy system (SES) and battery energy storage (BES) is highly essential than conventional grid connection. Few advantages are maintaining stable DC link capacitor voltage (DLCV) during the variations of loads, reducing the stress and ratings of the converters, PQ enhancement of gird, sensitive load safety against grid side disturbance, and the converter of high fault ride. Even though the artificial neural network (ANN) controller is an advanced intelligent controller by adopting the traditional training methods like back propagation (BP) and Levenberg-Marquardt (LM), it may get stuck in local optimal solution which motivates to the invention of ANN trained optimally by metaheuristic algorithms.
1.2. Literature Review
The recent advancement in the various control techniques and configurations of shunt active filter (SHAF) with three-phase distribution network was discussed in detailed [1]. The soccer league algorithm-based optimal design of hybrid controller was suggested for the solar battery-connected UPQC to eliminate PQ problems effectively for the unbalanced and nonlinear loads [2]. An ANN and fuzzy logic controller (FL-C) hybridized controller was designed for battery and solar-integrated self-tuning filter- (STF-) based UPQC with a goal of DLCV balancing with maximum reduction of voltage and current-related PQ issues [3]. Besides, the STF-based solar battery-connected SHAF was developed in view of regulating the reactive power and minimizing the current harmonics efficiently, while the Maxi kalman-type filter was engaged for the assessment of the reference current [4]. A fuzzy-integral-sliding mode controller was proposed for fuel cell and solar-integrated UPQC with a goal of DLCV balancing and minimizing THD with maximum elimination of voltage disturbances [5]. A neurofuzzy controller was designed for battery- and solar-integrated UPQC with a goal of DLCV balancing with maximum elimination of current waveform imperfections and voltage distortions [6]. The hybrid fuzzy-based sliding mode (F-SMC) controller was suggested for the wind battery-associated SHAF to reduce current-related distortions and improve power factor (PF) [7].
The solar system with maximum power tracking was integrated to UPQC, and its viability was investigated on various types of loads with an objective of reducing THD and enhancing the efficiency of UPQC [8]. Besides, the proportional integral controller (PI-C) based on synchronous reference frame theory (SRFT) was developed for the SHAF integrated to fuel cell with a motive of improving the shape of current waveforms and to maintain constant DLCV [9]. An evolutionary particle swarm optimization (PS-O) and grey wolf optimization (GW-O) algorithm was proposed for the optimal selection of Kp and Ki values of PI-C of SHAF with an aim of handling the reactive power effectively and reducing THD [10]. Besides, to maintain DLCV and to control the reactive power, the ANN controller was developed for wind- and solar-connected UPQC and performance was tested on various loading conditions [11].
A new adaptive control procedure was applied on the H-bridge UPQC with 8 switches with a goal of minimizing THD and supply voltage distortions efficiently [12]. Besides, a multilevel-UPQC connected to solar and wind with fuel cell was projected with an objective of suppressing voltage-related PQ issues and current waveform imperfections efficiently [13]. The UPQC was recommended in order to suppress the current/voltage harmonics for furnace load at steel power plant. However, to prove its superior performance, comparative analysis was carried out with distribution static compensator [14]. The development of efficient controller from the hybridization of both the properties of ANN controller and FL-C was carried out for the solar PV-integrated UPQC to address the PQ problems and to show that the viability of the proposed controller performance investigation was carried out for various combinations of the loads as well as supply voltages [15].
The STF-controlled SHAF was developed to avoid the necessity of low-pass filter (LPF) and phase-lock loop (PLL) and to minimize the current THD. However, to show its performance, theoretical and/practical performance investigation was done [16]. The FL-C-based UPQC was designed for R-L nonlinear load to minimize the imperfections in current waveforms [17]. The Fourier transform was suggested for the solar system with wind and fuel cell, along with battery to UPQC with an objective of diminishing voltage fluctuations in the source voltage and diminishing imbalances and harmonics in load current [18]. A novel technique was designed to UPQC for rapid response in fault identification with high accuracy. Additionally, a BBO algorithm was chosen to tune the Kp and Ki values of PI-C optimally with a goal of stabilizing the DC link oscillations [19]. UPQC was selected to reduce the voltage distortions and harmonics in current waveforms by adaptive neurofuzzy hybrid controller in addition to the improvement in the utilization of network [20]. The controller with a hybridization of both improved-bat and moth-flame algorithms was suggested to handle the PQ issues by appropriate tuning of Kp and Ki parameters [21]. The FL-C was designed for series active filters (SEAF) for three-phase distribution network to solve the voltage and current-related PQ issues successfully [22].
The predator-prey firefly optimization was chosen to obtain the optimal Kp and Ki values of PI-C for the SHAF with an intention of reducing the THD and in turn enhancing the PF [23]. Moreover, the traditional training methods like BP and LM may be trapped at local optimal solution. Therefore, the ANN trained by Lightning-Search Algorithm (LSA) was suggested with an objective of solving engineering problems effectively [24]. AC-O algorithm-based optimal tuning of Kp and Ki values of PI-C was developed for the SHAF with a goal to minimize THD under variable loading conditions [25]. A fuzzy back-propagation (BP) technique was developed to the 5-level UPQC with an aim of minimizing THD [26]. Ant-lion algorithm was chosen for training the feedforward- (FF-) based ANN to avoid getting stuck in local optimal solution [27]. GW-O was suggested for training the FF method-based ANN controller to solve multiobjective problems [28]. An atom search algorithm (AS-O) was suggested for tuning fractional-order proportional integral derivative (FOPID) of UPQC to address PQ issues effectively [29]. However, the detailed study was carried out on different types of phase synchronization methods that are applicable to control the operation of SHAF [30]. The new load equivalent conductance method was applied for UPQC for improving voltage quality with a view of regulating energy transfer between sources and loads [31]. An adaptive hysteresis band with FLC was introduced to solar-connected nine-level UPQC with an intention to obtain distortion-free voltage waveforms [32]. Besides, the grey wolf metaheuristic optimization algorithm-based PIC was presented for UPQC with an aim of reducing THD for both linear and nonlinear loads [33].
1.3. Key Contributions and Paper Alignment
Thus, the literature survey clearly portrays the existing conventional control schemes for UPQC. This manuscript develops a new optimal trained artificial intelligence-based control scheme for UPQC combined with SES and BES. However, from that literature review (Table 1), it is clearly observed that many works concentrated only on few objectives but the proposed work concentrated on multiobjectives simultaneously. The key contributions of this manuscript are as follows: (i)The nature-inspired metaheuristic firefly algorithm (FF-O) based on the behavior of fireflies is used to train feedforward- (FF-) based ANN in order to avoid the conventional methods like BP and LM which may get stuck in local optimal solution(ii)FF-ANNC is proposed for the SHAF and PI-C for SEAF of the proposed UPQC with an aim of diminishing the current THD thereby enhancing the PF; eliminating the troubles of grid voltage like interruption, sag or swell, and disturbance; and maintaining constant VLDC as multiobjective problem(iii)The SES and BSS system is connected to the DC link of UPQC to maintain stable VLDC during load variations and to meet the demand with lower stress on converts(iv)Moreover, the developed FF-ANNC-based UPQC with solar PV and BSS (U-SEBES) is studied on five test cases for various supply voltage conditions, solar irradiation variation, and loading variations to exhibit the superior performance with respect to THD and PF along with waveforms
The rest of the manuscript is arranged as follows: Section 2 gives the construction of proposed U-SEBES, Section 3 highlights on the proposed FF-ANNC in the shunt controller, Section 4 explains the control strategies of series controller, Section 5 demonstrates the results and discussion, and finally, Section 6 concludes the manuscript.
2. Construction of Proposed U- SEBES
The structure of the developed U-SEBES is illustrated in Figure 1. The SES and BES are connected to UPQC by means of a DC link through a B-C and B-B-C. The UPQC comprises of both SHAF and SEAF. The purpose of SEAF is to suppress the voltage allied fluctuations by supplying voltage series injected (VSE). Besides, the separation among the series connected converter and the supply line is carried out by the isolating transformer. Similarly, the prime goal of SHAF is to minimize the imperfections in current waveforms by supplying the required injected shunt current (ISH) and rapid action in regulating DLCV constant. The three-phase balanced, unbalanced, and electric furnace loads were chosen.
The SES and BES support externally to the DC link of UPQC through a B-C and BB-C with an aim of regulating constant DLCV during various load combinations and reduce the ratings of converters as illustrated in Figure 2. The SES and BES specifications were chosen in this paper are shown in Table 2. However, the power dispersion of U-SEBES at the DC link is exhibited by the following equation:
2.1. SES
The SES transforms the sun’s irradiation into electricity. The major components of this system are series and or parallel configured PV arrays with MPPT technique and B-C as given in Figure 2. The SPG mainly depends on the irradiation of sun on arranged PV modules. The integration of SES to the DC link minimizes the ratings, burden on power converters, and demand from utility. The P&O algorithm is suggested to attain the highest output from the PV system. The power output of solar PV system () is determined by the following equation:
2.2. BES System
BES controller is connected to B-B-C which charges and discharges according to the requirement. It maintains the stable DC link voltage as given in Figure 2. State of charge of battery () is evaluated by the following equation:
The output power produced by the SES will choose the state of working of a battery either charging or discharging by satisfying the upper and lower constraints given by equation (4). Table 3 explains the distribution of power across the DC link for different levels of solar power generation (SPG).
3. Shunt Controller
The prime goal of SHAF is to minimize the imperfections in current waveforms by injecting ISH and to stabilize the DLCV to constant value. It performs (i) and frame transformations; (ii) FF-ANNC is developed to achieve the desired objectives. The SHAF with the proposed FF-ANNC is given in Figure 3. As and conversions are already accessible in the literature survey, the control technique of suggested FF-ANNC is highlighted below.
The load current is transformed into frame by means of the pharos and frequency by supply voltage through PLL. The performance of SHAF is determined by the reference current generation and regulating the DLCV. However, in case if the load varies, the power flow in the SHAF may change which leads to voltage instability across the DC link. So, in order to maintain the DLCV, the real power in SHAF must be equal to the switching losses. The proposed FF-ANNC injects a DC error current signal , calculated from the difference of the reference and actual DLCV given by the following equation:
The th component of load current is summed with the error signal obtained from FF-ANNC. The sequence components are shifted into the frame and compared with the load current in a hysteresis current controller to generate the necessary gate signals.
3.1. Proposed FF-ANNC
ANN is one of the most well-known artificial intelligence techniques which is a human brain-inspired mathematical representation and highly flexible for application in power electronic control system. MLPs are the most famous neural network. The advantage of ANN consists of self-learning ability, fault tolerance, fast convergence, robustness, etc. The structure of ANN contains 3 layers: input layer (INL), hidden layer (HIL), and output layer (OL). The performance of ANN depends on the type of learning algorithm chosen for training the network. Training is a process of adjusting of weights that are associated with the neurons of the ANN between the layers to reduce the error. Supervised and unsupervised are most familiar training methods, where gradient search and metaheuristic are the two types in those methods. Generally, BP is the well-known gradient search–based traditional training method used for MLP. However BP has its own limitations: inaccurate primary guess on weights, higher time required for convergence, and probability of getting stuck in local solution is more.
Besides, the metaheuristic optimization-based training methods take initial guess of control variables randomly during their process of optimization which finds the global best optimal solution without any previous information about the selected problem. These metaheuristic algorithmic methods can be used for the optimal selection of weights, bias, and architecture of ANN. The goal of the supervised learning is to reduce the mismatches between the actual obtained and desired values.
In multilayer perceptron (MLP) network, neurons among the layers are connected by valued weights, where every neuron contains both summation and activation functions. The summation function sums up the product of the inputs and the weight, with bias as shown in equation (6), where is the weight connecting to neuron , is a bias, and is the number of input neurons. In general, a nonlinear sigmoid activation function is suggested as given in equation (7). Hence, the th neuron output can be determined as in equation (8).
In this paper, single-layer FF-based ANN is trained for DLCV balancing, reference DLCV is compared with actual DLCV, and its error is considered the input while the desired-output is considered the target to the ANN.
Figure 4 exhibits the developed ANN structure for DLCV balancing with 100 neurons in HIL, and Figure 5 gives the proposed architecture of FF-ANNC. It was proved [24] that the MLP with a one HIL is sufficient to estimate any function. The firefly-based optimization is a nature-inspired algorithm from the twinkling behavior of the group of fireflies. The selection of weights is considered a problem for optimization with a goal of diminishing the common mean squared error (MSE) through optimally choosing parameters.
Initially, a group of fireflies are randomly produced in the search space, where each firefly represents a suitable solution in the space, which depends on the quantity of control parameters considered. In this technique, each firefly () is a control variable given in the vector form in the following equation:
The constraints are represented as where nd stands for number of design variables.
This technique proposes bioluminescent communication for the movement of fireflies in the search space. Each of the fireflies is mesmerized by the glow of other fireflies and tries to move towards them. The brightness function (BF) of firefly determines the appropriate value of the selected problem. In the iteration process, the proposed algorithm calculates the BF and modifies their positions according to the obtained value. The BF can be formulated to minimize the MSE given in the following equation: where MSE is evaluated by equation (12), where is the actual output, is the forecasted one, and is the total instances.
The attractiveness between the and fireflies is represented by the following equation: where represents the Cartesian distance between and fireflies and is computed by the following equation:
In the team, the firefly moves towards the firefly and updates its position, if is greater than at the instant by the following equation:
The optimization begins with the generation of random values within their constraints and calculation of BF by running the proposed USB Simulink model by treating the values of each firefly as the optimal design parameters. Based on the BF value, each firefly is moved towards the brighter firefly that represents the best optimal solution. The iterative process is carried out until it gets converged. The main aim of suggesting firefly algorithm in this paper is its excellent performance in solving multiobjective optimization problems with faster convergence and high accuracy with the lowest sensitivity to the problem’s dimensions. It can also be applied for both linear and nonlinear loads. However, it has its own limitation like complexity as the number of control variables increases.
The chosen parameters of the proposed and compared optimization techniques are listed in Table 4. The flowchart of the developed algorithm is given in Figure 6. The th and th fireflies’ movement with brightness determines the best optimal solution.
4. Series Controller
The SEAF injects voltage to reduce grid voltage fluctuations and maintain constant load voltage. The control structure of series active power filter is shown in Figure 7. A PLL is used to extract the fundamental component of grid voltage, which is then used to generate the reference axis in the --0 domain. The data of phase and frequency retrieved from the PLL is used to produce the reference load voltage. The source voltages, load voltages, and reference load voltages are then converted into the --0 domain. The injected reference voltage is obtained from the difference between the reference and load voltages. The injected voltage is obtained by the difference between load and grid voltages. For both - and -axis signals, the difference between the reference and actual voltage of the series compensator is passed through aPI-C to produce reference injected voltages. Finally, the PWM voltage controller to generate the gating pulses (, , , , , and ) for series VSC.
5. Results and Discussions
The three-phase distribution network was considered to demonstrate the performance of the developed U-SEBES with the proposed optimally designed controller. The U-SEBES specifications are exhibited in Table 5. The proposed method was designed, and performance is analyzed on Simulink/MATLAB version 2016. The proposed UPQC with solar controller in the Simulink model is as given in Figures 8(a) and 8(b), respectively. Five test studies with several combinations of nonlinear balanced and unbalanced loads, source voltages, and conditions like swell/sag/disturbance with constant irradiation 1000 W/m2 and a temperature of 25°C were considered to prove the superior performance of designed FF-ANNC on developed U-SEBES as shown in Table 6. The source voltage is considered to be balanced for test studies 1-3 and unbalanced for 4 and 5. However, the THD of the source current is evaluated for all the case studies and compared with GA and AC-O methods and also with the controllers that are suggested in the literature as given in Table 7. Figure 9 gives the comparison of convergence plot of the proposed method with GA and AC-O-trained ANNC. However, it can be clearly seen that the suggested method converges to much lower MSE in a minimum number of iterations. The PF is evaluated from the THD by equation (16), and comparison with other controllers is shown in Figure 10.
(a) Simulink model of the proposed UPQC with loads
(b) Solar system Simulink model
Here, is the angle between current and voltage. The voltage sag/swell () is calculated by
The series compensated voltage of U-SEBES is given by
The shunt-compensated current is given by
In case 1, the was considered to be balanced and to evaluate the performance of SEAF, 30% of sag was introduced in the source voltage during the interval of 0.25-0.35 s, as illustrated in Figure 11(a). However, U-SEBES identifies the voltage dip and injects appropriate VSE via coupling transformer and maintains constant voltage across the load terminals. To investigate the performance of the SHAF, a rectifier-based three-phased balanced nonlinear load was considered. The load current during sag was found to be nonsinusoidal but balanced as given in Figure 11(b). The proposed U-SEBES reduces the imperfections in current waveform which is in turn reciprocated in the THD and PF. However, the THD of source current was decreased from 27.80% to 2.39%, which is less when compared to other controllers as given in Table 7 and the PF rises from 0.8536 to 0.9996. Additionally, the optimally designed controller maintains a stable DLCV as shown in Figure 11(c).
(a) Source voltage, injected voltage, and load voltage
(b) Load current, injected current, and source current
(c) Irradiation, temperature, and DLCV
In case 2, the was considered to be balanced and 30% of swell was introduced in the source voltage during the interval of 0.40-0.50 s as exhibited in Figure 12(a). However, U-SEBES identifies the voltage boost and injects appropriate VSE via coupling transformer and maintains constant voltage across the load terminals. The rectifier-based nonlinear balanced and unbalanced loads were considered here due to which the load current during swell was observed to be nonsinusoidal and unbalanced as presented in Figure 12(b). U-SEBES diminishes THD from 16.81% to 2.32% and thus increases the PF from 0.8013 to 0.9912. It is clearly visible that the proposed system addresses both voltage- and current-related PQ problems effectively. However, as demonstrated in Figure 12(c), suggested controller works efficiently in maintaining the constant DLCV during load variation.
(a) Source voltage, injected voltage, and load voltage
(b) Load current, injected current, and source current
(c) Irradiation, temperature, and DLCV
In case 3, the was considered to be balanced and disturbance was introduced during the time period of 0.7 to 0.8 s for a combination of 3ⱷ balanced rectifier-based load with unbalanced and induction furnace load simultaneously as given in Figure 13(a). The load current was found to be nonsinusoidal and balanced during the disturbance as in Figure 13(b). The FF-ANNC was able to diminish the THD from 19.90% to 2.27%, enhances PF from 0.8587 to 0.9997, and balances load voltage successfully. In addition, it also holds DLCV effectively during large nonlinear load as in Figure 13(c).
(a) Source voltage, injected voltage, and load voltage
(b) Load current, injected current, and source current
(c) Irradiation, temperature, and DLCV
In case 4, both the and load are considered to be unbalanced given in Figure 14(a). The U-SEBES eliminates voltage imbalances and provides three-phase constant voltage to the load. The load currents are observed to be sinusoidal but unbalanced as shown in Figure 14(b). The FF-ANNC is able to minimize the imperfections in current waveform and decreases THD from 9.33% to 2.45% while boosting up the PF from 0.83872 to 0.9988. Figure 14(c) exhibits its performance in regulating DLCV during load variation.
(a) Source voltage, injected voltage, and load voltage
(b) Load current, Injected current, and source current
(c) Irradiation, temperature, and DLCV
In case 5, the unbalanced was chosen with the combination of rectifier-based nonlinear load and induction furnace loads as shown in Figure 15(a). The U-SEBES eliminates voltage imbalances and provides three-phase constant voltage to the load. The load current was balanced with but with nonsinusoidal shape as in Figure 15(b). The developed system diminishes the THD from 21.86% to 2.66% and boosts up PF from 0.7925 to 0.9934 effectively.
(a) Source voltage, injected voltage, and load voltage
(b) Load current, injected current, and source current
(c) Irradiation, temperature, and DLCV
The suggested method effectively maintains constant voltage during the changes in irradiation with constant temperature as shown in Figure 16. However, Table 8 compares MSE of the developed method with other techniques. The regression plot of the FF-ANNC as an accuracy proof is given in Figure 17. The THD spectrum for test studies is given in Figure 18.
6. Conclusion
The FF algorithm-based optimally trained ANNC is developed for U-SEBES. The SES and BES controllers were also designed along with the FF-ANNC for SHAF and PI-C for SEAF with a prime goal of maintaining the DLCV during load and solar irradiation variation and suitable injection of voltages for maximum elimination of swell, sag, and disturbances; providing compensation for unbalances in the source voltage; removing imperfections in current waveforms thereby reducing THD; and enhancing the PF by taking minimizing of MSE of ANNC as an objective. By observing the performance of the proposed method on five test studies, it clearly exhibits that in the system without U-SEBES, the THD value was 27.80% for case 1, 16.81% for case 2, 19.90%, for case 3, and 9.33% and 21.86% for cases 4 and 5. By implementation of U-SEBES with FF-ANNC, the THD reduces to 2.39%, 2.32%, 2.27%, 2.45%, and 2.66%, respectively. It clearly exhibits that the proposed FF-ANNC was able to lower the THDs within acceptable levels and power factors to almost unity. Moreover, by the comparative investigation with GA and AC-O and other controllers in literature, it is proved that the performance was much better than other controllers. The proposed system can be further studied for multilevel UPQC with optimal design of shunt and series filter parameters as future work.
Nomenclature
| : | Supply voltage of phases -- |
| : | Supply current of phases -- |
| : | Resistance at source |
| : | Inductance at source |
| : | Load voltages in -- phases |
| : | Source voltage in domain |
| : | Load voltage in domain |
| : | Compensated series voltage in -- frame |
| : | Reference compensated series voltage in -- frame |
| : | Reference load voltage in frame |
| : | Reference load voltage in -- phases |
| : | Reference supply voltage in domain |
| : | Load current in -- phases |
| : | Load current in domain |
| : | Reference SHAF compensated current in -- phases |
| : | SHAF compensated current in -- phase |
| : | SHAF capacitance |
| : | SHAF resistance |
| : | SHAF inductance |
| : | SEAF capacitance |
| : | SEAF resistance |
| : | SEAF inductance |
| : | DC link capacitance |
| : | DC link voltage |
| : | DC link error voltage |
| : | Reference DC link voltage |
| : | DC link output error |
| : | DC link reference current |
| : | Power output of PV system |
| : | Voltage output of PV system |
| : | Current output of PV system |
| : | DC link power |
| : | Power output of battery system |
| : | Voltage of battery system |
| : | Current of battery system |
| : | Reference battery current |
| : | Error current of battery |
| : | Reference error current of battery |
| : | Battery’s capacity |
| : | Error |
| : | Change in error |
| : | State of charge of battery |
| : | Lower limit of SOCB |
| : | Upper limit of SOCB. |
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request (Baseem Khan, baseem.khan1987@gmail.com).
Conflicts of Interest
The authors declare no conflict of interest.