Fuzzy logic sliding mode controller based solar PV fed UPQC for improvement of dynamic performance and power quality enhancement in distribution power system

Abstract

The unified power quality conditioner (UPQC) makes use of a fuzzy logic sliding mode controller (FLSMC) in order to enhance the reliability and quality of the distribution power system. This is accomplished by addressing dynamic performance and power quality issues such as current disturbances, voltage sag, swell, and total harmonic distortion (THD) under nonlinear loads. When compared to traditional controllers, FLSMC-based UPQCs perform better in terms of dynamic performance and power quality. In order to reliably extract reference current and voltage signals for UPQC, the FSMPWM architecture makes use of sliding surface implementation. Similarly, control principles are derived for shunt converters and series converters. The Mamdani fuzzy rule basis for switching pulse generation was meant to be implemented at the sliding surface. Chattering is eliminated, and a fixed switching pulse is produced for shunt and series converters through the utilization of the method that has been provided. The results indicate that when a FLSMC controller is utilized, the total harmonic distortion (THD) values of the source voltage are 0.38%, and the THD values of the source current are 2.01%. Additional evidence demonstrates that the compensation utilized by this controller is successful for all parameters. As a result, the FLSMC controller is the most effective of the four options that have been offered. The FLSMC is superior to the FLC, ANFIS, and FOFLC in terms of its ability to increase dynamic performance and power quality. MATLAB/Simulink is used to actually implement the controller-based system architecture for the FOFLC and FLSMC applications.MATLAB/Simulink, Power Quality, and Fractional Order FLC, as well as Fuzzy Sliding Mode Controller, are some of the keywords that are associated with this topic.

Introduction

Electrical energy has emerged as the most popular power source in modern times. Without electricity, it is impossible to imagine living. The constancy and dependability of the electricity supplied to the end user are also essential to the equipment’s correct operation. Commercial and industrial loads frequently require a constant, uninterrupted power supply. Therefore, maintaining the electrical grid’s dependability is of utmost importance¹. The nonlinear components have a significant impact on the power supply’s dependability and efficiency. Electronic gadgets can be the source of a number of power quality issues. Poor power quality can be caused by voltage drops and spikes brought on by lightning, network outages, and switching capacitor banks². When used excessively, computers, laser printers, and rectifiers produce reactive and harmonic power. This kind of issue needs to be resolved right away to avoid more harm because it may worsen in the future. Despite their size, resonance issues, and the performance impact of source impedance, passive filters have been utilized for reactive power disturbances and harmonic production. In order to categorize active power filters, one has to look at the system setup. An active power filter can either be a series active power filter or a shunt active power filter.The combination of Series APF and shunt APF is known as UPQC. Distortions in voltage, current are both removed using UPQC³. Shunt Active Power Filter is able to enhance power factor, reactive power, harmonic current, whereas series Active Power Filters are able to correct voltage fluctuations at the load properly managed⁴. The distribution system is in series with the Series APF, and in shunt with Shunt APF. While hysteresis” band” controller in conventional control techniques uses “active-reactive theory” targeted at the SHAPF and the hysteresis band controller in conventional control techniques transforms Park transformation or dq0 for SAPF, improves dynamic performance and P.Q of system⁵. APF simulations are run in a shunt configuration first, and then in a series configuration. Eventually, these will be combined to form the UPQC model^6,7 It is the combination of the SAPF and the SHAPF designs⁸. In^9,10, Using the PCC as a framework, this design can be utilized to eliminate voltage sag/swell by injecting voltage proportional to source current (Is), injected series voltage. In¹¹PI controller’s inability to operate adequately in the face of very sensitive load interruption can be traced back to its reliance on separate linear numerical models, which are difficult to obtain. Controllers including state action controllers, self-calibration controllers, model-reference controllers (MRC) have lately been proposed by several writers for use in advanced control¹². Within the scope of this work proposal, a UPQC controller that is based on FOFL is designed. As^13,14 proposed, these controllers require numerical models as well, and as a result, they are sensitive to any changes in the parameters. The typical configuration of a UPQC consists of a SAPF, a SHAPF, and an adjoining mutual dc connection. This configuration is the standard¹⁵.Fig. 1 depicts a straightforward configuration of a conventional UPQC in its example. By utilizing the series active power filter that was proposed in, it is possible to isolate harmonics that are present between the distribution system and the sub transmission system¹⁶ At PCC, this filter helps reduce sag, swell, THD. Shunt APF is used to correct for harmonics of current¹⁷. The DC voltage that exists between the two filters is controlled by the DC connection¹⁸. The UPQC circuit consists of a pair of inverter-gate-transistor (IGBT)-based voltage-source bidirectional converters connected in series over a common DC bus. The load is wired into one inverter that is series-connected to the circuit and shunt-connected to the other¹⁹. The inverter can inject compensatory current ‘Ish’ when it is coupled in shunt with load. The source side inverter is connected in series with load to supply the latter with voltage. Insertion transformers provide this voltage to ‘Vsc’. This study discusses the use of FOFLC and FLSMC based UPQC for improving dynamic performance and addressing PQ problems.Compared to Interconnected Power System, the distribution side is more vulnerable to problems with power quality. The load side power quality problems are mostly caused by the introduction of power electronic equipment. For the purpose of injecting high-quality electricity into the utility grid, the Point of Common Coupling management must ensure this²⁰.PCC control and regulation must be given top priority by power quality engineers.The EN 50530 test technique is specifically created for the dynamic performance of PGSs, and it is used to suggest an effective MPPT approach that is built upon an adaptive type 2 fuzzy-neural network (AT2FNN). Using Matlab/Simulink, we compare the suggested method’s dynamic efficiency performance to that of more traditional MPPT techniques like incremental conductance (IC) and perturb and observe (P&O)²¹. it suggests an enhanced architecture for the MPPT of standalone PV systems using a hybrid intelligent controller. The AIC technique and the IT2-TSKFLC (Interval Type-2 Takagi-Sugeno-Kang Fuzzy Logic Controller) are both parts of the hybrid intelligent control framework. When compared to other intelligent controllers, the suggested hybrid one performs better in handling unexpected changes in a variety of environments²².The suggested EPT design incorporates a three-phase pulse width modulation rectifier at the input stage, a dual active bridge converter at the isolation stage, and a three-phase two-level inverter at the output stage to produce AC output. The input stage converts 800 Vrms AC to 2000 V DC bus. In the input and isolation phases, neural fuzzy controllers-which are durable and nonlinear in nature-are utilized instead of PI controllers to improve the dynamic performance of the EPT structure²³.

Fig. 1

General configuration of proposed system.

Motivation

Power factor has decreased due to an increase in industrial load; the significance of maintaining power quality is discussed in²⁴. Utility grid stability is preserved by power control, a decrease in harmonic content, and reduce in power quality interruptions’ is the FACTS device that is used on the distribution side of the electrical grid.

Literature review

Integrating Distributed Energy Resources (DER) with the UPQC is one of the most effective topologies for both active and Reactive power exchange¹⁸. The greatest substitute for conventional energy sources is DER. Due to the many detrimental effects that conventional energy sources have on the environment, both developed and developing nations are currently concentrating on substituting renewable energy sources for traditional energy sources. The widely used and conveniently existing renewable energy source is solar energy. Photovoltaic panels are used to capture solar energy from the Sun. Either immediate use or storage in a battery for later use is possible with this energy. Because the solar panels’ energy is sporadic, an MPPT Controller is used to maximize the power produced by the solar panels. The topic of maximizing solar panel power extraction is covered in the literature⁵. In addition to solar energy integration, UPQC is being utilized with wind energy^12,13and, more recently, with plug-in hybrid electric vehicles^13,14 (Tables 1 and 2).

Table 1 Comparative analysis of UPQC control strategies with PV integrating.

Key contribution

When running the UPQC system, controllability and reference current generation are the two most crucial factors to take into account. The most widely used control method for UPQC systems is reactive power theory, or p-q theory^15,16.The p-q theory work on a similar premise. The Unit Vector Template Control scheme¹⁷ and the p-q theory¹⁸ are the methods used in the proposed study to control the UPQC series and shunt converters, respectively.¹⁹talks about the UPQC’s stronghold. One popular controller that uses mathematical modeling of a system is the proportional-integral controller²⁰. Efficiency of the system is impacted by variations in nonlinear loads and the constraints of the PI controller throughout short operation. Machine learning controllers have replaced PI controllers in the modern world. Power quality has been enhanced by the development of an efficient controller. In order to achieve better dynamic response and improved power quality under extremely nonlinear and unpredictable operating conditions, the proposed work is unique in that it integrates Fuzzy Logic Control (FLC) and Sliding Mode Control (SMC) in a solar PV-fed Unified Power Quality Conditioner (UPQC) that operates in a distribution power system.

Paper organization

Designing a PV connected UPQC system with a synergetic controller is the focus of the proposed paper. The PV-UPQC system’s design and operation are covered in “UPQC system” through “Control methods”, while “Results and discussions” addresses PV incorporation. “THD comparison with FOFLC and FLSMC” describes the structure and control of the synergetic controller. In “Conclusions”, the PV integrated UPQC system is examined under various load scenarios, and MATLAB/Simulink has been used to conduct and validate the power quality experiments.

UPQC system

A unique power FACTS device that permits bidirectional power flows is called a UPQC. Reactive power is balanced and power quality is enhanced using UPQC, which raises system reliability. By installing the UPQC on the utility grid’s distribution side, the PCC’s voltage and current quality are enhanced. The Distributed Static Compensator (DSTAT-COM), a shunt compensator, and the Static Synchronous Compensator (SSSC), a series compensator, are combined in UPQC²⁴. These two compensators are directly linked to each other. The type of link DC depends on the type of converter that is being used. VSC are frequently used for this purpose since they require fewer electrical components, do away with the need for blocking diodes, provide a greater degree of control, and can operate on many levels. A DC link capacitor, which functions as a storage component, connects the VSC’s to one another²⁹.

Fig. 2

Configuration of the UPQC system.

Figure 2 displays the UPQC system’s structural diagram.A three-phase unbalanced system’s source current $V_{grid}$(t) is composed of fundamental and harmonic elements in the positive, negative, and zero sequences. Equation (1) determines the system’s current for the analog circuit.

$$\begin{aligned} V_{g(t)} = V_{g+(t)} + V_{g-(t)} + V_{g0(t)} +V_{sh} \end{aligned}$$

(1)

where $V_{g+(t)}$, $V_{g-(t)}$, $V_{g0(t)}$ are components of $V_{sh}$. The voltage that the serial compensator induces is specified by Eq. (2).

$$\begin{aligned} V_{secomp(t)} = V_{L(t)} - V_{g(t)} \end{aligned}$$

(2)

If $V_{g(t)}$ represents the system Voltage, $V_{L(t)}$ the load Voltage, and $V_{secomp(t)}$ the series compensation factor. The difference between the load current and the current flowing through the grid is known as the shunt compensated current, and it is determined by Eq. (3).

$$\begin{aligned} I_{sh(t)} = I_{L(t)}- I_{g(t) } \end{aligned}$$

(3)

where $I_{g(t)}$ is grid current, The compensating current is $I_{sh(t)}$, while the load current is $I_{L(t)}$. The grid obtains current injection from the shunt compensator. The injected current possesses negligible harmonic content. Equation (4) yields the distorted load current.

$$\begin{aligned} I_{L(t)} = I_{L+(t)} + I{_{L-(t)}} + I_{L0(t)} + I_{sh(t)} \end{aligned}$$

(4)

When the load current is positive (represented by IL(t), negative (represented by $I_{L(t)}$), and the null (represented by $I_{L0(t)}$) component is the load current. The symbol for the current in the Shunt Compensation Device is $I_{sh(t)}$. In this system, a three-phase dual wire system, is being used. The effort is a non-linear, inductive effort.

Series converter

It eliminates voltage disturbances such as voltage swell and sag, hence improving the quality of power. The voltage consistently sustained using the series converter. With the aid of a series injection transformer, the series converter is accountable for injecting current into the PCC³⁰. The series converter charges the DC-link element while converting the AC amount to DC quantity. The transfer of actual power is also made possible by the series adapter. An example of a vectorial unit model is the tension converter in series control mechanism. Voltage sensors measure the inaccurate and essential voltage component at the common coupling point. Differentiates the detected distorted Voltage by the maximum Voltage entry value³¹.

$$\begin{aligned} V_{Max}=\sqrt{\frac{2}{3}}(V_{a_s}+V_{b_s}+V_{c_s}) \end{aligned}$$

(5)

Three phases can be synchronized with frequency using the PLL circuit. The inaccurate voltage is divided by the maximum tension before to entering the PLL. The equation indicates that the phase vectors must be separated by a difference in phase angle (6,7,8).

$$\begin{aligned} & V_{PLL_a}=\sin {(\omega t)} \end{aligned}$$

(6)

$$\begin{aligned} & V_{PLL_b}=\sin {(\omega t-\frac{2\pi }{3})} \end{aligned}$$

(7)

$$\begin{aligned} & V_{PLL_c}=\sin {\left( \omega t+\frac{2\pi }{3}\right) } \end{aligned}$$

(8)

To obtain the reference signals described in Eq. (9), multiply the PLL circuit’s output by the fundamental voltage.

$$\begin{aligned} V_{L_abc}^*=V_{peak}*V_{PLL_abc} \end{aligned}$$

(9)

To create an error signal, the created reference signal is compared to the load signal. The obtained error signal is sent into a PWM signal generator, which outputs the output signal to the series converter. The construction of the control scheme is shown in Fig. 3 of the Unit Vector Template.

Fig. 3

working of series APF.

Shunt converter

Rectify reactive power and eliminate current harmonics via shunt converters. Shunt Converters supply or absorb power for the DC-Link Capacitor’s series converter. A Shunt Converter converts DC-Link-Power-Demand from Series-Converters to AC to enable their operation³². Shunt converters adjust load power consumption via shunt inductance. The p-q theory uses Clark’s Transformation to convert electrical variables from a-b-c coordinates to $\alpha$-$\beta$ dimensions. Electrical values are given in $\alpha$-$\beta$ coordinates using formulae 10 and 11.

$$\begin{aligned} & \left( \begin{matrix}v_{\alpha load}\\ v_{\beta load}\\ \end{matrix}\right) =\sqrt{\frac{2}{3}}\left( \begin{matrix}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\\ \end{matrix}\right) \left( \begin{matrix}v_{aload}\\ v_{bload}\\ v_{cload}\\ \end{matrix}\right) \end{aligned}$$

(10)

$$\begin{aligned} & \left( \begin{matrix}i_{\alpha load}\\ i_{\beta load}\\ \end{matrix}\right) =\sqrt{\frac{2}{3}}\left( \begin{matrix}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\\ \end{matrix}\right) \left( \begin{matrix}i_{aload}\\ i_{bload}\\ i_{cload}\\ \end{matrix}\right) \end{aligned}$$

(11)

From Eqs. (12) and (13), one can calculate the real and reactive power by considering the current and voltage at any point in the coordinates $\alpha$-$\beta$.

$$\begin{aligned} & p_{load}(t)=v_{\alpha load}(t)i_{\alpha load}(t)+v_{\beta load}(t)i_{\beta load}(t) \end{aligned}$$

(12)

$$\begin{aligned} & q_{load}(t)={-v}_{\alpha load}(t)i_{\alpha load}(t)+v_{\beta load}(t)i_{\beta load}(t) \end{aligned}$$

(13)

Similar to the Synchronous Reference Frame Theory, the pq theory comprises a standard component and an oscillatory factor pertaining to actual and reactive power, as delineated in Eqs. (14) and (15).

$$\begin{aligned} & p_{load}={\bar{p}}_{acload}+{\bar{p}}_{dcload} \end{aligned}$$

(14)

$$\begin{aligned} & q_{load}={\bar{q}}_{acload}+{\bar{q}}_{dcload} \end{aligned}$$

(15)

The reference current that is created can be transformed from $\alpha$-$\beta$ coordinates to a-b-c coordinates using Eq. (16).

$$\begin{aligned} \left( \begin{matrix}i_{aload}^*\\ i_{bload}^*\\ i_{cload}^*\\ \end{matrix}\right) =\sqrt{\frac{2}{3}}\left( \begin{matrix}1& -\frac{1}{2}& -\frac{1}{2}\\ 0& \frac{\sqrt{3}}{2}& -\frac{\sqrt{3}}{2}\\ \end{matrix}\right) \left( \begin{matrix}{-i}_{oload}\\ i_{\alpha load}^*\\ i_{\beta load}^*\\ \end{matrix}\right) \end{aligned}$$

(16)

The shunt converter must sustain a stable DC connection voltage. The variation in real and reactive power control is determined by the phase angle $\delta$. Reference signals can be generated and transmitted to the PWM generator through contrasting the reference current with the load current. The shunt voltage source converter obtains its gating pulses from the PWM generator. Figure 4 presents a block design of the shunt converter.

Fig. 4

Working of shunt APF.

PV fed UPQC

Solar power will soon overtake all other traditional energy sources. Because it is clean and doesn’t harm the environment, solar power is favoured over traditional energy sources³³. Listed below are some of the reasons why distributed energy resources (DERs) like solar power can be linked with the UPQC using the DC-Link element. Alongside electricity generation from photovoltaic panels, the Shunt Converter simultaneously mitigates harmonics in the load current. To generate the necessary DC power, the photovoltaic panels may be configured in a series-parallel layout. DC-DC converters facilitate impedance matching and enhance power output from solar panels. The predominant variety of DC-DC converter is referred to as a boost converter. In order to balance supply and demand, the PV panels must be loaded into the DC-Link capacitor in addition to being connected to the actual power exchange. As a result, optimizing the solar panel’s performance is essential. The Maximum Power Point (MPPT) Controllers help make this happen. Among the most popular MPPT techniques is the observe-and-perturb algorithm³³. It is possible for the voltage on the grid side to fluctuate if there is an overload or underload on the load side. In the event that there is a reduction in grid voltage fluctuations, the series converter outputs the series compensation. It is clear from Fig. 5 that the Shunt-Converter is used to transfer power from the solar modules.

Fig. 5

General configuration of PV-UPQC system.

Control methods

Design of FLC

FLC evaluates input data in terms of logical variables with continuous values ranging from zero to one. The operation of the controller in a fuzzy logic control system based on fuzzy rules generated using fuzzy set theory. In order to compensate PQ a fuzzy logic controller is used. Fuzzification, decision making, defuzzification are steps in FLC³². Fuzzification is technique for transforming crisp value into fuzzy value³⁴. Figure 6 shows fuzzy logic controller block diagram. The fuzzification, defuzzification, input, and output variables make up FLC³⁵ (Fig. 7). The membership function for constructing a fuzzy set is shown in Figs. 8 and 9 for inputs and Fig. 10 depicts for the output. In FIS one input is $V_{dc,ref}$, another input is $\delta$ $V_{dc,re f}$, output is $P_{loss}$. For a high level of FLC.

Fig. 6

Block diagram of fuzzy logic controller.

Fig. 7

Fuzzy inference system.

Fig. 8

Membership functions for error.

Fig. 9

Membership functions for change in error.

Fig. 10

Membership functions for output.

Table 2 Fuzzy logic rule table.

FLC refers to algorithm of process is based on fuzzy inference. Fuzzy logic control is nonlinear adaptive control that provides reliable results for a linear or nonlinear plant with parameter change. To put the FLC into practice with seven membership functions are selected. The inputs are error voltage V(k), its progressive variation $\Delta$V(k), both are obtained from voltage applied to the DC link and may be represented as follows:

$$\begin{aligned} & V(k)=V_{dc}^*-Vdc(k) \end{aligned}$$

(17)

$$\begin{aligned} & \mathrm {\Delta V}(k)=V(k)-V(k-1) \end{aligned}$$

(18)

The output is amplitude of source current $I_{sp}(n)$. The “min” operator is employed for implication, continuous universe of discourse is utilized for fuzzification. The foundation of inference is fuzzy implications. The defuzzification process employs the “Centroid” method. The membership functions for all fuzzy variables are Negative Big (NB), Negative medium (NM), Negative small (NS), Zero (ZE), Positive small (PS), Positive medium (PM) and Positive Big (PB).

Fuzzy sliding mode controller

The fuzzy sliding mode controller is also known as variable structure control. System reliability is increased by combining traditional Sliding Mode Control (SML) with Fuzzy Logic control. The Fuzzy SML is capable of handling high-class and quadratic uncertainty. Compared to more Fractional order Fuzzy logic controller or other proposed controllers, its control effect is more progressive³³.

Fig. 11

Sliding mode operation.

The sliding surface, control rule needs to be designed in order for a fuzzy SML to work correctly. Every state trajectory in system tends to converge at s=0 superficies. Every trajectory has a certain amount of time to get to sliding manifold, after which the control law permits it to stay there permanently³⁶. The transition from an initial state to a moving matrix is called the moving phase, or the moving phase, in which the state’s trajectory remains in moving matrix. Both the raising and sliding phases are determined by the regulation law. The sliding mode functioning is shown in Fig. 11.

$$\begin{aligned} & u(t) = u_{eq} - M\,\textrm{sign}(s), \end{aligned}$$

(19)

$$\begin{aligned} & \textrm{sign}(s) = {\left\{ \begin{array}{ll} \;\;1, & \text {if } s > 0,\\ -1, & \text {if } s < 0. \end{array}\right. } \end{aligned}$$

(20)

Everything that produces the oscillation phenomena known as chattering should be avoided by electrical drives. Their boundaries are wholly arbitrary³⁷. By adding or replacing the sigmum function with continuous functions like saturation, this effect can be lessened. There can be a limited boundary layer in a system that changes with these uninterrupted functionalities. Figure 12 shows the effect of buzzing.

Fig. 12

Chattering phenomenon.

Modified control law

$$\begin{aligned} & u(t) = u_{eq} - M\,\textrm{sat}\!\left( \frac{s}{\phi }\right) , \end{aligned}$$

(21)

$$\begin{aligned} & \textrm{sat}\!\left( \frac{s}{\phi }\right) = {\left\{ \begin{array}{ll} \dfrac{s}{\phi }, & \left| \dfrac{s}{\phi }\right| \le 1,\\ \textrm{sign}(s), & \left| \dfrac{s}{\phi }\right| \ge 1. \end{array}\right. } \end{aligned}$$

(22)

where $\phi$ unity factor, $u_{eq}$ equivalent control

By modifying constant “M” in accordance with amplitude, rate of change of error signal, control system’s performance can be maximized. Figure 11 shows the FSMC management structure. The switching surface is defined by the rotor error speed. The regulation law’s objective is to get rid of the false output and its corresponding derivative.

$$\begin{aligned} & e\left( M\right) =w_{ref}\left( M\right) -w\left( M\right) \ \ \ \end{aligned}$$

(23)

$$\begin{aligned} & s={\dot{e}}+\delta _1{e+\delta }_2\int edt\ \ \ \ \ \ \ \ \ \end{aligned}$$

(24)

$w_{ref\}}$ -actualspeed and reference speed $\delta _1$,$\delta _2$ are surface parameters (Fig. 13)

Fig. 13

Proposed controller.

Sliding surface definition

Assume that the tracking error is

$$\begin{aligned} e(t) = x(t) - x^{*}(t). \end{aligned}$$

(25)

One option for the sliding surface is to use

$$\begin{aligned} s(t) = {\dot{e}}(t) + \lambda e(t), \quad \lambda > 0. \end{aligned}$$

(26)

As soon as $s(t)=0$, the reduced-order dynamics transforms into

$$\begin{aligned} {\dot{e}}(t) + \lambda e(t) = 0, \end{aligned}$$

(27)

the tracking error is guaranteed to converge exponentially.

Lyapunov-based convergence

Take into account the candidate function of Lyapunov

$$\begin{aligned} V(t) = \frac{1}{2}s^{2}(t). \end{aligned}$$

(28)

By calculating the time derivative, one gets

$$\begin{aligned} {\dot{V}}(t) = s(t){\dot{s}}(t). \end{aligned}$$

(29)

It is decided that the law of sliding mode control will be

$$\begin{aligned} u = u_{\text {eq}} - K \, \text {sat}\!\left( \frac{s}{\phi }\right) , \quad K > 0, \end{aligned}$$

(30)

where $\phi$ denotes the boundary layer thickness.

When the control law is replaced, it results in

$$\begin{aligned} {\dot{s}}(t) = -K \, \text {sat}\!\left( \frac{s}{\phi }\right) . \end{aligned}$$

(31)

Therefore,

$$\begin{aligned} {\dot{V}}(t) = -K |s| \left| \text {sat}\!\left( \frac{s}{\phi }\right) \right| \le 0, \end{aligned}$$

(32)

This ensures that the sliding surface is globally asymptotically stable.

Chattering reducing mechanism

Saturation functions are used in place of discontinuous sign functions to reduce chattering.

$$\begin{aligned} \text {sat}\!\left( \frac{s}{\phi }\right) = {\left\{ \begin{array}{ll} -1, & s < -\phi , \\ \dfrac{s}{\phi }, & |s| \le \phi , \\ 1, & s > \phi . \end{array}\right. } \end{aligned}$$

(33)

Furthermore, the switching gain is deceptively tuned using fuzzy logic as

$$\begin{aligned} K(t) = K_{0} + \Delta K_{\text {FLC}}(s,{\dot{s}}), \end{aligned}$$

(34)

where huge mistakes are used to hasten convergence with a larger gain and chattering is minimized with a lower gain near the sliding surface.

Finite-time reachability

The reachability condition

$$\begin{aligned} s{\dot{s}} < 0 \end{aligned}$$

(35)

is satisfied by the proposed control law, yielding

$$\begin{aligned} s{\dot{s}} = -K(t)|s| < 0, \quad \forall s \ne 0. \end{aligned}$$

(36)

Because of this, the paths taken by the system eventually come to rest on the sliding surface.

Results and discussions

Voltage swells, voltage sags compensation with FLSMC

Figure 14 shows that swell formed in 0.2–0.4 seconds. It was found that the FLSMC-based UPQC sufficiently corrects for signal-input sag and voltage swells. the outcomes of the simulation’s execution. The swell scenario affects the quantity of electrical power that may be produced, as shown in Fig. 12. Following the use of FLSMC-based UPQC, Swell experienced no negative effects. The waveform displays the adjusted load voltage, the injected voltage, and the Source voltage with swell and sag. Sag has produced in between 0.5 and 0.7 seconds, as seen in Fig. 12. It demonstrates how successfully adaptable FLSMC-based UPQC compensates for voltage sag. The results of the model and the impact of the sag condition on power output. Sag remains unchanged when UPQC based on FLSMC is utilized.

Fig. 14

Voltage swells during 0.2 to 0.4 sec, sags during 0.5 to 0.7 sec with FLSMC.

Voltage swells, voltage sags compensation with FOFLC

Figure 15 shows that swell formed in 0.2–0.4 seconds. It was found that the supplied signal’s voltage swells and sags are efficiently compensated for by the FOFLC-based UPQC. the outcomes of the simulation’s execution. The swell scenario affects the quantity of electrical power that may be produced, as shown by Fig. 15. Swell received better load compensation after using FOFLC-based UPQC. The waveform displays the adjusted load voltage, the injected voltage, and the grid voltage with swell and sag. Sag has produced during those 0.5 and 0.7 seconds, as seen in Fig. 15. It demonstrates how successfully adaptable FOFLC-based UPQC compensates for voltage sag. The results of model and the impact of the sag condition on power output.

Fig. 15

Voltage swells during 0.2 to 0.4 s, sags during 0.5 to 0.7 s with FOFLC.

Voltage swells, voltage sags compensation for unbalanced load

Fig. 16

Voltage swells during 0.2 to 0.4 s, sag during 0.5 to 0.7 s with FLSMC.

Figure 16 shows the outcomes of a control method for the UPQC that handles voltage sags and swells all at once. Figure 16 displays the source voltage waveform, which includes the sag range (0.5–0.7 s) and the swell range (0.2–0.4 s). The compensating voltage waveform shown in Third waveform is used to adjust for the sag and swells, and the resulting load voltage waveform is also displayed in Second waveform. Figure 16 displays the results of the simulation as well as the enhanced voltage sag/swell correction achieved using the FLSMC.

Current harmonics compensation with FLSMC

The input current becomes sinusoidal when FLSMC-based UPQC is implemented, as seen in Fig. 17. Right now, harmonics are taken into consideration. $I_{s}$, $I_{L}$, and filter current simulation results are displayed in Fig. 17.

Fig. 17

$I_{s}$ , $I_{L}$ and $I_{f}$ with FLSMC.

Current harmonics compensation with FOFLC

The input voltage turns oscillatory when FOFLC-based UPQC is implemented, as seen in Fig. 18. The outcomes of simulation for the $I_{s}$, $I_{L}$, filtering present are displayed in Fig. 18.

Fig. 18

$I_{s}$ , $I_{L}$ and $I_{f}$ with FOFLC.

Current harmonics compensation for unbalanced load with FLSMC

Fig. 19

$I_{s}$ , $I_{L}$ and $I_{f}$ with FOFLC.

Controlled by AI-driven techniques, the Shunt Active Power Filter (ShAPF) successfully injected compensatory currents to alleviate power quality issues connected to current, including harmonics, reactive power, and load unbalance1. In Fig. 19 , it is shown that the FLSMC was able to lower the compensatory current’s THD, as demonstrated in the simulation results.

Source voltage, source current after compensation with FLSMC

Figure 20 depicts FOFLC simulation for $V_{S}$, $I_{S}$, $V_{L}$, and $I_{L}$. It was discovered after applying the FoFLC , the source, load side voltages and currents are balanced.

Fig. 20

$V_{s}, I_{s}, V_{L}, I_{L}$ with FOFLC.

Figure 21 depicts FLSMC simulation for $V_{S}$, $I_{S}$, $V_{L}$, and $I_{L}$. It was discovered after applying the FLSMC , the source, load side voltages and currents are balanced.

Fig. 21

$V_{s}, I_{s}, V_{L}, I_{L}$ with FLSMC.

Regulation of $V_{DC-Link}$ voltage

Comparing of VDC-Link Regulation Variations with FOFLC and FLSMC is shown in Fig. 22. To create a controlled DC bus, the voltage across the capacitor is measured periodically and adjusted using closed loop control. DC link voltage, or $V_{dc}$, is measured on a regular basis with respect to the standard value, $V_{dc}*$. An error signal is processed in a FLSMC. To ensure that the source can provide the active power for the load, UPQC’s DC bus, a restriction is placed on the controller’s output. A part of the active power provided by the source is used to build the DC link of UPQC. Through a series inverter and a shunt inverter, respectively, the DC link provides support on both the source and load sides..

Fig. 22

Comparison variation of VDC-Link regulation.

THD comparison with FOFLC and FLSMC

The THD results of source and load-side voltages and currents are shown in Figs. 23, 24, 25, 26, 27, 28, 29 and 30. The findings indicate that the source voltage THD values are 0.38% and the source current THD values are 2.01% when utilizing a FLSMC controller. It is further shown that this controller’s compensation for all parameters is successful. Consequently, out of the four suggested alternatives, the FLSMC controller is the most effective. The installation of the Synergetic Controller considerably enhanced the power quality of the solar-fed distribution system. Reducing the source current’s THD to 2.01% demonstrated a significant reduction in harmonic distortion. The ability of the FLSMC to precisely describe and regulate the nonlinear dynamics of the system was a crucial element of its outstanding performance. We evaluated the performance of the suggested AI-driven control strategies for the UPQC in a metro train system using MATLAB Simulink. We examined how successfully each controller mitigated the effects of various power quality disruptions when testing the system. The primary performance indicator that gauged the degree of harmonic pollution in the system was the source current’s Total Harmonic Distortion (THD).

Fig. 23

FFT analysis(THD) for $I_{L}$ with FOFLC.

Fig. 24

FFT analysis (THD) for $V_{S}$ with FOFLC.

Fig. 25

FFT analysis (THD) for $I_{S}$ with FOFLC.

Fig. 26

. FFT analysis (THD) for $V_{L}$ with FOFL.

Fig. 27

FFT analysis (THD) for $I_{S}$ with FLSMC.

Fig. 28

FFT analysis (THD) for $I_{L}$ with FLSMC.

Fig. 29

FFT analysis (THD) for $V_{s}$ with FLSMC.

Fig. 30

FFT analysis (THD) for $V_{L}$ with FLSMC.

Table 3 Dynamic performance for DC-link voltage regulation using FLC, ANFIS, FOPI, FOFL and FLSMC during swell.

Table 4 Dynamic performance for DC-link voltage regulation using FLC, ANFIS, FOP and FOFL and FLSMC during sag.

Table 5 Dynamic performance for DC-link voltage regulation using FLC, ANFIS, an FOFL and FLSMC during source.

Table 6 Comparison THD with all the controllers.

Dynamic performance for Dc link voltage regulation during Swell,sag and Source Voltage using FLC,ANFIS,FOPI anf FLSMC is shown in Table 3., Table 4. and Table 5. respectively and THD comparison shown in Table 6.

Conclusions

The purpose of this work is to provide a FLSMC-based UPQC in order to address the concerns of dynamic performances and V DC-Link control, both of which have been identified as key challenges in the power quality improvement. The operation of UPQC is comprised of four controllers: the fuzzy logic controller, the adaptive FLC, the fractional order FLC, and the fractional order fractional control (FLSMC) controller. Following the development of the model using MATLAB/Simulink, the results of the simulation are examined. The THD values of each controller are computed and compared to one another. In addition to that, the Dynamic performance metric incorporates itself. The results indicate that when a FLSMC controller is utilized, the total harmonic distortion (THD) value of the source voltage is 0.38%, and the THD value of the source current is 2.01%. Additional evidence demonstrates that the compensation utilized by this controller is successful for all parameters. As a result, the FLSMC controller is the most effective of the four options that have been offered.