SELF-ADAPTİVE FAULT-TOLERANT CONTROL STRATEGY OF SHUNT ACTİVE POWER FİLTER BASED ON MULTİCELLULAR CONVERTER

The use of multicellular topology in power quality enhancement can reduce the power loss and also dv/dt of power switches, minimize the electromagnetic interference. However, the failure of flying capacitors can reduce the active filtering efficiency and affect the power quality by injecting currents with wave-form distortion (harmonics, notching, noises etc.) in power distribution grid. Therefore, this study presents a fault-tolerant control strategy (FTC) allowing to keep the normal operation conditions of a multicellular converter even under failure mode. The obtained results show that the proposed FTC strategy enhances the power quality of power distribution grid when a fault in flying capacitors occurs.


INTRODUCTION
Recently, the increasing use of nonlinear loads such as uninterruptible power supplies, adjustable speed drives, furnaces and so on in domestic and industrial appliances, leads to propagate current harmonics in the grid [1][2][3][4] and due to the sensitivity of modern industry to power quality problems, these current harmonics can increase the thermal stress, mechanical vibrations, noise in communication systems and electromagnetic interference [5][6][7][8].Shunt Active Power Filters (SAPF) are proposed in many research works in order to solve all these problems, mitigate harmonics and improve power quality [9][10][11][12].The performance of SAPFs are depends on the control methods, harmonic detection algorithms; in [13] a pq theory is used to extract harmonics of nonlinear loads and regulate the dc capacitor voltage of, in [14] an active power filter and multicellular topology are used with sliding mode control.In order to exploit the advantageous of neural networks, in [15][16][17][18][19] artificial neural network is applied to three phase shunt active power filter in order to reduce calculation time in estimation of harmonic components.In [20] an artificial neural network method used to drive shunt active power filter for minimizing the harmonic currents in industrial systems, and in [21] the obtained results show the effectiveness of hysteresis current control to compensate reactive power and mitigate harmonics using shunt active power filter.The performance of SAPF is depends also to the topology of power converter used (classical two level converter or multilevel converter).
The multilevel power converters are used in shunt active power filters in order to reduce switching power loss and increase the switching frequency [22][23][24][25][26]; among the multilevel topologies of power converter, flying capacitor or multicellular topology has various advantages in comparison to other multilevel topologies such as small dv/dt, it combine between high switching frequency capability and reduced voltage on the power switches [27].In [28] an active power filter with multicellular topology proves the robustness against variations of nonlinear load and minimize the switching losses.However, during a failure in power capacitor, the multicellular converter injects faulty current harmonics and affects the power quality of electric power grid, therefore the use of fault tolerant control in modern industry is very important [29][30][31].In [32][33] a multicellular converter with fault tolerant control used in wind energy conversion system and solar photovoltaic system.
In this paper, a shunt active power filter with three cells multicellular converter used to enhance power quality of 50 Hz grid, self-adaptive FTC is DIAGNOSTYKA, Vol. 24, No. 4 (2023) Bouhafs A, Rouabah B, Kafi MR, Louazene L: Self-adaptive fault-tolerant control strategy of shunt active … 2 proposed to enhance the power quality of electric power grid under failure flying capacitor conditions.
The organization of this paper is as follow: in section-2 material and methods which present the modeling of shunt active power filter based on three cells multicellular converter, sliding mode control is applied in both of healthy and different failure modes of three cells multicellular converter, and the applying of self-adaptive fault tolerant control to proposed topology with one or two flying capacitor failure, in section 3 results and discussion with the comparison between THD values of deferent operating modes of shunt active power filter and finally the conclusion of this work in section 4. Fig. 1, shows the proposed topology of shunt active power filter.

MATERIAL AND METHOD
2.1.Modeling of three cells multicellular power converter Figure 1 show a three phase shunt active power filter based on multicellular converter, this later topology is used in order to compensate current harmonics generates from inductive nonlinear load [6].Flying capacitors currents are given by: Flying capacitors voltages are expressed by: From Figure 1 the output voltage VOG of multicellular converter can be expressed by: ) Output current of multicellular converter if or filter current is given by: The nonlinear form of proposed shunt active power filter is:

DC Capacitor voltage regulation
In order to mitigate the harmonic currents of nonlinear load, DC side capacitor must be regulated at fixed voltage Vdc [14].In this work, the instantaneous power theory is used to extract the filter currents references and to regulate the dc side capacitor as detailed in [18].The filter currents in αβ frame can be expressed as: ∆P: represent the active power necessary to keep the voltage of dc capacitor constant.The output current ifabc can be expressed as:

Multicellular Converter with Sliding Mode Control (Healthy mode)
Equation 6 represent a nonlinear model of shunt active power filter based on multicellular converter expressed in can be written as: With x=[V C1 V C2 i f ] T is the state vector.

xref=[
i fref ] T reference state vector.
DIAGNOSTYKA, Vol. 24, No. 4 (2023) Bouhafs A, Rouabah B, Kafi MR, Louazene L: Self-adaptive fault-tolerant control strategy of shunt active … Where error vector e is expressed by In this work, sliding surface is considered as the error vector.Therefore, in order to assure the stability according to LYAPUNOV theory, we define a new positive function V: The first derivation of function V is given in equations (12,13): V ̇= e (ẋ− ẋ ) V ̇= e ( f(x) + g(x) u + H − ẋ ) The output of sliding mode control: u= u eq +u n (14) Where the control un represent sliding surface sign, ueq is the control which forces the state variables to the origin.ueq led to e=0 and "e" "=0" So, According to equations 16 and 13 V ̇= e g (x) u (17) In order to assure the stability according to Lyapunov theory, derivative of function V must be negative.
Figure 2 shows sliding mode control of shunt active power filter based on multicellular converter.

RESULTS AND DISCUSSION
System parameters used in simulation are given in table .1.

Failure of one flying capacitor
In this section, we consider the failure of C2 as shown in Figure 9.
The voltages VC1 and VC2 are not regulated to their desired values (Figure 10), also the multicellular converter injects faulty currents in the grid (Figure 11).Therefore, the grid current is not sinusoidal with THDig=15.52%(Figures 12 and 13) this THD value does not satisfies the IEEE limits.
The results confirm that the failure of one capacitor destabilize the active power filtering operation and make the multicellular converter affect the power quality instead of power quality improvement.During the failure of C2, the elimination of second cell of multicellular converter by changing the control algorithm is necessary.Therefore, S2 and S3 have the same switching function.In this case, the equation 6 can be expressed by: x =[ V C1 i f ] T is the state vector.
xref=[ i fref ] T reference state vector.
where vector of error e is expressed by Equation 22-23 gives LYAPUNOV positive function and its derivative: V ̇= e ė (23)

Substitution of equation 26 in equation 23
V ̇= e g(x)u DIAGNOSTYKA, Vol. 24, No. 4 (2023) Bouhafs A, Rouabah B, Kafi MR, Louazene L: Self-adaptive fault-tolerant control strategy of shunt active … In order to assure the stability of shunt active power filter the derivative of V must be negative.
Figure 19 shows the sliding mode control of multicellular converter used in shunt active power filter during one capacitor failure mode.Simulation results during failure of one flying capacitor with FTC In this section, the failure of C2 is considered, and the FTC is used.In simulation results, between 0.45s and 0.5s the shunt active power filter without FTC.After 0.5s, the self-adaptive FTC is applied by eliminating the cell with failure capacitor.with switching functions S2=S3.
During the application of self-adaptive FTC (instance 0.5s), Vdc regulates at its reference (Vdcref=1000V).VC1 regulates at its new reference (VC1ref=Vdc/2=500V) as shown in Figure 20.Also, after 0.5s shunt active power filter generates the desired currents (Figure 21) and improve the form of grid current with THDig=2.70% (Figure 22 and figure 23).During the failure of two capacitors.Selfadaptive FTC based on hysteresis control is applied.In this case, S1=S2=S3, therefore, the multicellular converter operates as two-level classical converter as presented in Figure 24.

Simulation results during failure of two capacitors failure with FTC
In this section, the failure of capacitors C1 and C2 is considered.Therefore, S1=S2 =S3 and multicellular converter operates as classical topology.at the instance 0.5s the self-adaptive FTC based on hysteresis control is applied.Vdc regulated at its desired value (Vdc=Vdcref=1000V) as shown in Figure 25, and the power quality is enhanced by injecting the desired current in the grid (Figure 26) and the grid current has a sinusoidal form (Figure 27) with acceptable THD (figure 29).

Analysis of simulation results
In this paper, the proposed structure is shunt active power filter used to improve power quality of power grid.So, a sophisticated multicellular power converter and its control algorithm are used to have a sinusoidal grid current phase with grid voltage.However, according to the obtained results, during the failure of one or more flying capacitors, the THD of grid current exceeds the limits of the standards, and the multicellular converter becomes a source of instability instead of being a power enhancement tool.Therefore, the self-adaptive fault tolerant control (FTC) without changing the structure is applied.The obtained simulation results, proves that the FTC allows the multicellular converter with defected flying capacitor to enhance the power quality of power grid, this enhancement is justified by reducing the THD value of grid current under the threshold of standard as detailed in simulation results.

Benefits of society from this paper
The benefits of society from this paper are: Reduce the cost of failure in active power filter especially the proposed FTC does not require to changing the structure as well as optimize the energy consumption, extend the life time of electric machine in both domestic and industrial use.

CONCLUSION
This research paper represented a significant advancement in power quality enhancement and fault tolerant control in shunt active power filters.The proposed self-adaptive FTC was found to be highly robust and responsive to the dynamic conditions presented by the failure of flying capacitors, and preventing the injection of undesirable currents into the power grid.
The obtained simulation results provided solid evidence of the FTC's efficacy in enhancing power quality during fault scenarios.This research contributes to assure that power distribution systems adhere to the power quality standards and remain it reliable even in the face of component failures.

Fig. 3 .Fig. 4 .Fig. 6 . 5 Fig. 7 .Fig. 8 .
Fig. 3. Multicellular converter with sliding mode control In healthy mode operation the dc side voltage is regulated at Vdc=1000V which equal to Vdcref=1000V and the flying capacitors are regulated at their references VC1=VC1ref=Vdc/3 and VC2=VC2ref=2*Vdc/3 as represented in Figure 4.In the Figure 5 the nonlinear load current is deformed and

Fig. 14 .
Fig. 14.Multicellular converter under two flying capacitors failure Simulation results of shunt active power filter based on multicellular converter under two flying capacitors failure in (Figures 15-18) presents the divergence of VC1 and VC2 from their desired values and the multicellular converter injects the unwanted currents and affect the power quality of power grid with non-sinusoidal grid currents and high THD value (THDig=15.70),the spent coast in order to enhance the power quality with multicellular converter can affect the power quality and

Fig. 19 .
Fig. 19.Shunt active power filter with selfadaptive FTC and one capacitor failure mode 3.4.2.Simulation results during failure of oneflying capacitor with FTC In this section, the failure of C2 is considered, and the FTC is used.In simulation results, between 0.45s and 0.5s the shunt active power filter without FTC.After 0.5s, the self-adaptive FTC is applied by eliminating the cell with failure capacitor.with switching functions S2=S3.During the application of self-adaptive FTC (instance 0.5s), Vdc regulates at its reference (Vdcref=1000V).VC1 regulates at its new reference (VC1ref=Vdc/2=500V) as shown in Figure20.Also, after 0.5s shunt active power filter generates the desired currents (Figure21) and improve the form of grid current with THDig=2.70% (Figure22and figure23).

Table 2
gives the THD values of different state of multicellular converter compared to threshold of IEEE-519, this table demonstrate the effectiveness of proposed self-adaptive FTC in power quality enhancement.