Analysis and Mathematical Model for Restitution of Voltage Using Dynamic Voltage Restorer

Voltage sag and swell have amajor concern in the distribution systems. In order tomitigate the voltage sag and swell, a custompower device called dynamic voltage restorer (DVR) is used.The proposed system is a polymer electrolytemembrane (PEM) fuel cell based DVR.The energy from the fuel cell is stored in the super capacitor to restitute the voltage. In this proposed DVR, Z-source inverter is used instead of traditional inverter because of buck-boost and shoot through capability. The simulation is performed using three controller topologies: PI controller, synchronous reference frame controller and fuzzy controller and the results are verified using Matlab-Simulink environment.


Introduction
Recently series type voltage compensators are used to solve the voltage quality problems.Voltage sags and swells were the most frequent disturbances in the industrial sites.Voltage sags become disruptive, when the RMS (root mean square) magnitude dropped lower than 90% of the nominal voltage.Usually, there is significant phase unbalance than the balanced faults [1].Dynamic voltage restorers (DVR) is an effective and economic way to compensate for voltage sags and swells [2,3].
The voltage sags as defined by IEEE is "a decrease in RMS voltage or current at the power frequency for durations from 0.5 cycles to 1 minute, reported as the remaining voltage." Typical values are between 0.1 p.u. and 0.9 p.u., and fault clearing times range from three to thirty cycles depending on the fault current magnitude and the type of overcurrent detection and interruption [1][2][3].DVR is used in low and medium voltage distribution network to protect sensitive load from sudden voltage sag or swell [4,5].Pulse width modulation inverter is used to vary amplitude and phase angle of injected voltages, thus allowing control of real and reactive power exchange between distributed system and load [6].For proper voltage sag compensation, it is necessary to derive suitable and fast control scheme for inverter switching [7,8].A fuel cell converts chemical energy into electric energy by electrochemical conversion.In this system, electric energy is generated as long as fuel is supplied continuously.It can also be considered a generating system similar to conventional generating systems [9].
Fuel cells produce DC output voltages.Polymer electrolyte membrane (PEM) fuel cells are attractive because they are modular, capable, and environmentally friendly.PEM operating temperature is 60-100 ∘ C and efficiency is 50-60%.The control circuit monitors the utility and the fuel cell status continuously [9,10].The traditional inverters are voltage source inverter (VSI) which consists of a diode rectifier, dc link, and inverter bridge.In order to improve the power factor, either an ac inductor or dc inductor is normally used.The VSI is a buck converter and can only produce an ac voltage limited by the dc link voltage.Because of this nature, VSI is characterized by relatively low efficiency because of switching losses and considerable EMI generation.Since the switches are used in the main circuit, each is traditionally composed of power transistors and antiparallel diode.It provides bidirectional current flow and unidirectional voltage blocking capability.Thus, inverter presents negligible switching losses and EMI generation at the line frequency.The proposed Z-source inverter (ZSI) has the unique feature that it can boost/buck the output voltage by introducing shoot through operation mode, which is forbidden in traditional voltage source inverters [11].With this feature, the ZSI provides a cheaper, simpler, buck-boost inversion by single power conversion stage, strong EMI immunity, and low harmonic distortion [12].Super capacitor can store energy at a higher density than a normal capacitor [13,14].When the amount of energy to be stored in a capacitor which increases the size of the capacitor, whereas super capacitor is compact.It has rapid charging and discharging capabilities, so that the efficiency of supercapacitor is higher than the conventional capacitor [15,16].In this paper, dynamic voltage restorer uses fuel cell, super capacitor, and ZSI for the compensation of voltage sag and swell.The PI controller converts the phase voltages into their respective d-q components and generates a PWM signal based on the magnitude and angle of the d-q components.The synchronous reference frame (SRF) technique is based on the instantaneous values of the supply voltage.In fuzzy logic, phase locked loop for each phase which tracks the phase of network voltage phasor generates a reference signal for each   phase, based on the fuzzy matrix.The supply voltage for each phase is converted to p.u and error is obtained.

Proposed Method
The most of the power quality problems are due to different fault conditions.These cause voltage sag and swell.Dynamic voltage restorers (DVR) can provide the cost effective solution to mitigate voltage sag by establishing the appropriate voltage quality level [8].This compensation voltage is provided with the help of a fuel cell [13].The overall block diagram of proposed fuel cell based compensation is given in Figure 1.
The DC voltage from the fuel cell is stored in a super capacitor.Super capacitors are new generation energy storage devices which store energy via charge separation at the electrode-electrolyte interface and they can withstand a large number of charge/discharge cycles without degradation.The major advantages of super capacitors include higher capacitance density, higher charge-discharge cycles, reliable, long life and maintenance-free operation, environmentally safe, wide range of operating temperature, high power density, and good energy density [14].The dc voltage is converted using an impedance source inverter.The proposed Z-source inverter has the unique features that it can boost/buck the output voltage by introducing shoot through operation mode, which is forbidden in traditional voltage source inverters.
With this unique feature, the Z-source inverter provides a cheaper, simpler, buck-boost inversion by single power conversion stage, strong EMI immunity, and low harmonic distortion.
2.1.Super Capacitor.Electrical double layer capacitors (EDLCS) are popularly known as ultracapacitor (UC) or super capacitor (SC) as shown in Figure 2.These devices are emerging very fast as green energy storage devices in the field   of hybrid electrical vehicle, UPS system, along with FACTS devices in power system, drive applications, and utility applications [16].Attractive features of ultracapacitor are its high capacitance, short duration peak power delivery capacity, that is, high power density, reduced space, environmentally safe, low power to weight ratio, and very long cycle life.
Various time domain models of ultracapacitor have been proposed by different authors to study its electrical behavior under various operating conditions [14][15][16].The proposed method overcomes both these limitations and it is also verified by the simulation results.The purpose of UC detailed modeling is to predict its electrical and energetic behavior with high accuracy before implementation of UC in the actual system.The proposed model takes into account temperature effect and it fits in various operating conditions more accurately; the identification process is much simpler and it does not require very sophisticated instrumentation.

Fuel Cell.
PEM stands for polymer electrolyte membrane or proton exchange membrane.Sometimes they are also called polymer membrane fuel cells or just membrane fuel cells.PEM fuel cells use a proton conductive polymer membrane as electrolyte.This technology has drawn the most attention because of its simplicity, viability, and quick startup and it has been used in almost any conceivable application from powering a cell phone to a locomotive.The structure of fuel cell is shown in Figure 3.At the heart of a PEM fuel cell is a polymer membrane that has some unique capabilities.It is impermeable to gases but it conducts protons (proton exchange membrane).The membrane, which acts as the electrolyte, is squeezed between the two porous, electrically conductive electrodes.These electrodes are typically made out of carbon cloth or carbon fiber paper [9,10].At the interface between the porous electrode and the polymer membrane there is a layer with catalyst particles, typically platinum supported on carbon.Electrochemical reactions occur at the surface of the catalyst at the interface between the electrolyte and the membrane.
Hydrogen which is fed on one side of the membrane splits into its primary constituents, protons and electrons.Each hydrogen atom consists of one electron and one proton.Protons travel through the membrane, while the electrons travel through electrically conductive electrodes, through current collectors and through the outside circuit where they perform useful work and return to the other side of the membrane.At the catalyst sites between the membrane and the other electrode they meet with the protons that went through the membrane and oxygen that is fed on that side of the membrane.Water is created in the electrochemical reaction and then pushed out of the cell with an excess flow of oxygen.The net result of these simultaneous reactions is current of electrons through an external circuit, direct electrical current.The hydrogen side is negative and is called  the anode, while the oxygen side of the fuel cell is positive and is called the cathode [9].
The maximum amount of electrical energy generated in a fuel cell corresponds to Gibbs free energy [10]: Potential of fuel cell, , is where  is the number of electrons and is equal to 2 and  is Faraday's constant (96,485 coulombs/electron-mol).Then, potential can be calculated as

Control Algorithm
3.1.PI Controller.Sag occurs when there is increase in load or during the occurrence of fault and swell occurs when there is a sudden removal of load or due to addition of capacitor banks.This sag or swell in load voltage is sensed and its magnitude is compared with a reference voltage and the error signal is given to the PI controller as shown in Figure 4.The output of error detector is where  ref is the reference voltage and  in is the load voltage.
The difference between load voltage,  in , and reference voltage,  ref , is supplied to the PI controller.From the controller, the voltage magnitude is taken as feedback.The IGBT inverter is triggered from the pulse generated by the PWM generator.The IGBTs are triggered depending on the firing angle, , which introduces additional lag or lead in the voltage [6]: The supply side voltages,  ,   , and   , are transformed into d-q values of positive sequence: () is a matrix that rotates by phase angle .Subscripts  and  represent the direct and quadrature axes. 0 is the output voltage.

Synchronous Reference Frame Method.
The general principle of DVR is that whenever the system detects a voltage sag/swell, the DVR should react as fast as possible and inject an ac voltage into the grid.It can be implemented using the synchronous reference frame (SRF) technique based on the instantaneous values of the supply voltage.The control algorithm produces a three-phase reference voltage to the PWM inverter that tries to maintain the load voltage at its reference value.The voltage sag/swell is detected by measuring the error between the supply voltage and the reference value.The reference component is set to a rated voltage.The SRF method can be used to compensate all types of voltage disturbances, voltage sag/swell, voltage unbalance, and harmonic voltage.The difference between the reference voltage and the supply voltage is applied to the ZSI to produce the load rated voltage, with the help of pulse width modulation (PWM) through the PI controller: where  = rotation speed (rad/s) of the rotating frame.We have

Fuzzy Logic
Algorithm.PI controller is the most frequently used controller in DVRs.But one disadvantage of this PI controller is its inability to work well under a wider range of operating conditions.So, as a solution fuzzy controller is proposed.The fuzzy table and its membership function are shown in Figure 5.In this method, PLL for each phase tracks the phase of network voltage phasor and generates a reference signal with magnitude of unit to supply frequency for each phase.The supply voltage for each phase is converted to pu and error is obtained from the difference of reference PLL generated signal and actual supply voltage converted to pu.Error and error rate are the inputs for the FL controller.Output of the FL controller is fed to the PWM generator to produce switching pulses for ZSI.The desired response from DVR-PLL system is quite different from other applications.This is because the phase of the supply voltage prior to the sag is generally preferred and if the PLL reacts quickly to changes in the phase during sag, the post-sag phase may be used.Therefore, the DVR would not be able to compensate for the phase jump.Conventionally, once sag is detected, the target phase of the voltage reference is fixed to the pre-sag phase to ensure that if the reference is correctly tracked, then the load voltage phase will remain unaffected.Through a suitable choice of the time constant of the PLL, the DVR restores the instantaneous voltage waveform in the sensitive load side to the same phase and magnitude as the initial pre-sag voltage.

Simulation Results
A 3-phase, 415 V, 50 HZ supply line can be connected to more than one load, that is, due to addition of load or due to fault occurrence on the distribution side, voltage gets distorted; this can be mitigated with the help of DVR.The fuel cell based DVR is simulated with the help of three controllers for sag and swell compensation using Matlab/Simulink platform.In this paper, increase in load or fault occurs at the interval of 0.05 sec to 0.2 sec.During that time, DVR is activated and they are deactivated during the rest of the time.In this paper DVR uses energy storage device as super capacitor.By using controllers, when fault occurs or increase in load they provide the error signal for the pulse generator which produces the pulses for the  source inverter which injects the three-phase output voltage into the distribution line via injection transformer.Figures 6,7,8,9,10,and 11 show the Simulink model for sag, swell, and fault compensation.

PI Controller
Case 1. Case 1 is as follows: compensation of 40% three-phase voltage sag (Figure 12) and 10% three-phase voltage swell (Figure 13), under condition of adding an additional load to Case 2. Case 2 is as follows: compensation of variable threephase voltage sag under different fault conditions.The load chosen is a linear R-L load ( = 500 Ω,  = 30 −3 H).

Case 1
Sag Compensation.A sudden increase in load occurs at 0.05 s to s; voltage dropped to 249 V (40% sag) from 415 V.The DVR is activated at 0.05 second and injects a voltage of 149 V up to 0.2 second.The load voltage is not compensated to 415 V.

Swell Compensation (Capacitive Load).
A sudden addition of capacitive load at 0.05 second occurred; voltage swelled to 456.5 V (10% swell).DVR is activated at 0.05 second and injects negative voltage of 50.5 V up to 0.2 second.The load voltage is not compensated to 415 V.

Swell Compensation (Removal of Load).
A sudden removal of load at 0.05 second causes voltage swell to 456.5 V (10% swell).DVR is activated at 0.05 second and injects negative voltage of 64.5 V to phase A, 86.5 V to phase B, and 74.5 V to phase C. The load voltage is not compensated to 415 V (Figure 14).

Case 2
Three-Phase Fault Compensation.A three-phase fault occurred at 0.05 s and the voltage in all the three phases are dipped to 210 V. DVR is activated at 0.05 s and it injects a voltage of 190 V in all the three phases.Load voltage is not compensated to 415 V (Figure 15).

Line to Line Fault Compensation.
A line to line (LL) fault occurred at 0.05 s; the voltage in phase A dipped to 340 V and the voltage in phase B dipped to 330 V. DVR is activated at 0.05 s and it injects a compensating voltage of 65 V to phase A and 70 V to phase B. Load voltage is not compensated to 415 V (Figure 16).

Single Line to Ground Fault Compensation.
A single line to ground (LG) fault occurred at 0.05 s; voltage dipped to 225 V from 415 V in phase A. The compensating voltage is provided by a fuel cell for that phase.DVR is activated at 0.05 s and the load voltage is not compensated to 415 V (Figure 17).

Double Line to Ground Fault Compensation.
A double line to ground (LLG) fault occurred at 0.05 s and the voltage in phase A dipped to 310 V and the voltage in phase B dipped to 320 V. DVR is activated at 0.05 s and it injects a compensating voltage of 95 V in phase A and a voltage of 85 V in phase B. Load voltage is not compensated to 415 V (Figure 18).

Synchronous Reference Frame Method
Case 1. Case 1 is as follows: compensation of 40% three-phase voltage sag and 10% three-phase voltage swell, under condition of adding an additional load to existing load/removal of load.The existing load is a linear R-L load ( = 250 Ω,  = 30 −5 H).
Case 2. Case is as follows: compensation of variable threephase voltage sag under different fault conditions.The load chosen is a linear R-L load ( = 500 Ω,  = 30 −5 H).

Case 1
Sag Compensation.Additional load is added during the period of 0.05 s to 0.2 s so sag occurs and the voltage in all 3 phases drops to 249 V. DVR is activated at 0.05 s and it provides the compensating voltage of 141 V to phase A, 137 V to phase B, and 120 V to phase C (Table 1).The load voltage is not compensated to 415 V (Figure 19).

Swell Compensation (Capacitive Load).
Additional capacitive load is added during the period of 0.05 s to 0.2 s so swell occurs and the voltage increases to 456.5 V. DVR is activated at 0.05 s and it provides the compensating voltage of 51.5 V to phase A, 76.5 V to phase B, and 66.5 V to phase C (Table 2).The load voltage is not compensated to 415 V (Figure 20).

Swell Compensation (Removal of Load).
A sudden removal of load at 0.05 second causes voltage swell to 456.5 V (10% swell).DVR is activated at 0.05 second and injects negative voltage of 53.5 V to phase A, 81.5 V to phase B, and 66.5 V to phase C. The load voltage is not compensated to 415 V (Figure 21).

Double Line to Ground Fault Compensation.
A double line to ground fault occurs during the period of 0.05 s to 0.2 s so sag occurs and the voltage drops to 410 V in phase A, 310 V in phase B, and 320 V in phase C. DVR is activated at 0.05 s and it provides the compensating voltage of 5 V to phase A, 101 V to phase B, and 93 V to phase C. The load voltage is not compensated to 415 V (Figure 22).

Fuzzy Algorithm
Case 1. Case 1 is as follows: compensation of 40% three-phase voltage sag and 10% three-phase voltage swell, under condition of adding an additional load to existing load/removal of load.The existing load is a linear R-L load ( = 250 Ω,  = 30 −5 H).Case 2. Case 2 is as follows: compensation of variable threephase voltage sag under different fault conditions.The load chosen is a linear R-L load ( = 500 Ω,  = 30 −3 H).

Case 1
Sag Compensation.Additional load is added during the period of 0.05 s to 0.2 s so sag occurs and the voltage drops to 249 V. DVR is activated at 0.05 s and it provides the compensating voltage of 166 V.The load voltage is compensated to 415 V (Figure 23).

Swell Compensation (Capacitive Load).
Additional capacitive load is added during the period of 0.05 s to 0.2 s so swell occurs and the voltage increases to 456.5 V. DVR is activated at 0.05 s and it provides the compensating voltage of 41.5 V.The load voltage is compensated to 415 V (Figure 24).

Swell Compensation (Removal of Load).
A sudden removal of load at 0.05 second causes voltage swell to 456.5 V (10% swell).
DVR is activated at 0.05 second and injects negative voltage of 41.5 V up to 0.2 second.The load voltage is compensated to 415 V (Figure 25).

Case 2
Fault Compensation: Three-Phase Fault Compensation.A three-phase fault occurs during the period of 0.05 s to 0.2 s so sag occurs and the voltage drops to 210 V in all the phases.DVR is activated at 0.05 s and it provides the compensating voltage of 215 V to phase A, 215 V to phase B, and 215 V to phase C (Table 3).The load voltage is compensated to 415 V (Figure 26).compensating voltage of 2 V to phase A, 63 V to phase B, and 72 V to phase C. The load voltage is not compensated to 415 V (Figure 27).

Line to Line Fault
Line to Ground Fault Compensation.A line to line fault occurs during the period of 0.05 s to 0.2 s so sag occurs and (i) A sudden removal of load at 0.05 sec causes voltage swell (10% swell).(ii) DVR is activated at 0.05 sec and injects negative voltage up to 0.2 sec.(iii) From the three control methods, it is evident that the fuzzy is superior to the other methods.(iv) With the fuzzy controller, voltage restoration is maximum.
The comparative analysis of various control methods for sag compensation (LG fault) is shown in Figure 32.
(i) Single line to ground fault occurs during the period of 0.05 sec to 0.2 sec, so sag occurs and the voltage drops in phase A and phase C. (ii) DVR is activated at 0.05 sec and it provides the compensating voltage.(iii) From the three control methods, it is evident that the fuzzy is superior to the other methods.(iv) With the fuzzy controller, voltage restoration is maximum.
The comparative analysis of various control methods for sag compensation (LL fault) is shown in Figure 33.(ii) DVR is activated at 0.05 sec and it provides the compensating voltage.
(iii) From the three control methods, it is evident that the fuzzy is superior to the other methods.
(iv) With the fuzzy controller, voltage restoration is maximum.
The comparative analysis of various control methods for sag compensation (LLG fault) is shown in Figure 34.
(i) A double line to ground fault occurs during the period of 0.05 sec to 0.2 sec, so sag occurs and the voltage drops in phase A, phase B, and phase C.
(ii) DVR is activated at 0.05 sec and it provides the compensating voltage.
(iii) From the three control methods, it is evident that the fuzzy is superior to the other methods.
(iv) With the fuzzy controller, voltage restoration is maximum.
The comparative analysis of various control methods for sag compensation (three-phase fault) is shown in Figure 35.
(i) A three-phase fault occurs during the period of 0.05 sec to 0.2 sec, so sag occurs and the voltage drops in all the phases.
(ii) DVR is activated at 0.05 sec and it provides the compensating voltage.(iii) From the three control methods, it is evident that the fuzzy is superior to the other methods.

Mathematical Problems in Engineering
(iv) With the fuzzy controller, voltage restoration is maximum.

Conclusion
This paper has proposed a DVR with polymer electrolyte membrane (PEM) fuel cell to mitigate the voltage sag and swell.Three different voltage controllers were designed for DVR voltage regulation.PI Controller, SRF controller, and fuzzy logic controller are the three voltage controllers used.
After a detailed analysis it is found that fuzzy logic controller is the best.The simulation result shows both the balanced and unbalanced faults sag compensation and the swell compensation for the addition of capacitive load.The simulation results validate the efficiency of the DVR which is able to compensate 40% voltage sag and 10% swell.Time domain simulations of the DVR under different conditions have validated the operation of the proposed DVR.PI controller provides sag compensation of 34% in phase A, 33% in phase B, and 28% in phase C. It provides swell compensation of 16% in phase A, 20% in phase B, and 18% in phase C. A synchronous reference frame controller (SRF) provides sag compensation of 35% in phase A, 34% in phase B, and 30% in phase C and provides swell compensation of 12% in phase A, 19% in phase B, and 16% in phase C. Fuzzy controller provides sag compensation of 40% in all phases and swell compensation of 10% in all phases.
In PI controller, voltage sag caused by LG fault is compensated by 20% in phase A. Voltage sag caused by LL fault is compensated by 15% in phase B and 17% in phase C. Voltage sag caused by LLG fault is compensated by 21% in phase B and 16% in phase C. Voltage sag caused by three-phase fault is compensated by 51% in phase A, 49% in phase B, and 40% in phase C.
In SRF controller, voltage sag caused by LG fault is compensated by 45% in phase A. Voltage sag caused by LL fault is compensated by 17% in phase B and 20% in phase C. Voltage sag caused by LLG fault is compensated by 24% in phase B and 22% in phase C. Voltage sag caused by threephase fault is compensated by 52% in phase A, 48% in phase B, and 40% in phase C.
In fuzzy controller, voltage sag caused by LG fault is compensated by 45% in phase A. Voltage sag caused by LL fault is compensated by 18% in phase B and 20% in phase C. Voltage sag caused by LLG fault is compensated by 25% in phase B and 23% in phase C. Voltage sag caused by threephase fault is compensated by 51% in all the phases.From above results, it is clear the fuzzy controller is the most efficient in voltage sag and swell compensation.

Line to Line Fault
Fault resistance ron: 100.

Figure 5 :
Figure 5: Fuzzy table and its membership function.

Figure 16 :
Figure 16: Line to Line fault sag compensation.

Figure 22 :
Figure 22: A double line to ground fault sag compensation.

Figure 27 :
Figure 27: A line to line fault sag compensation.
Compensation.A line to line fault occurs during the period of 0.05 s to 0.2 s so sag occurs and the voltage drops to 413 V in phase A, 340 V in phase B, and 330 V in Phase C. DVR is activated at 0.05 s and it provides the

Figure 28 :
Figure 28: A line to ground fault sag compensation (fuzzy).
(i) A line to line fault occurs during the period of 0.05 sec to 0.2 sec, so sag occurs and the voltage drops in phase A, phase B, and phase C.

Figure 35 :
Figure 35: Comparative analysis for three-phase fault sag compensation.

Table 1 :
Comparison of distorted voltage, injected voltage, and load voltage for different controllers (sag compensation).

Table 2 :
Comparison of distorted voltage, injected voltage, and load voltage for different controllers (swell compensation).

Table 3 :
Comparison of distorted voltage, injected voltage, and load voltage for different controllers (fault compensation).
Figure 32: Comparative analysis for LG fault sag compensation.