# Novel PLL With Fuzzy Logic Controller Computer Science Essay

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AuthorAbstract- This paper proposed a novel Fuzzy Logic Controller (FLC) in conjunction with Phase Locked Loop (PLL) synchronization based three-phase shunt Active Power Line Conditioners (APLC) for power quality improvements in the transmission and distribution grid due to the non-linear loads. The Mamdani-type fuzzy logic is developed and this controller is linguistic description, so it does not require a mathematical calculations. The active power filter is implemented with current controlled voltage source inverter (VSI) and is connected at the point of common coupling for filtering the current harmonics and compensating the reactive power. The desired reference current(s) are extracted using FLC with PLL algorithm and VSI gate switching signals are derivates from hysteresis current controller (HCC). This method maintains the dc-side capacitance voltage of the inverter constant and it is observed less time to settle. The shunt APLC system is investigated and the performances of parameters are verified under different non-linear load conditions.

Index Terms- Shunt Active Power Line Conditioners (APLC), current harmonics, Hysteresis Current Controller (HCC), Fuzzy Logic Controller (FLC), PLL

## INTRODUCTION

Power distribution and transmission system has raised significant interest of power quality problems due to non-linear loads. The most of the industrial load is non-linear, such as rectifiers, welding equipment, incandescent lighting, switched mode power supply (SMPS), ac motor drives and etc. These non-linear loads lead to harmonic or distortion current and reactive power troubles [1-2]. Many countries have set electrical criteria to limit the harmonics and power factor at the point of common coupling (PCC) or on the supply side of electric equipment. Conventionally passive LC filters have been used to eliminate line current harmonics; however in practical applications these passive filters introduce resonance and tuning problems, large size, and it's also limited to few harmonics [3]. Active power filters (APF) or active power-line conditioners (APLC) are recently developed power-electronic equipment for solving these problems. The APLC has ability to compensate current-harmonics and reactive power simultaneously; it can keep the mains current balanced after compensating either the non-linear load is balanced or unbalanced [4]. The shunt APLC can be executed with current converter or voltage converter. The voltage converters have three inductors in series with the ac side and a capacitor on the dc side. The current converters have three capacitors in parallel with the ac side and an inductor in series with the dc side. Generally the voltage converter type is preferred for the shunt active power circuit due to the lower losses in the dc side [5-7].

The controller is the most important part of the APF and currently lot of research is being conducted in this area. Conventional PI and PID controllers have been used to suppress the harmonic current and dc-side capacitor voltage of the shunt active power filter [8]. However, these controllers requires precise linear mathematical model of the system, which is difficult to obtain under parameter variations, nonlinearity, and load disturbances. Recently, fuzzy logic controllers (FLC) are used in power electronic systems and adjustable motor drive applications. The advantages of FLC's over the conventional controllers are: It does not need accurate mathematical model; it can handle nonlinearity and is robust than conventional controllers [9-11].

This paper presents a novel fuzzy logic along with PLL synchronization controller based shunt active power filter for the harmonics and reactive power mitigation of the non-linear loads. The phase locked loop (PLL) can operate satisfactorily under highly distorted and unbalanced system voltages or currents. The shunt active filter is implemented with current controlled voltage source inverter and connected at the point of common coupling for current harmonics by injecting equal but opposite harmonic compensating current. The reference currents are extracted using fuzzy logic with PLL algorithm and inverter switching signals are generated from hysteresis current controller. The shunt APLC is validated and investigated in terms of order of harmonics and VDC settling time under various non-linear load conditions.

## Design of shunt APLC systems

Shunt APLC is connected in the distribution network at the point of common coupling through filter inductances with power inverter and operates in a closed loop. The three phase active power filter comprises of six power transistors with power diodes, a dc capacitor, RL-filter, compensation controller (PLL synchronization with fuzzy logic controller) and switching signal generator (hysteresis current controller) shown in the fig 1. The reference current extracted from the non-linear load using Fuzzy logic controller. The RL-filter suppresses the harmonics caused by the switching operation of the IGBTs inverter. The filter provides smoothing and isolation for high frequency components and the current wave shape is limited by the switching frequency of the inverter. The current harmonics is achieved by injecting equal but opposite current harmonic components at the point of common coupling, there by canceling the original distortion and improving the power quality on the connected power distributed system.

## 6

## VDC,ref

## isa*,isb*,isc*

## PWM-VSI

## Vsa,Vsb,Vsc

## isa,isb,isc

## ica,icb,icc

## Rs,Ls

## PCC

## Reference current generator

## Current

## Sensor

## Voltage

## Sensor

## N

## Unbalanced load

## RL, LL

## Vdc Sensor

## CDC

## iLa, iLb, iLc

## RL

## LL

## Non-sinusoidal Load

## 3-phase supply

## PLL Synchronization Technique

## Fuzzy Logic Controller

## Hysteresis current controller

## Fig 1 shunt active power line conditioners system

Current supplied by shunt APLC:

The three phase supply source connected to the non-linear load (fig 1); the instantaneous source current can be written as

The instantaneous source voltage is given by

The nonlinear load current will have a fundamental component and harmonic current components, which can be represented as

The instantaneous load power can be multiplied from the source voltage and load current and the calculation is given as

This load power contains fundamental (active power), reactive power and harmonics power. From this equation only the real (fundamental) power drawn from the load is

From this equation, the source current drawn from the mains after compensation should be sinusoidal; this is represented as

If the active power filter provides the total reactive and harmonic power, source current will be in phase with the utility voltage and would be sinusoidal. At this time, the active filter must provide the compensation current:

The desired source currents, after compensation, can be written as

This peak value of the reference current has been estimated by regulating the DC-side capacitor voltage of the inverter using fuzzy logic controller.

## Proposed control strategies

The proposed control system is consists of reference current control strategy using PLL synchronization technique with fuzzy logic controller and voltage source inverter switching control method using hysteresis current modulator. In this section describes the FLC, PLL and HCC design for active power line conditioners.

A) Fuzzy Logic Controller:

Fuzzy logic control is deduced from fuzzy set theory; it was introduced by Zadeh in 1965 [5]. In fuzzy set theory concept that transition is between membership and non membership function. Therefore, limitation or boundaries of fuzzy sets can be undefined and ambiguous; it is useful for approximate systems design. FLC's are an excellent choice when precise mathematical formula calculations are impossible. Fig 1 shows the active power filter compensation system and the fuzzy logic control scheme. In order to implement the control algorithm of a shunt active power filter in a closed loop, the dc capacitor voltage is sensed and then compared with the desired reference value. The compared error signal that allows only the fundamental component using the Butterworth 50 Hz low pass filter (LPF). The error signaland integration of error signal is called change of error signalthat are used as inputs for fuzzy processing shown in fig. 2. The output of the fuzzy logic controller limits the magnitude of peak reference current. This current takes care of the active power demand of the non-linear load and losses in the distribution system. The switching signals for the inverter are generated by comparing the actual source currents with the reference current using the hysteresis band current controller method.

## e(n)

## ce(n)

Defuzzification

Data Base

Rule Base

Fuzzification

Rule Evaluator

(Decision making

## +

## -

## -

Vdc

Vdc,ref

LPF

Integrator

Fig 2 Fuzzy logic controller

The proposed fuzzy logic controller characteristics are; (1) Seven fuzzy sets (NB, NM, NS, ZE, PS, PM, PB) for each input and output variables. (2)Triangular membership function is used for the simplicity (3) Implication using mamdani-type min operator (4) Defuzzification using the height method.

Fuzzification:

Fuzzy logic uses linguistic variables instead of numerical variables. In a control system, error between reference signal and output signal can be assigned as negative big (NB), negative medium (NM), negative small (NS), zero (ZE), positive small (PS), positive medium (PM), positive big (PB). The triangular membership function used in fuzzifications. The processes of fuzzification are numerical variable (real number) convert to a linguistic variable (fuzzy number).

Rule Elevator:

In conventional controllers PI and PID having control gains or control rules which are combination of numerical values. In fuzzy logic controller uses linguistic variables on nature instead of the numerical variables. A typical fuzzy set rule can be written as follows;

: If is and is then output is

Where,, are the linguistic variables of error ,change of error and output respectively. Here and output represents degree of membership function. The basic fuzzy logic controller operations required for evaluation of fuzzy set rules are, and for intersection, union and complement functions respectively, it can be derived as

-Intersection:

-Union:

-Complement:

Defuzzification:

The rules of fuzzy logic controller generate required output in a linguistic variable (Fuzzy Number), according to real world requirements; linguistic variables have to be transformed to crisp output (Real number). This selection of strategy is compromise between accuracy and computational intensity.

Database:

The Database stores the definition of the triangular membership function required by fuzzifier and defuzzifier. Storage arrangement is compromise between available memory and microprocessor stages of the digital controller chip for fuzzification and defuzzification.

Rule Base:

The Rule base stores the linguistic control rules required by rule evaluator (decision making logic). The rules used in this proposed controller are shown in table 1.

Table 1 Rule base table

ce(n) e(n)

NB

NM

NS

ZE

PS

PM

PB

NB

NB

NB

NB

NB

NM

NS

ZE

NM

NB

NB

NB

NM

NS

ZE

PS

NS

NB

NB

MN

NS

ZE

PS

PM

ZE

NB

NM

NS

ZE

PS

PM

PB

PS

NM

NS

ZE

PS

PM

PB

PB

PM

NS

ZE

PS

PM

PB

PB

PB

PB

ZE

PS

PM

PB

PB

PB

PB

The output of the fuzzy controller is estimate the magnitude of peak reference current. This current takes response of the active power demand of the non-linear load and losses in the distribution system. The peak reference current multiply with PLL synchronizing output current for determine the desired reference current.

B) PLL Synchronization

The phase locked loop circuit design should be consists perfect operation under distorted and unbalanced voltages [6]. The PLL-synchronizing circuit shown in fig 3, determines automatically the system frequency and the fundamental positive sequence components of three phase line voltages and. The outputs of the PLL synchronizing circuit areof the three phase currents. This algorithm is based on the instantaneous active three-phase power expression, it's written by

The current feedback signals and is built up by the PLL circuit and time integral of output calculated of the proportional integral (PI)-controller. It is having unity amplitude and lead to 1200 these represent a feedback from the frequency.

Sin (ωt - π/2+2π/3)

Sin (ωt - π/2-2π/3)

Sin (ωt - π/2)

Sin (ωt)

Sin (ωt+2π/3)

PI

Controller

Vab

Vcb

## ∑

ia1

ib1

ic1

Fig 3 synchronizing PLL circuit

The PLL synchronizing circuit can reach a stable point of operation when the input of the PI controller has a zero average value () and has minimized low-frequency oscillating portions in three phase voltages. Once the circuit is stabilized, the average value of is zero and the phase angle of the supply system voltage at fundamental frequency is reached. At this condition, the currents become orthogonal to the fundamental phase voltage component. The PLL synchronizing output currents are set as

Therefore the PLL output current signals and the distorted/unbalanced source voltages of the power supply are measured and which are in phase with the fundamental component. The PLL output current multiply with fuzzy logic controller output of peak reference currentfor determine the desired reference current.

C) Hysteresis current modulator:

The hysteresis band current control for active power filter line currents can be carried out to generate the switching pattern the inverter. There are various current control methods proposed for such active power filter configurations but in terms of quick current controllability and easy implementation hysteresis current control method has the highest rate among other current control methods. Hysteresis band current control is the robustness, excellent dynamics and fastest control with minimum hardware. The three-level voltage source inverter systems of the hysteresis current controller are utilized independently for each phase. Each current controller directly generates the switching signal of the phases.

## Lower Band

## Upper Band

## Actual Current

## Reference Current

Fig 4 Diagram of hysteresis current control

In the case of positive input current, if the error current between the desired reference current and the actual source current exceeds the upper hysteresis band limit (+h), the upper switch of the inverter arm is become OFF and the lower switch is become ON. As a result, the current starts to decrease. If the error current crosses the lower limit of the hysteresis band (-h), the lower switch of the inverter arm is become OFF and the upper switch is become ON. As a result, the current gets back into the hysteresis band and the cycle repeats.

Here the hysteresis band limit h=0.5. The range of the error signaldirectly controls the amount of ripple voltage in the output current from the voltage source inverter.

## Simulation result and analysis

The performance of the proposed control strategy is evaluated through digital simulation using Matlab/Sim power tools in order to model and test the system under non-linear load conditions. The system parameters values are; Line to line source voltage is 440 V; System frequency (f) is 50 Hz; Source impedance of RS, LS is 1 Ω; 0.1 mH; Filter impedance of Rc, Lc is 1 Ω; 1 mH respectively; Diode rectifier RL, LL load: 20 Ω; 200 mH respectively; DC side capacitance (CDC) is 1200 μF; Reference voltage (VDC, ref) is 400 V; Power devices build by IGBTs with freewheeling diodes.

The diode rectifier RL non-linear load connected with ac main network and active power filter connected in parallel at the PCC for suppress the harmonics and reactive power. The diode rectifier R L values 20 ohms and 200 mH respectively. The simulation result of source current after compensation is presented in fig 5 (a) that indicates the current is sinusoidal. The six-pulse diode rectifier load current or source current before compensation is shown in fig 5 (b). The desired reference current is shown in fig. 5(c), this current is obtained from our proposed PLL synchronization with fuzzy logic controller. The shunt active power filter supplies the compensating current that is shown in fig. 5(d). These current waveforms are for a particular phase (phase a). Other phases are not shown as they are only phase shifted by 1200

(a)

(d)

(c)

(b)

Fig.5 Simulation results for three-phase active-power-line conditioners under Non-sinusoidal load condition (a) Source current after active power filter (b) Load currents or source current before compensation, (c)Reference currents extracted by the FLC with PLL control algorithm and (d) Compensation current by active power filter

The three phase unbalanced RL load connected parallel with diode rectifier non-linear load in the three phase ac main network. The unbalanced load condition studied and simulated without and with active power line conditioners. Unbalanced three phase RL load impedance are R1=10 Ω, R2=50 Ω, R3=90 Ω and 10 mH respectively. The unbalanced RL load current or source current before compensation is shown in 6 (a). The three-phase source current after compensation is presented in fig 6 (b) that indicates the current becomes sinusoidal. The shunt active filter supplies the compensating current based on the proposed controller that is shown in fig. 6(c). This system achieved power factor correction as shown in fig 6(d) that shows a-phase voltage and a-phase current are in phase.

(b)

(a)

(c)

(d)

Fig.6 Simulation results for three-phase active-power-line conditioners under Non-linear with Unbalanced load condition (a) RL Load current or Source current before active power filter compensation, (b) Source current after active filter (c) Compensation current generated by active filter and (d) unity power factor waveforms.

The dc side capacitance voltage (Cdc) and its settling time are controlled by fuzzy logic controller (FLC). This controller reduces the ripple to certain level and makes settling time to a low value in both non-linear (t= 0.23s) and non-linear with unbalanced load condition (t=0.031s) and it's plotted in fig 7.

(b)

(a)

Fig 7 the DC side capacitor voltage settling time controlled by FLC a) Non-sinusoidal (t= 0.23s) and b) non-linear with Unbalanced load (t=0.031s)

The Fast Fourier Transform (FFT) is used to measures the order of harmonics with the fundamental frequency 50 Hz at the source current. This order of the harmonics plotted under non-linear and non-linear with unbalanced load condition in the distribution supply current that is shown in fig 8. From the result, we can observe that fuzzy logic with PLL controller based shunt APLC is compensating the harmonics effectively.

(b)

(a)

(c)

Fig 9 Order of harmonics (a) non-sinusoidal load condition; the source current without APLC (THD=26.88%), (b) non-sinusoidal condition; with APLC (THD=2.11%) and (c) non-linear with unbalanced load condition; source current with APLC compensation(THD=3.53%)

The Real (P) and Reactive (Q) power is calculated and given in the table 2. This result measured under non-sinusoidal and unbalanced load conditions using fuzzy logic controller with phase locked loop (PLL) synchronization controller based shunt APLC system. These results indicate that reactive power suppressed by active filter and improve the power quality.

Table 2 Real (P) and Reactive (Q) power measurement

Condition

Real (P) and Reactive (Q) power measurement

Without APF

With APF

Non-sinusoidal load

P=9.15 kW

Q= 697 VAR

P=10.81 kW

Q= 366 VAR

Non-linear with unbalanced load

P= 10.40 kW

Q= 416 VAR

P= 11.50 kW

Q=108 VAR

The total harmonic distortion measured from source current on the ac main network. The current of the THD is defined as the root mean square value of the total harmonics of the signal divided by the RMS value of its fundamental signal The fuzzy logic controller and PLL synchronizing control based compensator filter made sinusoidal source current in the supply. The total harmonic distortion measured and compared, shown in table 3.

Table 3 FFT analysis of Total harmonic distortion (THD)

Condition(THD)

Source Current(IS) without APF

Source Current(IS) with APF

Non-linear load

26.88 %

2.11%

Non-linear with Unbalanced load

22.98%

3.53%

Power factor

Lagging

Unity

The simulation is done various Non-sinusoidal and unbalanced load conditions. The obtained result shows the source current and load current is small variation in balanced and unbalanced conditions. The fuzzy logic controller with PLL synchronizing control based compensator filter made balance responsibility even the system is unbalanced. FFT analysis of the active filter brings the THD of the source current less than 5% into compliance with IEEE-519 standards harmonic under balanced/unbalanced conditions.

## Conclusion

The investigation demonstrates a novel fuzzy logic controller is conjunction with the PLL synchronizing circuit facilitates APLC practicality. The FLC ensures that the dc-side capacitor voltage is nearly constant with very little ripple besides extracting fundamental reference currents. The PLL synchronizing circuit assists the APLC to function even under distorted voltage or current conditions. The shunt APLC is implemented with three phase current controlled voltage source inverter and is connected at the point of common coupling for compensating the current harmonics and reactive power. The VSI gate control signals are derived from hysteresis band current controller. The proposed controller based shunt active power filter performs perfectly under different load conditions. Important performance parameters are presented graphically. This approach brings down the THD of the source current to become 2.11 % under non-linear load that is compliance with IEEE-519 and IEC 61000-3 standards. This fuzzy logic with PLL control algorithm based APLC system can be implemented field programmable gate array (FPGA) devices in the future work.