# Compensating Reactive Power And Harmonics Computer Science Essay

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## 1. Introduction

AC power supply feeds different kind of linear and non-linear loads. The non-linear loads produce harmonic and reactive power problems in the distribution system [1] [2]. The harmonics and reactive power are primary concern for poor power factor and these loads distort the power supply at the common coupling point (PCC). This distortion is mainly due to the line impedance or the distribution transformer leakage inductance. Traditionally Passive L-C filters are used to compensate the lagging power factor and harmonic currents, but there are definite drawbacks such as resonance, large size, weight and limited compensation. So the alternative solution is an active power line conditioners (APLC) or active power filter (APF) that provides an effective solution for harmonics and reactive power compensation produced by the non-linear loads [3-4].

The controller plays a vital role in the functioning of the active power filter and currently lot of research is being conducted. Conventional PI and PID controllers have been used to extract the fundamental component of the load current thus facilitating reduction of harmonics; in addition it also controls the dc capacitor voltage on the dc side of the PWM-inverter of the shunt APF [5-6]. However, the conventional PI and PID controller requires precise linear mathematical model of the system, which is difficult to obtain under parameter variations, nonlinearity, and load disturbances. Another drawback of this system is that the proportional, integral and derivative gains are to be chosen heuristically. Recently, fuzzy logic controllers (FLC) are used in power electronic systems and variable speed motor drive applications. The advantages of fuzzy logic controller over the conventional controllers are: it does not need accurate mathematical model; it can work with imprecise inputs; it can handle nonlinearity, and it is more robust than conventional nonlinear controllers [1-4].

This paper describes the possibility and feasibility of fuzzy logic control schemes for harmonic current reduction and reactive power mitigation by shunt APLC. The FLC controller is capable of controlling dc side capacitor voltage of the inverter which in turn helps to improve the power quality. The performance of fuzzy logic controller is evaluated through computer simulation under different non-linear load conditions. The results clearly indicate that the proposed active power filter with fuzzy logic controller is capable of providing sinusoidal source current(s) with low harmonic distortion and the current is in phase with the corresponding line voltage.

## 2. Design of APLC system

Active power filter comprises six IGBTs along with freewheeling diodes, a dc capacitor, and RL-filter. The design of the dc side capacitor is based on the principle of instantaneous power flow. The choice of capacitor is governed by the amount of ripple that can be allowed on the dc side capacitor without affecting the performance. The RC-filter facilitates suppressing the higher order harmonic currents caused by the switching operation of the power devices. Reduction of 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. The block diagram of the proposed APLC is shown in fig 1. The APLC consists of a gating signal generator, current reference generator and dc voltage controller that are implemented using fuzzy logic controller. The three phase distribution grid connected to the non-linear load; the instantaneous source current can be written as

From the equation (1), the harmonic or filter current can be obtained by subtract the fundamental component current from the load current. The instantaneous supply voltage is given by

PWM-VSI Inverter

VDC

6-pulse gate drive signal generator

VDC,ref

Vsa,Vsb,Vsc

isa,isb,isc

ica,icb,icc

Rs,Ls

Filter

isa*,isb*,isc*

RL

LL

C

B

A

Voltage sensor

Current sensor

## Fuzzy Logic Controller

Reference Current generator

CDC

A

B

C

G

## 3-Phase Source

A

B

C

Fig 1 Shunt APLC implemented with PWM-VSI in the distribution ac network

If a nonlinear load is connected to the power supply, then the load current will have a fundamental component and harmonic components, which can be represented as

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

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

From this equation the source current supplied by the main source, after compensation the source current should be sinusoidal is written as

where,

The total peak current supplied by the source is

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

Therefore the APLC extracts the fundamental component of the load current and compensates the harmonic current and reactive power. The desired source currents, after compensation, can be given as

Where is the amplitude of the desired source current, while the phase angle can be obtained from the source voltages [3]. This peak value of the reference current has been estimated by regulating the DC side capacitor voltage of the PWM-voltage source inverter using fuzzy logic controller

## 3. Proposed Control scheme

The proposed control system consists of reference current generator using unit sine vector technique with fuzzy logic controller and PWM voltage source inverter switching signals derived from hysteresis current modulator.

## 3.1 Fuzzy Logic Control

Fuzzy logic control is derived from fuzzy set theory introduced by Zadeh in 1965. In fuzzy set theory, the transition between membership and non-membership can be gradual. Therefore, boundaries of fuzzy sets can be vague and ambiguous, making it useful for approximate systems. FLC's are an attractive choice when precise mathematical formulations are not possible. Fig. 1 shows the active power filter compensation system and the fuzzy control scheme. In order to implement the control algorithm of shunt active power line conditioners in a closed loop, the dc capacitor voltage is sensed and then compared with the reference value. In case of a fuzzy logic control scheme, the error and integration of error signal are used as inputs for fuzzy processing shown in fig 2. The output of the fuzzy controller after a limit is considered as 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 PWM inverter are obtained by comparing the actual source currents with the reference current templates using the hysteresis band current controller.

Defuzzification

Fuzzification

Rule Evaluator

(Decision making

## -

Vdc

Vdc,ref

Integrator

LPF

Rule Base

Data Base

Fig 2 block diagram of Fuzzy logic controller

The proposed fuzzy logic controller characteristics are; (1) Seven fuzzy sets for each input and output variables. (2)Triangular membership function is used for 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 can be labeled as zero (ZE), positive small (PS), negative small (NS), positive medium (PM), negative medium (NM), positive big (PB), negative big (NB). The processes of fuzzification is numerical variable (real number) convert to a linguistic variable (fuzzy number), shown in fig 3.

(b)

(a)

(c)

Fig 3 FLC membership functions (a) the input variables error e (n) (b) change of error ce (n) and (c) output variable defuzzification

Rule Elevator:

In conventional controllers, we have control gains or control laws which are combination of numerical values. In FLC, the equivalent term is rules and they are linguistic in nature. A typical rule can be written as follows;

: If is and is then output is

Where,, are the labels of linguistic variables of error,change of errorand output respectively. Hereand the output represents degree of membership. The basic fuzzy set operations needed for evaluation of rules are,and

-Intersection:

-Union:

-Complement:

Defuzzification:

The rules of FLC generate required output in a linguistic variable, according to real world requirements, linguistic variables have to be transformed to crisp output (Real number). The choices available for defuzzification are numerous. So far the choice of strategy is a compromise between accuracy and computational intensity

Database:

The Database stores the definition of the membership function required by fuzzifier and defuzzifier. Storage format is a compromise between available memory and MIPS of the digital controller chip.

Rule Base:

The Rule base stores the linguistic control rules required by rule evaluator (decision making logic). The rules used in this paper 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

## 3.2 Unit sine vector

The source voltages are converted to the unit current(s) while corresponding phase angles are maintained. The unit current is defined as

The amplitude of the sine current is unit or 1 volt and frequency is in phase with the source voltages. This unit current multiplies with peak value of fuzzy logic control output for generate the reference current.

## 3.3 Hysteresis Band Current Control:

Hysteresis current control is the softest control method to implement [5-6]. A hysteresis current controller is implemented with a closed loop control system and is shown in diagrammatic form in fig 4. An error signal e (t) is used to control the switches in an inverter. This error is the difference between the desired current and the actual current.

Lower Band

Upper Band

Actual Current

Reference Current

Fig 4 hysteresis current control

If the error current exceeds the upper limit of the hysteresis band (h=0.5), the upper switch of the inverter leg is turned OFF and the lower switch is turned ON. As a result, the current starts to decay. If the error current exceeds the lower limit of the hysteresis band (h=-0.5), the lower switch of the inverter leg is turned OFF and the upper switch is turned ON. As a result, the current gets back into the hysteresis band. The minimum and maximum values of the error signal are and respectively. The range of the error signaldirectly controls the amount of ripple in the output current from the inverter.

## 4. Simulation Result and Analysis

The performance of the proposed fuzzy logic control strategy is evaluated through digital simulation using SIMULINK toolbox in the MATLAB. This software is used 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 1300 μF

Reference voltage (VDC, ref) is 400 V

Power devices build by IGBT with anti parallel diode.

Fuzzy logic controlled APLC system comprises of a three-phase source with nonlinear load (six pulse diode Rectifier Bridge feeding an RL load) and a PWM voltage source inverter with a inductive filter. The simulation time is counted from T=0 to T=0.1s. The source current after compensation is presented in fig 5 (a) that indicates the source current becomes sinusoidal. The non-linear load current is shown in fig 5 (b). The each phase is shifted by 1200 and we have considered a balanced load. The actual reference currents derived from fuzzy logic controlled value multiply with unit sine vector current, shown in fig 5(c). The APLC supplies the compensating current that is shown in fig 5(d). The current after compensation is as shown in (a) which would have taken a shape as shown in (b) without APLC. It is clearly visible that this waveform is sinusoidal with some high frequency ripples.

(d)

(c)

(b)

(a)

Fig 5 Simulation results for three-phase active-power-line conditioners under non-linear load condition (a) Source current after APLC compensation, (b) Non-linear load current or source current before APLC (c) reference current and (d) Compensation current by APLC.

The proposed fuzzy logic controller achieved power factor correction as shown in fig 6(e). The figure represent a-phase voltage and current are in phase.

Fig 6 Simulation results for unit power factor

The dc side capacitance voltage (Cdc) and its settling time are controlled by fuzzy logic controller (FLC). This controller reduces the ripple voltage to certain level and makes settling time to a low value in the non-linear load condition (t= 0.123s) and it's plotted in fig 7.

Fig 7 the DC side capacitor voltage settling time controlled by fuzzy logic controller (t= 0.123s)

The Fourier analysis of the source current with the fundamental frequency is plotted in fig 8. The Fourier can be calculating the magnitude and the fundamental or harmonic component of the signal f (t) is given as,

Where n represents the order of the harmonics, this order of the harmonics plotted under Non-linear load condition using fuzzy logic controller based shunt APLC system.

(a)

(b)

Fig 8 Order of harmonics under the non-linear load condition, (a) the source current without APLC (THD=26.88%), (b) with APLC (THD=1.59%)

Total Harmonic distortion (THD) of the source current measured and verified without and with APLC using fuzzy logic controller algorithm.

Table 2 comparision of without/with APLC in non-linear load condition

Measurement

Without APLC

With APLC

THD

26.92%

2.203%

Power factor

0.913

0.999

The proposed controller based compensator filter made balance responsibility in the non-linear load conditions. FFT analysis of the active power line conditioners brings the THD of the source current less than 5 % into compliance with IEEE-519 standards harmonic limits.

## 5. Conclusions

A fuzzy logic controller is implemented for three phase shunt active power filter to obtain dc capacitor voltage and estimate the peak value of reference current. This facilitates to improve the power quality parameters such as reactive power and harmonics due to nonlinear load. The reference current generated from the FLC output of peak current multiply with the unit sine vector current. Hysteresis current controller is used for generate switching signals to PWM-VSI. The obtained results indicate that DC capacitor voltage and the harmonic current control can be adapted easily even under balanced or unbalance conditions. The performance of a fuzzy logic controlled shunt active power is verified the simulated various non-linear load conditions. The THD of the source current after compensation is 2.203% which is less than 5%, the harmonic limit imposed by the IEEE-519 and IEC 61000-3 standards. The fuzzy logic controller is a good candidate for controlling APLC to solve power quality problems. This proposed fuzzy logic control algorithm based APLC system can be implemented field programmable gate array (FPGA) devices to attempt as a future work.