Unity power factor Converter based on a Fuzzy controllerand Predictive Input Current

Amar Bouafassa a, Lazhar Rahmani a, Abdelhalim Kessal b,n, Badreddine Babes a

a Automatic Laboratory of Setif, University of Setif 1, Algeriab University of Bordj Bou Arreridj, Algeria

a r t i c l e i n f o

Article history:Received 4 July 2014Accepted 1 August 2014This paper was recommended forpublication by Jeff pieper

Keywords:PFCTHDFuzzyPredictiveUnity power factor

a b s t r a c t

This paper proposes analysis and control of a single-phase power factor corrector (PFC). The proposedcontrol is capable of achieving a unity power factor for each DC link voltage or load fluctuation. Themethod under study is composed of two intelligent approaches, a fuzzy logic controller to ensure anoutput voltage at a suitable value and predictive current control. The fuzzy controller is used withminimum rules to attain a low cost. The method is verified and discussed through simulation on theMATLAB/Simulink platform. It presents high dynamic performance under various parameter changes.Moreover, in order to examine and evaluate the method in real-time, a test bench is built using dSPACE1104. The implantation of the proposed method is very easy and flexible and allows for operation underparameter variations. Additionally, the obtained results are very significant.

& 2014 ISA. Published by Elsevier Ltd. All rights reserved.

1. Introduction

Recently, power converters have been employed in a widerange of industrial sectors and energy conversions. Due to increas-ing energy demands and the appearance of renewable energy(photovoltaic and wind), studies regarding power converters havebecome a topic of interest. Moreover, more than 60% of utilitypower is dissipated before it is finally consumed due to: networkpollution, harmonic distortion and the insufficiency of powersupplies; for these reasons, many countries around the worldhave created laws to limit energy dissipation. One of these lawsenforces that electronic appliances produced must have high-performance with low harmonic distortion. To fulfill these goals,power factor correctors (PFC) appear to be an enabling technologyfor the improvement of power supplies. A switching mode opera-tion in the latest power converts has improved the efficiency andspeed of their performance. This operation includes two states(ON/OFF) and has been developed due to new inventions insemiconductor technologies [1].

In the literature, there are many types of power converters.Among these converters, the boost converter is currently the mostpopular and is used in a wide range of electronic appliances.

To ensure the converted AC/DC, usually a bridge of diodes isused; this tends to have a non-sinusoidal current and a low power

factor, nearly 0.6, due to the nonlinear behavior of the circuit. Tosolve this problem, one possibility is to add a PFC circuit. Moreover,the global cost of devices will be increased by 10 to 25%; however,the cost of the energy saved will cover the cost of the PFC.

Active PFCs have increasingly been used in the last few years ina wide range of industrial power supplies. This involves a pre-regulator between the rectifier and the load (Fig. 1) [2]. Bycontrolling the applied switching, the current will take a sinusoi-dal shape like the source voltage; also, the total harmonic distor-tion (THD) will be decreased. Several control strategies have beenproposed for the control of boost converters, such as PI control [3],neural networks [4], predictive control [5–8], fuzzy logic control[9] sliding mode control [2], and others [10–11]. Taking intoaccount the efficiency of devices, they ensure conversion with lessweight and cost. The fuzzy logic with predictive method can be asuitable solution.

Fuzzy logic is considered a solution when a high nonlinearityand ambiguity of the system have been considered. It is used inmany areas, such as: identification, control and diagnostic of acomplex system [12]. Fuzzy logic was created by Zadeh in 1963[13]. Construction and understanding are very easy because thecontroller does not need mathematical modeling. According toZadeh’s concept, the system behavior is converted to linguistrules; these rules are used to develop a control strategy [14]. Theapplication of fuzzy logic for a power factor corrector can yieldimprovements [9] because it can enhance the performance of thesystem and can offer good responses during the variation of loadvalues or output voltage reference value. There are several works

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ISA Transactions

http://dx.doi.org/10.1016/j.isatra.2014.08.0010019-0578/& 2014 ISA. Published by Elsevier Ltd. All rights reserved.

n Corresponding author.E-mail address: Abdelhalim.kessal@yahoo.fr (A. Kessal).

Please cite this article as: Bouafassa A, et al. Unity power factor Converter based on a Fuzzy controller and Predictive Input Current. ISATransactions (2014), http://dx.doi.org/10.1016/j.isatra.2014.08.001i

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that use fuzzy logic for APFC, but these works apply a high numberof rules, which will exhibit an additional cost and decrease therapidity of devices. Thus, in this work, we try using FLC with asmall number of rules compared to previous works. Meanwhile,the predictive control has been introduced to the current control;this later has been extended for a wide range of power convertersand electric devices. This type of control allows the system topresent good robustness.

The primary task of this work is to develop a new methodbased on predictive control and Takagi Sugeno Fuzzy logic forsingle-phase active power factor correction in order to supply asinusoidal current in phase with the grid voltage. The simulationin MATLAB/Simulink and its implementation in real-time by usingdSPACE1104 are carried out to improve the efficiency and possi-bility of commercialization for this technique in the future.Additionally, several robustness tests have been conducted bythe changing load values and the output voltage reference.

2. Mathematical modeling

The basic conception of the boost converter is illustrated inFig. 1. According to the state of the switch, two function modes arefounded. The first mode of operation is shown in Fig. 1b; in thiscase, the switch S is turned on (S¼1), and the current willaccumulate. Additionally, the energy has been saved in theinductor, and the capacitor supplies the load. In the second modeof operation, shown in Fig. 1c, the switch S is turned off (S¼ 0).The quantity of stored energy in the inductor and the sourceenergy will both be transferred to the output (capacitor–load).Moreover, the power circuit has been changed for this mode. Themodel of the boost PFC can be represented by Eqs. (1) [2,3,9].

Cdvodt ¼ ð1�SÞiL� io

LdiLdt ¼ vin�ð1�SÞvo

8<: ð1Þ

To get a sinusoidal current in phase with the source voltage, acontrol law has been introduced to achieve a manner by which theresistive load is made equal to the ratio of vin and iL.

3. Predictive current control

Predictive control has become increasingly popular over aperiod of decades, but its application for power electronics israther new. Due to its attractive characteristics, the predictivecontrol changes the concept of a classical controller, which unableor less able to achieve good performance if it’s integrated with thenew power converters that use a switching mode operation. In thiswork, predictive control has been used for control of the converterswitch. Taking into account the state of the switch from the circuitshown in Fig. 1, the equations of the current of inductor iL(t) foreach state can be expressed as [8]:

For the case in which switch S is turned on:

LdiLdt

¼ vinðtÞ f or tðkÞrtotðkÞþdðkÞ:Ts ð2Þ

For the case in which switch S is turned off:

LdiLdt

¼ vinðtÞ�voðtÞ f or tðkÞþdðkÞ:Tsrtotðkþ1Þ ð3Þ

where t(k) and t(kþ1) are the starting time of the kth and (kþ1)th

switching cycle, respectively, and d(k) and Ts are the duty cycle andswitching period, respectively.

Since the switching period is more than the input voltagefrequency, Eq.(3) and Eq.(4) can be rewritten as:

LiL t kð Þþd kð Þ:Tsð Þ� iLðt kð ÞÞ

d kð Þ:Ts¼ vinðt kð ÞÞ ð4Þ

LiL t kþ1ð Þð Þ� iLðt kð Þþd kð Þ:TsÞ

ð1�d kð ÞÞ:Ts¼ vin t kð Þð Þ�voðt kð ÞÞ ð5Þ

The diagram shown in Fig. 2 presents the inductor current duringone switching cycle [8].

At the instant t(k)þd(k).Ts, the inductor current can be derivedas (6):

iL t kð Þþd kð Þ:Tsð Þ ¼ iL t kð Þð Þþ1Lvin t kð Þð Þ:d kð Þ:Ts ð6Þ

At the start time of the (kþ1)th switching cycle, the inductorcurrent can be derived as follow:

iL t kþ1ð ÞÞð ¼ iL t kð Þþd kð Þ:Tsð Þþ1Lðvin t kð Þð Þ�voðt kð ÞÞ:ð1�d kð ÞÞ:Ts ð7Þ

Substituting (6) and (7), the inductor current can be derived as:

iL t kþ1ð ÞÞð ¼ iL t kð ÞÞð Þþ1Lvin t kð Þð Þ:Ts�1

Lvoðt kð ÞÞ:ð1�d kð ÞÞ:Ts ð8Þ

The discrete form of (8) can be expressed as

iL kþ1ð Þ ¼ iL kð Þþvin kð Þ:Ts

L�vo kð Þ:ð1�d kð ÞÞ:Ts

Lð9Þ

According to (9), the inductor current at the next switching cycle iscalculated by the inductor current at the present switching cycle.

To calculate the duty cycle, d(k), Eq. (8) can be rewritten as:

d kð Þ ¼ LTs:iL kþ1ð Þ� iL kð Þ

vo kð Þ þvo kð Þ�vin kð Þvo kð Þ ð10Þ

Through the boost circuit parameters, such as input voltage,output voltage and inductor current, the duty cycle d(k) for theactual switching cycle has been calculated.

For designing the boost converter with APFC, the inductorcurrent iL(kþ1) has been forced to follow this reference iref(kþ1),which has a sinusoidal form.

Substituting V0, iL(kþ1) in (10) by his references, the duty cyclecan be expressed as:

d kð Þ ¼ LTs:iref kþ1ð Þ� iL kð Þ

Vref kð Þ þVref kð Þ�vin kð ÞVref kð Þ ð11Þ

The reference current iref in (11) has been calculated as (12):

Iref kþ1ð Þ ¼ Kfuzzy: sin ðωline:tðkþ1Þ�� �� ð12Þ

Fig. 1. PFC pre-regulator.

Mode 1 Mode 2

iL(t(k)+d(k)*Ts)iL(t(k)+1)

iL(t(k))

t(k) t(k)+d(k)*Ts t(k+1)

iref(k+1)

iref(k)

Fig. 2. Inductor current during one switching cycle.

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Kfuzzy is the peak value of the reference current that is given by theoutput of the voltage loop controller, which is detailed in thefollowing section.

4. Fuzzy logic-Based DC Bus Voltage Controller.

Due to its simple structure and robustness, FLC has becomevital in very important research studiers in many fields ofelectrical engineering. The research for enhancing the character-istics of FLC has not abated since 1973. In this work, FLC has beenused in order to regulate and maintain dc-link voltage of the boostconverter that is depicted in Fig. 1 in the desired value. FLCcontains two inputs variables, as shown in Fig. 3: the first is the

KΔe

Ke

Ku ++

d/dt

d/dt

Vin

Vref+

-u

Fig. 3. Fuzzy logic controller.

Table 1Fuzzy rules table.

Error e(k) Change in error Δe(k)

NB NS ZE PS PB

NB NB NB NS NS ZENS NB NB NS ZE PSZE NB NS ZE PS PBPS NS ZE PS PS PBPB ZE PS PS PB PB

Fig. 4. Membership functions for input variables.

Fig. 5. Membership functions for output variable.

Paramaters identification

Initialization of duty cycle table

Measurement of output voltage

FLC for output voltage

Predictive loop controller

All duty cyclescalculated

End

No

YES

Fig. 6. Flowchart of applied method.

1 1.02 1.04 1.06 1.08-10

0

10

20

30

Time (s)

Vdc/5 (V)

Vs/10 (V)

is (A)

Fig. 7. Simulation results, input and output voltage, input current.

Table 2Circuit parameters.

Switching frequency 20 KHzResistance load 200 ΩOutput capacity 1100 μFInput inductance 20 mHDC-link voltage reference 110 VSource voltage frequency 50 HzSupply voltage (RMS) 50 V

0 2 4 6 8 100

50

100

150

200

Time (S)

Out

put V

olta

ge (V

)

Fig. 8. Variation of output voltage from 110 V to 160 V.

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error, e(k), which is calculated as the difference between themeasured dc-link voltage and the desired reference voltage; thesecond input consists of the change in the voltage error, Δe(k),which helps the controller to be fast and efficient. As output, thereference current iref is produced.

According to Fig. 3, the controller is normalized by usingscaling factors to obtain optimal performance as follows:

uk ¼ uk�1þKu:uk

e¼ Ke:e

Δe¼ KΔe:Δe

8><>:

ð13Þ

A total of 25 rules are designed to achieve the best performance ofthe controller, as illustrated in Table 1, Figs. 4 and 5.

All steps of the proposed method are presented in Fig. 6.

� Step 1: Identification of the parameters.� Step 2: Determine the suitable voltage and introduce FLC for

regulation.

0 2 4 6 8 1040

60

80

100

120

140

Time (S)

Out

put V

olta

ge (V

)Decrease Load Increase Load

Fig. 9. Variation of load from 200 Ω to 100 Ω and from 100 Ω to 200 Ω.

Fig. 10. Experimental test bench components: 1: PC, 2: dSPACE I/O connectors, 3:Power Analyzer, 4: Scope, 5: transformer, 6: resistive load, 7: inverter, 8: voltagesensor, 9:current sensor.

is

vdc

vs

iL

5ms

Fig. 11. Experimental results without APFC: Source voltage (50 V/div), input andinductor current (1 A/div) and DC voltage (100 V/div).

Fig. 12. Experimental measurement: PF, voltage and current of source.

vdc

vs

is

iL

10ms

Fig. 13. Experimental results: Source voltage (50 V/div), source current (5 A/div)inductor current (2 A/div) input voltage and output DC voltage (50 V/div).

vdc

is

Increase loadDecrease load

250ms

Fig. 14. Experimental results for load variation, output DC voltage (50 V/div) andinput current (2 A/div).

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� Step 3: Determine Iref through FLC for efficient use of thesuitable mode, and introduce predictive control.

� Step 4: Verify that all duty cycles are calculated by predictivecontrol.

� Step 5: Exploitation of the converter

5. Simulation results

The simulation of the model was conducted with the MATLAB/Simulink environment with a fixed-step size of 40 e-6 s; the mainparameters of the model are given in Table 2. Simulation results ofthe system with constant load (200Ω) and constant DC link voltage(110 V) are shown in Fig. 7. Moreover, various simulation tests havebeen performed to evaluate the dynamic performance of the con-troller during the variation of the DC link voltage reference, as shownin Fig. 8, and the steps of load, as shown in Fig. 9

According to the previous figures, it can observed that theproposed control strategy is robust and was not influenced duringthe changes in parameters (load, output voltage reference), thecurrent take a sinusoidal form and is in phase with the gridvoltage, the steady state error and settling time are enhanced andthe output voltage follows the reference value perfectly.

6. Experimental results and discussion

To validate the proposed method, an experimental test bench hasbeen developed, as shown in Fig. 10, in the LAS laboratory, Setif1 University, Algeria. The prototype contains: an inverter (SEMIKRON,20 KVA, 1200 V, 50 A) used as a rectifier, a transformer (12 KVA, 380/220 V), current sensors, and voltage sensors. The control program hasbeen simulated in the MATLAB/Simulink environment and has beenimplemented in real-time via dSPACE RTI1104.

Test 1: The first test was performed without the APFC con-troller, and the experimental results are presented in Fig. 11. Thisconfiguration presents poor performance, and a high THD,approximately 52.8% with a lower PF of approximately 0.78, wasinduced. Additionally, the current takes a bad waveform due to theload influence. These results affirm the importance of APFC.

Test 2: Here, the model is tested with APFC, and the results arepresented in Figs. 12 and 13. The results highlight the effect ofAPFC with fixed load (200Ω) and output voltage (110 V); it isobserved that the output voltage follows the desired reference,and the source current is in phase with the input voltage. Hence,the THD is approximately 5% and PF is nearly 0.992, an improve-ment compared to the previous test.

Test under load changes: in this test a load variation was appliedin order to test the influence of the load perturbation. Fig. 14shows a slight remoteness of the output voltage due to suddenload changes, but the system performance was not decreased.

Test under voltage reference changes: the value of the outputvoltage reference has risen by roughly (160 v). The results arepresented in Fig. 15, and they show that the output voltage followsthe reference with a lower settling time.

7. Conclusion

In this work, the control of single-phase power factor correc-tion has been studied. The control consists of two intelligentcontrollers, fuzzy logic and a predictive technique, which is simpleand yet efficient. The proposed techniques have successfullysimulated and implemented in real-time via dSPACE 1104. Thesimulation results have been presented and confirmed by experi-mental tests; in both, high efficiency is obtained, which results in aunity power factor, reduced harmonic distortion, and robustnessduring parameter variations (time response). As a future perspec-tive, an artificial neural network will be introduced to optimize thescaling factor of fuzzy logic in cases where there is ambiguity inmeasurements.

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is

vdc250ms

110V

160V 250ms

160V

110V

Fig. 15. Experimental results for voltage variation, increasing from 110 V to 160 V and decreasing from 160 V to 110 V.

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Please cite this article as: Bouafassa A, et al. Unity power factor Converter based on a Fuzzy controller and Predictive Input Current. ISATransactions (2014), http://dx.doi.org/10.1016/j.isatra.2014.08.001i