Power Factor Correction based on Fuzzy Logic Controller with Fixed Switching Frequency

Pristatomas skirtingų metodų taikymas AC-DC konverterio su galios koeficiento reguliatoriumi isėjimo įtampai reguliuoti. Klasikinis PI ir neraiskiosios logikos reguliatoriai buvo panaudoti įtampos kilpoje. Siekiant sumažinti harmoninius įėjimo srovės iskraipymus, buvo naudojama histerezės juostų kontrolė. Kintamos juostos histerezės rezultatai būna geresni nei kitų juostų. Visi sie valdikliai buvo patikrinti „Simulink“ modeliavimu ir eksperimentiskai. Neraiskiosios logikos valdiklis gali pasiekti geresnes dinamines charakteristikas nei PI valdiklis esant dideliems trikdžiams ir jėgainės neapibrėžtumams. Be to, kintamų histerezės juostų kontrolė srovės kilpoje sukelia nedaug harmoninių iskraipymų, palyginti su klasikine juostų kontrole. Il. 12, bibl. 10, lent. 2 (anglų kalba; santraukos anglų ir lietuvių k.). DOI: http://dx.doi.org/10.5755/j01.eee.118.2.1176


Introduction
Single-phase power factor correction (PFC) circuits provide rectification of the line voltage to a regulated dc voltage while shaping the input current to be a sinusoid and in phase with the line voltage [1].Often, the PFC acts as a pre-regulator to a dc-dc converter that may be used to provide additional regulation and ohmic isolation [2].Due to adoption of IEC 1000-3-2 as the EN61000-3-2 norm in Europe and the formulation of the IEEE 519 [3] in USA, these circuits are increasingly being used in the front-end of electronic equipments.Among the several possible topologies [2], the boost PFC shown in Fig. 1 is most commonly used.The control objectives are to track the inductor current to a rectified Sinusoid (the line current is sinusoidal and in phase with the line voltage) and to regulate the average output voltage to desired magnitude with fast response to the load variation [4].
Recent research has been directed at applying nonlinear control principles to the dynamic control of converters.The system is controlled by fuzzy control algorithm, in which a set of linguistic rules written in accordance to experience and intuitive reasoning.However, if the control methodology is directly applied to classical ac-dc converters with APFC [5], it might impose considerable computation time to deal with the fast-varying current loop.Fuzzy logic control has been investigated for applications such as motor drives and dc-dc converters [6].Objectives include tight output voltage regulation, high rejection of reference output voltage variations and load transients.The improvement in the transient response of the controller voltage loop decreases the quality of the input current (High THD).On the other hand, PI controller design in current loop requires an accurate mathematical model of the plant and it failed to perform satisfactorily under parameter variation, nonlinearity (two multiplications), load disturbance, etc [7].Hysteresis current controller (bang-bang hysteresis (BBH) technique) has an advantage in coping with the time varying nonlinearity of switches in PFC pre-regulator, and it does not require an accurate mathematical model of the PFC pre-regulator when the controller is being designed [8].Also this technique has an advantage of yielding instantaneous current control, which results in very fast response and increased switch reliability.However, it has a serious disadvantage in that the switching frequency of the boost switch f sw is not constant and varies in a wide range during each half cycle of the ac input voltage [9].The switching frequency is also sensitive to circuit component values, design parameters and difficult for EMI filter design.The novel feature of the proposed method resides in the fact that unity power factor and nearly sinusoidal input current are obtained at constant switching frequencies [10].Moreover, the method exhibits an instantaneous control of current, which results in very fast response and increased switch reliability.This paper presents a systematic design, digital implementation and experimental comparison, in first a PI and fuzzy logic controllers with a 100Hz notch filter for a voltage loop of the regulated dc voltage, then the standard hysteresis controller and redesign with some modifications for improved performance in the current loop.All these controllers are verified by detailed MATLAB/Simulink based simulations through the use of a continuous time plant model and a discrete time controller.Design is comprehensive in the sense that it accounts for sampling effects, computation delays, hardware filtering for antialiasing and software filtering for measurement noise reduction.Real-time implementation is done on an experimental test bench using the dSPACE DS1104 controller board.These controllers are experimentally compared for steady-state performance and transient response over the entire range of input and load conditions for which the system is designed.The system in Fig. 1 is modeled as a first order system * = 4 * 1 + 2 = 1 + . ( Pole and gain are chosen to obtain a sufficient phase margin gain (≈45°) and bandwidth in the 5Hz to 20Hz range.The bandwidth is intentionally kept very low since the compensator gain at 100Hz effectively determines the third harmonic to be expected in the input current.Since the outer loop has a finite dc gain, the voltage reference is pre-compensated to avoid a steady state voltage error at nominal operation.With f CV =10Hz, K i =2.0160 and T i =0.0494, the closed loop transfer function with the design example given in table 1 The circuit is designed with the following specification (Table 1).
Fuzzy Logic-Controller.The fuzzy logic controller unlike conventional controllers does not require a mathematical model of the system that should be controlled.However, a comprehending of the system and the control requirements is necessary.The fuzzy controller designer must clarify how the information is processed (control strategy and decision), and information flows out of the system (solution/output variable).The fuzzy logic controller consists of three basic blocks: Fuzzification; Inference Mechanism and Defuzzification

Current-loop controller
The PFC circuit analyzed here has a feedback loop such that the switching mode is determined by comparison of the actual current and sinusoidal reference current supplied form voltage loop controller in both ways the actual current oscillates in fixed band hysteresis (FBH) as shown in Fig. 4. In the second way, the actual current oscillates in variable band hysteresis (VBH).
If > , = 0, then = , (5) where β=2ΔI is band hysteresis.From Fig. 4 and Fig. 5 by considering the output voltage constant (U 0 ) over a switching period we can write: From Fig. 1, is given For the ideal PFC, we assume to the reference rectifier sinusoidal shape , the equation ( 9) becomes From ( 9) and (10) where = − -the error current in hysteresis band, * -the interrupter reference voltage.
From (11), if we assume the quantity − * constant during the switching period, then the error current ( ) varied as triangular form as shown in Fig. 5.
From Fig. 6 and (11), become and : From ( 11) and ( 13), switching frequency is where To investigate the control characteristics of a PFC, the variation of maximal switching frequency (MSF) with the inductance L of ΔI parameter for FBH is evaluated in Fig. 6.The charts of ( ) = ( ) of parameter ΔI for FBH, informs us about the value of L to choose to limit the excursion in frequency to a compatible value.With 0,1H, the MSF is about 5 kHz.This relatively low frequency shows well the control by hysteresis.A more realistic simulation with L=0,0225H and thus an MSF of 20 kHz would allow faster variations of current around his reference current .Hysteresis current control with constant switching frequency.From (14), if β is constant and the time t varies, then the switching frequency also varies.To get constant, the hysteresis band has to be dynamically changes, according (15) where is the desired switching frequency.(15) gives a very simple control law with constant switching frequency allowing the improvement of characteristics of hysteresis current controller in terms of switching loss, audible noise and EME related problems.

Simulation and experimental results
Steady-state performance.Fig. 7 illustrate dc-bus voltage, line voltage, line current and his associated spectrum, for the Fuzzy_Hysteresis control with FBH and VBH, respectively at nominal load and nominal line voltage.From these figures, it can be seen that the results obtained with the proposed Fuzzy_Hysteresis control are much better than the international norms.Line current is very close to sine wave and in phase with the power source voltage, the THD is less than 4%.It is important to note that at nominal line and load condition, the Fuzzy_Hysteresis control with variable band hysteresis has THD number about 2,01% even with the limited bandwidth that is allowed by the digital implementation.With the variable band hysteresis control, THD of the input current is match better than with the fixed band hysteresis control; the steady-state error is 1V.10.The output voltage reached to the new value after 400ms.On the other hand, it can be observed that the input current is maintained in sinusoidal waveform during the transient period.When the system becomes stable, U 0 * is returned to 160V again.The settling time is about 400ms for the output voltage to attain the old value.Nevertheless, the input current is still sinusoidal and in phase with the input voltage during transient.It can be seen from the above that the system is stable during the large-signal change in the reference output voltage and the output load.Further research will be dedicated into the optimization of the fuzzy rules, in order to have further improvement in the transient behaviors.Fig. 11 show experimental results for PI and fuzzy logic controller respectively of a step response against the disturbance load under the unity power factor operation.It can be observed from these results that the unity power factor operation is successfully achieved, PF=0,997, the reactive power is approximately equal to zero (0,3VAR) and the DPF=1 (DPF displacement power factor) even in this transient state.Notice that, after a short transient, the dc-bus voltage is maintained close to their reference values.

Conclusions
The main goal of the control system is to maintain the dc-bus voltage at the required level, using conventional PI controller or fuzzy logic controller in the dc-bus voltage control loop, while input currents drawn from the power supply should be sinusoidal and in phase with respective phase voltages to satisfy the unity power factor (UPF) operation of the converter.The proposed variable band hysteresis controller, different to the conventional fixed band hysteresis controller, is synthesized by analyzing the instantaneous inductance current.The proposed VBH was simulated and implemented in real-time for both conventional PI and fuzzy logic controller.The presented results indicate that the VBH is much better than the classical one in steady and transient states (dc-bus voltage error =1V, THD of line currents = 2,10%).Near unit power factor can be achieved.Moreover, fuzzy logic controller gives excellent performance in transient state, a good rejection of impact load disturbance, and a good robustness.

Fig. 1 .
Fig. 1.APFC pre-regulator Voltage-loop controller PI-Controller.As shown in Fig. 2, the dc-bus voltage u 0 is sensed and compared with a reference value * .The obtained error is used as input for the PI controller, the output of the controller * multiplied by |sin | obtained from PLL stage with sensing of the input voltage is the instantaneous reference current command i ref .

Fig. 2 .
Fig. 2. PI-Controller for APFC is the transfer function of the PI-Controller; = , = * : are the PI parameters; f CV is the voltage closed loop crossover frequency.The system in Fig.1is modeled as a first order system

Fig. 3 .
Fig. 3. shows the block diagram of the proposed fuzzy logic control scheme of the boost rectifier with APFC.The dc-bus voltage is scaled and is sampled by the digital apparatus and compared with a reference value * .The obtained error ( ) = * ( ) − ( ) and its incremental variation ( ) = ( ) − ( − 1) at the k th sampling instant are used as inputs of fuzzy controller.The output is the variation magnitude of reference current * .The dcbus voltage is controlled by adjusting the magnitude of reference current * .Where ρ and σ are constants used to normalize the error and the change of error.

Fig. 6 .
Fig. 6.Variation of switching frequency with L

Fig. 7 .
Simulated waveforms: a) using FBH, b) using VBH Transient performance.As previously stated, step load changes are effected by connecting (or disconnecting) parallel load.The reference current amplitude is limited to 3,5A in the control for the Fuzzy and PI control designs.When the system has been entered into steady state, there is large step change in the load R from 212Ω to 312Ω with constant reference output voltage.The waveforms of the input current and the output voltage during transient period are shown in Fig. 9.After a short transient, the dc-bus voltage is maintained close to its reference value with a good approximation and stability.Afterwards, the load resistance is switched back to 212 Ω.Another test on large-signal change of U 0 * has been performed, U 0 * is changed from 160V to 192V with R unchanged.The transient output voltage and the input current are shown in Fig.

Fig. 10 .
Fig. 10.Output voltage, input current (reference changes) Fig. 12 show experimental results for PI and fuzzy logic controller respectively of a step response against the step change of U 0 * .Notice that, after a short transient, the dc-bus voltage is maintained close to their new reference values.

Table 1 .
Design specification and circuit parameters

Table 2 .
Fuzzy control rules