Survey

Document related concepts

Ground (electricity) wikipedia, lookup

Control system wikipedia, lookup

Spark-gap transmitter wikipedia, lookup

Control theory wikipedia, lookup

Utility frequency wikipedia, lookup

Immunity-aware programming wikipedia, lookup

Ground loop (electricity) wikipedia, lookup

Stepper motor wikipedia, lookup

Mercury-arc valve wikipedia, lookup

Power engineering wikipedia, lookup

Electrical ballast wikipedia, lookup

Power inverter wikipedia, lookup

Electrical substation wikipedia, lookup

History of electric power transmission wikipedia, lookup

Current source wikipedia, lookup

Power MOSFET wikipedia, lookup

Integrating ADC wikipedia, lookup

Schmitt trigger wikipedia, lookup

Resistive opto-isolator wikipedia, lookup

Distribution management system wikipedia, lookup

Variable-frequency drive wikipedia, lookup

Pulse-width modulation wikipedia, lookup

Voltage regulator wikipedia, lookup

Three-phase electric power wikipedia, lookup

Surge protector wikipedia, lookup

Stray voltage wikipedia, lookup

Switched-mode power supply wikipedia, lookup

Buck converter wikipedia, lookup

Opto-isolator wikipedia, lookup

Voltage optimisation wikipedia, lookup

Transcript

Transactions on Electrical Engineering, Vol. 2 (2013), No. 1 10 Control Techniques of Grid Connected PWM Rectifiers under Unbalanced Input Voltage Conditions Martin Bejvl 1), Petr Šimek 2), Jiří Škramlík 3), Viktor Valouch 4) Institute of Thermomechanics AS CR, v. v. i., Department of Electrical Engineering and Electrophysics, Dolejškova 1402/5, 182 00 Praha 8, Czech Republic, www.it.cas.cz 1) [email protected], 2) [email protected], 3) [email protected], 4) [email protected] Abstract — Current-controlled voltage source converters are widely used in grid-connected applications, for example for ac drives with indirect frequency converters. The structure and parameters of the PLL are developed and proposed in order to cope with the grid containing both the positive and the negative sequence components, and minimize the wrong frequency transients during phase angle steps and also in the start-up stage. The DSC (Delayed Signal Cancellation) technique was realised. There is also necessary to compensate the negative sequence component in the grid voltage. The negative sequence component of the grid voltage causes ripples of the dc voltage in the DC link. Several sophisticated topologies of converter current controller were developed, simulated and tested for this purpose. Results of simulation and experimental tests are provided to evaluate different current control schemas and phase locked loop techniques. Keywords — Phase Locked Loop (PLL), DSC, Current Controller, PWM rectifier. I. INTRODUCTION The ac/dc rectifiers are often used in many applications, especially in electric drives with ac motors. The rectifier works at these drives as an input part of the indirect frequency inverter. In an ideal situation, the 3-phase grid voltage is harmonic, shifted by 120° phase-by-phase, and the voltage and current are in phase. The track of the space vector of the 3-phase voltage transformed to αβ coordinates has a form of the circle. In a real situation, the 3-phase grid voltage is distorted by a negative sequence component, high-order harmonics and by a shift between voltages and currents in the phases, which produces a reactive power and also ripples in the voltage on the capacitors in the DC link. The track of the space vector of the 3-phase voltage transformed to αβ coordinates has a deformed form. This deformed track of the voltage space vector, with harmonics neglected, consists of the positive and negative superposed components. The first component is equal with the ideal circle shape of the space vector track and is running by frequency 50 Hz. This is so called positive sequence component. The second component of the space vector is running in the opposite direction with the frequency 50 Hz and represents the negative sequence component of the grid voltage. The second component is called negative sequence component. Now, our object is an analysis of the positive and negative sequence component control of the ac current in order to eliminate reactive power, high-order harmonics and the ripples of the voltage in the dc link. The current also consists of the positive and the negative sequence components similarly like the voltage. Both components of the current are controlled separately and simultaneously. The positive sequence component of the current is controlled in the positive coordinates, which looks like the dc control. The negative sequence component of the current is controlled in the negative coordinates, which looks like the dc control too. Both of these controls are realized simultaneously by separate PI controllers. This system is very effective because it permits the complete control by one chip and one program without additionally SW or HW devices. The necessary condition of a reliable operation of an electronic power converter connected to the grid is an effective synchronization of the control system, usually to the positive sequence component of the grid voltage. We present a several possibilities of the synchronization by Phase Locked Loop (PLL) strategies in the text below. Transactions on Electrical Engineering, Vol. 2 (2013), No. 1 11 Fig. 1: Control schema of rectifier with standard dual current controller; reproduced from [1] From many methods published recently only those were selected for an analysis which are suitable for three phase systems and do not need tuning of many parameters (like e.g. those with varying switching periods, with adaptive parameter tuning, with many low- or high-pass filters, etc.). These selected PLL techniques have been more or less verified by simulations or experiments and recommended to use not only by their authors too. can cause dc voltage ripples. It means that the control system based on calculation from ea , eb , ec is not usable for an extremely unbalanced grid. B. Nonlinear dual current controller A new method, which calculates current references idqp∗ pn idqn∗ with help of the output voltage vdq , was proposed in II. CURRENT CONTROLLER: INVESTIGATED AND TESTED METHODS A. Standard dual current controller displays the schema of the control algorithm, which is considered to be a standard dual current controller [1]-[2]. This control system is based on calculation of the reference currents with help of the grid voltages ea , eb , ec . For the exactly working control system it is necessary to compute the current references from voltages va , v b , vc , thus from voltages at the ac poles of the converter, because v a , v b , v c , together with phase currents, are responsible for an active power that [3]. The output voltage pn vdq is expressed by pn pn vdq = edq ± ωLiqdpn , where pn edq is measured. The disadvantage of this method consists in necessity to solve nonlinear equations, what is very difficult and complicated. C. Dual current controller with feedback from PWM This method will avoid the nonlinearity of the previous one [4]. The nonlinearity is transformed to linearity by use an additional feedback path for pole voltages Transactions on Electrical Engineering, Vol. 2 (2013), No. 1 Phase error Input v1(t) v2(t) 12 Phase detector ϑe Loop filter (PI Controler) ω VCO Fig. 2: Basic structure of closed loop PLL (va , v b , vc ) . So, the algorithm for calculation of the which is dissipated in filters, are used: current references becomes simpler. The four sequence In the first case (case 1), the dc side of the converter supplies oscillating power to the filter, it means that the oscillating powers are set to zero on the grid side, i.e. components of the pole voltages vdp , v qp , vdn , vqn , are extracted from the space vector PWM block and fed back to the algorithm for calculation of the current references. Ps2in = Pc2in = 0 . A disadvantage of the methods is that oscillating powers that have been dissipated in the input filtering inductors are neglected. In the second case (case 2), the oscillating power flows from the grid into the filter, i.e. the oscillating powers are forced to zero at the converter terminals and Pcin2 = - ∆Pc2 Psin2 = - ∆Ps2 . D. Dual current controller with calculation of dissipated power This method [5] comes from calculation of the power, which is dissipated in the input inductors. The method calculates the current references with the help of the measured voltage e. The difference is considered between the power at the grid side and power at the ac side of the converter. So the regard to losses at the inductors is assumed. But the equations for the power are still nonlinear. The authors avoided the nonlinearity by giving the previous patterns of the calculated reference current to the equations for calculating the actual current references. So nonlinearity (multiplying unknown components of the current with unknown components of the current) is replaced by linearity. This is the difference between this work and the nonlinear controller. Two different methods for calculation of the power, Input vabc(t) III. GRID SYNCHRONISATION The PLL unit can be described by the basic structure shown in the block diagram in Fig. 2 This PLL structure comprises a phase detector (PD), a loop filter (LF), and a voltage controlled oscillator (VCO). Each part of which can be implemented in several different forms. The block diagram in Fig. 2 shows a basic structure of the closed loop synchronization block. The input (reference) signal is compared with the internal (estimated) signal in the phase detector (PD), called also phase comparator. The phase error being the output of this block is used as the input signal for the frequency controller (PI). Frequency from this controller is used for the control of the Voltage Controlled Oscillator (VCO). The output of the VCO is compared with the input signal in the PD block. When the input and internal signal are in the same vsd=Vs abc abc→dq dq vsq→0 ω PI ϑcont ∫ dt Fig. 3: Block structure of the SFR-PLL ϑ ϑ to 0..2π Transactions on Electrical Engineering, Vol. 2 (2013), No. 1 angular frequency and phase angle, the error signal is zero and PLL is in steady state. 13 Voltage Vd, Vq 10000 Vq 5000 A. SFR (Synchronous Frame Reference) A basic closed loop technique is the SFR-PLL (Synchronous Frame Reference PLL) where the reference frame is synchronized by the vector of the grid threephase voltage. It is the most extended technique used for frequency and phase angle detection in three phase systems. The input voltage is transformed to the synchronous reference frame. One of two synchronous components is required to be zero (in Fig. 3 vsq). If the first component is (nearly) equal zero the second component represent magnitude Vs of the grid voltage vector and the angle ϑ represents the instantaneous phase angle of this vector. Vd 0 -5000 1.4 1.5 1.6 1.7 1.8 1 1.9 2 2.1 2.2 2.3 Vabc 4 x 10 Va Vb 0 Vc -1 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 error of angle (in degrees) 1 Source SFR 0.5 0 -0.5 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 frequency 52 Under ideal grid conditions (without harmonic distortion and negative sequence component) a high bandwidth of the SFR-PLL feedback loop yields a fast and precise detection of the phase and amplitude of the grid voltage vector. In case when utility is distorted with high order harmonics, the SFR-PLL can operate satisfactorily only if this bandwidth is reduced. Fig. 4 shows typical waveforms obtained by using the SFR PLL. The upper graph shows the detected voltages in the synchronous frame (vd, vq). The lower graph shows the instantaneous angle error (top), and the instantaneous detected frequency (middle). Here, the blue lines sign the theoretically correct values. The bottom graphs in both diagrams show the phase voltages. Between 1.5 and 2.5 s the voltage negative sequence component of the magnitude 10 % was added. The negative sequence component is transferred as a second order harmonic in the transformed voltages, and manifests itself in the detected frequency and phase waveforms. B. DDSFR (Double Decoupled Synchronous Frame Reference) In [11] the method for decoupling the positive and negative sequence voltage components was described. This method uses the filtered negative and positive sequence components to eliminate (decouple) them in the input signal. A decoupling cell is used for the cancellation of the coupling effect between signals in the two different frames. Block diagram of the DDSFR-PLL is shown in Fig. 5. The decoupling cell for decoupling signals between Source SFR 51 50 49 1.4 1.5 1.6 1.7 1.8 1 1.9 V 4 x 10 2 2.1 2.2 2.3 abc V V 0 V -1 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 a b c 2.3 Fig. 4: SFR-PLL under unbalanced grid conditions. The negative sequence component of magnitude 10 % was added between 1.5 and 2.0 s positive and negative sequence components can be expressed as v*d + vd + cos2ϑ sin2ϑ vd − * + = v + − vq q −sin2ϑ cos2ϑ vq− (1) v*d − vd − cos ( −2ϑ) sin ( −2ϑ) vd + * = − vq− vq− −sin ( −2ϑ) cos ( −2ϑ) vq+ The low pass filters at the outputs of the decoupling block stop (or attenuate) the transformed negative sequence component (it is transferred as a component with double frequency). All the frequencies at the input that are greater than this frequency (i.e. harmonics) are attenuated too. But only the negative sequence component is decoupled and quite suppressed. The PLL filter is situated outside of the control loop. Thus, the loop bandwidth of the PLL is not reduced. The simulation of this type of PLL was performed with the recommended LPF type (Butterworth of the 4th order) and cut-off frequency value. The Fig. 6 shows transient Transactions on Electrical Engineering, Vol. 2 (2013), No. 1 abc dq+ vabc v*d + vdq + abc dq− 14 v*q + Decoupling v*d − cells vdq − v*q − LPF LPF Vs = vd vd + vq + PI LPF LPF ω 1 s ϑ vd − vq − Fig. 5: Block diagram of the DDSFR-PLL strategy response after applying an unsymmetrical voltage component. Positive sequence 10000 V q+ 5000 V d+ 0 -5000 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 Negative sequence C. DSC (Delayed Signal Cancellations) The DSC (Delayed Signal Cancellation) strategy represents an effective and robust method for the detection of the positive and negative sequence components of the voltage in the three-phase system. The positive sequence vector appears as a dc component in the synchronous reference frame. 500 V q0 V d- -500 -1000 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 V abc 4 1 x 10 Va 0.5 Vb 0 + vαβ ( t ) = 0.5 ( vαβ ( t ) + jvαβ ( t − T4 ) ) Vc -0.5 -1 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 The voltage vector in a stationary α-β reference frame is delayed. This technique is based on a combination of the positive- and negative-sequence components with a time delay of one quarter of a period (5 ms at 50 Hz). 2.3 (2) − vαβ ( t ) = 0.5 ( vαβ ( t ) − jvαβ ( t − T4 ) ) error of angle (in degrees) 0.6 Source DDSFR 0.4 0.2 D. PLL based on the pq theory [14] 0 -0.2 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 frequency Source DDSFR 50.65 50.6 The phase detector operation is based on the product of the space vectors v1(t) and v2(t). Its output can be obtained from 50.55 50.5 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 x 10 e j ( Φ1 −Φ 2 ) (3) where the asterisk (*) denotes the complex conjugate quantity. Alternatively, the phase error signal can be expressed in rectangular form as Va 0.5 Vb 0 Vc -0.5 -1 1.4 j (ω1 −ω2 ) V abc 4 1 vd ( t ) = v1 ( t ) ⋅ v2 ( t ) = V1V2 e * 50.45 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 Fig. 6: Detection of positive and negative sequence in the synchronous frames (dq+ and dq-) with DDSFR-PLL vd ( t ) = ( v1α v2α + v1β v2 β ) + j ( v1β v2α − v1α v2 β ) (4) It is evident from (4) that the real and imaginary components of vd(t) have, respectively, the same form as the p and q power components from Akagi’s instantaneous power theory. Transactions on Electrical Engineering, Vol. 2 (2013), No. 1 fiα vabc abc cos(ϑ) vα PI controller fp αβ 15 vβ fiβ ϑ ω ∫ dt sin(ϑ) Fig. 7: PLL based on the pq theory Two different approaches can be adopted: if the real part of vd(t) is used as the feedback error signal, then we have the so called p-type PLL system. Using the imaginary part of vd(t) yields the so called q-PLL. (stationary α-β and synchronous d-q). The extracted positive sequence voltage component is the input to an SFR-PLL for detecting the frequency and the angle of the desired voltage vector. Now considering that ω1=ω2 = ω0 (i.e. the p-type PLL is nearly locked at the centre frequency), then the phase error signal given by (3) can be simplified to It is possible to obtain the symmetrical phasor components (s+, s- and s0) of a three-phase signal from vd = VV 1 2con (ϑ1 − ϑ2 ) S%+ 1 1∠120° 1∠ − 120° S%a % 1 % S − = 3 1 1∠ − 120° 1∠120° S b S%0 1 S%c 1 1 (5) For small deviations it can be approximated linearly by vd ( t ) ≈ K dϑe ( t ) (6) (6) The negative and positive components can be extracted in the abc system by where ϑe is the phase error and Kd = V1V2. Block diagram is showed in the Fig. 7. The resulting quantity can also be interpreted as being analogous to the instantaneous real power according to Akagi’s pq theory. E. Simple mathematical transformations for canceling some harmonics [15] This is the next method for elimination of the negative sequence component and most harmonics. The method is based on different ways of obtaining the positive and negative sequence components of the grid voltage, by applying the symmetric component theory to the voltage vector transformed into different reference frames vabc αβ S%a− 1∠60° 1∠− 60° S%a −1 %− 1 −1 1∠60° S%b (8) Sb = 3 1∠− 60° S%c− 1∠60° 1∠− 60° −1 S%c S%a+ 1∠− 60° 1∠60° S%a −1 %+ 1 −1 1∠− 60° S%b (9) Sb = 3 1∠60° S%c+ 1∠− 60° 1∠60° −1 S%c The operations (8) and (9) can be written in different ways for obtaining the same response if the phase signals contain only the fundamental frequency components. vq αβ abc Cαβ Dαβ dq (7) Aαβ Bαβ Fig. 8: Block diagram of the PLL which uses the mathematical transformations MDC ϑ ω PI ∫ dt Transactions on Electrical Engineering, Vol. 2 (2013), No. 1 16 However, the harmonics presented in the original signals are differently modified by each of such operations. the corresponding values in degrees. The negative advance is used to indicate delayed instantaneous signal. The Eq. (8) can be rewritten as (in the instantaneous values) The formulas (10) - Chyba! Nenalezen zdroj odkazů. can be used to improve the operation under harmonics of the SFR-PLL after the transformation to the stationary αβ frame [15] (Fig. 8). Most of the harmonics has been suppressed (all odd except 12n+1, (n is an integer)) or sa sa− sa 60 sa −60 1 − sb = − 3 A1 sb + A2 sb 60 + A3 sb − 60 (10) s sc− sc 60 sc − 60 c AB 1 0.8 sa− sa sa −90 1 − sb = 3 − B1 sb + B2 sb −90 sc− sc sc −90 0.6 (11) (11) 0.4 0.2 0 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 The Eq. (9) can be rewritten as (in the instantaneous values) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Fig. 9: Gain of the operation A and B in cascade sa sa+ sa −60 sa 60 1 + sb = − 3 C1 sb + C2 sb −60 + C3 sb 60 (12) s sc+ sc −60 sc 60 c CD 1 0.8 0.6 0.4 0.2 sa+ sa sa 90 1 + sb = 3 − D1 sb + D2 sb 90 sc+ sc sc 90 0 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 (13) Fig. 10: Gain of the operation C and D in cascade attenuated. where the matrixes −1 0 0 A1 = C1 = 0 −1 0 0 0 −1 0 1 0 A2 = C2 = 0 0 1 1 0 0 0 0 1 A3 = C3 = 1 0 0 0 1 0 1 −1 12 2 1 1 B1 = D1 = 2 −1 2 1 12 −1 2 0 B2 = D2 = − 23 3 2 3 2 0 − 3 2 3 2 0 − Due to the synchronous d-q frame transformation the harmonic order of a component in the input signal is decreased. Then, even harmonics become odd and vice versa. The signals in the synchronous d-q reference frame go through the operation A and B in cascade. The gain of this operation is shown in Fig. 9. Then the odd harmonics (even harmonics in the original signal) are eliminated. The gain of the operation A and B in the cascade is shown in Fig. 10. The eleventh negative and thirteenth positive (and all other harmonics 12n+1) get through without attenuation, as well as the fundamental harmonic. This harmonic cannot be suppressed by use of this method. 3 2 (14) The subscripts 60 and 90 are used to indicate instantaneous signals advanced from the original ones by F. PLL with moving average value The integral of the voltage of any harmonic frequency in the full period of the fundamental frequency is zero. This mathematical knowledge is used in the Frequency Transactions on Electrical Engineering, Vol. 2 (2013), No. 1 Input vabc(t) 17 vsd=Vs abc abc→dq dq vsq AVG ω PI ∫ dt ϑ Fig. 11: Block structure of the SFR-PLL Fig. 12: Dip response under single current controller in comparison to standard dual current controller; reproduced from [1] Variable Average PLL (FVAVG-PLL). This technique is capable to suppress all harmonics components (Fig. 11). IV. SIMULATION AND EXPERIMENTAL RESULTS A. Standard dual current controller The 50 % dip has been simulated in order to test the effectiveness of the dc controller under the condition of an unbalanced voltage [1]. The current of the dc-link load is constant 0.5 p.u. Fig. 12 displays response of the output dc voltage to the described dip, where the single current controller and standard dual current controller have been used. The dip starts at 20ms and ends at 180ms. It is obvious that the dc voltage ripple is almost zero under the dual controller. For the single current controller system, the dc-voltage ripple oscillates with twice the grid frequency and the amplitude of the ripple is 4 %. So, possibilities of the single current controller system are limited in the presence of negative sequence components. Fig. 13: Simulation waveforms for the single controller under unbalance; reproduced from [3] Transactions on Electrical Engineering, Vol. 2 (2013), No. 1 18 B. Nonlinear dual current controller This type of the dual current controller was tested under Fig. 16: Simulation waveforms of the dual current controller with feedback from PWM controller with a compensation for the 15 % one phase unbalance; reproduced from [4] Fig. 14: Simulation waveforms for the nonlinear dual current controller under unbalance; reproduced from [3] conditions of 15 % decrease of the voltage amplitude in one phase [5]. This type of unbalance appears often in a weak ac system. The simulation results are displayed in Figs. 13, 14. The figures display waveforms of the dc voltage vdc, phase current ia and grid voltage ea. Fig. 13 displays results if the simple single PI controller without any compensation of the unbalance in the control program is used. Fig. 14 displays results of the dual current controller. Fig. 17: Grid current (top) and dc voltage (bottom) with single current controller; reproduced from [5] It is obvious that the output voltage vdc has a strong ripple in its waveform in Fig. 13. The output voltage vdc has any ripple in its waveform in Fig. 14. C. Dual current controller with feedback from PWM The dual current controller with the feedback from PWM was tested under conditions of 15 % decrease of the voltage amplitude in one phase [4]. Fig. 15: Simulation waveforms of the single controller without a compensation for the 15 % one phase unbalance; reproduced from [4] Fig. 15 and Fig. 16 display simulation the waveforms of the line voltage wave form in phase a (ea), line current in phase a (ia) and output dc voltage (vdc). Fig. 15 displays results of the conventional single PI controller use without unbalance compensation. Fig. 16 displays results of the dual current controller use. We can see that the dual current controller provides much lower ripple of the vdc than the conventional controller. Transactions on Electrical Engineering, Vol. 2 (2013), No. 1 19 1 x 10 4 v alpha, sine, cosine v alpha sine cosine 0 -1 0.3 0.31 0.32 0.33 0.34 0.35 theta 0.36 0.37 0.38 0.39 10 0.4 theta 5 0 0.3 1 0.31 x 10 0.32 0.33 4 0.34 0.35 0.36 v d, v q, v+ d, v+ q 0.37 0.38 0.39 0.4 vd v+ d vq v+ q 0 -1 0.3 0.31 0.32 0.33 0.34 0.35 0.36 Time(s) 0.37 0.38 0.39 0.4 Fig. 20: Waveforms of DSC-PLL after unbalance is added to input voltage (vd, vq – input voltages, v+d, v+q – detected positive sequence) Fig.18: Grid current (top) and dc voltage (bottom) with dual current controller with calculation of dissipated power in method 1; reproduced from [5] It is obvious that the use of this algorithm results in quality current references. On the other side, the dc side supplies the oscillating powers and therefore the dc ripple is about to 20 %. Fig. 19 displays waveforms of the grid currents and output dc voltage for the dual current controller algorithm of the method 2. With the oscillating powers supplied by the grid, the dc voltage is smoothed out, apart from the transients at the beginning and end of the dip. The currents are almost the same in magnitude in both cases, but they are more smoothed in the case 2. Fig. 19: Grid current (top) and dc voltage (bottom) with dual current controller with calculation of dissipated power in method 2; reproduced from [5] D. Dual current controller with calclatiton of dissipated power Several simulations were realized in order to test the controller [5]. There was a 40 % dip in the phases B and C. Fig. 17 displays waveforms of the grid currents and output dc voltage for the single current controller. The unbalance of the grid voltage causes the ripple in the output dc voltage of about 6.5 %. Fig. 18 displays waveforms of the grid currents and output dc voltage for the dual current controller algorithm. The dual current controller algorithm of the method 1 was used here. Fig. 21: Measured time responses of DSC-PLL after changing grid voltage in unbalanced form: a) upper part: grid voltage component va (1000 V/div), sinΘ, cosΘ; b) middle part: angle Θ (π/div); c) lower part: grid voltage components vd, vq (250 V/div) – time scale 10 ms/div E. Phase Locked Loop strategies All proposed PLL strategies were simulated with different parameters and by several voltage distortions. Fig. 20 shows the response of the DSC-PLL to the unsymmetrical voltage (the magnitude of the voltage in the phase a was rapidly decreased). In Fig. 20, lower part, Transactions on Electrical Engineering, Vol. 2 (2013), No. 1 20 Frequency Frequency 50.4 50.15 Source DSC DDSFR 50.2 Source FVAVG SFR 50.1 50.05 50 50 49.8 49.95 49.6 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 1.4 1.5 1.6 Angle Error (in Degrees) 1 0.5 0.5 0 0 -0.5 -0.5 1.5 1.6 1.7 4 1 1.8 1.9 2 2.1 -1 1.4 2.2 1.5 1.6 1.7 4 Voltage x 10 1.8 1.9 2 2.1 2.2 2.1 2.2 Angle Error (in Degrees) 1 -1 1.4 1.7 1 1.8 1.9 2 Voltage x 10 Va 0.5 Vb Vc 0 -0.5 -1 1.4 Va 0.5 Vb Vc 0 -0.5 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 -1 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 Fig.22: Waveforms obtained by applying DSC-PLL, DDSFR-PLL, FVAVG-PLL, SFR-PLL strategies when unbalance is added to input voltage two pairs of the d, q grid voltage components are + d depicted: vd, vq of the real grid voltage and v , + q v of the extracted positive symmetrical voltage sequence component only, which are used in the DSC-SPLL algorithm to synchronize the controller to the grid. The DSC-PLL method was adopted as the most suitable for a practical realisation. Fig. 21 presents captured time responses of the DSC-PLL variables under the same conditions as those in Fig. 20. High frequency disturbances at the instant of a voltage system change result from the switch process in the programmable power source. Nevertheless, even by this dramatic voltage change, the synchronization was reached in circa half of the fundamental period (that is, + the components v d , v q+ V. CONCLUSION It has been introduced that the unbalanced input voltage causes wrong work of the rectifier. So the unbalance must be compensated. These compensations are really very important for a good function of the PWM rectifier. The compensation method must be tested in different nonstandard states and also in transient processes. Therefore, a lot of efforts have been made to propose a control schema, which would make possible to compensate the input voltage unbalance reliably. In the second part of the paper an overview of different synchronizations techniques suitable for the three phase PWM rectifiers were presented. Most of the techniques were simulated too. The DSC-PLL technique was realized in the control system with the DSP. were again constant). Fig. 22 shows the responses of different PLL’s by an unsymmetrical input voltage. The DSC-PLL, DDSFRPLL, FVAVG-PLL, SFR-PLL strategies were simulated and compared. The responses of the estimated frequency, angle error, and three-phase voltages are presented. The negative sequence component was added between 1.5 and 2.0 s. ACKNOWLEDGEMENT With institutional support RVO//:61388998. Financial support of the Ministry of Industry and Trade of the Czech Republic, through grant number FR-TI1/330, is highly acknowledged. Transactions on Electrical Engineering, Vol. 2 (2013), No. 1 21 REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] Hong-seok Song, Kwanghee Nam: “Dual current control scheme for PWM converter under unbalanced input voltage conditions” IEEE transactions on industrial electronics, vol. 46, No. 5, October 1999. Giuseppe Saccomando, Jan Svensson: “Transient operation of grid-connected voltage source converter under unbalanced voltage conditions”. Industry applications conference, 2001. 36th IAS annual meeting. Conference record of the 2001 IEEE, vol.4, 30th September – 4th October 2001. Pages 2419 - 2424. Yongsuh Suh, Valentin Tijeras, Thomas Lipo: “A nonlinear control of the instantaneous power in dq synchronous frame for PWM AC/DC converter under generalized unbalanced operating conditions”. Conference record of the industry applications conference, 2002. 37th IAS annual meeting, vol. 2, 13th – 18th October 2002. Pages 1189 – 1196. Yongsuh Suh, Thomas Lipo: “A control scheme of improved transient response for PWM AC/DC converter under generalized unbalanced operating conditions”. 2004 35th annual IEEE Power electronics specialists conference. Fainan Magueed, Ambra Sanino, Jan Svensson: “Transient performance of voltage source converter under unbalanced voltage dips”. IEEE 35th annual power specialists conference (PESC´04). Aachen, Germany. 20-25 June 2004. Pages: 1163 – 1168. Hong-seok Song, Kwanghee Nam: “Dual current control scheme for PWM converter under unbalanced input voltage conditions” IEEE transactions on industrial electronics, vol. 46, No. 5, October 1999. Giuseppe Saccomando, Jan Svensson: “Transient operation of grid-connected voltage source converter under unbalanced voltage conditions”. Industry applications conference, 2001. 36th IAS annual meeting. Conference record of the 2001 IEEE, vol.4, 30th September – 4th October 2001. Pages 2419 - 2424. Yongsuh Suh, Valentin Tijeras, Thomas Lipo: “A nonlinear control of the instantaneous power in dq synchronous frame for PWM AC/DC converter under generalized unbalanced operating conditions”. Conference record of the industry applications conference, 2002. 37th IAS annual meeting, vol. 2, 13th – 18th October 2002. Pages 1189 – 1196. [9] [10] [11] [12] [13] [14] [15] Yongsuh Suh, Thomas Lipo: “A control scheme of improved transient response for PWM AC/DC converter under generalized unbalanced operating conditions”. 2004 35th annual IEEE Power electronics specialists conference. Fainan Magueed, Ambra Sanino, Jan Svensson: “Transient performance of voltage source converter under unbalanced voltage dips”. IEEE 35th annual power specialists conference (PESC´04). Aachen, Germany. 20-25 June 2004. Pages: 1163 – 1168. Rodriguez, Pedro Pou, Josep Bergas, Joan Candela, J. Ignacio Burgos, Rolando P. Boroyevich, Dushan "Decoupled Double Synchronous Reference Frame PLL for Power Converters Control", IEEE Transactions on Power Electronics, Vol.22, Iss.2, pp.584, 2007, ISSN: 08858993 G. Saccomando and J. Svensson, "Transient operation of gridconnected voltage source converter under unbalanced voltage conditions," in Proc. of IEEE-IAS Annual Meeting, vol. 4, Sept. 2001, pp. 2419-2424. H. Award, J. Swenson J., “Phase locked loop for static series compensator” in EPE2003 Toulouse L. G. B. Barbosa Rolim , D. R. Rodrigues da Costa Jr.and M. Aredes "Analysis and software implementation of a robust synchronizing PLL circuit based on the pq theory", IEEE Trans. Ind. Electron., vol. 53, p.1919 , 2006. H. E. P. de Souza, F. Bradaschia, F. A. S. Neves, M. C. Cavalcanti, G. M. S. Azevedo, and J. P. Arruda, "A Method for Extracting the Fundamental Frequency Positive-Sequence Voltage Vector Based on Simple Mathematical Transformations," IEEE Transactions on Industrial Electronics, vol. 56, no. 5, pp. 1539-1547, May 2009 The contribution was presented on the conference ELEN 2012, PRAGUE, CZECH REPUBLIC