Search This Blog

Monday, 31 December 2018

Virtual flux direct power control for PWM rectifiers based on an adaptive sliding mode observer


 In the traditional virtual flux estimation for a three-phase PWM rectifier, the integration element causes problems for the initial value and DC bias, and the unstable grid voltage induces a non-constant flux amplitude. To address these issues, an improved direct power control (DPC) scheme based on an adaptive sliding mode observer (ASMO) is proposed in this work. The observer employs a sigmoid function as switch function to estimate the grid side source voltage. Meanwhile, an adaptive compensator instead of pure integral element is also designed to dynamically adjust compensation. The stability of this observer is proved by the Lyapunov function; moreover, simulations and experimental results indicate that this new virtual flux observer substantially improves the observation accuracy based on voltage sensorless control. The application of this strategy successfully suppresses the fluctuation of the dynamic voltage response in the DC bus, eliminating high-frequency noise from the grid side, whilst simultaneously boosting the power quality.

1.       PWM rectifier
2.      Virtual flux
3.      Adaptive sliding mode observer
4.      DPC



Fig. 1. System structure of traditional voltage sensor-less (VF-DPC)


Fig. 2. Comparison of steady-state curve under four methods.

Fig. 3. Dynamic simulation I of saturation suppression and adaptive sliding mode.

Fig. 4. Dynamic simulation II of saturation suppression and adaptive sliding mode.

Fig. 5. Dynamic simulation of traditional voltage sensorless control.

Fig. 6. Dynamic simulation of adaptive sliding mode.

Fig. 7. Comparison of bus voltage during load step.

Fig. 8. Comparison of phase current and voltage during load step.


This paper introduces sliding mode control in a virtual flux observer, based on the three-phase PWM rectifier model under virtual flux DPC; moreover, the systematic design of an orthogonal feedback compensation method to calibrate the flux estimation has been proposed. An improved sensorless control algorithm with an adaptive sliding mode observer has been simulated and experimentally verified. Results show that the combination of sliding control and virtual flux observer has improved dynamic response over traditional control strategies. This scheme can significantly improve the observation accuracy and dynamic response performance of the observer, and suppress the dynamic fluctuation and harmonic disturbance, increasing the overall power quality and delivery.


[1] J. W. Kolar, T. Friedli, J. Rodriguez, and P. W. Wheeler, “Review of three-phase PWM AC-AC converter topologies,” IEEE Transactions on Industrial Electronics, vol. 58, no. 11, pp. 4988–5006, Nov. 2011.
[2] Y. Zhang, Z. Li, Y. Zhang, W. Xie, Z. Piao, and C. Hu, “Performance improvement of direct power control of PWM rectifier with simple calculation,” IEEE Transactions on Power Electronics, vol. 28, no. 7, pp. 3428–3437, Jul. 2013.
[3] B. Singh, B. N. Singh, A. Chandra, K. Al-Haddad, A. Pandey, and D. P. Kothari, “A review of three-phase improved power quality ac-dc converters,” IEEE Transactions on Industrial Electronics, vol. 51, no. 3, pp. 641–660, Jun. 2004.
[4] A. Rahoui, A. Bechouche, H. Seddiki and D. O. Abdeslam, “Grid Voltages Estimation for Three-Phase PWM Rectifiers Control Without AC Voltage Sensors,” IEEE Transactions on Power Electronics, vol. 33, no. 1, pp. 859–875, Jan. 2018.
[5] A. Bechouche, H. Seddiki, D. Ould Abdeslam and K. Mesbah, “Adaptive AC filter parameters identification for voltage-oriented control of three-phase voltage-source rectifiers,” International Journal of Modelling Identification and Control, vol. 24, no. 4, pp. 319–331, 2015.

Variable Switching Frequency PWM Strategy of Two-Level Rectifier for DC-link Voltage Ripple Control

The switching frequency is an important control parameter of PWM rectifier to reduce switching losses and EMI noise. This paper proposed a variable switching frequency PWM (VSFPWM) strategy for DC-link voltage ripple control in two-level rectifier. DC-link voltage ripple is determined by the DC-link current directly, and can be predicted synchronously with PWM signals. A real-time prediction model of DC-link voltage ripple is derived for a common voltage oriented control (VOC) PWM rectifier. Then, VSFPWM control is introduced, which changes the switching frequency cycle to cycle with a restriction of DC-link voltage ripple peak value. Furthermore, the dynamic behavior is also observed when the proposed VSFPWM control scheme is adopted. Detail simulation and experimental comparisons are carried out between VSFPWM and normal constant switching frequency PWM (CSFPWM), which demonstrate the advantages of the proposed method.
1.      Voltage ripple
2.      Prediction
3.      Variable switching frequency
4.      PWM rectifier
5.      Switching losses
6.      EMI



Fig.1 Control structure of AFE rectifier

Fig.2 Comparison between the prediction and the simulation results of the
DC-link voltage ripple in one line-cycle

Fig.3 DC-link voltage ripple comparison

Fig.4 Switching frequency comparison

Fig.5 AC-side current

Fig.6 Spectrum comparison (a) AC-side (2) DC-link

Fig.7 Step response (a) Step response of DC-link voltage (f) The change of
switching frequency with VSFPWM

The contribution of this paper is develop the VSFPWM strategy for DC-link voltage ripple control. Different from the previous work on the AC-side current ripple or torque ripple, the DC-link voltage ripple is nearly not affected by the PWM current ripple of AC-side. In a rectifier system, the DC-link voltage ripple is determined by the PWM method and load current, and the peak value of it is important for DC-link capacitor design or selection. The proposed VSFPWM fully utilizes the freedom of switching frequency, which is often neglected in the PWM module. However, the proposed VSFPWM is different from the random PWM [24], which changes the switching frequency based on the statistics and no prediction model is used. It should be noted that the proposed technique can be applied to a different power factor than the unitary one and not can be applied direct to the rectifier with neutral wire (four wire). Few conclusions can be derived as follows:
(1) DC-link voltage ripple prediction model can be built in the time-based-domain. With the three-phase duty cycles, AC-side current and load current measured by the current sensors, the DC-link voltage ripple peak can be predicted for updating the switching frequency in next cycle. The prediction method also applies to other PWM methods, and also be used for design and analysis of DC capacitors and DC battery reliability.
(2) In a whole line period, the switching frequency of VSFPWM continuously varies below the designed constant switching frequency, keeping the DC-link voltage ripple always under the requirement. Using the proposed VSFPWM strategy, the switching losses decrease significantly, and EMI noise reduces markedly.
(3) The dynamic property of VSFPWM is firstly investigated in a typical closed-loop control system. In fact, VSFPWM still has a good dynamic response, without nearly impairing the tracking performance shown in common CSFPWM. The open-loop Bode plot indicates the VSFPWM methods just decrease a little bit of bandwidth of both voltage control loop and the current in CSFPWM because of the reduction of average switching frequency.
[1] J. Rodriguez, J. Dixon, J. Espinoza, J. Pontt, and P. Lezana, “PWM regenerative rectifiers: State of the art,” IEEE Trans. Ind. Electron., vol. 52, no. 1, pp. 5–22, Feb. 2005.
[2] B., Singh; B. N., Singh; K., Al-Haddad; A., Pandey; and D. P., Kothari,“A Review of Three-Phase Improved Power Quality AC-DC Converters,” IEEE Trans. on Industrial Electronics, Vol.51, pp.641–660, June 2004.
[3] A. Marzouki, M. Hamouda, and F. Fnaiech, “Sensorless Nonlinear Control for a Three-Phase PWM AC-DC Converter,” in Industrial Electronics (ISIE), 2010 IEEE International Symposium, Bari, Italy, pp. 1052-1057, July 2010.
[4] M.Malinowski, M.P.Kazmierkowski, andA.M.Trzynadlowski, “Acomparative study of control techniques for PWM rectifiers in ac adjustable speed drives,” IEEE Transaction on Power Electronics,vol.18,no.6,pp.1390–1396, Nov. 2003.
[5] Joerg Dannehl, Christian Wessels, and Friedrich Wilhelm Fuchs, “Limitations of Voltage-Oriented PI Current Control of Grid-Connected PWM Rectifiers With LCL Filters”, IEEE Transactions on Industrial Electronics, Vol.56, pp. 380-388, Feb. 2009.

Three-Phase Unidirectional Rectifiers with Open-End Source and Cascaded Floating Capacitor H-Bridges

This paper presents two topologies of three-phase semicontrolled rectifiers suitable for open-end ac power sources. The rectifiers are composed by a combination of two-level three phase bridges (controlled, semicontrolled or uncontrolled), and three single-phase floating capacitor h-bridges (controlled). These topologies generate two powered dc-links, each one belonging to a three-phase bridge. They present a reduced number of controlled power switches if compared to other open-end configurations of similar complexity found in the literature. It is also proposed a space-vector pulse width modulation (SV-PWM) approach and a method of floating capacitor voltage control dedicated to the topologies, with an equivalent approach based on the level-shifted PWM (LS-PWM). The proposed SV-PWM solving method is based on a redundant state selection (RSS) technique, which allows the floating capacitors voltage regulation. On the other hand, the LS-PWM solving method is based on the neutral voltage selection, which is shown to be equivalent to the SVPWM RSS technique seen from the control system. Simulation results are shown to validate proposed topologies, as well as the SV-PWM and LS-PWM techniques, and the control strategy. Experimental results are shown to demonstrate proposed configurations feasibility.
1.      Power electronics
2.      Ac-dc power conversion
3.      Unidirectional converters
4.      Cascade systems
5.      Multilevel systems
6.      Pulse width modulated power converters
7.      Space vector pwm
8.      Level shifted pwm
9.      Floating capacitor control
10.  Redundant state selection


Fig. 1: Proposed configurations with open-end power source and cascaded floating h-bridges. (a) Configuration 1, where converter A is a three-phase diode bridge. (b) Configuration 2, where converters A and B have semi-controlled legs.


Fig. 2: Simulation graphics for the conventional configuration 0. (a) Currents ik. (b) Voltages vk, vrk and v0s0. (c) Mean voltages vk, vrk and v0s0.

Fig. 3: Currents ik from simulation results for both proposed configurations with the LS-PWM. (a) For configuration 1. (b) For configuration 2.

Fig. 4: Voltages v1, vr1 and v0b0a from simulation results for both proposed configurations. (a) For configuration 1 with SV-PWM. (b) For configuration 1 with LS-PWM. (c) For configuration 2 with SV-PWM. (d) For configuration 2 with LS-PWM.

Fig. 5: Mean voltages v1, vr1 and v0b0a for both proposed configurations. (a) For configuration 1 with SV-PWM. (b) For configuration 1
with LS-PWM. (c) For configuration 2 with SV-PWM. (d) For configuration 2 with LS-PWM.

Fig. 6: DC capacitors voltages vCck from simulation results for both proposed configurations with the LS-PWM. (a) For configuration 1. (b) For configuration 2.

Fig. 7: Pole voltages va10a, vb10b, vcp10c1 and vcn10c1 for both proposed configurations. (a) For configuration 1 with SV-PWM. (b) For configuration 1 with LS-PWM. (c) For configuration 2 with SV-PWM. (d) For configuration 2 with LS-PWM.
In this paper, two configurations of unidirectional rectifiers were proposed. They were based on the cascaded connection of two three-phase bridges with three floating capacitor h bridges (one per-phase), which was allowed by the open-end configuration of the three-phase power source. The voltage regulation of the floating capacitor h-bridges was realized by two proposed PWM solving techniques. The first was applied to the SV-PWM, where methods for redundancy selection and state switching minimization were also proposed. The second was proposed for the LS-PWM as an alternative to the SVPWM. In this case, the floating capacitors voltage regulation was based in solving the PWM for appropriately selected neutral voltage references. Simulation results were provided to supply evidence that proposed topologies are viable and that proposed SV-PWM redundancy selection technique is effective within the control system. It was also shown that the control based on the LS-PWM was effective and equivalent to the SV-PWM. It could be concluded that the proposed configurations could present lower current THD and voltage WTHD with fixed switching frequency, as well as lower semiconductor losses with matched current THD, if compared to the conventional three-phase IBGT rectifier bridge. Experimental results were also provided to show the feasibility of proposed topologies and control strategy.
[1] S. Debnath, J. Qin, B. Bahrani, M. Saeedifard, and P. Barbosa, “Operation, control, and applications of the modular multilevel converter: A review,” IEEE Transactions on Power Electronics, vol. 30, no. 1, pp. 37–53, Jan 2015.
[2] R. A. Krishna and L. P. Suresh, “A brief review on multi level inverter topologies,” in 2016 International Conference on Circuit, Power and Computing Technologies (ICCPCT), March 2016, pp. 1–6.
[3] F. Z. Peng, W. Qian, and D. Cao, “Recent advances in multilevel converter inverter topologies and applications,” in Power Electronics Conference (IPEC), 2010 International, June 2010, pp. 492–501.
[4] J. Rodriguez, J.-S. Lai, and F. Z. Peng, “Multilevel inverters: a survey of topologies, controls, and applications,” Industrial Electronics, IEEE Transactions on, vol. 49, no. 4, pp. 724–738, Aug 2002.
[5] M. Diaz, R. Cardenas, M. Espinoza, F. Rojas, A. Mora, J. C. Clare, and P. Wheeler, “Control of wind energy conversion systems based on the modular multilevel matrix converter,” IEEE Transactions on Industrial Electronics, vol. 64, no. 11, pp. 8799–8810, Nov 2017.

Study on PWM Rectifier without Grid Voltage Sensor Based on Virtual Flux Delay Compensation algorithm


At present, virtual flux voltage oriented control strategy is one of the widely used control strategies without grid voltage sensor. To solve the dc bias resulting from voltage vector integration in vector calculation of virtual flux and further avoid the steady state error, a virtual flux observer with negative feedback resonant filter is presented in this paper based on virtual flux principle and a delay compensation algorithm is also proposed to solve the delay of virtual flux. In addition, the control system diagram of PWM rectifier without grid voltage sensor is brought forth. Then, simulation system and experimental platform are both established to simulate and test the rectifier. Eventually, the correctness and feasibility of the proposed algorithm are verified through the analysis of simulation and experimental results.

1.      Virtual flux
2.      Sensorless
3.      PWM rectifier



Fig.1 The diagram of control system of rectifier without grid voltage sensor based on virtual Flux.


Fig. 2 DC Side Voltage and AC Side Current.

Fig. 3 Harmonic Analysis of A Phase Current.

Fig. 4 The Output Angle of Phase-Locked Loop and that of Virtual Flux During Uncontrolled Rectifier

Fig. 5 The Output Angle of Phase-Locked Loop and that of Virtual Flux During Controlled Rectifier.

Fig.6 The Output Angle of Phase-Locked Loop and that of Virtual Flux During Uncontrolled Rectifier after Compensation.

Fig.7 The Output Angle of Phase-Locked Loop and that of Virtual Flux During Controlled Rectifier after Compensation.


Mathematical model of virtual flux algorithm is analyzed in this paper. The improvement is made to the existing virtual flux observer, and then the virtual flux observer with negative feedback resonant filter is proposed in this paper. The simulation and experimental results show that the proposed virtual flux observer can realize flux estimation without steady state error and it has better dynamic characteristics than series algorithm of dual low pass filter. Furthermore, relevant parameters of the observer are adjusted. Eventually, a delay compensation algorithm is brought forward to solve the delay of virtual flux, which can effectively compensate the error caused by system delay to flux observation. In this paper, the aging of electric reactor is not taken into account. The estimated value of virtual flux is bounded to change with the change of inductance.


[1] Chuan-jin Zhang, Yi Tang et al.,“A Novel Virtual Space Vector Modulation Strategy for the Neutral-Point Potential Comprehensive Balance of Neutral-Point-Clamped Converters,” Journal of Power Electronics, Vol.16, no.3, May. 2016, pp.946-959.
[2] Hui Zhang, Chuan-da Sun et al.,“Voltage Vector Error Fault Diagnosis for Open-Circuit Faults of Three-Phase Four-Wire Active Power Filters ," IEEE Trans. Power Electron, vol. 32, no.3, pp.2215-2226, March, 2017.
[3] S. Eren, M. Pahlevaninezhad, A. Bakhshai, and P. Jain, “Grid-connected voltage source inverter for renewable energy conversion system with sensorless current control, ” in Proc. 25th Annu. IEEE APEC, 2010,vol. 1, pp. 768-772.
[4] Hung-Chi Chen, Che Yu Lu, “Digital Current Sensorless Control for Dual-Boost Half-Bridge PFC Converter with Natural Capacitor Voltage Balancing,” IEEE Trans. Power Electron, pp.768-772,Mcrch. 2016.
[5] Krishan Kant1, Sabha Raj Arya, “Current Sensorless Control Algorithm of DSTATCOM for Power Quality Improvement,” in Proc. Annu. IEEE INDICON, Dec.2015, pp.2325-9418.

Sliding-Mode Observer Based Voltage-Sensorless Model Predictive Power Control of PWM Rectifier Under Unbalanced Grid Condition

A sliding-mode grid voltage observer (SMGVO) is proposed and experimentally verified in this paper for voltage-sensorless operation under an unbalanced network. Fundamental positive sequence component (FPSC) and fundamental negative sequence component (FNSC) are inherently separated in the observer without employing any additional filters. Due to embedded filtering effect, high frequency chattering and harmonic ripples can be well suppressed. Additionally, DC component can be completely rejected. As a result, DC offset would not cause fundamental frequency oscillations in magnitude and frequency of the estimated FPSC and FNSC. Owing to the predictive ability of SMGVO, one-step delay can be directly compensated using state variables in the observer. By combining estimation and prediction into one stage, the designed SMGVO turns out to be a compact solution for finite control set-model predictive power control (FCS-MPPC) without voltage sensors. Theoretical proof is derived to verify that FPSC and FNSC can be accurately estimated and separated. Experimental results obtained from a two-level PWM rectifier confirm the effectiveness of the whole control system.

1.      Predictive power control
2.      Unbalanced grid
3.      Voltage observer
4.      Voltage sensorless


Fig. 1. Control diagram of SMGVO based FCS-MPPC.


Fig. 2. Startup responses with 50% voltage dip in phase A. (a) Actual grid voltages, currents and estimated voltages; (b) comparison between estimated voltages from SMGVO and calculated voltages from DSOGI.

Fig. 3. Operation from balanced condition to unbalanced condition. (a) Actual grid voltages, currents and estimated voltages; (b) comparison with usogi p and usogi n calculated from actual voltage by DSOGI.

Fig. 4. Dynamic responses when Pref steps from 600 W to 1000 W.

Fig. 5. Steady state responses with 1.5 V DC component and 50% AC voltage dip in phase A.

Fig. 6. Average switching frequency fsw when Pref = 1 kW.

Fig. 7. Spectrum analysis of (a) grid voltage, (b) ^up and (b) ^un under unbalanced and distorted grid conditions.

Fig. 8. Estimated grid frequency with sudden frequency step change of +10 Hz under unbalanced and distorted grid conditions.


A SMGVO is designed and experimentally verified in this paper. It has the following properties: 1) inherent separation of FPSC and FNSC without utilizing any filters; 2) no high frequency chattering; 3) satisfactory DC component rejection; 4) comparable performance with DSOGI based sequence separation using measured voltage; 5) predictive ability to compensate one-step delay in predictive control. FCS-MPPC is implemented based on SMGVO and tested on a two-level PWM rectifier to verify the effectiveness of the control system. Experimental results show that FPSC and FNSC can be accurately estimated and separated. The dynamic performance of SMGVO during voltage sag is similar to that of DSOGI. The implemented voltage sensorless FCSMPPC presents fast dynamic responses which can track power reference quickly. Direct start without initial knowledge of grid voltage is possible due to fast converging rate of SMGVO and high regulation bandwidth of FCS-MPPC.


[1] Z. Zhang, H. Xu, M. Xue, Z. Chen, T. Sun, R. Kennel, and C. M. Hackl, “Predictive control with novel virtual-flux estimation for backto- back power converters,” IEEE Trans. Ind. Electron., vol. 62, no. 5, pp. 2823–2834, May 2015.
[2] A. M. Razali, M. A. Rahman, G. George, and N. A. Rahim, “Analysis and design of new switching lookup table for virtual flux direct power control of grid-connected three-phase PWM AC - DC converter,” IEEE Trans. Ind. Appl., vol. 51, no. 2, pp. 1189–1200, March 2015.
[3] J. Kukkola and M. Hinkkanen, “State observer for grid-voltage sensorless control of a converter equipped with an LCL filter: Direct discretetime design,” IEEE Trans. Ind. Appl., vol. 52, no. 4, pp. 3133–3145, July 2016.
[4] H.-S. Song, I.-W. Joo, and K. Nam, “Source voltage sensorless estimation scheme for PWM rectifiers under unbalanced conditions,” IEEE Trans. Ind. Electron., vol. 50, no. 6, pp. 1238–1245, Dec 2003.
[5] K. H. Ahmed, A. M. Massoud, S. J. Finney, and B. W. Williams, “Sensorless current control of three-phase inverter-based distributed generation,” IEEE Trans. Power Del., vol. 24, no. 2, pp. 919–929, April 2009.