A Systematic Method for Designing a PR Controller and Active Damping of the LCL Filter for Single-Phase Grid-Connected PV Inverters

ABSTRACT:

The Proportional Resonant (PR) current controller provides gains at a certain frequency (resonant frequency) and eliminates steady state errors. Therefore, the PR controller can be successfully applied to single grid-connected PV inverter current control. On the contrary, a PI controller has steady-state errors and limited disturbance rejection capability. Compared with the L- and LC filters, the LCL filter has excellent harmonic suppression capability, but the inherent resonant peak of the LCL filter may introduce instability in the whole system. Therefore, damping must be introduced to improve the control of the system.

PV INVERTER

Considering the controller and the LCL filter active damping as a whole system makes the controller design method more complex. In fact, their frequency responses may affect each other. The traditional trial-and-error procedure is too time-consuming and the design process is inefficient. This paper provides a detailed analysis of the frequency response influence between the PR controller and the LCL filter regarded as a whole system.

LCL FILTER

In addition, the paper presents a systematic method for designing controller parameters and the capacitor current feedback coefficient factor of LCL filter active-damping. The new method relies on meeting the stable margins of the system. Moreover, the paper also clarifies the impact of the grid on the inverter output current. Numerical simulation and a 3 kW laboratory setup assessed the feasibility and effectiveness of the proposed method.

 KEYWORDS:

  1. Single phase
  2. Grid-connected
  3. LCL filter
  4. Active damping
  5. Proportional resonant (PR) controller

SOFTWARE: MATLAB/SIMULINK

CIRCUIT DIAGRAM:

 

 Figure 1. Two-stage single-phase PV system with LCL-filter control scheme.

EXPECTED SIMULATION RESULTS:

 

Figure 2. Grid voltage and injected current at full load with nominal parameters: simulation results. (a) Grid voltage sag; (b) grid voltage swell.

Figure 3. Grid voltage and injected current at full load with inductor L1 variation: simulation results. (a) Inductor L1 increased by 20%: grid voltage sag; (b) Inductor L1 increased by 20%: grid voltage swell; (c) Inductor L1 decreased by 20%: grid voltage sag; (b) Inductor L1 decreased by 20%: grid voltage swell.

Figure 4. Grid voltage and injected current at full load with inductor L2 variation: simulation results. (a) Inductor L2 increased by 150%: grid voltage sag; (b) inductor L2 increased by 150%: grid voltage swell; (c) inductor L2 decreased by 20%: grid voltage sag; (b) inductor L2 decreased by 20%: grid voltage swell.

Figure 5. Grid voltage and injected current at full load with capacitor C variation: simulation results. (a) Capacitor C increased by 20%: grid voltage sag; (b) capacitor C increased by 20%: grid voltage swell; (c) capacitor C decreased by 20%: grid voltage sag; (b) capacitor C decreased by 20%: grid voltage swell.

CONCLUSION:

The stability analysis of the system composed by a PR controller and an LCL filter together is not easy: the frequency responses may affect each other and the PR controller design becomes complex. The traditional method based on trial-and-error procedures, is too time-consuming, and the design process is inefficient. This paper provides a detailed analysis of the frequency response influence between the PR controller and the LCL filter.

PR CONTROLLER

In addition, the paper presents a systematic design method for the PR controller parameters and the capacitor current feedback coefficient, used in the active damping of the LCL filter. Using the new parameters, a numerical simulation shows that the system meets the requirements of stable margins and current tracking steady-state error. The robustness of the current controller is verified through several experimental tests carried out on a 3 kW platform varying the system parameters.

INDUCTOR

The Bode diagrams of the system varying inductor, capacitor, and grid impedance values confirmed that the controller parameters enhance robustness against the system parameters variation. Moreover, the system remains stable even in case of grid voltage fluctuation. Both the simulation and the experimental results assess the validity of the proposed design method.

REFERENCES:

  1. Carrasco, J.M.; Franquelo, L.G.; Bialasiewicz, J.T.; Galvan, E.; Guisado, R.C.P.; Prats, A.M.; Leon, J.I.; Moreno-Alfonso, N. Power-electronic systems for the grid integration of renewable energy sources: A survey. IEEE Trans. Ind. Electron. 2006, 53, 1002–1016.
  2. Wessels, C.; Dannehl, J.; Fuchs, F.W. Active Damping of LCL-Filter Resonance based on Virtual Resistor for PWM Rectifiers—Stability Analysis with Different Filter Parameters. In Proceedings of the 2008 IEEE Power Electronics Specialists Conference, Rhodes, Greece, 15–19 June 2008; pp. 3532–3538.
  3. Castilla, M.; Miret, J.; Matas, J.; de Vicuna, L.G.; Guerrero, J.M. Control design guidelines for single-phase grid-connected photovoltaic inverters with damped resonant harmonic compensators. IEEE Trans. Ind. Electron. 2009, 56, 4492–4501.
  4. Yi, L.; Zhengming, Z.; Fanbo, H.; Sizhao, L.; Lu, Y. An Improved Virtual Resistance Damping Method for Grid-Connected Inverters with LCL Filters. In Proceedings of the 2011 IEEE Energy Conversion Congress and Exposition (ECCE 2011), Phoenix, AZ, USA, 17–22 September 2011; pp. 3816–3822.
  5. Parker, S.G.; McGrath, B.P.; Holmes, D.G. Regions of Active Damping Control for LCL Filters. In Proceedings of the Energy Conversion Congress and Exposition (ECCE), Raleigh, NC, USA, 15–20 September 2012; pp. 53–60.

Single-Phase Active Power Filtering Method Using Diode-Rectifier-Fed Motor Drive

2013, IEEE

ABSTRACT: This paper presents a single-phase high power factor motor drive system with active power filter function. Since most of electrical equipment connected to the grid must comply with regulations regarding grid current harmonics, motor drive systems are generally equipped with Power Factor Corrector (PFC) which is comprised of power switches and reactive components, e.g., inductor and capacitor. The reactive components are bulky and increase the system cost especially in low-cost applications such as electrical home appliances. In this paper, a new motor drive algorithm which is capable of both driving a permanent magnet motor and filtering the harmonic currents produced by other non-linear loads belong to the system is proposed. Since the input current of the drive system is directly controlled by manipulating not the motor current reference but the output voltage reference of the inverter, it is possible to achieve exact and immediate control of the grid current. The effectiveness of the proposed algorithms is validated by experiments with a permanent magnet motor drive system.

KEYWORDS:

  1. Active damping
  2. Constant power load
  3. Dc-link capacitor
  4. Dc-link voltage stabilization
  5. Electrolytic capacitor
  6. Power factor corrector

 SOFTWARE: MATLAB/SIMULINK

BLOCK DIAGRAM:

                    Figure 1. Block diagram of the input current control and the active power filter function.

 EXPECTED SIMULATION RESULTS:

 

Figure 2. (a) Motor currents (a-phase current in the stationary frame and d-q axes currents in the syncronous reference frame) with the proposed input current control, and (b) grid current, dc-link voltage, speed error and estimated torque.

Figure 3. Experimental results : input current of non-linear load and motor drive, grid current, dc-link voltage of both diode-rectifier (a) with the input current control algorithm, (b) with both the input current control and the active harmonic filtering algorithms, (c) three-phase motor currents (ia, ib, ic), grid voltage and current.

Figure 4. (a) PFC operation at light motor load (15% motor load) , and (b) during load change from 15% to 100% motor load.

CONCLUSION:

In motor drive systems supplied by a single-phase grid, the problems of input harmonic currents have been mitigated by a PFC, which makes the system bulk and expensive. In this paper, a power factor correction method for motor drive systems without PFC has been proposed. In the proposed system, the dc-link capacitor is reduced for continuous conduction of diode rectifier front end. And, the input current is controlled by directly manipulating the inverter output voltage according to the motor currents and the input current reference. Since the input current can be shaped into any waveforms using the proposed input current control method, it is also possible to eliminate the harmonics in the grid current that other electric loads generate by injecting the opposite harmonics. It was validated by experiments that the input current can be controlled using the proposed algorithm and the harmonic currents from other non-linear loads can be actively suppressed.

REFERENCES:

[1] Electromagnetic Compatibility (EMC), Part 3-2: Limits-Limits for Harmonic Current Emissions (Equipment Input Current≤ 16 A Per Phase), International Standard IEC 61000-3-2, 2005, 2013.

[2] H. Endo, T. Yamashita and T. Sugiura, “A high-power-factor buck converter”, in Proc. IEEE Power Electron. Spec. Conf. (PESC), pp.1071 -1076 Jun. /Jul., 1992.

[3] L. Yen-Wu and R. J. King, “High performance ripple feedback for the buck unity-power-factor rectifier”, IEEE Trans. Power Electron., vol. 10, no. 2, pp.158 -163, 1995

[4] B. Chen , Y. Xie , F. Huang and J. Chen, “A novel single-phase buck PFC converter based on one-cycle control”, in Proc. IEEE Power Electron. Motion Control Conf. (IPEMC), vol. 2, pp.1 -5 Aug., 2006.

[5] W. W. Weaver and P. T. Krein, “Analysis and applications of a current-sourced buck converter”, in Proc. IEEE Appl. Power Electron. Conf. (APEC), pp.1664 -1670 Feb. /Mar., 2007.

Deadbeat Weighted Average Current Control with Corrective Feed-forward Compensation for Microgrid Converters with Non-Standard LCL Filter

ABSTRACT

Microgrid converters are required to have the capability of both grid-tied mode and islanding mode operation. For this dual-mode operation, large shunt capacitors are often used in the interfacing converter output LCL filter, as it can help to stabilize supply voltage and to reduce switching ripple pollutions to sensitive loads during autonomous islanding operation. At the same time, this modification causes a few challenges, including the low frequency harmonic distortions, the steady-state tracking errors and the slow dynamic response, to the line current regulation during grid-tied operation. To overcome these drawbacks, a modified weighted average current controller is developed. First, to realize a fast line current response, a deadbeat control of weighted average current is developed based on a reduced-order virtual filter plant. Second, a grid voltage feed-forward term is added to the weighted average current reference to mitigate the steady-state line current tracking errors. Note that this compensation term is directly added to the current reference, thus, it is very well decoupled from the closed-loop current regulator. In addition, it can be seen that the low-order line current harmonics caused by grid voltage distortion is inherently compensated by this proposed corrective feed-forward control.

KEYWORDS:

  1. Virtual filter
  2. Deadbeat control
  3. Weighted average current control
  4. Active damping
  5. LCL filter
  6. Microgrid

SOFTWARE: MATLAB/SIMULINK

CIRCUIT DIAGRAMS:

Fig. 1. Diagram of a grid-tied converter controlled by conventional weighted average current feedback.

Fig. 2. Diagram of the proposed control deadbeat scheme with weighted average current feedback and line current tracking error compensation.

EXPECTED SIMULATION RESULTS:

Fig.3. Performance of the system using the proposed deadbeat control method (compensation term is activated in 0.5sec). (from top to bottom: (1) grid voltage Vgrid; (2) line current I2 ; (3) output current I1 ; (4) current tracking errors ( Iref-I2).)

Fig. 4. Performance of the system using the proposed deadbeat control method and the method in [14]. (from top to bottom: (1) grid voltageVgrid ; (2) line current I2; (3) output current I1 ; (4) current tracking errors ( ).)

Fig. 5. Performance of the system using the proposed method, operating in a distorted grid with grid impedance variation

Fig. 6. Performance of the system using the proposed deadbeat control method with feed-forward control. Grid frequency changes from 50Hz to 50.15Hz at 0.2sec. (from top to bottom: (1) Grid voltage Vgrid; (2) line current I2 ; (3) output current I1; (4) weighted average current I12 .)

Fig. 7. Performance of the system using the proposed deadbeat control method but without feed-forward control. Grid frequency changes from 50Hz to 50.15Hz at 0.2sec. (from top to bottom: (1) Grid voltage Vgrid ; (2) line current I2; (3) output current I1; (4) weighted average current I12 .)

Fig. 8. Performance of the system using the PI control for weighted average current regulation, with feed-forward control. Grid frequency changes from 50Hz to 50.15Hz at 0.2sec. (from top to bottom: (1) Grid voltage Vgrid ; (2) line current I2; (3) output current I1; (4) weighted average current I12.)

CONCLUSION

An enhanced current controller is proposed in this paper. The research work of this paper is summarized here as:

1) In order to realize rapid control of converter current, the deadbeat control is applied to regulate the weighted average current based on a virtual filter plant.

2) The feed-forward compensator is developed to mitigate the steady-state fundamental current tracking errors caused by conventional weighted average current control.

3) The frequency-selective capacitor leg current estimation is proposed and the corresponding compensation term can be used to increase the robustness of the converter against grid harmonic distortions. The design and implementation of this compensator are highly decoupled from the closed-loop deadbeat current regulator. Thus, both the current regulator and the compensator can be independently designed.

REFERENCES

  • Blaabjerg, Z. Chen, and S. B. Kjaer, ―Power electronics as efficient interface in dispersed power generation systems,‖ IEEE Trans. Power Electron., vol. 19, no. 5, pp. 1184-1194, May. 2004.
  • Rocabert, A. Luna, F. Blaabjerg, and P. Rodriguez, ―Control of power converters in AC microgrids,‖ IEEE Trans. Power Electron., vol. 27, no. 11, pp. 4734–4749, Nov. 2012.
  • W. Li, D. M. Vilathgamuwa and P. C. Loh, ―Design, analysis and real-time testing of a controller for multibus microgrid system,‖ IEEE Trans. Power Electron., vol. 19, pp. 1195-1204, Sep. 2004.
  • M. Guerrero, L. G. Vicuna, J. Matas, M. Castilla, and J. Miret, ―A wireless controller to enhance dynamic performance of parallel inverters in distributed generation systems,‖ IEEE Trans. Power Electron., vol. 19, no. 4, pp. 1205-1213, Sep, 2004.