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In Chapter 3 a control scheme for a three-phase PV inverter has been designed and analyzed. A linear model of the LCL filter is presented. An active damping scheme for the inverter is proposed and described. This method uses feedback of both the inverter-side current and the

filter capacitor current to damp the resonance of the LCL filter. Because two feedback variables are used, the damping ratio can be directly specified and no iteration is required in calculating the feedback gains. Using the inner inductor current in addition to the capacitor current increases the phase margin and reduces the low frequency gain. Using the transfer function of the damped LCL filter, a method of calculating the gains for a PR controller based on phase and gain margin specifications has been shown. The current control loop had a ½ cycle step response time. A modification is proposed for a PR controller to prevent resonator windup. The proposed anti-windup scheme compares the output of the active damping loop to a maximum and minimum value based on the DC link voltage. If the limits are exceeded, the difference is subtracted from the input of the resonator. Compared to previously proposed anti-windup methods for PR controllers, the scheme presented in this chapter has been shown to more accurately track the phase of the current reference. The DC link voltage control scheme discussed in [1] is considered. An FLL was designed to estimate the grid frequency. Finally, the well-known P&O technique for maximum power point tracking has been adopted.

3.9 References

[1] A. Yazdani and R. Iravani, Voltage-Sourced Converters in Power Systems. Toronto,

Canada: Wiley, 2010.

[2] K. Ogata, “Basic Control Actions and Response of Control Systems,” in Modern Control Engineering, 3rd ed., Upper Saddle River, NJ: Prentice Hall, 1997, pp. 230.

[3] J. Dannehl, F.W. Fuchs, S. Hansen, and P.B. Thøgersen, "Investigation of Active Damping Approaches for PI-Based Current Control of Grid-Connected Pulse Width Modulation Converters With LCL Filters," IEEE Trans. Ind. Applicat., vol.46, no.4, pp.1509-1517, Jul.-Aug. 2010.

[4] J. Xu, S. Xie and T. Tang, "Evaluations of current control in weak grid case for grid- connected LCL-filtered inverter," IET Power Electron., vol. 6, no. 2, pp. 227-234, Feb. 2013.

[5] C. Bao, X. Ruan, X. Wang, W. Li, D. Pan and K. Weng, "Step-by-Step Controller Design for LCL-Type Grid-Connected Inverter with Capacitor–Current-Feedback Active-Damping," IEEE Trans. Power Electron., vol.29, no.3, pp.1239-1253, Mar. 2014.

[6] X. Yuan, W. Merk, H. Stemmler and J. Allmeling, "Stationary-frame generalized integrators for current control of active power filters with zero steady-state error for

current harmonics of concern under unbalanced and distorted operating conditions," IEEE Trans. Ind. Applicat., vol. 38, no. 2, pp. 523-532, Mar. 2002.

[7] B.A. Francis and W.M. Wonham, “The internal model principle for linear

multivariable regulators,” Appl. Math. Optimization, vol. 2, no. 2, pp. 170-194, 1975. [8] F. Liu, Y. Zhou, S. Duan, J. Yin, B. Liu and F. Liu, "Parameter Design of a Two- Current-Loop Controller Used in a Grid-Connected Inverter System With LCL Filter," IEEE Trans. Ind. Electron., vol. 56, no. 11, pp. 4483-4491, Nov. 2009.

[9] A.G. Yepes, F.D. Freijedo, O. Lopez and J. Doval-Gandoy, "High-Performance Digital Resonant Controllers Implemented With Two Integrators," IEEE Trans. Power Electron., vol. 26, no. 2, pp. 563-576, Feb. 2011.

[10] S. A. Richter and R. W. De Doncker, "Digital proportional-resonant (PR) control with anti-windup applied to a voltage-source inverter," in Proc. 14th European Conf. Power Electron.and Applicat.(EPE), 2011, pp. 1-10.

[11] A.G. Yepes, F.D. Freijedo, J. Doval-Gandoy, O. López, J. Malvar and P. Fernandez-

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[12] N. Bottrell and T.C. Green, "Comparison of Current-Limiting Strategies During Fault Ride-Through of Inverters to Prevent Latch-Up and Wind-Up," IEEE Trans. Power Electron., vol. 29, no. 7, pp. 3786-3797, July 2014.

[13] R. Teodorescu, F. Blaabjerg, U. Borup and M. Liserre, "A new control structure for grid-connected LCL PV inverters with zero steady-state error and selective harmonic compensation," in Proc. IEEE 19th Annu. Appl. Power Electron. Conf. and Expo.(APEC), 2004, vol.1, pp. 580-586.

[14] A. Ghoshal and J. John, "Anti-windup schemes for proportional integral and proportional resonant controller," presented at Nat. Power Electron. Conf., IIT- Roorkee, 2010.

[15] R. Mishra and A. Shukla, "A Proportional Resonator-based control scheme to suppress AC components in circulating current of Modulator Multilevel Converter," in Proc. IEEE 39th Annu. Conf. Ind. Electron. Soc.(IECON), 2013, pp.6170-6175.

[16] R. Peña-Alzola, M. Liserre, F. Blaabjerg, M. Ordonez and T. Kerekes, "A Self- commissioning Notch Filter for Active Damping in a Three-Phase LCL -Filter-Based Grid-Tie Converter," IEEE Trans. Power Electron., vol. 29, no. 12, pp. 6754-6761, Dec. 2014.

[17] T. Messo, J. Jokipii, J. Puukko and T. Suntio, "Determining the Value of DC-Link Capacitance to Ensure Stable Operation of a Three-Phase Photovoltaic Inverter," IEEE Trans. Power Electron., vol. 29, no. 2, pp. 665-673, Feb. 2014.

[18] P. Rodríguez, A. Luna, I. Candela, R. Mujal, R. Teodorescu and F. Blaabjerg, "Multiresonant Frequency-Locked Loop for Grid Synchronization of Power Converters Under Distorted Grid Conditions," IEEE Trans. Ind. Electron., vol.58, no.1, pp.127-138, Jan. 2011.

[19] A.K. Abdelsalam, A.M. Massoud, S. Ahmed and P. Enjeti, "High-Performance Adaptive Perturb and Observe MPPT Technique for Photovoltaic-Based Microgrids," IEEE Trans. Power Electron., vol. 26, no. 4, pp. 1010-1021, Apr. 2011.

[20] M.A.G. de Brito, L. Galotto, L.P. Sampaio, G. de Azevedo e Melo and C. A. Canesin,

"Evaluation of the Main MPPT Techniques for Photovoltaic Applications," IEEE Trans. Ind. Electron., vol. 60, no. 3, pp. 1156-1167, Mar. 2013.

[21] K.H. Hussein, I. Muta, T. Hoshino and M. Osakada, "Maximum photovoltaic power

tracking: an algorithm for rapidly changing atmospheric conditions," IEE Proc. Gener. Transm. Distrib., vol. 142, no. 1, pp. 59-64, Jan. 1995.

[22] S.K. Kollimalla and M.K. Mishra, "A Novel Adaptive P&O MPPT Algorithm Considering Sudden Changes in the Irradiance," IEEE Trans. Energy Convers., vol. 29, no. 9, pp. 602-610, Sept. 2014.

[23] Yihua Hu, Wenping Cao, Jiande Wu, Bing Ji and D. Holliday, "Thermography-Based

Virtual MPPT Scheme for Improving PV Energy Efficiency Under Partial Shading Conditions," IEEE Trans. Power Electron., vol. 29, no.11, pp. 5667-5672, Nov. 2014.

[24] Q. Mei, M. Shan, L. Liu and J.M. Guerrero, "A Novel Improved Variable Step-Size

Incremental-Resistance MPPT Method for PV Systems," IEEE Trans. Ind.

Electron., vol. 58, no. 6, pp. 2427-2434, June 2011.

[25] F. Liu, S. Duan, F. Liu, B. Liu and Y. Kang, "A Variable Step Size INC MPPT Method for PV Systems," IEEE Trans. Ind. Electron., vol. 55, no. 7, pp. 2622-2628, July 2008.

[26] K. Sundareswaran, S. Peddapati and S. Palani, "MPPT of PV Systems Under Partial

Shaded Conditions Through a Colony of Flashing Fireflies," IEEE Trans. Energy Convers., vol. 29, no. 6, pp. 463-472, June 2014.

[27] V.V.R. Scarpa, S. Buso and G. Spiazzi, "Low-Complexity MPPT Technique

Exploiting the PV Module MPP Locus Characterization," IEEE Trans. Ind. Electron., vol. 56, no. 5, pp. 1531-1538, May 2009.

[28] N. Femia, G. Petrone, G. Spagnuolo and M. Vitelli, "Optimization of perturb and observe maximum power point tracking method," IEEE Trans. Power Electron., vol. 20, no. 7, pp. 963-973, July 2005.

[29] D. Sera, L. Mathe, T. Kerekes, S.V. Spataru and R. Teodorescu, "On the Perturb-and- Observe and Incremental Conductance MPPT Methods for PV Systems," IEEE J. Photovolt., vol. 3, no. 3, pp. 1070-1078, July 2013.

Chapter 4

4 Calculation of the Negative Sequence Current Component

In this chapter the method used for calculating the negative sequence of the load current is shown and compared to existing techniques for calculating negative sequence components. For control applications the calculation of sequence components must be accomplished in real time using no more than the available processing power. Several techniques for the calculation of symmetrical components were presented in Chapter 2. In this chapter, the work presented in [1] is extended for the calculation of the negative sequence current component using a compensated Half-Cycle Discrete Fourier Transform (HCDFT). Section 4.1 provides a brief introduction to the Discrete Fourier Transform (DFT). The method for calculating the accurate negative sequence components is then derived. This method is evaluated and compared with existing algorithms in section 4.2. Section 4.3 describes the integration of the HCDFT into the inverter control structure.