Design of Quadratic Optimal Regulator System for State Space Model of Single phase Inverter both in Standalone and Gridtie Modes

Nagulapati Kiran, V.Anil Kumar, Dhanamjaya Appa Rao


Since in 3-phase systems, the reliability of 3-phase Inverter is not good, under such situations Paralleled Inverter Systems are used. Parallel Inverter operation has a major role in uninterruptible power system (UPS) applications. Most of the standalone inverter systems use a LC filter and proportional-integral (PI) controller in their control loops. When connecting the paralleled inverters to utility grids, the capacitor becomes redundant and thus either a pure inductor or an LCL filter can be used as inverter output stage. Compared with the L filter, the LCL filter is more attractive because it cannot only provide higher harmonics attenuation with same inductance value, but also allow inverter to operate both in standalone and grid-tie modes, which makes it a universal inverter for distributed generation applications. Output of Inverter should always be checked. In this paper State Space Model of Single phase Inverter is analysis in two modes which are: a) Grid-tie Mode b) Standalone Mode.A Quadratic Optimal Regulator System is designed and its unit step response is obtained to validate whether the whole system (inverter system along with designed QOR) is a stable system or not.  This is done using MATLAB Program.

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Chien Liang Chen, Jih-Sheng Lai, Martin.D, “State-space modeling, analysis and implementation of

paralleled inverters for micro grid applications”, Applied Power electronics Conferences and

Exposition(APEC), 2010,Twenty-Fifth Annual IEEE:pp.619-626.

Hoff,E.,Skjellnes,T. &Norum,L, “Paralleled three-phase inverters”, Department of Electrical power

Engineering, Norwegian University of Science and technology, NTNU;

Chien-Liang Chen, Jih-Sheng Lai ,Yu-Bin Wang, Sung-Yeul Park Miwa,H. “ Design and Control for

LCL-Based Inverters with Both Grid-Tie and Standalone Parallel Operations”, Industry Applications

Society Annual Meeting 2008, IAS ’08. IEEE;1-7

Anderson, B.D.O., and J.B Moore, Linear Optimal Control: Upper Saddle River,NJ; Prentice Hall,1971

Katsuhiko Ogata, Modern Control Engineering, 5th Edition

Athans,M., and P.L. Falb, Optimal Control: An Introduction to the Theory and its Applizations, New

York: McGraw-Hill Book Company, 1965.

Brogan,W.L., Modern Control Theory, Upper Saddle River,NJ: Prentice Hall,1985

Enns,M.,J.R. Greenwood III, J.E, Matheson and F.T Thompson,”Practical Aspects of State Space

Methods Part I: System Formulation and Reduction”, IEEE Trans, Military Electronics,(1964);81-93.

Ogata, K.,Designing Linear Control Systems with MATLAB, Upper Saddle River,NJ: Prentice Hall,1994.

Xunbo Fu, Chunliang.E, Jianlin Li, Modeling and simulation of parallel-operation grid connected

inverter”, Industrial Technology,2008.ICIT 2008,IEEE Conference

Talebi.N, Sadrina,M.A, Rafiei,S.R.M, “Current and Voltage control Paralleled Multi module inverter

systems”, Control and Automatation,2009.MED’09. 17th Mediterranean Conference

Xunbo,Chunliang.E,Jianlin Li,Honghua Xu,“ Modelling and simulation of parallel operated grid-

connected inverter”, IEEE Conference on Industrial Technology, ICIT 2008,April 2008;1-6.

Sun, Y. S. Lee, and D. H. Xu, “Modeling, analysis, and implementation of parallel multi-inverter

systems with instantaneous Average-current-sharing scheme,” IEEE Trans. Power Electron., May

,vol.18, pp. 844-856.

Zhilei Yao, Lan Xiao, Yangguang Yan,”Seamless Transfer of Single phase Grid-Interactive Inverters

between Grid-connected and Standalone modes”,IEEE Transactions on Power Electronics”,June


Alberto Bemporad, Manfred Morari, Vivek Dua, Efstratios N. Pistikopoulos,” The explicit linear

quadratic regulator for constrained systems”, 2001 Elsevier Science,Automatica 38 (2002) 3-20.

Yunying Mao, Zeyi Liu, The optimal feedback control of the linear-quadratic control problem with a

control inequality constraint, Journal “Optimal Control Applications and Methods”,Vol.22, Issue 2, 2001,


Debayan Bhattacharya, Debabrata Hazra, Pranay Pratim Das, Sumana Chowdhuri, “A Novel

Standalone and GRID-tied Single Phase SPWM Inverter”, ISSN 0973-4562, Volume 9,

Number 3 (2014) pp. 267-274.

Amakye Dickson Ntoni, “Control of Inverters to support Bidirectional power flow in Grid Connected

system”, IJERT,May 2014,Vol 3(7),pp 458-462.

Mohamad Reza Rahimi Khoygani, Saeide Hajighasemi, Davoud Sanaei, “Designing and Simulation

for Vertical Moving Control of UAV System using PID, LQR and Fuzzy logic”, IJECE, Vol. 3, No. 5,

October 2013, pp. 651~659. [20] Ganesh Dharmireddy,Moorthi.S, Sudheer Hanumanthakari,”A Voltage Controller in Photo-Voltaic

System with Battery Storage for Standalone Applications”,IJPEDS, Vol.2, No.1, March 2012, pp. 9~18.



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