Decentralized Carrier Phase Shifting for Optimal Harmonic Minimization in Asymmetric Parallel-Connected Inverters

Jason Poon, Brian Johnson, Sairaj V. Dhople, Juan Rivas-Davila

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


This article presents a carrier phase shifting technique for minimizing the aggregate harmonics in networks of asymmetric parallel-connected inverters for distributed power generation system applications. The proposed technique is: 1) implemented in a decentralized manner, relying only on local voltage and current measurements, and 2) optimal in the sense that it minimizes a cost function representing the carrier-frequency current harmonics. The analysis indicates that the proposed optimal carrier phase shifting technique can enable order-of-magnitude reductions in harmonic power, and also universal improvements compared to symmetric carrier interleaving for asymmetric inverter networks. Moreover, compared to existing methods that require either centralized communication or information exchange between inverters to coordinate carriers, the proposed technique is completely decentralized, which provides important practical benefits for implementation, including improved robustness and reduced cost. The technique is experimentally validated on a network of three single-phase 2-kW inverters and demonstrates a 36.5% reduction in the weighted total harmonic distortion factor of the aggregate inverter current, and the ability to converge to the optimal carrier phase spacing dynamically in less than one line frequency cycle (16.7 ms) in steady state and transient operating conditions.

Original languageEnglish (US)
Article number9219168
Pages (from-to)5915-5925
Number of pages11
JournalIEEE Transactions on Power Electronics
Issue number5
StatePublished - May 1 2021
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received May 6, 2020; revised August 6, 2020 and September 25, 2020; accepted October 6, 2020. Date of publication October 9, 2020; date of current version January 22, 2021. This work was supported in part by the U.S. Department of Energy (DOE) Office of Energy Efficiency and Renewable Energy administered by the Oak Ridge Institute for Science and Education (ORISE), Oak Ridge Associated Universities (ORAU) under DOE Contract DE-SC0014664. The work of Brian Johnson was supported in part by the U.S. Department of Energy’s Office of Energy Efficiency and Renewable Energy (EERE) under Solar Energy Technologies Office (SETO) Agreement No. EE0008346, and in part by the Washington Research Foundation. The work of Sairaj V. Dhople was supported in part by the National Science Foundation under Grant 1453921. Recommended for publication by Associate Editor B. Peter. (Corresponding author: Jason Poon.) Jason Poon and Juan Rivas-Davila are with the Electrical Engineering Department, Stanford University, Stanford, CA 94305 USA (e-mail:;

Publisher Copyright:
© 1986-2012 IEEE.


  • DC-AC power converters
  • harmonic distortion
  • optimization methods
  • power conversion harmonics


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