Doctoral Dissertations

Keywords and Phrases

Grid-tied inverter; Islanded inverter; Microgrid; Reduced order modeling; Small-signal model; Stability


This dissertation focuses on small-signal modeling and analysis of inverter based microgrid systems. The proposed microgrid consists of two microsources placed on two different buses. The buses are connected using a distribution feeder with some impedance. The proposed microgrid can operate with the grid support, or without the grid support. When operated without the grid support, the standalone system’s microsources participate in controlling the system voltage and frequency. For a non-inertia source, such as the inverter, the load perturbations play an important role in system dynamics. In paper-I, such complex system was studied.

In the grid-tied mode, the microsources share the load demand with other sources that are present in the main grid. The control algorithm for such system is much simpler than that of the islanded system. However, when aggregated in multi-bus system, prohibitively higher order state-space models are formed. In paper-II, a reduced order modeling of such systems was considered. Singular perturbation method was applied to identify the two time-scale property of the system. In paper-III, a similar approach was taken to develop a reduced order model of the islanded system that was developed in paper-I. Application of such reduced order models were illustrated by using them to simulate a modified IEEE-37 bus microgrid system.

The islanded microgrids system’s stability is characterized in paper-IV by the Markov Jump Linear System Analysis. Conservative bounds on the expected value of the state were determined from a combination of the Markov process parameters, the dynamics of each linear system, and the magnitude of the impulses. The conclusions were verified with the simulation results. "--Abstract, page iii.


Kimball, Jonathan W.

Committee Member(s)

Crow, Mariesa
Ferdowsi, Mehdi
Shamsi, Pourya
McMillin, Bruce M.


Electrical and Computer Engineering

Degree Name

Ph. D. in Electrical Engineering


National Science Foundation (U.S.)


This project was supported in part by the FREEDM Systems Center, funded by the National Science Foundation under award EEC-0812121.


Missouri University of Science and Technology

Publication Date

Summer 2015

Journal article titles appearing in thesis/dissertation

  • An Accurate Small-Signal Model of Inverter-Dominated Islanded Microgrids Using dq Reference Frame
  • Reduced Order Small-Signal Model of Micro-grid Systems - Part I
  • Reduced Order Small-Signal Model of Micro-grid Systems - Part II
  • Markov jump linear system analysis of microgrid stability


xii, 107 pages

Note about bibliography

Includes bibliographic references.


© 2015 Md. Rasheduzzaman, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Subject Headings

Distributed generation of electric power
Smart power grids
Electric inverters
Small power production facilities
Electric current converters -- Stability

Thesis Number

T 10765

Electronic OCLC #