Modeling and control of a three phase voltage source inverter with an LCL filter

This thesis addresses the design and control of three phase inverters. Such inverters are

used to produce three-phase sinusoidal voltages and currents from a DC source. They

are critical for injecting power from renewable energy sources into the grid. This is

especially true since many of these sources of energy are DC sources (e.g. solar

photovoltaic) or need to be stored in DC batteries because they are intermittent (e.g. wind

and solar). Two classes of inverters are examined in this thesis. A control-centric design

procedure is presented for each class. The first class of inverters is simple in that they

consist of three decoupled subsystems. Such inverters are characterized by no mutual

inductance between the three phases. As such, no multivariable coupling is present and

decentralized single-input single-output (SISO) control theory suffices to generate

acceptable control designs. For this class of inverters several families of controllers are

addressed in order to examine command following as well as input disturbance and noise

attenuation specifications. The goal here is to illuminate fundamental tradeoffs. Such

tradeoffs include an improvement in the in-band command following and output

disturbance attenuation versus a deterioration in out-of-band noise attenuation.

A fundamental deficiency associated with such inverters is their large size. This can be

remedied by designing a smaller core. This naturally leads to the second class of inverters

considered in this work. These inverters are characterized by significant mutual

inductances and multivariable coupling. As such, SISO control theory is generally not

adequate and multiple-input multiple-output (MIMO) theory becomes essential for

controlling these inverters.