EEEE4116 MATLAB

Java Python Advanced Control (EEEE4116)
Coursework 1
Modelling and Advanced Controller Design for a 2-Level Grid-Feeding Inverter
In this assignment you will bring together your skills of state-space equation development and controller
design to control a grid-tied 2-Level Converter. The design will make use of transforming the 3-phase
behaviour of this converter into the dq frame and use the dq equivalent circuit to develop controls. If you
have not yet read the coursework summary, it is highly recommended you read this prior to get the
understanding of what dq transforms are and why we are developing a control system in this way.
Figure 1- Notional System Diagram: DC Source interfaced with 3-phase 2-Level Inverter interfaced to the grid.
The system under investigation is a very common application when trying to link renewable energy sources
such as solar panels, or energy storage systems to interface them to the national grid, or even microgrid
applications where small remote communities rely on generating their own power.
We are converting DC power into 3-phase AC power to connect to the national grid. The parameters which
will be used in the design is as follows:
Vdc DC Supply Voltage = 400V
Vgrid Grid RMS Voltage = 230Vrms
L Output Filter Inductance = 470mH
R Intrinsic Filter Resistance = 2Ω
C Output Filter Capacitance = 33uF
ω Grid Frequency (rads-1
) = 100π rads-1
fs
Switching Frequency = 20kHz
Exercise 1 – System Modelling
As per the coursework summary, we wish to develop our control strategy using the dq equivalent model. It
can be shown in [ X ] that an equivalent 3-phase inverter can be modelled using the following circuits when
observing converter dynamics in the dq domain:
Figure 2- 3-Phase Inverter dq equivalent average model.
Where:
• md: d-axis modulation index.
• mq: q-axis modulation index.
• ω: frequency of phase voltages (rads-1
)
• Vcd / Vcq: d-axis and q-axis voltage respectively across capacitor
• Iid / Iiq: d-axis and q-axis input current respectively from inverter
• Icd / Icq: d-axis current respectively flowing into capacitor.
• Iad / Iaq: d-axis and q-axis output currents after filter.
• represents a virtual voltage source in the system (due to changing currents in inductor)
• represents a virtual current source in the system (due to changing voltages in capacitor)
Hint: Note the directions of the virtual voltage and current sources. Vital to this exercise.
Using Kirchhoff’s current and voltage laws on the two circuits shown in Figure 2, develop state-equations for d and q
axis voltage and currents.
In our system, we will treat the modulation indexes as inputs to our system. Using your state equations, go on to
show that the state-space equation defining the model can be shown to be as:
As you may have recognised, although Iad and Iaq are variables in our dq model, this variable is not included within
the state-equation. Similar could be said about Icd, and Icq. Explain why these terms are not present in the final
state-space equation.
In addition, what sources of error do you think could be attributed in the model, and what effect do you think this
could have on the system?
Exercise 2 – Transfer Function Depiction
Whilst state-space can describe the system with differential equations, it still does not fully replace the
transfer function for model development. In fact, often a transfer function block diagram is first developed
to visualize the behaviours of a system and help formulate state-space models.
In the first part of this exercise, analyse Fig 2 and construct a transfer block dia