MultiLevel Converter Modeling

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Multi-Level Converter Modeling

• GRA Xi Zhu
• Prof. A. P. Meliopoulos
• Prof. G. J. Cokkinides

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Motivation of Research

• Multi-level converter is an emerging technology.
• Benefits of Multilevel Converter Design
• Less harmonics contents
• Possible Transformerless connection
• Lower switching ra te
• Reduced switching loss
• Lower dv/dt, Less EMI

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Motivation of Research (cont.)

• Develop a physically-based multi-level converter
  models for VTB to study its behavior and control
  in an integrated power system
• There Exist Several Topologies. Our Work is on
  Tri-Level Converter using Diode-Clamp Topology

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Tri-Level Converter ofDiode-Clamp Type

• It contains 12 valve sub-circuits, 6 clamping
  diodes and 2 Smoothing capacitors
• Assume each smoothing capacitor has voltage E,
  then phase voltage has three levels 0, E and 2E
• Valves must follow certain rules to avoid short
  circuit or invalid state
• ( See Demo )

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Proposed Approach Application Tri-Level Converter
Hardware Manager
Application Manager
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Power Section Model

• Determine individual device circuit model
  (Devices include Valves, Clamping Diodes and
  Smoothing Capacitors)
• Write state equations and create connectivity
  pointer for each device
• Apply connectivity constrain and use device
  pointers to form overall state equations
• Compute Algebraic Companion Form for the
  converter for each time step.

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Tri-Level ConverterPower Section

• Power Section Model contains
• 12 valve sub-circuits
• 6 clamping diodes
• 2 Smoothing capacitors

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Valve State Equations
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Valve Connectivity Table
Blue number state index within valve Red number
state index of converter
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Clamping Diode Model
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Smoothing Capacitor Model
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Converter State-Space Model
Application of connectivity constraints to the
valve, diode and capacitor models yields the
overall converter state space model.
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Converter Algebraic Companion Form
Application of trapezoidal integration yields the
Algebraic Companion Form
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Multi-Rate Simulation

• Switching can occur between two fixed time steps.
  Using fixed time step will generate erroneous
  results
• Our solution
• Detect upcoming switching in next time step
• Apply sub-step integration for t-h,t period.

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Monitoring Estimation Section

• Purpose
• To derive control reference(s) from system
  sampled data that may be corrupted by transients,
  harmonics and may come from three phase
  unbalanced system
• Two advanced approaches are used
• Run-time Discrete Fourier Analysis
• Two-pass State Estimation

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Run-time Discrete Fourier Analysis (DFA)

• Equations for Vab(t) as an example

• Compute base frequency using DFA.
• Extract the positive sequence component as
  control reference
• Pros and Cons simple computation but needs
  minimum one cycle sampled data

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Two-Pass State Estimation

• Two-pass state estimation approach
• Pass One
• Estimate phase voltage/current magnitude,
  frequency and phase angle using state estimation
  techniques for all phases
• Pass Two
• Compute the average frequency from Pass one
• Fix frequency and estimate only magnitude and
  phase angle for all phases
• Extract the positive sequence component as
  control reference
• Pros and Cons No need for whole cycle data
  samples but computation is intensive

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Controller/Hardware Manager

• Controller model determines the switching
  sequence of all the valves in the converter for a
  specific objective
• Controller model is application and objective
  dependent
• Example presented here
• Tri-level Inverter using PWM control with 3
  controllable switching angles
• Objective Elimination of 5th and 7th harmonics
  with a specified Modulation Index

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Tri-Level Converter Controller Example PWM with
Elimination of 5th and 7th Harmonics
(1). Phase A to Neutral Voltage Waveform is shown
in the right (2).Switching angles are to be
computed to eliminate 5th and 7th harmonics for a
specific Modulation Index.
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Solution of Switching Angles
(1). Fourier Series Coefficients of 1st, 5th and
7th are shown here, where E is the actual
smoothing capacitor DC voltage
(2). By specifying a proper a1 value or
Modulation Index m value, and setting a5 a7
0, switching angles can be solved. Modulation
Index is defined as
(3). Above transcendental equations are solved
using Sylvester Resultant Criterion. When m
0.7, solutions are
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Results of Switching Angles vs. Modulation Index m
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Output voltages and Valve Switching Sequence (m
0.7 and 5th and 7th Harmonics are eliminated)
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Summary

• Multilevel converter is an emerging technology.
  It offers a lot of benefits. Computer model
  enables the study of its behavior and control in
  an integrated power system by simulation
• A versatile methodology for computer modeling of
  multilevel converter is presented which is
  divided into three sections (1). Power Section
  (2). Control Section (3). Monitoring and
  Estimation Section. Multi-rate simulation
  algorithm is implemented.
• Tri-Level converter is used to exemplify the
  methodology. A controller employing PWM with
  selected harmonics elimination is used in the
  example. Sylvester Resultant Criterion is used to
  solve the transcendental equations for firing
  angles.