© Per Karlsson Small Signal Modelling and Analysis of DC Distributed Power Systems

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IE http://www.iea.lth.se/

Per Karlsson

Small-Signal Modelling and Analysis of DC Distributed Power Systems

© Per Karlsson Small Signal Modelling and Analysis of DC Distributed Power Systems

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Presentation Outline

• Introduction

• DC power distribution

• DC bus voltage control

• Small-signal modelling

• Small-signal models compared to previous work

© Per Karlsson Small Signal Modelling and Analysis of DC Distributed Power Systems

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Energy Supply in the Future

http://www.toshiba.com

© Per Karlsson Small Signal Modelling and Analysis of DC Distributed Power Systems

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Renewable Energy Sources &Distributed Generation

• Several renewable energy sources need assistance from power electronics

• Most consumer and office electronic equipment operate on rectified AC

DC might as well be used for local distribution systems

© Per Karlsson Small Signal Modelling and Analysis of DC Distributed Power Systems

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DC Distributed Power SystemRing Bus

http://www.bigfrogmountain.com/

http://www.cogreenpower.org/

http://www.tecowestinghouse.com/

http://networkpower.exide.com/

http://www.elektro-helios.se/

© Per Karlsson Small Signal Modelling and Analysis of DC Distributed Power Systems

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Droop DC Bus Voltage Control

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© Per Karlsson Small Signal Modelling and Analysis of DC Distributed Power Systems

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nConverterBode-Diagrams

Bode diagram of the closed loopsystem from id,ref to iq.

Bode diagram of the closed loopsystem from iq,ref to iq.

Solid: dead-beat gain (ki = 1), Dashed: half dead-beat gain (ki = 0.5)Dash-dotted: 25% of dead-beat gain (ki = 0.25).

© Per Karlsson Small Signal Modelling and Analysis of DC Distributed Power Systems

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nConstant Power Load

- Negative Small-Signal Resistance

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© Per Karlsson Small Signal Modelling and Analysis of DC Distributed Power Systems

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nTwo-Converter System

Bode-Diagrams

Bode diagram for the completesystem from iqr,ref to vs forRdc = 1.0 and Ldc = 0.3 - 32 mH

Note that the transformers needed for galvanic separation are not included in the small-signal model!

© Per Karlsson Small Signal Modelling and Analysis of DC Distributed Power Systems

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Droop DC Bus Voltage ControlDynamic Properties of the Two-Converter System

Measured (left) and simulated (right) sending end (blue) and receiving end (red) voltage (top) and power (bottom), in the case of Rdc=1.0 , Ldc=32 mH and Zsc=0.25+j0.25 .

© Per Karlsson Small Signal Modelling and Analysis of DC Distributed Power Systems

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Small-Signal Modellingvs Switch Mode Modelling and Measurements

Sending end voltage in the case of Rdc=1.0 and Ldc=32 mH.Green: Experiment,Blue: Switch-mode simulationRed: Small-signal simulation

• The dominant poles are the same as the ones found in earlier investigations.

• The converter dynamics do not have to be included in the analysis.

• The assumption that Gconv = 1 is applicable due to the low bandwidth.

• A constant power load results in a unstable pole of the DC power system.

• The unstable node is cancelled for the closed loop system.