1. Industrial Electrical Engineering and Automation © Per KarlssonSmall Signal Modelling and Analysis of DC Distributed Power Systems http://www.iea.lth.se/ Per Karlsson Small-Signal Modelling and Analysis of DC Distributed Power Systems

2. Industrial Electrical Engineering and Automation © Per KarlssonSmall Signal Modelling and Analysis of DC Distributed Power Systems Presentation Outline Introduction DC power distribution DC bus voltage control Small-signal modelling Small-signal models compared to previous work

3. Industrial Electrical Engineering and Automation © Per KarlssonSmall Signal Modelling and Analysis of DC Distributed Power Systems Energy Supply in the Future http://www.toshiba.com

4. Industrial Electrical Engineering and Automation © Per KarlssonSmall Signal Modelling and Analysis of DC Distributed Power Systems 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

5. Industrial Electrical Engineering and Automation © Per KarlssonSmall Signal Modelling and Analysis of DC Distributed Power Systems DC Distributed Power System Ring Bus http://www.bigfrogmountain.com/ http://www.cogreenpower.org/ http://www.tecowestinghouse.com/ http://networkpower.exide.com/ http://www.elektro-helios.se/

6. Industrial Electrical Engineering and Automation © Per KarlssonSmall Signal Modelling and Analysis of DC Distributed Power Systems Droop DC Bus Voltage Control

7. Industrial Electrical Engineering and Automation © Per KarlssonSmall Signal Modelling and Analysis of DC Distributed Power Systems Converter Bode-Diagrams Bode diagram of the closed loop system from i d,ref to i q. Bode diagram of the closed loop system from i q,ref to i q. Solid: dead-beat gain (k i = 1), Dashed: half dead-beat gain (k i = 0.5) Dash-dotted: 25% of dead-beat gain (k i = 0.25).

8. Industrial Electrical Engineering and Automation © Per KarlssonSmall Signal Modelling and Analysis of DC Distributed Power Systems Constant Power Load - Negative Small-Signal Resistance

9. Industrial Electrical Engineering and Automation © Per KarlssonSmall Signal Modelling and Analysis of DC Distributed Power Systems Two-Converter System Bode-Diagrams Bode diagram for the complete system from i qr,ref to v s for R dc = 1.0  and L dc = 0.3 - 32 mH Note that the transformers needed for galvanic separation are not included in the small-signal model!

10. Industrial Electrical Engineering and Automation © Per KarlssonSmall Signal Modelling and Analysis of DC Distributed Power Systems Droop DC Bus Voltage Control Dynamic 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 R dc =1.0 , L dc =32 mH and Z sc =0.25+j0.25 .

11. Industrial Electrical Engineering and Automation © Per KarlssonSmall Signal Modelling and Analysis of DC Distributed Power Systems Small-Signal Modelling vs Switch Mode Modelling and Measurements Sending end voltage in the case of R dc =1.0  and L dc =32 mH. Green: Experiment, Blue: Switch-mode simulation Red: 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 G conv = 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.