1. Metamodeling of Power System Components S. Sudhoff, L. Ruiyang, R. Sahu - Purdue E. Broughton, R. Leonard, B. Langland - USC January 11, 2015

2. Mass, Loss, and S3D In early stage design, we wish to populate the ship with equipment We need mass, loss, volume, etc.

3. Catalogs The good: high confidence The (sometimes) bad: discrete design The (sometimes) ugly: confined to what exists

4. Densities Base size and loss calculations on rules of thumbs X kg/kW, Y kW/kW The good: simple The bad: component design space unexplored (X and Y can usually be traded off) The ugly: fundamentally misleading

5. Problems with Density Consider a 1 MW high-speed (15,000-35,000 rpm) generator design

6. Metamodeling Consider an simple inductor …

7. Scaling To scale – Dimensions, areas, volumes, mass: – Current, current density: – Power, energy, time: – Time, frequency: Not scaled – Magnetic Flux density – Voltage

8. Inductor Metamodel

9. Of Interest …

10. Scaled Machine Design To scale – Dimensions, areas, volumes, mass: – Force, torque: – Current, current density: – Power, energy, time: – Frequency, speed Not scaled – Magnetic Flux density – Voltage Base 10

11. Assumptions Three-phase, surface mounted permanent magnet machine Steel, conductor, magnet type fixed a-priori Slots are not individual represented (spatially averaged) Hysteresis loss model is simplified

12. Metamodel Formulation

13. Using the Metamodel Initial Inputs – Motor Rated speed Rated torque Conservativeness factors – Generator Rated speed Rated power Conservativeness factors Final Input – Torque density – Aspect ratio

14. Example Generator Design What is the torque density you would like (Nm/l)? 30 Choose diameter/length aspect ratio Enter "pancake" for D/L=2; "boxy" for D/L=1; "pencil" for D/L=0.5: pencil Design Summary – Rated Power = 20 MW – Rated Speed = 5000 rpm – Rated Loss = 155 kW – Rated Torque = 38.5 kNm – Rated Resistive Loss = 119 kW – Rated Hysteresis Loss = 24.5 kW – Rated Eddy Loss = 11 kW – Rated Efficiency = 99.2% – Rated Current Density = 20.8 A/mm^2 – Total Mass = 6300 kg – Cuboidal Circumscribing Volume = 1.98 kl – Height and Width = 0.997 m – Length = 1.99 m 14

15. Partial Load Power Loss Model Motor Generator 15