Preliminary Sizing Design of a 1 MW Low Duty Cycle Switched Reluctance Generator for Aerospace Applications

Preliminary Sizing Design of a 1 MW Low Duty Cycle Switched Reluctance Generator for Aerospace Applications Jin-Woo Jung, Ph. D. Student Advisors: Prof. Ali Keyhani Adjunct Prof. Tomy Sebastian Oct. 25, 2002 (IAB 02) Department of Electrical Engineering The Ohio State University

TABLE OF CONTENTS 1. Design Requirements 2. Research Focus 3. Design Specifications 4. Design Guideline 4. 1 Sizing Equation 4. 2 Design Inputs 5. Preliminary Sizing Design 5. 1 First Pass Sizing Design 5. 2 Second Step Sizing Design 6. Redesign Results 7. Conclusions 8. Future works 9. Statement of Work for Phase II Design of a Laboratory 5 kw Model for Experimental Study

1. DESIGN REQUIREMENTS 1). Generate preliminary sizing dimensions of a 1 MW low duty cycle SR generator 2). Consider the hot spot in the conductor and the life time of commercially available insulation materials 3). Obtain the maximum current density in a stator under the liquid-cooled method 4). Redesign the generator to reflect the maximum allowable current density

2. RESEARCH FOCUS 1). Assumptions! Low Duty Cycle ( t on (5 sec.), t off (30 sec.) )! Limited life expectancy (about 100 hr.)! Internal heat removed by liquid-cooled method 2). Effects by the above assumptions! Increase maximum permissible temperature of commercially available insulation material! Increase hot-spot temperature limit in the conductor! Increase maximum permitted current density 3). Research Focus! To maximize the area of the slot to ensure more effective cooling in the winding! To minimize the weight of the copper and the rotor diameter to reduce the windage loss " SR generator can be reduced in weight and volume 4). Objective! To obtain the preliminary sizing dimensions of a 1 MW low duty cycle SR generator using a D 2 L sizing equation and a Matlab before an optimal complete set of dimensions

3. DESIGN SPECIFICATIONS Design Specifications (assumptions):!three-phase SR Generator Rated Power (P): 1 MW! DC-link Output Voltage (V DC ): 300 V! Rated RPM: 30,000 [Rev/min]! Life time: 100 hours! w m = RPM*(2*pi/60) = 3.1416e+003 [rad/s]! Efficiency: 85%! Gas Turbine Supply Power (P s ) = 1 MW/0.85 = 1.1765 MW! Gas Turbine Supply Torque (T s ) = Ps/wm = 374.4822 [N m]! Number of stator poles (N s ): 6! Number of rotor poles (N r ): 4! Phase current waveform: rectangular (360/N r /3 = 30 [Mech.])! Low Duty Cycle: 5 seconds (operating)/30 seconds (standstill)! f m (Fundamental Phase Frequency [Mech.]) = w m /(2 pi) = 500 Hz! f (Fundamental Phase Frequency [Elec.]) = w m N r = 2 khz! Cooling: liquid (oil) cooling

4. DESIGN GUIDELINE 4. 1 Sizing Equation! Variation of inductance and current Fig. 1 Variation of inductance and current with rotor position. (Upper: Ideal inductance variation, Lower: Ideal phase current waveforms for motoring and generating) Fig.2 Inductance variation by flux linkage vs. phase current

4. DESIGN GUIDELINE 4. 1 Sizing Equation! Saturation Factor:! Voltage equation:! Resistance ignored: dψ V = dt ψ = ( Las Lu ) i ( θoff θon ) Stator _ Pole _ Arc β s t = = ω ω ω ( Las Lu ) iω ω 1 V = = ilas (1 ) βs βs σ! Flux linkage at maximum inductance: ψ = L asi = NΦ = NBs As! Cross sectional area of the stator pole: D βs DβsL As = 2 sin( ) L 2 2 2! Sizing equation constant: K 2 1 L = (1 ) = 1 σ L Las σ = Lu dψ V = ir + dt u as [0.65-0.9]! New voltage equation: 1 V = ωnb DLK s 2 2! Power equation: P = mkdviη where, θc Kd =, i 2π I = m K N! Magnetic loading: r B =! Electric loading: Bs B 2NI Q = π D 2 πd L Q P = Kd KBK2ωη BQ = ωt 4 T Q L = K K K BQ π 2 η 4 D d B 2

4. DESIGN GUIDELINE 4. 2 Design Inputs Design Inputs to be Selected: 1). Selection of Magnetic Steel Material 2). Selection of Stator Winding Conductor 3). Number of Poles and Phases 4). Airgap 5). Stator/Rotor Pole arcs 6). Rotor Slot Depth (Rotor Pole Height) 7). Stator Slot Depth (Stator Pole Height) 8). Rotor/Stator Yoke Thickness 9). Number of Turns 10). Stator Outside Diameter and Stack Length

4. DESIGN GUIDELINE 4. 2 Design Inputs 4. 2. 1 Selection of Magnetic Steel Material! Cobalt-iron alloy: Hiperco Alloy 50HS (2V49FeCo) manufactured by Carpenter Co. : high magnetic saturation, high stress and temperature capability 2.5 2 1.5 B [T] 1 0.5 0 0 2 4 6 8 10 12 14 16 H [ka/m] Fig. 3 B-H curve for Alloy 50HS

4. DESIGN GUIDELINE 4. 2 Design Inputs 4. 2. 2 Selection of Stator Winding Conductor! Litz-wire conductor # Multi-strand conductor # Minimize the core losses by eddy-current and/or circulating currents in the windings # Less effective heat removal compared to hollow conductor! Hollow conductor # More core losses compared to Litz-wire conductor # More effective heat removal by direct cooling Table 1 Litz-wire manufactured by New England Electric Wire CorporationMechatronics Laboratory

4. DESIGN GUIDELINE 4. 2 Design Inputs 4. 2. 3 Number of Poles and Phases! 6/4 topology: To ensure the maximum area in slot m Ns Nr stroke angle strokes/ rev 3 6 2 60 6 3 6 4 30 12 3 3 6 12 8 8 15 15 24 24 2π Stroke _ Angle = mn r 3 18 12 10 36 Stroke / rev. = m N r 3 24 16 7.5 48 Table 2 Feasible stator/rotor pole combinations 4. 2. 4 Airgap! T. J. E Miller # Reasonable airgap length: 0.5% of the rotor diameter in proportion to L stk /D r

4. DESIGN GUIDELINE 4. 2 Design Inputs 4. 2. 5 Stator/Rotor Pole arcs! Minimum pole arc (β s_min, β r_min ) β s min = 2π min ( β, β ) > s r mn! The line XZ (β s, min ), line XY (β r, min ) 2π mn r ( β + β ) s r β 2π N r r r min = 2π mn! Relationship between the stator and rotor poles in the unaligned position! Feasible area: triangle XWZ, r! Pole widths from the pole-arcs t s = ( r + g) β sin 2 β s 2 r r t r = 2r r sin 2 Fig. 4 Lawrenson s feasible triangle

4. DESIGN GUIDELINE 4. 2 Design Inputs 4. 2. 6 Rotor Slot Depth (Rotor Pole Height)! T. J. E Miller # At least 20 30 times the airgap length # Half the rotor pole width 4. 2. 7 Stator Slot Depth (Stator Pole Height) 1 d s = s r 2 + 2 ( D D ( g y )) 4. 2. 8 Rotor/Stator Yoke Thickness s! Rotor Yoke Thickness # At least half the rotor tooth width # 1.4 times half the rotor tooth width # Design factors: magnetic constraint (saturation), mechanical constraints (stress)! Stator Yoke Thickness # 0.6 ~ 1.2 times the stator tooth width [1.0] # Design factors: magnetic constraint (saturation), mechanical constraints (vibration, noise)

4. DESIGN GUIDELINE 4. 2 Design Inputs 4. 2. 9 Number of Turns! Flux linkage ψ ψ peak peak V = s ω = t L B 2N s stk s p Assumption: - Back EMF is equal to the supply voltage - Phase resistance is ignored! Number of turns per phase N p 2πV s = ω( t L N B )m s stk r s 4. 2. 10 Stator Outside Diameter and Stack Length! Constraint: either outside diameter of the stator or stack length

5. 1 First Pass Sizing Design 5. 1. 1 Conduction Angle! Conduction angle: 30 (Mech.) 5. 1. 2 Slot Fill Factor 2π 360 Stroke _ Angle = = = 30 mn r 3 4! Slot fill factor (ksf) : 0.05 (bare conductor area)/0.2 (real total area) 5. 1. 3 Current Density Cooling method Without cooling Air over; fan-cooled External blower; through-cooled Liquid-cooled A/in 2 (RMS) 3000-3500 5000-7000 9000-10000 15000-20000 A/mm 2 (RMS) 4.7-5.4 7.8-10.9 14.0 15.5 23.3-31 Table 3 Typical Empirical Values of Current Density [13]

5. 1 First Pass Sizing Design 5. 1. 4 Efficiency! Efficiency: 85% (based on two papers [17, 18]) # stator core loss: 5.3% # rotor core loss: 4.4% # friction & windage loss: 6% # copper loss: only 0.6% (Litz-wire) 5. 1. 5 First Pass Design Results! Number of stator poles (N s ): 6! Number of rotor poles (N r ): 4! Stator Outside Diameter (Sod): 350 mm! Rotor Outside Diameter (D): 210 mm! Stack Length (L): 267.6 mm! Stator Tooth width (bs): 40.6 mm! Rotor Tooth width (br): 43.8 mm! Stroke Angle per phase (Conduction angle): 30 deg.! Stator pole arc (bs_arc): 24 deg.! Rotor pole arc (br_arc): 26.4 deg.

5. 1 First Pass Sizing Design 5. 1. 5 First Pass Design Results (continued)! Stator Pole height (hs): 37.5 mm! Rotor Pole height (hr): 21.9 mm! Stator Yoke thickness (hc): 39.8 mm! Rotor Yoke thickness (hcr): 30.6 mm! Number of turns per phase (N): 2 [Turns]! Slot fill factor (ksf, bare conductor): 0.05! Current Density: 31 [A/mm 2 ]! Slot cross-sectional area (s): 3600 mm 2! Peak Current per phase (I pk ): 3900 A! RMS Current per phase (Irms): 2251 A! Ampere Turn (NI) per phase: 7800 [A turn]! Unaligned Inductance (L u ): 4.2 µh! Aligned inductance (L as ): 48.9 µh! K 2 (1-L u /L as ): 0.914! Flux Density in aligned position (Bs): 2.41 T! Shaft Diameter: 86.4 mm! Airgap: 2 mm

5. 1 First Pass Sizing Design 5. 1. 5 First Pass Design Results (continued)! Weight/Volume Parts Stator Rotor Conductor (copper + insulation material) Total Weight [kg] 103.8 32.44 12.94 149.18 Volume [m 3 ] 0.0128 0.004 0.0033 0.0201 Table 4 Weight/Volume for each part

5. 2 Second Step Sizing Design 5. 2. 1 Maximum Permitted Temperature in Insulation Material! Normal life expectancy per the insulation classes: 20,000 (2 years) to 40,000 hr (5 years).! The life is inversely in proportion to the temperature # 10 C increase (temperature) " 50 % decrease (life time of insulation material)! Class N (200 C): Teflon # 100 hr (life time) " 270 C (estimated maximum permitted temperature of insulation) # maximum permissible temperature in insulation: 260 C because Teflon has the maximum operating temperature at 260 C 5. 2. 2 Loss Calculations! Copper Losses # Current density: i = i 0 e x δ # Skin depth: 2ρ δ = = 503 ω µ ρ f µ r [ m]

5. 2 Second Step Sizing Design 5. 2. 2 Loss Calculations (continued) # Resistivity: ρ = ρ 0 (1 + αt) [nω m] where, ρ 0 : resistivity at 0 C [15.88 nω m], α: temperature coefficient at 0 C [0.00427]. x i= i0 e - ρ = 21.3 nω m at 80 C 33.51 nω m at 260 C. i 0 x r 0 # Phase Resistance: R ph ( 1.583) N L 9 2 = ρ = 33.51 10 4 A 1.7793 10 = 5.9626e- 004 [ Ω] i 0 0 # Copper loss: Fig. 5 Current distribution in a conductor P cu = m R ph I rms2 = 3 (5.9626 10-4) (2251)2 = 9.064 [kw] 0.77% of total input power

5. 2 Second Step Sizing Design 5. 2. 2 Loss Calculations (continued)! Stator/Rotor Core Losses # Stator Core loss: P sc = (0.0128 m 3 ) ( 8108.8 kg/m 3 ) (900 W/kg) = 93.4 [kw] " 7.9% # Rotor Core loss: P rc = (0.004 m 3 ) ( 8108.8 kg/m 3 ) (900 W/kg) = 29.2 [kw] " 2.4% # Friction & windage loss: about 6% # Efficiency: Calculated 83% Assumed 85% Fig. 6 Core losses vs. flux density and frequency

5. 2 Second Step Sizing Design 5. 2. 3 Thermal Modeling 5. 2. 3. 1 Thermal Equivalent Circuit! Heat transmission # Conduction # Convection # Radiation Fig. 7 Heat transmission by conduction, convection, and radiation

5. 2 Second Step Sizing Design 5. 2. 3. 1 Thermal Equivalent Circuit (continued)! Simplified Thermal equivalent circuit # Lumped-parameter model # Heat source: all losses # Thermal resistance/capacitance! Analogy Thermal Heat flow rate [W] Temperature [ C] R [ C/W] C [W s/ C] Electric Current [A] Voltage [V] R [Ω] C [F] Fig. 8 Simplified thermal equivalent circuit

5. 2 Second Step Sizing Design 5. 2. 3. 1 Thermal Equivalent Circuit (continued) Fig. 9 Detailed thermal equivalent circuit for direct cooling of conductor

5. 2 Second Step Sizing Design 5. 2. 3. 2 Maximum Permitted Current Density! Assumptions # Engine oil is used as liquid coolant # Ambient temperature means that of liquid coolant inside the generator # Initial ambient temperature is 80 C [17-18] # In the steady-state average ambient temperature (T 0 ) is about 85 C [17-18] (5 C temperature rise by all heat sources such as copper, core, windage & friction losses) # Temperature rise in stator winding conductors is only analyzed # Considered heat transfer by only convection of liquid coolant for t off # Considered heat transfer by only conduction and convection for t on Fig. 10 Power losses/temperature curve vs. time

5. 2 Second Step Sizing Design 5. 2. 3. 2 Maximum Permitted Current Density (continued)! Temperature -T 0 : ambient temperature [85 C] -T c : lowest temperature in the conductor -T max : hottest temperature in the conductor Fig. 11 Power losses/temperature curve vs. time in the conductor after the ambient temperature (T 0 ) reaches at the steady-state

5. 2 Second Step Sizing Design 5. 2. 3. 2 Maximum Permitted Current Density (continued)! Material properties used for the calculation of R and C Material Specific heat capacity [kj/kg C] Thermal conductivity [W/m C] Density [kg/m 3 ] Copper 0.38 394 8950 Teflon 0.2 1.2 2150 Cobalt-iron (Hiperco Alloy 50HS) 0.42 30 8108.8 Engine oil 1.88 0.0037 888 Mica 0.36 2800 Table 5 Material properties [13, 14]

5. 2 Second Step Sizing Design 5. 2. 3. 2 Maximum Permitted Current Density (continued) Temperature fall in the winding during OFF! Assumption: # Heat transfer by only convection of liquid coolant for t off! Thermal convective resistance 1 R oil = / ha [ C W ] where, h: convection heat transfer coefficient [W/m 2 / C], A: appropriate surface area for convective heat transfer [m 2 ]! Temperature equation (T c ) for t off Fig. 12 Thermal equivalent model for t off T c t off τ ( T T ) e T = 0 max 0

5. 2 Second Step Sizing Design 5. 2. 3. 2 Maximum Permitted Current Density (continued) Temperature fall in the winding during OFF (continued)! Liquid Coolant (Convection): R 1 1 = = = 0.0288 oil ha 100W / m / C 0.3477m / 2 2! Conductor: [ C W ] Volume = (1.7793 10-4 m2) 3 (1.583 m) = 0.000845 [m 3 ] Weight = (0.000845 m3) (8950 kg/m3) = 7.56 [kg] C cu = (7.56 kg) (0.38 kj/kg/ C) = 2.87 103 [W s/ C]! Insulation in Conductor (Conduction): t 0.0113m R in _ con = = = 0.0867 / 2 ka 0.2W / m/ C 0.6519m Volume = (5.3379 10-4 m 2 ) 3 (1.583 m) = 0.0025 [m 3] Weight = (0.0025m 3 ) (2150 kg/m 3 ) = 5.375 [kg] C in_con = (5.375 kg) (1.2 kj/kg/ C) = 6.45 10 3 [W s/ C] [ C W ]

5. 2 Second Step Sizing Design 5. 2. 3. 2 Maximum Permitted Current Density (continued) Temperature fall in the winding during OFF (continued)! Total thermal resistance and capacitance R = R oil + R in_con = 0.1155 [ C/W] C = 1/(1/C cu + 1/C in_con ) = 1.9862 103 [W s/ C]! The time constant (τ) τ = RC = 3 ( 0.1155) ( 1.9862 10 ) = 229.4 [ sec]! Lowest temperature (T c ) for t off t off τ 229. 4 ( T T ) e = 85 + ( 260 85) e = 238.5 [ C] Tc = T0 + max 0 30

5. 2 Second Step Sizing Design 5. 2. 3. 2 Maximum Permitted Current Density (continued) Temperature rise in the winding during ON! Assumption: # All the heat in the winding during t on is transmitted by only conduction and convection # Copper loss and stator/rotor core losses generated by current are only considered as heat sources! Calculation equations of P loss, R, and C P loss = P cu + P sc + P rc R = (R in_con + R in )//(R oil ) C = 1/(1/C cu + 1/C in_con ) + C s + C r! Thermal contact resistance (heat flow rate, Q) T t R = / Q ka [ C W ] = where, Q: heat flow rate [W], A: appropriate surface area, t: thickness, and k is thermal conductivity with units (W/m C).! Thermal convective resistance 1 R oil = / ha [ C W ] where, h: convection heat transfer coefficient [W/m 2 / C], A: appropriate surface area for convective heat transfer [m 2 ]

5. 2 Second Step Sizing Design 5. 2. 3. 2 Maximum Permitted Current Density (continued) Temperature rise in the winding during ON (continued)! Liquid Coolant (Convection): R 1 1 = = = 0.0288 oil ha 100W / m / C 0.3477m / 2 2! Copper: t 0.0113m = = ka 0.2W / m/ C 0.6519m [ C W ] Volume = (1.7793 10-4 m2) 3 (1.583 m) = 0.000845 [m 3 ] Weight = (0.000845 m3) (8950 kg/m3) = 7.56 [kg] C cu = (7.56 kg) (0.38 kj/kg/ C) = 2.87 103 [W s/ C]! Insulator in Conductor: [ C W ] R in con = 0.0867 / _ 2 Volume = (5.3379 10-4 m 2 ) 3 (1.583 m) = 0.0025 [m 3] Weight = (0.0025m 3 ) (2150 kg/m 3 ) = 5.375 [kg] C in_con = (5.375 kg) (1.2 kj/kg/ C) = 6.45 10 3 [W s/ C]

5. 2 Second Step Sizing Design 5. 2. 3. 2 Maximum Permitted Current Density (continued) Temperature rise in the winding during ON (continued)! Slot liner (mica): 3 R t 1 10 m = = = 0.02 in ka 0.36W / m / C 0.1386m / 2! Stator: [ C W ] Volume = (0.0479 m 2 ) (0.35 m) = 0.017 [m 3 ] Weight = (0.017 m 3 ) (8108.8 kg/m 3 ) = 135.9 [kg] C s = (135.9 kg) (0.42 kj/kg/ C) = 57.1 103 [W s/ C]! Rotor: Volume = (0.0151 m 2 ) (0.35 m) = 0.0053 [m3] Weight = (0.0053 m 3 ) (8108.8 kg/m 3 ) = 42.86 [kg] C r = (42.86 kg) (0.42kJ/kg/ C) = 18 103 [W s/ C]

5. 2 Second Step Sizing Design 5. 2. 3. 2 Maximum Permitted Current Density (continued) Temperature rise in the winding during ON (continued)! Total thermal resistance and capacitance R = (Rin_con + Rin)//(Roil) = (0.1067)//(0.0288) = 0.0227 [ C/W] C = 1/(1/Ccu + 1/Cin_con) + Cs + Cr = 77.08 103 [W s/ C]! Time constant (τ) τ = RC =! Total power losses (P loss ) 3 ( 0.0227) ( 77.08 10 ) = 1750 [ sec] T t τ max T0 = RPloss 1 e + c 0 t τ ( T T ) e on t on on τ ( T T ) ( T T ) e ( 260 85) ( 238.5 85) 1750 max 0 c 0 e Ploss = = = 338.73 ton 5 1750 R 1 τ e ( 0.02775) 1 e 5 [ kw ]

5. 2 Second Step Sizing Design 5. 2. 3. 2 Maximum Permitted Current Density (continued) Temperature rise in the winding during ON! Maximum copper loss (P cu ) P cu = P loss -P sc -P sr = 338.73 kw 93.4 kw 29.2 kw = 216.13 [kw]! Maximum current density (J) P c = P cu /total weight = 216.13 [kw]/7.56 [kg] = 28.59 [kw/kg] P c = 1000 J 2 ρ/ζ [W/kg] where, ρ: resistivity [nω m] ζ: density [kg/m 3 ] ( 28.59) ( 8950) Pc ζ J = = = 87.38 1000 ρ 33.51 [ A/ mm 2 ]

6. REDESIGN RESULTS Redesign dimensions:! Number of stator poles (N s ): 6! Number of rotor poles (N r ): 4! Stator Outside Diameter (Sod): 320 mm! Rotor Outside Diameter (D): 180.2 mm! Stack Length (L): 286.8 mm! Stator Tooth width (bs): 38.2 mm! Rotor Tooth width (br): 41.1 mm! Stroke Angle per phase (Conduction angle): 30 deg.! Stator pole arc (bs_arc): 24 deg.! Rotor pole arc (br_arc): 26.4 deg.! Stator Pole height (hs): 30.9 mm! Rotor Pole height (hr): 20.5 mm! Stator Yoke thickness (hc): 37.3 mm! Rotor Yoke thickness (hcr): 28.7 mm! Number of turns per phase (N): 2 [Turns]! Slot fill factor (ksf, bare conductor): 0.023! Current Density: 87.38 [A/mm 2 ]! Slot cross-sectional area (s): 2700 mm 2! Peak Current per phase (Ipk): 3854 A

6. REDESIGN RESULTS Redesign dimensions (continued)!rms Current per phase (Irms): 2225 A! Ampere Turn (NI) per phase: 7709 [A turn]! Unaligned Inductance (L u ): 4.37 µh! Aligned inductance (L as ): 48.6 µh! K 2 (1-L u /L as ): 0.9102! Flux Density in aligned position (Bs): 2.42 T! Shaft Diameter: 81 mm! Airgap: 2 mm! Weight/Volume Parts Stator Rotor Conductor (copper + insulation material) Total Weight [kg] 81.9 30.8 4.67 117.37 Volume [m 3 ] 0.0101 0.0038 0.0012 0.0151 Table 6 Weight/Volume for each part

7. CONCLUSIONS! Preliminary sizing design using D 2 L sizing equations and a Matlab program! Calculation of unaligned inductance (L u ) and aligned saturated inductance (L as )! Design guideline and the preliminary sizing dimensions of the machine under specified conditions such as the limited life expectancy, low duty cycle, and liquid-cooled method! Calculation of maximum permissible current density using the simplified thermal equivalent circuit! Reduction of the size of the conductor and slot " Reduction of the weight/volume of the generator! Sizing program still needs many design inputs to be selected

8. Future Works! A starting point to start more accurate design! Prediction of accurate inductance to evaluate the generator performance! Optimal shape design of rotor to minimize the windage loss due to a high speed! Verification and redesign of the sizing dimensions by Finite Element Analysis (FEA) and experiment! More detailed thermal equivalent model to analyze the heat removal more accurately

9. STATEMENT OF WORK FOR PHASE II Tasks to be performed: 1). Design of Stator 2). Design of Rotor 3). Copper Loss Computation 4). Finite Element computation of Stator and Rotor Core Losses 5). Matlab analysis of thermal model 6). Finite Element Analysis of thermal model 7). Iterative optimum design of steps 1 6 through material selection 8). Final Design 9). Construction of Prototype Machine 10). Experimental Evaluation of the machine performance Duration: 15 Months