Hollow cylinder flywheels

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1 Hollow cyliner flyweels Magnus Helun February 22, Introuction 1.1 Applications Two main applications ave been ientifie, along wit oter so-calle sie-applications. Wen eploying a flyweel site, one soul try to cover as many applications as possible to maximize profit. Power quality An EIT contact (Krzysztof Cmielowiec) from AGH in Polan reports 150 billion euros are lost yearly in power quality issues (in Europe alone). Leonary Energy reports a number of 80 billion. Several reports (EPRI among tem) says tat >95% of power outages are less tan 3s. More tan 99% is less tan one minute. Hence, a flyweel can be an insurance against most external power failures. Flyweels can be mae to ave excellent stanby times, an can provie ig power for a sort uration. Tere are several players in tis fiel alreay, among tem are PowerTru flyweels, wic ave a moel wit te followings specs: PowerTru Flyweel Power 190 kw Stanby losses 300 W Stanby efficiency 99.8% Discarge efficiency 89% Pricing $ 60k USD Maintenance 5% per annum Response time Full power in 5 ms Design Life 20 years Discarge uration 10 secons Bearings Fully magnetic Frequency Responsive Reserve Frequency is maintaine by running generators on part-loa. Stuies sow tat fast time response units suc as flyweels can be up to 40 times more efficient tan steam turbine base plants an twice as efficient as yro power at restoring frequency 1. Te report conclues tat 10MW of flyweels correspon to 14 MW yro power, 22 MW of combustion turbine power, 240 MW of combine cycle (gas turbine+steam from waste eat) an 228 MW of steam turbine power, wen it comes to frequency regulation. Te frequency regulation application is extra relevant since it requires a ig amount of cycles per year (est. 3000[ref]), wic rules out batteries an oter storage tecnologies. Energy requirements for tis applications is aroun 15 min, prefferably more. One actor (Beacon Power) is in te frequency regulation market in te New York region. Recently a bill was passe ( Payfor-performance ) tat increase teir profits foursome. Some specifications for state-of-te-art in tis fiel: Beacon Power Smart Energy 25 Beacon Next-Gen Power 100 kw 100 kw Energy 25 kw 100 kw Type PM semi-soli PM ollow Bearings Mecanical raial, Magnetic axial Fully magnetic Design Life 20 year 20 year, cycles Cost 27 SEK/kW 3.4 SEK/kW Diameter 0.81 m 1.77 m Rotor weigt 1134 kg 1814 kg 1 Assessing te Value of Regulation Resources Base on Teir Time Response Caracteristics, PNNL 1

Power quality An EIT contact (Krzysztof Cmielowiec) from AGH in Polan reports 150 billion euros are lost yearly in power quality issues (in Europe alone).

2 Intermittent prouction support, sort-uration Stabilizing te gri in remote areas as become an important topic for some gri operators. Wit increase win penetration, tis nee is expecte to grow. See market analysis below. Market analysis Sania Laboratories reporte te following market (early 2010): Benefit Type Discarge Dur. Capacity Benefit ($/kw) Pot. US (MW, 10y) $Million, 10y Electric Energy Time-sift MW Electric Supply Capacity MW Loa Following MW Area Regulation min 1-40 MW Electric Supply Reserve Capacity MW Voltage Support 15 min MW Transmission Support 2-5 sec MW Transmission Congestion Relief MW T&D Upgrae Deferral 50t % MW T&D Upgrae Deferral 90t % MW Substation On-site Power kw Time-of-use Energy Cost Manag kw Deman Carge Management MW Electric Service Reliability 5 min kW-10MW Electric Service Power Quality 10sec-1 min 0.2kW-10MW Renewables Energy Time-sift MW Renewables Capacity Firming MW Win Gen. Gri Integration, sort 10sec-15 min MW Win Gen. Gri Integration, long MW Main reason: Price efficiency Te primary reason for ollow esign is reuce cost an better utilization of energy storing material. Hollow cyliner type flyweels are being researce by inustrial leaers 2. Te cost optimization can be unerstoo as in te following iscussion. Soli vs Hollow comparison For simplicity, assume a cylinrical flyweel consisting of aluminium proviing te motor-generator structure, as well as some energy-bearing material. Ten, te cost as a function of raius can be written as (were p enotes price per volume) a volume integral: ˆ C cost,total = p price (r)rrϕz = 2πrp price (r)r (1) cost(r) = 2πrp price (r) = Te energy ensity of te material can be escribe as follows: { 2πrp alu, 0 < r < r alu (2) 2πrp T 1000, r alu < r < r outer U = 1 2 v2 m v = rω m = ρ ensity V U = 1 2 ρr2 ω 2 V U = 2 as reporte in Macine Design Digital Eition, August 11, ρr2 ω 2 rrϕz 2

US (MW, 10y) $Million, 10y Electric Energy Time-sift 2-8 1-500 MW 400-700 18417 10129 Electric Supply Capacity 4-6 1-500 MW 359-710 18417 9838 Loa Following 2-4 1-500 MW 600-1000 36834 29467 Area

3 ˆ U = ˆ e r = πρω 2 r 3 r e = πω 2 r 3 ρ(r) = Te following table contains some prices for relevant materials (source: Bolun). { πω 2 r 3 ρ(r), 0 < r < r alu πω 2 r 3 (3) ρ(r), r alu < r < r outer Material Price / kg Price / m 3 Ligtweigt ig-strengt Alu SEK SEK Hig-en carbon fibre Toray 1000G SEK SEK Using suggeste macine parameters below, te cost an energy ensity analyis above yiels (assuming aluminium is use up to 0.2m): SEK/m 3 & J/m Cost soli 10 2 Energy soli Cost ollow Energy ollow raius [m] Togeter wit: Soli esign Hollow esign Cost SEK SEK Mass kg 2169 kg Useful Energy 273 kw 94 kw Cost/kW SEK/kW SEK/kW Te compute material costs per kw of a ollow flyweel is ten 57% of te soli esign. However, te simulation is one for a realistic ollow esign, wereas te soli esign is overestimate largely (it woul crack long before reacing te same rotational spees). Te energy content of te soli esign soul be lower ue to raial stresses increasing wit raius (tickness). Terefore, te actual price tag is iger for soli esign, an te ollow esign case as an even larger margin. 3

8 SEK 1282680 SEK Using suggeste macine parameters below, te cost an energy ensity analyis above yiels (assuming aluminium is use up to 0.

2 Suggeste ollow macine A escriptive rawing of te macine can be seen in te Figure below. Analytical estimations an simulations ave been one, an te following setup is currently suggeste.

4 2 Suggeste ollow macine A escriptive rawing of te macine can be seen in te Figure below. Analytical estimations an simulations ave been one, an te following setup is currently suggeste. Energy-carrying material T1000G Heigt 2 m Diameter 2 m Rim wit 0.2 m Max rim spee: 680 m/s Energy Capacity 161 kw Mass 4072 kg Rotor energy ensity 40 W/kg Max. oop stress 760 MPa (25% of max) Max. raial stress MPa (252% of max) * Est. amount of cycles 40k ** Approx. total T1000G price 2.9 MSEK Material cost / Cycle 29 SEK/cycle * Beräkna utan förspäna kolfiberlager (som är state-of-te-art), något som kommer sänka enna siffra markant. Beräkningar me förspänning görs just nu av en exjobbare i samarbete me leverantör. Förspänning omvanlar gör raiell stress cirkumferentiell, är et finns mer marginal. ** Value base on typical flyweel manufacturer ata. 3 Motor-Generator esign 3.1 Coosing macine Bolun, Bernoff, Leijon suggests an efficient ig-voltage PM macine, an rejects inuction macine ue to losses. Te natural coice is ten a PM macine. However, Neoymium-magnets are very brittle, an wen glue to te inner part of te ollow flyweel tey crack ue to te expansion of te energy-carrying material (reporte 1% sift at top spee). Beacon Power ave recieve a uge grant from US DOE to evelop magnets wic are more elastic, since no magnet istributor coul provie tis. Procentuell längföränring Stress i ϕ-le Följane formel relaterar kraft till circumferentiell stress i en iålig cyliner: σ ϕ = F tl (4) 4

raial stress 12.59 MPa (252% of max) * Est. amount of cycles 40k ** Approx. total T1000G price 2.

5 är F är kraft, t tjocklek oc l öj. Hoop stress vi rotation ges av följane samban: är ρ är ensitet, ω rotationsastiget, r är raien. Deformationsgraen ges av: σ ϕ = ρω 2 r 2 (5) ɛ = δ L 0 är δ är eformationen oc L o är ursprungslängen. ɛ kan ses som en per-unit-föränring. Elasticitetsmoulen efinieras som: Vilket ger en relativa längföränringen som: E = σ ɛ ɛ = σ E = ρω2 r 2 Utifrån formeln ovan kan relativ längföränring beräknas. Antag ω = 400ra/s = 3820rpm samt r = 1. Även, maximal relativ längföränring kan fås om σ = tensilstyrkan. Källa: ttp:// Magnetiskt Rotormaterial Magnetiskt material Tensilsty. MPa Kompr. sty. MPa Youngmo. GPa ρ kg/m3 ɛ % ɛ max % Ceramic (Har Ferrite) ~ Alnico (sintere) Alnico (cast) NeDyFeB ~ SmCo Typ 1 ~ SmCo Typ 2 ~ Sanvik Safeni Källa: extermag.com & Design of Rotating Electrical Macines Kolfiber-material Alla fibrer sammansatta me 60% epoxy. Namn Tensilstyrka i ˆϕ MPa Elasticitetsmoul GPa Densitet kg/m3 ɛ % ɛ max % T1000G (60% epoxy) T800S (billigare, 60% epoxy) M60J (ög moulus) Glasfiber Stål (A36) Titanlegering Stål (A514) Stål (bok) Aluminium (bok) Kolfiber (bok) Källa: ttp:// ttp://k-mac-plastics.net/, Boken Grunläggane Hållfastetslära, övriga wikipeia, (elastic steel) ttp:// E 5

Elasticitetsmoulen efinieras som: Vilket ger en relativa längföränringen som: E = σ ɛ ɛ = σ E = ρω2 r 2 Utifrån formeln ovan kan relativ längföränring beräknas. Antag ω = 400ra/s = 3820rpm samt r = 1.

6 3.2 Reluctance macine parameters Region A is te volume not occupie by any rotor steel, region B is elsewere. Amperes law for an airgap fiel B = B z ẑ wit zero leakage flux gives: { B A = µ0ni H s = NI (6) B B = Eq 1 yiels te system energy: Wic, in turn yiels te force (F = ± U): Te torque is ten easily compute as: Inuctance is ten compute as: U = 1 2 µ 0N 2 I 2 ( V olumea 2 µ0ni + V olume ) B = 1 ( ( b ρ 2 µ 0N 2 I 2 ϕ a + ρ ) 2 + a l ϕ ) a { ( Fϕ = U ϕ = 1 2 µ 0N 2 I 2 b ρ F ρ = U ρ = 1 2 µ ( 0N 2 I 2 ϕ a 2 τ = rf ϕ = r 2 µ 0N 2 I 2 ( b ρ 2 + ρ a 2 1 ) (7) ) (8) + ρ 2 a ) L = Φ I = 1 I (Φ A + Φ B ) = 1 I (B AA A + B B A B ) = (9) Macine parameters N 700 Airgap 1 mm = µ 0 N [ ( b ρ ϕ a + ρ ) + (l ϕ a ) a ] (10) 6

is ten easily compute as: Inuctance is ten compute as: U = 1 2 µ 0N 2 I 2 ( V olumea 2 µ0ni + V olume ) B = 1 ( ( b ρ 2 µ 0N 2 I 2 ϕ a + ρ ) 2 + a l ϕ ) a { ( Fϕ = U ϕ = 1 2 µ 0N 2

EPIKOTE TM Resin MGS RIM 235

2.1-1 EPIKOTE TM Resin MGS RIM 235 EPIKURE TM Curing Agent RIM H 235-238 page Caracteristics 1 Application 11 Specifications 12 Processing details 13 Mixing ratios 13 Temperature development 13 Viscosity