Renewable Generation and Conversion B31GC Renewable Energy Fundamentals Learning Objectives This session • We will review key system components for renewable energy applications • We will understand the fundamental working principle of different generator types • We will understand the operating principles of different power converter types 22/01/2022 B31GC Renewable Generation and Conversion 2 Principles of electromagnetism Some basics Complex impedance General Resistor ๐ฃาง = ๐.าง ๐ าง Sinusoidal form ๐ ๐ก = ๐ด0 ๐๐๐ (2๐๐๐ก + ๐แป ๐ฃ ๐ก = ๐ . ๐ ๐ก = ๐ . ๐ผ๐๐๐ (๐๐ก + ๐แป ๐ฃาง = ๐ ๐ผ๐ ๐๐ We choose: ๐ ๐ก =๐๐๐ผ๐๐๐ (๐๐ก + ๐แป Phasor ๐๐ = ๐ ๐ าง = ๐ผ๐ ๐ าง = ๐ด๐๐๐ ∠๐ or ๐ าง = ๐ด0 ∠๐ Inductance Capacitance 1 1 ๐ เถฑ๐ ๐ก ๐๐ก = ๐ผ๐๐๐ ๐๐ก + ๐ − ๐ถ ๐ถ๐ 2 1 1 ๐๐ = −๐ ๐ฃาง = −๐ ๐าง ๐ถ๐ ๐ถ๐ ๐ฃ ๐ก = ๐ฃาง = ๐ฟ๐๐ผ๐ ๐ด๐๐๐ = ๐ด0 2 = 1 ๐ เถฑ ๐ (๐กแป2 ๐๐ก ๐ 0 ๐ ๐(๐+ แ 2 = ๐๐ฟ๐๐ าง ๐๐ฟ = ๐๐ฟ๐ 4 Laws Electric and magnetic circuits Ohm’s law ๐ฃ ๐ก =๐ ๐ก ๐ Impedance ๐ ๐ฃ ๐ก = ๐ ๐ก (๐ + ๐๐ค๐ฟ − แป ๐ค๐ถ 22/01/2022 B31GC Renewable Generation and Conversion 5 Laws Electric and magnetic circuits ๐๐๐ = ๐. ๐๐ ๐๐๐ = ๐. ℜ = ๐ ℜ1 + ℜ2 + 2ℜ3 ๐1 ๐2 ๐3 = ๐( + +2โ แป ๐ด๐๐น๐ ๐ด๐๐น๐ ๐ด๐๐ด๐๐ 22/01/2022 B31GC Renewable Generation and Conversion 6 Laws Electric and magnetic circuits Ni = mmf = ๐ โ ℜ ๐1 ๐2 ๐3 = ๐( + +2โ แป ๐ด๐๐น๐ ๐ด๐๐น๐ ๐ด๐๐ด๐๐ 22/01/2022 B31GC Renewable Generation and Conversion 7 22/01/2022 B31GC Renewable Generation and Conversion 8 Michael Faraday was born in England in 1791 Faraday’s law Electric and magnetic circuits Faraday’s Law:“When the magnetic flux linking a circuit is varied, an emf is induced in the circuit” emf = − ๐๐ ๐๐ก Lenz’s law:“The direction of an induced emf is always such that it tends to set up current opposing the change of the flux” 22/01/2022 Emil Lenz was born in the Russian Empire in 1804 B31GC Renewable Generation and Conversion 9 Generator effect Motor and generator effect • Applied magnetic field • Applied motion • Resultant electric current ๐น = ๐ต๐๐ 22/01/2022 B31GC Renewable Generation and Conversion 10 Motor effect Motor and generator effect • Applied magnetic field • Applied electric current • Resultant motion ๐น = ๐ต๐๐ 22/01/2022 B31GC Renewable Generation and Conversion 11 Motor and generator effect ๐๐ ๐๐๐ = −๐ ๐๐ก = −๐๐๐๐ ๐๐๐ ๐๐ก ๐๐ ๐ = −๐ฟ ๐๐ก ๐๐ ๐ฟ=๐ ๐๐ For a linear magnetic circuit: −๐ฟ = ๐๐ ๐ Inductance = number of flux linkage per unit current 22/01/2022 B31GC Renewable Generation and Conversion 12 Power generation and transmission 22/01/2022 B31GC Renewable Generation and Conversion 13 Advantages AC power generation DC Resistive losses Materials used AC Transformer 3 phase AC Deliver more power per cabling Constant power 22/01/2022 B31GC Renewable Generation and Conversion 14 AC transmission High voltage transmission 22/01/2022 B31GC Renewable Generation and Conversion 15 AC transmission Equivalent circuit per-phase diagram 22/01/2022 B31GC Renewable Generation and Conversion 16 AC transmission Single line per-phase diagram 22/01/2022 B31GC Renewable Generation and Conversion 17 High voltage transmission The ideal transformer (IT) -> operation Transformer ratio: α= ๐1 ๐2 ๐ผ Power in = Power out ๐ = ๐ผ2 = ๐1 1 2 Windings have no resistance Core of transformer has infinite permeability: • It takes zero mmf to create flux • All flux is confined to the core Transformer core lacks losses: no hysteresis or eddy currents 22/01/2022 B31GC Renewable Generation and Conversion 18 Open circuit or no-load test Real transformers - Core losses (magnetising current losses) Rc and Xm • Hysteresis (non-linear magnetic effects in core) • Eddy current losses (Joule heating of the core) Measured: V1,I1,P1,V2 Calculated: Rc=V12/P1 , Xm=V12/Q1 Short-circuit or full-load test - Windings’ losses R1, X1 and R2, X2 Measured: V1,I1,P1 Calculated: R1eq= P1 /I12 , Z1eq= V1 /I1 , Z1eq= Q1 / I12 22/01/2022 B31GC Renewable Generation and Conversion 19 Synchronous generators Single-phase synchronous generators 22/01/2022 B31GC Renewable Generation and Conversion 21 Single-phase synchronous generators 60๐ 60๐ ๐๐ = = ๐ ๐2๐ 22/01/2022 B31GC Renewable Generation and Conversion 22 Single-phase synchronous generators 22/01/2022 B31GC Renewable Generation and Conversion 23 Single-phase synchronous generators 22/01/2022 B31GC Renewable Generation and Conversion 24 Single-phase synchronous generators I๐๐๐๐๐๐๐๐ โถ ๐ = ๐ + ๐๐ Complex number Not a phasor as it does not change with time 22/01/2022 B31GC Renewable Generation and Conversion 25 Phasor notation and diagrams Single-phase synchronous generators 22/01/2022 B31GC Renewable Generation and Conversion 26 Single-phase synchronous generator Find Ea, rms, pf and power delivered to load 22/01/2022 B31GC Renewable Generation and Conversion Single-phase synchronous generator Find Ea, rms, pf and power delivered to load 22/01/2022 B31GC Renewable Generation and Conversion Single-phase synchronous generators 22/01/2022 B31GC Renewable Generation and Conversion 29 Three-phase synchronous generators 22/01/2022 B31GC Renewable Generation and Conversion 30 Three-phase synchronous generators 22/01/2022 B31GC Renewable Generation and Conversion 31 Three-phase synchronous generators 22/01/2022 B31GC Renewable Generation and Conversion 32 Three-phase synchronous generators 22/01/2022 B31GC Renewable Generation and Conversion 33 Three-phase synchronous generators 22/01/2022 B31GC Renewable Generation and Conversion 34 Connecting threephase systems 1. Y (wye) 2. D (Delta) 3. Conversion from D to Y Y connection 22/01/2022 B31GC Renewable Generation and Conversion 35 Connecting threephase systems 1. Y (wye) 2. D (Delta) 3. Conversion from D to Y Y connection 22/01/2022 B31GC Renewable Generation and Conversion 36 Connecting threephase systems 1. Y (wye) 2. D (Delta) 3. Conversion from D to Y Y with neutral connection 22/01/2022 B31GC Renewable Generation and Conversion 37 Connecting threephase systems 1. Y (wye) 2. D (Delta) 3. Conversion from D to Y Δ connection 22/01/2022 B31GC Renewable Generation and Conversion 38 Connecting threephase systems Za 1. Y (wye) 2. D (Delta) 3. Conversion from D to Y Zb Zc • For balanced wye-connected load: • For balanced delta-connected load • Conversion 22/01/2022 B31GC Renewable Generation and Conversion 39 Break Induction generators The induction machine 22/01/2022 B31GC Renewable Generation and Conversion 42 The stator 22/01/2022 B31GC Renewable Generation and Conversion 43 The stator 22/01/2022 B31GC Renewable Generation and Conversion 44 The stator 22/01/2022 B31GC Renewable Generation and Conversion 45 The rotor Squirrel Cage Wound rotor 22/01/2022 B31GC Renewable Generation and Conversion 46 The rotor 22/01/2022 B31GC Renewable Generation and Conversion 47 Synchronous speed Machine operation 60๐ 60๐ 120๐ ๐๐ = = = ๐ ๐2๐ ๐ ๐ ๐๐ = ๐ p = pair poles P = number of poles 22/01/2022 e.g. 60 × 50 1 = 3000๐๐๐ 50 60 × = 1500 ๐๐๐ 2 B31GC Renewable Generation and Conversion 48 Induced current Machine operation Fleming’s right-hand rule 22/01/2022 B31GC Renewable Generation and Conversion 49 Induced motion Machine operation Fleming’s left-hand rule 22/01/2022 B31GC Renewable Generation and Conversion 50 Slip (fractional slip Machine operation ๐= 22/01/2022 B31GC Renewable Generation and Conversion ๐๐ − ๐๐ ๐๐ − ๐๐ = ๐๐ ๐๐ 51 Equivalent circuits 52 22/01/2022 B31GC Renewable Generation and Conversion 52 Machine operation Power to stator Pi 22/01/2022 is2Rs loss Pg = Tωs ir2Rr loss Pm = Tωr Windage loss P0 = T0ω0 B31GC Renewable Generation and Conversion Core loss Frictional loss 53 Mechanical power as a function slip Machine operation ๐๐ = ๐๐ − 3๐ผ๐2 ๐ ๐ = ๐๐ − ๐๐ ๐๐๐ = ๐๐๐ − ๐๐ ๐๐ = ๐ ๐๐ − ๐๐ = ๐๐๐ ๐ ๐ = ๐๐ ๐๐ = ๐๐๐ ๐๐ 3๐ผ๐2 ๐ ๐ ๐๐ = ๐๐ − ๐๐ = ๐๐ 1 − ๐ = (1 − ๐ แป ๐ 22/01/2022 B31GC Renewable Generation and Conversion 54 Machine operation Load 1−๐ ( แป๐ ๐ ๐ 22/01/2022 B31GC Renewable Generation and Conversion 55 Machine operation 1−๐ ๐ ๐ ๐ 22/01/2022 B31GC Renewable Generation and Conversion 56 Machine operation 22/01/2022 ๐ ๐′ ๐ = ๐ ๐ + + ๐(๐๐ + ๐๐′ แป ๐ B31GC Renewable Generation and Conversion 57 Machine operation ๐ผ๐′2 ๐ ๐′ ๐ ๐= ๐ ๐ ๐ ๐ ๐ + ๐ ๐′ =๐= + ๐(๐๐ + ๐๐′ แป ๐ผ′ ๐ 3๐ ๐2 ๐ ๐′ ๐= ( แป ′ ๐ ๐ ๐ + ๐ ๐ 2 ๐ ( แป + (๐๐ + ๐๐′ แป2 ๐ 22/01/2022 B31GC Renewable Generation and Conversion 58 Machine operation 3๐ ๐ฃ2 ๐๐ = ( แป 2๐ ๐ ๐ + ๐ ๐ 2 + (๐๐ + ๐๐′ แป2 ๐๐ = 22/01/2022 ๐ ๐′ ๐ ๐ 2 + ( ๐๐ + ๐๐′ แป2 B31GC Renewable Generation and Conversion 59 Machine operation 22/01/2022 B31GC Renewable Generation and Conversion 60 Power electronics Converters Semiconductor devices 1. Rectifiers (AC to DC) 2. Choppers (DC to DC) 3. Inverters (DC to AC) 4. Cyclo-converters (AC to AC) 22/01/2022 B31GC Renewable Generation and Conversion 62 Rectifier Converters 3-phase full-wave rectifier with diodes 22/01/2022 B31GC Renewable Generation and Conversion 63 Rectifier Converters For 30o: 22/01/2022 B31GC Renewable Generation and Conversion 64 Rectifier Average output voltage ๐๐ท๐ถ +๐ 6 1 = ๐เถฑ −๐ 3 6 3 2๐๐ฟ cos(๐ค๐กแป +๐ 6 3 6๐๐ฟ = เถฑ cos(๐ค๐กแป −๐ ๐ 6 3 6 = ๐ = 2.34๐๐ฟ ๐ ๐ฟ ๐๐๐๐๐ = 2๐๐๐๐ ๐๐๐๐๐−๐ก๐−๐๐๐๐ = 3๐๐๐๐๐−๐ก๐−๐๐๐ข๐ก๐๐๐ ๐๐ฟ๐ผ๐๐ธ = 3๐๐๐ป๐ด๐๐ธ 22/01/2022 B31GC Renewable Generation and Conversion 65 Rectifier Converters • Fully-controlled 3-phase bridge rectifier – replacing diodes with thyristors • Control of voltage level 3 3 2 ๐๐ท๐ถ = ๐๐ฟ cos ๐ผ ๐ = 2.34๐๐ฟ ๐๐๐ ๐ผ 22/01/2022 B31GC Renewable Generation and Conversion 66 Inverter 22/01/2022 B31GC Renewable Generation and Conversion 67 Inverter 22/01/2022 B31GC Renewable Generation and Conversion 68 Inverter (120o mode of operation) 22/01/2022 B31GC Renewable Generation and Conversion 69 Inverter (180o mode of operation) fd 22/01/2022 B31GC Renewable Generation and Conversion 70 DC linked converter 22/01/2022 B31GC Renewable Generation and Conversion 71
