Lecture Notes EEE 360 TOPIC 4 Synchronous Machine - Lecture 13 docx

Lecture Notes EEE 360 George G Karady TOPIC Synchronous Machine Read Chapter: 7.1, 7.2, 7.4, 7.6, 5.6, 5.7 06/29/14 360 Topic Synchr • Lecture 13 06/29/14 360 Topic Synchr • Animation Voltage induced in a rotating loop 06/29/14 360 Topic Synchr • Energy Conversion Concept: • Generators convert mechanical energy to electric energy • Motors convert electric energy to mechanical energy • The construction of motors and generators are similar • Every generator can operate as a motor and vice versa • The energy or power balance is : – Generator: losses Mechanical power = electric power + – Motor: losses Electric Power = Mechanical Power + 06/29/14 360 Topic Synchr • Energy Conversion Voltage generation (Generator) • A wire loop is rotated in a magnetic field – N is the number of turns in the loop – L is the length of the loop – D is the width of the loop – B is the magnetic flux density – n is the number of turns per seconds 06/29/14 360 Topic Synchr B L D • Energy Conversion Voltage generation (Generator) • • B A wire loop is rotated in a magnetic field The magnetic flux through the loop changes by the position B Φ ( t ) = B D L cos ( ω t ) ω = 2π n 06/29/14 D L cos ωt 360 Topic Synchr • Energy Conversion Voltage generation (Generator) • • • Position all flux links with the loop cos ωt Position the flux linkage reduced The change of flux linkage induces a voltage in the loop V( t ) = N 06/29/14 B dΦ ( t ) d [ cos ( ω t ) ] = N B DL = N B D L ω sin ( ω t ) dt dt 360 Topic Synchr • Energy Conversion Voltage generation (Generator) • • • The induced voltage is an ac voltage The voltage is sinusoidal The rms value of the induced voltage loop is: Vrms 06/29/14 N B DL ω = B cos ωt • View the animation of voltage generation 360 Topic Synchr • SYNCHRONOUS MACHINES Concept (two poles) Round Rotor Machine • • • • The stator is a ring shaped laminated ironcore with slots Three phase windings are placed in the slots Round solid iron rotor with slots A single winding is placed in the slots Dc current is supplied through slip rings 06/29/14 A Stator with laminated iron-core Slots with winding B A - C + Rotor with dc winding C A - B 360 Topic Synchr + S N C B - + • SYNCHRONOUS MACHINES • Salient Rotor Machine • Concept (two poles) The stator has a laminated ironcore with slots and three phase windings placed in the slots B- C+ N • The rotor has salient excited by dc current poles • DC current is supplied to the rotor through slip-rings and brushes • A+ AS The number of poles varies between - 128 06/29/14 360 Topic Synchr C- B+ • 10 SYNCHRONOUS MACHINES Student class room exercise • A two pole, three phase, wye connected, round rotor synchronous generator data are: • Stator (armature): Length L = 1.2 m, Number of turns per phase Na = 50, Load current is 300 A • Rotor: Diameter 75 cm, gap = 20 mm, field current If = A, Number of turns in the field winding Nf = 600 • • Draw a sketch of the machine Calculate: – mmf produced by the three phase load currents, the magnetic field, magnetic field intensity, and flux – synchronous reactance per phase 06/29/14 360 Topic Synchr • 63 Lecture 16 06/29/14 360 Topic Synchr • 64 SYNCHRONOUS MACHINES Power angle Characteristics Round Rotor Machine • A synchronous machine supplies an electric network with constant voltage under steady state conditions • The terminal voltage in the machine is kept constant by the regulation of the field current • The generator speed is constant, at the synchronous speed determined by the network frequency and the number of poles in the machine • An increase of input mechanical power increases the torque Calculate the output power variation with the input power 06/29/14 360 Topic Synchr • 65 SYNCHRONOUS MACHINES Power angle Characteristics Round Rotor Machine • The external network is represented by a voltage source and an equivalent reactance A large network’s impedance is very small, we assume Xe = and Ven = Vt n The equivalent circuit is: Generator Generator Bus • Network Using the equivalent circuit the current is: 06/29/14 Xe=0 Network jXs δ E fn Ia tn V Ven Efn ei δ − Vtn I= i Xsyn + i Xnt 360 Topic Synchr • 66 SYNCHRONOUS MACHINES Power angle Characteristics Round Rotor Machine • The complex power delivered by the generator is:  Efn e −i δ − Vtn  S = Vtn I = Vtn   − i Xs     • After simplification we get: Generator Xs = Xsyn + Xnt  Efn Vtn Efn ⋅ Vtn Vtn  S=3 ⋅ sin δ + j ⋅ ⋅  ⋅ cos δ −  Xs Xs Xs     Generator Bus 06/29/14 Xe = Network jXs Network δ E Ia fn 360 Topic Synchr tn V Ven = Vtn • 67 SYNCHRONOUS MACHINES Power angle Characteristics Round Rotor Machine • The real and reactive power are P=3 Efn ⋅ Vtn ⋅ sin δ Xs  Efn Vtn Vtn  Q = j⋅ 3⋅  ⋅ cos δ −  Xs Xs     • The real power is maximum if δ = 900 • The maximum torque is: Tmax = Pmax / ω 06/29/14 360 Topic Synchr • 68 SYNCHRONOUS MACHINES Power angle Characteristics • Round Rotor Machine The P(δ) curve shows that the increase of power increases the angle between the induced voltage and the terminal voltage Pmax 100 • The power is maximum when δ =90o 80 • The further increase of input power 60 forces the generator out of P( δ ) 40 synchronism This generates large current and mechanical forces • This angle corresponds to the angle between the field flux and the stator 20 0 30 generated rotating flux 06/29/14 360 Topic Synchr 60 90 120 15 180 δ • 69 SYNCHRONOUS MACHINES Power angle Characteristics • • • Round Rotor Machine The angle δ, called power angle and it corresponds to the angle between the field flux and the stator generated rotating flux The maximum power is the static stability limit of the system Safe operation requires a 1520% power reserve Pmax 100 80 P( δ ) Safe operation limit 60 40 20 0 30 60 90 120 15 180 δ 06/29/14 360 Topic Synchr • 70 SYNCHRONOUS MACHINES Operation concept Student numerical exercise • A three-phase, pole, 10 MVA, 2400 V, 80% generator supplies a 60Hz, 2300V network • Calculate the synchronous reactance in ohm and the line to ground terminal voltage • Draw the equivalent circuit • The field current is adjusted that the Ef induced voltage (line to ground ) is 3500V Calculate the generate or produced active and reactive power, power factor, if the power angle is 20 deg • Calculate the maximum power that the generator can supply to the network Assume that the field current and network voltage are constant 06/29/14 360 Topic Synchr • 71 SYNCHRONOUS MACHINES Power System Operation • In a network several hundred synchronous generators operate in parallel • Each generator operates with the same speed • The load increase is achieved by increasing the input power, that increases the power angle δ The speed remain constant • The power angle must be less than 90 degrees The load should be 30-20% less than the maximum power (δ = 90o) • The reactive power is regulated by the control of the field current that varies the induced voltage 06/29/14 360 Topic Synchr • 72 SYNCHRONOUS MACHINES Power System Operation • When the induced voltage is: – larger than the terminal voltage the generator produces reactive power (capacitance) – smaller than the terminal voltage the generator absorbs reactive power (inductance) • The synchronous generator starting torque is zero, the machine has to be driven by a mechanical device (turbine, recipricating engine, etc) • The proper interconnection of a rotating machine with the network is called synchronization 06/29/14 360 Topic Synchr • 73 SYNCHRONOUS MACHINES Synchronization • The steps are: – Verify that the phase sequence of the two systems are the same – Adjust the machine speed with the turbine that drive the generator until the induced voltage and network frequency are nearly the same – Adjust the terminal voltage of the generator by changing the field current until the terminal voltage is almost equal to the network voltage Acceptable limit is 5% – Adjust the phase angle of the generator to be nearly equal with the phase angle of the network voltage 06/29/14 360 Topic Synchr • 74 SYNCHRONOUS MACHINES Synchronization • The voltages between the terminals of the circuit breaker are measured, when this voltages are small, about 5% and the two frequencies are nearly equal the circuit breaker is closed • In the past lamps, connected across the open breaker, were used to detect the voltage differences • Today electronic circuits compare the voltages and control the generator However some operators still prefers to synchronize the generator manually with an out of range synchronizer overriding 06/29/14 360 Topic Synchr • 75 SYNCHRONOUS MACHINES Student class room exercise • A three phase, wye connected, four pole, 40 MVA, 13.8 kV generator is operating at half load with pf = 0.8 lagging The synchronous reactance is 115% • Calculate: – Synchronous reactance in ohm – Draw the equivalent circuit – Rated, load currents and line to neutral terminal voltage – Machine speed – Induced voltage – Output active and reactive power 06/29/14 360 Topic Synchr • 76 SYNCHRONOUS MACHINES GENERATOR CONSTRUCTION VIDEO 06/29/14 360 Topic Synchr • 77 ... machine 06/29/ 14 360 Topic Synchr • 20 Animation Generator Operation 06/29/ 14 360 Topic Synchr • 21 Test Transformer 06/29/ 14 360 Topic Synchr • 22 Lecture 14 06/29/ 14 360 Topic Synchr • 23 SYNCHRONOUS. .. zero, when Θ is + /-9 00 Magnetic axis of phase Α Θ = 00 m Magnetic axis of phase Α Θm= 900 C+ B- C+ B- N N A+ A- A+ A- S S C- 06/29/ 14 B+ C- 360 Topic Synchr B+ • 40 SYNCHRONOUS MACHINES • The flux... are closed by wedges and re-enforced with steel rings 06/29/ 14 360 Topic Synchr • 15 SYNCHRONOUS MACHINES Rotor Details 06/29/ 14 360 Topic Synchr • 16 SYNCHRONOUS MACHINES Round rotor Steel ring