Jan 15, 2016 ... LESSON 20 ALTERNATOR OPERATION OF. SYNCHRONOUS MACHINES. ET 332b. Ac Motors, Generators and Power Systems. 1. Lesson 20_et332b.pptx. ...
Phasor diagram of a synchronous generator. (similar to that of a transformer). Since the voltages in a synchronous generator are AC voltages, they are usually expressed as phasors. A vector plot of voltages and currents within one phase is called a p
(c). (d)phasor diagram for R-L load. Figure 30: Equivalent circuits. The synchronous generator, under the assumption of constant synchronous reactance, may be considered as representable by an equivalent circuit comprising an ideal winding in which a
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1/15/2016
Lesson 20_et332b.pptx
ET 332b Ac Motors, Generators and Power Systems
LESSON 20 ALTERNATOR OPERATION OF SYNCHRONOUS MACHINES 1
Lesson 20_et332b.pptx
LEARNING OBJECTIVES After this presentation you will be able to:
Interpret alternator phasor diagrams under different load conditions. Explain the infinite bus concept and compute power delivered to an infinite bus. Explain how alternators are synchronized. Define alternator stiffness.
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ALTERNATOR OPERATION Synchronous machines can convert from motor to generator operation by having the shaft driven by a source of mechanical power
Current exits for generator operation
Note: reversal of current direction in machine electrical model 3
Lesson 20_et332b.pptx
PHASOR DIAGRAMS OF MACHINE OPERATION Motor operation: d lags the terminal voltage V T. Armature current Ia can either lead or lag V T depending on value of excitation. Leading Ia
Lagging Ia
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PHASOR DIAGRAMS OF MACHINE OPERATION Machine with no mechanical load or power output. The torque/power angle, d is 0 in this case
Ef1
d=0
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PHASOR DIAGRAMS OF MACHINE OPERATION Generator operation (Alternator)
Ef1 leads the terminal voltage for generator operation
Power factor angle can either lag or lead depending on field excitation 6
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ALTERNATOR CIRCUIT MODEL Synchronous Generator Equations and Model Circuit Power equation (Watts/phase)
Pin
VT Ef
sin(d)
Xs
Note: equation is positive and d is positive for Alternator (generator) operation Ia reversed
Where:
Voltage equation
VT E f Ia jX s V T = terminal voltage/phase (V) Ef = excitation voltage/phase (V) Ia = armature current/phase (A) Xs = synchronous reactance/phase (ohms) 7
Lesson 20_et332b.pptx
GENERATOR LOADING Mechanical power converted to active power
Exciter
Excess field flux converted to reactive power
Idc Pmech Pe Prime Mover
Prime Mover Torque
Governor
ELECTRIC LOADS
Generator
Q Electrical load produces counter-torque
Speed Governor – device that regulates Increased electrical load produces counter torque that speed to match electric load prime mover must overcome or prime mover slows down 8
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INFINITE BUS CONCEPT In large power systems, V T and system frequency are assumed constant. Individual generators added to large system can not change V T and f. Good approximation when generator small with respect to all other generation connected
System Tie Bus Power Grid (100’s of interconnected generators. Psys = sum of all generator’s outputs) V T and f constant here
Local Generator Po <<< Psys
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Lesson 20_et332b.pptx
INFINITE BUS EXAMPLE Example 20-1: 3-phase, 460 V, 2-pole, 60 Hz, wye-connected, synchronous alternator. Xs = 1.26 ohm/phase. Connected to an infinite bus and supplies 117 kW with a power angle of 25 degrees. Neglect losses and find: a.) turbine torque supplied to alternator; b.) excitation voltage; c.) active, reactive power and machine power factor; d.) neglecting saturation effects of the field, the excitation voltage if the field current is reduced to 85% of its original value in part a; e.) the turbine speed for 60 Hz operation
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EXAMPLE 20-1 SOLUTION (1) Find torque developed by prime mover to generate 117 kW neglecting losses
Need synchronous speed
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EXAMPLE 20-1 SOLUTION (2) Find the excitation voltage Ef
Solve for Ef
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EXAMPLE 20-1 SOLUTION (3) Part c.) Find Sout Pout and Qout of generator. Need armature current
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EXAMPLE 20-1 SOLUTION (4) Find the power phasor using the following formulas
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EXAMPLE 20-1 SOLUTION (5) Find the power factor and the change in excitation voltage
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PARALLELING SYNCHRONOUS GENERATORS :Required initial conditions : Machines must have same phase sequence (order of voltages) (ABC) or (BAC). Incorrect phase sequence causes short circuit.
Turbine speed should be a fraction of Hz faster than system to prevent motoring of generator
VT
3.) Close generator breaker
1.) Adjust voltage of incoming machine to match system voltage
2.) Adjust frequency of incoming generator to match system f (Synchronize to system) 16
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MEASURING SYSTEM/MACHINE FREQUENCY Synchroscope - instrument to determine if machine frequency is the same as system frequency. Instrument indicates fast-slow operation by comparing the frequencies of the two voltages (system-generator)
Mathematically, phase shift is integral of frequency change
t
f s f g ( t ) dt Where: = phase shift 0
fs = system frequency fg(t) = generator frequency 17
Lesson 20_et332b.pptx
SYNCH EXAMPLE Generator voltage lagging system voltage - crosses zero later in time Also cause rotor oscillations which cause the generator to be unstable D
Closing Generator breaker with phase shifts of greater than 10 degrees causes high armature currents and will trip the generator off line
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SYNCHRONIZING GENERATOR TO SYSTEM Increasing speed of prime mover increases frequency which reduces phase difference
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SYNCHRONIZING GENERATOR TO SYSTEM Phase shift near zero at ts. Prime mover is accelerating the rotor ahead of the system voltage after this point. (Vg leads Vs)
Close generator breaker when phase is slightly leading system
Machine will remain locked to system frequency after breaker is closed assuming infinite bus 20
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STIFFNESS OF SYNCHRONOUS MACHINES Stiffness -Ability of a synchronous machine to resist forces that pull it out of synchronism. Slope of the power-angle curve around a given operating point
Operating point in graph above is at do 21
Lesson 20_et332b.pptx
STIFFNESS OF SYNCHRONOUS MACHINES Remember power equation P
3 VT Ef
sin(d)
Xs
To find slope, take derivative of P with respect to d. This is defined as the stiffness Ps
DP dP 3 VT E f cos(d) Dd dd Xs
Units of Ps are watts/radian (or degree)
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STIFFNESS OF SYNCHRONOUS MACHINES Example 20-2: A 3-phase 13.2 kV 60 Hz, 50 MVA wyeconnected cylindrical rotor synchronous generator has Xs = 2.49 ohms/phase and an internally generated voltage at the operating point of 15,767 VLL with a power angle of 11.1 degrees. The machine has 8 poles. Determine:
a.) the synchronizing power in MW/rad and MW/ mechanical degree b.) synchronizing torque in N-n/radian
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EXAMPLE 20-2 SOLUTION (1) Find the per phase quantities of V T and Ef from the line-to-line values
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EXAMPLE 20-2 SOLUTION (2) Number of poles is 8, so... de= (dm) ∙(P/2)
b.) Now compute the synchronizing torque Compute synchronous speed Convert to Radians/second
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ET 332b Ac Motors, Generators and Power Systems
END LESSON 20 ALTERNATOR OPERATION OF SYNCHRONOUS MACHINES
