Chapter 5 Electrical Machines PDF

  137   5. Electrical  machines     Learning objectives of the chapter By completing this ch...

  137   5. Electrical  machines     Learning objectives of the chapter By completing this chapter, the student will able to: understand the basic priniples behind electrical machines understand the basic operation of induction machines understand different types of induction machines and their properites understand the basic operation of synchronous machines compare the both types of machines The electrical machines as explained in this chapter are to be understood as a converter: electrical machine can be a generator and thus convert mechanical energy in electrical energy, or be a motor which converts electrical to mechanical energy. The main difference to the transformer is, beside the fact that the energy in transformer before and after conversion is the same form – electrical energy, both generator and motor involve “moving parts”. If we analyze the power systems, than you will note that majority of power plants transformers mechanical energy (in conventional power plants the thermal energy is “converted” in mechanical, in wind power plant the rotor movement) into electrical. So basically, without electrical machines no power supply would be possible. On the other hand electric motors consume approximately 50% – 60% of all electricity produced. This means that on the both sides of the power system (generation and demand) electrical machines are involved. Irrespective of manifold features, for instance the external shapes of the electrical machines, they all comprise moving part and two electric circuits, which have been coupled through a magnetic circuit. Each electrical machine has a stationary component and a moving component. The motion of the moving machine component can be linear, oscillatory or rotational and the most common type of motion is rotational. Any rotating machine consists of two basic parts: The not moving, stationary (outside) part of the machine is called the stator. The rotating (inside) part is known as rotor and is typically mounted on a shaft. In between the stator and the rotor there is an air gap. Figure  5.1:  Common  parts  of  electrical  machine   The shaft is connected directly to the rotor. With regard to the rotational velocity of the machine (actually rotor), the equivalent terms “machine speed, “rotor speed” and “shaft speed” are used.    138   Stator and Rotor are mainly consisting of three components: - Core: a ferromagnetic material used to effectively conduct the magnetic fields through the windings (coils). - Winding: typically copper or aluminum, the winding currents are the sources of magnetic fields in the machine - Insulation In practice three different types of rotational machines can be found: - Synchronous machines – mainly three-phase machines, the most common application is in the power grid as a three-phase generator. - Induction (asynchronous) machines – are the most widely used rotating machines in industry. Single-phase induction motors are also being used for most household applications (requiring a motor). - DC machines – mainly used as a motor in applications where DC sources are only available (e.g. automotive systems) or a high degree of flexibility in the control of speed and torque are needed. Common for all machines is a rotating magnetic field. 5.1. Rotating  magnetic  field   The rotating magnetic field describes a field with rotating, moving polarities. Ideally, the rotation changes direction of the magnetic field at a constant angular rate. This rotating magnetic field can be created through: - Rotation of the (permanent) magnet or - Polyphase AC-System with specific spatial layout Both principles are actually used: For example, some synchronous generators use permanent magnets as rotor. The inductance and synchronous machines have stationary windings in stator, which are supplied with AC-current. The most obvious way to create a rotating magnetic field is the use of a permanent magnet, rotated at (constant) speed: Figure  5.2:  Magnetic  field  of  the  rotating  permanent  magnet   Of course, we can also use a current in a wire wounded around the core which than rotates at (constant) speed:    139   Figure  5.3:  Magnetic  field  of  the  rotating  single-­phase  coil       Now, let’s assume following arrangement (see Figure 5.4): Three coils are spatially so arranged that between them an angle of 120 degrees can be observed. On the terminals of the coils the three-phase system is connected (means between phases electrically 120°) Figure  5.4:  Three  coils  in  star,  connected  to  a  three-­phase  system  [5-1]     The currents in these three windings have the shape indicated in Figure 5.5.     Figure  5.5:  Currents  in  the  three-­phase  system  [5-1]     Now, let us check how the magnetic field “created” by those currents will look like (for each single time indicated from 1 to 12). The black color in Figure 5.6 indicates positive current, hatched area the negative direction, the magnitude is indicated with the color level. The arrow in the middle is the sum of the three magnetic fields resulting from these currents.      140       Figure  5.6:  Rotating  magnetic  field  as  a  result  of  the  AC,  three-­phase  current  flow  [5-1]     From this we can also see that the rotational speed of the resulting field is proportional to the frequency of the three-phase system. This speed is called synchronous speed and in our setup if we assume the grid frequency is 50Hz, we would see 50 rotations per second or 3000 rotations per minute. In total, in this arrangement we see only two poles (north and south) or one pole pair. However, if we place more windings (for example a second 3-coils system), than we would increase the number of poles to 4 or rather the number of pole pairs to 2. In this case the resulting rotational field will have the speed, which is the half of our basic arrangement. The rotation speed of the stators magnetic field is depending on the construction - means number of poles. The speed of it is defined as the synchronous speed: f ns = 5.1   P           where f is the frequency of the AC- stator (grid) current and P the number of pole pairs. In terms of revolutions per minute (rpm), the synchronous speed is given as: € f n s = 60⋅ 1      5.2   P                 €      141       Exercise  5.1:   Assume following arrangement:     What would be the direction of the total magnetic field at time t1, t2, t3 and t4?    142   5.2. Inductance  (asynchronous)  machines   The induction machine gets its name from the manner in which it operates. If we assume it operates as a motor an external AC current is provided to the stator windings of an induction motor but no external current is provided to the rotor windings. The AC currents, which than can be observed in the rotor, are the result of the induction: due to the rotation of the magnetic field created by the stator the current in a conductor/coil of the rotor is induced. An induction machine is also known as asynchronous machine due to the fact that the operating speed (rotor speed) differs the speed of the rotating magnetic field of the stator: it is slightly less if operated as motor and slightly more if operated as generator. Stator is the outer stationary part of the machine, which consists of: - The outer cylindrical frame of the machine – made of welded sheet steel or cast iron or cast aluminum alloy. - Stator core – provides the basic magnetic path. In order to reduce the losses (see chapter “Transformer”) comprises a set of slotted steel laminations pressed into the cylindrical space inside the outer frame. The slots for the winding and their number depend on the type of the machine and the design requirements. The main types of slots used are open type (rectangular in shape) or semi-closed (slot opening is much smaller than the width of the slot, also as tapered slot, where width will be varying from top of the slot to bottom of the slot with minimum width at the bottom) - A set of insulated electrical windings – placed inside the slots of the laminated stator. Stator windings is a set of conductors wound in the form of coils, placed in slots (typically double layer) and connected in a suitable way to obtain required voltage if used as generator or to work on required applied voltage if in motor-use. The cross-sectional area of these windings must be large enough for the power rating of the motor. The stator winding is the most critical component of the stator (very costly component) and most stator problems occur with the winding. Figure  5.7:  Stator  core  (left  hand  side),  wound  stator  [5-2]   There are two types of rotors used in induction machines: - Squirrel-cage rotor – conducting bars that are electrically connected at both ends of the rotor by end rings. This kind of construction does not admit any access to the rotor windings during operation. As a result there is no possibility of a direct influence on the operational characteristics of the engine. For large machines copper rotor bars as well as    143   short-circuit rings are characteristic, whereas die-cast aluminum cages for machines with smaller nominal power are used. - Wound rotor – polyphase windings connected to slip rings at both ends of the rotor. Through slip rings the connection to external resistances is possible and with their adjustment the control of the speed/torque of the motor. During normal operation the rotor windings are short-circuited directly. While starting they may be connected via slip- rings and brushes to resistors or they may be supplied by external voltage. Both are methods to control rotary speed and torque.       Figure  5.8:  Rotor  types,  left-­hand  side  wound  (slip-­ring)  rotor,  right-­hand  side  squirrel-­cage  rotor     Between stator and rotor is the air gap, which is a very critical part. The performance parameters of the motor like magnetizing current, power factor, over-load capacity, cooling and noise are affected by length of the air gap.   5.2.1. Basic  operation   The stator of the inductance machine is connected to the three-phase system with the frequency f1 and creates inside the air gap a rotating magnetic field Bs with the synchronous rotary speed n1. The conductors of the rotor experience this rotating field, and as we already know that the changes in magnetic field will lead to induction, in rotor the voltage is induced and the short-circuit current flows with a frequency f2. The rotor currents according to the Lenz’s Law counteract their cause, which is based on relative motion between the rotor and the stator field. As a consequence rotor currents and stator rotary field, which revolves with synchronous speed, create torques driving the rotor towards the stator rotary field and try to    144   adapt their speed to that of the stator rotary field. If the squirrel cage is rotating at the same angular velocity as the stator magnetic flux density, then the loops of the squirrel cage experience a constant magnetic field, and no current flows through the bars of the cage. Under this condition, the squirrel cage generates no magnetomotive force and no torque on the rotor exists. The rotor then begins to slow down relative to the stator magnetic field. As is does so, the magnetic flux density for a given loop of the squirrel cage changes (some loops experiencing an increase in magnetic flux density, and some loops experiencing a decrease in magnetic flux density). The response to this change in magnetic field is a current that flows in the bars of the squirrel cage so as to oppose this change in magnetic field. Because the induction effect would disappear if there would be no difference between the rotary speed of the rotor and that of the stator field, it is impossible that the rotor reaches stator field rotational speed. Rotors show a certain amount of slip s as against the synchronous stator field – their kind of running is called asynchronous. Therefore this kind of machine is called induction machine (asynchronous machine). The more torque by the rotor is required, the larger the slip, which occurs in the machine. The difference between the synchronous speed (stator field) and the motor speed (speed of the rotor) is defined as the slip speed (nslip) and given by: n slip = n s − n (rpm)    5.3             It the slip speed is defined on a per-unit basis (which means normalized to the synchronous speed), the resulting value is defined as the slip (s): € n −n s= s ns    5.4               If the motor speed equals the synchronous speed, than slip would be zero, s=0. If the motor is stationary the slip is one, s=1. € The frequency of the current and voltage in the rotor circuit (f2) is dependent on the relative speed between the stator magnetic field and the machine speed. Using the relationship between frequency, pole-pair number and rotation speed, we can write: P P P f2 = ⋅ n 2 = ⋅ ( n s − n ) = ⋅ s⋅ n s 60 60 60    5.5   f 2 = s⋅ f1       So, the frequency of the voltage and current in the rotor equals frequency of the excitation in the stator times the slip.   € Exercise  5.2:   A three-phase 50Hz, four-pole induction machine delivers rated output power at a slip of 0.05. Determine the: a) Synchronous speed and motor speed b) Speed of the rotating air gap field c) Frequency of the rotor circuit d) Slip rpm e) Speed of the rotor field relative to the rotor structure, the stator structure and the stator-rotating field.    145   Depending on the specific range of the slip, the induction machine has different modes of operation: ⎧ s = 0; coil ⎪ s = 1; transformer n s − n ⎪⎪ s= ⎨ s < 0; generator n s ⎪ 0 < s < 1; motor ⎪ ⎪⎩ s > 1; break When the induction machine is in motor operation, the motor speed is between zero and the synchronous speed while the slip ranges between 1 and 0. When the induction machine is operated as a generator, € the stator is connected to a constant frequency voltage source and the rotor is driven by the mechanical power. In order to “generate” electricity the rotating directions must be the same, however the speed of the rotation of the rotor must be above synchronous speed. That means that the slip of the induction machine is negative when operated as a generator. In case that the induction motor is running at normal speed, and the leads on the stator winding are suddenly reversed, than the rotation of the stator magnetic field is suddenly reversed. The resulting slip is greater one and the motor will come to an abrupt stop since the force on the rotor now would oppose the normal rotation. This method of stopping a rotor is commonly known as plugging. Please note, that if only stopping is intended, than the machine has to disconnect from the voltage source before it starts to rotate in the reverse direction. From the standpoint of the operation, the stator winding of the induction machine has the same function as the primary winding in a transformer. When we apply voltage on the winding, the current is driver through the stator windings and creates a magnetic flux in the core (in the case of the induction machine stator / air gap / rotor). The stator has a winding resistance leakage resistance and as well as core resistance and a magnetization reactance. The equivalent circuit of the stator winding per phase corresponds exactly than to equivalent circuit of the transformer primary winding. Important is to note, that stator winding reactance are defined in terms of the stator source frequency f1. Figure  5.9:  Equivalent  circuit  of  the  per-­phase  stator  winding   In Figure 5.9, V1 is per-phase stator terminal voltage, I1 is per-phase stator terminal current, R1 describes per-phase stator winding resistance, X1s is per-phase stator leakage reactance, the per-phase stator core loss resistance is given by R1c and X1m is per phase stator magnetizing reactance. One significant difference between the transformer and the induction machine is the magnitude of the current in the excitation branch. In induction machines this current is much higher than in transformers and can be up to 50% of the rated input current. Also the leakage reactance of the induction machine is larger than that of the transformer primarily due to the air gap. The equivalent circuit of the rotor contains the rotor winding resistance and rotor leakage    146   reactance connected in series. If we assume the squirrel cage rotor, than the ends are short- circuited. That means (at lease theoretically speaking) we could use the schematics of the short-circuited secondary side of the transformer. As long as the rotor is not moving this is true, however when the rotor is moving, please take into account that the frequency seen by the rotor (which is important for the calculation of reactance etc.) is not equivalent to the primary side but is the relative difference between the rotational frequencies of the start magnetic field and rotor. The equivalent circuit of the rotor is presented in Figure 5.10: Figure  5.10:  Equivalent  circuit  of  the  per-­phase  rotor  winding   As long as the rotor stands still (not moving, s=1), the induced voltage will be depending only on the magnetic field of the stator (like transformer). We can write: V2m = s⋅ V2still s⋅ V2still V2still I2 = =    5.6   R2 + jsω1L2σ R2 + jω1L2σ s         Now, as already done with transformers, we can use the impedance reflection technique, to reflect back all the quantities on the rotor side of the machine to the stator side of the circuit. Using already known € relationships we can write: N ʹ′ ʹ′ ⎛ N1 ⎞ 2 ʹ′ ⎛ N1 ⎞ 2 I = 2 I2 ; 2 R = R2 ⎜ ⎟ ; 2 X 2σ = X 2σ ⎜ ⎟ N1 ⎝ N 2 ⎠ ⎝ N 2 ⎠ Please note that the N2 and N1 in this case represent the effective number of turns1 € Figure  5.11:  Equivalent  circuit  of  the  rotor  reflected  to  the  stator  phase     Note that the power dissipated in the equivalent circuit resistance R2/s (R´2/s) includes both copper losses in the rotor and the developed mechanical power. Therefore we can write following:                                                                                                                 1 Effective number of turns is taking into account not only the number of turns but also taking into account the winding coefficient    147   R2 R2 ⎛ R ⎞ R = + ( R2 − R2 ) = R2 + ⎜ 2 − R2 ⎟ = R2 + 2 (1 − s)   s s ⎝ s ⎠ s In this case R2 represents the copper losses of the rotor and the slip-dependant part the developed mechanical power. The overall€equivalent circuit of the inductance machine is represented in Figure 5.12:   Figure  5.12:  Equivalent  circuit  of  the  inductance  machine  per  phase     The parameters in this equivalent circuit for an induction machine can be determined using specific tests in the motor. No-load test Balanced voltages are applied to the stator terminals at the rated frequency with the rotor uncoupled from any load. Therefore the slip of the induction motor at no-load is very low (s tends to 0). If we take a closer look to the equivalent circuit in Figure 5.12, we can see that the value of the equivalent resistance (representing load) is very high. The no-load rotor current is negligible and the rotor branch of the equivalent circuit can be neglected. However, as the rotor rotates almost synchronously with the magnetic field, some losses due to rotational movement will appear. The no-load rotational losses, which are windage, friction and core losses, will be seen, when no-load test is performed. Blocked Rotor Test This could be understood as a “transformer” test since the rotor is stationary. In order to prevent the rotation, the rotor is blocked and balanced voltages are applied to the stator terminals with only 25% of the rated frequency, with voltage supplied in a way that the rated current is achieved. The speed dependant equivalent resistance in rotor goes to zero and the resistance of the rotor branch is only depending on winding losses in core, and is therefore very small. Thus, the rotor current is much larger that the magnetization current, so that the excitation branch can be neglected. 5.2.2. Power  flow  and  efficiency  of  induction  motor   If the induction machine operate as a motor, than electrical energy from the grid provided to the stator is transformed in mechanical energy (work) provided by rotor. In-between, electrical power was used to create rotating magnetic field, which induces electrical currents in rotor, which are then together with a stator magnetic field causing the rotation of the rotor, which can be used for the mechanical work. Each of these steps will be accompanied by losses (see Figure 5.13).    148   Figure  5.13:  Power  flow  in  induction  motor   In a first step power is “supplied” to the stator. This input, electrical power can be calculated as: Pin = Pel = 3⋅ V1 ⋅ I1 ⋅ cosϕ The power available at the air-gap is smaller: the current flow in stator will result in stator copper losses and also the core losses. Therefore: € Pairgap = Pel − 3⋅ (R1 ⋅ I12 + Pcore ) On the other hand (check Figure 5.11) the rotating field/air-gap power can be expressed as: € R2ʹ′ ʹ′2 Pairgap = 3⋅ ⋅ I2 s As we already discussed, the copper losses of the rotor are represented with a resistance R´2 so that we can write: € Pcopper2 = 3⋅ R2ʹ′ ⋅ I2ʹ′2 = s⋅ Pairgap The mechanical power of the rotor can than be expressed as: € Pmech = Pairgap − Pcopper2 = (1 − s)⋅ Pairgap However, the mechanical losses developed by the rotor, due to rotation of the rotor structure must be subtracted from Pmech in order to obtain the net power Pout delivered to the coupling, € shaft or load. sprocket on the drive Mechanical losses, caused by rotation of the rotor body, are sufficiently significant that their effect must be considered. Rotation of the rotor structure results in the production of friction and windage losses, which equal almost 1% of the output rating of the machine. Such frictional losses are manifest as heat energy, and a power loss must be subtracted from the total power developed by the rotor. Pout = Pmech − Pfriction €    149   5.2.3. Torque  Development   It was already mentioned in chapter “Magnetism” that if a magnetic field and a current- carrying conductor are so positioned, that the field and current direction are mutually perpendicular, than a useful force would be obtained in a direction perpendicular to both. If there is force acting tangentially on the rotor structure than a useful torque will be seen. Torque is and important machine quantity as the machine output torque must be matched with the load torque requirements – torque is a basic application requirement. The torque of the motor can be derived from the power produced by the rotor. The relationship between rotor power and torque include rotor speed: Pmech = ω 2 ⋅ τ = 2πn⋅ τ = 2πn s (1 − s)⋅ τ Pmech (1 − s)⋅ Pairgap Pairgap τ= = = 2πn s (1 − s) 2πn s (1 − s) 2πn s Knowing that the power of the air-gap can be expressed as function of the rotor current and resistance we finally can write: Pairgap 3I2ʹ′2 ⋅ R2ʹ′ € τ= =    5.7   2πn s s⋅ 2πn s             An inspection of equation 5.7 shows that starting torque is proportional to the rotor winding losses at blocked-rotor condition. This fact presents an apparent dilemma in the design of induction machines. €It is obviously necessary to have sufficient starting torque to meet the requirements of the application. On the other hand, it is important to keep the rotor-winding losses, at full-speed operation, as low as reasonably possible, because of efficiency and heating considerations. If an induction motor has been operating at some given load point and the external load is then increased by some increment, the speed of the rotor will decrease and the slip will increase. An increase in slip will cause the voltage induced in the rotor to increase, which will tend to increase the rotor current and with that also the torque developed by the machine. However, an increase in slip will also increase the leakage reactance component of the rotor impedance, which will decrease the rotor current and hence the torque. The net effect of these two opposing interactions is that the torque produced by the machine will increase with increasing external load and increasing slip, until a maximum value of torque is reached, after which the motor becomes unstable as the load and slip are increased further. The point at which this effect starts to occur is called the maximum or breakdown torque of the machine. The starting torque, maximum torque and full-load torque can be calculated by using a value of slip equal to 1, smax and rated. Actually, any value of slip can be used to calculate the corresponding torque. Normally however, speed vs. torque is plotted, and the speed-torque curve is a significant application tool in matching the drive motor to the driven equipment. Common features of interest in the curve (see Figure 5.14) are: - τrated – the rated torque of the machine. This is the design operating point. This torque corresponds to the nominal/rated slip of the machine - τstart – the start torque of the machine, when the machine is at standstill. This means the torque in case the slip equals 1. - τmax, τpo or τbreak – the maximum torque or pull-out torque. Once a machine has reached rated operating point, this is the maximum torque that can be applied without stopping the machine (pulling out). In reality, since this torque is significantly more than the design    150   rated torque, operation at maximum torque is not possible due to thermal heating issues. (Currents will be above rated values and I2R losses will be excessive.) This torque corresponds to the breakdown slip. - τpu – the pull-up torque of the machine. In some machines, the lowest point on the torque speed curve between starting and pullout is not the start torque. In this case it is important to know the pull-up torque. This is the minimum torque that the motor can accelerate up to the desired operating speed. Figure  5.14:  Torque-­Speed  Curve  of  an  induction  machine     In steady state operation, an induction motor will operate at the speed where the mechanical load torque equals the torque developed by the motor. At low speeds, the difference between the motor torque and the load torque accelerates the machine. Normal operation is to the right of the maximum torque. In this region, an increase in the load torque will cause the motor to slow, increasing the motor torque until equilibrium is reached. To the left of the pullout torque, no such equilibrium can be reached. If the slip rings of the wound-rotor machine are shorted (means if no external resistance is inserted into the rotor circuit), the resulting speed-torque characteristic will, in general, resemble that of a squirrel-cage but will typically have less starting torque. However, a wound-rotor motor is not normally operated without external resistance in the rotor-circuit. It is normal practice to have considerable external resistance inserted during acceleration. This is done to reduce the kVA requirements on the stator bus and, at the same time, to develop adequate starting torque. Subsequent to acceleration, the external resistance is set to match the speed and torque requirements of the driven equipment. The speed-torque curve of a wound- rotor motor is illustrated in Figure 5.15. Since the slip at which maximum torque occurs is proportional to the total rotor-circuit resistance, the amount of external rotor resistance    151   inserted into the rotor circuit will affect the speed at which maximum torque occurs. Figure  5.15:  Speed-­torque  curve  of  the  wound-­rotor  machine  [5-3]   From the figure above it can be seen that: - The slip at which maximum torque occurs is proportional to rotor resistance but - The magnitude of the maximum torque is independent of rotor resistance If we only “play” with the rotor resistance and all other parameters remain constant, then increasing the rotor resistance will: - Reduce the speed at which maximum torque occurs - Increase the starting torque - Increase slip for a given torque - Reduce the speed for a given torque and - Increase the rotor losses at a given torque – this can be obtained from the torque equation: if slip increases, losses must increase to maintain the torque. It can be seen from the plots that a high rotor resistance will provide a high starting torque, leading to rapid acceleration of the mechanical system: Rapid acceleration of the mechanical systems means stress reduction on the power system caused by high currents and starting current is significantly above the rated current. Short acceleration times reduce the stress on the power system caused by high currents. While high starting torques are desirable, high rotor resistance results in a relatively high slip during normal running operation. As torque is proportional to rotor joule losses divided by slip, high resistance causes increased losses and reduced efficiency during normal operation. The above points cause a conflict as for most applications it is desirable to have: - High starting torque and - High efficiency at rated speed In order to deal with these conflicting requirements, it is necessary to understand the application requirements and carefully design the motor with variable rotor resistance.    152   5.2.4. Motor  Design  Classes   Since different applications need different characteristics from induction motors, the motors have been specified (for example by NEMA2 Standard Publication MG-1) in different classes with different characteristics. For example, cranes that have to start with full loads imposed may require motors with operating characteristics much different from what is required for pumps and blowers. Motor performance characteristics can be altered by design changes in lamination, winding, rotor, or any combination of these three items. Typical torque speed-curves for classes A-D used by NEMA are sketched below. Figure  5.16:  Torque-­speed  curves  according  to  NEMA  classification  [5-4]   The most of the motors used are class B. The main attributes of the classes are described in Class A Class B Class C Class D Type General Purpose General Purpose High Starting Torque Very High Starting Torque Applications Fans, Blowers, Fans, Blowers, Compressors, pumps, High inertia Pumps, Machine Pumps, Machine conveyors applications, e.g. Tools Tools mechanical punches Notes High starting inrush Replacement for Applications that Very high inertia current causes power Class A due to lower require high start applications. e.g. in a system problems; it start current. The torques. The pull-up punch or reciprocal can cause the supply standard off-the shelf and pull-out torque pump where the slip voltage to sag and commodity motor. can both be lower may vary between 0 requires special than the start torque. and 0.50 Much less starting techniques. Less efficient than efficient than other More efficient than B class B designs Table 5.1: Different motor classes according to NEMA [5-5]                                                                                                                   2 In general terms the standards applying for motors use either IEC/EN (International Electrotechnical Commission, typically used in Europe and Asia) and NEMA (National Electrical Manufacturer Association, typically used in Americas)    153   5.3. Induction  Generators   If the rotor of an induction machine rotates above synchronous speed, slip is negative, as are torque, mechanical output power and air gap power, i.e. the machine is operating as a generator. If slip is negative, the "input power" to the electrical terminals will be negative, implying that power is flowing out of the electrical terminals. Exercise  5.3:     Consider a 480V, 60Hz, 6-pole, three-phase, delta-connected induction motor with the following parameters: R1=0.461 Ω, R2=0.258 Ω, X1=0.507 Ω, X2=0.309 Ω, Xm=30.74 Ω Rotational losses are 2450W. Suppose that the machine is being driven by a mechanical system and rotating at 1224 rpm. Calculate the following information: a) Slip b) Line Current c) Power and Reactive Power at the terminals d) Airgap Power e) Torque Developed f) Mechanical Power g) Efficiency 5.3.1. Basic  principle,  induction  generator One of the real charming issues about the induction machines is that the same induction machine can be used as an induction motor as well as an induction generator (also called asynchronous generator), without any internal modifications. Consider an AC supply (the grid) is connected to the stator terminals of an induction machine. The produced rotating magnetic field pulls the rotor to run behind it (the machine is acting as a motor). Now assume that the rotor is attached to a prime mover and can be accelerated to the synchronous speed (means slip zero and net torque also zero) and beyond it. If the rotor rotates at the speed more than the synchronous speed the slip becomes negative and the rotor current is generated in opposite direction! This generated rotor current produces a rotating magnetic field in the rotor, which pushes onto the stator field – induced stator voltage and current flowing out of the stator winding against the applied voltage. The simplest way to understand is to follow the steps: h) A three-phase set of voltages is applied to the stator i) A three-phase set of stator currents is flowing j) A rotating magnetic field is produced with the speed n0 =f /p k) This rotating magnetic field passes over the rotor bars and induces a voltage in them l) The rotor current flow produces a rotor magnetic field m) The induced torque in the machine is given by τ~BRx BS n) The rotor of the induction machine will be accelerated by the prime mover to n > n0 o) The rotor magnetic field induces three-phase set of voltages in the stator    154   If carefully analyzing the steps you will discover that induction generator is not a self-excited machine. Therefore, when running as a generator, the machine takes reactive power from the AC power line, and supplies active power back into the line. In order to operate – that means for producing rotating magnetic field, reactive power is needed. The active power supplied back in the line is proportional to slip above the synchronous speed. 5.3.2. Self-­excited  induction  generator   It is clear that, an induction machine needs reactive power for excitation (magnetization current), regardless whether it is operating as a generator or a motor. When an induction generator is connected to a grid, it takes reactive power from the grid. But if we want to use an induction generator to supply a load without any grid connection (off-grid or island power supply systems) we need a “source” of reactive power. One option is to use a capacitor bank connected across the stator terminals to supply reactive power to the machine as well as to the load. Figure  5.17:  Self-­excitation  with  capacitor  bank     When the prime mover starts to turn and achieves a certain speed, the residual magnetism in its field circuit (in rotor) induces a small voltage in the stator. That means that self-excitation is initiated by the residual flux in the induction generator rotor iron. When the generator is accelerated to a certain speed, the residual flux will induce a voltage in the stator. If capacitors are connected at the generator terminals, the induced stator voltage will cause the flow of a current into the capacitors. Depending on the generator parameters, the value of the capacitors and the generator speed, a transition from the synchronous operating mode to the asynchronous operating mode may take place at some point leading to the self-excitation of the induction generator. Saturation dependent machine reactance and external capacitors form a resonating circuit, which is able to oscillate at driven rotor if it is excited by remanent magnetization. Once the self-excitation process has started, the induction generator voltage builds up. The voltage build up can be understood by considering the Figure 5.18. The induced stator voltage causes a capacitor current that generates a flux into the generator with the same direction as the residual flux. Therefore, the current circulating in the stator reinforces the residual flux. This in turn causes a higher induced stator voltage leading to a successive increase in current and flux. This voltage build up process comes to a halt when the capacitor voltage curve intersects the no-load curve of the induction generator. This point is a stable operating point and it is the steady-state operating point of the self-excited induction generator running at no-    155   load with the shunt-connected capacitors. At this point, the capacitors supply exactly the reactive power needed by the induction generator at no-load. The no-load steady-state operating point is determined by the no-load curve of the induction generator, by the value of the capacitors and by the generator speed. Increasing the value of the capacitors has the effect of shifting the no-load steady-state point towards higher voltages. Increasing the generator speed, i.e. the frequency of the induced voltage, shifts the no-load curve of the generator upwards, while the slope of the capacitor voltage curve decreases. The net result is still an increase in the no-load steady-state voltage. Figure  5.18:  Voltage  build-­up  of  self-­exited  induction  generator     Besides „starting“ the operation it is important to know how the machine operates under load. For example a sudden connection of a resistance close to the generator base impedance results in the demagnetization of the generator and a subsequent very low residual flux in the rotor iron. Figure 5.19 shows that if the machine is loaded with current I1, the amount of required reactive current increases by about ΔI1R. Since the capacitor is not able to provide more reactive current, voltage drops to U1.     Figure  5.19:  Stability  of  the  self-­exited  induction  generator       5.3.3. Doubly-­fed  induction  generator   Doubly-fed electric machines are basically electric machines that are fed AC-currents into both the stator and the rotor windings. Most doubly-fed electric machines in industry today are three-phase wound-rotor induction machines. Although their principles of operation have been known for decades, doubly-fed electric machines have only recently entered into    156   common use. The DFIG is an induction generator with a wound rotor where the rotor and stator are both connected to electrical sources, hence the term ‘doubly-fed’. The rotor has three phase windings, which are energized with three-phase currents. These rotor currents establish the rotor magnetic field. The magnetic field created in the rotor is not static (as it is created using three-phase AC-current instead of DC-Current) it rather rotates at a speed n ,rotor proportional Φ to the frequency of the AC-Current fed into the generator rotor windings. This means that the rotating magnetic field passing through the generator stator windings not only rotates due to the rotation of the generator rotor, but also due to the rotational effect produced by the AC- current fed into the generator rotor windings. Therefore, in a doubly-fed induction generator, both the rotations speed nrotor of the rotor an the frequency frotor of the AC-currents fed into the rotor windings determine the speed n ,stator of the rotating magnetic field passing through the Φ stator winding, and thus the frequency fstator of the alternating voltage induced across the stator windings. If the magnetic field at the rotor rotates in the same direction as the rotor the frequency at stator is calculated as: n rotor ⋅ P f stator = + f rotor    5.8   60           Conversely, when the magnetic field at the rotor rotates in the direction opposite to the rotor movement, the rotor speed and the speed of the rotor magnetic field subtract from each other: € n rotor ⋅ P f stator = − f rotor 60 In other words, the frequency fstator of a doubly-fed induction generator is proportional to the speed of the resulting rotating magnetic field at the stator, which itself depend on the rotor speed – resulting from the mechanical power at the rotor shaft and the frequency of the AC- € Currents fed into the generators rotor. This is very important feature of the DFIG: Generally the DFIG is used to produce three- phase voltage whose frequency fstator is constant i.e. whose frequency is equal to fgrid of the ac- grid to which the generator is connected, despite variations in the generator rotor speed nrotor caused by fluctuations of the mechanical power provided by the prime mover (e.g. a wind turbine) driving the generator. To achieve this purpose, the frequency frotor of the AC-currents fed into the rotor winding of the DFIG must be continually adjusted to counteract any variation in the rotor speed nrotor caused by fluctuating mechanical power of the prime mover. The frequency frotor of the AC-Current applied to the rotor winding to maintain the generators output frequency (fstator or fgrid) depends on the rotation speed of the rotor nrotor and can be calculated using the following equation: n rotor ⋅ P f rotor = f grid − 60 Exercise  5.4:   Consider a DFIG having 8 magnetic poles. The generator supplies power to a 50Hz AC power grid. The prime mover rotates € at the speed of 900rpm. Calculate the frequency of the AC- currents supplied to the rotor so that the generator is synchronized with the grid. Also, determine the direction of the rotation of the rotating magnetic field created by the AC- currents fed into rotor windings.    157   Exercise  5.5:   Consider a DFIG having 4 magnetic poles. The generator supplies power to a 60Hz AC power grid. The prime mover rotates at the speed of 1530rpm. Calculate the frequency of the AC- currents supplied to the rotor so that the generator is synchronized with the grid. Also, determine the direction of the rotation of the rotating magnetic field created by the AC- currents fed into rotor windings. The DFIG system has to control the magnitude, frequency and phase of the applied rotor current. Most DFIG systems utilize closed-loop current control using a voltage-source inverter (VSI). At this stage, the voltage source inverter can be viewed as a three-phase voltage source whose magnitude and phase can be altered instantaneously and can be used to regulate the rotor current. In order to properly position the rotor current knowledge of the physical position of the rotor is required using a mechanical position sensor, for example. Figure  5.20:  Doubly-­fed  induction  generator  [5-6]   As indicated in the figure above the AC-DC-AC converter used on the rotor, which consists of two voltage-sourced converters, i.e., rotor-side converter and grid-side converter (GSC), which are connected “back-to-back.” Between the two converters a dc-link capacitor is placed, as energy storage, in order to keep the voltage variations (or ripple) in the dc-link voltage small. With the rotor-side converter it is possible to control the torque or the speed of the DFIG and also the power factor at the stator terminals, while the main objective for the grid-side converter is to keep the dc-link voltage constant regardless of the magnitude and direction of the rotor power. The grid-side converter works at the grid frequency (leading or lagging in order to generate or absorb a controllable magnitude of reactive power). The rotor- side converter works at different frequencies, depending on the wind speed.    158   Induction generation used to be relatively rare. However, it is becoming increasingly common, as induction generators are the generator of choice for large wind turbines. The requirement of an induction generator to have an independent reactive power supply has caused significant research into the impact of large wind farms of power system stability. DFIGs have a number of advantages over other types of generators when used in wind turbines. The primary advantage of DFIGs when used in wind turbines is that they allow the amplitude and frequency of their output voltages to me maintained at a constant value, no matter the speed of the wind blowing on the wind turbine rotor. Because of this, DFIGs can be directly connected to the ac power network ad remain synchronized at all times with the ac power gird. Their advantages include the ability to control the power factor (e.g. to maintain the power factor at unity), while keeping the power electronics in the wind turbine at a moderate size. The doubly-fed induction generator may also operate as a stand-alone generator. Such an operation is preferred for low reactive power requirements at low negative slips. Constant frequency, constant voltage output in the stator with autonomous load does not seem to be advantageous when the speed varies by more than +- 5%.    159   5.4. Single-­phase  motors   A lot of common loads in a household are actually using electric motors in order to provide needed energy form (for example electric motor is used to provide mechanical power for the compressor in refrigerator etc.). Most of those loads are however not connected to the three- phase power supply but use a common, single-phase electrical socket. These motors are commonly fractional-kW types, though integral sizes are generally available to several kW. But, if only single-phase is available, how can we create a rotating (changing) magnetic field. Exercise  5.6: Assume following arrangement: How would the magnetic field of such an arrangement look like? The most common single-phase motor types are: - Shaded pole motors - they have a continuous copper loop wound around a small portion of each pole (see Figure 5.21). This loop causes the magnetic field through the ringed portion to lag behind the field in the unringed portion. This produces a slightly rotating field in each pole face, sufficient to turn the rotor. Shaded pole motors have low starting torque and are available only in fractional and sub-fractional horsepower sizes. Slip is about 10%, or more at rated load. - Split phase motor – they have an auxiliary (starting) winding, which is displaced 90 electrical degrees from the main (running) winding. The main (running) winding has many turns of large diameter wire wound in the bottom of the stator slots to get high reactance. Therefore, the current in the auxiliary winding leads the current in the main winding, causing a rotating field. During startup, both windings are connected to the line. As the motor comes up to speed (at about 25% of full-load speed), a centrifugal switch actuated by the rotor, or an electronic switch, disconnects the auxiliary winding. Split phase motors are considered low or moderate starting torque motors and are limited to about 200 W. - Capacitor-start motor – they also have an auxiliary (starting) winding similar to split phase motors (see Figure 5.22). The main difference is that a capacitor is placed in series with the auxiliary winding. This type of motor produces greater locked rotor and accelerating torque than the split phase motor. Sizes range from fractional to 5 kW. - Permanent split-capacitor motors (capacitor start capacitor run CSCR) - they also have an auxiliary winding with a capacitor, but they remain continuously energized and aid in    160   producing a higher power factor than other capacitor designs. This makes them well suited to variable speed applications. Figure  5.21:  Shaded  pole  and  split  phase  induction  motor       Figure  5.22:  Capacitor  start  and  permanent  split  capacitor  single-­phase  machine      161   5.5. Synchronous  machines   Synchronous machines or rather synchronous generators are the “workhorse” of the power generation arena. A machine is classified as a synchronous machine if its operating speed is directly proportional to the frequency of the electrical system. The speed of operation for a synchronous machine is thus designated as synchronous speed. The geometry of a synchronous machine is quite similar to that of the induction machine. The stator core and windings of a three-phase synchronous machine are practically identical to that of a three-phase induction machine. In both cases (induction or synchronous machine) the function of the stator is to provide a rotating magnetic force to the rotor. The main constructional difference between induction and synchronous machine is the rotor. Synchronous machine use an electromagnet/permanent magnet rotor. On smaller synchronous motors, the permanent rare-earth magnets are glued onto the rotor. An electromagnet with north and south poles is established when DC voltage is applied to the rotor. Thus, the synchronous machine requires, if designed as electromagnet one, a DC excitation of the rotor (field) windings. The resultant magnetic field is static (non-rotational). When the stator windings are energized, a rotating magnetic field is established. The permanent magnet rotor has its own magnetic field that interacts with the rotating magnetic field of the stator. The north pole of the rotating magnetic field attracts the south pole of the permanent magnet rotor. As the rotating magnetic field rotates, it pulls the permanent magnet rotor, causing it to rotate. In other words, the magnetic fields of the stator and the rotor tend to align themselves. Therefore, under steady state conditions given a constant frequency AC source, the machine speed (n) of a synchronous machine is equal to the synchronous speed (ns) defined by: f ns = 5.9 P where f is the frequency of the AC signal at the stator, and P is the number of poles in the synchronous machine. € Thus, the fundamental difference between a synchronous machine and an induction machine is that the rotor currents of the induction machine are induced while those of the synchronous machine are not. There are fundamentally two types of rotors used in synchronous machines: salient pole rotors and cylindrical (or non-salient pole) rotors. These rotors are each well suited for different applications based on their physical characteristics. - Salient pole rotor - the individual rotor poles protrude from the center of the rotor, characterized by concentrated windings, non-uniform air gap, larger rotor diameters, used in applications requiring low machine speed and a large number of machine poles (example - hydroelectric generation, diesel gensets). The salient pole rotor does not provide the mechanical strength necessary for the high-speed applications and presents too much wind resistance when rotating at high speeds.    162   - Cylindrical rotor - the individual rotor poles are produced using a slotted cylindrical rotor, characterized by distributed windings, nearly-uniform air gap, smaller rotor diameters, used in applications requiring high machine speed and a small number of machine poles, typically 2 or 4 poles (example - steam or gas turbine generators). The cylindrical rotor is typically a solid piece of steel for reasons of strength given the high rotational speeds to which the rotor is subjected.   Figure  5.23:  Synchronous  Machine  Rotor  Types  [5-7],  [5-8]     Typically, synchronous machines will use DC-Current for the exiting circuit. However, in the last decade the development in the field of permanent magnets comprising rare-earth elements (e.g. neodymium -iron-boron) including both the quality of the material (chemical, temperature stability), increasing of (BH)max product (by more than factor 2) and reduction in price (factor of ten!) will probably increase the popularity of this solution. The DC current required for the rotor is typically provided by an external DC source (commonly referred to as an exciter) that is connected to the rotor windings by means of conducting rings (slip rings) that are mounted concentrically on the machine shaft (the slip rings are electrically insulated from the shaft). The stationary contact required to connect the DC source with these slip rings is achieved by means of carbon brushes that make physical contact with the slip rings as they rotate. The carbon brushes make good electrical contact with low friction. The DC rotor current can also be provided by a rectifying source (AC/DC- converter) mounted directly to the machine shaft. This type of configuration is known as brushless excitation. Both of those options need an external power source to make the    163   generator work. One option to avoid the need for external power and to enable completely independent system is to use a pilot exciter. It consists of a small AC generator with permanent magnets mounted on the rotor shaft and a three-phase winding on the stator. The pilot exciter produces the power required by the field circuit of the exciter that is used to control the field circuit of the main generator. When a pilot exciter is used, the generator can operate without any external electric power. Figure  5.24:  Excitation  with  brushes  and  brushless  configuration 5.5.1. Basic  operation   The synchronous machine can be operated as a motor or a generator, but the most common application of the synchronous machine is in the power industry as a three-phase generator. The synchronous generator is also sometimes referred to as an alternator. In a synchronous generator, the magnetic field created by the DC current in the rotor is static in nature (magnetostatic field). However, if the rotor is set in motion by some external force (wind, water, turbine, etc.), the rotating magnetic field produced by the synchronous generator rotor looks like the rotational field produced by the AC current in the stator of the induction motor. This rotating field changes the magnetic flux with time through the stator windings, inducing voltage in the stator terminals according to Faraday’s law. The frequency f of the voltage produced at the stator windings is directly related to the mechanical speed of the rotor rotation. The magnitude of the voltage induced voltage in the given stator (armature) phase can be written as: E A = KΦω                 5.10 where K represents the constant depending on the generator construction, Φ the flux in the machine and ω the speed € of rotation. The flux in the machine will depend on the field current and also the induced voltage. The dependency between the flux and the field current is represented by the magnetization curve and this means that in case of open circuit conditions, the curve showing dependency between induced voltage and field current looks quite similar.      164   Figure  5.25:  Synchronous  generator:  (a)  Plot  of  flux  versus  field  current,  (b)  Induced  voltage  (open   circuit  versus  field  current  [5-9]   The voltage that appears on the terminal of the generator however, differs from the variable, internal generated voltage induced in one phase of a synchronous generator. The main factors influencing it are: - The armature reaction – the current flowing in the stator (armature) creates magnetic flux and thus the distortion of the air-gap magnetic field - The self-inductance of the armature (stator) windings - The resistance of the armature windings The armature reaction has the largest impact on the difference between the induced voltage EA and the terminal voltage V. The three-phase current flowing in the stator will produce its own magnetic field in the machine, which tends to distort the magnetic field created by the rotor resulting in a change of the phase voltage. This effect is known as the armature reaction because the current in the armature (stator) affects the magnetic field that produced it in the first place. The current in the armature (and also the effect on the terminal voltage) is however depending on the load connected to the generator. If we neglect in a first moment the self- inductance and resistance of the armature windings, than the terminal voltage will correspond to the voltage induced by the total magnetic flux, which is a superposition of the fluxes due to the rotor current (field current) and stator current (armature reaction). The very simple equivalent circle of this circumstance is shown in Figure 5.26. Figure  5.26:  Simple  equivalent  circuit  for  armature  reaction   This means that if the terminal voltage must correspond to the grid voltage, the speed of the rotor must correspond to the grid frequency and we have to supply different loads (size and    165   type – capacitive, inductive etc.) the induced voltage in stator must be adapted. This means that the field current of the machine must be controlled. Figure 5.27 illustrates the influence on the induced voltage (and thus field current) as well as on angle between terminal voltage and induced voltage δ, known as the power angle or torque angle. Figure  5.27:  The  phasor  diagram  of  a  synchronous  generator  at  unity  (a),  lagging  (b)  and  leading   (c)  power  factor  neglecting  self-­inductance  and  resistance  of  the  stator  windings.       Exercise  5.7:   Show the effect of an increase in generator loads at constant-power factor upon induced voltage and power angle if the terminal voltage is constant for (a) Lagging power factor; (b) unity power factor; (c) leading power factor. If we now remember that not only the armature reaction but also the self-inductance and resistance of the armature (stator) windings have influence on the terminal voltage of the synchronous machine, than we can use for the calculation the following equivalent circuit: Figure  5.28:  Equivalent  circuit  per  phase  of  the  synchronous  machine     Exercise  5.8:   Draw phasor diagrams of a synchronous generator at unity (a), lagging (b) and leading (c) power factor according to the equivalent circuit indicated in Figure 5.9. Quite similar to the other machines, also with the synchronous machines typically two tests – open-circuit and short circuit tests are performed to determine the important machine’s properties.    166   Open circuit test With the stator windings open-circuited, the synchronous machine is driven at synchronous speed while the field current If is varied. In this case there is no influence according to the load current (no armature reaction) and the open-circuit voltage V voltage across the stator windings will correspond to the induced voltage. This test provides data for a plot of V vs. If, that is known as the open-circuit characteristic (OCC) and represents the variation of the generator voltage with respect to the field current. Typically OCC  will be nonlinear due to the saturation of the magnetic core at higher levels of field current. Short circuit test With the stator input terminals short-circuited (the stator windings connected in parallel), the synchronous machine is driven at synchronous speed while the field current If is varied. The current I1 in each of the three (stator) windings is measured and an average value is determined. This test provides data for a plot of I1 vs. If, that is known as the short-circuit characteristic (SCC) and represents the variation of the armature (stator) current with respect to the field current. The SCC shows unlike the OCC linearity since the magnetic core does not saturate under short-circuit conditions. 5.5.1. Power  flow  and  efficiency  of  synchronous  machine   A synchronous generator is a machine that converts mechanical power to three-phase electrical power. A turbine usually gives the mechanical power. Figure 5.29 shows the power flow in the synchronous generator. Please remember, that in order to stay connected to the grid, the rotational speed n must remain constant to maintain a steady frequency f. Figure  5.29:  Power  flow  in  a  synchronous  generator     The input power of a synchronous generator is the mechanical power provided by the prime driver: Pin = Pmech = 2πn⋅ τ           5.11   The output power of the generator is given by: Pout = Pel = 3V1I1 cosϕ €           5.12             If we ignore armature resistance, than the output power Pel equals Pairgap. €    167   Figure  5.30:  Phasor  diagram  of  the  synchronous  generator  (ignoring  stator  resistance)   If we check the Figure 5.30 than we can see that the current can be expressed by induced voltage and the power angle so we can write: E A sin δ X sI1 cosϕ = E A sin δ ⇒ I1 cosϕ = Xs 3V1 E A sin δ       5.13   Pel = Xs The output power equation shows that the power produced depends on the angle (Power angle or torque angle) between V and EA. € On the other hand, the airgap power in the machine will be the result of the induced torque in the generator and can be expressed as: 3V1 E A sin δ Pairgap = 2πn⋅ τ ind = Xs       5.14   Therefore the induced torque in terms of electrical quantities can be written as 3V E sin δ € τ ind = 1 A = τ max sin δ 2πn⋅ X s         5.15   Figure 5.31 shows the dependance between the torque and the power or torque angle. € Figure  5.31:  Torque  and  torque/power  angle  diagram      168   5.5.2. Stand  alone  operation  of  the  synchronous  generator     When a synchronous generator is operating under load, its behavior varies greatly depending on the power factor of the load and also if the generator is operating alone or in parallel with other synchronous generators. Figure  5.32:  Stand-­alone  operating  synchronous  generator   What would be the effect of the load change if the synchronous generator were operating alone? If the load increases – the generator current output must increase. Since the prime mover governing system maintains the mechanical speed constant, the magnitude of the internal generator voltage is constant and the flux will also remain constant as the filed resistor did not change and that means the field current is constant. So if the induced voltage EA is constant, which parameter is varying with the changing load? Figure  5.33:  Terminal  voltage  depending  on  load   If the generator is operating at a lagging power factor and an additional load is added at the same power factor, then the magnitude of I1 increases, but angle between I1 and V1 remains constant. The armature reaction voltage has increased due to increased current and this means that the voltage will decrease. Exercise  5.9:   Draw a phasor diagram of the stand-alone operating synchronous generator at unity power factor if the load doubles. During normal operation, it is desirable to maintain constant the voltage that is supplied to the load even when the load varies. The terminal voltage variations can be corrected by varying the magnitude of the induced voltage EA to compensate for changes in the load. Since we cannot change the constructional properties or the rotational speed, we can only control the induced voltage by varying the flux in the generator. For example, when a lagging load is added to the generator, the terminal voltage will fall. In this case, the field resistor RF is decreased to increase the field current IF and thus restore the terminal voltage to its previous level.    169     Figure  5.34:  Voltage  control  trough  adaptation  of  field  current     If the armature current is plotted versus field current for several power levels, the regulating plots are the so-called V-curves shown in Figure 5.34. Typically, the synchronous machine V- curves are provided by the manufacturer so that the user can determine the resulting operation under a given set of conditions. 5.5.3. Parallel  operation  of  synchronous  generators   In most generator applications, there is more than one generator operating in parallel to supply power to various loads – this is how typically the power grid works. Some of the advantages for operating generators in parallel are: - The liability of the power system increases when many generators are operating in parallel, because the failure of any one of them does not cause a total power loss to the loads. - When many generators operate in parallel, one or more of them can be taken out when failures occur in power plants or for preventive maintenance. - If one generator is used, it cannot operate near full load (because the loads are changing), and then it will be inefficient. When several machines are operating in parallel, it is possible to operate only a fraction of them. The ones that are operating will be more efficient because they are near full load. Ensuring that each of the three phases has the same voltage magnitude and phase angle as the conductor to which it is connected is prerequisite for the smooth parallel operation. To ensure this match, these four paralleling conditions must be met: - The two generators must have the same line voltages – the terminal voltage of the oncoming generator should be adjusted by changing the field current until it is equal to the line voltage of the running system - The phase sequence must be the same in the two generators – can be checked with phase sequence indicators - The two a phases must have the same phase angles.    170   - The frequency of both generators after connection must be the same – typically before connecting the frequency of the oncoming generator should be slightly higher than the frequency of the running system, so it will come on-line supplying power as a generator, instead of consuming it as a motor. 5.5.4. Synchronous  motor   Synchronous motor construction, design and analysis is very similar to that used for synchronous generators. Insight into principles of motor operation can be found by considering that the torque in the machine is produced by two magnetic fields – rotor and stator field. In a generator torque opposes motion, so the rotor flux density must lead the stator flux density. In a motor, the torque is in the same direction as motion, therefore the rotor flux density must lag the stator flux density. As in a synchronous generator, induced voltage EA is in phase with rotor flux density and terminal voltage V1 in phase with resulting field. This means that in generator operating mode as the torotr filed leads the stator field also induced voltage EA leads stator voltage V1. In motor operation as the stator field pulls the rotor field, the induced voltage EA lags stator voltage V1. The simplest way to understand the operation of the synchronous motor is to follow the steps: a) A three-phase set of voltages is applied to the stator b) A three-phase set of stator currents is flowing c) A rotating magnetic field is produced with the speed n0 =f /P d) Rotor DC-Current is applied to the rotor winding e) The rotor current flow produces a rotor magnetic field, which is NOT moving f) There is a reaction/attraction between the rotating field from the stator side and “stationary” field from the rotor side: actually the rotor north pole would be attracted by the south pole of the stator which rotates and would like to follow it. But if the rotor has got no initial rotation and since the rotor has got some inertia, the starting moving speed will be very low. By this time South Pole of rotating magnetic field will be replaced by a north pole. So it will give repulsive force. This will make the rotor move backward. As a net effect the rotor won’t be able to start. So basically, the synchronous motors are not self-starting. In order to overcome the “inertia”-problem, the synchronous motor can be mechanically powered from another motor, so that the DC-exitation is applied, when rotor is almost on synchronous speed. Another way of starting the synchronous motor is the use of damper winding, which mainly follows the principle of the induction motor – in this case also in damper winding the voltage will be induced and the required starting torque will result from it. As speed of the rotor increases, the induced voltae and torque from the damper winding will reduce and finally be zero at synchronous speed. g) The rotor of the synchronous generator is at n =n0 h) The induced torque in the machine is given by τ~BSx BR i) The power output (mechanical power) depends on this torque and thus on induced voltage EA, grid-voltage and the power angle. In some cases no load is connected to the shaft of the synchronous motor. They are used for the power factor improvement as they can work at any electrical power factor. In some cases, such as pumped storage hydro schemes, the synchrone machines can be    171   operated as both motors and generators. Figure 5.35 shows the different operating modes of the synchrone machine: motor and generator, over or under exited. Figure  5.35:  Operating  modes  of  the  synchronous  machine    172     5.5.5. Power  Limits  of  the  synchronous  machine   For the operation of a synchronous machine there are three basic types limiting the power of it: - Thermal limit - the maximum temperature rise is defined and therefore the maximum power loss in different parts of the machine. For example in rotor the major cause of losses is the field winding resistive loss. If the field current is above a certain level, the I2R losses will be high, and eventually causing insulation failure in the field winding. In order to manage thermal conditions, field current is limited which means that the induced excitation in the armature winding will also be limited. The rotor heating limit sets EAmax. The same applies on the stator side: very high armature currents will cause the stator temperature to rise beyond a safe level. The stator heating limit sets IAmax. In steady state, this limit is the rated current of the machine. - Mechanical and electromagnetic limit - the input power to the generator is limited by the physical capacity of the prime mover. As a result, the prime mover limit sets the maximum output power from the generator, Pmax≈Emaxsinδmax. If the generator is operating with δ close to 90° when the rotor speeds up, δ increases past 90° (as a reaction of the relationship between mechainical and electromagnetic torque), the electromagnetic torque falls (as the sinus or the angle becomes smaller) and positive feedback occurs, causing the rotor to accelerate further, pull out of synchronism and result in zero output power and possibly catastrophic failure. The static stability limit is set at δ=90°. Especially regarding the thermal limits, it is necessary to provide suitable ventilation and cooling for the machines so that the temperature rise at any part of the machine does not go beyond the permissible limit depending on the type of insulation used in the construction. Electrical machines are also classified depending on the type of ventilation and cooling system used for the machines. The cooling of electrical machines by means of an air-stream is called ventilation. The circulation of the air in the machine can be arranged by the use of a built in fan or fan with separate drive. Machines with an open-circuit are those in which heat is given up directly to the cooling air; the air is being replaced continuously. In self-ventilated the internal surface is cooled by a built-in fan.      173   Short check at the end of the chapter: 5-1 How can the rotating magnetic field be created? 5-2 What is a basic principle behind the induction machines? 5-3 Is it possible to use an induction motor as a generator? How can this be done? Is any additional equipment needed? 5-4 What are the main advantages of using doubly-fed induction generators instead of asynchronous generators in wind turbines? 5-5 What is a basic principle behind the synchronous machines? 5-6 Compare both type of machines and name their advantages and disadvantages!    174     Bibliography Chapter 5: [5-1] Klaus Fuest: Elektrische Maschinen und Antriebe, Vieweg Verlag, 3. Auflage 1989 [5-2] www.valco.eu [5-3] Paul Cochran: Polyphase Induction Motors, Analysis: Design, and Application, Marcel Dekker Inc, 1989 [5-4] www.ecmweb.com [5-5] http://people.ucalgary.ca/~aknigh/electrical_machines/machines_main.html [5-6] Festo Didactic 86376-10: Electricity and New Energy, Principles of Doubly-Fed Induction Generators (DFIG), Courseware Sample [5-7] http://www.gepowerconversion.com [5-8] www.abb.com/motors&generators [5-9] Philip Kiameh: Power generation handbook, McGraw-Hill 2002