Synchronous Machines Synchronous Generators Construction of synchronous machines In a synchronous generator, a DC current is applied to the rotor winding producing a rotor magnetic field. The rotor is then turned by external means producing a rotating magnetic field, which induces a 3-phase voltage within the stator winding. • Field windings are the windings producing the main magnetic field (rotor windings) • armature windings are the windings where the main voltage is induced (stator windings) Construction of synchronous machines Construction of synchronous machines The rotor of a synchronous machine is a large electromagnet. The magnetic poles can be either salient (sticking out of rotor surface) or nonsalient construction. Non-salient-pole rotor: usually two- and four-pole rotors. Salient-pole rotor: four and more poles. Rotors are made laminated to reduce eddy current losses. Construction of synchronous machines Two common approaches are used to supply a DC current to the field circuits on the rotating rotor: 1. Supply the DC power from an external DC source to the rotor by means of slip rings and brushes; 2. Supply the DC power from a special DC power source mounted directly on the shaft of the machine. Slip rings are metal rings completely encircling the shaft of a machine but insulated from it. Graphite-like carbon brushes connected to DC terminals ride on each slip ring supplying DC voltage to field windings. Construction of synchronous machines On large generators and motors, brushless exciters are used. A brushless exciter is a small AC generator whose field circuits are mounted on the stator and armature circuits are mounted on the rotor shaft. The exciter generator’s 3-phase output is rectified to DC by a 3phase rectifier (mounted on the shaft) and fed into the main DC field circuit. It is possible to adjust the field current on the main machine by controlling the small DC field current of the exciter generator (located on the stator). Construction of synchronous machines A brushless exciter: a low 3-phase current is rectified and used to supply the field circuit of the exciter (located on the stator). The output of the exciter’s armature circuit (on the rotor) is rectified and used as the field current of the main machine. Construction of synchronous machines To make the excitation of a generator completely independent of any external power source, a small pilot exciter is often added to the circuit. The pilot exciter is an AC generator with a permanent magnet mounted on the rotor shaft and a 3-phase winding on the stator producing the power for the field circuit of the exciter. Construction of synchronous machines A rotor of large synchronous machine with a brushless exciter mounted on the same shaft. Construction of synchronous machines Exciter Salient poles. Rotation speed of synchronous generator By the definition, synchronous generators produce electricity whose frequency is synchronized with the mechanical rotational speed. p fe = nm 120 Where fe is the electrical frequency, Hz; nm is the rotor speed of the machine, rpm; p is the number of poles. • Steam turbines are most efficient when rotating at high speed; therefore, to generate 60 Hz, they are usually rotating at 3600 rpm (2-pole). • Water turbines are most efficient when rotating at low speeds (200-300 rpm); therefore, they usually turn generators with many poles. The induced voltage in a 3-phase set of coils In three coils, each of NC turns, placed around the rotor magnetic field, the induced in each coil will have the same magnitude and phases differing by 1200: eaa ' (t ) = NCm cos mt ebb ' (t ) = NCm cos (mt −120 ) ecc ' (t) = NCm cos (mt − 240 ) Peak voltage: Emax = NCm RMS voltage: Emax = 2 NC f Internal generated voltage of a synchronous generator The magnitude of internal generated voltage induced in a given stator is where K is a constant representing the construction of the machine, is flux in it and is its rotation speed. Since flux in the machine depends on the field current through it, the internal generated voltage is a function of the rotor field current. Magnetization curve (open-circuit characteristic) of a synchronous machine Equivalent circuit of a synchronous generator The internally generated voltage in a single phase of a synchronous machine EA is not usually the voltage appearing at its terminals. It equals to the output voltage V only when there is no armature current in the machine. The reasons that the armature voltage EA is not equal to the output voltage V are: 1. Distortion of the air-gap magnetic field caused by the current flowing in the stator (armature reaction); 2. Self-inductance of the armature coils; 3. Resistance of the armature coils; Equivalent circuit of a synchronous generator Armature reaction: • When the rotor of a synchronous generator is spinning, a voltage EA is induced in its stator. • When a load is connected, a current starts flowing creating a magnetic field in machine’s stator. • This stator magnetic field BS adds to the rotor (main) magnetic field BR affecting the total magnetic field and, therefore, the phase voltage. Lagging load Equivalent circuit of a synchronous generator The load current IA will create a stator magnetic field BS, which will produce the armature reaction voltage Estat. Therefore, the phase voltage will be V = EA + Estat The net magnetic flux will be Bnet = BR + BS Rotor field Stator field Equivalent circuit of a synchronous generator Since the armature reaction voltage lags the current by 90 degrees, it can be modeled by Estat = − jXI A The phase voltage is then V = EA − jXI A However, in addition to armature reactance effect, the stator coil has a self-inductance LA (XA is the corresponding reactance) and the stator has resistance RA. The phase voltage is thus V = EA − jXI A − jX A I A − RI A Equivalent circuit of a synchronous generator Often, armature reactance and selfinductance are combined into the synchronous reactance of the machine XS = X + XA Therefore, the phase voltage is V = EA − jX S I A − RI A The equivalent circuit of a 3-phase synchronous generator is shown. The adjustable resistor Radj controls the field current and, therefore, the rotor magnetic field. Equivalent circuit of a synchronous generator A synchronous generator can be Y- or -connected: The terminal voltage will be Equivalent circuit of a synchronous generator Since – for balanced loads – the three phases of a synchronous generator are identical except for phase angles, per-phase equivalent circuits are often used. 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 phasor diagram. A phasor diagram of a synchronous generator with a unity power factor (resistive load) Lagging power factor (inductive load): a larger than for leading PF internal generated voltage EA is needed to form the same phase voltage. Leading power factor (capacitive load). Measuring parameters of synchronous generator model The three quantities must be determined in order to describe the generator model: 1. The relationship between field current and flux (and therefore between the field current IF and the internal generated voltage EA); 2. The synchronous reactance; 3. The armature resistance. Open circuit Test The generator is rotated at the rated speed, • all the terminals are disconnected from loads, • the field current is set to zero first. • Next, the field current is increased in steps and the phase voltage (whish is equal to the internal generated voltage EA since the armature current is zero) is measured. Since the unsaturated core of the machine has a reluctance thousands times lower than the reluctance of the air-gap, the resulting flux increases linearly first. When the saturation is reached, the core reluctance greatly increases causing the flux to increase much slower with the increase of the mmf. Short Circuit Test In here, • the generator is rotated at the rated speed, with the field current is set to zero first, and all the terminals are shortcircuited through ammeters. • Next, the field current is increased in steps and the armature current IA is measured as the field current is increased. The plot of armature current (or line current) vs. the field current is the short-circuit characteristic (SCC) of the generator. Short Circuit Test The SCC is a straight line since, for the short-circuited terminals, the magnitude of the armature current is The equivalent generator’s circuit during SC The resulting phasor diagram Short circuit test An approximate method to determine the synchronous reactance XS at a given field current: 1. Get the internal generated voltage EA from the OCC at that field current. 2. Get the short-circuit current IA,SC at that field current from the SCC. 3. Find XS from Since the internal machine impedance is >> OCC and SCC A drawback of this method is that the internal generated voltage EA is measured during the OCC, where the machine can be saturated for large field currents, while the armature current is measured in SCC, where the core is unsaturated. Therefore, this approach is accurate for unsaturated cores only. The approximate value of synchronous reactance varies with the degree of saturation of the OCC. Therefore, the value of the synchronous reactance for a given problem should be estimated at the approximate load of the machine. The winding’s resistance can be approximated by applying a DC voltage to a stationary machine’s winding and measuring the current. However, AC resistance is slightly larger than DC resistance (skin effect). Example Example 7.1: A 200 kVA, 480 V, 50 Hz, Y-connected synchronous generator with a rated field current of 5 A was tested and the following data were obtained: 1. VT,OC = 540 V at the rated IF. 2. IL,SC = 300 A at the rated IF. 3. When a DC voltage of 10 V was applied to two of the terminals, a current of 25 A was measured. Find the generator’s model at the rated conditions (i.e., the armature resistance and the approximate synchronous reactance). Since the generator is Y-connected, a DC voltage was applied between its two phases. Therefore: Example (cont.) The internal generated voltage at the rated field current is The synchronous reactance at the rated field current is precisely We observe that if XS was estimated via the approximate formula, the result would be: Which is close to the previous result. The error ignoring RA is much smaller than the error due to core saturation. The Synchronous generator operating alone The behavior of a synchronous generator varies greatly under load depending on the power factor of the load and on whether the generator is working alone or in parallel with other synchronous generators. Although most of the synchronous generators in the world operate as parts of large power systems, we start our discussion assuming that the synchronous generator works alone. Unless otherwise stated, the speed of the generator is assumed constant. The Synchronous generator operating alone A increase in the load is an increase in the real and/or reactive power drawn from the generator. Since the field resistor is unaffected, the field current is constant and, therefore, the flux is constant too. Since the speed is assumed as constant, the magnitude of the internal generated voltage is constant also. Assuming the same power factor of the load, change in load will change the magnitude of the armature current IA. However, the angle will be the same (for a constant PF). Thus, the armature reaction voltage jXSIA will be larger for the increased load. Since the magnitude of the internal generated voltage is constant EA = V + jX S I A Armature reaction voltage vector will “move parallel” to its initial position. The Synchronous generator operating alone Increase load effect on generators with Lagging PF For lagging (inductive) loads, the phase (and terminal) voltage decreases significantly. The Synchronous generator operating alone Increase load effect on generators with Unity PF For unity power factor (purely resistive) loads, the phase (and terminal) voltage decreases slightly. The Synchronous generator operating alone Increase load effect on generators with Leading PF For leading (capacitive) loads, the phase (and terminal) voltage rises The Synchronous generator operating alone Generally, when a load on a synchronous generator is added, the following changes can be observed: 1. For lagging (inductive) loads, the phase (and terminal) voltage decreases significantly. 2. For unity power factor (purely resistive) loads, the phase (and terminal) voltage decreases slightly. 3. For leading (capacitive) loads, the phase (and terminal) voltage rises. Effects of adding loads can be described by the voltage regulation: Where Vnl is the no-load voltage of the generator and Vfl is its full-load voltage. The Synchronous generator operating alone A synchronous generator operating at a lagging power factor has a fairly large positive voltaje regulation. A synchronous generator operating at a unity power factor has a small positive voltage regulation. A synchronous generator operating at a leading power factor has a small negative voltage regulation. The Synchronous generator operating alone Normally, a constant terminal voltage supplied by a generator is desired. Since the armature reactance cannot be controlled, an obvious approach to adjust the terminal voltage is by controlling the internal generated voltage EA = K. This may be done by changing flux in the machine while varying the value of the field resistance RF, which is summarized: 1. 2. 3. 4. Decreasing the field resistance increases the field current in the generator. An increase in the field current increases the flux in the machine. An increased flux leads to the increase in the internal generated voltage. An increase in the internal generated voltage increases the terminal voltage of the generator. Power and torque in synchronous generators A synchronous generator needs to be connected to a prime mover whose speed is reasonably constant (to ensure constant frequency of the generated voltage) for various loads. Pin = appm The applied mechanical power is partially converted to electricity Where is the angle between EA and IA. The power-flow diagram of a synchronous generator. Pconv = ind m = 3EA I A cos Power and torque in synchronous generators The real output power of the synchronous generator is The reactive output power of the synchronous generator is Recall that the power factor angle is the angle between V and IA In real synchronous machines of any size, the armature resistance RA << XS and, therefore, the armature resistance can be ignored. Thus, a simplified phasor diagram indicates that I A cos = EA sin XS Power and torque in synchronous generators Then the real output power of the synchronous generator can be approximated as 3VEA sin Pout XS We observe that electrical losses are assumed to be zero since the resistance is neglected. Therefore: Pconv Pout Here is the torque angle of the machine – the angle between V and EA. The maximum power can be supplied by the generator when = 900: Power and torque in synchronous generators The maximum power specified is called the static stability limit of the generator. Normally, real generators do not approach this limit: full-load torque angles are usually between 150 and 200. The induced torque is ind = kBR BS = kBR Bnet = kBR Bnet sin Notice that the torque angle is also the angle between the rotor magnetic field BR and the net magnetic field Bnet. Alternatively, the induced torque is MOTOR INTRODUCTION Synchronous motors are widely used in the industry for high-precision applications. This motor runs at constant speed and it does not depend on the torque acting on it. So, it has a constant-speed torque characteristic. The efficiency of synchronous motor is around 90%– 93%. MOTOR INTRODUCTION Synchronous motor is a doubly fed motor; three-phase power is given to the stator while the rotor is fed from a DC source for excitation of the field winding. MOTOR CONSTRUCTION There is no constructional difference between synchronous motor and synchronous generator MOTOR CONSTRUCTION •The stator has a laminated core with slots to hold the three-phase windings. • Rotor holds the field winding. The rotor can be of salient-pole type or cylindrical type. • Synchronous motor is likely to hunt, and so damper windings are also provided in the rotor poles. MOTOR PRINCIPLE OF OPERATION •When a three phase-supply is given to the stator of the synchronous motor, it produces a rotating magnetic flux of magnitude, rotating at synchronous Constant speed. MOTOR PRINCIPLE OF OPERATION •DC supply on the rotor will also produce a flux of constant magnitude. Brushless exciter Static exciter MOTOR PRINCIPLE OF OPERATION • If the rotor of the synchronous motor is rotated by some external means at the start, there will be a continuous force of attraction between the stator and the rotor. • This is called magnetic locking. • Once is this stage is reached, the rotor pole is dragged by the revolving stator field and thus the rotor will continue to rotate. MOTOR PRINCIPLE OF OPERATION The different methods that are generally followed to start the synchronous motor are i) ii) By using a pony motor (Small motor) Motor Starting by Reducing the supply Frequency iii) By using a damper winding iv) Starting as an induction motor MOTOR PRINCIPLE OF OPERATION By using a pony motor (Small induction motor) In this method, the rotor of the synchronous motor is brought to its synchronous speed with the help of an external induction motor. This external motor is called the pony motor. MOTOR PRINCIPLE OF OPERATION By using DC motor In this method of starting, the synchronous motor is brought to its synchronous speed with the help of a DC motor coupled to it. Once the rotor of the synchronous motor attains synchronous speed, the DC excitation to the rotor is switched off. MOTOR By using a motor This method is usually followed in the laboratory- the synchronous machine is started as a generator and is then connected to the supply mains by following the synchronization or paralleling procedure. Then the power supply to the prime mover is disconnected so that the synchronous machine will continue to operate as a motor. MOTOR PRINCIPLE OF OPERATION By using a damper winding The damper windings are provided on the pole face slots in the fields. These windings are short-circuited at both ends with the help of end rings, thus forming a squirrel-cage system. MOTOR PRINCIPLE OF OPERATION By using a damper winding Now, when a three-phase supply is given to the stator of a synchronous motor, it will start as a three-phase induction motor. MOTOR PRINCIPLE OF OPERATION Starting as an induction motor The synchronous motor is started as a squirrelcage induction motor. When the synchronous motor is started as a slip-ring induction motor, the three ends of the windings are connected to an external resistance in series through slip-rings. MOTOR PRINCIPLE OF OPERATION by Reducing the supply Frequency If the rotating magnetic field of the stator in a synchronous motor rotates at a low enough speed, there will be no problem for the rotor to accelerate and to lock in with the stator’s magnetic field. The speed of the stator magnetic field can then be increased to its rated operating speed by gradually increasing the supply frequency f up to its normal value. MOTOR PRINCIPLE OF OPERATION V-Curve generator MOTOR PRINCIPLE OF OPERATION Inverted V-Curve motor MOTOR Application of Synchronous Motor Synchronous motor having no load connected to its shaft is used for power factor improvement. Synchronous motor finds application where operating speed is less, and high power is required. such as rolling mills, chippers, mixers, pumps, compressors etc. MOTOR Application of Synchronous Motor As synchronous motor is capable of operating under either leading or lagging power factor, it can be used for power factor improvement. A synchronous motor under no-load with leading power factor is connected in a power system where static capacitors cannot be used. Why Use Synchronous Motors? Power factor correction Synchronous motors can help to reduce energy costs and improve the power system efficiency by correcting the power factor of the power line where they are installed. In a few years, the power savings can match the amount invested in the motor. Constant speed Synchronous motors maintain a constant speed under overload conditions and also during moments of voltage variations, observing the limits of maximum torque (pullout). variations. 2 Why Use Synchronous Motors? High efficiency Synchronous motors are more efficient in the conversion of electric into mechanical energy, resulting in greater energy savings. Synchronous motors are designed to operate with high efficiency over a wide speed range and provide a better use of energy for a wide variety of loads. High torque capacity Synchronous motors are designed with high torque on duty, keeping the speed constant even in applications with great load variations. 2 Why Use Synchronous Motors? Greater stability in the operation with frequency inverters It can operate in a wide speed range, while maintaining stability regardless load variation (e.g.: rolling mills, plastic extruders, etc.). 2 Principle of Operation 1) From the external source, the field winding is supplied with a DC current (excitation current) that generates a DC flux. 2) Rotor (field) windings are mechanically turned (rotated) at synchronous speed. 3) The rotating magnetic field produced by the field current induces voltages in the outer stator (armature) windings. The frequency of these voltages is in synchronism with the rotor speed. Principle of Operation 𝒇𝒔=𝑵s𝒑/𝟏𝟐𝟎 fs : electrical frequency, in Hz Ns : mechanical speed of magnetic field, in rpm (equals speed of rotor for synchronous machines) P : number of poles Principle of Operation The Equivalent Circuit of Synchronous Machine 𝐸𝐴 = 4.44𝑁s 𝜙f Ia Ra jXal Esa Va If Er EA 𝑋𝑠= 𝑋𝑎𝑙+ 𝑋𝑚 jXm AC The full equivalent circuit of synchronous machine per phase Rf Vf Principle of Operation The Equivalent Circuit of Synchronous Machine 𝐸𝐴 = 4.44𝑁s 𝜙f Ia Ra jXal Va : armature rms terminal voltage/phase. Ia: armature current/phase. Va Ra: armature resistance. Xal: armature leakage reactance. Xm: armature magnetizing reactance Esa jXm If Er EA AC Rf Vf 𝑉𝑎= 𝐼𝑎(𝑅𝑎+ 𝑗𝑋𝑎𝑙)+ 𝐸𝑠𝑎+ 𝐸A 𝑍𝑠= 𝑅𝑎+ 𝑗𝑋𝑎𝑙+ 𝑗𝑋𝑚= 𝑅𝑎+ 𝑗𝑋𝑠 Zs : synchronous impedance. Principle of Operation Ia Ra jXal Esa Va If Er EA δ=positive: generator. δ =negative: motor. δ =zero: compensator. jXm AC Rf Vf The Equivalent Circuit of Synchronous Machine For Synchronous Motor 𝑬𝑨 ∠𝜹 = Va∠0− Ia∠Φa × Zs∠𝜶 Ia Pin : input power/phase. 𝑃𝑖n = 𝑉𝑎 𝐼𝑎 cos Φ 𝑎 = 𝑉𝑎 𝐸𝐴 𝑋s sin𝛿 Pin Tg = 3 Pg/ωs Tload : load torque. Tloa𝑑 = η: efficiency. Pm: mechanical Power 𝜂= 3𝑃m 3𝑃in + 𝑉f I f 𝑉f 𝐼f = 𝐼²f R f 100% 3Pm 𝜔s jXm If Er EA 𝑃g = 𝐸𝐴 𝐼𝑎 cos(Φ𝑎 − 𝛿 ) Tg : air gap torque. jXal Esa Va Pg : air gap power/phase. Ra Rf AC Pg Vf The Equivalent Circuit of Synchronous Machine For Synchronous Motor SR : speed regulation. Nnl: no load speed. Nfl: full load speed. Input Power 𝑃𝑖n = 𝑉𝑎 𝐼𝑎 cos 𝜙𝑎 Armature Cu Losses Ia2Ra Ia Ra Iron, Excitation and Friction Losses jXal Esa jXm If Er Va EA Rf AC Pin Pg Dr Firas Obeidat Air Gap Power 𝑃g = 𝐸 𝐴 𝐼𝑎 cos(𝜙𝑎− δ) Vf Mechanical Power (Pm) The Effect of Load Changes on Synchronous Motor Ia Va Phasor diagram of synchronous motor operating at a leading power factor. -𝛿 EA Ia1 Ia2 Ia3 Va Ia4 P ∝ 1 P2 ∝ EA1 EA2 EA3 EA4 ∝P3 P4 ∝ The effect of an increase in load on the operation of a synchronous motor. The Effect of Field Current Changes on a Synchronous Motor What effect does a change in field current have on a synchronous motor? An increase in field current increases the magnitude of EA but does not affect the real power supplied by the motor. The power supplied by the motor changes only when the shaft load torque changes. Since a change in If does not affect the shaft speed Ns and since the load attached to the shaft is unchanged, the real power is unchanged. Va is also constant, since it is kept constant by the power source supplying the motor. A synchronous motor operating Va at a lagging power factor. 𝛿 EA Ia ∝P=constant Ia4 Ia3 Ia2 Va ∝P=constant Ia1 EA1 EA2 EA3 EA4 The effect of an increase in field current on the operation of the motor. GENERADOR Actividad Un generador síncrono de seis polos de 480 V, 50 Hz y conexión en Y tiene una reactancia síncrona por fase de 1,0 Ω. Su corriente de armadura de plena carga es 60A a 0.8 PF en retraso. Este generador tiene pérdidas de fricción y rozamiento con el viento de 1,5-kW y pérdidas de núcleo de 1,0 kW a 50 Hz a plena carga. Puesto que la resistencia de la armadura está siendo ignorada, se asume que las pérdidas I²R son insignificantes. La corriente de campo se ha ajustado de modo que la tensión terminal sea de 480V sin carga. (a) ¿Cuál es la velocidad de rotación de este generador? (b) ¿Cuál es la tensión terminal de este generador si se cumple lo siguiente? 1. Se carga con la corriente nominal en 0.8 PF en retraso. 2. Se carga con la corriente nominal a 1.0 PF. 3. Se carga con la corriente nominal a 0.8 PF adelanto. c) ¿Cuál es la eficiencia de este generador (ignorando las pérdidas en el cobre) cuando está operando a la corriente nominal y 0.8 PF en retraso? (d) ¿Cuánto par de eje debe aplicar el motor principal a plena carga? ¿Cuánto es el par en el entrehierro? (e) ¿Cuál es la regulación de voltaje de este generador a 0.8 PF retraso? ¿A 1.0 PF? ¿A 0,8 PF adelanto? Principle of Operation Actividad Una máquina síncrona de 208 V, 45 hp, 0,8-PF en adelanto conectada en triángulo, a 60 Hz tiene una reactancia síncrona de 2,5Ω y una resistencia de armadura insignificante. Sus pérdidas de fricción y rozamiento son de 1,5 kW, y sus pérdidas de núcleo son de 1,0 kW. Inicialmente, el eje está suministrando a una carga de 15 hp, y el factor de potencia del motor es 0.80 en adelanto (a) Esbozar el diagrama fasorial de este motor, y encontrar los valores de IA, IL y EA. (b) Supongamos que la carga del eje ahora se ha aumentado a 30 hp. dibujar el comportamiento del diagrama fasorial en respuesta a este cambio. (c) Encontrar IA, IL y EA después del cambio de carga. ¿Cuál es el nuevo factor de potencia del motor? Principle of Operation Actividad Una máquina síncrona de 208 V, 45 hp, 0,8-pf en adelanto, conectada en triángulo a 60 Hz tiene una reactancia síncrona de 2,5 Ω y una resistencia de armadura insignificante. Sus pérdidas de fricción y rozamiento son de 1,5 kW, y sus pérdidas de núcleo son de 1,0 kW. Inicialmente, el eje está suministrando una carga de 15 hp con factor de potencia de 0,85 en retraso. La corriente de campo If en estas condiciones es 4.0 A. (a) Dibuje el diagrama fasorial de este motor y encuentre los valores de Ia y Ea (b) Si el flujo del motor aumenta en un 25 por ciento, esboce el nuevo diagrama fasorial del motor. Cuáles son ahora IA, EA y el factor de potencia del motor?
