Electrical Drives I Week 3: SPEED-TORQUE characteristics of Electric motors
b- Shunt DC motor: I f Series and shunt field resistances are connected in shunt (parallel) Exhibits identical characteristics as that of the separately excited motor The field current is constant regardless of the loading of the machine. Shunt DC motor Shunt DC motor Speed Control: 1. Field resistance control 2. Terminal voltage control ω = kφ Vt K R a K 2 T d 3. Series resistance insertion in armature (less common practice due to the added losses accompanied by the insertion of new resistance)
b- Shunt DC motor: 1- Field resistance I f Control When field resistance increases, field current I f decreases and so the flux φ f decreases. Since flux decreases, induced emf decreases and thus the armature current increases I f = = kφω = Shunt DC motor Since flux φ f decreased while the armature current increased, how will this affect the developed torque T d??? T d = kφ It is also called field weakening
b- Shunt DC motor: 1- Field resistance Control Example: Assume = 0.25Ω, terminal voltage = 250V, induced emf = 245V. I f φ decreased by 1% = 250 245 0.25 = 20 A T d = kφ The torque will increase. Since T d > T L motor speeds up decreased by 1% = 0.99 *245= 242.55V = 250 242.55 = 29.8 A 0.25 ω increases, increases, decreases, T d decreases till T d = T L at a higher speed So what happens if the flux decreased by 1%? Armature current increased by 49% for a decrease in flux by 1 Shunt DC motor
T b- Shunt DC motor: 1- Field resistance I f Control y = C + mx ω = kφ No load speed= C intercept kφ 2 T d Slope of a st. line= m V 1 > 2 1 2 T L Not possible for PM motor Shunt DC motor As the field resistance increase, the flux K slope K 2 decreases, and the no-load speed of the motor increases, while the slope of the torque speed curve becomes steeper
b- Shunt DC motor: 2- Terminal voltage control When increases, increases, field current I f remains unchanged and so I f T d increases making T d > T L and thus the speed of the motor increases. = V t T d = kφ Shunt DC motor When the speed of the motor increases, the induced emf increases causing the armature current to decrease and thus decreases the developed torque T d until T d = T L at a higher speed. = kφω
b- Shunt DC motor: 2- Terminal voltage I f control ω = kφ kφ 2 T d No load speed= CHANGES Slope = UNCHANGES Requires variable DC supply Shunt DC motor V a K T L V a T e
b- Shunt DC motor: 3- Armature resistance I f control ω = kφ kφ 2 T d K V a slope 2 K Simple control Losses in external resistor Rarely used. T L Shunt DC motor T e
b- Shunt DC motor: Is the choice REALLY that simple? Can I either choose field control or armature control or is there a hidden secret Field control: The lower the field, the faster the machine turns and vice versa. Therefore at minimum value for speed, the field current is maximum. For very very low values of speed, the field winding might be damaged due to the high field current Armature control: The lower the terminal voltage, the slower the machine is and vise versa. The maximum achievable speed is related to the maximum terminal voltage the machine can withstand. For very very high values of speed, the armature winding might be damaged due to the high terminal voltage.
b- Shunt DC motor: Field control (field weakening control): used for operation above the base speed Armature control (terminal voltage control): used for operation below the base speed Combining two together it is possible to control the machine in a good operating range. Separately excited and shunt DC motor have an excellent speed control range BUT. There are torque and power limitations for each type
b- Shunt DC motor: Combined control Base speed base = Speed at rated, I f and = 0 to base speed control by > base speed control by flux weakening () T control base control
b- Shunt DC motor: Armature and Field Control Limitations 1- Armature voltage control at constant φ:, ω, E, constant There are limiting factors in either case which is the heating effect of the armature conductors which places an upper limit to the magnitude of the armature current For armature voltage control and at constant flux operation, the maximum developed torque is obtained by: T dmax = kφmax Maximum developed torque is Constant regardless the speed of rotation of the motor The maximum power at any given speed under armature voltage control will be: Maximum output power P max = T dmax ω is directly proportional m to the speed of rotation of the motor
b- Shunt DC motor: Armature and Field Control Limitations 1- Field control at constant : φ, ω, E constant, constant Flux changes and the speed is related to the flux level (speed increases when field is decreased) Torque limits decreases as the speed of the motor increases P max = T dmax ω m Maximum output power is constant regardless of the motor speed T dmax = kφ Maximum developed torque varies inversely with the motor speed
b- Shunt DC motor: Armature and Field Control Limitations Maximum Torque T max Maximum Power P max T max = constant P max = constant T max = constant so P max = T max ω P max = constant = control = control = control = control n base speed n base speed
c- Series DC motor: Series and shunt field resistances are connected in series φ Series field resistance is composed of a small number of turns as compared to that of the shunt field resistance Current in the series winding is equal to that of the armature current. Hence the series field resistance carries much larger current than that of the shunt field. I f The series machine has field current varying with the Saturation Curve loading of the motor- the heavier the load, the stronger the field. At light or no load conditions, the field of the Series DC motor series motor is very small. The effect of high field current must be taken into consideration when operating with series motor as to avoid saturation due to high field current
c- Series DC motor: = kφω T d = kφ = + T d = kφ kφω + ω = kφ + kφ 2 T d Modify the separately φ Series DC motor If we assume that the motor operates in the linear region of the saturation curve. Flux proportional to armature current φ = C T d = kφ = kc 2 Saturation Curve I f
c- Series DC motor: T d = kφ = kc 2 ω = kφ + kφ 2 T d φ = C Speed at no load (or light load) is excessively high. For this reason, series motors must always be connected to a mechanical load. ω = kφ ω = ω = kφ 2 T d + kc kc + kct d kc Separately excited Series DC motor 2 kφ = kc kφ= kc 1 Ia = kc kφ T d =kφ kφ = kφ 2 kc kc
c- Series DC motor: Methods of Speed control Unlike the shunt machine, there is only one way which is changing the armature voltage (terminal voltage change). Increasing the terminal voltage, will increase the first term of the equation and will result in higher speed for any given torque ω ω = + kct d kc Series DC motor Terminal voltage change Torque Torques speed characteristics series motor Inserting another resistance can be used in speed control but will account for additional losses Until the last 40 years, there was no convenient way to change, so the only method was through the resistance change. Everything changes today with the introduction of solid state control circuits
d- Series and Shunt DC motor: STARTING I st = + s 2 T st = kφi st = kci st = kc +s 2 I st = T st = kφ = kc sh = kc 2 sh Starting of series DC Motor Starting of shunt DC Motor Starting is computed when is equal to zero, since ω = 0. s = series field resistance sh = shunt field resistance
What makes the series motor more popular than the shunt? 1. sh is usually a few hundred times larger than the resistance of the series field s 2. If we assume that kc is constant, then the starting torque in the series is much larger than that of the shunt. However, the starting current in the series is much lower than that of the shunt. I st = T st = kc + s +s Series DC motor 2 I st = T st = kc 2 sh Shunt DC motor
d- Compound DC motor: I f I s The compound excitation characteristic in a dc motor can be obtained by combining the operational characteristic of both the shunt and series excited motor. The compound wound self excited dc motor or simply compound wound dc motor essentially contains the field winding connected both in series and in parallel to the armature winding. When the shunt field flux assists the main field flux, produced by the main field connected in series to the armature winding then its called cumulative compound dc motor. sh φ totalcum = φ series + φ shunt In case of a differentially compounded self excited dc motor i.e. differential compound dc motor, the arrangement of shunt and series winding is such that the field flux produced by the shunt field winding diminishes the effect of flux by the main series field winding. The net flux produced in this case is lesser than the original flux and hence does not find much of a practical application. φ totaldiff = φ series φ shunt Series field Shunt field Compound DC motor
d- Compound DC motor: Cumulative Compound I f I s Cumulative Compound DC motor = + + = I s I f sh I f = V f sh In cumulative compound DC motor there is a component of flux which is constant (not dependent on load) and another component which depends on load (armature current) Cumulative Compound DC motor φ totalcum = φ series + φ shunt Load dependent Load independent
d- Compound DC motor: Cumulative Compound I f I s Original separately excited equation Compound (cumulative) ω = kφ sh ω = ( + ) k φ total ω = k φ series + φ shunt ( + ) k φ series + φ shunt Cumulative Compound DC motor Assuming that the terminal voltage, is constant as well as the φ shunt are constant: φ series = C ω = kc + kφ shunt (+ ) kc + kφ shunt
I s d- Compound DC motor: Cumulative Compound I f ω = kc + kφ shunt (+ ) kc + kφ shunt sh Previously we concluded ω = T d = k φ series + φ shunt = k φ series + φ shunt T d k φ series + φ shunt ( + ) k φ series + φ shunt Cumulative Compound DC motor ω = k φ series + φ shunt ( + )T d k φ series + φ shunt 2
d- Compound DC motor: Cumulative Compound ω = k φ series + φ shunt At no-load when T d =0, armature current is zero, and φ series =0 ( + )T d k φ series + φ shunt 2 φ total = φ series + φ shunt ω 0 = =0 k φ shunt φ total = φ shunt No load speed using cumulative compound same as shunt Also, the speed drop is avoided which occurs in series motor connection ω = kφ + kφ 2 T d Series Motor Bigger speed drop shunt Motor ω = kφ kφ 2 T d
d- Compound DC motor: Cumulative versus Differential Compound ω = ( + ) k φ total φ total = φ series + φ shunt Cumulative compound Load dependent Load independent Load increase, armature current increase, series field increases, total flux increases, speed decreases φ total = φ series φ shunt Differential compound Load dependent Load independent Load increase, armature current increase, series field increases, total flux decreases, speed increases
d- DC motor characteristics: All types Speed torque characteristics of DC motor
d- Compound DC motor: STARTING I f I s From the circuits, starting armature current is : I st = + Starting current in cumulative compound same as series sh From the circuits, starting torque is : T st = k φ series + φ shunt I st = kc + 2 + kφ shunt + Cumulative Compound DC motor Starting torque in cumulative compound higher than series