Why should we maintain the v/f constant during the Induction motor control?
Reason:
Induction motor control revolves around the formula of synchronous speed i.e., Ns = 120*f/p.
As frequency is the only variable to be controlled other than the poles (p), I used to think how it can be sufficient to just vary the frequency of the supply and increase the speed. I reached to a satisfying level of understanding that “it is sufficient”. This is how I understand.
The formula quoted above is the synchronous speed i.e., the speed of the stator flux revolving in the air-gap and not the actual speed of the motor (rotor). If the frequency of the stator current is increased, obviously the revolving speed of the air-gap flux will increase as it has no other constraints but to satisfy the relation depending on the number of poles. But, our induction motor control doesn’t mean just to increase the speed of the air-gap flux but to increase the motor speed i.e., the rotor speed which we do it by increasing the asking speed i.e., the synchronous speed. (Air-gap flux asks the rotor to rotate at its speed via the induction principle)
To do that, let us recollect the principle of induction motor. The torque required to drive the rotor depends on the rotor current which in turn depends on the emf developed in the rotor (because of the induction principle). This torque producing component of current magnitude depends on the cause i.e., the air gap flux strength. The current should be sufficient to drive the rotor (motor) to attain the speed at which the air-gap flux is asking it to rotate. Just asking the rotor to rotate at its speed is not adequate. It has to be given enough energy (current) to achieve that. This poses a requirement that the flux should be strong enough to develop a strong emf. In turn the magnitude of the current given to the stator is to be increased which can be done by increasing stator voltage. This is how the voltage is varied along with the frequency to maintain the ratio v/f constant. This in short, the text books tell us in a sentence which is well-known i.e., “in order to maintain the magnetizing current.”
Conversely, if only the voltage is increased then it means that energy is fed to the stator and rotor which is more than required for that speed. Increasing voltage doesn’t result in increase in speed as voltage holds no direct relation with the synchronous speed. It results in excess current which results in heating up the windings.
Why are system models and control theories not sufficient for analysis & design?
Reasons:
1. No mathematical system model is perfect
2. Dynamic systems are driven not only by our own control inputs, but also by disturbances which we can neither control nor model deterministically.
3. Sensors do not provide perfect and complete data about a system.
How is Speed, N converted from RPM to rad/s i.e,ω?
N is rotational speed and ωis angular speed.
Rotational speed tells as how many rotations(revolutions) have been completed per minute or per second. The standard unit is Revolutions per minute. RPM.
Angular speed tells the change(shift or displacement) in degrees per seconds.
one complete revolution is 360 degrees i.e. 2π radians.
one revolution per second is 2π radians per second.
one revolution per minute is 2π/60 rad/s.
N rpm is 2π x N/60 rad/s.
Similarly angular frequency (cycles per second) is calculated.
1 cycle per second = 2π radians per second.
f cycles per sec (Hz) = 2πf radians per second.
What is the difference between MV7000 (Voltage Source Inverter (VSI)) & SD7000 Current Source Inverter (CSI)?
The DC link after the converter (network) bridge in the VSI is made up of capacitors with voltage available for the inverter (machine) bridge. So, the voltage source is presented for the inverter. Hence, the voltage source inverter, VSI. In the CSI, the DC link is made up of a reactor which is to smoothen the current and give good DC current to the inverter bridge. It acts as a current source for the inverter present after the DC link. Hence, the current source inverter.
1. Disadvantage of high current THD (Total Harmonic Distortion) in a Drive - Derating of the machine and Torque pulsations at the shaft. 2. A phasor is a rotating vector. The benefit of using phasors in electrical engineering analysis is that it greatly simplifies the calculations required to solve circuit problems.
3. The angle between the applied voltage and the current depends on certain characteristics of the circuit. These characteristics can be classified as being resistive, capacitive, and inductive.
4. The angle between the voltage and the current in the circuit is called the power angle.
5. Apparent power and reactive power does not represent any measure of real energy.
6. Power Triangle - The relationship between apparent power (S), reactive power (Q) and real power (P) can be shown like this. By convention, Q is shown positive for inductive circuit and negative for capacitive circuit. Q - generated power losses in the circuit and voltage drops in the lines and cables.
7. The “neutral” wire of a three-phase system will conduct electricity if the source and/or the load are unbalanced.
8. In three-phase systems two sets of voltages and currents can be identified. These are the phase and line voltages and currents.
9. Three-phase circuits can have their sources and/or loads connected in wye (star) or in delta.
10. Almost without exception, turbine-driven generators have their windings connected in wye (star).
The AC induction motor is the workhorse of industrial and residential motor applications due to its simple construction and durability.
Advantages: No brushes to wear out or magnets to add to the cost. Rotor assembly is a simple steel cage.
ACIMs are designed to operate at a constant input voltage and frequency, but you can effectively control an ACIM in an open loop variable speed application if the frequency of motor input voltage is varied. Motor speed is roughly proportional to the input frequency. For example, you decrease the frequency of the drive voltage (for reducing speed), you also need to decrease the amplitude of the drive voltage by a proportional amount. Otherwise, the motor will consume excessive current at low input frequencies. This control method is called "Volts-Hertz control" (v/f control).
The Volts-Hertz (v/f) method works very well for slowly changing loads such as fans or pumps. But, it is less effective when fast dynamic response is required.
Limitation of Volts-Hertz (v/f) control method: Dynamic (quick) response is not achieved.
Good dynamic response can be realized if both the torque and flux of the motor are controlled in a closed loop manner. This is accomplished using Vector Control techniques.
Vector Control is also commonly referred to as Field Oriented Control (FOC).
As it is a known fact that the speed control of DC motor is easier compared to the ACIM. Vector Control principles enable us to control an AC motor similar to the way of controlling a DC motor.
Motor current can be broken down into 2 components:
1. Excitation, magnetization or flux current (similar to field current of a DC motor).
2. In-phase current (similar to armature current of a DC motor).
Vector Control principle:
Traditional control methods, such as v/f control methods control the frequency and amplitude of the motor drive voltage whereas vector control methods control the frequency, amplitude and phase of the motor drive voltage.
The key principle of vector control is to generate 3-phase voltage as a phasor to control the 3-phase stator current as a phasor that controls the rotor flux vector and finally the rotor current phasor.
Ultimately, the components of the rotor current need to be controlled. The rotor current cannot be measured because there is no direct electrical connection. So, they are indirectly computed using the parameters that can be measured.
This technique is indirect vector control because there is no access to rotor currents.
Indirect vector control is accomplished using the following data:
The motor must be equipped with sensors to monitor the 3-phase stator currents and rotor speed for feedback.
Key to understanding how vector control works:
The key to understanding how vector control works is to form a mental picture of the coordinate reference transformation process. If you picture how an AC induction motor works, you might imagine the operation from the perspective of the stator. From this perspective, a sinusoidal input current is applied to the stator. This time variant signal causes a rotating magnetic flux to be generated. The time variant signal causes a rotating is going to be a function of the rotating flux vector. From a stationary perspective, the stator currents and the rotating flux vector look like AC quantities.
Now, instead of the previous perspective, imagine that you could climb inside the motor. Once you are inside the motor, picture yourself running alongside the spinning rotor at the same speed as the rotating flux vector that is generated by the stator currents. Looking at the motor from this perspective during steady state conditions, the stator currents look like constant values, and the rotating flux vector is stationary! Ultimately, you want to control the stator currents to get the desired rotor currents (which cannot be measured directly). With the coordinate transformation, the stator currents can be controlled like DC values using standard control loops.
Vector Control Summary:
To summarize the steps required for indirect vector control:
1. 3-phase stator currents (Ia, Ib, Ic) and rotor speed are measured.
2. The 3-phase stator currents are transformed to a 2-axis time varying quadrature current values (I I α, I β)as viewed from the stator perspective.
3. The 2-axis coordinate system is rotated to align with the rotor flux using a transformation angle information calculated at the last iteration of the control loop. This conversion provides quadrature components of currents (Id, Iq) transformed to the rotating co-ordinate system. Id and Iq will be constant at steady-state.
4. Id reference controls rotor magnetizing flux. Iq reference controls the torque output of the motor. The error signals computed after comparison are input to PI controllers. The output of the controllers provide Vd and Vq, which is a voltage vector.
5. A new coordinate transformation angle is calculated. The motor speed, rotor electrical time constant, Id and Iq are the inputs to this calculation. The new angle tells the algorithm where to place the next voltage vector to produce an amount of slip for the present operating conditions.
6. The Vd and Vq output values from the PI controllers are rotated back to the stationary reference frame using the new angle. This results in the quadrature voltage values Vα and Vβ.
7. The Vα and Vβ are transformed back to 3-phase values Va, Vb and Vc. These 3-phase voltage values are used to calculate new PWM duty cycle values that generate the desired voltage vector.
VECTOR CONTROL BLOCK DIAGRAM
Coordinate Transforms
Through a series of coordinate transforms, the torque and flux can be controlled indirectly within the control loops. The process starts out by measuring the three phase motor currents. Practically, there is an advantage of the constraint that in a balanced 3-phase system - the sum of the 3 instantaneous current values will be zero. Thus, by measuring only two of the three currents, you can know the third. Hence, the cost of hardware is reduced.
CLARKE TRANSFORM
The first transform is to move from a 3-axis 2-dimensional coordinate system referenced to the stator of the motor to a 2-axis system also referenced to the stator. This is by using Clarke Transform.
PARK TRANSFORM
At this point, we have the stator current phasor represented on a 2-axis orthogonal system with the axis called α-β. The next step is to transform into another 2-axis system that is rotating with the rotor flux. This uses the Park Transform. From this perspective, the components of the current phasor in the d-q coordinate system are time invariant. Under steady state conditions, they are DC values. The stator current component along the d-axis is proportional to the rotor torque, and the component along q-axis proportional to the rotor torque. Now that you have these components represented as DC values, they can be controlled using the classic control loops.
INVERSE PARK
The output of the control loop have two voltage component vectors in the rotating d-q axis. You will need to go through complementary inverse transforms to get back to the 3-phase motor voltage. First you transform the 2-axis rotating d-q frame to the 2-axis stationary frame α-β. This is done using Inverse Park Transformation.
INVERSE CLARK
The next step is to transform from the stationary 2-axis α-β frame to the stationary 3-axis, 3-phase reference frame of the stator. Mathematically, this transformation is accomplished with the Inverse Clarke Transform.
Flux Estimator
Park and Inverse Park transformation require an angle θ. The variable θ represents the angular position of the rotor flux vector. The correct angular position of the rotor flux vector must be estimated on know values and motor parameters. This estimation uses a motor equivalent circuit model. The slip required to operate the motor is accounted for in the flux estimator equations and is included in the calculated angle.
The flux estimator calculates a new flux position based on stator currents, the rotor speed and the rotor electrical time constant. This implementation of the flux estimation is based on the motor current model and in particular these three equations.
where :
Imr = Magnetizing current (as calculated from measured values)
fs = Flux speed (as calculated from measured values)
T = Sample (loop) time parameter in the simulation or program
n = Rotor speed (measured with encoder or estimated)
Tr = Lr/Rr = Rotor time constant (motor data sheet)
θ = Rotor flux position (output variable from this module)
ωb = Electrical nominal flux speed (from motor name plate)
Ppr = Number of pole pairs (from motor name plate)
During steady state conditions, the Id current component is responsible for generating the rotor flux. For transient changes, there is a low-pass filtered relationship between the measured Id current component and the rotor flux. For transient changes, there is a relationship between the measured Id current and the rotor flux. The magnetizing current, Imr, is the component of Id that is responsible for producing the rotor flux. Under steady state conditions, Id is equal to Imr. Equation 1 relates Id and Imr. This equation is dependent upon accurate knowledge of the rotor electrical time constant. Essentially, Equation 1 corrects the flux producing component of Id during transient changes.
The computed Imr value is then used to compute the slip frequency as shown in Equation 2. The slip frequency is a function of the rotor electrical time constant, Iq, Imr and the current rotor velocity.
Equation 3 is the final equation of the flux estimator. It calculates the nex flux angle based on the slip frequency calculated in Equation 2 and the previously calculated flux angle.
