The chopper was operated at high frequency due to which it upgrade the motor performances by decreasing the ripple and removing the discontinuous conduction. The most important feature of chopper control is that the regenerative braking is carried out at very low generating speed when the drive is fed from a fixed voltage to low DC voltage.

Motoring Control

The transistor chopper controlled separately excited DC motor is shown in the figure below. The transistor T_r is operated periodically with period T_r and remains open for a duration T_on.The waveforms of motor terminal voltage and armature current are shown in the figure below. During on the motor terminal voltage is V and operation of the motor is described as

In this interval, the armature current raises from i_a1 to i_a2. This interval is called duty interval because the motor is directly connected to the source.

At t = t_on, T_r is turned off. Motor current freewheels through diode D_f and motor terminal voltage is zero during interval t_on≤ t ≤ T. Motor operation during this interval is known as freewheeling interval and is described by

Motor current decreases from i_a2 to i_a1 during this interval.The ratio of duty interval t_on to chopper period T is called duty cycle.

Regenerative Braking

Chopper for regenerative braking operation is shown in the figure below. The transistor T_r is operated periodically with a period T and on-period of t_on. The waveform of motor terminal voltage v_a and armature current i_a for continuous conduction is shown in the figure below. The external inductance is added to increase the value of L_a. When the transistor is on, i_a increased from i_a1 to i_a2.

The mechanical energy is converted into electrical energy by the motor, now working as a generator, partly increased the stored magnetic energy in the armature circuit inductance and the remainder is dissipated in armature and transistors.

When the transistor is turned off, the armature current flows through diode D and the source V and reduces from i_a2 to i_a1. The stored electromagnetic energy and the energy supplied by the machine are fed to the source. The interval  0  ≤ t  ≤ t_on is called energy storage interval and the interval t_on ≤ t ≤ T called the duty interval.

Forward Motoring and Braking Control

The forward motoring operation of the chopper is obtained by the transistor T_r1 with the diode D₁.The transistor T_r2 and diode D₂ provide the control for forward regenerative braking operation.

For the motoring operation, transistor T_r1 is controlled, and for braking operation, the transistor T_r2 is controlled. Shifting of control from T_r1 to T_r2 shift the operation from motoring to braking and vice versa.

Dynamic Control

The dynamic braking circuit and its waveform are shown in the figure below. During the interval between 0 ≤ t ≤T_on, i_a increases from i_a1 to i_a2. The part of the energy is stored in inductance and rest is dissipated in R_a and T_R.

During the interval T_on≤ t ≤ T, i_a decreases from i_a2 to i_a1.The energies generated and stored in inductances are dissipated in braking resistance R_B, R_a and diode D.Transistor T_r control the magnitude of energy dissipated in R_B and therefore control its effective value.

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If the load has different parts, their speed may be different. Some part of the rotor may rotate while others may go through a translational motion. The equivalent load system of the motor is shown in the figure below.

Where J – the polar moment of inertia of motor-load system, referred to the motor shaft, kg-m²
ω_m – instantaneous angular velocity of the motor shaft, rad/sec.
T – the instantaneous value of developed motor torque, N-m.
T₁ – the instantaneous value of load torque, referred to a motor shaft, N-m.

The equation shown below described the motor load equation.This equation is applicable for variable inertia drives such as mine, winders, reel, drives, industrial robots. In this equation, the load torque includes friction and windage torque of the motor.

For constant inertia drive dj/dt = 0. Therefore the equation becomes

The above equation shows that the load developed by the motor is counter-balanced by a load torque T₁ and a dynamic torque jdω_mt/dt.The torque component j(dω_mt/dt) is called dynamic torque because it is present only during transient operations.

The acceleration or deacceleration of the drive mainly depends on whether the load torque is greater or less than the motor torque. During acceleration, the motor supplies the load torque along with an additional torque component jdω_mt/dt to overcome the drive inertia.

The drives which have a large inertia must increase the load torque by a large amount for getting sufficient acceleration. The drive which requires a fast transient response, their motor torque should be maintained at the excessive value and motor load system should be designed with a lower possible inertia.

The energy associated with dynamic torque is stored in the form of kinetic energy and given by the equation jdω²_m/dt. During the deacceleration, the dynamic torque has a negative sign. Thus it assists the motor developed torque T and maintains the drive motion by extracting energy from stored kinetic energy.

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1. Regenerative Braking
2. Plugging or reverse voltage braking
3. Dynamic Braking
   • AC dynamic braking
   • Self-dynamic braking
   • DC dynamic braking
   • Zero sequence braking

The braking of an induction motor is explained below in details.

1. Regenerative Braking

The input power of the induction motor drive is given by the formula shown below

Where φ_s is the phase angle between stator phase voltage and the stator phase current I_s. For motoring operation, the phase angle is always less than the 90º. If the rotor speed becomes greater than synchronous speed, then the relative speed between the rotor conductor and air gap rotating field reverse.

This reverse the rotor induces emf, rotor current and component of stator current which balances the rotor ampere turns. When the φ_s is greater than the 90º, then the power flow to reverse and gives the regenerative braking. The magnetising current produced the air gap flux.

The nature of the speed torque curve is shown in the figure above. When the supply frequency is fixed, the regenerative braking is possible only for speeds greater than synchronous speed. With a variable frequency speed, it cannot be obtained for speed below synchronous speed.

The main advantage of regenerative braking is that the generated power is fully used. And the main drawback is that when fed from a constant frequency source the motor can not employ below synchronous speed.

2. Plugging

When the phase sequence of supply of the motor running at speed is reversed by interchanging the connection of any two phases of the stator on the supply terminal, operation change from motoring to plugging as shown in the figure below. Plugging is the extension of motoring characteristic for a negative phase sequence from quadrant third to second. The reversal of phase sequence reverses the direction of a rotating field.

3. Dynamic Braking

•  AC Dynamic Braking – The dynamic braking is obtained when the motor is run on the single phase supply by disconnecting the one phase from the source and either leaving it open or connecting it with another phase. The two connections are respectively known as two and three lead connection.

When connected to a one phase supply the motor can be considered as to be fed by positive and negative sequence three phase set of voltage. The total torque produced by the machine is the sum of torque due to positive and negative sequence voltage. When the rotor has high resistance, then the net torque is negative, and the braking operation is obtained.

Assume the phase A of the star connected motor is open circuited. Then the current flow through the phase A becomes zero, i.e., I_a = 0 and current through the other two phases is I_B = – I_C.

The positive and negative sequence component I_p and I_n are represented by the equation.

Where α = e^j20°

•  Self Excited Braking Using Capacitor – In this method the three capacitors are permanently connected to the motor. The value of the capacitor is so chosen that when disconnecting from the line, the motor works as a self-excited induction generator. The braking connection and self-excitation process is shown in the figure below.

The curve A is the no load magnetisation curve and line B represent the current through the capacitor. E is the stator induced voltage per phase of the line. The capacitor supplies the necessary reactive current for excitation.

•  DC  Dynamic Braking – In this method, the stator of induction is connected across the DC supply. The method for getting DC supply with the help of a diode bridge is shown in the figure below.

The direct current flow through the stator produces a stationary magnetic field, and the motion of the rotor in this field produces induces voltage in the stationary windings. The machine therefore works as a generator and the generated energy is dissipated in the rotor circuit resistance, thus giving the dynamic winding.

•  Zero Sequence Braking – In this braking, the three phases of the stator are connected in series across either a single AC or DC source. Such type of connection is known as zero sequence connection because the current in all the three phases is co-phase. The nature of speed-torque curve for AC and DC supply is shown in the figure below.

With the AC supply, the braking could be used only up to one-third of synchronous speed. The braking torque produces by this connection are considerable larger than motoring. With DC supply braking is available the entire speed range and the braking are essential a dynamic braking as all the generated energy is wasted into rotor resistance.

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The induction motor drive has many applications like it is used in fans, blowers, mill run-out tables, cranes conveyers, traction, etc. The induction motor drive is self-starting, or we can say when the supply is given to the motor, it starts rotating without any external supply.

The initial resistance of the supply is zero, and hence large current flows through the motor, which damages the windings of the motor. For reducing the flow of starting current, the different starting methods are used. These methods keep the magnitude of starting current within a prescribed limit such that it does not cause the overheating.

Starting Methods

The methods employed for starting motors are:

1. Star-delta starter
2. Auto-transformer starter
3. Reactor starter
4. Saturable reactor starter
5. Part windings starter
6. AC voltage controller starter
7. Rotor resistance starter for wound rotor motor

The starting methods are explained below in details.

Star-Delta Starter

In this method, an induction motor designed to operate normally with delta connection is connected in a star during starting. Thus the stator voltage and current are reduced by 1/√3. The motor torque is proportional to stator terminal voltage, starting torque is reduced to one-third.

A circuit diagram for a star-delta starter is shown in the figure below. The circuit breaker CB_m and CB_s are closed to start the machine with star connection. When the steady state speed is reached, CB_s is opened, and CB_r is closed to connect the machine in Delta.

Auto-Transformer Starter

In this method, the starting current and motor terminal voltage are reduced by an autotransformer. The torque is proportional to the square of the motor terminal voltage, and hence it is also reduced. When the motor reaches its steady states, it is connected to the full supply voltage. An auto-transformer starter is shown in the figure below.

In the starting, the CB_s1 and CB_s2 are closed, and CB_m is open. When the motor accelerates at its full speed, the CB_s2 is opened, and CB_m closed. Now CB₁ is opened to disconnect auto-transformer from the supply.

Reactor Starter

The starting current is reduced by connecting the three phase reactor in series with the starter. When the motor reaches its steady state, the reactor is removed from the circuit. The reactor starter circuit is shown in the figure below.

The circuit breaker CB_s is closed to start the machine. When the motor reaches its full speed, the CB_s is closed to introduce the reactor at the neutral end of the stator winding. Thus, the starting current of the motor is reduced to its minimum value.

Saturable Starter Reactor

The saturable reactor is introduced in series with the stator, and it gives the soft start to the motor. The saturable reactor has DC control winding which controlled the torque of the motor steplessly. The reactance of the saturable reactance can be varied steplessly by changing the control winding current.

In the starting, the reactance is set at the higher value, and hence the starting torque is close to zero. The reactance is controlled smoothly by increasing the winding control current, and this gives the step less variation of starting torque. Thus motor starts without any jerks and accelerates smoothly.

Part Winding Starting

Some squirrel cage motors have two or more stator windings, and these windings are connected in parallel during the normal operation. During starting only one winding is connected, which increases the starter impedance and reduces the starting current. This starting scheme is called part winding starting. The machine starts with winding 1 when the CB_m is closed and after the full speed is reached the CB_s is closed to connect winding 2.

Rotor Resistance Starter

This method connects the rotor resistance in the external circuit. The highest value of current is chosen to limit the current at zero speed within the safe value. The rotor resistance starter is shown in the figure below.

As the motor accelerates the external resistance are cut one by one by closing contacts and hence the rotor current is limited between specified maximum and minimum value.

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The brushless DC motor drive is used in record players, the tape drive for recorders, spindle drive in hard disks for computers, and low power drives in computers peripherals instruments and control systems. They also have applications in aerospace, in biomedical and in driving cooling fans, etc.

The cross section of a three-phase two pole trapezoidal PMAC motor is shown in the figure below. This drive has a permanent magnet rotor with wide pole arc. The stator of the drive has three poles winding which is displaced by 120º and each phase winding spans 60º on each side.

The voltage induces in three phases are shown in the figure below. The reason for getting the trapezoidal waveform is that when the rotor revolving in a counter-clockwise direction, then up to 120º rotation from the position all the top conductor of phase A will linking the south pole and all the bottom of phase A will be linking the north pole.

The voltage induces in phase A will be the same during 120º rotations and beyond the 120º some conductors in the top link north pole and others the south pole. Similarly, the voltage induces in the bottom conductors. The wave voltage induces in phase A linearly reverse in next 60º rotation. Similarly, the voltage induces in the phases B and C.

The brushless DC motor drive uses voltage source inverter and trapezoidal PMAC motor shown in the figure below. The stator windings are star connected. The phase voltage waveform for a trapezoidal PMAC motor is shown in the figure below.

The stator winding is fed with a current pulse, and each of the pulses had duration 120º and located in the region where induced voltage is constant and maximum. The polarity of the current pulse is same as that of the induced voltage. The air gap flux is constant and the voltage induced is proportional to the speed of the rotor.

During each 60º internal the current enters one phase and come out of another phase, therefore power supplied to the motor in each such interval is expressed as

The torque developed by the motor

The waveform of the torque is given by the figure shown below. The torque is proportional to the current flows in the DC power links. The regenerative breaking of the drive is obtained by reversing the phase current and hence the current source I_d will also reverse. The power flows from the machine to inverter and from the inverter to DC source.

When the drive speed reversed the polarity of induces voltages reversed and the drive gives regenerative braking operation, and when the current direction is reversed the motoring operation is obtained. The current waveforms are shown in the figure below.

Types of Brushless DC Motor Drive

The brushless DC motor drive is mainly classified into two types, i.e., the low-cost brushless dc motor drive and the single-phase brushless dc motor drive.Their types are explained below in details.

Low-Cost Brushless DC Motor Drive

This drive has only three transistors and three diode converter which can supply only positive current or voltage to three phase motor. The induced voltage and current supplied to the motor for motoring and braking operation. When 120º positive current pulses are supplied to the motor, then the motoring action is obtained in a counter-clockwise direction. When these pulses are shifted to 180º, then the braking action is obtained

The current of phase A is controlled by the thyristor T_r1 and the diode D₁. When T_r1 is on source V_d is connected across winding A and rate of change of I_A is positive. When T_r1 is turned off current i_A freewheels through diode D₁ and rate of change of i_A is negative. Thus, during the period from 0 to 120º, T_r1 can be alternately turn on and off. So that current I_A is made to follow a rectangular reference current i_A within a hysteresis band.

Single-Phase Brushless DC Motor Drive

The single-phase brushless DC motor drive is shown in the figure below. Let us consider the motor is supplied from the half bridge single phase converter with a rectangular current waveform as shown in the figure.

The torque produced by the motor has a large ripple. When the motor is running at large speed, the torque rippled will be filtered out by the inertia of the motor load system which is giving a uniform speed.

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The static Kramer-drive converts the slip power of an induction motor into AC power and supply back to the line. The slip power is the air gap power between the stator and the rotor of an induction motor which is not converted into mechanical power. Thus, the power is getting wasted. The static Kramer drives fed back the wasted power into the main supply. This method is only applicable when the speed of the drive is less than the synchronous speed.

Static Kramer Drive Working

The rotor slip power is converted into DC by a diode bridge. This DC power is now fed into DC motor which is mechanically coupled to an induction motor. The torque supplied to the load is the total sum of the torque produced by the induction and DC motor drive.

The figure shown below represents the variation of V_d1 and V_d2 with a speed of two values of DC motor field current. When the value of V_d1 is equal to the value of V_d2 then the steady state operation of the drive is obtained, i.e., at A and B for field current of I_f1 and I_f2.

The speed control is possible only when speed is less or half of the synchronous speed. When the large range speed is required, the diode bridge is replaced by the thyristor bridge. The relationship between the V_d1 and the speed can be altered by controlling the firing angle of thyristor amplifier. Speed can now be controlled up to stand still.

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The feedback power is controlled by controlling the inverter counter emf V_d2, which is controlled by controlling the inverter firing angle.The DC link inverter reduced the ripple in DC link current I_d. The slip power of the drive is fed back to the source due to which the efficiency of the drive increases.

The drive input power is the difference of the DC input power and the power fed back. Reactive input power is the sum of the motor and input reactive power.Thus, the drive has poor power factor throughout the range of its operation.

Where α is the inverter firing angle and n, and m are respectively the stator to the rotor turn ratio of motor and source side to convert side turns ratio of the transformer. The neglecting drop across the inductor.

Substituting the equation (1) and (2) in the above equation we get

where a = n/m

The maximum value of alpha is restricted to 165º for safe commutation of inverter thyristor. The slip can be controlled from 0 to 0.966α when α is changed from 90º to 165º.The appropriate speed range can be obtained by choosing the appropriate value of α.

The transformer is used to match the voltage from V_d1 and V_d2. At the lowest speed required from the drive, V_d1 will have the maximum value V_d1m, and it is given by

Where S_m is the value of slip at the lowest speed. If α is restricted to 165, m is chosen such that the inverter voltage has a value V_d1m when α is 165º, i.e.,

The value of m determines the highest firing angle at the lower motor speed. It also gives the highest firing angle and the lowest reactive power at the lowest speed.

Considered the circuit of the motor, which is neglecting the magnetising branch. When referred to DC link, resistance (sR_s + R_r) will be 2(sR’_s + R_r). This gives the equivalent circuit of the drive, where V_d1 and V_d2 are given. R_d is the resistance of the DC link inductor.

If rotor copper loss is neglected

The nature of the speed torque curve is shown in the figure below.

The drive has application in pump drive which requires the speed control in the narrow range only. The drive is widely used in medium and high power fan and pump drives, because of high efficiency and low cost.

Operating Modes of Static Scherbius Drives

The following are the operating modes of Static Scherbius Drives.

Sub-synchronous Motoring – In this mode of operation the slip and torque both are positive and hence the injected voltage is in phase with rotor current. The power flows into the stator and feedback into the rotor circuit.

Super-synchronous Motoring – When the speed of the motor is above the synchronous speed, then the slip is negative. Thus, the voltage and current are out of phase with each other.The power feeds into the rotor from the drive circuit along with input power flowing into the stator.

Sub-synchronous Generating – For sub-synchronous speed, the torque is required to be positive, although the slip is positive. The power is fed into the rotor through the slip ring.

Super-synchronous Generating – When the speed of the motor above the synchronous speed, then the slip and torque becomes negative. Thus, the injecting voltage is in phase with the rotor. The mechanical power is injected by the shaft and the output power is obtained from the stator and rotor circuit.

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The figure below shows a voltage source inverter employing transistor.

The voltage source inverter use self-commutated device like MOSFET, IGBT, GTO, etc. It is operated as a stepped-wave inverter or a pulse width modulation. When the voltage source inverter is operated as a stepped-wave inverter, then the transistor is switched in the sequence of their number with a time difference of T/6.

The each of the transistors is kept on for the duration of T/2, where T is the period for one cycle. The waveform of the line voltage is shown in the figure below. The frequency of the inverter is varied by varying T, and the output voltage of the inverter is varied by varying DC input voltage.

When the supply is DC, then the variable DC input is obtained by connecting a chopper between DC supply and inverter.

When the supply is AC, then the DC input voltage is obtained by connecting the controlled rectifier between the AC supply and inverter shown in the figure below.The capacitor C filter out the harmonics in DC link voltage.

The main drawback of the VSI induction motor drive is the large harmonics of the low frequency in the output voltage. The harmonics increases the loss in the motor and cause the jerky motion of the rotor at low speed.

Braking of VSI Induction Motor Drives

Dynamic Braking:  In dynamic braking, the switch SW and a self-commutated switch in series with the braking resistance R are connected across the DC links. When the operation of the motor is shifted from motoring to braking switch SW is opened. The energy flowing through the DC link charges the capacitors and its voltage rises.

When the voltage crosses the set value, switch S is closed, connecting the resistance across the link. The energy which is stored in the capacitor flows into the resistance and reduces the DC link voltage. When it falls to its nominal value S is opened.Thus the closing and opening of the switch depends on the DC link voltage, and the generated energy is dissipated in the resistance gives dynamic braking.

Regenerative Braking:  Let us consider the regenerative braking of pulse width modulation of inverter drive. When the operation shift from motoring to braking, the DC link current I_d reverse and flows into the DC supply feeding the energy to the source.Thus the drive already has the regenerative braking capability.

In regenerative braking the, the power supply to the DC link must be transferred to the AC supply. When the operation shift from motoring to braking, the DC link current I_d reverse, but the V_d remain in the same direction. Thus, for regenerative braking, a converter is required for converting the DC voltage and direct current in either direction.

Four Quadrant Operation

Braking capability obtains the four quadrant operation of the drive. The reduction of the inverter frequency makes the synchronous speed less than the motor speed. Thus the operation of the motors is transferred from quadrant 1 (forward motoring) to quadrant 2 (forward braking).

The inverter frequency and voltage are progressively reduced as the speed falls, to brake the machine from zero speed. The phase sequence of the output voltage is reversed by interchanging the firing pulse of the thyristor. Thus, the operation of the motor is transferred from the second quadrant to the third quadrant (reverse motoring). The inverter frequency and voltage are increased to get the required speed in the reverse direction.

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Where μ is the coefficient of adhesion and M_d the adhesive weight or weight on the driving wheel.

Functions of the Tractive effort

The following are the functions perform by the tractive effort on the vehicles.

1. Tractive effort required to accelerate the train mass horizontally (in newtons) at an acceleration of α is

Where M is the mass in tonnes

2. The tractive effort required to accelerate the rotating parts: The rotating parts consist of wheels, gears, axles and rotor of the motor. The moment of inertia of the wheel is expressed by the formula shown below.

Where J_w is the moment of inertia of the wheel, kgm² and N_x is the number of axles on the wheel.

N – the number of driving motor.
n₁ – teeth on motor gear wheel
n₂ – teeth on axle gear wheel

R – radius of the wheel, m
J_m – moment of inertia of one motor, kg-m²

Then moment of inertia of motor referred to wheels

Traction effort for driving rotating partsTotal tractive effect required for accelerating the train on a level track.

Where M_e is the effective mass of the train.The above equation can also be written as

3. The tractive effort required to overcome the force due to gravity: When moving up in the slope the drive has to produce tractive effort to overcome the force due to gravity.In railway, the gradient or slope is expressed as a rise in meters in a track distance of 1000 m and is denoted by G.The tractive force required to overcome the force due to gravity will be

4.The tractive effort required to overcome train resistance: The resistance of the train is mainly due to various kinds of friction. The three basic types of friction responsible for the train resistances are Coulomb friction, viscous friction and air friction.

The Coulomb friction is produced by the relative motion of the two surfaces. It does not depend on the speed of the train. The viscous friction is directly proportional to the speed of the train, and the air friction is independent of the speed square.

Where V is the speed of the train, and A, B, C are constants.

5. The total tractive effort required to move the train:

The positive sign is used for the train movement up-gradient and negative for down gradient.

6. Motor Torque Rating:

Total torque at the rim of the driving wheels = Total tractive effort X R

where R is the radius of the driving wheels in meters.Total torque referred to the motor shaft is expressed by the equation

where η_t is the efficiency of transmission.

Torque per motor

where N is the number of motors

When deciding motor rating, maximum gradient allowed while laying out down the track should be considered.

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Current Source Inverter Control

A thyristor current source inverter is shown in the figure below. The diodes D₁-D₆ and capacitor C₁-C₆ provide commutation of thyristor T₁-T₆, which are fired with a phase difference of 60º in the sequence of their number. It also shows the nature of the output current waveform. The inverter act as a current source due to large inductance L_D in DC link. The fundamental component of motor phase current is shown in the figure below.

The torque is controlled by varying DC link current I_d by changing the value of V_d. When the supply is AC, a controlled rectifier is connected between the supply and inverter. When the supply is, DC a chopper is interposed between the supply and inverter.

The major advantage of current source inverter is its reliability. In the case of current source inverter a commutation failure in the same leg does not occur due to the presence of a large inductance Ld.

In an induction motor, the rise and fall of current are very fast. This rise and fall of current provide large motor spikes. Therefore a motor of low leakage inductance is used. The commutation capacitance C₁-C₆ reduce the voltage spikes by reducing the rate of rising and fall of the current. A large value of capacitance is required to sufficiently reduced the voltage spikes.

Regenerative braking and Multiquadrant Operation of CSI

When the motor speed is less than the synchronous speed, machine work as a generator. The power flows from machine to DC link and DC link voltage V_d reverse. If a fully controlled converter is made to work as an inverter, then the power supply to DC link will be transferred to AC supply, and regenerative braking will take place. Hence no additional equipment is required for regenerative braking of DC motor drive.

The drive can have regenerative braking capability and four quadrant operation if a two-quadrant chopper provides current in one direction, but voltage in either direction is used.

Closed Loop Speed Control of CSI Drives

The closed loop CSI drive is shown is shown in the figure below. The actual speed ω_m is compared with the reference speed ω*_m. The speed error is controlled through PI controller and slip regulator. The slip regulator sets the slips speed command ω*_sl. The synchronous speed obtained by adding ω_m, ω*_sl determines the inverter frequency.

Constant flux is obtained when slip speed ω_sl and I_s have the relationship. Since I_d is proportional to I_s, according to the equation shown below a similar relation exists between ω_sl and I_d for constant flux operation.

Based on the value of ω*_sl, the flux control flux produces a common reference current I*_d, which through a closed loop current control adjust the DC link current I_d to maintain a constant flux. The limit imposed on the output of slip regulator, limit I_d at the inverter rating flux. Therefore, any correction in speed error is carried out at the maximum permissible inverter current and maximum available torque, giving a fast transient response and current protection.

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