STEADY STATE AND TRANSIENT ANALYSIS OF CHOPPER CONTROLLED KRAMER DRIVE

Abstract

Over years efforts have been made to devise methods through which variable speed feature could be introduced in a.c. drives. In the process, a rumber of methods have come up for both cage and wound-rotor type of induction motors. Whereas, normally, the cage type of induction motors are run from variable frequency voltage or current source, the wound rotor type induction motors are run from fixed frequency source and speed control is exercised from rotor side. When principle of slip-power recovery is employed, the drive may be run in constant power or constant torque mode depending upon whether the recovered slip energy is returned to shaft or supply mains, respectively. Von Ch. Kramer introduced in 1908, a constant power type of slip energy recovery drive in which the slip power of wound rotor induction motor (main motor) is rectified and fed to a d.c. motor which is directly coupled to the main motor. Speed control in subsynchronous region is accomplished by varying the field current of d.c. motor. The size of d.c. motor goes on increasing as speed range is increased. For a speed range from synchronous to half synchronous speed, a d.c. motor of same rating as that of induction motor is required. For greater speed range, d.c. motor size becomes uneconomically large. In the present work a modification has been introduced in the Kramer drive to enhance its capability in terms of speed control range. An electronically monitored d.c. chopper is introduced, series connected, in the d.c. link of the drive. By reducing the duty cycle of the chopper, the effective arma ture voltage of the d.c. motor and hence the speed of the drive may be reduced. Chopper control, however, results in increased copper losses in the rotor circuit. It is therefore used only when the drive is to be operated at speeds which are less than the lowest obtainable by field control alone. The modified drive can provide speed control in the entire sub synchronous region with a d.c. motor of same size as that of induction motor. The aim of present study is to develop the analytical tool for analysing the steady state and transient behaviour of chopper-controlled Kramer drive system. An idealised model describing the behaviour of the system has been developed based on the concept of coupled circuit approach. The system is analysed in a synchronously rotating reference frame. The generalised two-axes non-linear differential equations of the system are established from the equations of the symmetrical induction machine and from the equations which express relation ship between rectifier, chopper and d.c. motor variables. The parameters involved in these equations are such that they can be easily measured experimentally at the terminals of the induction and d.c. machines. The steady state equations of the system are obtained by setting the time rate of change of all currents to zero in the generalised system equations. The expressions have been developed for the supply current, power factor, efficiency and various copper losses in the drive. Using these equations steady state operating characteristics of the drive are determined both under field control and chopper control and plotted against slip. The effect of rotor current time harmonics has also been investigated by developing the harmonic equivalent circuit of the drive. The ~ system having an•-induction motor of 3-75 KW and a d.c. motor of same size, is fabricated using power diodes in the bridge rectifier, SCRs in the chopper and operational amplifiers in the control circuit. The fabrication work also includes a current feedback and a speed feedback loop for closed loop operation. The open loop results of steady state performance have been obtained experimentally. A good correlation is obtained between computed and experimental results. The reasons for discrepancies observed, have also been explained with the help of oscillograms of voltages and currents at different points of the drive's circuit under field control and chopper control. The development of adjustable speed a.c. drives has led to an Increased interest ii the stability considerations. It is now well known that instability can exist, even in symmetrical induction machines, if the parameters of the machine are incorrectly chosen. Stability behaviour of chopper controlled Kramer drive has, therefore, been investigated. The perturbation equations are derived by linearizing the dynamic equations of the system about an operating point. The characteristic equation is then developed directly from these perturbation equations. This system is represented by fifth order characteristic equation, which is then solved to obtain the eigenvalues. Drive's relative stability is examined by dominant eigenvalue approach. Effect of varying drive s parameters on movement of eigenvalues with respect to imaginary axis is noted. The results so obtained have -ivbeen verified by observing drive's computed transient response upon application of a sudden increase in load by a small amount. The transient response to sudden increase in load has also been obtained experimentally and the oscillograms of speed signal recorded under variation of supply voltage, field current and chopper duty cycle- The nature of the oscillograms is discussed from the viewpoint of relative stability and results compared with theoretical findings. The investigation of transient behaviour of the system is of great practical importance, because of severe instantaneous torque generation during the transition period imposing undue strain on the mechanical parts of the drive. To investigate the' transient behaviour,the non-linear differential equations des cribing the dynamics of the system have been simulated on a digital computer and solved by the application of Runge-Kutta method. As the most important transients from electromechanical considerations are those of electromagnetic torque and speed, these are investigated in detail when the system is started from rest under no load and loaded condition. The transients in supply currents are also computed. The effect of variation in supply voltage, system inertia, d.c. link reactance, settings of field current and chopper duty cycle on these transients following a switching operation have been investigated. The current transients have been recorded experimentally also and the oscillograms are compared with computed transients for peak values and settling time.The drive has also been provided with speed and current feedbacks for closed loop speed control. Speed is regulated by speed controller and the current controller checks the drive from drawing dangerously high currents during the process of speed correction- The parameters of speed and current controllers should be such as to provide stable operation with good transient response, under all possible operating condition. This has been graphically examined by the D-partition technique. Stability contours are plotted in the plane of controller parameters, gain and time constant, for different operating conditions and the common area is picked up for selecting the values of controller parameters. This process yields a design that offers good damping as well as less settling time. PI type of controllers are used for both current and speed loops. The correctness of design has been verified from the transient response, obtained from state model of the drive with feedback loops. Oscillograms showing drive s response to change in reference speed and change in load are recorded which exhibit the effectiveness of the closed loop operation. The drive has been found to be a good proposition as a variable speed, first quadrant drive which exhibits very good stability and transient response and offers steady state operation at good efficiency and power factor. The harmonics reflected into the power system on account of this drive are negligible.