The Per Unit Notation

It is better to design the current loop first before the outer loop design is attempted. But it is necessary to describe the per unit notation that is adopted here. Let the rated armature voltage V_RA be the base voltage. Then equation (16) is valid. As shown in equation (17), the rated armature current I_RA is chosen to be the base current.

Per Unit Value of Rated Armature Voltage = 1 (16)

Per Unit Value of Rated Armature Current = 1 (17)

Then the base impedance for the armature circuit is obtained as shown in equations(18) whereas equation (19) shows how the per unit value of armature resistance can be obtained if it is r_a W. Given that the inductance present in the armature circuit is L_a H, the voltage across it is obtained as shown in equation (20). Equation (21) is obtained by dividing both sides of equation (20) by V_RA. Equation (21) uses symbol t_a, representing the time constant of the armature circuit and it is defined by equation (22).

For a 3-phase controlled-bridge rectifier circuit, the maximum average output voltage that can be obtained at 0^o firing angle is shown in equation (23). Then the amplitude of line voltage of 3-ph supply is described by equation (24). The per unit value of the peak line voltage is obtained from equation (25).

We have seen so far how voltages, currents and impedances related to armature circuit can be expressed in per unit values. Next, it is shown how the torque developed, moment of inertia J and friction coefficient B can be expressed in per unit values. Let the torque developed by motor be M_e N-m. Then when the motor is operating with the nominal or the rated flux, the torque developed by motor is defined by equation (26), where i_a is the armature current. Also, let w_r be the armature shaft speed in rad/s. Then the per unit value of the torque developed is expressed as shown in equation (27), where I_RA is the rated armature current.

The per unit value of moment of inertia is obtained as follows. Let W_R be the rated shaft speed in rad/s, and the moment of inertia of motor and the coupled load be J kg-m2. Let the torque required to accelerate this moment of inertia be MJ. Then equation (28) can be used to relate J and MJ. Dividing both sides of equation (28) by the rated torque, we get equation (29). From equation (29), it is seen how the per unit value of the moment of inertia can be obtained. Similarly, we can get an expression for friction coefficient, as shown by equation (30).

It is necessary to state how the parameters for the current controller should be specified. The gain, K_I , is just a ratio whereas the time constant, T_I , should be specified in seconds.

 
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