Slip power recovery: static Kramer drive

Slip power recovery is a speed control method for wound-rotor (slip ring) induction motors in which the slip power $sP_g$, which would be wasted as heat in rotor resistance control, is taken out of the rotor and returned to the supply (or to the shaft). Speed is reduced by extracting power at slip frequency, so efficiency stays high.

Static Kramer drive

 3-ph supply ----+------------------+
                 |                  |
              stator          [step-up/match
             [ WRIM ]          transformer]
              rotor                 ^
                 |                  |
          [diode bridge] -- Ld -- [line-commutated
           (rectifier)    smoothing  thyristor inverter]
             Vd = 1.35 s E2          Vi = -1.35 VL' cos(alpha)

Working

1. Rotor voltage $sE_2$ at slip frequency ($E_2$ = standstill rotor line voltage) is rectified by an uncontrolled diode bridge:

$$V_d = \frac{3\sqrt2}{\pi}\, s E_2 = 1.35\, s E_2$$

2. A thyristor bridge working as an inverter ($90^\circ < \alpha < 180^\circ$) returns this dc power to the ac mains through a transformer ($V_L'$ = inverter-side ac line voltage):

$$V_i = -1.35\, V_L' \cos\alpha$$

3. Neglecting the drop in the dc link, $V_d = V_i$:

$$s E_2 = V_L' |\cos\alpha| \quad\Rightarrow\quad s = \frac{V_L'}{E_2}|\cos\alpha|$$

So the inverter firing angle sets the slip and hence the speed. At $\alpha = 90^\circ$ the counter voltage is zero and the motor runs near synchronous speed (as if the rotor were shorted); increasing $\alpha$ towards 180° increases the slip and lowers the speed. 4. Torque is proportional to the dc link current, $T \propto I_d$, so the drive behaves like a separately excited dc motor with armature voltage control. 5. The recovered power $\approx sP_g$ goes back to the supply, so overall efficiency is high.

Features: the converters are rated only for the slip power (e.g. a 30 % speed range needs about 30 % rating), so the drive is economical for limited speed ranges on large pumps, fans and compressors. Drawbacks: poor power factor (the inverter draws reactive power), harmonics, and a separate starting resistance is needed because the converter is not rated for full rotor voltage at standstill.

Can super-synchronous speed be obtained?

No. The diode bridge in the rotor allows power to flow only out of the rotor. Super-synchronous speed requires slip power to be fed into the rotor (negative slip). Therefore the static Kramer drive gives only sub-synchronous speed control in one direction (motoring, quadrant I). For super-synchronous operation the diode bridge must be replaced by a controlled converter so that power can flow both ways, i.e. the static Scherbius drive (a cycloconverter or two back-to-back thyristor/PWM converters, as in a doubly fed induction machine).