The document discusses the Static Kramer drive system, which allows a motor to operate at sub-synchronous speeds. It does this by converting the slip power in the rotor circuit into AC line power and returning it to the line using an inverter. At zero speed, the motor acts as a transformer and transfers all real power back to the line. Speed is controlled by varying the firing angle of the inverter, which adjusts the rotor slip and synchronous speed. The load torque is directly proportional to the DC link voltage and current, rotor speed, and inversely proportional to the turns ratio between the stator and rotor windings.

1. STATIC KRAMER SYSTEM

2. Slip power recovery
 Instead of wasting the slip power in the rotor circuit resistance, a better approach is
to convert it to ac line power and return it back to the line. Two types of converter
provide this approach:
1) Static Kramer Drive - only allows
operation at sub-synchronous speed.
2) Static Scherbius Drive - allows
operation above and below
synchronous speed

3. Static kramer system

4. At zero speed (s=1) the motor acts as a transformer and all the real power is
transferred back to the line (neglecting losses). The motor and inverter only
consume reactive power.
At synchronous speed (s=0) the power factor is the lowest and increases as slip
increases. The PF can be improved close to synchronous speed by using a
step-down transformer. The inverter line current is reduced by the
transformer turns ratio -> reduced PF.

5. SPEED CONTROL
 The average o/p voltage of the diode bridge connected to the slip rings is given by
 𝑉𝐶 =
3 2𝐸2 𝑠
𝜋
 𝑉𝐶 =1.35 𝐸2 s
 𝐸2= RMS line voltage on the rotor side
 S=slip
 Inverter mode:
 𝑉𝑖𝑛 =
3 2𝐸 𝑙 𝑠
𝜋
cos 𝛼 𝐸2= RMS line voltage of ac supply
 𝑉𝑖𝑛 =1.35 𝐸𝑙 cos 𝛼 𝛼=firing angle of the inverter

6.  𝑉𝐶 = −𝑉𝑖𝑛
1.35 𝐸2 s = - 1.35 𝐸𝑙 cos 𝛼
 𝑠 = −
𝐸 𝑙
𝐸2
cos 𝛼
 𝑠 = −
𝑁1
𝑁2
cos 𝛼
 Where
𝑁1
𝑁2
is the turns ratio of the stator to rotor winding which is fixed

7. SPEED CONTROL WITH LOAD
 Neglecting all losses in the diode and SCR bridges
Rotor slip power=DC link power
𝑠𝑃𝑅 = 𝑉𝐶 𝐼 𝐶
𝑠𝜔𝑠 𝑇 = 𝑉𝐶 𝐼 𝐶
𝑇 =
𝑉𝐶 𝐼 𝐶
𝑠𝜔𝑠
𝑉𝐶 = 𝑉𝑖𝑛 = 1.35 𝐸𝑙 cos 𝛼 & 𝑠 = −
𝑁1
𝑁2
cos 𝛼
𝑇 =
1.35𝐸𝑙 𝐼 𝐶
𝑁1
𝑁2
𝜔𝑠

8. Torque speed characteristics of static
Kramer system