1. No category

A. Static Kramer drive in general
A static kramer drive is a method to obtain an injected voltage that is in phase with the
rotor current. The voltage at the slip rings is forced to be in phase with the rotor currents by the
diode rectifier. The magnitude of the slip ring voltage is set by the DC link voltage, which is in
turn set by the inverter connected back to the AC supply. In the diagram above and the analysis
presented, the inverter used is a thyristor converter. However, a PWM inverter can also be used.
1. Schema of the system ;
!
!
!
!
!
!
!
!
!
!
2. The motor fundamental phasor diagram (referred to the stator) ;
Vs = stator phase voltage,
Is=stator current,
Irf’ = fundamental rotor current referred to the
stator,
g
= air gap flux, Im=magnetizing current, and =PF
angle.
3. Torque expression ;
!
1/9
!
!
4. The phasor diagram for a static Kramer drive at rated voltage ;
!
!
!
!
!
!
!
!
5. AC Equivalent Circuit of Static Kramer Drive
-The two components are ;
- Thus the rotor power per phase is given
by ;
!
Ir=rms rotor current per phase,
Rr = rotor resistance, and
Pm’ = mech. output power per phase.
B.
MATHEMATICAL MODEL OF THE STATIC KRAMER SYSTEM
!
To develop the mathematical model of the Static Kramer system, the main elements of
the system will be analysed separately. Those main elements are the motor, the rectifier circuit
and the inverter circuit. Also the methodology for solving the system equations of the developed
model will be presented. [1]
2/9
a. Mathematical Model of the Induction Motor
b. Mathematical model of the Rectifier
c. Mathematical model of the Inverter
d. Solution of the Static Kramer Mathematical Model
!
1-
D-Q Model of Static Kramer Drive
!
That interest has been promoted by the need for more efficient and reliable drive systems.
The Static Kramer drive system is shown in fig. 1. In this system, the change in the rotor's
voltage is obtained through a change in the slip. Thus, the speed control of the induction motor
can be accomplished by varying the firing angle of the inverter.
There have been many attempts to propose a simplified model of the Static
Kramersystem. The use of the reference frame theory to develop the equations, which could be
used to predict the dynamic and steady state behaviour of an ordinary induction motor drive
system is very well, establishedUnfortunately, the derivation of the system voltage equations in
that model is incorrect and the resulting voltage equations are invalid this model has ignored the
effects ofthe commutation overlap angle and the harmonics associated with the inverter and the
rectifier lcircuits. Neglecting the commutation overlap angle may account for intolerable errors
in the computation of the electromagnetic torque.
To develop the
mathematical model of the Static
Kramer system shown in Fig. 1,
the main elements of the system
will be analyzed separately.
Those main elements are
the motor, the rectifier circuit, the
inverter circuit, and the smoothing
inductor.
Next, the implementation
of the commutation overlap angle
of the rectifier into the model will
3/9
be presented.
!
The drive system model can be obtained as:
where X, = --Xm,, X,, = X, + X,, X:, = Xir +
XAi , and p is the operator d/dt. X, , XI, and rs
are the magnetisation reactance, the leakage
reactance and the resistance of a stator phase
winding, respectively.
XI, and r, are the leakage reactance and the
resistance of a rotor phase winding referred to the
stator, respectively. Ob , we , and w, are the base
radian electrical frequency (the rated machine
frequency), the radian electrical frequency of the
supply voltage and the electrical angular speed of
the rotor, respectively.
To investigate the validity of the d-q model presented in the previous section, the Static
Kramer system is simulated mathematically and experimentally.
The simulated drive involves a three-phase, 380V, 5OHz, four pole, 4KW, 9.3A, slip ring
induction motor.
The measured parameters of the motor are; r, =1.31Q7 rT=2.04R, XI, =2.23Q7 X1,'=21.7Ll2,
X~=53.75!2, J=0.116 Kg.m2 (motor and load), and P=0.01536N.m/(rad/ sec). The simulated system
also includes a smoothing inductance (X'L = 803.7Q and f'L = 12.1552) and a three-phase
transformer (a=0.36). The motor speed is measured using an optical shaft encoder which
produces180 pulse/revolution.
!
For a= 120", fig. 2 shows that at t=5 Sec., the
calculated speed is equal to 674 rpm and the
measured speed is approximately equal to 680
rpm
!
!
!
4/9
!
!
For a= 120" the torque reaches l7N.m and at
steady state it decreases to 1.2N.m which is
sufficient to cove the friction losses.
As expected, the maximum torque may be
reduced by increasing a. However, as a gets
smaller, the torque oscillation gets larger.[2]
!
!
C. Fields of Usage
1- Kramer Drive Usage in Wind Turbines
!
An induction generator is identical to an
induction motor in construction. The squirrel cage
induction generators, double-fed induction
generators and wound rotor induction generators are
the commonly used induction generators. The power
is generated when the induction generator is made to
rotate above the synchronous speed by a source of
mechanical torque such as the wind turbine. Fig. 1
illustrates the torque-speed characteristics of an
induction generator.
!
From Fig. 1, it can be noted that
below the synchronous speed, the
machine operates as an induction
motor and above the synchronous
speed, the machine acts as an
5/9
induction generator. In the motoring mode, power is fed into the machine and in the
generating mode, the power flows from the machine to the grid. In the generating mode,
reactive power is consumed and hence it is compensated by providing compensating
capacitors.
!
The DFIG can also be viewed as the evolution of the SCIG and the WRIG made to
run at super-synchronous cascade, with bidirectional partially rated power converters. The
principle of operation of the DFIG is discussed in many papers. The stator circuit of the
DFIG is directly connected to the grid while the rotor is connected by means of a power
electronics converter.
!
The back-to-back converters consists
of two converters namely the machine side
converter and the grid side converter.
Between these two converters, a capacitor is
connected in order to maintain the DC-link
voltage constant or to keep the voltage
ripples as small as possible. With the
machine side converter, it is possible to
control the speed or the torque of the
machine and also to maintain the power factor at the stator terminals of the machine. In
addition, the function the grid side converter is to keep the DC-link voltage constant.
The DFIG generates power for speed up to 30% above and 30% below the
synchronous speed Ns. The three modes of operation of the DFIG are well explained at
below the synchronous speed, at the synchronous speed and above the synchronous speed.
For illustration purpose, consider a 60 Hz, 6-pole machine whose synchronous speed of
1200 rpm.
!
!
6/9
Fig. 5 shows the DFIG operation for speeds below the
synchronous speed. If the machine runs at 800 rpm, then
according to the related equations, the frequency of rotor
currents induced in the machine can be calculated.
Fig. 6 shows the DFIG operation at synchronous speed.
If the machine runs at its synchronous speed of 1200
rpm, then according to the related equations, the
frequency of rotor currents induced in the machine can be
calculated as Fig. 6.
!
Fig. 7 shows the DFIG operation for speeds above the
synchronous speed. If the machine runs above the
synchronous speed at 1600 RPM, then according to the
related equations, the frequency of the rotor currents induced
in the machine can be calculated as Fig. 7. [4]
2- Double Kramer Cascade Usage in the Differential Electrical Shafts
A new Electrical transmission drive that insures an adjustable constant speed difference between a
pair of mechanical shafts independent of load conditions or speed levels. This generalised electrical shaft
comprises two rotor interconnected induction machines, fed from different frequencies and two dc machines
forming a double Kramer cascade .
Advantages of Applying the Kramer Cascade to the system
The use of the Kramer cascades offers many important advantages over the alternative simpler
scheme of using resistors in the rotor circuit, namely, higher efficiency, much lower speed dependence on
load, and speed level adjustability in the subsynchronous range.
Various electrical shafts providing
exact speed correspondence in a pair of
mechanical systems have been investigated.
!
7/9
Two such well-known schemes are shown in Figures.
Connecting the induction machines to sources of different frequencies results in a constant speed difference
between the two rotors, irrespective of load
conditions or speed levels.
Why using Kramer Cascade on differential electrical shaft (DES) ;
•
The inherent performance is poor because of the need for the induction motors to develop synchronising
torques and their need for running at higher slip percentages which is done by using large value of
external rotor resistances.
•
Speed change is achieved by
changing the load which decreases
the efficiency (%50-60 at full load).
To overcome these
disadvantages the resistors in Fig.2 are
replaced by two Kramer cascades. Thus
the slip power wasted in the resistors are
recovered as added mechanical power to
the shafts through the dc machines
which is shown in Fig.3.[3]
8/9
References:
1-
Modeling and Speed Control Scheme for the Static Kramer Drive, Amr M. A. Amin, (Department
of Electric Power and Machines Faculty of Engineering and Technology Helwan University Cairo, Egypt)
2D-Q Model of the Static Kramer Drive System, Amr M. A. Amin, (Faculty of Engineering
and Technology Helwan University Cairo, Egypt)
3Differential Electrical Shaft Combined with Double Kramer Cascade ,Daniel Sharon,VOL.
IA-12. NO. 3,MAY/JUNE 1976
Doubly Fed Induction Generator for Wind Energy Conversion System – A Survey,Ram
4Meenakshi, (EE Department SSN College of Engineering Tamilnadu,India)
!
!
!
!
!
!
9/9