1. (Systems And Control Engineering) (Deptartment of Electrical Engg.)
Design of Decentralized Power System Stabilizer for Multi Machine System using Fast Output Sampling Feedback Technique
Authors
RAJEEV GUPTA
B. BANDYOPADHYAY
(Systems And Control Engineering)
A. M. KULKARNI
(Deptartment of Electrical Engg.)
I.I.T.Bombay, MUMBAI
INDIA

2. Introduction Modeling of Multi machine system
Decentralized Fast output sampling feedback control method
Numerical Example
Conclusion
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3. General methods used for PSS design
Phase compensation method
Root locus method
State feedback method
H based optimal control method
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4. Power System Stabilizer
Basic Concept
Performance Objective
Classical Stabilizer implementation procedure
Transfer function of PSS is
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5. State space model of Multi Machine System
For kth machine
Complete state space model
Continued…
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6. 4 Machine 10 Bus system AREA 1 AREA 2 To Load 7 9 10 1 3 6 8 25 9 10 1 3 6 8 2 4
To Load
4 Machine 10 Bus system
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7. Fast Output Sampling Feedback
Consider a plant described by a linear model
Assume the plant is to be controlled by a digital controller,
with sampling time t and a state feedback gain F such that the
closed loop system
has desired properties
Continued…
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8. Instead of using a state observer, the following sampled data
control can be used to realize the effect of the state feedback
gain F by output feedback Let D =t/N,
For
Continued…
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9. Fast Output Sampling Feedback Method
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10. To show how a fast output sampling controller can be designed to
realize the given sampled-data state feedback gain, we construct a
fictitious, lifted system for which can be interpreted as static
output feedback.
Let ( F,G ,C ) denote the system at the rate 1/D
where
Continued…
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11. LC=F Assume that the state feedback gain F has been designed that
(F t+G t F) has no eigenvalues at the origin.
Then, assuming that in intervals k t < t < kt +t
one can define the fictitious measurement matrix
which satisfies the fictitious measurement equation yk =Cxk.
For L to realize the effect of F, it may satisfy
LC=F
for N >n
Continued…
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12. LMI Formulation of above equations are
To reduce this effect we relax the condition that L exactly satisfy the above linear equation and include a constraint on the L
LMI Formulation of above equations are
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13. Decentralized Fast Output Sampling Feedback
In fast output sampling feedback for multi machine system, gain matrix is generally full
This results in the control input of each machine being a function of outputs of all machines.
Due to the geographically distributed nature of power system and lack of communication system (unavoidable delays), the decentralized control scheme may be more feasible than the centralized control scheme.
Decentralized fast output sampling feedback control can be achieved by making the off diagonal elements L= [L0 L1 L2 …..L N-1] of matrices zero.
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14. Numerical Examples Decentralized Fast output sampling feedback method
The 4 machines, 10 bus Multi- Machine Power System data are considered.
Discrete model is obtained for the sampling time t =0.01 sec.
Stabilizing state feedback gain matrix F (4x16) is obtained.
Using LMI approach, decentralized fast output sampling feedback gain matrix L ( 4x16) is obtained.
The closed loop responses with this decentralized gain L for
linearized model of all four machines are satisfactory and able to
stabilize the outputs. The eigenvalues of (FN+GLC) are found to
be within the unit circle.
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15. Nonlinear Simulations
The slip of the machine is taken as output and the initial value of slip is taken as zero
The output slip signal with decentralized gain L and a limiter is added to Vref signal which is used to provide additional damping
The disturbances considered is self clearing fault at third bus cleared after 0.1 second
The limits of PSS output are taken as to +0.1.
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16. Open and closed loop response using decentralized FOS Method
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17. Open and closed loop response with fault using decentralized FOS
method
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18. Concluding Remarks
Decentralized fast output sampling feedback method can be used for designing power system stabilizers for multi machine power system.
The control input for these generators are required of small magnitudes.
The method is more general than static output feedback .
This controller can be applied simultaneous to all machines.. This single controller gives the effect of 4 individual controller for each machine.
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