(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

Introduction Modeling of Multi machine system Decentralized Fast output sampling feedback control method Numerical Example Conclusion Syscon, IIT Bombay

General methods used for PSS design Phase compensation method Root locus method State feedback method H based optimal control method Syscon, IIT Bombay

Power System Stabilizer Basic Concept Performance Objective Classical Stabilizer implementation procedure Transfer function of PSS is Syscon, IIT Bombay

State space model of Multi Machine System For kth machine Complete state space model Continued… Syscon, IIT Bombay

4 Machine 10 Bus system AREA 1 AREA 2 To Load 7 9 10 1 3 6 8 2 5 9 10 1 3 6 8 2 4 To Load 4 Machine 10 Bus system Syscon, IIT Bombay

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… Syscon, IIT Bombay

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… Syscon, IIT Bombay

Fast Output Sampling Feedback Method Syscon, IIT Bombay

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… Syscon, IIT Bombay

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… Syscon, IIT Bombay

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 Syscon, IIT Bombay

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. Syscon, IIT Bombay

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. Syscon, IIT Bombay

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 - 0.1 to +0.1. Syscon, IIT Bombay

Open and closed loop response using decentralized FOS Method Syscon, IIT Bombay

Open and closed loop response with fault using decentralized FOS method Syscon, IIT Bombay

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. Syscon, IIT Bombay