DESIGN AND COMPARISON OF POWER SYSTEM STABILIZER BY CONVENTIONAL AND ROBUST H LOOP SHAPING TECHNIQUE

DESIGN OF POWER SYSTEM STABILIZER USING ROBUST CONTROL TECHNIQUESPRESENTED BY SOUMYABRATA BARIKNIT CALICUTM120193EEGUIDED BYDr. ABRAHAM T. MATHEW1ORGANIZATION OF THE PRESENTATIONObjectivesSmall Signal StabilityIntroduction to PSSRobust Control Techniques in Power SystemModeling of Power system for Small signal Stability Analysis (SMIB System)Simulation & Results for SMIB SystemModeling of Power system for Small signal Stability Analysis (Multimachine System)Simulation & Results for Multimachine SystemConclusion References

OBJECTIVESTo design a CPSS for SMIB by using conventional lag-lead compensator & eigenvalue analysis.

To find out a design strategy of PSS for SMIB by Robust Loop-Shaping Method.

H Robust Loop Shaping Power System Stabilizer design for Multi-Machine (3 Machines 9 Buses) Power System.

SMALL SIGNAL STABILITYAbility of power system to maintain synchronism under small disturbances.Low frequency oscillations occurs due to high gain fast responding AVR, the effect of transmit bulk power over long distance etc.Instability may be of two formIncrease in rotor angleRotor oscillation of increasing magnitude INTRODUCTION TO PSSA PSS is the most effective approach toIncrease the positive damping.Improve the steady state stability margin.Suppress the low frequency oscillation of power system.Provide additional damping torque without affecting synchronizing torque to improve power system stability.ROBUST CONTROL TECHNIQUE IN POWER SYSTEM

Mc-Farlene Glover Loop Shaping TechniqueROBUST CONTROLThe goal of Robust systems design is to retain assurance of system performance in spite of model inaccuracies & changes.

Robust control system exhibits the desired performance despite the presence of significant plant (process) uncertainties.

Mc-Farlane Glover Loop Shaping Method. STEPS TO DESIGN ROBUST LOOP SHAPING CONTROLLERMcFarlane Glover Loop Shaping Robust design can be divided into three stepsLoop Shaping.

Robust Stabilization

Design of The Final Robust Controller.

LOOP SHAPING DESIGNClosed loop performance is specified in terms of requirements on the open loop singular values.

Shaping of open loop singular value to give desired high or low gain at frequencies of interest.

Selection of compensators(W1 & W2) iteratively.

ROBUST STABILIZATION denotes stability margin for the normalized co-prime factor Robust Stabilization. provides a stability guarantee for the closed loop system.

Provides stability guarantee for closed loop system. can be uniquely determined by solving the following equation

CONTD.

Where denotes the maximum eigen value and X & Z are the solution of the two Riccati- Equations given as below

Where A,B,C are the state space coefficients of the system.

FINAL ROBUST CONTROLLERW1 is pre-compensator, designed in such a way that gain at low frequency range is very high to take into account the disturbances.

W2 is known as post-compensator. When we are not considering sensor noise W2 can be taken as Identity Matrix.

The final feedback controller is

FLOW CHART FOR RPSS DESIGN

MODELLING OF POWER SYSTEM FOR SMALL SIGNAL STABILITY ANALYSIS

Single Machine Infinite Bus SystemINTRODUCTIONDisturbances are so small that the linearization of system equation is permissible.Small signal analysis is based on linearization of a group of ODE (Ordinary Deferential Equation)that characterize the power system dynamics.Eigen value analysis can provide valuable information about inherent dynamic characteristics.SINGLE MACHINE INFINITE BUS

HEFFRON PHILLIPS MODEL To design the PSS first of all small signal model should be obtained for SMIB which is as below

STATE SPACE MODEL

And the State Variables areSIMULATION DIAGRAM

Simulation & Results PSS FOR SMIB SYSTEMFor Single Machine Infinite Bus System the PSS has been designed by Conventional Method and Robust Method.Conventional Bode Plot based Lag-Lead Compensator.Robust Mc-Farlene Glover Loop Shaping Technique Method.

CONVENTIONAL METHODThe delay introduced by Automatic Voltage Regulator can be obtained from GEP(s) of the system.Input of PSS Speed, Output Voltage

GEP(S)

DESIGNED PSS PARAMETERSNoParametersValues1420.249230.168341054.8827621.935970.675680.2560

ROBUST METHODFrom Eigen Value Analysis The System has poor damping at frequencies 1/0.2 and 1/0.06.Gain has to be increased at those points.Pre-compensator

As the sensor noise has been neglected

CONTD.

ROBUST CONTROLLERThe final Robust Controller is of the order of 9.The order is reduced by Hankel Norm Reduction Method. Reduced order is of 4.

The stability limit .

SPEED RESPONSE

TORQUE RESPONSE

LOAD ANGLE RESPONSE

MODELLING OF POWER SYSTEM FOR SMALL SIGNAL STABILITY ANALYSIS

Multimachine (3 Machines 9 Buses) Power SystemMULTIMACHINE POWER SYSTEM

POWER FLOW SOLUTION

HEFFRON-PHILLIPS MODELSynchronous machine model for small perturbation, developed by Heffron Phillips & Concordia doesnt include dynamic interaction between the machines. These interactions could have large effect on small and large and small machines.So a modification will be required which include these interactions. SMALL SIGNAL BLOCK DIAGRAM

INITIAL CONDITIONSTo find out the Heffron-Phillips constants in the above mentioned block diagram, initial conditions are required.

Initial conditions can be calculated from the load flow analysis of the Multimachine system by considering the steps as below

DETERMINATION OF INITIAL CONDITIONSSTEP 1: Generator current STEP 2: The machine rotor angle

STEP 3:

CONTD.STEP 4: The d and q axis component of the internal voltage for individual machine can be calculated as below

STEP 5: The equivalent field voltage for individual machine is

DETERMINATION OF P-H CONSTANTSK1 & K2: The constants can be found from electric torque equation

for all the values of i=1,2,.,j,.,n

CONTD.K3 & K4: The constants can be obtained from the internal voltage equation

for all the values of i=1,2,.,j,.,n

CONTD.K5 & K6: K5 and K6 can be obtained from the terminal voltage relation

for all the values of i=1,2,.,j,.,n

PARTICIPATION FACTORGives the relationship among the states and the Eigen mode.Participation factor can be formulated as

Normalized values to study the active influence of different state variables on a particular mode.

Simulation & Results INITIAL CONDITIONSPARAMETERSMACHINE--1MACHINE--2MACHINE--3-20.10296.984511.83362.390923.910916.11170.29920.46340.06230.72251.52260.83340.04340.25860.20281.03910.99191.004701.01790.8399.1.12161.18291.09021.14711.54241.1607

HEFFRON-PHILLIPS CONSTANTS

MATLAB SIMULINK MODEL

SIMULINK DIAGRAM FOR SUBSYSTEM

ROBUST METHODFrom Eigen Value Analysis The System has poor damping at frequencies 1/0.0763 and 1/0.34962.Gain has to be increased at those points.Pre-compensator

As the sensor noise has been neglected

CONTD.

ROBUST CONTROLLER FOR MULTIMACHINE SYSTEMThe final Robust Controller is of the order of 15.The order is reduced by Hankel Norm Reduction Method. Reduced order is of 3.Machine-1

CONTD.Machine-2

Machine-3

VOLTAGE RESPONSEMachine-1

VOLTAGE RESPONSEMachine-2

VOLTAGE RESPONSEMachine-3

SPEED RESPONSEMachine-1

SPEED RESPONSEMachine-2

SPEED RESPONSEMachine-3

ACCELERATING POWERMachine-1

ACCELERATING POWERMachine-2

ACCELERATING POWERMachine-3

CONCLUSIONFor SMIB system initially it was unstable but after introducing RPSS it is getting stable within 10 seconds.Comparison of the robust controller with the CPSS shows that H controller can achieve excellent robustness provided that the design of pre-compensator W1 is proper.The designed Robust controller is feasible according to Mc-Farlane Glover loop shaping technique cause stability margin is within limit.

CONTD.Pre-Compensator W1 has been designed by taking the uncertainty model (Load Variation).After applying the RPSS in Multimachine system it can be shown from the response curves that the parameters are settled down within 5 seconds.REFERENCESA.Jonaitis, Impact of Increased Frequency Excitation System on Stability of Synchronous Generator, ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN: 1392-1215, VOL. 19, NO. 4, 2013.

Dr. Ramesh Kumar, Mithilesh Das, R.K.Mandal, Ruchita, A Technique for Enhancement of power System Dynamics, INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE INVENTION, ISSN: 2319-6734, VOL. 2, Issue 3, March 2013, PP.47-55.

CONTD.Dordala. Pratap Hari Krishna, B N S P Venkatesh, G.Sai Sudheer, Design of Power System Stabilizer to Improve Small Signal Stability by Using Modified Heffron-Phillips Model, INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE & TECHNOLOGY,ISSN: 0975-5462, VOL. 3, NO. 6, June 2011.

Balwinder Singh Surjan, Ruchira Garg, Power System Stabilizer Controller Design for SMIB Stability Study, INTERNATIOINAL JOURNAL OF ENGINEERING & ADVANCED TECHNOLOGY, ISSN: 2249-8958, VOL.2, Issue 1, October 2012.CONTD.Chuanjiang Zhu, Mustafa Khammash, Robust Power System Stabilizer Design using H Loop Shaping Approach, IEEE TRANSACTION ON POWER SYSTEM, Vol. 18, No. 2, pp 810-819, May, 2003.

Dr. J. K. Mendiratta, Jayapal R. , H Loop Shaping Based Robust Power System Stabilizer for Three Machine Power System, INTERNATIONAL JOURNAL OF COMPUTER APPLICATION, Vol. 1, No. 7.