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Electrical Engineering

, Volume 101, Issue 3, pp 943–967 | Cite as

Multi-band power oscillation damping controller for power system supported by static VAR compensator

  • Wesley PeresEmail author
Original Paper
  • 76 Downloads

Abstract

Low-frequency electromechanical oscillations damping is powerfully crucial in power system operation. In order to fulfill this requirement, power oscillation damping (POD) controllers are installed in synchronous generators and flexible alternating current transmission system devices. These controllers can have either a conventional fixed structure composed by stages of gain and phase compensation or a multi-band modern structure (PSS4B) composed by three bands that correspond to a specific frequency range (low, intermediate and high frequency). In the PSS4B structure, each band consists of two branches based on differential filters (with a gain, lead–lag blocks and a hybrid block). This paper investigates the application of PSS4B as a POD controller for the static VAR compensator (PSS4B-SVC-POD) to damp oscillations in multi-machine power systems. The proposed PSS4B-SVC-POD and power system stabilizers (fitted on generators) are simultaneously designed through an optimization approach aiming at maximizing the closed-loop damping ratio. Modal analysis, frequency responses and time simulations for the well-known two-area four-generator power system show the good performance of the proposed controller fitted on static VAR compensator.

Keywords

Power oscillation damping controller Static VAR compensator Multi-band PSS4B Power system stabilizers Coordinated design 

List of symbols

General

AVR

Automatic voltage regulator

FACTS

Flexible alternating current transmission systems

MB-PSS

Multi-band power system stabilizer (PSS4B)

POD

Power oscillation damping

PSM

Power sensitivity model

PSO

Particle swarm optimization

PSS

Power system stabilizers

PSS4B

Modern multi-band power system stabilizer (MB-PSS)

PSS4B-POD

Proposed POD controller based on the multi-band PSS4B

PSS4B-SVC-POD

Proposed POD controller for SVC based on the multi-band PSS4B

SSSC

Static synchronous series compensator

STATCOM

Static synchronous compensator

SVC

Static VAR compensator

SVC-POD

Conventional POD fitted on SVC

TCR

Thyristor-controlled reactor

TCSC

Thyristor-controlled series compensator

Number of devices

nb

Number of busses

ng

Number of generators

npod1

Number of conventional POD controllers

npod2

Number of multi-band PSS4B-POD controllers

npss

Number of conventional power system stabilizers

nsvc

Number of static VAR compensators

Power system variables

\( \varOmega_{k} \)

Set of nodes connected to bus k

Dk

Damping constant of generator k (pu)

EFDk

Field voltage (exciter output) of generator k (pu)

Eqk

Internal voltage of generator k, proportional to the rotor field flux in the direct axis (pu)

Hk

Inertia constant of generator k (s)

Idk

d-axis stator current of generator k (pu)

KAk, TAk

Gain (pu) and time constant (s) of AVR at generator k

KSVCi, TSVCi

Gain (pu) and time constant (s) of the dynamic model of SVC i

PGk, QGk

Real and reactive generated powers at node k (pu)

PLk, QLk

Real and reactive power loads at node k (pu)

Pkm, Qkm

Real and reactive power flows from node k to node m (pu)

Pmk

Mechanical power of generator k (pu)

QSVC

Injected reactive power at node k (pu)

Td0 k

d-axis open-circuit time constant of generator k (s)

VPOD i

Supplementary stabilizing signal (POD output) of SVC i (pu)

VPSS k

Supplementary stabilizing signal (PSS output) of generator k (pu)

VREF1 k

Reference voltage of AVR of generator k (pu)

VREF2 i

Reference voltage of SVC i (pu)

Vk

Voltage magnitude at node k (pu)

Xdk

d-axis synchronous reactance of generator k (pu)

Xdk

d-axis transient reactance of generator k (pu)

Xqk

q-axis synchronous reactance of generator k (pu)

bSVC

Susceptance of SVC (pu)

δk

Internal angle of generator k (degrees)

θk

Voltage phase at node k (degrees)

ωs

Synchronous speed (rad/sec)

Δ

Deviation operator (used in linearized system of equations)

\( \Delta \omega_{puk} \)

Rotor speed deviation of generator k (pu)

\( \varvec{f}\left( {\varvec{x},\varvec{z},\varvec{u}} \right) \)

Set of first-order nonlinear differential equations

\( \varvec{g}\left( {\varvec{x},\varvec{z},\varvec{u}} \right) \)

Set of nonlinear algebraic equations

u

Vector of input variables

x

Vector of state variables

z

Vector of algebraic variables

Modal analysis

\( \xi_{\hbox{min} } \)

Damping ratio associated with the dominant eigenvalue in closed-loop operation

\( \varvec{J}_{1} ,\varvec{ J}_{2} ,\varvec{J}_{3} ,\varvec{J}_{4} \)

Derivative matrices

A

State space matrix

B

Input matrix

\( \lambda = \sigma \pm j\omega_{d} \)

Complex eigenvalue with real (\( \sigma \)) and imaginary (\( j\omega_{d} \)) components

\( \xi \)

Damping ratio of any complex eigenvalue

Power system controllers

FLi, FIi, FHi

Low-, intermediate- and high-band central frequencies of PSS4B-POD i (Hz)

KH11 i, KH17 i

High-band first lead–lag blocks coefficients of PSS4B-POD i (pu)

KH1 i, KH2 i

High-band differential filter gains of PSS4B-POD i (pu)

KI11 i, KI17 i

Intermediate-band first lead–lag blocks coefficients of PSS4B-POD i (pu)

KI1 i, KI2 i

Intermediate-band differential filter gains of PSS4B-POD i (pu)

KL11 i, KL17 i

Low-band first lead–lag blocks coefficients of PSS4B-POD i (pu)

KL1 i, KL2 i

Low-band differential filter gains of PSS4B-POD i (pu)

KLi, KIi, KHi, KGi

Low-band, intermediate-band, high-band and series gains of PSS4B-POD i (pu)

KPOD i

Gain parameter of conventional POD i (pu)

KPSS k

Gain parameter of conventional PSS k (pu)

T1iT2iT3iT4i

Time constants of conventional POD i (s)

T1kT2kT3kT4k

Time constants of conventional PSS k (s)

TH1 i, TH2 i, TH7 i, TH8 i

High-band time constants of PSS4B-POD i (s)

TI1 i, TI2 i, TI7 i, TI8 i

Intermediate-band time constants of PSS4B-POD i (s)

TL1 i, TL2 i, TL7 i, TL8 i

Low-band time constants of PSS4B-POD i (s)

Twi

Washout time constant of conventional POD i (s)

Twk

Washout time constant of conventional PSS k (s)

V1ckV2ckVPSSk

Algebraic variables of conventional PSS k (pu)

V1 ckV2 ckVPSS k

State variables of conventional PSS k (pu)

V1iV2iV3iV4iV5iV6i

Algebraic variables of PSS4B-POD i (pu)

V1iV2iVPODi

Algebraic variables of conventional POD i (pu)

V1iV2iV3iV4iV5 iV6 i

State variables of PSS4B-POD i (pu)

V1 iV2 iVPODi

State variables of conventional POD i (pu)

VPOD_LiVPOD_IiVPOD_Hi

Algebraic variables of PSS4B-POD i (pu)

VPOD i

Supplementary stabilizing signal (POD output) of SVC i (pu)

VPSS k

Output voltage of conventional PSS k (supplementary stabilizing signal) (pu)

Δyi

Input signal of POD i (pu)

Metaheuristics and optimization

c1, c2

Positive acceleration constants (PSO)

pbesti

Best location in history associated with the ith particle (PSO)

tmax

Maximum number of generations

wmaxwmin

Inertia weight bounds (PSO)

wt

Inertia weight (PSO)

\( \varvec{x}_{\varvec{i}}^{\varvec{t}} \), \( \varvec{v}_{\varvec{i}}^{\varvec{t}} \)

Position and velocity of the ith individual in the tth generation

gbest

Best location among all particles in history (PSO)

Notes

Acknowledgements

This work was supported by the following Brazilian Agencies: FAPEMIG (APQ-02245-18), CNPq and Capes (Finance Code 001). Besides, the technical support from GOCES (Optimization, Control and Power System Stability Research GroupUFSJBrazil) is greatly acknowledged.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electrical Engineering (DEPEL)Federal University of São João del-Rei (UFSJ)São João del-ReiBrazil

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