ECE 576 POWER SYSTEM DYNAMICS AND STABILITY Lecture 33 Power System Stabilizers (PSS) Professor M.A. Pai Department of Electrical and Computer Engineering © 2000 University of Illinois Board of Trustees, All Rights Reserved

Functions of a PSS PSS adds a signal to the excitation system proportional to speed deviation. This adds positive damping. Signal is generated locally from the shaft. Both local mode and inter-area mode can be damped. When oscillation is observed on a system or a planning study reveals poorly damped oscillations, use of participation factors helps in identifying the machine(s) where PSS has to be located. Tuning of PSS regularly is important. Modal Analysis technique forms the basis for multi-machine systems.

Basic Approach DAE Model Linearizing about an operating point PSS principles are best understood for a single machine infinite bus (SMIB) system.

SMIB System (Flux Decay Model) Flux Decay Model and Fast Exciter ~ How are computed for a multi-machine system?

Computation of Suppose at generator i we wish to obtain Consider rest of the machines as infinite buses with voltages fixed. From the physical terminal of generator i, obtain a Thevenin equivalent (i.e. short circuit all other generators and do network reduction) to get This can be repeated for all other generators to get the SMIB equivalents.

Stator Equations Assume Stator Algebraic Equations are:

Network Equations The network equation is (assuming zero phase angle at the infinite bus and no local load) Simplifying, ~

Complete SMIB Model Machine Stator equations Network equations ~

Linearization of SMIB Model

Linearization (contd) Final Steps involve Linearizing Machine Equations Substitute (1) in the linearized equations of (2).

Linearization of Machine Equations Symbolically we have Substitute (3) in (2) to get linearized model.

Linearized SMIB Model Excitation system is yet to be included. K1 – K4 constants are:

K1 – K6 Constants K1 – K4 only involve machine and not the exciter.

Computing Before linearizing exciter equations, compute is an algebraic variable in the Excitation System.

Computing While linearizing stator algebraic equations, we had Substitute this in expression for to get We thus have K1 – K6 constant. Next construct the Heffron – Philips model.

Heffron – Phillips Model Add a fast exciter Linearize This together with Gives SMIB Model

Block Diagram K1 – K6 affected by system loading and

Numerical Example Initial conditions ~

Initial Conditions (contd) From the stator algebraic equation,

Initial Conditions (contd) From non linear model, setting derivatives = 0, This completes the calculation of the initial conditions.

Computation of K1 – K6 Constants The formulas are used.

Effect of Field Flux on System Stability With constant field voltage, ,from block diagram are usually positive. For low frequencies and in steady state, Field flux variation due to feedback.(Armature reaction) introduces negative synchronizing torque.

Effect of Field Flux At higher frequencies This is a phase with Hence results in a positive damping component. In general, positive damping torque and negative synchronizing torque due to at typical oscillation frequencies (1-3 Hz).

Effect of Field Flux There are situations when can become negative. Case1. A hydraulic generator without damper winding, light load ( is small) and connected to a line with high ratio and large system. Case 2. Machine is connected to a large local load, supplied partly by generator and partly by remote large system. If , damping due to is negative

Effect of Excitation System Ignore dynamics of Gain through is If , then gain becomes positive. Large enough K5 may make system unstable

Numerical Example (Effect of ) Test system 1 Test System 2 Eigen Values Test System 1 Test System 2 unstable