power system stability

Classification of power system stability-Angle and Voltage stability-

SMIB: Development of swing equation

SUBMITTED TO:MRS. ANJALI BHATNAGARRESEARCH SCHOLAR

SUBMITTED BY: ROHIT KUMAR

IC 1ST YR

Content

a) Classification of stabilityb) Dynamics Of A Synchronous Machinec) Synchronous Machine Swing Equationd) Single Machine Infinite Bus Bar Systeme) Small-signal Angle Stability

Introduction

Power System Stability Definition By IEEE Power system stability is the ability of an electric power

system, for a given initial operating condition, to regain a state of operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically the entire system remains intact. The disturbances mentioned in the definition could be faults, load changes, generator outages, line outages, voltage collapse or some combination of these.

ClassificationPower System Stability

Voltage Stability

Rotor Angle Stability Frequency Stability

Small DisturbanceStability

TransientSignal

TransientSignal

Small DisturbanceStability

Short term Short term orLong Term

Short term orLong Term

Rotor Angle Stability

It is the ability of the system to remain in synchronism when subjected to a disturbance. The rotor angle of a generator depends on the balance between the electromagnetic torque due to the generator electrical power output and mechanical torque due to the input mechanical power through a prime mover. Remaining in synchronism means that all the generators electromagnetic torque is exactly balanced by the mechanical torque. If in some generator the balance between electromagnetic and mechanical torque is disturbed, due to disturbances in the system, then this will lead to oscillations in the rotor angle. Rotor angle stability is further classified into small disturbance angle stability and large disturbance angle stability.

Voltage Stability

Voltage Stability Definition By IEEE: Voltage stability refer to the ability of power system to

maintain steady voltages at all buses in the system after being subjected to a disturbance from a given initial operating point. The system state enters the voltage instability region when a disturbance or an increase in load demand or alteration in system state results in an uncontrollable and continuous drop in system voltage.

Rotor Angle Stability Analysis

Assumptions:a) Balanced 3-phase system and balanced disturbances

considered.b) Deviation of frequency is small.c) Dc offset current and Harmonics are neglected.d) Network & impedance load are sane as steady state.e) Voltage &current& power flow can be computed by power

flow equations

Dynamics Of A Synchronous Machine

Continue…………

Synchronous Machine Swing Equation

Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The angle between the two is known as the power angle or torque angle. During any disturbance, the rotor decelerates or accelerates with respect to the synchronously rotating air gap mmf, creating relative motion. The equation describing the relative motion is known as the swing equation, which is a non-linear second order differential equation that describes the swing of the rotor of synchronous machine.

Swing Equation Without Damper Torque

A synchronous generator is driven by a prime mover. The equation governing the rotor motion is given by:

wherea) J is the total moment of inertia of the rotor mass in kgm2

b) Tm is the mechanical torque supplied by the prime mover in N-m

c) Te is the electrical torque output of the alternator in N-md) m is the angular position of the rotor in rad(Mech)

Swing Equation With Damper Torque

Problem

A 50Hz,20 pole hydro-electric generator rated at 500MVA ,20Kv has H=2MJ/MVA . Determine following:

a) Ws and Wsmb) Write swing equation for this generatorc) The generator is initially working at Pm=Pe=1.0 P.U with

δ0=10deggree when a 3-phase short circuit occurs at this terminals which result in its electrical output reduing to 0 for t>0. Determine its power angle δ, 3 cycle after the short circuit . Assume the mechanical input power Pm remains constant at 1.0P.U during this time.

Infinite Bus

A system having a constant voltage and constant frequency regardless of the load is called an Infinite Bus bar system. Thus, an infinite bus has a large power system. The amount of real and reactive power is drawn or supplied, does not affect its voltage and frequency. They both remain constant. In a power system, normally more than one alternators operate in parallel. The machine may be located at different places. A group of machines located in one place may be treated as a single large machine. The machine connected to the same bus, but separated by transmission lines of low reactance, may be grouped into one large machine. The operation of one machine connected in parallel with such a large system comprising many machines is of great interest. The capacity of the system is so large that its voltage and frequency is considered constant. The connection or disconnection of a single small machine or a small load on such a system would not affect the magnitude and phase of the voltage and frequency. The system behaves like a large generator having internal impedance zero and infinite rotational inertia.

Single Machine Infinite Bus Bar System

Equivalent Circuit Diagram

Explanation On Board

a) Swing equation for Two –machine Systemb) Swing equation for Multi machine Systemc) Swing equation for Coherently swinging of machines

Problem

A power plant has two 3-phase ,50 Hz generators with following rating:

Gen-1: 500MVA ,20Kv, 20Poles , H=3 SGen-2: 200MVA ,15Kv, 2Poles , H=6 Sa) Write the swing equation for each machine on a system base

of 100MVAb) If the machines are assumed to swing together (Coherent ) write the swing equation for the equivalent machine.

Small-disturbance or small-signal angle stability

It is the ability of the system to remain in synchronism when subjected to small disturbances. If a disturbance is small enough so that the nonlinear power system can be approximated as a linear system, then the study of rotor angle stability of that particular system is called as small-disturbance angle stability analysis. Small disturbances can be small load changes like switching on or off of small loads, line tripping, small generators tripping etc. Due to small disturbances there can be two types of instability: non-oscillatory instability and oscillatory instability. In non-oscillatory instability the rotor angle of a generator keeps on increasing due to a small disturbance and in case of oscillatory instability the rotor angle oscillates with increasing magnitude.

Problem

A 50Hz synchronous generator having inertia constant H=5MJ/MVA and a transient reactance Xd=0.2P.U is connected to an infinite bus through a purely reactive circuit as shown in figure. Reactance values are 0.4 P.U for each line .The diagram on a common real power of

a) P=0.6 P.U at 0.8 P.F lagging to the infinite bus at a voltage of V=1.0P.U and Δδo=10deggre , D(Damping coefficient )=0.15

b) P=0.6 P.U at 0.8 P.F lagging to the infinite bus at a voltage of V=1.0P.U , D(Damping coefficient )= -0.01 P.U

power system stability

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