Slide matlab based transient stability analysis of a power system

Power-system stability is a term applied to alternating-current electric power systems, denoting a condition in which the various synchronous machines of the system remain in synchronis

MATLAB-based transient

stability analysis of a power system

A PROJECT

ON:-MD SAMAR AHMAD (807056)

MUKESH KUMAR (807057) ADITYA SAHAY (807007)

JYOTI MAYEE PANI (807042)

PROJECT MENTOR:- Dr.C.K.Panigrahi

By:-1) ABSTRACT

3) LITERATURE RIVIEW &

MOTIVATION OF THE PRESENT

5) CASE STUDY

8) CASE STUDY OF A MACHINE NINE-BUS SYSTEM

THREE-9) SIMULINK

10) REFERENCES

CONTENTS:

Power-system stability is a term applied to

alternating-current electric power systems, denoting a

condition in which the various synchronous machines of the system remain in synchronism, or "in step," with each other Conversely, instability denotes a condition involving loss of synchronism, or falling "out of step."

Occurrence of a fault in a power system causes transients To stabilize the system load flow analysis is done Actually in

practice the fault generally occurs in the load side As

we controlling load side which will lead to complex problem in order avoid that we are controlling the

generator side

A MATLAB simulation has been carried out

to demonstrate the performance of the three-machine nine-bus system.

ABSTRACT

 BACK GROUND

The classical model of a multi machine may be used to study the stability of

a power system for a period of time during which the system dynamic

response is dependent largely on the kinetic energy in the rotating

masses

The classical three-machine nine-bus system is the simplest model

used in studies of power system dynamics and requires of minimum

amounts of data Hence such studies can be connected in a relatively short time under minimum cost

Among various method of load flow calculation Newton Raphson method is

chosen for calculation of load flow study If the oscillatory response of a power system during the transient period following disturbance is damped and the system settles in a finite time to a new steady operating condition, we say the system is stable If the system is not stable, it is

considered unstable This primitive definition of stability requires that the system oscillations should be damped This condition is

sometime called asymptotic stability and means that the system contains inherent forces that tend to reduce oscillation

INTRODUCTION

 In recent years, energy, environment, right-of-way, and cost problems

have delayed the construction of both generation facilities and new transmission lines, while the demand for electric power has

continued to grow This situation has necessitated a review of the

traditional power system concepts and practices to achieve greater

operating flexibility and better utilization of existing power systems

 Transient stability of a transmission is a major area of

research from several decades Transient stability restores the

system after fault clearance Any unbalance between the

generation and load initiates a transients that causes the rotors of the

synchronous machines to “swing” because net accelerating torques are exerted on these rotors If these net torques are sufficiently large to cause some of the rotors to swing far enough so that one or more

machines “slip a pole” and synchronism is lost So the calculation of

transient stability should be needed A system load flow analysis is required for it .The transient stability needs to be enhanced to optimize the load ability of a system, where the system can be loaded

closer to its thermal limits

LITERATURE RIVIEW & MOTIVATION

OF THE PRESENT WORK

 Occurrence of fault may lead to instability in a

system or the machine fall out of synchronism Load flow study should be done to analyze the transient stability of the power system If the system can’t

sustain till the fault is cleared then the fault in-stabilize the whole system If the oscillation in rotor angle around the final position go on increasing and the change in angular

speed during transient condition go on increasing then system never come to its final position The unbalanced condition

or transient condition may leads to instability where the machines in the power system fall out of

synchronism Calculation of load flow equation by

Newton Raphson method, Runge Kutta method, and

decoupled method gives the rotor angle and initial condition.

PROBLEM STATEMENT

 Each generator operates at the same synchronous speed

and frequency of 50 hertz while a delicate balance between

the input mechanical power and output electrical power is

maintained

 Whenever generation is less than the actual consumer

load, the system frequency falls On the other hand,

whenever the generation is more than the actual load, the

system frequency rise The generators are also

interconnected with each other and with the loads

they supply via high voltage transmission line.

 An important feature of the electric power system is that

electricity has to be generated when it is needed because

it cannot be efficiently stored Hence using a

sophisticated load forecasting procedure generators are scheduled for every hour in day to match the load

In addition, generators are also placed in active

standby to provide electricity in times of emergency This is referred as spinning reserved.

TRANSIENT STABILITY

• The power system is routinely subjected to a

variety of disturbances Even the act of switching on an appliance in the house can be regarded as a disturbance

• However, given the size of the system and the scale

of the perturbation caused by the switching of an appliance in comparison to the size and capability of the interconnected system, the effects are not

measurable Large disturbance do occur on the system These include severe lightning strikes, loss of transmission line

carrying bulk power due to overloading

• The ability of power system to survive the transition

following a large disturbance and reach an acceptable

operating condition is called transient stability

TRANSIENT STABILITY(cont.)

The physical phenomenon following a large disturbance can be

described as

follows:-•Any disturbance in the system will cause the imbalance between the

mechanical power input to the generator and electrical power output of the generator to be affected As a result, some of the generators will

tend to speed up and some will tend to slow down.

• If, for a particular generator, this tendency is too great, it will no longer

remain in synchronism with the rest of the system and will be

automatically disconnected from the system This

phenomenon is referred to as a generator going out of step.

TRANSIENT STABILITY(cont.)

Transient instability refers to the condition where there is a

disturbance on the system that causes a disruption in the

synchronism or balance of the system The disturbance can be a number of types of varying degrees of severity:

• The opening of a transmission line increasing the X L of the

system

• The occurrence of a fault decreasing voltage on the system (The

voltage at the fault goes to zero, decreasing all system voltages in the area.)

• The loss of a generator disturbing the energy balance and

requiring an increase in the angular separation as other generators

adjust to make up the lost energy

• The loss of a large block of load in an exporting area

TRANSIENT INSTABILITY

Acceleration or deceleration of these large generators

causes severe mechanical stresses

Generators are also expensive Damage to generators

results in costly overhaul and long downtimes for repair As a

result, they are protected with equipment safety in mind

As soon as a generator begins to go out-of-step, sensor in the system

sense the out-of-step condition and trip the generators In addition, since the system is interconnected through transmission lines, the imbalance in the generator electrical output power and mechanical input power is reflected in a change in the flows of power on

transmission lines

As a result, there could be large oscillations in the flows on the

transmission lines as generator try to overcome the imbalance and their output swing with respect to each other

EFFECT OF TRANSIENT INSTABILITY

ELEMENTARY VIEW OF TRANSIENT STABILITY

Consider the very simple power system of Fig

2.2, consisting of a synchronous generator

supplying power to a synchronous motor over

a circuit composed of series inductive

reactance X

Each of the synchronous machines may be

represented, at least approximately, by a

constant voltage source in series with a

constant reactance

Thus the generator is represented by EG and

XG ; and the motor, by EM and XM

Upon combining the machine reactance and

the line reactance into a single reactance, we

have an electric circuit consisting of two

constant-voltage sources, EG and EM,

connected through reactance

X =X G + XL + XM

It is shown that the power transmitted from the generator to the motor depends upon the phase difference δ of the two voltages EG and EM Since these voltages are generated by the flux produced by the field windings of the machines, their

phase difference is the same as the electrical angle between the

 The electromechanical equation describing the relative motion of the rotor load angle (δ) with respect to the stator field as a function of time is known

 Pt = Shaft power input corrected for rotational loss

 Pu = Pm sin(δ)=electric power output corrected for rotational losses

 Pm= amplitude of power angle curve

 δ = rotor angle with respect to a synchronously rotating referance

SWING EQUATION

EQUAL AREA CRITERION

• (lim δo,δ1) ∫ Pa (d δ ) =A1 (positive area);

• (lim δ1,δ2) ∫ Pa (d δ) =A2 (negative area);

A 1= Area of acceleration

A2= Area of deceleration

If the area of acceleration is larger than the area of deceleration, i.e.,

A 1 > A2 The generator load angle will then cross the point δm, beyond which the electrical power will be less than the mechanical power forcing the

accelerating power to be positive

The generator will therefore start accelerating before is slows down

completely and will eventually become unstable If, on the other hand, A1< A2, i.e., the decelerating area is larger than the accelerating area, the machine will decelerated completely before accelerating again

The rotor inertia will force the subsequent acceleration and deceleration areas

to be smaller than the first ones and the machine will eventually attain the steady state If the two areas are equal, i.e., A 1 = A 2 , then the accelerating area is equal

to decelerating area and this is defines the boundary of the stability limit

EQUAL AREA CRITERION (cont.)

curves of all the machines of a system will show whether the

machines will remain in synchronism after a disturbance In a multi machines system , the output and hence the accelerating power of each machine depend upon the angular positions –and also upon the angular speeds-of all the machines of the system

POINT-BY-POINT SOLUTION OF THE SWING EQUTION

i. M1(d2 δ)1 /dt2) =Pi1 – PU1 (δ1 , δ2 , δ3 , dδ1 /dtdt , dδ2 /dtdt , dδ3 /dtdt )

ii.M2(d2 δ)2 /dt2) =Pi2 – PU2 (δ1 , δ2 , δ3 , dδ1 /dtdt , dδ2 /dtdt , dδ3 /dtdt )

iii.M3(d2 δ)3 /dt2) =Pi3 – PU3 (δ1 , δ2 , δ3 , dδ1 /dtdt , dδ2 /dtdt , dδ3 /dtdt )

Formal solution of such a set of equations is not feasible even the simplest

case.so we go for point to point solution which is most feasible and widely

used way of solving the swing equations such solution which are also called step by step solutions ,are applicable to the numerical solution of all sorts of differential equations Good accuracy can be attained and the computational are simple

In a point by point solution one or more of the variables are assumed either to

be constant or to vary according to assumed laws throughout a short interval

of time ∆t , so that as a result of the assumptions made the equations can be solved for the changes in the other 2variables during the same time interval Then, from the values of the other variables at the end of the interval, new value can be calculated for the variables which were assumed constant These new value are then used in the next time interval



In a multi-machine system ,there

are three simultaneous differential equations likes :-

In applying the point by point method to the solution of

swing equations, it is customary to assume that the accelerating power is constant during each time constant during each time

interval, although it has different values in different variables.

The point by point solution of swing curve consists of two

processes which are carried out

alternately:- The first process is the computational of the angular positions,

and perhaps also of the angular speeds at the end of the time

interval from a knowledge of the positions and speeds at the

beginning of the interval and the accelerating power assumed

constant for interval

 The second process is the computational of the accelerating

power of each machine from the angular position of all machines

of the system The second process requires knowledge of network solution.

Methods of solution of swing

equations:

 Dividing the time interval t in n intervals

 From equations (1) &(2)

 The equations 3,4,5&6 are suitable for point-by-point calculation.

the preceding interval can be calculated as

δn - δn-1 = ∆δn ;

or, δ n-1 - δ n-2 = ∆δ n-1 ;

or, ωn -1 - ωn-2 = ∆ωn-1 ; From equation (5)

∆ ω n-1 = (P a(n-2) ∆t /dtM); ………….(10) using eq (9) &(10)

∆ δn = ∆δn-1 + ∆t Pa(n-2) ∆t /dtM +(Pa(n-1) - Pa(n-2)) (∆t ) 2 /dt2M;

Or, ∆t(ω δn = ∆t(ωδn-1 +(Pa(n-1) + Pa(n-2)) (∆t(ωt )2/2M; …… (final eq for point by point soln.)

Mathematical derivation for computational algorithm



A synchronous machine performing oscillation of small amplitude with respect to an infinite bus ,its power output may be assumed to be directly proportional to its angular

displacement from the infinite bus considering a 50 cycle machine for which H = 2.7

Mj-per Mva And which is operating in the steady state with input and output of 1.00

pu and angular displacement of 45 o (elec.) with respect to an infinite bus Upon

occurrence of a fault ,we assume that the input remains constant and that output is given

The inertial constant is

M = H /dt(pi*f) =2.7/dt(pi*50) = 017188( unit power sec 2 per elec.rad )

or ,M = H/dt(180*f) =0.30micro ( unit power sec 2 per elec.deg )