power system simulation - 2 lab manual (electrical engineering - power systems)

Power System Simulation Lab - 2

M.E (Power Systems Engineering) MATHANKUMAR.S, AP/EEE

EXPERIMENT: Date:

TRANSIENT ANALYSIS: SINGLE - MACHINE

INFINITE BUS SYSTEM

AIM

To become familiar with various aspects of the transient analysis of Single-

Machine Infinite Bus (SMIB) system.

OBJECTIVES

i. To understand modelling and analysis of transient stability of a

SMIB power system.

ii. To examine the transient stability of a SMIB and determine the

critical clearing time of the system through simulation by trial and

error method and by direct method.

iii. To determine transient stability margin (MW) for different fault

conditions.

iv. To obtain linearised swing equation and to determine the roots of

characteristics equation, damped frequency of oscillation and

undamped natural frequency.

SOFTWARE REQUIRED

TRANSIENT -SMIB module of AU Powerlab or equivalent

THEORETICAL BACK GROUND

Stability:

Stability problem is concerned with the behaviour of power system

when it is subjected to disturbances and is classified into small signal

stability problem if the disturbances are small and transient stability

problem when the disturbances are large. The description of the problems

are as follows.



Transient Stability

When a power system is under steady state, the load plus transmission

loss equals to the generation in the system.

The generating units run at synchronous speed and system frequency,

voltage, current and power flows are steady. When a large disturbance

such as three phase fault, loss of load, loss of generation etc., occurs the

power balance is upset and the generating units rotors experience either

acceleration or deceleration. The system may come back to a steady state

condition maintaining synchronism or it may break into subsystems or one

or more machines may pull out of synchronism. In the former case the

system is said to be stable and in the later case it is said to be unstable.

Mathematical Modelling For Transient Stability

Consider a single machine connected to an infinite bus shown in

fig. 1. An infinite bus is a source of invariable frequency and voltage.

Fig. 1. Single machine connected to infinite bus system

The equivalent circuit with the generator represented by classical model

and all resistances neglected is shown in fig. 2.

Fig. 2. Equivalent circuit



E‟ = E t + jX‟dIt

X = X‟d +XE where XE = Xtr + X1 || X2

Pe = |E‟||E B max (1)

X

Where, E‟ = e.m.f behind machine transient reactance

δ = rotor angle with respect to synchronously rotating reference

phaser EB L00. E‟ leads EB by δ

ωo = synchronous speed of rotor

Pe = electrical power output of generator in p.u

(2)

(2)

(3)



(4)

(5)

Swing Equation

During any disturbance in the system, the rotor will accelerate or decelerate

with respect to synchronously rotating axis and the relative motion begins. The

equation describing the relative motion is called as swing equation.

The following assumptions are made in the derivation of swing equation

1. Machine represented by classical model

2. Controllers are not considered

3. Loads are constants

4. Voltage and currents are sinusoids

The fundamental equation of motion of the rotor of the synchronous machine is

given by

(6)



Where, Pm = Mechanical power input in p.u

Pmax = Max. Electrical power out in p.u

H = Inertia constant in seconds.

δ = rotor angle in electrical radian measured from synchronous

by rotating reference frame.

ωo = Synchronous angular velocity rad / sec.

Rewriting equation (6) in state variable form

(7)

Changing rotor speed in to per unit and introducing damping torque, equation (7)

become

(8)

Where, Δωr = rotor speed deviation in p.u

Pm = mechanical input in p.u

KD = damping co-efficient in p.u

Numerical Integration Techniques

The differential equations (8) are to be solved using numerical techniques. There are

several techniques available and two of them are given below.

I. Modified Euler Method

Consists of the following steps

(i) Compute the derivative at t: PX(t) = f[X(t), Δt]

(ii) Compute first estimate : X1(t+Δt) = X(t) + PX(t) Δt

(iii) Compute the derivative : PX (t+ Δt)= f[X1(t + Δt), t+Δt]

(iv) Compute the average derivative : PXav (t) = ½ [PX(t) + PX(t+ Δt)

(v) Compute the final estimate : X(t+Δt) = X(t) + PXav(t) Δt

II. Fourth order Runge-Kutta Method

This is an explicit algorithm. The general formula giving the value of X

for the (n+1)th step is

Xn+1 = Xn + 1/6 (K1+ 2K2 +2K3 + K4) (9)

K1 = f(Xn, tn) Δt

K2 = f(Xn + K1/2, tn+ Δt/2) Δt

K3 = f(Xn + K2/2, tn + Δt

K4 = f (Xn + K3, tn + Δt) Δt



Determination of Critical Clearing Time

Critical clearing time is the maximum allowable time between the occurrence of a

fault and clearing of the fault in a system for the system to remain stable. For a given

load condition and specified fault, the critical clearing time for a system is found out

as follows. Choose a large clearing time say 30 cycles and decrease the clearing time

in steps of say two cycles and check for stability at each time step until the system just

becomes unstable. Vary the clearing time around this point in small step till you find

the clearing time which is just critical. The clearing time margin for a fault may be

defined as

Clearing time margin = critical clearing time – clearing time specified

= tc (critical) - tc (clearing)

Stability Margin in MW

Consider that the machine connected to infinite bus delivers Po MW (Fig. 1) and a

fault is specified at the end of line no. 1 with a clearing time tc = 0.3 seconds.

Suppose the MW output of the machine is increased in steps and stability is checked

for each step of load with the same clearing time and fault, then the system becomes

just stable at a loading say Pm and a small increase in load beyond Pm

causes instability; then the MW stability margin is defined as Ps = Pm - Po

Critical Clearing Time and Clearing Angle from Equal Area Criteria

This method can be used for quick prediction of stability but is applicable only to

single machine connected to infinite bus. The fundamental concepts and principles of

stability can be explained very well. Consider the system shown in fig. 1 . and its

model in .5. The terminal power is given by equation (1) and the power angle curves

for various operating condition is given in fig. 3.

Fig.3. Power angle curve

The steady state operating condition is given by point a and the corresponding

rotor angle is δo. Consider a three phase fault at location F on line 2 as shown in

fig. 1 . The fault is cleared by opening the circuit breakers at both ends of the line.

The p-δ plot for three network conditions are shown in fig. 3.

When the fault occurs, the operating point changes from a to b. Since Pm >

Pe, the rotor accelerates until the operating point reaches c where the fault is

cleared at δ1. The operation shifts to e. Now Pe>PM the rotor decelerates, but δ

continues to increase until the kinetic energy gained during the period of

acceleration (Area A1) is transferred to the system.



The operating point moves from e to f such that area A2 is equal to A1. The rotor

angle will oscillate back and forth around at its natural frequency such that

|area A1| = |area A2|. This is known equal area criterion.

Fig. 4. Equal area criterion for critical clearing angle

Critical Creating Angle an Time

With delayed fault clearing as shown in fig. 4 , the area A2 just equals to A1

at clearing angle equal to δc. Any further delay in clearing causes area A2 above

Pm less than A2 resulting in loss of synchronism, this angle δ c for which A1 = A2

is called critical clearing angle. The critical clearing angle can be computed as

Applying equal area criterion to fig. 4.

Integrating both sides and solving for δc

(10)

The corresponding critical clearing time is given by

Similarly you can find out δc and tc for the different types of faults.



Exercise

A power system comprising a thermal generating plant with four 555 MVA, 24kV,

and 60HZ Units supplies power to an infinite bus through a transformer and two

transmission lines

FIG: Single Machine Infinite Bus System

The data for the system in per unit on a base of 2220 MVA, 24 kV is given below:

An equivalent generator representing the four units, characterized by classical model:

Xd‟ = 0.3 p.u ;

H= 3.5 MW-s/MVA ;

Transformer: X = 0.15 p.u

Line 1 : X = 0.5 p.u ;

Line 2 : X = 0.93 p.u

Plant operating condition:

P = 0.9 p.u ;

Power factor: 0.9 lagging;

Et = 1.0 p.u

It is proposed to examine the transient stability of the system for a three-phase-to ground

fault at the end of line 2 near H.T bus occurring at time t= 0 sec. The fault is cleared at 0.07

sec. by simultaneous opening of the two circuit breakers at both the ends of line 2.



Viva Questions

1. Define critical clearing time.

2. What is transient stability limit?

3. Define critical clearing angle.

4. Write the expression for the critical clearing angle

5. What is power angle equation?

6. Define transient stability.

7. Write any three assumptions made upon transient stability.

8. Define Modified Eulers method.

9. List the methods of improving transient stability limit of a power system?

10. Define power angle diagram.

11. What is Voltage Collapse?

12. Define Runge – Kutta method.

13. What is meant by voltage instability?

14. What are the essential factors affecting the stability?

15. How will the transient stability limit of power system can be improved?

16. When is a power system said to be transiently stable?

17. What is transient state of power system?

18. What are the factors that affect the transient stability?

19. List the types of disturbance that may occur in a single machine infinite bus bar

system of the equal area criterion stability.

20. What are various faults that increasing severity of equal area criterion?



Result:

Marks split-up Marks

Secured

Marks

Awarded

Basic understanding 15

Theoretical Calculation 20

Conducting 15

Software output with graph 20

Comparison Results 10

Record 10

Viva - voce 10

Total Marks 100



EXPERIMENT: Date:

SMALL SIGNAL STABILITY ANALYSIS: SINGLE

- MACHINE INFINITE BUS SYSTEM

AIM

To become familiar with various aspects of the small signal stability analysis of

Single-Machine Infinite Bus (SMIB) system.

OBJECTIVES

i. To understand modelling and analysis of small signal stability of a SMIB

power system.

ii. To examine the small signal stability of a SMIB and determine the critical

clearing time of the system through simulation by trial and error method

and by direct method.

iii. To obtain linearised swing equation and to determine the roots of

characteristics equation, damped frequency of oscillation and undamped

natural frequency.

SOFTWARE REQUIRED

SMALL SIGNAL STABILTIY - SMIB module of AU Power lab or equivalent

THEORETICAL BACK GROUND

Stability:

Stability problem is concerned with the behavior of power system when it is

subjected to disturbances and is classified into small signal stability problem if

the disturbances are small and transient stability problem when the disturbances

are large. The descriptions of the problems are as follows.

Small Signal Stability

When a power system is under steady state, normal operating condition, the

system may be subjected to small disturbances such as variation in load and

generation, change in field voltage, change in mechanical torque etc. The

nature of system response to small disturbances depends on the operating

condition, the transmission system strength, types of controllers e t c .

Instability that may result from small disturbances may be of two forms

(i) Steady increase in rotor angle due to lack of synchronising torque.

(ii) Rotor oscillations of increasing magnitude due to lack of sufficient damping

torque.



Lack of sufficient synchronising torque results in instability through non-

oscillatory mode shown in fig.1., Fig.2. Shows the instability of a synchronous

machine through oscillations of increasing amplitude.

Fig.1 Non-Oscillatory instability Fig.2. Oscillatory instability

Swing Equation

During any disturbance in the system, the rotor will accelerate or decelerate

with respect to synchronously rotating axis and the relative motion begins. The

equation describing the relative motion is called as swing equation.

The following assumptions are made in the derivation of swing equation

1. Machine represented by classical model

2. Controllers are not considered

3. Loads are constants

4. Voltage and currents are sinusoids

The fundamental equation of motion of the rotor of the synchronous machine is

given by

(1)

Where, Pm = Mechanical power input in p.u

Pmax = Max. Electrical power out in p.u

H = Inertia constant in seconds.

δ = rotor angle in electrical radian measured from synchronous

by rotating reference frame.

ωo = Synchronous angular velocity rad / sec.

Rewriting equation (1) in state variable form

(2)



Changing rotor speed in to per unit and introducing damping torque, equation (2)

become

(3)

Where, Δωr = rotor speed deviation in p.u

Pm = mechanical input in p.u

KD = damping co-efficient in p.u

Modelling For Small Signal Stability

The electrical power output of the generator in p.u. is

Pe = |E‟ EB| sinδ (4)

X

In p.u. the air-gap torque is equal to air-gap power, Hence

(5)

Linearising equation (5) about in initial operating condition at δ = δ0

(6)

ΔTe = KS ΔS

Where, , called synchronising coefficient.

The state equations (3) are rewritten as

(7)

(8)

Where Tm , Te are in p.u. Δωr is per unit speed deviation, δ is the rotor angle in

electrical radians, ω0 is the base (rated) rotor speed in electrical radians per second,

KD is the damping coefficient in p.u., H is in p.u (seconds).



Linearising equation (7) and using (8) we get,

(9)

(10)

Fig.3 Block Diagram for Equation (10)

Taking Laplace transform for the above equation,

(12)

(13)

(14)

(15)



Damping ratio = ξ

The roots of characteristic equation are

S1 = ξ ωn + jωd

S2 = ξ ωn - jωd

Where, ωd is the damped frequency of oscillation given by

ωd = ωn - √1-ξ2

Taking inverse Laplace transform of equation (14) and (15) and taking Δ δ o = 10o

= 0.1745 radians; we get the equation for motion of rotor relative to

synchronously revolving field and the rotor angular frequency

(16)

(17)

Where θ = cos-1ξ

The response time constant τ = (1/ ξωn) = 2H / πf0 D)



EXERCISE

A power system comprising a thermal generating plant with four 555 MVA, 24kV,

60HZ units supplies power to an infinite bus through a transformer and two

transmission lines

FIG : Single Machine Infinite Bus System

The data for the system in per unit on a base of 2220 MVA, 24 kV is given below:

An equivalent generator representing the four units, characterized by

classical model:

Xd‟ = 0.3 p.u

H= 3.5 MW-s/MVA

Transformer: X = 0.15 p.u

Line 1 : X = 0.5 p.u

Line 2 : X = 0.93 p.u

Plant operating condition:

P = 0.9 p.u ; Power factor: 0.9 lagging;

Et = 1.0 p.u

It is proposed to examine the small-signal stability characteristics of the system

given in this problem about the steady-state operating condition following the loss

of line 2; Assume the damping coefficient KD = 1.5 p.u torque / p.u speed

deviation.

(a) Write the linearized swing equation of the system. Obtain the characteristic

equation, its roots, damped frequency of oscillation in Hz, damping ratio and

undamped natural frequency. Obtain also the force-free time response ∆δ(t) for an

initial condition perturbation ∆δ(0) = 5˚ and ∆ω(0)=0,using available software.



Viva Questions

1. Define power system stability.

2. What are the methods of maintaining stability?

3. How stability studies are classified, what are they?

4. What is steady state stability limit?

5. Define steady state stability.

6. What is stability study?

7. Given an expression for swing equation. Explain each term along with their units.

8. What are the assumptions that are made in order to simplify the computational

task in stability studies?

9. How is the machine connected to infinite bus?

10. What is meant by an infinite bus?

11. Give the control schemes included in the stability control techniques.

12. What are various faults that increase severity of equal area criterion?

13. State the applications of the equal area criterion.

14. What are the essential factors affecting the stability?

15. Define Inertia constant (H) & Movement of inertia (M).

16. What are the machine problems seen in the stability study?

17. What is small disturbance? Give some example.

18. How to you classify steady state stability limit. Define them.

19. When is a power system said to be steady state stable?

20. What are the system design strategies aimed at lowering system reactance?



Result:


Secured

Marks

Awarded



Conducting 15



Record 10

Viva - voce 10

Total Marks 100



EXPERIMENT: Date:

LOAD-FREQUENCY DYNAMICS OF SINGLE-AREA

POWER SYSTEMS

AIM

To become familiar with the modelling and analysis of load-frequency and

tie-line flow dynamics of a power system with load-frequency controller (LFC)

under different control modes and to design improved controllers to obtain the

best system response.

OBJECTIVES

i. To study the time response (both steady state and transient) of area

frequency deviation and transient power output change of regulating

generator following a small load change in a single-area power system with

the regulating generator under “free governor action”, for different

operating conditions and different system parameters.

ii. To study the time response (both steady state and transient) of area

frequency deviation and turbine power output change of regulating

generator following a small load change in a single- area power system

provided with an integral frequency controller, to study the effect of

changing the gain of the controller and to select the best gain for the

controller to obtain the best response.

iii. To analyse the time response of area frequency deviations and net

interchange deviation following a small load change in one of the areas

in an inter connected two-area power system under different control

modes, to study the effect of changes in controller parameters on the

response and to select the optimal set of parameters for the controller to

obtain the best response under different operating conditions.

SOFTWARE REQUIRED

„LOAD FREQUENCY CONTROL‟ module of AU Powerlab or equivalent.

THEORETICAL BACKGROUND

Introduction

Active power control is one of the important control actions to be performed

during normal operation of the system to match the system generation with the

continuously changing system load in order to maintain the constancy of system

frequency to a fine tolerance level. This is one of the foremost requirements in

providing quality power supply. A change in system load causes a change in the

speed of all rotating masses (Turbine – generator rotor systems) of the system

leading to change in system frequency. The speed change from synchronous

speed initiates the governor control (Primary control) action resulting in all the

participating generator – turbine units taking up the change in load, stabilizing

the system frequency. Restoration of frequency to nominal value requires



secondary control action which adjusts the load-reference set points of selected

(regulating) generator – turbine units. The primary objectives of automatic

generation control (AGC) are to regulate system frequency to the set nominal

value and also to regulate the net interchange of each area to the scheduled

value by adjusting the outputs of the regulating units. This function is referred

to as load – frequency control (LFC). The details of modelling and analysis of

LFC are briefly presented in the following sections.

Load-Frequency Control in an Interconnected Power System

An interconnected power system is divided into a number of “control areas” for

the purpose of load- frequency control. When subjected to disturbances, say, a

small load change, all generator – turbine units in a control area swing together

with the other groups of generator – turbine units in other areas. Hence all the

units in a control area are represented by a single unit of equivalent inertia and

characterized by a single (area) frequency. Since the area network is “strong”(all

the buses connected by adequate capacity lines), all the bus loads in a control

area are assumed to act at a single load point and characterized by a single

equivalent load parameter. The different control areas are connected by relatively

“weak” tie-lines. A typical n-area power system is shown in Fig.1.

Area 1

Other areas

Area i PNIi

Area n

Fig .1 Multi- Area Power System

For successful operation of an interconnected power system the following

operating principles are to be strictly followed by the participating areas:

i. Under normal operating conditions each control area should strive to meet

its own load from its own spinning generators plus the contracted

(scheduled) “interchange” (import / export) between the neighboring

areas.

ii. During emergency conditions such as sudden loss of generating unit, area

under emergency can draw energy as emergency support from the

spinning reserves of all the neighboring areas immediately after it is

subjected to the disturbances but should bring into the grid the required

generation capacity from its “hot” and “cold” reserves to match the lost

capacity and to enforce operating principle



(i) Satisfaction of principle (ii) during normal operation requires a load-

frequency controller for each area which not only drives the area

frequency deviation to zero but also the “net interchange” of that

area to zero under steady- state condition. “Net interchange” of area i, NIi

is defined as the algebraic sum of the tie- line flows between area i and other

connected areas (Fig .1) with tie-line flow out of area i taken as positive and

is given by

NIi = ΣPij (1)

j € αi

where αi is the set of all areas connected to area i

Modelling of Governor and Turbine

Governor with speed – droop characteristics

Governor is provided with a speed- droop characteristics so as to obtain stable

load deviation between units operating in parallel. The ideal steady- state speed

versus load characteristics of the generating unit is shown in Fig.2.

fNL

Frequency or

speed (p.u) Slope = -R

fFL

0 1.0

Power output (or) valve / gate position (p.u)

Fig .3 Steady-State Speed-Load Characteristics of

a Governor with Speed Droop

The negative slope of the curve, R, is referred to as “ Percent speed regulation or

droop” and is expressed as

Percent R = Percent speed or frequency change x 100

Percent power output change

=((fNL – fFL) / f0 ) x 100 where

fNL = steady-state frequency at no load

fFL = steady- state frequency at full load

f0 = nominal or rated frequency

For example a 5% droop means that a 5% frequency deviation causes 100%

change in valve position



Control of generating unit power output

The output of a generating unit at a given system frequency can be varied only

by changing its “load reference point” which is integrated with the speed

governing mechanism. The block diagram of a governor with the governor

droop R, the time constant of hydraulic amplifier TG and the load reference set

point is shown in Fig .4

GG(s)

-

∆f 1/R 1/(1+sTG) ∆Xv

+

Load reference

Fig.4 Governor with Speed Load Reference Set Point

The adjustment of load reference set point is accomplished by operating the

“speed changer motor”. This in effect moves the speed droop characteristics up

and down.

Turbine model

For the purpose of load-frequency dynamics the turbine may be modelled by

an approximate model with a single time constant TT as given by equation

∆PT(s) = GT(s) ∆Xv(s) = (1/(1+sTT)) ∆Xv(s) (2)

The block diagram for single-area load-frequency control is assembled by

combining equation (2) and Fig. 4. The block diagram is given in Fig. 5.

Modelling and Analysis of Single-Area Load-Frequency Control

Fig.5 Block Diagram for Single-Area Load – Frequency Control

In the above diagram, all powers are in per unit to area rated capacity and

the frequency deviation is in hertz.

Kp = 1/D Hz / p.u.MW

Tp = (2H/f0 D) s e c

The load damping constant D is normally expressed in percent and typical

values of D are 1 to 2 percent. A value of D = 1.5 means that 1.0 percent

change in frequency would cause a 1.5 percent change in load.



The dashed portion of the diagram marked as the secondary loop

represents the integral controller whose gain is KI. This controller actuates the

load reference point until the frequency deviation becomes zero.

Steady-state analysis with governor control

Let the disturbance be a step increase in load, M p.u. MW. With only governor

control (integral controller deactivated) the frequency deviation will not be made

zero. The steady-state frequency deviation ∆fs can be determined by applying

final value theorem in s-domain

∆fs = Lim s{∆fs } (3)

s >0

(4)

∆PD(s) = (M/s) (5)

Substituting equations (4) and (5) in equation (3) we obtain

∆fs = -(M / ß) Hz (6)

ß = Area Frequency Response Coefficient (AFRC)

ß = D +(1/R) Hz / p.u. MW

M is in p.u. MW



Example:

The data for a single-area power system is given below

Rated area capacity = Pr = 2000MW

Nominal operating load = P0D = 1000MW

f0 = 50 Hz; D=1 %; R = 3%; H = 5 sec

Load increase = M= 20 MW. Compute steady-state frequency deviation.

Solution:

Steady-state analysis with integral control

By reducing the full block diagram Fig .5. and by applying final value theorem in

s-domain, one can show that the steady-state frequency deviation is made zero.

Transient analysis

The block diagram Fig. 5 can be used to derive the state variable model with the

following four states:

x1 =∆fs = frequency deviation

x2 =∆PT = Turbine power deviation

x3 =∆Xv = Steam valve/water gate position x4

∆Pref = Load-reference setting

Transient response for step change in load can be obtained by numerically

integrating the four state equations through Runge – Kutta fourth order method

or any other method. AU Power lab or any available software can be used for

this purpose.



EXERCISES

It is proposed to simulate using the software available the load-frequency

dynamics of a single-area power system whose data are given below:

Rated capacity of the area = ________ MVA

Normal operating load = ________ MW

Nominal frequency = 50 Hz

Inertia constant of the area = ________sec

Speed regulation (governor droop)

of all regulating generators = ________

Percent Governor Time Constant = ________sec

Turbine Time Constant = ________ sec

Assume linear load–frequency characteristics which means the connected

system load increases by one percent if the system frequency increases by one

percent.

The area has a governor control but not a load-frequency controller. The area

is subjected to a load increase of 20 MW.

(a) Simulate the load-frequency dynamics of this area using available software

and check the following:

(i) Steady – state frequency deviation ∆fs in Hz. compare it with the hand-

calculated value using “Area Frequency Response Coefficient” (AFRC).

(ii) Plot the time response of frequency deviation ∆f in Hz and change in

turbine power ∆PT in p.u MW upto 20 sec. What is value of the peak

overshoot in ∆f?

(b) Repeat the simulation with the following changes in operating condition,

plot the time response of ∆f and compare the steady-state error and peak

overshoot.

(i) Speed regulation = 3 percent

(ii) Normal operating load = 1500MW



Viva Questions

1. What is the function of load frequency control?

2. How is the real power in a power system controlled/

3. What is meant by fly ball governor?

4. Define inertia constant.

5. What is area control error?

6. Define per unit droop.

7. Write the principle of tie line bias control.

8. State the basic role of ALFC.

9. What is meant by control area?

10. Write the tie line power deviation equation in terms of frequency.

11. Differentiate static and dynamic response of an ALFC loop.

12. What are the assumptions made in dynamic response of uncontrolled case?

13. Define Speed regulation.

14. What is mean by AFRC?

15. Draw a block diagram for single area load frequency control.

16. What is a need of speed changer?

17. Why load frequency control is important in operation of power systems?

18. What is ALFC?

19. Define time constant.

20. What is meant by frequency deviation?



Result:


Secured

Marks

Awarded



Conducting 15



Record 10

Viva - voce 10

Total Marks 100



EXPERIMENT: Date:

ECONOMIC DISPATCH IN POWER SYSTEMS

AIM

To understand the basics of the problem of Economic Dispatch (ED) of optimally

adjusting the generation schedules of thermal generating units to meet the system

load which are required for unit commitment and economic operation of power

systems.

To understand the development of coordination equations (the mathematical

model for ED) without losses and operating constraints and solution of these

equations using direct and iterative methods

OBJECTIVES

i. To solving ED problem without transmission losses for a given load condition /

daily load cycle using

(a) Direct

(b) Lambda-iteration method

ii. To study the effect of reduction in operation cost resulting due to changing

from simple load dispatch to economic load dispatch.

iii. To study the effect of change in fuel cost on the economic dispatch for a

given load.

SOFTWARE REQUIRED

„ECONOMIC DISPATCH‟ module of AUPowerlab or equivalent.




Mathematical Model for Economic Dispatch of Thermal Units without

Transmission Loss

Statement of Economic Dispatch Problem

In a power system, with negligible transmission loss and with N number of

spinning thermal generating units the total system load PD at a particular interval

can be met by different sets of generation schedules

{PG1(k), PG1(k), PG1(k),…………………………………….. PG1(k) }; where k = 1,2,3,……..NS.

Out of these NS sets of generation schedules, the system operator has to choose

that set of schedule which minimizes the system operating cost which is essentially

the sum of the production costs of all the generating units. This economic dispatch

problem is mathematically stated as an optimization problem.

Given: the number of available generating units N, their production cost

functions, their operating limits and the system load PD,

To determine: the set of generation schedule,

PGi ; i = 1,2,……N (1)

Which minimizes the total production cost,

N

Min : FT =Σ Fi(PGi) (2)

i = 1

and satisfies the power balance constraint

(3)

and the operating limits

PGi, min ≤ PGi ≤ PGi, max (4)

The unit production cost function is usually approximated by a quadratic function

Fi (PGi) = ai PG2i + bi PGi +ci ;i =1,2, …….N (5)

Where, ai, bi and ci are constants.



Necessary conditions for the existence of a solution to ED problem

The ED problem is given by the equations (1) to (4). By omitting the inequality

constraints (4) tentatively, the reduced ED problem (1),(2) and (3) may be

restated as an unconstrained optimization problem by augmenting the objective

function (1) with the constraint function Φ multiplied by LaGrange Multiplier λ to

obtain LaGrange function L as,

(6)

The necessary conditions for the existence of solution to (6) are given by

(7)

(8)

The solution to ED problem can be obtained by solving simultaneously the

necessary conditions (7) and (8) which state that the economic generation

schedules not only satisfy the system power balance equation (8) but also

demand that the incremental cost rates of all the units be equal to λ which can be

interpreted as “incremental cost of received power”

When the inequality constraints (4) are included in the ED problem the

necessary condition (7) gets modified as

(9)

Methods of Solution for ED Without Loss

The solution to the ED problem with the production cost function assumed to be

a quadratic function, equation (5), can be obtained by simultaneously solving

equations (7) and (8) using a direct method as given below.

(10)

From equation (10) we obtain

(11)



Substituting equation (1) in equation (8) we obtain

(12)

The method of solution involves computing λ using equation (12) and then

computing the economic schedules PGi; i = 1, 2, . . . . . . . . . . . . . . N using

equation (11). In order to satisfy the operating limits (4) the following iterative

algorithm is to be used.

Algorithm for ED without loss (For quadratic production cost function)

Step 1: Compute λ using equation (12)

Step 2: Compute using equation (11) the economic schedules

PGi ; i=1,2,…..N

Step 3: If the computed PGi satisfy the operating limits

PGi, min ≤ PGi ≤ PGi, max ; i=1,2,…..N (13)

then stop, the solution is reached. Otherwise proceed to step 4

Step 4: Fix the schedule of the NV number of violating units whose

generation PGi violates the operating limits (13) at the respective

limit, either PGi,max or PGi,min

Step 5: Distribute the remaining system load PD minus the sum of the fixed

generation schedules to the remaining units numbering NR (= N-NV)

by computing λ using equation (12) and the PGi;

P

Gi

i ∈ α NR using equation (11) where α NR is the set of remaining units.



Step 6: Check whether optimality condition (9) is satisfied.

If yes, stop the solution is reached. Otherwise, release the generation

schedule fixed at PGi,max or PGi,min of those generators not satisfying

optimality condition (9), include these units in the remaining units, modify

the sets αNV, αNR and the remaining load. Go to step 5

λ – Iteration Algorithm



Procedure

Using available software to solve the Economic Dispatch problem of a power

system with thermal units only for a given daily load cycle. Assume that the

production cost function of these units is quadratic and the transmission

loss of the system is negligible. Use the algorithm given in b e l o w

e x e r c i s e .

The program should have three sections: input section, compute section and

output section.

I. Input Section

The data to be read from an input file should contain the following:

(i) Number of thermal units in the system

(ii) Cost coefficients ai , bi , and ci , with cost in hundreds of rupees per

hour for all the units.

(iii) Maximum and minimum MW operating limits of all the units.

(iv) Daily load cycle in MW.

II. Compute Section

economic generation schedules for each one of the load levels in the load cycle

using the algorithm given in section 10.4.

III. Output Section

Create an output file in a report form comprising the following:

(i) Student information: as specified in exercise under experiment 3.

(ii) Input data: with proper headings

(iii) Results obtained: with proper headings for each load level

(a) Economic generation schedule of each unit

(b) Incremental fuel cost of each unit at economic schedule

(c) Incremental cost of received power.



Exercise

In a power system with negligible transmission loss, the system load varies

from a peak of 1200 MW to a valley of 500 MW. There are three thermal

generating units which can be committed to take the system load. The fuel

cost data and generation operation limit data are given below.

In hundreds of rupees per hour:

F1 = 392.7 + 5.544 P1 + 0.001093 P1 2 ; P1 in MW

F2 = 217.0 + 5.495 P2 + 0.001358 P2 2 ; P2 in MW

F3 = 65.5 + 6.695 P3 + 0.004049 P3 2 ; P3 in MW

Generation limits:

150 ≤ P1 ≤ 600 MW

100 ≤ P2 ≤ 400 MW

50 ≤ P3 ≤ 200 MW

There are no other constraints on system operation. Obtain an optimum

(minimum fuel cost) unit commitment table for each load level taken in

steps of 100 MW from 1200 to 500. Adopt “brute force enumeration”

technique. For each load level obtain economic schedules using the

Economic Dispatch Program developed in exercise for each “feasible”

combination of units and choose the lowest fuel cost schedule among

these combinations.

Show the details of economic schedule and the component and total costs

of operation for each feasible combination of units for the load level of 900

MW.



Viva Questions

1. What is the purpose of economic dispatch?

2. In which condition, the transmission losses are negligible in economic dispatch

problem?

3. What is unit commitment?

4. Name the methods of finding economic dispatch.

5. What do you mean by base load method?

6. What is meant by total generator operating cost?

7. List the various constraints in the modern power systems.

8. What are the disadvantages of using participation factor?

9. What is the difference between load frequency controller and economic

dispatch controller?

10. What is Lagrangian multiplier?

11. Write the coordination equation neglecting losses.

12. What are the assumptions for deriving loss coefficients?

13. Draw incremental fuel cost curve.

14. Write the quadratic expression for fuel cost.

15. What is system incremental cost?

16. Write the relationship between λ and power demand when the cost curve is

given.

17. What is base load?

18. Define Lamda – iteration method

19. What is minimum fuel cost?

20. What are the difference between simple load dispatch and economic load

dispatch?



Result:


Secured

Marks

Awarded



Conducting 15



Record 10

Viva - voce 10

Total Marks 100



EXPERIMENT: Date:

ELECTROMAGNETIC TRANSIENTS IN POWER

SYSTEMS

AIM

To study and understand the electromagnetic transient a phenomenon in

power systems caused due to switching and faults by using Electromagnetic

Transients Program (EMTP).

OBJECTIVES

i. To study the transients due to energization of a single-phase and

three-phase load from a non- ideal source with the line represented by

Π model.

ii. To study the transients due to energization of a single-phase and

three-phase load from a non-ideal source and line represented by

distributed parameters.

SOFTWARE REQUIRED:

ELECTROMAGNETIC TRANSIENTS PROGRAM – UBC version module of

AU Power lab or equivalent


Solution Method for Electromagnetic Transients Analysis

Intentional and inadvertent switching operations in EHV systems initiate

over voltages, which might attain dangerous values resulting in destruction

of apparatus. Accurate computation of these over voltages is essential for

proper sizing, coordination of insulation of various equipment‟s and

specification of protective devices. Meaningful design of EHV systems is

dependent on modelling philosophy built into a computer program. The

models of equipment‟s must be detailed enough to reproduce actual

conditions successfully – an important aspect where a general purpose

digital computer program scores over transient network analysers.



The program employs a direct integration time-domain technique evolved

by Dommel [2]. The essence of this method is discretization of differential

equations associated with network elements using trapezoidal rule of

integration and solution of the resulting difference equations for the

unknown voltages. Any network which consists of interconnections of

resistances, inductances, capacitance, single & multiphase Π circuits,

distributed parameter lines, and certain other elements can be solved. To

keep the examinations simple, however, single phase network elements will

be used, rather than the more complex multiphase network elements.

Figure: Part of the Network around a Node of Large System



EXCERCISES

Prepare the data for the network given in the Annexure and run EMTP.

Obtain the plots of source voltage, load bus voltage and load current

following the energisation of a single-phase load. Comment on the results.

Double the source inductance and obtain the plots of the variables

mentioned earlier. Comment on the effect of doubling the source inductance.

ANNEXURE

Energization of a single phase 0.95 pf load from a non ideal source and a

more realistic line representation (lumped R, L, C)

Circuit Diagram

Figure: Energization of 0.95 pf load



Viva Questions

1. Define transient network analyser.

2. What is electromagnetic transient?

3. List out the advantage & disadvantage of EMT.

4. What are the differences between nodal and modified nodal analysis in

electromagnetic transient?

5. Develop the model for transmission system with lumped parameters.

6. What are the applications of EMT?

7. What is called as multi step method?

8. What is surge impedance?

9. Define Eigen value of power transients.

10. What is the importance of transients?

11. What are the requirements for transients in power system?

12. What is meant by thermal breakdown?

13. Mention the two components of voltage in power systems during transient period.

14. What is called as switching transients?

15. What are the sources of transients?

16. Define harmonics.

17. What is the need for harmonics and list out the types?

18. What is the significance of resistance in transients?

19. Define transient voltage & transient current.

20. What are the various types of power system transients?



Result:


Secured

Marks

Awarded



Conducting 15



Record 10

Viva - voce 10

Total Marks 100