INTRODUCTION

1.1 LOAD FREQUENCY CONTROL PROBLEM

Power system authorities have the responsibility to ensure that adequate

power is delivered to the load reliably and economically. In order to ensure

adequate delivery of power to the load reliably and economically, an electric

energy system must be maintained a t the desired operating level characterized

by nominal frequency, voltage profile and load flow configuration. It is kept in

this nominal state by close control of the real and reactive powers generated in

the controllable sources of the system. The generation changes must be made

to match the load perturbations at the nominal conditions, if the nominal state

is to be maintained.

Power system control is required to maintain a continuous balance

between electrical generatior and a varying load demand, while system

frequency, voltage levels and security are maintained. Further, it is desirable

that the cost of such generation should be minimum. The variable nature of the

consumer power demand necessitates changes in the total generation in order

that the power balance is maintained.

The system frequency fluctuations should be kept within strict limits

because of the following reasons:

1. Most types of a.c. motors run at speeds that are directly related to the

frequency.

2. The generator turbines, particularly steam-driven ones, are designed to

operate a t a very precise speed and hence constant turbine speed is an

important requirement in thermal stations.

The velocity of the expanding steam is beyond the control of the operator

and the turbine efficiency requires the perfect speed match. A turbo-rotor with

its many huge turbine blades constitutes a mechanical system of many natural

frequencies. These frequencies are quite undamped and they are each subject

to resonance at various rotor speeds. It is important under load that the rotor

never drifts into a speed range where building of dangerous amplitude would

result. Hydro-turbines are not subject to this type of danger.

3. A large number of electrically operated clocks are driven by synchronous

motors, and the accuracy of these clocks is a function not only of the

frequency error but, actually, of the integral of this error.

4. The overall operation of a power system can be better controlled if the

frequency error is kept within strict limits.

The last reason is equally important. Unusual deviations in frequency

indicates that something is basically wrong with the system. In modern electric

energy systems the frequency constancy is normally kept within % 0.05 Hz.

The frequency is closely related to the real power balance in the overall

network. Under normal operating conditions the system generators run

synchronously and generate together the power that at each moment is being

drawn by all loads, plus the real power losses. The ideal way to operate the

system would therefore be to instruct the machine operators to set all

watergates and steam valves of the various generators a t values that would

exactly correspond to the load demand. We would then have a perfect real

power balance with constant frequency.

Unfortunately, reality is not so accommodating. As it is well known that

the system load can be predicted only to within certain limits. Its fluctuations

are entirely random in character, and it is indeed impossible to accomplish a

perfect instant by instant match between generation and demand. There will

always be a small surplus or deficiency in the generation and this ever present

mismatch will cause frequency fluctuations.

In any power system, it is a desirable feature to achieve a better

frequency constancy than is obtained by the speed governing system alone. In

an interconnected power system, it is also desirable to maintain the tie-line

power flow at a given level irrespective of load changes in any area. To

accomplish this it becomes necessary to automatically manipulate the operation

of main steam valves or hydro-gates in accordance with a suitable control

strategy, which in turn controls the real power output of electric generators.

The controlling of real power output of electric generators in this way is termed

as automatic generation control (AGC) or Automatic Load Frequency Control

(ALFC).

Most large Generators are equipped with two major control loops. The

automatic voltage regulator (AVR) loop controls the magnitude of the terminal

voltage V. The voltage is continuously sensed, rectified and smoothed. This d.c

signal, being proportional to I V I , is compared with d.c reference V, the

resulting "error voltage" after amplification and signal shaping, serves as the

input to the exciter which finally delivers the voltage to the generator field

winding. This excitation control loop controls the reactive power.

The Automatic Load-Frequency Control loop regulates the megawatt

output and frequency (speed) of the generator. The loop is not a single one as

in the case of AVR. A relatively fast primary loop responds to a frequency

signal which is an indirect measure of megawatt balance. Via the speed

governor and the control valves the steam (or hydro) flow is regulated with the

intent of matching the megawatt output to relatively fast (one to several

seconds) load fluctuations. Thus tending to maintain megawatt balance, this

primary loop performs indirectly a course speed or frequency control.

A slower secondary loop maintains the fine adjustment of the frequency,

and also by "reset" action maintains proper megawatt interchange with other

pool members. This loop is insensitive to rapid load and frequency changes but

focuses instead a driftlike changes which take place over periods of minutes.

The AVR and ALFC control loops are loosely coupled. The AVR loop

mainly controls the reactive power through excitation input and ALFC loop

controls the active power output. However the AVR loop is much faster than

ALFC loop and there is, therefore, a tendency for the AVR dynamics to settle

down before they can make themselves felt in the slower load-frequency control

channel. So AVR and ALFC loops are treated independently.

A control area is defined as a power system, a part of a system, or a

combination of systems to which a common generation control scheme is

applied. The electrical interconnections within each control area are very strong

as compared to the ties with the neighbouring areas. All the generators in a

control area swing in unison or coherently, and it is characterized by a single

frequency. It is necessary to consider as many control areas as the number of

such coherent groups. Automatic Generation Control problem of a large

interconnected power system has been studied by dividing the whole system

into a number of control areas.

A power system area generally has interconnections which are physically

remote from the controlling station or dispatching center. Feedback regulatory

control of the system required the measurement of tie-line flows a t

interconnections and the transmission of measured data over data links to the

controlling plant or dispatching center.

During normal operating conditions, Automatic Generation Control is

characterized by random variation of loads in each control area. AGC matches

area generation to area load plus scheduled net interchange by controlling

generation to maintain the net interchange schedule and scheduled power

system frequency. For normal operating conditions, it is important to minimize

from below 1 cycle per minute (CPM) to about 10 CPM. The lower frequencies

are associated with random load changes caused by AGC, while the higher

frequencies are associated with random load changes caused by the primary

speed governor control.

Proper selection of frequency bias setting is extremely important for

AGC of interconnected systems. The bias responses of an area to a sudden load

or generation change in a remote area is preceded by a natural governing

response of the area. The bias setting will determine whether the bias response

remains that of the natural governing response, or whether the bias response

is in a direction to add to it or subtract from it.

In order to study the effect of frequency bias setting on the system

performance, M.L.Kothari (133) analyzed AGC problem of Zequal area reheat

thermal system in the discretemode. A practical sampling period of 2 seconds

is chosen. Detailed investigations reveal that

(a) Frequency bias setting, B, which match the prevailing area frequency

response characteristic 13, impose no further change on frequency, tie-line

flow, and local generation.

(b) Frequency bias settings which are less than 13 impose further decrease

in frequency tie-line flow and local generation and thus amount to

withdrawing assistance to needy area.

(c) Frequency bias settings which are greater than 13, cause reduction in

frequency deviation, increase in tie-line flow and decrease local

generation. This is desirable since the assistance to needy area is

enhanced.

The main problem faced in practice is due to the fact that the area

frequency response characteristic is not constant over the operating period

since it depends on number of generating units talung part in the regulation

process, and the prevailing load characteristics. Number of regulating units in

a area change, their regulating characteristic vary over a wide limits, load

varies over a wide range and hence 13 varies over a wide range. Obvious remedy

to this problem is to set frequency bias setting equal to the highest possible

value of 13, thus ensuring 13213 for all operating conditions.

Control action is conventionally based on the Area Control error

computation. A time deviation term is added in the western North American

interconnected systems. Present industry practice is to set the frequency bias

coefficient approximately equal to the "natural" system frequency characteristic,

during heavy load conditions. The natural characteristic is measured for large

disturbances, with bias coefficients normally changed only a t the start of a new

calendar year. Power networks consist of number of utilities interconnected

together and power is exchanged between the utilities over the tie-lines by

which they are interconnected. The net power flow on tie-lines is scheduled on

apriori contract basis. It is, therefore, important to have some degree of control

over the net power flow on the tie-lines. Load-frequency control allows

individual utilities to interchange power to aid in overall security while

allowing the power to be generated most economically.

For a number of years, the problem of Load Frequency Control has been

one of the most accentuated topics in the operation of autonomous and

interconnected systems. The solution of this problem has been one of the first

practical applications of the decentralized control of large scale dynamic

systems. The development of modern computers facilitated the design of all

digital AGC systems. The computerized AGC can incorporate the traditional

load frequency control, which is designed to match the generation to the

varying system demand, and an Economic Dispatch program that distributes

the generation and the generating units so that the total system cost is

minimized.

Load-frequency control is very important item in power system operation

and control for supplying sufficient and reliable electric power with good

quality. Many control strategies have been proposed to achieve better

performance. Due to the non-linearities of various components of power

systems, a linear model obtained by linearization around an operating point is

usually adopted for the controller design. However, because of the inherent

characteristics of changmg loads, the operating point of a power system may

vary very much during a daily cycle. As a result, a fixed controller which is

optimal under one operating condition may no longer be suitable in another

status. In view of this, some authors have applied the variable structure control

to make the control insensitive to the plant parameter changes. However, this

method requires the information of the system states which are not easily

measurable. On the other hand, recently, various adaptive control techniques

have been proposed for dealing with large parmeter variations. Basically,

adaptive control systems can be classified into two categories, namely the self-

tuning regulators and the model reference control systems. The former which

is based on explicit identification of the system transfer function has the

difficulty in designing an efficient on-line identifier. As to the latter, due to the

requirement of satisfying the perfect model following conditions and the state

information of the system, it is rather difficult to be applied to LFC in the

sense of practical implementation.

Most of the work reported in the literature pertaining to LFC of

interconnected power systems is centered around tie-line frequency bias control

strategy. Supplementary controllers are designed to regulate the area control

errors to zero effectively. Several modern design techniques have been used to

optirnize the parameters of the supplementary controllers. Supplementary

controllers regulate the generation so as to match load variation, the frequency

and tie-power deviation from scheduled values. This would result in

accumulations of time error and inadvertent interchange accumulations would

also occur due to errors in measurements of frequencies and tie-powers,

scheduled frequency and tie-power scheduled frequency and tie-power settings

or internal offsets in scheduled settings. It is expected that individual areas will

make all reasonable efforts to minimize time error and inadvertent interchange

accumulations by minimizing or eliminating source causes. Accumulations will

nevertheless occur and there is a need for correcting them. Such corrections are

achieved by making appropriate offsets in system frequency schedules to

compensate for time error accumulations and offsets in area net interchange

schedules to cornpensate fcr ~nsdvertent interchange accumulations. Detailed

literature survey shows that the above mentioned two-step correction scheme

has been used for illustrations in spite of practical difficulties. In order to avoid

such practical difficulties, the utilities are looking forward for a control strategy

that not only maintains constancy of system frequency and desired tie-line

power flow but also zero steady state error. It is essentially in this direction,

the investigations have been carried out by many researchers.

Load frequency control in electric power systems represents the first

realization of a higher level control system. It has made the operation of

interconnected systems possible and today it is still the basis of any advanced

concept for the guidance of large system. A peculiarity of LFC lies in the fact

that each partner in the interconnection has equal rights and possibilities,

being limited only by the installed power in the area and the capability of the

tie-lines. Thus it is not a centralized control system when the total

interconnection is considered. Economic dispatch control and security control

schemes demand the system as a prerequisite for LFC. In the historical

development, LFC systems were installed because of stability problems and the

need for better control of the active power. In Europe the relative ease of

controlling hydraulic power stations has contributed very much to the success

of LFC. In the United States LFC has gained an importance with the growth

of interconnected systems mainly supplied by thermal power stations.

1.2 STATEMENT OF THE PROBLEM

The control of frequency during load variations in a power system is one

of the major problems encountered in the operation of the system as of most

of the electrical appliances need a constant frequency. The development of

design technique for load-frequency control of large interconnected systems is

an important control problem in power system. Many techniques and models

have been proposed in the last few decades using conventional and modern

control concepts for load frequency control problem for improving dynamic

response and stability of the system. However the classical techniques are

having their own drawbacks. In recent literature many people applied modern

control theory for solving LFC problem.

The present work deals with new control strategy of quenching

transients of a load frequency control problem. The load-frequency problem is

represented by a new state space model for a single area and for two area

electric power systems. The state variables selected in this model are frequency,

first and second derivatives of frequency. The steady state operating points

before and after the load disturbance are named as initial state and final states

of the system. Now the problem is to move the system from this initial to the

final state in a definite time without any oscillations. Hence the LFC problem

is restructured as a state transition problem (initial and final states) using a

suitable control parameters. With the help of pontryagin's Maximum PrincipIe

the optimal control is proved to be bang-bang control by minimizing the time

of state transfer. The control parameter taken in this work is the position of

speed changer which is not an external parameter.

A single area power system is considered and the optimal controllers are

synthesized for increase in load position of the system. The switching instants

for the control strategy are evaluated. It is observed that the frequency

transients are quenclred at much faster rates without any oscillations.

The above technique of designing an optimal controller has been

extended for decrease in load position. It is observed that the frequency

transients are quenched at much faster rates. In this analysis the transients a t

switching are not considered. The amount of deviation may be upto 50% of load

disturbance.

For single area power system, studies have been conducted to find the

control strategies to determine the control vector u, and up with different step

load disturbances starting from 0.01 per unit to 0.05 per unit in steps of

0.01 per unit. For each load disturbance, the control inputs for bang-bang

control have been determined. Curves have been drawn between Af on x-axis

and AD.f on y-axis showing the trajectory of operating point.

For optimum LFC, the time taken for the system from disturbed state

to the equilibrium state (Af = 0) should be minimum. To achieve this two

control inputs ul and u2 have been selected. The magnitude and the instant a t

which these controls are to be applied have been different for various load

disturbances. The control input u l is applied after some elapsed time from the

instant of occurrence of load disturbance. This delay has been assumed, as the

time required for sensing the disturbance and changng control position.

The philosophy of the proposed control strategy for increased load

changes is depicted in fig 1.1.

fig. 1.1

'0' is the initial and final equilibrium state after disturbance. 'OA' is the trajectory of the uncontrolled system for step load change. 'AB' is the trajectory of the system with control u,. 'BO' is the trajectory of the system with control u,.

For each load disturbance, the control input u, is changed to a value

equal to a t least the load disturbance. The trajectory of the operating point is

plotted. The time at which u, is to be applied is determined with the help of the

curves plotted with initial state (Af=O) and backward integration of system

equations. The intersection of this trajectory with the u, trajectory gives the

time a t which u, is to be applied for minimum time of transfer. If the curves

don't intersect, the LFC with Af=O is not possible.

From the graphs drawn for different load disturbances, the following

observations are made.

The minimum value of u, or u2 should be at least equal to the magnitude

of the load disturbance.

If the magnitude of u, or u, is increased, the total time taken for the

system to come back to equilibrium state with Af=O decreases.

From time response curves, it can be seen that for higher value of u, and

u,, the system response is fast in returning to the equilibrium state.

For the implementation of the optimal LFC, for different load

disturbances, the control strategies u, and u, magnitudes and the time a t which

they are to be applied can be stored in a look up table of the computer. When

there is a disturbance, the computer can select appropriate optimal values of

u, and u, and apply a t proper instants so that the system may be restored to

new equilibrium state.

13

The method suggested in this provides optimal load frequency controller,

which takes minimum time to come to new equilibrium state with Af=O

compared to methods suggested by others. In addition, LFC controller

suggested can easily by implemented as it does not require a feed back system

or state estimator.

The review of literature of load frequency control is presented in the I1

chapter.

A new state space model for load frequency control is presented in the

chapter 111. The model presented is tested for different load disturbances

ranging from 0.01 per unit upto 0.05 per unit in steps of 0.01 per unit and

compared with the model given by 0.E.Elgerd. rB.11

Chapter N deals with the design of optimum speed regulation constant

R for uncontrolled and controlied mode for various load disturbances from 0.01

per unit upto 0.05 per unit in steps of 0.01 per unit with the present model.

The results are discussed in the same chapter.

The synthesis of optimal controllers of a single area power system, for

an increase and decrease of load disturbances, the strategy, the control inputs

and the switching instants are presented in the chapter V. An attempt is made

to find control inputs for two area power system and results for the both cases

are evaluated and presented in this chapter.

The conclusions and further scope of the proposed strategy are presented

in the chapter VI.