Real power and frequency control

1. UNIT II
REAL POWER - FREQUENCY CONTROL
SYLLABUS
Basics of speed governing mechanism and modeling - speed-load characteristics –
load sharing between two synchronous machines in parallel. Control area concept
LFC control of a single area system. Static and dynamic analysis of uncontrolled
and controlled cases. Integration of economic dispatch control with LFC. Two-area
system – modeling - static analysis of uncontrolled case - tie line with frequency
bias control of two-area system - state variable model.

2. Speed
changer
Lower
Raiser
XA
XB
XC
XD
XE
Speed
Governor Pilot
valve
High pressure oil
To Turbine
Steam
Steam valve
Main
piston
Hydraulic amplifier
l1
l2 l3
l4
Fundamentals of Speed Governing System
2

4. The system consists of following components
1. Fly ball governor
2. Hydraulic amplifier
3. Linkage mechanism
4. Speed changer
Fly ball speed governor:
1. This is the heart of the system which senses the change in speed of the
system.
2. As the speed increases, the fly ball moves outwards and the point B on
linkage mechanism moves downwards. The reverse happens when the speed
decreases.
Hydraulic amplifier
1. It consists of pilot value and main piston.
2. Low power level pilot valve movement is converted into high power level
pilot valve movement.
3. This is necessary in order to open or close the steam value against high
pressure system.
Linkage mechanism
1. ABC is a rigid link pivoted at B and CDE is another rigid Link pivoted at D.
2. This link mechanism provides a movement of control valve in proportion to
the change in speed. 4

5. N
&
F
L
Raise
command
A point
Move
Downwards
Xc point
move
upwards
Xe point
move
downwards
Valve move
downwards
Getting
more inputs
To restore the freq. we increase
the generation

6. Speed Governor Model
The governor compensates for changes in the shaft speed
1. Changes in load will eventually lead to a change in shaft speed.
2. Change in shaft speed tends to change in system frequency.
Turbine model
1. The prime mover driving a generator unit may be a steam turbine or a hydro
turbine.
2. The models for the prime mover must take account of the steam supply and boiler
control system characteristics in the case of steam turbine on the penstock for a
hydro turbine.
3. The dynamic response of steam turbine in terms of changes in generator power
output ΔPG to change in steam valve opening ΔXE.
6

7. Generator load or Power system model
1. To develop the mathematical model of an isolated generator, which is only
supplying local load and is not supplying power to another area,
2. Suppose there is a real load change of ΔPD.
3. Due to the action of the turbine controllers, the generator increases its output by
an amount ΔPG.
4. The net surplus power (ΔPG - ΔPD) will be absorbed by the system in two ways.
i. By increasing the kinetic energy in the rotor.
ii. As frequency changes, the motor load changes being sensitive to speed.
7
Model of Load frequency control of single area

8. Speed-Load characteristics
The parameter R is referred to as speed regulation or droop. It can be
expressed in percent as

9. Requirements of parallel operation of Alternators
Alternators to be operated in parallel should meet the following requirements.
1. They must have the same output voltage rating.
2. The rated speed of the machines should be such as to give the same frequency.
3. The prime movers of the alternators should have same speed load drooping
characteristics, so as to load the alternators in proportion to their output rating.
4. The alternators should be of the same type so as to generate voltages of the
same waveform.
5. They may be differ in KVA rating.
Load sharing between two synchronous machines in parallel
1. If two or more generators with drooping governor characteristics are connected
to a power system, there will be a unique frequency at which they will share a
load change
2. They are initially at nominal frequency f0, with outputs P1 and P2.
3. When a load increases ΔPL causes the units to slow down, the governors
increase output until they reach a new common operating frequency f’.
4. The amount of load picked up by each unit depends on the droop
characteristics:

10. 5.If the percentage of regulation of the units are nearly equal, the change in the
outputs of each unit will be nearly in proportion to its rating.
EX.01.Two identical 60 MW synchronous machines are operate in parallel, the
governor settings on the machines are such that they have 4% and 3% droops no load
to full load % speed drops. Determine (a) the load taken by each machine for a total
load of 100 MW. (b) The % no-load speed to be made by the speeder motor if the
machines are to share the load equally. A
B C
D
E F
G
60MW 60MW
100MW
x 100-x
104
103

12. EX.02.Two turbo-alternators are rated at 25 MW each. They are running in parallel. The
speed-load characteristics of the driving turbines are such that the frequency of
alternator 1 drops uniformly from 50 Hz on no load to 48 Hz on full load, and that of
alternator 2 from 50 Hz to 48.5 Hz: (a) how the two machines will share a load of
30MW and find the bus-bar frequency at this load? (b) Compute the maximum load that
these two units can deliver without overloading either of them.

13. System frequency=48.5

14. Steady state response of Uncontrolled case
Consider speed changer has a fixed speed setting. ▲Pc=0
Reduced Block diagram is
General block diagram for LFC

16. When several generators are with governor
speed regulation R1 , R2 …. Rn

17. Block diagram of Load frequency control
Block diagram reduces to

20. Kp=1/B=1/.01=100 Hz/p.uMW

26. Dynamic Analysis of Uncontrolled Case (Single Area)
1. A static response of ALFC loop will inform about frequency accuracy, whereas, the
dynamic response of ALFC loop will inform about the stability of the loop.
2. To obtain the dynamic response representing the change in frequency as a function
of time for a step change in load. The block diagram reduces as shown in below.
Taking Inverse Laplace transform for an expression ▲F(s) is tedious, because the
denominator will be third order. We can simplify the analysis by making the following
assumptions.
1. The action of speed governor and turbine is instantaneously compared with rest
of the power system.
2. The time constant of the power system Tp= 20 sec
Time constant of governor TG= 0.4 sec
Time constant of turbine Tt=0.5 sec

30. Important Points for Uncontrolled Single Area
1. By reducing value of 'R', it is possible to increase AFRC (Area Frequency
Response Characteristics). Hence static frequency error may be reduced.
2. With smaller time constant TG and Tt, the system response shows some oscillations
before settling down with a drop-in frequency. But if these time constants are
neglected, response is purely exponential.
3. If the overall closed loop system time constant is calculated from the response
curve, it is found to be much smaller than the open loop time constant Tps of the
power system. This has been possible due to the feedback loop as provided through
the speed governing system. From the nature of the system response equation it
may be observed that system may be made still faster by reducing 'R'.
4. For the uncontrolled system there exists a steady state frequency error as a result of
increase in load demand, however small it may be.
5. When the load demand increases speed or frequency of the system drops though
initially kinetic energy of rotating inertia may be used to meet up the demand.
Eventually it will be balanced by an increase in system generation and decrease in
load as associated with the dropping frequency.

31. Ex.01: For a system of regulation = 4 Hz / p. u MW, kp = 150, Tp = 18 sec,
▲PD = 0.01 p.u.find the dynamic response for uncontrolled case.

32. Integral control of single area system.
1. There is a considerable droop in speed on frequency of the turbine for a given
speed changer setting. Such a large deviation '(± 0.5 Hz) cannot be tolerated and we
must develop some suitable control strategy to achieve much better frequency
constancy.
2. For this purpose, a signal from ▲f is fed through an integrator to the speed
changer. The Integral controller actuates the load reference point until the
frequency deviation becomes zero. Integral controller gives zero steady state error.
The negative polarity means positive frequency error to give rise to a negative or
decrease command.

33. Static Analysis or Steady State Response (Uncontrolled Case)
Put ΔPc=0, the block diagram reduces as shown in below

35. Equating the coefficients,

36. Equating the coefficients,

37. MULTI AREA SYSTEM
Introduction
 Interconnected power system
 Control Area
 Tie line
 Normal condition Operation
 Emergency condition
Operation
 Net area interchange

38. AGC of Two area interconnected power system
1. An extended power system can be divided into a number of load frequency control
areas interconnected by means of tie lines.
2. Without loss of generating, we shall consider a two-area case connected by a single
tie line has illustrated in below figure.
3. It is conveniently assumed that each control area can be represented by an equivalent
turbine, generator and governor system. Symbols used with suffix ‘1’ refers to area
‘1’ and those suffix ‘2’ refers to area ‘2’.
4. In an isolated control area case, the incremental power (ΔPG-ΔPD) was accounted for
by the rate of increase of stored kinetic energy and increase in area load caused by
increase in frequency.
5. Since a tie line transports power in or out of an area, this fact must be accounted for
in the incremental power balance equation of each area.
6. Power transported out of area 1 is given by

44.  
 
)
(
1 s
F

)
(
2 s
F

1
1
1 p
p
sT
k

1
1
1
t
sT

2
1
1
g
sT

1
1
1
g
sT

2
1
1
t
sT
 2
2
1 p
p
sT
k

s
T12
2
)
(
1 s
Ptie

12
a

)
(
1 s
PC

+
1
1
R
-
)
(
2 s
PC

+
2
1
R
-
-
)
(
1 s
PD

-
)
(
2 s
Ptie

-
)
(
2 s
PD

-

-
+
+
ΔPG1(s)
+
ΔPG2(s)

51. Frequency Response of AGC without IC

53. Frequency Response of AGC with IC

55. AGC in two area system

56. AGC in two area system with IC

57. Power variation in Multi area system

65. Tie-line With Frequency Bias Control Of Two area systems.
1. The persistent static frequency error is intolerable in the single control area
case.
2. A persistent static error in tie-line power flow called "inadvertent exchange" -
would mean that one area would have to support the other on a steady state
basis.
3. The basic principle in good operation of pool must be that each area absorbs
its own load in normal steady state.
4. In two area- system, we could conceive of the arrangement that area '1 ‘ be
responsible for frequency reset and area '2' take care of the tie line power.
5. The ACE's would be fed via slow integrators or to the respective speed
changers. But this arrangement is not so good.
6. The block diagram of two area LFC with tie-line bias control is shown in
below.
7. The control strategy is termed as tie line bias control, and is based upon the
principle that all operating pool members must contribute their share to
frequency control, in addition to taking care of their own net interchange .

66.  

 2
1
1
g
sT

2
1
1
t
sT
  2
2
1 p
p
sT
k

s
T12
2
)
(
1 s
Ptie

12
a

)
(
1 s
F

)
(
2 s
F

1
1
1 p
p
sT
k

1
1
1
t
sT

1
1
1
g
sT

)
(
1 s
PC

+
1
1
R
-
)
(
2 s
PC
 +
2
1
R
-
-
-
)
(
1 s
PD

-
)
(
2 s
Ptie

-
)
(
2 s
PD

-
+
+
ΔPG1(s)
+
ΔPG2(s)
s
KI 2

-b1
s
KI1



+
+
-b2
)
(
1 s
Ptie

)
(
2 s
Ptie


67. Determination of Tie Line with Frequency Bias Control of Two Area System
Principle: All operating pool members must contribute their share to frequency
control, in addition to taking care of their own net interchange.
ACE is the change in area frequency which, when used in integral control loop
forced the steady state frequency error to zero.
In order to make the steady state tie line power error to zero, another integral
control loop (one for each area) must be introduced to integrate the incremental tie
line power signal and feed it back to the speed changer.

68. Speed changer commands are,
Steady State Response

70. The reset control is implemented by sampled data techniques.
At sampling intervals of one second, all tie-line power data are fed into the central
energy control area, where they are added and compared with predetermined
power.
Now this error is added with biased frequency error, to give ACE results.
If optimum dispatch is employed, a tertiary slower loop is added.
1. Under normal operating conditions, besides meeting respective area loads,
scheduled interchange between areas can take place.
2. Under abnormal conditions, such as loss of generation in area, power can flow
from other areas, through the interconnection.
3. Such pool operation where mutual assistance is possible which reduces the
reserve capacity needed.
4. For a large system with many areas, the kinetic energy of the rotatory inertia is
high. A sudden load change may not cause any considerable transient frequency
deviation.

71.  

 2
1
1
g
sT

2
1
1
t
sT
  2
2
1 p
p
sT
k

s
T12
2
)
(
1 s
Ptie

12
a

)
(
1 s
F

)
(
2 s
F

1
1
1 p
p
sT
k

1
1
1
t
sT

1
1
1
g
sT

)
(
1 s
PC

+
1
1
R
-
)
(
2 s
PC

+
2
1
R
-
-
-
)
(
1 s
PD

-
)
(
2 s
Ptie

-
)
(
2 s
PD

-
+
+
ΔPG1(s)
+
ΔPG2(s)