LOAD FREQUENCY CONTROL (SINGLE AREA CASE):
Load Frequency Control (Single Area Case):
Load Frequency Control – Let us consider the problem
of controlling the power output of the generators of a closely-knit electric
area to maintain the scheduled frequency. All the generators in such an area
constitute a coherent group so that all the generators speed
up and slow down together maintaining their relative power angles. Such an area
is defined as a control area. The boundaries of a control area
will generally coincide with that of an individual Electricity Board Company.
To understand the load frequency control problem, let
us consider a single turbo-generator system supplying an isolated load.
Turbine Speed
Governing System
1. Fly ball speed governor:
This is the heart of the system which senses the
change in speed (frequency). As the speed increases the fly balls move outwards
and the point B on the linkage mechanism moves downwards. The reverse happens when the speed
decreases.
2. Hydraulic amplifier:
It comprises a pilot valve and main piston Low power
level pilot valve movement is converted into high power level piston valve
movement. This is necessary to open or close the steam valve against
high-pressure steam.
3. Linkage mechanism:
ABC is a rigid link pivoted at B and CDE is another rigid
link pivoted at This linking mechanism provides a movement to the control valve in
proportion to change in speed. It also provides feedback from the steam valve
movement (link 4).
4. Speed changer:
It provides a steady-state power output setting for
the turbine. Its downward movement opens the upper pilot valve so that more
steam is admitted to the turbine under steady conditions (hence more steady power
output). The reverse happens for the upward movement of the speed changer.
Model of Speed Governing System
Assume that the system is initially operating under
steady conditions. the linkage mechanism is stationary and the pilot valve is closed, a steam valve is opened by a definite magnitude, turbine running at a constant speed
with the turbine power output balancing the generator load. Let the operating
conditions be characterized by
We shall obtain a linear incremental model around
these operating conditions.
Let point A on the linkage mechanism is moved downwards by a small amount ΔyA. It is a command which causes the turbine power output to change and can therefore be written as
where ΔPC is the commanded increase
in power.
The command signal ΔPC (i.e. ΔyE) sets into motion a sequence of events. the pilot valve moves upwards, high-pressure oil flows onto
the top of the main piston moving it downwards; the steam valve opening
consequently increases, the turbine generator speed increases, i.e. the
frequency goes up. Let us model these events mathematically.
Two factors contribute to the movement of C:
The movement ΔyD depending upon its
sign opens one of the ports of the pilot valve admitting high-pressure oil into
the cylinder thereby moving the main piston and opening the steam valve by ΔyE. Certain justifiable
simplifying assumptions, which can be made at this stage, are:
·
Inertial
reaction forces of the main piston and steam valve are negligible compared to the
forces exerted on the piston by high-pressure oil.
·
Because
of (i) above, the rate of oil admitted to the cylinder is proportional to port
opening ΔyD.
The volume of oil admitted to the cylinder is thus
proportional to the time integral of ΔyD,. The movement ΔyE is
obtained by dividing the oil volume by the area of the cross-section of the
piston. Thus
It can be verified from the schematic diagram that a
positive movement ΔyD causes negative (upward) movement ΔyE accounting
for the negative sign used in Eq. (8.4).
Taking the Laplace transform of Eqs. (8.2), (8.3) and
(8.4), we get
Eliminating ΔYC(s) and ΔYD(s), we can write
Where
Equation (8.8) is represented in the form of a block diagram in Fig. 8.3.
The speed governing system of a hydro-turbine is more
involved. An additional feedback loop provides temporary droop compensation to
prevent instability. This is necessitated by the large inertia of the penstock
gate which regulates the rate of water input to the turbine. Modeling a
hydro-turbine regulating system is beyond the scope of this book.
Turbine Model
Let us now relate the dynamic response of a steam
turbine in terms of changes in power output to changes in the steam valve opening
ΔyE. Figure
8.4a shows a two-stage steam turbine with a reheat unit. The dynamic response
is largely influenced by two factors, (i) entrained steam between the inlet
steam valve and the first stage of the turbine, (ii) the storage auction in the
reheater which causes the output of the low-pressure stage to lag behind that
of the high-pressure stage. Thus, the turbine transfer function is
characterized by two-time constants. For ease of analysis, it will be assumed
here that the turbine can be modeled to have a single equivalent time
constant. Figure 8.4b shows the transfer function model of a steam turbine.
Typically the time constant Tt lies in the range of 0.2 to 2.5
sec.
Generator Load Model
The increment in power input to the generator-load
system is
where ΔPG = ΔPt incremental
turbine power output (assuming generator incremental loss to be negligible) and
ΔPD is the load increment.
This increment in power input to the system is
accounted for in two ways:
·
Rate of
increase of stored kinetic energy in the generator rotor. At scheduled
frequency (f° ), the
stored energy is
where Pr is
the kW rating of the turbo-generator and H is defined as its inertia constant.
The kinetic energy is proportional to the square of
speed (frequency), the
kinetic energy at a frequency of (f°+Δf) is given by
The rate of change of kinetic energy is therefore
·
As the
frequency changes, the motor load changes being sensitive to speed, the rate of
change of load concerning frequency, i.e. δPD/δf can be
regarded as nearly constant for small changes in frequency Δf and can be
expressed as
where the constant B can be determined empirically. B is positive for a
predominantly motor load.
Writing the power balance equation, we have
Dividing throughout by Pr and
rearranging, we get
Taking the Laplace transform, we can write ΔF(s) as
Where
Equation (8.13) can be represented in block diagram form as in Fig. 8.5.
Complete Block Diagram Representation of Load Frequency Control of an Isolated Power System
A complete block diagram representation of an
isolated power a system comprising the turbine,
generator, governor, and load is easily obtained by combining the block diagrams
of individual components, i.e. by combining Figs. 8.3, 8.4, and 8.5. The
complete block diagram with feedback loop is shown in Fig. 8.6.
Steady States Analysis
The model of Fig. 8.6 shows that there are two
important incremental inputs to the load frequency control system -ΔPC, the change in speed
changer setting; and ΔPD, the
change in load demand. Let us consider a simple situation in which the speed
changer has a fixed setting (i.e. ΔPC = 0) and the load demand changes.
This is known as free
governor operation. For such an operation the steady change in
system frequency for a sudden change in load demand by an amount
is obtained as follows:
While the gain Kt is fixed for the
turbine and Kps is fixed for the power the system, Ksg, the speed
governor gain is easily adjustable by changing the lengths of various links. Let it
be assumed for simplicity that Ksg is so adjusted that
It is also recognized that Kps = 1/B,
where B = δPD/δf / Pr (in
pu MW/unit change in
frequency). Now
The above equation gives the steady-state changes in frequency caused by changes in load
demand. Speed regulation R is
naturally so adjusted that changes in frequency are small (of the order of 5%
from no load to full load). Therefore, the linear incremental relation (8.16)
can be applied from no load to full load. With this understanding, Fig. 8.7
shows the linear relationship between frequency and load for free governor
operation with speed changer set to give a scheduled frequency of 100% at full
load. The ‘droop’ or slope of this relationship is
Power
system parameter B is generally much
smaller* than 1/R (a typical value is B = 0.01 pu MW/Hz and
1/R = 1/3) so that B can
be neglected in comparison. Equation (8.16) then simplifies to
The droop of the load frequency curve is thus mainly
determined by R, the
speed governor regulation.
It is also observed from the above that increase in
load demand (ΔPD) is met under steady
conditions partly by increased generation (ΔPG) due to the opening of
the steam valve and partly by decreased load demand due to drop in system
frequency. From the block diagram of Fig. 8.6 (with KsgKt≈1)
Of course, the contribution of the decrease in system
load is much less than the increase in generation. For typical values of B and R quoted earlier
Consider now the steady effect of changing speed
changer setting
with load demand remaining fixed (i.e. ΔPD =
0). The steady-state change in frequency is obtained as follows.
If
If the speed changer setting is changed by ΔPC while
the load demand changes by ΔPD, the steady frequency change is obtained by superposition, i.e.
According to Eq. (8.21), the frequency change caused
by load demand can be compensated by changing the setting of the speed changer,
i.e.
Figure 8.7 depicts two load frequency plots—one to
give scheduled frequency at 100% rated load and the other to give the same frequency at 60% rated load.
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