Station Performance and Operation Characteristics Performance of generating plants is compared by their average thermal efficiencies over a period of time. The measure of performance varies with: Cooling Water Temperature Shape of load duration curve Total output Quality of fuel

1. Station Performance
and Operation
Characteristics

2. Performance Characteristics
Performance of generating plants is compared by their
average thermal efficiencies over a period of time.
The measure of performance varies with:
• Cooling Water Temperature
• Shape of load duration curve
• Total output
• Quality of fuel
periodthatforinputenergyTotal
periodtheduringoutputenergyUseful
EffciencyThermal.Avg 

3. Input output Curve
Plant performance is most
precisely described by the input
output curve derived from tests.
General equation for input and
output curve of an equipment
can be described as
y = a + bx + cx2 + dx3 +
………………+ nxr
Y corresponds to input (I) =>
BTU/hr
X corresponds to output (L) =>
kW

4. Efficiency
Efficiency can be derived from
input-output curve
Efficiency =
• e = ; at any load
• The efficiency curve is the plot
of e against the value of L
** 1kw = 3413 BTU/hr
** The British thermal unit (BTU) is a traditional
unit of energy equal to about 1.055 K Joules.
%100
/
/
X
PI
PO
%100
3413
X
I
L

5. Heat Rate
The heat rate curve is derived by taking at each load the
corresponding input; then
• HR= (I/L) BTU per kWhr
• HR is plotted against the
corresponding value of L
• HR = (I/L) = 341300/e
• HR is inversely proportional to e.
• If the input-output curve is defined
by; I = a + bL + cL2 + dL3
HR = (a/L) + b + cL +dL2

6. Incremental Rate
It is derived form the input-output curve by finding at any
load the additional input required for a given additional
load.
• The incremental rate is defined by IR = BTU/kWhr
and plotted against the load L for the full range of I/O
curve.
• IR is the slope of I/O curve at given load.
• Physically the incremental rate expresses the amount of
additional energy required to produce an added unit of
output at any given load
dL
)I(d

7. Incremental Rate
If the input output curve, I = a + bL + cL2 + dL3
Then IR = = b + 2cL + 3dL2





2
1
2
1
2
1
L
L
12
L
L
I
I
IRdLII
IRdLdI
IRdLdI
dL
)I(d

8. Mathematical Problem - 1
Example 32-1: A 20MW station has a n input-output curve is defined by
I = 30 + 0.5L + 0.65L2 + 0.001L3
Where I => million of BTU/hr
L => megawatts
Find the increase in input required to increase the station output from 7 to 9 MW by
means of the
(i) input-output curve and also by
(ii) incremental-rate curve
Solution:
(i)
At L= 7; I1 = 30 + 0.5*7 + 0.65*72 + 0.001*73 = 68.78 X 106 BTU/hr
At L= 9; I2 = 30 + 0.5*9 + 0.65*92 + 0.001*93 = 94.44 X 106 BTU/hr
Increment input for 2MW increased output = (94.44-68.78) X 106 = 25.66 X 106
BTU/hr

9. Mathematical Problem - 1
(ii)
Following the above two equations IR = 0.5 + 1.3L + 0.03L2
I2 -I1 = = 25.66 X 106 BTU/hr
Another way to perform this is to assume that from L=7 to L=9 the IR curve is a
straight line.
IR at L=8 is = 0.5 + 1.3*8 + 0.03*82 = 12.82 X 106 BTU/hr
Then the increment input for 2MW increased output is = 2 X 12.82 X 106 BTU/hr
= 25.64 X 106 BTU/hr


2
1
L
L
12 IRdLII
dL
)I(d
IR
 
9
7
2
)dL0.03L1.3L(0.5

10. Relation Between Heat Rate and I/O Curve
If the tangent of I/O curve at point Lm is straight line
through the origin, then the equation of the tangent is
Im = aLm ;
so, at Lm, HRm = Im/Lm = a
Where a = slope of the tangent
• Now if the tangent were considered as I/O curve then the
corresponding HR and IR curve would be a horizontal line
with a value of Im/Lm
• Since the actual I/O curve lies above this tangent at all
other loads except for Lm, HR curve must be higher than
Im/Lm at all other loads. Then the HR is minimum when
HRm = a

11. Relation Between Heat Rate and I/O Curve
• The slope of the tangent to the
actual I/O curve at Lm is the
slope of the curve at Lm
• Therefore, the IR at this load;
a = IRm = at Lm
But a = HRm at Lm
So HRm = IRm
HR of the I/O curve is
minimum when it is equal to IR.
m
m
dL
dI

12. Relation Between Heat Rate and
Incremental Rate
• Using Calculus
• At minimum HR the slope of the HR curve is zero
imumminaisHRWhen;HRIR
L
I
dL
dI
IdLLdI
0IdLLdI
0
L
IdLLdI
0)
L
I
(
dL
d
0)HR(
dL
d
2










13. Average Heat Rate

17. Suppose that the station operates at only two different loads
during an entire period such as at La and Lb.
The locus of the average heat rates operating at the two load
levels exclusively can be demonstrated as follows:

23. Mathematical Problem - 2