Electrical Engineering Department Sanjay Ghodawat ... · CFLs, Fans, Electrical Motors, Socket...

Mr. Nitin S. Patil Electrical Engineering Department

Sanjay Ghodawat Polytechnic, Atigre

Economics of Power Generation

SGP-Atigre Electrical Engg.Dept.

Mr. N.S.Patil 2

Chapter No. 6

Economics of Power Generation

Hours: 08 Marks = 12

INDEX

Sr. No.

Particulars Page No.

1 Definition of Economics of Power Generation 1

2 Variable Load on Power Station 1

3 Terms commonly used in system operation: connected load, firm power, cold reserve, hot reserve, spinning reserve

1-4

4

Curves used in system operation such as Load-curve, load duration curve, integrated duration curve. (Simple numerical based on plotting above curves

5-11

5

Factors affecting the cost of Generation: Average demand, Maximum demand, demand factor, plant capacity factor, plant use factor, diversity factor, load factor and plant load factor (Simple numerical based on above)

12-19

6 Solved Examples 20-36

7 Important Technical Words & its Meaning 37


Mr. N.S.Patil 3

1. Definition of Economics of Power Generation:

The art of determining the per unit (i.e. one kWh) cost of production of

Electrical Energy is known as Economics of Power Generation.

2. Variable Load on Power Station:

The load on Power Station varies from time to time due to uncertain demands

of the consumers and is known as variable load on power station.

3. Terms commonly used in system operation: connected load,

firm power, cold reserve, hot reserve, spinning reserve.

1. Connected Load:

Definition: The Sum of Continuous rating of all the equipments (bulbs, tubes,

CFLs, Fans, Electrical Motors, Socket Outlets, and Power Plugs etc) connected to

Electrical Supply System is known as Connected Load.

, , ,

,

For Example: Students considered your house, in your house consist of

number of lamps=6, tubes=4, fans=5, 5A socket outlet=10, power plug=3 etc.


Mr. N.S.Patil 4

Then we have to calculate the Connected Load by using above mention

example.

Step-I: Assume Suitable Wattage for the above mentioned electrical accessories.

Step-II: Calculate used appliance total Load:

No. of Lamps = 6 (Each Lamp Wattage = 60 W), 6 x 60 = 360 Watts.

No. of Tubes= 4 (Each Tube Wattage = 40 W), 4 x 40 = 160 Watts.

No. of Fans= 5 (Each Fan Wattage = 60 W), 5 x 60 = 300 Watts.

No. of Socket Outlet = 10 (Each Socket outlet Wattage = 100 W), 10 x 100

= 1000 Watts.

No. of Power Plug = 3 (Each Power Plug Wattage = 1000 W), 3 x 1000 =

3000 Watts.

Step-III: (By using definition of Connected Load) Add all connected load:

Addition= 360W + 160W + 300W + 1000W + 3000W = 4820 W

Total Connected Load = 4820 Watt.

2. Firm Factor:

Definition: It is defined as, the theoretical (imaginary) value of power which a

power plant (Hydro, Thermal etc) is supposed to produce throughout a year or at

all time is known as firm power.

,

For Example: In Case of hydro power plant with reservoir, the firm power is that

power which a hydro electric plant supplies for 95% of the time. However, it is not


Mr. N.S.Patil 5

necessary that firm power should be produces throughout the year & available

under emergency conditions.

3. Cold Reserve:

Definition: It is defined as the reserve generating capacity which is available for

service but is not in operation.

,

4. Hot Reserve:

Definition: It is defined as the reserve generating capacity which is available in

operation but is not in service.

5. Spinning Reserve:

Definition: It is defines as the generating capacity which is connected to bus and is

ready to take load.


Mr. N.S.Patil 6

4. Curves used in system operation such as Load-curve, load

duration curve, integrated duration curve. (Simple numerical

based on plotting above curves.

1. Load Curve [ ]

Definition: The Load Curve is a Graph, which represents load on the generation

station (the load is in kW/MW) recorded at the interval of half hour or hour (time)

against the time in chronological order.

Or

The Load Curve is defined as the curve which is drawn between loads versus

time in sequential order. We have to draw the load curve on daily basis data,

weekly, monthly basis data.

Or

The curves showing the variation of load on the power station with respect

to time is known as load Curves.


Mr. N.S.Patil 7

The Load Curve gives following Information:

The daily load curve shows the variation of load on the power station during

different hours of the day.

The area under the daily load curve gives the number of unit generated in the

day. Unit generated/day= Area (in kWh) under daily load curve.

The highest point on the daily load curve represents the maximum demand

on the station on that day.

The area under the daily load curve divided by the total number of hours

gives the average load on the station in that day.

Average Load =

The ratio of the area under the load curve to the total area of the rectangle in

which it is contained gives the load factor.

Load Factor = =

=


Mr. N.S.Patil 8

The load curves helps in selecting the size & number of generating units.

The load curve helps in preparing the operation schedule of the station.

The curve which gives idea of load of a whole day with respect to time (24

Hours or 12 Hours of the day) is known as daily load curve.

The monthly load curve can be obtained from the daily load curve of the

month. For this purpose, average values of power over a month at different

times of the day are calculated.

The yearly load curve is obtained by considering the monthly load curve of

that particular year. The yearly load curve is generally used to determine

annual load factor.

Maximum Demand)

Average

Demand)

,


Mr. N.S.Patil 9

2. Load Duration Curve

Definition: When the load elements of a load curve are arranged in the order of

descending magnitudes, the curve thus obtained is called a load duration curve.

The load duration curve is obtained from the same data as load curve but the

ordinate representing the maximum load is represented to the left and the

decreasing loads are represented to the right in the descending order.

,

From the above figure (i) shows the daily load curve, the daily load duration

curve can be readily obtained from it.


Mr. N.S.Patil 10

From fig (ii), it is clear from the daily load duration curve that the

magnitudes of load elements are in descending order. The magnitudes are 20MW

for 8 Hours, 15MW for 4 hours & remaining 5 MW from 12 hours.

MW , MW , MW

Plotting these loads in order of descending magnitude, we get Daily Load

Duration Curve. (Shown in Fig. ii)

The Load Duration Curve gives following information:

The load duration curve readily shows the number of hours during which the

given load has prevailed.

The area under daily load duration curve (in kWh) will give the units

generated on that day.

The load duration curve, which helps to give information about annual load

duration curve.

. .


Mr. N.S.Patil 11

3. Integrated Duration Curve

Definition: The curve which represents the total number of units generated for the

given demand is called as Integrated Load Curve.

Fig. A Integrated Duration Curve

The above figure shows the Integrated Duration Curve, its X-axis represents units

generated in kWh & Y-axis represents Demand of load in kW.

Such type of curve can be drawn with the help of Load Duration Curve.

Fig B: Load Duration Curve


Mr. N.S.Patil 12

Consider Fig. B, let the demand of load can be represented at point A & it

corresponds to line AG (Refer Fig. A) on the load duration curve.

The number of unit generated (P1) corresponding to this load demand are

represented by area OAGF, it corresponds to point P1 on integrated duration curve.

Consider Fig B, let the demand of load can be represented at point B & it

corresponds to line BH (Refer Fig. A) on the load duration curve.

The number of unit generated (P2) corresponding to this load demand are

represented by area OAHF, it corresponds to point P2 on integrated duration curve.

Similarly, all the above mentioned sequence will help to draw Integrated Duration

Curve.

,

Integrated Duration Curve) X Axis

, Axis kW)

Integrated Duration Curve)

,

A Integrated Duration Curve)

B

B A AG

A P1 OAGF

. P2 , P3 Points


Mr. N.S.Patil 13

5. Factors affecting the cost of Generation: Average demand,

Maximum demand, demand factor, plant capacity factor, plant

use factor, diversity factor, load factor and plant load factor

(Simple numerical based on above)

1. Average Demand or Load: ( )

Definition: The average of loads occurring on the power station in a given period (day or

month or year) is known as average load or average demand.

The Average Demand is Calculated by using given formula:

a. Daily Average Load =

=

b. Monthly Average Load =

=

c. Yearly or Annual Average Load =

=


Mr. N.S.Patil 14

2. Maximum Demand (MD):

Definition: It is the greatest demand of load on the Power Station during a giving period

is known as Maximum Demand.[

]

Or The maximum demand of the power station is equal to maximum load on the station

considered in a given period of time.[

Maximum Demand ]

Fig: Load Curve

We know that, the load on every power station in not constant. The load varies

from time to time. The variation of load on the power station is depends upon the demand

of load with respect to time.

Consider, the above figure, the figure X-axis Represents Time in Hours & Y-axis

represents Load in MW. In this figure, at every two hours give information about how

much load generated. Out of the 6MW load generated during evening period. So that

maximum Demand is 6MW.

The Knowledge of Maximum Demand is very important as it helps in

determining the installed capacity of the power station.

X-Axis Y-Axis

MW

Maximum Demand MW


Mr. N.S.Patil 15

3. Demand Factor:

Definition: It is the Ratio of Maximum Demand on the Power Station to its Connected

Load.

Demand Factor =

=

The value of Demand factor is usually less than 1. It is excepted because maximum

demand on the power station generally less than the connected load.

The knowledge of Demand Factor is vital in determining the capacity of the plant

equipments.


Mr. N.S.Patil 16

4. Plant Capacity Factor:

Definition: The Plant Capacity Factor is the ratio of average demand on the Power Station

divided by the maximum installed capacity of the power station.

.

Plant Capacity Factor =

=

Or

It is the ration of actual energy produced to the maximum possible energy that could have

been produced during a given period. [

].

Plant Capacity Factor =

=

The plant capacity factor is an indication of the reserve capacity of the plant.

,

Reserve Capacity = Plant Capacity Factor – Maximum Demand

=


Mr. N.S.Patil 17

5. Plant Use Factor:

Definition: It is the ratio of kWh generated to the product of plant capacity and

the number of hours for which the plant was in operation.

kWh X

Plant Use Factor =

=

Or

Plant Use Factor =

=

Plant use factor indicated how much is the plant capacity utilized, but it does not

indicate the time for which the plant remained idle.

.


Mr. N.S.Patil 18

6. Diversity Factor:

Definition: The Ratio of the sum of individual maximum demands to the

maximum demands on power station is known as Diversity Factor.

=

For the above mentioned formulae the value of diversity factor is more than 1

Or

Diversity Factor =

=

For the above mentioned formulae the value of diversity factor is less than 1

.


Mr. N.S.Patil 19

7. Load Factor:

Definition: The ratio of number of units actually generated in a given period to

number of units which could have been generated with the same maximum

demands is called as load factor for the station.

Or

The Ratio of Average Load to the Maximum Demand during a given period is

known as load factor.

Load Factor =

=

Assume that the plant is operation for ‘T’ Hours

T

Load Factor =

=

The load factor may be daily, monthly or yearly load factor, if the time period

considered is a day or month or year. The value of load factor is always less than 1

, ,

.


Mr. N.S.Patil 20

8. Plant Load Factor:

Definition: The Plant Load Factor is defined as the ration of output of power

station in kWh to the rated capacity of the plant.

.

Plant Load Factor =

=

The plant load factor indicated how best the plant capacity has been utilized but it

does not indicate the time for which the plant remained idle.

9. Unit Generated per Annum:

It is often required to find the kWh generated per annum form maximum demand

& load factor.

Load Factor =

Average Load = Maximum Demand X Load Factor

Units Generated/Annum = Average Load in kW X No. of Hours in a Year

Units Generated/Annum = Maximum Demand in kW X Load Factor X 8760

(No. of Hours in a Year)


Mr. N.S.Patil 21

6. Solved Examples:

1. The maximum demand on power station is 100 MW. If the annual load

factor is 40%, calculate the total energy generated in a year.

Given Data:

Maximum Demand = 100MW = 100 x 103 kW

Annual Load Factor = 40% = = 0.4

Total no. of days in year = 365

Total no. of hours in year = 365 X 24 hours of the day = 8760

To Find:

Total Energy Generated in a Year.

Formulae Used:

Energy generated in a year or Unit Generated/Annum = Maximum Demand

(in kW) X Load Factor X Number of hours in a Year

Solution:

Substitute all the values in given data to the above mentioned formula.

= (100 x 103) x 0.4 x 8760

Answer:

Energy generated in a year = 3504 x 105 kWh

[ MW

x ^ kW

]


Mr. N.S.Patil 22

2. A generating station has a connected load 120MW & it supplies

maximum demand 60 MW. The numbers of units generated in a year

are 48 X 107 Calculate load & demand factor of generating station.

Given Data:

Connected Load = 120 MW = 120 x 103 kW.

Maximum Demand = 60 MW = 60 x 103 kW.

Number of units generated in a year = 48 X 107

To Find:

Load Factor

The demand factor of generating station.

Formula Used:

Load Factor =

Demand Factor =

Solution:

To calculate load factor by using above formula, substitute the value.

Load Factor = = 0.9132

To Calculate Demand Factor:

Demand Factor = = 0.5

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Example for Practice: A generating station has a connected load 43MW & it

supplies maximum demand 20 MW. The numbers of units generated in a year are

61.5 X 106 Calculate load & demand factor of generating station. [

MW KW

]


Mr. N.S.Patil 23

3. A power supply agency, supplies the following load to different

consumers, its details given below:

o Domestic Load: Maximum Demand = 20000 kW, Diversity Factor

= 1.5, Demand Factor = 0.7

o Commercial Load: Maximum Demand = 20000 kW, Diversity

Factor = 1.4, Demand Factor = 0.8

o Industrial Load: Maximum Demand = 50000kW, Diversity Factor

= 1.2, Demand Factor = 0.9

If overall diversity factor is 1.6, determine:

1. Maximum Demand

2. Connected Load of each type of Consumer.

Given Data:

Sr.No. Particulars Domestic

Load

Commercial

Load

Industrial

Load

System

Diversity

Factor

1 Maximum

Demand 20000kW 20000 kW 50000 kW

1.6 2 Diversity

Factor 1.5 1.4 1.2

3 Demand

Factor 0.7 0.8 0.9

To Find:

Maximum Demand

Connected load of Domestic, Commercial & Industrial Load.

Formula Used:

System Diversity Factor =

Connected Load =

Solution:


Mr. N.S.Patil 24

To Find System Diversity factor using above formula

Given System Diversity factor= 1.6 =

Maximum Demand of System = = 56250 kW

To find out connected load of Domestic type:

Connected load of Domestic Type = = 42857.14 kW

To find out connected load of Commercial type:

Connected load of Commercial Type = = 35000 kW

To find out connected load of Industrial type:

Connected load of Industrial Type = = 66666.67 kW

----------------------------------------------------------------------------------------------------

Example for Practice:

A power supply system having the following loads:

Type of Load Maximum

Demands

Diversity

Factor

Demand

Factor

Domestic 1500 1.2 0.8

Commercial 2000 1.1 0.9

Industrial 10000 1.25 1

If the Overall System Diversity Factor is 1.35, determine the maximum demand &

connected load of each type.

, ,

,


Mr. N.S.Patil 25

4. A 200 MW power station delivers loads as detailed below:

o 180 MW for 3 Hours during a day.



o 5 MW for Remaining Hours during a day

The Plant is shut down for repair or maintenance work for a period of 30 days

in a year. Calculate the annual load factor of the plant.

Given Data:

200 MW Power Station Delivered Load given Below:

Delivered Load in MW No. of Hours

180 3

100 6

20 3

5 Remaining Hours

To Find:

The annual load factor of the plant.

Formula Used:

Annual Load Factor =

Energy generated/Year = Maximum Demand x load Factor x No. of hours plant works

Solution:

We know that the Maximum Demand is 200MW = 200 x 103 kW.

In one total year number of days = 365

But our plant is shut down for repair or maintenance = 30 Days

Total Number of Days in which Plant Work = 365-30 = 335 Days


Mr. N.S.Patil 26

Calculate Energy Generated/Annum:

By using above formula find out Energy Generated/Year:

= [(180 x3(hours)) + (100 x 6) + (20 x 3) + (5 x 12)] X 103

= 1260 x 106 kWh

Total Energy Supplied in Year = 1260 X 106 x 335 Days of Plant Works

Total Energy Supplied in Year = 1260 x 106 x (335 x 24 Hour) = 422100 x 10

3 kWh

Annual Load Factor = = 0.2625

----------------------------------------------------------------------------------------------------

Example for Practice: A 100 MW Power Station delivers 100 MW for 2 Hours,

50MW for 6 Hours, and is shut down for the rest of each day. It is also shut down

for maintenance off 45 days each year calculates its annual load factor.

,


Mr. N.S.Patil 27

5. A generating plant works on a maximum demand of 600MW. The

annual load factor being 60% and capacity factor is 30%. Find the

reserve capacity of the plant.

Given Data:

Maximum Demand = 600MW

Annual load factor = = 0.6

Capacity factor = = 0.3

To Find: Reserve Capacity of the Plant

Formula Used:

Reserve Capacity = Plant Capacity – Maximum Demand

Plant Capacity =

Energy Generated per annum = Maximum Demand x Load Factor x Number

of hours in a year

Solution:

Energy generated per annum = (600x103) x 0.6 x 8760 = 3153600 x 10

3kWh

Plant Capacity = = 1200 x 103kW = 1200 MW

Reserve Capacity = 1200 – 600 = 600MW

------------------------------------------------------------------------------------------------------------


Mr. N.S.Patil 28


1. A Power Station has maximum demand of 15000kW. The annual load factor

is 50% & Plant Capacity factor is 40%. Determine the Reserve Capacity of

the Plant.

2. A Power Station has a maximum demand 0f 10 MW. The annual load factor

is 60% & plant capacity factor is 50%. Determine the reserve capacity of

plant.

----------------------------------------------------------------------------------------------------

,

---------------------------------------------------------------------------------------------------------------------

, ,

,


Mr. N.S.Patil 29

6. A generating station has a maximum demand of 40000kW and a

connected load of 70000kW. The number of units supplied annually is

28 x 107 Calculate load & Demand Factor.

Given Data:

Maximum demand = 40000kW

Connected load = 70000kW

Unit supplied per year = 28 x 107

To Find:

Load Factor

Demand Factor

Formula Used:

Load Factor =

Demand Factor =

Solution: Load Factor = = 0.799


--------------------------------------------------------------------------------------------

Example for Practice: A generating station has maximum demand of 20MW &

connected load of 40MW. The units generated being 60x106 per annum. Calculate

demand factor & load factor.


Mr. N.S.Patil 30

7. A generating station supplies the following loads:

Domestic Load 2000kW, Maximum Demand

Industrial Load 10000kW, Maximum Demand

Commercial Load 6000kW, Maximum Demand

Irrigation Load 3000kW, Maximum Demand

The diversity factor of these loads at the generating station is 1.5 &

average annual load factor is 55%. Calculate the maximum demand on the

station & total energy supplied by the plant in year.

To Find: Diversity Factor, Maximum Demand, Average load Factor & total

energy supplied by the plant in a year.

Formula used:

Diversity Factor =

Average Load Factor =

Energy Supplied per Year = load factor x Maximum Demand x Hours in Year

Solution:

By using Diversity Factor Formula:

1.5 =

Maximum Demand = = 1400 kW

By using Average Load Factor Formula

0.55 =

Total Energy Supplied in a Year = 0.55 x 1400 x 8760 = 6745200kWh

---------------------------------------------------------------------------------------------------

Example for Practice: A diesel station supplies following loads to various consumers:

Domestic=100kW, Commercial=750kW, Industrial=1500kW & Domestic light = 450kW. If the

maximum demand of the station is 2500 kW& Energy generated per year is 45 x 105 Calculate

Diversity & Load Factor.


Mr. N.S.Patil 31

8. The peak load on a power station is 30MW. The loads having maximum

demands of 25, 10, 5 & 7 MW are connected to the power station.

Capacity of the power station is 40MW & annual load factor is 50%.

Calculate: average load, energy supplied per year, demand factor &

diversity factor.

Given Data:

Peak Load or Maximum Demand = 30MW

Capacity of Power Station = 40 MW

Annual Load Factor = 50% = = 0.5

To Find:

Average Load

Total Energy Supplied per Year

Demand Factor

Diversity Factor

Formula Used:

Load Factor =

Energy Supplied /Year = Load factor x Maximum Demand x Hours in year

Demand Factor =

Diversity Factor =

Solution:

By using the formula of load factor:

0.5 =

Average load = x 0.5 = 15 x 103

kW


Mr. N.S.Patil 32

Energy Supplied per Year = 0.5 x 30 x 103 x 8760 = 131,400,000 kWh


Diversity Factor = = 1.56

----------------------------------------------------------------------------------------------------


The peak load on power station is 40 MW. The loads having maximum

demands of 30 MW, 5MW, 8MW are connected to power station. The annual

load factor is 50%. Find: Average load on Power Station, Demand Factor,

diversity Factor & Load Factor.

, ,


Mr. N.S.Patil 33

9. A Generating Station has the Following Daily Load Cycle:

Time in Hours 0-6 6-10 10-12 12-16 16-20 20-24

Load in MW 40 50 60 50 70 40

Draw the load curve and Find: Maximum Demand, Unit Generated per

annum, average load & load Factor.

For all above the given problem is totally different from other.

Given Data: Required data is given to the above table

To Find: Maximum Demand, Unit Generated per annum, average load & load

Factor

Formula Used:

Unit Generated/Annum = Maximum Demand x Load Factor x Hours in day

Average Load =

Load Factor =

Solution:

Draw the Load Curve:

In previous section we have studied what is meant by load curve & what it

indicates or how it can be drawn.

With reference to the given data in the above table, we draw the load curve. For

this purpose we take shows on X-axis Time & Y-Axis Load.

There are total 24 hours of the day, for X-Axis it is divided into TWO hours &

load is in increasing order of 10 on Y-Axis.


Mr. N.S.Patil 34

Fig: Load Curve

Maximum Demand: From the above curve it is clear that, the maximum load is 70 MW.

Unit Generated per Annum: = Area (in kWh) under the daily load curve.

= [(40 x 6) + (50 x 4) + (60 x 2) + (50 x 4) + (70 x 4) + (40 x 4)] x 103

Unit Generated per Annum = 12 x 105

Average Load = = 50,000 kW

Load Factor = = 0.714

----------------------------------------------------------------------------------------------------

Example for Practice: The daily load curve on a generating station is as given below:

Draw the Load Curve & Calculate: Load Factor, Average Demand & Energy Generated

per Day.

Time in Hours 0 to 5 5-7 7-10 10-13 13-15 15-19 19-22 22-00

Load in MW 5 7 10 12 8 12 15 10


Mr. N.S.Patil 35

, , ,

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,


Mr. N.S.Patil 36

10. A Power Station has the Following Daily Load Cycle:

Time in Hours 6-8 8-12 12-16 16-20 20-24 24-6

Load in MW 20 40 60 20 50 20

Plot the Load Curve & Load Duration Curve. Calculate the Energy

Generated per Day.

Given Data: Required Data is given in above Table:

To Find: Energy Generated per Day.

Formula used:

Energy Generated per Day = Area under (in kWh) daily load curve.

Energy Generated per Day = Area under (in kWh) daily load duration curve.

Solution:

While draw the load curve, first up all we need to axis X & Y respectively.

Take Time in Hours in X-Axis & load in MW in Y Axis & Draw the load

curve.

Fig: Load Curve


Mr. N.S.Patil 37

While Drawing the Load Duration Curve, same procedures repeat. Take

Time in Hours in X-Axis & Load in MW in Y Axis.

In load duration curve, we know that to arrange all the load order in

descending magnitude (take highest load first then order in descending

magnitude)

Fig: Load Duration Curve

For load curve & load duration curve calculate Energy Generated per Day

Energy Generated per Day = Area (in kWh) under daily load or load duration curve

= [(60 x 4) + (50 x 4) + (40 x 4) + (20 x 12)] x 103 = 840 x 10

3 kWh

---------------------------------------------------------------------------------------------------

Example for Practice: A Generating Station has the Following Daily Load Cycle:

Time in Hours 0-6 6-10 10-12 12-16 16-20 20-24

Load in MW 50 70 90 75 100 40

Plot the Load Curve & Load Duration Curve. Calculate the Energy

Generated per Day.


Mr. N.S.Patil 38

7. Important Technical Words & its Meaning

Economics of Power

Generation:

Cost of Generation:

Factor:

Connected Load:

Load duration curve:

Average demand:

Maximum demand:

Demand Factor:

Capacity factor:

Use Factor:

Diversity Factor:

Load Factor:

Variable load:

Kilo watt hour:

Consumer:

Definition:

Daily:

Monthly:

Annual or yearly:

X 8760

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