The document discusses variable load problems in power plants. It defines key terms related to loads and demand such as load curve, load duration curve, load factor, demand factor, diversity factor, and plant factor. It explains that load varies over time due to different factors like type of service, day of week, season, and weather. Load curves graphically represent the variation in demand over time and are used to calculate important metrics. The document also provides examples of calculating metrics like load factor and presents sample problems.

1. Power Plant Engineering
VARIABLE LOAD PROBLEMS

2. Load Distribution Diagram of a Power Plant:
Chapter 2: Variable Load Problem

3. Electric Power Substation:
- a grouping of electrical equipment through which electric energy is
passed for the purpose of switching or of transforming voltage levels. General
classifications includes primary substations (interconnection between high
voltage and medium voltage) and secondary substations (interconnection
between medium and low voltage).
Chapter 2: Variable Load Problem

4. Chronological Load Curve:
- a graphical representation of the variation in demand with respect to clock
time.
Variation in demand may be due to one or
more of the following factors:
• type of service (residential, industrial,
commercial, etc.)
• day of the week
• season of the year
• weather conditions
Chapter 2: Variable Load Problem

5. Load-Duration Curve:
- represents the data of the chronological load curve with the ordinates
rearranged in order of decreasing values. The horizontal distance of any point
from the load axis indicates the duration of all loads equal to and greater than that
indicated on the ordinate. The coordinates of any point on the curve are
determined by the value of the load, and the length of the horizontal line at that
load level as limited by the chronological load curve.
Load-Energy Curve:
- indicates the total energy for a given load and all values less than that load.
Chapter 2: Variable Load Problem

6. Chronological Load Curve, Load-Duration Curve and Load-Energy Curve:
Chapter 2: Variable Load Problem

7. Comparison of Ideal Load and Realized Load:
Chapter 2: Variable Load Problem
• Constant magnitude and steady duration • Load varies with time

8. Important Terms and Factors:
1. Load (on a machine or apparatus)
- is the power which it delivers.
2. Power – is the time rate of transferring or transforming energy.
3. Demand (of an installation or system)
– is the load at the receiving terminals averaged over a specified interval
of time.
4. Maximum Demand, MD
– is the greatest demand of loads on the power station during a given
period (say in 24 hrs.). It is also called “Peak Load”. It may be the
maximum instantaneous load or the maximum average load over a
designated interval of time.
Chapter 2: Variable Load Problem

9. Important Terms and Factors:
5. Base Load, BL
– is the minimum load over a given period of time.
6. Connected Load, CL
– is the sum of all continuous ratings of all utilization equipment in the
consumer premises connected to the supply system.
7. Load Curve - is a graph used to represent the relationship between the
demanded load and time sequence.
 Monthly Load Curve – is a curve representing the average of the daily
load curves over a one-month period used in establishing rates.
 Annual load curve – is a curve representing the average of the daily
load curves over a one-year period used for annual load factor.
Chapter 2: Variable Load Problem

10. Example of a monthly load curve:
A comparison of the actual load curves of
two towns A and B of about 4000
population each, situated 45 miles apart,
and having similar community life. Both
served by municipality owned and
operated Diesel plants. (Source: Power
Plant Engineering by Frederick T. Morse)
Chapter 2: Variable Load Problem

11. Important Terms and Factors:
8. Average Load
– is the average of loads occurring on the power station in a given
period (say a day, a month, or minutes).
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐿𝑜𝑎𝑑 =
𝑇𝑜𝑡𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑
𝑃𝑒𝑟𝑖𝑜𝑑 ℎ𝑜𝑢𝑟𝑠 𝑖𝑛 𝑎 𝑑𝑎𝑦, 𝑚𝑜𝑛𝑡ℎ 𝑜𝑟 𝑦𝑒𝑎𝑟
where:
Total Energy Produced = total area under the curve, kW-hr
Period = length of abscissa under the curve, hrs
Example:
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐿𝑜𝑎𝑑 =
10,620 𝑘𝑊−ℎ𝑟
24 ℎ𝑟
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐿𝑜𝑎𝑑 = 442 𝑘𝑊
Chapter 2: Variable Load Problem

12. Important Terms and Factors:
9. Load Factor
– is the ratio of the average load to the maximum demand during a given
period.
𝐿𝑜𝑎𝑑 𝐹𝑎𝑐𝑡𝑜𝑟 =
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐿𝑜𝑎𝑑
𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝐷𝑒𝑚𝑎𝑛𝑑
< 1.0
where:
Average load = 442 kW
Maximum demand or peak load = 1040 kW
Example:
𝐿𝑜𝑎𝑑 𝐹𝑎𝑐𝑡𝑜𝑟 =
442 𝑘𝑊
1040 𝑘𝑊
𝐿𝑜𝑎𝑑 𝐹𝑎𝑐𝑡𝑜𝑟 = 0.424
peak load = 1040 kW
Chapter 2: Variable Load Problem

13. Important Terms and Factors:
10. Demand Factor
– is the ratio of the maximum demand on the power station to its
connected load.
Demand 𝐹𝑎𝑐𝑡𝑜𝑟 =
𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝐷𝑒𝑚𝑎𝑛𝑑
𝐶𝑜𝑛𝑛𝑒𝑐𝑡𝑒𝑑 𝐿𝑜𝑎𝑑𝑠
, < 1.0
11. Diversity Factor
– is the ratio of the sum of individual maximum demands of subdivision
systems to the simultaneous maximum demand on the power station.
Diversity 𝐹𝑎𝑐𝑡𝑜𝑟 =
σ 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑑𝑒𝑚𝑎𝑛𝑑𝑠 𝑜𝑓 𝑠𝑢𝑏𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛𝑠
𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑑𝑒𝑚𝑎𝑛𝑑 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑢𝑝𝑝𝑙𝑦 𝑤ℎ𝑜𝑙𝑒 𝑠𝑦𝑠𝑡𝑒𝑚
, > 1.0
Chapter 2: Variable Load Problem

14. Important Terms and Factors:
12. Coincidence Factor
– is the reciprocal of diversity factor.
13. Plant Factor
– is the ratio of the average load on the plant for the period of time
considered, to the aggregate rating of all the generating equipment
installed in the plant.
𝑃𝑙𝑎𝑛𝑡 𝐹𝑎𝑐𝑡𝑜𝑟 =
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐿𝑜𝑎𝑑
𝐼𝑛𝑠𝑡𝑎𝑙𝑙𝑒𝑑 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦
Coincidence 𝐹𝑎𝑐𝑡𝑜𝑟 =
𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑑𝑒𝑚𝑎𝑛𝑑 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑢𝑝𝑝𝑙𝑦 𝑤ℎ𝑜𝑙𝑒 𝑠𝑦𝑠𝑡𝑒𝑚
σ 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑑𝑒𝑚𝑎𝑛𝑑𝑠 𝑜𝑓 𝑠𝑢𝑏𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛𝑠
, < 1.0
Coincidence 𝐹𝑎𝑐𝑡𝑜𝑟 =
1
𝐷𝑖𝑣𝑒𝑟𝑠𝑖𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟
, < 1.0
Note: Installed Capacity = Peak Load + Reserved Load
Chapter 2: Variable Load Problem

15. Important Terms and Factors:
Chapter 2: Variable Load Problem

16. Important Terms and Factors:
14. Capacity Factor
– is the ratio of the average load on a machine or equipment for the
period of time considered, to the rating of the machine or equipment.
15. Plant Use Factor or Plant Output Factor
– is the ratio of the actual energy generated to the product of plant
installed capacity and the number of hours for which the plant was in
operation.
Plant 𝑈𝑠𝑒 𝐹𝑎𝑐𝑡𝑜𝑟 =
𝐴𝑐𝑡𝑢𝑎𝑙/𝑇𝑜𝑡𝑎𝑙 𝐸𝑛𝑒𝑟𝑔𝑦 𝑃𝑟𝑜𝑑𝑢𝑐𝑒𝑑
𝐼𝑛𝑠𝑡𝑎𝑙𝑙𝑒𝑑 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑥 𝑆𝑒𝑟𝑣𝑖𝑐𝑒 𝐻𝑜𝑢𝑟𝑠
𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝐹𝑎𝑐𝑡𝑜𝑟 =
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐿𝑜𝑎𝑑 𝑜𝑛 𝑀𝑎𝑐ℎ𝑖𝑛𝑒 𝑜𝑟 𝐸𝑞𝑢𝑖𝑝𝑚𝑒𝑛𝑡
𝑅𝑎𝑡𝑖𝑛𝑔 𝑜𝑓 𝑀𝑎𝑐ℎ𝑖𝑛𝑒 𝑜𝑟 𝐸𝑞𝑢𝑖𝑝𝑚𝑒𝑛𝑡
Chapter 2: Variable Load Problem

17. Important Terms and Factors:
16. Utilization Factor
– is the ratio of the maximum generator demand to the generator
capacity.
17. Operating Plant Factor
– is the ratio of the average load for a given period of time to the
operating capacity in actual service only.
Operating Plant 𝐹𝑎𝑐𝑡𝑜𝑟 =
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐿𝑜𝑎𝑑
𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑃𝑙𝑎𝑛𝑡 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦
𝑈𝑡𝑖𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝐹𝑎𝑐𝑡𝑜𝑟 =
𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝐷𝑒𝑚𝑎𝑛𝑑
𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑜𝑟 𝐼𝑛𝑠𝑡𝑎𝑙𝑙𝑒𝑑 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦
Chapter 2: Variable Load Problem

18. Important Terms and Factors:
18. Operating Load Factor
– is the ratio of the average load for a given period of time to the average
of daily maximum demand during the same period (say for 30 days period
of time).
O𝐿𝐹 =
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐿𝑜𝑎𝑑
(𝑀𝐷1 + 𝑀𝐷2 + 𝑀𝐷3 + ⋯ + 𝑀𝐷30)/30
=
(𝑇𝑜𝑡𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑)/30
(𝑀𝐷1 + 𝑀𝐷2 + 𝑀𝐷3 + ⋯ + 𝑀𝐷30)/30
19. Plant Service Factor
– is the ratio of the Plant Capacity Factor to the Plant Use Factor.
Plant Service 𝐹𝑎𝑐𝑡𝑜𝑟 =
𝑃𝑙𝑎𝑛𝑡 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝐹𝑎𝑐𝑡𝑜𝑟
𝑃𝑙𝑎𝑛𝑡 𝑈𝑠𝑒 𝐹𝑎𝑐𝑡𝑜𝑟
Chapter 2: Variable Load Problem

19. Important Terms and Factors:
20. Plant Ratio
– is the per annum measure of the plant’s capacity factor. It is the ratio of
the net KWH output for the year to the nameplate capacity of the plant
times the number of hours in a year.
Plant 𝑅𝑎𝑡𝑖𝑜 =
𝑇𝑜𝑡𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑/𝑦𝑒𝑎𝑟
𝐼𝑛𝑠𝑡𝑎𝑙𝑙𝑒𝑑 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑥 8760
Chapter 2: Variable Load Problem

20. Sample Problems:
1. A 24-hr load curve is drawn to scale of 1 cm = 2 hr and 1 cm = 1000 kW. Determine the load factor if
the maximum demand is 15,000 kW and the area under the curve found using a planimeter is
75.60 sq. cm.
Chapter 2: Variable Load Problem

21. Sample Problems:
2. A central steam power station with a rated capacity of 200 MW generates 962,000 MW-hrs of
energy in a year. What is the capacity factor of the plant?
A. 52% B. 55% C. 48% D. 45%
Chapter 2: Variable Load Problem

22. Sample Problems:
3. The annual peak load on a 15,000 kW power plant is 10,500 kW. Two substations are being
supplied by this plant. Annual energy dispatched through substation A is 27,500,000 kW-hrs
with a peak at 8900 kW, while 16,500,000 kW-hrs are sent through substation B with a peak at
6650 kW. Neglecting line losses, find the capacity factor of the power plant.
A. 0.335 B. 0.353 C. 0.533 D. 0.535
Chapter 2: Variable Load Problem

23. Sample Problems:
3. The annual peak load on a 15,000 kW power plant is 10,500 kW. Two substations are being
supplied by this plant. Annual energy dispatched through substation A is 27,500,000 kW-hrs
with a peak at 8900 kW, while 16,500,000 kW-hrs are sent through substation B with a peak at
6650 kW. Neglecting line losses, find the capacity factor of the power plant.
A. 0.335 B. 0.353 C. 0.533 D. 0.535
Chapter 2: Variable Load Problem

24. Sample Problems:
4. A provincial power station supplies the following loads to its major clients: Consumer A =
2500 kW ; Consumer B = 1250 kW; Consumer C = 500 kW; Consumer D = 700 kW. The station’s
maximum demand is 3700 kW. Determine the annual load factor and diversity factor if the
annual energy generated is 6,225,000 kW-hr.
A. 0.20, 1.37 B. 0.17, 1.24 C. 0.18, 1.31 D. 0.19, 1.34
Chapter 2: Variable Load Problem

25. Sample Problems:
4. A provincial power station supplies the following loads to its major clients: Consumer A =
2500 kW ; Consumer B = 1250 kW; Consumer C = 500 kW; Consumer D = 700 kW. The station’s
maximum demand is 3700 kW. Determine the annual load factor and diversity factor if the
annual energy generated is 6,225,000 kW-hr.
A. 0.20, 1.37 B. 0.17, 1.24 C. 0.18, 1.31 D. 0.19, 1.34
Chapter 2: Variable Load Problem

26. END.
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