Economic Load Dispatch (Without Losses) | Power Systems - Electrical Engineering (EE) PDF Download

 Page 1


ECONOMIC DISPATCH AND UNIT COMMITMENT ECONOMIC DISPATCH AND UNIT COMMITMENT
Page 2


ECONOMIC DISPATCH AND UNIT COMMITMENT ECONOMIC DISPATCH AND UNIT COMMITMENT
1 INTRODUCTION 
 
A power system has several power plants. Each power plant has several 
generating units. At any point of time, the total load in the system is met by 
the generating units in different power plants. Economic dispatch control 
determines the power output of each power plant, and power output of 
each generating unit within a power plant , which will minimize the overall 
cost of fuel needed to serve the system load. 
 
• We study first the most economical distribution of the output of a • We study first the most economical distribution of the output of a 
power plant between the generating units in that plant. The method 
we develop also applies to economic scheduling of plant outputs for 
a given system load without considering the transmission loss.  
• Next, we express the transmission loss as a function of output of the 
various plants.  
• Then, we determine how the output of each of the plants of a system 
is scheduled to achieve the total cost of generation minimum, 
simultaneously meeting the load on the system. 
Page 3


ECONOMIC DISPATCH AND UNIT COMMITMENT ECONOMIC DISPATCH AND UNIT COMMITMENT
1 INTRODUCTION 
 
A power system has several power plants. Each power plant has several 
generating units. At any point of time, the total load in the system is met by 
the generating units in different power plants. Economic dispatch control 
determines the power output of each power plant, and power output of 
each generating unit within a power plant , which will minimize the overall 
cost of fuel needed to serve the system load. 
 
• We study first the most economical distribution of the output of a • We study first the most economical distribution of the output of a 
power plant between the generating units in that plant. The method 
we develop also applies to economic scheduling of plant outputs for 
a given system load without considering the transmission loss.  
• Next, we express the transmission loss as a function of output of the 
various plants.  
• Then, we determine how the output of each of the plants of a system 
is scheduled to achieve the total cost of generation minimum, 
simultaneously meeting the load on the system. 
2 INPUT – OUTPUT CURVE OF GENERATING UNIT 
 
Power plants consisting of several generating units are constructed 
investing huge amount of money. Fuel cost, staff salary, interest and 
depreciation charges and maintenance cost are some of the components 
of operating cost. Fuel cost is the major portion of operating cost and it of operating cost. Fuel cost is the major portion of operating cost and it 
can be controlled. Therefore, we shall consider the fuel cost alone for 
further consideration. 
Page 4


ECONOMIC DISPATCH AND UNIT COMMITMENT ECONOMIC DISPATCH AND UNIT COMMITMENT
1 INTRODUCTION 
 
A power system has several power plants. Each power plant has several 
generating units. At any point of time, the total load in the system is met by 
the generating units in different power plants. Economic dispatch control 
determines the power output of each power plant, and power output of 
each generating unit within a power plant , which will minimize the overall 
cost of fuel needed to serve the system load. 
 
• We study first the most economical distribution of the output of a • We study first the most economical distribution of the output of a 
power plant between the generating units in that plant. The method 
we develop also applies to economic scheduling of plant outputs for 
a given system load without considering the transmission loss.  
• Next, we express the transmission loss as a function of output of the 
various plants.  
• Then, we determine how the output of each of the plants of a system 
is scheduled to achieve the total cost of generation minimum, 
simultaneously meeting the load on the system. 
2 INPUT – OUTPUT CURVE OF GENERATING UNIT 
 
Power plants consisting of several generating units are constructed 
investing huge amount of money. Fuel cost, staff salary, interest and 
depreciation charges and maintenance cost are some of the components 
of operating cost. Fuel cost is the major portion of operating cost and it of operating cost. Fuel cost is the major portion of operating cost and it 
can be controlled. Therefore, we shall consider the fuel cost alone for 
further consideration. 
C
i
  
in Rs / h 
To get different output power, we need to vary the fuel input. Fuel input can 
be measured in Tonnes / hour or Millions of Btu / hour. Knowing the cost of 
the fuel, in terms of Rs. / Tonne or Rs. / Millions of Btu, input to the 
generating unit can be expressed as Rs / hour. Let  C
i
 Rs / h  be the input 
cost to generate a power of P
i
 MW in unit i. Fig.1 shows a typical input – 
output curve of a generating unit.  For each generating unit there shall be a 
minimum and a maximum power generated as  P
i min
 and  P
i max
. 
 
 
 
in Rs / h 
P
i min 
P
i 
 in MW 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig.1 Input-Output curve of a generating unit 
max i
P 
Page 5


ECONOMIC DISPATCH AND UNIT COMMITMENT ECONOMIC DISPATCH AND UNIT COMMITMENT
1 INTRODUCTION 
 
A power system has several power plants. Each power plant has several 
generating units. At any point of time, the total load in the system is met by 
the generating units in different power plants. Economic dispatch control 
determines the power output of each power plant, and power output of 
each generating unit within a power plant , which will minimize the overall 
cost of fuel needed to serve the system load. 
 
• We study first the most economical distribution of the output of a • We study first the most economical distribution of the output of a 
power plant between the generating units in that plant. The method 
we develop also applies to economic scheduling of plant outputs for 
a given system load without considering the transmission loss.  
• Next, we express the transmission loss as a function of output of the 
various plants.  
• Then, we determine how the output of each of the plants of a system 
is scheduled to achieve the total cost of generation minimum, 
simultaneously meeting the load on the system. 
2 INPUT – OUTPUT CURVE OF GENERATING UNIT 
 
Power plants consisting of several generating units are constructed 
investing huge amount of money. Fuel cost, staff salary, interest and 
depreciation charges and maintenance cost are some of the components 
of operating cost. Fuel cost is the major portion of operating cost and it of operating cost. Fuel cost is the major portion of operating cost and it 
can be controlled. Therefore, we shall consider the fuel cost alone for 
further consideration. 
C
i
  
in Rs / h 
To get different output power, we need to vary the fuel input. Fuel input can 
be measured in Tonnes / hour or Millions of Btu / hour. Knowing the cost of 
the fuel, in terms of Rs. / Tonne or Rs. / Millions of Btu, input to the 
generating unit can be expressed as Rs / hour. Let  C
i
 Rs / h  be the input 
cost to generate a power of P
i
 MW in unit i. Fig.1 shows a typical input – 
output curve of a generating unit.  For each generating unit there shall be a 
minimum and a maximum power generated as  P
i min
 and  P
i max
. 
 
 
 
in Rs / h 
P
i min 
P
i 
 in MW 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig.1 Input-Output curve of a generating unit 
max i
P 
If the input-output curve of unit i  is quadratic, we can write 
i i i
2
i i i
? P ß P a C + + =   Rs / h                                                                   (1) 
A power plant may have several generator units. If the input-output 
characteristic of different generator units are identical, then the generating 
units can be equally loaded. But generating units will generally have 
different input-output characteristic. This means that, for particular input 
cost, the generator power P
i
 will be different for different generating units 
in a plant. 
  
3 INCREMENTAL COST CURVE 
As we shall see, the criterion for distribution of the load between any two 
units is based on whether increasing the generation of one unit, and 
decreasing the generation of the other unit by the same amount results in 
an increase or decrease in total cost. This can be obtained if we can 
calculate the change in input cost ?C
i
 for a small change in power ?P
i
. 
Since  
i
i
dP
dC
 = 
i
i
?P
?C
 we can write ?C
i
 = 
i
i
dP
dC
 ?P
i