UNSW - SCHOOL OF ELECTRICAL ENGINEERING AND TELECOMMUNICATIONS

ELEC4612 POWER SYSTEM ANALYSIS LABORATORY

LABORATORY 8
ECONOMIC DISPATCH AND OPTIMAL POWER FLOW

1. AIMS:

With the aid of the PowerWorld Simulator program, the objectives are:
▪ To analyse the problem of economic dispatch.
▪ To analyse the problem optimal power flow.

2. BACKGROUND:

2.1 Economic Dispatch:

Economic dispatch is a method that determines the allocation of the loads to the electricity
generation resources in the power system and minimizes the generation cost. Consider an
ideal system with n generating units, neglecting unit constraints and system losses. The
operating cost of generator i is C i , which varies with the real power output Pi of the
generator, and
Ci = ( a + bPi + cPi 2 + dPi 3 )  ( fuel cost ) ( $/hr ) (1)
where a, b, c, d are the coefficients of the cost curve.

Generally, “a” represents the fixed costs that do not vary with the generator output, such as
the cost of installing the generators; “b”, “c”, “d” are coefficients related to generator power
outputs. The fuel input to the generator is in Btu/hr and represented by bPi + cPi 2 + dPi 3 . The
fuel cost is in $/Btu. The operating cost can be reduced by optimizing the operation strategies.

Practically, the curve of operating cost C i versus generator output is a piecewise-continuous

and monotonically increasing curve. The discontinuities may be caused by the incremental
firing of the equipment, like additional boilers or condensers. The incremental cost curve,
dCi dPi versus Pi , which indicates the cost of producing one more MW power by the
electricity generating unit, can be obtained by taking the slope or derivative of the operating
cost curve. When C i consists of only fuel costs, dCi dPi specifies the heat rate of the unit.
Heat rate is the ratio of the amount of heat energy required in Btu to generate one more MW
of power, which indicates the fuel efficiency of the generator over its operating range. The
lower this number is, the higher the efficiency of the unit is. Generally, generators reach their
highest efficiency somewhere in the middle of their operating range and become least
efficient at the minimum and maximum MW output.

For an area consisting of n units which operate on economic dispatch, the total operating cost
of the area is
n
CT =  C i = C1 (P1 ) + C 2 (P2 ) +  + C n (Pn ) $/hr (2)
i =1
Neglecting system losses, the total load demand in the area is

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 n
PT =  Pi = P1 + P2 +  + Pn (3)
i =1

Assuming the load demand PT is constant, the economic dispatch problem becomes the
determination of the values P1 , P2 , Pn that minimize the total area operating cost CT , and the
sum of unit outputs should be equal to the total load demand.

The minimum total operating cost occurs when

C C C
dCT = T dP1 + T dP2 +  + T dPn = 0 (4)
P1 P2 Pn
From Equation 2, the above can be written as:
dC dC 2 dC n
dCT = 1 dP1 + dP2 +  + dPn = 0 (5)
dP1 dP2 dPn
Since the load demand PT is assumed constant,
dP1 + dP2 +  + dPn = 0 (6)
Multiplying Equation 6 by  and subtracting the resulting equation from Equation 5, the
following equation can be obtained,
 dC1   dC   dC 
 −  dP1 +  2 −  dP2 +  +  n −  dPn = 0 (7)
 dP1   dP2   dPn 
According to Equation 6, Equation 7 is satisfied when
 dC1   dC   dC 
 −   =  2 −   =  =  n −   = 0 (8)
 dP1   dP2   dPn 
Thus,
dC1 dC 2 dC n
= == = (9)
dP1 dP2 dPn
Therefore, all units in the system should operate at the same incremental operating cost under
economic dispatch, which is a criterion for the solution to economic dispatch problem.
dC1 dC 2 dC n
= == (10)
dP1 dP2 dPn

The criterion given in the Equation 10 can be explained as follows: neglecting the system
loss, if a unit operates at a higher incremental cost than others, the output power shift from
this unit to the unit with lower incremental cost will certainly reduce the total operating cost
in the system. Thus, all the electricity generating units must operate at the same incremental
cost to achieve the minimum operating cost.

If the unit’s output constraint, Pi min  Pi  Pi max , is considered, the units that have reached
their limit values are held at their limits, and the others that are not at their limits will
distribute remaining loads equally. In this case, the incremental operating cost of the area is
determined by the units that are not at their limits.

When the transmission losses are included, the problem becomes more complicated. The total
cost of transmitting 1MW power includes the incremental cost and the cost due to the
transmission losses. The unit with lower incremental operating cost may be so far away from
the load centre that the total cost is higher than those with higher incremental cost. The total
load demand is as follows:
n
PT =  Pi − PL = P1 + P2 +  + Pn − PL (11)
i =1

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where PL is the total transmission loss in the system. Generally, PL depends on the unit
outputs P1 , P2 ,, Pn . Equation 6 can be rewritten as
 
(dP1 + dP2 +  + dPn ) −  PL dP1 + PL dP2 +  + PL dPn  = 0 (12)
 P1 P2 Pn 
Thus, Equation 7 can be rewritten as
 dC1 P   dC P   dC P 
 +  L −   dP1 +  2 +  L −   dP2 + +  n +  L −   dPn = 0 (13)
 dP1 P1   dP2 P2   dPn Pn 
According to Equation 12, Equation 13 is satisfied when
dC1 P dC P dC P
+ L − = 2 + L − = = n + L − = 0 (14)
dP1 P1 dP2 P2 dPn Pn
or
dC1 dC 2 dC n  P 
= == =  1 − L  (15)
dP1 dP2 dPn  Pn 

Equation 15 is the new criterion when the transmission losses are considered. When the
transmission losses are negligible, which means PL P1 = 0 , this equation reduces to
Equation 9.

3. PRE-LAB QUESTIONS
1. What are the two different methods to solve Economic dispatch problem? Compare the
differences (in terms of implementation) among these two techniques.
2. Define penalty factor? How does distance of load from generation affect the penalty
factor of generator?
3. What are the differences between unit commitment and economic dispatch in power
systems?
4. SIMULATIONS:

Procedure:

This experiment involves the use of PowerWorld Simulator. This system consists of 10 buses,
and three generators (G1 at bus 1, G2 at bus 10, G3 at bus 3). The corresponding data of the
system is listed in Table 1 and Table 2. AGC are available for all the generators and enforced
MW limits are applied.
Table 1: Bus data
P P P Q Q Q Voltage
Bus Bus
Generated Generated Load Load Generated Generated Level
No. Type*
max.(MW) min.(MW) (MW) (MVar) max.(MVar) min.(MVar) (kV)
1 300.0 80.0 0.0 0.0 2 50.0 -6.0 13.8
2 0.0 0.0 21.7 12.7 3 0.0 0.0 13.8
3 200.0 60.0 54.8 19.0 2 60.0 -6.0 13.8
4 0.0 0.0 77.3 16.6 3 0.0 0.0 13.8
5 0.0 0.0 0 0 3 0.0 0.0 13.8
6 0.0 0.0 0 0 3 0.0 0.0 13.8
7 0.0 0.0 9 5.8 3 0.0 0.0 13.8
8 0.0 0.0 6.1 1.6 3 0.0 0.0 13.8

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 9 0.0 0.0 57 5.8 3 0.0 0.0 13.8
10 150.0 30.0 14.9 5.0 1 80.0 -6.0 13.8
*Bus Type: (1) swing bus, (2) generator bus, (3) load bus.

A 10-bus power system is shown in Figure 1 below.

Figure 1: A 10-bus power system.

Table 2: Line data
From Bus To Bus Resistance (p.u.) Reactance (p.u.) Line Charging (p.u.)
1 2 0.01938 0.05917 0.0528
1 5 0.05403 0.22304 0.0492
2 3 0.04699 0.19797 0.0438
2 4 0.05811 0.17632 0.0374
2 5 0.05695 0.17388 0.034
3 4 0.06701 0.17103 0.0346
4 5 0.01335 0.04211 0.0128
4 7 0.03181 0.08450 0.0
4 10 0.12711 0.27038 0.0
5 6 0.09498 0.1989 0.0
5 8 0.12291 0.25581 0.0
5 9 0.06615 0.13027 0.0
6 7 0.08205 0.19207 0.0
8 9 0.22092 0.19988 0.0
9 10 0.17093 0.34802 0.0
*Rating for transmission lines are 150MVA.

ELEC4612 Lab 8 – Economic dispatch and optimal power flow Page 4

In order to enter cost model for generators, double click the generator to open Generators
Option dialog, go to Cost tab, choose Output Cost Model and select Cubic Cost Model.
Assuming fixed cost is zero and fuel cost is 1.00 $/Mbtu, the operating costs of the generators
can be specified as follows:
C1 = ( 2 P1 + 0.375P12 )  ( fuel cost ) ( $ / hr )
C2 = (1.75P2 + 1.75P22 )  ( fuel cost ) ( $ / hr )
C3 = ( 3.25P3 + 0.834 P32 )  ( fuel cost ) ( $ / hr )
where P1 , P2 , P3 are in MW units.
Bring up some important information fields to simulation file:
- AGC Status: In Edit Mode, go to Draw tab, choose Field > Area Field, then click
anywhere on simulation file to show up dialog and select AGC Status
- Similarly, add the following fields: Load Scheduled Multiplier, MW Losses, MVAr
Losses, Total Load and Hourly Cost
- Marginal Cost: Go to Draw tab, choose Field > Area Field, then click anywhere on
simulation file to show up dialog and click Find Field button; scroll down and select
OPF > lambda

1. Obtain all generators Incremental Cost curves by right clicking any generator on Run
Mode and choose All Area Gen IC Curves. Then obtain the Fuel Cost curve of each
generator by right clicking that generator and choosing Fuel-Cost Curve. Note that all
generator Fuel-Cost Curve need to be plotted using the same scale. Make this graph 1.

2. To run the Economic Dispatch for this system, go to Case Information tab →
Aggregation →Areas, and then double-click on the Automatic Generation Control
(AGC) Status field and choose ED mode. Run the simulation and write down the total
MW losses, the total MVar losses, the hourly cost and marginal cost of the system.

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