Energy and Power En gi neering, 2011, 3, 17-23
doi:10.4236/epe.2011.31003 Published Online February 2011 (http://www.SciRP.org/journal/epe)
Copyright © 2011 SciRes. EPE
Cost Control of the Transmission Congestion Management
in Electricity Systems Based on Ant Colony Algorithm
Bin Liu, Jixin Kang, Nan Jiang, Yuanwei Jing
Faculty of Information Science and Engineering, Northeastern University, Shenyang, China
E-mail: jiangnan@ise.neu. edu.cn
Received October 8, 2010; revised November 3, 2010; accepted November 4, 2010
Abstract
This paper investigates the cost control problem of congestion management model in the real-time power
systems. An improved optimal congestion cost model is built by introducing the congestion factor in dealing
with the cases: opening the generator side and load side simultaneously. The problem of real-time congestion
management is transformed to a nonlinear programming problem. While the transmission congestion is
maximum, the adjustment cost is minimum based on the ant colony algorithm, and the global optimal solu-
tion is obtained. Simulation results show that the improved optimal model can obviously reduce the adjust-
ment cost and the designed algorithm is safe and easy to implement.
Keywords: Electricity Systems, Congestion Management, Ant Colony Algorithm, Minimax, Adjustment
Cost
1. Introduction
With the open of transmission network, the problem of
transmission congestion becomes very serious under power
market environment. When the active tidal current in line
surpasses the limiting value, the net side will adjust various
units’ output allocative decision to avoid transmission con-
gestion as much as possible for safety [1-3]. When the unit
output distribution plan is adjusted, the transaction cost of
network side will rise due to the emergence of congestion
cost. However, adjustment schemes in many cases are not
unique, different adjustment programs will lead to different
congestion costs, so there exists an optimal strategy [4-7].
It is important that how to choose the optimal adjustment
program to ensure the loss caused by network’s plan failure
is the least [8,9].
Reference [4,10,11] studied congestion management al-
gorithm problem and power system economic dispatch
problem, but the optimization models considered do not
cover the cost of load side. Reference [12] d esigned a rela-
tively simple regulation for blocking costs against the op-
timization model of transmission congestion management.
Reference [13,14] proposed a kind of generator adjustment
expense smallest optimization model. Reference [15] pro-
posed an optimization model using sensitivity factor to
solve the blocking problem existing regional electricity
market based on AC power flow model.
However, these traditional optimizations of transmission
congestion mostly focused on the trend of the objective
function or as a percentage of the basic constraints to the
introduction of the congestion management model. This
approach increases the difficult to solving the model in
virtually.
This paper presents the congestion cost optimal models
for the case: open the generate side and the load side at the
same time. The greatest feature of this model is that the
power flow percentage is involved in the calculation of
blocking cost in order to make the power flow limit’s li-
ability more clearly. The optimal solution is obtained by
using the ant colony algorithm which has the global search
ability. Finally, the model is simulated for two cases: the
load of 982.4 MW and 1052.8 MW. Simulation results
show that the improved optimal model can obviously re-
duce the cost of electricity.
2. Problem Statement
Congestion management is a complicated systematic
work, including the interest of the generate side and the
load side at the same time.
Transmission congestion management principles:
1) Transmission congestion is eliminated by adjusting
the unit output distribution program.
2) Transmission congestion is also eliminated by using
B. LIU ET AL.
18
the safety margin transmission in line to avoid power
cuts (focus to reduce the load demand) , but make sure
that the percentage of the absolute value of the trend ex-
ceeding the limit value in each line is as small as possi-
ble.
3) If the percentage of the absolute value of the trend
exceeding the limit value in each line is greater than rela-
tive safety margin no matter how to distribute the unit
output, the power should be cut in the load side.
3. Congestion Management Optimal Model
Traditional congestion management model based on
nodal price has a strong practical, but the model con-
straints have nonlinear expressions, which makes solving
the biggest problem. Because the trends affect the cost of
congestion management based on the generator side, the
traditional model needs quadratic programming, which
means complex. When there is interruptible load in the
load side, the model only focuses on the minimum power
purchase cost of the network and more importantly it
doesn’t reflect the current contribution of the ob struction
charges. Therefore, this paper will improve the inter-
ruptible load with opening the generator side and load
side simultaneously, focusing on the influence to conges-
tion cost when the trend is inevitable. The new model’s
objective function is the minimum congestion cost.
3.1. Current Ratio Factor
Generally, researchers use the percent of effective power
flow exceeding the safe threshold value in each line to
measure the congestion degree, here called transmission
congestion rate. It could be expressed as:
kk
kk
yu
u
(1)
where k represents the effective power flow in the
main lines in power network, k represents the limited
value of power flow in the wiring, which means security
margin in the wiring, .
yu
,ks1,
Obviously, when the effective power flow is smaller
than the safe threshold value, then 0
k
; when the
effective power flow exceeds the safe threshold value,
then 0
k
. Let k
max ,1k, ,s
. We study the
state when the transmission congestion is maximum.
Therefore
is a positive number in this paper.
The power flow describes the distributions of voltage
(including the amplitude and phase), active power and
reactive power in power network. Assume there are eight
generators and six main lines. It can be seen from the
observation data that active power flow
1, 2,,
k
y
k
1, 2,,
i
s
and the generator o utp ut
x
in
i
are linear relation- ship as follows,
1
ni
kk
i
y
x
(2)
where i
k
represents the linear relevant coefficient of
the active power flow relating to the output of each gen-
erator.
3.2. The Improved Transmission Congestion
Control Model
The influence of power flow on congestion cost can’t be
reflected fully when only power flow violation is taken
as the constrain condition. Therefore, transmission con-
gestion rate (power flow proportion coefficient) is intro-
duced into the target function of cost model in this paper.
The congestion cost is larger with the increase of the
proportion coefficient. The responsibility of the power
flow violation can be ascertained by using the assump-
tion, and the partners of power market can be constrained
and the process of solution can be simplified. It has the
direct meaning to the commercialization of power ma rket.
The goal of real-time congestion management is to
eliminate the congestion with the minimum cost. In this
section, we consider the two cases: generation bidding
only, and generation and auxiliary power bidding at the
same time. Considering the adjustment of the minimum
cost as the target function, the optimal model can be in-
vestigated when the transmission congestion rate is as
large as possible.
If the transmission congestion rate is beyond the safe
margin, the worst congestion occurs. Then we should
adjust the output plan and interrupt parts of the load and
compensate for it. The congestion cost including the
compensation fee paid for consumers. In order to get th e
minimum of the sum of adjustment cost, the generator
and load side should be adjusted simultaneously.
Assumption
j
Q is the compensation price for the
reason of power interruption,
j
is the adjusted inter-
ruption load, and then
j
j
Q
is the compensation fee for
the reason of power interruption. Considering the effect
of power flow coefficient on congestion cost, the target
function can be defined as follows:
*
1,2, ,11
min maxnl
kii jj
in ij
J
PQ
 






(3)
1
1
1
0
..
i
n
i
i
n
i
i
iiii
s
iijij
j
xB
st
CTV xCTV
xxd

where, i
x
s the output in the next time-interval of gen-
Copyright © 2011 SciRes. EPE
B. LIU ET AL.
Copyright © 2011 SciRes. EPE
19
erator in the distribution preplan, i represents the
corresponding price of i
i P
x
which locates the generator
s the adjusted distribution replant,
i
is the change
value of generator of adjusted output plan com-
pared with original plan after the congestion happen.
is the number of the consumers who participate the in-
terruption load management and bid successfully in
il
ancillary service market. is the total amount of gen-
erators that participate in the output adjustment.
n
s
is
the number of main lines, is the load requirement of
next time-interval forecast, i s the output of generator
, i s the length of one time-interval, i is th e climb
rate, ij is the interval capability from generator to
generator .
B
C
iT dVi
jij
x
is defined as follows:
1output of -nehrval
0out output o-th ge-inter
ij
x
th ge
f
rato
ene
r in
rator
ij-t
in
tim
-tij
e-inte
h timwithval
where .
2,, ,,in1,j2,s
Constraint conditions
1
n
i
i
x
B
and
1
n
i
i
0
CTV
ensure the load forecasting always to meet the require-
ments, i.e. the adjustment of each generator output al-
ways to meet the load requirements when the require-
ment is . Constraint condition iiii
describes the generator climb rate i.e. if the output is i
at present, in the next time-interval the generator set
output will lies within the range of
Bi
TV
C
xC

,
iii
CTVCT
i
V.
Constraint co ndition
1
s
iijij
j
x
xd
restricts the capability of generator output, i.e. the gen-
erator output can’t exceed the sum of every time-interval
output.
Remark 1: the vector will increase correspondingly
with the increase of the rate of transmission congestion.
As a result, the adjustment cost will increase. However,
our final goal is to reduce the congestion cost. Then this
problem could be considered as a typical mini-max
problem. We will solve the set models in the following
section to verify their security and reliability.
4. Model Solution
4.1. Characteristics of Ant Colony Algorithm
1) Positive feedback mechanism. The more ants after the
path chosen by the ants follow-up more likely, by con-
tinuously updated information on the optimal path of
Convergence.
2) Generality. The algorithm model has a good adapta-
tion for other o pt imization problem.
3) Distributed parallel computing. The algorithm sear-
ches solution in the global context of multi-location si-
multaneously. It is a global optimization heuristic algo-
rithm, both for single objective optimization problem and
for multi-objective optimization or constrained optimiza-
tion problem conditions.
4.2. Transmission Congestion Model Based on
Improved Ant Colony Algorithm
Based on the improved congestion management model,
the model’s objective function value is set to the
shortest path on which ants find food. Above the
analysis, we can reach a conclusion: ant colony algo-
rithm solving process has the two major cycles. Circu-
lation is controlled by the change of cities’ number
while the outer loop is controlled by the change of
ants’ number. The parameters have a significant impact
on path of ants searching food.
1) Initial control parameter is chosen as large as possi-
ble.
2) Attenuation function con trols the ants’ number. It is
defined as follows:
M
*dkM
. Where d is close to
1. This value is closer to 1 that participate in the more
ants find food, the better the optimal solution obtained,
because it determines the number of outer loop.
k
3) There are many options to terminate the conditions.
A variety of conditions on the performance of the algo-
rithm has great influence on the quality of reconciliation.
This paper sets the number of iterations and comparison
as both internal and external conditions.
The ant colony algorithm process of the improved
blocking model:
1) Initialization of variable. Set
M
ants, cities
(units) and pheromone matrix system be 1. In this paper,
we suppose there are eight generating units and six
transmission lines.
N
M
2) Set ants to cities. Generate an initial solu-
tion set (the starting point for the algorithm) according to
the constraints random variable of the improved model
(the output of new programs).
N
12
,,,
n
X
xx xis the
output matrix of redistribution preplan of generators.
Firstly, restrict the output of generator n within the
range of
,
nn
according to the known data and ine-
quality constraint conditions. Where,
ab
,
n
ab
n
is inter-
B. LIU ET AL.
20
section of
,
nnnn
CTVCTV and 1
s
nnj
jnj
x
xd
. Ant
colony.
3) Algorithm has a major advantage which is the final
result of optimization has nothing to do with the initial
value. So with the generated solution
is set with the random number. It shows as follows:
. At the same time, we
can use the other output to express the output of genera-
tor in order to satisfy the equation constraint condi-
tion:
1, 2,, 7
i
xi


0,1
ii ii
xaba random 
n

8 1234567
x
Bxxxxxxx 
4)
M
ants select to the next city with a certain
probability to complete their tour, so the new output
scheme is obtained. The congestion cost of the new and
the corresponding output program’s difference is called
evaluation function: **
11 1
J
JJ .
5) If the evaluation function is a negative number, the
current efforts contributing to the program is accepted to
the new program; else, accept it as the new one accord-
ing the probability:

 
1
0,1
k
i
pk
p random
pk

The new program is the local optimal solution. Where



ij
ij
pk L
is a sequence consisting of after some iterative
optimizations.

pk
6) The number of the searching city increasing, from
to , pheromone is updated. Deter-
mine whether the conditions meet the above. Jump out of
circulation and turn to the next step when it doesn’t meet.
Repeat the two steps above until the maximum number
of iterations and record the best path in this iteration.
j
1, 2,,jj n
7) The number of foraging ants increasing, record
every round each ant foraging route and feeding distance,
which means the unit costs under the current combined
output. Select the minimum number of optimal solutions
and repeat (3-6) steps until reaching the maximum num-
ber of iterations.
8) Getting results. By the Step 3 and Step 4, get the
optimal distance of each ant, step 3 and 6 control the
change of the size of
M
, to seek the global opti mal so-
lution.
5. Simulation Examples
According to the characteristics of Ant Colony Algo-
rithm, the three examples will be simulated, combining
with the proposed model. Main purpose is to compare
the costs resulting from the current output matrix with
costs resulting from the previous output matrix, and
choose the smaller the cost. Finally, Minimum cost is
found and after a finite number of iterations, and it as an
optimal solution of the example.
5.1. Example 1: Load Requirement is 982.4 MW
We identify the simple feasibility and safe reliability of
the proposed congestion optimal model by simulation
examples.
Table 1 gives the output of each generator and the cor-
responding climb rate. Table 2 gives the output distribu-
tion preplan and corresponding price each generator
when the load forecasting is 982.4 MW.
If the output preplan does not change, i.e., the output
of each generator according to Table 1, this preplan is
decided by the transaction rul es of power market.
Let max 0.22
k
According to the safety and trans-
action rules of power market, we can get the original cost
597.694” for the increase of load requirement by the
formula.
Then we resolve the preplan aiming to minimize the
preplan cost using the simulation annealing algorithm.
Where, let the current output matrix
120,73,180,80,125,125,81,90c, the revolution of the
generator unit
2.1,1,3.1,1.3,1.8,2,1.4,1.8v, the target
output
15fprice 0,79,180,99.5,125,140,95,113.9 , the
252,300,233,302,215,252,260
.95 ,303 , the pphero-
mone parameter 0
.
The simulation result is as follows:
The X-axis represents the iteration times and the
Y-axis represents the target function.
It can be seen from Figure 1 that the cost is
478.5872 and the saving cost is 119.106. The out-
Table 1. The present climb rate of each generator output.
1 2 3 4 5 6 7 8
Present
output (MW)1207318080 125 125 81.190
Rate
MW/min 2.11 3.1 1.3 1.8 2 1.4 1.8
Table 2. The distribution preplan each generator when load
forecasting is 982.4 MW.
1 23 4 5 6 7 8
Forecasting
outpout MW15079180 99.5 125 140 95113.9
Price
(Yuan/MW.hour)252300 233 302 215 252 260303
Copyright © 2011 SciRes. EPE
B. LIU ET AL.21
Figure 1. The adjustment cost when load is 982.4 MW.
put of each generator is as follows:
147.3545,69.1272,228.5268,64.0073,
149.2004,155.6027,10 1.9507,66.6304
X
We can see that the process of decreasing temperature
is reasonable and the annealing can jump out the local
optimal solution. Therefore, the final minimum value is
reliability after enough iteration times.
5.2. Example 2: Load Requirement is
1052.8 MW
Table 3 gives the output distribution preplan when the
load requirement is 1052.8 MW. Let max 0.22
k
.
According to the safety and transaction rules of power
market, we can get the original cost “3845.814” for the
increase of load requirement. Where, let the current out-
put matrix
150,81,21 8.2,99.5,135,150,102.1,117c,
the revolution of the generato r unit
2.1,1,3.v
1,1.3,1.8,2,1.4,1.8 , the target output
150,79f
,180,99.5,125,140,95,113.9, the price
252,30p0,233,302,21 5,252,260,303
0.95 , the pheromo-
ne parameter
.
The simulation result using matlab is as follows:
The X-axis represents the iteration times and the
Y-axis represents the target function.
It can be seen from Figure 2 that the cost is 3784.6
and the saving cost is 61.214. The output of each
generator is as follows:
151.9448,83.9114,197.8033,97.749 8,
151.4479,156.3922,10 2.4476,118.8128
X
We can also see form Figure 2 that the larger load re-
quirement corresponds the higher generator cost. There-
fore, we consider the method of interruptible load in or-
der to realize the cost management of high load require-
ment.
Table 3. The generator forecasting output when load re-
quirement is 1052.8 MW.
1 2 3 4 5 6 7 8
Forecasting
Output MW15081218.299.5 135 150 102.1117
Price (Yuan/
MW.hour) 252320356302 310 305 306303
Figure 2. The adjustment cost when load is 1052.8 MW.
5.3. Example 3: Simulation of Interruptible
Load Model
Assume the present output is described by Table 1, the
load requirement is 1052.8 MW. The consumer side ex-
ists the interruptible load according to the interrupt
agreement, and the interruptible quantity is 30.4 MW.
Because of the implementation of interruptible load, the
distribution preplan of each generator output can be en-
forced according to the residual load requirement. At the
same time, corresponding max 0.02
k
, load require-
ment decrease dramatically compare with the 1052.8
MW. Where, let the current output matrix
120,73,18 0,80,125,12c5,81,90 , the revolution of the
generator unit
2.1,1,3.1,1.3,1.8,2,1.4,1.8v, the target
output
150,79,180,99.5,125,140,95,113.9fthe
price ,
252,300,233,p302,215,252,260
0.95 ,303 , the
pheromone parameter
.
The compensation fee for the interrupt is calculated as
follows:


1
max
0.0225.8640003.5541 1.04 154
2109.8732
l
kjj
jQ

 
The simulation result using MATLAB is:
The X-axis represents the iteration times and the
Y-axis represents the target function.
Copyright © 2011 SciRes. EPE
B. LIU ET AL.
22
Figure 3. The adjustment cost when consumer side exist the
interruptible load.
We can get the result using the calculation function of
MATLAB, the generator cost is 2592.701. The gen-
erator cost decreases dramatically compare with
3780.9 without the interruptible road. The saving cost
is 1188.199.The output of each generator is as fol-
lows:
153.1424,65.5055,227.4673,61.3641,
151.0063,145.5638,101.3008,79.0498
X
Therefore, signing the appropriate interruptible load
agreement can decrease the congestion cost and improve
the social benefits.
6. Conclusion
In this paper, an improved optimal congestion cost model
is built by introducing the congestion factor in dealing
with the cases: opening the generator side and load side
simultaneously. The optimal solution is obtained based
on the ant colony algorithm. The model is simulated for
two cases: the load of 982.4 MW and 1052.8 MW. The
results show that the model can significantly reduce the
cost of electricity. As the load demand increasing, a cor-
responding increase in congestion costs, the effective
interruptible load is used to reduce the cost and control
the adjustment effectively.
7. Acknowledgment
This work is supported by the Fundamental Research
Funds for the Central Universities, under grant
090304004, and the National Natural Science Foundation
of China, under grant 60274009, and Specialized Re-
search Fund for the Doctoral Program of Higher Educa-
tion, unde r gr ant 2002014 5007.
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