 Open Access
 Total Downloads : 681
 Authors : K. Venkatesan, C. Christober Asir Rajan
 Paper ID : IJERTV1IS8486
 Volume & Issue : Volume 01, Issue 08 (October 2012)
 Published (First Online): 29102012
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Ant Colony Search Algorithm For Solving Multi Area Unit Commitment Problem With Import And Export Constraints
K. Venkatesan, C. Christober Asir Rajan
Research Scholar, Dept. Of Elect. Engg., J.N.T.U. Anantapur, Anantapur, 515 002, A.P., India Associate Professor,Department of EEE, Pondicherry Engg. College, Puducherry, 605 014, India.
Abstract Nomenclature
This paper presents a new approach to solve the multi area unit commitment problem (MAUCP) using a Ant Colony Search Algorithm (ACSA). The objective of this paper is to determine the optimal or a near optimal commitment schedule for generating units located in multiple areas that are interconnected via tie lines. The Ant Colony Search Algorithm is used to solve multi area unit commitment problem, allocated generation for each area and find the operating cost of generation for each hour. Joint operation of generation resources can result in significant operational cost savings. Power transfer between the areas through the tie lines depends upon the operating cost of generation at each hour and tie line transfer limits. The tie line transfer limits were considered as a set of constraints during optimization process to ensure the system security and reliability. The overall algorithm can be implemented on an IBM PC, which can process a fairly large system in a reasonable period of time. Case study of four areas with different load pattern, each containing 26 units connected via tie lines has been taken for analysis. Numerical results showed comparing the operating cost using Ant Colony Search method with conventional evolutionary programming (EP) and dynamic programming (DP) method. Experimental results shows that the application of this Ant Colony Search method have the potential to solve multi area unit commitment problem with lesser computation time.
Keywords
Ant Colony Search Algorithm (ACSA), Dynamic Programming (DP), Evolutionary Programming (EP), Multi Area Unit Commitment Problem (MAUCP).
F (Pk )
g
i
P
k gi
ak ,bk , ck
i i i
X
off i, j
P
k i, j
I
k
i, j
Pg
k i, j
D
k j
R
k j
E
k j
Pj
k
max
Pj
k
min
T
on
T
i off
i
Lj
k
max
Wj
sys
Pg
k
i max
Pg
k
i min
Production cost of unit i in area K
Power generation of unit i in area K
Cost function parameters of unit i in area K
Time duration for which unit i have been off at jth hour.
Power generation of unit i in area K at jth hour
Commitment state (1 for ON, 0 for OFF)
Power generation of unit i in area K at jth hour
Total system demand of area K at jth
hour
Spinning reserve of area K at jth hour
Total export power to area K at jth
hour
Maximum power generation in area K at jth hour
Minimum power generation in area K at jth hour
Minimum up time of unit i Minimum down time of unit i
Maximum total import power in area K at jth hour
Net power exchange with outside system
Marginal cost of supplying the last incremental energy to meet entire system demand.
Maximum power generation at area K at ith hour
Minimum power generation at area k at ith hour

Introduction
In multi area, several generation areas are interconnected by tie lines, the objective is to achieve the most economic generation to meet out the local demand without violating tieline capacity limits constraints [1]. The main goal of this paper is to develop a multi area generation scheduling scheme that can provide proper unit commitment in each area and effectively preserve the tie line constraints.
In an interconnected multi area system, joint operation of generation resources can result in significant operational cost savings [2]. It is possible by transmitting power from a utility, which had cheaper sources of generation to another utility having costlier generation sources. The total reduction in system cost shared by the participating utilities [3].
The exchange of energy between two utilities having significant difference in their marginal operating costs. The utility with the higher operating cost receives power from the utility with low operating cost. This arrangement usually on an hour to hour basis and is conducted by the two system operators.
In the competitive environment, customer request for high service reliability and lower electricity prices. Thus, it is an important to maximize own profit with high reliability and minimize overall operating cost [4]. Multi Area unit commitment was studied by dynamic programming and was optimised with local
this work, the parents are obtained from a predefined set of solution (i.e., each and every solution is adjusted to meet the requirements). In addition, the selection process is done using evolutionary strategy [8][10].
For the last few years, the algorithms inspired by the observation of natural phenomena to help solving complex combinatorial problems have been increasing interest. In this study, a new Ant Colony Search Algorithm (ACSA), which was derived by the observation of the behaviors of ant colonies, is proposed [11]. In analyzing the behaviors of real ants, it was found that the ants are capable of finding shortest path from food sources to the nest without using visual cues. In the application of this method to UC problem, the initial population of colony can be first randomly generated within the search space of problem. Then, the fitness of ants is individually assessed based on their corresponding objective function. With the selection of trial, the ant dispatch can be activated based on the level of pheromone and the distance of selected trial in order to find the best tour or the shortest path.

Problem Formulation
The cost curve of each thermal unit is in quadratic form [1]
demands with a simple priority list scheme on a personal computer with a reasonable execution time [5]. Even though the simplicity and execution speed are well suited for the iterative process, the commitment schedule may be far from the optimal, especially when
F(Pgik ) ak (Pg k )2 bk (Pg k ) ck
i i i i i
k = 1 NA
Rs/hr (1)
massive unit on/off transitions are encountered. The tie line constraint checking also ignores the network topology, resulting in failure to provide a feasible generation schedule solution [5]. The transportation model could not be used effectively in tie line constraints, as the quadratic fuel cost function and exponential form of start up cost were used in this study.
An Evolutionary algorithm is used for obtaining the
The incremental production cost is therefore
i i i
2ak Pg k bk
(or)
i i
Pgik bk / 2ak
(2)
(3)
initial solution which is fast and reliable [6]. Evolutionary Programming (EP) is capable of
The startup cost of each thermal unit is an exponential function of the time that the unit has been off
o ff
determining the global or near global solution [7]. It is based on the basic genetic operation of human chromosomes. It operates with the stochastic
S ( X off )
A B (1 exi , j i )
(4)
i, j
i
i
mechanics, which combine offspring creation based on the performance of current trial solutions and competition and selection base on the successive generations, from a considerably robust scheme for large scale real valued combinational optimization. In
The objective function for the multiarea unit commitment is to minimize the entire power pool generation cost as follows [1].
k k k
X on
T on I
I 0
N A t
Nk Ii, j Fj (Pi, j
i, j1 i
i, j 1
i, j
(12)
min
I,P
k 1 j1i1I
(1I
)S (X off
))
X off
T off I I
0
i, j
i, j1 i
i, j1
(5)
i, j 1 i
i, j
i, j1
(13)
To decompose the problem in above equation (5), it is rewritten as

In each area, power generation limits caused by tie line constraints are as follows
Upper limits
t
min
F (P
)
Pk
Dk E k
(14)
j 1
gi , j
(6)
gi , j
i
j jmax
N A
k k
g
Lower limits
F Pg
i , j
F
k 1
P
i , j
(7)
P
j
k gi , j
Dk
j

Lk
max
(15)
F P
Subject to the constraints of equations (9), (11) and i
(1418). Each
k k
gi , j
for K=1 NA is
Import/Export balance
represented in the form of schedule table, which is the solution of mixed variable optimization problem
Ek Lk W
0 (16)
min I k F k Pk I 1 I S X off (8)
j j j
i k
I ,P i
i, j i
i, j
i, j
i, j1 i
i, j


Area generation limits
Subject to following constraints are met for optimization.
P

System power balance constraint
k gi , j
P
i
k gimax
P
i
Rk ; k=1. N
j A
j=1.t (17)
j
g j
k Dk
k k
(9)
k gi , j
P
i
k
P
gi min
i
; k=1. NA
Sum of real power generated by each thermal unit must be sufficient enough to meet the sum of total demand of each area while neglecting transmission losses.
j=1.t (18) The objective is to select sys at every hour to minimize the operation cost.

Spinning reserve constraint in each area
k Dk
P
j
g
j

E k

Lk
(19)
Pk
Dk Rk E k Lk
(10)
j
j
gi , jmax
i

j j j
where
Nk
P
P

k
g j gi , j
(20)



Generation limits of each unit
i1
Since the local demand D k is determined in
P
P
k jmax
k i, j
Pk
j
min
(11)
j
accordance with the economic dispatch within the pool,
i=1..Nk, j=1.t, k=1NA
changes of P k
g
j
will cause the spinning reserve

Thermal units generally have minimum up time Ton and down time Toff constraints, therefore
constraints of equations (10) to change accordingly and redefine equation (8). Units may operate in one of the following modes when commitment schedule and unit generation limits are encountered [16].

Coordinate mode : The output of unit i is determined by the system incremental cost
An area may reach its lower generation limit according to equation (15) or (18) in this case because
min,i sys max,i
(21)
of higher generation cost

Minimum mode : Unit i generation is at its minimum level
k
min
sys
(27)
min,i sys
(22)




Tie Line Constraints
To illustrate the tieline flow in a multiarea system, the four area system given in Fig.1 is studied.

Maximum mode : unit i generation is at its
maximum level
An economically efficient area may generate more power than the local demand, and the excessive power
max,i sys
(23)
will be exported to other areas through the tielines [1]. For example assume area 1 has the excessive power the tie line flows would have directions from area1 to other

Shut down mode : unit i is not in operation,
Pi = 0
Besides limitations on individual unit generations, in a multi area system, the tieline constraints in equations (12), (13) and (15) are to be preserved. The operation of each area could be generalized into one of the modes as follows.

Area coordinate mode
areas, and the maximum power generation for area1 would be the local demand in area1 plus the sum of all the tieline capacities connected to area1.
If we fix the area 1 generation to its maximum level than the maximum power generation in area 2 could be calculated in a similar way to area 1. Since tie line C12 imports power at its maximum capacity, this amount should be subtracted from the generation limit of area

According to power balance equation (9) some areas must have a power generation deficiency and requires generation imports. The minimum generation limits in these areas is the local demand minus all the connected
k
sys
tieline capacities. If any of these tielines is connected to an area with higher deficiencies, then the power flow directions should be reserved.
Dk Lk
Pk
Dk E k
(24)
j max
gi , j
i
(or)
j max
1
100 300

L
k
max
k gi , j
P
i

Dk
k
E
max
(25)
4
300
150
2
100
j



Limited export mode
When the generating cost in one area is lower than the cost in the remaining areas of the system, that area may generate its upper limits according to equations
(14) or (17) therefore
3
Figure 1. Multiarea connection and tieline limitations
k
sys
(26)

ACSA Paradigm
For area k, area k is the optimal equal incremental cost which satisfies the generation requirement.


Limited import mode
4.1. Behavior of Ants
Ant colony search (ACS) studies are inspired from the behavior of ants colonies that are used to solve
function or combinatorial optimization problems. Currently, most work has been done in the direction of applying ACS to combinatorial optimization. The first ACS system was introduced by Marco Dorigo [12] and was called ant system. Ant colony search algorithm, to some extent; mimic the behavior of real ants. As is well known, real ants are capable of finding the shortest path from food sources to the nest without using visual cues. They are also capable of adapting to changes in the environment. Pheromone trails, which ants use to communicate information among individuals regarding path and to decide where to go. Ants deposit a certain amount of pheromone while walking, and each ant probabilistically prefers to follow a direction rich in pheromone rather than a poorer one. The behavior of ant is given in fig. 2.
(a)
(b)
(d)
Figure 2: Behavior of ants : (a) Real ants follows a path between nest and food source. (b) An obstacle appears on the path: ants choose whether to turn left or right with equal probability. (c) Pheromone is deposited more quickly on the shorter path. (d) All ants have chosen the shorter path.

Ant colony search Algorithm

ACS State Transition Rule
In ACS the state transition rule is as follows: An ant positioned on node choose the city S to move by applying the given rule, if q qo
Where
q is a random number uniformly distributed in (0..1) q0 is a parameter (0qo1)
S is random variable selected according to the probability distribution given in (28)
The state transition rule used by ant system, called a random proportional rule, is given by Eq(8), which gives the probability with which ant k in city r chooses to move to the city s.
r, s.r, s
r,u.r,u
ifsJ ( r) (28)
pk r, s
uJk r
r k
0 otherwise
(c)
Where
is the pheromone
Jk(r) is the set of cities that remain to be visited by ant k positioned on city r (to make the solution feasible)
is a parameter, which determines the relative importance of pheromone versus distance (>o)
1/ is the inverse of the distance (r,s)

ACS Global Updating Rule
Global updating is performed after all ants have completed their tours. The pheromone level is updated by applying the global updating rule of equation (29).
(r,s) (1)(r,s)+ (r,s) (29)
Step 2 : Assessment of Fitness
In this step, the fitness of all ants is assessed based on the corresponding objective function, which can be expressed as following:
where
L
1
f () tcs
i
, s i1
(31)
(r, s) =
gb
0 otherwise
if(r,s) globalbesttour
Where
tc(si,sj) is the transition cost between state si and sj
is the pheromone decay parameter
Lgb is the length of the globally best tour from the beginning of trial

ACS Local Updating Rule
While building a solution of the MAUCP, ants visit edges and change their pheromone level by applying the local updating rule of equation (30)
(r,s) (1)(r,s)+ (r,s) (30)
where
is a heuristically defined coefficient o – is the initial pheromone level

ACS Parameter Setting

In this program of the following sections the numeric parameters, except when indicated differently, are set to the following values: =2, qo= 0.9, ==0.1.
4.3. Ant Colony Search General Algorithm
To solve MAUCP by ACSA, the search space of generation scheduling problem is established using multiprocess decision making concept. The main computations are discussed below.
Step 1 : Ant Generation
In the first step, the colonies of ants are first generated. Ants are positioned on initial state while the initial pheromone value of 0 is also given at this step. Based on the concept multi state process, the search space of thermal generation scheduling problem can be established. All the possible permutations constitute this search space. Each stage contains several states, while the order of state selected at each stage can be combined as an achievable tour that is deemed a feasible solution to the problem.
Âµ(i) for i=1.n defines a permutation
With the evaluated fitness of the corresponding ants, the pheromone can be added to the particular direction in which the ants have selected.
Step 3: Ant Dispatch
In this step, the ants are dispatched based on the level of pheromone and distance. Each ant chooses the next state to move taking into account of ij and ij values. When the value of ij gets larger, there has been a lot of traffic on this edge; hence it is more desirable to reach the optimal solution. When the value of ij increases, it represents that the closer state should be chosen with a higher probability.
Step 4: Convergence
The computation process continues until the number of iterations reaches the predefined maximum threshold, of the iteration counter without improving the best objective function reaches the maximum allowable value. All the tour visited by ants in each iteration should be evaluated. If a better path found in the process, it will be saved for later reference. The best path selected among all iterations implies the optimal scheduling solution to the problem.
Algorithm for ACSA for SCUC Step 1 : Ant generation
Step 2 : Assessment of fitness
Step 3 : Ant dispatch
Step 4 : Update pheromone by applying local updating rule
Step 5 : Check for all ants are completed their tours.
If No go to step 3
Step 6 : Apply Global pheromone update rule
Step 7 : Check for convergence. If No go to step 2

Ant colony search algorithm for MAUCP
ACSA is conducted to solve MAUCP by following sequence of operations.

Initialize area A=1.

Read unit data, tieline data, load demand profile and number of iterations to be carried out.

Find initial feasible solution.

Colonies of ants are generated and ants are positioned with initial phermone value of 0 .

Calculate the fuel cost and start up cost of each power plant at each ant position.

Calculate total production cost.

Calculate the fitness function of all ants.

Update ant position based on ij and ij values.

Update phermone by applying local updating rule.

Check for all ants completed their tour. IF No go to step 8. Otherwise go to next step.

Apply global phermone update rule.

Check for N number of areas completed. If yes go to step 2, else go to step 14.

Export power from lower operating cost areas to higher operating cost area by following tieline constraints.

Print the commitment schedule of N areas and tie line flows

Repair mechanism
A repair mechanism to restore the feasibility of the constraints is applied and described as follows

Pick at random one of the OFF units at one of the violated hours.

Apply the rules in section 4.2 to switch the selected units from OFF to ON keeping the feasibility of the down time constraints.

Check for the reserve constraints at this hour. Otherwise repeat the process at the same hour for another unit.


Making Offspring Feasible
While solving the constrained optimization problem, there are various techniques to repair an infeasible solution [8] [11]. In this paper, we have chosen the technique, which evolves only the feasible solutions. That is, the schedule which satisfies the set of constraints as mentioned earlier. Here, in this paper,
the selection routine is involved as curling force to estimate the feasible schedules. Before the best solution is selected by evolutionary strategy, the trial is made to correct the unwanted mutations.

Implementation
Software program were developed using MATLAB software package, and the test problem was simulated for ten independent trials using Ant Colony Search Algorithm (ACSA). The training and identification part as implemented in the ACSA technique is employed here and considered as a process involving random recommitment, constraint verification, and offspring creation.
6. Numerical Results
The test system consists of four areas, and each area has 26 thermal generating units [1]. Units have quadratic cost functions, and exponential start up cost functions. Table 1 lists generating unit characteristics like the minimum up/down times, initial conditions and generation limits of units in every area. Table 2 to Table 5 lists the cost functions of units given in the four area [1], where variables ai, bi and ci are defined in equation 1. Ai, Bi and Ci are defined in equation 4. Load demand profile for each area is different and is given in Fig. 3. The hourly operating cost of four areas by Dynamic Programming (DP), Evolutionary Programming (EP) and Ant Colony Search Algorithm (ACSA) method is given in Table 6 to Table 8 respectively. The total operating cost in pu coparison between DP, EP and ACSA method is shown in Table
9. Comparison of total operating cost in each area by DP, EP and ACSA method is shown in Fig. 4. The proposed algorithm quickly reaches smallest total operating cost compared to DP and EP method, which indicates that the proposed algorithm could determine the appropriate schedule within a reasonable computation time. It is noted that cost in one iteration may be lower than that of the previous iteration, indicating that our optimization rules always comply with the equal incremental cost criterion for dispatching power generation among thermal units. The tieline flow pattern at 11 am and 4 pm are shown in Fig. 5 and Fig. 6 respectively.
Figure 3. Load demand profile in each area
Figure 4. Comparison of Total Operating cost by DP, EP and ACSA method
598 Area Generation
1
81 0
846 4
89 2
1200
20 20
3
857
Figure 5. Tie line flow pattern at 11 am
Table 1. Generating unit characteristics
Unit No. 
Minimum up time(hour) 
Minimum down time (hour) 
Initial condition (hour) 
Minimum Generatio n(MW) 
Maximum Generation (MW) 
1 
0 
0 
1 
2.40 
12 
2 
0 
0 
1 
2.40 
12 
3 
0 
0 
1 
2.40 
12 
4 
0 
0 
1 
2.40 
12 
5 
0 
0 
1 
2.40 
12 
6 
0 
0 
1 
4.00 
20 
7 
0 
0 
1 
4.00 
20 
8 
0 
0 
1 
4.00 
20 
9 
0 
0 
1 
4.00 
20 
10 
0 
2 
3 
15.20 
76 
11 
3 
2 
3 
15.20 
76 
12 
3 
2 
3 
15.20 
76 
13 
3 
2 
3 
15.20 
76 
14 
3 
2 
3 
25.00 
100 
15 
4 
2 
3 
25.00 
100 
16 
4 
2 
3 
25.00 
100 
17 
4 
3 
5 
54.25 
155 
18 
4 
3 
5 
54.25 
155 
19 
5 
3 
5 
54.25 
155 
20 
5 
3 
5 
54.25 
155 
21 
5 
4 
4 
68.95 
197 
22 
5 
4 
4 
68.95 
197 
23 
5 
4 
4 
68.95 
197 
24 
8 
5 
10 
140.00 
350 
25 
8 
5 
10 
140.00 
350 
26 
8 
5 
10 
140.00 
350 
Table 2. Cost functions for generating units in area 1
td>
175.057
Unit No. 
Gen. cost coeffi. a($/MW2) 
Gen. cost coeffi. b($/MW) 
Gen. cost coeffi. c ($) 
Start up Cost coeffi.A($) 
Start up Cost co effi.B($) 
Start up time constant 
1 
24.360 
25.237 
0.0120 
0 
0 
1 
2 
24.379 
25.255 
0.0121 
0 
0 
1 
3 
24.395 
25.273 
0.0125 
0 
0 
1 
4 
24.420 
25.299 
0.0129 
0 
0 
1 
5 
24.434 
25.321 
0.0130 
0 
0 
1 
6 
117.121 
37.000 
0.0060 
20 
20 
2 
7 
117.239 
37.132 
0.0062 
20 
20 
2 
8 
117.358 
37.307 
0.0064 
20 
20 
2 
9 
117.481 
37.490 
0.0066 
20 
20 
2 
10 
81.000 
13.322 
0.0046 
50 
50 
3 
11 
81.028 
13.244 
0.0047 
50 
50 
3 
12 
81.104 
13.300 
0.0049 
50 
50 
3 
13 
81.176 
13.350 
0.0052 
50 
50 
3 
14 
217.000 
18.000 
0.0042 
70 
70 
4 
15 
217.100 
18.100 
0.0044 
70 
70 
4 
16 
217.200 
18.200 
0.0047 
70 
70 
4 
17 
142.035 
10.394 
0.0043 
150 
150 
6 
18 
142.229 
10.515 
0.0045 
150 
150 
6 
19 
142.418 
10.637 
0.0047 
150 
150 
6 
20 
143.497 
10.708 
0.0048 
150 
150 
6 
21 
256.101 
22.000 
0.0025 
200 
200 
8 
22 
257.649 
22.100 
0.0026 
200 
200 
8 
23 
258.176 
22.200 
0.0026 
200 
200 
8 
24 
10.462 
0.0016 
300 
200 
8 

25 
305.036 
7.486 
0.0019 
500 
500 
10 
26 
306.910 
7.493 
0.0019 
500 
500 
10 
Table 3. Cost functions for generating units in area 2
Unit No. 
Gen. cost co effi.a($/MW2) 
Gen. cost co effi.b($/MW) 
Gen. cost coeffi.c ($) 
Start up Cost coeffi.A($) 
Start up Cost coeffi.B($) 
Start up ti constant ( 
me ) 
1 
24.389 
25.547 
0.0123 
0 
0 
1 

2 
24.411 
25.675 
0.0125 
0 
0 
1 

3 
24.638 
25.803 
0.0130 
0 
0 
1 

4 
24.760 
25.932 
0.0134 
0 
0 
1 

5 
24.488 
26.061 
0.0136 
0 
0 
1 

6 
117.755 
37.551 
0.0059 
20 
20 
2 

7 
118.108 
37.664 
0.0066 
20 
20 
2 

8 
118.458 
37.777 
0.0066 
20 
20 
2 

9 
118.821 
37.890 
0.0073 
20 
20 
2 

10 
81.136 
13.327 
0.0047 
50 
50 
3 

11 
81.298 
13.354 
0.0049 
50 
50 
3 

12 
81.464 
13.380 
0.0051 
50 
50 
3 

13 
81.626 
13.407 
0.0053 
50 
50 
3 

14 
217.895 
18.000 
0.0043 
70 
70 
4 

15 
218.355 
18.100 
0.0051 
70 
70 
4 

16 
218.775 
18.200 
0.0049 
70 
70 
4 

17 
142.735 
10.695 
0.0047 
150 
150 
6 

18 
143.029 
10.715 
0.0047 
150 
150 
6 

19 
143.318 
10.737 
0.0048 
150 
150 
6 

20 
143.597 
10.758 
0.0049 
150 
150 
6 

21 
259.131 
23.000 
0.0026 
200 
200 
8 

22 
259.649 
23.100 
0.0026 
200 
200 
8 

23 
260.176 
23.200 
0.0026 
200 
200 
8 

24 
177.057 
10.862 
0.0015 
300 
200 
8 

25 
310.002 
7.492 
0.0019 
500 
500 
10 

26 
311.910 
7.503 
0.0019 
500 
500 
10 
Table 4. Cost functions for generating units in area 3
td>
150
Unit No. 
Gen. cost coeffi. a($/MW2) 
Gen. cost coeffi. b($/MW) 
Gen. cost coeffi. c ($) 
Start up Cost coeffi.A($) 
Start up Cost coeffi.B($) 
Start up ti constant ( 
me ) 
1 
24.451 
26.547 
0.0123 
0 
0 
1 

2 
24.395 
26.675 
0.0125 
0 
0 
1 

3 
24.738 
26.803 
0.0130 
0 
0 
1 

4 
24.861 
26.932 
0.0134 
0 
0 
1 

5 
24.988 
27.061 
0.0136 
0 
0 
1 

6 
118.755 
38.551 
0.0069 
20 
20 
2 

7 
119.108 
38.664 
0.0076 
20 
20 
2 

8 
119.458 
38.777 
0.0076 
20 
20 
2 

9 
119.821 
38.890 
0.0083 
20 
20 
2 

10 
82.136 
14.327 
0.0047 
50 
50 
3 

11 
82.298 
14.354 
0.0059 
50 
50 
3 

12 
82.464 
14.481 
0.0061 
50 
50 
3 

13 
82.626 
14.407 
0.0063 
50 
50 
3 

14 
218.895 
19.000 
0.0053 
70 
70 
4 

15 
219.355 
19.100 
0.0061 
70 
70 
4 

16 
219.775 
19.200 
0.0059 
70 
70 
4 

17 
143.735 
11.695 
0.0056 
150 
150 
6 

18 
144.029 
11.715 
0.0057 
150 
6 

19 
144.318 
11.737 
0.0058 
150 
150 
6 

20 
144.597 
11.758 
0.0059 
150 
150 
6 

21 
259.131 
24.000 
0.0036 
200 
200 
8 

22 
259.649 
24.100 
0.0036 
200 
200 
8 

23 
260.176 
24.200 
0.0036 
200 
200 
8 

24 
177.057 
11.862 
0.0015 
300 
200 
8 

25 
310.002 
7.692 
0.0019 
500 
500 
10 

26 
311.910 
7.703 
0.0019 
500 
500 
10 
Table 5. Cost functions for generating units in area 4
Unit No. 
Gen. cost co effi. a($/MW2) 
Gen. cost coeffi. b($/MW) 
Gen. cost coeffi. c ($) 
Start up Cost coeffi.A($) 
Start up Cost coeffi.B($) 
Start up ti constant ( 
me ) 
1 
24.389 
25.202 
0.0123 
0 
0 
1 

2 
24.411 
25.255 
0.0125 
0 
0 
1 

3 
24.638 
25.273 
0.0130 
0 
0 
1 

4 
24.760 
25.342 
0.0134 
0 
0 
1 

5 
24.888 
25.366 
0.0136 
0 
0 
1 

6 
117.755 
37.012 
0.0059 
20 
20 
2 

7 
118.108 
37.055 
0.0066 
20 
20 
2 

8 
118.458 
37.098 
0.0066 
20 
20 
2 

9 
118.821 
37.156 
0.0073 
20 
20 
2 

10 
81.136 
13.261 
0.0047 
50 
50 
3 

11 
81.298 
13.278 
0.0049 
50 
50 
3 

12 
81.464 
13.295 
0.0051 
50 
50 
3 

13 
81.626 
13.309 
0.0053 
50 
50 
3 

14 
217.895 
17.500 
0.0043 
70 
70 
4 

15 
218.355 
17.600 
0.0051 
70 
70 
4 

16 
218.775 
17.700 
0.0049 
70 
70 
4 

17 
142.735 
10.210 
0.0047 
150 
150 
6 

18 
143.029 
10.268 
0.0047 
150 
150 
6 

19 
143.318 
10.307 
0.0048 
150 
150 
6 

20 
143.597 
10.375 
0.0049 
150 
150 
6 

21 
259.131 
22.500 
0.0026 
200 
200 
8 

22 
259.649 
22.600 
0.0026 
200 
200 
8 

23 
260.176 
22.700 
0.0026 
200 
200 
8 

24 
177.057 
10.462 
0.0015 
300 
200 
8 

25 
310.002 
7.492 
0.0019 
500 
500 
10 

26 
311.910 
7.503 
0.0019 
500 
500 
10 
Table 6. Hourly cost of each area by DP method
HOURS (24) 
AREA1 (26 unit) 
AREA2 (26 unit) 
AREA3 (26 unit) 
AREA4 (26 unit) 
1 
36394.904 
24678.309 
29112.227 
22128.126 
2 
32398.748 
23221.985 
22898.975 
19312.818 
3 
31714.449 
23121.988 
23694.843 
19163.999 
4 
31723.462 
18350.520 
26238.838 
18774.766 
5 
32023.452 
18364.520 
25612.969 
19065.740 
6 
35712.469 
19012.524 
23593.510 
19715.542 
7 
38904.904 
28196.592 
21832.636 
24921.278 
8 
39680.722 
34467.091 
20119.855 
21974.690 
9 
41896.216 
34791.559 
19316.373 
21367.342 
10 
37900.709 
32945.357 
22168.596 
24306.437 
11 
37917.621 
32869.634 
20322.082 
23391.572 
12 
37958.864 
32865.094 
20984.893 
21272.693 
13 
33762.144 
34214.477 
18212.821 
26541.176 
14 
33613.449 
37582.461 
17814.931 
25892.619 
15 
31918.347 
33706.661 
17895.408 
23704.434 
16 
37482.917 
33472.179 
22519.578 
2306.943 
17 
37416.541 
33621.180 
23718.580 
25778.726 
18 
36267.023 
39914.137 
27489.760 
19513.752 
19 
36216.023 
39893.695 
23899.842 
22287.661 
20 
36249.123 
32892.034 
21933.391 
16016.417 
21 
38230.836 
31482.461 
19897.539 
20245.248 
22 
30217.685 
14517.871 
21107.431 
21796.720 
23 
32112.343 
18698.415 
19989.213 
22319.124 
24 
30219.685 
14516.872 
19742.613 
18318.498 
Table 7. Hourly cost of each area by EP method
HOURS (24) 
AREA1 (26 unit) 
AREA2 (26 unit) 
AREA3 (26 unit) 
AREA4 (26 unit) 
1 
36967.398 
23978.521 
28416.216 
21898.126 
2 
24332.916 
22896.680 
22740.900 
19324.823 
3 
27998.167 
23114.640 
23667.246 
19245.978 
4 
29612.861 
18326.321 
26117.837 
18417.701 
5 
29363.621 
18316.323 
25472.429 
18553.713 
6 
35721.176 
18312.326 
23869.510 
19573.596 
7 
39617.164 
28143.146 
21845.592 
24765.272 
8 
39328.856 
38076.468 
19905.851 
21123.616 
9 
38549.734 
34843.238 
18245.373 
21291.120 
10 
37219.318 
32416.347 
22163.591 
24207.432 
11 
37184.469 
31691.375 
20612.082 
23542.570 
12 
38316.472 
31581.138 
20979.893 
21262.693 
13 
33116.354 
34120.029 
18127.822 
26401.178 
14 
31630.279 
37051.828 
17124.939 
25704.619 
15 
30466.627 
33150.817 
17878.473 
23576.431 
16 
36281.163 
32861.752 
22306.578 
25204.946 
17 
36894.174 
32860.606 
23648.580 
25226.725 
18 
35696.310 
39439.616 
27612.752 
19314.724 
19 
34975.326 
39811.059 
23799.842 
22343.624 
20 
35766.320 
32081.951 
21834.391 
15868.403 
21 
38622.479 
29125.272 
19798.539 
20118.242 
22 
30614.829 
15108.122 
20985.432 
21816.770 
23 
31483.724 
18412.089 
19896.273 
22294.078 
24 
29540.211 
15162.711 
19716.613 
18314.498 
Table 8. Hourly cost of each area by ACSA method
HOURS (24) 
AREA1 (26 unit) 
AREA2 (26 unit) 
AREA3 (26 unit) 
AREA4 (26 unit) 
1 
34336.423 
22618.345 
28411.822 
21921.265 
2 
24262.626 
22458.681 
22243.927 
19427.375 
3 
27232.561 
23006.322 
22958.254 
19224.418 
4 
29216.527 
18168.468 
25996.688 
17884.585 
5 
28936.816 
18831.753 
25114.074 
18503.871 
6 
35682.305 
18131.933 
23618.551 
19367.459 
7 
39161.916 
28214.713 
20158.592 
23247.172 
8 
38913.128 
37866.544 
19118.348 
20751.954 
9 
38165.517 
34595.109 
17878.902 
20129.412 
10 
36701.131 
31341.347 
21021.759 
23988.243 
11 
36221.045 
31260.137 
20245.147 
22754.326 
12 
37831.964 
31058.831 
20701.164 
21123.106 
13 
32391.863 
34650.702 
18098.751 
26324.891 
14 
31596.124 
36715.018 
16871.612 
25216.106 
15 
30431.216 
33681.628 
17212.824 
23175.934 
16 
35816.616 
32162.904 
22136.345 
25047.745 
17 
36289.017 
32238.516 
23146.727 
25526.217 
18 
35116.523 
38149.046 
27176.607 
19643.724 
19 
34239.063 
39780.612 
23467.218 
22934.162 
20 
35174.314 
32163.595 
21608.239 
15238.124 
21 
38136.164 
29212.972 
19179.052 
21294.524 
22 
30114.339 
15212.172 
20298.102 
20918.107 
23 
31348.171 
18041.106 
19638.927 
22396.343 
24 
29345.852 
15426.107 
19307.116 
18231.542 
Table 9. Comparison of total operating cost for 26 unit
System 
Method 
Total Operating Cost (pu) 
Area 1 
Area 2 
Area 3 
Area 4 

DP 
1.00000 
1.00000 
1.00000 
1.00000 

26 Unit 
EP 
0.97377 
0.98783 
0.98618 
0.98926 
ACSA 
0.95405 
0.96260 
0.97250 
0.95407 
466
1
19 0
784 4
177
2 1177
0 0
3
787
Figure 6. Tie line flow pattern at 4 pm
7. Conclusion
This paper presents ACSA method for solving multi area unit commitment problem with import and export constraints. In comparison with the results produced by the technique DP and EP method obviously proposed method displays satisfactory performance. Test results have demonstrated that the proposed method of solving multi area unit commitment problem with import and export constraints reduces the total operating cost of the plant. An effective tieline constraint checking procedure is implemented in this paper. This method provides more accurate solution for multi area unit commitment problem with import and export constraints.
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