less start up cost are selected and then generation units with higher start-up cost ..... programming: an application to unit commitment". IEEE. Trans. Power syst.
International Review of Electrical Engineering (I.R.E.E.), Vol. 4, n. 3
Cost-Based Unit Commitment considering Prohibited Zones and Reserve Uncertainty A.Abdollahi1, M.Ehsan2, M.Rashidinejad3, M.Pourakbari-kasmaei4 IAEEE (Iranian Association of Electrical and Electronics Engineers)
Abstract – Generation scheduling is a crucial challenge in power systems especially under new environment of liberalization of electricity industry. This paper is focused on the economical aspect of UC problem, while the next load demand as a very important issue and prohibited operation zones and spinning reserve uncertainty as practical constraints have been taken in to account. The impacts of hot/cold start-up cost have been considered in this paper. Numerical results show a significant improvement in the solutions of a cost-based unit commitment in comparison with the other studies.
Keywords: Unit commitment, Spinning reserve uncertainty, Economic dispatch, Generation scheduling, prohibited zone
I.
Introduction
Fast growing load in power systems associated with a large gap between heavy load and light load periods, generating scheduling and unit commitment (UC) problem has become a crucial issue in operation time horizon .So unit commitment problem has always been an important research challenge in power systems especially under restructured environment. In a vertically integrated power system, unit commitment determines when to start-up or shut-down units and how to dispatch online generators over a given scheduling horizon in order to minimize the operating costs, satisfying the prevailing constraints such as load balance, system reserve requirement, ramp rate limits, minimum up/down time limits [1-5]. Since the unit commitment is a mixed integer programming, it is very hard to get an exactly optimal solution and it has been viewed as a very complex optimization problem. Variant methods have been implemented to solve such a complicated problem which are classical optimization or heuristic as well as hybrid techniques. Dynamic programming (DP) is the earliest conventional optimization method that can be applied to solve the dissimilar size UC problem .The other classical optimization methods are as follows: priority list (PL) [6], Lagrangian relaxation (LR), mixed integer programming [7] and branch and bound (B&B) [8]. The classical optimization techniques, in general, might not be able to find a solution within a significant computational time for the medium or large scale UC problem. These limitations have been redounded to introduce the heuristic optimization methods. With the emergence of metaheuristic and evolutionary algorithm in modern optimization technique such as: simulated Manuscript received January 2007, revised January 2007
annealing (SA), tabu search (TS), fuzzy logic, genetic algorithm (GA), artificial neural network (ANN) and ant colony (AC) have been used to solve the UC problem [9]. Moreover, in some methods more than one algorithm has been incorporated together and forms a hybrid technique to meet the industry requirements [10]. The hybrid methods are also applied to handle more complicated constraints, and are claimed to have a better performance. In one hand, evolutionary algorithms may seem simple but their solution might be suboptimal and on the other hand, they might be complicated with more accurate results [11]. The hybrid methods such as fuzzy dynamic programming [12], genetic-based neural network [13], Lagrangian relaxation associated with genetic algorithm [14], and annealing genetic algorithm [15] are experienced to tackle to the UC problem. In this paper a new approach considering next hours demand by minimizing the operating costs considering reserve uncertainty and prohibited zones is presented. By including next hours demand at a scheduling horizon the online units that are not optimal to be turned off kept continuing. On the other hand, in the proposed formulation a new objective function that comprises start-up cost is used in order to select the best chromosomes to get better results. So at first units with less start up cost are selected and then generation units with higher start-up cost may have a chance to be turned on in order to minimize total scheduling horizon costs . The generating units may have certain ranges where operation is restricted based upon physical limitations of machine components or instability, e.g. due to steam valve or vibration in shaft bearings. Using prohibited zone may increase the total operation cost, but the UC problem will be more practical. . Therefore prohibited operating zones as a prominent constraint has been considered .There are mainly two different approaches Copyright © 2009 Praise Worthy Prize S.r.l. - All rights reserved
A. Abdollahi, M. Ehsan, M. Rashidinejad, M .Pourakbari-kasmaei
to calculate spinning reserve requirement either through deterministic or probabilistic models. Deterministic technique is used as a rule of thumb for SRR, while it might be more conservative than necessity. A probabilistic approach generally is based upon the design and operating constraints on the criterion that the risk of certain events must not exceed pre-selected limits. Utilization of probabilistic techniques will permit the capture of the random nature of system components and load behavior in a consistent manner .So, in this study the hourly probability that spinning reserves are called and generated can be estimated using artificial neural network (ANN) to manage reserve uncertainty [16]. Using reserve uncertainty in the proposed method may decrease the costs of operation considerately. The present paper is organized as follows: Section II formulates the UC problem, while in section III the problem is decomposed to different solving stages. Section ΙV presents case studies and results analysis, concluding remarks are driven in section V.
NOMENCLATURE Artificial Neural Network a i , bi , c i : Fuel cost coefficients for unit i Cost (chr, itr ) : Cost of chromosome Cold start-up cost of unit i CSCi : Cold start time of unit i CSTi : Demand during hour t Dt : Hot start-up cost of unit i HSCi : Duration during which the ith unit is MDiON : continuously on Duration during which the ith unit is MDiOFF : continuously off Minimum Down Time MDT : Minimum Up Time MUT : Number of units N: Power output of unit i at hour t Pi o, t : ANN :
P i ,t : P i ,t : PZ
Rt : RDRi :
RTS :
Minimum generation of unit i Maximum generation of unit i Prohibited Zone Reserve requirement during hour t Ramp down rate limit of unit i
RURi :
Reliability Test System Ramp up rate limit of unit i
SDCi ,t :
Shut-down cost of unit i at hour t
SRC :
Spinning Reserve capacity Spinning Reserve Probability Spinning Reserve Requirement SRR : SUC i ,t : Start-up cost of unit i at hour t Unit commitment horizon T: SRP :
Copyright © 2009 Praise Worthy Prize S.r.l. - All rights reserved
TiD :
Minimum down-time of unit i
U
Ti :
Minimum up-time of unit i
u i ,t :
On or off status of unit i at hour t
αi , βi :
Coefficient of start-up cost function
τi :
Time constant in the start-up cost function for
unit i
II.
Problem Formulation
Unit commitment involves determining generation outputs of all units from an initial hour to satisfy load demands associated with a start-up and shut-down schedule over a time horizon. The objective is to find the optimal schedule such that the total operating costs can be minimized while satisfying the load demand, spinning reserve requirement as well as other operational constraint. A. Objective function The outage cost as well as fuel cost of generation units should be considered in power system operation as an objective function of a UC problem .The objective function is a function that comprises the fuel costs of generating units, the start-up costs of the committed units and shut-down costs of decommitted units. The start-up cost is presented in two schemes: hot start-up costs and cold start-up costs, while the shut-down cost is assumed to be fixed. Nevertheless the objective function in common form is expressed by Eq. (1). T
{
Minimize
T
+
N
∑ ∑
F i , t ( p it ) * u
i ,t
t =1 i =1 N
∑ ∑
SUC
i ,t
* u
i ,t
∑ ∑
SDC
i ,t
* u
i ,t − 1
* (1 − u
i ,t − 1
)
(1)
t =1 i =1 T N
+
* (1 − u
i ,t
t =1 i =1
)}
(1)
The production cost is typically expressed as a quadratic function of the power output, while the startup cost is usually modeled as a nonlinear (exponential) function of the offline time prior to the startup [17]. B. Thermal Constraints • Initial Condition Initial conditions of generating units include the number of hours that a unit consequently has been on-line or offline and its generation output at an hour before the scheduling.
•
Power balance constraint N
∑ ( Pi ,t ) ∗ u i ,t
= Dt
1 ≤ t ≤ T , i ∈ N (2)
i =1
International Review of Electrical Engineering, Vol. 4, n. 3
A. Abdollahi, M. Ehsan, M. Rashidinejad, M .Pourakbari-kasmaei
•
Unit output limit
P i , t * u i , t ≤ Pi , t * u i , t ≤ P i , t * u i , t
(3)
1≤ t ≤ T , i∈ N
•
Unit ramp-up constraint Pi ,t ≤ P i ,t P i ,t = Min { Pi o,t −1 + RUR i , P i }
(4)
1≤ t ≤ T , i∈ N
•
Therefore, in practical operation, adjusting the generation output of a unit must avoid all capacity limits and unit operations in prohibited zones. The feasible operating zones of a unit can be described as follows: P ≤ P ≤ P Lower i i ,1 i Upper Lower , j = 2, . . . , PZ z Pi , j −1 ≤ Pi ≤ Pi , j Upper Pi , PZi ≤ Pi ≤ Pi (10)
Unit ramp-down constraint
P it ≤ Pi ,t P it = Max { Pi o,t − 1 − RDR i , P i }
(5)
1≤ t ≤ T ,i∈ N •
Minimum up time limit ON i
MD
≥TiU ,
i =1,..., N
(6)
• Minimum down time limit M D OFF ≥ T D , i = 1,..., N i i
(7)
•Spinning reserve capacity Spinning reserve capacity at each hour is the total amount of maximum capacity of all synchronized units minus the total generating output in that hour. SR must be sufficient enough to maintain the desired reliability of a power system. Spinning reserve requirement is usually a pre-specified amount or it is equal to the largest unit or a given percentage of the forecasted load. Total spinning reserve capacity can be given by Eq. (8). N
∑
P
i ,t
*u
i ,t
= D
t
+ SR C
(8)
t
i =1
Fig 1. Prohibited zones and output limit of a generator
III. Optimization Technique The optimization model consists of some steps that are shown in Fig 2 and explained in the following steps. In each step related constraints are taken into account while
1 ≤ t ≤ T , i ∈ N
finally the objective function associated with all
On the other hand, the probability of calling spinning may decrease the total operating costs. In order to find SRP in usually of a day scheduling it is needed to study in a larger horizon like a week or a month. In this paper SRC t as the total spinning reserve capacity is defined
probability that spinning reserve is called and generated
by Eq. (9).
(SRP).
SRC t ≥ SRPt * SRRt 1 ≤ t ≤T
(9)
•
Prohibited Zone Each generator has its generation limit, which cannot be exceeded at any time. Moreover, a typical thermal unit may have a steam valve in operation, or a vibration in a shaft bearing, which may result in interference and discontinue input– output performance-curve sections, called prohibited zones, as shown in Fig 1. Copyright © 2009 Praise Worthy Prize S.r.l. - All rights reserved
constraints is minimized via genetic algorithm (GA). Step 1. Call load and units data and forecasted
Step 2. Initialization: at this step an initial population is generated such that some information for first hour is obtained from initial condition Step 3. Update units data: update some of the units' data like the time that a unit continuously has been on/off according to the previous hour's scheduling. Step 4. GA procedure: Genetic algorithm is a random and robust search technique that guides a population International Review of Electrical Engineering, Vol. 4, n. 3
A. Abdollahi, M. Ehsan, M. Rashidinejad, M .Pourakbari-kasmaei
towards an optimum using the principles of natural
d. Fitness evaluation: In this step, the fitness
evolution. This process is facilitated through a fitness
value of each chromosome should be
evaluation procedure, which determines the fitness value
calculated.
of each member of the population the so-called
convergence of the proposed method the
chromosome. Each chromosome contains a number of
fitness function is adopted as follows:
gens. In this simulation the chromosome is corresponds
adopted
In
fitness
order
robustness of GA and its capability across a broad range of problems make GA as general problem solving techniques in many applications (18). So in this paper according to the complexity of unit commitment considering prohibited zones, GA is used to solve this complicated and non-convex optimization problem. The flowchart of the proposed GA-based solution approach for UC includes the following steps:
accelerate
the
A 1 + Cost ( chr , itr )
(11) Where: A is the big positive number (assumed
1E+4),
chromosomes
chr
and
and
iteration
itr
are
counter
respectively. Thus a modified cost function is shown by Eq. (12). Since in scheduling problems the objective is to minimize the operating costs, those units with more expensive start-up costs may have
a. Initialize the iteration counter as a stopping criterion: in this paper according to the number of units the number of iterations is set to 80 and at first the iteration counter is set to one. b. Economic
=
function
to a plant and a gen is corresponds to a unit. The
to
no chance to be turned on before they must be, while they may impose less total operating costs .So, in this paper a modified objective function is defined in order to select the best chromosomes for crossover and mutation to
dispatch:
Economic
dispatch
determines the output of all online units with
generate new chromosomes for achieving optimum scheduling.
the objective of minimum total operating
T
costs at a given hour, which is subjected to
Cost ( chr , itr ) = Min
the power balance constraint Eq. (2) and
+ SUC
N
∑ ∑ F i , t ( p i ,t ) * u i ,t t =1 i =1
i ,t
* u i ,t * (1 − u i , t −1 )}
output limits Eq. (3). For each chromosome
(12)
of the generated population in step 2 of the main flowchart the ED is applied and the output power of each gens of chromosome is obtained. A lambda iteration method is
Where: CSCi,t MDiOFF > Ti D + CSTi,t SUCi,t = MDiOFF ) HSC Ti D ≤ MDiOFF ≤ Ti D + CSTi,t (1 + D T i + CSTi ,t
applied in this paper to determine the optimal (13)
economic dispatch. c. Prohibited Zone check: after ED, for each gens of chromosome, the prohibited zone check is taken into consideration. If any of gens violated the PZ, the PZ is applied to that gen and ED is repeated for the aforementioned chromosome.
In this paper the cold start-up cost (CSC) is considered twice of hot start-up cost (HSC).
e. Mating: The mating process consists of three operators: selection, crossover and mutation. f. Modification: After crossover and mutation processes
Copyright © 2009 Praise Worthy Prize S.r.l. - All rights reserved
for
achieving
feasible
International Review of Electrical Engineering, Vol. 4, n. 3
A. Abdollahi, M. Ehsan, M. Rashidinejad, M .Pourakbari-kasmaei
chromosomes two following tasks should be handled.
• Chromosomes elimination: infeasible chromosomes that can not satisfy the SRR constraint will be eliminated as redundant.
• Chromosome modification: since the
Fig. 3. Forecasted probability that spinning reserve is called and generated (first day).
number of chromosomes must be remained constant, chromosomes with the best fitness are replaced instead of eliminated chromosomes. g. Stopping criterion: for stopping GA Procedure it is needed to have a criterion, in this study a constant number of iteration has been used. Step 5: Best cost selection: in this step the
Case 1: IEEE 10-Unit test system without considering SRP and PZ The proposed method has been applied to solve a commonly UC problem that so-called 10-unit base system with the given data presented in the appendix where in this case the PZ and SRP are not taken in to account. The result of the units output power is given in Table 1 and total cost comparison of several techniques is shown in Table 2.
chromosome with the least cost is selected and the output power of each generator is kept as the best answer.
IV. Case studies and Result Analysis The proposed methodology is implemented to a standard IEEE 10-Unit test system while four states have been studied. The first study is only about a commonly unit commitment problem without considering SRP and Prohibited zone. For the second test, the PZ is taken in to account in the formulation and after that, for the third study the SRP is considered in the problem formulation as the input data. At last, both of SRP and prohibited zones check are taken into account as a practical and redundant limitation. Figure 3 presents the forecasted probability of calling SR for the first day[16]. The PZ employed in the paper is not an accurate representation which will be shown in Appendix.
Copyright © 2009 Praise Worthy Prize S.r.l. - All rights reserved
Case 2: IEEE 10-Unit test system considering PZ In practice each generator has its generation limit, which cannot be exceeded at any time. Moreover, a typical thermal unit may have a steam valve in operation, or a vibration in a shaft bearing, which may result in interference and discontinue input–output performance-curve sections, called prohibited zones (PZ), so it seems be essential to study the PZ as a practical limitation. The result of the units' output power is given in Table 3 for 24-h time horizon with a total operating cost 564714 $.No study has been done before considering PZ .So ,establishing a table for comparison of total cost is impossible in this case. By comparison of UC cost with the result of Table.2, it is clearly seen that there is no main difference between them which present the effectiveness of UC. The PZ employed in the paper is not an accurate representation which is given in Appendix. However, there is no great difficulty in making some changes in the formulations developed so that the proposed approach can employ different PZ representation.
International Review of Electrical Engineering, Vol. 4, n. 3
International Review of Electrical Engineering (I.R.E.E.), Vol. 4, n. 3
Fig 2
Main flowchart of proposed Method
Manuscript received January 2007, revised January 2007
Copyright © 2009 Praise Worthy Prize S.r.l. - All rights reserved
A. Abdollahi, M. Ehsan, M. Rashidinejad, M .Pourakbari-kasmaei
Table 1.
Units output power for the 10-unit case H U
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
1
455 455
2
245 295 370 455 455 455 455 430 455 455 455 455 455 455 455 315 260 360 455 455 455 455 425 345
455 455 455 455 455 455 455 455 455 455 455 455 455 455 455 455 455 455 455 455 455 455
3
0
0
0
0
0
4
0
0
0
0
0
130 130 130 130 130 130 130 130 130 130 130 130 130 130
0
0
0
130 130 130 130 130 130 130 130 130 130 130 130 130 130 130 130
0
0
0
0
0
5
0
0
25
40
70
40
90
25
85
162 162 162 162
85
30
25
25
25
30
162
85
145
0
0
6
0
0
0
0
20
20
20
20
20
33
68
80
33
20
0
0
0
0
0
33
20
20
20
0
7
0
0
0
0
0
0
0
0
25
25
25
25
25
25
0
0
0
0
0
25
25
25
0
0
8
0
0
0
0
0
0
0
0
0
10
10
43
10
0
0
0
0
0
0
10
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
10
10
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
Table 2. Total cost comparison of several techniques Method Cost Method Cost
SPL [19] 564950
EP [20] 565352
ALR [25] 565508
GA [12] 565825
Total cost of different methods PSO BPSO [21] [22] 574153 565804 Total cost of different methods BCGA ICGA [26] [26] 567367 566404
PSO-LR [23] 565869
LR [23] 566107
DP [12] 565825
MA [27] 565827
LRGA [24] 564800 PM 564703
Table 3. Units output power for the 10-unit case considering PZ H
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
1
447.9999 455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
2
252.0001 295
370
455
455
455
455
430
455
455
455
455
455
455
455
315
260
360
455
455
455
455
425
345
0
0
0
0
0
130
130
130
130
130
130
130
130
130
130
130
130
130
130
0
0
0
U
1
2
3
0
0
4
0
0
0
0
0
130
130
130
130
130
130
130
130
130
130
130
130
130
130
130
130
0
0
0
5
0
0
25
40
70
40
90
25
85
162
162
162
162
85
30
25
25
25
30
162
85
145
0
0
6
0
0
0
0
20
20
20
20
20
33
68
77.9999
33
20
0
0
0
0
0
33
20
20
20
0
7
0
0
0
0
0
0
0
0
25
25
25
25
25
25
0
0
0
0
0
25
25
25
0
0
8
0
0
0
0
0
0
0
0
0
10
10
45.0001
10
0
0
0
0
0
0
10
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
10
10
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
Copyright © 2009 Praise Worthy Prize S.r.l. - All rights reserved
International Review of Electrical Engineering, Vol. 4, n. 3
A. Abdollahi, M. Ehsan, M. Rashidinejad, M .Pourakbari-kasmaei
References
Case 3: IEEE 10-Unit test system considering SRP The result of the units' output power is given in Table 4 for 24-h time horizon with a total operating cost 556306 $. No study has been done before considering SRP .So, establishing a table for comparison of total cost is impossible in this case, too. By comparison of UC cost with the result of previous cases, it is clearly seen that there is obvious difference between them which may offer a significant performance. It is clearly seen that considering SRP decreases the total cost, significantly which the obtained result is better than all methods that have been applied until now.
Case 4: IEEE 10-Unit test system considering SRP and PZ: The result of the units' output power is given in Table 5 for 24-h time horizon with a total operating cost 556310 $. No study has been done before considering SRP and PZ .So, establishing a table for comparison of total cost is impossible in this case, too .By comparison of UC cost in this case with the result of case 3, it is clearly seen that the operation cost increases about 4 $ which is the effect of considering PZ in order to have more practical unit commitment problem.
V. Conclusion In this paper a reliable and efficient method using heuristic technique for unit commitment as well as scheduling problem is presented. It has presented a new approach to select best chromosomes via GA, where the objective function in GA has comprised start-up cost to give a chance to those units that have higher start-up cost and the search area will be extended. On the other hand, in this paper prohibited zone and spinning reserve probability as a practical constraint have been considered. The proposed methods is successfully applied to a standard 10-unit system considering practical constraints which are PZ and SRP and the satisfactory results are compared with the other methods reported in literature. The results also can offer the usefulness of the proposed method which can consider as practical technique. The results shown that the PM has the following merits in UC problem: efficient searching ability, robustness in result.
Copyright © 2009 Praise Worthy Prize S.r.l. - All rights reserved
Tsung-Ying Lee, Chun-Lung Chen. "Unit commitment with probabilistic reserve" An IPSO approach. EC&M.48 (2006)486-493. [2] K. Afshar, M. Ehsan, M. Fotuhi-firuzabad, A. Ahmadi-khatir and N. Bigdeli. "A new approach for reserve market clearing and cost allocating in a pool model",IJST, B: Engineering.31 (B3) (2007)593-602. [3] H. Y. Yamin, Q. E1-Dwairi, S. M. Shahidehpour. "A new approach for GenCos profit based unit commitment in day-ahead competitive electricity markets considering reserve uncertainty". EPES.29 (2007) 609-616. [4] C. Wang, S.M. Shahidehpour. "Effect of ramp-rate limits on unit commitment and economic dispatch". IEEE Trans on Power Syst. 8(3) (1993) 1341-1350. [5] Vo Ngoc Dieu, Weerakorn Ongsakul, Ramp rate constrained unit commitment by improved priority list and augmented Lagrange Hopfield network, EPSR.78 (3) (2008) 291-301. [6] A.I. Cohen, M. Yoshimura, A branch-and-bound algorithm for unit commitment, IEEE Trans. Power App. Syst. 102 (2) (1983) 444–451. [7] Narayana Prasad Padhy, “Unit commitment-A bibliographical Survey”, IEEE Trans. Power syst. 19(2) ( 2004)1196-1205. [8] H.Li,P.Chen,and H.Huang,Fuzzy Neural Intelligence Systems. Boca Raton, FL: CRC. (2001). [9] N.P.Padhy,V.Ramachandran and S.R.Paranjothi,"A hybrid fuzzy neural network expert system for short-term unit commitment problem,"Int.J.Microelectronics Reliability.37(5)(1997) 733-737. [10] C. C. Su and Y. Y. Hsu. "Fuzzy dynamic programming: an application to unit commitment". IEEE Trans. Power syst. 6(1991)1231-1237. [11] S. J. Huang and C. L. Huang. "Application of genetic-based neural network to thermal unit commitment". IEEE Trans. Power syst. 12(1997) 654660. [12] H.Y Yamin, S.M. Shahidehpour. "Unit commitment using a hybrid model between Lagrangian relaxation and genetic algorithm in competitive electricity markets". EPSR.68 (2004)83-92. [13] C. P Cheng, C. W. Liu and G. C. Liu. "Unit commitment by annealing-genetic algorithm". EPES.24 (2000) 149-158. [14] IEEE Reliability Test System Task Force, IEEE Reliability Test System , IEEE Trans Power syst.98 (1979)2047–2054. [1]
International Review of Electrical Engineering, Vol. 4, n. 3
A. Abdollahi, M. Ehsan, M. Rashidinejad, M .Pourakbari-kasmaei
Table 4. Units output power for 10-unit base system considering SRP H
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
1
455 455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
2
245
295
370
455
455
455
455
430
455
455
455
455
455
455
455
315
260
360
455
455
455
455
425
345
3
0
0
0
0
0
0
0
0
130
130
130
130
130
130
0
0
0
0
0
130
130
130
130
88
4
0
0
0
0
0
130
130
130
130
130
130
130
130
130
130
0
0
0
0
0
130
130
130
107
5
0
0
0
40
90
60
110
160
130
162
162
162
162
130
160
140
90
162
162
162
105
0
0
0
6
0
0
0
0
0
0
0
0
0
68
80
80
0
0
0
0
0
28
80
80
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
38
33
68
25
0
0
0
0
48
63
25
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
55
0
0
0
0
0
0
0
55
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
U
1
2
Table 5. Units output power for 10-unit base system considering SRP and PZ H U
1
1
2
447.9 455
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455 150
2
252
295
395
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
455
385
185
3
0
0
0
0
0
0
0
0
130
130
130
130
130
130
0
0
0
0
0
130
130
130
130
88
4
0
0
0
0
0
130
130
130
130
130
130
130
130
130
130
0
0
0
0
0
130
130
130
107
5
0
0
0
40
90
60
110
160
130
162
162
162
162
130
160
140
90
162
162
162
105
0
0
0
6
0
0
0
0
0
0
0
0
0
68
80
80
0
0
0
0
0
28
80
80
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
38
33
68
25
0
0
0
0
48
63
25
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
55
0
0
0
0
0
0
0
55
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
[15] Juste
KA, Kita H, Tanaka E, Hasegawa J. An evolutionary programming solution to the unit commitment problem. IEEE Trans Power Syst.18 (1)( 2003)229–37. [16] H.Y. Yamin , Q. El-Dwairi , S.M. Shahidehpour," A new approach for GenCos profit based unit commitment in day-ahead competitive electricity markets considering reserve uncertainty"". EPES.29 (2007)609-616. [17] A. J. Wood and B. F. Wollenberg, Power Generation, Operation, and Control, 2nd ed. New York: Wiley, 1996. [18] Swarup, K.S. and S. Yamashiro, 2002. Unit commitment Solution Methodology Using Genetic Algorithm. IEEE transactions on power system, 17(1):87-91. DOI: 10.1109/59.982197. [19] T. Senjyu, T. Miyagi, A. Y. Saber, N. Urasaki, and T. Funabashi. "Emerging solution of large-scale unit commitment problem by stochastic priority list". Elect Power Syst. 76(2006)283–292. [20] K.A. Juste, H. Kita, E. Tanaka, J. Hasegawa. "An evolutionary programming to the unit commitment problem". IEEE Trans. Power Syst. 14(1999) 1452– 1459. [21] B. Zhao, C. X. Guo, B. R. Bai, and Y. J. Cao. "An improved particle swarm optimization algorithm for unit commitment". EPES. 28(2006) 482-490. Copyright © 2009 Praise Worthy Prize S.r.l. - All rights reserved
Z. Gaing. "Discrete particle swarm optimization algorithm for unit commitment". IEEE Power Eng. Soc. General Meeting. (2003) 418-424. [23] H. H. Balci and J. F. Valenzuela. Scheduling electric power generators using particle swarm optimization combined with the lagrangian relaxation method. Int. J. Appl. Math. Comput. Sci.14 (3)(2004) 411-421. [24] C. P. Cheng, C. W. Liu, and G. C. Liu. "Unit commitment by lagrangian relaxation and genetic algorithms". IEEE Trans. Power Syst.15 (2)(2000)707-714. [25] W. ongsakul and N. Petcharaks. "Unit commitment by enhanced adaptive Lagrangian relaxation". IEEE Trans. Power Syst19 (1) (2004) 620-628. [26] I. G Damusis, A. G. Bakirtizis, and P.S. Dokopoulos. "A solution to the unit commitment problem using integer-coded genetic algorithm". IEEE Trans. Power Syst.19 (2)(2004) 1165-1172. [27] J Valenzuela and A. E. Smith. "A seeded memetic algorithm for large unit commitment problems". J. Heurist.8 (2002)173-195. [22]
International Review of Electrical Engineering, Vol. 4, n. 3
A. Abdollahi, M. Ehsan, M. Rashidinejad, M .Pourakbari-kasmaei
Appendix
Table 6. Unit characteristic and cost coefficient of 10-unit base problem Unit No 1
5
Init condition 8
Prohibited operating Zones [150 165], [448 453]
5000
5
8
[90 110], [240 250]
1100
550
4
-5
-------
5
1120
560
4
-5
-------
6 3 3
1800 340 520
900 170 260
4 2 2
-6 -3 -3
-------
1
1
60
30
0
-1
[20 30], [40 45]
1
1
60
30
0
-1
-------
-1
[12 17],[35 45]
Pmax
Pmin
A
B
c
TU
TD
HSC
CSC
CST
455
150
1000
16.19
0.00048
8
8
9000
4500
2
455
150
970
17.26
0.00031
8
8
10000
3
130
20
700
16.6
0.002
5
5
4
130
20
680
16.5
0.00211
5
5 6 7
162 80 85
25 20 25
450 370 480
19.7 22.26 27.74
0.00398 0.00712 0.00079
6 3 3
8
55
10
660
25.92
0.00413
9
55
10
665
27.27
0.00222
10
55
10
670
27.79
0.00173
1
1
60
30
0
-------------
Table 7. Load demand of 10-unit base problem Hour
1
2
3
4
5
6
7
8
9
10
11
12
Load
700
750
850
950
1000
1100
1150
1200
1300
1400
1450
1500
Hour
13
14
15
16
17
18
19
20
21
22
23
24
Load
1400
1300
1200
1050
1000
1100
1200
1400
1300
1100
900
800
SPL
Table 8. Abbreviation Of UC Solution Techniques Stochastic Priority List (Senjyu et al. 2006)
EP
Evolutionary programming (Juste et al. 1999)
PSO
Particle Swarm Optimization (Zhao et al. 2006)
BPSO
Binary Particle Swarm Optimization (Gaing, 2003)
PSO-LR
Particle Swarm Optimization combined with Lagrangian Relaxation (Balci and Valenzuela, 2004)
LR
Lagrangian Relaxation (Balci and Valenzuela, 2004)
LRGA
Lagrangian Relaxation combined with Genetic Algorithm (Cheng, 2000)
DP
Dynamic Programming (Kazarlis et al., 1996)
ALR
Augmented Lagrangian Relaxation (Ongsakul and Petcharaks, 2004)
GA
Genetic Algorithm(Kazarlis et al., 1996)
BCGA
Binary Coded Genetic Algorithm (Sun et al., 2006)
ICGA
Integer Coded Genetic Algorithm (Ongsaku land Petcharaks, 2004)
MA
Memetic Algorithm (Valenzuela and Smith, 2002)
PM
Proposed Method
Copyright © 2009 Praise Worthy Prize S.r.l. - All rights reserved
International Review of Electrical Engineering, Vol. 4, n. 3
International Review of Electrical Engineering (I.R.E.E.), Vol. 4, n. 3
Authors’ information
4
1
Amir Abdollahi received the B.S degree in Electrical Engineering from Shahid Bahonar University of Kerman, Iran, 2007.He is currently pursuing the M.S. degree in the Electrical Engineering Department at Sharif University of Technology, Tehran, Iran. His research interests include power system operation, Simulation, optimization, planning and economics.
Mehdi Pourakbari-Kasmaei received his B.S degree in Electrical Engineering from Azad University of Lahijan, Iran, 2005. He received his M.S. degree in Control Engineeering from Shahid Bahonar University of Kerman, Iran, 2008. His research interests include power system reliability, optimization, operation, Simulation and economics.
2
Mehdi Ehsan received B.S and M.S degrees in Electrical Engineering from Technical College of Tehran University 1963.He received his PhD and DIC degrees from Imperial College, University of London in 1976. Since then He has been with EE Dept of Sharif University of Technology in different responsibilities. He has an extended cooperation with research centers in Iran and also abroad. Currently he is a professor in EE Department of Sharif University. His research interests include Power system Simulation, Dynamic and Transient Stability, Application of Expert systems in Identification, Operation, Planning and Control of power system.
3
Masoud Rashidinejad received his B.S. degree in Electrical Engineering and M.S. degree in Systems Engineering Isfahan University of Technology, Iran. He received his PhD in Electrical Eng. from Brunel University, London, UK, 2000. He is currently associate professor at Electrical Eng. Dept., Shahid Bahonar University of Kerman, Iran. His area of interests is power system planning, electricity restructuring and energy management.
Manuscript received January 2007, revised January 2007
Copyright © 2009 Praise Worthy Prize S.r.l. - All rights reserved
