UNIT COMMITMENT USING PARTICLE SWARM OPTIMIZATION

VINOD PURI¹*, NITIN NARANG², JAIN S.K.³, CHAUHAN Y.K.^4
1Department of Electrical and Electronics Engineering, SRM University, NCR Campus, Ghaziabad, India.
²Department of Electrical and Instrumentation Engineering, Thapar University, Patiala, India.
³Department of Electrical and Instrumentation Engineering, Thapar University, Patiala, India.
⁴School of Engineering, Gauttam Buddha University, Greater Noida, Uttar Pradesh, India.
* Corresponding Author : vinod_tu24@yahoo.co

Received : 13-02-2012     Accepted : 09-03-2012     Published : 15-03-2012
Volume : 2     Issue : 1       Pages : 9 - 16
Bioinfo Comput Optim 2.1 (2012):9-16

An important criterion in power system operation is to meet the power demand at minimum fuel cost using an optimal mix of different power plants. Moreover, in order to supply electric power to customers in a secured and economic manner, thermal unit commitment is considered to be one of the best available options. It is thus recognized that the optimal unit commitment of thermal systems results in a great saving for electric utilities. Unit Commitment is the problem of determining the schedule of generating units subject to device and operating constraints. The formulation of unit commitment has been discussed and the solution is obtained by classical dynamic programming method. An algorithm based on Particle Swarm Optimization technique, which is a population based global search and optimization technique, has been developed to solve the unit commitment problem. The effectiveness of these algorithms has been tested on systems comprising three units and four units and compared for total operating cost.

Unit commitment, dynamic Programming, PSO.

Unit commitment (UC) is a nonlinear mixed integer optimization problem to schedule the operation of the generating units at minimum operating cost while satisfying the demand and other equality and inequality constrains. Several solution strategies have been proposed to provide quality solutions to the UC problem and increase the potential savings of the power system operation. These include deterministic and stochastic search approaches. Deterministic approaches include the priority list method, dynamic programming, Lagrangian Relaxation and the branch and- bound methods. Although these methods are simple and fast, they suffer from numerical convergence and solution quality problems. The stochastic search algorithms such as particle swarm optimization, genetic algorithms, evolutionary programming, simulated annealing, ant colony optimization and tabu search are able to overcome the shortcomings of traditional optimization techniques. These methods can handle complex nonlinear constraints and provide high quality solutions. This formulation drastically reduces the number of decision variables and hence can overcome the shortcomings of stochastic search algorithms for UC problems. Due to simplicity and less parameter tuning, particle swarm optimization is used for solving the unit commitment problem. In this thesis we have to study the algorithm of particle Swarm optimization and formulate the algorithm for solving unit commitment using PSO. In the results we have to find the variation in the results of total operating cost of the system in the given time horizon and compare it with the results of the already existing method like dynamic programming.

The objective of the UC problem is to minimize the total operating costs subjected to a set of system and unit constraints over the scheduling horizon. It is assumed that the production cost, PCi for unit ‘i’ at any given time interval is a quadratic function of the generator power output, pi. [eq-1] ai, bi, ci are the unit cost coefficients. The generator start-up cost depends on the time the unit has been switched off prior to the start up, Toff. The start-up cost SCi at any given time is assumed to be an exponential cost curve. [eq-2] σi is the hot start-up cost, δi the cold start-up cost and τi is the cooling time constant
The total operating costs, OCT for the scheduling period T is the sum of the production costs and the start-up costs. [eq-3] Ui,t is the binary variable to indicate the on/off state of the unit i at time t. Ui,t =1 if unit i is committed at time t, otherwise Ui,t=0.
The overall objective is to minimize OCT subject to a number of system and unit constraints. All the generators are assumed to be connected to the same bus supplying the total system demand. Therefore, the networks constraints are studied above are as follows briefly.

The total generated power at each hour must be equal to the Load of the correspondinghour, D. [eq-4]

The generation of the unit is under its minimum and maximum limit [eq-5]

This constraint signifies the minimum time for which a committed unit should be turned off and removed from online. [eq-6]

This constraint signifies the minimum time for which a de-committed unit should be turned on and brought on-line. [eq-7]

Spinning reserve is the term used to describe the total amount of generation available from all the units synchronized on the system minus the present load plus losses being incurred. Spinning reserve must be carried so that the loss of one or more units does not cause too far a drop in system frequency [eq-8]

Dynamic programming acts as an important optimization technique with broad application areas. It decomposes a problem into a series of smaller problems, solves them, and develops an optimal solution to the original problem step-by-step. The optimal solution is developed from the sub problem recursively. In its fundamental form, the dynamic programming algorithm for unit commitment problem examines every possible state in every interval. Some of these states are found to be infeasible and hence they are rejected instantly. But even, for an average size utility, a large number of feasible states will exist and the requirement of execution time will stretch the capability of even the largest computers. Hence many proposed techniques use only some part of simplification and approximation to the fundamental dynamic programming algorithm. Dynamic programming has many advantages over the enumeration scheme. The chief advantage of this technique is the reduction in the dimensionality of the problem. Suppose we have found units in a system and any combination of them could serve the single load. A maximum of 2N-1 combinations are available for testing. The imposition of priority list,
arranged in order of the full load average cost rate would result in a theoretically correct dispatch and commitment only if
• No load costs are zero.
• Unit input-output characteristics are linear between zero output and full load.
• There are no other restrictions.
• Start-up costs have a fixed amount

In dynamic programming algorithm:
• A state consists of an array of units with only specified units operating at a time and rest off-lin
• The start-up cost of a unit is independent of the time it has been off-line (i.e., it is a fixed amount).
• There are no costs for shutting down a unit.
• There is a strict priority order, and in each interval a specified minimum amount of capacity must be operating.

A feasible state is one in which the committed units can be supply the required load and that meets the amount of capacity at each period The dynamic programming algorithm can be run backward in time starting from the final hour to be studied, back to the initial hour. Conversely, we have set the algorithm to run forward in time from the initial hour to the final hour. DP approach has distinct advantages in solving generator unit commitment. For example, if the start-up cost of a unit is a function of time it has been off-line (i.e., its temperature), then a dynamic programming approach is more suiTable since the previous history of the unit can be computed at each stage. There are other practical reasons for going for D.P. The initial conditions are easily specified and the computations can go forward in time as long as required. The flowchart for the Dynamic programming approach to Unit commitment problem is given below in [Fig-1]

Particle swarm optimization is a stochastic, population-based search and optimization algorithm for problem solving. It is a kind of swarm intelligence that is based on social-psychological principles and provides insights into social behaviour, as well as contributing to engineering applications. The particle swarm optimization algorithm was first described in 1995 by James Kennedy and Russell C. Eberhart. The techniques have evolved greatly since then, and the original version of the algorithm is barely used at present. Social influence and social learning enable a person to maintain cognitive consistency. People solve problems by talking with other people about them, and as they interacts their beliefs, attitudes, and behaviour changes, the changes could typically be depicted as the individuals moving toward one another in a socio-cognitive space.
The particle swarm simulates a kind of social optimization. A problem is given, and some way to evaluate a proposed solution to it exists in the form of a fitness function. A communication structure or social network is also defined, assigning neighbours for each individual to interact with a population of individuals defined as random guesses as the problem solutions is initialized. These individuals are candidate solutions and are also known as the particles, hence the name particle swarm. An iterative process to improve these candidate solutions is set in motion. The particles iteratively evaluate the fitness of the candidate solutions and remember the location where they had their best success. The individual's best solution is called the particle best or the local best. Each particle makes this information available to their neighbours. They are also able to see where their neighbours have had success. Movements through the search space are guided by these successes, with the population usually converging, by the end of a trial, on a problem solution better than that of non-swarm approach using the same methods.The particle swarm optimization (PSO) algorithm is a population-based search algorithm inspired by the social behaviour of birds within a flock. The initial intent of the particle swarm concept was to graphically simulate the graceful and unpredicTable choreography of a bird flock, the aim of discovering patterns that govern the ability of birds to fly synchronously, and to suddenly change direction with a regrouping in an optimal formation. From this initial objective, the concept evolved into a simple and efficient optimization algorithm. In PSO, individuals, referred to as particles, are "flown" through hyper dimensional search space. Changes to the position of particles within the search space are based on the social-psychological tendency of individuals to emulate the success of other individuals. The changes to a particle within the swarm are therefore influenced by the experience, or knowledge, of its neighbours. The search behaviour of a particle is thus affected by that of other particles within the swarm therefore PSO is the kind of symbiotic cooperative algorithm. The consequence of modelling this social behaviour is that the search process is such that particles stochastically return toward previously successful regions in the search space. The operation of the PSO is based on the neighbourhood principle as social network structure.

• Initialize the swarm, p(t), of particles such that the position xi(t) of each particle . p(t) is random within the hyperspace, with t = 0.
• Evaluate the fitness function for each particle and find out the pbest.
• For each individual particle, compare the particle’s fitness value with its pbest. If the current value is better than the pbest value, then set this value as the and the current particle’s position, xi, as pi.
• Identify the particle that has the best fitness value. The value of its fitness function is identified as gbest and its position as pg.
• Update the velocities and positions of all the particles.
vi(t)=vi(t-l)+C1(xpbesti-xi(t))+C2(xgbest-xi(t)) (9)

Where C1 and C2 are random variables. The second term above is referred to as the cognitive component, while the last term is the social component.
xi (t) = xi(t - 1) + vi(t) (10)
The flow chart is given as under.“Fig. (2)”

According to the discussion in above sections, the following procedure can be used for implementing the PSO algorithm.
• Initialize the swarm by assigning a random position in the problem search space to each particle.
• Evaluate the fitness function for each particle and find out the pbest.
• For each individual particle, compare the particle’s fitness value with its pbest. If the current value is better than the pbest value, then set this value as the and the current particle’s position, xi, as pi.
• Identify the particle that has the best fitness value. The value of its fitness function is identified as gbest and its position as pg.
• Update the velocities and positions of all the particles using equation (9) and (10).
• Repeat steps b-e until a stopping criterion is met (e.g., maximum number of iterations or a sufficiently good fitness value). The flow chart is given above in [Fig-2]

The Particle swarm optimization (PSO) has been briefed earlier.PSO is a population based searching algorithm. This approach simulates the simplified social system such as fish schooling and birds flocking. PSO is initialized by a population of potential solutions called particles. Each particle flies in the search space with a certain velocity. The particle’s flight is influenced by cognitive and social information attained during its exploration. It has very few tuneable parameters and the evolutionary process is very simple. It is capable of providing quality solutions to many complex power system problems. One such problem is the unit commitment of thermal units in the power system. PSO is used to minimize the total operating cost by committing those optimal combinations of the units which satisfy the constraints and gives the minimum cost corresponding to that combination.
Our main aim is to minimise the operating cost, so we are using the ALM method for handling equality and in equality constraints. In this problem the up and down time of the units are not taken into consideration. the algorithm for UC is detailed as follows

The following steps are used by the PSO technique to solve the unit commitment problem
• Initialize a population of particles pi and other variables. Each particle is usually generated randomly with in allowable range. [eq-11] Here pi represented as ith unit in the power system.
• Initialize the parameters such as the size of population, initial and final inertia weight, random velocity of particle, acceleration constant, the max generation, Lagrange’s multiplier (λi), etc.
• Calculate the fitness of each individual in the population using the fitness function or cost function. [eq-12] Where PCi,t is represented as [eq-13] With equality constraint as [eq-14] Where Pi is the ith generators and P_D is the load or demand. And inequality constraints as [eq-15] 15.
• Compare each individual’s fitness value with its pbest. The best fitness value among pbest is denoted as gbest.
• Modify the individual’s velocity vid of each individual pi as [eq-16] 16.
• Modify the individual’s position pi as [eq-17] where i is the ith unit and t is the hour
• If the evaluation value of each individual is better than the previous ppbest, the current value is set to be ppbest. If the best ppbest is better than pgbest the value is set to be pgbest.
• Modify the λ and α for each equality and Inequality constraint
For Inequality Constraint [eq-18] [eq-19] 19.
• For equality Constraint [eq-20] 20.
• Minimize the fitness function using PSO method for the number of units running at that time.
• If the number of iteration reaches the maximum then go to step k. Otherwise go to step c.
• The individual that generates the latest is the optimal generation power of each unit with the minimum total generation cost.
The flow chart of the above mention steps is developed as under in [Fig-3]

The performance has been studied for three generator and four generator test data. The results for the respective systems are discussed as in [Table-1] [Table-2] and [Table-3] respectively

Three units are to be committed to serve 15-h load pattern. Data on the units and load pattern are contained in the given Table(1).The details of fuel cost components, initial conditions and load pattern are given

The results obtained for the test system1 using dynamic programming are summarized in [Table-4]

The results obtained from PSO are detailed in [Table-5] for tree generator system. Correspondingly, the variation of fitness and Xgbest are shown in [Fig-4] and [Fig-5] respectively. The total operating cost is calculated,
the unit combination selected in each hour and the distribution of load among each unit. From [Fig-4] it is concluded that at first there is variation in the operating cost (fitnessgbest) and after some iteration the operating cost is set to its optimal point. i.e. The operating cost is minimized. Same is the case with [Fig-5] there are three units i.e. Unit1, Unit2, Unit3. As these are denoted by Xgbest1, Xgbest2, Xgbest3, the behaviour of these three units are also varying at first and then these are set to their optimal point.

Four units are to be committed to serve an 8-h load pattern. The details of unit characteristics, fuel cost components, initial
conditions and load pattern are given in [Table-6] [Table-7] [Table-8] [Table-9] respectively

The results obtained for the test system2 using dynamic programming are summarized above in [Table-10]

Results are coming according to given data for the four generator unit commitment problem. Here the total operating cost is calculated, the unit combination selected in each hour and the distribution of load among each unit. It is seen from the [Table-11] that the total operating cost in this case is minimum as compared to the results obtained as seen in the [Table-10] in case of dynamic programming Now, in [Fig-6] As at first the there is variation in the operating cost of the four units, but after few iteration the operating cost is minimized as it is set to its optimal point. In [Fig-7] Units (Xbgest) also shows the random behaviour at first then they also reach their optimal point.

It is recognized that the optimal unit commitment of thermal systems results in a great saving for electric utilities. Unit Commitment is the problem of determining the schedule of generating units subject to device and operating constraints. The formulation of unit commitment has been discussed and the solution is obtained by classical dynamic programming method. An algorithm based on Particle Swarm Optimization technique, which is a population based global search and optimization technique, has been developed to solve the unit commitment problem. The effectiveness of these algorithms has been tested on systems comprising three units and four units and compared for total operating cost. It is found that the result obtained from the unit commitment using particle swarm optimization are minimum than the results obtained from classical Dynamic programming.

[1] Kerr R.H., Scheidt J.L., Fontana A.J. and Wiley J.K. (1966) IEEE Transactions on Power Apparatus and Systems. PAS-85(5), 417-421.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[2] Hara K., Kimura M. and Honda N. (1966) IEEE Transaction on Power Apparatus And Systems, PAS-85(5), 421-436.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[3] Lowery P.G. (1966) IEEE Transaction on Power Apparatus And Systems, PAS-85, No. 5, pp. 422-426.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[4] Guy J.D. (1971) IEEE Transactions on Power Apparatus and Systems, 90, 1385-1389.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[5] Fang C.K., Sheble G.B. and Albu F. (1989) IEEE Transactions on Power Apparatus and Systems. 100(3), 1212-1218.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[6] Lauer G.S., Sandell N.R., Jr. Bertsekas and Posbergh T.A. (1982) IEEE Transactions on Power Apparatus and Systems, 101, 79-96.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[7] Lee K.D., Vierra R.H., Nagel G.D. and Jenkins R.T. (1985) IEEE Transactions on Power Apparatus and Systems, 104(8), 2072-2078.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[8] Van den Bosch P.P.J. and Honderd G. (1985) IEEE Transactions on Power Apparatus and Systems, 104, 1684-1690.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[9] Kusic G.L. and Putnam H.A. (1985) IEEE Transactions on Power Apparatus and Systems,104, 2408-2412.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[10] Walter L., Snyder. Jr., David Powell H., and John C. Rayburn (1987) IEEE Transaction on Power System. 2, 339-347.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[11] Nieva R., lnda A. and Guillen I. (1987) IEEE Transaction on Power System, 2, 465-473.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[12] Cohen A.I. and Wan S.H. (1987) IEEE Transaction on Power System, 2, 608-614.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[13] Mukhtari S., Singh J. and Wollenberg B. (1988) IEEE Transaction on Power System, 3(I), 272-277.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[14] Fred. N. Lee (1988) IEEE Transaction on Power System, 3, 421-428.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[15] Walter J. Hobbs, Gary Hermon, Stephen Warner and Gerald B. Sheble (1988) IEEE Power Engineering Review, 70.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[16] Aoki K., Itoh M., Satoh T., Nara K. and Kanezashi M. (1989) IEE Gener. Tansnm. Distrib., 136©, 162-174.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[17] Tong S.K. and Shahidehpour (1989) IEEE Transaction on Power System, 4, 1065-1073.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[18] Sudhir Virmani, Eugene C. Adrian, Karl Imhof and Shishir Muhhejee (1989) IEEE Transaction on Power System, 4, 1373-1384.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[19] Chowdhury N. and Billinton R. (1990) IEEE Transaction on Power System, 5, 1231-1238.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[20] Handschin E. and Slomski (1990) IEEE Transaction on PowerSystem, 5, 1470.1477.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[21] Khadim Hussain (1991) IEEE Computer Applications in Power, 16-20.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[22] Slobodan Ruic and Nikola Rajakovic (1991) IEEE Transaction on Power System, 6, 269-275.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[23] Fred N. Lee (1991) IEEE Transaction on Power System, 6, 691-698.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[24] Chung-Ching Su and Yuan-Yih Hsu (1991) IEEE Transaction on Power System, 6, 1231-1237.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[25] Ouyang Z. and Shahidehpaur S.M. (1991) IEEE Transaction on Power System, 6, 1203-1209.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[26] Md-Sayeed Salam abdul-Razak Hamdan and Khalid Mohamed Nor (1991) IEE, 138, 553-559.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[27] Ouyang Z. and Shahidehpour S.M. (1992) IEEE Transaction on Power System, 7, 236-242.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[28] Sasaki H., Watanak M. and Yokoyama R. (1992) IEEE Transaction on Power System. 7, 974-981.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[29] Dasgupta D. and McGregor D.R. (1994) IEEE Proc.-Gener. Transm. Distrib., 141, 459-465.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[30] Ma X., El-Keib A.A., Smith R.E. and Ma H. (1995) Electric Power System Research, 34, 29-36.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[31] Ross Baldick (1995) IEEE Transaction on Power System, 10, 465-475.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[32] Tim T. Maifeld and Gerald B. Sheble (1996) IEEE Transaction on Power System, 11, 1359-1370.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[33] Li C. and Johnson R.B. (1996) IEEE PES Summer Meeting.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[34] Seyedrasoul Saneifard, Nandipuram R. Prasad and Howard A. Smolleck (1997) IEEE Transaction on Power System, 12, 988-995.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[35] Walsh M.P. and Mallry M.J.O. (1997) IEEE Transaction on Power System, 12, 1765-1774.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[36] Ma H. and Shahidehpour S.M. (1997) IEE Pro.-Gener. Trans. Distrib., 144(2), 113-117.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[37] Mantawy A.H., Youssef L. Abdel-Magid and Shokri Z. Selim (1998) IEEE Transaction on Power System, 13, 197-204.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[38] Kun-Yuan Hung, Hong -Tier Yang and Ching-Lien Hung (1998) IEEE Transaction on Power System, 13, 936-945.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[39] Mantawy A.H., Yousnef L. Abdel-Magid and Shakri Z. Selim (1999) IEEE Transaction on Power System, 14, 829-836.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[40] Juste K.A., Kita H., Tanaka E. and Hasegawa J. (1999) IEEE Transactions on Power System, 14, 1452.1459.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[41] Samer Takriti and John R. Birge (2000) IEEE Transactions on Power Systems, 15, 151-156.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[42] Liang R.H. and Kang F.C. (2000) IEE On Gener. Transm. Distrib., 147, 164.170.]  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[43] Charles W. Richter, and Gerald B. Sheble (2000) IEEE Transactions on Power Systems, 15, 715.721.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[44] Swarup K.S. and Yamashiro S. (2002) IEEE Transaction on Power System, 17, 87-91.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[45] Sum-im. T. and Ongsakul .W (2003) IEEE International Conference, 1, 72 -77.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[46] Sriyanyong P., Song Y.H. (2005) IEEE Power Engineering Society General Meeting, 3, 2752-2759  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

[47] Samudi C., Das G.P., Ojha P.C., Sreeni T.S. and Cherian S. (2008) IEEE/PES Transmission and Distribution Conference and Exhibition, 1-5.  
» CrossRef   » Google Scholar   » PubMed   » DOAJ   » CAS   » Scopus  

	Fig. 1- Unit commitment by dynamic programming
	Fig. 2- PSO Algorithm
	Fig. 3- Flow chart for solving unit commitment using PSO
	Fig. 4- Variation of fitness global best (Total Operating Cost)
	Fig. 5- Variation of Xgbest ( Generating Units)
	Fig. 6- Variation of Fitness global best (Total Operating Cost)
	Fig. 7- Variation of X global best (Generation Units)
	Table 1- Fuel cost component
	Table 2- Initial conditions.
	Table 3- Units characteristics, load pattern and initial status of the unit.
	Table 4-Result of 3-units, unit commitment problem using Dynamic Programming
	Table 5- Result of 3-units, unit commitment problem using PS0
	Table 6- Unit characteristics
	Table 7- Fuel cost components
	Table 8- Start up and start down costs and Initial conditions
	Table 9- load pattern
	Table 10- Result of Dynamic Programming
	Table11- Results of unit commitment using PSO