910s-2

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CHAPTER 2

Unit Commitment Problem --- A Brief Literature Survey

2.1 Introduction

The Unit Commitment Problem (UCP) is a large scale, non-linear, 0-1 combinatorial

optimization problem.

This chapter presents an overview and literature survey on UCP. Final section includes

the directions on which the new approaches evolved with time, discussion and potential avenues

for further investigations including hybrid approaches.

2.2 Power System Operational Planning

The objectives of the power system operational planning involves the best utilization of

available energy resources subjected to various constraints and to transfer electrical energy from

generating stations to the consumers with maximum safety of personal/equipment, continuity,

and quality at minimum cost.

The operational planning involves many steps such as short term load forecasting, unit

commitment, economic dispatch, hydrothermal coordination, control of active/reactive power

generation, voltage, and frequency as well as interchanges among the interconnected systems in

power pools etc.

In the early days the power system consisted of isolated stations and their individual

loads. But at present the power systems are highly interconnected in which several generating

stations run in parallel and feed a high voltage network which then supplies a set of consuming

centers. Such system has the advantages of running the number of stations with greater reliability

and economy, but at the same time the complexity in the operational and control procedures has

increased. The power industry therefore requires the services of the group of men who are

specially trained to look after the operation of the system. These men are known as the system

engineers and are responsible for the operation, control and operational planning of the system.

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Unit Commitment involves the hour-to-hour ordering of the units on/off in the system to

match the anticipated load and to allow a safety margin. Having solved the unit commitment

problem and having ensured through security analysis that present system is in a secure state

then the efforts are made to adjust the loading on the individual generators to achieve minimum

production cost on minute-to-minute basis. This loading of generators subjected to minimum

operation cost is in essence the economic dispatch.

Load forecasting gives an accurate picture of the expected demand over the following

few hours. In an anticipation of the variations in demand and for reasons of economic operation

of the system the unit commitment activity is carried out.

The solution methods being used to solve the UCP can be divided into three categories as:

• Single classical/Deterministic approaches: A variety of classical/deterministic single

techniques in this context have been reported such as: Priority List (PL), Dynamic

Programming (DP), Exhaustive Enumeration (Brute Force Technique), Branch and

Bound (B&B), Integer /Mixed integer programming (IP/MIP), Lagrangian Relaxation

(LR), Straight Forward (SF) and Secant Methods.

• Single non classical approaches: The popular single non classical approaches which got

attention in recent years are such as: Tabu Search (TS), simulated annealing (SA), Expert

System (ES), Artificial Neural Networks (ANN), Evolutionary Programming (EP),

Genetic algorithms (GA), Fuzzy Logic (FL), Particle Swarm Optimization (PSO), Ant

Colony Optimization (A.C.O), and Greedy Randomized Adaptive Search Procedure

(GRASP).

• Hybrid techniques based on classical and non-classical approaches: More recently

hybrid techniques combining two or more of the above mentioned optimization

techniques were proposed to solve UCP such as: Particle Swarm Optimization Based

Simulated Annealing, Enhanced Lagrange Relaxation, Augmented Lagrange Relaxation,

Fuzzy Adaptive Particle Swarm Optimization, Hybrid Particle Swarm Optimization,

Lagrange Relaxation Parallel Particle Swarm Optimization, Lagrange Relaxation Parallel

Relative Particle Swarm Optimization, Unit Characteristics Classification-Genetic

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Algorithm, Tabu Search based Hybrid Particle Swarm Optimization, Annealing Genetic

Algorithm, Ant Colony Simulated Annealing, Dynamic Programming- Lagrange

Relaxation, Lagrange Relaxation- Genetic Algorithm, Lagrange Relaxation-Particle

Swarm Optimization, Enhanced Merit Order- Augmented Lagrange Hopfield Network,

Priority List based Evolutionary Algorithm, Memetic Algorithm seeded with Lagrange

Relaxation, Dynamic Programming based Hopfield Neural Network etc.

2.3 Unit commitment --- Literature Survey

Unit commitment is the problem to determine the optimal subset of units to be used

during the next 24 to 168 hours [1]. This section presents a survey of the research work based on

techniques both using conventional as well as Artificial Intelligence (AI) approaches.

Traditionally the UC problem is to minimize the total production costs (TPC), (operating

fuel cost, start-up and shut-down costs) and is referred as the cost-based-unit-commitment

(CBUC) problem [2–3]. A 0.5 percent saving of the operating fuel cost gives savings of millions

of dollars per year for large utilities [4]. A number of methodologies to solve the UCP exist and

are under investigation [5-14].

The next section gives the review of several classical approaches which have been reported

in the literature

2.4 Single Classical/Deterministic Approaches

Classical methods give good results. They are heuristic and have dimensionality problem.

2.4.1. Priority List

In 2003, T. Senjyu, et al. [15] introduced extended priority list (EPL) method. The

approach consists of two steps. The initial UC schedules are produced by priority list method and

then modified using the problem specific heuristics to fulfill unit and system constraints. Some

heuristics are also applied. The Economic Dispatch is performed only on the feasible schedules.

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In 2006, T. Senjyu, et al. [16] proposed Stochastic Priority List (SPL) method. Some

initial feasible UC schedules are generated by Priority List method and priority based stochastic

window system. Some heuristics are used to reduce search space and computational time.

2.4.2. Dynamic Programming

In 1966, P. G. Lowery, [17] proposed DP in solving UCP. The main concern was to

determine the feasibility of using Dynamic Programming to solve the UCP. Results of the study

show that simple, straightforward constraints are adequate to produce a usable optimum

operating policy. The computer time to produce a solution is small.

In 1981, C. K. Pang, et al. [18] presented a study of three different DP algorithms. The

Dynamic Programming-Sequential Combinations (DPSC) and Dynamic Programming-Truncated

Combinations (DP-TC) and Dynamic Programming-Sequential/Truncated Combinations (DP-

STC), is a combination of the DP-SC and DP-TC methods. Four methods were used to establish

the savings and computer resource requirements.

In 1986, S. D. Bond, et al. [19] presented a dynamic programming which is capable of solving

the generation scheduling problem. The solutions are guaranteed to be optimal and are obtained

by using a state definition which includes the length of time a unit has been on or off. This

information is required to assess the effect of present commitment decisions on future flexibility.

When similar combinations of with the lowest accumulated cost is pursued further. The reduced

search effort lowers run times by an order of magnitude compared with a mixed integer-linear

programming approach relying mainly on constraint violations as a truncation mechanism.

Storage requirements are reduced even more significantly. The algorithm has been tested

successfully on data for a small and medium sized thermal power system. In addition to the usual

upper and lower limits on unit outputs, emergency reserve and MUT and MDT down time

constraints were incorporated.

In 1987, W. L. Snyder, et al. [20] proposed an approach to save computational time. This

algorithm incorporates a number of special features and effectively deals with the control of

problem size. To achieve the computational time saving, individual units were assigned status

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restriction in any given hour. This approach features the classification of units into groups so as

to minimize the number of unit combinations. Programming techniques are described which

maximize efficiency. This approach has been proved on a medium size utility for which sample

results were presented.

In 1988, W. L. Hobbs, et al. [21] developed an enhanced DP approach. This approach

saves predecessor options. The approach was implemented in an on-line energy management

system. A merit order list is formed which excludes all unavailable, fixed output, peaking, and

must run units. Subsequent combinations of units are formed by decommitting one unit at a time.

The method creates several states from each unique combination and links each state to one of

the possible paths to that combination.

In 1991, C. C. Su, et al. [22] developed a technique using fuzzy DP. The errors in the

forecasted load are considered and membership functions are derived for the load demand, the

total cost, and the spinning reserve using fuzzy set notations. With these membership functions at

hand, a recursive algorithm for fuzzy dynamic programming is presented. The developed

algorithm is used to solve the unit UC of Taiwan power. The proposed fuzzy dynamic

programming approach requires more computer time than the DP approach.

In 1991, Z. Ouyang, et al. [23], presented a heuristic improvement of the truncated

window DP and used a variable window size according to forecast load demand increments. The

corresponding experimental results show a considerable saving in the computation time.

2.4.3 Branch and Bound

In 1983, A. I. Cohen, et al. [24] proposed a new approach based on branch-and-bound

techniques. The method incorporates start-up costs, load demand, spinning reserve, MUT and

MDT constraints.

2.4.4 Integer and Mixed Integer programming

In 1978, T. S. Dillon, et al. [25] proposed an extended and modified version of applying

branch and bound technique for Integer Programming and treats the commitments of both hydro

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and thermal systems. The method is computationally practical for realistic system. The present

method constitutes a basis for the development of unit commitment programs using integer

programming for practical use in electric utilities.

In 2000, S. Takriti, et al. [26] presented a technique for refining the schedules obtained

by Lagrangian method. Given the schedules generated by Lagrangian iterations, and improved

schedule was found by solving the mixed integer program. The model was an integer program

with non linear constraints and solved for optimal solution using branch and bound technique.

The method gives a significant improvement in terms of quality of the solution for large number

of units.

In 2005, Li Tao, et al. [27] formulated the price-based unit commitment problem based

on the mixed integer programming method. The proposed PBUC solution is for a generating

company having cascaded-hydro, thermal, pump storage and combined-cycle, units. The results

are compared with LR method. The major obstacles are more computation time and memory

requirement to solve large UC problems.

In 2007, B. Venkatesh, et al. [28] demonstrated advantages of using the fuzzy

optimization model and presents fuzzy linear optimization formulation of UC using a mixed

integer linear programming (MILP) routine. In this formulation, start up cost is modeled using

linear variables. The fuzzy formulation provides modeling flexibility, relaxation in constraint

enforcement and allows the method to seek a practical solution. The use of MILP technique

makes the proposed solution method rigorous and fast. The method is tested on a 24 h, 104-

generator system demonstrating its speed and robustness gained by using the LP technique. A

five-generator system is additionally used to create a see-through example demonstrating

advantages of using the fuzzy optimization model.

2.4.5 Lagrange Relaxation Method

In 1983, A. Merlin, et al. [29] proposed a new implementation in solving UCP by

Lagrangian relaxation method. Numerous developments were envisaged, to make the algorithm

flexible such as simultaneous management of pumping units, probabilistic determination of the

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spinning reserve. This decomposition method used is flexible and Lagrange multiplier provides a

new solution to the conventional problem.

In 1987, R. Nieva, et al. [30] proposed an approach to solve very large and complex

UCP. The proposed approach gives an estimate of suboptimality that indicates the closeness of

the solution near to the optimum. In contrast with the technique of Lagrangian Relaxation, this

approach makes no attempt of maximizing the dual function.

In 1988, F. Zhuang, et al. [31] presented an LR method for large scale problem. The

algorithm in divided into three phases. First the Lagrangian dual of the unit commitment is

maximized with standard subgradient techniques, second a reserve-feasible dual solution is find,

and finally ED is performed. On 100 units to be scheduled over 168 hours, gives a reliable

performance and low execution times. Both spinning and time-limited reserve constraints are

treated.

In 1989, S. Virmani et al. [32] presented a paper in which they provide an understanding

of the practical aspects of the Lagrangian Relaxation methodology for solving the thermal UCP.

In 1995, R. Baldick [33] formulated UCP in generalized form and solved using LR

method. The algorithm, presented, approximately solves the dual optimization problem. The

algorithm was slower in solving the special cases of the generalized UCP than algorithms

demonstrated by other authors. The approach has been tested for ten units for a time period of 24

hours.

In 1995, W.L. Peterson, et al. [34] proposed a Lagrange Relaxation to incorporate unit

minimum capacity and unit ramp rate constrains. The proposed method is used in finding a

feasible UC schedule considering a new approach for ramping constraints. The algorithm

incorporates other practical features such as boiler fire-up characteristics and non-linear ramp up

sequences.

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In 2000, A. G. Bakirtzis, et al. [35] demonstrated the difference between the lambda

values of the economic dispatch and the UCP based on economic interpretation of the

Lagrangian Relaxation solution framework. During the LR solution of the UCP two sets of

lambdas are used. Although both set of lambdas represent marginal cost of electricity. The first

one, is assigned as a Lagrange multiplier (Lambda) to the UC power balance equations and

second one, is the Lagrange multiplier of the power balance equation in the economic dispatch

problem.

In 2004, W. P. Ongsakul, et al. [36] proposed an enhanced adaptive Lagrangian

relaxation (ELR). Enhanced LR approach consists of heuristic search and adaptive LR. ALR is

enhanced by introducing new 0-1 decisions. After the ALR the best feasible schedule is obtained.

The heuristic search is used to fine tune the schedule. The total system production costs are less

for the large scale system. The computational time is much less compared with others

approaches.

In 2005, D. Murtaza, et al. [37] presented an algorithm for the unit commitment schedule

using the Lagrange relaxation method by taking into account the transmission losses. For better

convergence and faster calculation, a two stage Lagrange relaxation was provided. First,

conventional Lagrange relaxation was applied in order to determine the unit commitment

schedule neglecting transmission loss. The results are then input to the proposed method, and the

unit commitment schedule including transmission losses was produced.

2.4.6 Straight Forward Method

In 2007, S. H. Hosseini, et al. [38] presented, a novel fast straightforward method (SF).

This new approach decomposes the UCP into three sub-problems. The quadratic cost functions

of units are linearized and hourly optimum solution of UC is obtained considering all constraints

except the MUT and MDT constraints and then the MUT/MDT constraints are introduced by

modifying the schedule obtained in the first step through a proposed novel optimization

processing. Finally, by using a new de-commitment algorithm the extra spinning reserve is

minimized.

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2.4.7 Secant Method

In 2008, K. Chandram, et al. [39] proposed an application of Secant method and

Improved Pre-Prepared Power Demand (IPPD) table (based on the units having low minimum

incremental cost) for solving the UCP. The problem is divided into two sub problems, the unit

on/off scheduling and ED sub problem. Initially, IPPD table obtains the unit 0-1 status

information and then the optimal solution is achieved by Secant method. For solving large scale

problems the convergence is in less iteration.

2.5 Non classical approaches

The growing interest is the application of non classical approaches like Artificial

Intelligence (AI) and Swarm Intelligence (SI) in solving the UCP. AI methods like Neural

Networks, Simulated Annealing, Genetic Algorithm, expert system, evolutionary programming,

and fuzzy logic are used to solve the UCP. The SI techniques like PSO and ACO also gained

prominence for solving UCP. In the following section a survey of the AI and SI methods for

UCP are presented.

2.5.1 Tabu search

In 1998, A. H. Mantawy, et al. [40] presented an approach based on the Tabu Search

method. Initial feasible UC schedules are generated randomly using new proposed rules. TSA is

used to solve the combinatorial optimization sub problem while the quadratic programming is

used to solve the EDP subproblem. Numerical results show an improvement in the quality of

solution compared with other approaches.

2.5.2 Simulated Annealing (SA)

In 1990, F. Zhuang, et al. [41] presented a general optimization method, known as

simulated annealing, and is applied to generation unit commitment. SA was used to generate

feasible solutions randomly and moves among these solutions using a strategy leading to a global

minimum with high probabilities. The method assumes no specific problem structures and is

highly flexible in handling unit commitment constraints. Numerical results on test systems of up

to 100 units were reported.

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In 1998, A. H. Mantawy, et al, [42] presented a Simulated Annealing Algorithm (SAA)

and proposed new rules for randomly generating initial feasible UC schedules. SAA is used to

solve the combinatorial optimization sub problem while the quadratic programming is used to

solve the EDP subproblem. Numerical results show an improvement in the total production cost

compared with other approaches.

In 1998, S. Y. W Wong, [43] developed an enhanced SA-approach for solving the UCP

by adopting mechanisms to ensure that the candidate solutions produced are feasible and satisfy

all the constraints. During the solution process, the solutions are generated in the neighbor of the

current one and the extent of perturbation of the solutions decreased with decreasing

temperature.

In 2006, D. N. Simopoulos, et al. [44] developed a new enhanced SA combined with a

dynamic ED method. SA is used for generator scheduling. The dynamic ED method is used to

incorporate the ramp rate constraints in the UCP. New rules for the tuning of the control

parameters of the SA algorithm are also presented.

In 2006, A. Y. Saber, et al. [45] presented fuzzy UCP using the absolutely stochastic

simulated annealing method.

2.5.3 Expert System

In 1988, S. Mokhtari, et al. [46] presented in setting up an expert system which combines

the knowledge of the unit commitment programmer and an experienced operator. In scheduling

units an expert system based on consultant has been formulated. This expert system will lead an

inexperienced operator to a better unit schedule. The basic expert system used 56 rules for the

experiments. The authors estimate that 300 rules will be required to satisfy all operational

requirements.

In 1991, S. K. Tong, et al. [47] demonstrated PL based heuristic to form initial UC

schedules based on the given forecasted load. A new expert system approach was used to handle

short term UC problem. In the proposed approach one of the previous schedules as the staring

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point is used to find the new schedule that will satisfy the present load requirements. A rule

based approach is applied to implement PL scheme for modifying the previous schedule so that a

sub-optimal feasible schedule can be obtained quickly.

In 1993, S. Li, et al. [48] presented a graphics package and a new heuristic method for

unit commitment. The principles of this method can be expanded to consider more complicated

cases with additional constraints. The units are divided into three categories the base, medium

and peak. The computational time is less than two seconds.

2.5.4 Artificial Neural Network (ANN)

In 1992, Sasaki, et al. [49] explored the feasibility of using the Hopfield neural network

to unit commitment in which a large number of inequality constraints are handled by the

dedicated neural network instead of including them in the energy function. Once the states of

generators are determined, their outputs are adjusted according to the priority order in fuel cost

per unit output.

In 1999, T. Yalcinoz, et al. [50] presented an improved Hopfield neural networks method.

A new mapping process was used and a computational method for obtaining the weights and

biases using a slack variable technique for handling inequality constraints. Transmission

capacity, transmission losses, start-up and shutdown costs and MUT/MDT constraints have been

taken into account. The HFNN approach has been tested on a 3 unit and a 10 unit systems.

In 2000, M. H. Wong, et al. [51] used GA to evolve the weight and the interconnection of

the neural network to solve the UC problem. The back-propagation was used to train the weights.

Three selection methods Roulette Wheel, Tournament and Ranking was used as well as two

options for Weight and Connections are combined for running the GA. Roulette Wheel has the

best performance.

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2.5.5 Evolutionary Programming (EP)

In 1999, K. A. Juste, et al. [52] proposed an algorithm that uses the EP technique in

which populations of initial population is generated randomly and then the solutions are evolved

through selection, competition, and random changes.

2.5.6 Genetic Algorithm (GA)

In 1993, D. Dasgupta et al. [53] presented a genetic approach for determining the priority

order in the commitment of thermal units in power generation. The paper examined the

feasibility of using genetic algorithms and reports some simulation results in near optimal

commitment of thermal units. The genetic-based UC system evaluates the priority of the units

dynamically considering the system parameters, operating constraints and load profile at each

time period in the scheduling horizon.

In 1995, X. Ma, et al. [54] developed a forced mutation operator and the efficiency of the

GA was improved significantly using this operator. Two different coding schemes were devised

and tested. It was observed that the two-point crossover operation is considerably more efficient

than the single-point crossover commonly used in GAs In addition, the effects of GA’s control

variables on convergence were extensively studied. The approach was tested on a 10 unit system.

Test results clearly reveal the robustness and promise of the proposed approach.

In 1996, S. O. Orero, et al. [55] presented an enhanced genetic algorithm incorporating

sequential decomposition logic for faster search mechanism Unit commitment constraints

including ramp rates are considered. The method relies on the selection and grading of the

penalty functions to allow the fitness function to differentiate between good and bad solutions.

The method guarantees the production of solutions that do not violate system or unit constraints,

so long as there are enough generators available in the selection pool to meet the required load

demand. The algorithm has been tested on 26 generators.

In 1996, S. A. Kazarlis, et al. [56] presented Genetic Algorithm by using Varying Quality

Function technique and adding problem specific operators. The coding was implemented in a

binary form. With the technique of varying quality function, the GA finally manages to locate

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the exact global solution. A nonlinear transformation was used for fitness scaling. New operators

swap-mutation and swap-window hill-climb was implemented. The algorithm is applied to 100

units.

In 2002, T. Senjyu, et al. [57] presented new genetic operator based on unit characteristic

classification and intelligent technique for generating initial populations. The initial population is

generated base on load curve. To handle MUT/MDT constraints new mutation operators were

introduced. New cross over operator, shift operator, and intelligent mutation operators were

proposed. Units are classified in several groups depending upon their MUT/MDT constraints.

For every violated constraint, a penalty term is added to the total cost.

In 2003, E. Gil, et al. [58] proposed a new method for hydrothermal systems. The

proposed GA, using new specialized operators, has demonstrated excellent performance in

dealing with this kind of problem, obtaining near-optimal solutions in reasonable times.

In 2004, G. Loannis, et al. [59] presented a new solution based on an integer-coded

genetic algorithm (ICGA), in which the chromosome size is reduction compared to the binary

coding. The non linear MUT and MDT constraints are directly coded in the chromosome. The

use of penalty functions is avoided because they distort the search space. The ICGA is robust and

execution time is less than other approaches.

In 2006, C. Dang, et al. [60] proposed a floating-point genetic algorithm (FPGA). In

which a floating-point chromosome representation is used based on the forecasted load curve. To

handle MUT and MDT constraints encoding and decoding schemes are used. The fitness

function, constraints, population size, selection, crossover and mutation probabilities are

characterized in detail. The FPGA is also applicable for non-convex cost function.

In 2006, L. Sun, et al. [61] introduced a matrix real-coded genetic algorithm (MRCGA).

A real number matrix representation of chromosome is used that can solve the UC problem

through genetic operations. The search performance is improved through a window mutation.

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The proposed new mechanism of chromosome repair guarantees that the UC schedule satisfies

unit and system constraints.

2.5.7 Fuzzy logic

In 1997, S. Saneifard, et al. [62] formulated the fuzzy logic to the UCP. A comparison of

results presented in the paper indicates that the use of fuzzy logic provides outcomes comparable

to those of conventional dynamic programming. It is claimed that this approach gives

economical cost of operation.

In 2004, S. C. Pandian, et al. [63] presented a fuzzy logic approach that is very useful to

consider the uncertainty in the forecasted load curve, derating and line losses. Numerical results

are compared w.r.t the operating cost and computation time obtained by using fuzzy dynamic

programming and other conventional methods like dynamic programming, Lagrangian relaxation

methods. For validation of the approach in respect of total production cost and computational

time, case studies on 10, 26 and 34 units have been performed.

2.5.8 Particle Swarm Optimization (PSO)

In 2003, Z. L. Gaing, [64] proposed binary particle swarm optimization (BPSO). The

BPSO is used to solve the combinatorial unit on/off scheduling problem for operating fuel and

transition costs. The ED subproblem is solved using the lambda iteration method for obtaining

the total production cost.

In 2006, B. Zhao, et al. [65] presented an improved particle swarm optimization

algorithm (IPSO) for UC which utilizes more particles information to control the process of

mutation operation. For proper selection of parameters some new rules are also proposed. The

proposed method combines LR technique to 0-1 variable.

In 2007, T. Y. Lee, et al. [66] presented a new approach for UCP named the iteration

particle swarm optimization (IPSO). The proposed method improves the quality of solution in

terms of total production cost and also improves the computation efficiency. A standard 48 unit

system has been tested for validation.

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In 2009, X. Yuan, et al. [67] proposed a new improved binary PSO (IBPSO). The

standard PSO is improved the using the priority list and heuristic search to improve the MUT and

MDT constraints. The 10-100 units have been tested to validate the proposed approach.

Numerical performance shows that the proposed approach is superior in terms of low total

production cost and short computational time compared with other published results.

2.5.9 Ant Colony Optimization (ACO)

In 2003, T. Sum-im, et al. [68] proposed, ant colony search algorithm (ACSA), which is

inspired by the observation of the behaviors of real ant colonies, and is a new cooperative agent’s

approach based on parallel search. In the proposed approach, a set of cooperating agents called

“ants” cooperates to find good unit schedules the ED sub-problem is solved by the λ-iteration

method.

In 2008, A.Y. Saber, et al. [69] proposed memory-bounded ant colony optimization

(MACO). The proposed approach is applicable for large number of units and solves the

computer memory limit requirements. A heuristic is also incorporated to enhance local search.

2.5.10 Greedy Randomized Adaptive Search Procedure (GRASP)

In 2003, A Viana, et al. [70] presented, an adaptive algorithmic framework based on

another meta-heuristic principle (GRASP – Greedy Randomized Adaptive Search Procedure).

The philosophy applied is slightly different from standard meta-heuristics, the decisions taken by

the method, when building a solution, are somehow adapted according to decisions previously

taken. This dynamic learning-process often leads to very good solutions.

2.6 Hybrid approaches

Hybrid approaches are also used to solve many difficult engineering problems. The aim

of the hybrid methods is to improve the performance of single approaches. The objective of

hybrid of two or more methods is to speed up the convergence and to get better quality of

solution compared with single approaches. A brief review of different hybrid approaches which

have been reported in the literature is presented in this section.

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In 1992, Z. Ouyang et al. [71] utilized neural networks to generate a pre-schedule

according to the forecasted load curve. The proposed approach significantly reduced the

computational time. Case studies are performed on 26 unit system. A 35 training pattern are used

in the study. The training of each load takes approximately eight to ten minutes.

In 1992, Z. Ouyang, et al. [72] proposed a multi-stage Neural Network-expert system

approach. Through inference the feasible UC schedule is obtained. A load pattern matching

scheme is performed at the pre-processor stage. The trained network performs adjustments in

the schedule to achieve the optimal solution at the post processor stages.

In 1995, D. P. Kothari, et al [73] described a hybrid expert system dynamic programming

approach. The output scheduling of the usual dynamic programming is enhanced by

supplementing it with the rule based expert system. The proposed system limits the number of

constraints and also checks the possible constraint violations in the generated schedule. The

expert system communicates with the operator in a friendly manner and hence the various

program parameters can be adjusted to have an optima1, operationally acceptable schedule.

In 1997, H. Shyh-Jier, et al. [74] proposed genetic algorithm based neural network and

dynamic programming approach for UCP. At the initial stage a set of feasible UC schedules are

generated by genetic-enhanced neural networks. In the second stage these schedules are

optimized by using the DP approach. The computational efficiency is more compared with other

methods.

In 2000, M. H. Wong, et al. [75] presented a technique in which genetic algorithm is

evolved to intelligently decide the initial weights and the connections in the ANN. This approach

prevents the stagnation during training. The approach converges into global minimum for a given

range of space. The evolving neural network has lower training error compared to neural

network with random initial weights.

In 2000, R. Nayak, et al. [76] proposed a hybrid of feed forward neural network and the

simulated annealing. The ANN is used to solve the unit scheduling sub problem and the SA is

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used to solve the ED sub problem. A set of inputs based on the forecasted load curve and

corresponding UC schedules as outputs satisfying the system and unit constraints are used to

train the network. A reduction in computational time is achieved by this approach.

In 2000, C. P. Cheng, et al. [77] presented an application of Genetic Algorithms and

Lagrangian Relaxation (LRGA) method. The proposed approach incorporates GA into LR

method to improve the performance of LR and to update the Lagrangian multipliers. The method

is easy to implement, better in convergence.

In 2002, C. P. Cheng, et al. [78] proposed the application of the annealing–genetic (AG)

algorithm. The AG is a hybrid of GA into the SA to improve the performance of the SA

approach. The method improves the computational time of the Simulated Annealing and the

quality of solution of Genetic Algorithm and gives near optimal solution of a large scale system.

In 2002, J. Valenzuela, et al. [79] presented memetic algorithm, a hybrid of GA, and LR

is efficient and effective for solving large UC problems. The implementations of standard GA or

MA are not competitive compared with the traditional methods of DP and LR. However, an MA

incorporated with LR proves to be superior to other approaches on large scale problems.

In 2003, T. O. Ting, et al. [80] proposed a Hybrid Particle Swarm Optimization (HPSO).

Problem formulation, representation and the numerical results for a 10 unit are presented. Results

shown are acceptable at this early stage.

In 2003, C. C. A. Rajan, et al. [81] presented a neural based tabu search (NBTS) method.

The algorithm is based on the short term memory procedure of the tabu search method. Systems

consisting of 10, 26, and 34 units have been tested and the results are compared with other

approaches. The results in terms of total production cost and computational time are better than

single approaches like DP and LR.

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In 2004, D. Srinivasan, at al. [82] proposed an efficient algorithm for aiding unit

commitment decisions. To solve the UCP an evolutionary algorithm with problem specific

heuristic and genetic operators has been employed

In 2004, L. Shi, et al. [83] developed and demonstrated a novel ant colony optimization

algorithm with random perturbation behavior (RPACO). The approach is based on the

combination of colony optimization and stochastic mechanism is developed for the solution of

optimal UC with probabilistic spinning reserve.

In 2004, H. H. Balci, et al. [84] presented a hybrid of PSO and LR. UCP is divided into

sub problems and each sub problem is solved using DP. PSO is used to update the Lagrangian

multipliers. The comparison of results shows that the proposed approach uses less computational

time and gives good quality solutions.

In 2005, T.A.A Victoire, [85] introduced an application of hybrid-PSO and sequential-

quadratic programming technique (SQP) guiding the tabu search (TS). The unit scheduling

problem is solved using an improved random-perturbation scheme. A simple procedure for

generating initial feasible UC schedules is proposed for the TS method. The nonlinear ED

subproblem is solved using the hybrid PSO-SQP technique.

In 2005, S. Chusanapiputt, et al. [86] presented Parallel Relative Particle Swarm

Optimization (PRPSO) and LR for a large-scale system. To reduce the dimensionality problem

and to improve the UC schedules the neighborhood solutions are divided into sub-

neighborhoods.

In 2005, P. Sriyanyong, et al. [87] proposed PSO based LR method for optimal setting of

Lagrange multipliers. In the proposed work, the PSO was used to adjust the lagrange multipliers

in order to improve the performance of lagrange relaxation method.

In 2005, T. Aruldoss, et al. [88] presented a solution model using fuzzy logic. Hybrid of

Simulated annealing, particle swarm optimization and sequential quadratic programming

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technique (hybrid SA-PSO-SQP) is used to schedule the generating units based on the fuzzy

logic decisions.

In 2006, T. O. Ting, et al. [89] introduced a hybrid particle swarm optimization (HPSO)

which is a combination of binary and real coded particle swarm optimization (BPSO and

RCPSO). The term “hybrid particle swarm optimization” was first mentioned by S. Naka, et al.

where by the term hybrid meant the combination of PSO and GA. The BPSO is used to solve

unit scheduling problem and RPSO is used to solve the ED subproblem.

In 2006, V.N. Dieu et al. [90] proposed an enhanced merit order (EMO) and augmented

Lagrange Hopfield network (ALHN) for solving hydrothermal scheduling (HTS) problem with

pumped-storage units. The proposed approach is based on merit order approach enhanced by

heuristic search based algorithms. The ALHN is a continuous Hopfield network and its energy

function is based on augmented Lagrangian function. EMO is efficient in unit scheduling,

whereas ALHN can properly handle generation ramp rate limits, and time coupling constraints.

In 2007, A. Y. Saber, et al. [91] presented a twofold simulated annealing (twofold-SA)

method. A hybrid of SA and fuzzy logic is used to obtain SA probabilities from fuzzy

membership function. The initial feasible UC schedules are generated by a priority list method

and are modified by de-composed SA using a bit flipping operator. Results indicate a low total

production cost and low execution time compared with other approaches.

In 2007, S. Nasser, et al. [92] presented hybrid particle swarm optimization based

simulated annealing (PSO-B-SA) approach. The unit scheduling sub problem is solved by using

binary PSO and ED sub problem is solved by using real valued PSO. Numerical results

demonstrated show that the PSO-B-SA approach can perform well compared with the other

solutions.

In 2007, A. Y. Saber, et al. [93] proposed a fuzzy adaptive Particle Swarm Optimization

(FAPSO) for UCP. FAPSO precisely tracks a changing schedule. Based on the diversity of

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fitness the fuzzy adaptive criterion is used for the PSO inertia weight. Using fuzzy IF/THEN

rules the weights are dynamically adjusted.

In 2007, S. S. Kumara, et al. [94] developed DP based direct Hopfield computation method. The

proposed approach solves the UCP in two steps. The generator scheduling problem is solved

using DP and generation scheduling problem is solved using Hopfield neural network.

2.7 Unit Commitment --- Issues and Bottlenecks

The issues and bottlenecks in the UCP may be listed as:

1. High dimensionality

2. Handling of cost base and profit base unit commitment

3. Handling of non convex fuel cost function

4. Generation of infeasible solutions

5. Handling of constraints such as:

i. Minimum up and down time

ii. Transmission

iii. Emission

iv. Security

2.8 Discussion

The global optimal solution of the UCP can be obtained by Brute Force (complete

enumeration) technique, which is not applicable for a power system having large number of units

due to its long computational time. Priority list (PL) methods are highly heuristic but very fast

and give UC solutions with high total production cost. The DP methods are based on

enumeration and PL, but suffer from the curse of dimensionality. Integer programming (IP) and

Mixed-integer programming (MIP) require considerable computational efforts when dealing with

large-scale problems. The main problem with Lagrangian relaxation (LR) method is the

difficulty in obtaining the feasible UC schedules.

The non classical approaches such as Evolutionary Computation, Genetic Algorithm, and

Particle Swarm Optimization etc. attract much attention, because they are able to solve convex

and non-convex fuel cost functions, have the ability to search for near global and can deal easily

with non linear constraints. In case of large-scale problem these single approaches consume long

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computational time. The main difficulty is their sensitivity on the choice of parameters. Hence,

there is an incentive to explore hybrid algorithms. From the selected above mentioned literature

review, it is observed that the hybrid techniques reduce the search space are more efficient and

have better quality of solutions for small and large scale problems, gives solution in an

acceptable computation time and can accommodate more constraints. Thus enhancing existing

classical and non classical optimization approaches and exploring new single and hybrid

approached to solve unit commitment problem has great importance. Among the hybrid

approaches the Swarm Intelligence techniques are new to apply to the UC problem. PSO is new,

flexible and efficient tool for UCP. The potential avenues for further exploration may be listed

as:

1. How to generate initial feasible schedules considering spinning reserve requirements.

2. How to satisfy MUT and MDT constraints.

3. Exploration of new operators for MUT and MDT constraint handling.

4. To reduce the high dimensionality of the UCP.

5. Hybrid methodology is the useful tool for efficient solution by exploiting the strength of

single classical approaches, and non classical approaches.

6. Exploration of fast and efficient method for utility system.

7. Exploration of PSO based approaches.

8. Hybrid models based on the integration of classical and non classical approaches for

enhancing the computational efficiency and handling of non-convex cost function for the

UC problem.