Optimal Unit Commitment Based on Economic Dispatch Using Improved Particle Swarm Optimization Technique

ISSN 2349-7815
International Journal of Recent Research in Electrical and Electronics Engineering (IJRREEE)
Vol. 3, Issue 1, pp: (50-56), Month: January - March 2016, Available at: www.paperpublications.org
Page | 50
Paper Publications
Optimal Unit Commitment Based on Economic
Dispatch Using Improved Particle Swarm
Optimization Technique
Neha Thakur1
, L. S. Titare2
1,2
Deptt. of Electrical Engineering, JEC, Jabalpur (M.P.), India
Abstract: In this paper, an algorithm to solve the optimal unit commitment problem under deregulated
environment has been proposed using Particle Swarm Optimization (PSO) intelligent technique accounting
economic dispatch constraints. In the present electric power market, where renewable energy power plants have
been included in the system, there is a lot of unpredictability in the demand and generation. This paper presents an
improved particle swarm optimization algorithm (IPSO) for power system unit commitment with the
consideration of various constraints. IPSO is an extension of the standard particle swarm optimization algorithm
(PSO) which uses more particles information to control the mutation operation, and is similar to the social society
in that a group of leaders could make better decisions. The program was developed in MATLAB and the proposed
method implemented on IEEE 14 bus test system.
Keywords: Unit Commitment, Particle Swarm Optimisation. Best individual particle, Best group particle, Voltage
Security.
1. INTRODUCTION
Over the years, power systems had seen an immense shift from isolated systems to huge interconnected systems. These
interconnected power systems are more reliable and at the same time have brought up many challenges in the operation
from economics and system security perspective. Power systems can be divided into three main sub-systems called the
Generation, Transmission and the Distribution systems apart from the power consumption at the end. The behaviour of all
sub-systems is interdependent. Each of the sub-systems has its own behavioural attributes and constraints which govern
overall system operation. Power systems have expanded the reach over a large geography for years to supply and cater to
the ever increasing load demand. With this vast spread due to continuously growing power requirements, every utility in
the world is facing a problem in reliable operation of system.
The need to supply of electricity to consumers with utmost importance towards reliability inclines utilities to plan at every
level. In addition to reliability, an aspect that concerns utilities in planning is the economics involved in system operation.
From the stage of power generation to the supply at consumer level, there exist many economic considerations. Thus, the
planning steps followed should enable system reliable operation while optimizing the economics needed. The power
system is subjected to a varying electric load demand with peaks and valleys at different times in a day completely based
on human requirements. This urges the company to commit (turn ON) sufficient number of generating units to cater to
this varying load at all times. The option of committing all of its units and keeping them online all the time to counter
varying nature of load is economically detrimental [1] for the utilities.
A literature survey on unit commitment reveals that several methods have been developed to solve unit commitment [2,
3].They include dynamic programming method, It is a stochastic search method which searches for solution from one
state to the other. The feasible states are then saved [4, 5]. Dynamic programming was the earliest optimization-based
method to be applied to the UC problem. It is used extensively throughout the world. It has the advantage of being able to

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Paper Publications
solve problems of a variety of sizes and to be easily modified to model characteristics of specific utilities. But the
disadvantage of this method is curse of dimensionality. i.e., the computational effort increases exponentially as problem
size increases and solution is infeasible and its suboptimal treatment of minimum up and downtime constraints and time-
dependent start-up costs. Lagrange Relaxation method, In this method the constraints are relaxed using Lagrange
multipliers. Unit commitment is written as a cost function involving a single unit and coupling constraints. Solution is
obtained by adjoining coupling constraints and cost by Lagrange multipliers. Mixed Integer Linear Programming method,
the method is widely used in the commitment of thermal units. It uses binary variables (0 or 1) to represent start up, shut
down and on/off status of units. Even it guarantees optimal solution in finite number of steps; it fails when number of
units increases because they require large memory space and suffer from great computational delay [6]. While considering
the priority list method for the committing the units, replication time and memory are saved, and it can also be pertained
in a genuine power system. In contrast, the priority list method has shortcomings that consequence into suboptimal
solutions since it won’t consider each and every one of the possible combinations of generation [7].
Section -2 presents problem formulation. Section-3 presents problem solution using DP algorithm. Section-4 gives
implementation of developed algorithm on IEEE-14-bus system and section-5 gives conclusion.
2. FORMULATION OF UNIT COMMITMENT PROBLEM
Unit commitment can be defined as the selection of generators that must be operated to meet the forecasted load demand
on the system over a period of time so that fuel cost is minimum [9,10]. The Unit Commitment Problem (UCP) is to
determine a minimal cost turn-on and turn-off schedule of a set of electrical power generating units to meet a load demand
[12] while satisfying a set of operational constraints. It is a well-known problem in power industry and helps in saving
fuel cost if units are committed correctly so that fuel cost is saved.
A. Need for Unit Commitment:
(i) Enough units will be committed to supply the load.
(ii) To reduce loss or fuel cost.
(iii) By running the most economic unit load can be supplied by that unit operating closer to its better efficiency.
B. Factors Considered In Unit Commitment:
(i) For finding the nature of fluctuating load as well as to commit the units accordingly a graph is drawn between load
demand and hours of use. This graph is known as load curve. In the solution load pattern for M period is formed using
load curve.
(ii)The possible numbers of units are committed to meet the load.
(iii)The load dispatch is calculated for all feasible combinations and operating limits of the units have to be calculated.
Unit Commitment is considered as a complex optimization problem where the aim is to minimize the objective function
in the presence of heavy constraints The objective function is given by Minimize Total cost = Fuel cost + Start-up cost
+Shut down cost
C. The input-output characteristic of a generating unit is obtained by combining directly the input-output characteristics of
boiler and that of turbine-generator set [13]. A typical input-output characteristic also called fuel cost curve of a thermal
generating unit is convex as shown in Fig. 1
Figure 1. Input-output characteristics of thermal generator

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This non liner curve can be approximated to a quadratic equation (1)
( ) (1)
Where ( ) represents the cost function, is the power output and , and are the coefficients of input-output
characteristic of ith unit. These cost coefficients are determined experimentally. The constant is equivalent to the fuel
consumption or cost incurred in operating the unit without power output. The slope of this input-output curve is called the
incremental fuel cost of unit.
Start- up cost: When the unit is at rest, some energy is required to bring the unit online. It is maximum when the unit is at
cold start (start- up cost when cooling). The unit is given sufficient energy input to keep it at operating temperature (start-
up cost when banking). So it requires some energy input to keep it at operating temperature.
Shut down cost: It is the cost for shutting down the unit. Sometimes during the shutdown period boiler may be allowed to
cool down naturally and thus no shut down cost will be incurred.
The two costs are as shown, and are compared while determining the UC schedule and a best approach among them is
chosen [1].
Start-up cost for cold start: ( ⁄
) (2)
Start-up cost for hot start: (3)
Where STC is the Start-up cost, Cc is the cold start cost in MBtu, F is the fuel cost, Cf is the fixed cost that includes crew
expenses and maintenance expenses, Ct is cost in Mbtu/hour for maintaining the unit at operating temperature, α is the
thermal time constant of the unit and t the time in hours the unit was allowed to cool. Shutdown cost is generally taken as
a constant value.
D. constraints in unit commitment [11]:
1. Power balance: the total generated load and demand at corresponding hours must be equal
∑ (4)
2. Minimum capacity committed: : It is the total power available from all units synchronised on the system minus present
loads plus the losses. It is given by
∑ (5)
3. Thermal constraints: The temperature and pressure of units increase gradually as the units are started. So they must be
synchronised before bringing online.
4. Must run units: Some of the units must be given a must run status in order to provide voltage support for the network.
For such units =1.
5. Minimum up/down time:
(6)
(7)
6. Unit generation limits: The generated power of a unit should be within its minimum and maximum power limits.
(8)
7. Ramp rate constraints: The ramp rate constraint ensures that sufficient ramp rate capacity is committed to accommodate
required generation changes. Any generation changes beyond the required changes are due strictly to economics of the
committed generators.
(9)
8. Fuel constraints: The constraint means limited availability of fuel or burning of some amount of fuel.

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Objective function: so the total cost can be represented by
∑ ∑ [ ( ) ( ) ] (10)
3. PROBLEM SOLUTION USING PARTICLE SWARM OPTIMISATION METHOD
Since all the previous methods suffer from dimensionality and computation problems, a new method has been evolved in
solving the unit commitment. It is known as Particle Swarm Optimisation method.[15].The method was developed by
simulation of social model. The method is inspired from social behaviour such as “bird flocking‖” or “fish schooling”[8].
The method consists of a group of particles in a given dimension moving towards optimal solution. The particles move
based on their previous best position, the position of neighbours and the best among all particles [14].Each particle move
towards the optimal solution based on its previous best position given by Pbest, position of other particles and the best
among all the other particles given by Gbest. The search is continued until a globally best solution is obtained or specific
number of iteration is reached.
A. Algorithm of PSO:
It is known that a particle in the swarm flies through hyperspace and alters its position over the time iteratively, according
to its own experience and that of its neighbours. Velocity is the factor responsible for this and which reflects the social
interaction. If xj represents particle x in iteration j, it is modified for the next iteration or it can be said that it is moved to a
new location as shown, where vj+1 is the velocity term derived for j+1 iteration.
(11)
A particle x flying in hyperspace has a velocity v. The best success attained by the particle is stored as pbest and the best
among all the particles in the swarm is stored as gbest.
Step1: Initialize the swarm or population Pop randomly of desired size, let K in the hyperspace.
* +
Step 2: Calculate the fitness value of each particle f(xij).
Step 3: Compare the fitness of each particle with its own best attained thus far as illustrated below
if ( ) {
( )
(12)
else : no change in pbest and
Step 4: Compare the fitness values of all particles and find gbest as shown
if ( ) {
( )
(13)
else : no change in gbest and
Step 5: Change the velocity of each particle for the next iteration as under, where w is inertia weight, c1, c2 are constants,
rand is random variable which assumes uniformly distributed values between 0 and 1.
( ) ( ) (14)
Step 6: Move each particle to a new position
(15)
Step 7: Repeat step 2 to 6 until convergence.
Inertia weight w: Controls the influence of previous velocity on the new velocity. Large inertia weights cause larger
exploration of search space, while smaller inertia weights focus the search on a smaller region. Typical PSO starts with a
maximum inertia weight wmax which decreases over iterations to a minimum value wmin as shown.

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(16)
Where it represents the current iteration count and itmax is the maximum iterations allowed.
Reference [15] gives the best values of wmax and wmin as 0.9 and 0.4 respectively for most of the problems.
B. Advantages Of PSO Compared To Conventional Methods:
1. Easy to implement and potential to achieve a high quality solution with stable convergence characteristics.
2. The particles are treated as volume less and each particle update position and velocity according to its own experience
and partners experience.
3. PSO is more capable of maintaining diversity of the swarm.
4. One of reasons that PSO is attractive is that there are very few parameters to adjust [16]
Figure 2. Flow Chart of PSO Applied To Unit Commitment

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4. TEST SYSTEM AND SIMULATION RESULTS
Table 1 shows the 24 hour UC schedule for standard IEEE 14 bus test data given in Appendix B. Results given in the
table are self-explanatory with hourly load demand, unit status, and power output from each committed unit. Total cost of
UC schedule along with hourly production costs and total transitional cost are listed. In order to indicate the effectiveness
of proposed UC algorithm, the maximum and minimum load bus voltages attained during every hour in the system are
shown in the Table 2 that follows the voltages at the load buses in the system during 24 hour time period attained as high
as 1.0751 PU and as low as 1.0017 PU.
Table 1. UC for IEEE 14 Bus Test System
Hour Load Unit Status Power Output (MW) Cost($)
(MW) X10^31 2 3 6 8 1 2 3 6 8
1 181.30 0 1 1 1 1 0 33.47 64.54 43.90 39.99 0.9618
2 170.94 1 0 1 1 1 60.00 0 52.70 27.19 32.14 0.9506
3 150.22 1 1 1 1 0 62.84 20.00 47.64 21.20 0 0.8415
4 103.60 1 0 0 1 1 64.49 0 0 22.23 18.00 0.6392
5 129.50 1 0 1 1 1 58.06 0 32.00 14.45 25.99 0.7710
6 155.40 1 0 1 1 0 71.19 0 54.79 30.92 0 0.8321
7 181.30 1 0 1 0 0 104.1 0 80.00 0 0 0.9551
8 202.02 1 0 1 0 0 125.7 0 80.00 0 0 1.0823
9 212.38 1 0 1 1 0 117.6 0 80.00 18.00 0 1.1479
10 227.92 1 0 1 1 0 115.1 0 80.00 36.00 0 1.2155
11 230.51 1 1 1 0 1 116.1 20.00 80.00 0 18.00 1.2824
12 217.56 1 0 1 0 1 104.1 0 80.00 0 36.00 1.1681
13 207.20 1 0 1 1 1 83.40 0 66.35 18.00 41.16 1.1271
14 196.84 1 0 1 0 0 120.4 0 80.00 0 0 1.0496
15 227.92 1 1 1 0 1 113.4 20.00 80.88 0 18.00 1.2667
16 233.10 1 1 1 0 1 89.37 37.90 72.54 0 36.00 1.2584
17 220.15 1 0 1 1 1 88.59 0 71.11 18.00 44.29 1.1944
18 230.51 1 1 1 1 1 76.95 20.00 61.76 36.00 37.70 1.2616
19 243.46 1 0 1 1 1 86.76 0 70.44 45.00 43.23 1.3026
20 253.82 1 1 1 1 1 82.58 20.00 67.30 45.00 41.11 1.3782
21 259.00 1 0 1 1 1 94.07 0 77.19 45.00 45.00 1.3857
22 233.10 1 1 1 0 1 94.16 20.00 76.45 0 45.00 1.2638
23 225.33 1 0 1 0 1 102.8 0 80.00 0 45.00 1.2067
24 212.38 1 1 1 1 0 97.98 20.00 79.35 18.00 0 1.1559
Transitional Cost 2.7198
Total Cost 29.418
Table 2. Hourly Min. and Max. Load Bus Voltages for IEEE 14 Bus Test Systems
Hour Vmax Vmin Hour Vmax Vmin
1 1.0779 1.0358 13 1.0704 1.0275
2 1.071 1.0286 14 1.0325 0.9974
3 1.0651 1.0269 15 1.0529 1.0114
4 1.0737 1.0323 16 1.0535 1.0123
5 1.0722 1.0307 17 1.0700 1.0273
6 1.0631 1.0270 18 1.0709 1.0291
7 1.036 1.0135 19 1.0704 1.0277
8 1.0353 1.0144 20 1.0705 1.0293
9 1.0659 1.0209 21 1.0697 1.0275
10 1.0626 1.0210 22 1.0541 1.0151
11 1.0659 1.0244 23 1.053 1.0127
12 1.0546 1.0204 24 1.0582 1.0239

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5. CONCLUSION
The optimal unit commitment of thermal systems resulted in enormous saving for electrical utilities. The formulation of
unit commitment was discussed and the solution is obtained using the Particle Swarm Optimization method. It is found
that the total operating cost obtained from the solution of unit commitment using particle swarm optimization is minimum
compared to the outcomes obtained from conventional methods. And also the computation time is less.
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Optimal Unit Commitment Based on Economic Dispatch Using Improved Particle Swarm Optimization Technique

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