IRJET- Optimal Generation Scheduling for Thermal Units

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 05 Issue: 04 | Apr-2018 www.irjet.net p-ISSN: 2395-0072
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Optimal Generation Scheduling For Thermal Units
Nitish R. Patel1, Nilesh K. Patel2
1PG student, Department of Electrical Engineering, Sankalchand Patel College of Engineering, Gujarat, India
2Associate professor, Department of Electrical Engineering, Sankalchand Patel College of Engineering,
Gujarat, India
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Abstract - The main aim of this paper is to develop short-
term generation scheduling. The scheduling problem is
formulated by considering productioncostandstart-upcostof
generating units and satisfying all equality and inequality
constraint. A PSO techniques is used to obtain optimal
scheduling of ten generating unit. Results generated are
compared with other techniques. It was found that PSO
technique are very effective and efficient to solved short term
generation scheduling problem andprovideeconomic benefits
to the system operator to developed optimal scheduling.
Key Words: short-term scheduling,PSO,Economic Dispatch
1. INTRODUCTION
In deregulated power system, all the generating company
are independently and separately operated. The system
operator plan day ahead scheduling, that how many
generating units are carried out to satisfy load demand. A
short-term scheduling also known as day ahead scheduling.
In power system, consumer demand changes continuously,
its varied according to day-time, evening and morning
time[1]. Thus, system operator has to plan enoughunitsthat
required for next day to fulfill load demand. The generation
scheduling of power system is necessary to maintain a
balance between supply and demand, due to the fact that no
practical technology is available for large scale storage of
electricity. In day-ahead scheduling, a day-ahead unit
commitment program is executed to decide the most
economic unit combination with considerations of various
restrictions of units. Previously, a unit can usemultiplesfuel
constrained and it is assumed that only one fuel is
constrained. Adding fuel constraints severely complicates
the unit commitment problem. Thus author[2], utilized
Lagrange multipliers which tackle the unit responsibility
issue within the sight of fuel constraint. when a unit
supplying multiple fuels, the price of fuel at a unit is not
readily available and fuel pricecouldvaryoverdifferenttime
intervals of the study period resulting in an increase in the
complexity of the problem. Thus, in [3] divides the fuel
constrained unit commitment problem into a linear fuel
dispatch (FD) issue and a unit commitment (UC) issue. The
Fuel Dispatch issue improves framework fuel cost and
fulfilling fuel required. It is very difficult aspect of the power
system to incorporating a ramping costs into a scheduling
procedure, since the ramping costs vary with the generation
schedule. By presenting ramping costs, the unit on or off
states can be determined more economically by the
lagrangian method in [4], this method is developed for unit
commitment and economic dispatch problem. A short-term
scheduling issue is solved in [5] by dynamic programming,
and the economic dispatch with transmission and
environmental constraints is solved by an efficient network
flow programming algorithm. An economic dispatch
considering the generator constraints can solved by using
Particle Swarm Optimization in[6,7]. In this method for
practical application of generator operations, a many
nonlinear characteristics of generator, such as ramp rate
limits, prohibited operating zone, and non-smooth cost
functions is considered. Static economic dispatch(SED) can
handle only a single load level at a certain time. However,
SED may fail to deal with the large variations of the load
demand due to the ramp rate limits of the generators,
moreover, it doesnothavethelook-aheadcapability[3,4].For
large variation in load demand and the dynamic nature of
the power systems, it necessary for development of optimal
dynamic dispatch (ODD) problem. ODD is a new update of
SED to determine the generation scheduling of the
committed units, so as to meet the load demand over a time
horizon at minimum operating cost under ramp rate and
other constraints. The dynamic dispatching was first
introduced in [8] and was followed by [9,10]. Inthesepaper,
optimal control dynamic dispatch (OCDD) formulation
models the power system generation by means of state
Equations, where the state variables aretheelectrical power
outputs of the generators and the control inputs are the
ramp rates of the generators. In OCDD the optimization is
done with respect to the ramp rates and the solution
produces an optimal output generator. In[11] the DED
problem the optimization is done with respect to the
dispatch able powers of the units. Some researchers have
considered the ramp rate constraints by solving SED
problem interval by interval and enforcing the ramp rate
constraints from one interval to the next. However, this
approach can lead to suboptimal solutions trajectory for a
given initial generation in the optimal dynamic dispatch
problem is to determine underwhatconstraintstheproblem
will be solved. Broadly, these constraints can be classified
into three kinds: equality constraints, inequalityconstraints,
and dynamic constraints. Some of these constraints such as
load demand balance, and spinning reserve constraints can
be modified when the DED problem is solved in the
deregulated market Environment. The dynamic economic
and emission dispatch is an extension of the conventional
economic dispatch problem [12]. It is used to determine the
optimal generation schedule of on-line generators.
A main aim of this paper is to developed short-term
generation scheduling also known as day ahead scheduling
for ten generating units. All equality and inequality

constrained is taken to obtained optimal short-term
generation scheduling. PSO techniques are used to make
optimal scheduling, due to its efficienttimecomputationand
required less parameter to developed algorithm.
2. PROBLEM FORMULATION
The objective function is to minimize operating cost are as
follows[13]:
where, FCij and SCij are operating cost(OC) of ith unit in jth
hour and start-up costs of ith unit in jth hour ,Pij its power
output. The Fuel cost as follows:
(1)
Where, a, b and c are cost coefficient. The start up cost
characteristic as follows:
(2)
Where, α is hot start up cost, β is cold start up cost and τ is
cooling time constant. Tij turn off time of ith unit in jth time
period.uij is status of unit ith in jth time period.
The following are the system constraints which are
considered in this problem formulation:
1) Real power balance constraint:
Where, Pij is ith generating unit in jth time period and PD is
power demand.
2) Real power operating limits of units are:
(4)
Where,Pi
min and Pi
max is minimum and maximum generating
power.
3) Unit minimum up/downtimeforthermal generatingunits
and is given as:
(5)
(6)
Where, Ton/TOFF is the unit turn on and turn off time.
4) Spinning reserve constraints:
(7)
Where, Xij is status of generating unit, Di is load demand of
ith unit and R is reserve of generating unit.
3. Overview of Particle Swarm Optimization
Particle swarm optimization wasintroducedbyDr.Eberhart
and Dr. kennedy[14].It is an evolutionary computation type
of new method and population based optimization tool like
GA.PSO is adopted from the naturebehaviorofsocial system
such as bird flocking and fish schooling. The PSO algorithm
requires less memory because ofitssimplicity.PSOissimilar
to the other evolutionary algorithms in that the system is
initialized with a population of random solutions called
particle. These particles flies over fitness function according
to its neighborhood experiences. It moves according to
update velocity vg
n+1 and positionupdatexg
n+1 tofindparticle
best values.
(8)
A position update equation represent as:
(9)
Here, w is the inertia weight parameter which controls the
global and local exploration of the particle. c1 and c2 are
acceleration coefficients respectively, and Rand() are
random numbers between 0 and 1. c1 pulls the particles
towards local best position, c2 pulls towards the global best
position. In particle swarm optimization, a particle velocity
Vmax determines the resolution. If Velocity is too high,
particles may fly past good solutions. If velocity is too small,
particles may not explore a local solutions. Thus, the system
parameters Vmax has the beneficial effect of the preventing
explosion and scales the exploration of the particle
search[15].Thus, inertia weight w provides a balance
between global exploitation and local explorations, which
requiring less number of iteration to find a sufficiently
optimal solution. Since, W indicates decreases linearly from
about 0.9 to 0.4 approx during a run, which determines
follows,
(10)
where, w is inertia weight constant of particle, an
exploration of search space is controlled by inertia constant
is given in[5]. wmax is maximum weight and wmin is minimum
weight.
A. Algorithm of particle swarm optimization for Scheduling
Step by Step procedure as follows:
Step-1: Initialization of the particles: For a populationsizeP,
the particles are randomly generated and located between
the maximum and the minimum operating limits of the
generators units.

Step-2: Define fitness function:a randomparticlesgenerated
start moving towards fitnees function according to define
velocity. It is define to minimize cost function.
Step-3:Initialization of Pbest and Gbest: The fitness values
obtained for the initial particles are set as the initial Pbest
values of the particle. The best value among all particle
called Gbest.
Step-4: update velocity using equation(8) to move particles
towards neighborhood best position.
Step-5:update position using equation (9) according to
update velocity .
Step-6:If the fitness value of each individual is better than
previous P-best, the current value is set to be P-best. If the
best P-best is better than G-best, the best P-best is set to be
G-best. The value of fitness function is to analyzes.
Step-7: If number of iteration reaches its maximum value
than stop iteration. Otherwise, repeat from step-2. Thus, at
the end Gbest obtain is considered as optimal value of
generating units.
4. Results and Discussion
A system of ten generating unit data are used to obtain
optimal scheduling using particle swarm optimization
technique. Unit data for 10 generating unit and loaddemand
over 24 time horizon in[16]. Unitcommitmentandeconomic
dispatch is main important task for preparing generation
scheduling. A system operator which plan an optimal
scheduling by considering both unit commitment and
economic dispatch problems. It is possible to ON all
generating unit over all time period, but it is not economical
to keep all unit ON. Thus, for obtaining best generation
scheduling it is essential to commit enough generating unit
for required load, are shown in table 1.
Table-1: unit commitment for ten generating unit
UNITS HOUR(1-24)
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
3 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0
4 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0
5 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0
6 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0
7 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0
8 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0
9 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
Unit ON and OFF status is indicated by 1 and 0 respectively.
The binary number 1 indicated that unit is available for
required time slots, while 0 indicates that unit is not
generate any power for particular time periods. Unit 1 and2
are consider as base load power plant, which is available at
all time and unit 9 and 10 are costly unit, so it is ON over a
peak time period at 12th hour respectively. These unit are
able to supply for dynamic load demand The dynamic load
demand over 24 time period is shown in fig(1) a different
load at each time intervals. A maximum load is 1500 MW
Fig(1) Load curves for different time periods
at 12th hour and minimum load is 700MW at 1st hour . A PSO
method is utilize for ten generatingunit,whichtakenvarious
parameter data: such as population size is 70, particle is 10
unit , wmax and wmin are 0.9 and 0.4 respectively, velocity is
10%, acceleration constant c1 and c2 are 2.0 and number of
iteration is 100. Operating cost oftengeneratingunitinclude
production cost and start up cost both followsquadraticcost
function and exponential function, which are utilizes by
satisfying all constraints for calculations.Implementingdata
of ten generating unit in PSO method and individually
analyzes results for all time period for differentloads.Result
of all unit and their operating cost is shown in table(2).

Table -2: result of different generating unit over a different time period and total operating cost
Hour
(hr)
p1
(MW)
p2
(MW)
p3
(MW)
p4
(MW)
p5
(MW)
p6
(MW)
p7
(MW)
p8
(MW)
p9
(MW)
p10
(MW)
Load
(MW)
Cost
($)
Start
up cost
($)
total
cost
($)
1 454.21 245.79 0 0 0 0 0 0 0 0 700 13674 0 13674
2 449.09 300.919 0 0 0 0 0 0 0 0 750 14541 0 14541
3 455 367.25 0 0 27.75 0 0 0 0 0 850 16790 1298 18088
4 442.59 385.59 0 0 121.82 0 0 0 0 0 950 18540 0 18540
5 455 381.64 0 130 33.36 0 0 0 0 0 1000 20001 807 20809
6 455 357.97 130 130 27.03 0 0 0 0 0 1100 22355 793 23148
7 455 455 94.33 120.67 25 0 0 0 0 0 1150 23171 0 23171
8 455 455 130 102.7 57.3 0 0 0 0 0 1200 24140 0 24140
9 440.28 418.2 120 130 88.52 80 25 0 0 0 1300 27200 768 27968
10 455 455 120.78 130 120 44 25 50.22 0 0 1400 29950 90 30040
11 455 455 130 130 119.55 80 25.45 55 0 0 1450 31449 0 31449
12 455 455 130 130 162 80 25.46 17.25 29 17 1500 33700 180 33880
13 455 455 120.78 130 120 44 25 50.22 0 0 1400 29950 0 29950
14 440.28 418.2 120 130 88.52 80 25 0 0 0 1300 27200 0 27200
15 455 455 130 102.7 57.3 0 0 0 0 0 1200 24140 0 24140
16 455 455 20.33 95 25.67 0 0 0 0 0 1050 21500 0 21500
17 455 381.64 0 130 33.36 0 0 0 0 0 1000 20001 0 20001
18 455 357.97 130 130 27.03 0 0 0 0 0 1100 22355 0 22355
19 455 455 130 102.7 57.3 0 0 0 0 0 1200 24140 0 24140
20 455 455 120.78 130 120 44 25 50.22 0 0 1400 29950 858 30808
21 440.28 418.2 120 130 88.52 80 25 0 0 0 1300 27200 0 27200
22 455 357.97 130 130 27.03 0 0 0 0 0 1100 22355 0 22355
23 455 410 0 0 35 0 0 0 0 0 900 17595 0 17595
24 454 346 0 0 0 0 0 0 0 0 800 15410 0 15410
557319 4794 562113

Result obtained by using approach method, it is found that
fuel cost for differenet generating unit and start up cost are
$ 5,57,319 and $ 4794 repectively. Total operating cost for
the generating unit is $ 5,62,113. A PSO convergence
characteristic shown in fig(2), which shown that PSO is able
Fig(2) convergence of PSO
to converge successfully at each iteration. Result of cost
obtained are compared with other techniques, which used
same data to obtain generation scheduling problems. PSO
result are verify with genetic algorithm[16], evolutionary
programming[17] and genetic algorithm based
lagrangian[18], shown in table-3.
Table-3: Comparison of PSO result with GA and GA-LR
A comparison shows effectiveness of this method, which is
roboust and efficient towards useful minimization of
operating cost and time required for computational is less.
5. CONCLUSION
This paper solved optimal scheduling problem along with
economic problem using PSO method. From experimental
result, total operating cost obtained is $ 5,62,113 and best
optimal generation for ten different unit is generated, which
is found better than result obtained by using other
techniques suchas GA ,EP and LR-GA. Thus, it was concluded
that this approach method isvery useful forsystemoperator
to obtained short-term scheduling along with economic
benefit forsatisfying dynamic load over 24 hourtimeperiod.
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Technique GA EP LR-GA PSO
Cost 5,65,825 5,65,352 5,64,800 5,62,113
Time 211 100 518 95

[14] James kennedy and rusel Eberhart , particle swarm
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BIOGRAPHIES
Nitish R. Patel
M.Tech, Research scholar,
Department of EE, SPCE,
Visnagar,Gujarat,India.
Nilesh K. Patel
Associate Professor,
Department of EE, SPCE,
Visnagar, Gujarat, India
2nd
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IRJET- Optimal Generation Scheduling for Thermal Units

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