An Improved Particle Swarm Optimization for Proficient Solving of Unit Commitment Problem

ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010

An Improved Particle Swarm Optimization for
Proficient Solving of Unit Commitment Problem
R.Lala Raja Singh1 and Dr.C.Christober Asir Rajan2
1
Research Scholar, Department of EEE, Sathyabama University, Chennai – 600 119
E-mail: lalrajasingh@yahoo.com
2
Associate Professor, Department of EEE, Pondicherry Engineering College, Pondicherry – 605 014
E-mail: asir_70@pec.edu

Abstract—This paper presents a new approach to solving the dispatch the generation optimally in the most economical
short-term unit commitment problem using an improved way [4].
Particle Swarm Optimization (IPSO). The objective of this Power system operators have to face the decision-making
paper is to find the generation scheduling such that the total problems extensively because of these difficulties. The
operating cost can be minimized, when subjected to a variety
of constraints. This also means that it is desirable to find the
scheduling of generators in a power system at any given
optimal generating unit commitment in the power system for time is one of the decision making problems. Running all
the next H hours. PSO, which happens to be a Global the units is not economical for a power system which is
Optimization technique for solving Unit Commitment required to satisfy the peak load during low load periods
Problem, operates on a system, which is designed to encode [5]. The main objective is to reduce the power generation
each unit’s operating schedule with regard to its minimum costs when meeting the hourly forecasted power demands.
up/down time. In this, the unit commitment schedule is coded UCP is the method of finding an optimal turn on and turn
as a string of symbols. An initial population of parent off schedule for a group of power generation units for each
solutions is generated at random. Here, each schedule is time window over a given time horizon [10]. The UCP is a
formed by committing all the units according to their initial
status (“flat start”). Here the parents are obtained from a pre-
vital area of research which concerns more attention from
defined set of solution’s i.e. each and every solution is adjusted the scientific community because of the fact that even
to meet the requirements. Then, a random decommitment is small savings in the operation costs for each hour can lead
carried out with respect to the unit’s minimum down times. A to the major overall economic savings [6]. In order to
thermal Power System in India demonstrates the effectiveness decide which of the available power plants should be
of the proposed approach; extensive studies have also been involved to supply the electricity, the best choice is the UC
performed for different power systems consist of 10, 26, 34 which is called as Unit Commitment [7]. UCP is an area of
generating units. Numerical results are shown comparing the production scheduling which is related to decide the
cost solutions and computation time obtained by using the ON/OFF status of the generating units during each interval
IPSO and other conventional methods like Dynamic
Programming (DP), Legrangian Relaxation (LR) in reaching
of the scheduling period. This is done in order to meet the
proper unit commitment. system load and reserve requirements and minimum cost
which are exposed to many types of equipment, system and
Index Terms—Unit Commitment, Particle Swarm environmental constraints [8]. The UC should
Optimization, Legrangian Relaxation, Dynamic Programming simultaneously reduce the cost of the system production
when it satisfies the load demand, spinning reverse, ramp
I. INTRODUCTION constraints and the operational constraints of the individual
unit [9].
In power stations, the investment is pretty costlier and
Some of the recent research works related to solving the
the resources in operating them are considerably becoming UCP is discussed as follows. A novel approach for solving
sparse of which focus turns on to optimizing the operating the short- term commitment problem using the genetic
cost of the power station [1]. The demand for the electricity
algorithm based tabu search method with cooling and
is varying in a daily and weekly cyclic manner and this banking constraints was proposed [2]. The main aim of his
creates a problem for the power system in deciding the best work is to find the generation scheduling so that the total
way to meet those varying demands [2]. The demand
operating cost can be reduced, when subjected to a variety
knowledge in the future is the main problem of the of constraints. A two- layer approach for solving the UCP
planning. With an accurate forecast, the basic operating in which the first layer utilizes a Genetic Algorithm to
functions like thermal and hydrothermal UC, economic
decide the onoff status of the units and second layer
dispatch, fuel scheduling and unit maintenance can be utilizes an Improved Lambda- Iteration technique to solve
performed efficiently [3]. The energy production cost the Economic Dispatch Problem was presented [11]. Their
varies considerably between all the energy sources approach satisfies all the plant and system constraints. UCP
available on a power system. Moreover it requires a tool in for four-unit Tuncbilek thermal plant which was in
order to balance the demand and generation and also to
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Kutahya region in Turkey, was solved [3] for an optimum fish schooling, and swarm theory to produce the best of the
schedule of generating units based on the load data characters among comprehensive old populations [17-20].
forecasted by using the conventional ANN (ANN) and an The basic PSO algorithm can be described as follows: Each
improved ANN model with Weighted Frequency Bin particle in the swarm represents a possible solution to the
Blocks (WFBB). They have used Fuzzy Logic (FL) existing optimization problem. During PSO iteration, every
method for solving the UCP. Three evolutionary particle accelerates independently in the direction of its
computation techniques, namely Steady-State Genetic own personal best solution which is found so far, as well as
Algorithms, Evolutionary Strategies and Differential the direction of the global best solution which is discovered
Evolution for the UCP have compared [12]. Their so far by the other particles. Therefore, if a particle finds a
comparison was based on a set of experiments conducted promising new solution, all other particles will move closer
on benchmark datasets as well as on real-world data to it, exploring the solution space more thoroughly [22].
obtained from the Turkish Interconnected Power System. Computation in PSO is based on a population (swarm) of
An algorithm which is used to solve security constrained processing elements called particles in which each particle
UCP with both operational and power flow constraints represent a candidate solution [18]. The PSO algorithm
(PFC) have been proposed [9] for planning a secure and depends on the social interaction between independent
economical hourly generation schedule. Their algorithm particles, during their search for the optimum solution [19].
introduces an efficient unit commitment (UC) approach PSOs are initialized with a population of random
with PFC which obtains the minimum system operating solutions and search for optima by updating generations
cost which satisfies both unit and network constraints when [21]. All particles have fitness values which are estimated
contingencies are included. by the fitness function to be optimized, and have velocities
Alternative strategies with the advantages of Genetic which direct the flying of particles [20]. The fitness
Algorithm for solving the Thermal UCP and in addition to function is evaluated for each particle in the swarm and is
these they have developed [8]. Parallel Structure to handle compared to the fitness of the best previous result for that
the infeasibility problem in a structured and improved particle and to the fitness of the best particle among all
Genetic Algorithm (GA) which provides an effective particles in the swarm [24]. The algorithm iterates by
search and therefore greater economy. A novel approach updating the velocities and positions of the particles, until
for solving the Multi- Area Commitment problem using an the stopping criteria is met [25]. The position (i.e. solution)
evolutionary programming technique has proposed [13]. of every individual particle will be attracted stochastically
Their technique was used to improve the speed and towards their related best positions (i.e. best solutions) in
reliability of the optimal search process. A dynamic multidimensional solution space [20]. The PSO algorithm
programming algorithm for solving the single-UCP (1- is becoming very popular due to its simplicity of
UCP) which efficiently solves the single-unit economic implementation and ability to quickly converge to a
dispatch (ED) problem with ramping constraints and reasonably good solution. Nowadays, PSO algorithm is
arbitrary convex cost functions have proposed [14]. The effectively applied in power system optimization, traffic
analytical and computational necessary & sufficient planning, engineering design and optimization, and
conditions to determine the feasible unit commitment states computer system etc [23].
with grid security constraints have presented [15]. The
optimal scheduling of hydropower plants in a hydrothermal III. PROBLEM FORMULATION
connected system has considered [16]. In their model they
have related the amount of generated hydropower to The main aim is to find the generation scheduling so that
the total operating cost can be reduced when it is exposed
nonlinear traffic levels and also have taken into account the
hydraulic losses, turbine- generator efficiencies as well as to a variety of constraints [26]. The overall objective
multiple 0-1 states associated with forbidden operation function of the UCP is given below,
T N
(Fit (Pit )U it + S itVit ) Rs
zones.
From the surveyed research works it can be understood FT = ∑ ∑ h
(1)
that solving the UCP gains high significance in the domain t =1 i =1
of power systems. Solving the UCP by a single Where
optimization algorithm is ineffective and time consuming. Uit ~ unit i status at hour t=1(if unit is ON)=0(if unit is
Hence, we are proposing a UCP solving approach based on OFF)
improved PSO which provides an effective scheduling with Vit ~ unit i start up / shut down status at hour t =1 if the unit
minimum cost. The proposed approach solves the UCP is started at hour t and 0 otherwise.
with less time consumption rather than the approaches FT ~ total operating cost over the schedule horizon (Rs/Hr)
solely based on a single optimization algorithm. Sit ~ start up cost of unit i at hour t (Rs)
For thermal and nuclear units, the most important
II. PARTICLE SWARM OPTIMIZATION component of the total operating cost is the power
production cost of the committed units. The quadratic form
PSO first introduced by Eberhart and Kennedy in 1995
for this is given as
which uses the natural animal’s behavior like bird flocking,
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Rt ~ spinning reserve at time t (MW)
Fit (Pit ) = Ai P 2 it + Bi Pit + Ci
Rs
(2) T ~ scheduled time horizon (24 hrs.)
h
Ai, Bi, Ci ~ the cost function parameters of unit i (Rs./MW2hr, Rs./MWhr, D. Thermal Constraints
Rs/hr)
The temperature and pressure of the thermal units vary
F it(P it ) ~ production cost of unit i at a time t (Rs/hr) very gradually and the units must be synchronized before
P it ~ output power from unit i at time t (MW) they are brought online. A time period of even 1 hour is
The startup value depends upon the downtime of the unit. considered as the minimum down time of the units. There
When the unit i is started from the cold state then the are certain factors, which govern the thermal constraints,
like minimum up time, minimum down time and crew
downtime of the unit can vary from a maximum value. If
constraints.
the unit i have been turned off recently, then the downtime
of the unit varies to a much smaller value. During the Minimum up time:
downtime periods, the startup cost calculation depends If the units have already been shut down, there will be a
upon the treatment method for the thermal unit. The startup minimum time before they can be restarted and the
cost Sit is a function of the downtime of unit i and it is constraint is given in (6).
given as
Toni ≥ Tupi (6)
⎡ ⎛ − Toff i ⎞⎤
S it = Soi ⎢1 − Di exp ⎜
⎜ Tdown ⎟⎥ + Ei Rs
⎟ (3) Where
⎢
⎣ ⎝ i ⎠⎥⎦ Toni ~ duration for which unit i is continuously ON (Hr)
Where Tup i ~ unit i minimum up time (Hr)
Soi ~ unit i cold start – up cost (Rs) Minimum down time:
If all the units are running already, they cannot be shut
Di, Ei ~ start – up cost coefficients for unit i
down simultaneously and the constraint is given in (7).
A. Constraints Toffi ≥ Tdown
i (7)
Depending on the nature of the power system under Where
study, the UCP is subject to many constraints, the main T down i ~ unit i minimum down time (Hr)
being the load balance constraints and the spinning reserve T off i ~ duration for which unit i is continuously OFF (Hr)
constraints. The other constraints include the thermal E. Must Run Units
constraints, fuel constraints, security constraints etc. [26] Generally in a power system, some of the units are given
B. Load Balance Constraints a must run status in order to provide voltage support for the
network.
The real power generated must be sufficient enough to
meet the load demand and must satisfy the following F. Ramping Constraints
factors given in (4). If the ramping constraints are included, the quality of the
N solution will be improved but the inclusion of ramp-rate
∑P U
i =1
it it = PDt (4) limits can significantly enlarge the state space of
production simulation and thus increase its computational
Where requirements. And it results in significantly more states to
PD t ~ system peak demand at hour t (MW) be evolved and more strategies to be saved. Hence the CPU
N ~ number of available generating units time will be increased.
U(0,1) ~ the uniform distribution with parameters 0 and 1 When ramp-rate limits are ignored, the number of
UD(a,b) ~ the discrete uniform distribution with parameters generators consecutive online/offline hours at hour t,
a and b provides adequate state description for making its
commitment decision at hour (t+1). When ramp-rate limits
C. Spinning Reserve Constraints are modeled, the state description becomes inadequate. An
The spinning reserve is the total amount of real power additional status, generators energy generation capacity at
generation available from all synchronized units minus the hour t is also required for making its commitment decision
present load plus the losses. It must be sufficient enough to at hour (t+1). These additional descriptions add one more
meet the loss of the most heavily loaded unit in the system. dimension to the state space, and thus significantly increase
This has to satisfy the equation given in (5). the computational requirements. Therefore, we have not
included in this algorithm.
N

∑P max U
i =1
i it >= (PDt + Rt );1 ≤ t ≤ T (5)
IV. IMPROVED PSO ALGORITHM FOR SOLVING UCP
Where The proposed IPSO Algorithm is to determine the units
Pmaxi ~ Maximum generation limit of unit i and their generation schedule for a particular demand with
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minimum cost. In this manner, with the assistance of PSO algorithm. In parallel, random velocities are also generated
we determine the same for different possible demands. The for the corresponding particles as follows
problem is divided into two stages; one is for determining
the minimum cost for a particular demand and another is [
vi = v1i ) , v2i ) , L , v ni )
( ( (
] (11)
for determining the minimum cost for unit commitment In equation (14), the velocities for each particle element are
during all the periods. But the demand varies during all the randomly generated within the maximum and minimum
periods. Hence, different possible demands are need to be limit and so the each element of the velocity vector vi
generated which can be performed by the IPSO algorithm.
PSO is used to determine the optimal generation schedule satisfies v min ≤ vi ( j ) ≤ v max . After determining the
for a particular demand. The steps of the algorithms which
is used for our approach is demonstrated in the “Fig. 1”. initial particles and their corresponding velocities, the
particles are evaluated by the evaluation function which is
As depicted in “Fig. 1”, for a power demand of Pd , given by
initially, a population of random individuals is taken. The n
Rs
random individuals include random particles and their min ∑ ( Fit ( Pit )U it + SitVit ) (12)
velocities. Hereby, a logical algorithm is utilized to i =1 h
generate the initial random solutions of particles which can
be discussed as follows
1. Generate an arbitrary integer r which satisfies the
condition r ≤ n .
th
2. For the r unit, generate a random integer
indicating the power generated by the unit which
should essentially satisfy the condition
Pg(min) ≤ Pg r ≤ Pg(max)
r r

3. The remaining power to be generated i.e.
Pd − Pg r is subjected for the following decision,
⎧ Pd − Pg r ; if Pd − Pg r < Pth
⎪
Pd = ⎨ Pd − Pg (8)
⎪
r
; else
⎩ 2
4. Allot Pd to the next unit to generate (now, let the
next unit as r ) whose maximum limit of power
generation is greater than the remaining free units.
The allotment of Pd to the unit is based on the
following condition Figure 1. Steps involved in PSO to determine the optimal generation
schedule
⎧ Pd ; if P ≤ Pd ≤ P
(min)
gr
(max)
gr
⎪ (min)
⎪
Based on the evaluation function given in equation (15),
Pg r = ⎨ Pg r ; if Pd < Pg(min)
r
(9) pbest and g best for the initial particles are determined.
⎪ (max) Then new velocities are determined as
⎪ Pg r
⎩ ; if Pd > Pg(max)
r
vinew( j) = w* vicnt ( j) + c1 * a1 *
5. Determine Pd − Pg r . If Pd − Pg r < 0 , go to step (13)
[ pbesti ( j) − Pi cnt ( j)] + c2 * a2 *[gbest ( j) − Pi cnt ( j)]
1; If Pd − Pg r > 0 , go to step 3; If Pd − Pg r = 0 ,
then terminate the criteria. where, 1 ≤ i ≤ l , 1 ≤ j ≤ n , vicnt ( j ) stands for current
By the above mentioned algorithm, a vector is obtained
which represents the amount of power to be generated by velocity of the particle,vinew ( j ) stands for new velocity
each unit. Hence, some different possible vectors are of a particular parameter of a particle, a1 and a 2 are
generated by repeating the algorithm and it can be given as
[
Pi = Pg i ) , Pg i ) , L, Pg i )
(
1
(
2
(
n
] (10)
arbitrary numbers in the interval [0,1] , c1 and c 2 are
acceleration constants (often chosen as 2.0) and w is the
Equation (13) represents the initial particles that are
inertia weight that is given as
satisfying the constraints given in equation (4) and (5) are
generated as random initial solutions for the PSO
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w − wmin Table I
w = wmax − max ×I (14) Operation Data Of Seven Units Utility System
I max
where, wmax and wmin are the maximum and minimum
inertia weight factors respectively which are chosen
randomly in the interval [0,1] , I is the current number of
iteration and I max is the maximum number of iterations.
The velocity of such newly attained particle should be
within the limits. Before proceeding further, this would be
checked and corrected.
⎧v max ( j )
⎪ ; vinew ( j ) > v max ( j ) Table II
vinew ( j ) =⎨ (15) Daily Generation of 10,26,34 Unit System
⎪v min ( j )
⎩ ; vinew ( j ) < v min ( j )
Depend upon the newly obtained velocity vector, the
particles are updated and obtained as new particles as
follows
Pinew ( j ) = Pinew ( j ) + vinew ( j ) (16)
Then the parameter of each particle is checked whether it
is ahead the lower and upper bound limits. The minimum
and maximum generation limit of each unit is referred by
the lower and upper bound values respectively. If the new
particle infringes the minimum and maximum generation
limit, then a decision making process is performed as
follows
⎧P (max) ; if P new ( j ) > P (max)
⎪ gi gi gi
Pi new
( j) = ⎨ (17)
(min) (min)
⎪Pgi ; if Pg ( j ) < Pg
new
⎩ i i
The newly obtained particles are evaluated as mentioned
earlier and so pbest for the new particles are determined.
With the concern of pbest and the g best , new g best is
determined. Again by generating new particles, the same
process is repeated until the process reaches the maximum The simulated demand set, corresponding generation
iteration I max . Once the iteration reaches the I max , the schedule, the minimum operating cost and the
process is terminated and so that a generation schedule of computational time for the utility system is given in the
all the units with minimum cost is obtained which will Table III. The status of unit i at time t and the start-up /
meet the demand at the particular period. In the similar shut - down status obtained are the necessary solutions and
fashion, the optimum generating schedule for all the are obtained for DP, LR, PSO, IPSO methods for utility
possible demand set is determined. So, a complete training system.
set which includes the various possible demands and the Table III
corresponding optimum generation schedule is generated. Optimal Generation Schedule For Utility System Satisfying 24 Hour
Demand Along With Its Total Operating Cost
V. RESULTS AND DISCUSSION
The proposed intelligence technique for UCP which is
based on the IPSO has been implemented in the working
platform of MATLAB (version 7.8). We have considered
an Indian thermal power system with seven unit’s utility
system for a time span of 24 hours for evaluating the
performance of the proposed technique. The operation data
for the system is given in the Table I. The daily load data of
10, 26, 34 unit systems are shown in Table II.
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reduced. After a certain number of iterations, the cost
remains constant for all the remaining iterations, which
means that there no more generation schedule is available
with cost which lesser than the previous cost. For the
evaluation of performance, we have solved the UCP by
IPSO only and thus we have compared the total production
cost and computational time taken by the proposed
approach and by the PSO to solve the problem and found
that it was reduced for the IPSO method for all the systems.

CONCLUSION
The proposed approach IPSO has performed well in
solving the UCP by recognizing the optimal generation
schedule. The approach has been tested for the seven unit’s
utility system with the consideration of load balance and
spinning reserve constraints, which are the most significant
constraints. Prior to test the system, we have trained the
Figure 3. The normalized cost for an optimal generation schedule versus network by different possible combinations of the demand
the number of iterations of the PSO operation set and its corresponding optimal schedule using the BP
The comparison of the total costs and Central Processing algorithm.
unit (CPU) time is shown in Table IV for utility system, 10, For the test demand set which consists of demand for 24
26, and 34 generating unit power systems. The demand for periods, the hybrid approach effectively yields optimal
24 hour time horizon is just simulated and it is not the generation schedule for the periods. In comparison with the
actual demand which is practically satisfying by the units. results produced by the referenced techniques (DP, LR,
An optimal generation schedule for each period and the PSO), the IPSO method obviously displays a satisfactory
total operating cost for the whole 24 periods are obtained. performance. There is no obvious limitation on the size of
The IPSO algorithm contributes in determining the optimal the problem that must be addressed, for its data structure is
generation schedule for a particular demand. The such that the search space is reduced to a minimum; No
performance of PSO for a particular demand is depicted in relaxation of constraints is required; instead, populations of
the “Fig. 3”. feasible solutions are produced at each generation and
throughout the process.
Table IV
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