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ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011



       Profit based unit commitment for GENCOs using
              Parallel PSO in a distributed cluster
                                       C.Christopher Columbus* and Sishaj P Simon
          National Institute of Technology/Electrical and Electronics Engineering, Tiruchirapalli, Tamil Nadu, India
                                    Email: christoccc@gmail.com, sishajpsimon@nitt.edu


Abstract— In the deregulated electricity market, each                   The basic idea of LR is to relax the UCP constraints into a
generating company has to maximize its own profit by                    small sub-problem, which is much easier to solve, and then
committing suitable generation schedule termed as profit                coordinated by a master problem via properly adjusting a
based unit commitment (PBUC). This article proposes a                   factor called Lagrangian multiplier. For all that, it has proven
Parallel Particle Swarm Optimization (PPSO) solution to the
                                                                        to be a very difficult task that may come sometime from oscil-
PBUC problem. This method has better convergence
characteristics in obtaining optimum solution. The proposed             lation of their solution by slight change of the multiplier. In
approach uses a cluster of computers performing parallel                order to overcome these complex mathematical problems, there
operations in a distributed environment for obtaining the               are other method of computational methodology, which is
PBUC solution. The time complexity and the solution quality             shared by popular artificial intelligence such as genetic algo-
with respect to the number of processors in the cluster are             rithm and evolutionary programming.
thoroughly tested. The method has been applied to 10 unit                   Charles W. Richter et.al presented a PBUC problem
system and the results show that the proposed PPSO in a                 formulation using genetic algorithm (GA) which considers
distributed cluster constantly outperforms the other methods            the softer demand constraints and allocates fixed and
which are available in the literature.
                                                                        transitional costs to the scheduled hours [6]. Pathom
Index Terms—deregulated market, profit based unit                       Attaviriyanupap et.al proposed a method that helps GENCO
commitment, particle swarm optimization, distributed                    to make a decision on how much power and reserve that
environment, parallel processing, parallel particle swarm               should be sold in markets, and how to schedule generators
optimization.                                                           in order to receive the maximum profit [7]. Here the authors
                                                                        have considered both power and reserve generation at the
                       I. INTRODUCTION                                  same time. In [8], H.Y. Yamin et.al proposed an auxiliary hybrid
                                                                        model using LR and GA to solve UCP. GA is used to update
     The GENCOs objective is to maximize the profit and to
                                                                        the Lagrangian multiplier also presented their view on the
place proper bid in the market. In order to do this generation
                                                                        profit based unit commitment in day- ahead electricity markets
companies need to determine the schedule and operating
                                                                        considering the reserve uncertainty [9].
points based on the load and price forecasted. The traditional
                                                                            The optimization method known as particle swarm
unit commitment problem objective is minimizing the cost of
                                                                        optimization (PSO) algorithm developed by Eberhart and
operation subject to fulfillment of demand. However in a
                                                                        Kennedy is successfully applied to solve nonlinear
deregulated environment the traditional unit commitment
                                                                        optimization problems. Therefore an attempt is made to solve
objective needs to be changed to maximize the profit with
                                                                        the PBUC problem using this algorithm. The swarm-based
relaxation of the demand fulfillment constraint. This unit
                                                                        algorithm described in this paper is a search algorithm capable
commitment is referred to as profit based unit commitment.
                                                                        of locating optimal solutions efficiently.
[1].
                                                                            The proposed method is applied to solve PBUC problem
     A competitive and deregulated framework is replacing
                                                                        with ten-unit and hundred-unit-test systems. The performance
traditional and centralized regulation in many electric power
                                                                        of the PPSO algorithm in terms of solution quality is compared
systems around the world. With the promotion of deregulation
                                                                        with that of other algorithms reported in literature for the
of electric power systems, operation, planning and control
                                                                        above mentioned problem in power system operation.
aspects in traditional power system need to be changed [2-
                                                                        Likewise, simulation results demonstrate the feasibility and
3]. In this new paradigm, the signal that would enforce a
                                                                        effectiveness of the proposed method, as compared with the
unit’s on/off status would be the price, including the fuel
                                                                        results available in the literature.
purchase price, energy sale price, ancillary service sale price,
and so on. There are many solution techniques such as
                                                                                          II. PROBLEM FORMULATION
integer programming; dynamic programming, Lagrangian
relaxation and genetic algorithms are available to solve the                The objective of the PBUC problem is to obtain the optimal
PBUC problem [4-6]. Researchers also presented a review on              unit commitment schedule thereby maximizing GENCOs profit.
deterministic, meta-heuristic and hybrid approaches of                  The problem formulation is given as follows:
generation scheduling in both regulated and deregulated                 Maximize PF  RV  TC                                      (1)
power markets [7].                                                        or
  *Corresponding author
© 2011 ACEEE                                                       24
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ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011


  Minimize                             TC  R V          (2)                                                                 III. PARLLEL CLUSTERING ENVIRONMENT
where PF is the total profit ($), RV is the total revenue ($)                                                        In clusters, powerful low cost workstations and/or PCs
and TC is the total cost ($).                                                                                    are linked through fast communication interfaces to achieve
Here,                                                                                                            high performance parallel computing. Workstation clusters
                 T       N
                                                                                                                 have become an increasingly popular alternative to traditional
  TC              [C                i   ( P( i ,t ) I ( i ,t ) )  ST t ]                          (3)        parallel supercomputers for many workloads requiring high
                 t 1 i 1                                                                                       performance computing. The use of parallel computing for
           T      N                                                                                              scientific simulations has increased tremendously in the last
RV    [( g (t )P(i,t ) I (i,t) )]                                                                 (4)        ten years, and parallel implementations of scientific simulation
           t 1 i 1                                                                                             codes are now in widespread use [10, 11]. There are two
                                                                                                                 dominant parallel hardware/software architectures in use
where C i is the production cost which is calculated by using                                                    today are Distributed memory, and Shared memory. In shared
the equation (10). P( i ,t ) is the power level of i th generator                                                memory systems, parallel processing occurs through the use
                                                                                                                 of shared data structures, or through emulation of message
unit at t th hour (MW), I (i , t ) is the commitment state of i th unit                                          passing semantics in software. Distributed memory systems
                                                                                                                 are composed of a number of interconnected computational
at t th hour, STt is the startup cost ($), t is the index for time,                                              nodes, which do not share memory, but can communicate
T is the dispatch period in hours, i is the index for generator                                                  with each other through a high-performance ether net switch
                                                                                                                 (HPES) as shown in Figure 1. Parallelism is achieved on
unit, N is the total number of generating units and  g (t ) is
                                                                                                                 distributed memory systems with multiple copies of the
the forecasted market price for energy at time t.                                                                parallel program running on different nodes, sending
     Ci ( P( i ,t ) )  a  b * P( i ,t )  c * P( 2,t )                                              (5)        messages to each other to coordinate computations. The
                                                   i
                                                                                                                 cluster should perform as a parallel computing resource,
where a , b and c are the fuel cost co-efficients.                                                               achieving higher performance than possible using
System Constraints                                                                                               workstations configured in a more standard way. The nodes
Demand constraints                                                                                               in the cluster are always used in groups, not individually as
           N                                                                                                     in a general purpose workstation laboratory.
       P  i1
                         I
                  ( i , t ) (i , t )    Dt              t  1.....T                                  (6)        Speedup factor and efficiency:
                                                                                                                    To evaluate the parallel performance of the PPSO
where Dt is the total system demand at time t.
                                                                                                                 algorithm, the speedup factor SWh and efficiency EWh of the
Here, demand and reserve constraints are different from                                                          cluster [12-13] is calculated as follows;
traditional UC problem because GENCO can now select to
produce demand and reserve less than forecasted level if it                                                                  SWh  Wt Wht                                        (10)
creates more profit.                                                                                                       EW h  SW h W h                              (11)
 Unit constraints
                                                                                                                 where Wt and Wht are the execution time of single processor
1. Unit power limit
                                                                                                                 and cluster respectively.
     Pi,min  P(i,t) I (i,t )  Pi,max                                                                (7)

where Pi , min is the minimum power output of i th generator

unit (MW) and Pi , max is the maximum power output of
generator unit (MW).
2. Minimum Up and Down time constraints
     on                                      on
[X         ( i , t  1)  T                       ( i )] * [ I ( i , t  1 )  I ( i , t ) ]  0      (8)
     off                                       off
[X          ( i , t  1)  T                         ( i )] * [ I ( i , t )  I ( i , t  1 ) ]  0   (9)
where Xon(i,t) is the “On” duration of i th generator unit till
time t, Xoff (i, t) is the “Off” duration of i th generator unit till
time t, T on (i) is the minimum up-time of i th generator unit
and T off (i) is the minimum down-time of i th generator unit.



                                                                                                                      Figure 1. Distributed cluster of workstations (20 Nodes)
© 2011 ACEEE                                                                                                25
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ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011


         III. PARTICLE SWARM OPTIMIZATION ALGORITHM                                  x, if particles divisible by Wh
                                                                                    
                                                                              PSP   x  1 for the first hx slaves and
    Particle Swarm Optimization (PSO) is an optimization                            
                                                                                                                                           (14)
                                                                                                      x for the remaining , Otherwise
technique inspired from bird flocking which is developed by
Dr Eberhart and Dr. Kennedy way back in the year 1995 [14].                   where
It is a population based algorithm where each individual                      x  floor ( N Particles / Wh )                               (15)
(particle) in the population is a potential solution, flies in the
                                                                               hx  N Particles  ( x * Wh )                                (16)
D dimensional problem space with a velocity which is
dynamically adjusted according to the flying experiences of                   Master node allocate (x+1) particles to the first hx slaves in
its own and its colleagues.                                                   the Wh cluster (W1 ...Whx ....Wh ) and x ants to the remaining
                                                                              slaves (Whx+1 ....Wh ) . Where NParticles=population.
A) Standard PSO algorithm
   Suppose that the search space is D-dimensional and m
particles form the colony. The ith particle represents a D
dimensional vector Xi (i=1, 2… m). It means that the ith particle
positions at X i  ( xi 1 , xi 2 ,......., xiD ) (i=1, 2… m) in the
searching space. The position of each particle is a potential
result. The calculation of the particle’s fitness is carried out
by putting its position value into a designated objective
function. When the fitness is higher, the corresponding Xi is
“better”. The ith particle’s “flying” velocity is also a D-
dimensional vector, denoted as Vi  (vi 1 , vi 2 ,......., v i D )
Denote the best position of the i th particle as
Pi  ( pi1 , pi 2 ,....., piD ) and the best position of the
colony as Pg  ( p g1 , p g 2 ,......., p gD ) respectively. The
PSO algorithm can be performed by the following equations
(12, 13).
Vid (k1) Vid (k)c1r1 (P (k)- xid (k))c2r2 (Pgd (k)- xid (k)
                          id                                      (12)
    xid (k  1)  xid (k )  vid (k  1)                     (13)
Where k represents the iterative number,
c1, c2 are learning factors. Usually c1= c2=2, r1, r2 are random
numbers between (0, 1).The termination criterion for the
iterations are determined according to whether the max
generation or a designated value of the fitness of Pg is reached
B) Parallel PSO algorithm
    PPSO algorithm is implemented to determine the
commitment status of each unit over a scheduled period of
(24 hours) time in order to maximize the profit. The procedure
of the proposed algorithm to solve PBUCP is as follows.
Step 1: Generator and PSO Parameters Specification
    Specify the generator minimum and maximum generation
limits, minimum up and down time constraints and start up
cost of each unit. Specify the PPSO parameters such as
population size (M), inertia weight factor (w), dimension of
the system (D), acceleration constants (c1 and c2), velocity
maximum and minimum limits, maximum iterations (Max iter).
Set iteration number iter=1 and time t=1.                                                     Figure 2. Flowchart of PPSO for PBUC
Step 2: Particles sharing policy                                              Step 3: Initialization of Individual in the swarm
    Master node decides the sharing of particles by particles                 The initial solution of each individual Uj=[un1 un2 … unT], (j=1,
sharing policy (PSP).Therefore the number of particles                        2, …,M), (n=1, 2, ….., N)) for complete M population is
allocated in a slave processors or workers is given by                        generated randomly. The position of each unit unt of each
                                                                              particle is generated using uniformly distributed random
© 2011 ACEEE                                                             26
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ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011


function, which generates either 0 or 1. Similarly the initial           is found to be more than the maximum total profit computed
velocity of each particle is generated randomly using                    so far, then the present global best is memorized, or else the
uniformly distributed random function, which generates a                 previous maximum total profit solution is retained as global
real value between Vmin and Vmax. The representation of each             best. The new global best is sent to the workers and the
individual for ‘N’ number of generating units for a scheduled            workers saved the received global best as their global best.
period of time is as follows:                                            Step 8: Memorize the best solution obtained so far and
                                                                         increment iteration number. Stop the process if iteration
                                                                         number is equal to the maximum number of cycles. Otherwise
      u 11           u 12        .   .    u1N                          go to step 4.
     u               u 22        .   .    u2N                          Step 9: Increment the time and repeat step 3 to step 8 for the
      21                                                               given scheduled period (24 hours) of time.
  U  .                .         .   .      .    
                                                             (17)
                                                                         The flowchart of the proposed method is shown in the Figure
                                                                       2.
      .                .         .   .      .    
     u T 1
                     uT 2        .   .    u TN   
                                                                                            IV. NUMERICAL RESULTS
                                                                             The PABC method for PBUC is first tested on 10 unit
Step 4: Defining the evaluation function                                 system available in the literature as Case 1. It is also validated
    The merit of each individual particle in the swarm is found          on multiple test systems of 100 units in Case 2. The parallel
using a fitness function called evaluation function.        Each         computation is carried out in the MATLAB® environment of
particle in the population is evaluated using the objective              R2007b using distributing computing toolbox. The parallel
function given by (1).                                                   computation is carried out through distributed memory
Step 5: Repair Minimum up and down time constraints                      environment. In a distributed environment, a cluster with the
violation                                                                maximum size of 20 nodes/processors (Pentium - IV 3.40 GHz,
    Repair each unit for each particle in the swarm for minimum          1GB RAM) is used.
up and down time constraints violation.                                  A. Case 1: 10 Unit System
Step 6: Modifying best particle position (Pbest)
    To modify the position of each individual in the next stage              In order to participate in the market, GENCOs have to
is obtained from equation (12).                                          prepare a self commitment according to the forecasted load
The weighting function is defined as follows                             and price. In this case, the commitment schedule is prepared
                                                                         to maximize the GENCOs’ profit by calculating the generator
               w  wmin                                                coefficients with the satisfaction of constraints. Here the profit
   w  wmax   max
               iter               iter
                                                            (18)
                   max                                                 of the company gets the first priority and the demand
Where,                                                                   satisfaction is not mandatory. So, GENCOs will make the self
                                                                         commitment depending upon the forecasted price to get
 wmax , wmin      - Initial, final weights
                                                                         surplus profit. The test system consists of 10 generating
 itermax             - Maximum iteration number                          units. Here the generating unit data and load data are taken
                                                                         from [15]. The constraints included for PBUC in [15] are
 iter            - Current iteration number                              considered. Based on the forecasted market price of energy
To control excessive roaming of particles, velocity is restricted        information, the proposed PPSO model is used to generate
between - V max and  V max .                                            dispatch schedule for 24 hours time horizon. The dispatch
The maximum velocity limit for the jth generating unit is                schedule of ten unit system is given in TABLE I. Optimal
computed as follows:                                                     parameters obtained by trial and error for PPSO is as follows:
                                                                         Population size=200, Acceleration coefficients, c1=0.2, c2=0.2,
                Pj max  Pj min
      V max                                                 (19)        Inertia weight: W max=0.9, W min=0.2 and Maximum
                      R
                                                                         iteration=300.
The particle position vector is updated using equation (13).                 The comparison of the proposed method with other
The values of the evaluation function are calculated for the             existing methods given in TABLE II proves that PPSO gives
updated positions of the particles. Evaluate each particle using         better solution, i.e. a difference in profit of $1260.23 is
object function. Compare each particle evolution value with              achieved when compared to Muller method [15]. The time
its own best position (Pbest or BS). If the present particle             taken to get the best schedule is 168 sec. The PPSO yields a
position is better than the old value set new particle position          higher profit of 1.2 % than the Muller method. Figure 3 shows
as Pbest, otherwise retain old value.                                    the execution time achieved by the different cluster sizes.
Step 7: Computation of global best
                                                                         The execution time will reduce, when the cluster size
    Master receives the information of local best solutions
                                                                         increases. TABLE III shows the speedup factor and efficiency
(BSI, BS2,…..,BSh) from the workers and computes the best
                                                                         achieved by different sizes of cluster. When the cluster size
solution among them as the global best. Whenever a global                increases the speedup factor also increases. i.e., performance
best solution is selected by the master, and if the total profit         of the cluster will increase, when its size increases.
© 2011 ACEEE                                                        27
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ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011

                                                     TABLE I. D ISPATCH SCHEDULE FOR 10    UNIT SYSTEM




        TABLE II . COMPARISON OF PBUC SOLUTIONS (10 UNIT SYSTEM)                    B. Case 2: 100 Unit Syatem
                                                                                        This test system consists of multiple generating units
                                                                                    such as 100 generating units. More number of generating
                                                                                    units is considered in order to validate the feasibility of the
                                                                                    application of PPSO for large scale power system. The data
                                                                                    for different groups of generating units are obtained by
                                                                                    duplicating the 10 unit system data. The demand is multiplied
                                                                                    with respect to the system size; however the generating limits,
                                                                                    the minimum up/down time constraints remain the same.
                                                                                    Based on the forecast market price of energy information, the
                                                                                    proposed PPSO model is used to generate dispatch schedule
                                                                                    for 24 hours time horizon. The parameter setting of the 10
                                                                                    unit system is extended for the multiple test systems.




        Figure 3.   Execution time chart for 10 unit system

TABLE III. COMPARISION OF   SPEEDUP FACTOR AND CLUSTER EFFICIENCY   (10 UNIT
                                 SYSTEM)
                                                                                           Figure 4.     Execution time chart for 100 unit system




© 2011 ACEEE                                                                   28
DOI: 01.IJEPE.02.03.512
ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011

                                                    TABLE   IV.   COMMITMENT STATUS FOR 100 UNIT SYSTEM




TABLE V. C OMPARISION OF   SPEEDUP FACTOR AND CLUSTER EFFICIENCY   (100 UNIT        and efficiency achieved by different sizes of cluster. When
                                 SYSTEM)
                                                                                    the cluster size increases the speedup factor also increases.
                                                                                    i.e., performance of the cluster will increase, when its size
                                                                                    increases. When a single processor is used, it consumes
                                                                                    more time for execution, i.e., 1728.01 sec for 100 units. The
                                                                                    execution time for the 20 node cluster of 100 units are around
                                                                                    156.38 sec. It clearly shows the execution time decreases as
The Commitment status of 100 unit system is given in TABLE                          the number of processor increases. Each test system has
IV. Figure 4 shows the execution time achieved by the differ-                       been tested for 30 trial runs and the best results are pre-
ent cluster sizes. The execution time will reduce, when the                         sented.
cluster size increases. TABLE V shows the speedup factor
© 2011 ACEEE                                                                   29
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ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011


                        V. CONCLUSIONS                                    [11] Weiwei Lin, Changgeng Guo, Deyu Qi, Yuchong Chen and
                                                                          Zhang Zhili, “Implementations of grid-based distributed parallel
   This paper proposes a MPI based PPSO model for PBUC,                   computing”, First International Multi-Symposiums on Computer
computing in parallel, in a distributed environment. The                  and Computational Sciences, pp. 312-317, 2006.
approach is simple, efficient, and economic and can be                    [12] H. T. Kumm and R. M. Lea, “Parallel computing efficiency:
extended for making smarter decisions in a large scale power              climbing the learning curve”, TENCON’94, pp. 728-738, 1994.
system. Simulation results obtained from the cluster                      [13] X.-H. Sun, L.M. Ni, “Scalable problems and memory-bounded
demonstrate the accuracy of the proposed algorithm and its                speedup”, Journal of Parallel and Distributed Computing, vol. 19,
capability of greatly reducing the execution time.                        no. 1, pp. 27–37, 1993.
                                                                          [14] J. Kennedy and R. C. Eberhart, “Particle swarm optimization,”
                                                                          IEEE international Conference on Neural Networks, vol. 4,
                          REFERENCES                                      pp.1942-1948, 1995.
[1] Eric H. Allen and Marija D. Ilic, “Reserve markets for power          [15] Chandram K, Subrahmanyam N, Sydulu M, “New approach
systems reliability”, IEEE Trans. on Power Systems, vol. 15 no 2,         with Muller method for profit based unit commitment”, Power
pp. 228-233, 2000.                                                        and Energy Society General Meeting - Conversion and Delivery of
[2] M. Shahidehpour and M. Mawali, Maintenance scheduling in              Electrical Energy in the 21st Century, pp. 1-8, 2008.
restructured power systems, Nowell, MA Kluwer, 2000.                      [16] Victoire T. A. A, Jeyakumar A. E, “Unit commitment by a
[3] G.B. Sheble and G.N. Fahd, “Unit commitment literature                tabu-search-based hybrid-optimization technique”, IEE Proc.
synopsis”, IEEE Trans. on Power Systems, vol. 9, pp. 128-135,             Gener. Transm. Distrib., vol. 152, pp. 563-570, 2005.
1994.
[4] Narayana Prasad Padhy, “Unit commitment - A bibliographical                                 AUTHORS    BIOGRAPHY
survey”, IEEE Trans. on Power Systems, vol. 19, no. 2, pp. 1196-
1205, 2004.                                                               C. Christopher Columbus was born in India and received his
[5] Narayana Prasad Padhy, “Unit commitment problem under                 Bachelors of Engineering (Electrical and Electronics Engineering) in
deregulated environment- a review”, Power Engineering Society             M. S University, Tirunelveli and Masters of Engineering (Computer
General Meeting, 2, pp. 1088-1094, 2003.                                  Science and Engineering) at Anna University, Chennai, India in the
[6] Charles W. Richter and Gerald B. Sheble, “A Profit based Unit         years 1998 and 2005 respectively. He is currently pursuing his
Commitment GA for Competitive Environment”, IEEE Trans. on                research degree in the Department of Electrical and Electronics
Power Systems, vol. 15, no. 2, pp. 715-721, 2000.                         Engineering, National Institute of Technology, Tiruchirappalli,
[7] Pathom Attaviriyanupap, Hiroyuki Kita, Eiichi Tanka and               Tamil Nadu, India. His research interest includes Deregulation of
Jun Hasegawa, “A hybrid LR-EP for solving new profit –based UC            Power system and Parallel computing applications in Power
problem under competitive environment”, IEEE Transaction on               Systems.
Power Systems, vol.18, no. 1, pp. 229-237, 2003.
[8] H.Y. Yamin and S.M. Shahidehpour, “Unit commitment using              Sishaj Pulikottil Simon was born in India and received his
a hybrid model between Lagrangian relaxation and genetic algorithm        Bachelors of Engineering (Electrical and Electronics Engineering)
in competitive electricity markets”, Electric Power Systems               and Masters of Engineering (Applied Electronics) at Bharathiar
Research, vol. 68, pp. (83-92, 2004.                                      University, Coimbatore, India in the years 1999 and 2001
[9] I. Jacob Raglend, C. Raghuveer, G. Rakesh Avinash, N.P. Padhy         respectively. He obtained his Ph.D., (Power System Engineering)
and D.P. Kothari, “Solution to profit based unit commitment               at Indian Institute of Technology (IIT), Roorkee, India in 2006.
problem using particle swarm optimization”, Applied soft                  Currently, he is an Assistant professor in the Department of
computing, vol. 10, pp. 1247-1256, 2010.                                  Electrical and Electronics Engineering at National Institute of
[10] Dingju Zhu and Jianping Fan, “Application of parallel                Technology (NIT), Tiruchirappalli, Tamil Nadu, India.
computing in digital city”, The 10th IEEE International Conference
on High Performance Computing and Communications, pp. 845-
848, 2008.




© 2011 ACEEE                                                         30
DOI: 01.IJEPE.02.03.512

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Profit based unit commitment for GENCOs using Parallel PSO in a distributed cluster

  • 1. ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011 Profit based unit commitment for GENCOs using Parallel PSO in a distributed cluster C.Christopher Columbus* and Sishaj P Simon National Institute of Technology/Electrical and Electronics Engineering, Tiruchirapalli, Tamil Nadu, India Email: christoccc@gmail.com, sishajpsimon@nitt.edu Abstract— In the deregulated electricity market, each The basic idea of LR is to relax the UCP constraints into a generating company has to maximize its own profit by small sub-problem, which is much easier to solve, and then committing suitable generation schedule termed as profit coordinated by a master problem via properly adjusting a based unit commitment (PBUC). This article proposes a factor called Lagrangian multiplier. For all that, it has proven Parallel Particle Swarm Optimization (PPSO) solution to the to be a very difficult task that may come sometime from oscil- PBUC problem. This method has better convergence characteristics in obtaining optimum solution. The proposed lation of their solution by slight change of the multiplier. In approach uses a cluster of computers performing parallel order to overcome these complex mathematical problems, there operations in a distributed environment for obtaining the are other method of computational methodology, which is PBUC solution. The time complexity and the solution quality shared by popular artificial intelligence such as genetic algo- with respect to the number of processors in the cluster are rithm and evolutionary programming. thoroughly tested. The method has been applied to 10 unit Charles W. Richter et.al presented a PBUC problem system and the results show that the proposed PPSO in a formulation using genetic algorithm (GA) which considers distributed cluster constantly outperforms the other methods the softer demand constraints and allocates fixed and which are available in the literature. transitional costs to the scheduled hours [6]. Pathom Index Terms—deregulated market, profit based unit Attaviriyanupap et.al proposed a method that helps GENCO commitment, particle swarm optimization, distributed to make a decision on how much power and reserve that environment, parallel processing, parallel particle swarm should be sold in markets, and how to schedule generators optimization. in order to receive the maximum profit [7]. Here the authors have considered both power and reserve generation at the I. INTRODUCTION same time. In [8], H.Y. Yamin et.al proposed an auxiliary hybrid model using LR and GA to solve UCP. GA is used to update The GENCOs objective is to maximize the profit and to the Lagrangian multiplier also presented their view on the place proper bid in the market. In order to do this generation profit based unit commitment in day- ahead electricity markets companies need to determine the schedule and operating considering the reserve uncertainty [9]. points based on the load and price forecasted. The traditional The optimization method known as particle swarm unit commitment problem objective is minimizing the cost of optimization (PSO) algorithm developed by Eberhart and operation subject to fulfillment of demand. However in a Kennedy is successfully applied to solve nonlinear deregulated environment the traditional unit commitment optimization problems. Therefore an attempt is made to solve objective needs to be changed to maximize the profit with the PBUC problem using this algorithm. The swarm-based relaxation of the demand fulfillment constraint. This unit algorithm described in this paper is a search algorithm capable commitment is referred to as profit based unit commitment. of locating optimal solutions efficiently. [1]. The proposed method is applied to solve PBUC problem A competitive and deregulated framework is replacing with ten-unit and hundred-unit-test systems. The performance traditional and centralized regulation in many electric power of the PPSO algorithm in terms of solution quality is compared systems around the world. With the promotion of deregulation with that of other algorithms reported in literature for the of electric power systems, operation, planning and control above mentioned problem in power system operation. aspects in traditional power system need to be changed [2- Likewise, simulation results demonstrate the feasibility and 3]. In this new paradigm, the signal that would enforce a effectiveness of the proposed method, as compared with the unit’s on/off status would be the price, including the fuel results available in the literature. purchase price, energy sale price, ancillary service sale price, and so on. There are many solution techniques such as II. PROBLEM FORMULATION integer programming; dynamic programming, Lagrangian relaxation and genetic algorithms are available to solve the The objective of the PBUC problem is to obtain the optimal PBUC problem [4-6]. Researchers also presented a review on unit commitment schedule thereby maximizing GENCOs profit. deterministic, meta-heuristic and hybrid approaches of The problem formulation is given as follows: generation scheduling in both regulated and deregulated Maximize PF  RV  TC (1) power markets [7]. or *Corresponding author © 2011 ACEEE 24 DOI: 01.IJEPE.02.03.512
  • 2. ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011 Minimize TC  R V (2) III. PARLLEL CLUSTERING ENVIRONMENT where PF is the total profit ($), RV is the total revenue ($) In clusters, powerful low cost workstations and/or PCs and TC is the total cost ($). are linked through fast communication interfaces to achieve Here, high performance parallel computing. Workstation clusters T N have become an increasingly popular alternative to traditional TC    [C i ( P( i ,t ) I ( i ,t ) )  ST t ] (3) parallel supercomputers for many workloads requiring high t 1 i 1 performance computing. The use of parallel computing for T N scientific simulations has increased tremendously in the last RV    [( g (t )P(i,t ) I (i,t) )] (4) ten years, and parallel implementations of scientific simulation t 1 i 1 codes are now in widespread use [10, 11]. There are two dominant parallel hardware/software architectures in use where C i is the production cost which is calculated by using today are Distributed memory, and Shared memory. In shared the equation (10). P( i ,t ) is the power level of i th generator memory systems, parallel processing occurs through the use of shared data structures, or through emulation of message unit at t th hour (MW), I (i , t ) is the commitment state of i th unit passing semantics in software. Distributed memory systems are composed of a number of interconnected computational at t th hour, STt is the startup cost ($), t is the index for time, nodes, which do not share memory, but can communicate T is the dispatch period in hours, i is the index for generator with each other through a high-performance ether net switch (HPES) as shown in Figure 1. Parallelism is achieved on unit, N is the total number of generating units and  g (t ) is distributed memory systems with multiple copies of the the forecasted market price for energy at time t. parallel program running on different nodes, sending Ci ( P( i ,t ) )  a  b * P( i ,t )  c * P( 2,t ) (5) messages to each other to coordinate computations. The i cluster should perform as a parallel computing resource, where a , b and c are the fuel cost co-efficients. achieving higher performance than possible using System Constraints workstations configured in a more standard way. The nodes Demand constraints in the cluster are always used in groups, not individually as N in a general purpose workstation laboratory. P i1 I ( i , t ) (i , t )  Dt t  1.....T (6) Speedup factor and efficiency: To evaluate the parallel performance of the PPSO where Dt is the total system demand at time t. algorithm, the speedup factor SWh and efficiency EWh of the Here, demand and reserve constraints are different from cluster [12-13] is calculated as follows; traditional UC problem because GENCO can now select to produce demand and reserve less than forecasted level if it SWh  Wt Wht (10) creates more profit. EW h  SW h W h (11) Unit constraints where Wt and Wht are the execution time of single processor 1. Unit power limit and cluster respectively. Pi,min  P(i,t) I (i,t )  Pi,max (7) where Pi , min is the minimum power output of i th generator unit (MW) and Pi , max is the maximum power output of generator unit (MW). 2. Minimum Up and Down time constraints on on [X ( i , t  1)  T ( i )] * [ I ( i , t  1 )  I ( i , t ) ]  0 (8) off off [X ( i , t  1)  T ( i )] * [ I ( i , t )  I ( i , t  1 ) ]  0 (9) where Xon(i,t) is the “On” duration of i th generator unit till time t, Xoff (i, t) is the “Off” duration of i th generator unit till time t, T on (i) is the minimum up-time of i th generator unit and T off (i) is the minimum down-time of i th generator unit. Figure 1. Distributed cluster of workstations (20 Nodes) © 2011 ACEEE 25 DOI: 01.IJEPE.02.03. 512
  • 3. ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011 III. PARTICLE SWARM OPTIMIZATION ALGORITHM  x, if particles divisible by Wh  PSP   x  1 for the first hx slaves and Particle Swarm Optimization (PSO) is an optimization  (14)  x for the remaining , Otherwise technique inspired from bird flocking which is developed by Dr Eberhart and Dr. Kennedy way back in the year 1995 [14]. where It is a population based algorithm where each individual x  floor ( N Particles / Wh ) (15) (particle) in the population is a potential solution, flies in the hx  N Particles  ( x * Wh ) (16) D dimensional problem space with a velocity which is dynamically adjusted according to the flying experiences of Master node allocate (x+1) particles to the first hx slaves in its own and its colleagues. the Wh cluster (W1 ...Whx ....Wh ) and x ants to the remaining slaves (Whx+1 ....Wh ) . Where NParticles=population. A) Standard PSO algorithm Suppose that the search space is D-dimensional and m particles form the colony. The ith particle represents a D dimensional vector Xi (i=1, 2… m). It means that the ith particle positions at X i  ( xi 1 , xi 2 ,......., xiD ) (i=1, 2… m) in the searching space. The position of each particle is a potential result. The calculation of the particle’s fitness is carried out by putting its position value into a designated objective function. When the fitness is higher, the corresponding Xi is “better”. The ith particle’s “flying” velocity is also a D- dimensional vector, denoted as Vi  (vi 1 , vi 2 ,......., v i D ) Denote the best position of the i th particle as Pi  ( pi1 , pi 2 ,....., piD ) and the best position of the colony as Pg  ( p g1 , p g 2 ,......., p gD ) respectively. The PSO algorithm can be performed by the following equations (12, 13). Vid (k1) Vid (k)c1r1 (P (k)- xid (k))c2r2 (Pgd (k)- xid (k) id (12) xid (k  1)  xid (k )  vid (k  1) (13) Where k represents the iterative number, c1, c2 are learning factors. Usually c1= c2=2, r1, r2 are random numbers between (0, 1).The termination criterion for the iterations are determined according to whether the max generation or a designated value of the fitness of Pg is reached B) Parallel PSO algorithm PPSO algorithm is implemented to determine the commitment status of each unit over a scheduled period of (24 hours) time in order to maximize the profit. The procedure of the proposed algorithm to solve PBUCP is as follows. Step 1: Generator and PSO Parameters Specification Specify the generator minimum and maximum generation limits, minimum up and down time constraints and start up cost of each unit. Specify the PPSO parameters such as population size (M), inertia weight factor (w), dimension of the system (D), acceleration constants (c1 and c2), velocity maximum and minimum limits, maximum iterations (Max iter). Set iteration number iter=1 and time t=1. Figure 2. Flowchart of PPSO for PBUC Step 2: Particles sharing policy Step 3: Initialization of Individual in the swarm Master node decides the sharing of particles by particles The initial solution of each individual Uj=[un1 un2 … unT], (j=1, sharing policy (PSP).Therefore the number of particles 2, …,M), (n=1, 2, ….., N)) for complete M population is allocated in a slave processors or workers is given by generated randomly. The position of each unit unt of each particle is generated using uniformly distributed random © 2011 ACEEE 26 DOI: 01.IJEPE.02.03.512
  • 4. ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011 function, which generates either 0 or 1. Similarly the initial is found to be more than the maximum total profit computed velocity of each particle is generated randomly using so far, then the present global best is memorized, or else the uniformly distributed random function, which generates a previous maximum total profit solution is retained as global real value between Vmin and Vmax. The representation of each best. The new global best is sent to the workers and the individual for ‘N’ number of generating units for a scheduled workers saved the received global best as their global best. period of time is as follows: Step 8: Memorize the best solution obtained so far and increment iteration number. Stop the process if iteration number is equal to the maximum number of cycles. Otherwise  u 11 u 12 . . u1N  go to step 4. u u 22 . . u2N  Step 9: Increment the time and repeat step 3 to step 8 for the  21  given scheduled period (24 hours) of time. U  . . . . .  (17) The flowchart of the proposed method is shown in the Figure   2.  . . . . .  u T 1  uT 2 . . u TN   IV. NUMERICAL RESULTS The PABC method for PBUC is first tested on 10 unit Step 4: Defining the evaluation function system available in the literature as Case 1. It is also validated The merit of each individual particle in the swarm is found on multiple test systems of 100 units in Case 2. The parallel using a fitness function called evaluation function. Each computation is carried out in the MATLAB® environment of particle in the population is evaluated using the objective R2007b using distributing computing toolbox. The parallel function given by (1). computation is carried out through distributed memory Step 5: Repair Minimum up and down time constraints environment. In a distributed environment, a cluster with the violation maximum size of 20 nodes/processors (Pentium - IV 3.40 GHz, Repair each unit for each particle in the swarm for minimum 1GB RAM) is used. up and down time constraints violation. A. Case 1: 10 Unit System Step 6: Modifying best particle position (Pbest) To modify the position of each individual in the next stage In order to participate in the market, GENCOs have to is obtained from equation (12). prepare a self commitment according to the forecasted load The weighting function is defined as follows and price. In this case, the commitment schedule is prepared to maximize the GENCOs’ profit by calculating the generator  w  wmin  coefficients with the satisfaction of constraints. Here the profit w  wmax   max  iter  iter  (18)  max  of the company gets the first priority and the demand Where, satisfaction is not mandatory. So, GENCOs will make the self commitment depending upon the forecasted price to get wmax , wmin - Initial, final weights surplus profit. The test system consists of 10 generating itermax - Maximum iteration number units. Here the generating unit data and load data are taken from [15]. The constraints included for PBUC in [15] are iter - Current iteration number considered. Based on the forecasted market price of energy To control excessive roaming of particles, velocity is restricted information, the proposed PPSO model is used to generate between - V max and  V max . dispatch schedule for 24 hours time horizon. The dispatch The maximum velocity limit for the jth generating unit is schedule of ten unit system is given in TABLE I. Optimal computed as follows: parameters obtained by trial and error for PPSO is as follows: Population size=200, Acceleration coefficients, c1=0.2, c2=0.2, Pj max  Pj min V max  (19) Inertia weight: W max=0.9, W min=0.2 and Maximum R iteration=300. The particle position vector is updated using equation (13). The comparison of the proposed method with other The values of the evaluation function are calculated for the existing methods given in TABLE II proves that PPSO gives updated positions of the particles. Evaluate each particle using better solution, i.e. a difference in profit of $1260.23 is object function. Compare each particle evolution value with achieved when compared to Muller method [15]. The time its own best position (Pbest or BS). If the present particle taken to get the best schedule is 168 sec. The PPSO yields a position is better than the old value set new particle position higher profit of 1.2 % than the Muller method. Figure 3 shows as Pbest, otherwise retain old value. the execution time achieved by the different cluster sizes. Step 7: Computation of global best The execution time will reduce, when the cluster size Master receives the information of local best solutions increases. TABLE III shows the speedup factor and efficiency (BSI, BS2,…..,BSh) from the workers and computes the best achieved by different sizes of cluster. When the cluster size solution among them as the global best. Whenever a global increases the speedup factor also increases. i.e., performance best solution is selected by the master, and if the total profit of the cluster will increase, when its size increases. © 2011 ACEEE 27 DOI: 01.IJEPE.02.03. 512
  • 5. ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011 TABLE I. D ISPATCH SCHEDULE FOR 10 UNIT SYSTEM TABLE II . COMPARISON OF PBUC SOLUTIONS (10 UNIT SYSTEM) B. Case 2: 100 Unit Syatem This test system consists of multiple generating units such as 100 generating units. More number of generating units is considered in order to validate the feasibility of the application of PPSO for large scale power system. The data for different groups of generating units are obtained by duplicating the 10 unit system data. The demand is multiplied with respect to the system size; however the generating limits, the minimum up/down time constraints remain the same. Based on the forecast market price of energy information, the proposed PPSO model is used to generate dispatch schedule for 24 hours time horizon. The parameter setting of the 10 unit system is extended for the multiple test systems. Figure 3. Execution time chart for 10 unit system TABLE III. COMPARISION OF SPEEDUP FACTOR AND CLUSTER EFFICIENCY (10 UNIT SYSTEM) Figure 4. Execution time chart for 100 unit system © 2011 ACEEE 28 DOI: 01.IJEPE.02.03.512
  • 6. ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011 TABLE IV. COMMITMENT STATUS FOR 100 UNIT SYSTEM TABLE V. C OMPARISION OF SPEEDUP FACTOR AND CLUSTER EFFICIENCY (100 UNIT and efficiency achieved by different sizes of cluster. When SYSTEM) the cluster size increases the speedup factor also increases. i.e., performance of the cluster will increase, when its size increases. When a single processor is used, it consumes more time for execution, i.e., 1728.01 sec for 100 units. The execution time for the 20 node cluster of 100 units are around 156.38 sec. It clearly shows the execution time decreases as The Commitment status of 100 unit system is given in TABLE the number of processor increases. Each test system has IV. Figure 4 shows the execution time achieved by the differ- been tested for 30 trial runs and the best results are pre- ent cluster sizes. The execution time will reduce, when the sented. cluster size increases. TABLE V shows the speedup factor © 2011 ACEEE 29 DOI: 01.IJEPE.02.03. 512
  • 7. ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011 V. CONCLUSIONS [11] Weiwei Lin, Changgeng Guo, Deyu Qi, Yuchong Chen and Zhang Zhili, “Implementations of grid-based distributed parallel This paper proposes a MPI based PPSO model for PBUC, computing”, First International Multi-Symposiums on Computer computing in parallel, in a distributed environment. The and Computational Sciences, pp. 312-317, 2006. approach is simple, efficient, and economic and can be [12] H. T. Kumm and R. M. Lea, “Parallel computing efficiency: extended for making smarter decisions in a large scale power climbing the learning curve”, TENCON’94, pp. 728-738, 1994. system. Simulation results obtained from the cluster [13] X.-H. Sun, L.M. Ni, “Scalable problems and memory-bounded demonstrate the accuracy of the proposed algorithm and its speedup”, Journal of Parallel and Distributed Computing, vol. 19, capability of greatly reducing the execution time. no. 1, pp. 27–37, 1993. [14] J. Kennedy and R. C. Eberhart, “Particle swarm optimization,” IEEE international Conference on Neural Networks, vol. 4, REFERENCES pp.1942-1948, 1995. [1] Eric H. Allen and Marija D. Ilic, “Reserve markets for power [15] Chandram K, Subrahmanyam N, Sydulu M, “New approach systems reliability”, IEEE Trans. on Power Systems, vol. 15 no 2, with Muller method for profit based unit commitment”, Power pp. 228-233, 2000. and Energy Society General Meeting - Conversion and Delivery of [2] M. Shahidehpour and M. Mawali, Maintenance scheduling in Electrical Energy in the 21st Century, pp. 1-8, 2008. restructured power systems, Nowell, MA Kluwer, 2000. [16] Victoire T. A. A, Jeyakumar A. E, “Unit commitment by a [3] G.B. Sheble and G.N. Fahd, “Unit commitment literature tabu-search-based hybrid-optimization technique”, IEE Proc. synopsis”, IEEE Trans. on Power Systems, vol. 9, pp. 128-135, Gener. Transm. Distrib., vol. 152, pp. 563-570, 2005. 1994. [4] Narayana Prasad Padhy, “Unit commitment - A bibliographical AUTHORS BIOGRAPHY survey”, IEEE Trans. on Power Systems, vol. 19, no. 2, pp. 1196- 1205, 2004. C. Christopher Columbus was born in India and received his [5] Narayana Prasad Padhy, “Unit commitment problem under Bachelors of Engineering (Electrical and Electronics Engineering) in deregulated environment- a review”, Power Engineering Society M. S University, Tirunelveli and Masters of Engineering (Computer General Meeting, 2, pp. 1088-1094, 2003. Science and Engineering) at Anna University, Chennai, India in the [6] Charles W. Richter and Gerald B. Sheble, “A Profit based Unit years 1998 and 2005 respectively. He is currently pursuing his Commitment GA for Competitive Environment”, IEEE Trans. on research degree in the Department of Electrical and Electronics Power Systems, vol. 15, no. 2, pp. 715-721, 2000. Engineering, National Institute of Technology, Tiruchirappalli, [7] Pathom Attaviriyanupap, Hiroyuki Kita, Eiichi Tanka and Tamil Nadu, India. His research interest includes Deregulation of Jun Hasegawa, “A hybrid LR-EP for solving new profit –based UC Power system and Parallel computing applications in Power problem under competitive environment”, IEEE Transaction on Systems. Power Systems, vol.18, no. 1, pp. 229-237, 2003. [8] H.Y. Yamin and S.M. Shahidehpour, “Unit commitment using Sishaj Pulikottil Simon was born in India and received his a hybrid model between Lagrangian relaxation and genetic algorithm Bachelors of Engineering (Electrical and Electronics Engineering) in competitive electricity markets”, Electric Power Systems and Masters of Engineering (Applied Electronics) at Bharathiar Research, vol. 68, pp. (83-92, 2004. University, Coimbatore, India in the years 1999 and 2001 [9] I. Jacob Raglend, C. Raghuveer, G. Rakesh Avinash, N.P. Padhy respectively. He obtained his Ph.D., (Power System Engineering) and D.P. Kothari, “Solution to profit based unit commitment at Indian Institute of Technology (IIT), Roorkee, India in 2006. problem using particle swarm optimization”, Applied soft Currently, he is an Assistant professor in the Department of computing, vol. 10, pp. 1247-1256, 2010. Electrical and Electronics Engineering at National Institute of [10] Dingju Zhu and Jianping Fan, “Application of parallel Technology (NIT), Tiruchirappalli, Tamil Nadu, India. computing in digital city”, The 10th IEEE International Conference on High Performance Computing and Communications, pp. 845- 848, 2008. © 2011 ACEEE 30 DOI: 01.IJEPE.02.03.512