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


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In the deregulated electricity market, each
generating company has to maximize its own profit by
committing suitable generation schedule termed as profit
based unit commitment (PBUC). This article proposes a
Parallel Particle Swarm Optimization (PPSO) solution to the
PBUC problem. This method has better convergence
characteristics in obtaining optimum solution. The proposed
approach uses a cluster of computers performing parallel
operations in a distributed environment for obtaining the
PBUC solution. The time complexity and the solution quality
with respect to the number of processors in the cluster are
thoroughly tested. The method has been applied to 10 unit
system and the results show that the proposed PPSO in a
distributed cluster constantly outperforms the other methods
which are available in the literature.

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

  1. 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:, sishajpsimon@nitt.eduAbstract— In the deregulated electricity market, each The basic idea of LR is to relax the UCP constraints into agenerating company has to maximize its own profit by small sub-problem, which is much easier to solve, and thencommitting suitable generation schedule termed as profit coordinated by a master problem via properly adjusting abased unit commitment (PBUC). This article proposes a factor called Lagrangian multiplier. For all that, it has provenParallel 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 convergencecharacteristics in obtaining optimum solution. The proposed lation of their solution by slight change of the multiplier. Inapproach uses a cluster of computers performing parallel order to overcome these complex mathematical problems, thereoperations in a distributed environment for obtaining the are other method of computational methodology, which isPBUC 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 presented a PBUC problemsystem and the results show that the proposed PPSO in a formulation using genetic algorithm (GA) which considersdistributed cluster constantly outperforms the other methods the softer demand constraints and allocates fixed andwhich are available in the literature. transitional costs to the scheduled hours [6]. PathomIndex Terms—deregulated market, profit based unit Attaviriyanupap proposed a method that helps GENCOcommitment, particle swarm optimization, distributed to make a decision on how much power and reserve thatenvironment, parallel processing, parallel particle swarm should be sold in markets, and how to schedule generatorsoptimization. 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 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 theplace proper bid in the market. In order to do this generation profit based unit commitment in day- ahead electricity marketscompanies 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 swarmunit commitment problem objective is minimizing the cost of optimization (PSO) algorithm developed by Eberhart andoperation subject to fulfillment of demand. However in a Kennedy is successfully applied to solve nonlinearderegulated environment the traditional unit commitment optimization problems. Therefore an attempt is made to solveobjective needs to be changed to maximize the profit with the PBUC problem using this algorithm. The swarm-basedrelaxation of the demand fulfillment constraint. This unit algorithm described in this paper is a search algorithm capablecommitment 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 performancetraditional and centralized regulation in many electric power of the PPSO algorithm in terms of solution quality is comparedsystems around the world. With the promotion of deregulation with that of other algorithms reported in literature for theof 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 and3]. In this new paradigm, the signal that would enforce a effectiveness of the proposed method, as compared with theunit’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 FORMULATIONinteger programming; dynamic programming, Lagrangianrelaxation and genetic algorithms are available to solve the The objective of the PBUC problem is to obtain the optimalPBUC 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 24DOI: 01.IJEPE.02.03.512
  2. 2. ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011 Minimize TC  R V (2) III. PARLLEL CLUSTERING ENVIRONMENTwhere PF is the total profit ($), RV is the total revenue ($) In clusters, powerful low cost workstations and/or PCsand TC is the total cost ($). are linked through fast communication interfaces to achieveHere, high performance parallel computing. Workstation clusters T N have become an increasingly popular alternative to traditional TC    [C i ( P( i ,t ) I ( i ,t ) )  ST t ] (3) parallel supercomputers for many workloads requiring high t 1 i 1 performance computing. The use of parallel computing for T N scientific simulations has increased tremendously in the lastRV    [( g (t )P(i,t ) I (i,t) )] (4) ten years, and parallel implementations of scientific simulation t 1 i 1 codes are now in widespread use [10, 11]. There are two dominant parallel hardware/software architectures in usewhere C i is the production cost which is calculated by using today are Distributed memory, and Shared memory. In sharedthe equation (10). P( i ,t ) is the power level of i th generator memory systems, parallel processing occurs through the use of shared data structures, or through emulation of messageunit at t th hour (MW), I (i , t ) is the commitment state of i th unit passing semantics in software. Distributed memory systems are composed of a number of interconnected computationalat t th hour, STt is the startup cost ($), t is the index for time, nodes, which do not share memory, but can communicateT 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 onunit, N is the total number of generating units and  g (t ) is distributed memory systems with multiple copies of thethe 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 usingSystem Constraints workstations configured in a more standard way. The nodesDemand 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 PPSOwhere Dt is the total system demand at time t. algorithm, the speedup factor SWh and efficiency EWh of theHere, demand and reserve constraints are different from cluster [12-13] is calculated as follows;traditional UC problem because GENCO can now select toproduce 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 processor1. 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 generatorunit (MW) and Pi , max is the maximum power output ofgenerator 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 tilltime t, Xoff (i, t) is the “Off” duration of i th generator unit tilltime t, T on (i) is the minimum up-time of i th generator unitand T off (i) is the minimum down-time of i th generator unit. Figure 1. Distributed cluster of workstations (20 Nodes)© 2011 ACEEE 25DOI: 01.IJEPE.02.03. 512
  3. 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 , Otherwisetechnique inspired from bird flocking which is developed byDr Eberhart and Dr. Kennedy way back in the year 1995 [14]. whereIt 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 isdynamically adjusted according to the flying experiences of Master node allocate (x+1) particles to the first hx slaves inits 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 mparticles form the colony. The ith particle represents a Ddimensional vector Xi (i=1, 2… m). It means that the ith particlepositions at X i  ( xi 1 , xi 2 ,......., xiD ) (i=1, 2… m) in thesearching space. The position of each particle is a potentialresult. The calculation of the particle’s fitness is carried outby putting its position value into a designated objectivefunction. 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 asPi  ( pi1 , pi 2 ,....., piD ) and the best position of thecolony as Pg  ( p g1 , p g 2 ,......., p gD ) respectively. ThePSO 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 randomnumbers between (0, 1).The termination criterion for theiterations are determined according to whether the maxgeneration or a designated value of the fitness of Pg is reachedB) Parallel PSO algorithm PPSO algorithm is implemented to determine thecommitment status of each unit over a scheduled period of(24 hours) time in order to maximize the profit. The procedureof the proposed algorithm to solve PBUCP is as follows.Step 1: Generator and PSO Parameters Specification Specify the generator minimum and maximum generationlimits, minimum up and down time constraints and start upcost of each unit. Specify the PPSO parameters such aspopulation size (M), inertia weight factor (w), dimension ofthe system (D), acceleration constants (c1 and c2), velocitymaximum and minimum limits, maximum iterations (Max iter).Set iteration number iter=1 and time t=1. Figure 2. Flowchart of PPSO for PBUCStep 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 isallocated 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 26DOI: 01.IJEPE.02.03.512
  4. 4. ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011function, which generates either 0 or 1. Similarly the initial is found to be more than the maximum total profit computedvelocity of each particle is generated randomly using so far, then the present global best is memorized, or else theuniformly distributed random function, which generates a previous maximum total profit solution is retained as globalreal value between Vmin and Vmax. The representation of each best. The new global best is sent to the workers and theindividual 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 unitStep 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 parallelusing a fitness function called evaluation function. Each computation is carried out in the MATLAB® environment ofparticle in the population is evaluated using the objective R2007b using distributing computing toolbox. The parallelfunction given by (1). computation is carried out through distributed memoryStep 5: Repair Minimum up and down time constraints environment. In a distributed environment, a cluster with theviolation 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 SystemStep 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 tois obtained from equation (12). prepare a self commitment according to the forecasted loadThe 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 demandWhere, 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 energyTo control excessive roaming of particles, velocity is restricted information, the proposed PPSO model is used to generatebetween - V max and  V max . dispatch schedule for 24 hours time horizon. The dispatchThe maximum velocity limit for the jth generating unit is schedule of ten unit system is given in TABLE I. Optimalcomputed 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 otherThe values of the evaluation function are calculated for the existing methods given in TABLE II proves that PPSO givesupdated positions of the particles. Evaluate each particle using better solution, i.e. a difference in profit of $1260.23 isobject function. Compare each particle evolution value with achieved when compared to Muller method [15]. The timeits own best position (Pbest or BS). If the present particle taken to get the best schedule is 168 sec. The PPSO yields aposition is better than the old value set new particle position higher profit of 1.2 % than the Muller method. Figure 3 showsas 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 sizesolution among them as the global best. Whenever a global increases the speedup factor also increases. i.e., performancebest solution is selected by the master, and if the total profit of the cluster will increase, when its size increases.© 2011 ACEEE 27DOI: 01.IJEPE.02.03. 512
  5. 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 systemTABLE III. COMPARISION OF SPEEDUP FACTOR AND CLUSTER EFFICIENCY (10 UNIT SYSTEM) Figure 4. Execution time chart for 100 unit system© 2011 ACEEE 28DOI: 01.IJEPE.02.03.512
  6. 6. ACEEE Int. J. on Electrical and Power Engineering, Vol. 02, No. 03, Nov 2011 TABLE IV. COMMITMENT STATUS FOR 100 UNIT SYSTEMTABLE 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 asThe Commitment status of 100 unit system is given in TABLE the number of processor increases. Each test system hasIV. 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 29DOI: 01.IJEPE.02.03. 512
  7. 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 Computercomputing 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-boundeddemonstrate 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 approachsystems reliability”, IEEE Trans. on Power Systems, vol. 15 no 2, with Muller method for profit based unit commitment”, Powerpp. 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 BIOGRAPHYsurvey”, 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) inderegulated environment- a review”, Power Engineering Society M. S University, Tirunelveli and Masters of Engineering (ComputerGeneral 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 hisCommitment GA for Competitive Environment”, IEEE Trans. on research degree in the Department of Electrical and ElectronicsPower 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 ofJun Hasegawa, “A hybrid LR-EP for solving new profit –based UC Power system and Parallel computing applications in Powerproblem 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 hisa 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 BharathiarResearch, 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 ofcomputing, 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 Conferenceon High Performance Computing and Communications, pp. 845-848, 2008.© 2011 ACEEE 30DOI: 01.IJEPE.02.03.512