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A Layered Matrix Cascade Genetic Algorithm and Particle Swarm Optimization Approach to Thermal Power Generation Scheduling By Neoh Siew Chin Dr. Zalina Abdul Aziz Associate Prof. Norhashimah Morad Associate Prof. Lim Chee Peng 1 1

Thermal Power Generation Scheduling Thermal Power Generation Scheduling Thermal power scheduling � can be separated into two sub problems: (1) Unit Commitment (2) Economy Power Dispatch Unit commitment refers to Unit commitment refers to � � number of power generation number of power generation units dedicated to serve the units dedicated to serve the load demand whereas load demand whereas economic power dispatch economic power dispatch refers to the allocation of refers to the allocation of power generation to power generation to different generator units different generator units 2 2

Thermal Power Generation Scheduling Thermal Power Generation Scheduling � Thermal power generation scheduling has commonly been formulated as a nonlinear, large scale, mixed- integer combinatorial optimization with constraints. � There are a number of approaches used to address the power scheduling problem, e.g. dynamic programming, mixed-integer programming, Lagrangian relaxation, Simulated Annealing etc. � In our research, a Layered Matrix Cascade Genetic Algorithm and Particle Swarm Optimization (GA- PSO) Approach is proposed. 3 3

Layered Matrix Cascade GA-PSO � Layered Matrix Cascade GA-PSO is a hybrid approach of GA and PSO which employ a layered matrix encoding structure for problem representation. � The hybridization of GA and PSO in the cascade format based on layered encoding structure is mainly developed to allowed a more thorough search of solution space. � GA is a stochastic search method that mimics the metaphor of natural biological evolution, whereas PSO is an optimization tool driven by the social behavior of organisms. � Both methods are combined in this case study to give balance exploration and exploitation of search. 4 4

Layered Matrix Encoding Structure � In combinatorial problems, multi-dimensional encoding structure is sometimes required to incorporate all required constraints and decisions into one single combinatorial solution representation structure. � The conventional multi The conventional multi- -dimensional encoding dimensional encoding � however makes the fitness evaluation and problem however makes the fitness evaluation and problem analysis tedious when the number of dimension analysis tedious when the number of dimension increases (e.g. 4 or 5 dimensions). increases (e.g. 4 or 5 dimensions). � Layered matrix encoding structure is different from Layered matrix encoding structure is different from � the existing multi- -dimensional encoding approaches dimensional encoding approaches the existing multi in which it separates different decision outputs into in which it separates different decision outputs into 5 5 different layers. different layers.

Layered Matrix Encoding Structure � As a result, layered matrix encoding structure As a result, layered matrix encoding structure � simplify the problem representation and at the simplify the problem representation and at the same time allow optimization to be done on each same time allow optimization to be done on each stage of the decision output. stage of the decision output. � Instead of increasing the dimensions, the layered Instead of increasing the dimensions, the layered � structure allows constraints and decision outputs structure allows constraints and decision outputs to be analyzed more effectively. to be analyzed more effectively. � In addition, layers enhanced the construction of In addition, layers enhanced the construction of � hybrid approach to solve combinatorial problem hybrid approach to solve combinatorial problem where different optimizer can be employed in where different optimizer can be employed in different layer to optimize both local and global different layer to optimize both local and global search. search. 6 6

Layered matrix encoding structure Z Y Layer 3 Layer 2 Layer 1 Resource Period ( R k ) ( P i ) R 1 R 2 …… R r P 1 S 1 1 S 1 2 …… S 1 r P 2 S 2 1 S 2 2 …… S 2 r P 3 : : …… : P 4 : : …… : P n S n1 S n2 S n3 S nr X 7 7

Period Resource ( R k ) ( P i ) R 1 R 2 R 3 R r Layer 1 P 1 S 1 1 S 1 2 S 1 3 S 1 r P 2 S 2 1 S 2 2 S 2 3 S 2 r P 3 : : : : P n S n1 S n2 S n3 S nr Period Resource ( R k ) ( P i ) R 1 R 2 R 3 R r Layer 2 P 1 X 1 1 X 1 2 X 1 3 X 1 r P 2 X 2 1 X 2 2 X 2 3 X 2 r P 3 : : : : P n X n1 X n2 X n3 X nr Period Resource ( R k ) ( P i ) R 1 R 2 R 3 R r Layer 3 P 1 N 1 1 N 1 2 N 1 3 N 1 r P 2 N 2 1 N 2 2 N 2 3 N 2 r P 3 : : : : P n N n1 N n2 N n3 N nr 8 8

Layered Matrix GA-PSO in Thermal Power scheduling � In this case study, thermal power generation schedule is represented by a two layers 2D matrix with layer 1 stands for unit commitment and layer 2 stands for power dispatch. � PSO is used to optimize unit commitment (layer 1) whereas GA is used to optimize economy power dispatch (layer 2) � Layers in the layered matrix structure can be viewed as the optimization stages in cascade optimization. 9 9

Period Generator, G k Electricity (P i ) G 1 G 2 G 3 Demand (D i ) Layered P 1 n 11 n 12 n 13 D 1 P 2 n 21 n 22 n 23 D 2 P 3 n 31 n 32 n 33 D 3 Matrix P 4 n 41 n 42 n 43 D 4 P 5 n 51 n 52 n 53 D 5 Encoding Structure in Period Generator, G k Electricity this case (P i ) G 1 G 2 G 3 Demand (D i ) P 1 x 11 x 12 x 13 D 1 study P 2 x 21 x 22 x 23 D 2 P 3 x 31 x 32 x 33 D 3 P 4 x 41 x 42 x 43 D 4 P 5 x 51 x 52 x 53 D 5 10 10

11 11 optimization Cascade GA-PSO model

Thermal Power Scheduling Generator Units Minimum Maximum Cost per Cost per hour Start-up Type Available Level Level hour at per megawatt Cost (MW) (MW) minimum above (£) (£) minimum (£) Type 1 12 850 2000 1000 2 2000 Type 2 10 1250 1750 2600 1.30 1000 Type 3 5 1500 4000 3000 3 500 12 12

Input and Output Parameters for Power Scheduling Optimization Minimize Generator Type Total Production Cost Layered Power Demand Utilize Available Matrix-based Capacity GA-PSO Cascade Business/ Optimization Meeting extra Production (Thermal Power 15% demand Rules Scheduling) based on selected generator units Constraints 13 13

Evaluation Function Objective Function ⎧ = ⎡ = ⎤ i 5 k 3 ( ) ∑ ∑ = + + ⎨ minimize C (x - m n ) E n F z ⎢ ⎥ k ik k ik k ik k ik ⎣ ⎦ ⎩ = = i 1 k 1 C k is the cost per hour per megawatt above the minimum � level of generator k multiplied by the number of hours in period i E k is the cost per hour for operating at the minimum level � of generator k multiplied by the number of hours in period i F k is the start up cost of generator k � 14 14

Thermal Power Scheduling Thermal Power Scheduling Layered Matrix Method LP Cascade GA-PSO Total Daily Cost £ 988,540 £ 954,260 IMPROVEMENT = £ 34,280 SAVED DAILY 15 15

Conclusion � Layered matrix encoding structure that separates different decision outputs into different layers simplify problem representation and at the same time allow multi stage cascade optimization. � The combination of GA and PSO provides a good The combination of GA and PSO provides a good � balance between exploration and exploitation which balance between exploration and exploitation which leads to a balanced individuality and sociality of the leads to a balanced individuality and sociality of the search. search. � Based on the result obtained, the proposed layered matrix cascade GA-PSO is an alternative approach of solving unit commitment and power dispatch problem in thermal power generation scheduling. 16 16

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