A Layered Matrix Cascade Genetic Algorithm and Particle Swarm - - PowerPoint PPT Presentation

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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

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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

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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.

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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.

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Layered Matrix Encoding Structure

In combinatorial problems, multi-dimensional

encoding structure is sometimes required to incorporate all required constraints and decisions into

• ne 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 the existing multi-

• dimensional encoding approaches

dimensional encoding approaches in which it separates different decision outputs into in which it separates different decision outputs into different layers. different layers.

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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.

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Layer 1 Layer 2 Layer 3

Period Resource ( Rk) ( Pi) R1 R2 …… Rr P1 S1 1 S1 2 …… S1 r P2 S2 1 S2 2 …… S2 r P3 : : …… : P4 : : …… : Pn Sn1 Sn2 Sn3 Snr

Layered matrix encoding structure

Y X Z

8 8 Period Resource ( Rk) ( Pi) R1 R2 R3 Rr P1 S1 1 S1 2 S1 3 S1 r P2 S2 1 S2 2 S2 3 S2 r P3 : : : : Pn Sn1 Sn2 Sn3 Snr Xnr Xn3 Xn2 Xn1 Pn : : : : P3 X2 r X2 3 X2 2 X2 1 P2 X1 r X1 3 X1 2 X1 1 P1 Rr R3 R2 R1 ( Pi) Resource ( Rk) Period N nr N n3 N n2 N n1 Pn : : : : P3 N 2 r N 2 3 N 2 2 N 2 1 P2 N 1 r N 1 3 N 1 2 N 1 1 P1 Rr R3 R2 R1 ( Pi) Resource ( Rk) Period

Layer 1 Layer 2 Layer 3

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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.

10 10 Period Generator, Gk Electricity (Pi) G1 G2 G3 Demand (Di) P1 x11 x12 x13 D1 P2 x21 x22 x23 D2 P3 x31 x32 x33 D3 P4 x41 x42 x43 D4 P5 x51 x52 x53 D5 Period Generator, Gk Electricity (Pi) G1 G2 G3 Demand (Di) P1 n11 n12 n13 D1 P2 n21 n22 n23 D2 P3 n31 n32 n33 D3 P4 n41 n42 n43 D4 P5 n51 n52 n53 D5

Layered Matrix Encoding Structure in this case study

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Cascade GA-PSO

• ptimization

model

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Thermal Power Scheduling

Generator Type Units Available Minimum Level (MW) Maximum Level (MW) Cost per hour at minimum (£) Cost per hour per megawatt above minimum (£) Start-up Cost (£) 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

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Input and Output Parameters for Power Scheduling Optimization

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

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Evaluation Function

• Ck is the cost per hour per megawatt above the minimum

level of generator k multiplied by the number of hours in period i

• Ek is the cost per hour for operating at the minimum level
• f generator k multiplied by the number of hours in period i
• Fk is the start up cost of generator k

( )

) n m

• (x

C minimize Function Objective

5 1 3 1 ik k ik k

⎩ ⎨ ⎧ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + + =

∑ ∑

= = = = i i k k ik k ik k

z F n E

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Thermal Power Scheduling Thermal Power Scheduling

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

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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.

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