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Distribution System Expansion PlanningUsing a GA-Based Algorithm

Shiqiong Tong , Yiming Mao, Karen Miu

Center for Electric Power EngineerDrexel University

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• Introduction

• Problem Formulation

• Solution Algorithm

• Simulations

• Conclusions

Outline

ControlVariables

DG ControlVariables

Feeder UpgradeControl Variables

GeneticAlgorithm

HeuristicAlgorithm

GA-BasedAlgorithm

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• Careful DG placement is an option to - expand generation capacity - release transmission and distribution system capacity - delay equipment upgrade - enhance system reliability

• New strategies and methods for distribution system expansion planning need to be developed

Introduction

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Introduction

Previous work about DG placement

• Grffin et. al. [6] provided a method based on loss sensitivity or load distribution to reduce losses. (2000)

• Nara et. al. [7] applied tabu search to minimize interruption cost. (2001)

• Kim et. al. [8] used fuzzy-GA method to minimize distribution loss cost. (2002)

• Teng et. al. [9] proposed a GA to maximize the benefit/cost ratio of DG placement. (2002)

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• We proposed a cost-based problem formulation including:

- feeder upgrade costs

- DG installation costs

- DG operating costs

- wheeling costs

• A GA-based algorithm is designed to solve this problem

Introduction

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Problem Formulation

,min ( , )

x uf x u

( , ) 0F x u

( , ) 0G x u

st.

aggregate objective function

where: x : continuous state variables u : discrete control variables

Constrained Optimization Problem:

voltage magnitude, current magnitude, feeder capacity , DG penetration constraints

3 power flow equations

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Problem Formulation

[ ]loc type fDG DG Gu u u P u

1 1 2[ ] [ , , , ]DG DG

loc loc loc locDG n nu u u u

1 1 2[ ] [ , , , ]DG DG

type type type typeDG n nu u u u

1 1 2 21 1 1 1[ ] [ , , , , , ] 'l l

DG l DG DG DG

n nG n n G Gn G Gn G GnP P P P P P P

, , , , , ,2 1 1 1 2 2[ ] [ , , , , , , ] '

branch branch branch

f f R f X f R f X f R f Xn n nu u u u u u u

DG location:

DG type:

DG output:

Feeder upgrade:

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Objective Function:

Problem Formulation

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1

( , ) ( , )ii

f x u C x u

where:

C1(x,u) : total feeder upgrade cost

C2(x,u) : total DG installation cost

C3(x,u) : total DG operating cost

C4(x,u) : total wheeling cost

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• DG model

- P|V| bus

- same type DG can be installed on one bus

• Balanced three-phase transformer and branch upgrades

• Keep original configuration of radial distribution power system

Modeling Issues

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• GA-based algorithm Design

- Genetic Algorithm Determine DG control variables DG initial locations are bias using available feeder

capacities

- Heuristic Algorithm Determine feeder upgrade control variables

- using three-power flow studies with DG

information to decide upgrade options

Solution Algorithm

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• GA-based Algorithm Design (Continued)– Coding

Solution Algorithm

location 1 location 2 location 3

type onlocation 1

type onlocation 2

type onlocation 3

output onlocation 1

output onlocation 2

output onlocation 3

output onlocation 1

output onlocation 2

output onlocation 3

Load Leval lnLoad Level 2Load Level 1

DG location substring

DG type substring

DG output substring

GA controlvariables

(Binary code)

options forbranch 1

options forbranch 2

options forbranch 3

Options forbranch nb

Feeder upgradesubstring

Dependent controlvariables

(Integer code)

output onlocation 1

output onlocation 2

output onlocation 3

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• A 20-bus distribution system• Two 4MVA transformers• 17 line feeders ( total length about 7.18 miles)• 12 loads

Simulations

1 2 3

4 5 6 7 8 9 10 11

12 13 14

15 16 17 18

19 20Transformer

Closed Switch

Load

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• Loads

- The total three-phase base load 5.8610 MW and 2.104 Mvar

- Three load levels Low: 0.7 times of the base load Medium: the base load High: 1.1 times of the base load

- Each load level lasts one year

Simulations

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• Cost data

- Wheeling cost $0.065 per KWh

- Transformer upgrade cost $400,000 for each

- Line upgrade cost: $30,000 per 1000 feet

- DG cost: see Table 2 on the paper

Simulations

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• Transformer between Bus 2 and Bus 4 is over-loaded

- Transformer capacity: 4 MVA

- Medium-load level:

= 4.1789 MVA > 4 MVA

- High-load level:

= 4.6519 MVA > 4 MVA

SimulationsCase 1. Original system

32 4S

32 4S

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• Upgrade the transformer between Bus 2 and Bus 4• Total cost: $11,320,006

Total cost = Wheeling costs + Upgrade costs

= $10,920,006 + $ 400,000

= $11,320,006

Simulations

Case 2. Feeder upgrade without DG placement

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• Use proposed GA-based algorithm• Solution: - No feeder upgrade - One DG on bus 8:

0.5 MW reciprocating operating outputs: 0,0.5 and 0.5 MW

- Total cost: $11,043,429

Total cost = Wheeling costs + DG installation costs + DG operating costs = $10,182,569 + $ 217,000 + $643,860 = $11,043,429

Simulations

Case 3. Feeder upgrade with DG placement

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Simulations

0 50 100 150 200 250 300 3501.1

1.11

1.12

1.13

1.14

1.15

1.16

1.17

1.18

1.19

1.2x 10

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To

tal

Co

st,

$

generation

Algorithm performance

Case 2: feeder upgrade without DG placement

Case 3: feeder upgrade with DG placement

C=$276,577

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• The proposed GA-based algorithm successfully generate high quality solutions

• DG placement with feeder upgrade can provide more diverse expansion solutions

• DG placement can avoid or delay equipment upgrades

• Considering DGs’ impacts to outage cost may further decrease cost for utilities.

Simulations

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• In this paper, a problem formulation of distribution expansion planning with DG placement was proposed.

• A cost-based objective function considering feeder upgrade costs, DG installation costs, DG operating costs, and wheeling costs were discussed.

• A GA-based algorithm was discussed

• The simulation results using different methods were compared

Conclusions