Corridor Method heuristics to solve rural electrification projects

Joan Triadó Aymerich, Dra. Laia Ferrer Martí, Dr. Alberto García Villoria,

Dr. Rafael Pastor Moreno

Universitat Politècnica de Catalunya- Barcelona Tech.

Institut d’Organització i Control

With the support of:

2013 ICSO-HAROSA International Workshop on Simulation-Optimization & Internet Computing

BARCELONA 10-12 July 2013

Ministerio de Ciencia e Innovación de España, proyecto ENE2010-15509, cofinanciado por FEDER.

Summary

1. Introduction

2. Technical considerations

3. Objectives

4. MILP model

5. Heuristics based on Corridor method

6. Instances

7. Analysis of results

8. Conclusions

3

Electrification systems using renewable energies are a suitable solution to provide electricity to communities independently.

– They use local resources.– At a lower cost than extending the grid.

Hybrid systems (wind and solar) are one of the possible techniques.

– Recently, hybrid systems have been implemented in Cajamarca.

1. Introducción

Currently, more than 1.3 billion people have no access to electricity (IEA 2011)– Especially in rural areas in developing countries

Due to the dispersion between housings, the trend in electrification projects is to use individual systems.

This work considers the design of projects of electricity supply that combine micro-grids and isolated points generation, considering the resource (wind and sun) at each point.

– No consumption is limited in a point to available resource in your housing.– Money can be saved using large equipment. – May be more easily adaptable to increases in consumption.

4

Types of micro wind turbinesTypes of consumption points

Types of solar panels

1. Introduction

2. Technical considerations

Wind turbine, power generated depends on the type and location. Solar panel, power generated depends on the type. Solar controller, controls the charge / discharge of the battery. Battery, considers capacity and autonomy demand. Inverter, DC/AC conversion to the nominal distribution voltage. Meter, measures the energy consumed at the point of microgrid. Wire, used to distribute energy in the form of radial microgrid.

InverterBattery

Solar controller

Wind turbine

Solar Panel Consumption point Meter

Consumption pointMeter Consumption point

Meter

Consumption pointMeter

Consumption point Meter

5

3. Objectives

Designing an autonomous power system with renewable energy (solar and wind).– Determining

• the location, number and type of elements forming the system.

• the distribution microgrids to use– Considering

• the situation and demand of consumption points• the energy resources (solar and wind above all) at each point

– At a minimum investment cost.

Developing heuristics based on linear programming to solve the design.

4. MILP model

Variables:xp: Existence of generation at p (binary)

Xapa : No. of wind turbines at p of type a

xbpb: No. of batteries at p of type b

xipi: No. of inverters at p of type i

xrspz: No. of solar controllers at p of type z

xcpdc: Existence of wire connecting p and d of type c (binary)

xccpd : Existence of wire connecting p and d (binary)

fepd : Energy flow from p to d

fppd : Power flow from p to d

vp : Voltage at p

xmd : Existence of a meter at d (binary)

4. MILP model

Objective function (investment cost):

Constraints

wind turbines wires batteries

inverters solar controllersmeters solar panels

I

ipii

B

bpbb

Pp

C

cpdccpd

DdPp

A

apaa

Pp

xiCI

xbCBxcCCLxaCAZMIN

1

111

Z

zpzz

Pp

S

spss

PpDdd xrsCZxsCSxmCM

11

- Demand

- Batteries

- Voltage drops

)(1

11

11

PpfexED

xsESxaEAfePd Dq

pqpccib

pS

spsps

A

apapadp

)()1(1

PpEDfeDB

VBx

ED

DB

VBxbEB

Dqppqp

Pj cib

jB

bpbb

),...1:;(1minmax CcDdPpxcVVV

fpRCLvv pdc

n

pdcpddp

The Corridor method (Sniedovich and Vos, 2006) is based on the idea of using an exact method on restricted portions of the solution space of the given problem. The method is an iterative improvement result of exploring neighborhoods. It is characterized by the way in which the neighborhood is defined.

The neighborhood is generated from the previous values of decision variables, xj, of the model. The constraints that define neighborhoods are:

5. Heuristics based on Corridor Method

,j j jx R x x R j

xj : variable values confined in the neighborhood

j: index of the set of variables which define the neighborhoodRZ+: parameter that determines the size of the neighborhood.

Corridor constraints used in the project

5. Heuristics based on Corridor Method

( , )pd

p d MX

xcc nc R

( , )mn

m n MX

xcc R

xccpd: existence of wire connecting p and d (binary).RZ+ is a parameter that determines the size of the neighborhood.nc: number of wires of the incumbent solution. MX: set of all pairs of points (p, d) of the incumbent solution that

are interconnected by a wire, p is the source and d is the destination.

Constraints that deny the possibility of connection between points outside MX.

• Constraints added to accelerate the computing and to allow the achieving of a local optimal solution

5. Heuristics based on Corridor Method

xccmn: existence of wire connecting m and n (binary).X: set of points p of the incumbent solution that are connected

with another point.MX: set of all pairs of points (p, d) of the incumbent solution that

are interconnected by a wire, p is the source and d is the destination.

0mnm X n X

xcc

Constraints that maintain the basic structure of the microgrids

• These constraints do not allow the change of direction of the connection, and so the basic structure of microgrids remains intact. On the other hand the generation points may be the same as in the incumbent solution or may change to some new added points.

• Constraints added to accelerate the computing and to allow the achieving of a local optimal solution

5. Heuristics based on Corridor Method

xccdp: existence of wire connecting d and p (binary)MX: set of all pairs of points (p, d) of the incumbent solution that

are interconnected by a wire, p is the source and d is the destination.

0dpxcc (p,d)MX

Additional constraints that limit the distance of connection (optional).

• Constraints added to accelerate the computing and to allow the achieving of a local optimal solution

– Option 1: fixed limit distance

– Option 2: equivalent limit distance

5. Heuristics based on Corridor Method

xcpdc: existence of wire connecting p and d of type c (binary)L[p,d]: distance from p to d.dmax: distance limit allowed for connectiondmax_eq: equivalent distance is worth to connect two points

1

* [ , ] maxC

pdcc

xc L p d d

p, d

1

* [ , ] max_eq[p,d]C

pdcc

xc L p d d

p, d

Additional constraints that limit cost (optional). • Constraints added to accelerate the computing and to allow the achieving of

a local optimal solution

5. Heuristics based on Corridor Method

1 1 1

1

A C B

a pa pd c pdc b pbp P a p P d D c p P b

I

i pii

CA xa L CC xc CB xb

CI xi

1 1

_S Z

d s ps z pzd D p P s p P z

CM xm CS xs CZ xrs z incumbent

Algorithm Stage 1

Proposed relaxation:• xapa, xsps, xp: not relaxed given that obtained solutions tend to determine

fractions of generators avoiding the creation of microgrids.

• Xccpd not relaxed, for an excessive number of connections are created and all the points are supplied by a single point of generation.

• xbpb, xcpdc, xipi, xrspr and xmd: relaxed variables.

Stage 2. Taking advantage of the initial solution obtained from stage 1

Addition of new constraints • Corridor constraints• Constraints that deny the possibility of connection between points outside MX• Constraints that maintain the basic structure of the microgrids

Local neighborhood searching

5. Heuristics based on Corridor Method

6. Instances

Characteristics of instances– Randomly generated based on real project in El Alumbre (Perú):

• Number of consumption points: 10, 20, 30, 40, 50, 60, 70, 80 and 90.• Consumption points concentrations:

– Low density; 25% of consumption points concentrated in 20% of area. – High density; 50% of consumption points concentrated in 20% of area.

• Energy and power demand by consumption point: – 280Wh/day and 200W respectively. – 420Wh/day and 300W respectively.

• Wind potential: – Normal (as wind map). – High (multiplying by 1,5 the wind map values).

– For each combination of the 4 parameters (number of points of consumption, consumption points concentration, energy and power demand and wind potential) were generated 5 instances:Total 9 x 2 x 2 x 2 x 5 = 360 instances

7. Analysis of results

Heuristic evaluation comparing with H0 (MILP model resolution for 1 hour).

Characteristics of heuristics implemented

CM1, CM2 and CM3: Different heuristics based on Corridor method Trm: Computing limit of time of relaxed model (stage 1)GAPrm: GAP of relaxed model (stage 1)R: number of connection changes allowed between iterations (stage 2)Ti: Computing limit of time for stage 2GAPi: GAP of stage 2dmax: maximum distance of connection allowed

Heuristics Trm GAPrm R Ti GAPi dmax Z limited

CM1 2700 25% 5 900 1% 500 No

CM2 2700 25% 5 900 1% No

CM3 2700 25% 5 900 1% equivalent

Yes

7. Analysis of results

Results at the end of stage 2CM1

No. Housings

% z

Impro-vement

T

average

No.

instances

St Dv CM2

No.

Housings

% z

Impro-vement

T averag

e

average

No.

instances

St Dv

10 -0,51 53 40 1,38 10 -0,64 151 40 1,48

20 -0,46 1056 40 1,08 20 -0,51 2067 40 1,10

30 -0.93 2159 40 1,81 30 -1,12 2232 40 1,83

40 -1,15 2308 40 3,76 40 -1,83 2322 40 3,67

50 1,74 3015 40 4,68 50 -0,27 3127 40 4.22

60 4,42 3187 40 4,93 60 0,01 3167 40 5.65

70 6,08 3468 40 5,17 70 0,98 3426 40 3.83

80 5,46 3600 40 5,17 80 0,08 3600 40 2.36

90 1,15 3600 40 2,69 90 -0,37 3600 40 1.87

7. Analysis of results

Results at the end of stage 2CM1

No. Housings

% z

Impro-vement

T

average

No.

instances

St Dv CM3

No.

Housings

% z

Impro-vement

T averag

e

average

No.

instances

St Dv

10 -0,51 53 40 1,38 10 -0,50 130 40 1,39

20 -0,46 1056 40 1,08 20 -0,48 1952 40 1,12

30 -0.93 2159 40 1,81 30 -0,66 3044 40 1,89

40 -1,15 2308 40 3,76 40 -0,83 3191 40 3,72

50 1,74 3015 40 4,68 50 1,97 3342 40 4.36

60 4,42 3187 40 4,93 60 4,66 3332 40 4.65

70 6,08 3468 40 5,17 70 5,67 3600 40 4,99

80 5,46 3600 40 5,17 80 4,98 3600 40 5,09

90 1,15 3600 40 2,69 90 1,19 3600 40 2,75

7. Analysis of results

CM1 and CM3 give better results than H0

The best results were achieved for CM1: 6.08% of average improvement comparing with H0 for instances of 70 consumption points

8. Conclusions

In this paper we present a heuristics based on MILP design for rural electrification systems.

The MILP heuristic provide the location of the generators and the design of possible microgrid considering wind and solar resource

There has been a computing experience over 360 instances generated based on a real project

The results have been satisfactory for the heuristic studied

Thank you for your attention

Corridor Method heuristics to solve rural electrification projectsJoan Triadó Aymerich, Dra. Laia Ferrer Martí, Dr. Alberto García Villoria,

Dr. Rafael Pastor Moreno

Universitat Politècnica de Catalunya- Barcelona Tech.

Institut d’Organització i Control

With the support of:

2013 ICSO-HAROSA International Workshop on Simulation-Optimization & Internet Computing

BARCELONA 10-12 July 2013

Ministerio de Ciencia e Innovación de España, proyecto ENE2010-15509, cofinanciado por FEDER.