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Evolutionary algorithm based Optimization approach

for Energy Management in Microgrid

V.Geetha Minmini

Power System Engineering

Kamaraj College of Engineering and Technology

Virudhunagar

[email protected]

B.Noorul Hamitha M.E.,

AP/EE

Kamaraj College of Engineering and Technology

Virudhunagar

[email protected]

Abstract— Micro grid is an emerging technology for

the future solution. Microgrid can be created by

integrating distributed energy resources and energy

storage systems for reliable operation and to serve the

load. A microgrid not only provides backup for the grid

during emergencies, it can be used to cut the costs, or

connect to a local resource that is too small or unreliable

for traditional grid use. This paper discusses about the

minimization of system cost that is the addition of

conventional energy fuel cost and degradation cost of the

storage system, and to satisfy the load demand. This has

been proposed using evolutionary algorithm such as

Particle swarm optimization (PSO) and Grey wolf

optimizer (GWO). The unit commitment has been done

based on basic concept of Multi Agent System (MAS).

Keywords— Particle Swarm Optimization(PSO), Grey Wolf

Optimizer(GWO), Multi Agent System(MAS), Economic

dispatch(ED), Unit Commitment(UC).

I. INTRODUCTION

In all over the world the electric power is generated

by the conventional generation plant that uses fuel as a coal,

diesel etc. But these resources are exhausting and it is

available for only 60years. So, the conventional energy fuel

cost increases very high, we have to move on to the

renewable. And cost also increases because of the high usage,

mining operation, extraction, transportation etc. In order to

reduce the conventional cost we can use renewable energy

resources like wind, solar, biomass etc. The importance of

incorporating renewable has been defined in the paper[1].

The wind power plants are old ideas. It has been used

worldwide on the coastal area. But During the non windy

period, we may face the power shortage. At that time, either

we need to purchase power from our own grid or another grid.

In order to avoid it, installing solar plant gives much benefit. It

increases the Energy availability. The Energy requirement will

be satisfied. In case of using the conventional grid ,the cost

will be high for transmission installation etc.

In order to avoid this long transmission problem, A

microgrid can be used at the distribution side it will reduce the

transmission losses. Microgrid structure has been explained in

the paper[2],[3].A typical microgrid consist of Distributed

Generators (DGs), that are dispatch able units Renewable

Energy sources , that are non controllable devices; and

controllable loads, which can be cut down as per our

requirement . If excess power is available it can be sell to the

nearby power system or load. If the excess power is required it

can by buy from other suppliers [4].The optimization of the

microgrid operations is extremely important, for managing

cost-efficiently and energy resources.

II. ECONOMIC DISPATCH

The purpose of economic dispatch or optimal dispatch to

reduce the fuel cost for power system. By load scheduling, we

need to find the generation of different generators or plants, so

that the fuel cost is minimum and at the same time the total

demand and losses at any instant must be met by total

generation[5]. And the conventional generators are used for

maintaining the base load condition. The average load demand

has been calculated with the forecasted demand level.

The output from the each unit will be depends upon the

input (i.e.) fuel. For mathematically speaking the objective

function is to minimize the fuel cost. Power generated must be

equal to the load including the transmission losses without

violating the operating limits.

(1)

(2)

In order to establish the necessary condition with constraint

function as an objective function. It has been multiplied by

undetermined multiplier. This is Lagrange function [4].

  t L F

(3)

Kron and Kirchmayer is developed the loss co- efficient

method, that includes the effect of losses in the transmission

line .B matrix which is known as the transmission loss coefficient

,matrix is a square matrix which a dimension of n*n,

While n = the number of generation unit in the system .

Applying B matrix gives a solution with generated powers of

different units as the variables shows the function of

calculating P loss as the transmission loss through B matrix [6].

ij j

n

i

n

j

loss i p PB P

 

1 1

(4)

0

min ( ( ))

1

1

 

n

i

d i

n

i

P P

f Pi

International Journal of Applied Engineering Research, ISSN 0973-4562 Vol. 10 No.88 (2015)

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264

III. UNIT COMMITMENT WITH MULTI AGENT SYSTEM

A. Unit commitment

Economic dispatch gives optimum schedule corresponding

to one particular load. But load varies for each time

throughout the day. Different combination of loads is

connected in the system for various loads are known as unit

commitment. The Unit Commitment involves Turing

ON/OFF the generated as per the Forecasted Load for each

time. The Unit commitment saves much fuel consumption so

that minimize production cost.

There are many techniques are available to solve Unit

Commitment problem they are Brutes technique, Priority list

method, Dynamic programming technique. In this paper only

3 conventional sources are considered so simply brute’s

technique has been used. The UC problem includes the

following constraints Thermal constraints, minimum up time,

minimum down time, hot start cost, Cold Start Cost. The data

are taken from the paper [7]. And for the efficient dispatching,

consider environmental condition. Depending upon the

environmental condition and during the combination of Wind

and Solar power the decision should be taken. For that multi

agent system is used in this paper.

B. Multi Agent System

A multi-agent system is a loosely coupled network of

problem-solving entities (agents) that work together to find

answers to problems that are beyond the individual

capabilities or knowledge of each entity (agent). The MAS

technology for power engineering applications are explained

in the paper[8] . Multiple agents working together to achieve a

common goal

The MAS modelling is one of the best techniques to take

decision for the allocation of energy as per the demand

requirement on the system for each time period. It provides

mathematical model and artificial intelligence to select the

agents .the agents are nothing but a sensors. In this paper the

agent is taken as the conventional power. Basic concept o f the

multi agent system has been used in this paper.

When the complex task is provided then it splits into

several independent tasks to complete it. In order that, the

overall efficiency of the system increases. That leads to

increase in problem solving ability.

MAS is based on such thinking, for the completion of tasks,

many agents in coordination and cooperation, greatly

improving the problem-solving abilities [9].

Properties of MAS:

1. Reactive

2. Autonomous

3. Goal-oriented Pro-active,

4. Communicative Socially

5. Learning Adaptive

6. Flexible

IV. STORAGE MODEL

The storage is modeled to represent the dynamic variation

on the system. The Battery performance can be represented by

the efficiency described for each storage system. The storage

model has been referred from the paper[10][11]. The efficiency

denotes how much energy lost during the charging and

discharging process. And The Storage device should not

completely charge or discharged. The complete discharge may

drain out the storage device, if battery completely drained out

it cannot be charged without proper maintenance. The

minimum and maximum storage level can be denoted

as ( ), ( ) min max St t St t . Here t denotes time slots. The

equation (5), (6) denotes Battery stored power during charging

and discharging operation.

For charging period:

(5)

For Discharging period:

(6)

The Storage device is selected as per the available surplus

energy. It is denoted in the equation (7) .If it is positive value

that means load demand is higher than the available resources.

If  is negative, it meant there is some surplus energy is

available.

(7)

The degradation cost of the battery is also considered.

There are 2 types one is Entry cost and the another is usage

cost[12]. Entry cost is the fixed cost due to charging and

discharging activity. It has been represented in equation

(8),(9).

Entry cost:

(8)

(9)

Charging and the discharging function:

(10)

The fast charging or discharging, leads to usage

cost ( )

2

u t , has a more detrimental effect on the battery life

time. The equation (11) and (12) represents charging effect on

the battery. And the usage cost shows in equation (13)

Average charging and discharging amount:

(11)

(12)

Usage cost:

(13)

( )

( )

( 1) ( )

effd t

Bop t

St t   St t 

St(t 1)  Stteffc(t)Bin(t)

P (t) (P (t) P (t) P (t)) d t s w     

      C rc D dc e t  E t E  E t E 1

e t 

N

e

N

t 

1

1 1

 1

 

  1, _ 0, ,0

1, _ 0, ,0

E t if otherwise

E t if otherwise

D

C

 

 

u t  BoptorBint 2

x t 

N

u

N

t 

1

2 2

 1

  2 2 g u ku

 

International Journal of Applied Engineering Research, ISSN 0973-4562 Vol. 10 No.88 (2015)

© Research India Publications; http/www.ripublication.com/ijaer.htm

265

Fuel cost $/day

Total number of slots

Energy stored at time t

Conventional power in MW at

slot t (KW)

surplus power at slot t

solar power in KW at slot t

Load demand in KW at slot t

wind power in KW at slot t

e t  1

Entry cost of battery usage at

time slot t. ($/hr)

E t  E t  C D , Charging and discharging

function.

 rc dc E ,E Charging and discharging cost

coefficient

 1 e

Entry cost

 2 u

Usage cost

k  Battery cost coefficient

   2 g u

 Usage cost($/day)

V. IMPLEMENTATION WITH ALGORITHM

A. Problem Formulation

This paper deals with the System cost that is the

combination of fuel cost of the conventional generator and

the degradation cost of the battery for N number of slots.

(14)

(15)

(16)

And it is subjected to the following constraints

Constraints:

(17)

(18)

B. Particle Swarm Optimization(PSO)

In the algorithm, the swarm (bird) movement has been

modeled according to the possible best position, where the

whole swarm tries to reach the best position .The each swarm

updates its position and velocity in order to reach the best

value. The swarms are coordinated and leads to the best

position that is known as gbest [13]

Step I: Initialization

Initialize population size, number of iteration and

variables, upper and lower limits [14].

Fig.1.PSO Flowchart

Step II: Generation

The particles size and velocity are generated randomly

according to the population size within the allowable range.

The variables of each particle in the population are

conventional grid power

Step III : Fitness Function Calculation

PSO considers the variable as continuous. When the power

is tried by each population it is checked whether it is within

the limit & the unit commitment is also done for each

iteration. The power and the fuel cost values are updated.

The best position that is associated with the best

fitness encountered so far is called the Pbest. For each particle

P (t)  t

(t) 

P (t)  w

P (t)  s

P (t)  d

S (t)  t

N 

( )  i f G

min {( ( )) }

1

bat

N

t

t DEG P f  

f P aP bP c t t t    2 ( )

    1 2 DEG x t g x bat  

( ) ( ) ( ) min max P t P t P t t t t  

( ) ( 1) ( ) min max St t  St t   St t

International Journal of Applied Engineering Research, ISSN 0973-4562 Vol. 10 No.88 (2015)

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266

in the population, Pbest can be determined and updated during

the search. Gbest is the best position among all the individual

best position achieved so far.

Step IV : Velocity and particle updating

The particle velocity and position is updated[15].

    id id id id gd id v  w v  c r p  x  c r p  x 1 1 2 2 *

(19)

Step V: Stopping criteria

The procedures mentioned in Steps III and IV is

repeated until the variables converge to a stable point.

C. Grey Wolf Optimizer

Grey wolf algorithm is a meta-heuristic optimization

technique, which is based on wolf behavior. It is developed by

Mirjalili et.al in 2014[16]. The hierarchy of wolf is ordered

as ,  , , . The fittest solution is considered as

follows ,  , . The rest of the candidates are considered

as . The four types can be used for simulating the leadership

hierarchy. GWO algorithm provides competitive results . The

solution of the problem is to find the prey, which is nothing

but an optimal solution. The hunting behavior of the wolf is

given as follows,

 Encircling

 Hunting

 Attacking

 Exploring

a. Encircling:

During hunt the grey wolf encircles the prey, which

is mathematically modeled. To detect the distance of the prey

D C X t  Xt  P

  

 . 

(20)

X t 

=position of the wolf

X t  P =position of the prey

C 

, A 

=Vector coefficient

t=current iteration for identifying the next position

where the wolf should move

Xt  X t  AD P

   

1   . (21)

For A ar a

  

  1 2 (22)

2 C 2.r

 

 (23)

a

=decreased from 2-0

1 r , 2 r =[0,1] (random numbers)

b. Hunting

Hunting means ability to find the location of the prey.

For simulating hunting in mathematically alpha, beta and delta

should have good knowledge about location of prey. So it has

to be stored the previous location.

D C X X

   

    . 1 (24)

D C X X

   

    . 2 (25)

D C X X

   

    . 3 (26)

.( ) 1  1  X X A D

   

 

(27)

.( ) 2  2  X X A D

   

 

(28)

.( ) 3  3  X X A D

   

 

(29)

Where,

1 2 3 X , X , X -

the position vectors of grey

wolves

1 2 3

1 2 3

, ,

, , ,

C C C

A A A

- the coefficient vectors

   X , X , X -

the position vectors of alpha,

beta and delta

X - Position vector of a grey wolf

t - Current iterations

1 2 r , r - Random vectors

c. Attacking prey (Exploitation):

The grey wolfs stops the hunt by attacking the prey.

A 

is a random value in the interval [-2a, 2a] where a and it

should satisfy the condition A 1 that Forces the wolf to

attack the prey.

d. Search for prey:

Grey wolf mostly search based on the position of the

alpha, beta and delta. They deviate from each other and

focalize to attack the prey. A <1 forces the wolf to diverge

from the prey with an assumption of getting a fitter victim. C 

also helps in exploration. C 

contain random values in [0,2].

TheC 

is can also be considered as the effect of obstacles to

approaching prey in nature. Depending on the position of prey

it gives a weight to the prey and makes it tougher and farther

to reach for wolves and vice versa.

Pseudo code of the GWO algorithm:

Initialize the grey wolf population i X (i 1,2,...n)

For n=1<N

Initialize a, A and C

Find out the fitness of each search agents

  X the best search agent

 X = the second best search agent

 X = the third best search agent

Evaluate the fitness

Find Unit commitment by MAS

while (t< maximum number of iterations)

for each search agent

Update the position of search agent

end for

update a, A, and C

find out the fitness of all search agents

International Journal of Applied Engineering Research, ISSN 0973-4562 Vol. 10 No.88 (2015)

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267

update    X , X , X

t=t+1end while

n=n+1

return  X

VI. RESULT AND DISCUSSION

A. Tools and Test System.

The programming codes were developed using MATLAB.

And The Decision making is done with Multi agent system

concept and the units are allocated as per the power and the

load data. Here the conventional generators data are taken

from the paper [15] .The bus system used here is a 12 bus

system. The wind and a solar plant are assumed to be

connected in fourth and fifth bus and its rating is about 1 MW

and 2 MW. Power varies according to the wind speed.

Simulations are performed in computer with Intel i3 processor

2.40 GHz and 3.00 GB RAM.

B. Simulation results of PSO& GWO

The Table I represents the initialized parameters in

two algorithms. It includes population size, number of

iteration number of variables. And the boundary values are

given as per the fuel cost limits.

TABLE I. INITIAL PARAMETER VALUES FOR PSO AND GWO

Parameters PSO GWO

Population Size 100 100

Number of Iterations 100 100

Number of variables 1 1

The table II represents the total grid power utilized by the

load. It has been compared with both PSO and GWO. The

power varies as per the load requirement.

TABLE II. CONSUMED GRID POWER COMPARISION BY PSO AND

GWO

Hour Consumed grid power

using PSO(KW)

Consumed grid power

using GWO(KW)

1 3550 3069.672

2 2250 1900

3 3550 1900

4 3550 1900

5 3550 3069.672

6 3550 3069.672

7 3550 3069.672

8 3550 3069.672

9 3550 3069.672

10 3550 3069.672

11 3550 3069.672

12 3550 3069.672

13 3550 3069.672

14 3550 3069.672

15 3550 3069.672

16 3550 3069.672

17 3550 3069.672

18 3550 3069.672

19 3550 3069.672

20 3550 3069.672

21 3550 3069.672

22 3550 3069.672

23 2250 1900

24 2250 1900

TABLE III. SYSTEM COST COMPARISION BETWEEN PSO AND GWO

Algorithm used

System cost(fuel cost

&battery degradation

cost)($/day)

PSO 35368.9

GWO 36430.0

In TABLE III, The system cost comparison. The cost has

been found by two algorithms for a day period. And the PSO

gives minimum cost than GWO.

Fig.2.convergence graph for PSO

Fig.3. convergence graph of GWO

The figure 2 and 3 shows the convergence graph

using PSO and GWO. And it has been converged at 100th

iteration. And figure 4 and 5 shows the consolidated output of

available wind power, solar power, load variation etc.

International Journal of Applied Engineering Research, ISSN 0973-4562 Vol. 10 No.88 (2015)

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268

Fig.4. consolidated output for N number of slots by PSO

Fig.5. consolidated output for N number of slots by GWO

Without the storage device there is surplus energy is available on applying both PSO and GWO has shown in the figure 6 and 7. And in some of the place the available sources are not enough to satisfy the demand that is represented in figure 8 and 9.

Fig.6. excess energy available by using PSO

Fig.7. Excess energy available using GWO

Fig.8. required discharge level using PSO

Fig.8. required discharge level using GWO

After charging the excess power in the storage system, it satisfies load the demand using PSO. But the load demand could not meet the effectively using GWO. That has been shown in the figure 9 and 10. International Journal of Applied Engineering Research, ISSN 0973-4562 Vol. 10 No.88 (2015)

© Research India Publications; http/www.ripublication.com/ijaer.htm

269

Fig.9. Load satisfied using stored energy in the storage system (PSO)

Fig.10. Load satisfied using Stored energy in the storage system (GWO)

.

VII. CONCLUSION

This paper has presented an effective method for solving load management problem. The grey wolf optimizer and the Particle swarm optimization algorithms are implemented and the Multi Agent System (MAS) basic concept has been used to allocate the solar and wind power as per the load. The objective function is taken as the minimization of fuel cost and the degradation cost of the battery. The numerical result shows that the PSO gives better result than GWO. And the demand has been satisfied perfectly using Particle swarm optimization approach.

VIII. REFERENCES

[1] Kai Strunz, Ehsan Abbasi, and Duc Nguyen Huu,‖ DC Microgrid for Wind and Solar Power Integration‖ IEEE journal of emerging and selected topics in power electronics, vol. 2, no. 1, march 2014,pp.115-126

[2] Nikos Hatziargyriou, Hiroshi Asano, Reza Iravani, and Chris Marnay,‖Micro grid‖ IEEE Power Magazine 1540-7977/07©2007

[3] Ramon Zamora a,b, Anurag K. Srivastava,‖ Controls for microgrids with storage: Review, challenges, and research needs‖ Renewable and Sustainable Energy Reviews 14 (2010) 2009–2018

[4] Alessandra Parisio and Luigi Glielmo,‖ A Mixed Integer Linear Formulation for Microgrid Economic Scheduling‖ Virtual Power Plants, Distributed Generation, Microgrids, Renewables and Storage (IEEE SmartGridComm)

[5] M.Jeraldin Ahila,―Power System Cperation and Control‖

[6] Revathy K, Nithiyanandham C,‖ Economic Dispatch Using Particle Swarm Optimization‖ International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering Vol. 3, Special Issue 4, May 2014

[7] T. Logenthiran, Dipti Srinivasan, Ashwin M. Khambadkone,‖ Multi-agent system for energy resource scheduling of integrated microgrids in a distributed system‖ Electric Power Systems Research 81 (2011) 138–148

[8] Stephen D. J. McArthur, Euan M. Davidson, Victoria M. Catterson, , Aris L. Dimeas, Nikos D. Hatziargyriou, Ferdinanda Ponci, Toshihisa Funabashi ,‖Multi-Agent Systems for Power Engineering Applications—Part I: Concepts, Approaches, and Technical Challenges‖ IEEE transactions on power systems, vol. 22, no. 4, november 2007.

[9] Sufang Chen,‖ Power Dispatching Sheet Generation System based Multi-Agent‖ 2010 International Conference on Computer, Mechatronics, Control and Electronic Engineering (CMCE)

[10] Tianyi Li, Min Dong,‖ Real-Time Energy Storage Management:Finite-Time Horizon Approach‖ 2014 IEEE International Conference on Smart Grid Communications.

[11] Katayoun Rahbar,,Jie Xu,Rui Zhang,‖ Real-Time Energy Storage Management for Renewable Integration in Microgrid: An Off-Line Optimization Approach‖ IEEE TRANSACTIONS ON SMART GRID, VOL. 6, NO. 1, JANUARY 2015

[12] Minh Y Nguyen, Dinh Hung Nguyen and Yong Tae Yoon,‖ A New Battery Energy Storage Charging/Discharging Scheme for Wind Power Producers in Real-Time Markets’Energies 2012, 5, 5439-5452.

[13] Yimin Zhou, Guoqing Xu, Ming Chang,‖ Demand Side Management for EV Charging/Discharging Behaviours with Particle Swarm Optimization‖,Proceeding of the 11th World Congress on Intelligent Control and Automation Shenyang, China, June 29 - July 4 2014.

[14] S. Nagalakshmi, N. Kamaraj,‖ Comparison of computational intelligence algorithms for loadability enhancement of restructured power system with FACTS devices‖ Swarm and Evolutionary Computation 5 (2012) 17–27.

[15] Revathy K, Nithiyanandham.C,‖ Economic Dispatch Using Particle Swarm Optimization‖ International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering Vol. 3, Special Issue 4, May 2014.

[16] Seyedali Mirjalili,Seyed Mohammad Mirjalili, ndrew Lewis,‖ Grey Wolf Optimizer‖ Advances in Engineering Software , vol. 69, pp. 46-61, 201.

International Journal of Applied Engineering Research, ISSN 0973-4562 Vol. 10 No.88 (2015)

© Research India Publications; http/www.ripublication.com/ijaer.htm

270

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