An Emission Constraint Environment Dispatch Problem Solution with Microgrid using Whale

Optimization Algorithm

Indrajit N. Trivedi

Department of Electrical Engineering GEC, Gandhinagar (Gujarat) India

forumtrivedi@gmail.com

Motilal Bhoye Department of Electrical Engineering L.E. College, Morbi (Gujarat) India

mtbhoye@gmail.com

R. H. Bhesdadiya Department of Electrical Engineering L.E. College, Morbi (Gujarat) India

rhblec@gmail.com

Pradeep Jangir Department of Electrical Engineering L.E. College, Morbi (Gujarat) India

pkjmtech@gmail.com

Narottam Jangir Department of Electrical Engineering L.E. College, Morbi (Gujarat) India

nkjmtech@gmail.com

Arvind Kumar Department of Electrical Engineering

SSEC Bhavnagar, (Gujrat) India akbharia8@gmail.com

Abstract—In this work, microgrid is modern small scale power system of the centralized electricity for a small community such as villages and commercial area. Microgrid consists of microsources like distribution generator, solar and wind units, etc., and different loads. In the microgrid, the energy management system (EMS) having a problem of Combined Economic Emission Dispatch (CEED) and it is optimized by metaheuristic techniques. The CEED is the procedure to scheduling the generating units within their bounds together with minimizing the fuel cost and emission values. The Whale Optimization Algorithm (WOA) is applied for the solution of CEED problem in the MATLAB environment. The minimization of total cost and total emission are obtained for all sources included. The result shows the comparison of WOA with the Gradient Method (GM), Ant Colony Optimization (ACO) and Particle Swarm Optimizer (PSO) technique for the two different cases which are Economic Load Dispatch (ELD) without emission and with emission. The results are calculated for different power demand of 24 hours. The results obtained with WOA gives better cost reduction in less iterations as compared to GM, ACO and PSO which shows the effectiveness of the given algorithm. The key objective of this work is to solve the CEED problem to obtained optimal system cost.

Keywords— Microgrid; Combined Economic Emission Dispatch; Solar Generation Forecast; Wind Generation Forecast; Whale Optimization Algorithm.

I. INTRODUCTION

Electrical power utilities need to guarantee that electrical power necessity from the consumer end is fulfilled in accordance with the reliable power quality and minimum cost. Due to increasing technological research, industrial development and population, the power demand increases.

With increasing electrical power demand worldwide, the non-renewable energy sources are reducing day after day. To solve the problem of increasing electrical power demand more renewable energy sources (RES) should be used. With the use of more RES, the power generation can be increase which is the modern research scenario at the present time.

In this paper, the analysis of isolated mode microgrid (MG) is considered. Combined Economic Emission Dispatch (CEED) is an elementary problem in the microgrid, which can be optimized by meta-heuristic optimization techniques. The CEED is the procedure to scheduling the generating units within their bounds together with the minimization of fuel cost and emission [1]. Hence, for the solution of CEED problem Whale Optimization Algorithm [2] is used. This algorithm is always trying to find accurate value in less iteration.

II. MICROGRID STRUCTURE

The Distributed Energy Resources (DERs) are used in a specific small area which is known a microgrid. A microgrid is consummate specific purposes like reliability, cost reduction, emission reduction, efficiency improvement, use of renewable sources and continuous energy source [3]. Microgrid consists of DG units like Wind unit, Solar unit, hydro unit, Biomass unit, Natural gas generator, Diesel generator, Combined Heat and Power(CHP) and Battery energy storage. The Microgrid also connected different types of loads like Agriculture, Industrial, Commercial, Residential, University and Vehicle charging. The microgrid is connected to the micro-sources like as Wind turbine, Solar Cell, CHP and battery Storage with supply produced power to the different loads through the point of common coupling (PCC) [4].

978-1-4799-5141-3/14/$31.00 ©2016 IEEE

The main advantage of a microgrid is combine all benefits of renewable energy sources to reduce the carbon generation and power generation efficiency improvement. Microgrid has two modes of connection: first is Grid coupled mode and second is isolated mode [5]. In the first mode, Microgrid is connected to the main grid via PCC. In the isolated mode, microgrid is not connected from the main grid.

Micro-source controllers used in MG controls the micro-source and loads. In the isolated mode, MG is isolated from the utility grid and deliver power to the important loads. Rating of this critical loads is considered equal to 240MW. A microgrid is an answer to energy crisis in the power system. Reduced transmission loss to the DERs (microgrid) connection of transmission line in a different location [6]. Power generation cost is reduced using distributed energy resources in microgrid as well as microgrid uses many renewable energy resources. Environmental emission is more reduced to be using microgrid in power system and achieve high quality and reliable energy supply to the critical loads [7].

III. MATHEMATICAL MODEL OF ISOLATED MODE MICROGRID

A. Generation Fuel Cost Function

The main objective of the Economic Load Dispatch (ELD) problem solution is to examine the generation levels of every on-line unit which decreases the total generation fuel cost and reduces the emission level of the system, together with satisfying a system constraint [1]. The objective of ELD is to reduce the generation fuel cost together with satisfying the power demand of a modern power system during a given duration of time considering the power system operating constraints. ELD formulation of the generators for Microgrid is given in. The Fuel cost function of Generators quadratic equation is [5]:

C1

( )NG

i ii

F F P=

= (1)

Where, CF = Total fuel cost, NG = Number of generators

( )i iF P = Fuel cost of the ith generator

iP = Active power generation of ith generator 2( )i i i i i i iF P u P v P w= + + (2)

iu = Cost coefficient of ith generator in [$/MW2h]

iv = Cost coefficient of ith generator in [$/MWh]

iw = Cost coefficient of ith generator in [$/h]

2

1

( )NG

C i i i i ii

Min F u P v P w=

= + + (3)

The various pollutants like Carbon dioxide, Sulphur dioxide and Nitrogen oxide are released as a result an operation of the diesel generator, gas Generator, CHP [8]. Reduction of these pollutants is compulsory for every generating unit. To achieve this goal, new criteria are included in a formulation of the ED problem as follows.

( )2

1

n

T i i i i ii

E x P y P z=

= + + (4)

Where, TE = Total Emission Value

ix = Emission coefficient of ith generator in [kg/MW2h]

iy = Emission coefficient of ith generator in [kg/MWh]

iz = Emission coefficient of ith generator in [kg/h]

Price penalty factor (PPF) hi is used to convert multi-objective CEED problem into a single objective optimization problem [9].

( ) ( )2 2

1

n

T i i i i i i i i i i ii

F u P v P w h x P y P z=

= + + + + + (5)

Where, TF = Total CEED Cost

ih = Price penalty factor (PPF)

The function of PPF is to transfers the physical sense of emission measure from a mass of the emission to the fuel cost for the emission. The variance among these penalty factors is in the fuel cost mass for emission in the last optimal fuel cost for generation and emission [10]. The PPF for multi-objective ED problem is formulated taking the ratio fuel cost to emission value of the corresponding generators as follows [11]:

Min-Max price penalty factor is formulated as:

( )( )

2min min

2max max

i i i i i

i

i i i i i

u P v P wh

x P y P z

+ +=

+ + [$/kg] (6)

B. Solar Generation Forecast

The cost function is [4]:

( ) p ESolar Solar SolarF P aI P G P= + (7)

[1 [(1 ) ]N

ra

r −=− +

(8)

Where, SolarP =Solar generation in [kW]

r = Interest scale = 0.09, a = Annuitization coefficient N = Investment duration = 20 years

pI = Ratio of Investment cost to unit establish power = 5000$/kW

EG = Operational cost and maintenance cost = 0.016$/kW. The cost function for solar energy can be calculated as:

( ) 547.7483 *Solar SolarF P P= (9)

The 24 hours’ data of solar generation are shown in Table I.

C. Wind Generation Forecast

The cost function is [5]:

( ) p EWind Wind WindF P aI P G P= + (10)

pI = Ratio of Investment cost to unit establish power = 1400$/kW

The cost function for wind energy can be calculated as:

( ) 153.3810*Wind WindF P P= (11)

TABLE I. SOLAR GENERATION [1]

TABLE II. WIND GENERATION [1]

The 24 hours’ data of wind generation are shown in Table II. D. Constraint Function (a) Isolated type of MG: No trading of energy from the main grid [5]. (b) Power Balance constraint:

1 2 3 4 5LoadP P P P P P= + + + + (12)

(c) Power Generation constraint: Each generator output bounded by minimum and maximum boundaries.

min maxi i iP P P≤ ≤ (13) max

iP = Max. output power of ith generator, m iniP = Min.

output power of ith generator.

IV. WHALE OPTIMIZATION ALGORITHM (WOA)

In meta-heuristic algorithm, a newly purposed optimization algorithm called Whale Optimization Algorithm (WOA) [2], which inspired from the bubble-net hunting strategy. Algorithm describes the special hunting behaviour of humpback whales; the whales follows the typical bubbles causes the creation of circular or ‘9-shaped path’ while encircling prey during hunting. Simply bubble-net feeding/hunting behaviour could be understanding such that humpback whale went down in water approximate 10-15 meter and then after start to produce bubbles in a spiral shape encircles prey and then follows the bubbles and moves upward

the surface. Mathematic model for Whale Optimization algorithm (WOA) is given as follows [2]:

A. Encircling prey equation

Humpback whale encircles the prey (small fishes) then updates its position towards the optimum solution over the course of increasing number of iteration from start to maximum number of iteration.

. * ( ) ( )D C X t X t= −

(14)

( 1) * ( ) .X t X t A D+ = −

(15)

Where: A

, D

are coefficient vectors, t is current iteration,

* ( )X t

is position vector of optimum solution so far and

( )X t is position vector.

Coefficient vectors A

, D

are calculated as follows:

2 *A a r a= −

(16)

2*C r=

(17)

Where: is a variable linearly decrease from 2 to 0 over the course of iteration and r is a random number [0, 1].

B. Bubble-net attacking method

In order to mathematical equation for bubble-net behaviour of humpback whales, two methods are modelled as:

1. Shrinking encircling mechanism: This technique is employed by decreasing linearly the

value of a

from 2 to 0. Random value for vector in rang between [-1, 1].

2. Spiral updating position: Mathematical spiral equation for position update between

humpback whale and prey that was helix-shaped movement given as follows:

( 1) '* * cos(2 ) * ( )btX t D e l X tπ+ = +

(18) Where: l is a random number [-1, 1], b is constant defines

logarithmic shape, ' * ( ) ( )D X t X t= −

expresses the

distance between ith whale to the prey mean best solution so far.

We assume that there is 50-50% probability that whale either follow the shrinking encircling or logarithmic path during optimization. Mathematically we modelled as follows:

*( ) . 0.5( 1)

'. .cos(2 ) *( ) 0.5bl

X t AD if pX t

D e l X t if pπ

− < + = + ≥

(19)

Where: p expresses random number between [0, 1]. 3. Search for prey

A

Vector can be used for exploration to search for prey;

vector A

also takes the values greater than one or less than -1. Exploration follows two conditions

. randD C X X= −

(20)

Time (Hrs)

Solar generation

(MW)

Time (Hrs)

Solar generation

(MW)

Time (Hrs)

Solar generation

(MW) 1 0 9 24.05 17 9.57

2 0 10 39.37 18 2.31

3 0 11 7.41 19 0

4 0 12 3.65 20 0

5 0 13 31.94 21 0

6 0.03 14 26.81 22 0

7 6.27 15 10.08 23 0

8 16.18 16 5.30 24 0

Time (Hrs)

Wind generation

(MW)

Time (Hrs)

Wind generation

(MW)

Time (Hrs)

Wind generation

(MW)

1 1.7 9 20.58 17 3.44 2 8.5 10 17.85 18 1.87 3 9.27 11 12.80 19 0.75 4 16.66 12 18.65 20 0.17

5 7.22 13 14.35 21 0.15

6 4.91 14 10.35 22 0.31 7 14.66 15 8.26 23 1.07

8 26.56 16 13.71 24 0.58

( 1) . randX t X A D+ = −

(21)

Finally, follows these conditions [2]:

1A >

enforces exploration to WOA algorithm to

find out global optimum avoid local optima.

1A <

for updating the position of current search

agent/best solution is selected.

TABLE III. CONTROL PARAMETER OF WOA

Control Parameter Value

Population Size 50

Maximum Iteration (N) 500

Number of variable (d) 3

Random number (r) (0 to 1)

V. DATA OF MICROGRID

TABLE IV. GENERATION POWER MIN-MAX LIMITS [1]

Min Power (MW) Max Power (MW)

Generator-1 37 150

Generator-2 40 160

Generator-3 50 190

The min. limit and max. limit of the output power of all micro-sources is shown in Table IV.

TABLE V. FUEL COST COEFFICIENT OF THREE GENERATORS [1]

u ($/MW2h)) v ($/MWh) w ($/h)

Generator-1 0.024 21 1530

Generator-2 0.029 20.16 992

Generator-3 0.021 20.4 600

Table V shows fuel cost coefficient of three generators. Table VI shows emission coefficient of three generators. Table VII shows the system power demand for 24 hours of a day.

TABLE VI. EMISSION COEFFICIENT OF THREE GENERATORS [1]

TABLE VII. POWER DEMAND FOR 24 HOURS [1]

VI. RESULTS OF MICROGRID ED AND CEED PROBLEM

A. All sources included

1. WITHOUT EMISSION

TABLE VIII. ALL SOURCES INCLUDED WITHOUT EMISSION

Time (Hrs)

PD (MW) Generation (MW) GM Cost ($/hr)

[1] ACO Cost ($/hr)

[1] PSO Cost ($/hr) WOA Cost ($/hr)

G1 G2 G3

1 140 48 40 50 6297 6134 6117 6113 2 150 51 40 50 6474 6312 6292 6192 3 155 56 40 50 6565 6439 6292 6295 4 160 54 41 51 6650 6512 6235 6228 5 165 63 44 50 6759 6682 6544 6577

6 170 64 48 51 6867 6807 6737 6742 7 175 62 42 50 7209 6837 6491 6489 8 180 47 40 50 7762 6780 6093 6093 9 210 65 50 51 8649 7457 6751 6750

10 230 67 52 54 9713 7852 6923 6912

11 240 74 68 77 8722 8358 8034 8052

12 250 76 71 80 8794 8594 8150 8278 13 240 70 59 65 9654 8146 7409 7417

x (kg/MW2h)) y (kg/MWh) z (kg/h)

Generator-1 0.0105 -1.355 60

Generator-2 0.008 -0.6 45

Generator-3 0.012 -0.555 30

Time (Hrs)

Load (MW)

Time (Hrs)

Load (MW)

Time (Hrs)

Load (MW)

1 140 8 210 17 170 2 150 10 230 18 185 3 155 11 240 19 200 4 160 12 250 20 240 5 165 13 240 21 225 6 170 14 220 22 190 7 175 15 200 23 160 8 180 16 180 24 145

14 220 68 57 58 9013 7760 7101 7224 15 200 68 55 59 7905 7424 7133 7120 16 180 64 46 52 7268 6943 6652 6661 17 170 62 44 50 7276 6756 6554 6561 18 185 68 55 57 7288 7146 7117 7129 19 200 71 61 67 7544 7538 7541 7535

20 240 77 75 86 8567 8517 8751 8530 21 225 75 70 79 8167 8153 8404 8294 22 190 69 58 62 7314 7316 7330 7311 23 160 63 46 50 6674 6605 6588 6594 24 145 54 41 50 6389 6275 6261 6259

Total 4580 1536 1243 1399 183520 173343 167500 167356

Table VIII shows that cost of all sources included without emission. This table also shows cost of GM, ACO, PSO, WOA. The cost of the all sources included in MG shows that ED problem to be optimal for WOA compare to other techniques.

2. WITH EMISSION

TABLE IX. ALL SOURCES INCLUDED WITH EMISSION

Time (Hrs)

PD (MW) Generation (MW)

GM Cost ($/hr) [1]

ACO Cost ($/hr) [1]

PSO Cost ($/hr) WOA Cost ($/hr)

G1 G2 G3

1 140 48 40 50 8529 7250 7153 7120

2 150 51 40 50 8648 7511 7203 7186

3 155 56 40 50 8675 7704 7278 7282

4 160 54 41 51 8795 7742 7234 7233

5 165 63 44 50 8758 8211 7516 7545

6 170 64 48 51 8848 8459 7729 7737

7 175 62 42 50 8964 8406 7457 7455

8 180 47 40 50 9308 7923 7138 7138

9 210 65 50 51 9609 9040 7745 7665

10 230 67 52 54 10049 9599 7920 7947

11 240 74 68 77 11520 11184 9240 9337

12 250 76 71 80 12098 11616 9386 9335

13 240 70 59 65 10676 10320 8483 8496

14 220 68 57 58 9982 9707 8124 8014

15 200 68 55 59 9569 9351 8195 8378

16 180 64 46 52 9030 8469 7633 7638

17 170 62 44 50 8872 8189 7525 7528

18 185 68 55 57 9273 9061 8146 8156

19 200 71 61 67 9990 9852 8639 8665

20 240 77 75 86 12646 11897 10353 10112

21 225 75 70 79 11496 11101 9710 9625

22 190 69 58 62 9534 9488 8390 8430

23 160 63 46 50 8667 8077 7846 7590

24 145 54 41 50 8517 7498 7254 7252

Total 4580 1536 1243 1399 232053 217655 193297 192864

Table IX shows that cost of all sources included with emission.

The cost the all sources included in microgrid shows that CEED problem to be optimal for WOA compare to other Techniques.

Fig. 1 shows the comparison of cost saving of ED and CEED using WOA with a different algorithms like GM, ACO and PSO.

Fig. 1. Comparison of WOA Vs Other Techniques.

VII. CONCLUSION

In this paper, Combined Economic Emission dispatch (CEED) problem is considered in isolated mode microgrid. The WOA is applied to achieve the minimal cost of the considered system compare to GM, ACO and PSO. The prior goal of the work is to solve the CEED problem to obtain an optimum cost of the microgrid using WOA. The minimization of total cost and total emission are obtained for all sources included. Result shows the comparison of WOA with the GM, ACO and PSO for the two different cases which are ELD without emission and with emission. The results are calculated for different power demand of 24 hours. The results obtained with WOA gives better cost reduction in less iterations as compared to GM, ACO and PSO which shows the effectiveness of the given algorithm. The key objective of this work is to solve the CEED problem to obtained optimal system cost.

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