# A Domestic Microgrid with Optimized Home Energy Management System

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## Abstract

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## 1. Introduction

- We proposed three hybrid schemes: WDGA, WDGWO and WBPSO.
- This work considered the grid-connected microgrid system with multiple appliances.
- Our proposed work minimized the electricity cost and PAR.
- By implementing our proposed schemes, user can enjoy maximum comfort.
- Imported electricity was also reduced by integrating microgrid.

## 2. Literature Review

## 3. Motivation and Problem Description

## 4. Formulation of the Problem Statement

#### 4.1. PV Generation

#### 4.2. Wind Generation

#### 4.3. BBS

#### 4.4. Energy Consumption

#### 4.5. Energy Pricing and Electricity Cost

#### 4.6. PAR

#### 4.7. AWT

#### 4.8. Objective Function

## 5. System Model

## 6. Optimization Techniques

#### 6.1. GWO

#### 6.2. GA

#### 6.3. BPSO

#### 6.4. WDO

#### 6.5. WDGA

#### 6.6. WDGWO

#### 6.7. WBPSO

Algorithm 1 WDGA | |

Input: set of appliances $\alpha $ or population; | |

Initialization genetic parameters: peak hour, off peak hour, t = 0, H, vmax, vmin, no of iteration; Initialization wind driven parameters: dimMin, dimMax, dim, param.rt, param.g, param.alp, param.c; | |

1: | for$t=1\to 24$do |

2: | for $h=1\to H$ do |

3: | Generate population randomly; |

4: | for $h=1\to P$ do |

5: | Fitness calculation; Select best population, pop save in pop1; Status check of appliance using peak hour and off peak hour; |

6: | if t == peak hour then |

7: | Shift on RESs and BBS; |

8: | OR wait for off peak hour; |

9: | if Consumption == high then |

10: | Check remaining t of all App and check LOT until it is 0; |

11: | end if |

12: | end if |

13: | end for |

14: | Generate new population; |

15: | Replace the genetic operators by particles pressure; |

16: | Evaluate and find air parcels (population) pressure; |

17: | for $K=1\to swarm$ do |

18: | for $h=1\to n$ do |

19: | x(K,h) = (dimMax - dimMin) * ((x(K,h)+1)./2) + dimMin; |

20: | Pres(K,h) = sum $\left(x(K,h){.}^{2}\right)$; |

21: | end for |

22: | end for |

23: | Save air parcels value in pop2; |

24: | Check and find air parcels velocity; |

25: | Vel = min(vel, maxV); and vel = max(vel, -maxV); |

26: | Find and update air parcel positions; |

27: | x = x + vel; and x = min(x, 1.0); and x = max (x, -1.0); |

28: | Finding best particle in population |

29: | Globalpres, indx = min (pres); and globalx = x (indx, :); |

30: | Find min location for this iteration |

31: | Minpres, indx = min (pres); and minpos = x (indx, :); |

32: | Rank the air parcels: sortedpres rankind = sort (pres); |

33: | Sort the air parcels position, velocity and pressure: |

34: | Pres = sortedpres; |

35: | Updating the global best: |

36: | Better = minpres < globalpres; |

37: | if Solution = better then |

38: | Globalpres = minpres; |

39: | Globalpos = minpos; |

40: | end if |

41: | Save the velocity and position value in pop3; |

42: | Select from pop2 and pop3; |

43: | New velocity and position of air parcels; |

44: | if Solution == infeasible then |

45: | Update solution; |

46: | Update with sol in pop2 and pop3; |

47: | end if |

48: | Update pop best solution; |

49: | Update t = t+1 till 24 h; |

50: | Terminate when t = 24 h or iter = Max; |

51: | end for |

52: | end for |

Algorithm 2 WDGWO | |

Input: set of appliances $\alpha $ or population; | |

Initialization grey wolf parameters: Max iter, Np, D, alpha, beta, delta, search agents; | |

Initialization wind driven parameters: dimMin, dimMax, dim, param.rt, param.g, param.alp, param.c; | |

1: | Randomly initialize the position of search agents i.e., positions = rand (Np, D); |

2: | Evaluate the position of search agents |

3: | while$iter<{\mathit{iter}}_{max}$do |

4: | for $i=1\phantom{\rule{4pt}{0ex}}:\phantom{\rule{4pt}{0ex}}size\phantom{\rule{4pt}{0ex}}(positions,1)$ do |

5: | Calculate objective function for each search agent Fitness = sum (electricity cost * positionsx); Update alpha, beta and delta |

6: | if $Fitness<alpha-score$ then |

7: | $Alpha-score=fitness;$ |

8: | $Alpha-pos=positions(i:1);$ |

9: | end if |

10: | if $Fitness<alpha-score\phantom{\rule{4pt}{0ex}}and\phantom{\rule{4pt}{0ex}}fitness<beta-score$ then |

11: | $Beta-score=fitness;$ |

12: | $Beta-pos=positions(i:1);$ |

13: | end if |

14: | if $Fitness>alpha-score\phantom{\rule{4pt}{0ex}}andfitness>beta-score\phantom{\rule{4pt}{0ex}}andfitness<delta-score$ then |

15: | $Delta-score=fitness;$ |

16: | $Delta-pos=positions(i:1);$ |

17: | end if |

18: | end for |

19: | $a=2-l\ast \left(\right(2)/Max-iter)$; a value linearly from 2 to 0 |

20: | for $i=1:\phantom{\rule{4pt}{0ex}}size\phantom{\rule{4pt}{0ex}}(positions,1)$ do |

21: | for $j=1:\phantom{\rule{4pt}{0ex}}size\phantom{\rule{4pt}{0ex}}(positions,\phantom{\rule{4pt}{0ex}}2)$ do |

22: | r1, r2 randomly initialize the value between 0 to 1 |

23: | Vel = maxV * 2 * (rand (Np, D)-0.5) |

24: | for $i=1\to Np$ do |

25: | for $j=1\to D$ do |

26: | Velot (i, j) = vel (i, j); |

27: | Vel (i, j) = ( 1 - alp ) * vel (i, j) - ( g * positions (i, j)) + abs (1 - 1/i) * (((positions (i, j) - positions (i, j))).* RT ) + ( c * velot (i, j) / i) |

28: | if ((vel (i, j) < vmax) and (vel (i, j) > vmin)) then |

29: | Velot (i, j) = vel (i, j); |

30: | else if ( vel (i, j) < vmin ) then |

31: | Vel (i, j) = vmin |

32: | else if (vel (i, j) > vmax) then |

33: | Vel (i, j) = vmax; |

34: | end if |

35: | Position updating |

36: | Sig (i, j) = 1/(1+exp (-vel (i, j))); |

37: | if rand (1) < sig (i, j) then |

38: | Positions (i, j) = 1; |

39: | else |

40: | Positions (i, j) = 0; |

41: | end if |

42: | end for |

43: | end for |

44: | end for |

45: | end for |

46: | end while |

Algorithm 3 WBPSO | |

Require: Number of particles, swarm size, ${t}_{max}$, electricity price, LOT and appliance power consumption rating | |

Require: vmax, vmin, no of iter, c1, c2, param.RT, param.g, param.alp, param.c, dimMin, dimMax, dim | |

1: | Randomly generate the particles’ positions and velocities |

2: | ${P}_{gbest}\leftarrow \infty $ |

3: | for$t=1$to$swarmsize$do |

4: | Initialize (swarmsize, tbits) |

5: | ${P}_{vel}\leftarrow randomvelocity\phantom{\rule{4pt}{0ex}}\left(\right)$ |

6: | ${P}_{pos}\leftarrow randomposition\phantom{\rule{4pt}{0ex}}\left(swarmsize\right)$ |

7: | ${P}_{lbest}\leftarrow {P}_{pos}$ |

8: | end for |

9: | for h = 1 to 24 do |

10: | Validate constraints |

11: | for $i=1$ to M do |

12: | if $f\left({\sigma}_{i}\right)<f\left({p}_{lbest,\phantom{\rule{4pt}{0ex}}i}\right)$ then |

13: | ${p}_{lbest,\phantom{\rule{4pt}{0ex}}i}\leftarrow {\sigma}_{i}$ |

14: | end if |

15: | if $f\left({P}_{lbest,\phantom{\rule{4pt}{0ex}}i}\right)<f\left({P}_{gbest,\phantom{\rule{4pt}{0ex}}i}\right)$ then |

16: | ${P}_{gbest,\phantom{\rule{4pt}{0ex}}i}\leftarrow {P}_{lbest,\phantom{\rule{4pt}{0ex}}i}$ |

17: | else |

18: | ${P}_{gbest,\phantom{\rule{4pt}{0ex}}i}\leftarrow {P}_{gbest,\phantom{\rule{4pt}{0ex}}i}$ |

19: | end if |

20: | Decrement one from the TOT of the working appliance |

21: | if ${E}_{cost}$ > ${E}_{maxcost}$ then |

22: | if ${E}_{TO{T}_{RESs}}>{E}_{loa{d}_{h}}$ then |

23: | Switch the load to RESs and BBS |

24: | else |

25: | Consume the grid energy |

26: | end if |

27: | end if |

28: | Return ${P}_{gbest,\phantom{\rule{4pt}{0ex}}i}$ |

29: | Vel = maxV * 2 * (rand (swarm, n)-0.5); |

30: | for i = 1 : swarm do |

31: | for j = 1 : n do |

32: | Velot (i, j) = vel (i, j); |

33: | Vel (i, j) = ( 1 - param.alp ) * vel (i, j) - ( param.g * pres (i, j)) + abs (1 - 1/i) * (((pres (i, j) - pres (i, j))).*param.RT) + (param.c * velot (i, j) /i); |

34: | if ((vel (i, j) < = vmax) and (vel (i, j) >= vmin)) then |

35: | vel (i, j) = vel (i, j); |

36: | elseif ( vel (i, j) < vmin); vel (i, j) = vmin; elseif ( vel (i, j) > vmax); vel (i, j) = vmax; |

37: | end if |

38: | Sig (i, j) = 1 / ( 1 + exp ( -vel (i, j))); |

39: | if rand (1) < sig (i, j) then |

40: | x (i, j) = 1; |

41: | else |

42: | x (i, j) = 0; |

43: | end if |

44: | end for |

45: | end for |

46: | Check velocity: vel = min (vel, maxV); vel = max (vel, -maxV); |

47: | Update air parcel positions: x = x + vel; x = min (x, 1.0); x = max (x, -1.0); |

48: | Evaluate population: (pressure) |

49: | Finding best particle in population |

50: | Globalpres, indx = min (pres); globalx = x (indx, :); |

51: | Min location for this iteration |

52: | Minpres, indx = min (pres); minpos = x (indx, :); |

53: | Rank the air parcels; |

54: | Sorted-pres rank-ind = sort (pres); |

55: | Sort the air parcels position, velocity and pressure; |

56: | Pres = sorted-pres; |

57: | Updating the global best; |

58: | Better = minpres < globalpres; |

59: | if Better then |

60: | Globalpres = minpres; globalpos = minpos; |

61: | end if |

62: | end for |

63: | end for |

## 7. Simulation Results and Discussion

#### 7.1. RTP Scheme

#### 7.2. Energy Consumption Profile

#### 7.2.1. Energy Consumption with and without RESs

#### 7.3. Electricity Cost

#### Electricity Cost Profile with and without RESs

#### 7.4. PAR

#### PAR with and without RESs

#### 7.5. AWT

#### 7.6. Energy Generation Profile of Microgrid

#### 7.6.1. Energy Generation with Wind Turbine and Solar Panel

## 8. Conclusion and Future Work

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

Acronyms | Description |

$AC$ | Alternate current |

$AD$ | Autonomy days |

$AINA$ | Advanced Information Networking and Applications |

$AMI$ | Advanced metering infrastructure |

$AWT$ | Appliances waiting time |

$BBS$ | Battery bank storage |

$BEV$ | Battery electric vehicle |

$BFA$ | Bacterial foraging algorithm |

$BPSO$ | Binary particle swarm optimization |

$CBPSO$ | Chaos BPSO |

$CP$ | Convex programming |

$CPP$ | Critical peak pricing |

$CPP-R$ | Critical peak price with rebate |

$DAP$ | Day-ahead pricing |

$DC$ | Direct current |

$DEMS$ | Distributed energy management strategy |

$DERs$ | Distributed energy resources |

$DG$ | Distributed generation |

$DOD$ | Depth of discharge |

$DP$ | Dynamic programming |

$DR$ | Demand response |

$DSM$ | Demand side management |

$EC$ | Energy consumption |

$ECG$ | Energy consumption and generation |

$EMC$ | Energy management controller |

$EMS$ | Energy management system |

$EP$ | Electricity price |

$ESS$ | Energy storage system |

$EV$ | Electric vehicle |

$GA$ | Genetic algorithm |

$GWO$ | Grey wolf optimization |

$HP$ | Hourly pricing |

$HPS$ | Hybrid power system |

$HEMS$ | Home energy management system |

$ICTs$ | Information and communication technologies |

$IL$ | Interruptible load |

$ILA$ | Interruptible load appliances |

$ILP$ | Integer linear programming |

$IPSO$ | Improved PSO |

$KW$ | Kilowatt |

$KWh$ | Kilowatt hour |

$LMP$ | Locational marginal pricing |

$LOT$ | Length of operation time |

$LP$ | Linear programming |

$MIP$ | Mixed integer programming |

$MILP$ | Mixed-integer linear programming |

$MINLP$ | Mixed integer nonlinear programming |

$MKP$ | Multiple knapsack problem |

$MPC$ | Model predictive control |

$MPP$ | Multi-parametric programming |

$MRL$ | Must-run load |

MRLA | Must run load appliances |

$MTPSO$ | Multi-team PSO |

$NCP$ | Non-critical peak |

$NDL$ | Non-deferrable load |

$NDLA$ | Non-deferrable load appliances |

$OCM$ | Optimal control method |

$PAR$ | Peak-to-average ratio |

$PEV$ | Plug-in electric vehicle |

$PC$ | Personal computer |

$PCPM$ | Predictor corrector proximal multiplier |

$PHEV$ | Plug-in hybrid electric vehicle |

$PMU$ | Phaser measurement unit |

$PMU$ | Power management unit |

$PP$ | Peak pricing |

$PS$ | Price signal |

$PSO$ | Particle swarm optimization |

$PV$ | Photovoltaic |

$AD$ | Autonomy days |

$HP$ | Hourly pricing |

$PS$ | Price signal |

$RE$ | Renewable energy |

$RESs$ | Renewable energy sources |

$RTMP$ | Real-time market pricing |

RTP | Real time pricing |

SCADA | Supervisory control and data acquisition |

SI | Set of IL appliances |

SM | Smart meter |

SM | Set of must-run appliances |

SMSU | Smart schedular unit |

SN | Set of NDL appliances |

T | Temperature |

TOU | Time of use |

UC | User comfort |

USA | United States of America |

WBPSO | Wind driven BPSO |

WDGA | Wind driven genetic algorithm |

WDGWO | Wind driven GWO algorithm |

WDO | Wind driven optimization |

Symbol | Description |

${P}_{PV-out}$ | PV panel output power |

${G}_{ref}$ | Solar radiation at reference conditions |

${K}_{T}$ | Temperature coefficient of the PV panel |

$\sigma $ | Air density |

${P}_{coff}$ | Wind turbine power coefficient |

S | Set of appliances $\alpha $ |

${v}_{cut-in}$ | Cut-in wind speed |

$\left({C}_{Wh}\right)$ | BBS storage capacity |

${\eta}_{V}$ | BBS voltage |

${C}_{B}\left(t\right)$ | Available power from BBS at time slot t |

$\lambda $ | BBS self-discharge rate |

${C}_{Bmin}$ | Minimum allowable energy level remain in the BBS |

$\alpha $ | Appliance |

$P{S}^{rtp}\left(t\right)$ | Real time PS in time slot t |

${Y}_{ilSI\alpha}\left(t\right)$ | ON/OFF state of IL appliances |

${E}_{ps}^{ndl}\left(t\right)$ | EP of NDL appliances in time slot t |

${E}_{ps}^{mrl}\left(t\right)$ | EP of MRL appliances in time slot t |

$SN\alpha $ | Represents NDL appliances |

$SM\alpha $ | Represents MRL appliances |

$ilSI\alpha $ | SI represents the number of appliances of IL |

${\mathsf{\Gamma}}_{PAR}$ | PAR of the demanded load |

$\mathsf{{\rm Y}}{t}_{\alpha wt}$ | Waiting time of appliance |

${T}_{\alpha w}^{st}$ | Appliance $\alpha $ start time |

${T}_{mw}$ | Appliance $\alpha $ maximum waiting time |

${E}^{il}\left(t\right)$ | EC of IL appliances in time slot t |

${E}^{PV}\left(t\right)$ | Available energy from PV in time slot t |

$BS\left(t\right)$ | Available energy from battery in time slot t |

${E}_{ug}\left(t\right)$ | Available energy from utility grid in time slot t |

${t}_{0}$ | Lower limit of scheduling horizon |

${t}_{sch}$ | Scheduling time of appliance |

${X}_{id}(t-1)$ | Position of particle i in the d dimension at time slots t |

${V}_{id}(t-1)$ | Velocity of particle i in the d dimension at time slots t-1 |

${g}_{bestid}(t-1)$ | Best positions obtained by particle i and swarm in d dimension in time slot t-1 |

c | Coriolis force |

r | Variable value for the rank of air parcels |

${F}_{Cr}$ | Coriolis force |

$\nu $ | Wind velocity |

$\eta $ | Air density |

g | Acceleration of gravity |

$\Delta $ | Pressure gradient |

$\phi $ | Friction coefficient |

${\nu}_{i+1}^{p}$ | Current and new velocity of the air parcels |

${x}_{gbest}$ | Global best position |

${P}_{N-PV}$ | Rated or nominal power of PV cell at reference conditions |

${E}_{\alpha}^{NDL}$ | Energy consumption by NDL appliances |

${E}_{\alpha}^{MRL}$ | Energy consumption by MRL appliances |

${L}_{A}$ | Average load |

$\overrightarrow{X}\left(t\right)$ | In $\overrightarrow{X}\left(t\right)$, t is current iteration |

${\overrightarrow{X}}_{p}$ | Prey position vector |

${X}_{\alpha}$ | Best search agent |

${X}_{\delta}$ | Third best search agent |

G | Solar radiation |

${T}_{ref}$ | Cell temperature at reference conditions |

${A}_{rs}$ | Rotor swept area |

${V}^{3}$ | Average wind velocity |

${v}_{rated}$ | Rated wind speed |

${v}_{cut-out}$ | Cut-out wind speed |

${P}_{rated-wt}$ | Wind turbine rated output power |

${E}_{L}$ | Daily EC |

${\eta}_{B}$ | BBS efficiency |

${C}_{B}(t-1)$ | Available power from BBS at time slot (t-1) hour |

${P}_{BAT}\left(t\right)$ | BBS power in time slot t |

${C}_{Bmax}$ | Maximum allowable energy level remain in the BBS |

${E}_{\alpha}\left(t\right)$ | Energy consumed by appliance $\alpha $ in time slot t |

${Y}_{ndlSN\alpha}\left(t\right)$ | ON/OFF state of NDL appliances |

${Y}_{mrlSM\alpha}\left(t\right)$ | ON/OFF state of MRL appliances |

${E}_{ps}^{il}\left(t\right)$ | EP of IL appliances in time slot t |

ps | Price signal |

$SI\alpha $ | Represents the set of IL appliances |

$ndlSN\alpha $ | SN represents the set of NDL appliances |

$mrlSM\alpha $ | SM represents the set of MRL appliances |

${L}_{t}$ | Total load of all consumers |

${T}_{\alpha w}^{o}$ | Appliance $\alpha $ ON time |

${T}_{l}$ | Appliance $\alpha $ Length of operation time |

${E}^{ndl}\left(t\right)$ | EC of NDL appliances in time slot t |

${E}^{mrl}\left(t\right)$ | EC of MRL appliances in time slot t |

${E}^{WD}\left(t\right)$ | Available energy from wind in time slot t |

${E}^{nim}\left(t\right)$ | Total EC of NDL, IL and MRL appliances in time slot t |

${E}_{unsch}^{min}$ | Minimum amount of EC in unscheduled case |

${t}_{max}$ | Upper limit of scheduling horizon |

${X}_{id}\left(t\right)$ | Position of particle i in the d dimension at time slots t |

${V}_{id}\left(t\right)$ | Velocity of particle i in the d dimension at time slots t |

${P}_{bestid}(t-1)$ | Best positions obtained by particle i and swarm in d dimension in time slot t-1 |

${c}_{1}$ and ${c}_{2}$ | Acceleration coefficients |

${r}_{1}$ and ${r}_{2}$ | Random numbers between 0 and 1 |

${V}_{i}^{t+1}$ | Velocity of particle in particular time slot |

$\mathsf{\Omega}$ | Earth rotation |

${F}_{Gv}$ | Gravitational force |

$\psi \nu $ | Air finite volume |

${F}_{prg}$ | Pressure gradient force |

${F}_{Fr}$ | Friction force |

${\nu}_{i}^{p}$ | Current and new velocity of the air parcels |

${x}_{t}^{p}$ | Current and new positions of the air parcels |

R | Universal gas constant |

${T}_{c}$ | Temperature of PV cell ${}^{\circ}$C |

${E}_{\alpha}^{IL}$ | Energy consumption by IL appliances |

${L}_{p}$ | Peak load |

${T}_{\alpha w}$ | A term used for AWT |

$\overrightarrow{A},\overrightarrow{C}$ | Coefficient vectors |

$\overrightarrow{X}$ | Position vector of grey wolf |

${X}_{\beta}$ | Second best search agent |

D | Encircling of prey |

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Technique(s) | Objective(s) | Finding(s) | Limitation(s) |
---|---|---|---|

GA [18] | Electricity cost and PAR reduction | Cost and PAR is reduced using RTP and TOU | UC is not considered |

MILP [19] | PAR and cost reduction with RESs integration | Cost is reduced | Expensive for small scale residential users |

OCM and MPC [20] | Electricity bill reduction | Optimal energy management solution and cost saving | AWT for UC is not taken into account |

MIP [21] | Optimal scheduling of energy resources among users | Maximizes energy utilization | UC is not considered |

SCADA [22] | A hybrid power generation model | Design of hybrid power system | UC is not considered |

MILP [23] | HEMS modeling and techno-economic sizing | Used single step methodology to size additional PV and ESS | UC and cost reduction are ignored |

PSO and GA [24] | To minimize electricity cost | Cost is reduced using PSO and GA | To reduce cost UC is compromised |

MILP [25] | Reduction of $C{O}_{2}$ emission and cost | $C{O}_{2}$ emission and cost minimization | UC and PAR are not considered |

PCPM [26] | Design of a distributed EMS | EMS is designed using optimal operation of microgrids | PAR and UC are not addressed |

MTPSO [27] | Cost reduction | Cost reduction achieved | UC is not discussed |

IPSO [28] | Peak load reduction | They achieve desired objectives | UC is compromised and only passive appliances is considered. |

PMU [29] | To reduce electricity cost | Cost is reduced by peer-to-peer electricity sharing | UC is decreased |

Component | Rating |
---|---|

Battery | 1.2 kWh |

Wind turbine | 10 kW |

Solar panel | 230 W |

Non-Deferrable Loads | Interruptible Loads | Must-Run Loads |
---|---|---|

Home lightings | Water heater | Fans |

Fan | PEV | Optional lightings |

Exhaust fan | Iron | Heated towel rails |

Desktop PC | Pool Pump | Personal computer |

ESS | Refrigerator | Television |

Washing machine | Out-door lightings | Electric clock |

Parameters | Value |
---|---|

Total iterations | 50 |

Population size | 200 |

$\overrightarrow{\alpha}$ | 2 to 0 |

Random vectors r1, r2 | 0, 1 |

n | 18 |

Parameters | Value |
---|---|

Number of iterations | 50 |

Population size | 200 |

Probability of mutation | 0.1 |

Probability of crossover | 0.9 |

n | 18 |

Parameters | Values |
---|---|

Number of iterations | 50 |

Swarm size | 200 |

Maximum velocity | 4 |

Minimum velocity | −4 |

Initial weight constant | 2 |

Final weight constant | 0.4 |

Local pull | 2 |

Global pull | 2 |

n | 18 |

Parameters | Values |
---|---|

Total iterations | 50 |

Population size | 200 |

dimMin | −5 |

dimMax | 5 |

vmin | −0.3 |

vmax | 0.3 |

Universal gas constant | 3 |

n | 18 |

Gravity | 0.2 |

Coefficient of friction | 0.4 |

Parameters | Values |
---|---|

Number of iterations | 50 |

Parcels size | 200 |

Dimensions | [−1, +1] |

Maximum velocity | 0.4 |

Universal gas constant | 3.0 |

Gravity | 0.2 |

Coefficient of friction | 0.4 |

Crossover rate | 0.9 |

Mutation rate | 0.1 |

Parameters | Values |
---|---|

Number of iterations | 50 |

Population size | 200 |

Dimensions | [−1, +1] |

Maximum velocity | 0.4 |

Universal gas constant | 3.0 |

Gravity | 0.2 |

Coefficient of friction | 0.4 |

$\overrightarrow{\alpha}$ | 2 to 0 |

Random vectors r1, r2 | 0, 1 |

n | 18 |

Parameters | Values |
---|---|

Number of iterations | 50 |

Population size | 200 |

Dimensions | [−1, +1] |

Maximum velocity | 0.4 |

Minimum velocity | −4 |

Initial weight constant | 2 |

Final weight constant | 0.4 |

Local pull | 2 |

Global pull | 2 |

Gravity | 0.2 |

Coefficient of friction | 0.4 |

n | 18 |

Technique | Total Energy Demand(kW) | Imported Energy from Utility (kW) | Difference (kW) | Reduction (%) |
---|---|---|---|---|

Unscheduled | 156.5000 | 156.5000 | 0.0000 | 0.0000% |

GA scheduled | 156.5000 | 156.5000 | 0.0000 | 0.0000% |

BPSO scheduled | 156.5000 | 156.5000 | 0.0000 | 0.0000% |

WDO scheduled | 156.5000 | 156.5000 | 0.0000 | 0.0000% |

GWO scheduled | 156.5000 | 156.5000 | 0.0000 | 0.0000% |

WDGA scheduled | 156.5000 | 156.5000 | 0.0000 | 0.0000% |

WDGWO scheduled | 156.5000 | 156.5000 | 0.0000 | 0.0000% |

WBPSO scheduled | 156.5000 | 156.5000 | 0.0000 | 0.0000% |

Unscheduled + RESs | 156.5000 | 103.5+53 | 53.0000 | 33.860% |

GA scheduled + RESs | 156.5000 | 103.5+53 | 53.0000 | 33.860% |

BPSO scheduled + RESs | 156.5000 | 103.5+53 | 53.0000 | 33.860% |

WDO scheduled + RESs | 156.5000 | 103.5+53 | 53.0000 | 33.860% |

GWO scheduled + RESs | 156.5000 | 103.5+53 | 53.0000 | 33.860% |

WDGA scheduled + RESs | 156.5000 | 103.5+53 | 53.0000 | 33.860% |

WDGWO scheduled + RESs | 156.5000 | 103.5+53 | 53.0000 | 33.860% |

WBPSO scheduled + RESs | 156.5000 | 103.5+53 | 53.0000 | 33.860% |

Technique | Cost (Cents/hour) | Difference (Cents/hour) | Reduction (%) |
---|---|---|---|

Unscheduled | 103.9500 | 0.0000 | 0.0000% |

GA scheduled | 84.6842 | 0.0000 | 0.0000% |

BPSO scheduled | 64.3556 | 0.0000 | 0.0000% |

WDO scheduled | 96.3625 | 0.0000 | 0.0000% |

GWO scheduled | 77.9125 | 0.0000 | 0.0000% |

WDGA scheduled | 83.1125 | 0.0000 | 0.0000% |

WDGWO scheduled | 71.2750 | 0.0000 | 0.0000% |

WBPSO scheduled | 73.1100 | 0.0000 | 0.0000% |

Unscheduled + RESs | 72.8857 | 31.0643 | 42.6205% |

GA scheduled + RESs | 55.9129 | 28.7713 | 33.9700% |

BPSO scheduled + RESs | 44.0948 | 20.2608 | 31.4800% |

WDO scheduled + RESs | 51.5500 | 44.8125 | 46.0500% |

GWO scheduled + RESs | 53.6400 | 24.2725 | 31.1500% |

WDGA scheduled + RESs | 54.0355 | 29.0770 | 34.9800% |

WDGWO scheduled + RESs | 41.2500 | 30.0250 | 42.1200% |

WBPSO scheduled + RESs | 32.8900 | 40.2200 | 55.0100% |

Technique | Cost (Cents/day) | Difference (Cents/day) | Reduction (%) |
---|---|---|---|

Unscheduled | 2494.8000 | 0.0000 | 0.0000% |

GA scheduled | 2032.4000 | 0.0000 | 0.0000% |

BPSO scheduled | 1544.5000 | 0.0000 | 0.0000% |

WDO scheduled | 2257.7000 | 0.0000 | 0.0000% |

GWO scheduled | 1869.9000 | 0.0000 | 0.0000% |

WDGA scheduled | 2174.7000 | 0.0000 | 0.0000% |

WDGWO scheduled | 1870.6000 | 0.0000 | 0.0000% |

WBPSO scheduled | 1474.7000 | 0.0000 | 0.0000% |

Unscheduled + RESs | 1781.0814 | 713.7186 | 40.0722% |

GA scheduled + RESs | 1341.9000 | 690.5000 | 33.9700% |

BPSO scheduled + RESs | 1058.3000 | 486.2000 | 31.4700% |

WDO scheduled + RESs | 1237.4000 | 1020.3000 | 45.1900% |

GWO scheduled + RESs | 1287.4000 | 582.5000 | 31.1500% |

WDGA scheduled + RESs | 1196.9000 | 977.8000 | 44.9600% |

WDGWO scheduled + RESs | 810.0805 | 664.6195 | 35.5200% |

WBPSO scheduled + RESs | 900.5800 | 574.12000 | 38.9300% |

Technique | PAR | Difference | Reduction (%) |
---|---|---|---|

Unscheduled | 5.2915 | 0.0000 | 0.0000% |

GA scheduled | 4.6095 | 0.0000 | 0.0000% |

BPSO scheduled | 2.7294 | 0.0000 | 0.0000% |

WDO scheduled | 5.2915 | 0.0000 | 0.0000% |

GWO scheduled | 4.2426 | 0.0000 | 0.0000% |

WDGA scheduled | 3.2915 | 0.0000 | 0.0000% |

WDGWO scheduled | 2.6095 | 0.0000 | 0.0000% |

WBPSO scheduled | 1.6518 | 0.0000 | 0.0000% |

Unscheduled + RESs | 5.2915 | 0.0000 | 0.0000% |

GA scheduled + RESs | 1.8199 | 2.7896 | 60.5100% |

BPSO scheduled + RESs | 2.0211 | 0.7083 | 74.0400% |

WDO scheduled + RESs | 2.5024 | 2.7891 | 47.2900% |

GWO scheduled + RESs | 1.6265 | 2.6161 | 38.3300% |

WDGA scheduled + RESs | 1.2474 | 2.0441 | 62.1000% |

WDGWO scheduled + RESs | 1.3251 | 1.2844 | 49.2200% |

WBPSO scheduled + RESs | 1.3427 | 0.3091 | 81.2800% |

Wind Generation (kWh) | Wind Speed (m/s) | PV Generation (kWh) | Temperature (${}^{\circ}$C) |
---|---|---|---|

0.1838 | 1.0000 | 0 | 18.0000 |

0.1103 | 0.6000 | 0 | 18.5000 |

0.1838 | 1.0000 | 0 | 19.0000 |

0.2021 | 1.1000 | 0 | 20.0000 |

0.2205 | 1.2000 | 0.0622 | 21.0000 |

0.4447 | 2.4200 | 0.5988 | 22.0000 |

1.1111 | 6.0470 | 1.0475 | 24.0000 |

1.3331 | 7.2550 | 1.5535 | 25.0000 |

1.8945 | 10.3100 | 1.9714 | 25.5000 |

2.8481 | 15.5000 | 2.2306 | 26.0000 |

2.9400 | 16.0000 | 2.3946 | 27.0000 |

3.2156 | 17.5000 | 2.4600 | 28.0000 |

2.3704 | 12.9000 | 2.3126 | 29.0000 |

1.7640 | 9.6000 | 2.0132 | 30.0000 |

1.9661 | 10.7000 | 1.6314 | 29.8000 |

2.5725 | 14.0000 | 1.1918 | 29.5000 |

2.4990 | 13.6000 | 0.7123 | 29.2000 |

0.7901 | 4.3000 | 0.1831 | 29.0000 |

1.2495 | 6.8000 | 0 | 28.5000 |

2.1131 | 11.5000 | 0 | 27.0000 |

0.2205 | 1.2000 | 0 | 25.0000 |

0.2205 | 1.2000 | 0 | 23.0000 |

0.1929 | 1.0500 | 0 | 21.0000 |

0.1470 | 0.8000 | 0 | 18.0000 |

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## Share and Cite

**MDPI and ACS Style**

Iqbal, Z.; Javaid, N.; Iqbal, S.; Aslam, S.; Khan, Z.A.; Abdul, W.; Almogren, A.; Alamri, A. A Domestic Microgrid with Optimized Home Energy Management System. *Energies* **2018**, *11*, 1002.
https://doi.org/10.3390/en11041002

**AMA Style**

Iqbal Z, Javaid N, Iqbal S, Aslam S, Khan ZA, Abdul W, Almogren A, Alamri A. A Domestic Microgrid with Optimized Home Energy Management System. *Energies*. 2018; 11(4):1002.
https://doi.org/10.3390/en11041002

**Chicago/Turabian Style**

Iqbal, Zafar, Nadeem Javaid, Saleem Iqbal, Sheraz Aslam, Zahoor Ali Khan, Wadood Abdul, Ahmad Almogren, and Atif Alamri. 2018. "A Domestic Microgrid with Optimized Home Energy Management System" *Energies* 11, no. 4: 1002.
https://doi.org/10.3390/en11041002