Smart Home Battery for the Multi-Objective Power Scheduling Problem in a Smart Home Using Grey Wolf Optimizer
Abstract
:1. Introduction
2. Power Scheduling Problem in Smart Home Formulation
2.1. Power Consumption
2.2. Electricity Bill (EB)
2.3. Peak-to-Average Ratio (PAR)
2.4. User Comfort (UC) Level
3. Multi-Objective Approach for PSPSH
3.1. Multi-Objective Approach: Overview
3.2. Multi-Objective Approach for PSPSH (MO-PSPSH)
- Step 1:
- Choosing a convenient method to address MO-PSPSH.The first step of formulating MO-PSPSH is to choose a method to solve the problem. As mentioned previously, the weighted sum method is the simplest method because it is easy to implement and has no complexity. Besides, this method is mostly used by PSPSH state-of-the-art methods. Therefore, this method is chosen to address the proposed MO-PSPSH. The procedure of the weighted sum method is to assign a convenient weight to each objective function as follows:
- Step 2:
- Normalize the objective functionThe second step of formulating MO-PSPSH is normalize the fitness values of EB, PAR, WTR, and CPR to equate their value ranges. In PSPSH, the value ranges of WTR and CPR are between 0 and 1, whereas the value ranges of EB and PAR are unknown. EB and PAR have unknown values of and . Therefore, their fitness values can be normalized using Equation (25), as follows:
- Step 3:
- Modeling the MO-PSPSH
4. Smart Home Battery (SHB)
4.1. Smart Home Battery (SHB): Overview
4.2. Smart Home Battery for MO-PSPSH (BMO-PSPSH)
- Step 1:
- Initialize the SHB parametersAs discussed previously, the charging operations of SHB will be scheduled as SAs in the smart home. Several SHB parameters should be initialized, including the maximum amount of power that can be stored in SHB, known as the capacity of SHB (), the charging and discharging efficiency, known as the round trip of SHB efficiency (), the number of charging operations (CO) represented as , the beginning and ending OTP of each charging operation and represented as and respectively, and LOC for each charging operation (), such that . The and are initialized by users, whereas CO, , , and are initialized by the proposed BSA.A constraint of the total number of COs (u) should be considered in this step as follows:and for each CO are initialized to be the beginning and ending, respectively, of the available period for SHB to be charged. is set to the beginning of T, and is set to to ensure that SHB not charging at the last time slot. For , each is set to be one-time slot (the smallest period to be scheduled).Algorithm 1 shows the pseudocode for initializing the SHB parameters.
Algorithm 1 Pseudocode of SHB parameters initialization - Parameters initialized by users ()
- Parameters initialized by BSA () with respecting the
- Return SHB parameters;
- Step 2:
- Initialize the SHB charging populationEach solution of charging operations is represented as a vector containing the starting time for each charging operation (). The population of charging operations contains an N number of solutions initialized randomly, as shown in Equation (32).Algorithm 2 shows the pseudocode for generating the SHB charging population.
Algorithm 2 Pseudocode for generating the SHB charging population - Create a charging operations population matrix of size ()
- for each solution (y) do
- for each charging operation (c) do
- Initialize the values () randomly with respecting , , and of c
- end for
- end for
- Return SHB charging population;
- Step 3:
- Calculate the power consumed by the SHB charging operationsIn this step, the power charged in SHB by charging operation c at time slot j () is calculated. can be calculated as follows:u and are generated randomly by the BSA to increase their flexibility and allow the adapted algorithm to deal with the four objectives of PSPSH. After the PBco for all COs are calculated, the BSA will send COs to the adapted algorithm to be scheduled.Algorithm 3 shows the pseudocode for calculating the power consumed by the SHB charging operation.
Algorithm 3 Pseudocode for calculating power consumed by the charging operation - for each solution (y) do
- for each charging operation (c) do
- end for
- end for
- Return charged SHB
- Return for all
- Send to the adapted algorithm to be scheduled
- Step 4:
- Discharge the SHBAs mentioned previously, the discharging mode of SHB is considered as an additional source. In other words, discharging operations will not be scheduled by the adapted algorithm. However, the discharging mode is managed by the BSA to discharge power using the roulette wheel method, where the charged power will be discharged on the basis of the sizes of the parts on the wheel assigned for each time slot with considering the amount of power consumed at that time slots. In the roulette wheel method, big parts are assigned to high-pricing time slots and small parts to low-pricing time slots. The reason for assigning the part sizes this way in the distribution is to reduce the amount of power consumed at high-pricing time slots due to its effect on the stability of the power system and EBs. The roulette wheel method is used in this study due to its popularity and its performance in distributing individuals on the basis of their importance. Therefore, it gives a high chance for BSA to reduce the amount of power consumed at high-pricing time slots.The possible time slots for SHB to be discharged is calculated using Equation (36).After choosing a time slot to discharge SHB using the roulette wheel method, BSA will define the amount of power to discharge on the basis of the power consumed at that time slot as follows:will be released from SHB on the basis of Equation (38). BSA will keep choosing the discharging time slots and update the value of until all of the power stored in SHB is discharged.However, if the value of is equal to 0 and some power is still considered as stored in SHB, then BSA will update the power of the last CO (i.e., ) to be equal to 0 and release it from SHB. The BSA will repeat this process until all of the remaining power in SHB is releasedshould not exceed the maximum allowable discharge at time slot j as follows:DIS is the maximum allowable discharge. Note that the capacity of any SHB is defined according to the amount of power that can be discharged and not the amount that can be stored. For instance, the capacity of an SHB is 5 kWh, but the usable power is 4.5 kWh. Therefore, of the proposed SHB is set equal to , while the is set equal to 1 [74].
Algorithm 4 Pseudocode of discharge the SHB |
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Algorithm 5 Pseudocode of the four steps of the proposed BSA |
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5. Grey Wolf Optimizer for PSPSH
5.1. Grey Wolf Optimizer (GWO)
- Social Hierarchy
- The pack of grey wolves has an austere social hierarchy, which is classified into alpha (), beta (), delta (), and omega (). Wolves belong to the class alpha are considered as the leader of the grey wolves’ hierarchy due to their domination and power to manage the pack. The beta wolves are playing the primary role in support the alpha in leading the pack. Delta wolves are in the third level of the hierarchy, and they in charge of leading the lowest level in the hierarchy. Omega wolves are considered as the lowest level in the hierarchy.In GWO, the solutions are represented as grey wolves in the social hierarchy, where the best solution is represented as wolf, and wolves are the second and third best solutions, respectively, and wolves are considered as the rest of the solutions.
- Encircling Prey
- In addition to this deep social hierarchy, the intelligent behavior of group hunting is also procedurally modeled. This behavior involves three main phases: chasing, encircling, and attacking.The grey wolves can change/update their locations closer to the prey by encircling the prey mechanism. The encircling behavior of grey wolves is formulated as follows:The coefficient vectors and are calculated as
- Search for Prey (Exploration)
- The grey wolves searching mechanism for prey can be done on the basis of the wolves’ positions, where the wolves diverge and converge to find the best position to attack prey. The coefficient vectors and manage the divergence (exploration) and convergence (exploitation) of the wolves in GWO. GWO exploit a search space if and explore a search space if .The changing values in is not similar to , where is changing randomly to emphasize exploration/exploitation and local optima stagnation avoidance throughout iterations.
- Hunting
- As mentioned previously, in GWO, the best three solutions are , , and wolves, respectively, and wolves are the rest of the solutions.Owing to the domination and leadership of wolf on the pack, usually guides the hunting. and wolves occasionally can engage in hunting to help wolf. wolves are usually changing their location according to the three best solutions (, and ).The hunting mechanism on the basis of these wolves (solutions) is formulated as follows:To change the location of the wolves for hunting in accordance with the and wolves, the location of the prey should be estimated by these three wolves.
Grey Wolf Optimizer for PSPSH
- GWO adaptation for MO-PSPSH (MO-PSPSH-GWO)The adaptation of the GWO for MO-PSPSH is discussed in this section. This adaptation contains five main steps, which are illustrated below.The flowchart of the proposed MO-PSPSH-GWO is provided in Figure 4.
- Step 1:
- Initialize MO-PSPSH-GWO parametersThe adaptation the MO-PSPSH-GWO is started by initializing the parameters of PSPSH and GWO. The PSPSH parameters are , , , , , , , , and . The GWO parameters are , , , , , the minimum () and maximum () ranges for the search agent, the maximum number of iterations (), and the number of search agents in the pack ().
- Step 2:
- Initialize MO-PSPSH-GWO populationEach wolf in the pack is presented as a solution of MO-PSPSH-GWO, and each solution is containing the starting time for each appliance i, as shown in Figure 5.The MO-PSPSH-GWO population is containing of y number of solutions initialized randomly as shown in Equation (51).
- Step 3:
- Fitness function calculationThe fitness value of each solution is calculated on the basis of Equation (29). In the MO-PSPSH-GWO method, the best solution and its fitness value are assigned to and ,respectively, and the second and third best solutions and their fitness values are assigned to , , and , , respectively.
- Step 4:
- Update the MO-PSPSH-GWO populationThe MO-PSPSH-GWO population is updated in the step, where the Equations (42)–(50) are in charge of this update.The updating mechanism of MO-PSPSH-GWO is utilized to estimate the distance between solutions and the solution and then generate a new solution Equations (42)–(44) and (47). The same steps for are repeated for and to generate using Equations (42), (43), (45) and (48) and to generate using Equations (42), (43), (46) and (49). In Equation (50), a new solution is generated based on , , and .
- Step 5:
- Check the stop criterionSteps 3 and 4 of MO-PSPSH-GWO are repeated until the stop criterion is met.Algorithm 6 presents the pseudocode of the five steps of the proposed MO-PSPSH-GWO.
Algorithm 6 Pseudocode of the five steps of the proposed MO-PSPSH-GWO - 1:
- Step 1: Initialize MO-PSPSH-GWO parameters;/
- 2:
- Initialize all PSPSH parameters ()
- 3:
- Initialize all GWO parameters ()
- 4:
- Step 2: Initialize MO-PSPSH-GWO population
- 5:
- Initialize MO-PSPSH-GWO population matrix of size ()
- 6:
- Step 3: Social Hierarchy
- 7:
- while (itr I) do
- 8:
- for each solution (y) do
- 9:
- Calculate the fitness of each solution
- 10:
- = the best fitness value
- 11:
- = the second fitness value
- 12:
- = the third fitness value
- 13:
- = the best solution
- 14:
- = the second best solution
- 15:
- = the third best solution
- 16:
- end for
- 17:
- Step 4: Update MO-PSPSH-GWO population
- 18:
- for each solution (y) do
- 19:
- for each appliance (i) do
- 20:
- Update (Random number in [0, 1])
- 21:
- Update the value of (Equation (42))
- 22:
- Update the value of (Equation (43))
- 23:
- 24:
- Update (Random number in [0, 1])
- 25:
- Update the value of (Equation (42))
- 26:
- Update the value of (Equation (43))
- 27:
- 28:
- Update (Random number in [0, 1])
- 29:
- Update the value of (Equation (42))
- 30:
- Update the value of (Equation (43))
- 31:
- 32:
- Generate a new solution (Equation (50))
- 33:
- end for
- 34:
- end for
- 35:
- Step 5: Check the stop criterion
- 36:
- if The maximum number of the iteration is not reached then
- 37:
- 38:
- end if
- 39:
- end while
- 40:
- Return and
- GWO adaptation for BMO-PSPSH (BMO-PSPSH-GWO)BMO-PSPSH-GWO has six main steps, which will be thoroughly discussed below.The flowchart of BMO-PSPSH-GWO is provided in Figure 6.
- Step 1:
- Initialize BMO-PSPSH-GWO parametersThe adaptation of BMO-PSPSH-GWO is started by initializing the parameters of SHB, PSPSH, and GWO. The SHB parameters are and . The PSPSH and GWO are the same as initialized in the first step of MO-PSPSH-GWO, including and for PSPSH and and for GWO.
- Step 2:
- Initialize BMO-PSPSH-GWO populationIn this step, BMO-PSPSH-GWO solutions are initialized randomly, where each solution is presented as two vectors. The first vector contains the starting time for SAs and second vector contains the starting time for charging operations, as shown in Figure 7The BMO-PSPSH-GWO population is presented as a matrix of size , in which m is the number of SAs, u is the number of charging operations, and N is the number of solutions. Equation (52) shows the presentation of the BMO-PSPSH-GWO population.
- Step 3:
- Calculate the power consumed by the charging operationsIn this step, the power charged in SHB by each charging operation will be calculated as discussed in the third step of designing BSA in Section 4.2.
- Step 4:
- Calculate the fitness valuesThis step is divided into two parts, namely, discharging the SHB and calculating the fitness values of the solution in the population. As discussed in Section 4.2, the time slots for discharging the SHB are determined using the roulette wheel method and the amount of power chosen randomly on the basis of several equations and constraints. In this step, the processes of discharging the SHB are the same as discussed in Section 4.2. For calculating the fitness values, the three best fitness values and their solutions are assigned as , , and , and , , and , respectively.
- Step 5:
- Update BMO-PSPSH-GWO populationThe BMO-PSPSH-GWO population is updated in the step, where the Equations (42)–(50) are in charge of this update.The updating mechanism of BMO-PSPSH-GWO is utilized to estimate the distance between solutions and the solution and then generate a new solution Equations (42)–(44) and 47. The same steps for are repeated for and to generate using Equations (42), (43), (45) and (48) and to generate using Equations (42), (43), (46) and (49). In Equation (50), a new solution is generated on the basis of , , and .
- Step 6:
- Check the stop criterionSteps 4 and 5 of BMO-PSPSH-GWO are repeated until the stop criterion (maximum number of iterations) is met. The resulting BMO-PSPSH-GWO solution is .Algorithm 7 presents the pseudocode of the six steps of the proposed BMO-PSPSH-GWO.
Algorithm 7 Pseudocode of the six steps of the proposed BMO-PSPSH-GWO - 1:
- Step 1: Initialize BMO-PSPSH-GWO parameters
- 2:
- Initialize PSPSH parameters()
- 3:
- Initialized SHB parameters ()
- 4:
- Initialize GWO parameters()
- 5:
- Step 2: Initialize BMO-PSPSH-GWO population
- 6:
- Initialize a BMO-PSPSH-GWO population matrix of size ()
- 7:
- Step 3:Calculate the power consumed by charging operations
- 8:
- for each solution (y) do
- 9:
- for each charging operation (c) do
- 10:
- 11:
- end for
- 12:
- end for
- 13:
- Step 4: Calculate the fitness values
- 14:
- while (itr I) do
- 15:
- for each solution (y) do
- 16:
- Discharge the SHB of the solution
- 17:
- Calculate the fitness of the solution
- 18:
- = the best fitness value
- 19:
- = the second best fitness value
- 20:
- = the third best fitness value
- 21:
- = the best solution
- 22:
- = the second best solution
- 23:
- = the third best solution
- 24:
- end for
- 25:
- Step 5: Update BMO-PSPSH-GWO population
- 26:
- for each solution (y) do
- 27:
- for each appliance (i) do
- 28:
- Update (random number in [0, 1])
- 29:
- Update the value of (Equation (42))
- 30:
- Update the value of (Equation (43))
- 31:
- 32:
- Update (random number in [0, 1])
- 33:
- Update the value of (Equation (42))
- 34:
- Update the value of (Equation (43))
- 35:
- 36:
- Update (random number in [0, 1])
- 37:
- Update the value of (Equation (42))
- 38:
- Update the value of (Equation (43))
- 39:
- 40:
- Generate a new solution (Equation (50))
- 41:
- end for
- 42:
- end for
- 43:
- Step 6: Check the stop criterion
- 44:
- if The maximum number of the iteration is not reached then
- 45:
- 46:
- end if
- 47:
- end while
- 48:
- Return and
6. Experiments and Results
6.1. Dataset Description
6.2. Experimental Evaluation
6.2.1. Effect of The Proposed Approaches on EB
6.2.2. Effect of The Proposed Approaches on PAR
6.2.3. Effect of The Proposed Approaches on UC Level
6.2.4. Discussion
6.3. Comparative Evaluation
6.3.1. Comparison with State-of-the-Art Methods Using Their Datasets
6.3.2. Comparison with State-of-the-Art Methods Using the Proposed Datasets
7. Conclusions and Future Research
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
BFOA | Bacterial Foraging Optimization Algorithm |
BMO-PSPSH | Smart Home Battery for MO-PSPSH |
BSA | SHB Scheduling Algorithm |
CPP | Critical Period Price |
CPR | Capacity Power Limit Rate |
CO | Charging Operations |
EB | Electricity Bill |
GA | Genetic Algorithm |
GWO | Grey Wolf Optimizer |
HEMS | Home Energy Management System |
HSA | Harmony Search Algorithm |
IBR | Inclining Block Rate |
LOC | Length of Operation Cycle |
MO-PSPSH | Multi-Objective Approach for PSPSH |
MOP | Multi-objective Optimization Problem |
NSA | Non-Shiftable Appliance |
OTP | Operation Time Period |
PAR | Peak-to-Average Ratio |
PSC | Power Supplier Company |
PSO | Particle Swarm Optimization |
PSPSH | Power Scheduling Problem in Smart Home |
PSPSH-GWO | Grey Wolf Optimizer for PSPSH |
RES | Renewable Energy Source |
RTP | Real Time Price |
SA | Shiftable Appliance |
SG | Smart Grid |
SHB | Smart Home Battery |
TOU | Time-Of-Use |
UC | User Comfort |
WTR | Waiting Time Rate |
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NO. | Appliance | l | OTPs–OTPe | Power (kW) | NO. | Appliance | l | OTPs–OTPe | Power (kW) |
---|---|---|---|---|---|---|---|---|---|
1 | Dishwasher | 105 | 540–780 | 0.6 | 19 | Dehumidifier | 30 | 1–120 | 0.05 |
2 | Dishwasher | 105 | 840–1080 | 0.6 | 20 | Dehumidifier | 30 | 120–240 | 0.05 |
3 | Dishwasher | 105 | 1200–1440 | 0.6 | 21 | Dehumidifier | 30 | 240–360 | 0.05 |
4 | Air Conditioner | 30 | 1–120 | 1 | 22 | Dehumidifier | 30 | 360–480 | 0.05 |
5 | Air Conditioner | 30 | 120–240 | 1 | 23 | Dehumidifier | 30 | 480–600 | 0.05 |
6 | Air Conditioner | 30 | 240–360 | 1 | 24 | Dehumidifier | 30 | 600–720 | 0.05 |
7 | Air Conditioner | 30 | 360–480 | 1 | 25 | Dehumidifier | 30 | 720–840 | 0.05 |
8 | Air Conditioner | 30 | 480–600 | 1 | 26 | Dehumidifier | 30 | 840–960 | 0.05 |
9 | Air Conditioner | 30 | 600–720 | 1 | 27 | Dehumidifier | 30 | 960–1080 | 0.05 |
10 | Air Conditioner | 30 | 720–840 | 1 | 28 | Dehumidifier | 30 | 1080–1200 | 0.05 |
11 | Air Conditioner | 30 | 840–960 | 1 | 29 | Dehumidifier | 30 | 1200–1320 | 0.05 |
12 | Air Conditioner | 30 | 960–1080 | 1 | 30 | Dehumidifier | 30 | 1320–1440 | 0.05 |
13 | Air Conditioner | 30 | 1080–1200 | 1 | 31 | Electric Water Heater | 35 | 300–420 | 1.5 |
14 | Air Conditioner | 30 | 1200–1320 | 1 | 32 | Electric Water Heater | 35 | 1100–1440 | 1.5 |
15 | Air Conditioner | 30 | 1320–1440 | 1 | 33 | Coffee Maker | 10 | 300–450 | 0.8 |
16 | Washing Machine | 55 | 60–300 | 0.38 | 34 | Coffee Maker | 10 | 1020–1140 | 0.8 |
17 | Clothes Dryer | 60 | 300–480 | 0.8 | 35 | Robotic Pool Filter | 180 | 1–540 | 0.54 |
18 | Refrigerator | 1440 | 1–1440 | 0.5 | 36 | Robotic Pool Filter | 180 | 900–1440 | 0.54 |
Scenarios | Appliances |
---|---|
1 | 1, 3, 4, 5, 6, 7, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 35 |
2 | 1, 2, 4, 5, 6, 7, 10, 11, 12, 18, 25, 26, 27, 28, 29, 31, 32, 33, 34, 36 |
3 | 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 23, 24, 25, 26, 27, 28, 31, 32, 33, 34, 35 |
4 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36 |
5 | 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 23, 24, 25, 26, 27, 28, 31, 32, 33, 34, 35 |
6 | 1, 2, 3, 8, 9, 10, 11, 12, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35 |
7 | 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36 |
No. | Appliances | Power (kW) |
---|---|---|
1 | Light [16] | 0.6 |
2 | Attic Fan [76] | 0.3 |
3 | Table Fan [76] | 0.8 |
4 | Iron [16] | 1.5 |
5 | Toaster [76] | 1 |
6 | Computer Charger [76] | 1.5 |
7 | Cleaner [15] | 1.5 |
8 | TV [76] | 0.3 |
9 | Hair Dryer [76] | 1.2 |
10 | Hand Drill [76] | 0.6 |
11 | Water Pump [76] | 2.5 |
12 | Blender [76] | 0.3 |
13 | Microwave [16] | 1.18 |
14 | Electric Vehicle [77] | 1 |
Parameter | Value |
---|---|
N | 40 |
I | 1000 |
lb | |
ub |
Parameter | Value |
---|---|
13.5 kWh | |
5 kW | |
5kW | |
90% |
Scenarios | MO-PSPSH-GWO | BMO-PSPSH-GWO |
---|---|---|
S 1 | 43.5041 | 41.9042 |
S 2 | 64.5597 | 59.6252 |
S 3 | 66.1138 | 62.7707 |
S 4 | 62.5916 | 55.9692 |
S 5 | 46.2879 | 43.6999 |
S 6 | 52.2998 | 49.1431 |
S 7 | 62.6367 | 56.4908 |
Average | 56.8562 | 52.8004 |
Total | 397.993 | 369.603 |
Scenarios | MO-PSPSH-GWO | BMO-PSPSH-GWO |
---|---|---|
S 1 | 2.6002 | 2.9418 |
S 2 | 2.4451 | 2.4796 |
S 3 | 2.2267 | 2.5710 |
S 4 | 2.2277 | 2.3167 |
S 5 | 2.2310 | 2.5207 |
S 6 | 2.5233 | 2.5375 |
S 7 | 2.0423 | 2.4931 |
Average | 2.3280 | 2.5515 |
Scenarios | MO-PSPSH-GWO | BMO-PSPSH-GWO |
---|---|---|
S 1 | 0.0658 | 0.0645 |
S 2 | 0.1030 | 0.0534 |
S 3 | 0.0889 | 0.0629 |
S 4 | 0.1358 | 0.0787 |
S 5 | 0.0872 | 0.0695 |
S 6 | 0.1004 | 0.0598 |
S 7 | 0.1310 | 0.0771 |
Average | 0.1017 | 0.0666 |
Scenarios | MO-PSPSH-GWO | BMO-PSPSH-GWO |
---|---|---|
S 1 | 0.3206 | 0.3216 |
S 2 | 0.3528 | 0.3529 |
S 3 | 0.3913 | 0.3871 |
S 4 | 0.5236 | 0.5062 |
S 5 | 0.3924 | 0.3880 |
S 6 | 0.3647 | 0.3546 |
S 7 | 0.4857 | 0.4590 |
Average | 0.4044 | 0.3956 |
Scenarios | MO-PSPSH-GWO | BMO-PSPSH-GWO |
---|---|---|
S 1 | 80.67 | 80.68 |
S 2 | 77.20 | 79.67 |
S 3 | 75.98 | 77.49 |
S 4 | 67.02 | 70.75 |
S 5 | 76.01 | 77.12 |
S 6 | 76.74 | 79.27 |
S 7 | 69.16 | 73.18 |
Average | 74.68 | 76.88 |
Study | Method | Appliances | Pricing Scheme | Time Slot |
---|---|---|---|---|
[42] | HSA, BFOA | 13 | TOU | 1 h |
[80] | GA, BPSO, WDO | 9 | RTP | 1 h |
[81] | GA, GWO | 12 | RTP, CPP | 1 h |
[82] | GOA, CSA, ACO, FA, MFO | 6 | RTP | 1 h |
[83] | GA, DA | 12 | RTP | 1 h |
Study | Algorithm | EB | PAR |
---|---|---|---|
HSA | 1523.9 | 2.24 | |
[42] | BFOA | 1558.8 | 2.15 |
(Summer Scenario) | HBH | 1557.2 | 2.12 |
B-PSPSH-GWO | 1082.4 | 2.47 | |
HSA | 1155.8 | 3.26 | |
[42] | BFOA | 1082.9 | 3.18 |
(Winter Scenario) | HBH | 1143.6 | 3.5 |
B-PSPSH-GWO | 954.8 | 3.7 | |
GA | 64 | 2.2 | |
BPSO | 42 | 2 | |
[80] | WDO | 41.6 | 1.9 |
GWDO | 37 | 1.7 | |
B-PSPSH-GWO | 30.2 | 2.28 | |
[81] | GA | 462.67 | 3.639 |
(RTP Scenario) | GWO | 474.06 | 3.774 |
HGWGA | 449.35 | 3.108 | |
B-PSPSH-GWO | 426.18 | 3.95 | |
GA | 523.96 | 3.639 | |
[81] | GWO | 541.45 | 3.774 |
(CPP Scenario) | HGWGA | 508.35 | 3.108 |
B-PSPSH-GWO | 474.21 | 3.95 | |
[82] | GOA | 1768.27 | 7.41 |
CSA | 2147.28 | 9.47 | |
ACO | 2001.16 | 4.13 | |
FA | 2104.23 | 8.02 | |
MFO | 1794.61 | 8.31 | |
B-PSPSH-GWO | 1673.79 | 8.50 | |
GA | 1.683 | 3.56 | |
[83] | DA | 1.561 | 3.76 |
B-PSPSH-GWO | 1.23 | 3.94 |
Scenarios | GWO | GA | PSO | HSA | BFOA |
---|---|---|---|---|---|
S 1 | 41.90 | 44.54 | 42.05 | 43.72 | 42.39 |
S 2 | 59.62 | 62.00 | 59.76 | 61.46 | 60.18 |
S 3 | 62.77 | 65.10 | 63.01 | 63.92 | 63.24 |
S 4 | 55.96 | 56.56 | 56.14 | 56.44 | 56.32 |
S 5 | 43.69 | 47.90 | 43.77 | 44.96 | 43.93 |
S 6 | 49.14 | 52.55 | 49.21 | 50.86 | 49.95 |
S 7 | 56.49 | 59.22 | 56.60 | 58.11 | 57.10 |
Average | 52.80 | 55.41 | 52.93 | 54.21 | 53.30 |
Scenarios | GWO | GA | PSO | HSA | BFOA |
---|---|---|---|---|---|
S 1 | 2.94 | 2.96 | 2.89 | 2.95 | 2.94 |
S 2 | 2.47 | 2.57 | 2.49 | 2.53 | 2.50 |
S 3 | 2.57 | 2.92 | 2.58 | 2.86 | 2.61 |
S 4 | 2.31 | 2.33 | 2.30 | 2.35 | 2.33 |
S 5 | 2.52 | 2.73 | 2.54 | 2.71 | 2.59 |
S 6 | 2.53 | 2.70 | 2.55 | 2.72 | 2.65 |
S 7 | 2.49 | 2.65 | 2.51 | 2.62 | 2.54 |
Average | 2.54 | 2.694 | 2.55 | 2.691 | 2.58 |
Scenarios | GWO | GA | PSO | HSA | BFOA |
---|---|---|---|---|---|
S 1 | 0.064 | 0.102 | 0.072 | 0.100 | 0.084 |
S 2 | 0.053 | 0.135 | 0.061 | 0.112 | 0.076 |
S 3 | 0.062 | 0.100 | 0.065 | 0.083 | 0.069 |
S 4 | 0.078 | 0.142 | 0.083 | 0.122 | 0.089 |
S 5 | 0.069 | 0.098 | 0.070 | 0.081 | 0.080 |
S 6 | 0.059 | 0.088 | 0.062 | 0.085 | 0.077 |
S 7 | 0.077 | 0.110 | 0.078 | 0.095 | 0.091 |
Average | 0.066 | 0.110 | 0.070 | 0.096 | 0.080 |
Scenarios | GWO | GA | PSO | HSA | BFOA |
---|---|---|---|---|---|
S 1 | 0.321 | 0.340 | 0.322 | 0.339 | 0.328 |
S 2 | 0.352 | 0.361 | 0.357 | 0.363 | 0.357 |
S 3 | 0.387 | 0.401 | 0.386 | 0.400 | 0.390 |
S 4 | 0.506 | 0.519 | 0.505 | 0.519 | 0.510 |
S 5 | 0.388 | 0.411 | 0.393 | 0.409 | 0.399 |
S 6 | 0.354 | 0.370 | 0.355 | 0.373 | 0.361 |
S 7 | 0.459 | 0.469 | 0.460 | 0.463 | 0.463 |
Average | 0.395 | 0.410 | 0.396 | 0.409 | 0.401 |
Scenarios | GWO | GA | PSO | HSA | BFOA |
---|---|---|---|---|---|
S 1 | 80.68 | 77.90 | 80.30 | 78.05 | 79.4 |
S 2 | 79.67 | 75.20 | 79.10 | 76.25 | 78.35 |
S 3 | 77.49 | 74.95 | 77.45 | 75.85 | 77.05 |
S 4 | 70.75 | 66.95 | 70.60 | 67.95 | 70.05 |
S 5 | 77.12 | 74.55 | 76.85 | 75.50 | 76.05 |
S 6 | 79.27 | 77.10 | 79.15 | 77.10 | 78.10 |
S 7 | 73.18 | 71.05 | 73.10 | 72.10 | 72.30 |
Average | 76.88 | 73.95 | 76.65 | 74.68 | 75.90 |
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Makhadmeh, S.N.; Al-Betar, M.A.; Alyasseri, Z.A.A.; Abasi, A.K.; Khader, A.T.; Damaševičius, R.; Mohammed, M.A.; Abdulkareem, K.H. Smart Home Battery for the Multi-Objective Power Scheduling Problem in a Smart Home Using Grey Wolf Optimizer. Electronics 2021, 10, 447. https://doi.org/10.3390/electronics10040447
Makhadmeh SN, Al-Betar MA, Alyasseri ZAA, Abasi AK, Khader AT, Damaševičius R, Mohammed MA, Abdulkareem KH. Smart Home Battery for the Multi-Objective Power Scheduling Problem in a Smart Home Using Grey Wolf Optimizer. Electronics. 2021; 10(4):447. https://doi.org/10.3390/electronics10040447
Chicago/Turabian StyleMakhadmeh, Sharif Naser, Mohammed Azmi Al-Betar, Zaid Abdi Alkareem Alyasseri, Ammar Kamal Abasi, Ahamad Tajudin Khader, Robertas Damaševičius, Mazin Abed Mohammed, and Karrar Hameed Abdulkareem. 2021. "Smart Home Battery for the Multi-Objective Power Scheduling Problem in a Smart Home Using Grey Wolf Optimizer" Electronics 10, no. 4: 447. https://doi.org/10.3390/electronics10040447
APA StyleMakhadmeh, S. N., Al-Betar, M. A., Alyasseri, Z. A. A., Abasi, A. K., Khader, A. T., Damaševičius, R., Mohammed, M. A., & Abdulkareem, K. H. (2021). Smart Home Battery for the Multi-Objective Power Scheduling Problem in a Smart Home Using Grey Wolf Optimizer. Electronics, 10(4), 447. https://doi.org/10.3390/electronics10040447