Optimal Scheduling of Hybrid Energy Resources for a Smart Home
Abstract
:1. Introduction
1.1. Background and Motivation
1.2. Literature Review
- The inclusion of an EV exerts a unique stress on the house loads. It raises the electrical demand while the thermal load remains unchanged. Hence, the feasibility of its responsive behavior must be explored.
1.3. Contribution and Paper Organization
- A model of an SH is developed. The SH is equipped with an EV, a BESS, and an FC-based micro-CHP system which is powered by natural gas. Two typical tariffs (flat and variable) of the utility are realized, and the effect of responsive nature of the EV is explored.
- An optimization problem for the economic operation of the hybrid energy system of the SH is developed, and the constraints are defined for the systems and the devices. The problem is modeled to utilize the real coded genetic algorithm (RCGA) to optimally schedule the resources and the responsive loads.
- A comprehensive simulation results of six test cases reveal interesting features of the developed model and optimization process. The necessary conditions for the optimal operation of the energy resources are also discussed.
2. Development of SH Model
2.1. FC Model
2.2. EV Model
PEVi | EV charging power at interval i (kW) |
SOCEV.i | EV SOC at interval i (%) |
SOCEVpi | EV SOC at plugging-in time (%) |
SOCEVpo | EV SOC at plugging-out time (%) |
SOCEVmin | Minimum SOC of the EV (%) |
d | Trip distance of the EV |
ηEV | Overall electric drive efficiency |
CEV | Capacity of the EV (kWh) |
2.3. BESS Model
2.4. TOU Tariff
3. Optimization Model
- The forecasted data for the thermal and electrical loads is available.
- The initial conditions of the SOC of the BESS and trip distance of the EV is available.
- All the devices are already installed. Therefore, the installation costs are not considered.
3.1. Objective Function
n | Number of hours |
T | Length of a time interval (h) |
α,β | Startup, Shutdown costs of the FC |
CFC.i | Cost of the FC operation for interval i kWh) |
CBL.i | Cost of the boiler operation for interval i kWh) |
CU.i | Cost of the utility power for interval i kWh) |
Cgas | Cost for purchasing the gas kWh) |
CUb | Base cost for purchasing the power from utility |
PFCe.i | Electrical power from the FC at interval i (kW) |
PBL.i | Heating provided by the boiler at interval i (kW) |
PU.i | Electrical power provided by the utility at interval i (kW) |
Tp.v | Multiplier for the peak-valley price as provided in Table 1 |
ηFC.i | Efficiency of the FC |
3.2. Constraints
3.2.1. Constraints of Power Balance
Electrical demand at interval i (kW) | |
Power being delivered to the EV at interval i (kW) | |
BESS power at interval i (kW). It is negative in charging mode and positive in discharging mode | |
Heating demand at interval i (kW) | |
Heating produces by the FC at interval i (kW) | |
Charging efficiency of the BESS | |
Discharging efficiency of the BESS |
PDh.i | Heating demand at interval i (kW) |
PFCh.i | Heating produced by the FC at interval i (kW) |
PBL.i | Heating produced by the auxiliary boiler at interval i (kW) |
3.2.2. Constraints of Devices
ΔPFCup | FC ramp rate limit for increasing power |
ΔPFCdn | FC ramp rate limit for decreasing power |
PFCmin | FC minimum power limit |
PFCmax | FC maximum power limit |
WB.i | BESS energy at interval i (kWh) |
WBmin | BESS minimum energy limit (kWh) |
WBmax | BESS maximum energy limit (kWh) |
PBchmax | BESS minimum charging rate limit (kW) |
PBdchmax | BESS maximum discharging rate limit (kW) |
T | Length of time interval |
4. Real Coded Genetic Algorithm
4.1. Initialization
4.2. Dimensionality
4.3. Implementation of the Constraints
- Constraints of FC
- Constraints of the BESS
- For each interval i, if exceeds the battery capacity limit in charging mode i.e., , then and h to satisfy the upper limit of (21).
- For each interval i, if depletes more than battery minimum limit in discharging mode, i.e., then and to satisfy the lower limit of (21).
- If the battery is in charging mode i.e., , then the difference between values of battery energy in two consecutive intervals should not exceed according to (22). Otherwise h.
- If the battery is in discharging mode i.e., , then the difference between the values of battery energy in two consecutive intervals should be less than according to (23). Otherwise h.
- Constraints of the EV
5. Simulation Results
5.1. Case 1: Base Case
5.2. Case 2: Installation of FC
5.3. Case 3: Addition of EV
5.4. Case 4: Considering Variable Tariff
5.5. Case 5: Scheduling the EV Charging
5.6. Case 6: Adding the BESS
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Tarrif Type | Time Range | Normalized Price |
---|---|---|
Peak | [09:00–12:00] | 1 |
[17:00–22:00] | ||
Plain | [13:00–16:00] | 0.9 |
Valley | [01:00–08:00] | 0.78 |
[23:00–24:00] |
Case No | FC | EV | Variable Tariff | Scheduling of EV | BESS |
---|---|---|---|---|---|
1 | x | x | x | x | x |
2 | o | x | x | x | x |
3 | o | o | x | x | x |
4 | o | o | o | x | x |
5 | o | o | o | o | x |
6 | o | o | o | o | o |
Parameter Description | Value | Unit | |
---|---|---|---|
Electric Vehicle | |||
Trip distance of EV | d | 60 | mi |
Overall electric drive efficiecy | 6.2 | - | |
Capacity of EV | 16 | kWh | |
EV maximum charging power | 3.3 | kW | |
Minimum SOC of EV | 3.3 | % | |
Maximum SOC of EV | 100 | % | |
EV SOC at plugging-out time | 100 | % | |
Plug-in time | 17:00 | hour | |
Plug-out time | 7:00 | hour | |
Fuel Cell | |||
FC maximum power limit | 2 | kW | |
FC minimum power limit | 0.05 | kW | |
FC ramp rate limit for increasing power | 1.25 | kW | |
FC ramp rate limit for decreasing power | 1.5 | kW | |
FC startup cost | 0.15 | $ | |
FC shutdown cost | 0 | $ | |
Battery Energy Storage System | |||
Maximum energy limit | 3 | kWh | |
Minimum energy limit | 0 | kWh | |
Minimum charging rate limit | c/4 | kW | |
Maximum discharging rate limit | c/2 | kW | |
Charging efficiency of Battery | 0.927 | - | |
Discharging efficiency of Battery | 0.971 | - | |
General | |||
Number of hours | n | 24 | hour |
Length of time interval | T | 1 | hour |
Cost for purchasing gas | 0.05 | $/kW | |
Base cost for purchsing power from utility | 0.13 | $/kW | |
Genetic Algorithm | |||
Crossover probability | 0.5 | - | |
Mutation probability | 0.1 | - |
Powers (Demand and Generation) | Costs | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Total | ||||||||||||
h | (kW) | (kW) | (kW) | (kW) | (kW) | (kW) | (kW) | (kW) | ($/day) | ($/day) | ($/day) | ($/day) |
1 | 1.55 | 0.91 | 1.35 | −0.15 | 2.16 | 2.45 | 0.66 | 1.79 | 0.09 | 0.12 | 0.22 | 0.42 |
2 | 1.51 | 0.83 | 1.77 | −0.25 | 2.72 | 2.41 | 0.59 | 1.82 | 0.09 | 0.1 | 0.28 | 0.47 |
3 | 1.49 | 0.98 | 1.63 | −0.53 | 2.70 | 2.38 | 0.73 | 1.65 | 0.08 | 0.13 | 0.27 | 0.48 |
4 | 1.50 | 1.03 | 3.16 | −0.35 | 4.01 | 2.34 | 0.77 | 1.57 | 0.08 | 0.13 | 0.41 | 0.62 |
5 | 1.53 | 1.02 | 1.53 | −0.59 | 2.67 | 2.30 | 0.76 | 1.54 | 0.08 | 0.13 | 0.27 | 0.48 |
6 | 1.66 | 1.03 | 3.30 | −0.25 | 4.20 | 2.28 | 0.76 | 1.51 | 0.08 | 0.13 | 0.43 | 0.64 |
7 | 1.91 | 1.09 | 1.75 | −0.26 | 2.85 | 2.25 | 0.82 | 1.43 | 0.07 | 0.14 | 0.29 | 0.5 |
8 | 2.15 | 1.08 | 0.00 | −0.62 | 1.74 | 2.29 | 0.81 | 1.48 | 0.07 | 0.14 | 0.18 | 0.39 |
9 | 2.30 | 1.62 | 0.00 | 0.65 | 0.05 | 2.30 | 1.39 | 0.91 | 0.05 | 0.23 | 0.01 | 0.28 |
10 | 2.38 | 1.74 | 0.00 | 0.42 | 0.23 | 1.95 | 1.56 | 0.39 | 0.02 | 0.25 | 0.03 | 0.3 |
11 | 2.40 | 1.61 | 0.00 | 0.68 | 0.12 | 1.98 | 1.38 | 0.60 | 0.03 | 0.23 | 0.02 | 0.27 |
12 | 2.35 | 1.54 | 0.00 | 0.58 | 0.25 | 2.15 | 1.28 | 0.87 | 0.04 | 0.21 | 0.03 | 0.29 |
13 | 2.33 | 1.58 | 0.00 | −0.03 | 0.77 | 2.20 | 1.34 | 0.86 | 0.04 | 0.22 | 0.09 | 0.35 |
14 | 2.30 | 1.56 | 0.00 | 0.01 | 0.73 | 2.23 | 1.31 | 0.91 | 0.05 | 0.22 | 0.09 | 0.35 |
15 | 2.28 | 1.54 | 0.00 | 0.04 | 0.70 | 2.23 | 1.28 | 0.95 | 0.05 | 0.21 | 0.08 | 0.34 |
16 | 2.31 | 1.56 | 0.00 | 0.02 | 0.73 | 2.23 | 1.31 | 0.91 | 0.05 | 0.22 | 0.08 | 0.35 |
17 | 2.50 | 1.68 | 0.00 | 0.63 | 0.21 | 2.23 | 1.47 | 0.76 | 0.04 | 0.24 | 0.03 | 0.3 |
18 | 2.48 | 1.68 | 0.00 | 0.00 | 0.80 | 2.24 | 1.46 | 0.78 | 0.04 | 0.24 | 0.1 | 0.38 |
19 | 2.44 | 1.69 | 0.00 | 0.00 | 0.74 | 2.26 | 1.49 | 0.78 | 0.04 | 0.24 | 0.1 | 0.38 |
20 | 2.30 | 1.78 | 0.00 | 0.00 | 0.52 | 2.29 | 1.62 | 0.67 | 0.03 | 0.26 | 0.07 | 0.36 |
21 | 2.28 | 1.79 | 0.00 | 0.00 | 0.49 | 2.40 | 1.62 | 0.78 | 0.04 | 0.26 | 0.06 | 0.36 |
22 | 2.13 | 1.74 | 0.00 | 0.00 | 0.39 | 2.45 | 1.55 | 0.90 | 0.05 | 0.25 | 0.05 | 0.35 |
23 | 1.93 | 0.96 | 1.00 | 0.00 | 1.97 | 2.50 | 0.70 | 1.80 | 0.09 | 0.12 | 0.2 | 0.41 |
24 | 1.75 | 0.92 | 0.00 | 0.00 | 0.83 | 2.45 | 0.67 | 1.78 | 0.09 | 0.12 | 0.08 | 0.29 |
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Rafique, M.K.; Haider, Z.M.; Mehmood, K.K.; Saeed Uz Zaman, M.; Irfan, M.; Khan, S.U.; Kim, C.-H. Optimal Scheduling of Hybrid Energy Resources for a Smart Home. Energies 2018, 11, 3201. https://doi.org/10.3390/en11113201
Rafique MK, Haider ZM, Mehmood KK, Saeed Uz Zaman M, Irfan M, Khan SU, Kim C-H. Optimal Scheduling of Hybrid Energy Resources for a Smart Home. Energies. 2018; 11(11):3201. https://doi.org/10.3390/en11113201
Chicago/Turabian StyleRafique, Muhammad Kashif, Zunaib Maqsood Haider, Khawaja Khalid Mehmood, Muhammad Saeed Uz Zaman, Muhammad Irfan, Saad Ullah Khan, and Chul-Hwan Kim. 2018. "Optimal Scheduling of Hybrid Energy Resources for a Smart Home" Energies 11, no. 11: 3201. https://doi.org/10.3390/en11113201