Grey Wolf Optimization-Based Optimum Energy-Management and Battery-Sizing Method for Grid-Connected Microgrids
Abstract
:1. Introduction
2. Mathematical Problem Formulation
2.1. Objective Function
2.2. Constraints
2.2.1. Balance of Electrical Load Demands
2.2.2. Boundaries of Distributed Generation (DG) Constraints
2.2.3. Grid Constraints
2.2.4. Operation Reserve (OR) Constraints
2.2.5. Battery Energy Storage (BES) Constraints
3. Grey Wolf Optimizer (GWO)
Mathematical Formulation of GWO
Algorithm 1 GWO pseudo-code |
Initialize the locations of the grey wolf population Xi (i = 1, 2, …, n Initialize a, A and C Calculate the objective function value for each grey wolf agent Set: Xα as best result of the search agents Xβ as the second best result of the search agents Xδ as the third best result of the search agents While (t < max number of iteration) the termination criterion is not satisfied do Initialize r1 and r2 values Update a by Equation (30) Update A by Equation (28) Update C by Equation (29) For i For j Update the positions of each grey wolf agent by using Equations (31)–(37) End j End i Calculate the fitness of all agents with the new positions t = t + 1 End while return Xα |
4. The GWO Implementation of the Optimal Operation Management of the Microgrid
Algorithm 2 Function handle |
For t = 1 to NT do For m = 1 to NOA do Part 1: power balance and generation source capacity handling Calculate the power difference between the generation sources and load demand Pdiff = (P_MT,t u_MT,t + P_FC,t u_FC,t + P_PV,t + P_WT,t + P_BES,t u_BES,t + P_grid,) − PD,t; Select random generation sources based on their capacity While P_diff ≠ 0 do Subtract P_diffm,t from the selected units Check the capabilities of the generation units based on lower and upper limits as follows: If Pm,FC,t < PFC,min then Pm,FC, = PFC,min; or Pm,MT,t < PMT,min then Pm,MT,t = PMT,min; or Pm,grid,t < Pgrid,min then Pm,grid,t = Pgrid,min; or Pm,BES,t < PBES,min then Pm,BES,t = PBES,min; Elseif Pm,FC,t > PFC,max then Pm,FC, = PFC,max; or Pm,MT,t > PMT,max then Pm,MT,t = PMT,max; or Pm,grid,t > Pgrid,max then Pm,grid,t = Pgrid,max; or Pm,BES,t < PBES,max then Pm,BES,t = PBES,max; End if Calculate P_diffm,t Select another generation units randomly End while Part 2: ORs handling Calculate objective function (ft) by using Equation (2) If P_MT,t u_MT,t + P_FC,t u_FC,t + P_PV,t + P_WT,t + P_BES,t u_BES,t + P_grid,t < PD,t + ORt Then ft = ft + Penalty_Factor ×(P_MT,t u_MT,t + P_FC,t u_FC,t + P_PV,t + P_WT,t + P_BES,t u_BES,t + P_grid,t – (PD,t + ORt)) End if End for m Calculate Equation (1) End for t |
5. Numerical Results and Discussion
Description of the Microgrid Test System and the Data Inputs
- Scenario A: The microgrid operates without BES.
- Scenario B: The microgrid’s BES does not have an initial value (uncharged).
- Scenario C: The microgrid’s BES has an initial value equal to its size (fully charged).
Scenario A
Scenario B
Scenario C
6. Conclusions
Author Contributions
Conflicts of Interest
Nomenclature
Indices | |
ADNs | Active distribution networks |
ASO | Adaptive storage operation |
BA | Bat algorithm |
BBO | Biogeography- based optimisation |
BES, grid | Battery energy storage and grid indices, respectively |
BESS | Battery energy storage system |
DE | Differential evolution |
DG | Distribution generation |
DP | Dynamic programming |
ESS | Energy storage system |
FC, MT | Fuel cell and micro-turbine indices, respectively |
GA | Genetic algorithm |
GHG | Greenhouse gas |
GWO | Grey wolf optimizer |
HBB-BC | Hybrid big bang–big crunch |
t | time index |
T | Operation time horizon (h) |
TLBO | Teaching-learning based optimisation |
TPC | Total present cost |
TS | Tabu search |
iter | iteration index of the GWO algorithm |
MAS | Multi-agent system |
MGCC | Microgrid central controller |
MILP | Mixed-integer linear programming |
NOA | Number of agents |
PSO | Particle swarm optimization |
PV, WT | Photovoltaic and wind turbine indices, respectively |
SD | Storages devices |
SDO | Simulink design optimization |
IBA | Improved bat algorithm |
IR | Interest rate for financing the installed BES |
RES | Renewable sources |
Constants | |
Bgrid,t, BBES,t, BMT,t, BFC,t, BPV,t, BWT,t | Bid of utility, BES, MT, FC, PV and WT, respectively, at time t (€ct/kWh). |
CBES,min, CBES,max | Minimum and maximum size of BES (kWh) |
CSD_Max | Maximum capacity of storage device |
CSD_Min | Minimum capacity of storage devices |
FCBES, MCBES | Fixed and maintenance cost for BES, respectively (€ct/kWh) |
Iter_max | Maximum number of iteration for the GWO algorithm |
LT | Lifetime of the installed BES (year) |
OMDG | Fixed operation and maintenance cost of distributed generators (DGs; €ct) |
OMMT, OMFC OMPV, OMWT | Fixed operation and maintenance cost of MT, FC, PV and WT, respectively (€ct/kWh) |
ORt | Minutes operating reserve requirements (kW) |
PBESmax,t PBESmin,t | Maximum discharge and charge rates of BES, respectively, at time t (kW) |
ηd, ηc | Discharge and charge efficiencies of BES, respectively |
SDCMT,t, SDCFC,t | Shutdown cost for MT and FC, respectively, at time t (€ct) |
SDMT, SDFC | Shutdown cost coefficient for MT and FC, respectively (€ct) |
SUCMT,t, SUCFC,t | Startup cost for MT and FC, respectively, at time t (€ct) |
SUMT, SUFC | Startup cost coefficient for MT and FC, respectively (€ct) |
tax | Tax rate of utility power grid |
Δt | Time interval duration |
Pgrid,max, Pgrid,min | Maximum/minimum limits of power production for utility, respectively (kW) |
PMT,max, PFC,max, PPV,tmax, PWT,t max, PBES,max | Maximum producible power of MT, FC, PV, WT and BES respectively (kW) |
PMT,min, PFC,min, PPV,tmin, PWT,t min, PBES,min | Minimum producible power of MT, FC, PV, WT and BES respectively (kW) |
PSD_Max | Maximum power of storage device |
Variables | |
CostDG,t, CostBES,t | Cost of fuel and operating power of DGs and BES, respectively, at time t (€ct) |
F | Total costs (€ct) |
Pgrid,t, PBES,t, PMT,t, PFC,t PPV,t, PWT, t | Power of utility, BES, MT, FC, PV, and WT, respectively (kW) |
PSD_min | Minimum power of storage device |
TCPDBES | Total cost per day of BES (€ct) |
Up | Utility price |
X | Position vector of a grey wolf in GWO algorithm |
XP | Position vector of the prey in GWO algorithm |
Gp | Gas price |
Costgrid,t | Cost of trade with the upstream grid at time t (€ct) |
CSD_Max | Maximum capacity of storage device |
PD,t | Electrical load demand at time t (kW) |
CBES,t | Energy stored in BES at time t (kWh) |
uBES,t, uMT,t, uFC,t | Status (on or off) of BES, MT, and FC, respectively, at time t |
Sg | Dispatch of storage device |
Appendix A
Method | Method Mode | Generation SOURCE | Analysis | Objective Function | CONSTRAINTS | Ref. | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Single | Hybrid | PV | WT | DG | FC | MT | HB | Wave | SD | |||||
Adaptive Storage Operation | √ | √ | √ | √ | √ | Techno-Economic | Forecast accuracy | Energy balance | [7] | |||||
PSCAD/EMTDC Software | √ | √ | √ | √ | √ | √ | Techno | Primary frequency control | Overloading characteristics and limitations of the state of charge (SOC) of SD | [8] | ||||
Mixed Integer Linear Programming | √ | √ | √ | Economic | Microgrid operation cost | Non-linear loads | [9] | |||||||
√ | √ | √ | √ | √ | Economic | Minimization of the levelized cost of energy (LCOE) | Renewable sources intermittency | [10] | ||||||
√ | √ | √ | √ | √ | Techno-Economic | Optimal design of standalone microgrid | Uncertainty of the generation sources | [11] | ||||||
√ | √ | √ | √ | √ | √ | Economic | Optimal size of storage device based on cost-benefit | Unit commitment problem with spinning reserve of microgrid | [12] | |||||
√ | √ | Economic | Minimizes the annualized investment and operation costs | Optimal type, size and allocation of distributed generators in radial distribution system | [13] | |||||||||
√ | √ | Techno-Economic | Non-convex economic dispatch (ED) | Ramp rate constraints, valve-point effect (VPE), prohibited operating zones (POZs), transmission loss, and spinning reserve constraints. | [14] | |||||||||
Linear Programing | √ | √ | √ | √ | √ | Techno-Economic | Maximizing the economic and minimize the annual cost | energy prices, ambient conditions, energy demand, units’ characteristics, electricity grid constraints | [15] | |||||
Cuckoo Search | √ | √ | √ | √ | Economic | Minimize the operational costs | System reliability | [16] | ||||||
Inventory Models | √ | √ | √ | Economic | Minimize the operational costs | Energy source cost and availability | [17] | |||||||
Self-Adaptive Mutation Strategy | √ | √ | √ | √ | √ | √ | Economic | Cost minimization | Ramp rate of generation sources | [18] | ||||
Distributed Economic Model Predictive Control | √ | √ | √ | Economic | Cost minimization | System stability | [19] | |||||||
Multi-Objective Evolutionary Algorithm | √ | √ | √ | Techno-Economic | Decreasing switching operation | System stability | [20] | |||||||
Dynamic Programming Algorithm | √ | √ | √ | √ | Techno-Economic | Maximize the power rating | Reliability and system efficiency | [21] | ||||||
Self-Adaptive Dynamic Programming | √ | √ | √ | Economic | Cost minimization | System stability | [22] | |||||||
Genetic Algorithm | √ | √ | √ | √ | Techno-Economic | Maximize the power rating | System stability | [23] | ||||||
√ | √ | √ | √ | √ | Economic | minimization of life-cycle cost of the generation sources | Limitation of battery state of charge | [24] | ||||||
Particle Swarm Optimization | √ | √ | √ | √ | Techno-Economic | Cost minimization | System stability | [25] | ||||||
√ | √ | √ | √ | Techno-Economic | Improve system stability and performance | System frequency control | [26] | |||||||
Particle Swarm–Nelder–Mead | √ | √ | Techno-Economic | Cost minimization | System stability | [27] | ||||||||
Big Bang–Big Crunch algorithm | √ | √ | √ | √ | Economic | Cost minimization | System reliability | [28] | ||||||
Non-Linear Programming Optimization | √ | √ | √ | √ | Economic | Maximize the revenues of the renewable farm | System stability | [29] | ||||||
Alternating Direction Method of Multipliers | √ | √ | √ | √ | Techno-Economic | Minimize network losses and energy cost | Network voltage limitation | [30] | ||||||
Differential Evolution algorithm | √ | √ | √ | √ | Techno-Economic | Reducing power losses, improving voltage stability of the system and reducing charging costs | Network voltage limitation | [31] | ||||||
Fuzzy Logic–Genetic Algorithm | √ | √ | √ | Economic | Predicting storage device lifetime and minimize the costs | Unit commitment problem | [32] | |||||||
Photovoltaic-Trigeneration Optimization Model | √ | √ | √ | Economic | Minimize operational costs and emissions | Renewable sources intermittency | [33] | |||||||
Simulink Design Optimization | √ | √ | √ | √ | Economic | Cost minimization | Renewable sources intermittency | [34] | ||||||
Fuzzy Logic–Particle Swarm Optimization | √ | √ | √ | √ | √ | Economic | Minimize operational costs and emissions | System stability | [35] | |||||
Fuzzy Logic–Multi Agent System | √ | √ | √ | √ | √ | Economic | Cost minimization | System stability | [36] |
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Time (hour) | MT | FC | PV | WT | Utility Grid |
---|---|---|---|---|---|
1 | 0 | 1 | 0 | 1 | 1 |
2 | 0 | 1 | 0 | 1 | 1 |
3 | 0 | 1 | 0 | 1 | 1 |
4 | 1 | 1 | 0 | 1 | 1 |
5 | 1 | 1 | 0 | 1 | 1 |
6 | 1 | 1 | 0 | 1 | 1 |
7 | 1 | 1 | 0 | 1 | 1 |
8 | 1 | 1 | 1 | 1 | 1 |
9 | 1 | 1 | 1 | 1 | 1 |
10 | 1 | 1 | 1 | 1 | 1 |
11 | 1 | 1 | 1 | 1 | 0 |
12 | 1 | 1 | 1 | 1 | 0 |
13 | 1 | 1 | 1 | 1 | 0 |
14 | 1 | 1 | 1 | 1 | 0 |
15 | 1 | 1 | 1 | 1 | 1 |
16 | 1 | 1 | 1 | 1 | 1 |
17 | 1 | 1 | 1 | 1 | 1 |
18 | 1 | 1 | 0 | 1 | 1 |
19 | 1 | 1 | 0 | 1 | 1 |
20 | 1 | 1 | 0 | 1 | 1 |
21 | 1 | 1 | 0 | 1 | 1 |
22 | 1 | 1 | 0 | 1 | 1 |
23 | 1 | 1 | 0 | 1 | 1 |
24 | 1 | 1 | 0 | 1 | 1 |
Methodology | Best operation Cost (€ct) | Mean Operation Cost (€ct) | Worst Operation Cost (€ct) |
---|---|---|---|
GA | 1041.8376 | 1196.3251 | 1361.2437 |
PSO | 968.0190 | 1081.8351 | 1241.7459 |
BA | 933.8145 | 989.3718 | 106.9860 |
IBA | 825.8849 | 825.8849 | 825.8849 |
GWO | 813.6850 | 815.5231 | 816.8512 |
Time (hour) | Microturbine (MT) | Fuel Cell (FC) | Photovoltaic (PV) | Wind Turbine (WT) | Battery-Energy Storage (BES) | Utility Grid |
---|---|---|---|---|---|---|
1 | 1 | 1 | 0 | 1 | 1 | 1 |
2 | 1 | 1 | 0 | 1 | 1 | 1 |
3 | 1 | 1 | 0 | 1 | 1 | 1 |
4 | 1 | 1 | 0 | 1 | 1 | 1 |
5 | 1 | 1 | 0 | 1 | 1 | 1 |
6 | 1 | 1 | 0 | 1 | 1 | 1 |
7 | 1 | 1 | 0 | 1 | 1 | 1 |
8 | 1 | 1 | 1 | 1 | 1 | 1 |
9 | 1 | 1 | 1 | 1 | 1 | 1 |
10 | 1 | 1 | 1 | 1 | 1 | 1 |
11 | 1 | 1 | 1 | 1 | 1 | 1 |
12 | 1 | 1 | 1 | 1 | 1 | 1 |
13 | 1 | 1 | 1 | 1 | 1 | 1 |
14 | 1 | 1 | 1 | 1 | 1 | 1 |
15 | 1 | 1 | 1 | 1 | 1 | 1 |
16 | 1 | 1 | 1 | 1 | 1 | 1 |
17 | 1 | 1 | 1 | 1 | 1 | 1 |
18 | 1 | 1 | 0 | 1 | 1 | 1 |
19 | 1 | 1 | 0 | 1 | 1 | 1 |
20 | 1 | 1 | 0 | 1 | 1 | 1 |
21 | 1 | 1 | 0 | 1 | 1 | 1 |
22 | 1 | 1 | 0 | 1 | 1 | 1 |
23 | 1 | 1 | 0 | 1 | 1 | 1 |
24 | 1 | 1 | 0 | 1 | 1 | 1 |
Methodology | Best Operation Cost (€ct) | Mean Operation Cost (€ct) | Worst operation Cost (€ct) |
---|---|---|---|
GA | 615.9034 | 623.4835 | 638.6436 |
PSO | 567.5185 | 575.1266 | 592.8787 |
BA | 520.2354 | 532.1278 | 550.6589 |
IBA | 497.0082 | - | - |
GWO | 445.3254 | 450.6587 | 465.2154 |
Time (hour) | MT | FC | PV | WT | BES | Utility Grid |
---|---|---|---|---|---|---|
1 | 0 | 0 | 0 | 1 | 1 | 1 |
2 | 0 | 0 | 0 | 1 | 1 | 1 |
3 | 0 | 0 | 0 | 1 | 1 | 1 |
4 | 0 | 0 | 0 | 1 | 1 | 1 |
5 | 0 | 0 | 0 | 1 | 1 | 1 |
6 | 1 | 1 | 0 | 1 | 1 | 1 |
7 | 1 | 1 | 0 | 1 | 1 | 1 |
8 | 1 | 1 | 1 | 1 | 1 | 1 |
9 | 1 | 1 | 1 | 1 | 1 | 1 |
10 | 1 | 1 | 1 | 1 | 1 | 1 |
11 | 1 | 1 | 1 | 1 | 1 | 1 |
12 | 1 | 1 | 1 | 1 | 1 | 1 |
13 | 1 | 1 | 1 | 1 | 1 | 1 |
14 | 1 | 1 | 1 | 1 | 1 | 1 |
15 | 1 | 1 | 1 | 1 | 1 | 1 |
16 | 1 | 1 | 1 | 1 | 1 | 1 |
17 | 1 | 1 | 1 | 1 | 1 | 1 |
18 | 1 | 1 | 0 | 1 | 1 | 1 |
19 | 1 | 1 | 0 | 1 | 1 | 1 |
20 | 1 | 1 | 0 | 1 | 1 | 1 |
21 | 1 | 1 | 0 | 1 | 1 | 1 |
22 | 1 | 1 | 0 | 1 | 1 | 1 |
23 | 0 | 1 | 0 | 1 | 1 | 1 |
24 | 0 | 0 | 0 | 1 | 1 | 1 |
Methodology | Best Operation Cost (€ct) | Mean Operation Cost (€ct) | Worst Operation Cost (€ct) |
---|---|---|---|
GA | 499.0665 | 506.4029 | 523.5212 |
PSO | 459.8236 | 466.6086 | 485.2675 |
BA | 436.7845 | 446.3267 | 456.2547 |
IBA | 424.1339 | - | - |
GWO | 297.5429 | 299.3274 | 312.8742 |
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Nimma, K.S.; Al-Falahi, M.D.A.; Nguyen, H.D.; Jayasinghe, S.D.G.; Mahmoud, T.S.; Negnevitsky, M. Grey Wolf Optimization-Based Optimum Energy-Management and Battery-Sizing Method for Grid-Connected Microgrids. Energies 2018, 11, 847. https://doi.org/10.3390/en11040847
Nimma KS, Al-Falahi MDA, Nguyen HD, Jayasinghe SDG, Mahmoud TS, Negnevitsky M. Grey Wolf Optimization-Based Optimum Energy-Management and Battery-Sizing Method for Grid-Connected Microgrids. Energies. 2018; 11(4):847. https://doi.org/10.3390/en11040847
Chicago/Turabian StyleNimma, Kutaiba Sabah, Monaaf D. A. Al-Falahi, Hung Duc Nguyen, S. D. G. Jayasinghe, Thair S. Mahmoud, and Michael Negnevitsky. 2018. "Grey Wolf Optimization-Based Optimum Energy-Management and Battery-Sizing Method for Grid-Connected Microgrids" Energies 11, no. 4: 847. https://doi.org/10.3390/en11040847