Structure Optimization of StandAlone Renewable Power Systems Based on Multi Object Function
Abstract
:1. Introduction
2. StandAlone Hybrid PV/Wind/Diesel/Battery System
2.1. System Configuration
2.2. Operation Strategies
3. Modelling of Hybrid Power System Components
3.1. Wind Turbine System
3.2. Photovoltaic System
3.3. Diesel Power System
3.4. Battery Model
4. Cost Modelling of Hybrid Power System
4.1. Annualized Capital Cost (ACS)
4.2. Replacement Capital Cost
4.3. Loss of Power Supply Probability (LPSP)
5. PopulationBased Optimization Algorithm
5.1. Genetic Algorithm
Begin 
t: = 0 
P(t): = InitPopulation(); 
Evaluate(P(t)) 
While (stop criteria unsatisfied) 
P’(t) = Select(P(t)); 
P’(t) = Crossover(P’(t)); 
P’(t) = Mutate(P’(t)) 
Evaluate(P’(t)); 
P(t + 1) = UpdateNewPop(P(t),P’(t)); 
t = t + 1; 
end 
5.2. Particle Swarm Optimization
For each particle 
Initialize particle 
END 
Do For each particle 
Calculate fitness value 
If the fitness value is better than the best fitness value (p_{Best}) in history, set current value as the new p_{Best} 
End 
Choose the particle with the best fitness value of all the particles as the g_{Best} 
For each particle 
Calculate particle velocity according Equation (a)
V(t + 1) = w * v(t) + c_{1} * rand() * (pbest(t) – present(t)) + c_{2} * rand() * (g_{best}(t) − present(t))

Update particle position according Equation (b)
present(t + 1)= present(t) + v(t + 1)

End 
While maximum iterations or minimum error criteria is not attained 
w is inertia weight; c_{1}, c_{2} is the learning factor, or accelerated variable; rand () is a random number between (0,1). 
5.3. Teaching LearningBased Optimization
5.4. Clonal Selection Algorithm
 1)
 Initialization of antibodies;
 2)
 Cloning and selection (proliferation and differentiation on the encounter of cells with antigens);
 3)
 Maturation and diversification of antibody types by performing affinity maturation process through random genetic changes;
 4)
 Removal of differentiated immune cells that possess low affinity.
5.5. The Proposed Hybrid Optimization
 Step 1:
 Initialize the learners (i.e., the population) and design variables of the optimization problem (i.e., the number of subject) by random generation.
 Step 2:
 Evaluate the initial learner and select the best learner (i.e., the best solution) as a teacher and assign learners in descending order.
 Step 3:
 Clonal selection (CS) step
 CSstep 31:
 Select clones from the assigned learners for clonal selection optimization;
 CSstep 32:
 Differentiation step (i.e., duplicate the best learners);
 CSstep 33:
 Mutation step (reproduce the clones by mutation);
 CSstep 34:
 Evaluate the clones and compare the performance of the teacher (the best learner) with the clones. If the best clone is better than the teacher, assign it as the teacher, otherwise the teacher in Step 2 is retained.
 Step 4:
 Teacher Phase: Update each learner’s knowledge with the help of the teacher’s knowledge using Equation (15).
 Step 5:
 Learner Phase: Update the learners’ knowledge by utilizing the knowledge of some other learner of the same class using Equation (16) or (17).
 Step 6:
 Repeat the procedure from Step 3 to 5 until the termination criterion is met.
5.6. The Object Function of Proposed Hybrid Optimization Algorithm
6. Simulation and Results
7. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Parameters  Values  Parameters  Values 

$i$  5%     
$n$  20 years     
Wind turbine  
${P}_{r}$  1 kW  ${C}_{Wind}$  3200$ 
${\mathsf{\upsilon}}_{cutin}$  2.5 m/s  ${C}_{mtn}^{Wind}$  100$ 
${\mathsf{\upsilon}}_{cutout}$  13 m/s  ${C}_{rep}^{Wind}$  0$ 
${\mathsf{\upsilon}}_{r}$  11 m/s  Life Span  20 years 
PV panel  
${P}_{r}$  120 W  A  1.07 m^{2} 
${C}_{PV}$  614$  Efficiency  12% 
${C}_{mtn}^{PV}$  0$  Life Span  20 years 
${C}_{rep}^{PV}$  0$     
Diesel generator  
${P}_{N}^{D}$  1.9 kW  ${C}_{rep}^{Diesel}$  0$ 
${C}_{Diesel}$  1713.15$  Life Span  8,760 h 
${C}_{Mtn}^{Diesel}$  0.2 $/h  ${P}_{fuel}$  1.24 $/L 
Power converter/inverter  
Rated power  3 kW  Life Span  10 years 
${\mathsf{\eta}}_{inv}$  95%  ${C}_{Conv/Inv}$  2000$ 
Battery  
Voltage  12 V  ${C}_{rep}^{Batt}$  130$ 
${S}_{Batt}$  1.35 kWh  Life Span  5 years 
${\mathsf{\eta}}_{Batt}$  85%  $\mathsf{\sigma}$  0.0002 
${C}_{Batt}$  130$     
Method  Parameter  Values 

GA  Population size  100 
Probability of crossover  0.65  
Probability of mutation  0.05  
Iteration  100  
PSO  Particle size  100 
Inertia weight $\mathsf{\omega}$  1  
c_{1}, c_{2}  2, 2  
Iteration  100  
Proposed method  Class size  100 
The No. of clones  5  
Probability of Mutation for clonal selection  0.25  
SV1 and SV2  1 × 10^{6} 
GA  PSO  TLBO  

Constraints  Best Structure [N_{wind}, N_{pv}, N_{batt}, N_{DG}]  Total Cost  LPSP (%)  Best Structure [N_{wind}, N_{pv}, N_{batt}, N_{DG}]  Total Cost  LPSP (%)  Best Structure [N_{wind}, N_{pv}, N_{batt}, N_{DG}]  Total Cost  LPSP (%)  
LPSP = 0  Mean  [37.4, 253, 7.2, 13]  8.94 × 10^{4}  0.00%  [14.8, 237.6, 8, 10.4]  9.03 × 10^{4}  0.00%  [18, 225, 1.6, 9.2]  8.91 × 10^{4}  0.00% 
Best  [41, 215, 1, 11]  8.86 × 10^{4}  0.00%  [23, 214, 10, 11]  8.88 × 10^{4}  0.00%  [17, 214, 1, 21]  8.85 × 10^{4}  0.00%  
LPSP < 1%  Mean  [36.5, 257, 7.1, 11.8]  8.92 × 10^{4}  0.98%  [12.40, 256.4, 1.6, 9]  8.94 × 10^{4}  0.98%  [17.8, 228, 1.8, 9.2]  8.89 × 10^{4}  0.92% 
Best  [38, 240, 7, 9]  8.86 × 10^{4}  0.90%  [17, 217, 1, 9]  8.86 × 10^{4}  0.78%  [8, 218, 1, 1]  8.85 × 10^{4}  0.67%  
LPSP < 2%  Mean  [37.1, 252, 77.6, 11.3]  8.91 × 10^{4}  1.92%  [21.4, 280, 14.4, 7.4]  9.00 × 10^{4}  1.95%  [18, 225, 1.8, 6.4]  8.88 × 10^{4}  1.82% 
Best  [29, 255, 4, 8]  8.83 × 10^{4}  1.86%  [19, 273, 12, 8]  8.96 × 10^{4}  1.79%  [8, 218, 1, 1]  8.83 × 10^{4}  1.79%  
LPSP < 3%  Mean  [37.8, 246, 7.5, 12]  8.92 × 10^{4}  2.86%  [25.8, 280, 29.2, 6.4]  9.18 × 10^{4}  2.61%  [20.6, 225.8, 1.8, 6.5]  8.856 × 10^{4}  2.77% 
Best  [29, 255, 4, 8]  8.83 × 10^{4}  1.86%  [18, 242, 1, 8]  8.83 × 10^{4}  2.37%  [22, 215, 1, 8]  8.82 × 10^{4}  2.24%  
LPSP < 4%  Mean  [37.8, 246, 7.5, 12]  8.92 × 10^{4}  2.85%  [15.6, 302.4, 19, 8.2]  9.12 × 10^{4}  2.47%  [21.6, 218, 1.6, 6.2]  8.851 × 10^{4}  2.89% 
Best  [29, 255, 4, 8]  8.83 × 10^{4}  1.86%  [13, 263, 1, 8]  8.87 × 10^{4}  2.57%  [22, 215, 1, 8]  8.82 × 10^{4}  2.24%  
LPSP < 5%  Mean  [37.8, 246, 7.5, 12]  8.92 × 10^{4}  2.85%  [19.2, 256.6, 6.6, 8.2]  8.93 × 10^{4}  2.42%  [21.6, 218, 1.6, 6.2]  8.851 × 10^{4}  2.89% 
Best  [29, 255, 4, 8]  8.83 × 10^{4}  1.86%  [26, 207, 1, 8]  8.82 × 10^{4}  2.10%  [22, 215, 1, 8]  8.82 × 10^{4}  2.24% 
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Cho, J.H.; Chun, M.G.; Hong, W.P. Structure Optimization of StandAlone Renewable Power Systems Based on Multi Object Function. Energies 2016, 9, 649. https://doi.org/10.3390/en9080649
Cho JH, Chun MG, Hong WP. Structure Optimization of StandAlone Renewable Power Systems Based on Multi Object Function. Energies. 2016; 9(8):649. https://doi.org/10.3390/en9080649
Chicago/Turabian StyleCho, JaeHoon, MyungGeun Chun, and WonPyo Hong. 2016. "Structure Optimization of StandAlone Renewable Power Systems Based on Multi Object Function" Energies 9, no. 8: 649. https://doi.org/10.3390/en9080649