Optimization of Renewable Energy Systems: The Case of Desalination
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8/18/2019 Serdar ıplıkçı Optimization Applications in the Renewable Energy Systems
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The 4th Renewable Energy Systems Winter School │ Prof. Dr. Serdar İPLİKÇİ
OPTIMIZATION in RENEWABLE
ENERGY SYSTEMS
OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
1/3316/01/2015
Prof. Dr. Serdar İPLİK Çİ
Pamukkale University, Dept. of Electrical and Electronics Eng., Kınıklı Campus, 20040, Denizli
e-mail: [email protected]
web: www.pau.edu.tr/iplikci
phone: +90 (258) 2963197
8/18/2019 Serdar ıplıkçı Optimization Applications in the Renewable Energy Systems
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The 4th Renewable Energy Systems Winter School │ Prof. Dr. Serdar İPLİKÇİ
OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
2/3316/01/2015
CONTENTS1. Introduction
2. Optimization Techniques1. Introduction
2. Heuristic Optimization
3. Gradient-Based Optimization
3. Optimization Applications in the Renewable and
Sustainable Energy Systems1. Wind Power
2. Solar Energy
3. Geothermal Energy
4. Bioenergy
5. Hybrid Systems
4. Modeling and Prediction
5. Conclusions
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The 4th Renewable Energy Systems Winter School │ Prof. Dr. Serdar İPLİKÇİ
OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
3/3316/01/2015
1) Introduction1.1) Why Optimization?
• Due to the increasing demand and limited sources worldwide, sustainability is of great
importance
• It is necessary to develope efficient methods that allow us to produce and consume
the energy very effectively.
• The extension of energy sources and the information structure allow a fine screening
of energy resources, but also require the development of tools for the analysis and
understanding of huge datasets about the energy grid.• Key technologies in future ecological, economical and reliable energy systems are
• Energy prediction of renewable resources
• Prediction and monitoring of energy consumption
• Efficient planning and control strategies for network stability
• To enable ecologically and financially feasible projects, optimization methods have
taken over a key role for planning, optimizing and forecasting sustainable systems.
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The 4th Renewable Energy Systems Winter School │ Prof. Dr. Serdar İPLİKÇİ
OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
4/3316/01/2015
1) Introduction1.2) Optimization in the Literature
Source: Web of Science
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OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
5/3316/01/2015
2) Optimization Techniques2.1) Introduction
2.1.1) General Format and Short Notation
Objective Function Design Variables
min ()s . t . : () 0 ∈ ℰ
() ≥ 0 ∈ ℐ
min,,…,(, , … , )
s. t: (, , … , ) 0 ∈ ℰ(, , … , ) ≥ 0 ∈ ℐ
: ℝ ⟼ ℝ ∈ ℝ 1,2, … ,
⋮
()
Local minimum
Global minimum
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The 4th Renewable Energy Systems Winter School │ Prof. Dr. Serdar İPLİKÇİ
OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
6/3316/01/2015
2) Optimization Techniques2.2) Heuristic Optimization
2.2.1) Introduction
•
Heuristic methods are the methods that produce sufficient (even if not optimum)solutions to the large scale problems very rapidly.
• Meta-heuristics are generalizations of heuristics in the sense that they can be applied
to a wide set of problems.
• Heuristic methods can be categorized as follows:• Trajectory vs population
• memory-based vs memoryless
• nature-inspired vs non-nature-inspired
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OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
7/3316/01/2015
2) Optimization Techniques2.2) Heuristic Optimization
2.2.2) Trajectory Methods
Trajectory methods start the search process with a single solution. During the search
process, the solution is updated iteratively and the thus the outcome is also a single
optimized solution. Most of them are extensions of simple iterative improvement
procedures that incorporate techniques that enable the algorithm to escape from local
optima. Some of the trajectory methods are:
•
Hill Climbling (HC)• Simulated Annealing (SA)
• Tabu Search (TS)
• Greedy Randomized Adaptive Search Procedures (GRASP)
• Variable Neighborhood Search (VNS)
Some of the meta-heuristics trajectory methods are :
• Iterated Local Search (ILS)
• Pareto Archived Evolution Strategy (PAES)
• Multi-Objective Simulated Annealing (MOSA)
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OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
8/3316/01/2015
2) Optimization Techniques2.2) Heuristic Optimization
2.2.3) Population-based Meta-Heuristics Methods
Population-based heuristics use a population of solutions which evolve during a given number of
iterations, also returning a population of solutions when the stop condition is fulfilled. Themain population-based heuristics include:
• Genetic Algorithms (GA)
• Evolutionary Algorithms (EA)
• Scatter Search (SS)
• Path Relinking (PR)
• Memetic Algorithms (MA)
• Ant Colony Optimization (ACO)
• Particle Swarm Optimization (PSO)
• Estimation of Distribution Algorithm (EDA)
• Differential Evolution (DE)
• Artificial Bee Colony Optimization (ABCO)
Population-based meta-heuristics are:• The Multiobjective Tabu Search (MOTS)
• Non-dominated Sorting Genetic Algorithm (NSGA/NSGA-II)
• Pareto Simulated Annealing (PSA)
• Single Front Genetic Algorithm (SFGA)
• Strength Pareto Evolutionary Algorithm (SPEA/SPEA-II)
• Pareto Envelope-based Selection Algorithm (PESA/PESA-II).
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OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
9/3316/01/2015
2) Optimization Techniques2.2) Heuristic Optimization
2.2.4) Genetic Algorithm Cycle
Table of fitness values
N F F F ,,,
21 calculate
Sort from smallest to highest
Population
selection
crossover
roulette wheel
1 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1
1 1 0 0 1 0 1 1 0 1 1 1 0 1 0 0
Parent 1
Parent 2
Offspr ing1
Offspr ing2
1 0 0 1 1 1 0 1 0 1 1 1 0 1 0 0
0 0 1 0 1 1 0 11 1 0 0 1 0 1 1
2X
N X
3X
1X
mutation
1 0 1 1 1 0 1 0 0 1 0 1 1 0 1or iginal
mutated 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 0
GENETIC ALGORITHM CYCLE
fitness function
number of population
fitness of the i th solution
i th individual (solution)
binary counterpart of the
i th solution
0
(, , … , )
N
(, , … , )
decimal2binary
⋮
OPTIMIZATION i RENEWABLE ENERGY SYSTEMS
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OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
10/3316/01/2015
2) Optimization Techniques2.3) Gradient-Based Optimization
2.3.1) Mathematical Basics
, , … ,
, , … ,
, , … ,
⋮ , , … ,
Gradient Vector
, , … ,
, , … ,
, , … ,
⋯ , , … ,
, , … ,
, , … ,
⋯ , , … ,
⋮ ⋮ ⋱ ⋮
, , … ,
, , … ,
⋯ , , … ,
Hessian Matrix
, , … ,
, , … ,
, , … ,
⋯ , , … ,
, , … ,
, , … ,
⋯ , , … ,
⋮ ⋮ ⋱ ⋮ , , … ,
, , … ,
⋯ , , … ,
Jacobian Matrix
OPTIMIZATION i RENEWABLE ENERGY SYSTEMS
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OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
11/3316/01/2015
2) Optimization Techniques2.3) Gradient-Based Optimization
2.3.2) Taylor Expansion, Descent Direction and Optimality Conditions
Taylor Expansion
∆ ∆ 12 ∆ ∆ ℎ. .
Descent Direction
First-order Optimality Conditions: ∗
Optimality Conditions
Update Rule
If one can find a search direction that satisfies <
+ ← kuralı ile güncelleme yapılır.
Second-order Optimality Conditions : ∗ positive definite
≅
< →
< 0
OPTIMIZATION i RENEWABLE ENERGY SYSTEMS
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OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
12/3316/01/2015
2) Optimization Techniques2.3) Gradient-Based Optimization
2.3.3) First- and Second-order Methods
Steepest Descent:
Conjugate Gradient: −
Newton: −
Modified Newton: −
First-order Methods
Second-order Methods
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OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
13/3316/01/2015
2) Optimization Techniques2.3) Gradient-Based Optimization
2.3.4) Quasi-Newton Methods and Second-order Approximate Methods
Davidon-Fletcher-Powell (DFP) :
, + ∆ ∆ ∆
, +
Gauss-Newton (GN):
−
Levenberg-Marquardt (LM): − .
Quasi-Newton Methods
Second-order Approximate Methods
Broydon-Fletcher-Goldfarb-Shanno (BFGS) :
− , + ∆ , +
OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
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OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
14/3316/01/2015
3) Optimization App. in the Renewable and Sustainable Energy Systems
PROBLEM ÇÖZÜM
Community-scale renewable energy systems planning is an
important problem consisting of justifying the allocation
patterns of energy resources and services, formulation of localpolicies regarding energy consumption, economic
development and energy structure, and analysis of
interactions among economic cost, system reliability and
energy-supply security.
• Interval Linear Programming (ILP)
• Chance-Constrained Programming
• Mixed Integer-Linear Programming (MILP)
a long-term dynamic multi-objective planning model for
distribution network expansion along with distributed energy
options
Immune Genetic Algorithm (I-GA)
minimum cost expansion of power transmission networks
under carbon emission trading programs
• Mixed-Integer Programming (MIP)
• Genetic Algorithms (GA)
• Simulated Annealing (SA )
• Tabu Search (TS)
annual peak load forecasting in an electrical power system
with the aim of minimizing the error associated with the
estimated model parameters
Particle Swarm Optimization (PSO)
new renewable energy sources penetration
and congestion management so that electricity supply and
demand are always evenly balanced
• Nelder–Mead Simplex (NMS) and PSO
• Honey Bee Mating Optimization (HBMO)
• Ant Colony Optimization (ACO), ANN, GA
Energy demand prediction • Yapay Sinir Ağları (ANN)
• Destek Vektör Makineleri (SVM)
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OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
15/3316/01/2015
3) Optimization App. in the Renewable and Sustainable Energy Systems3.1) Wind Power
3.3.1) Introduction
•
Wind is a periodical phenomenon for large geographical areas like Mexico.• the increasing sizes of turbines and the lower prices per installed production
capacity of electricity.
• Wind energy systems may not be technically viable in all locations because of
low wind speeds and the fact that it is more unpredictable than solar energy
• Areas where winds are stronger and more constant, such as offshore and high
altitude sites, are preferred locations for wind farms.
•
An accurate estimation of wind speed distribution
the site selection of windfarms
• Bayesian modelmodeling long-term wind speed distributions
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OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
16/3316/01/2015
3) Optimization App. in the Renewable and Sustainable Energy Systems3.1) Wind Power
3.3.1) Optimization in Wind Turbine Design
• In particular, two important problems are often considered: wind turbine and wind farm layout
The power output of a turbine is a function of the:• density of the air
• area swept out by the turbine blades
• cube of the wind speed
• Numerous metrics are used to measure the power quality of a wind turbine, such as
• the power factor, reactive power,
• Harmonic distortion
the optimization of the geometrical parameters of the rotor
configuration of stall-regulated horizontal-axis wind turbines with
the aim of achieving the best trade-off performance between the
total energy production per square meter of wind park and cost
Multi-Objective Evolutionary Algorithm
(MOEA)
the optimization of the ranges of gearbox ratios and power ratings
of multihybrid permanent-magnet wind generator systems
Genetic Algorithms (GA)
determining the optimum capacity taking into account uncertainties
arising from wind speed distribution and power–speed
characteristics
Mixed-Integer Nonlinear Programming
(MINLP)
prediction of wind speed at a selected location based on the data
collected at the neighbouring locations
Fuzzy Logic Modelling
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OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
17/3316/01/2015
3) Optimization App. in the Renewable and Sustainable Energy Systems3.1) Wind Power
3.3.2) Optimization in Wind Farm Layout
• Wind farm layout consists of determining the optimum positions of wind turbines
within the farm in order to maximize energy production.
optimal placement of wind turbines for maximum production capacity while
limiting the number of turbines installed and the acreage of land occupied by
each wind farm
Genetic Algorithms (GA)
optimum wind farm configuration problem which is driven by an integralwind farm cost model based on the cumulative net cash flow value
throughout the wind farm’s lifespan
Evolutionary Algorithms (EA)
wind turbine placement based on wind distribution with the aim of both
maximizing the wind energy capture and minimizing an index that
determines constraint violations
Multi-Objective Evolutionary
Algorithm (MOEA)
determining the optimal type, number and placement of wind turbines
considering the given wind conditions and wind park area
Mixed-Integer Nonlinear
Programming (MINLP)
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OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
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3) Optimization App. in the Renewable and Sustainable Energy Systems3.2) Solar Energy
3.2.1) Introduction
• Solar energy is radiant energy that is produced by the sun. In many parts of the world,
direct solar radiation is considered to be one of the best prospective sources of energy.
• The main ways to convert solar radiation into energy are active and passive solar
design.
• Passive solar design is often based on the optimal design of buildings that capture the
sun’s energy in order to reduce the need for artificial light and heating. Regarding
passive solar systems, a primary interest for researchers in solar energy is related to
the design and optimization of solar energy homes.
• Active solar design is based on water heating converting solar radiation into heat using
photovoltaic panels and solar cells to convert the solar radiation into energy.
•
In order to design both active and passive solar energy systems, radiation data areneeded for the studied location.
calculating solar radiation levels over complex mountain terrains using data from only
one radiometric station
ANN, Neuro-Fuzzy
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OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
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3) Optimization App. in the Renewable and Sustainable Energy Systems3.2) Solar Energy
3.2.2) Active Solar Design
• An interesting problem related to photovoltaic systems is the optimal determination of
their size. The sizing optimization of a stand-alone photovoltaic system is a complex
optimization problem which aims to obtain acceptable energy and economic cost for
the consumer, and a relatively correct energy supply quality.
identifying the electrical parameters of photovoltaic solar cells and modules to
determine the corresponding maximum power point from the illuminated current –
voltage characteristic
Genetic Algorithms
(GA)
maximizing the thermal performance of flat plate solar air heaters by considering
the different system and operating parameters
Genetic Algorithms
(GA)
determining the tilt angle of photovoltaic modules with the aim of maximizing the
electrical energy output of the modules
Particle Swarm
Optimization (PSO)
Optimal sizing of photovoltaic systems ANN ve GA
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OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
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3) Optimization App. in the Renewable and Sustainable Energy Systems3.3) Bioenergy
3.3.1) Introduction
• Bioenergy is renewable energy made available from materials derived from biological
sources. Biomass, a renewable energy source, is biological material from living, orrecently living organisms, including plants and animals.
• Biomass is one of the most promising renewable energy sources, but more research is
required to prove that power generation from biomass is both technically and
economically viable
• Biomass can be burned to produce steam for making electricity, or to provide heat to
industries and homes.• In addition biomass can be converted to other usable forms like methane gas, ethanol
fuel and biodiesel fuel.
• Biomass power plants exist in over 50 countries around the world and supply a
growing share of electricity.
• The sustainability of electricity generation from biomass must be assessed according
to the key indicators of price, efficiency, greenhouse gas emissions, availability,
limitations, land use, water use and social impacts.
Finding optimal location of biomass-fuelled systems for distributed power generation
with forest residues as biomass source
binary PSO-based
method
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OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
21/3316/01/2015
3) Optimization App. in the Renewable and Sustainable Energy Systems3.4) Geothermal Energy
3.4.1) Introduction
• Geothermal energy is the energy contained as heat inside the Earth. Geothermal heat
pumps are a highly efficient, renewable energy technology for heating and cooling.
• This technology relies on the fact that, at depth, the Earth has a relatively constant
temperature, warmer than the air in winter and cooler than the air in summer.
• The main advantage of using geothermal energy is that this renewable energy source
can provide power 24 h a day due to it is constant, without intermittence problems
compared to other renewable resources such as wind or solar energy.
• It is expensive to build a power station but operating costs are low, resulting in low
energy costs for suitable sites.
• Geothermal power plants now exist in 19 countries, and new plants are commissioned
annually. However, only a small fraction of the geothermal potential has beendeveloped so far, and there is ample space for an accelerated use of geothermal energy
both for electricity generation and direct applications.
optimization of the exploitation system of a low enthalpy geothermal aquifer, with
the aim of determining the annual pumping cost of the required flow and the
amortization cost of the pipe network, which carries the hot water from the wells
to a central water tank, situated on the border of the geothermal field
Genetic Algorithms (GA)
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OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
22/3316/01/2015
3) Optimization App. in the Renewable and Sustainable Energy Systems3.5) Hybrid Systems
3.5.1) Introduction
• In the last decade, there has been a spectacular increase the interest in optimizing the design and
control of stand-alone hybrid power generation systems in order to manage energy between themaximum energy captured and consumed energy.
• The aim of optimizing the mix of the renewable system is maximizing its contribution to the peak
load, while minimizing the combined intermittence at a minimum cost.
the economic environmental dispatching of a hybrid power system
including wind and solar thermal energies.
Multi-Objective Evolutionary
Algorithm (MOEA) and GA
the multi-objective design of isolated hybrid systems where the
objectives to minimize are the total cost throughout the useful life of
the installation and the pollutant emissions
Multi-Objective Evolutionary
Algorithm (MOEA) and Strength Pareto
Evolutionary Algorithm (SPEA)
Optimal sizing a hybrid solar–wind-battery system with the aim of
minimizing the annualized cost system and the loss of power supply
probability
Genetic Algorithms (GA)
Solving the wind-photovoltaic capacity coordination for a time-of-use
rate industrial user with the aim of maximizing the economic benefitsof investing in a wind generation system and a photovoltaic
generation system
Particle Swarm Optimization (PSO)
Optimal sizing of stand-alone photovoltaic-wind generator systems,
which selects the optimal number and type of units to minimize the
cost subject to the constraint that the load energy requirements are
completely covered
Genetic Algorithms (GA)
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The 4th Renewable Energy Systems Winter School │ Prof. Dr. Serdar İPLİKÇİ 23/3316/01/2015
4) Modeling and Prediction4.1) Introduction
4.1.1) The Concept of Modeling
• Modeling is a method that is used when a real-world «process» cannot be described
analytically or mathematically. Here, the «process» can be all sorts of biological,physical, chemical, electrical, mechanical, meteorological, social and financial
dynamical systems.
• There are many such systems in the real world. For instance, dynamics of weather
conditions is so complex that it cannot be described mathematically, and thus it should
be modeled.similarly, stock market is a very complex system that incorporates manyvariables and parameters. There some problems in the energy systems that need
modeling:
• Electrical load prediction
• Energy demand prediction
• Therefore, when needed, we have to collect sufficient data from such energy systems
and then try to obtain a reliable model.
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4) Modeling and Prediction4.1) Introduction
4.1.2) Data Types
Input-Output Data
⋮
⋮
MM Input Data Output Data
... ...
1 ... ...
2
...
...
⋮ ⋮ ⋮
N ... ...
∈ ℝ ∈ ℝ
unknown system
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The 4th Renewable Energy Systems Winter School │ Prof. Dr. Serdar İPLİKÇİ 25/3316/01/2015
4) Modeling and Prediction4.1) Introduction
4.1.2) Data Types Time Series
1 2 3 4 5 6
… 1
?
Input Data Output Data
...
1
1
2 ...
1
2 2 3 ... 1 2
⋮ ⋮ ⋮ 1 ... 1
OPTIMIZATION in RENEWABLE ENERGY SYSTEMS
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The 4th Renewable Energy Systems Winter School │ Prof. Dr. Serdar İPLİKÇİ 26/3316/01/2015
4) Modeling and Prediction4.2) Modeling and Model Selection
4.2.1) Generalization, Approximation and Prediction Errors
MM Input Data Output Data Model Output
... ... ...
1 ... ... ...
2 ... ... ...
⋮ ⋮ ⋮ ⋮ N ... ... ...
∈ ℝ ∈ ℝ
MM , =
⋮
⋮
real model
optimum model
HYPOTHESIS SPACE
predicted model
TARGET SPACE
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The 4th Renewable Energy Systems Winter School │ Prof. Dr. Serdar İPLİKÇİ 27/3316/01/2015
4) Modeling and Prediction4.2) Modeling and Model Selection
4.2.1) Emprical Error, Overfitting and Splitting Data
ℎ
Over-learning Under-learning
model complexityEmprical error
training
validation
test
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The 4th Renewable Energy Systems Winter School │ Prof. Dr. Serdar İPLİKÇİ 28/3316/01/2015
4) Modeling and Prediction4.2) Modeling and Model Selection
4.2.2) Objective Function
min , ,
∈
=
∈
=
1
, ,
∈VL
=
Complexity
best model
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The 4th Renewable Energy Systems Winter School │ Prof. Dr. Serdar İPLİKÇİ 29/3316/01/2015
4) Modeling and Prediction4.3) Example: Chaotic Time Series Predictyion by Artificial Neural Nets
4.3.1) Architecture of an Artificial Neural Network
Σ
1
ℎ
Σ
1
ℎ
Σ
−
1
ℎ
Σ
1
ℎ
⋮ Σ
ç
1
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,ç
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,ç
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−
,
,
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−
,
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,
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⋮
,
⋮,
⋮
,ç
⋮,ç
ç
+ ←
1
ℎ
ç
Σ
i n p
u t s i g n a l s
output signal
⋮
input weight
summing block
bias weight
activation
function
output weight
input weight
Single neuron
Neural network
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The 4th Renewable Energy Systems Winter School │ Prof. Dr. Serdar İPLİKÇİ 30/3316/01/2015
4) Modeling and Prediction4.3) Example: Chaotic Time Series Predictyion by Artificial Neural Nets
4.3.2) Data
0 20 40 60 80 100 120 140 160 180 2000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
k
x k
Chaotic Logistic Map + 3.9 1 , 0.2
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The 4th Renewable Energy Systems Winter School │ Prof. Dr. Serdar İPLİKÇİ 31/3316/01/2015
4) Modeling and Prediction4.3) Example: Chaotic Time Series Predictyion by Artificial Neural Nets
4.3.3) Model Output
0 50 100 150 200 2500
0.2
0.4
0.6
0.8
1LM VERI:logistic EGITIM VERISI SAYISI=119 TEST VERISI SAYISI=80 NORON SAYISI=10 GURULTU GENLIGI=0.01
gercek yorunge
en iyi model cikisi
tahmin cikisi
50 100 150 200 250
0
0.05
0.1
0.15
0.2
iterasyon
h a t a
egitim hatasi
training error
test error
190 192 194 196 198 200 202 204 2060
0.2
0.4
0.6
0.8
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The 4th Renewable Energy Systems Winter School │ Prof. Dr. Serdar İPLİKÇİ 32/3316/01/2015
5) Conclusions
• The optimization methods that have beenn used for solving optimization problems inrenewable energy systems have been developed day-by-day. They are especially used
in hybrid systems.
• Some of these methods are based on the traditional methods like mixed-integer,interval linear-programming, Lagrangian relaxation, quadratic programming, andNelder–Mead Simplex, while others are based on some heuristics methods such as GAand PSO.
•
On the other hand, the multi-objective function problems in the energy systems havebeen solved by Pareto-optimization techniques.
• The problems in the renewable energy systems that can be solved by optimizationtechniques are• Planning• Management of supply-demand balance• Optimization of design parameters
• Prediction of power curve• Configuration• Optimization of economical load distribution• Wind-photovoltaic capacity coordination• Modeling and prediction
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THANKS...